1

INTRODUCTION

The basic aim of aerodynamics is to obtain the flow quantities (especially, pressure

distribution and skin friction) about a body immersed in fluid. Very often, the interest is

limited only to obtain the overall forces and moments acting on the body.

There are two main ways these quantities can be found; theoretically and experimentally.

Both the procedures have their relative advantages and disadvantages and have acted and

are going to act as supplementary to each other in foreseeable future

The limitation of theoretical methods basically stems from the fact that the governing

equation of real fluid about a body the Navier-Stokes equation can not, in general, be

solved theoretically. The theoretical methods are usually based on some simplified form

of this equation. With the assumption of inviscid (infinite Reynolds Number) and

incompressible (zero Mach number) flow, i.e., the ideal flow, the Navier Stokes equation

can simplified to Laplaces equation. The solution of this ideal flow, because of the above

simplification, differs from the experimental results. Efforts are then made to employ

some corrections due to the effects of viscosity and compressibility.

Even with simplification of inviscid incompressible flow, it is not easy to solve the

problem. For a few simple configurations, exact analytic solutions exist (Chap. 5).

Configurations of arbitrary shape are not amenable to analytic methods and demand

numerical solution. In the early days, a variety of approximate numerical methods were

developed. Examples are the different variants of linearised theory by Munk, Weber etc.

for aerofoil problems, Prandtls lifting line theory, Multhopps lifting surface theory,

Jones slender wing theory etc. for wing problems. With the advent of high speed digital

computers, more sophisticated exact numerical methods (Panel method) have been

developed. A variety of computer based theoretical schemes are also developed for

effecting the corrections due to viscosity and compressibility to these solutions.

Alternatively, attempts have been made to develop Euler as well as Navier-Stokes codes

with or without turbulence modeling.

2

It is almost certainly the case that however sophisticated these theoretical methods may

eventually become the engineer will always wish to validate his design, prior to

manufacture, by means of physical experiment. In this respect, in aircraft industry, the

wind-tunnel experimentation will always play the superior role of the two.

Wind-tunnel testing, like the theoretical calculations, has its own deficiencies and

difficulties. Broadly speaking these are : the high capital and running cost associated with

a wind tunnel, the expenses, elapsed time and skill needed in manufacturing accurate

scale models, the difficulty in obtaining the adequate data (forces, pressure distribution

etc.), the difficulty of interrogating this data.

Students of aeronautical engineering are well aware of the fact that the forces and

moments etc. experienced in flight on an aircraft depends primarily on two non-

dimensional parameters : Reynolds number and Mach number. Reynolds number

expresses the relative contributions of inertia and friction forces in the motion of the

fluid. The Mach number is the ratio of the flight speed and the speed of sound. In general

it can be stated that only a full scale model operating at full scale speed can give a totally

correct simulation of a real aircraft in flight. However, because of power conservation

problem (specially for high-speed flow) the wind-tunnel model is generally constructed at

a much smaller scale than the real aircraft. This in itself presents numerous difficulties

associated with the acquisition of sufficiently detailed data on such a small model.

However a more serious problem arises in simultaneously recreating the Mach number

and Reynolds number experienced in flight.

If the working medium and its temperature are the same in the wind-tunnel as in full-

scale flight in the atmosphere, then proper matching of the Mach numbers requires the air

speeds to be the same in both cases. If this is not achieved, then at Mach numbers of

interest of most aircrafts, the effects of compressibility will be different between the

wind-tunnel and flight.

On the other hand, if the speeds are kept same for Mach number simulation, the Reynolds

number in the wind-tunnel will be reduced (proportional to the geometric scale of model)

relative to the real aircraft. Clearly, if the wind-tunnel speed is increased to approach

full-scale Reynolds number then the Mach number will be incorrectly simulated.

3

Now many vital phenomena depend strongly on the Reynolds number and these include :

development of boundary layer, transition from laminar to turbulent boundary layer,

separation of boundary layer, vortex formation at high angle of attack etc. If the Reynolds

number is not matched properly, viscosity will be incorrectly simulated.

Numerous technological approaches have been proposed to overcome such difficulties.

One of these consists of modifying the properties of working medium and in particular

working at very low temperature or at high pressure. These approaches, in turn, present

other difficulties. However, since the present study is restricted to low speed regime

where compressibility effects are negligible, matching of both parameters is not

necessary and simulation of Reynolds number alone is sufficient.

The other difficulties associated with wind tunnel testing arise from the fact that the flow

conditions inside the tunnel are not exactly the same as those in the free air. Primarily, the

air in the tunnel is considered to be more turbulent than the free air this turbulence being

produced in the tunnel by propeller, vibrations of the tunnel walls etc. This consequently

increases the effective Reynolds number of the tunnel (Section 3.5). Excessive turbulence

makes the test data unreliable and difficult to interpret.

Secondly, the wind-tunnel model experiences spurious constraint effects due to wind-

tunnel walls (chapter 10 and 11) which will be absent in free air. These extraneous forces

must be calculated and subtracted out. These forces arise from two sources. Due to

formation and growth of boundary layer in the test section, the effective area is

progressively reduced resulting in increase of velocity and decrease of static pressure

downstream. This variation of static pressure produces a drag force known as horizontal

buoyancy. Again, the presence of a model in the test section reduces the area through

which air flows. This blockage caused by the model and its wake effectively increases

the average air speed in the vicinity of the model than they would be in free air, thereby

increasing all forces and moments at a given angle of attack.

Thirdly, the model in a tunnel is usually installed by some supports which in turn affect

the flow. The effect of this supports (the so-called Tare and Interference effects,

section 6.4) need to be calculated carefully and eliminated from observed values.

4

The procedure involved in wind-tunnel testing may now be summarized. The prerequisite

of any experimental work is the calibration and evaluation of the tunnel (Chapter 3)

itself. The wind-tunnel must be pre-calibrated to give the velocity of air flow during any

testing (since it is not practical to measure the velocity by pitot-static tube while the

model is in tunnel). The flow characteristics of the tunnel must be ascertained by

measuring the variation of velocity (static pressure) in the test section, flow angularity

and the turbulence level of the tunnel.

Wind-tunnel testing, then, involves model making, installation of model in the tunnel and

measuring forces, moments, pressure distribution etc. the forces and moments may be

obtained by any of the three methods :

a) Measuring the actual forces and moments with wind-tunnel balance

b) Measuring the effects that the model has on the airstream by wake survey (profile

drag, section 12.2)

c) Measuring the pressure distribution over the model by means of orifices

connected to manometer and integrating the pressure distribution over the model

surface.

The data acquired is then to be corrected for the tunnel boundary and support effects.

5

Chapter 1

WIND-TUNNEL

1.1 Introduction : The wind-tunnel is one of the most important facilities available for experimental work in

aerodynamics. Its purpose is to provide a region of controlled airflow into which models

can be inserted. This region is termed the working section or test section. For aeronautical

work, the flow in the test section should ideally be perfectly uniform in speed, direction

and vorticity. Such perfection can never be achieved in practice and the quality of a wind-

tunnel is related to the closeness to which the airflow in the test section approaches the

ideal.

1.2 Wind Tunnel Classification : Wind-tunnels are usually classified according to the three main criteria :

i) the type of test section

ii) the type of return circuit

iii) the speed of flow in the test section

1.2.1 The type of test section:

The cross sectional form of a test section may be square, rectangle, octagonal, circular or

elliptic. Again, it can be closed or open. A closed test section is one which is completely

enclosed within solid walls, the airflow therefore being constrained by these walls. An

open test section is one which is not enclosed within solid walls (Fig. 1.1). Because the

flow is not constrained, it usually tends to expand, partly due to pressure difference and

partly due to mixing between the air in the test section and that outside. To allow for this

expansion, the downstream part of the tunnel is bell-mouthed.

6

Figure 1.1 Open test section

Comparing these two types of test section, the closed type has the following advantages :

a) greater efficiency (i.e. reduced power losses)

b) better control of air flow

c) no loss of air

d) less noise

On the other hand, the open type of test section allows easier access to the model and

easier visual study of the flow.

1.2.2 The type of return circuit

A wind tunnel may either be open-circuit or closed-circuit tunnel. The open circuit tunnel

which is open at the both ends has no guided return of the air (Fig. 1.2). After the air

leaves the tunnel it circulates by devious paths back to intake.

7

Figure 1.2 Open circuit tunnel

The closed circuit tunnel has, as the name implies, a continuous path for the air (Fig. 1.3).

The whole circuit, except possibly the test section, is enclosed.

1.2.3 The speed of flow in the test section:

Five categories of speed are usually recognized :

a) low speed (up to about 60 or 70 m/s)

b) high speed subsonic (but Mach number less than 0.9)

c) transonic (Mach number between 0.9 and 1.2)

d) supersonic (Mach number between 1.2 and 5)

e) hypersonic (Mach number greater than 5)

8

Figure 1.3 Close circuit tunnel

The first two categories, low speed and high speed subsonic, are often taken together as

subsonic tunnels.

1.3 Types of Wind Tunnel :

1.3.1 Subsonic Wind Tunnel :

The simplest kind of subsonic tunnel consists of a tube, open at both ends, along which

the air is propelled. The propulsion is usually provided by a fan downstream of the test

section (a fan upstream would create excessive turbulence in the working section. Fig. 1.2

represents a tunnel of this type.

The following description relates to Fig. 1.2. The mouth is shaped to guide the air

smoothly into the tunnel; flow separation here would give excessive turbulence and non-

uniformity in velocity in the test section.

To make the flow parallel and more uniform in speed and top give a little time for

turbulence to decay, the mouth is followed by a settling chamber. The settling chamber

usually includes a honeycomb and wire-mesh screens.

9

A honeycomb is a coarse mesh made of thin, broad plates set edgewise to the flow. It has

two purposes. First, it helps to guide the air to flow parallel to the tunnel axis. Second, if

there are any large eddies in the incoming flow, the honeycomb cuts them into smaller

ones which can decay more rapidly than would the original larger ones.

The mesh-screens are fitted to reduce non-uniformities in flow speeds. A typical

installation might have one or two. The effects of screens on dynamic pressure variation

in the test section is shown in Fig. 1.4. The screen also serves to reduce the turbulence

level of the tunnel.

Figure 1.4 Effect of screen

The contraction followed by the settling chamber improves the quality of flow in the test

section. The air flows from the mouth of the tunnel at low speed into a comparatively

short settling chamber with a honeycomb and mesh screens. It is then accelerated rapidly

in the contraction. The contraction reduces turbulence and also non-uniformities in flow

speed and direction.

The test section is followed by a divergent duct, the diffuser. The divergence results in a

corresponding reduction in the flow speed, which has two principle effects. Firstly, it

enables an increased fan efficiency to be achieved. Secondly, the reduction in dynamic

pressure leads to reduced power losses at the exit from the tunnel in the laboratory.

10

Leaving the diffuser, the air enters the laboratory, along which it flows slowly back to the

mouth of the tunnel.

A typical tunnel will have a working section of about 1 meter square and an overall

length of some 5 to 7 meters. The speed in the test section, will be controllable, upto

about 30 m/s.

1.3.2 Transonic Tunnel:

The main special feature of a transonic wind-tunnel is its test section. In this, test section

walls are neither open nor closed but a combination of both. The walls usually have

perforation or streamwise slots. The reason is as follows :

If, as an Fig. 1.5 an aerofoil is being tested in a transonic flow, shock waves occur. If the

walls were solid these shockwaves would be reflected from them and would impinge on

the model. The flow over the model would therefore be very different from that in free

flight and the test would be invalid.

If the test section were open, there would be a boundary between the jet and the

surrounding atmosphere; the shock (compression) waves would be reflected from this

boundary as expansion (rarefaction) waves. These would impinge on the model, so again

the test would be invalidated.

Figure 1.5 Reflection of shock wave

11

If the walls are perforated or slotted (i.e., the test section is partly opened and partly

closed), the reflections are mixtures of compression waves and rarefaction waves and so,

depending on the degree of perforation, these tend to cancel each other out. The flow

over the model therefore approximates more closely to that in free flight.

1.3.3 Supersonic Wind Tunnel:

The simplest form of supersonic wind-tunnel is the blow-down type (Fig. 1.6). It consists

of a convergent-divergent duct whose upstream end is connected to a tank filled with

compressed air. The downstream end is usually open to the atmosphere. The air in the

tank then discharges through the duct. This means, of course, that the pressure in the tank

fall continuously, and therefore a reducing valve is fitted to maintain a constant pressure

at the inlet of the duct. The duration of each test run is necessarily limited with this type

of tunnel.

The blow-down type of tunnel is relatively cheap. In particular, a relatively low-powered

pump can be used to pressurize the tank taking, of course, a correspondingly long time to

do so. The power expanded in driving the tunnel during a test Is many times greater than

the power of the pump.

The test section of this type of tunnel is followed by a convergent-divergent duct. It can

be shown that if the pressure ratio between the two ends of a convergent-divergent duct

exceeds 1.892, the flow is sonic (M=1) at the throat and supersonic downstream. A plane

downstream of the throat can therefore be used as a test section in which the flow is

supersonic.

12

Figure 1.6 Supersonic wind tunnel

The Mach number at the test section will depend only on the cross-sectional areas at the

throat and the test section.

32

.

651

+=

MMA

A ST (1.1)

This shows that the test section Mach number is determined solely by the shape of the

tunnel (provided the pressure ratio is sufficient to maintain supersonic flow through the

test section). Because of this supersonic tunnels frequently consist of a basic frame to

which various liners can be fitted. Each liner gives a unique area ratio and therefore a

unique Mach number in the test section. The shapes of some different liners for various

Mach number are illustrated in Fig. 1.7.

13

Figure 1.7 Shapes of liners

1.3.4 Hypersonic Wind Tunnel :

The main special feature of hypersonic wind tunnel is that provision must be made for

preheating the air before entering the tunnel.

By suitable design of lines i.e. providing the large area ratio AT*S/ A* for generating high

Mach number, the Mach number in the test section of a supersonic wind-tunnel may be

increased to hypersonic regime. But another consequence of expanding air to high speed,

namely its change in temperature, becomes limiting criterion. The equation for the

temperature ratio along a streamline originating in a region where the flow is at rest with

temperature T0 and terminating where the temperature is T is given by

5

12

0 MTT

+= (1.2)

For M = 10, this equation gives T =T0/21. Now if T0 be the absolute temperature 228k

then the wind temperature in the test section will be 13.5K. This is well below the

temperature where air becomes liquid. Thus a limiting Mach number in the test section

would be one at which air remains gaseous.

14

The obvious choice for increasing this limiting Mach number is not preheat the air to be

used in the tunnel to such an extent that the very low temperature in the test section is not

realized. Another choice is to use a gas which has very much lower condensation

temperature than air, e.g. helium. The majority of hypersonic tunnels, however use the

preheating method. The preheating of air may be done by heating the reservoir air or

alternatively to allow the air to pass through a heat exchanger as it leaves the reservoir to

enter the working section.

Apart from these wind tunnels, other types of wind tunnels are also designed and

fabricated. The effort to simulate both Mach number and Reynolds number of free flight

in wind-tunnel has resulted in development of two types of tunnels :

1. Full Scale Tunnel

2. Compressed Air Tunnel

1.3.5 Full Scale Tunnel :

The Full Scale Tunnel is capable of testing actual aircrafts of moderate size under near

flight condition. The wind tunnel, developed at Langley Field, U.S.A., attains wind

velocities up to 53m/s with an open jet 18m wide and 9m high. Apart from providing a

total simulation of Mach number and Reynolds number, such wind tunnels also serve a

useful purpose in giving a correlation between flight and small model tests.

1.3.6 Compressed Air Tunnel :

The use of high pressure and therefore a high density in the test section can help to

achieve full scale Reynolds number with relatively small and low speeds. Some tunnels

are therefore completely enclosed in a large tank which can be pumped up to several

times atmospheric pressures. Such tunnels are termed compressed air tunnels.

It is worth mentioning that high pressure is no cure-all for getting a high Reynolds

number since model strength may be a limiting factor.

15

1.3.7 Other Tunnels :

There are also other types of tunnels built for various purposes. Some of these tunnels

are:

Smoke tunnel : For flow visualization

Spin Tunnel : For studying spin recovery

Low Turbulence tunnel : For testing at high Reynolds number

Stability Tunnel : For studying dynamic stability

Gust Tunnel : For studying effects of gust on models

V/STOL : For studying V/STOL configurations

Ice Tunnel : For studying formation and removal of ice on models

subjected to icing condition.

Automobile Wind Tunnel : For testing full scale automobiles.

16

Chapter 2

WIND TUNNEL INSTRUMENTATION 2.1 Introduction Instrumentation plays an important role in wind tunnel testing. The accuracy of

experimental results depends not only on the quality of the tunnel but also on the

performance of he measuring equipments.

The quantities which are frequently measured in wind tunnel testing are generally

pressure distribution and over all forces and moments acting on a model. Velocity, in

general, can be calculated from the pressure and hence need not be measured. However,

in some cases velocity itself (for example, fluctuating velocity components in turbulent

flow) may be of importance and need to be measured. Also, measurement of skin friction

may be necessary in some experiments.

Measuring instruments may, broadly, be classified as two types: mechanical and

electronic. Examples of mechanical type of instruments are the liquid-level manometers

for pressure measurement and wind-tunnel mechanical balances for measurement of

overall forces and moments. Such instruments lack the first response, capability of

measuring high and low values and amenability to automation required for unsteady or

short-duration high speed tunnel.

All these limitations may be overcome in electronic instrumentation system. An

electronic system usually consist of:

a) pick-up or transducer

b) signal conditioner

c) data acquisition system

The pick-up or transducer receives the physical quantity (pressure/force) under

measurement and delivers a proportional electrical signal to the signal conditioner. Here

17

the signal is amplified, filtered or otherwise modified to a format acceptable to the data

acquisition system. The data acquisition system may be a simple indicating meter, an

oscilloscope or a chart recorder for visual display. Alternatively, it may be a magnetic

tape recorder for temporary or permanent storage of data or a digital computer for data

manipulation or process control.

2.2 Pick-up or Transducer:

A transducer may be defined as a device which provides an electrical output signal for a

physical quantity (pressure/force), whether or not auxiliary energy is required. Many

other physical parameters (such as heat, light, intensity, humidity) may also be converted

into electrical energy by means of transducers. Transducers used in wind tunnel testing

may be classified according to the electrical principles involved, as follows:

1) Variable resistance transducer (resistance strain gauge)

2) Variable capacitance transducer

3) Variable reluctance transducer

4) Piezoelectric transducer

Of all these transducers, resistance strain gauge, because of its unique set of operational

characteristics, has dominated in transducer field for the past twenty years.

2.2.1 Variable Resistance Transducer:

The strain gauge is an example of variable resistance transducer that converts a physical

quantity into a change of resistance. A strain gauge is a thin, wafer-like device that can be

attached (bonded) to a variety of materials. Metallic strain gauges are manufactured from

small diameter resistance wire such as constantan, or etched from thin foil sheets (Fig.

2.1). For simultaneous measurement of strain in more than one direction, two-element or

three-element rosettes are used. The resistance of the wire or metal foil changes with

length as the material to which the gauge is attached undergoes tension or compression.

In a gauge diaphragm pressure transducer, strain gauges are directly bonded on the

diaphragm while in a sting balance used for force measurement, strain gauges are bonded

on he sting (Fig. 2.2). While the load is applied, the resistances of the strain gauges

increase or decrease, depending on nature of stress (tensile or compression). The

18

sensitivity of a strain gauge is described in terms of characteristics called the gauge

factor, G, defined as the unit change in resistance per unit change in length

Or, G = (R/R) / (L/L) (2.1)

where G = Gauge factor

R = Gauge resistance

R = change in gauge resistance

L = normal length (unstressed condition)

L = change in length.

The term L/L is the strain , so that equation (2.1) may be written as

G = (R/R) / (2.2)

Where = strain in the lateral direction.

Figure 2.1 Strain gauges (a: wire, b: foil)

The resistance R of a wire of length L can be calculated by using the expression for the

resistance of conductor of uniform cross-section.

2

4d

Larea

lengthR

== (2.3)

Where = specific resistance of conductor material

19

L = length of the conductor

=d diameter of the conductor

Figure 2.2 Sting balance

Tension on the conductor causes an increase L in its length and a decrease d in its

diameter. The resistance of the conductor then changes to

( )( )( )

( )( ) ( )ddd

LLLdd

LLRR

2141.

4. 22

+=

+=+ (2.4)

Equation (2.4) may be simplified by using Poissons ratio, , defined as a ratio of strain

in lateral direction to strain in axial direction. Therefore,

( ) ( )LLdd = (2.5) Substituting equation (2.5) in equation (2.4) gives

( )

( ))21(

14 2 LL

LLd

LRR

+

=+

( )( )LLLLR 211 ++= ( )( )LLR 211 ++= [neglecting higher order term] The gauge factor can now be obtained as

20

( ) ( ) ( ) 21/ +== LLRRG (2.6) Poissons ratio for most metals vary from 0.25 to 0.5 and the gauge factor is then of the

order of 1.5 to 2.0. For strain-gauge application, a high sensitivity is very desirable. A

large gauge factor means a relatively large resistance change which can be more easily

measured than a small resistance change. Semi-conductor gauges are now developed,

which have gauge factor of the order of 120.

The semi-conductor strain gauges are however neither so practical nor so widely used as

the conventional metallic gauges in general purpose, high accuracy transducers. It is

worth nothing that semi-conductor gauges were originally considered advantageous

because of their high output. This has less importance today because the same

semiconductor technology which created the type of gauge has also created smaller and

less expensive amplifiers high gain for use with conventional strain gauges.

Conventional metallic strain gauges are generally of four types : Constantan, Karma,

Isoelastic and platinum-tungsten. Constantan, a copper nickel alloy, of gauge factor 2.0 is

the most popular alloy for transducer gauges. It possesses an exceptional linearity over a

wide strain range and is readily manufactured. It is also easily solderable. Its primary

limitation in precision applications is a slow irreversible drift in grid resistance when

exposed to temperature above 75 C. Because the drift rate increases exponentially with

temperature, Constantan is not recommended for transducers operating continuously at

high temperature.

Karma (gauge factor 2.1) is a nickel-chromium alloy used in a variety of modified forms

for strain sensing. Like Constantan it displays extremely good linearity over a wide strain

range. It has greater resistivity than Constantan making higher grid resistance feasible. A

major advantage is its improved resistive stability, particularly at high temperature.

Isoelastic alloy offers exceptionally good fatigue life and a gauge factor 3.1, about 50%

higher than Constantan or Karma alloys. It has limited use in transducers because of its

poor zero stability with temperature variation. Because of its good fatigue life, it is

normally used for dynamic measurements.

Platinum-tungsten alloys, like Isoelastic, find their primary use in dynamic transducer

applications. With a gauge factor approximately two times greater than Constantan and

21

Karma, and with very good fatigue life, platinum-tungsten gauges are used almost

exclusively in fatiguerated dynamic transducers.

2.2.1.1 The Wheatstone Bridge principle :

The change in resistance due to applied load can be converted into a change in voltage by

the Wheatstone bridge circuit. Two types of Wheatstone bridge circuits are possible :

summing circuit and differencing circuit. Generally, in wind tunnel testing,

differencing circuit is used for measuring moment.

2.2.1.2 Summing Circuit :

In the summing circuit, resistance undergoing tension and compression are connected in

opposite sides of the Wheatstone bridge. Four unstressed strain gauges R1, R2, R3, R4 are

connected to form a Wheatstone bridge in summing circuit is shown in Fig. 2.3.

The current passing through the resistance R1 and R3 is I13 where

31

13 RRVI+

= (2.7)

Similarly, the current passing through resistances R4 and R2 is I42 where

24

42 RRVI+

= (2.8)

Figure 2.3 Summing circuit

22

The voltage at A is therefore,

131

113 .RRRVVRIVVA +

==

The voltage at B is,

424

442 .RRRVVRIVVB +

==

The voltage across A and B is,

+

+

=== 421

131

RRR

VVRRR

VVVVVV BAAB

+

+

=31

1

4

4

2 RRR

RRV

( )( )42312143

RRRRRRRRV++

=

or, ( )( )42312143

RRRRRRRRVV++

= (2.9)

Now, the output voltage V will be exactly zero, if

(1) 02143 = RRRR or, 2

4

3

1

RR

RR

=

or, (2) RRRRR ==== 4321 (say)

no matter what the input voltage V may be.

If any of the resistance changes due to applied load, the output voltage V will change.

Provision may be made to change only one resistance (quarter active bridge) or two

resistance (half active bridge) or three resistance (three-quarter bridge) or all four

resistances (fully-active bridge).

For the fully active bridge (Fig. 2.2), the output voltage due to applied load is calculated

in a simple manner. The resistance R1 and R2 are subjected to compression and will

therefore have a decrease in resistance value while resistance R4 and R3 will have a

increase in resistance.

23

The changed values of the resistances may be written as

RRRRRRRRR

+=

=

=

3

2

1

RRR += 4 (2.10)

RR , are the changes in resistances due to changes in strain at positions 1 and 2 (Fig.

2.2).

Substituting the values in equation (9) yields

( )( ) ( )RRRRRRRRRRRRRRRR

VV

++++++

=

)())((

( )224

22RRRRRRR

+=

( )r

RRR4

2 +=

R

RR2

+=

(2.11)

If the strain gauges are bounded very close to each other, it can be assumed

RRR ==

and the equation (2.11) is reduced to

244

RRR

VV

=

or, RR

VV

= (2.12)

The equation shows a linear relationship. However, for quarter-bridge and half bridge a

non linearity appears in the expression for output voltage. For example, if only R4 is

active (quarter-bridge) and the other three resistance are passive (not bonded on the

sting), the expression for output voltage is

( )RRR

VV

+

=4

(2.13)

For a half-bridge (taking only R4 and R3 active)

24

( )RRR

VV

+

=2

(neglecting higher order terms) (2.14)

Similarly, for a three-quarter bridge (taking R4, R3 and R2 )

( )RRR

VV

+

=4

3 (2.15)

Because of the linearity in relationship, fully-active bridge is usually used in

measurement techniques. It also has another advantage compared to others i.e. the

temperature compensation effect. In a fully active bridge, all resistances have same

temperature (neglecting the thermal e.m.f. effect) while in other bridges, the temperature

of active gauges may be different from those of the passive gauges which will cause a

change in resistance values resulting in further non-linearities.

2.2.1.3 Differencing Circuit :

The arrangement of resistance in the Wheatstone bridge in differencing circuit is shown

in Fig. 2.4. Using the similar procedure, the output voltage V in this circuit is obtained

as

Figure 2.4 Differencing circuit

25

( )( )34213142

RRRRRRRR

VV

++

=

= ( )( ) ( )( )( )RRRRRRRRRRRRRR

++++

2.2(

( )( )224

2RRR

RRR+

=

( )242

RRRR

= [neglecting ( )2RR + with respect to 4R2]

R

RR2

=

(2.16)

If the strain gauges are pasted close to each other, the output voltage will be virtually zero

since R will be almost equal to R.

2.2.2 Variable Capacitance Transducer :

The capacitance of parallel-plate capacitor is given by

)(.. 0 faradsd

AkC =

Where A = area of each plate (m2)

=d distance between the plates (m)

0 = 9.85 10 -12 (F/m)

=k dielectric constant

Since the capacitance is inversely proportional to the spacing of the parallel plates, d, any

variation in d causes a corresponding variation in the capacitance. This principle is

applied in the variable capacitance pressure transducer (Fig. 2.5). A pressure, applied to a

diaphragm that functions as one plate of a simple capacitor changes the distance between

the diaphragm and the static plate. The resulting change in capacitance can be measured

with an AC bridge but it is usually measured with an oscillator circuit. The transducer, as

a part of the oscillatory circuit, causes a change in the frequency of the oscillator. This

change in frequency is a measure of the magnitude of the pressure applied.

26

Figure 2.5 Variable capacitance transducer

2.2.3 Variable Reluctance Transducer :

Such transducers employ magnetic diaphragms as sensing element (Fig. 2.6). When a

differential pressure deflects the magnetic diaphragm, the air gaps (initially about 0.025

mm) also changes differentially and so does the reluctance. The two coils are connected

on a two-active arm bridge so that an output proportional to pressure is obtained.

Figure 2.6 Variable reluctance transducer

27

Another type of variable reluctance transducer is based on linear variable differential

transformer (LVDT). The LVDT is a three-coil device with a movable magnetic core

(Fig. 2.7). Two outer coils are connected in opposition so that induced voltages are 180

out of phase with each other. When the armature is centered, these voltages are equal in

magnitude giving zero output. The pressure activates the diaphragm and when it moves

the magnetic fluxes are unbalanced to produce an output proportional to the pressure

applied.

Figure 2.7 Linear variable differential transducer

2.2.4 Piezoelectric Transducer:

The Greek word piezo means to squeeze. The piezoelectric effect is appropriately

described as generating electricity by squeezing crystals. This type of sensor is self-

generating, that is, it does not require external electrical power as do the variable

resistance or variable reluctance sensors.

A piezoelectric transducer is illustrated schematically in Fig. 2.8. The sensitivity can be

enhanced at the expense of resonant frequency by stacking a series of elements together

with the appropriate electrical connection.

28

Figure 2.8 Schematic diagram of piezoelectric transducer

A variety of piezoelectric materials are used, with quartz being most popular. Although

piezo-electric transducers may be used for near static pressure measurements, they are

more frequently employed for transient measurement.

2.3 Signal Conditioner: Signal originating from the transducer is fed to the signal conditioner in which it is

transformed into a form acceptable to the data acquisition system. Broadly speaking, the

signal conditioner provides circuitry for amplification, noise suppression, filtering,

excitation, zeroing, ranging, calibration and impedance matching. Because the operating

principles of the different transducers are different, a variety of signal conditioners have

been developed. The different types of signal conditioner for different transducers are

outlined below.

2.3.1 Signal conditioner for Variable Resistance Transducer :

The signal conditioner usually provides supporting circuitry for resistance strain gauge

transducer. Usually, the equipment is able to accept quarter-bridge, half-bridge and full-

bridge by providing appropriate dummy gauges. The circuitry usually provides excitation

power, balancing circuits, calibration elements, signal amplification etc.

2.3.1.1 Excitation Supply :

Normally DC excitation is used for resistance strain gauge transducer. Although AC

excitation can be used, the disadvantages outweigh the advantages. The accuracy of an

AC system is not as good as that of DC system. Also the noise rejection near the carrier

frequency is poor. Earlier DC amplifier circuit was based on the chopper principle in

29

which the DC is first converted to AC and then amplified and later converted to DC.

Such a DC amplifier is fairly expensive. However, with the advent IC chips, DC

amplifiers are no longer more costly than AC system.

However, the DC power supplied must have high stability. To achieve this, the power

supply should be isolated from all other common lines and from the AC power line. In

the other words, it should have a very low coupling to the power line and to the ground.

2.3.1.2 Bridge Balance :

The Wheatstone bridge circuit should ideally have zero voltage output under no load

condition, equation (2.9). However, because of normal gauge-to gauge resistance

variations and additional resistance changes during gauge installation, the bridge circuit is

usually in a resistively unbalanced state when first connected. It is advantageous to have

a balancing network to nullify any residual signal.

Figure 2.9 Parallel balance network

The most common arrangement uses a shunt on one side of the bridge as shown in Fig.

2.9, the fixed resistor in the potentiometer wiper lead being used to omit the loading

effect on the active arms of the bridge.

If all the resistance strain gauges are of exact equal values, the voltage at A and B will be

0.5 V and the output V will be zero. In this hypothetical case, the potentiometer wiper

30

lead will be at the center (position C) and the voltage there will also be 0.5 V and

therefore there will be no current through R4.

However, if due to any of reasons mentioned above, the output V is not zero, the voltage

at A is then either higher or lower than the voltage at B. in either case, bridge can be

balanced by moving the wiper lead downward (C2) or upward (C1) respectively.

The range of he balance network is given by

44R

RVV

= if R4>>R

where V is the maximum out-of balance (zero offset) that can be nullified. The range

can be extended by decreasing the value of R4. However, R4 can not be decreased

indefinitely because it will then have loading effect on the power supply. Usually, to limit

the loading effect, R4 is many times higher than R (of the order of 75 k to 100 k ).

2.3.1.3 Shunt Calibration :

Usually, in all signal conditioners, shunt resistors are provided across the arms connected

to balance network. The shunt resistor, when connected, can usually accommodate a

0.4% change of resistance of the arm shunted. This actually amounts to simulating 2000

strain on the arm shunted as shown in Fig. 2.10. From equation (2.2), = (R/R)/G. For

R = 120 , G = 2.0, R = 0.48, becomes 0.002 or 2000.

31

Figure 2.10 Shunt calibration

2.3.1.4 Signal Amplification :

Signal amplification is the major function of a signal conditioner. Usually, the output

voltage V (equations 2.12, 2.16) of a wheatstone bridge circuits is of the order of

microvolts since the change in resistance is usually of the order of 10 5 to 10 6 ohms.

Such a weak signal may not be accepted by the data indicator or recording system

(although microvoltmeters are now available) and therefore the signal originating from

transducer need to be amplified.

Signal requirements for amplifier are quite stringent. These include impedance matching

with the data indicator or recording device, high signal-to-noise ratio (SNR), low drift

(change in output voltage with time is called drift) etc.

With low impedance devices such as resistance strain gauges, no special problems arise

in the operational mode. A fairly conventional voltage amplifier with an input impedance

of 100k or greater in suitable for use with the data indicator system (such as DVM) or

32

C.R.O. For bridge circuits in which neither output terminal is grounded, a differential

amplifier is needed. Such amplifiers offer good common mode rejection characteristics.

The philosophy underlying noise cancellation is outlined in Fig. 2.11.

Figure 2.11 Noise cancellation by amplifier common-mode rejection

If the common mode rejection ratio is of the order of 105, the noise that appears at the

output terminal is largely eliminated. Such transducers have the ability to handle direct

coupled signals, the D.C. drift being less than 10V/hour after allowing one hour warm-

up. Low drift rates are fairly difficult to achieve and the cost of D.C. amplifier with this

sort of performance is comparatively high.

2.3.2 Signal Conditioner for Variable Capacitance Transducer :

A number of signal conditioner is available based on the following schemes

i) D.C. polarization as the input circuit for an amplifier.

ii) An A.C. bridge circuit for use with and amplitude modulation system.

iii) A frequency modulating oscillator circuit.

iv) A pulse modulating circuit.

The D.C. polarization circuit, the simplest of these, is described here. It is effected by the

circuit shown in Fig. 2.12. in which C represents the capacitance of the transducer

together with that of the connecting cable and any stray parallel capacitance. The

polarizing voltage V is usually a few hundred volts. If it is assumed that the capacitance

C can be represented by a constant portion C0 plus a sinusoidally varying part C1 sinwt,

then

33

C = C0 + C1 sinwt

If C1

34

amplified by an A.C. amplifier and demodulated. It is then filtered to remove any ripple

from the carrier wave.

Figure 2.13 Carrier wave amplifier system

2.3.4 Signal Conditioner for Piezo-electric Transducer :

Piezo-electric transducers are self-generating; they do not require an external source of

energy. However, using them poses some special problem. In order to measure the charge

separation which occurs when the piezo-electric material is mechanically strained, a

measured circuit must be connected to it. The measuring circuit draws some current so

that the charge, Q, leaks away. To minimize this leakage, the input impedance of the

circuit must be made very large. Early approaches to this problem involved the use of

valve voltmeters. The input impedance of such valves are very high so that negligible

current is drawn less than 10-12 Amp. Used in a simple voltage amplification circuit, Fig.

2.14, the output signal is function of cable capacitance CC, and any stray capacitance CS between the input and ground as well as on the range- setting capacitor C1

35

Figure 2.14 Voltage amplifier

Thus, CS CCCC

mQV+++

=

10

This strong dependence on cable and stray capacitance is circumvented by using a

charge-amplifier. This is an operational amplifier, in which the high input impedance is

retained but strong negative capacitive feedback is employed as shown in Fig. 2.15.

For such an arrangement, the output voltage V is given by

( ) ( ) inF CmmCQV

111 ++

=

If the open loop gain m, of the amplifier is very large (m > 50000), the output becomes

FC

QV =

Thus a voltage proportional to charge Q is produced.

Figure 2.15 Charge amplifier

2.4 Data Acquisition System :

Data acquisition systems are used to measure, indicate and/or record signals originating

from transducers and signal conditioning process. Such systems can be categorized into

36

two major classes : analog system and digital system. The type of data acquisition

system, whether analog or digital, depends largely on the intended use of the recorded

input data. In general, analog systems are used when wide bandwidth is required or when

lower accuracy can be tolerated. Digital systems are used when the physical process

being monitored is slowly varying (narrow bandwidth) and when high accuracy and low

pre-channel cost is required. Digital data acquisition systems are in general more

complex than analog systems both in terms of instrumentation involved and the volume

and complexity of input data they can handle.

2.4.1 Analog System

An analog system may be defined as continuous function such as a plot of voltage versus

load (Fig. 2.16) or displacement versus pressure. Examples of the analog systems are the

analog panel meter, CRO, strip-chart recorder, X-y plotter etc.

Figure 2.16 Analog system

A complete analog instrumentation system used in wind tunnel testing may consist of

some or all of the following elements :

a) Transducers: for translating physical parameters into electric signal.

b) Signal Conditioners: for amplifying, modifying etc. of these signals.

37

c) Visual Display Devices: for continuous monitoring of the input signals. These

devices may include single or multi-channel CRO, storage CRO, panel meter,

numerical display and so on.

d) Graphic Recordings Instruments: for obtaining permanent records. These

instruments include strip chart recorder to provide continuous records on paper

charts, X-y plotter, ultraviolet recorders etc.

e) Magnetic Tape Instruments: for acquiring data, preserving their original

electrical form and reproducing them at a later data for more detailed analysis.

2.4.2 Digital System :

Digital systems handle information in digital form. A digital quantity may consist of a

number of discrete and discontinuous pulses (Fig. 2.17) which contains information about

the magnitude or nature of quantity. Digital system may consist of digital panel meter,

data-logger, computer etc. It is worth noting that if a digital system is employed, an

analog-to-digital (A/D) converter must be used before since the output signal from the

signal conditioner is in analog form.

Figure 2.17 Digital system

A complete digital instrumentation system may include some or all of the following

elements (Fig. 2.18).

a) Transducers: for translating physical parameters into electrical signals.

b) Signals Conditioners: for amplifying, modifying, etc. of these signal.

38

c) Scanner or Multiplexer: for sequentially connecting multiple analog signals to

one measuring/recording system.

d) Signal Converter: translates the analog signal to a form acceptable by analog-to-

digital converter. An example of signal converter is an amplifier for amplifying

log-level voltages generating by strain gauges.

e) Analog to Digital (A/D) converter: converts the analog voltage to its equivalent

digital form.

f) Digital Recorder: records digital information on punched cards, perforated

paper tape, magnetic tape, or a combination of these systems.

g) Auxiliary Equipment: this section contains instruments for system

programming functions and digital data processing. These functions may be

performed by individual instruments or by a digital computer.

Figure 2.18 Complete digital instrumentation system

Transd-ucer

Signal Condit-ioner

Scanner/Multiple-xer

Signal Conver-ter

A/D Conver-ter

Digital Record-er

Auxiliary Equipment and

System Programming

39

Chapter 3

TUNNEL CHARACTERISTICS

3.1 Introduction : Once a wind tunnel is designed and constructed, the primary task is to calibrate and

evaluate the tunnel characteristics in terms of uniformity in wind speed and direction, and

also level of turbulence. A wind tunnel can be considered to have good characteristics if

the flow in the test section has uniform speed, no angular variation in direction and low

level of turbulence. Four tests are generally necessary for calibrating and evaluating a

tunnel. These are:

1. Air speed calibration.

2. Determination of velocity variation in the test section.

3. Determination of angular flow variation in the test section.

4. Determination of turbulence level.

3.2 Air Speed Calibration : In any experiment, the wind tunnel flow speed (or dynamic pressure) must be known for

calculation of flow quantities. However, it is not desirable top insert a pitot-static tube in

the tunnel in the presence of a model. This is because of two reasons; firstly, the tube will

interfere with the model and secondly the tube will not read true owing to the effect of

model on it. It is therefore necessary to determine the airflow speed during an experiment

without using the pitot-static tube. This is possible by a prior calibration of a wind tunnel

manometer with respect to air speed.

The pitot-static tube (Fig.3.1) at station J is considered. If P0 be the total pressure, pj be

the static pressure and UJ be the oncoming flow speed at the test section, then from

Bernoullis equation

40

20 21

JJ UpP +=

or, ( ) JJ PPU = 02 (3.1)

Figure 3.1 Calibration of wind tunnel manometer

The pitot-static tube is connected to manometer M1 which shows a difference in water-

level of hJ , then

ghPP JwaterJ = 0

The manometer M1 is inclined at an angle of 600,

gSinhPP JWaterJ =0

0 60 (3.2)

From equation (3.1) and (3.2)

41

gSinhU JWaterJ =0602 (3.3)

The air flow speed at test section can now be calculated from equation (3.3)

The calibration of flow speed UJ or dynamic pressure

= 2

21

JJ Uq can now be

calibrated with the help of another manometer M2 . Applying Bernoullis equation at L

and S stations gives

2221

21

SSLL UpUp +=+

or, SSLL qpqp +=+ where q is the dynamic pressure.

If the pressure drop between S and L stations due to friction is considered, total head at L

will be slightly smaller by an amount (say qSK1 where K1is he loss coefficient), then

1kqqpqp SSSLL +=+

or, ( ) LSSL qkqpp = 11

Applying equations of continuity between stations L and S

LLSS UAUA = ; ( ) SLSL UAAU =

Therefore, ( )[ ]211 LSSSL AAkqpp = (3.4) Applying equation of continuity between S and J

JJSS UAUA = ; ( ) JSJS UAAU =

or, ( ) JSJS qAAq 2=

Putting in equation (3.4)

( ) ( )[ ]212 1 LSJSJSL AAkqAApp = jqk2=

or, ( ) 2kppq SLJ = where k2 is a constant.

Now, if another manometer M2 is connected to stations L and S, then

ghpp LSwaterSL =

or, ( ) 2kghq LSwaterJ =

LSkh= (3.5)

where k is a constant.

42

Equation (3.5) shows that the free stream dynamic pressure is linearly proportional to the

pressure difference in terms of manometer water level difference hLS. Free stream speed

(U) at station J Is also therefore directly related to pressure difference (in terms of hLS )

between two points L and S.

The lows peed wind tunnel (LSWT) in the department can be run at 11 different speed

setting. For 11 different speeds a table can be made concerning free stream speed C at

station J and hLS, as shown in Table 3.1.

Table 3.1. : Calibration of tunnel speed

No. of runs hJ (cm) qJ (N/m2) U at J (m/s) hLS(cm)

1.

2.

3.

-

-

11.

Calibration graphs (Fig. 3.2) can now be made in terms of q vs hLS and U vs hLS. Using

these graphs velocity or dynamic pressure in any subsequent experiment can be obtained

simply from hLS (without using pitot-static tube).

43

q U (N/m2) (m/s)

hLS (cm) hLS (cm)

Figure 3.2 calibration graphs

3.3 Determination of Velocity variation in test section : Velocity in the test section, even in the absence of model, is not uniform either in

horizontal or vertical direction. Owing to the effects of viscosity, the velocity near the

tunnel wall will be slower than the velocity on the centerline and velocity at downstream

will be greater than at upstream. To achieve uniformity of speed various means like using

guide vanes, breathers or screens are used.

To check uniformity of speed in vertical direction velocity at different vertical positions

(for example, points 1, 2, 3, 4, 5, in Fig. 3.3) can be measured by pitot-static tube.

Velocity at these points for a particular tunnel speed setting can be obtained from

ghU water =060sin2 (3.6)

Tunnel Roof

0 5 Test Section

Exit 0 4 Entrance

0 0 0 3 0 0

5 4 3 2 1

0 2

0 1

Tunnel Floor

Figure 3.3 Velocity measurement at five vertical and five horizontal positions

44

Velocity in the wind tunnel varies in longitudinal directions (i.e. along the axis of the test

section) because of viscous effects. As the flow progresses towards the exit, the boundary

layer is thickened resulting in an effective reduction of area, increase in velocity and

decrease in static pressure. Because of the decrease of static pressure there is tendency of

the model to be drawn downstream. This creates a drag force acting on the body, termed

horizontal buoyancy (chapter 10, 11), which is to be calculated and subtracted in any drag

measurement experiment.

Velocities (dynamic pressure) at different points along the tunnel center line (1, 2, 3, 4,

5 in Fig. 3.3) can be measured using the pitot-static tube as before. Subtraction of

dynamic pressure from total pressure (atmospheric pressure) will give static pressure at

these points.

A table can now made for calculation of velocity variation in vertical and horizontal

directions as shown below.

Table 3.2: Calculation of velocity at 9 points

Stations y cm h cm U m/s Stations x cm h cm U m/s p (N/m2)

1. 1.

2. 2.

3. 3.

4. 4.

5. 5.

45

U U (m/s)

(m/s) p (N/m2)

Height from floor, Distance along tunnel

y (cm) Centerline, x (cm)

Figure 3.4 Velocity variation in vertical and horizontal direction

Velocity variation with tunnel height (y) and velocity and static pressure variation with

distance along tunnel center line (x) can now be plotted (Fig. 3.4). Static pressure

gradient (p/x) should be calculated and noted.

3.4 Determination of Angular Flow Variation in the Test Section :

Due to defectiveness in design and construction, the flow in the test section may not be

horizontal. It is therefore necessary to know whether such angularity in flow exists and if

it exists then to measure it so as to allow compensations due to this angularity of flow.

The angular variation in the flow can be checked by using a spherical yawhead as shown

in Fig. 3.5. The yawhead has two smooth orifices usually 900 apart on the forward face of

a sphere. Obviously, if they are exactly placed, they will read equal pressure when the

flow is directed along the axis of the yawhead. If the pressure at the two points a and b

are not equal then it will indicate that the flow is inclined at an angle. This angle of yaw

may then be determined by simply rotating the yawhead till the pressures at these points

become equal. The angle of rotation of yawhead is then the angle of yaw of the flow. A

similar procedure can be adopted for measuring yaw in the horizontal plane by measuring

pressure at two other points a and b in the horizontal plane again 900 apart.

46

Figure 3.5 Spherical yawhead

An alternative way of measuring yaw angle is to fix yawhead in tunnel and to determine

the flow angularity by reading the pressure difference between two orifices and

comparing with a previous calibration of the yawhead.

It is believed that accurate testing can not be done if the variation in angle is greater than

5.0 degree. The larger angles of yaw distorts the span load excessively.

Unfortunately, the variation of flow angle across the jet may change with the tunnel

speed. If such a change is noted, a testing speed must be selected and the guide and anti-

twist vanes should be adjusted to give smooth flow at that speed.

3.5 Turbulence Level : The flow conditions inside the wind tunnel are not exactly same as those in free air. The

flow inside the tunnel is more turbulent than the free air because of the effects of the

propeller, the guide vanes and the vibrations of tunnel walls. This discrepancy in the

turbulence level results in disagreement of tests made in the wind-tunnel and in the free

air at the same Reynolds number. By the same reasoning, tests made in different tunnels

at the same Reynolds number may not agree. A correction factor is therefore necessary

for compensating the turbulence created in the tunnel.

It is found that the flow pattern in the tunnel at a given Reynolds number corresponds

closely to the flow pattern in the free air at a higher Reynolds number. The increase ratio

is called the turbulence factor and the effective Reynolds number RNe of the tunnel can

be obtained from the calculated Reynolds number using the turbulence factor of the

tunnel from

RNTFRNe = (3.7)

47

The turbulence may be found with a sphere in two ways :

a) Drag sphere

b) Pressure sphere

3.5.1 Drag Sphere :

The drag coefficient of sphere is affected greatly by change in velocity. Contrary to the

laymans guess, CD for a sphere decrease with increasing airspeed since the result of

earlier transition to turbulent flow is that the air sticks longer to the surface of the sphere.

This action decreases form or pressure drag, yielding a lower total drag coefficient.

Obviously, the Reynolds number at which the transition occurs at a given point on the

sphere is a function of the turbulence already present in the air and hence the drag

coefficient of a sphere can be used to measure turbulence . The method is to measure the

drag, D, for a small sphere 15 or 20 cm in diameter, at many tunnel speeds. After

subtracting the horizontal buoyancy drag DB the drag coefficient may be computed

from

( ) 22 4

21

=

Ud

DDC BD

(3.8)

Figure 3.6 Variation of CD with Reynolds Number

48

The sphere drag coefficient is then plotted against the calculated Reynolds number, RN

(Fig.3.6). The Reynolds number at which the drag coefficient equals 0.30 is noted and

termed the critical Reynolds number, RNC. The above particular value of the drag

coefficient occurs in free air at RN = 385000, so it follows that the turbulence factor may

be given by

TF = 385000/RNC (3.9)

Once the turbulence factor (TF) is obtained from equation (3.9), the effective Reynolds

number, RNe, can now be calculated from equation (3.7).

3.5.2 Pressure Sphere :

An alternative method (which will be used) of measuring turbulence makes use of

pressure sphere. No force tests are necessary and the difficulty of finding the support

drag is eliminated. The pressure sphere has an orifice at the front stagnation point and

four more interconnected and equally spaced orifices at 0

2122 from the theoretical rear

stagnation point (Fig.3.7).

Figure 3.7 Pressure Sphere

A lead from the front orifices is connected across a manometer to the lead from the four

rear orifices. After the pressure difference due to the static longitudinal pressure gradient

is subtracted, the resultant pressure difference, p for each Reynolds number is divided

49

by the dynamic pressure for the appropriate Reynolds number, and the quotient is plotted

against Reynolds number (Fig. 3.8). It has been found that the pressure difference p/q

is 1.22 when the sphere drag coefficient is 0.30 and hence this value of p/q determines

the critical Reynolds number RNC. Once the turbulence factor is determined, the

turbulence factor may then be determined, as before, from equation (3.9).

Figure 3.8 Variation of p/q with Reynolds number

This experiment is carried out on a sphere of diameter 20 cm. The following table may be

made for plotting p/q vs Reynolds number.

50

Table 3.3 : Experimental measurement of turbulence factor

No.of

Runs

hLS (cm)

U from Fig.

1.2 b (m/sec)

q from

Fig.1.2 a

(N/m2)

hj

(cm)

p

= hjwg.sin600

(N/m2)

p/q RN

= UD/

1.

2.

3.

-

11.

Turbulence factor usually varies from 1.0 to 3.0. Values above 1.4 indicate that the tunnel

has too much turbulence for reliable testing. Low turbulence factor is necessary for the

test data to be reliable.

51

Chapter 4

FLOW VISUALISATION

4.1 Introduction : Flow visualization techniques are a means of obtaining the qualitative pattern of the flow

about a body. Flows encountered in engineering application are often complex in nature.

Such techniques of flow visualization helps in obtaining a better understanding of the

flow characteristics. Many a times suitable mathematical methods have been developed

for a particular flow problem based on such qualitative studies.

Flow visualisation techniques can be classified as follows :

Flow visualisation techniques

Incompressible flow Compressible flow

Entire flow field Only on model Flow pattern Shock visualisation

1. Smoke 1. Tuft 1. Oil flow 1. Shadowgraph

2. Tuft on wire mesh 2. Oil flow 2. Interferometer

3. Evaporation 3. Schlieren

52

4.2 Incompressible Flow Visualisation Techniques : 4.2.1 Smoke Method :

Flow visualisation with smoke is achieved in a smoke tunnel with a facility to emit

cleaned smoke in streamer form (Fig. 4.1). Smoke is generated by burning kerosene or

paraffin. Particular care is needed in introducing the smoke in the tunnel by a blower

without disturbing the flow in the tunnel. This smoke follows the air flow and makes the

flow pattern visible. Smoke tunnels are usually low-velocity tunnels and most of them

have two dimensional test sections. Such tunnels are usually open circuit type to prevent

accumulation of smoke in the tunnel. The walls of test section are made of glass so that

the flow can observed (Fig. 4.2) and/or photographed.

Figure 4.1 Smoke Tunnel

53

Figure 4.2 Flow separation at high angle of incidence

4.2.2 Tuft Method :

Tufts are simplest and most often used. A large number of silk tuft are pasted at one end

on the surface of the wing. The length of each tuft is taken about 2 cm. The most rapid

method of installing the tufts is to attach them about every one inch to the tape and

pasting the tape on the model (Fig. 4.3). To obtain clear photography the model is usually

painted black while the tufts used are white. Since the open ended tufts align with the

flow the general direction of he tufts indicate the direction of the flow on the surface of

the body. Motion of tufts usually means that the flow in the boundary layer has become

turbulent. Violent motion or tendency a tendency to lift from the surface and point

upstream indicates separation.

If the tufts are to be used to examine the entire flow field they may be supported on wires

on a mesh installed inside the tunnel. Complete grids of wires normal to the flow can be

fixed in the tunnel behind a wing model. Tufts attached on one end on the mesh junctions

will align with the flow direction and show up trailing vortices.

54

Figure 4.3 Visualisation of flow over a straked wing by tuft method

4.2.3 Oil Flow Method :

In this method the model is pasted with a semi-liquid mixture of mobil oil and grease

and a dye. The dye taken for this purpose is a chemical known as Rhodamin B. When the

model is installed in the tunnel, the air flow spreads the mixture along the streamlines so

that after the tunnel has been stopped the flow pattern remains. The process requires

about 30 minutes of continuous air flow in the tunnel. The model is thereafter removed

from the tunnel and the flow pattern (Fig. 4.4) can be examined afterwards under

ultraviolet light.

An alternative approach is to mix mobil oil and titanium dioxide (dye) and paste on the

model. In this case the mixture gets dried up in a few minutes and the flow pattern can be

observed without using ultraviolet light. Care must be taken so that the oil does not

follow machining marks on the surface.

Figure 4.4 Visualisation of flow over a straked wing by oil flow method

55

4.2.4 Evaporation Method :

Napthalin may be dissolved in acetone and pasted on a model. When the tunnel runs

napthalin evaporated quickly from the turbulent portion making that portion white. If the

model is painted black, transition from laminar to turbulent flow can be observed easily.

Among the incompressible flow visualization techniques it may to be noted that tuft, oil

flow and evaporation method gives pattern of flow on the surface of the model only while

the smoke method (and tuft on mesh screen) gives the picture of the entire flow field.

Among the compressible flow visualization techniques, only the oil flow method,

described in section 4.2.3, can be used. Other methods are not suitable because of the

high speed involved.

4.3 Compressible Flow Visualisation Techniques :

4.3.1 Shadowgraph Method :

A parallel beam of light is produced by a point source. It is passed through a converging

lens and then through the working section. Since the flow in the working section is

compressible, refraction of light rays through the compressible medium will be different.

The screen will be illuminated where rays have converged. Shock waves then appear on

the screen as two adjacent bands, one dark and one light, corresponding to the sudden

increase in density gradient at the front of the shock and the sudden decrease in gradient

at the rear.

56

Figure 4.5 Shadowgraph picture of flow about a sphere

4.3.2 Schlieren Method :

Schlieren method is most widely used. It is sensitive to density changes whereas

shadowgraph method is sensitive to change in density gradient. The light rays passing

through the varying density area (test section) will be deflected. The screen will be

illuminated or darkened depending on the deflection of the light beam. This method is

described in details in chapter 20.

4.3.3 Interferometer Method :

A direct response to density changes is given by the interferometer which depends on the

interference fringes formed on the recombination of two light rays from the same source

which have taken different times to make the journey.

If he two path lengths are same, interference fringes may be produced. The light paths are

adjusted with no airflow disturbance to produce a uniform and parallel set of interference

fringes on screen giving uniform illumination. When the tunnel is run with model

installed, fringe spacing will change by an amount proportional to the phase change by

the disturbance at any point which is in turn proportional to the change of fluid density

integrated along the light path. If the interferometer is pre-calibrated, it will give absolute

values of density.

57

Figure 4.6 Schematic diagram of the interferometer system

58

Chapter 5

PRESSURE MEASUREMENT BY MECHANICAL DEVICE

5.1 Introduction : Pressure, at different points on the surface of model, can be obtained by drilling holes on

the surface and connecting tubes from these points to a mechanical device like a multi-

tube liquid level manometer (Fig. 5.1). liquid levels, which are initially in the same level,

undergo changes in height proportional to the pressure applied and pressure at different

points in the surface can be calculated from the heights of the columns.

Figure 5.1 Liquid level manometer

Multi-tube, indicated schematically in Fig. 5.1 may be used in vertical position. For

increased sensitivity the manometer may be inclined at various angles in which readings

59

are multiplied by appropriate factors. Also, in stead of water, liquid of specific gravity

less than 1.0 may be used.

The reservoir for manometer liquid is usually mounted on a vertical rod at a height which

is adjustable. It is recommended that the reservoir be normally left open to atmospheric

pressures. Pressures p1, p2, p3,.are then gauge pressures i.e., pressures relative to

atmospheric datum. Pressure relative to some other chosen datum may be obtained by

connecting the reservoir and one manometer tube to the required datum.

Manometers are generally graduated so that height of liquid level may be read in cm and

the pressure is calculated from the height of the liquid column in the relevant tube. Some

manometers are graduated directly in N/m2 or in millibar (1mb = 100 N/m2 ).

5.2 Measurement of Cp : Pressure is usually expressed in non-dimensional form as pressure coefficient Cp . by

definition Cp is given by

2

21

=U

ppC p

(5.1)

Using a liquid-level manometer as shown in Fig. 5.1, pressure coefficient Cp can be

obtained in two ways depending on whether the tunnel is precalibrated or not.

5.2.1 Without Pre-Calibration of the Tunnel :

If the tunnel is not pre-calibrated to give U, two holes are to be drilled on the walls of

the settling chamber and the test section and directly connected to the manometer in

addition to connecting pressure port of the configuration.

Now, by Bernoullis theorem,

SPUpP =+= 2

0 21

where PS is the settling chamber pressure.

Or, = ppU S2

21

If the manometer is graduated in N/m2 ,(p - p) and (PS - p) can be obtained directly in

units of N/m2 and Cp can be obtained as the ratio of the two given by

60

=pPppC

Sp (5.2)

Non-dimensional pressure coefficient is thus obtained simply as a ratio of pressure

differences and value of U is not needed. If U is needed (e.g., to calculate Reynolds

number) U can be obtained in a simple manner by assuming no frictional loss between

settling chamber and test section.

Under this assumption, U can be obtained as

( ) = pPU S2 (5.3)

If the manometer is graduated to give height of liquid column, Cp can be obtained as ratio

of column heights as shown below.

( ) ghhpp liquid =

and ( ) == hhppU SliquidS 221

Where,

hS = height of column in the tube connected to settling chamber.

h = height of the water column in the tube connected to the pressure port on the

configuration where pressure is being measured.

h = height of the column in the tube connected to test section

This gives ,

=pPppC

Sp

( )( )

=

hhghhg

Sliquid

liquid

=hhhh

S

(5.4)

Cp is then obtained as ratio of height difference of liquid columns.

By assuming zero frictional loss between settling chamber and test section U can be

obtained as

( ) = pPU S2

61

( ) ghhSliquid = 2 (5.5)

5.2.2 With Pre-Calibration of the Tunnel :

If the tunnel is pre-calibrated to give U, pressure coefficient can be derived in terms of

U.

( )

22

21

21

=

=U

ghh

U

ppC liquidp

If the manometer is inclined at 600, then

( )

2

0

21

60sin

=U

ghhC liquidp

If the liquid is water, height is graduated in cm and density of air is taken as 1.225 kg/m3,

then

( )

2225.121

866.081.91000

=

U

hhC p

( ) 270.138 = Uhh (5.6) Experimental measurement of pressure distribution on a few simple models are described

in the following sections. In all models several holes are drilled on the surface and

connected to the multi-tube manometer. Pressure distribution can then be obtained from

equation (5.4) or (5.6) depending on whether the tunnel is pre-calibrated or not. These

models include :

a) Circular cylinder model

b) Elliptical cylinder model

c) Spherical model

5.3 Pressure Distribution on Circular Cylinder Model : Exact analytical solutions are available for limited cases of direct potential flow

problems. The problem of two dimensional flow about a cylindrical body is one of such

62

problems. For steady, inviscid, incompressible irrotational flow, for which the governing

equation is Laplaces equation, the non lifting two dimensional flow about a cylindrical

body can be simulated by placing a doublet in uniform flow. The total velocity at any

point P (Fig. 5.2) is obtained as

sin2 = Uqt (5.7)

Figure 5.2 Circular cylinder in uniform flow

The pressure distribution can be obtained from Bernoullis equation,

22

2sin411

21

=

=

=

Uq

U

ppC tP (5.7)

It may be noted that the expression for total velocity or pressure is independent of the

diameter of the cylinder.

The ideal pressure distribution, given by equation (5.8), over the surface of the cylinder

will be symmetrical about the axis in the direction of the flow and about the plane normal

to it. Consequently, the net forces, lift and drag, are zero.

An experimental study can be undertaken to check how far the real solution deviates

from the ideal solution. For the case of uniform flow of real fluid, both the effects due

to compressibility and viscosity are to be taken into account. For the low speed test case

(0.1 Mach number) the effect due to compressibility may be justifiably ignored.

However, effect of viscosity alone will change the flow pattern considerably.

63

Primarily, the flow will be asymmetric about the axis normal to the uniform stream and

hence pressure distribution will also be asymmetric resulting in a net force (drag) acting

on the cylinder along the flow direction. However, the flow is still symmetrical about the

axis in the direction of the flow and hence no lift force acts on the cylinder.

Secondly, while the ideal flow is always attached to the body surface, in real fluid, the

flow may separate under adverse pressure gradient. In the forward face of the cylinder (

between 00 to 900), the flow speed increases and pressure decreases, hence the flow is not

likely to separate in this region. In the backward face, ( between 900 to 1800), the speed

decreases and pressure increases. Under the action of this increasing pressure (i.e.

adverse pressure gradient), the flow is likely to separate.

This separation is the so-called boundary layer separation. Since the flow velocity is

less in the boundary layer than in the free stream outside the boundary layer, the flow

separates in the boundary layer. The exact process of separation is yet little understood.

Generally speaking, at low speed the flow in the boundary layer is laminar and will be

attached to the body. Since the flow speed is less, kinetic energy associated with the flow

is also less, and the laminar flow is more susceptible to separation. As the flow speed is

increased, the boundary layer becomes turbulent. Transition for laminar to turbulent flow

is governed primarily by the Reynolds number of the flow.

The model chosen for experimental work is a circular cylinder of diameter 10.8 cm and

span 60.8 cm which extends from wall to wall (so that the flow is two dimensional).

Sixteen pressure holes are equally spaced at 0

2122 apart (Fig. 5.3) on the surface of the

cylinder and are connected to a multi-tube manometer.

Advantage, however, can be taken for this circular cylinder model. Only one hole can be

drilled and pressure at different points on the circular section can be obtained by simply

rotating the model (chapter 12).

64

Figure 5.3 Pressure holes on cylinder surface

Both the theoretical and experimental Cp distribution can now be obtained from equation

(5.8) and equation (5.4) or (5.6) and plotted against . The difference is due to viscous

effects.

The following table may be made for plotting Cp vs. (Fig. 5.4).

Table 5.1 : Pressure distribution on circular surface

Tap

points

hLS U h h Cp

(Theoretical) eq. (5.7)

Cp

(Experimental) eq. (5.6)

1. 0

2. 22.50

3. 450

-

16. 337.50

65

Cp

-Ve

0 90 180 270 300 330 360

+Ve

Figure 5.4 Pressure distribution on cylinder surface

5.4 Pressure Measurement on Elliptical Cylinder Model :

Exact analytical solution exists also for the case of potential flow about elliptical;