A STUDY OF FLUIDIC OSCILLATORS AS AN ALTERNATIVE

PULSED VORTEX GENERATING JET ACTUATOR FOR FLOW SEPARATION CONTROL

A thesis submitted to the University of Manchester for the degree of Master of Philosophy

in the Faculty of Engineering and Physical Sciences

2011

Gi-Hun Kim

School of Mechanical, Aerospace and Civil Engineering

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Contents

List of figures ............................................................................................................ IV

List of tables ............................................................................................................. XI

Nomenclature .......................................................................................................... XII

Copyright ................................................................................................................ XIV

Declaration .............................................................................................................. XV

Acknowledgements ................................................................................................ XVI

Abstract ................................................................................................................. XVII

1 Introduction ...................................................................................................... 18

1.1 The need for flow separation control ....................................................... 18 1.2 Methods for flow separation control ......................................................... 18 1.3 Fluidic oscillators ..................................................................................... 20 1.4 The objectives of this project ................................................................... 23 1.5 The layout of this report ........................................................................... 23

2 Literature review .............................................................................................. 25

2.1 Boundary layer and its separation ........................................................... 25 2.2 Boundary layer transition ......................................................................... 26 2.3 Turbulent boundary layer ......................................................................... 30 2.4 Flow control ............................................................................................. 32

2.4.1 Definition and its classification ............................................................. 32 2.4.2 Classic methods and principles of operation ....................................... 33

2.4.2.1 Stability modifiers ......................................................................... 33 2.4.2.2 Turbulators ................................................................................... 40

2.5 Fluidics ..................................................................................................... 45 2.5.1 Definition and general principles of operation ...................................... 45 2.5.2 Analogue devices ................................................................................ 47 2.5.3 Digital devices ...................................................................................... 49

2.6 Bistable wall attachment fluidic oscillator ................................................. 50 2.6.1 Early history ......................................................................................... 50 2.6.2 The Coanda effect in bistable wall attachment devices ....................... 52 2.6.3 Jet switching method and mechanism ................................................. 54 2.6.4 Static characteristic .............................................................................. 58 2.6.5 Dynamic characteristic ......................................................................... 70 2.6.6 Steady-state design methodology ....................................................... 79

3 Experimental apparatus and methods ........................................................... 109

3.1 Experimental models ............................................................................. 109 3.1.1 The fluidic oscillator ........................................................................... 109

3.1.1.1 The design .................................................................................. 109 3.1.1.2 Test conditions ........................................................................... 111 3.1.1.2.1 Steady-state analysis ................................................................. 111 3.1.1.2.2 Oscillatory jet characteristic analysis .......................................... 113

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3.1.2 Fluidic amplifiers in an array .............................................................. 115 3.1.2.1 The design .................................................................................. 115 3.1.2.2 Test conditions ........................................................................... 116

3.2 Experimental methods ........................................................................... 118 3.2.1 Constant temperature anemometer (CTA) ........................................ 118

3.2.1.1 Principles of operation ................................................................ 119 3.2.1.2 Calibration .................................................................................. 121 3.2.1.3 Error analysis ............................................................................. 122

3.2.2 Orifice plate flowmeter ....................................................................... 124 3.2.2.1 Principles of operation ................................................................ 125 3.2.2.2 Calibration .................................................................................. 127 3.2.2.3 Error analysis ............................................................................. 127

4 The characteristics of the fluidic oscillator ..................................................... 130

4.1 Steady-state analysis ............................................................................. 130 4.1.1 Control flow rate at the point of jet switching ..................................... 130 4.1.2 The characteristics of output jets ....................................................... 133 4.1.3 Flow gain and fanout ratio ................................................................. 138

4.2 Oscillatory jet characteristic ................................................................... 140 4.2.1 Output jet characteristics ................................................................... 141 4.2.2 The frequency of oscillatory jets ........................................................ 143 4.2.3 The switching time ............................................................................. 150 4.2.4 Assessment of capability in driving other fluidic amplifiers ................ 153

4.3 Assessment for flow control applications ............................................... 154 4.4 Summary of findings .............................................................................. 156

5 An array of Fluidic amplifiers ......................................................................... 159

5.1 Effect of changing exit orifice diameter .................................................. 159 5.2 Effect of changing aspect ratio .............................................................. 162 5.3 Other observations ................................................................................ 163 5.4 Summary of findings .............................................................................. 165

6 Conclusions and future work ......................................................................... 166

6.1 Conclusions ........................................................................................... 166 6.2 Suggestions for future work ................................................................... 169

References ............................................................................................................ 171

Final word count : 40,932 words

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List of figures

Figure 1.1 Separated flow over an aerofoil at an angle from ................................... 18

Figure 1.2 Separation control of flow in a diffuser by suction. a) Separation at both walls; a’) Suction applied only at the upper wall; a’’) Suction at both wall (Schlichting and Gersten (2000)). Original picture taken by Prandtl and Tietjens (1931). .......... 19

Figure 1.3 Classic designs of fluidic oscillator. (Morris (1973)). .............................. 20

Figure 1.4 Schematic drawing showing the geometrical difference of a symmetric bistable and asymmetric monostable oscillator. ..................................................... 21

Figure 1.5 Microfabricated bistable vent-fed fluidic oscillator (Simões (2004)) ....... 22

Figure 2.1 Flow visualisation showing a development in time of the separation at the aft of an upper quadrature of a symmetric cylinder. a) The flow recirculation has just begun at the trailing edge shortly after the initiation of the boundary layer separation; b) The boundary layer has thickened and the start of the reversed motion moved forward with growing in its size; c) A large vortex has formed from the backflow; d) The vortex grows in its size; e) The vortex separates from the body and moves downstream changing the flow portrait at the rear of the body. Schlichting and Gersten (2000). ....................................................................................................... 26

Figure 2.2 Laminar to turbulent transition process in a boundary layer ................... 28

Figure 2.3 Hairpin vortices and turbulent spot ......................................................... 29

Figure 2.4 Flow past a sphere. a) Subcritical flow in subcritical Re regime; b) Supercritical flow in subcritical Re regime with a trip wire. Schlichting and Gesten (2000). Original Picture after Wieselsberger, C. (1914) .......................................... 29

Figure 2.5 Schematic representation of laminar and turbulent flow ........................ 30

Figure 2.6 Schematic representation of velocity profile in laminar and turbulent boundary layer ......................................................................................................... 31

Figure 2.7 Skin friction coefficient for a smooth flat plate at zero incidence ............ 31

Figure 2.8 Laminar and turbulent flow over a sharp corner and a curved surface. a) and a’) Show thinner laminar boundary layer and their separation; b) and b’) Thicker turbulent boundary layer, delayed and suppressed separation. Van Dyke (1982). . 32

Figure 2.9 Interrelation between flow control goals ................................................. 34

Figure 2.10 Classification of flow control strategies ................................................ 34

Figure 2.11 Slot suction wing glove on B-18 ........................................................... 36

Figure 2.12 Vampire III Wing glove with distributed porous suction ........................ 36

Figure 2.13 Predicted benefits of NLF, LFC and HLFC ........................................... 37

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Figure 2.14 HLFC in practice................................................................................... 38

Figure 2.15 Effect of HLFC during B757 flight test .................................................. 39

Figure 2.16 Spatial relation of VVGs and sketch of generated vortices pattern. ..... 41

Figure 2.17 Oil-flow visualisation showing the separation delay of 3D flow over a back ward facing ramp by co-rotating MVVGs. a) normal flow condition; b) with MVVGs having the height of 20% of BL thickness. Lin and Howard (1989) ............ 41

Figure 2.18 MVVGs on leading edge of trailing edge flap of Piper Malibu .............. 41

Figure 2.19 Definition of pitch and skew of an vortex jets orientation ..................... 42

Figure 2.20 Oil flow visualisation of steady PVGJs effectin delaying flow separation. a) Baseline case; b) Steady jets in action with VR=6.8, α=45o and=90o. Selby et al (1992) ...................................................................................................................... 43

Figure 2.21 Starting vortex ring of the pulsed jet. .................................................... 44

Figure 2.22 Tesla valve and its principle of operation ............................................. 46

Figure 2.23 typical geometry of beam deflection proportional amplifier .................. 48

Figure 2.24 Axial turbulence amplifier ..................................................................... 48

Figure 2.25 Typical wall attachment geometry ........................................................ 49

Figure 2.26 Typical geometry of vortex amplifier. .................................................... 50

Figure 2.27 Typical wall attachment device geometrical components and symbols. ................................................................................................................................ 51

Figure 2.28 Classic bistable fluidic oscillator designs .............................................. 52

Figure 2.29 Jet attachment in a bistable wall attachment device with schematic presentation of a separation bubble. Kirshner and Katz (1975). ............................. 52

Figure 2.30 Definition of clearance .......................................................................... 54

Figure 2.31 Sequential illustration of a contacting-both-wall switching process. ..... 56

Figure 2.32 Sequential illustration of a splitter switching process ........................... 57

Figure 2.33 Jet attachment to an offset parallel wall ............................................... 59

Figure 2.34 Effect of offset in jet attachment length ................................................ 61

Figure 2.35 Effect of attachment wall angle on the jet attachment length ............... 61

Figure 2.36 Comparison of experimentally measured jet attachment length with theoretical model of Levin and Manion based on attachment point method. .......... 63

Figure 2.37 Comparison of experimentally measured jet attachment length with theoretical model of Levin and Manion based on control volume method for =8. Levin and Manion (1962) ......................................................................................... 64

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Figure 2.38 Approximate value of for combinations of attachment wall angle and offset ratio for Levin and Manion’s control volume method ............................. 64

Figure 2.39 Theoretical results of jet attachment length for the cases of various offset parallel wall by Boucher’s compared with other experimental results ........... 65

Figure 2.40 Boucher’s theoretical results of jet attachment length for the cases of various attachment wall angle with offset wall compared with other experimental results. a) Zero offset case; b) for offset ratio of 2, 4 and 10. .................................. 66

Figure 2.41 Variation of the minimum Reynolds number based on the power nozzle width for the initiation of jet attachment with AR. Comparin et al (1962) ................. 67

Figure 2.42 General amplifier geometry and profiles of splitter and convex and concave attachment wall studied by Sparkaya and Kirshner. Sparkay and Kirchner (1968) ...................................................................................................................... 68

Figure 2.43Pressure recovery with active port flow ................................................. 69

Figure 2.44 Separation time variation with control flow level ................................... 70

Figure 2.45 Dynamic separation bubble area change with power jet Reynolds number. Johnston (1963) ........................................................................................ 71

Figure 2.46 Measured control flow level and calculated average entrained flow .... 71

Figure 2.47 Control pulse length variation with offset .............................................. 73

Figure 2.48 Effect of offset on dynamic flow gain .................................................... 74

Figure 2.49 Flow visualisation showing jet attachment to a splitter ......................... 75

Figure 2.50 Effect of splitter location on the switching time ..................................... 75

Figure 2.51 Flow visualisation showing the standing vortex formed near the splitter and their influence on the separation bubble........................................................... 76

Figure 2.52 Summary of geometrical influence on the performance of bistable wall attachment device. (Warren 1963) .......................................................................... 78

Figure 2.53 Attachment length with attachment wall angle for various offset .......... 79

Figure 2.54 Blocked bubble pressure with offset ..................................................... 80

Figure 2.55 Input characteristic curve for a bistable device .................................... 80

Figure 2.56 Control flow to switch with offset .......................................................... 81

Figure 2.57 Input and output characteristic curve for bistable device. .................... 82

Figure 2.58 Blocked output parameter with offset for various attachment wall angle. (Kirshner 1975) ........................................................................................................ 82

Figure 2.59 Configuration of model. a) step-wall oscillator, and b) plane-wall oscillator. Yang et al (2007) ..................................................................................... 84

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Figure 2.60 PIV laser display of fluidic oscillator. a) flow pattern of plane-wall oscillator, b) local flow structures of the circulation, and c) local flow structures of the inlet zone. Yang et al (2007) ................................................................................... 84

Figure 2.61 Operating ranges of step-wall oscillators. a) for span angle variation, and b) for splitter angle variation. Yang et al (2007) ................................................ 84

Figure 2.62 Spectra cascade. a) plane-wall oscillator, and b) step-wall oscillator. Yang et al (2007) ..................................................................................................... 85

Figure 2.63 Visualisation of the internal flow for comparison of flow structure. a) plane-wall oscillator, b) step-wall oscillator. Yang et al (2007) ................................ 85

Figure 2.64 Total pressure drop as a function of flow rate. Yang et al (2007) ......... 86

Figure 2.65 Geometrical specification of the model (dimensions in mm). a) global dimension, b) model with large control port width, and c) model with small control port width. Furlan et al (2006) ................................................................................. 87

Figure 2.66 Internal flow visualisation with liquid dye. i) operation of oscillator with control port width of 0.87 at Re=1038, ii) operation of oscillator with control port width of 0.87 at Re=9737, and iii) operation of oscillator with control port width of 0.4 at Re=1168. Furlan et al (2006) .............................................................................. 88

Figure 2.67 Photo and conceptual drawing of the embedded-fluidic-vane. Culley et al (2003) .................................................................................................................. 89

Figure 2.68 Unsteady output generated by embedded-fluidic-vane. Cμ=0.014 at F+ = 0.52. Culley et al (2003) ....................................................................................... 89

Figure 2.69 Comparison of loss reduction for the slot-vane, embedded-fluidic-vane and hole-vane at 5O restagger angle, steady injection, 56% span, φ=0.36. Culley et al (2003) .................................................................................................................. 90

Figure 2.70 Schematic showing design and operation of miniature fluidic device. a) schematic drawing of the model, and flow visualisation using water injection depicting square-wave behaviour of oscillatory jet exiting the nozzle, where supply pressure = 4psig. Raman and Raghu (2004) .......................................................... 91

Figure 2.71 Fluidic oscillator supply pressure and mass flow requirements for jet-cavity tone suppression. The main jet’s flow is at M=0.69. Raman and Raghu (2004) ................................................................................................................................ 92

Figure 2.72 Feedback fluidic oscillator in insert (A). a) velocity wave form and b) frequency response as a function of supply pressure. Cerretelli and Kirtley (2009) 93

Figure 2.73 Feedback fluidic oscillator in insert (B). a) velocity wave form and b) frequency response as a function of supply pressure. Cerretelli and Kirtley (2009) 93

Figure 2.74 Schematic drawing of the hump diffuser cross section. Cerretelli and Kirtley (2009) ........................................................................................................... 94

Figure 2.75 Diffuser pressure recovery curves for steady and unsteady blowing as a function of Cμ for α=0 deg. Cerretelli and Kirtley (2009) ......................................... 94

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Figure 2.76 U velocity fields and streamlines for unsteady flow control applies by inset (A) over the hump. Cerretelli and Kirtley (2009) ............................................. 95

Figure 2.77 Relative reduction with fluidic oscillator in momentum, power and velocity ratio as a function of Cp. Cerretelli and Kirtley (2009) ................................ 96

Figure 2.78 Velocity time history and frequency response of the fluidic oscillator output jet. a) velocity waveform as measured by the HWA, and b) frequency response as a function of supply pressure. Cerretelli et al (2010) .......................... 96

Figure 2.79 Improvements in max CL as a function of Re and velocity ratio for all tested configurations. High level of actuation refers to a mass flow of 69.9g/s, and low level refers to a mass flow of 51.4g/s. Cerretelli et al (2010) ............................ 97

Figure 2.80 Diagram of the piezo-fluidic actuator design. The piezoelectric bender is positioned in the diffuser, pointing upstream into the flow. Gregory et al (2009) ..... 98

Figure 2.81 Time history of the oscillator outputs simultaneously measured by hot-film probes. a) at pressure ratio of 1.69 and 10Hz, b) at pressure ratio of 1.69 and 200Hz, c) at pressure ratio of 1.14 and 1.0kHz, and d) at pressure ratio of 2.15 and 5Hz. Gregory et al (2009) ........................................................................................ 99

Figure 2.82 Step response of the piezo-fluidic oscillator to the piezo bender. Gregory et al (2009) .............................................................................................. 100

Figure 2.83 Frequency maps of the piezo-fluidic oscillator performance at a supply pressure ratio of 1.14. The ordinate indicates the driving frequency and the abscissa corresponds to the power spectral density. Gregory et al (2009) .......................... 100

Figure 2.84 Diagram of the plasma-fluidic actuator. Gregory et al (2007) ............. 101

Figure 2.85 Velocity measurements across nozzle opening, Pplenum = 0.15, Torr, Pdissipated = 400mW. Gregory et al (2007) ......................................................... 101

Figure 2.86 Plots of switching time for varied flow velocities and power settings. Gregory et al (2007) .............................................................................................. 102

Figure 2.87 Geometrical specification and photo of the model. a) geometry of the amplifier, and b) photograph of the assembled amplifier as used in the experimental investigations. Tesar et al (2006) .......................................................................... 103

Figure 2.88 Flow transfer characteristic of the amplifier in relative co-ordinates; the response to the control signal admitted to only one control terminal X1. Tesar et al (2006) .................................................................................................................... 104

Figure 2.89 Pathlines of flow in the state B. Tesar et al (2006) ............................. 104

Figure 2.90 An example of a typical oscilloscope record of generated oscillation. Tesar et al (2006) .................................................................................................. 105

Figure 2.91 The frequenct vs. loop length dependences obtained with the 10mm diameter loop tube at different supply flow rates. Tesar et al (2006) ..................... 105

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Figure 2.92 The experimental results obtained with the 10mm diameter loop tube at different flow rates re-plotted in terms of the Strouhal number as a function of Reynolds number. Tesar et al (2006) .................................................................... 106

Figure 2.93 The propagation velocity for different feedback tube diameters. Tesar et al (2006) ................................................................................................................ 107

Figure 2.94 Dependence of the propagation velocity in resonant conditions in the feedback loop tube on Stokes number for different tube diameters, d. Tesar et al (2006) .................................................................................................................... 107

Figure 3.1 Geometrical specification of the fluidic oscillator planform. (Dimensions in mm) ....................................................................................................................... 110

Figure 3.2 Geometrical specification of the fluidic oscillator interaction region. (Dimensions in mm) .............................................................................................. 110

Figure 3.3 Photos of the fluidic oscillator test model. ............................................ 110

Figure 3.4 Experimental set-up for the steady-state analysis ................................ 112

Figure 3.6 Geometrical specifications of a fluidic amplifier in the array ................. 115

Figure 3.7 3D drawing showing the general assembly of the test model. Tesar (2007) .............................................................................................................................. 116

Figure 3.10 A feedback circuitry for a constant temperature anemometer ............ 120

Figure 3.11 An example of a hotwire calibration graph. ........................................ 122

Figure 3.12 An example of the velocity sensitivity calculated for the case shown in Figure 3.11 ............................................................................................................ 123

Figure 3.13 An example of the relative standard uncertainty due to the resolution error for the case shown in Figure 3.12 ................................................................. 123

Figure 3.14 Homemade orifice plate flowmeter geometry and corresponding symbols ................................................................................................................. 125

Figure 3.15 The mass flow rate calibration graph of the homemade orifice plate. 127

Figure 3.16 Total relative standard uncertainty in the estimated flow rate over the range of the calibration flow rate ........................................................................... 129

Figure 4.1 Variations of the control mass flow rate, 1cm, at the switching point and

its ratio to the supply flow rate, 1,cm , with hDRe. ................................................. 131

Figure 4.2 Time-averaged velocity measured at the centre and 1DO downstream of the output orifice at Low state and corresponding time-averaged spatial mean velocity across the orifice assuming Hagen-Poiseuille flow. ................................. 135

Figure 4.3 The calculated mass flow rate through the inactive side exit orifice for both cases of flow being suction and spill as a function of the orifice Reynolds

number, ODRe. ...................................................................................................... 135

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Figure 4.4 The calculated mass flow rate through the inactive side exit orifice and its

ratio to the supply flow rate plotted against hDRe. ................................................ 136

Figure 4.5 The calculated mass flow rate through the active side output orifice and

its ratio to the supply flow rate as a function of the hDRe. ..................................... 137

Figure 4.6 The corrected mass flow rate ratio through the active side output orifice for the mass flow rate through the inactive side. ................................................... 138

Figure 4.7 Output mass flow rate at the high state side and flow gain .................. 140

Figure 4.8 Flow gain of the fluidic oscillator at the steady state test conditions. ... 140

Figure 4.9 The output jet characteristics of the fluidic oscillator model measured simultaneously at the two exit orifices at ReDh = 4.92x104 and L=1.16 and approximated T of 10.5ms. a). Instantaneous velocity profile; b) Phase-averaged velocity variation over a one cycle; c) Phase-averaged turbulence intensity over a one cycle. .............................................................................................................. 142

Figure 4.11 Instantaneous velocity fluctuations and power spectral density ......... 145

Figure 4.12 Instantaneous velocity fluctuations and power spectral density ......... 146

Figure 4.14 Correlation between Strouhal number and hDRe. .............................. 149

Figure 4.15 Correlation between modified Roshko number and hDRe. ................ 149

Figure 4.16 Correlation between normalised switching time and hDRe. ............... 151

Figure 4.17 Variations of T/2 as a function of the feedback loop length at different

hDRewhich are used to find the natural switching time ......................................... 152

Figure 4.18 Approximated fundamental switching time, n , of the test model ...... 153

Figure 5.1 Instantaneous velocity variation measured at the centre and 1DO downstream of an amplifier exit orifice with bS=2mm and AR=4 .......................... 161

Figure 6.1 Conceptual drawing of a monostable control loaded fluidic oscillator. a) Planform of the fluidic oscillator; b) 3D showing the modules forming the fluidic oscillator. ............................................................................................................... 170

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List of tables

Table 3.1 Experiment case summary for the study of the jet oscillation characteristic of a fluidic oscillator….............................................................................................113

Table 3.2 Summary of the test cases for the study of the fluidic amplifier………..118

Table 3.3 Summary of the estimated maximum errors in the velocity measurements through hotwire measurements with calibration graph shown in Figure 3.11…….124

Table 4.1 Fanout ratios of the fluidic oscillator calculated at variousRe ………..154

Table 5.1 The calculated values of the amplitude to time averaged velocity ratio for various DO values with bS=2mm and AR=4………………………………………….162

Table 5.2 The calculated values of the amplitude to time averaged velocity ratio at DO,min for different AR values of 2 and 4 with bS=2mm…………………………...163

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Nomenclature

Do Output orifice diameter

bS Power nozzle width

bc Control nozzle width

B Offset distance of an attachment wall from the power

nozzle

L Feedback loop length

h Power nozzle height

Dh Hydraulic diameter

AR Aspect ratio of power nozzle

Ao Cross sectional area of Output orifice

Aref Cross sectional area of the fluidic element output aperture

conduit at the location of the output port

US Power jet mean velocity at the exit plane of the power jet

nozzle

u Time-averaged jet velocity

mu Time-averaged jet mean velocity

u Difference between the high state velocity and the low

state velocity of the oscillating jet

<u> Phase-averaged velocity

f Frequency of jet oscillation

fsat Maximum attainable frequency

P Pressure

P Differential pressure

T Period of jet oscillation

xR Power jet attachment distance

mandqm Mass flow rate

qV Volume flow rate

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M Local Mach number

GF Flow gain

nF Fanout ratio

Tu Turbulence intensity

St Strouhal number based on US and L

SbRe Reynolds number based on bS

hDRe Reynolds number based on Dh

ODRe Reynolds number based on Do

CRe Critical Reynolds number based on Dh

Romod Modified Roshko number

Greeks

ξ Ratio of feedback loop length to power nozzle width

ρ Density of fluid

Dynamic viscosity of fluid

Kinematic viscosity of fluid

m Ratio of mass flow rate to supply flow rate

P Propagation time

S Switching time

n Fundamental switching time

L Switching delay time

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Copyright

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- XV -

Declaration

No portion of the work referred to in this thesis has been submitted in support of an

application for another degree or qualification of this or any other university or other

institution of learning

- XVI -

Acknowledgements

I would like to take this opportunity to express my sincere gratitude to my supervisor,

Dr. Shan Zhong, for her support and understandings throughout this interesting

project. I am also grateful to Prof. Vaclav Tesar from the Academy of Sciences of

the Czech Republic for providing the design of the model and his technical advice.

I feel very indebted to my family for their continuous encouragement and support to

my study in abroad.

Finally I would like to express my appreciation to my colleagues and technical staff

at the Goldstein Laboratory of Manchester University for their numerous advices on

the experimental setup and the manufacturing of the model.

- XVII -

Abstract The current study experimentally examines a control loaded bistable fluidic

oscillator and an array of bistable fluidic amplifiers driven by the control loaded fluidic oscillator to validate their potential as an alternative flow control actuator. These fluidic devices are considered to be able to generate a periodically oscillating jet without a necessity of any mechanical moving parts and their prototype designs are provided by Professor Vaclav Tesar from Academy of Sciences of the Czech Republic. The output jet characteristics of the control loaded fluidic oscillator has been experimentally evaluated by means of hotwire measurements with single wire probes oriented normal to the plane of output orifices for supply flow rate range of 0.7g/s ~ 6g/s with a feedback loop length as a parameter which varied from 0.3m ~ 1.78m. The experiment have successfully demonstrated that the prototype fluidic oscillator can generate periodically oscillating jets from its conjugating pair of orifices in an alternating manner with a 50% pulse duty cycle, which its amplitude varies proportionally to the supply flow rate. The period of the pulsation found to vary linearly with a supply flow rate up to a power nozzle Reynolds number of 3.0X104 where the frequency saturation initiates giving a constant Strouhal number of ~0.7 with further increase in supply flow rate. The experimental results demonstrate an existence of a strong correlation between the propagation time, P , and the

switching time, S , in determining the saturation frequency, fsat, for a chosen

feedback loop length. Furthermore the current study demonstrates a simple way of possibly approximating the natural switching time of a control loaded fluidic oscillator without making an internal flow measurements, which may require further verification though, and found it to be approximately 1ms for the current test model. In general, the frequency response of the oscillating output jet reduced linearly with increasing feedback loop length when running at a relatively low values of

hDRe ,

while changing inverse proportionally with L at high hDRe values.

The experimental study of an array of bistable fluidic amplifiers verified that there exists a load mismatching due to a concentric reduction in the output orifice diameter for its intended function of delaying flow separation over an aerofoil, which caused attenuation in the output pulse characteristic. Although this change in the output characteristic may not be crucial when it comes down to an actual flow control application or can even be advantageous in certain cases the author attempted to remove the disparity in the output jet characteristic with a normal operation condition and suggests a design modification as described in chapter 5. As a by-product of this study it was found that the ratio of the output orifice diameter to the cross sectional area of the exit aperture conduit of a device should be greater than ~0.5 to avoid attenuated output jet characteristic and as a supporting evidence it was found that amplifier with a smaller height, i.e., lower power nozzle aspect ratio, can accommodate a smaller orifice diameter without disturbed output jet characteristic.

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ader flight e

rcraft transp

l ng mid 190

been deve

ive tangen

ow (steady

flow near

y layer flow

h as what is

g and a red

n result in a

ow separat

ering.

gle from

31).

s improved

a greatly en

ntrol surface

ce a reduc

sed for sup

As a summa

envelope an

port industr

00s various

eloped (Gad

ntial blowing

VGJs), act

the wall an

w by enhan

s shown

uced lift

a loss of

tion is of

lift/stall

nhanced

es to be

ced fuel

personic

ary, flow

nd it can

y.

types of

d-el-Hak

g which

tive wall

nd vane

cing the

mixing wit

employed

this conte

requireme

level of m

separation

Figure 1.2both walls(Schlichtin(1931).

Since the

Vortex Ge

Pearcey 1

accomplis

using so

incorporat

Extensive

(Zhang an

1996; Am

the vane

exhibit an

arises fro

penetrate

improved

unsteady

steady VG

much mo

th the high

on aircraft

xt categoris

ents in their

modification

n control wit

a)

2 Separatios; a’) Sucting and Ge

demonstra

enerating J

1961), Puls

shing the co

lenoid/siren

ting a piezo

efforts on

nd Sheng 1

itay et al 19

vortex gen

improved p

m the fact

further into

mixing wit

pulsation,

GJs due to

re effective

energy ou

ts (Joslin 19

se flow con

r actuation.

of the flow

th a classic

on control ion appliedrsten (2000

ation of the

Jets (Pulse

sed VGJs h

ontrol. Gen

n valves o

oelectric dia

verifying t

987; Katz e

998; Glezer

nerators (VG

performanc

that they

o the boun

h an outer

a much gre

the genera

e in mixing,

- 19

uter flow. S

998). The p

ntrol method

. Figure 1.2

w that can b

c active suct

a’)

of flow ind only at th0)). Origina

capability i

ed VGJs) in

have been

neration of

or cylindri

aphragm o

their effecti

et al 1989;

r et al 2005

Gs) and th

ce in suppre

can gener

ndary layer

r layer. Als

eater mixin

ation of larg

, in additio

9 -

ome of the

passive and

ds dependi

2 provides

be achieved

tion method

)

a diffuserhe upper wal picture ta

n delaying

n late 195

regarded a

pulsed VG

cal pump.

r plasma e

veness and

Seifert et a

). Compare

e steady V

essing flow

ate convec

than those

so as a res

g can be a

ge scale tur

n to the cu

ese devices

d active cla

ng on the e

a reader w

d by the ap

d.

r by suctiowall; a’’) Suaken by Pr

the flow se

0’s (Wallis

as a promis

GJs are nor

Also, ad

electrode ar

d feasibility

al 1993; Mc

ed to its pre

VGJs, Pulse

separation.

ctive vortica

e of steady

sult of an

achieved co

bulent vorte

ustomary st

s are now r

assification

energy exp

with an idea

pplication o

a’’)

on. a) Sepauction at brandtl and

eparation of

and Stuar

sing alterna

rmally achie

dvanced a

re frequent

y have bee

cManus et

edecessors

ed VGJs a

. This impro

al structure

y VGs resu

impulsively

ompared to

ex rings, w

treamwise

routinely

used in

enditure

a of the

of a flow

ration at oth wall Tietjens

f Pulsed

rt 1958;

ative for

eved by

ctuators

ly used.

en made

al 1994,

such as

ctuators

ovement

s which

ulting an

y started

o that of

hich are

vortices

(Johari an

zero paras

In more re

classic m

(MEMS) b

increased

to deliver

MEMS tec

global inte

1.3 FluThe

generating

moving pa

Coanda ef

A fluidic o

control po

two classi

named as

fed oscilla

a) Con

F

nd McManu

site drag an

ecent years

methods to

based actu

need for th

an optimis

chnology an

erest in sea

uidic oscmost inge

g periodical

arts. A fund

ffect and th

oscillator us

orts along w

c designs a

s the contro

ator.

ntrol loaded

S –

Figure 1.3 C

us 1997). F

nd they also

s, the resea

developing

ation meth

he separatio

sed perform

nd the even

rching for m

illatorsnious featu

lly oscillatin

amental pri

is will be ex

sually cons

with their fee

as shown in

ol loaded flu

d fluidic osci

– supply por

Classic des

- 20

urthermore

o require mu

arch empha

g more effi

hods (Wars

on control d

mance at a

n increasing

more effectiv

ure of fluidi

ng pulsed je

inciple of th

xplained in

sists of one

edback loop

n Figure 1.3

uidic oscilla

illator

rt; C – cont

signs of flu

0 -

, Unlike the

uch less air

asis has bee

icient Micro

op et al, 2

devices to b

ll flight con

g demand fo

ve and robu

c oscillator

ets without a

heir operatio

details in C

e supply po

p. They can

, in which th

tor and tha

b) V

rol port; O –

uidic oscill

e VGs, Puls

supply than

en shifted f

o-Electro M

2007). This

be controlled

nditions. Th

or energy sa

ust actuator

s would be

a necessity

on is based

hapter 2.

ort, two out

n be genera

he oscillato

t in Figure

Vent-fed fluid

– output por

ator. (Morri

sed VGJs

n the stead

from optimi

Mechanical

is a resul

d on deman

he advance

aving have

rs for flow co

e their capa

y of any mec

d on the we

tput ports a

ally categori

or in Figure

1.3 b) as th

dic oscillato

rt

is (1973)).

produce

y VGJs.

sing the

System

lt of the

nd so as

s in the

led to a

ontrol.

ability of

chanical

ll known

and two

sed into

1.3 a) is

he vent-

or

- 21 -

Both types of the above fluidic oscillators share a common principle at the very

beginning stage of their operation which can be summarised as following. As the

power jet leaves the power nozzle (throat), owing to the Coanda effect it will choose

to attach to one side of the attachment walls. For a symmetric bistable oscillator, the

jet can attach equally well on to one of the both sides of the attachment walls, hence

the jet attachment would solely governed by a naturally introduced momentary

disturbances. However, in an asymmetric monostable oscillator the power jet will

always attach to the side where the entrainment is more restricted. This attached jet

will then initiate the habitual oscillation mechanism in the fluidic oscillator. Figure

1.34 shows schematic drawings of a symmetric bistable and symmetric oscillators.

a) Symmetric bistable oscillator b) Asymmetric monostable oscillator

Figure 1.4 Schematic drawing showing the geometrical difference of a symmetric bistable and asymmetric monostable oscillator.

In a control loaded fluidic oscillator, the separation bubble formed on the attached

side wall further increases the pressure difference hence a rarefaction wave

(expansion) is generated on that side of the control port while a pressure wave

(compression) grows on the opposite side. The continuous generation and

interaction of these waves through the time delay feedback loop is the fundamental

principle of operation of these types of oscillators. Due to this switching

characteristic, they are more appropriate to be regarded as a pressure driven

devices.

The switching mechanism in a vent-fed fluidic oscillator partially incorporates

pressure change but the oscillation is mainly driven by the momentum injection

through the control ports (momentum driven devices). In this type of oscillator, a

portion of the fluid captured from the attached flow will be fed back to the control

port and deflects the jet to the opposite side. The same process initiates on the

newly attached side and a replication of this cycle generates the periodic oscillation.

Ba Bb Ba Bb

The perio

pneumatic

interaction

As these

part, they

This woul

Furthermo

compartm

promises

up to a ra

1973; Rab

separation

oscillator i

In recent y

devices fo

fundamen

(Tesar et

laboratory

and Ragh

have been

actuators,

amplifier i

flow level

focused o

switching.

evaluation

Fluidic de

actuator m

od of the os

c resistanc

n region geo

devices can

offer many

ld include

ore, they u

ment space

to be low i

ange of se

ber and Sh

n control de

is shown in

years, there

or flow contr

ntal perform

al 2006; Y

y scale inter

u 2004; Ce

n made on s

such as

n order to g

(Gregory e

on fluidic de

Thereby t

n of a press

evices hold

mainly due

scillation in

ce and cap

ometry.

n generate

advantage

greater me

sually cons

and mainte

n long term

veral kilohe

hinn 1964),

evice. An e

Figure 1.5.

e has been

rol applicati

mance char

ang et al 2

rnal/externa

erretelli et al

studying the

piezoelectr

gain control

et al 2005, 2

evice emplo

the work sh

ure driven f

many pot

to their geo

- 22

both types

pacitance

pulsing jets

es compared

echanical a

sist of simp

enance wor

m. Also, wit

ertz is atta

, which is

example of

.

a lot of pub

ions. These

racteristics

2007; Furlan

al flow contr

l 2009, 201

e feasibility

ric transdu

l authority o

2007, 2009

oying the m

hown in thi

fluidic oscill

tential bene

ometrical s

2 -

s of the os

in the fee

s in an abs

d to other c

and environ

ple intercon

k. As a res

th microfabr

inable with

commonly

a microfab

Figure 1.5bistable veoscillator

blished wor

e research e

of innovati

n et al 200

rol applicatio

0). Also, no

of incorpor

ucer or pla

of the jet sw

9). However

omentum in

is thesis re

ator as an a

efits makin

implicity an

scillators are

dback loop

sence of a m

conventiona

nmental con

nnections h

ult, the cos

rication a fr

these fluid

required b

bricated bis

Microfabrent-fed flui(Simões (2

rk suggestin

efforts range

vely design

6) to valida

ons (Culley

otable numb

rating other

asma actua

witching inde

r, most of re

nteraction a

epresents a

alternative P

g them an

nd superior

e governed

p as well

mechanical

al PVGJs ac

ndition robu

hence requ

st of fluidic s

requency re

dic devices

by a PVGJs

stable vent-

ricated idic 004))

ng the use o

e from stud

ned fluidic

ation of a d

y et al 2003;

bers of pub

known flow

ator, into a

ependent o

research eff

as a princip

an early att

PVGJs actu

n attractive

physical du

d by the

as the

moving

ctuators.

ustness.

uire less

systems

esponse

(Morris

s based

fed fluic

of fluidic

dying the

devices

device in

Raman

lications

w control

a fluidic

of supply

forts are

ple of jet

tempt of

uator.

PVGJs

urability.

- 23 -

Nevertheless, our knowledge as how to design the fluidic devices which satisfy the

requirement on jet velocity, pulsing frequency and optimisation of actuator geometry

for flow control purposes is still lacking.

1.4 The objectives of this project As the result of a collaborative research with Czech Academy of Sciences, the

prototype of a bistable control loaded fluidic oscillator and the design of a fluidic

circuit consists of an array of bistable fluidic amplifiers with a potential application for

delaying flow separation on a 2D aerofoil section have become available.

The objectives of this work are;

1. To examine the jet characteristics of a single fluidic oscillator over a range of

supply flow rates and control loop length;

2. To examine the jet characteristics of the fluidic circuit at a range of supply

flow rates and actuation frequencies;

3. To propose the modification of the fluidic circuit so that it can deliver the

required jet characteristics when it is embedded in an aerofoil section to be

used in a flow separation control experiment.

All the experiments were conducted at the Goldstein Aeronautical Lab. The jet

characteristics were measured using a single-normal hotwire probe.

1.5 The layout of this report Chapter 2 describes the fundamentals of the boundary layer concept including

the definition, the nature of turbulent boundary layers and the separation

mechanism. A literature review of flow control and fluidics is also included

describing their classification, principles of operation and previous work that has

been undertaken as to demonstrate their capability.

Chapter 3 describes the experimental models and experiment methods used

to accomplish the aforementioned objectives.

Chapter 4 discusses the experimental findings attained from the study of the

single prototype fluidic oscillator. This includes its steady state performance

parameters, oscillation characteristics and exit jet responses. Chapter 5 presents

the experimental results gained from the study of an array of bistable fluidic

- 24 -

amplifiers driven by the prototype fluidic oscillator. Most of the section has been

devoted to show their oscillation and jet response to a driving actuator.

Chapter 6 shows the author’s perspective of the feasibility of the existing

control loaded bistable fluidic oscillator as a separation control device based on his

understanding gained through this project. Suggestions for future work are also

given.

- 25 -

2 Literature review

2.1 Boundary layer and its separation As the fluid moves over a solid surface, the fluid molecules in contact with

the surface adhere to the surface owing to fluid viscosity, resulting in the no-slip

condition. On the other hand, the effect of viscosity becomes negligible further away

from the surface, allowing the fluid to follow the speed of the freestream velocity.

Thereby a region exists in the vicinity of the surface where a steep velocity change

occurs. This region is commonly known as a boundary layer or wall-bounded shear

layer.

A detachment of the boundary layer from the surface can occur at some point (or

line) along the wall and the phenomenon is known as a flow separation. Prandtl

(1904) stated that the separation occurs owing to the development of an adverse

pressure gradient along the surface in the direction of flow, which is present in the

freestream flow. The presence of the adverse pressure gradient will resist the

motion of fluid and if the fluid particles within the boundary layer no longer possess

enough energy to overcome the resistance, the motion will be halted. Further

downstream the flow starts to deflect laterally and eventually recirculation is

generated causing the departure of the boundary layer from the surface and

resulting in greatly increased pressure and form drag. The flow visualisation

showing development at the time of boundary layer separation is shown Figure 2.1.

At this point, it would be worth reviewing the total drag components of an

aerodynamic body moving in a flow and their origin to aid understanding of their

interrelation with the boundary layer. The total drag components of an aerodynamic

body can be broadly divided into a profile drag and a lift-induced drag. When a fluid

flow moves over a finite length lifting surface/body the resulting pressure difference

between the suction surface and the pressure surface creates a vortical structure at

its tip known as a wing tip vortex and this is the major source of the lift-induced drag.

The profile drag is usually subdivided further into a skin friction drag, a form drag

and a pressure drag. The skin friction drag is governed by the fluid viscosity and a

surface roughness of the body, hence determining the magnitude of the shear

stress that develops between the body surface and fluid particles moving over its

vicinity. On the other hand, as a boundary layer develops over a body moving in a

fluid flow t

with a cor

effective b

easily und

body at a

from the b

in a consi

This caus

motion an

Figure 2.1at the afrecirculatioboundary reversed formed frofrom the bbody. Sch

2.2 BoBou

layer will a

controlled

turbulent t

number b

106 (Schli

Reynolds

pressure

roughness

this causes

rresponding

body shape

derstood by

an angle. A

body surfac

derable pre

es the body

d this force

1 Flow visuft of an uon has juslayer separmotion mo

om the bacbody and mhlichting and

undary lndary laye

always natu

. For a flat

transition in

ased on a

chting and

number, go

distribution

s (Schlichtin

s a physical

increase in

e is called a

y visualising

boundary

ce creating a

essure diffe

y to experie

is known a

ualisation supper quat begun at ration; b) Th

oved forwarkflow; d) Th

moves downd Gersten (2

ayer tranr can be e

urally devel

plate with a

n a normal a

distance fro

Gesten 20

overning th

n and turb

ng and Ges

- 26

l profile cha

n drag. This

a form drag

g a fluid flo

layer unde

a low press

erence betw

ence a pres

as a pressur

showing a adrature of the trailinghe boundarrd with grohe vortex gnstream cha2000).

nsition either lamin

op into a tu

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om the lead

000). There

e onset of

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sten 2000).

6 -

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. The origin

ow over a b

r this circu

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ween the for

ssure force

re drag.

developmef a symmg edge shory layer hasowing in itsrows in its anging the

ar or turbu

urbulent bo

ding edge a

akes place

ding edge e

e are many

the turbulen

tensity of

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drag owing

n of the pre

blunt body o

mstance w

at downstr

rward and t

in the oppo

ent in timemetric cylinortly after t thickened

s size; c) Asize; e) Thflow portrai

ulent and a

undary laye

at zero incid

at a point w

exceeds Re

other facto

nt boundary

the outer

pe making it

g to a chan

essure drag

or an aerod

ill usually s

ream, which

the aft of th

osite directi

e of the sepnder. a) Tthe initiationand the sta

A large vorhe vortex seit at the rea

a laminar b

er unless ot

dence, the

where the R

ex crit = 3.5 X

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y layer such

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paration The flow n of the art of the rtex has eparates ar of the

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Reynolds

X 105 to

from the

h as the

surface

- 27 -

The Tollmien-Schlichting (T-S) instability transition mechanism is proven by free

flight experiment that this dominates in most of subsonic boundary layers, except for

swept wing where cross-flow instability plays an important role (Schlichting and

Gesten 2000). For two-dimensional zero pressure gradient boundary layer, the

process can be summarised as follows; above the indifference Reynolds number

(Reind) the laminar boundary layer becomes sensitive to small disturbances, leading

to amplification of unstable two-dimensional linear T-S waves (primary instability).

Once these primary T-S waves exceed a threshold value of 1% of the freestream

velocity (King and Breuer 2002), they slowly become three-dimensional and form

hairpin vortices (non-linear secondary instability). These then interact together and

are intensified as they are stretched to form the turbulent spots. The turbulent spots

grow as they propagate downstream and they eventually merge, leading to a fully

turbulent flow. The sketch of the process is given in Figure 2.2 and some of the

pictures of structures developed in the boundary layer are shown in Figure 2.3.

Tollemien (1929) and Schlichting (1933) applied the Orr-Summerfield equation to

analysed the linear primary instability with the laminar Blasius boundary layer and

estimated theoretical Reind of 520 (Schlichting and Gesten 2000) based on the

boundary layer thickness using Eq. 2-1

Ux 0.5 Eq. 2-1

Most of their theoretical estimation of the essential points agreed well with

experimental data (Schlichting and Gesten 2000) of Dryden (1946, 1948) and the

existence of T-S waves in natural transition has also been experimentally confirmed

by Arnal et al (1977).

There is one other important transition mechanism, first verified by Morkovin (1988),

in the flow control point of view known as the bypassed transition. In this scheme

the aforementioned T-S instability is bypassed and the subcritical perturbation

introduced in the initial condition, such as turbulence intensity and/or surface

roughness, etc., directly amplifies the secondary instability or even turbulent spots,

leading to advancement in transition. An example of bypass transition is shown in

Figure 2.4 where transition is triggered by a tripwire placed around a sphere.

Figurre 2.2 Lamia)

O

inar to turb) Sketch of

SchlicOriginal pict

- 28

a)

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- 29

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r. The incre

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ntly the flow

boundary l

there is a da

the flow se

rag by prom

oning separa

t safety from

simplified a

ght.

ity profile

flat plate at

eased shea

surface un

w separation

layer, as s

anger of inc

eparation (p

moting the t

ation would

m buffeting,

and/or safe

in lamin

t zero incid

ar stress

nder the

n can be

hown in

creasing

pressure

urbulent

d include

, greater

er use of

nar and

dence

Figure 2.surface. aand b’) ThDyke (198

2.4 Flo

2.4.1 DeAft

presented

manipulat

the study

in the real

developm

achievable

of study ‘F

Th

wa

glo

The desir

accelerate

end result

noise, imp

a

a

.8 Laminara) and a’) hicker turbu82).

ow contro

efinition ater the pub

d the conce

ion by dela

of new tec

m of aerosp

ent of an

e by traditio

Flow Contro

he controlle

all-bounded

obal modific

red global

ed/delayed

ts of these c

proved man

a)

’)

r and turbShow thinn

ulent bound

ol

and its cllication by

ept of the

ying the flow

hnologies f

pace indust

aircraft wit

onal geome

ol’, which ca

d modificat

and/or fre

cation in the

changes

transition

consist of re

noeuvrabilit

- 32

bulent flowner laminar dary layer, d

assificatiLudwig Pra

boundary

w separatio

for flow con

try believed

h improved

etrical optim

an be define

tion of the

ee shear flo

e dynamics

usually inc

and preven

educed drag

ty, augmen

2 -

w over a sboundary

delayed and

ion andtl in 190

layer and

on by the us

ntrol took of

d that this un

d overall p

misation of t

ed as follow

local boun

ow fields in

of their flow

clude supp

nted/provok

g, enhanced

ted mass/m

b)

b’)

sharp cornlayer and td suppresse

04 of semin

the possi

se of slit su

ff. The majo

nique techn

erformance

the body an

ws;-

ndary layer

n order to

w characteri

ressed/enh

ked separat

d lift, suppre

momentum/e

ner and a their separaed separati

nal researc

bility of its

uction on a c

ority of rese

nology could

e beyond th

nd named t

flow cond

achieve a

istics.

hanced turb

tion. The p

essed flow-

/energy mix

curved ation; b) on. Van

ch which

s forced

cylinder,

earchers

d realise

he level

this field

itions of

desired

bulence,

potential

-induced

xing and

- 33 -

removal/simplification of control surfaces. One should, however, recognise the

interrelation between one control goal and another, as in Figure 2.9 in determining

the net performance gains.

For the past one century many different flow control strategies have been developed

and demonstrated their capabilities ranging from as simple as controlled surface

roughness to as advanced as feedback closed control loop MEMS(Micro-Electro-

Mechanical Systems) based actuators. These various flow control devices are

commonly categorised as shown in Figure 2.10

A technique that requires any form of energy expenditure in driving the actuator

would be classified as an active method while the term passive is used to describe

those which do not. Active control methods are subdivided further depending on the

capability of producing a dynamic response to changes of flow state, into

predetermined and reactive methods. The reactive system can be distinguished by

the use of sensors to make pre-specified flow measurements to adjust the control

input to vary accordingly, and the system can either be open or closed loop.

2.4.2 Classic methods and principles of operation In this section some of the historical developments of the classical and

recent flow control methods of the last century and their principles of operations are

discussed.

2.4.2.1 Stability modifiers Stability modifiers are those of flow control actuators/methods intended to

suppress the initiation of the boundary layer transition to benefit from the customary

lower skin friction in laminar boundary layer by controlling the primary instability

growth in the boundary layer. Although the ultimate goal of this method is to reduce

the skin friction, separation delay is another beneficial by-product. This scheme is

generally applied to a flow with a Reynolds number lower than 3x107 and various

techniques are available, such as moving wall, wall heating/cooling, aerodynamic

shaping, wave cancellation, etc.

Figur

Figur

re 2.9 Inter

re 2.10 Clas

- 34

rrelation beGad-el-Ha

ssification Gad-el-Ha

4 -

etween flowak (2000)

of flow coak (2000)

w control g

ntrol strate

goals

egies

- 35 -

For the completeness of the report the suction method (Laminar Flow Control),

which has been extensively studied and is still receiving considerable attention from

the industries, is reviewed in terms of its development and principles of operation.

The laminar flow control (LFC) by means of active suction has been studied

extensively and yielded many promising flight test results. Its ultimate goal was to

reduce the skin friction drag during level flight in cruise condition, given that this

drag accounts for 50% of the total drag of conventional subsonic transport aircraft

(Joslin 1998), mostly owing to the presence of a turbulent boundary layer (TBL),

which has 90% higher skin friction coefficient than that of a laminar boundary layer

(LBL).

The principle of the method is postponement of the laminar-turbulent transition over

the surfaces such as the wings, tailplane, fuselage nose and engine nacelle by

removing the low energy near wall flow in the boundary layer. Suction can be

applied through permeable surfaces (porous or slots or perforated) or by tangential

slit suction.

When a perforated surface is used, this will cause a thinning effect on the existing

LBL, hence giving a more favourable velocity profile curvature leading to greater

shear stress, but much smaller than the ones in TBL, that can resist increasing

pressure more effectively. This method, however, imposes one extra drag source

called a sink drag which results from the flow withdrawn just downstream of the

point of application. In the case of slit tangential suction, existing retarded flow will

be effectively removed, followed by the development of a newly-initiated LBL that

can overcome higher pressure increase than that achievable by the former

boundary layer.

The first flight test of the method was in 1941 with a Douglas B-18 via nine slots

placed between 20 to 60% chord, as in Figure 2.11. They were able to maintain

laminar flow up to 45% chord over the range of the Reynolds number when suction

was applied decreasingly from the leading edge (Joslin 1998). Braslow et al (1951)

used a porous surface in a low turbulence wind tunnel and they were able to

achieve full chord laminar flow up to Re of 24 x 106 and drag reduction by

approximately 60% as compared with a no-control case. This work was followed by

Head et al (1955), which studied the effectiveness of the continuous distributed

porous suction and the capability of its system design methodology by using

Vampire I

flow at a M

of 70 to 80

for optima

disparity b

Fig

II fitted with

Mach numb

0 percent a

al size and

between me

Fig

ure 2.12 Va

h wing glove

er of 0.7 giv

at lower Re.

spacing a

easured and

gure 2.11 S

ampire III W

- 36

e as in Figu

ving Re of 2

. In addition

and minimu

d estimated

Slot suctioChambers

Wing gloveBraslow

6 -

ure 2.12. Th

26 x 106 and

n, the inabil

m suction

velocity pro

n wing glos (2005)

e with distr(1999)

ey achieved

d overall pro

ity of the th

requiremen

ofile. (Joslin

ve on B-18

ibuted poro

d full-chord

rofile drag re

heoretical pr

nt were ver

n 1998)

8

rous suctio

laminar

eduction

rediction

rified by

on

Although

delaying t

transport

embedme

can trip th

In an effo

Hybrid La

active LFC

own the la

instability

small lead

believed t

simplificat

LFC, as s

there are

he transitio

aircraft ap

ent complex

e TBL and

rt to overco

aminar Flow

C in conjunc

atter also su

at high swe

ding edge ra

hat the HLF

tion by NFL

hown in Fig

Figure

many exp

n, the active

pplication, s

xity, accumu

maintenanc

ome these p

w Control (H

ction with N

uffered prac

eep angle, p

adius and n

FC method

L and enhan

gure 2.13

2.13 Predi

- 37

perimental r

e LFC meth

such as th

ulation of ic

ce cost of th

problems, e

HLFC) idea

Natural Lam

ctical difficu

poor high li

necessity fo

could bene

nced high A

cted benefJoslin (

7 -

results sho

hod raises m

he manufa

ce, insects a

he system.

except the a

a was introd

inar Flow a

lties such a

ft coefficien

or very smo

efit from the

AoA and sw

fits of NLF,1998)

owing prom

many issues

acturing diff

and atmosp

accumulatio

duced, sug

erofoil (NAC

as susceptib

nt (AoA) per

ooth surface

e compromi

weep angle

LFC and H

mising pote

s, especiall

fficulties an

pheric partic

on disturba

ggesting the

CA 6 series

bility to a cr

rformance o

e conditions

ised overall

e performan

HLFC

ntial for

y for the

nd cost,

cles that

nce, the

e use of

s). On its

oss flow

owing to

s. It was

l system

nce from

The capa

performed

shown in

and conto

Mach num

approxima

1991; Coll

a) conce

ability of th

d during 19

Figure 2.14

our. The res

mber 0.82, a

ately 6% ov

lier 1993).

eptual confi

he HLFC s

90 and 199

4 with perfo

sults showe

as shown in

verall drag

Figuriguration of

w

- 38

system was

91 on the B

orated surfa

ed existence

n Figure 2.1

reduction

a)

b)

re 2.14 HLFf HLFC (Joswing Chamb

8 -

s well dem

Boeing 757

ace suction

e of the lam

5 and drag

for the airc

)

)

FC in practslin 1998); bbers (2005)

monstrated

7, employing

n to origina

minar flow u

reduction o

craft, (Madd

tice b) HLFC win

by the fli

g the confi

l 757 wing

up to 65% c

of 25 percen

dalon 1991

ng glove on

ght test

guration

surface

chord at

nt giving

; Shifrin

B757

While the

application

direct ope

and engin

consumes

before it c

further stu

requireme

civil trans

possible o

and/or ant

Figur

e concept o

n of lamina

erating costs

ne nacelle

s 80% of tot

can be con

udy include

ents, high s

port config

optimisation

ti-attachme

re 2.15 Effe

of the HLF

ar flow cont

s, for exam

of the sub

tal fuel duri

sidered as

e long-term

sweep angl

uration and

n of extra

nt line turbu

- 39

ect of HLFCJoslin (

C greatly e

trol and is b

mple, a 14%

bsonic trans

ng cruise, t

a ready te

structural

e performa

d military u

system re

ulence cont

9 -

C during B1998)

enhances t

believed to

% drag reduc

sport aircra

the technolo

chnology fo

robustness

ance for fut

use, theoret

equirements

amination d

757 flight t

the feasibil

provide po

ction from t

ft A340 (R

ogy requires

or applicatio

s of the sys

ture applica

tical design

s, such as

devices.

test

ity of the p

otential redu

the wings, t

Robert 1992

s further ev

on. Areas r

stem, main

ation in hig

n methodolo

s anti-accum

practical

uction in

tailplane

2) which

valuation

requiring

tenance

h-speed

ogy and

mulation

- 40 -

2.4.2.2 Turbulators This term generally describes methods involving turbulence enhancement in

the boundary layer, usually to take advantage of increased mixing and tendency to

postpone the boundary layer separation. These devices are best applied within the

region where the transitional range of Reynolds number occurs, as they are prone

to disturbances.

In the realm of aerospace industry, passive vortex generators (VGs), such as vane

VGs, Leading Edge eXtension (LEX) and etc., are the most widely known and

routinely used example of the turbulators. Their application is relatively simple and

yet gives an acceptable performance when they are carefully oriented and located.

Since the first demonstration by Taylor (1948) in the late 1940s, who used a row of

small plates projected normal to the surface and placed at an angle to the local flow,

various shapes of conventional vane vortex generators have been developed and

are broadly used in delaying boundary layer separation (Schubauer and

Spangenber 1960), to enhance lift (Pearcey 1961 and Bragg and Gregorek 1987),

and to improve wing buffet characteristics (Pearcey 1961).

These devices, usually with height compatible with the local boundary layer

thickness, generate tip vortices travelling in streamwise direction and the retarded

near wall flow is energised by these vortices owing to the entrained high energy

freestream flow. Their performance is greatly governed by planform shape, section

profile and camber, yaw angle, aspect ratio and height in respect of boundary layer

thickness (Gad-el-Hak 2000). In addition, the orientation of devices relative to others

determines the directional nature of the trailing vortices, producing either co-rotating

or counter-rotating vortices as in Figure 2.16 and magnitude of vorticity by their

interactions with each other. It is generally known that counter-rotating VGs tend to

function more effectively in controlling 2D types of separation while co-rotating

provides better performance in 3D separation cases (Lin 2002).

Although they are effective in delaying the separation, these devices produce

considerable parasite drag during cruise condition unless they are retracted or

stowed. Recent work by Lin and Howard (1989) produced substantial reduction on

the size of conventional VVGs enabling the use of miniaturised VVGs with a height

of only 20% of the local boundary layer but giving comparable effect, as shown in

Figure 2.17 and these are known as Micro VVGs (MVVGs), as in Figure 2.18.

Figure

Figure 2.1back warMVVGs ha

Figu

2.16 Spatia

17 Oil-flowrd facing raving the he

ure 2.18 MV

al relation a) Co

a) w visualisat

ramp by ceight of 20%

VVGs on le

- 41

of VVGs ano-rotating; b

(ESDU

tion showico-rotating% of BL thic

eading edgeChambe

1 -

a)

b)

nd sketch ob) Counter rU 93024)

ng the sep MVVGs. a

ckness. Lin

e of trailingers (2005)

of generaterotating

paration dea) normal fand Howar

g edge flap

ed vortices

b) elay of 3D fflow condit

rd (1989)

p of Piper M

s pattern.

flow over ation; b) with

Malibu

a h

Unlike the

can be u

separation

upstream

2002) .

Neverthele

associated

control ov

conditions

idea of Vo

overcomin

When con

skewed a

Figure 2.1

with boun

literally a

Johnston

producing

Figu

e macro VV

used, as th

n point/line

of the base

ess, althou

d with VGs

ver its actua

s and room

ortex Gene

ng these dra

ntinuous air

and pitched

19, and this

dary layer f

nalogous e

(1992) fou

strong stre

ure 2.19 De

VGs, howev

hese device

are reason

eline separa

ugh this m

to some e

ation to give

m still existe

rating Jets

awbacks of

r jets are b

at an ang

s generates

flow as they

effect like

und the op

eamwise vo

efinition of Jo

- 42

ver, there is

es can on

nably fixed a

ation, usuall

method gr

extent, it did

e optimised

ed for furthe

triggered b

f the VGs.

blown throu

gle to local

s persistent

y are conve

that of con

ptimum pitc

rtices.

pitch and sohari and R

2 -

s a limitatio

ly be appl

and need to

ly 5 ~ 30 tim

reatly redu

d not satisf

d performan

er improvem

by Wallis (1

ugh an orif

onset flow

t longitudina

ected in stre

nventional

ch and ske

skew of anixon (2003)

on on the r

ied in situ

o be placed

mes the heig

uced habitu

fy the dema

ce over a w

ments in its

1952) provid

ice in a so

w, as schem

al vortices w

eamwise dir

passive VG

ew angle o

n vortex jets

regions whe

uations whe

d quite clos

ght of MVV

ual parasit

and for clos

wide range

s profile dr

ded a poss

olid surface

matically s

which then

rection prod

Gs. Compt

of 450 and

s orientatio

ere they

ere flow

se to the

VGs, (Lin

te drag

sed-loop

of flight

rag. The

sibility in

, that is

hown in

interact

ducing a

ton and

d 900 in

on

Selby et

suppressi

rearward f

its perform

application

Figure 2.separatioSelby et a

They hav

velocity ra

the 2D se

more effec

The overa

the use of

1958; Pea

as they e

tangential

capability

in lift. The

confirmed

They verif

steady jet

area on a

deeper str

the bound

have been

Johari and

al (1992)

ng the 2D f

facing ramp

mance para

n.

a).20 Oil flo

on. a) Baselal (1992)

e verified g

atio and ske

eparation it

ctive than th

all performa

f pulsing jet

arcey 1961)

essentially r

blowing ov

of the PVG

e potential

by McMan

fied that for

s in delayin

an aerofoil

reamwise v

dary layer (J

n demonstr

d McManus

successfully

flow separa

p using an a

ameters inc

) ow visualisline case; b

generally im

ew angle of

t was foun

hat of gener

ance efficien

ts was conc

), commonly

require less

ver the hing

GJs in delay

benefit of s

nus et al (

r a given flo

ng flow sepa

section. F

ortex penet

Johari and R

rated (Grow

s 1997). Als

- 43

y demonst

ation associa

array of ten

cluding velo

sation of sb) Steady je

mproved pe

orifice valu

nd orifice o

rating coun

ncy of the s

ceived inste

y known as

s flow supp

ge of the fl

ying flow sep

smaller flow

1995) throu

ow rate, PV

aration and

Furthermore

tration, that

Rixon 2003

w and Cham

so maximum

3 -

rated the e

ated with lo

n actuators

ocity ratio, j

steady PVts in action

erformance

ues of 600 to

rientation p

ter-rotating

steady VGJ

ead of cont

s Pulsed Vo

ply. Seifert

ap on an a

paration by

w requirem

ugh flow se

VGJs perfor

d can contro

e, enhanced

t is to say, a

), compared

mpagne197

m circulation

effectivenes

ow speed tu

as in Figur

jet orientati

b) VGJs effect

with VR=6.8

of VGJs w

o 900. Also,

producing c

vortices.

Js was furth

tinuous jets

ortex Gener

et al (199

aerofoil and

achieving u

ents of pul

eparation c

med more e

ol a significa

d entrainm

approximate

d with analo

1; Bremhor

n and peak

ss of the V

urbulent flow

re 2.20 and

ion and loc

ctin delayin8, α=45o an

with the inc

, since they

co-rotating

her improve

s (Wallis an

rating Jets

3) used os

d demonstra

up to 30% i

lsed jets ha

control over

effectively t

antly larger

ents as we

ely 50% fur

ogous stead

rst and Holl

vorticity du

VGJs in

w over a

studied

cation of

ng flow nd=90o.

creasing

y studied

vortices

ed when

d Stuart

(PVGJ),

scillatory

ated the

ncrease

as been

r a flap.

than the

surface

ell as a

ther into

dy VGJs

is 1990;

uring the

pulsation

(Johari an

This supe

in the free

onset of e

vortices as

The perfo

number of

and spac

neighbour

pulse duty

Many rese

parameter

one (God

counter-ro

condition,

terms of o

PVGJs ap

the local

respective

pulse duty

order of m

were found

nd Rixon 20

rior perform

e jet which

each pulsin

s shown in

Figu

ormance of

f parameter

cing), jet o

ring jets; co

y cycle and

earch effort

rs and in ge

ard and St

otating vort

but requir

other param

pplication. T

boundary

ely while th

y cycle of 5

magnitude a

d to be 30%

03)

mance of PV

is charact

ng cycle ac

Figure 2.21

re 2.21 StaJo

both the s

rs. Primary

rientation (

o-rotating o

frequency o

ts have bee

eneral a rou

tanislas 200

tices can

es extra ca

meters Wars

They stated

layer thickn

e jet freque

50% or less

s the local f

- 44

% greater t

VGJ is belie

terised by t

ccompanied

1 (Johari an

arting vorteohari and R

steady and

parameters

(pitch and

or counter-r

of the pulse

en directed

und jet orific

06). Godard

give comp

are in their

sop et al (2

that the dia

ness with

ency respo

s. Also the

freestream

4 -

han the me

eved arise f

the formatio

d by the u

d McManus

ex ring of thixon (2003)

d the pulse

s include jet

skew ang

rotating), jet

ed jet case.

d towards o

ce is found t

d and Stan

parable per

r spatial an

2007) provid

ameter of an

skew and

onse should

jet velocity

velocity.

ean values

from the str

on of a sta

sual pairs

s 1997).

he pulsed j

ed VGJs is

t geometry

le and the

t velocity a

optimising t

to be more

nislas also c

rformance

nd magnitud

de optimal v

n orifice sho

pitch angle

d attainable

should be

of the stea

ructural diss

arting vortex

of counter-

jet.

influenced

(orifice sha

eir correlati

and addition

the aforeme

efficient tha

concluded

to the co-

de optimisa

values for p

ould be 5 to

es of 900 a

e up to 500

close to th

ady jets.

similarity

x at the

-rotating

d by the

ape, size

ion with

nally the

entioned

an a slot

that the

-rotating

ation. In

practical

o 15% of

and 450

0Hz with

he same

- 45 -

Traditionally, solenoid valves are used in generating pulsing jets but recent notable

advances have been achieved in pulsed jet actuators by the use of synthetic jets,

which are otherwise known as massless jets. This method requires only an

electrical energy in the generation of pulsed jets, unlike others requiring a supply of

air, and has the characteristic zero time averaged mass flux through the orifice yet it

gives non-zero momentum flux. Its effectiveness in reducing the boundary layer

susceptibility to separation is well established in laboratory experiments by Amitay

et al (1998, 2000) and Smith et al (1998).

Although this innovative method enables simplification in interconnection and

reduced power requirements, there are several practical issues, which include

difficulty in controlling actuation frequency, speed of response and possible

ingestion of foreign particles in the air during suction cycle, (Lockerby et al 2002).

Also the diaphragm can be excited during the inactive state by Helmholtz resonance

(Lockerby and Carpenter 2004). Furthermore, in order to achieve the optimal

performance the diaphragm must be operated at the appropriate structural

resonance frequency of a diaphragm, which can lead to a fatigue failure resulting a

significant reduction in its lift cycle.

Developing a performance-optimised PVGJs actuator for incorporation in a MEMS

based reactive closed-loop control still presents a difficult question and there is

much room for improvements. The fluidic oscillator as an alternative possibility holds

many potential, such as zero electrical power requirement in giving periodic

oscillation to output jets, relatively simple connection, physical robustness giving a

long life cycle, low flow requirement in operation, ease of manufacture and

microfabrication.

2.5 Fluidics In this section literature reviews on the early history and the basic operation

concepts of fluidics are presented. Also principal devices to demonstrate the

application of the fundamentals of fluid dynamics as the basis for the fluidic

elements are described.

2.5.1 Definition and general principles of operation Fluidics (Fluid Logic) is the term given to the study of circuitries or elements,

which do not involve any mechanical moving parts and use flow or pressure of fluid

as a powe

devices. T

for the ‘Va

flow exper

as shown

new techn

(HDL) in

deflection

to this, ow

fluidics st

Extensive

superior e

(Greenwo

Primary fl

with eithe

perform c

elements

fundamen

Wa

no

Mo

un

Je

a l

Vo

ext

er supply m

The first pat

alvular Valv

rience a hig

in Figure

nology only

1959 of th

amplifier a

wing to the

arted to be

research w

environmen

od 1960; E

Figure

uidic eleme

r analogue

complex fun

generally e

ntal principle

all attachme

zzle to atta

omentum i

bounded je

t turbulence

arge radial

ortex effect

ternal force

medium to a

tent of a flui

ve’, which f

gh resistanc

2.22. Neve

y after the

he concept

nd a digital

progress of

e considere

was then in

tal toleranc

zekiel and G

2.22 Tesla

ents involve

or digital o

nctions such

employs one

e of operatio

ent (Coand

ch itself to t

nteraction

ets impinge

e – laminar

component

– the mom

es are introd

- 46

achieve ana

idic device w

functioned

ce owing to

ertheless, th

demonstra

ts of fluidic

wall attach

f the funda

ed as a po

nitiated act

ce, simplicit

Greenwood

a valve andTesla (1

e an amplif

output, whic

h as shift r

e or more o

on and they

da Effect) –

the wall and

– exchang

upon one a

flow can be

t of velocity

mentum of a

duced.

6 -

alogous ope

was issued

as a check

the vortica

he field of f

tion at the

c amplifiers

hment ampl

mental stud

ossible alte

ively in con

ty and cost

d 1961; Brow

d its princip1916)

ier, diode,

ch can then

register and

of four diffe

y can be sum

– tendency

d flow along

ge of mom

another.

e destroyed

.

a stream of

eration of e

in 1916 to

k valve by

l motion it n

fluidics star

Harry Diam

s utilising a

ifier (Horton

dy on fluidic

rnative for

nsideration

t-effectivene

wn 1962).

ple of opera

modulator,

n be cascad

d counter. E

erent fluid p

mmarised a

of turbulen

g it.

mentum wh

d when the f

fluid remai

electronic ci

Nikola Tes

making a r

needed to u

rted to evol

mond Labo

an analogu

n 1960). In

c amplifiers

a reliable

of the robu

ess of the

ation

sensor and

ded into a c

Each one o

phenomena

as:-

nt jet issued

hen two o

flow is distu

ns constan

rcuits or

la (1916)

returned

undergo,

lve as a

oratories

e beam

addition

s at MIT,

system.

ustness,

devices

d switch

circuit to

of these

as their

d from a

or more

urbed by

t unless

- 47 -

In general, fluidic elements can be categorised as analogue devices or digital

devices according to the nature of their output. The analogue devices generate a

smoothly varying output signal upon the receipt of control signal and the output is

proportional to the input signal. But this linearity starts to break after the input signal

exceeds the predefined value and further increase in input signal will result as an

output signal saturation giving a constant value. On the other hand, a digital device

can produce only two different states of output, i.e., on and off (high or low). The

other characteristic which distinguishes these devices from analogue devices is that

a change in output state from one to the other occurs rapidly through the application

of the control signal. A further increase in control signal after the required state

change has been accomplished has little effect on the output signal.

General examples of the analogue and the digital devices are presented in the

following sections with brief descriptions of how they incorporate the

aforementioned fluid phenomena in achieving their functions and a summary of the

operation mechanism.

2.5.2 Analogue devices Beam deflection proportional amplifier: – This type of fluidic device best represents

the use of momentum exchange as an operation principle. In Figure 2.23 the

general geometry of the device is presented. As the turbulent power jet issues from

the supply nozzle, the flow is evenly divided between output A and B in the absence

of the control flow. With the application of a control signal from the control port C1

the power jet starts to bend towards output port A as the control jet impinges onto a

power jet stream, hence increasing the output pressure at port A, while output from

port B decreases. The deflection of the power jet stream is proportional to the

momentum differential of the control jets while the output is proportional to this

deflection of the main jet.

Figur

Turbulenc

of laminar

much low

supply jet

very sens

appreciab

The geom

Turbulenc

Conseque

the contro

injection o

reduces th

then dump

a) P

re 2.23 typi

ce amplifier:

r jet transiti

er than the

is kept low

itive to distu

ble distance

metry of the

ce Amplifier

ently, most o

ol flow. This

of the contro

he output fl

ped through

Power jet pa

ical geome

: – The ope

ion to turbu

e supply flo

within the r

urbances (tr

after leavin

e device pr

owing to it

of the supp

s high outpu

ol flow, whi

ow (pressu

h a vent.

Figure 2.2th without c

Ra

- 48

etry of beamMorris (

erating princ

ulence by a

ow, as in Fi

range of 10

ransitional r

ng the orific

resented in

ts inline arra

ply jet will en

ut signal sta

ich increase

ure) practica

a)

b)

24 Axial turcontrol; b) Paber and Sh

8 -

m deflectio(1973)

ciple of this

application o

igure 2.24.

00 to 2000,

regime). Th

e until the c

n Figure 2.

angement o

nter into the

ate can then

es the main

ally to zero.

)

)

rbulence aPerturbed pohinn (1964)

on proportio

amplifier is

of a radial

The Reyno

, at which th

is jet then s

control flow

24 is usua

of the input

e output por

n be gradua

n jet spread

The flow f

mplifier ower jet wit

onal ampli

s based on

control flow

olds numbe

he jet is lam

stays lamina

is introduce

ally called a

and output

rt in the abs

ally change

d and conse

from the ma

th control flo

fier

the use

w that is

er of the

minar but

ar for an

ed.

an Axial

t nozzle.

sence of

d by the

equently

ain jet is

ow

2.5.3 DiWall attac

attachmen

to adhere

gradient d

process is

main jet a

placed mu

that of the

difference

bubble on

appreciab

level, is ad

The usual

is attache

signal from

from the C

wall. Now

state signa

Vortex am

of Figure

escape in

applied th

then effec

igital devchment bist

nt walls in th

to one of t

developed a

s unstable i

ttachment w

uch closer t

e beam de

e in their p

n that side

ble level of f

dmitted to th

l geometric

ed to the S

m the OS. A

CS will detac

the high st

al.

Fig

mplifier: – Th

2.26. The p

nto the out

he resulting

ctively incre

ices table amplif

he vicinity o

he attachm

across the s

in bistable d

will be initia

to the supp

flection pro

principle of

of the atta

flow or pres

his separati

al configura

et (S) side

Admission o

ch the jet fr

ate output s

gure 2.25 Ty

he principle

power jet w

tput port d

power jet i

eases the f

O

- 49

fier; – Owin

of the suppl

ent walls, d

stream as it

devices ma

ated. One ca

ply nozzle w

oportional a

operation.

achment w

ssure, whic

ion bubble.

ation is defi

e of the atta

of the stead

rom the S a

signal is ge

ypical wall(Morris

e of this dev

will continue

uring norm

is forced in

flow path le

OS

9 -

ng to the Co

ly nozzle wi

depending o

t leaves the

aking it hard

an also see

with a small

amplifier in

The attach

wall will ma

ch is usually

ined in Figu

achment w

dy or impuls

and attach i

nerated fro

attachmen1973)

vice is mos

e its origina

mal operatio

to spiral mo

ength and

OR

oanda effec

ill force the

on the insta

e supply noz

d to predict

e that the at

er angle wh

Figure 2.23

hed jet for

intain its a

y 5 to 15%

ure 2.25. Im

wall producin

sive apprec

t to the Re-

m the OR w

nt geometr

t easily exp

l path towa

on. When t

otion toward

accelerates

ct, the pres

turbulent p

antaneous p

zzle. There

t on which

ttachment w

hen compa

3 which is

rming a se

attachment

% of the sup

magine the

ng the high

ciable contro

-Set (R) sid

while OS give

ry

plained with

ards the cen

the control

rds the cent

s the flow

sence of

power jet

pressure

fore this

side the

walls are

red with

a major

paration

until an

pply flow

main jet

h output

ol signal

de of the

es a low

h the aid

ntre and

flow is

tre. This

as they

spiral tow

resulting e

Another c

the output

the vortex

achievable

2.6 BisTh

earlier. In

amplifier i

falls withi

review o

geometric

conceptua

2.6.1 EaEv

amplifiers

But its dis

of deflecti

wards the o

effects lead

Figu

crucial assu

t port is les

x chamber

e in real ap

stable wahe basic con

this section

s presented

n this cate

n their co

cal parametr

al design de

arly histover since th

received b

covery was

ng a fluid je

output port

a to pressu

re 2.26 Typ

mption in t

ss than that

without ev

plication.

all attachncepts of th

n of the rep

d, since the

egory of the

oncepts, p

ric consider

eveloping m

ory he introduct

by far the m

s rather acc

et with anot

- 50

owing to t

ure drop in t

pical geom(Morris

the principle

t of the limi

ver leaving

hment fluhe operation

port an exte

e actuator e

e fluidic ele

previous a

rations. The

methodology

tion of fluid

most attenti

idental. Afte

her jet of m

0 -

the centrifu

the main jet

metry of vor1973)

e of operat

t of a circle

g the outpu

uidic oscn of fluidic d

ensive study

employed f

ements. Th

nalytical a

e section wi

y of the unit

dics, the bi

on both fro

er Horton (1

much smalle

ugal effect

t.

rtex amplifi

ion is that w

e an inviscid

ut port. Ho

cillator devices hav

y of the wal

or the flow

he study in

and experim

ll end with a

.

stable wall

om industrie

1960) conce

er flow, man

and both o

ier.

when the r

d fluid whir

owever, this

ve been int

ll attachmen

control ap

ncludes a l

mental wo

a descriptio

attachmen

es and univ

eived the po

ny experime

of these

adius of

ls within

s is not

roduced

nt fluidic

plication

iterature

ork and

on of the

nt fluidic

versities.

ossibility

ents with

round jets

this metho

Raymond

changed t

proportion

1975). Th

developed

power jet

the power

desired m

symbols fo

This rathe

for the dev

sustained

Various de

though the

the two c

Figure 2.2

fed oscilla

bS - P

bC - C

B - O

lb - S

Figure 2symbols.

s have been

od was too

Warren an

the power n

nal beam d

his provide

d across the

nozzle. Ne

r jet to attac

onostability

orming the

er fortuitous

velopment o

periodic os

esigns of flu

ey are all b

classic desig

28 a) will be

ator is reserv

Power nozzl

Control nozz

Offset

Setback

.27 Typica

n performed

low.

nd Ronald B

nozzle to a

deflection a

ed an incre

e power jet

evertheless

ch to the wa

y. Figure 2.2

geometry o

s discovery

of a special

scillation in

uidic oscilla

ased on the

gns shown

known as a

ved for Figu

le width

zle width

al wall at

- 51

d. It was so

Bowles ma

a slit nozzle

amplifier su

eased gain

as the resu

, the press

all and giving

27 shows th

of wall attac

later gaine

l type of wa

its output, l

ators have b

e fundamen

in Figure

a control lo

ure 2.28 b).

ttachment

1 -

oon found, h

de use of c

e, as an effo

uggested by

n owing to

ult of an en

sure effect

g the amplif

he typical co

hment devic

ed wide reco

ll attachme

ater known

been sugge

ntal principl

2.28. Henc

aded fluidic

lS

xV

device ge

however, th

cover plates

ort to impro

y Horton (

o a pressu

ntrainment in

became mo

fier a bistab

omponents

ces.

ognition and

nt device th

as a bistab

ested and pa

e of operati

ceforth, for

c oscillator w

- Splitter lo

- Attachme

- Attachme

- Splitter a

eometrical

hat the effic

s, which ef

ove the gai

Kirshner a

ure gradien

n the vicinit

omentous,

bility rather

and corres

d formed th

hat produce

ble fluidic os

atented sin

ion associa

ease of re

while the te

ocation

ent wall len

ent wall ang

angle

compone

ciency of

ffectively

n of the

nd Katz

nt which

ty of the

causing

than the

ponding

he basis

ed a self-

scillator.

ce then,

ated with

eference

rm vent-

gth

gle

ents and

2.6.2 ThTh

well-know

states tha

surface o

displaced

angle to th

Figure 2schemati

Figure a) C

he Coandhe ground r

wn turbulent

t when a tu

r wall and

too far from

he centrelin

a

2.29 Jet ac presenta

a

2.28 ClassControl load

da effect irule of ope

t re-attachm

rbulent jet i

attach itse

m the orifice

e of the jet.

)

attachmentation of a se

- 52

sic bistableded oscillato

Morris (

n bistableration of w

ment princi

issues from

elf to it furt

e and/or is s

.

t in a biseparation b

2 -

e fluidic oscor; b) Vent-f1973)

e wall attwall attachm

ple (Coand

m a nozzle it

ther downs

sufficiently s

stable wabubble. Kir

b

cillator desfed oscillato

tachmentment device

da Effect).

t will bend to

stream, unle

short and/or

b)

ll attachmshner and K

signs or

t devices es is based

The coand

towards any

ess the su

r inclined at

ment devicKatz (1975)

d on the

da effect

y nearby

urface is

t a large

ce with ).

- 53 -

The Coanda effect was first noticed by Thomas Young as early as 1800 (Young

1800) and rediscovered by Chilowski and Coanda in 1930. In 1936, Henri Coanda

acquired a patent for a ‘Device for Deflecting a Stream of Elastic Fluid Projected into

an Elastic Fluid’ (Coanda 1936) and later the phenomenon was entitled the ‘Coanda

Effect’ by Metral and Zerner in 1948.

In bistable wall attachment devices, as the turbulent jet issues from the power

nozzle it entrains fluid from its surrounding which is confined by the presence of the

top and bottom plates and attachment walls. This enables low pressure regions to

develop between the jet and attachment walls, owing to the entrained fluids, causing

a counterflow to issue from the downstream of the wall towards the low pressure

region, as schematically shown in Figure 2.29 a).

Then a momentary disturbance, usually the turbulence in the jet, causes the jet to

bend towards one side of the wall, decreasing the recirculating flow and hence the

pressure on that side of the jet. As a result of this increased differential pressure

across the stream of the jet, it will bend towards that side of the wall further and

attaching itself on to the wall, as shown in Figure 2.29 b).

The jet attachment will lead to a formation of trapped pocket of fluid (henceforth a

separation bubble). The state of equilibrium is achieved at the point of attachment

when the mass flow in the bubble is constant, i.e. when the mass flow fed back into

the bubble from the jet owing to the vortex flow inside the bubble is equal to the

entrained flow by the power jet from the bubble.

For a symmetric bistable oscillator the side of the jet attachment is totally governed

by the naturally introduced momentary disturbances, hence making it an

indeterminable process. On the other hand, in an asymmetric monostable oscillator

the power jet will always attach to a predetermined side where the entrainment is

more restricted.

Other work forming the basis of a fundamental study of these devices was

published by Kline (1958). Effects of the diffuser angles on the Coanda effect were

presented. He showed how the flow can separate from one side and flow along the

other at an appreciable diffuser angle and that at wider diffuser angles the flow will

separate from both walls. Bourque and Newman (1960) concluded from their

experimen

a bistable

stated tha

separation

than the e

2.6.3 JePo

application

through th

the compl

excessive

the portion

states the

Although

marginal d

devices an

clearance

Figure 2.3

An instant

load on th

control sig

ntal results

e wall attac

at at an an

n bubble wi

entrained flo

et switchiower jet sw

n of posit

he control p

etion of the

ely strong si

n of the pow

typical ratio

any fluidic

difference i

nd moment

, D, betwee

30

taneous se

he output p

gnal, which

that the ma

hment devi

gle greater

ll begin to b

ow and mak

ng methowitching in

ive/negative

ports. Furth

e jet switchi

gnal is intro

wer jet out t

o of the con

oscillators

n the geom

tum-driven d

en the edge

Figure 2Kir

ealing of a

port of the

the sealing

- 54

aximum allo

ice with ze

r than 670,

break down

king the jet d

od and mn fluidic de

e pressure

her admissi

ng will not c

oduced this

to the inact

ntrol signal a

can utilise

metry of inte

devices. In

es of power

2.30 Definitrshner and

control por

active side

method kn

4 -

owable attac

ro offset, a

the state o

n owing to t

detach from

mechanismevices is

e and/or je

on or remo

cause any

s can overd

ive output p

as 5 to 15%

both types

eraction reg

general, m

r nozzle and

tion of cleaKatz (1975

rt on the ina

e can be re

own as vac

chment wal

s shown in

of equilibriu

the returned

m the wall.

m commonly

et moment

oval of the

changes in

rive the dev

port and/or

% of the sup

s of control

gion betwe

momentum d

d control no

arance )

active side

egarded as

cuum switch

ll angle was

n Figure 2.3

um conditio

d flow being

achieved

tum contro

control sign

its status,

vice which

vent. Morris

pply flow lev

signals, th

en pressur

devices hav

ozzles, as s

or increas

another fo

hing.

s 670 for

35 They

n of the

g higher

by the

l signal

nal after

but if an

forces a

s (1973)

vel.

ere is a

re-driven

ve larger

shown in

e in the

orm of a

- 55 -

Warren has established three different possible switching mechanisms in wall

attachment devices in a flow visualisation study and his classifications are described

below;

Terminated wall or bleed type switching – If vents or bleeds are introduced

upstream of a splitter and considerable offset is given, a gradual addition of control

flow into separation bubble will enlarge it hence delaying the attachment point. Once

the attachment point moves beyond the point where the vent intercepts the provided

attachment wall, flow through the vent is fed into the bubble, making the switching

process continue even if the control flow has ceased.

Contacting-both-wall switching – This mode of switching can be observed when an

amplifier has small offset, which makes the power jet to attach shortly after leaving

the power jet nozzle and hence the usual separation bubble dose not form and is

replaced by a small recirculation bubble formed within a control port. In this situation

slight application of a control signal will initiate development of a separation bubble

and its expansion from the originally attached side, causing a proportion of the

opposite side of the power jet to adhere to that side of the wall. Different from

terminated wall switching process, removal of the control signal at an early stage of

the jet switching will make the jet re-stabilise back to its initial state. A schematic

sketch of this switching process with descriptions can be found in Figure 2.31.

Splitter switching – When vents or bleeds are placed considerably further

downstream of the splitter, the separation bubble grows and makes contact with a

splitter. This then separates a proportion of the flow from the main jet and the

bubble starts to open up. If the control flow is withdrawn at this point flow from

upstream starts to fill the gap created as the bubble opens up and hence the

switching continues. A schematic sketch of this switching process with descriptions

can be found in Figure 2.32.

After the jet attachment in a control loaded oscillator, the separation bubble formed

on the attached side wall further increases the pressure difference, generating a

rarefaction wave (compression) on that side of the control port while a pressure

wave (expansion) grows on the opposite side. These waves travel in an opposite

direction along the feedback loop connecting the two control ports, and on its

completion, the power jet will detach from the initially attached side wall and attach

onto the other side. This detachment and attachment process continues, giving the

periodic o

mechanis

a) Initiaformvortezero

b) As tsepato mthe p

c) The vorteoutp

d) The the lwhile

e) The side

Figure 2.3

oscillation.

m allows th

a)

d

ally the powmation of a ex (recirculao offset. A st

the controlaration bub

make a contapower jet w

separation ex is suppreput. A recirc

power jet left side of e the standi

jet switchinwall. The s

31 Sequent

The involv

em to be re

d)

wer jet is atseparation ation bubbltanding vort

flow is able and expact with an ill re-stabilis

bubble expessed in itsulation bub

has now atthe jet enlaing vortex is

ng is complseparation b

tial illustra

- 56

vement of

egarded as

b)

ttached to bubble on e) formed a

rtex formed

applied the pands it. Thoff side wase itself bac

pands furthes size and itble starts to

ttached to targes furthes pushed ou

leted and thbubble now

ation of a c

6 -

the pressu

pressure-d

)

the left sidthe attach

at the contrfurther dow

recirculatiohis causes ll. If the conck to its initi

er and movts core starto form at the

the right waer and reacut to the left

he power jeforms a sta

ontacting-b

ure waves

riven device

e)

e attachmeed side warol nozzle o

wnstream ca

on bubble the right sid

ntrol signal cal state.

ves downstrts to shift toe right contr

all. The sepches the vict output.

et is now atanding vorte

both-wall s

in their os

es.

c)

ent wall. Thall is replacowing to a an also be s

transformsde of the pceases at th

ream. The sowards the rol.

paration bucinity of the

ttached to tex.

switching p

scillation

he usual ed by a small or seen.

s into a ower jet his point

standing left side

ubble on e splitter

the right

process.

a) Ini

co

b) As

an

vo

c) Th

flow

pre

de

co

rig

the

d) Po

lef

Fig

tially the po

nsiderable

s the contro

d a portion

rtex.

he separatio

w is captur

evious sep

tached from

ntact with t

ht and the

e left side. P

ower jet swi

ft side wall.

gure 2.32 S

a)

c)

ower jet is a

offset a sep

l flow is intr

n of the po

on bubble f

red by the

aration bub

m the initia

the left sid

left side of t

Power jet flo

itching is co

Sequential

- 57

attached to

paration bub

roduced to

ower jet is

further incre

splitter, for

bble is now

ally attache

e wall, pre

the power j

ow exits thro

ompleted a

illustration

7 -

o the right s

bble forms o

the separat

piled by th

eases its si

rming a larg

w opened

ed side). As

essure diffe

et causing

ough both o

nd a separ

n of a splitt

b)

d)

side of the n

on that side

tion bubble

e splitter, f

ze and mo

ger standing

(the jet is

s the stand

rence incre

the jet to be

of the outpu

ation bubbl

ter switchin

nozzle and

e.

it increases

forming a s

ost of the p

g vortex, w

now perm

ding vortex

eases betw

end further

ut conduit.

le is formed

ng process

given a

s in size

standing

ower jet

while the

manently

x makes

ween the

towards

d on the

s

- 58 -

The oscillation mechanism in a vent-fed oscillator partially incorporates pressure

change but is mainly driven by a momentum injection through the control ports

(momentum-driven devices). Following the initial attachment, part of the attached

flow will be captured by the vent port located on the corresponding side of the exit

conduit. This will then be fed to that side of the control port through the feedback

connection and once sufficient momentum has been injected the power jet will

detach to the opposite side. The same process takes place again and periodic

oscillation is generated.

In general, all three switching mechanisms described above participate to some

extent in power jet switching of most fluidic devices. The specific designs of fluidic

oscillators given in Figure 2.28 and the current test model, however, which have

small or zero offset and are without a vent orientation, will incorporate dominantly

the contacting-both-wall switching and the splitter switching mechanisms during

their oscillation process. Also their period of oscillation, T, can be approximated by

the Eq. 2-2 on the assumption that the propagation time, P , is the function of the

length of the feedback loop, L, and the local speed of sound, a, as in Eq. 2-3. The

S in Eq. 2-2 is the switching time of the device which is governed by the input and

output characteristics and the device and the feedback loop geometry. Further

details of the propagation time and the switching time can be found in Chapter 4.

PST 22 Eq. 2-2

a

LP Eq. 2-3

2.6.4 Static characteristic The first attempt to study the Coanda effect theoretically is known to be that

of Dodds (1960). His analysis is based on a principal assumption that the

momentum flux is conserved in a volume surrounding the attachment point, a5.

As shown in Figure 2.33, the input momentum J is divided into downstream and

upstream (recirculating) components of J1 and J2, giving the reduced equation as Eq.

2-4

21cos JJJ Eq. 2-4

and this approach is known as the attachment point model.

The angle

assumptio

distributio

of reattach

In addition

the analyt

Th

Th

Th

rea

Th

bu

Th

Th

Th

wa

Ch

ne

Based on

researche

Figure

e at wh

ons that the

n is the sam

hment

n, the follow

ical descrip

he jet flow is

he jet velocit

he jet entrai

attachment.

he jet veloc

bble.

he pressure

he shear for

he nozzle w

all length is

hanges in th

gligible.

these ass

ers and nota

e 2.33 Jet aKir

hich the je

e jet centreli

me as the fr

wing assum

ption of the s

s turbulent,

ty is uniform

ns the sam

.

city is indep

within the s

ce owing to

idth is smal

long compa

he jet struc

umptions, e

ably by Bou

- 59

attachmentrshner and

et strikes th

ine is a circ

ree jet, emp

mptions are

steady state

incompress

m at the noz

me mass flo

pendent of

separation b

o the wall is

l compared

ared with th

cture owing

extensive a

rque and N

9 -

t to an offsKatz (1975

he wall is

cular arc of

ploying roG

e generally

e character

sible and tw

zzle exit.

w from eac

the reduce

bubble is un

neglected.

d with the ar

e nozzle wi

to the cen

analyses ha

ewman (19

et parallel )

then foun

radius R a

stler' analy

made for th

istic, (Levin

wo-dimensio

ch boundary

ed pressure

niform.

rc radius r; a

idth.

ntrifugal forc

ave been p

960) and Sa

wall

d with the

nd that the

ysis, up to t

he develop

n and Manio

onal.

y up to the

e in the se

and the atta

ce of curva

performed b

awyer (1960

e further

velocity

the point

pment of

on 1962):

point of

paration

achment

ture are

by many

0, 1963).

- 60 -

Bourque and Newman (1960) first studied the case of parallel wall with an offset by

approximating the J1 and J2 as in Eq. 2-5 and Eq. 2-6 using the corresponding free

jet values and the jet stream velocity approximated using a srtleroG ' profile at a

distance 616 ccS along the jet centre line and over the distance 66acya normal

to the jet centre line as shown in Figure 2.33. The y in Eq. 2-5 and Eq. 2-6 is the

distance from the jet centre line to an arbitrary point on a line normal to the centre

line, i.e., the ya. For a detailed description of the srtleroG ' profile, please refer to

Kirshner and Katz (1975).

dyysuJay

,62

1 Eq. 2-5

dyysuJay

,62

2 Eq. 2-6

The resulting theory achieved good agreement with the experimental data when

choosing the jet spreading factor as an empirical constant of 12, as in Figure 2.34

and both experimentally and analytically demonstrated the functional relationship

between the attachment distance, xR, and the offset, B, as in Eq. 2-7.

SSR bBfbx Eq. 2-7

Figure 2.35 also shows that the maximum allowable inclination of the wall is around

67o and beyond this value the attachment length becomes infinite.

Figure

Figure

e 2.35 Effec

BrSolid line –

and Bou

e 2.34 EffecBour

ct of attachfor

roken line –– Bourque urque and N

- 61

ct of offsetrque and Ne

hment wallr various of– Sawyer’s (and NewmaNewman ‘s

Sawyer

1 -

t in jet attacewman (196

angle on tffset values(1963) analyan ‘s (1960(1960) exp(1963)

chment len60)

the jet attacs ytical result) theoreticaerimental re

ngth

chment len

t al results esults

ngth

- 62 -

They also attempted a different approach to the problem, namely the control volume

model. The major dissimilarity between the control volume model and

aforementioned approach is the negligence of the recirculating momentum flux and

introduction of the separation bubble pressure, PPP B , giving the resulting

expression for as in Eq. 2-8, on the assumption that the momentum flux returned

to the low-pressure region, PB, balances the pressure difference times the area

normal to the wall.

1cos JJ Eq. 2-8

The results of this model, however, were not as good as those of the attachment

point model and furthermore none of these models gave good representation of the

experimental data for the cases of inclined wall with/without offset.

Levin and Manion (1962) extended both models of Bourque and Newman to the

study of inclined offset wall cases, which led them to the following expression of

momentum relation for the cases of attachment point and control volume theory

respectively, as in Eq. 2-9 and Eq. 2-10.

21cos JJJ Eq. 2-9

13cos JJJ Eq. 2-10

They compared their theory with the experimental data obtained from a test

conducted with a 0.5 Mach air jet, varying the offset distances of 0, 2, 4 and 10

nozzle widths and the wall angles from 0o to 55o. The attachment point theory

achieved satisfying agreement with the experimental data for most of the offset

values except the value of 10 at angles up to 35 degrees, when chosen as 15

and/or 20 as in Figure 2.36 Their modified control volume theory only agreed with

experimental data when the spread parameter was assumed as a functional

variable of offset and wall inclination. Their results fro the control volume method

are shown in Figure 2.37 and the deduced representative values of for various

combinations of offset and attachment wall angle in Figure 2.38

Sawyer (1963) separately worked on developing the jet attachment model to

describe both the cases of offset parallel wall and inclined wall without offset based

on the work of Dodd. Major divergences from the work of Bourque and Newman

involve the appreciation of difference in the entrainment depending on the jet

curvature i.e. entrainment for the jet curving over a convex surface is greater than

that of the

inclusion

assumptio

His result

inclined w

to be an e

Figure 2.with theomethod.

e free jet a

of pressure

on that the p

matches w

wall, as in F

empirical co

a

.36 Compaoretical m

nd lower fo

e force in

pressure dis

well with ex

igure 2.35,

nstant but u

a)

arison of eodel of L

Le

- 63

or the jet cu

the vicinity

stribution is

perimental

without the

using that o

experimentLevin and

a) =15; bevin and Ma

3 -

urving with

y of the att

similar to t

data for bo

e necessity

of the free je

tally measManion b

b) =20 anion (1962

in a concav

tachment p

hat of the fo

oth the offse

of assumin

et value of ~

sured jet abased on

)

ve surface

point based

orced vortex

et parallel w

ng spreadin

~7.7.

b)

attachmentattachmen

and the

on the

x.

wall and

ng factor

t length nt point

Figure 2.with theofor =8.

Figure 2.angle and

37 Compaoretical mo

Levin and M

38 Approd offset rat

arison of edel of LeviManion (196

oximate vaio for Levi

Le

- 64

experimentin and Man62)

alue of in and Man

evin and Ma

4 -

tally measnion based

for combinion’s contanion (1962)

ured jet ad on contro

nations ofrol volume)

attachmentol volume m

f attachmee method

length method

ent wall

Boucher

parallel a

agreemen

seen from

Figure 2.various oresults

In his ana

used by

discrepan

model allo

the point w

the theory

From succ

effect of

emphasise

good agre

(1968) imp

and offset

nt with the e

m Figure 2.3

.39 Theoreoffset para

alysis he su

Sawyer, a

cy in entra

ows variatio

where un

y best repre

cessful rep

jet curvatu

ed the imp

eement with

proved and

with incline

experimenta

9.

etical resuallel wall by

bstituted Si

and further

ainment bet

on of the jet

cuu equals

sents the d

resentation

ure on the

ortance of

h experimen

- 65

d simplified

ed wall ca

al data for t

ults of jet y Boucher

Boucher

impson’s je

simplificat

tween both

width by de

s the empiri

ata.

n of the offs

entrainme

the apprec

ntal data.

5 -

d Sawyer’s

ases and h

the offset p

attachmenr’s compar

(1968)

et profile for

ion was a

sides of t

efining the i

ically determ

set parallel

ent rate is

ciation of th

model an

his theory

parallel wall

nt length red with ot

r the modifie

chieved by

he jet. In a

nner edge

mined cons

cases it wa

negligible,

he pressure

nd analyse

provides t

case, as it

for the cather exper

ed rtleroG '

y disregard

addition to

line of the j

stant. When

as verified

and Bouc

e force by s

d offset

he best

t can be

ases of rimental

s' profile

ding the

this the

et along

n n=0.05

that the

cher re-

showing

Boucher’s

up to 30 d

that this d

bubble as

much fast

pressure g

Figure 2.cases of experime

Following

fundamen

devices.

s analysis re

degrees exc

deficiency is

ssociated w

ter internal

gradient wil

a

.40 Bouchvarious at

ental results

these work

ntal parame

easonably m

cept for the

s because o

with zero o

flow move

l divert the j

a)

er’s theorttachment s. a) Zero o

ks, research

eters on th

- 66

matches we

zero offset

of the deve

offset incline

ement with

jet centre li

retical resuwall angle

offset case; Boucher

hers have

he performa

6 -

ell with data

t case as sh

elopment of

ed wall lea

hin the bub

ne from bei

ults of jet e with offse

b) for offse(1968)

now started

ance chara

a for offset

hown in Fig

f the much

ading to the

bble; therefo

ng the circu

b

attachmeet wall comt ratio of 2,

d to verify t

acteristics o

inclined wa

gure 2.40 H

smaller se

e establish

fore the de

ular arc.

b)

nt length mpared wit

4 and 10.

the effects

of wall atta

all cases

e states

paration

ment of

eveloped

for the th other

of other

achment

Comparin

which incl

angle and

jet attach

dominatin

His result,

to 2, the

increase w

trends in t

that the c

form the c

Figure 2.4nozzle wi

Sarpkaya

performan

amplifier

parameter

et al (196

udes powe

length (Ra

ment (critic

g effect wh

, as shown

critical Re

with further

the variatio

critical Reyn

configuration

41 Variatiodth for the

and Kirshn

nce charact

with a cus

rs and splitt

2) investiga

r nozzle asp

ber and Sh

cal Reynold

ile the rest o

in Figure 2

eynolds num

r reduction

n of critical

nolds numb

n of the dev

on of the me initiation o

ner (1968) s

teristics of

sped splitte

ter shape ca

- 67

ated the eff

pect ratio (A

hinn 1964), o

ds number)

of the param

2.41 indicate

mber does

in AR. Ev

l Reynolds

ber depend

vice under c

minimum Rof jet attac

studied the

a vented

er. Their d

an be found

7 -

fects of var

AR), splitter

on the minim

) and it wa

meters were

es that for p

not chang

ven though

numbers w

ds on many

consideratio

Reynolds nchment with

effects of

and unven

designs for

d in Figure 2

rious geom

r distance a

mum Reyno

as found th

e not signifi

power nozz

ge greatly,

this may

with AR, one

y interrelate

on.

number bash AR. Comp

attachment

nted wall a

r amplifiers

2.42

metrical para

and attachm

olds numbe

hat the AR

icant influen

zle aspect r

but then s

well repres

e should re

ed paramet

sed on theparin et al (

t wall profile

attachment

s with geo

ameters,

ment wall

er for the

R had a

nces.

ratios up

starts to

sent the

ecognise

ters that

e power (1962)

e on the

bistable

ometrical

Figure 2.4concave Kirchner (

They argu

extension

geometry.

improved

are shown

42 Generalattachmen1968)

ued that the

of the cor

. Also, they

performanc

n in Figure

amplifier gnt wall stu

e pressure

responding

have show

ce compare

2.43. As t

- 68

a)

b)

geometry audied by S

and power

g values of

wn that the u

ed with stra

they expec

8 -

)

)

and profileSparkaya

r recovery o

the vented

use of a con

aight and co

cted, a conc

s of splitteand Kirsh

of unvented

d amplifiers

nvex attach

oncave wal

cave wall p

er and convhner. Spark

d amplifiers

s sharing th

hment wall c

ls and thei

presented a

vex and kay and

s are an

he same

can give

r results

a similar

effect of

bubble siz

c) C

increasing

ze and henc

a)

Figurea) Straighb) Concav

Convex atta

the offset

ce increased

)

e 2.43Presht attachmeve attachmeachment wa

Sarpk

- 69

of the wal

d pressure

c)

sure recovent wall for cent wall for all for closedkaya and K

9 -

l which res

loss.

)

very with acclosed contclosed cond and open

Kirshner (196

sults as inc

b)

ctive port frol ports optrol ports opcontrol por

68)

creased se

flow peration peration rts operatio

paration

n

2.6.5 DyJo

amplifier w

detachme

and later

switching

control flo

where V

entrainme

control flo

V is ind

eavQ is ind

and the a

switching

ynamic chnston (196

without a s

ent occurs w

Katz and D

time is a fu

ow level. H

V is the vo

ent of the co

ow level. He

ependent o

dependent

axis labelled

time in this

Figure 2.4

haracteri63) studied

splitter and

when the se

Dockery (196

unction of th

e defined t

lume chan

ontrol flow i

e showed t

of the Reyn

of CQ . The

d as a sepa

report.

QSt

4 Separatio

- 70

stic the switchi

d a receive

eparation bu

64) arrived

he control f

the switchin

ge in the

nto the pow

that eavQ in

nolds numb

ese results

aration time

eavC Q-Q

V

on time vaJohnston

0 -

ng mechan

er. In his a

ubble has s

at the sam

low rate an

ng time of

separation

wer jet durin

ncreases w

ber and CQ

are shown

e in the Fig

riation withn (1963)

ism of a sin

analysis he

sufficiently e

me conclusio

d it decreas

the amplifi

bubble, Q

ng the switc

ith the Rey

C . Also he

in Figure 2

gure 2.44 is

h control fl

ngle-sided w

e assumed

enlarged. J

on, namely

ses with inc

ier as in E

eavQ is the

ching and Q

ynolds num

demonstra

2.44 to Figu

s equivalen

Eq. 2-

low level

wall fluid

that jet

ohnston

that the

creasing

Eq. 2-11,

average

CQ is the

ber and

ated that

ure 2.46

nt to the

-11

Figure 2.4number. J

Figure 2

45 DynamJohnston (1

.46 Measur

ic separati1963)

red contro

- 71

ion bubble

l flow levelJohnston

1 -

e area cha

l and calcun (1963)

nge with p

ulated avera

power jet R

age entrain

Reynolds

ned flow

- 72 -

Savkar (1966) carried out an extensive experimental study on the effects of various

geometrical parameters on switching time of bistable fluid amplifiers. This included

the variation of control to power nozzle width ratio of 1 ~ 0.25, setback between 0 ~

4bS, offset and splitter location from 6 ~ 39 bS.

He described the switching time as the sum of two components, as in Eq. 2-12

where l is the minimum pulse length of the control signal to initiate the switching

and b is the additional time required to receive the output signal down the inactive

conduit. The beginning of their switching time was defined as the instance of the

control signal application and its termination when the power jet reached a

predefined point within the inactive conduit.

bla Eq. 2-12

His results show the reduction in the switching time with the offset as this required

shorter control pulse and a significantly increased dynamic flow gain has been

achieved as in Figure 2.47 and Figure 2.48. He also concluded that the momentum

ratio of the control jet to the power jet plays an equally important role to that of the

flow rate ratio in determining the switching time. This was derived by recognising the

decrease in actual switching time as the width of the control nozzle reduced for a

given control flow rate and demonstrated the minimum momentum ratio of 0.2 for a

bistable amplifier without a splitter. Unlike other parameters studied in his work, the

setback presented a rather negligible effect on the switching time.

While none of the aforementioned parameters had direct effects on the power jet

attachment, the splitter location had considerable influence to a certain extent.

When the splitter is closer than 16 throat width from the plane of the control jet, the

power jet develops an increasing tendency to oscillate about the splitter before its

attachment. Moreover the jet attachment will completely cease if the splitter moves

further upstream than 2 throat width downstream of the centreline of the control jet,

as can be seen in Figure 2.49

Savkar also demonstrated increase in the switching time as the pointed splitter

moved upstream and his results can be found in Figure 2.50. He stated that this is

because of the increased adverse interference from the recirculation vortex forms

near the splitter, which suppresses the growth of the separation bubble under the

application of the control signal and this is demonstrated in Figure 2.51

Much effo

Drzewieck

switching

well with e

Their mod

status of

Drzewieck

the applica

ort (Lush 196

ki 1973) hav

in a bistab

experimenta

del can com

the power

ki (1973) fu

ation of suc

Figure

67, 1968; O

ve been ex

le fluid amp

al data with

mpromise th

jet (lamina

rther impro

ction to the i

2.47 Contr

- 73

Ogzu and St

xpended in

plifier. Goto

hout the nec

he effects o

r and turbu

oved the mo

inactive sid

rol pulse leSavkar (

3 -

tenning 197

developing

o and Drzew

cessity of e

of vents, sp

ulent) and i

odel to allow

e control po

ength varia(1966)

72; Goto an

a theoretic

wiecki’s (19

employing e

plitter, and

nput and o

w the analy

ort.

ation with o

d Drzewiec

cal modellin

973) results

empirical co

opposite w

output impe

ysis of switc

offset

cki 1973;

ng of the

s agreed

onstants.

wall, flow

edances.

ching by

Figure 2.48 Effe

- 74

ect of offseSavkar (

4 -

et on dynam(1966)

mic flow ga

ain

Figure 2.4when pladownstre

49 Flow visaced near team of the

Figure 2.5

sualisationto the powplane of th

50 Effect of

- 75

showing jwer jet nozzhe control n

f splitter loSavkar (

5 -

et attachmzle; Splittenozzle. Sav

ocation on t(1966)

ment to a spr located t

vkar (1966)

the switchi

plitter two nozzle

ing time

widths

Figure 2.splitter ana) 22 powwidth awa

51 Flow vind their inf

wer jet nozzlay from the

isualisationfluence on e width awapower jet no

- 76

a)

b)

n showingthe separa

ay from the ozzle. Savk

6 -

)

)

the standation bubbpower jet n

kar (1966)

ding vortexle nozzle; b) 14

x formed n

4 power jet

near the

nozzle

- 77 -

Early research works and their results verifying the effects of various geometrical

parameters associated with the designs of wall attachment fluidic oscillators have

been described so far. Although the effects of these parameters on the performance

of a device are strongly interrelated with each other and can only be optimised

empirically, in the following paragraphs a general overview of their effects is

provided and commonly used values are summarised for reference in the following

subsection 2.6.6.

The primary geometrical parameter is the power nozzle width and the rest of the

commonly employed values will be expressed in terms of this. Typical values of the

power nozzle width range from 0.25mm to 0.5mm with AR of 1 to 2, while the power

nozzle aspect ratio of two gives the maximum pressure gain. A very high AR (O(10))

can be used but a device employing high AR tends not to function very well,

possibly owing to its susceptibility to promoting a swirl flow in the power jet. At low

power nozzle aspect ratio, boundary effect at the power nozzle becomes important

and increases the critical Reynolds number for jet attachment to occur: this is

believed to be because of the turbulence attenuation caused by the boundary layer

and consequent reduction of the jet entrainment rate.

Offset and wall angle introduce similar effects to a device. At large offset and angle

the jet attachment may not occur at low supply flow level and at small values the jet

may attach to both of the attachment walls or can result in loss in steady-state

stability. The jet attachment length reduces with both of the parameters as less

entrainment is allowed and hence forms a smaller separation which results as

reduced pressure loss and increased control flow requirement. Commonly used

offset to power nozzle width ratio falls within zero to one and attachment wall angle

ranges from 12 to 150. These values should be kept to a minimum allowed value if

one requires to operate the device at low supply flow level but at the expense of

dynamic stability.

Usual splitter distance ratio lies between eight and fifteen. The effect of this value is

dependent, to some extent, on the offset and its shape. In general, at low splitter

distance higher level of control flow is required for power jet switching owing to the

increased adverse interference from the standing vortex formed near the splitter and

the strength of this vortex becomes stronger as its shape becomes blunter. General

splitter shapes are pointed, round, square or cusped. In addition, at low values

edgetone may occur and further reduction will cause the jet to attach to the splitter.

For prelim

power noz

attachmen

downstrea

exiting th

reduction

increased

increased

A vent ca

excessive

however,

The furthe

Figure 2.5

Figure 2.5wall attac

minary desig

zzle width w

nt and switc

am of the je

rough the

in the con

momentum

control noz

n make a d

e flow can

as one wou

er significan

52, which ha

52 Summachment dev

gn work, c

with a zero s

ching, but c

et attachme

control po

trol nozzle

m addition.

zzle size ow

device beco

be evacua

uld expect.

nce of these

as been qua

ry of geomvice. (Warre

- 78

control nozz

setback. Se

care must b

ent point, re

rt. For a g

width can

Increase i

wing to grea

ome output

ated. This

e parameter

alitatively su

metrical infen 1963)

8 -

zle width u

etback has n

be taken to

esulting in

given flow

lead to ea

n attachme

ater entrainm

load insen

greatly red

rs on wall a

ummarised

luence on

sually equa

negligible ef

avoid placi

part or mo

level of co

arlier switch

ent length c

ment being

sitive as th

uces perfo

ttachment d

by Warren

the perform

als the size

ffect both o

ing the con

ost of the p

ontrol and

hing as a r

can result f

allowed.

he reversing

ormance ef

devices is s

(1963).

mance of b

e of the

n the jet

ntrol port

ower jet

supply,

result of

from the

g flow or

fficiency,

shown in

bistable

2.6.6 StTh

Kirshner (

bistable a

the analyt

forming th

in determi

One can

the allowe

suit the fu

attachmen

xR, using

xR. This fa

the atmos

case and

Figure 2

teady-stahe steady-s

(1975). The

mplifier, wh

tically deter

he interactio

nation of th

start develo

ed ranges w

unctional p

nt wall leng

the Figure

actor of four

sphere the a

to ensure s

2.53 Attach

te designstate model

ey offer one

hich can ea

rmined and

on region of

he steady-st

oping a dev

with conside

urpose of t

gth based o

2.53, which

r is multiplie

attachment

tability.

hment lengKir

- 79

n methodlling proced

e the chan

asily be man

d commonly

f the device

tate input an

vice by spe

eration of th

the unit. Th

on the appro

h should be

ed to accou

length is tw

th with attarshner and

9 -

ology dures pres

ce to deve

nipulated fo

y used prin

e. Then thes

nd output c

ecifying the

heir general

his then all

oximated p

e four times

unt for the fa

wice as long

achment wKatz (1975

ented here

lop a conc

or a fluidic o

ncipal geom

se chosen v

haracteristic

ese fundam

l effect as d

ows an ap

ower jet att

s greater tha

act that whe

g as that of

wall angle fo)

e are acco

ceptual des

oscillator, b

metrical par

values can

cs.

ental value

discussed e

pproximation

ttachment d

an the valu

en controls

f the closed

or various

rding to

ign of a

ased on

rameters

be used

es within

earlier to

n of the

distance,

ue of the

open to

d control

offset

The appro

developed

Pg, can be

which is th

The contro

be estima

oximation o

d would be

e estimated

he blocked

Figu

Figure 2.5

ol flow requ

ated with Fi

of the inpu

the next ste

d allowing f

control con

ure 2.54 Blo

55 Input ch

uired on the

gure 2.56 t

- 80

ut characte

ep. Using F

for the app

dition, as a

ocked bubb(Kirshner

haracteristi(Kirshner

e active side

that is dedu

0 -

eristic curve

Figure 2.54,

proximation

starting po

ble pressurr 1975)

c curve forr 1975)

e to switch

uced from t

e for the p

the blocke

of point A

int of the ch

re with offs

r a bistable

the jet to th

the experim

particular g

ed control p

in the Figu

haracteristic

set

e device

he inactive s

mental data

eometry

ressure,

ure 2.55

c curve.

side can

of Lush

(1967 and

angle of 1

At the swi

side by 3

flow level

Then the

2-14 by a

pressure o

This then

coordinate

The final

characteri

d 1968), Mo

5o or can be

tching point

0% of CSq

of the inact

Fig

control pre

assuming th

of the contro

completes

es of the po

stage of

stic curve.

oses and M

e approxim

3.0 S

CS

q

q

t Drzewieck

(Kirshner 1

tive side con

gure 2.56 C

essure at th

hat the tota

ol flow with

2CSP

the input c

oints S and

the steady

The block

- 81

cRee (1969

ated using

16.0

SbB

ki noticed a

1975), whic

ntrol port as

Control flow(Kirshner

he switching

al pressure

an associa

7.0

CdC

CS

AC

q

characterist

R in Figure

y-state desi

ked output

1 -

9) and Kimu

the empiric

2

1

sudden dro

ch can be m

s 0.7 CSq .

w to switchr 1975)

g point, PC

is complete

ated dischar

2

tic curve ap

2.55.

ign is the

pressure re

ura (1972) f

ally derived

op in contro

manipulated

with offse

S, can be c

ely conserv

rge coefficie

pproximatio

approxima

ecovery, OP

for attachm

d Eq. 2-13

Eq. 2-

ol flow on th

d to determ

et

calculated w

ved in the d

ent, dCC .

Eq. 2-

on by provid

ation of the

Ob , as indic

ment wall

-13

he active

mine the

with Eq.

dynamic

-14

ding the

e output

cated by

point B in

theoretica

Figu

Figure 2.5angle. (Ki

n Figure 2

al model of G

ure 2.57 Inp

58 Blockedrshner 1975

.57 can be

Goto and D

put and out

d output pa5)

- 82

e deduced

rzewiecki (1

tput charac(Kirshner

arameter w

2 -

from Figu

1973) for lS/

cteristic cur 1975)

with offset

re 2.58 as

/bS between

urve for bis

for various

s predicted

n 8 and 16.

stable devic

s attachme

by the

ce.

ent wall

- 83 -

This then allows the estimation of the output flow at the switching point and

consequently the fan out ratio of the unit using Eq. 2-15 together with the fact that

CSO PP at the switching point with a square law impedance assumption for the

output.

2

2

o

OSObO A

qPP

Eq. 2-15

The output width, bO, in calculating the AO can be reduced by Eq. 2-16

SSSO l

bBbBlb

2/tansin)2( 12/122 Eq. 2-16

Then the fanout ratio, nF, can be found with Eq. 2-17

CS

OSF q

qn Eq. 2-17

2.7 Fluidic devices in flow control application In recent years, there has been a lot of published work suggesting the use of

fluidic devices for flow control applications. These research efforts range from

studying the fundamental performance characteristics of innovatively designed

fluidic devices to validation of a device in laboratory scale internal/external flow

control applications. Also, notable numbers of publications have been made on

studying the feasibility of incorporating other known flow control actuators, such as

piezoelectric transducer or plasma actuator, into a fluidic amplifier in order to gain

control authority of the jet switching independent of supply flow level.

Yang et al (2007) analysed the geometrical influences on the oscillation stabilities

and pressure loss of a single output beam deflection fluidic oscillator. For this study,

a single output vent-fed bistable fluidic oscillator is used, but with a novel design

step-shaped attachment wall and acute-angle splitters; its performance is compared

with a standard plane-attachment wall device. The schematic drawings of the fluidic

device are shown in Figure 2.59, while Figure 2.60 shows the general internal flow

pattern inside the fluidic oscillator.

Figure 2.5oscillator

Figure 2.oscillator, inlet zone

Prior to t

performed

varying th

shown in

would cau

oscillatory

a 10O spa

suggest th

it from dev

Figure 2.6and b) for

59 Configur. Yang et a

60 PIV lasb) local flow. Yang et al

the introduc

d geometric

he span ang

Figure 2.61

use the form

y motion ove

an angle doe

hat the opti

veloping a p

61 Operatinsplitter ang

uration of ml (2007)

ser displayw structuresl (2007)

ction of a

cal optimisa

gle (from 5

1. Yang et

mation of a

er the teste

es not prov

mum splitte

pressure dra

ng ranges gle variation

- 84

model. a) st

y of fluidic s of the circ

step-shape

ation work O to 45O) a

al (2007) s

large stand

ed flow rates

vide enough

er angle sho

ag exerted

of step-wan. Yang et a

4 -

tep-wall os

oscillator.culation, and

ed attachm

on the pla

and splitter

state that a

ding vortex t

s (0 ~ 20 L/

h space for

ould be bet

on the main

all oscillatoal (2007)

scillator, an

. a) flow pad c) local flo

ent wall, Y

ne-attachm

angle (from

span angl

that results

/min). Also,

stable oscil

ween 80O a

n flow.

ors. a) for s

nd b) plane

attern of plaow structure

Yang et al.

ment wall m

m 70 O to 1

e greater t

in a ceasin

they concl

llation. They

and 90O, to

span angle v

e-wall

ane-wall es of the

. (2007)

model by

20 O) as

han 40O

ng of the

ude that

y further

prevent

variation,

For furthe

angle of 8

plane-wall

an extra s

control flo

rates. The

models ar

Figure 2

oscillator

Figure 2.6a) plane-w

As can be

produced

achieved

er analysis,

80O. In an ef

l model, at

step to the a

ow not overc

e spectral m

re shown in

.62 Spect

r. Yang et a

63 Visualiswall oscillato

e seen from

and a reco

as expecte

Yang et al

ffort to remo

flow rate h

attachment

coming the

measureme

Figure 2.6

ra cascad

l (2007)

a)

sation of thor, b) step-w

m the above

ognisable r

ed by Yang

- 85

l. (2007) ch

ove the dev

igher than

wall. They

latching st

ents and th

62 and Figur

de. a) pla

e internal fwall oscillato

e results, st

reduction in

et al (2007

5 -

ose the sp

velopment o

15L/min, Ya

state that th

tability of th

he internal f

re 2.63.

ane-wall os

flow for coor. Yang et

table oscilla

n the stand

7) when us

an angle of

of an unstab

ang et al. (2

his instabilit

e standing

flow pattern

scillator, a

b)

mparison oal (2007)

ation (with c

ing vortex

ing a step-w

f 20O and a

ble oscillatio

2007) intro

ty arises du

vortex at h

n of the tw

and b) st

of flow stru

clear harmo

strength ha

wall oscillat

a splitter

on in the

duced a

ue to the

high flow

wo fluidic

tep-wall

ucture.

onics) is

as been

tor. This

effectively

65L/min. H

wall oscilla

Figure 2.6

The resu

characteri

author bel

stability w

effectively

channel, p

Furlan et

fluidic osc

Re < 1000

liquid dye

2.65. Thro

been perfo

the results

y widened t

However, a

ator, as Fig

64 Total pr

lts for Yan

stics with a

lieves the e

with an incre

y altered the

possible cha

al (2006)

cillator for R

00 (equival

method. Th

oughout the

ormed from

s of the two

the operatin

an increase

ure 2.64 sh

essure dro

ng et al (2

an introduct

effect is sim

ease in pre

e cross sec

ange in the

visualised

eynolds nu

ent to supp

he geometr

e evaluation

m ≈1.3mm to

configurati

- 86

ng range o

in pressur

hows.

op as a fun

2007) dem

tion of a ste

ilar to that o

essure loss

ctional area

control flow

the interna

mber (base

ply flow rate

rical specific

n a step red

o ≈0.4mm, h

on shown in

6 -

f the mode

re loss has

ction of flo

onstrate a

ep to attach

of an offset

. Also, as t

a of the ve

w momentu

al flow patte

ed on hydra

e range of 6

cation of the

uction in th

however Fu

n Figure 2.6

el giving a r

also been

ow rate. Ya

n improvem

hment walls

based on t

the introduc

nt connecte

m must hav

ern of a m

ulic diamete

60ml/min to

e model can

e width of t

urlan et al (2

65 (b) and (

range of 5L

noted with

ng et al (20

ment in os

s, nonethel

the gain of d

ction of a s

ed to the fe

ve been con

meso-scale

er) range of

o 600ml/min

n be seen in

the control

2006) only p

(c).

L/min to

a step-

007)

scillation

ess, the

dynamic

step-wall

eedback

nsidered.

vent-fed

f 1000 <

n) with a

n Figure

port has

presents

Figure 2.6global dimcontrol po

Figure 2.6

with a rela

regimes,

However,

narrow co

main jet fl

the outpu

Although,

intended j

retention o

Culley et

control of

three emb

connected

two plenu

achieve a

(0.73mm

leading ed

Figure 2.6

could not

65 Geometmension, b) ort width. Fu

66 visualise

atively large

showing a

close exam

ontrol port (≈

ow. This sh

t conduits

the model

jet oscillatio

of emulation

al (2003) a

a stator va

bedded bis

d to two sep

ums are se

spanwise

in diamete

dge on the s

67. The pha

be controlle

trical specimodel with

urlan et al (2

es successf

e control po

sequential

mination of t

≈0.4mm) m

hows rather

and almos

with a relat

on, Furlan e

n and/or pa

assessed t

ne in a low

table fluidic

parate plen

parated in

uniformity o

r with 30O

suction side

ase differen

ed due to th

- 87

ification of large contr

2006)

ful jet switc

rt width (≈0

ly guided m

the results

model, revea

r an even di

st a stagna

tively narrow

et al (2006)

rticles.

he use of

w speed axia

c oscillators

nums. Each

a streamw

of the exit j

pitch angl

e) is used o

nces, howe

he bistability

7 -

the modelrol port widt

ching of the

0.9mm) at b

main jet flo

shown in F

als an abse

istribution o

ating flow o

w control po

) recommen

a bistable

al compress

s with each

output ple

wise directio

jet flow, a r

e and at a

over the eac

ever, betwee

y of the dev

(dimensioh, and c) m

e meso-sca

both laminar

ow into bot

Figure 2.66

ence of the

of the main j

occurs in th

ort width fo

nd possible

fluidic oscil

sor. The va

h output po

num covers

on by a 4%

row of hole

a 35% chor

ch output pl

en the thre

ices.

ons in mm)model with s

ale fluidic o

r and turbu

th output p

iii), obtaine

jet switchin

jet flow into

he feedbac

und not to

e use of this

llator in se

ane design e

ort of the o

s 20% of sp

% chord len

es on the va

rd length f

lenum, as s

ee fluidic os

. a) mall

oscillator

lent flow

plenums.

ed with a

ng in the

o both of

ck arms.

produce

s for the

paration

employs

oscillator

pan and

ngth. To

ane skin

from the

shown in

scillators

i.

ii.

iii.

Figure 2.6with controwidth of 0at Re=116

66 Internaol port widt.87 at Re=968. Furlan e

l flow visuh of 0.87 at9737, and iiet al (2006)

- 88

ualisation wt Re=1038, i) operation

8 -

with liquid ii) operatio

n of oscillato

dye. i) open of oscillat

or with contr

eration of otor with conrol port wid

oscillator ntrol port th of 0.4

Figure 2.6Culley et a

The prelim

during the

shows sim

continuou

state (zero

output ple

device ha

2.1kHz, w

range of 3

Figure 2.6F+ = 0.52

Culley et a

the perfor

methods.

control jet

steady jet

mass flow

the jet. Th

67 Photo aal (2003)

minary hotw

e calibration

milar oscillat

s jet flow. C

o jet velocit

enum, does

s demonstr

which gives

3.3 ≤ F+ ≤ 3.

68 Unstead. Culley et a

al (2003) us

mance of th

The exper

t is advant

t actuation.

w in order to

he performa

nd concep

wire measu

n stage, hav

tory charact

Culley et al

ty) of the m

not empty

rated capab

s a reduced

9.

dy output gal (2003)

sed total pre

he embedd

imental res

tageous in

The stead

o achieve th

ance of the

- 89

ptual drawin

urements o

ve been vis

teristics to t

(2003) stat

modulation i

in the time

bility of gene

d frequenc

generated b

essure loss

ed-fluidic-va

sults demon

a sense o

dy jet cont

he same red

e embedde

9 -

ng of the e

of the outpu

sualised in

that of the m

e that the a

s due to th

e it takes th

erating a fre

cy number

by embedd

coefficient

ane and co

nstrated tha

of its energ

rol required

duction gain

d-fluidic-va

mbedded-f

ut jet from

Figure 2.68

modulating f

absence of a

e fact that

e device to

equency ran

(based on

ded-fluidic-

as a figure

ompared it w

at the harm

gy expendit

d a 56% in

ned by harm

ne in sepa

fluidic-van

the fluidic

8. The jet re

flow couple

a complete

the flow, w

o switch. Th

nge of 1.8k

injection l

-vane. Cμ=0

of merit to

with other a

monically os

ture over th

ncrease in

monically os

ration cont

e.

device,

esponse

ed with a

shut off

within the

he fluidic

kHz ≤ f ≤

ocation)

0.014 at

quantify

actuation

scillating

hat of a

injected

scillating

rol, at a

vane resta

reduction

Figure 2.6vane and

=0.36. C

Figure 2.6

rates pres

injection m

state that

fluid to a

viscous lo

arising fro

The emb

reduction

appreciab

flow rate

1.2).

The inves

control wh

shown in

of attenua

device, w

further su

agger angle

of total exit

69 Compard hole-vanCulley et al (

69 shows th

sent rather

momentum

actuation w

region that

oss. Wherea

om an intera

bedded-fluid

in total exit

ble 20% red

of approxim

tigated fluid

hen compar

Figure 2.69

ation in the

hich arises

uggest pos

e of 5O, can

pressure lo

rison of lose at 5 deg(2003)

hat the con

an adverse

coefficient

with a low in

t is already

as, an exce

action betwe

dic-vane m

t pressure l

uction in lo

mately 1%

dic model, h

red to othe

9). Culley e

e magnitud

from the s

ssibility of

- 90

n be seen in

oss relative

ss reductiog restagge

ntrol attemp

e effect, an

higher than

njection flow

y at (or nea

essive injec

een the inje

odel succe

loss of a low

oss compare

of the com

however, wa

r actuation

t al (2003)

e of harmo

small exit h

an improv

0 -

n Figure 2.6

to the non-

on for the ser angle, s

pts made w

nd loss red

n approxima

w rate simp

ar) separati

ction flow r

ected jet and

essfully de

w speed ax

ed to a non

mpressor thr

as found to

methods e

conclude th

onic oscilla

oles in the

ved perform

69; this show

-injection ca

slot-vane, esteady inje

with injection

duction star

ately 0.03.

ply adds mo

on, which

ate increas

d the freestr

emonstrates

xial compre

-control cas

rough flow

be less effe

examined du

hat this is d

ation genera

vane surfa

mance of

ws a chang

ase.

embeddedection, 56%

ns at very l

rts to reduc

Culley et a

ore low mo

leads to en

ses the mix

ream flow.

s its capa

essor. It rea

se with an

(velocity ra

ective in se

uring the st

due to an ex

ated by th

ace. Howev

the fluidic

ge in the

-fluidic-% span,

low flow

ce at an

al (2003)

mentum

nhanced

xing loss

bility of

alised an

injection

atio of ~

paration

tudy (as

xistence

e fluidic

ver, they

device

compared

design sta

Raman a

oscillator

freestream

fluidic dev

with a ph

water as a

spatially o

the fluidic

sawtooth o

Figure 2.device. ainjection dsupply pre

The fluidic

592Hz to

inherent f

rate of 0.7

The perfo

has been

on the up

length of

two differ

considere

d to the sire

age of the m

and Raghu

as a tool

m jet flow a

vice used b

oto showin

a working m

oscillating je

c model is

or sine wav

.70 Schema) schematdepicting sqessure = 4p

c oscillator

2760Hz, wi

requency s

75•10-3kg/s)

ormance of

examined b

pstream en

7.62cm). T

rent freest

d in the exp

n valve, wh

model.

(2004) int

to suppre

and cavity

y Raman a

ng the insta

medium. On

et with a squ

also capa

veform, whe

matic showic drawing uare-wave

psig. Raman

produced a

ith a supply

saturation in

.

the fluidic

by locating

d of the ca

his points p

ream Mac

periment.

- 91

hen its outpu

troduced a

ess the ca

interaction

and Raghu

antaneous o

ne can note

uare wavefo

able of gen

en the exit n

wing desigof the mobehaviour

n and Ragh

an unsteady

y pressure v

nitiated bey

oscillator in

the exit noz

avity base

perpendicu

ch number

1 -

ut load mat

a single ou

avity reson

. A schema

(2004) is s

output jet o

e that the m

orm. Rama

nerating an

nozzle desig

n and opeodel, and fof oscillatoru (2004)

y oscillatory

variation be

yond the su

n the cavity

zzle (1.693m

(depth of 1

lar to the m

cases of

ching is con

utput vent-f

nance tone

atic drawin

hown in Fig

oscillation v

model gene

n and Ragh

n oscillating

gn is altered

eration of low visualisry jet exiting

y jet in the f

etween 0.4p

upply pressu

y resonance

mm X 0.954

1.27cm, wid

main flow ov

M=0.485

nsidered du

fed bistable

e arising fr

ng of the m

gure 2.70, t

visualised b

erates a tim

hu (2004) s

g jet with

d.

miniaturesation using the nozzle

frequency r

psig and 40

ure of 15ps

e tone supp

4mm in dim

dth of 4.45

ver the cav

and M=0

uring the

e fluidic

rom the

miniature

together

by using

mely and

tate that

either a

e fluidic g water

e, where

range of

psig. An

sig (flow

pression

mensions)

5cm and

vity, and

.69 are

The fluid

freestream

shown in F

M=0.69. F

supply ma

flow. Ram

factor tha

initiation o

Raman a

method, b

addition a

Figure 2.7jet-cavity (2004)

Cerretelli a

attachmen

compared

In addition

studied an

namely: in

amplifier,

output jet

dependen

frequency

Figure 2.7

ranging fro

ic oscillato

m Mach num

Figure 2.71

Figure 2.71

ass flow rate

man and Ra

an the actu

of frequenc

nd Raghu

by stating

t a flow rate

71 Fluidic otone supp

and Kirtley

nt fluidic os

d its efficienc

n, the effec

nd, for this

nsert (A) an

but their fe

t frequency

nt on the s

y responses

73. The exit

om 35 to 60

or achieved

mber cases

, with the flu

clearly sh

e of 1.15•10

aghu (2004)

uation freq

cy saturatio

(2004) str

that 1dB to

e of 0.12% o

oscillator spression. T

(2009) exa

scillator as

cy with the

ctiveness of

reason, tw

nd insert (B

eedback pat

y character

supply flow

s of those

t jet profile

0% of the je

- 92

d noticeab

s. The meas

uidic oscilla

hows tone

0-3kg/s, wh

) remark tha

quency in j

on beyond

ress an eff

one reduct

of the main

supply preThe main je

mined the i

s an actuat

steady blow

f the reduce

wo different

B). Both sh

th geometry

ristic while

pressure.

fluidic osci

demonstra

et mean vel

2 -

ble resonan

surements o

ator actuatio

reduction o

hich is equiv

at the mass

jet-cavity to

the supp

ficiency of

tion is ach

jet flow.

ssure and et’s flow is a

mplementa

tor to cont

wing contro

ed frequenc

fluidic osci

are an iden

y differs. Th

the outpu

The gene

llators can

ates a stron

locity. Inser

nce tone

of the cavity

on levels at

of as much

valent to 0.1

s addition is

one suppre

ly pressure

an oscillat

ieved when

mass flowat M=0.69.

ation of a ve

rol flow se

l method.

cy number

llator desig

ntical basic

his gives in

ut frequenc

ral output j

be seen i

g modulatio

rt (A) is des

reduction

ty tone amp

the main je

as 10dB w

12% of the

s a more d

ession, not

e of 15psig

tory mass

n using ste

w requiremeRaman and

ent-fed bista

eparation a

(F+) has als

ns are con

planform o

nsert (A) a c

cy of inser

jet respons

n Figure 2

on with rms

signed to op

in both

plitude is

et flow of

with the

main jet

ominant

ting the

g. Also,

addition

eady jet

ents for d Raghu

able wall

nd then

so been

sidered,

of fluidic

constant

rt (B) is

ses and

2.72 and

s values

perate at

a constan

from F+ =3

inherent l

velocity) d

Figure 2.7frequency

Figure 2.7frequency

The fluidic

used in

schematic

D=0.25mm

α=0O. The

the leadin

nt reduced

3 to F+ =6.

eakage exi

during the je

72 Feedbacy response a

73 Feedbacy response a

c oscillator

boundary

cally shown

m used ups

e flow contro

g edge.

frequency

In addition,

isting with

et modulatio

ck fluidic oas a functio

ck fluidic oas a functio

models de

layer sepa

n in Figure

stream of t

ol inserts ar

- 93

number of

, Cerretelli

any fluidic

on can neve

oscillator inon of supply

oscillator inon of supply

eveloped b

aration con

e 2.74 for

the test se

re situated

3 -

≈0.7, while

and Kirtley

switch, a

er be attaine

n insert (A)y pressure. C

n insert (B)y pressure. C

by Cerretell

ntrol over

UFS=25.9m

ction to en

between 50

e insert (B)

(2009) rem

complete s

ed (Kirshne

). a) velocityCerretelli an

). a) velocityCerretelli an

i and Kirtle

a hump d

s-1 (Re =

sure turbul

0 and 62%

) covers th

mark that du

shut-off sta

r and Katz,

ty wave formnd Kirtley (2

ty wave formnd Kirtley (2

ey (2009) a

diffuser mo

3•105, trip

lent transiti

chord lengt

e range

ue to an

te (zero

1975).

m and b) 2009)

m and b) 2009)

are then

odel, as

wire of

on) and

ths from

Figure 2.7and Kirtley

Cerretelli

as a metri

measurem

2.75 and

momentum

up to a va

value of C

presence

Figure 2.7

perturbatio

Figure 2blowing a

74 Schemay (2009)

and Kirtley

ic measure

ments of the

Figure 2.7

m coefficien

alue Cμ ≈ 0

CP ≈ 0.75.

of a larger

76 (a). Ce

on introduce

.75 Diffusas a functio

atic drawin

(2009) exa

of the sepa

e jet interac

76. A tren

nt, Cμ, for a

.9; then, it s

The initial

re-circulatin

erretelli and

ed to the m

er pressuon of Cμ fo

- 94

ng of the h

amined the

aration con

ction flow fie

nd of chan

all three con

starts to inc

drops at lo

ng flow reg

d Kirtley (2

main flow by

re recoveor =0 deg.

4 -

hump diffu

overall pres

trol perform

eld. These r

ge in CP

ntrol metho

crease stee

ow injection

ion in Figur

2009) state

the low inje

ry curves Cerretelli a

user cross

ssure recov

mance and a

results are i

with an in

ds, show a

ply giving a

n levels are

re 2.76 (b),

e this is d

ection level

for steadand Kirtley (

section. C

very coeffic

also presen

illustrated in

ncreasing

an initial dro

a relatively c

e supported

when comp

ue to an

control flow

dy and un(2009)

Cerretelli

ient, CP,

nted PIV

n Figure

injection

op in CP

constant

d by the

pared to

adverse

w.

nsteady

Figure 2.7by insert

Also, Cerr

over inser

by couplin

layer has

To compa

blowing c

Figure 2.7

oscillator

reduction

required

coefficient

76 U veloc(A) over th

retelli and K

rt (B), and

ng between

not been ob

are the effic

control met

77) where t

and the x

of 60% in t

mass flow

t of 0.75.

ity fields ahe hump. C

Kirtley (2009

possible de

unsteady a

bserved as

ciency betw

hods, Cerr

the y-axis s

x-axis show

the required

are achie

- 95

nd streamlCerretelli and

9) demonstr

evelopment

actuation at

in Figure 2

ween the u

retelli and

shows the

ws the pres

d momentu

evable in

5 -

lines for und Kirtley (20

rated a sup

of large-sc

t low freque

.76.

nsteady flu

Kirtley (200

relative red

ssure reco

m and a co

attaining a

nsteady flo009)

erior perfor

cale global

ency (F+≤1)

uidic oscillat

09) presen

ductions ga

very coeffi

orrespondin

an overall

ow control

rmance of in

instability t

) and the b

tor and the

nted graphs

ained by th

icients. A

g 30% redu

pressure r

applied

nsert (A)

riggered

oundary

e steady

s (as in

e fluidic

possible

uction in

recovery

Figure 2.7velocity r

Compleme

validated

characteri

separation

0.8m). An

interspaci

chord from

pitch and

The fluidic

independe

general je

Figure 2oscillatorfrequency

The valida

covering t

4.8·106. M

77 Relativeratio as a fu

entary to C

the perfor

stic as tha

n control ov

n array of

ng of 5mm

m the leadi

yaw angles

c oscillator e

ent of the

et response

.78 Velocir output jey response a

ation work o

the Reynol

Measuremen

e reductionunction of

Cerretelli a

rmance of

at used for

ver a DU-96

f fluidic os

m between t

ng edge on

s of 30O.

employed in

driving pre

and freque

a)

ty time het. a) velocas a functio

of the fluidic

lds number

nts of lift an

- 96

n with fluidCp. Cerrete

and Kirtley

the fluidic

insert (A)

6 aerofoil m

scillators w

the exits w

n the suctio

n the study

essure. Fo

ncy respon

istory andcity wavefo

on of supply

c oscillator i

r (based o

nd drag hav

6 -

dic oscillatoelli and Kirtl

(2009), C

oscillator,

in Cerretel

model (span

with exit no

were used.

on surface

provided a

r the comp

se are show

d frequencorm as mey pressure. C

in separatio

n chord le

ve been ana

or in momeey (2009)

Cerretelli et

which has

li and Kirtl

of 0.73m a

ozzle diame

This is the

of the mod

a constant fr

pleteness o

wn in Figure

b)

cy responsasured by Cerretelli et

on control h

ngth) range

alysed for tw

entum, pow

t al (2010)

s a similar

ey (2009)

and chord le

eter of 3m

en installed

del with exi

requency re

of the revi

e 2.78.

se of thethe HWA,

t al (2010)

as been pe

e of 2·106

wo actuatio

wer and

) further

r output

in flow

ength of

mm and

at 60%

t nozzle

esponse

ew, the

fluidic and b)

erformed

≤ Re ≤

on levels

based on

refers to

Cerretelli

especially

studied. A

conditions

(2010) rep

with 10mm

Figure 2.7

generally

an early tr

Figure 2.7all testedand low le

Readers

frequency

conditions

separation

frequency

made in c

output flow

provide re

total mass

=69.9g/s a

et al (2010

y in post sta

A considera

s of the fluid

peated a sim

m spacing)

79 shows,

resulted in

ransition of

79 Improved configuraevel refers to

would hav

y and velo

s. This intr

n control ac

y number. I

combining th

w, with fluid

elatively larg

s flow rate

and low refe

0) success

all applicati

ble increase

dic actuato

milar experi

applied to

actuation o

further enh

the bounda

ements in mations. Higho a mass flo

ve recognis

ocity chara

rinsic chara

ctuator due

In this poin

he use of o

dic amplifie

ge amplifica

- 97

driving an

ers to =51

sfully demo

ions for all

e of 10 to 6

r, can be s

iment but w

the leading

of the fluidi

ancement o

ary layer.

max CL ash level of acow of 51.4g

sed the h

cteristics o

acteristic ca

e to the los

nt of persp

other flow c

r; this is ba

ation of a mi

7 -

array of fl

.4g/s.

nstrated im

Reynolds

60% in lift, d

seen in Figu

with an artifi

g edge of th

ic oscillator

of the lift. H

a functionctuation ref

g/s. Cerrete

habitual de

of fluidic d

an be disa

ss of contro

ective, som

ontrol actua

ased on the

inute level o

uidic oscilla

mprovement

numbers an

depending

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cial roughn

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r with a rou

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n of Re andfers to a malli et al (201

pendency

devices on

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ollability of

me research

ators, gene

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of flow.

ators, nam

ts in lift an

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upon the o

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aerofoil mo

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d velocity rass flow of 10)

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h work hav

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fluidic ampl

ely high

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elli et al

mp tapes

odel. As

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y due to

ratio for 69.9g/s,

utput jet

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potential

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mpulsive

ifier can

Gregory e

decouple

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piezoelect

frequencie

The piezo

fluidic dev

deflect un

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Gregory e

piezo-fluid

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Through t

characteri

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bender m

shows hot

Figure 2.bender is (2009)

et al (2009

the frequen

hance the o

ers. In this

tric bende

es and supp

o-fluidic osc

vice, but th

der an elec

cillator with

et al (2005)

dic oscillato

he upstream

this this, up

stics, includ

gn of the p

odel, in Gre

t-film measu

.80 Diagrapositioned

9) have ev

ncy respon

output mom

s study, th

r oscillatio

ply pressure

illator consi

e usual sp

ctric signal.

a piezoelec

. In the wo

or have bee

m of the po

pstream-poi

ding higher

piezo-fluidic

egory et al.

urements of

m of the in the diffu

- 98

valuated th

se of the f

mentum of th

he oscillato

on have b

es.

ists of a sim

litter replac

The fundam

ctric-bender

ork of Grego

en evaluate

ower jet wh

inting-bend

modulation

c oscillator

. (2009), is

f the output

piezo-fluiduser, pointin

8 -

e piezo-flu

luidic devic

he usual ac

ory jet resp

been eval

mple contro

ced by a pi

mental perfo

r idea have

ory et al (2

ed, which in

hile the othe

er found to

n index and

with an up

shown in F

t jet at vario

dic actuatong upstream

idic oscillat

ce from its

tuators driv

ponse cha

uated at

l free bistab

ezoelectric

ormance ch

e been eval

005), two d

ncludes one

er bender p

o provide s

frequency

pstream po

Figure 2.80

ous actuatio

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tor in an e

input chara

ven by piezo

aracteristics

various a

ble wall atta

bender wh

haracteristic

uated prev

different de

e with a be

points down

superior mo

roll-off (Gre

ointing piezo

0, while Figu

on condition

. The piezoflow. Grego

effort to

acteristic

oelectric

to the

actuation

achment

hich can

cs of the

iously in

signs of

ender tip

nstream.

odulation

egory et

oelectric

ure 2.81

s.

oelectric ory et al

Figure 2.8hot-film pand 200Hand 5Hz. G

It is obser

the output

increase i

decay tim

square wa

index of 0

sawtooth

demonstra

flow at son

Gregory e

flow signa

results are

an increas

that this is

a

c

81 Time hisprobes. a) z, c) at preGregory et

rved through

t jet wavefo

in the phas

es. At a low

aveform is g

0.8); wherea

signal is g

ates the ca

nic nozzle c

et al (2009)

al response

e shown in

sing pressu

s solely due

a)

c)

story of theat pressuressure ratio al (2009)

h increasing

orm occurs.

se delay fro

w driving fre

generated w

as, a high a

generated

pability of t

condition (P

also exami

time to the

Figure 2.82

ure ratio, i.e

to an incre

- 99

e oscillatore ratio of 1.6of 1.14 and

g the driving

. Yet, an in

om the con

equency ra

with a modu

actuation fre

as in Figu

the piezoele

P/Patm=2.15

ined the eff

e step input

2 and one c

e., a faster p

ease in conv

9 -

r outputs s69 and 10Hd 1.0kHz, a

g frequency

ncrease in d

ntrol signal,

nge (0 ~ 25

ulation leve

equency bo

re 2.81 c)

ectric bend

5).

fect of the a

s sent to th

can note a d

power jet flo

vection time

b)

d)

simultaneoHz, b) at prend d) at pre

y that a chan

driving frequ

with an in

50Hz), an o

l higher tha

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. In additio

er in contro

actuation pre

e piezoelec

decreasing

ow. Gregory

e within the

ously measessure ratioessure ratio

nge in the s

uency resu

ncrease in r

oscillatory je

an 80% (mo

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on, Figure

olling the p

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ry et al (200

output plen

ured by o of 1.69 o of 2.15

shape of

lts in an

rise and

et with a

odulation

milar to a

2.81 d)

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el on the

r. These

ime with

09) state

num.

Figure 2.8Gregory e

Gregory e

chosen pr

jet frequen

range of 0

and 500H

the exami

to oscillate

an energy

2.83, whic

Figure 2.supply prabscissa c

In addition

output pla

of a usua

model is s

82 Step reet al (2009)

et al (2009)

ressure rati

ncy shows

0 to 1.2kHz

z, where th

ned input f

e at its reso

y shift in the

ch is a pre-d

83 Frequeressure ratcorresponds

n to the pie

asma-fluidic

l bistable w

shown in F

sponse of

further eva

o of 1.14; t

one to one

. However,

he piezo ben

low conditio

onant freque

e power spe

defined reso

ncy maps tio of 1.14. s to the pow

ezo-fluidic o

oscillator b

wall attachm

Figure 2.84.

- 100

f the piezo

aluated a ba

the results

e linear relat

Gregory et

nder appea

on. They st

ency within

ectrum mea

onant freque

of the pieThe ordina

wer spectra

oscillator, G

by integratin

ment fluidic

. The work

0 -

-fluidic osc

andwidth of

are illustrat

tion to the e

t al (2009)

ars unable t

ate it is a p

this driving

asurements

ency of the

ezo-fluidic ate indicatesl density. G

Gregory et

ng a plasma

amplifier. T

of Gregory

cillator to t

f the unstea

ted in Figur

examined a

note a regi

o actuate th

possibility fo

g frequency

to 121Hz a

piezoelectr

oscillator s the driving

Gregory et a

al (2007) i

a actuator w

The concep

y et al (200

the piezo

ady output

re 2.83. The

actuation fre

on between

he jet oscill

or the piezo

y range, afte

as shown in

ric bender.

performang frequencyl (2009)

ntroduced

within a con

ptual drawin

07) focused

bender.

jet for a

e output

equency

n 250Hz

ation for

o bender

er noting

n Figure

nce at a y and the

a single

ntrol port

ng of the

d on the

verification

exit veloc

400mW).

fluidic osc

Figure 2.8

Figure 2.8

output pla

first jet pr

plasma ac

change in

separation

delay. Fig

the output

and t=25,

Gregory e

flow from

Figure 2.Torr, Pdis

n of the sw

ity range o

They also

cillator durin

84 Diagram

85 shows t

ane during t

rofile graph

ctuator initia

n output jet

n bubble to

ure 2.85 als

t jet travers

an increas

et al (2007)

the plasma

85 Velocityssipated =

itching cha

f 5 ~ 8ms-1

evaluated t

g the jet sw

m of the pla

the hotfilm

he jet switc

h includes t

ation. Grego

flow has n

grow along

so shows c

es across t

se in peak

concluded

actuator to

y measure400mW. G

- 10

racteristics 1) and elec

the jet prof

witching pro

asma-fluidi

measurem

ching proces

the measur

ory et al (20

not been de

g the attach

changes in p

the exit noz

k velocity a

that this in

o the main je

ements acrregory et al

1 -

at various

tric power

ile across t

cess.

c actuator.

ents of the

ss. As can

rements ma

007) state th

etected and

hment wall

peak velocit

zzle. By com

nd total mo

crease is a

et flow.

ross nozzlel (2007)

flow velocit

supply leve

he output p

. Gregory et

e output jet

be seen fro

ade at a tim

hat prior to

suggest th

is the domi

ty and the a

mparing the

omentum c

as a result o

e opening,

ty (equivale

els (at 345m

port of the

t al (2007)

t profile acr

om Figure 2

me 20ms a

this time an

he time tak

inant sourc

actual jet pr

e jet profiles

can be reco

of an added

, Pplenum

ent to an

mW and

plasma-

ross the

2.85, the

after the

n overall

en for a

e of this

rofile, as

s at t=20

ognised.

d control

= 0.15,

Figure 2.8

flow to rea

speed and

variance o

velocity an

the mome

available e

jet switchi

Figure 2.settings.

Although t

a confide

integration

prevent t

configurat

Yet, Greg

could cert

the fluidic

of a more

As a closu

this cover

Readers w

studying v

86 shows c

ach 63.2% o

d plasma ac

of the calc

nd/or with a

entum of the

electric pow

ng reduces

.86 Plots Gregory et

the results

nt level of

n of the plas

them from

tion), it suc

ory et al (2

tainly be im

amplifier a

efficient pla

ure of this s

rs the fund

would have

vent-fed flu

changes in j

or one time

ctuation pow

culated swit

a decrease

e induced c

wer to it, the

with increa

of switchial (2007)

in Gregory

f control m

sma electro

induced

ccessfully d

007) claim

mproved wit

nd the plas

asma actua

section, the

damental s

e noted tha

uidic oscilla

- 102

jet switchin

e constant o

wer level. A

tching time

in power le

control flow

e control au

asing flow v

ing time f

et al (2007

momentum

odes (a limit

arcing ac

demonstrate

that the pe

th careful r

ma actuato

ator.

e work of Te

study of th

at most of

ator. To the

2 -

ng time (the

of its final va

An increase

e can be se

evel. Gregor

w by the pla

uthority of th

elocity and

for varied

7) present s

with the p

tation in po

cross the

es a functio

erformance

review of th

or location, t

esar et al (2

he test mo

recent res

e author’s

e time taken

alue) with va

in both the

een with a

ry et al (200

sma actuat

he plasma a

vice versa.

flow veloc

some drawb

lasma actu

wer levels t

electrodes

oning plasm

of the plasm

he geometri

together wit

2006) is rev

del evalua

earch effor

best knowl

n for the o

ariations in

switching t

an increase

07) state th

tor is limited

actuator on

.

cities and

backs in ge

uator and

to the elect

of the c

ma-fluidic os

ma fluidic o

ical optimis

th the deve

viewed in de

ated in this

rts are focu

ledge, the

utput jet

the flow

time and

in flow

hat since

d by the

the min

power

nerating

physical

rodes to

confined

scillator.

oscillator

sation of

lopment

etails as

s thesis.

used on

work of

Tesar et a

loaded flu

The planfo

specificati

can be fou

pressure d

interaction

the perfor

Figure 2.8the ampliexperimen

They have

the results

7% of the

attached

shown in

pumping e

supply flow

al (2006) is

idic oscillato

orm of the

ons shown

und in Figu

driven oscil

n as a princ

mance of th

87 Geometifier, and bntal investig

e numerical

s are illustra

e supply fl

side contro

Figure 2.8

effect throu

w.

almost an o

or.

fluidic mod

in Figure 2

re 2.87 b).

lator unlike

cipal in achie

he model bo

trical specb) photogragations. Tes

lly evaluate

ated in Figu

low will ini

ol port. Als

89 illustrate

ugh the low

- 103

only recent

del studied

2.87 a) with

A distingui

e others rev

eving the je

oth as an am

(a)

(b)

cification aaph of thesar et al (20

ed the perfo

ure 2.88. Te

itiate the je

o, the com

e an existen

w state side

3 -

efforts dev

in Tesar et

h a height o

shable feat

viewed abov

et oscillation

mplifier and

)

)

nd photo oe assemble006)

ormance of

esar et al (2

et switching

mputed path

nce of a s

e output po

oted in inve

al (2006) f

of 6mm; pho

ture of the m

ve, which a

n. Tesar et a

d oscillator.

of the moded amplifie

the model a

2006) conc

g when inj

hlines of th

tanding vor

ort; approxim

estigating a

follows geo

oto of a bui

model is th

adopted mo

al (2006) ev

del. a) geomer as used

as an ampl

clude approx

jected thro

he internal

rtex resultin

mately 20%

control-

ometrical

lt model

at it is a

mentum

valuated

metry of d in the

ifier and

ximately

ugh the

flow as

ng a jet

% of the

Figure 2ordinatesX1. Tesar

F

Tesar et

control p

(2.5mm≤d

width) ran

measured

generation

.88 Flow s; the respo

et al (2006

Figure 2.89

al (2006) s

parameters

d≤10mm) f

nge of 1790

d with a pre

n of a very s

transfer conse to the 6)

9 Pathlines

studied the

of feedb

for supply f

0 to 14340.

essure tran

stable modu

- 104

characteriscontrol sig

s of flow in

e frequency

back loop

flow Reyno

General ou

sducer is s

ulation with

4 -

stic of thenal admitte

the state B

y bandwidth

length (

olds numbe

utput jet res

shown in F

square wa

e amplifieed to only o

B. Tesar et

h of the flu

(1m≤l≤52m

r (based on

sponse of t

igure 2.90.

veform.

er in relatone control

al (2006)

uidic oscilla

m) and d

n power je

the fluidic o

One can

ive co-terminal

ator with

diameter

t nozzle

oscillator

notice a

Figure 2oscillatio

Plot of fre

can be fo

frequency

the calcula

jet velocity

of Figure 2

Figure 2.10mm dia

.90 An exn. Tesar et

equency as

und in Figu

y with increa

ated Strouh

y, w) as a f

2.92 is defin

.91 The freameter loop

xample ofal (2006)

a function

ure 2.91. O

asing loop le

hal number

function of

ned in Eq. 2

equenct vsp tube at d

- 105

f a typica

of feedback

One can not

ength. Figu

(based on f

Reynolds n

2-18 as in T

s. loop lendifferent su

5 -

al oscillos

k loop leng

te the inver

ure 2.92 sho

feedback lo

number. The

Tesar et al (2

ngth depepply flow r

cope reco

th at variou

rse proporti

ows corresp

oop length, l

e term Sh s

2006).

ndences orates. Tesa

ord of ge

us supply flo

ionally redu

ponding cha

l, and powe

shown in th

obtained wr et al (2006

nerated

ow level

ucing jet

anges in

er nozzle

he y-axis

with the 6)

Figure 2.9tube at dfunction o

Tesar et a

interpolati

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is indepen

The effec

investigate

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remark th

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92 The expdifferent flof Reynold

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number in

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ct of feedba

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to the con

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Figure 2.94

perimentalow rates r

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any way.

xponent of t

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r this Reyno

loop length

2

ack loop d

results are

nstant propa

onsiderable

o the therm

e confineme

4.

- 106

l results ore-plotted i Tesar et a

h

e Strouhal n

they rema

Based on

the curve f

speed is co

olds numbe

h for the len

iameter on

e shown in

agation spe

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ent by the

6 -

btained wiin terms ol (2006)

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Figure 2.93

eed regime

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small diam

th the 10mf the Strou

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Reynolds n

hey state th

r than 5m.

agation spe

3. Tesar et

e is noticea

on speed i

stic change

eter; this is

mm diametuhal numb

Eq. 2-

of two to en

he behaviou

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he Strouhal

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eed has als

al (2006) s

able, but fo

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-18

able the

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Figure 2.9the feedbTesar et a

2.8 SumFun

reviewed

dynamic c

is provided

93 The proal (2006)

94 Dependback loop al (2006)

mmary odamental p

throughout

characterist

d.

opagation

dence of thtube on S

of fluidicsprincipals of

t this chapt

tics are wel

- 107

velocity fo

e propagaStokes num

s f operation

ter. Geome

ll understoo

7 -

or differen

tion velocimber for d

and class

etrical influe

od and stea

nt feedback

ty in resondifferent tu

ification of

ences on b

ady-state de

k tube dia

nant condiube diame

fluidic dev

both the sta

esign meth

ameters.

tions in eters, d.

ices are

atic and

hodology

- 108 -

Recently, considerable research efforts have been devoted in validating a feasibility

of fluidic oscillator as an alternative PVGJ actuator for flow control appreciating its

operational simplicity and robustness in generation of unsteady pulsing jet. Although,

these efforts resulted in notable findings; successful demonstration of separation

control; specifying the optimal reduced frequency number for operation; successful

development of functioning micro- to meso-scale oscillator giving frequency

bandwidth of several kilo hertz; effective removal of habitual coupling between input

and output characteristics, most of studies are focused on investigating momentum

driven oscillators.

To the author’s best knowledge, publication made by Tesar et al (2006) is almost an

only recent work suggesting the use of control-loaded fluidic oscillator for flow

control application. Although, Tesar et al (2006) provide some valuable results it

requires further analysis as to validate it feasibility.

Thereby, the author experimentally evaluates steady-state characteristics of the

oscillator in amplifier configuration and output jet characteristics to verify its

frequency bandwidth and governing parameter for jet switching.

- 109 -

3 Experimental apparatus and methods

3.1 Experimental models The design of the bistable fluidic oscillator and an array of fluidic amplifiers

studied in this report are provided by Prof. Vaclav Tesar from the Academy of

Sciences of the Czech Republic.

3.1.1 The fluidic oscillator

3.1.1.1 The design Figure 3.1and Figure 3.2 show the geometry of the planform and the

interaction region of the model respectively. The fluidic oscillator has a power jet

nozzle with a width of 2.0mm and two control nozzles with a width of 1.4mm. It has

a depth of 8.0mm giving a power nozzle aspect ratio of 4. A specially designed

concave bi-cusped shaped splitter is employed to give an extra latching stability and

is located at 11.63mm downstream of the exit plane of the power nozzle. The

planform of the device is manufactured by laser cutting four 2.0mm thick perspex

sheets, then piling them up to meet the required height. The manufacturing of the

oscillator is then completed by covering it with a top and a bottom plate each having

a thickness of 8.0mm.

All the input and output interconnection ports are made accessible by connecting

metal tubes oriented perpendicularly to the top cover plate. The tubes stand 20mm

above the upper surface of the top cover plate and have an internal orifice diameter

of 6mm, 5mm and 6mm for the supply, control and exit ports respectively. Figure

3.3 shows an assembly of the manufactured bench-top test model. The principle of

operations is described in Chapter 2. The time-delay feedback loop internal

diameter was fixed to the size of 5mm, while its impedance and capacitance varied

according to its length.

This model was tested so as to assess its steady-state dynamic performance such

as the control flow requirement in switching the power jet flow, the flow gain and the

fan-out ratio as a function of the power jet Reynolds number, hDRe . The

characteristics of the oscillatory jets, including the pulse transition, frequency

bandwidth and characteristic switching time are also examined.

Figur

Figure 3.2

re 3.1 Geom

2 Geometri

a

Figure

metrical sp

ical specifi

a)

3.3 Photos

- 110

pecification(Dimension

ication of t(Dimension

s of the flu

0 -

n of the fluns in mm)

the fluidic ons in mm)

idic oscilla

idic oscilla

oscillator in

b)

ator test mo

ator planfor

nteraction

odel.

rm.

region.

- 111 -

3.1.1.2 Test conditions

3.1.1.2.1 Steady-state analysis

This analysis has been performed to define the control flow rate requirement

for deflecting the power jet from the attached side to the opposite wall, gain and fan-

out ratio of the actuator as a function of the power jet Reynolds number. The power

jet Reynolds number is based on the power nozzle hydraulic diameter and it varies

from 3105.8 to 4105.6 equivalent to a supply mass flow rate range of 0.7 to 6g/s.

For this analysis, the feedback loop from the existing fluidic oscillator is removed to

allow the device to function as a fluidic amplifier, which reacts to an application of a

control signal fed directly into the control port. An air supply connection is made to

one of the control ports, while the other is open to atmospheric pressure. The

volume flow rates applied to both the supply and the control are measured with an

analogue flow meter. A precision flow regulation is achieved by the use of needle

valves.

A schematic drawing of the experimental set-up used for the steady-state analysis is

given in Figure 3.4. To calculate the mass flow rates going through the supply port

and control port, fluid density is required along with the measured volume flow rates.

The volume flow rates are measured using flow meters. The locations at which the

static pressure reading for fluid density calculation are different for the supply port

and the control port, as shown in Figure 3.4. For a flowmeter measuring low volume

flow rates it is recommended to read a fluid density upstream of the flowmeter,

which was the case for the control port flow. On the other hand, the fluid density of

the flow going into a supply port is measured at the output port of the volume

flowmeter, which was designed to measure high flow rates.

The jet mean velocity is estimated from the hotwire measurements of the exit

velocity taken at 1Do downstream of the centre of the output orifice (within the

potential core region). If the exit jet Reynolds number based on the exit orifice

diameter and jet mean velocity, ODRe is less than 3103.2 , the flow can be

assumed to be laminar. In this case, the Hagen-Poiseuille velocity profile as shown

in Eq.3-1 can be assumed and the jet mean velocity, omu , is equal to one half of the

maximum velocity at the jet centreline.

At this low

is not truly

length of

measured

if a symm

variation f

velocity ca

hotwire. F

with a top-

.

At a given

has comp

switching

flow rate.

data at bo

flowmeter

w Reynolds

y the centre

the hotwire

d velocity is

metric jet p

from the w

an be still r

For higher R

-hat velocity

(flFigure 3.4

n supply flow

pletely deta

the needle

Then simu

oth output

readings t

ru

number, ho

eline veloci

e probe (le

found to be

profile acro

wire tips to

easonably

ODRe values

y profile, the

uid flow lineExperimen

of

w rate, the c

ached from

valve for th

ltaneous m

ports are m

taken manu

- 112

2

2

1Rr

cu

owever, the

ty but rathe

ength of ho

e only 2.9%

oss the orif

the centre

taken as on

s, since the

e measured

e) ntal set-upf the fluidic

control flow

the origin

he control f

measuremen

made. The

ually for fut

2 -

e velocity m

er a space-

otwire being

% lower than

fice and si

are assum

ne half of th

e exit flow

d ocu , is ass

p for the stec oscillator

w is graduall

ally attache

flow is locke

nts of press

data are st

ture analyse

easured wi

-averaged v

g 1.25mm).

n the actual

mplified lin

med. There

he velocity

is a fully d

sumed to be

(deady-state .

y increased

ed wall sid

ed to a pos

sure reading

tored on a

es. Once th

Eq. 3-

ith the hot-w

value over

Neverthele

l centreline

near mean

efore, the je

measured

developed t

e equal to u

data line) analysis

d until the p

de. At the

sition to mai

gs and the

PC along

he data acq

-1

wire ocu ,

the wire

ess, the

velocity

velocity

et mean

with the

urbulent

omu ,

power jet

point of

intain its

hotwire

with the

quisition

- 113 -

has been completed the power jet is forced back to its initial state, i.e. to the closed

control port side.

For the data acquisition from the hotwire, the sampling frequency was set to 80kHz

and hotwire signal was low-pass filtered at 50kHz for supply flow rate higher than

2.1g/s ( 1, 30 msu oc ) and 40kHz and 20kHz for lower than 2.1g/s ( 1

, 30 msu oc )

respectively so as to capture the possible turbulent fluctuations. The pressure

reading was filtered at 100Hz using a digital filter. The total sampling time was given

as five seconds.

3.1.1.2.2 Oscillatory jet characteristic analysis

The purposes of this analysis are two-fold: Firstly, to define quantitatively the

effects of the flow rate and the length of the time delay feedback loop on the

frequency response of the periodic oscillation of the jet; Secondly, to verify the

characteristic switching time of the actuator that is determined by the geometrical

parameters of the actuator. In addition, at certain selected test points, jet

characteristics are also analysed, including the phase-averaged and time-averaged

jet centreline velocity, pulse transition characteristics and turbulence intensity over a

one cycle.

In the present experiment, the time delay feedback loop between the two control

ports is obtained with the use of a plastic tube with a bore size of 5mm with a length

varing from 0.3m to 2.0m. The supply flow rates range from 0.6g/s to 5g/s, which

gives a range of Reynolds number based on the hydraulic diameter of the tube of

6.5X103 to 7.3X104. The supply flow rate is regulated with a needle valve and

measured with an orifice plate flowmeter. 오류! 참조 원본을 찾을 수 없습니다.

shows a summary of the test cases and the general experimental set-up is

illustrated in Figure 3.5.

Supply Flow Rate (g/s)

Feedback Loop Length (m)

0.6 to ~5

(Power jet velocity from ~ 30ms-1 to ~170ms-1 with an incremental step

of approximately 5ms-1) Power nozzle 5.0M

0.3 0.58 0.78 1.0 1.16 1.58 1.78

Table 3.1 character

Figure 3

The jet o

spectrum

of the orifi

of freque

resonant

sound bas

possible f

this thesis

enhance t

were acqu

approxima

1.5kHz m

capture th

only when

of 2048 d

sets over

100Hz wit

Experimenristic of a f

(fl

3.5 Experim

oscillating fr

of the volta

ice. In orde

ncies to b

frequency

sed on resu

frequency to

s. Also, ove

the assuran

uired at the

ately 1.46H

mechanically

he possible

n a stabilise

ata points

the time. T

th a digital lo

nt case sumluidic oscil

uid flow line

mental set-fo

requency is

age signals

r to improve

be captured

of the dev

ults in Tesa

o be ~300H

ersampled

nce in dete

e rate of 3k

Hz. The sig

y and filtere

high freque

ed spectral

were fed to

The pressur

ow-pass filt

- 114

mmary for llator.

e)

for the studof a fluidic o

s determine

measured w

e the quality

d was pre

vice with fe

ar et al (200

Hz for the r

data prior

rmination o

kHz for 204

gnals were

ed further w

ency harmo

measureme

o fft functio

re measure

ter.

4 -

the study o

dy of the jeoscillator.

ed as the

with a hotw

y of the spe

determined

eedback loo

06); this eff

range of fee

to the fina

of the samp

8 points giv

then low-

with a digi

onics. Data

ents are vis

n in LabVIE

ements for

of the jet o

(d

et oscillatio

strongest p

wire placed a

ectral meas

by estima

op length a

ectively def

edback loo

al measurem

pling freque

ving a frequ

pass filtere

tal low-pas

are stored

sualised in L

EW, then it

the flowme

oscillation

data line)

on characte

peak in the

at 1Do dow

urement, th

ating the

and local s

fined the m

p length st

ments are

ncy. The fi

uency reso

ed close to

ss filter at

for further

LabVIEW; e

t averaged

eter were fil

eristic

e power

nstream

he range

possible

peed of

maximum

udied in

used to

nal data

lution of

o the at

1kHz to

analysis

each set

multiple

ltered at

The samp

80kHz wit

seconds.

3.1.2 Fl

3.1.2.1 TTh

the interac

it has a p

the outpu

orifices ca

spaced ac

each prov

diameter o

amplifier a

empty spa

streamwsi

control flow

Figur

pling freque

th a low-pa

uidic amp

The designhe planform

ction region

ower nozzl

t ports has

an be redu

cross the s

vide six out

of 7.6mm a

are indicate

ace represe

ie offset be

w to be sup

re 3.6 Geom

ency selecte

ass filter s

plifiers in

n of the fluid

n as the sing

e width of 2

s been mod

uced. The e

span. The a

put ports w

as shown in

ed by a cro

ent the exit

etween the

pplied from t

metrical sp

(Dimen

- 115

ed for the j

set at 50kH

n an array

dic amplifie

gle oscillato

2mm and a

dified so th

entire array

amplifiers a

with a spanw

n Figure 3.5

ss in the s

ports contr

e two contr

two separa

pecification

nsions in m

5 -

et velocity

Hz. The tot

y

r in the arra

or discusse

a height of

at the spac

y contains

are spaced

wise spacin

56. The loc

haded flow

ributed by t

rol ports is

te chamber

ns of a fluid

mm) (Tesar

analysis da

al sampling

ay shares t

d the previo

8mm. Howe

cing betwee

five fluidic

at 73.96mm

ng of 12.33

cations of th

path. The

the neighbo

also introd

rs.

dic amplifie

2007)

ata acquisit

g time was

the same d

ous section

ever, the d

en adjacen

c amplifiers

m in the ar

3mm with a

he exit port

two crosse

ouring amp

duced to a

er in the ar

tion was

s twelve

esign of

n. Hence

esign of

nt output

equally

rray and

n orifice

ts of the

es in the

lifiers. A

llow the

rray

Suco

Sm

The assem

plate cont

control ch

aluminium

manufactu

Manufactu

two contro

supply cha

separate m

core plate

found in F

Figure 3.7(2007)

3.1.2.2 TTh

mounted a

of 250mm

surface. T

7.6mm to

upply ports tontrol chamb

Supply port tomain supply c

Supply port fluidic ampl

mbly of flui

taining the

ambers an

m cover plat

ured by CN

uring and L

ol chamber

amber with

module and

e containing

Figure 3.8.

7 3D drawi

Test condihe assembly

as an inser

m and thickn

The orifice d

1.1mm thro

to the bers

Main supp

o the chamber

to the ifier

idic amplifie

array of th

d jet orifice

te (see Figu

C machinin

Laser Proce

rs have a

a dimensio

d clamped o

an array of

ng showin

itions y of the flu

rt in a 2D N

ess of 30m

diameter of

ough a dive

ply chamber

C

- 116

er array is

he fluid am

es, the main

ure 3.7). T

ng a 9mm a

essing grou

dimension

on of 22mm

on to the m

f fluidic amp

ng the gene

idic amplifi

NACA0012 a

mm. The exit

f the exit p

rgent chann

Control cham

6 -

made of fo

mplifiers, the

n supply ch

The core pla

nd a 14.5m

up at the U

of 24.5mm

mx38mmx55

middle plate.

plifiers and

eral assem

er array is

aerofoil sec

t orifice diam

ort of the f

nel of 8mm

Core plate array of flu

Covecontr

mbers

our separat

e middle pl

amber bloc

ate and the

m thick alu

University o

mx12.5mmx5

58mm was

Pictures o

other assoc

mbly of the

designed s

ction which

meter is 1.1

fluid amplifi

in length in

containing thuidic amplifie

Middlethe conand jet

r plate for thol chambers

te pieces; t

late contain

ck and a 2m

e middle pla

minium pla

of Manches

x556mm. Th

manufactur

of the manu

ciated parts

test mode

such that it

has a chor

1mm on the

er is reduc

nside the ae

the iers

e plate containtrol chambe

orifices

he

Arrayexit o

the core

ning the

mm thick

ate were

te at the

ter. The

he main

red as a

factured

s can be

el. Tesar

t can be

d length

aerofoil

ced from

erofoil.

ining rs

y of orifices

Hence th

performan

However,

which is c

outputs of

This effec

final exit d

modifying

fully pulse

exit orifice

Figure 3.amplifier nozzle pla

The modif

aspect rat

sectional

oscillatory

The oscil

diameter

from 2 to

없습니다..

the freque

oscillatory

In the pre

impulsive

he initial in

nce of the a

owing to t

caused by t

f the fluidic

ctively shifte

diameter siz

this design

ed jet respo

es on a fluid

8 Geometra) exit noz

ate section;

fication on

tio of the po

area ratio o

y jet amplitu

latory jet c

ranging fro

4. A summ

. The perfo

ency respo

y jet charact

esent study,

control sig

ntention of

rray of fluid

the introduc

the reductio

amplifiers,

ed the focu

ze which en

n so as to

onse. For th

dic amplifier

rical specizzle profiled). the fluid

design whic

ower nozzle

of the exit

de attenuat

characterist

om 1.1mm t

mary of the

rmance par

onse. There

terisation st

the jet swi

nal fed into

- 117

f this stud

d amplifiers

ction of the

on of the ex

a fully puls

us of this p

nables a fu

reduce the

his reason,

r via a moun

ification ofe; b) 3D viedic array wit

ch is consid

e in the flu

orifice to a

tion.

tics were s

to 3.5mm w

test points

rameters co

efore simila

tudy for the

itching in th

o the contro

7 -

y was to

with a final

e extra exit

xit diameter

sed exit jet

roject to fin

ully pulsed j

exit diame

six exit no

nting plate a

f the exit ew of an eth the exit n

dered feasi

idic amplifie

mplifier exi

studied for

with a pow

s is shown

onsidered w

ar data sam

single fluid

he fluid amp

ol chambers

d

examine

exit orifice

t load on t

r from 7.6m

response w

nding for a

jet for the e

eter while m

zzles and a

as shown in

nozzles foxit nozzle; ozzles in pl

ble in the p

er. This is b

t conduit a

various si

wer nozzle a

in 오류! 참

were the jet

mpling sett

ic oscillator

plifier array

s. The fluidi

the oscilla

diameter o

the fluid am

mm to 1.1mm

was not att

minimum

existing des

meeting the

are attache

n Figure 3.8

or a singlec) assemb

lace.

present stud

because th

also determ

izes of exi

aspect ratio

참조 원본을

t peak velo

ting as tha

r case was

y is governe

ic oscillator

atory jet

f 1.1mm.

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sign and

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.

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t orifice

o varing

찾을 수

ocity and

t of the

adopted.

ed by an

r studied

previously

connected

supply flow

regulated

Table 3.2

Figure 3

3.2 Exp

3.2.1 CoTh

measurem

constant t

was chose

y was used

d to the con

w level to t

separately,

Feedbaof fluidi

Summary

(fl

3.9 Experim

periment

onstant tehroughout t

ments at the

temperature

en for its sim

as the driv

ntrol chamb

he fluidic a

as illustrat

ack loop lengc oscillator (

(m)

1.16

of the test

uid flow line

mental set-u

tal metho

emperatuhe experim

e outputs of

e hotwire a

mplicity, reli

- 118

ving actuat

ber via a fix

mplifiers an

ted in Figure

gth L) AR

432

t cases for

e)

up for the c

ods

ure anemment reporte

f the actuat

nemometer

iable accura

8 -

tor for the a

xed feedba

nd a fluidic

e 3.9.

Exit ori

[start :[1[1[1

the study o

cascading

ometer (Ced in this

tors were a

r. This mea

acy and hig

array with e

ack loop len

oscillator w

fice diamete(mm)

: step size : e.1 : 0.1 : 3.6].1 : 0.2 : 3.0].1 : 0.2 : 2.6]of the fluid

(d

study of a

CTA) report, the

accomplishe

ans of fluid

h frequency

each of its

ngth of 1.16

were measu

er (DO)

end ] ] ] ]

dic amplifie

data line)

fluidic am

fluid flow

ed with the

diagnostic

y response

outputs

6m. The

ured and

er.

plifier.

velocity

aid of a

method

.

- 119 -

The hotwire probe was a standard DANTEC 55P11 single normal wire probe. The

sensor was a 5μm in diameter and 1.25mm long tungsten wire. The probe was

connected to a TSI IFA 300 constant temperature anemometer containing an on-

board signal conditioning unit of the SMARTTUNETM module and a thermocouple

circuit. The SMARTTUNETM module also automatically optimises the frequency

response of the IFA 300, which can be as high as 250 kHz or greater. The analogue

output from the unit was converted into a digital signal by a 16-bit PCI 6221

analogue-to-digital converter, which has the best resolution of 0.00153% at the ±5V

scale and maximum sampling rate of 250kS/s and stored in a PC for future analysis.

3.2.1.1 Principles of operation A constant temperature anemometer allows virtually instantaneous

measurements of velocity fluctuations in the flow at a given point by quantifying the

change as an analogue voltage which varies in a predictable manner at the

anemometer output. This fluid diagnostic method is fundamentally based on the

forced convective heat transfer from an electrically heated sensor (wire/film) to the

surrounding fluid as their rate of exchange varies with fluid velocity, temperature,

pressure and phase (density). Thereby if multiple changes of parameters occur

simultaneously relevant corrections must be made. In this report only the fluid

temperature correction will be considered in the error analysis section. One should

also remember the existence of other heat transfer mechanisms apart from the

forced-convection which includes conductive heat transfer from the sensor to

prongs, radiation heat transfer and buoyant convection.

In the constant temperature mode, the hotwire placed in a feedback circuit as

illustrated in Figure 3.10 forms one of the Wheatstone bridge resistors. In this mode,

the chosen sensor hot temperature is maintained at a constant value, and hence is

the hot resistance. When the wire is exposed to a varying flow condition the

selected wire temperature will alter correspondingly due to forced-convective heat

transfer. This then generates error voltage of e2 – e1 as in Figure 3.10, which is

compensated by feeding the required current change back to the circuit to maintain

the sensor temperature and the resistance at the same level. This results in a

change in the voltage output as expressed in Eq. 3-5

Figure

The mean

of the hotw

where the

are the va

0oC.

A simplifie

sensor ca

Combining

introducin

transfer re

as in Eq.

constants

performing

law. The e

0.4 and 0.

e 3.10 A fee

n wire (sens

wire, RW, as

e temperatu

alues at the

ed form of

n be expres

g the Eq. 3

g the wire

elation of th

3-6 by in

in the ca

g a simple

exponent, n

.45.

W IRE 2

edback circ

sor) temper

s in Eq. 3-2

aW RR 1

a

ure coefficie

e ambient c

a heat tra

ssed as in E

aW

W

RR

RI

2

3-2 and Eq.

voltage E

e hotwire in

clusion of

libration co

calibration

n, is a user-

WW RRR 2

E 2

- 120

cuitry for a(Bruun

rature, TW, c

Wa T

00 aR

R

ent of the w

condition w

ansfer relati

Eq. 3-4.

a

BUA

. 3-3 and s

WW IRE ,

n Eq. 3-5. In

the wire p

onstants A

analysis. T

-selected va

W TTR 00

nBUA

0 -

constant t1995)

can be relat

aT

wire materia

hile 0 and

onship for

nU

substituting

where I is

n practice t

roperty con

and B, wh

This relation

ariable whic

a BUAT

temperatur

ted to the e

al, a , and

d R0 stand f

a finite len

into Eq. 3-

s the curre

he Eq. 3-5

nstants and

hich can b

nship is the

ch common

n

re anemom

electrical res

Eq. 3-

Eq. 3-

wire resist

for those v

ngth active

Eq. 3-

-4 for WR

ent, yield t

is further s

d operation

be easily fo

e well know

nly ranges b

Eq. 3

Eq. 3

meter

sistance

-2

-3

ance Ra

alues at

hotwire

-4

aR and

he heat

implified

n setting

ound by

n King’s

between

-5

-6

- 121 -

3.2.1.2 Calibration For the calibration of the hotwire probe, a 55D41 calibration unit from

DANTEC was used by placing the probe at the centre and in the same axial plane

of the downstream pressure tap of the venturi nozzle. The calibration unit is capable

of giving an accurate velocity variation range of ~2ms-1 to ~120ms-1 and this

available full velocity span is used for the probe calibration. The velocity of the flow

going through the venturi nozzle is calculated from a differential pressure

measurement between the upstream and downstream of the venturi nozzle, made

available with a digital micromanometer.

King’s law is used to relate the measured velocity and anemometer output voltage.

In order to choose an optimal value for n in King’s law, the sum of error squared

(SES) value is examined by comparing the measured output voltage with calculated

output voltage for various n values raging from 0.4 to 0.45. A minimum SES is found

at n=0.43.

In finding the calibration constants as in Figure 3.11, the voltage reading at zero

velocity, EW,0, has been omitted since this reading is purely the result of the buoyant

convection rather than a forced convection, but this can be included by multiplying

the 20,WE by a correction factor of 0.8 as in Eq. 3-7 if required (Bruun 1995).

20,8.0 WEA Eq. 3-7

To account for the possible characteristic disparity between low and high flow speed

regions, two different relations are made producing separate expressions for flow

below and above ~30ms-1. The calibration data are acquired at every ~2ms-1 up to

30ms-1 then every ~4ms-1 for the high-speed region. The hotwire calibration data are

acquired at a sampling frequency of 80kHz for total sampling time of 5seconds.

They are then lowpass filtered at 50kHz for high-speed band and 20kHz for low-

speed band. A typical calibration curve is shown in Figure 3.11.

- 122 -

Figure 3.11 An example of a hotwire calibration graph.

3.2.1.3 Error analysis The major error sources associated with the calculated velocity arise from

the calibration unit, linearisation during the calibration and data conversion through

the A/D converter. For the uncertainty estimation of the calibration unit used in this

project which is based on the differential pressure reading method, the usual

relative standard uncertainty value of 2% has been used with normal distribution

assumption. The error associated with the linearisation, linU , is estimated to be

1.25% using Eq. 3-8, where UR is the measured velocity and UC is the calculated

velocity, and has a normal distribution. The velocity sensitivity of the employed

King’s law relation is deduced from Eq. 3-9 and is used in calculating the resolution

error, resU , together with the aforementioned A/D board input range, EAD, and its

data conversion resolution in bit, nAD, as in Eq. 3-10 These results are shown in

Figure 3.12 and Figure 3.13 and the maximum value reads about 0.23%, which

turns out to be negligible. For other associated errors, such as sensor and fluid

temperature fluctuation and ambient pressure variation, usual values from Bruun

(1995) and Jørgense (2002) are assumed and listed as in 오류! 참조 원본을 찾을 수

없습니다. with the corresponding coverage factors.

2

1

21

1100

N

iUU

lin C

R

NUU Eq. 3-8

E

nBU

dU

dES

n

u 2

1

Eq. 3-9

dE

dUEUU

ADnAD

res 2100 Eq. 3-10

y = 13.269x + 6.4042

y = 13.805x + 2.5712

0

20

40

60

80

100

120

0 1 2 3 4 5 6 7 8 9

U^0.43

E^

2

high speed band

low speed band

Figure 3.shown in

Figure 3.resolution

.12 An exaFigure 3.1

.13 An exn error for

ample of t1

xample of the case s

- 123

the velocit

the relatishown in Fi

3 -

ty sensitiv

ve standaigure 3.12

vity calcula

ard uncerta

ated for th

ainty due

he case

to the

- 124 -

Source of error Estimated standard

uncertainty (%) Calibrator 1.0

Linearisation 1.25

Resolution 0.23

Sensor temperature fluctuation (1o) 0.8

Fluid temperature fluctuation (1o) 0.2

Ambient pressure variation (10kPa) 0.6

Table 3.3 Summary of the estimated maximum errors in the velocity measurements through hotwire measurements with calibration graph shown in Figure 3.11.

These values are then used in finding the total expanded uncertainty with a normal

distribution assumption giving the 95% confidence level using Eq. 3-11. The

maximum value is found to be approximately equal to 3.8%.

N

iitot UUU 22 Eq. 3-11

3.2.2 Orifice plate flowmeter Johnston (1963) stated that ‘for a fluidic amplifier having an orientation such

as the supply and control flows are injected perpendicularly to the planar plane of

the device, the primary switching mechanism is governed by the mass flow rate

rather than the pressure’. Hence an accurate means of measuring and regulating

the flow rate is required for fluidic devices. A homemade orifice plate was

manufactured with a conduit diameter, DP, of 25mm, which is the minimum

allowable size according to British Standards, an orifice diameter, dor, of 12.5mm

and an orifice plate thickness, Eor, of 0.022DP. Owing to a difference in size between

DP and the diameter of the predefined interconnection ports of the test models, it

requires a concentric expander at the inlet of the upstream pipe and a reducer at the

exit of the downstream pipe. These have an expansion ratio of 4 and a reduction

ratio of 0.25. An upstream and downstream straight passage length of 20DP and

10DP are thus introduced respectively for the flow development. The general

geometries are given in Figure 3.14 below.

Figure 3.symbols

The afore

procedure

2 and ISO

downstrea

which reco

to 50mm.

are used.

The orifice

a straight

3.2.2.1 PTh

Bernoulli’s

velocity an

point refer

from the u

then be us

DP - cdor - o - oEor - o

l1 - uup

l’2 - ddo

.14 Homem

ementioned

es of the ori

O 15377). T

am pressur

ommends t

Owing, how

This additi

e plate is no

bore orifice

Principles his fluid flo

s principle.

nd consequ

renced as a

upstream o

sed in appro

F

conduit (piporifice diamorifice to coorifice thick

upstream prpstream surf

downstreamownstream s

made orifi

geometric

fice plate a

There is a m

re tappings

the use of c

wever, to th

onal error

ot bevelled

e was used

of operatow measur

As the fluid

uently its pr

a vena contr

of the orifice

oximating th

4

Cqm

Flow directio

- 125

pe) diametemeter = 0.5Donduit diameness = 0.02

ressure taprface of the

m pressure tsurface of th

ice plate f

cal values

re referred

minor depar

s from the

corner tapp

he manufac

has been c

owing to th

like that of a

ion rements te

d is forced

ressure cha

racta hence

e plate. Thi

he flow rate

2

1

2

4

Pdor

on

5 -

r DP eter ratio 22DP

pping locatioorifice plate

tapping locahe orifice pl

flowmeter

in the des

to the Britis

rture in the

specificatio

ings, for the

cturing com

corrected in

he difficulty

a bidirection

chnique is

out throug

ange. The m

e giving the

is differenti

e, qm, using

4

1

on measuree = DP

ation measate = DP/2

geometry

sign and th

sh Standard

locations of

ons given i

e pipe DP ra

mplexity, DP

n accordanc

in controllin

nal orifice p

based on

h a relative

maximum c

maximum p

al pressure

Eq. 3-12.

ed from

sured from

y and corr

he flow es

ds (ISO 516

f the upstre

in the ISO

ranging from

and DP/2 t

ce with ISO

ng its depth

plate flowme

n the well

ely small or

change occ

pressure di

e reading,

Eq. 3-

responding

stimation

67-1 and

eam and

15377,

m 25mm

tappings

O 12767.

, and so

eter.

known

rifice, its

curs at a

fference

P , can

-12

g

- 126 -

where ρ1 is the upstream fluid density, ε is the running fluid expansion factor, is

the orifice to pipe conduit diameter ratio and C is the discharge coefficient which can

be calculated using the Reader-Harris/Gallagher equation as in Eq. 3-13.

4.258.275.0011.0

8.0031.01

11.01123.0080.0043.0

Re

100063.00188.0

Re

10000521.0216.00261.05961.0

3.11.1'2

'24

4710

3.06

5.3

7.06

82

11

D

MMAee

AC

LL

DD PP

Eq. 3-13

where;

e - Orifice thickness (for current design, this equals Eor)

PDRe = 11

4 P

m

Dq

1L = PD

l1

'2L =

PDl '2

'2M =

PDL'

22

A = 8.0

Re19000

PD

It can be seen from the Eq. 3-13 that the discharge coefficient depends on the

Reynolds number and it therefore needs to be iteratively optimised. This is done by

grouping the dependent terms and independent terms in the Eq. 3-13 separately

then setting dependent terms to zero by making an initial guess of the Reynolds

number as infinite. The new value of the Reynolds number is then determined by

substituting the approximated discharge coefficient from the previously estimated

value of the Reynolds number into the Eq. 3-14. This iterative analysis is repeated

until the convergence criteria in Eq. 3-15 satisfied.

ACP

D

dC

P

orDP

4

1

1

2

1

2Re

Eq. 3-14

41

)(

101

Re

A

CAi

iDP Eq. 3-15

3.2.2.2 CAs

coefficient

prior to th

data acqu

iteratively

the downs

and viscos

orifice pla

cause and

negligible.

3.15. The

used in e

experimen

Figure 3.plate.

3.2.2.3 ETh

orifice pla

confidence

)(, 2

Q totm

In this rep

have been

Calibrations the flow

t, it was ca

he experime

isition. Flow

estimated

stream tem

sity. The te

ate to avoid

d assuming

. The flow

derived eq

estimating

nts.

qm

15 The ma

Error analyhe expande

te flowmete

e level.

2

C

C

port, only t

n estimated

n estimation

librated und

ents, enabl

w rate durin

discharge

mperature m

emperature

d the poss

g that the

rate is the

quation as

the flow ra

15.117 m

ass flow r

ysis d relative u

er can be a

4

42

1

2

he errors a

d. Owing, h

- 127

requires it

der the sam

ling the red

g the calibr

coefficient.

measuremen

measurem

sible disturb

temperatur

n plotted a

in Eq. 3-16

rate from t

5.01 P

rate calibra

uncertainty

pproximate

2

1

2

D

D

P

P

associated

however, to

7 -

terative app

me conditio

duction in t

ration is esti

Upstream

nts are use

ents are m

bance that

re change

against the

6 by curve

he pressur

3.42

ation grap

in the mas

d using Eq

2

4

2

d

d

or

or

with the es

the difficul

proximation

n as that o

he computa

imated with

pressure m

ed in deter

ade at the

a thermoc

from that o

1P a

fitting the d

re measure

h of the h

s flow rate

. 3-17 to ac

2

4

1

P

P

stimated dis

ty in quanti

n of the di

of the test c

ational time

h Eq. 3-12 u

measureme

rmining the

downstream

couple pock

of the upst

as shown in

data points

ements du

Eq. 3-

homemade

measured

chieve the u

21

2

1

1

E

scharge co

ifying the q

scharge

condition

e during

using the

ents with

density

m of the

ket may

tream is

n Figure

s is then

ring the

-16

e orifice

with an

usual 95%

Eq. 3-17

oefficient

uality of

- 128 -

the manufactured orifice plate flowmeter, such as the alignment of the orifice plate

and the pressure tappings, circularity and cylindricality of the pipe conduit and

orifice plate and orifice sharpness, some of these associated terms involved in

determining the overall uncertainty of the determined flow rate have been either

neglected or referenced to usual values or maximum allowable values specified by

British Standards where possible.

The uncertainty sources included in the approximation of the discharge coefficient

errors are the inherent 0.5% arising from the chosen orifice to pipe diameter ratio

and an additional 0.91% from the pipe diameter being less than the 50mm,

calculated by using Eq. 3-18 (ISO 15377 and 5167:2). Further correction has been

made owing to the aforementioned disparity between the pressure tapping location

with that of the recommendation using the Eq. 3-19 at every calibration point and

over the calibration range (ISO 12767). Also errors arising from possible elastic

deformation of the orifice plate have been considered, even though it was expected

to be small. The relative change in discharge coefficient owing to plate deformation

is calculated as a percentage using Eq. 3-20 before being converted into a

percentile error with Eq. 3-21 (ISO 12767).

4.258.275.09.05.0(%)

1

PD

C

C Eq. 3-18

125(%) 2

2C

PDandPD

C

C

C

C Eq. 3-19

2

21

2

2100a

E

Da

E

D

Y

PC

orordef Eq. 3-20

defCC

C 5.0(%)

3

Eq. 3-21

where;

Y - Young’s modulus

D2 - orifice plate support diameter

a1 = 155.0135.0

a2 = 3.106.117.1

2PD

P andDC - calculated discharge coefficient for DP and DP/2 pressure

tappings

CC - calculated discharge coefficient for corner pressure tappings

The total

are shown

with other

estimated

Figure 3.1the range

relative sta

n in Figure 3

r uncertain

mass flow

16 Total ree of the cal

andard unce

3.16 and th

ties gives

rate with a

elative stanibration flo

- 129

ertainties ov

e maximum

the total e

95% confid

ndard unceow rate

9 -

ver the ran

m value is a

expanded u

dence level.

ertainty in t

ge of the c

round 3%. T

ncertainty

the estimat

calibration f

This value t

of %33.2

ated flow ra

flow rate

together

% for the

ate over

- 130 -

4 The characteristics of the fluidic oscillator

4.1 Steady-state analysis The primary emphasis of this study is to define a flow gain, GF, and a fanout

ratio, nF, of the test model, which are often used as a figure of merit in comparing a

dynamic switching response of such devices. To do so, the fluidic oscillator model is

modified into a fluidic amplifier as described in Chapter 3 and a steady control flow

is introduced to a control port. The control flow volume flow rate is then gradually

increased until the switching of a steady attached power jet flow takes place. The

control flow rate at the switching point together with the corresponding output flow

rates from the both exit orifices of the device are measured at different supply flow

rates, allowing the aforementioned performance parameters to be determined.

4.1.1 Control flow rate at the point of jet switching From the previous work of Tesar et al (2006) and Warren (1963), a ratio of

the control to the supply mass flow rate is expected to be around 7% at a sbRe of

7.6X103 for a model which has a similar interaction region as the current model and

it will decrease with an increasing power nozzle Reynolds number, hDRe . Here

sbRe is based on the width of the power jet nozzle width and is calculated using Eq.

4-1. hDRe is the Reynolds number defined using the hydraulic diameter of the

power jet nozzle, Dh as shown in Eq.4-2. The hydraulic diameter of the power jet

nozzle , Dh is calculated using Eq.4-3.

h

sD

SSb D

bbUhs ReRe

Eq. 4-1

hb

mDU

s

shSDh

2Re Eq. 4-2

AR

bAR

hb

hbD s

s

sh

1

22 Eq. 4-3

Figure 4.1 presents the measured control mass flow rates through the active side

control port, c1, at the power jet switching point for different power jet Reynolds

numbers and its ratio to the supply mass flow rate, 1,cm . Throughout the analysis,

subscript 1 denotes an initial active side of the fluidic amplifier prior to the

(1

mc

completio

power jet

converted

as shown

Figure 4.1

and its ra

Figure 4.1

the switc

examinatio

4104.2 .

number, R

Reynolds

dynamics

apparent w

Reynolds

the supply

)/ sg

n of the jet

switching h

into the ma

in Eq. 4-4.

1 Variation

atio to the s

1 clearly sho

hing point

on reveals

This Reyn

Recrit, which

number reg

between th

when the co

number reg

y flow rate.

t switching

has taken pl

ass flow rat

is estima

m

ns of the co

supply flow

ows a trend

with an i

an abrup

nolds numb

h divides the

gimes. The

he two Rey

ontrol to the

gime, the c

About 0.08

- 13

while 2 den

lace. The m

te, m , with

ated from th

Vq

ontrol mas

w rate, 1,cm

d of increas

increasing

t jump in

ber is henc

e supply flo

presence o

ynolds num

e supply flow

control mass

87 near Re

1 -

notes an ac

measured vo

knowledge

he time-ave

s flow rate

, with DRe

ing control

supply flo

the magni

ceforth refe

ow level into

of a charact

mber regime

w rate ratio

s flow rate

crit, a furthe

ctive side a

olume flow

e of the den

raged static

e, 1cm , at th

hD .

mass flow r

w level. H

tude of cm

erred as the

o a low-ban

eristic chan

es separate

, 1,cm , is ex

is a consta

r increase i

after the su

rate, Vq , h

sity of the f

c pressure r

Eq. 4-

he switchin

rate require

However, a

1c at hDRe

e critical R

nd and a hig

nge in the sw

ed by Recrit

xamined. In

ant ratio of 0

in the supp

ccessful

as been

fluid, ,

reading.

-4

ng point

ement at

a closer

around

Reynolds

gh-band

witching

is more

n the low

0.071 of

ply mass

1,cm

- 132 -

flow rate results in a sudden increase in 1,cm . Beyond this point, the ratio of the

control to the supply flow rate at the switching point decreases almost linearly to

0.066 at hDRe =6.5X104.

Based on the typical 1,cm ratio being 0.05 to 0.15 as mentioned in the literature

review, the result shown above suggests that the existing model has a relatively low

or a moderate latching stability, i.e., relatively high tendency for power jet switching.

The trend of change in 1,cm with the power jet Reynolds number observed in Figure

4.1 at hDRe > Recrit is in accordance with the conclusion drawn by Warren (1963).

Tesar et al (2006) studied a bistable fluidic oscillator which shares a similar

interaction region geometry as that of the current design but with a different power

nozzle width, a nozzle aspect ratio and a control to power nozzle width ratio. The

most influential parameter which affects1,cm at the switching point is the control to

power nozzle width ratio which was about the half the size of the current model.

Although their 1,cm is expected to be higher than that of the current model, their

computed value of 1,cm of 7% for

sbRe =7.6X103 is in close agreement with the

result from the present experiment observed at hDRe < Recrit. Referring to the paper

by Savkar (1966), this is perhaps due to a corresponding increase in the relative

control to supply jet momentum ratio which arose from the use of a smaller control

to power nozzle width ratio in the work of Tesar et al (2006).

As it was described in the literature review, the value of 1,cm of a bistable fluidic

wall attachment device is predominantly determined by two factors, i.e. the size of

the separation bubble and the latching stability in the device. The separation bubble

size near the power jet attachment point is known to be strongly governed by the

geometrical parameters, such as the offset and the attachment wall angle, but

relatively independent of the power jet nozzle Reynolds number (Johnston, 1963).

Furthermore, for a device having a small or zero offset, given the moderate

attachment wall angle, the power jet will attach to the wall shortly after leaving the

power nozzle. Thereby a negligibly small separation bubble is formed or its

formation may even be suppressed within the attached side control nozzle as

schematically shown in Figure 2.31 a). On the other hand, the latching stability is

- 133 -

determined by the size and the strength of the standing vortex and since it is formed

as a portion of the power jet flow captured by the splitter, its growth is governed by

the power jet Reynolds number as well as the shape and the location of the splitter.

The standing vortex will influence the latching stability by counteracting the control

flow which enters from the attached side control nozzle, hence forces the power jet

to detach from the wall. Also depending on the output load condition and the use of

vent, a return flow may result which travels towards the upstream output aperture

that can effectively counteract the standing vortex, hence reducing the latching

stability.

Based on the above discussion, the observed changes in 1,cm with increasing

power jet Reynolds number may imply a possible characteristic variation in the

evolution of the standing vortex. One possible explanation would be a limitation in

the size and strength of the standing vortex by the physical confinement of the

device cavity. It is believed that structure of the standing vortex evolves consistently

with the supply flow level and hence the control flow levels out to compromise the

increasing latching stability in the sub-critical regime. With a further increase inhDRe ,

the structural evolution of the standing vortex may be halted or stabilised causing

that the control rate ceases to depend on the supply flow rate.

4.1.2 The characteristics of output jets The characteristics of the output jet were evaluated using the velocity data

obtained from a single normal probe placed at one orifice diameter downstream of

the centre of the exit orifice..

From the statements made by Morris (1973), Kirshner and Katz (1975) and Tesar et

al (2006), some induced flow motion is expected to occur at a low state side exit

port either in the forms of a spill flow of a small portion of the power jet flow or a

suction of the ambient fluid. Morris (1973) states that one of an intrinsic nature of a

wall attachment device is that a perfect zero-low state of output signal is

unattainable due to their inherent geometrical configuration. Hence a portion of the

power jet flow tends to escape through the low state side exit, which can sometimes

be disadvantageous. Also, however, Kirshner and Katz (1975) stated that a suction

flow is also possible from this side exit port if the pressure at its exit conduit

becomes substantially lower than that of the ambient or an interconnected element’s

cavity. Furthermore the numerical results of Tesar et al (2006) show that a suction

- 134 -

flow of approximately 20% of the supply flow rate occurs at the switching point with

a control flow and about 17% occurs during the steady state operation in the

absence of any control signals at sbRe of 7.6X103.

The flow motion that occur at the low state side output holds an equal possibility of

being a spill or a suction flow. However, due to a flow directional insensitiveness of

a single normal hotwire probe, both of the suction and spill cases are considered in

estimating its output flow rate, 1om , over the complete data analysis. These

assumptions are denoted with subscripts SU and SP respectively. For both cases

the mass flow rates are calculated using the time-averaged jet centreline velocity,

ocu , , but with different fluid density. The fluid density is assumed to be equal to that

of the ambient for suction assumption case, whereas the density of the power jet

flow is used for spill case.

The time-averaged jet centreline velocity, 1,ocu , obtained from the hotwire

measurements at 1DO downstream of the exit low state side orifice are presented in

Figure 4.2 as a function of supply mass flow rate, sm , together with a deuced time-

averaged spatial mean velocity across an orifice, 1,omu , from

1,ocu . These values

describe the induced flow motion after the completion of the power jet switching with

a control flow remaining active. Using 1,omu data the output mass flow rates, om ,

from a low state side output orifice are calculated and presented in Figure 4.3 as a

function of exit jet Reynolds number, ODRe , defined in Eq. 4-5. This confirms the

validity of making the Hagen-Poiseuille assumption by showing that all the

calculated ODRe being lower than 2.3X103.

oom

D

Duo

,Re Eq. 4-5

The calculated output mass flow rate, 1om , data and their ratio to the supply flow

rate, 1,om , of the low state side exit have been plotted in Figure 4.4 as a function of

a power jet Reynolds number to verify their correlation. The calculated mass flow

rate is found to increase with a supply flow level in general but shows a tendency of

its saturation beyond hDRe =4X104 as would expected from the previous analysis of

the jet centreline velocity variation. Also it is evident from examining 1,om variation

that 1om re

sudden ju

previously

Figure 4downstreaveragedflow.

Figure 4.3for both Reynolds

elative to its

ump in om

y defined Re

4.2 Time-aeam of the spatial me

3 The calccases of

s number, R

s sm decrea

1o is observ

ecrit.

averaged e output oean velocit

ulated masflow being

ODRe .

- 135

ases with in

rved at Re

velocity orifice atty across t

ss flow ratg suction a

5 -

ncreasing R

hDe =2.4X10

measured Low statethe orifice

e through and spill a

hDRe overal

04, which c

at the e and cor

assuming

the inactivas a funct

ll. In additio

coincides w

centre anrresponding Hagen-Po

ve side exittion of the

on to this

with the

nd 1DO g time-

oiseuille

t orifice e orifice

Figure 4.4and its ra

The outpu

by assum

shaped ba

shown in

proportion

seen.

4 The calcatio to the s

ut mass flow

ing 2,ocu as

ased on th

n Figure 4

nality betwe

ulated massupply flow

w rate from

s 2,omu since

heir ODRe b

4.5. By ex

een the high

- 136

ss flow ratw rate plott

a high state

e the jet ve

being gener

xamining

h state side

6 -

e through ed against

e side exit p

elocity profi

rally in the

2,om an ex

e output an

the inactivt

hDRe .

port, 2om , h

le is expect

orders of O

xistence of

d the supp

ve side exit

has been ca

ted to be a

O(104), and

f almost a

ly flow rate

t orifice

alculated

a top-hat

d this is

a direct

e can be

Figure 4.5and its ra

However,

secondary

complete

account th

describing

4.6.

As it can

through th

been inclu

assumed

a state of

develops w

5 The calcuatio to the s

the results

y flow from

jet switchin

hese flows

g the flow d

be noticed

he high state

uded in app

that this en

f equilibrium

within the a

ulated massupply flow

s shown in

the low sta

ng, 1cm . The

depending

directional n

2 , oSUo mm

2 , oSPo mm

from Eq. 4-

e side contr

proximating

ntrained flow

m that form

active side c

- 137

ss flow ratew rate as a

Figure 4.5

ate side ou

ereby 2om i

on the afo

natures of

12 ,SUoo m

12 ,SPoo m

-6 and Eq.

rol port, 2cm

the modifie

w is dispens

ms at the at

control nozz

7 -

e through tfunction o

5 do not ac

utput, 1om , a

is modified

orementione

1om and the

1cm

1cm

4-7, the en

2, subseque

ed output f

sed in main

ttached side

zle in the ca

the active sf the

hDRe

ccount the

and the con

as in Eq. 4

ed two diffe

e results ar

ntrained flow

ent to the je

low rate. Th

taining a se

e wall; or m

ase of the cu

side outpu.

previously

ntrol flow a

4-6 and Eq

erent hypoth

re shown in

Eq. 4-

Eq. 4-

w from the

et switching

his is beca

eparation b

more precis

urrent mode

t orifice

verified

added to

. 4-7 to

heses in

n Figure

-6

-7

ambient

has not

use it is

ubble at

sely that

el.

Although a

measurem

author ha

law. There

target valu

be an app

hypothesis

Figure 4.6orifice for

4.1.3 FlUs

performan

nozzle R

considere

a flow direc

ment of a st

s attempted

eby establis

ue and exa

propriate de

s describes

6 The corrr the mass

ow gain asing the res

nce parame

Reynolds n

d are the flo

ctional mea

teady flow w

d to define

shing the in

mining the

escription fo

s better for t

rected masflow rate t

and fanouults from th

eters of the

numbers ca

ow gain, GF

FG

Fn

- 138

asurement s

which made

the origin

put to mod

results sho

or low Reyn

the regime h

ss flow ratthrough the

ut ratio he previous

current mo

an be ob

F, and the fa

1

2

c

oF m

m

Sc

So

m

m

,

,

1

2

8 -

shall never

e with a sin

of 1om bas

ified output

own in Figu

olds numbe

having DRe

e ratio throe inactive s

sections of

odel and the

btained. Th

anout ratio,

be interpre

ngle normal

ed on the

mass flow

re 4.6, the

er regime w

hD greater th

ough the aside.

f this chapte

eir correlatio

he perform

nF, which a

eted from a

hotwire pro

mass cons

rate ratio o

spill assum

whereas the

han the Rec

active side

er, two stea

ons with th

mance par

are defined b

Eq. 4-

Eq. 4-

velocity

obe, the

servation

of 1 as a

mption to

e suction

crit.

e output

dy-state

e power

ameters

below.

-8

-9

- 139 -

Where 2om and

1cm are the mass flow rates across the high state side output orifice

and the control nozzle at the switching point respectively, and Som ,2 and Scm ,1

are

the corresponding total mass flow over the power jet switching period. Thereby the

flow gain describes the easiness of the power jet switching and/or the latching

stability in the device, whereas the fanout ratio describes the number of passive

devices that can be derived by its output. Those passive devices, however, must

have a similar size and shape and are operated at the same supply flow condition of

the driving device.

The high state side output mass flow rate data presented previously in Figure 4.5

are plotted as a function of its corresponding control mass flow rate from Figure 4.1

and shown in Figure 4.7. The slope of a straight line of a best fit drawn through

these data points enables an approximation of an averaged steady-state gain for

the current model which found to be equal to 14.86. However, Figure 4.7 also

shows a change in the flow gain with an increasing control flow rate and one can

recognise that its trend of change and values closely match the inverse of 1,cm

shown previously in Figure 4.1. This is more evident when GF is plotted as a

function of the supply flow level as in Figure 4.8 in which it appears to firstly have a

constant value of 14 at low Reynolds numbers then linearly increases with the

power jet Reynolds number. The correlation between the flow gain and the control

to supply flow rate ratio re-confirms an existence of a direct proportionality in the

device output with an input. The continuous increase of GF at the high Reynolds

numbers noticed in Figure 4.8 demonstrates a decrease in the latching stability

which indicates that the jet switching becomes more prone to a control signal with

increasing supply flow level.

Since the output of the fluidic amplifier in a steady-state operation is a continuous jet,

the averaged steady-state flow gain would effectively describe an averaged steady-

state fanout ratio, nF. Hence the output from the high state side of the current model

can control up to 14 identical passive devices when they are running at the same

supply flow condition. However, it should be stated that this would not describe the

fanout ratio of the fluidic oscillator used to drive an array of fluidic amplifiers and this

will be further described in the latter section of this chapter.

Figure 4.7versus co

Figure 4.8

4.2 OsIn t

transferred

with a tim

expected

with a 18

7 Output montrol mass

8 Flow gain

cillatory this section

d to a fluid

me delay fe

to generate

80o phase

mass flow ras flow rate

n of the flu

jet charan, the fluid

dic oscillato

eedback lo

e self excit

difference.

- 140

ate at the h.

idic oscilla

acteristidic amplifie

or by interco

oop. A fluid

ted pulsing

The purp

0 -

high state s

ator at the s

c er studied

onnecting t

dic oscillato

jets from i

ose of this

side and flo

steady stat

in the pr

he two con

or in such

ts conjugat

s study wa

ow gain

te test con

revious se

ntrol ports t

a configur

ting pair of

as to exam

ditions.

ection is

together

ration is

outputs

mine the

- 141 -

characteristics of the oscillatory jet, and the effect of hDRe and feedback loop length

on the oscillating frequency and switching time of the jet.

4.2.1 Output jet characteristics The results in this section of the chapter show the correlation between the

output jets produced from a conjugating pair of the output orifices and the pulse

transitional measurements over a one cycle.

The Figure 4.9 a) shows the instantaneous velocity fluctuations measured

simultaneously at the centre of the both exit orifices of the fluidic oscillator at hDRe

of 4.92x104 with a feedback loop length of 1.16m (ξ = 580). As expected the

periodic oscillatory outputs from a pair of conjugating output orifices show a 180O

phase difference. As the power spectral density shows in Figure 4.9 b), the

dominant fluctuation frequency is about 100Hz.

The phase-averaged velocity, <u>, profiles are shown in the Figure 4.9 c) while

Figure 4.9 d) showing a phase averaged turbulence intensity, Tu, calculated over

one cycle; usually a synchronised artificial reference signal is used for phase

analysis of a pulsing jet, however, due to an instability in velocity waveform a state

reference value is used in separating each cycle of pulsation. The phase-averaged

velocity profiles are then normalised by the time-averaged velocity, ocu , , and plotted

in Figure 4.10 together with state reference values which are used for verifying its

transitional characteristics.

It is common for the high and low references values to be 10% below and above of

the high and low state values (pulse peak and valley) respectively and being evenly

distributed about the middle reference value, however this gave rather an

inappropriate high reference value for the intended analysis as it can be seen in

Figure 4.10; this effectively distorted rise and decay times of the pulsation. Thereby

the high reference value has been systematically defined as 80% of the amplitude

whereas the usual 50% and 10% are used for mid and low references respectively.

Figure 4measuredand apprspectral Phase-av

.9 The oud simultaneroximated density; c)

veraged tur

c)

utput jet ceously at thT of 10.5m) Phase-av

rbulence in

- 142

a)

b)

characterishe two exit

ms. a). Insveraged ventensity ove

2 -

)

)

stics of tht orifices atantaneouselocity varer a one cy

d)

he fluidic t = 4.9s velocity iation ove

ycle.

)

oscillator 92x104 and

profile; b)r a one cy

model d L=1.16 ) Power ycle; d)

Figure 4.1velocity o

Figure 4.1

which agr

the rise a

oscillating

L , which

4.2.2 ThIn

length on

examined

switching

(2006) the

hDRe whil

existence

local spee

Figure 4.1

correspon

loop leng

measurem

existence

Figure 4.1

10 The norover a one

10 shows a

rees with th

nd fall time

output jet f

is determin

he frequethis sectio

n the frequ

. In additio

times of the

e frequency

le decrease

of frequenc

ed of sound

11 and Figu

nding spectr

gth of 1.16

ments at R

of a fundam

11 b). Howe

malised phcycle toge

square wa

e theoretica

e of 1.65ms

from the ex

ned by the f

ency of osn the effec

ency respo

on, the fre

e present flu

y of the self

e with feed

cy saturatio

.

ure 4.12 sho

ra at two dif

6m. The je

hDe =4.37X

mental frequ

ever, instab

- 143

hase-averaether with s

aveform sign

al assumpti

s and 1.62m

xisting mode

feedback lo

scillatorycts of the s

onse of th

equency me

uidic oscilla

f excited je

back loop

on at high s

ow the inst

fferent pow

et velocity

104 shown

uency supp

bility in the

3 -

aged velocistate refere

nal with an

on of 50%

ms respect

el is governe

op geometr

y jets supply flow

e periodica

easurement

ator. Referri

et oscillation

length. Also

upply flow r

tantaneous

er jet Reyn

variation

in Figure

ported by th

oscillation p

ty by the tience values

average du

as employe

ively. The w

ed by the sw

ry.

level and

ally oscillat

ts are use

ng to the re

n is expecte

o they have

rates and it

jet velocity

olds numbe

and powe

4.11 clear

e presence

period from

ime-averags

uty cycle of

ed in Eq. 4-

wave shap

witching de

the feedba

ting output

ed to estim

esults of Te

ed to increa

e demonstr

ts correlatio

y variations

ers with a fe

er spectral

rly demonst

e of its harm

m the instan

ged

f 50.6%,

-13, and

e of the

elay time,

ack loop

jet are

mate the

sar et al

ase with

rated an

on with a

and the

eedback

density

trate an

monics in

taneous

- 144 -

velocity measurements at hDRe of 7.54x103 can be noticed Figure 4.12 a), which in

fact indicating occasional switching failures. This is also apparent in the power

spectral density shown in Figure 4.12 b) in which a fundamental frequency and its

harmonics are less well defined.

This comparison partially demonstrates the existence of an oscillation instability that

constantly encountered throughout the experiments at a relatively low Reynolds

numbers. Generally, when hDRe is close to the order of ~O(104 ) unstable periodic

oscillations are noticed. But as the feedback loop length increases, this instability

starts to diminish at higher power jet Reynolds numbers. The critical Reynolds

number at which this instability starts to diminish has not been established in this

study, however, due to the difficulty in defining a quantitative measure of the jet

oscillation instability.

One possible cause for this would be related to the flow development of the supply

flow, especially for the current flow feeding method. At low supply flow rates,

secondary vortices may form (swirl flow) upstream of the power nozzle, which tend

to be suppressed as the supply flow rate increases. This swirl flow subsequently

disturbs the power jet flow development through the power nozzle hence

destabilising its flow entrainment at the downstream of the nozzle.

Figure 4.1for

hDRe =11 Instanta=4.37X104;

aneous veloL = 1.16; tt

- 145

a)

b)

ocity fluctu

total=4s.

5 -

)

)

uations and

d power sppectral density

Figure 4.1for

hDRe =

The variat

loop leng

7.3x104 a

been incl

numbers.

feedback

for the cu

ratio, ξ, of

The plots

linearly w

12 Instanta=7.54X103;

tions of the

ths in the

re shown in

uded, due

This sugge

loop for the

rrent desig

f 150.

of frequen

ith an incre

aneous veloL=1.16; ttot

oscillating

range of p

n Figure 4.

to unstab

ests an exis

e generation

n yields an

cy data in

easing pow

- 146

a)

b)

ocity fluctu

tal=4s.

frequency o

power jet

.13 a). The

ble jet osc

stence of a

n of a stabl

n approxima

Figure 4.13

wer jet Reyn

6 -

)

)

uations and

of the outpu

Reynolds n

e frequency

illations ex

a possible l

le oscillatin

ated minimu

3 a) shows

nolds numb

d power sp

ut jets for a

number, Re

response

xcept at ve

imit in the

g jet. Takin

um allowab

that the fr

ber up to Re

pectral den

a range of fe

hDe , of 6.5

at L=0.3m

ery high R

minimum le

ng 0.3m as

ble nozzle to

requency in

hDe of 3.5x

sity

eedback

5x103 to

has not

Reynolds

ength of

the limit

o length

ncreases

x10-3. As

- 147 -

hDRe increases further, there is a reduction in its gradient indicating frequency

saturation for all feedback loop lengths studied in this report. Also at a given power

jet Reynolds number, a higher jet oscillation frequency was obtained when a shorter

time delay feedback loop is used.

The same data are presented by plotting the frequency variations against L for

different hDRe in Figure 4.13 b). At

hDRe =1.0X104, the frequency seems to vary

with hDRe linearly whereas it varies inversely proportional reduction at higher

hDRe .

In Figure 4.13 b), a 4th order polynomial curve fitting has been performed over the

data points and used in approximating the frequency responses at a chosen

Reynolds numbers for each feedback loop length.

The frequency measurements shown in Figure 4.13 a) are also used in calculating

the Strouhal number, St, defined as.

SU

LfSt

Eq. 4-10

Where Us is the mean power jet velocity at the exit of the power nozzle. These

values are then plotted as a function of hDRe in Figure 4.14. Its trend of change

closely follows that of the St behaviour of a bluff body in the subcritical range of

Reynolds number. At hDRe of 3x104 , St appears to become a constant between 0.6

and 0.8.

The modified Roshko number, Romod, is defined as

h

D

DLfStRo

h

Remod Eq. 4-11

This result shows that there exists a linear relationship between Romod and hDRe

which can be described by a straight line found from a curve fitting of the data points.

3mod 1057.3Re76.0

hDRo Eq. 4-12

Figure produc

hDRe for

4.13 The frced from thr different L

requency mhe fluidic oL. b) Freque

- 148

a)

b)measuremeoscillator. aency variatio

8 -

)

) ents of the a) Frequencons as a fun

periodically variations

nction of L fo

ly oscillatis as a functfor different

ng jet ion of

hDRe .

Figu

Figure 4.14

ure 4.15 Co

4 Correlatio

rrelation be

- 149

on between

etween mo

9 -

n Strouhal

odified Ros

number an

shko numb

nd hDRe .

ber and DRe

hD .

- 150 -

4.2.3 The switching time

The frequency saturation noticed above can be explained by understanding the

terms governing the period of the jet oscillation. For a bistable feedback loop

oscillators, the oscillation period is usually expressed as in Eq. 4-13.

SPT 2 Eq. 4-13

P is the control signal propagation time around the feedback loop. The other term

S is the characteristic switching time of an element.

Since the control signal is transmitted by rarefaction waves and pressure waves, it

will always propagate at a local speed of sound and it can be estimated by diving

the feedback loop length, L, by the local speed of sound, a, as shown in Eq. 4-14.

a

LP Eq. 4-14

S is governed by the input and output characteristics, geometries of the device and

the feedback loop. The device geometry and the input and output characteristics will

govern the latching stability and the size of separation bubble. On the other hand,

the feedback loop diameter and its length determine the pneumatic resistance and

capacitance of the feedback loop hence they control the time required for a

sufficient level of pressure difference to be achieved to initiate the control signal

propagation. Hence S can be further subdivided into n and L , i.e. LnS ,

Here n stands for the fundamental switching time of the device determined by the

input and output characteristics and device geometry whereas L describes the

switching time ruled by the feedback loop geometry, henceforth is called a switching

delay time; here concept of L is introduced, although P involves feedback loop

length in its definition, to emphasise the geometrical influence of the feedback loop

while P stressing the thermal property of the flow within feedback loop.

S for different feedback loop lengths over the range of hDRe are calculated using

the oscillation period from the spectrum analysis with Eq. 4-13. These are then

normalised by the propagation time, P , as an effort to verify whether there exists a

dominant time parameter at two different Reynolds number regimes. The results

shown in

collapse o

hDRe incre

Figur

Since S i

hDRe < 3.0

by the sw

noticed in

to the prop

reaches a

value.

The satu

substitutin

where bS

width ratio

Figure 4.1

on the sam

eases.

re 4.16 Cor

is always fo

0X104, it is

witching time

Figure 4.1

pagation tim

approximate

ration freq

ng P

S

=1 in

is the powe

o and a is th

16 demons

me curve an

rrelation be

ound to be l

apparent th

e, where th

3 a),. As th

me, the freq

ely a value o

quency of

nto Eq. 4-13

satf

22

1

er nozzle w

he local spe

- 15

strate that

nd it also a

etween nor

larger than

hat the perio

he linearly i

he switching

quency satu

of 1 and the

a given f

3, i.e.

bP

4

1

2

1

width, ξ is th

eed of sound

1 -

P

S

for diff

asymptotica

rmalised sw

the propag

od of the jet

ncreasing f

g time reduc

uration start

e Strouhal n

fluidic osci

aS

he feedbac

d.

ferent feed

ally reduces

witching tim

gation time f

t oscillation

frequency r

ces and bec

s to initiate

number lock

llator can

k loop leng

dback loop

s close to

me and Re

for all test c

is mainly g

response ha

comes com

when the

ks on to a c

be estima

Eq. 4-

gth to powe

lengths

zero as

hDe .

cases at

overned

as been

mparable

P

S

ratio

constant

ated by

-15

r nozzle

From Eq.

propagatio

Thereby f

loop lengt

either be

the therma

As an effo

test mode

in Figure

parameter

through th

feedback

as a func

believed t

fluidic osc

shows tha

increasing

attainable

tested Re

Figured

4-15 one c

on speed o

for a given

th, i.e., fixe

promoted o

al propertie

ort to estim

el, T/2 value

4.13 b) and

r as shown

he data po

loop length

ction of a p

to describe

cillator that

at the fund

g power no

n of the c

hD .

e 4.17 Variaifferent Re

an notice th

of the contro

control load

ed n and L

or postpone

s of the wor

ate the afo

s are calcu

d plotted as

n in Figure

oints and e

h. The switc

power jet R

the fundam

governed s

damental s

ozzle Reyn

current mod

ations of T/

hDe which a

- 152

hat the loca

ol signal tim

ded fluidic

L hence S

ed by modify

rking fluid.

orementione

lated from t

s a function

e 4.17. An

extrapolated

ching time f

Reynolds n

mental swit

solely by th

switching ti

nolds num

del is appro

/2 as a funcre used to

2 -

al speed of s

me but the

oscillator p

, the onse

ying the loc

ed fundame

the oscillatio

n of feedbac

exponentia

d to find th

found by an

number as

ching time

he device p

me reduce

bers and

oximately e

ction of thefind the na

sound not o

saturation

lanform wit

t of freque

cal speed o

ental switch

on frequenc

ck loop leng

al curve fitt

e switching

n extrapola

in the Figu

of the exis

planform ge

es inverse

it seems t

equal to 2m

e feedbackatural switc

only determ

frequency

th a fixed fe

ncy saturat

of sound by

ing time, n

cy approxim

gth with Re

ting is then

g time at t

ation is then

ure 4.18, w

sting contro

eometry. Th

proportiona

that the m

ms for the r

k loop lengching time

ines the

as well.

eedback

tion can

altering

n , of the

mated as

hDe as a

n drawn

the zero

n plotted

which is

l loaded

he result

ally with

minimum

range of

th at

Figure 4

4.2.4 As

In the pre

array of s

same sup

phase fro

the results

doing so .

possible m

in Figure 4

The fanou

fluidic osc

calculated

output ma

switching

used with

the analyt

o

4.18 Approxat

ssessmen

esent study

seven fluidi

pply flow lev

m the fluid

s in Figure

The chose

maximum a

4.8.

ut ratio, nF,

cillator capa

d in two dif

ass flow ove

period. In t

an assum

tically appr

of the fluid

ximated fudifferent p

nt of capa

, the fluidic

c amplifiers

vel. In this s

ic oscillator

4.10 in ord

n hDRe val

nd minimum

at a given

ability in dr

fferent ways

er the blowin

his case, th

ption that t

roximated n

- 153

dic oscillato

ndamentalpower nozz

ability in

c oscillator

s which ha

section, the

r at three d

der to verify

ues are sel

m fanout ra

n operating

riving seven

s. One me

ng phase w

he control to

he switchin

natural swit

3 -

or by extra

l switchingzle Reynold

driving o

examined

ave an iden

e output ma

different Re

y the capab

ected to co

atio values

condition

n fluidic am

ethod involv

with the total

o supply flo

ng time of t

tching time

polation.

g time, n , ods number.

other fluid

here will be

ntical shape

ass flow rat

hDe values

bility of this

ver the sub

based on th

is used as

mplifiers sim

ves a comp

l control flow

ow rate ratio

he fluidic a

e, n , as in

of the test .

dic amplif

e used to d

e and runn

te over the

is calculate

s fluidic osc

b critical reg

he previous

a measure

multaneous

parison of t

w required

o from Figu

amplifier is e

n Figure 4.

model

fiers

drive an

ing at a

blowing

ed using

cillator in

ime and

s results

e of the

ly. nF is

the total

over the

re 4.1 is

equal to

18. The

- 154 -

other method of calculating the fanout ratio assumes the switching time of the

amplifier to be comparable to the blowing period. Thereby the control flow rate

required at the switching point has only been compared with the output flow rate

over the blowing period. However, it must be stated that none of these methods

gives an exact fanout ratio of the fluidic oscillator used in such operating condition

since the steady-state analysis with an impulsive control signal case is not

considered in this study. Nevertheless these two methods cover the two extreme

cases of the maximum and minimum possible fanout ratios, thereby the capability of

the oscillator in actuating seven fluidic oscillators can be approximated

Table 4.1 shows the three different hDRe cases considered and its corresponding

fanout ratios. Both Sc

Som

m,

, and Sc

Som

m,

,

values in Table 4.1 for all Reynolds numbers

considered found to be sufficiently higher than the targeted value of 7 and hence the

use of the existing fluidic oscillator as a driving actuator of seven fluidic amplifiers is

valid under the circumstance that they are not operating at a higher power jet

Reynolds number than that of the oscillator.

hDRe Tpulse (ms)

n

(ms)

mo,S (mg)

mc,S (mg) Sc

Som

m,

, Sc

Som

m,

,

1.58x104 ( 43.1sm g/s,

fact=32Hz ) 15.7 5.14 19.05 0.17 36.26 11.87

2.69x104 ( 69.2sm g/s,

fact=62Hz) 8.1 2.83 19.25 0.25 32.87 11.47

5.89x104 ( 34.5sm g/s,

fact=105Hz) 4.8 1.92 30.03 0.35 42.14 16.85

Table 4.1 Fanout ratios of the fluidic oscillator calculated at various .

4.3 Assessment for flow control applications The output jet oscillation characteristics of the fluidic oscillator model studied in this

report suggests its possibility to be used as an alternative PVGJ actuator for

separation control. In order to deliver the desired flow control effect for a given

application, the fluidic actuators are expected to satisfy at least three basic

requirements on their performance in terms of jet peak velocity, oscillating

frequency and exit orifice diameter.

- 155 -

The jet peak velocity to the freestream velocity ratio is in the range of 1 to 2 at which

the pulsed jets are reported to be effective in delaying flow separation and not

extensively energy demanding.

The required minimum actuation frequency for the purpose of flow separation

control would be to achieve a reduced frequency number, f+, of ~1. The reduced

frequency number is defined as in Eq. 4-16, where fact is the actuation frequency, c

is the characteristic length of the lifting surface and U is the freestream velocity.

U

cff act

Eq. 4-16

Many research results, however, demonstrate that PVGJ based separation control

actuators provide an optimal separation control when operated with f+ in the range

of 0.58~2 (Donovan et al, 1998 and Seifert et al, 1996). In addition to this other

researchers also showed a successful separation control by actuating at a reduced

frequency number in the order of magnitude of O(10) (Glezer et al, 2005). However,

Cerretelli and Kirtley (2009) have successfully demonstrated that the fluidic

oscillators produce superior performance in flow control when actuated within f+

range of 0.4~1.

In order to minimise the disturbance of the exit orifices to the flow on the surface to

be controlled, the orifice diameter is expected to be 5 to 20% of the local boundary

layer thickness. This usually will require the orifice diameter being in the range of

sub millimetre scales. As it is to be discussed in the next chapter, this will place an

additional demand on the design of the fluidic actuator in order to produce a fully

pulsed with a minimum jet velocity close to zero.

For the aerofoil model to be used in subsonic flow control experiments to be

undertaken in a laboratory, the freestream velocity is in the range of 10m/s in a wind

tunnel with a typical chord length of 0.3m and boundary layer thickness of 5mm.

According to the aforementioned criterion, this would require flow control jets of 10

to 20m/s issues from orifices of 1mm in diameter at a an oscillating frequency of 13

to 33Hz.

For flow separation control on the trailing edge flap of aircraft high-lift system at take

off or landing, the freestream velocity is in the range of 100m/s with a typical chord

- 156 -

length of 0.5m and boundary layer thickness of 5mm. this would require flow control

jets of 100 to 200m/s issues from orifices of 0.5mm in diameter at a an oscillating

frequency of 80 to 200Hz.

The existing model can be scaled down to the power nozzle width size of 0.25mm,

which is a commonly used value for a fluidic oscillator. This then provides an output

orifice with a diameter of 0.75mm based on the existing power nozzle width to

output orifice ratio of 3. Further reduction in the output orifice diameter

approximately by half is also possible by introducing a concentric reduction at its

outputs according to the findings from the study of an array of fluidic amplifiers. The

scaling in power nozzle width will also improve the maximum attainable oscillation

frequency, with an approximated saturation frequency of about 1.1KHz by

substituting the modified power nozzle width and the minimum ξ of 150 into Eq. 4-15

These values, which can easily be achieved by minor modifications to current model,

assures possible implementation for those flow control applications described above.

Moreover, further improvement in frequency bandwidth is possible by reducing the

output conduit length, i.e., reducing the convection time.

However, one may find the intrinsic coupling behaviour of a fluidic oscillator

between its supply flow rate and the output frequency for a chosen feedback loop

length disadvantageous as a potential separation control actuator. This practically

presents a difficulty in controlling the output jet to freestream velocity ratio

independently from an oscillation frequency. The simplest remedy to overcome this

issue would involve use of a secondary driving unit such as a fluidic oscillator to

control the actuation of the oscillator. Nevertheless the most preferable way would

be to improve the existing design so that one can attain the required minimum

frequency response at a relatively low supply flow rate. This can be achieved by

modifying the existing splitter location and its shape and/or the parameters

governing P as complementary efforts to scale reduction of the model as above.

4.4 Summary of findings Summary of findings from steady-state analysis of fluidic amplifier;-

At low Reynolds number regimes (hDRe <2.4X104), the necessary control

flow rate to complete the power jet switching is found to increase with the

supply flow rate at a constant gradient of change, while it increases with a

uniformly decreasing rate of change for higher Reynolds number regimes.

- 157 -

This trend of change in the relative control to supply flow rate ratio at the

switching point is in accordance with Warren (1963).

Approximately 7% of the supply flow is necessary as a control flow to onset

and complete the power jet switching for low Reynolds number regime while

it increases to a 9% at Recrit then starts to decrease uniformly to 6.6% at

hDRe =6.5X104. The necessary control flow as a percent of the supply flow in

the low Reynolds number regime is in accordance with Tesar et al (2006).

Purely based on the observation of a discontinuity in the functional variation

of the control to supply flow rate ratio with the supply flow, the author

suspects there exists a point where the size and strength of the standing

vortex reaches a stable condition. This hypothesis is made by knowing that

the standing vortex is the dominant source of the counteracting force to the

control flow momentum entering from the control nozzle forcing the power jet

detachment. This certainly requires a validation from possibly an internal

flow study

An almost a direct proportional relation between the supply flow and the

output flow from the high state side exit orifice have been verified

An induced flow motion at the low state side exit orifice has been observed.

Although attempts to verify its flow nature have been made and states that

spill flow occurs at hDRe < 2.4X104 while suction occurs at

hDRe > 2.4X104,.

Caution must be applied in its application as this solely based on an indirect

approximation made using the conservation of mass principle.

The mass flow from the low state side exit orifice increases with the supply

flow but shows a tendency of saturation at hDRe > 4X104. Also its output to

supply ratio continuously reduces with increasing supply flow.

The steady-state average flow gain is found by plotting the output flow from

the high state side exit orifice against the control flow at the switching point

and then by examining the gradient of a straight line drawn across the data

point. It was found to be equal to 14 to a first integer value.

As the output from the high state side exit orifice is directly proportional to

the supply flow, the functional variation of the gain is expected to follow that

of the inverse of the control to the supply flow rate ratio and the results

confirms their correlation.

To a first approximation the steady-state average flow gain has been

considered as the steady-state average fanout ratio.

- 158 -

Summary of finding from study of the control loaded fluidic oscillator;-

The oscillation frequency found to increases with power jet Reynolds

number while decreases with feedback loop length.

Functional variation of the non-dimensionalised frequency numbers with

hDRe follow that of a self excited oscillation of a bluff body in a cross flow

giving a constant strouhal number of 0.7 at hDRe > 3X104 and linearly

increasing Roshko number with hDRe .

Instability in the oscillation period has been observed at hDRe < O(104)

and/or with ξ<150. The instability in the low Reynolds number regime is

believed to be related to the flow development within the power nozzle. The

presence of secondary vortices at the upstream of the power nozzle results

as a swirl flow which possibly reflected as an unstable jet entrainment at the

downstream of the nozzle.

The non-dimensionalised switching time by the predefined theoretical control

signal propagation time demonstrates that the frequency saturation will

occur when this value reaches a unity.

The natural switching time of the existing design has been estimated using

the oscillation period data made available from the power spectrum

measurements then plotting it against the feedback loop length for hDRe

range of 1.0X104~6.0X104 with an incremental step of 2X103 and

extrapolating the exponential curve fit to find the switching time at zero

feedback loop length. This result approximates the fundamental switching

time of 2ms.

The wave shape of the periodically oscillating output jet is found to follow

that of a square wave signal due to the presence of the switching delay time,

L , with and average duty cycle of 50.6%.

A 180o phase difference has been observed from a conjugating pair of exit

orifices of the fluidic oscillator.

The fluidic oscillator is found to produce adequate output flow over its pulse

period to be used as an impulsive control signal to drive an array of seven

fluidic amplifiers having an identical shape and running at power nozzle

Reynolds number not exceeding that of the oscillator.

Although, fluidic oscillator has intrinsic coupling between output

characteristic and supply flow level it can be easily overcome with a careful

review of the design to meet the intended application criterions

- 159 -

5 An array of Fluidic amplifiers

The results in this section server to show the changes in the pulse

characteristics of the output jet from a fluidic amplifier, which are caused by possibly

a load mismatching as mentioned in Chapter 3 and to demonstrate a necessity of a

design modification of the existing amplifier. Thereby the results shown in this

section are only to demonstrate the validity of the remedy methods considered in

overcoming the output signal attenuation and caution must be applied as the

findings might not be transferable to other applications as the small number of test

cases considered.

5.1 Effect of changing exit orifice diameter The array of fluidic amplifiers was originally designed to accommodate a

concentric reduction in its exit orifice diameter from 7.6mm to 1.1mm through a

divergent 8mm in length. However, with this setup a fully pulsed output jet can not

be achieved at the jet orifice of 1.1mm. Instead an attenuated pulsation equivalent

to a continuous jet with a superimposed pulsation about its mean value is obtained.

The supply flow rate was reduced as a first attempt to achieve the fully pulsed jet

response. However this was found to not give an expected improvement. Hence it

was concluded that the supply flow rate is not responsible for the change of pulse

behaviour mentioned above. This led to an option of enlarging the exit orifice

diameter of the amplifiers based on the transmission line theory described by

Kirshner (1966). Kirshner stated that when pulsing signals are transmitted through a

channel terminated with an orifice, attenuation in the signal can occur if the cross-

sectional area of the orifice, Ao, is not properly matched with that of the chamber at

the plane of the orifice, Aref. He further stated that there only exists a single matched

point area ratio where the signal attenuation can be perfectly removed. According to

an illustration provided by Kirshner (1966), if the exit orifice is designed too large

relative to the size of the channel conduit then the pulsation will be superimposed to

oscillate about a lower mean value while too small orifice diameter will shift the

pulsation to occur at a higher mean value. Although the most promising remedy

method would involve making the amplifiers to become load insensitive by

introducing a vent to its configuration, but this will involve too much modification on

- 160 -

what is already manufactured and furthermore it is not an ideal option for the

amplifier’s intended application in flow control due to a loss in overall efficiency.

Two additional exit orifice diameters, i.e. Do=3.5mm and 2.5mm, have been tested

and the velocity fluctuations at the jet exit are measured. It can be seen in Figure

5.1 that a near fully pulsed jet is obtained at Do=7.6mm and 3.5mm. However

Do=2.5mm, the magnitude of the lowest velocity of the oscillating jet becomes

significant.

To assist the comparison of jet performance, the ratio of the jet oscillation amplitude,

ocu , , to its mean velocity, ocu , , value is taken as a measure of the extent of the jet

pulsation (modulation index). Here the amplitude of jet oscillation ocu , is defined as

the difference between the values of the high and low peak. In a fully pulsed

condition the modulation index should correspond to ococ uu ,, / = 2. The values of

ococ uu ,, / for different exit diameters are shown in 오류! 참조 원본을 찾을 수

없습니다.. At Do=3.5mm, ococ uu ,, / is nearly two confirming that the jet is fully

pulsed. At Do=2.5mm, however, ococ uu ,, / is much less than 2. It appears that for

the amplifier with an AR value of 4, the minimum exit orifice diameter for getting a

fully pulsed jet is around 3.5mm, giving Do/h of 0.43..

Figure 5.1downstre

1 Instantaneam of an a

(

neous velocamplifier ex(a). DO=7.6

- 16

(a)

(b)

city variatixit orifice w6mm and DO

1 -

)

)

on measurwith bS=2mO=2.5mm,

red at the cmm and AR

(b). DO=3.5

centre and R=4 5mm

1DO

Table 5.1 ratio for v

5.2 EffAlth

output sig

intended

experimen

the existin

expected

the exit or

to 4mm, re

By reduci

expected

to 2.1mm

are shown

for Do=2.1

Figu

The calcuvarious DO

fect of chough it wa

nal without

flow contr

nt, a jet orif

ng design o

exit orifice

rifice diame

esulting a re

ng the AR

fully pulsed

. The temp

n in Figure 5

1mm and 3.

ure 5.2 Velo

DO (mm)

7.6 3.5 2.5

lated valuevalues wit

hanging aas found th

signal atten

rol purpose

fice of the o

of the fluidi

diameter. T

eter the heig

eduction of

from 4 to

d exit jet res

oral variatio

5.2 and the

.5mm are g

ocity variat

- 162

hDO

0.90.40.3

es of the amth bS=2mm

aspect rat the exit

nuation, this

e on the

order of 1m

ic amplifiers

Therefore i

ght of the a

the nozzle

2, the min

sponse ach

ons of the j

e compariso

given in Tab

ions of out

2 -

h

5 3 1 mplitude to and AR=4

atio orifice dia

s is still con

aerofoil. F

m will be m

s in an arra

n order to

mplifier is r

aspect ratio

nimum exit

ieved is fou

jet exit velo

on of releva

ble 5.2.

tput jet wit

oc

ocu

u,

,

2.21 1.97 1.07

o time aver

meter of 3

nsidered to

For the ae

more desira

ay can not

achieve a f

educed from

o from 4 an

orifice dia

und to be re

ocity for Do=

nt paramete

h DO=2.1m

raged veloc

3.5mm can

be too large

erofoil flow

ble. It appe

accommod

further redu

m the origin

d 2,

meter at w

educed from

=2.1mm an

ers for AR=

mm and AR

city

provide

e for the

control

ears that

date the

uction in

nal 8mm

which an

m 3.5mm

nd AR=2

=2 and 4

R=2

- 163 -

Although the effect of reduced exit conduit cross sectional area, Aref, observed is in

consistence with the description given by Kirshner (1966), h

D

A

AO

ref

O found from this

study does not gave a constant value for AR=2 and AR=4. Further reduction in the

height of the amplifiers has not been considered due to a concern regarding the

possible change on the device performance caused by the increased boundary

layer effect in the power jet nozzle. Nevertheless, Do=2.1mm is seemed a great

improvement and an exit orifice of this size is considered acceptable for flow

separation control experiments over a flap which has a thicker incoming boundary

layer than on the aerofoil model.

AR DO,min (mm) h

DO ref

OA

A

Aref=(7.6xh)mm2 u

u

4 (h=8mm)

3.5 0.43 0.16 1.97

2 (h=4mm)

2.1 0.52 0.11 2.05

Table 5.2 The calculated values of the amplitude to time averaged velocity ratio at DO,min for different AR values of 2 and 4 with bS=2mm.

5.3 Other observations The instantaneous velocity measurements from a conjugating pair of exit orifices of

an amplifier with an AR of 2 and Do,min of 2.1mm are plotted in Figure 5.3 a) during

the supply mass flow rate to a supply chamber being 4.4g/s. This shows that there

exists a minor difference between their pulse amplitude, which effectively gave the

two different oc

ocu

u,

, values of 1.74 from the Set side and 2.05 from the Re-set side.

This is believed to arise from the fact that the current fluidic amplifier having a

multiple output ports.

The control signals to an array of amplifiers were generated by operating the fluidic

oscillator at hDRe of ~3.1x104 with a feedback loop length of 1.0m, which was

expected to generate a periodically oscillating control signals at a frequency of 83Hz

from an each exit ports. However, the spectral analysis shows the actuation

frequency of the amplifiers to be at 127Hz as in Figure 5.3 b). One possible

explanation of the discrepancy noticed in frequency synchronisation would involve

an extra output load introduced to the fluidic oscillator by an interconnection made

between it

was briefly

the active

an extra s

high load

oscillator f

Figure 5measuredorifices hdensity. Ta fluidic os

ts output po

y described

side outpu

switching fo

exit port (e

for power je

.3 The oud at the cehaving DO oThe supply mscillator run

orts and con

d that the je

t ports. The

orce to a flu

expansion w

et switching

utput jet centre and

of 2.1mm. amass flow rnning at DRe

- 164

ntrol chamb

et switching

ereby an inc

uidic oscilla

wave), whi

compared

a)

b)

characteris1DO down

a) Instantanrate to the s

hD of 3.1x10

4 -

ber of the flu

can be init

creased out

ator in the f

ch enhance

to its norma

)

)

stics of tnstream ofneous velocsupply cham04 with L=1.

uidic amplifi

tiated by int

tput load ma

orm of retu

es the tend

al operation

he fluidic f a conjugcity variationmber of an a.0m.

fiers. In Cha

troducing a

ay have int

urned flow f

dency of th

n condition.

amplifier gating pair n; b) Power array is 4.4

apter 2 it

load on

roduced

from the

e fluidic

model of exit

spectral 4g/s with

- 165 -

5.4 Summary of findings It is found that for the original fluidic amplifier with the nozzle aspect ratio of

4, a fully pulsed jet can only be obtained with DO/h ratio greater than 0.43.

Decreasing the nozzle aspect ratio from 4 to 2 leads to further reduction of

the minimum orifice diameter with which a full pulsed jet is obtained.

DO,min/h ratio for a fixed power nozzle width was found to vary with a nozzle

aspect ratio, i.e., DO,min/h=0.43 for AR=4 and DO,min/h=0.52 for AR=2.

However, it can be stated that as long as DO/h ratio is higher than 0.52 a

fully pulsed jet can be obtained with a AR lager than 2.

A 180o phase difference has been observed from a conjugating pair of exit

orifices of the fluidic amplifiers. A considerable difference in the pulsing jet

magnitude between the 6 exit orifices of a single fluidic amplifier has been

observed.

A disparity between the oscillation frequency of the output jet from an array

of fluidic amplifier and the actuation frequency of the fluidic oscillator, which

is approximated from its power nozzle Reynolds number, has been observed.

The discrepancy in the synchronisation of an actuation frequency is thought

to be due to the extra output load introduced to the fluidic oscillator by the

interconnection made with the control chambers of the array of fluidic

amplifier.

- 166 -

6 Conclusions and future work

The objectives of this study are twofold, a) to examine the jet characteristics of

a control loaded fluidic oscillator so as to gain an understanding of their fundamental

performance parameters and b) to evaluate the design of the array of fluidic

amplifiers and to propose necessary modification for their use on an aerofoil model

for flow control. These set objectives have been achieved. The conclusions from

this work are stated in this chapter which is followed a suggestions for future work.

6.1 Conclusions

6.1.1 Fluidic oscillator

The steady state analysis showed that the current fluidic oscillator model, in

general, requires a control mass flow rate of about 7% of the supply mass flow rate

to onset the power jet switching. This demonstrates that the existing model has a

relatively high tendency for the power jet switching when compared to a usual value

of 5~15%, which can provide broad oscillation frequency bandwidth in the output jet.

However at a high Reynolds number, hDRe > 4104.2 , a constant reduction in the

relative control to supply flow rate ratio at the power jet switching point is noticed.

The trend of change and values of the flow gain with an increasing power jet

Reynolds number are found to follow that of the inverse of the control flow rate.

They were found to increase linearly above the critical power jet Reynolds number,

while giving a relatively constant value of 14 at sub critical regime. This discontinuity

noticed in trends of changes of the flow gain is likely caused by the limited growth of

the standing vortex, which counteracts the control flow entering from the attached

side control nozzle, confined by physically by the cavity forming the interaction

region.

The fluidic oscillator model has successfully demonstrated a generation of a fully

pulsed jet with a square waveform, having duty cycle of 50% and an 180o phase

difference between its conjugating pair of output orifice. It was found that the cycle

averaged output jet velocity can vary from ~8ms-1 to ~72ms-1 with a maximum of

~50% unsteadiness. The frequency bandwidth of ~10Hz up to ~185Hz was

attainable when the shortest available feedback loop length of 0.5m is used for the

- 167 -

power jet Reynolds number range of 6.5X103 to 7.3X104. The maximum cycle peak

velocity measured in this study was approximately 185ms-1 and this falls within an

acceptable range for practical separation control application.

The most obvious findings to emerge from this investigation are the dependency of

the oscillation frequency of the fluidic oscillator on the supply flow rate and the

feedback loop length. In general, the frequency of the output jet oscillation increases

proportionally with the supply flow rate whereas it reduces inverse proportionally

with the feedback loop length. The effect of increasing the supply flow rate is to

increase the power jet entrainment of the fluid from its vicinity which in turn reduces

the switching time, S , of the device. On the other hand, increasing the feedback

loop length provides a larger volume of fluid for the entrainment. As a result of this,

the development of a sufficient level of a differential pressure across the feedback

loop which is required to onset the propagation of a control signals in the form of a

pressure wave and a rarefaction wave is delayed, thereby S increases. Also,

increasing the feedback loop length effectively means the control signal has to

travel longer distance and hence the control signal propagation time, P , increases

accordingly.

In addition to this, at a power nozzle Reynolds number greater than 3.0x104

frequency saturation starts to occur regardless the length of the feedback loop,

which gave a constant Strouhal number of 0.7. Also when the fluidic oscillator

operated at low hDRe ~O(103) and/or small feedback loop length to power nozzle

width ratio, ξ, ~ 150, a fluctuation in the pulse period have been noticed. The

existence of an instability in the oscillation period at low hDRe operation is thought

to be due to the swirl flow occurring at an upstream of the power nozzle which tends

to be suppressed as the supply flow rate increases.

The normalisation of the experimentally calculated switching time, S , by the

theoretical control signal propagation time, P , has gone some way towards

enhancing the understanding the principal cause of the saturation in the oscillation

frequency of the fluidic oscillator. It is concluded that the oscillation period of the

output jet is mainly governed by S in the Reynolds number regime lower than

3.0x104 whereas P becomes the major time parameter in the higher Reynolds

- 168 -

number regime as P

S

gets smaller than the unity hence resulting a frequency

saturation.

The output jet oscillation characteristics of the fluidic oscillator model studied in this

report suggests its possibility to be used as an alternative PVGJ actuator for

separation control. It produces unsteady output jet with a strong modulation and

turbulence intensity of 10~50% of the jet mean velocity during the blowing phase.

Also, the possibility of scaling of the current test model to a meso-scale structure

promises its reliable augmentation as a flow control actuator for practical application.

6.1.2 The array of fluidic amplifiers

The results from an analysis of an array of amplifiers having a concentric reduction

in their output ports demonstrate an existence of change in pulse characteristic in

the output jet, which effectively shifted a cycle mean velocity to a higher level while

retaining its amplitude. It is apparent by examining the diminishing of the

transfiguration in the output jet as the exit orifice diameter is enlarged that the extra

output load introduced by the concentric reduction in their output port is the cause of

the jet attenuation noticed. It is found that a minimum orifice diameter of 3.5mm is

required in order to ensure a fully pulsed jet with a minimum jet velocity near zero

with changing the design.

It was also shown that the minimum output orifice diameter that can be

accommodated by an amplifier without changing the output jet characteristics, can

be reduced by reducing the height of the fluidic amplifier, i.e., the power nozzle

aspect ratio. By reducing the aspect ratio of the amplifier from 4 to 2, the minimum

orifice diameter is reduced from 3.5mm to 2.1mm. Although the results do not

present a constant hDO min, ratio for the point where the jet attenuation becomes

negligible, it can be stated that this ratio generally requires to be higher than 0.52 for

the nozzle aspect ratios up to 2. An orifice diameter of 2.1mm is not ideal, but is

seemed a great improvement and an exit orifice of this size is considered

acceptable for flow separation control experiments over a flap which has a thicker

incoming boundary layer than on the aerofoil model.

The design of an array of fluidic amplifiers tested in this study requires the use of a

secondary control flow source in order to guarantee a phase

difference/synchronisation between the neighbouring amplifiers/outputs due to the

- 169 -

indeterminable initial jet attachment in each fluidic amplifier. However, this removes

one of the principal advantages of a fluidic device by requiring a secondary unit

which in most cases requires mechanical moving parts to generate pulsing control

signal. The results shows when a fluidic oscillator used as a driving unit the

switching characteristic of the device can be changed based on the disparity in the

actuation frequency for a given supply flow rate. Furthermore a disparity in the

pulsing jet magnitude between the 6 output orifices of a single fluidic amplifier used

in an array has been noticed when operated at a relatively low power jet Reynolds

number.

6.2 Suggestions for future work Although the existing model of the control loaded fluidic oscillator requires

some design modification they seem to be a more suitable for the flow separation

control application compared to a fluidic amplifier. The drawbacks of a fluidic

amplifier would include an intrinsic necessity of a secondary driving element, a

relatively large compartment space requirement arising from a necessity of control

flow chambers and complexity in its interconnection and load matching between

with a driving unit.

When adopting the existing fluidic oscillator for flow control application, the major

modification required by the current model involves removal of its bistability in the

power jet attachment. For this reason the author suggests to develop a monostable

fluidic oscillator where its conceptual schematic drawing is shown in Figure 6.1 a).

The monostability of this oscillator is achieved by the restriction introduced in the

one side of the control port. A traditional method of achieving a monostability by

having different offsets on each side of the power nozzle has not been considered

due to a possible pulse characteristic difference, such as a duty cycle, between jets

generated from a conjugating pair of output orifices. Its planform may follow that of

the fluidic oscillator studied in this report. This idea can be preliminary demonstrated

using the existing model by modifying the feedback loop accordingly.

Also for a laboratory demonstration of its capability in delaying flow separation,

scaling of the device must be considered to have an acceptable size of the output

orifice diameter and to improve its frequency response and oscillation stability at low

power jet Reynolds number. Also it would be valuable to build each component of

the test model of the fluidic oscillator as a separate module, as shown in Figure 6.1

b), which can allow a geometrical parametric study for performance optimisation

Fao

and study

modules

microscale

technique

characteri

incorporat

Once the

the effect

separation

flow visua

Figure 6.1 a) Planformoscillator.

y of a scalin

the complic

e model c

. In the dev

stic analys

ted and sup

model has

tiveness of

n of turbule

lisation.

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- 171 -

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