shock manual

8/13/2019 Shock Manual

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AER 304S

Aerospace Laboratory II

Supersonic Flow and Shockwaves

http://sps.aerospace.utoronto.ca/labs/raalExperiment Duration: 150 min

Instructor

M. R. Emami

Aerospace Undergraduate Laboratories

University of Toronto

Winter 2013
http://sps.aerospace.utoronto.ca/labs/raalhttp://sps.aerospace.utoronto.ca/labs/raalhttp://sps.aerospace.utoronto.ca/labs/raal


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1. Purpose

Some basic concepts of supersonic flow are demonstrated using a nominal Mach 1.6

wind tunnel. Impact and static pressure probes are employed to monitor velocities in thetunnel at various points along the flow. A variable valve is used for changing the flow

rate. A Schlieren camera system is used for the examination of shock waves from objects

placed in the test section. A computer-aided data acquisition system is used to collect and

record pressure data from the impact and static pressure probes.

2. Apparatus

Half section supersonic tunnel (M= 1.6) with fixed static pressure taps. Traversing Pitot impact probe and knife-edge model. Whispairblower, 12.2 kJ/s at 3520 rpm (P= 70 kPa). Axial cooling fan for Whispairblower. Intake filter/silencer. Exhaust muffler. Motorized intake flow ball valve. Probe manipulation system for vertical and longitudinal motion. Honeywell absolute pressure transducers model #142PC15A (0-775 mmHg). 24v Solenoid valve manifold (SMC Pneumatics SY100) Wallace & Tiernan dial pressure gages (0-400 and 400-800 mmHg). Schlieren camera system. Test section aperture 25 mm by 30 mm. Data acquisition system (PCIM-DAS1602/16 PCI Board). Power supplies and power control unit. Web cams and audio system.

3. Notation and Constants

a speed of sound (m/s)

A cross-sectional area (m2)A* throat area (m2)

specific heat ratio (air = 1.4)

M Mach number (V/a)

n refractive indexppressures (mmHg)p1 static pressure (mm Hg)

p02 Pitot tube stagnation pressure (mmHg)

density (kg/m3)

viscosity

R ideal gas constant = 287 J/kgK (dry air)T temperature (K)

U flow velocity (m/s)V flow velocity (m/s)


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4. Experiment Setup

The major elements which make up the aerospace undergraduate laboratory supersonicfacility are indicated in Fig. 1. The tunnel operates as open circuit, meaning air is drawn

from the laboratory and exhausted outside the building.

Figure 1: Aerospace Laboratory Supersonic Facility (M= 1.6)

4.1 Wind Tunnel

The power required to run a wind tunnel scales roughly as the third power of the flowvelocity. This factor is reflected in the test section dimensions which for the supersonic

facility are small compared with the other laboratory tunnels. However, the 20 HP (15

kW) motor required for starting and running at supersonic speeds is higher powered than

either of our other tunnels, although the latter have much larger test sections.

The design of a supersonic tunnel can be tricky, mainly due to viscous effects during thestarting process. Compression ratios required to start a high Mach number tunnel are

usually at least twice the normal shock pressure ratio and even at M= 1.5 approximately30% extra power is required. The transient starting phenomena are difficult to evaluate

theoretically, so a good mix of empiricism, experience, and some luck is needed in the

design and manufacturing of a good tunnel.

The laboratory tunnel incorporates a supersonic nozzle contour which has been designed

using methods of characteristics [1]. The nozzle coordinates that are listed in Table 1


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include an empirical correction for boundary layer growth, which is an important factor at

high speeds. The contoured tunnel floor is slotted and sealed to permit the insertion of a

traversing Pitot tube. The roof of the test section is plane and corresponds to thecenterline of a hypothetical symmetrical tunnel of twice the height.

Table 1: Static Pressure Tap Locations

TapNumber

x (mm)y

(mm)h

(mm)A/A

* A

*/A

M(theory)

0.0 3.45 26.55 1.58 0.632 .405

11.6 8.86 21.14 1.26 0.794 .545

1 24.7 12.17 17.83 1.06 0.942 .755

2 36.6 13.21 16.79 1.00 1.000 1.00

3 48.3 12.37 17.63 1.05 0.952 1.26

4 61.0 10.69 19.31 1.15 0.869 1.46

5 73.7 9.40 20.60 1.23 0.815 1.57

6 86.4 8.64 21.36 1.27 0.786 1.63

7 99.1 8.33 21.67 1.29 0.775 1.65

8 118.0 8.18 21.82 1.30 0.769 1.66

9 209.5 8.18 21.82 1.30 0.769 1.66

10 300.1 8.18 21.82 1.30 0.769 1.66

11 diffuser - - - - -

Figure 2: Supersonic Nozzle Geometry

Air is sucked through the Laval nozzle of the tunnel depicted in Figs. 1 and 2, but several

other methods of flow drive may be used. For example, a closed circuit tunnel reduces

the operating power requirement, permitting the pressure of the whole tunnel to be variedif desired; the necessity of continuously drying air is also eliminated for this design. In a

blow-down tunnel, power requirements are reduced by charging a compressed or reduced

pressure air storage tank which is then used to power the tunnel on an intermittent basis.

These and other variants are discussed in [1].

4.2 Data Acquisition System

The data acquisition system consists of a Pentium IV workstation equipped with a


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PCIM-DAS1602/16 data acquisition (DAQ) board from Measurement Computing. The

DAQ board has 32 digital I/O channels, and a 16 channel analog-to-digital (A/D)

converter with 16-bit resolution (i.e. 216

discrete voltage values over the measurementrange of 0 to 10V), which is equivalent to a voltage resolution of 0.15 mV. The DAQ

board allows the computer software to control electromechanical actuators and collect

data from a variety of analog and digital sensors.

The position of the flow intake valve (i.e. the percentage that the valve is open; 100%corresponding to fully open) is set through a computer-controlled DC gear-head motor.The position of the valve is measured using a rotary potentiometer that converts the valve

position to a voltage that can be read by the DAQ board. Therefore, to move the valve to

a desired position the software turns on the motor with a direction corresponding to

opening or closing the valve, while simultaneously reading the valve potentiometervoltage. Once the voltage corresponding to the desired valve position is reached the

software turns off the motor.

The pressure from the impact and static pressure probes is measured using pressuretransducers that convert pressure values to a voltage that can be read by the DAQ board.

Each pressure probe can also be connected to the Wallace & Tiernan dial gages throughan array of computer-controlled solenoid valves.

4.3 Probe Manipulator

The position of the impact pressure probe (Pitot tube) in the tunnel test section is changed

using a computer-controlled manipulation system that has 2 degrees of freedom, namely

x (horizontal) and y (vertical) translation. The manipulator consists of linear steppermotors to position the probe with an x-resolution of 0.006096 mm and y-resolution of

0.00075 mm. Limit switches are used for homing the actuators.

The computer software can control each component of the experiment individually, suchas in the case of moving the probe to a desired position or it can control multiple

components simultaneously allowing complex dynamic experiments to be performed.

The computer control system enables the experimenter to not only collect data moreaccurately, but also perform multiple tasks simultaneously.


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5. Experiment User Interface

1. Start or stop the wind tunnel. There is a 60-second delay between starting and stopping the tunnel.2. Save a snapshot image from the Schlieren camera.3. Start or stop recording a video from the Schlieren camera. The maximum length is 60 seconds.4. Move the probe in incremental steps. The number box indicates the incremental size of each step

in millimetres. Each button will move the probe one incremental step in the indicated direction.

5. To move the probe to a specific coordinate, enter it in the X and Y number boxes and clickMove.6. Return the probe to theHomeposition.7. Animation of the current probe position in the tunnel test section.8. History of previously executed commands.9. Live pressure data from the pressure transducers. Select pressure channels to display on the

pressure graph using the Graphcheckboxes (see 18).

10. Start or stop updating the live pressure data.11. Select the current pressure units; mmHg,psi, or kPa.12. Open or close the intake valve. The +and buttons open and close the valve in small increments.13. To move the valve to a specific position enter the value in the number box and click Move.14. Animation of the current valve position.15. Select between theExperimentandPressure Graphcontrol panels.


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6. Supersonic Flow Theory

Supersonic flow theory is extensive, and perhaps the best text for a first appreciation of

the topic is [2], which provides adequate information for the purpose of this experiment.

A more complete and lucid look at the field in somewhat greater depth is given in [3] (an

excellent text). It is recommended that the students consult with at least one of these

sources for background material.

In the nozzle shown in Fig. 3 sonic flow is assumed to exist at the throat where conditions

are denoted by the asterisk.

Figure 3: Supersonic Wind Tunnel Nozzle

The real flow for this case is nearly isentropic because only small quantities of heat are

exchanged through the nozzle walls, and the flow is assumed to be frictionless. The

following continuity relation, Equation (1), is necessary and leads to several other useful

formulas which are listed in Fig. 4.

uAAu (1)


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Figure 4: Variation ofM,P , T , through a Supersonic Nozzle

6.1 Area-Mach Number and Area-Velocity Relations

1

1

2

2

2

2

11

1

21

M

MA

A (2)

Equation (2) is called the Area-Mach number relation and leads to the remarkable

consequences that sinceM =f(A/A*) andA/A*

1:

a) For subsonic situations:M increases asA/A*decreases (i.e. the nozzle converges).b) ForM= 1,A/A*

= 1, sonic conditions prevail at the throat.

c) For supersonic situations:M increases asA/A*increases, (i.e. the nozzle diverges).The somewhat counter-intuitive conclusion which is enunciated by (c) may be

appreciated more readily by the examination of theArea-Velocity relation:


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V

dVM

A

dA1

2 (3)

In this expression it is evident that increases in velocity follow automatically from an area

enlargement. Also, if 0AdA

the nozzle has a minimum area (the throat) and at that

locationM= 1.

6.2 Determination of Isentropic Flow Properties in Nozzles

6.2.1 Use of the Table of Isentropic Flow Properties

A MATLABfile can be generated from the experiment user interface which computes

the predicted values for Mlisted in Table 1, using the tabulatedA/A* data from the same

table.

6.2.2 Tunnel Flow Measurements (Supersonic Regions)

In Fig. 5 the Pitot tube measures the stagnation or total pressure behind the shock. In thisdiagramp1corresponds to the static pressure in a plane which is tangent to the shock.

Figure 5: Pitot Impact Tube in Supersonic Flow

The following expression, known as the Rayleigh Pitot Relation is usually solved

recursively to obtainMoncep1andp02are known.

25

2

2

1

1

2

12

1

02

17

167

1

1

1

2

2

1

M

M

M

M

p

p

(4)


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6.2.3 Tunnel Flow Measurements (Subsonic Regions)

Equation (4) cannot be used for the determination of velocities upstream of the throatsince a shock wave cannot exist at these locations. The following expression from Fig. 4

should be used for such cases:

2

7

2

12

1

0

51

2

11

MM

pp

(5)

6.2.4 Optical Methods for Gas Dynamic Analysis

In fluids and solids, pressure and density changes propagate at the velocity of sound in

the medium. For an ideal gas the sound velocity is:

RTa (6)

Shock waves formed about a body in a supersonic flow are created because disturbancesat the body surface cannot propagate upstream since the maximum propagation speed is

limited to the local speed of sound. This principle is illustrated in Fig. 6, where the

crosses represent disturbances traveling at a velocity Uin each case.

Figure 6: Evolution of a Shock Wave

Shock waves are thin (about 0.0001 cm) but special diagnostic techniques are availablefor visualizing the variations in fluid density which accompanies shock formation. The

local change of refractive indexdue to gas compressioninterferes with the

transmission of an illuminating beam, and this provides a visual manifestation of the

shock.

Interferometers, Schlieren systems, and shadowgraphs are complementary methods to

monitor the gas density , the first derivative of gas density, and the second derivative,

respectively. A preliminary description of the Schlieren method will be given but adiscussion of other methods is beyond the scope of this manual. Their operating

principles are interesting and are well covered in [4].


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6.2.5 The Schlieren Method

Whenever there is a change in the local fluid density a concomitant change in the opticalrefractive index (n) is observed (remember n = 1.0 only for a vacuum). In Fig. 7(a) a

uniform fluid density is assumed to be present throughout the disturbance region, and the

resulting deflection of a light beam is shown by the solid line OP.

Figure 7: Light Refraction at a Disturbance

A Schlieren system responds to the first derivative of the density as implied in Fig. 7(b)

where the wedge density increases linearly with distancey.

The Schlieren apparatus for this experiment, shown schematically in Fig. 8, uses lenses.However, for larger systems with long focal lengths mirrors are customarily employed,

since these are less expensive than lenses for comparable size and optical performance.

Figure 8: Schlieren Optical System

In Fig. 8 a light source Sis imaged by the lens L1onto aperture A, which serves to definethe source and eliminate any spurious light due to reflections from the source envelope.

Lens L2collimates the light which then passes through the test section and is focused by

L3in the plane of a knife edge KE.

The knife edge is adjusted so that in the absence of any disturbance in the test section it

just occludes all the radiation that would normally pass to the viewing screen. A shock

wave or similar perturbation of the fluid density in the test section may then cause light topass around KEas explained in Fig. 7. If the location of the screen is chosen such that it


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displays a sharp image of the test section via L3and the previous conditions have been

met, then shock waves are readily observable.

An example where the Schlieren technique has been used to examine the flow conditions

around a double wedge is shown in Fig. 9. Intuitively one would suspect the shock angle

depicted in Fig. 9 to be proportionally related to the flow velocity, and indeed this is thecase. The , , Mrelation, given in the figure, can be used to determine the flow Mach

number, where , ,Mare defined as indicated.

Figure 9: Shock Waves with a Wedge


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7. Experiment Design

Some preparation and research will be required to design your experiments prior to

actually performing the tests in the wind tunnel. Each experiment should not be viewedas an independent activity. The results of one experiment mayprove useful in defining

the parameters of another test.

A MATLAB file can be generated by the interface to compute both theoretical andexperimental Mach numbers, but you need to complete collecting data for all tests before

running the file. The tests to complete for creating the MATLABfile are:

1. Static Pressure Measurement: To save the static pressure (p1) along the tunnelcentreline (roof) use the Static Pressure Measurement box under the

Experiment tab. Enter the number of samples to read from the pressure

transducer at each tap in the Samples box.

2. Horizontal Stagnation Pressure Measurement: To record the stagnationpressure (p02) at each tap location along the tunnel at a fixed height use the

Impact Tube Horizontal Pressure Measurement box under the Experimenttab, and enter the Pitot tube height (30 mm corresponds to the tunnel centreline).Enter the number of samples to read from the Pitot tube pressure transducer at

each tap location in the Samples box.

3. Vertical Stagnation Pressure Measurement: To record the stagnation pressure(p02) at a tap location along the tunnel at different heights use the Impact TubeVertical Pressure Measurement box under the Experiment tab, and enter the

tap (port) location and the number of transverse points at which the stagnation

pressure is measured. Enter the number of samples to read from the impact tube

pressure transducer at each vertical point in the Samples box.

Flow Variation Pressure Measurement: To record the pressure from the impact andstatic pressure probes, while opening or closing the flow intake valve, use the FlowVariation Pressure Measurementbox under the Experiment tab. Enter the starting

position of the valve and the ending position of the valve over which the pressures will be

recorded. This recording mode may take up to several minutes to complete if the valve ismoved through its full range.

Schlieren Camera Measurements: To record images or video from the Schlieren

camera use the Schlieren Camera box on the experiment interface. The Image buttonsaves a snapshot from the camera in JPEG format, whereas the Record Video button

records a short video from the camera in AVI format.

7.1 Verify the Theoretical Mach Number Formulation

Design an experiment to collect static and stagnation pressure data to compute the Machnumber. Compare the results with the Area-Mach number relation (Equation 2) and

address the questions in Section 8.1. Static pressures are measured at taps 1-11 along the

tunnel centerline (roof) that are connected to the pressure transducers. Stagnationpressure is measured using the Pitot impact tube that can be positioned at different


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coordinates in the tunnel and can also traverse the tunnel horizontally at a constant

height.

The MATLAB file generated by the interface can be used to compute both the

theoretical and experimental Mach numbers for this experiment, but you need to

complete collecting data for all tests before running the file.

7.2 Determine the Vertical Mach Number Profile

Design an experiment to collect static and stagnation pressure data to compute the Mach

number profile across a vertical section of the tunnel and address the questions in Section

8.2. Static pressures are measured at taps 1-11 along the tunnel centerline (roof) that areconnected to the pressure transducers. Stagnation pressure is measured using the Pitot

impact tube that can be positioned at different coordinates in the tunnel and can also

traverse the tunnel vertically at a specific tap (port) location.

The MATLABfile generated by the interface can be used to compute the experimental

Mach numbers for this experiment, but you need to complete collecting data for all tests

before running the file.

7.3 Determine the Effects of Flow Restriction

Design an experiment to collect static and stagnation pressure data to determine the

effects of flow restriction on Mach number, and to address the questions in Section 8.3.

Stagnation pressure is measured using the Pitot impact tube that can be positioned atdifferent coordinates in the tunnel. The flow is restricted by closing the flow intake valve

(i.e. closing the valve reduces the intake cross-sectional area of the blower).

Write a new MATLABfile to compute the Mach numbers for this experiment using the

MATLAB file generated by the interface as a template. Note, MATLAB performscalculations using matrix algebra. You can calculate the Mach number for all data points

simultaneously by entering the data as a vector and computing the Mach number for the

entire vector.

7.4 Flow Variation and Shockwaves

Design an experiment to measure the Mach number and to confirm when the flow

becomes supersonic using visual techniques (Schlieren camera) and address the questions

in Section 8.4. You maynot observe any visual changes in the flow over a large range of

valve positions. First determine the regime over which the flow changes by opening and

closing the valve all the way. Then use the fine adjustments (the + and buttons) toincrementally change the flow over that regime. Be aware that the valve has a significant

hysteresis between opening and closing.


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8. Discussion of Results

8.1 Verify the Theoretical Mach Number Formulation

1. How and why do the static and stagnation pressure measurements vary with theheight of the Pitot impact tube?

2. How does the number of samples per measurement affect the overall results?What is a suitable number of samples to have a statistically relevant

measurement?

3. Is the Mach number computed from your measurements at sections far from thetunnel throat smaller or greater than the theoretical value? Why?

4. At which tap (port) location is the deviation from the theoretical Mach numbermaximal? Why?

5.

Explain various sources that cause deviation from the theoretical value.

8.2 Determine the Vertical Mach Number Profile

1. How and why does the Mach number vary with the location of the Pitot impacttube along the tunnel (i.e. different tap locations)?

2. Discuss the variations in the vertical Mach number profile at tap (port) 7.3. From the vertical Mach number profile characterize the boundary layer along the

top and bottom walls of the tunnel.

4. Use dimensional analysis to show the tunnel power requirements scale as V3 .You may assume that the power required is directly proportional to the throat areaA*, and power/area is a function of density , viscosity ,and velocity V.

8.3 Determine the Effects of Flow Restriction

1. Characterize how the Mach number at the throat and two other locations along thetunnel is affected by restricting the intake flow.

2. At what valve position and pressures does the flow become supersonic? Does thisagree with theory?

3. Identify and explain each regime in a plot of Mach number vs. time at tap (port) 7,for opening and closing the valve. Is there a hysteresis?

4. What is the Mach number at the throat when the tunnel goes supersonic? Explainany discrepancies.


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8.4 Flow Variation and Shockwaves

1. Compare the Mach number that you measured in this experiment to the results ofthe previous experiments. Explain any variations between experiments.

2. What effects does varying the flow have on the shockwaves?3. What effect does the vertical and horizontal location of the pitot impact tube inthe test section have on the shockwaves?

9. References

[1] A. Pope and K. Goin,High-Speed Wind Tunnel Testing. New York, NY, USA: John

Wiley and Sons, 1965.[2] J. D. Anderson,Introduction to Flight. New York, NY, USA: McGraw-Hill Book

Company, 1978.[3] J. D. Anderson,Fundamentals of Aerodynamics. New York, NY, USA: McGraw-Hill

Book Company, 1984.[4] H. W. Liepmann and A. Roshko,Elements of Gas Dynamics. New York, NY, USA: John

Wiley and Sons, 1965.

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