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HIGHSPEED AERODYNAMICS

AER134 3 0 0 100

UNIT-5

5. HIGH SPEED WIND TUNNELS 9Blow down, indraft and induction tunnel layouts and their design features,

Transonic, supersonic and hypersonic tunnels and their peculiarities, Helium

and gun tunnels, Shock tubes, Optical methods of flow visualization.

Introduction to Wind Tunnel

The "Wind tunnel" is a facility, by artificially producing airflow relative to a

stationary body, that measures aerodynamic force and pressure distribution

to simulate the actual flight of airplane or orbiting plane in the air.

Francis Herbert Wenham (1824-1908), a Council Member of theAeronautical Society of Great Britain, reported as the inventor anddesigner of the first enclosed operating wind tunnel in 1871.

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A wind tunnel is a research tool developed to assist with studying theeffects of air moving over or around solid objects.

Ways that wind-speed and flow are measured in wind tunnels: Threads can be attached to the surface of study objects to detect flow

direction and relative speed of air flow.

Dye or smoke can be injected upstream into the air stream and thestreamlines that dye particles follow photographed as the experimentproceeds.

Pitot tube probes can be inserted in the air flow to measure static anddynamic air pressure.

Particle image velocimetry (PIV) can be used for flow visualization study.

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Different types of wind tunnels

Wind tunnels are often denoted by the speed in the test section relative to thespeed of sound. The ratio of the air speed to the speed of sound is called the Mach

number.Tunnels are classified as

subsonic (M < 0.8), transonic (0.8 < M < 1.2) , supersonic (1.2 < M < 5.0) , or hypersonic (M > 5.0).

The distinction by Mach number is caused by the relative importance ofcompressibility effects.

For subsonic flows, we may neglect the effects of compressibility. For transonic and supersonic flows, compressibility effects must be considered. For hypersonic flows, we must make additional considerations for the chemical

state of the gas. The scaling effects of the Mach number can be theoretically derived from theconservation of momentum of the air in the tunnel.

Compressibility affects the design of the test section of a wind tunnel: forsubsonic tunnels, the test section has the smallest cross-sectional area of thetunnel; for supersonic tunnels, the throat of the nozzle has the smallest area and

the test section area is chosen to achieve a desired Mach number in the test

section.

Wind tunnels in general are used for testing purposes and aero-dynamicaloptimization.

They are specially designed to simulate airflow like in open air and flow velocityas close as possible to reality.

It is of great importance to avoid non-uniformities, because a slight difference inairflow may change the behaviour of the tested object, and furthermore provide

false information to the aerodynamicist, who consequently make the wrongdecisions.

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There is always a small vent, called a "breather", somewhere in the circuit so that the

internal pressure does not increase as the air heats up during the run.The breather is best located in a part of circuit where inner air is close to atmospheric

pressure. Usually that is around the perimeter at the downstream end of the test section.

This compensating inflow through the breather is bad for diffuser performance but easy

to detect by releasing smoke just outside the breather.

Model Test and Scale Effect

Example on the importance of Reynolds Number

If an aero plane needs testing of its wing, one can make a scaled down small

model of the wing and test the wing as table top model in the lab with thesame Reynolds number the actual air plane is subjected to.

The results of the lab model will be exactly similar to that of the actual plane wingresults. Thus we need not bring a plane into the lab to test it actually. This is the

example of "dynamic similarity."

This is what Reynolds number is all about.

Since a real airplane is too large to be accommodated to a test section in the windtunnel, a reduced scale model with same shape as the real airplane is usually used.

In the wind tunnel test, two parameters, Mach and Reynolds numbers, musthave the same value to simulate real airplane flight with high fidelity.

Mach number is the ratio of flow velocity to sound velocity.

Mach number is assumed to be zero in low speed wind tunnel that does not takethe compressibility of airflow into account.

Reynolds number depends on velocity, density and viscosity of the flow (usuallyairflow) and model size.

But it is difficult to adjust the Reynolds number in the wind tunnel test to that ofreal airplane.

The wind tunnel test requires not only the production of airflow with good qualityand the accurate measurement of aerodynamic forces and pressure, but also theReynolds number correction to the data obtained.

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Differences between flight and wind tunnel tests are induced by not onlyReynolds number but also test section wall that does not exist in the flight test andmodel support system (strut etc.) in the test section.

Therefore high fidelity simulation of the flight of real airplane through the

removal of these adverse effects is the main technical problem of wind tunnel test.

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MEASURING AIR VELOCITY

AND PRESSURE

Consider the subsonic wind tunnel shown in the above figure. Often, the velocity of the

air in the test section (v2) is important to know. Also, many times it is desirable to changethe velocity of the air with in the test section and look at how our test object responds at

different velocities.

We can use the continuity equation and Bernoullis equation to help us measure thevelocity in the test section (v2).

Continuity equation:

v1A1= v2A2

Bernoullis equation:

p1+ v12

= p2+ v22

( )[ ]21221

2/1(

)(2

AA

ppv

=

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We can easily find the velocity of the test section, v2 with this equation. We know theratio of the area of the inlet to the ratio of the test section (A2/A1) by measuring. The

pressure difference between the test section and the inlet can be measured with a

manometer.

COEFFICENT OF PRESSURE CALCULATION

Coefficient of Pressure is a dimensionless number since the units in the formulaswill be in the form of a ratio and cancel out. The equation used to calculate thecoefficient of pressure is:

Where:Cp = Coefficient of Pressure

P = the pressure of the airfoil - the pressure of the wind tunnel

= densityv = velocity of the wind tunnel

Cp =P

1

2

v2

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Requirements of the wind tunnel models

The mass forces of the model must be as small as possible, in order to receive afavorable relationship from aerodynamic forces and moments to the mass and

inertial forces.

The elastic deformation should be as small as possible.

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Wind Tunnel Design

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Wind tunnels are designed for a specific purpose and speed range. Therefore,

there are many different types of wind tunnels and several different ways to

classify wind tunnels.

Blowdown tunnels are normally used from high subsonic to high supersonic flowconditions.

There are several possible configurations for a blowdown tunnel. On the figure,we show completely closed supersonic configuration. The test section sits at theend of a supersonic nozzle.

The Mach number in the test section is determined by pressure andtemperature in the plenum and the area ratio between the test section and

the nozzle throat.As the flow expands in the nozzle, the pressure decreases and

any moisture in the tunnel may condense and liquefy in the test section. To

prevent condensation, air is brought into the tunnel through a dryer bed. The air ispumped into a closed high pressure chamber upstream of the plenum. At the same

time, air is pumped out of a closed low pressure chamber downstream of the test

section.

Test times are limited in blowdown wind tunnels. At the beginning of the test run, valves are opened upstream and downstream of

the test section.

The pressure ratio establishes a supersonic flow in the test section and the airflows from the high pressure chamber to the low pressure chamber.

As air leaves the high pressure chamber, the pressure in the chamber decreases. Likewise, as air enters the low pressure chamber, the pressure in that chamber

increases.

Eventually, the pressure in the two chambers equalized, the flow stops, and thetest is finished.

To provide constant conditions in the test section, a pressure regulator valve isnormally installed in the plenum.

A second throat is often employed downstream of the test section to shock downthe supersonic flow to subsonic before entering the low pressure chamber.

A closed configuration with both high pressure and low pressure chambers isshown in the figure, but there are other configurations of blowdwon tunnels.

Some blowdown tunnels, called indraft tunnels, do not use a high pressurechamber, but open the plenum chamber to the atmosphere.

The indraft tunnel uses the low pressure (vacuum) chamber downstream of thetest section to produce flow.

The advantage of this configuration is that the conditions in the plenum remain

constant and there is no need for a pressure regulator. The disadvantage is that the pressure ratio across the test section is usually lower

than a closed configuration and therefore the maximum Mach number is lower. Another configuration retains the high pressure chamber, but exits to atmosphere

instead of into a low pressure chamber.

The advantage of this configuration is that it is cheaper than a closedconfiguration in both construction and operation. But the tunnel is very loud and

normally requires some type of muffler downstream of the test section.

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Advantages of the Blowdown Tunnel High Mach capability. Easy tunnel "starting". Lower construction and operating costs. Superior design for propulsion and smoke visualization. There is no accumulation

of exhaust products in an open tunnel. Smaller loads on model during startup because of faster starts.

Disadvantages of the Blowdown Tunnel Shorter test times require faster (often more expensive) instrumentation. Need for pressure regulator valves. Noisy operation.

Power requirements

The power required to run a supersonic windtunnel is enormous, of the order of50 MW per square meter of test section. For this reason most wind tunnels

operate intermittently using energy stored in high-pressure tanks.

These windtunnels are also called intermittent supersonic blowdown windtunnels. Another way of achieving the huge power output is with the use of a

vacuum storage tank. These tunnels are called indraft supersonic wind

tunnels.Other problems operating a supersonic wind tunnel include: enough supply of dry air wall interference effects fast instruments needed for intermittent measurements

Tunnels such as a Ludwieg tube have short test times (usually less than onesecond), relatively high Reynolds number, and low power requirements.

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Ludwieg tube

The Ludwieg Tube was invented by Hubert Ludwieg (1912-2000) in 1955 in response to

a competition for a transonic or supersonic wind tunnel design that would be capable of

producing high Reynolds number at low operating cost.

A Ludwieg tube is a cheap and efficient way of producing supersonic flow. Mach

numbers up to 4 are easily obtained without any additional heating of the flow, withheating Mach numbers of up to 11 can be reached.

Principle A Ludwieg tubeis a wind tunnel that produces supersonic flow for short periods

of time.

A large evacuated dump tank is separated from the downstream end of aconvergent-divergent nozzle by a diaphragm or fast acting valve.

The upstream end of the nozzle connects to a long cylindrical tube, whose cross-sectional area is significantly larger than the throat area of the nozzle.

Initially, the pressure in the nozzle and tube is high. To start the tunnel, the diaphragm is

ruptured, e.g., by piercing it with a suitable cutting device, or opening the valve

respectively.As always when a diaphragm ruptures, a shock wave propagates into the low-pressure

region (here dump tank) and an expansion wave propagates into the high-pressure region

(here the nozzle and long tube).As this unsteady expansion propagates through the long tube, it sets up a steady subsonic

flow toward the nozzle, which is accelerated by the convergent-divergent nozzle to a

supersonic condition.

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The flow is steady until the expansion, having been reflected from the far end of the tube,

arrives at the nozzle again.For practical reasons, flow times are on the order of 100 milliseconds. For many purposes

this is a flow duration that is quite sufficient.

Shock tube

A shock tubeis a device used primarily to study gas phase combustion reactions.Shock tubes (and related shock tunnels) can also be used to study aerodynamic

flow under a wide range of temperatures and pressures that are difficult to obtainin other types of testing facilities.

Working of Shock Tube

A simple shock tube is a metal tube in which a gas at low pressure and a gas athigh pressure are separated using a diaphragm. This diaphragm suddenly bursts

open under predetermined conditions to produce a shock wave that travels down

the low pressure section of the tube. This shock wave increases the temperature

and pressure of the gas and induces a flow in the direction of the shock wave,creating the conditions desired for the testing being done.

Once the incident shock wave reaches the end of the shock tube, it is reflectedback in to the already heated gas, resulting in a further rise in the temperature,pressure and density of the gas.

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Applications of Shock Tube

For aerodynamic testing, the fluid flow induced in the driven gas (The low-pressure gas, referred to as the driven gas) behind the shock wave can be used

much as a wind tunnel is used. Shock tubes allow the study of fluid flow at temperatures and pressures that

would be difficult to obtain in wind tunnels (for example, to replicate theconditions in the turbine sections of jet engines).

The duration of the testing is limited, though, by the time available between thepassage of the shock wave and the arrival of either the contact surface or the

reflection of the shock wave off the end of the tube. In practice, this usually limits the available test time to a few milliseconds. A further development for aerodynamic testing is the shock tunnel, where a

nozzle is placed between the end of the tube and a dump tank. As the shock wavereflects off the end of the tube it creates a region of very high pressure and

temperature. Since the dump tank is pumped down to a low pressure (nearvacuum), there is a very large pressure difference across the nozzle.

Using a shock tunnel, very high temperature hypersonic flow can be createdin the test section, located immediately behind the nozzle. This allows testing

in conditions that can simulate re-entry of spacecraft or hypersonic

transport; but again testing time is limited to the order of milliseconds.A hypersonic wind tunnelis designed to generate a hypersonic flow field in the working

section. The speed of these tunnels vary from Mach 5 to 15. As with supersonic wind

tunnels, these types of tunnels must run intermittently with very high pressure ratioswhen initializing. Since the temperature drops with the expanding flow, the air inside has

the chance of becoming liquefied. For that reason, preheating is particularly critical (the

nozzle may require cooling). High pressure and temperature ratios can be produced witha shock tube.

There are several technological problems in designing and constructing a hyper-velocitywind tunnel:

supply of high temperatures and pressures for times long enough to perform ameasurement

reproduction of equilibrium conditions

structural damage produced by overheating

fast instrumentation

power requirements to run the tunnel

Simulations of a flow at 5.5 km/s, 45 km altitude would require tunnel temperatures of as

much as 9000 K, and a pressure of 3 GPa.

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The precise Mach number at which a craft can be said to be flying at hypersonic speed

varies, since individual physical changes in the airflow (like molecular dissociation andionization) occur at different speeds; these effects collectively become important around

Mach 5. The hypersonic regime is often alternatively defined as speeds where ramjets do

not produce net thrust.

Subsonic tunnel

Low speed wind tunnels are used for operations at very low mach number, with speeds inthe test section up to 400 km/h (~ 100 m/s, M = 0.3). They may be of open-return type, orclosed-return flow with air moved by a propulsion system usually consisting of large

axial fans that also increase the dynamic pressure to overcome the viscous losses.

Open wind tunnel

The working principle is based on the continuity and Bernoulli's equation:

The continuity equation is given by:

The Bernoulli equation states:

Putting Bernoulli into the continuity equation gives:

The contraction ratio of a windtunnel can now be calculated by:

Closed wind tunnel

In a return-flow wind tunnel the return duct must be properly designed to reduce thepressure losses and to ensure smooth flow in the test section. The compressible flow

regime: Again with the continuity law, but now for isentropic flow gives:

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The 1-D area-velocity is known as:

The minimal area A where M=1, also known as the sonic throatarea is than given for aperfect gas:

Transonic tunnel

High subsonic wind tunnels (0.4 < M < 0.75) or transonic wind tunnels (0.75 < M < 1.2)are designed on the same principles as the subsonic wind tunnels. Transonic wind tunnels

are able to achieve speeds close to the speeds of sound. The highest speed is reached inthe test section. The Mach number is approximately one with combined subsonic andsupersonic flow regions. Testing at transonic speeds presents additional problems, mainly

due to the reflection of the shock waves from the walls of the test section (see figure

below or enlarge the thumb picture at the right). Therefore, perforated or slotted walls are

required to reduce shock reflection from the walls. Since important viscous or inviscidinteractions occur (such as shock waves or boundary layer interaction) both Mach and

Reynolds number are important and must be properly simulated. Large scale facilities

and/or pressurized or cryogenic wind tunnels are used.

de Laval nozzle

With a sonic throat, the flow can be accelerated or slowed down. This follows from the 1-D area-Velocity equation. If an acceleration to supersonic flow is required, a convergent-

divergent nozzle is required. Otherwise:

Subsonic (M < 1) then converging

Sonic throat (M = 1) where

Supersonic (M >1 ) then diverging

Conclusion: The Mach number is controlled by the expansion ratio

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Schlieren technique:In this technique the density gradient in the flowfield is obtained in terms of the varying degree of the brightness on the screen; the degree

of brightness or intensity of illumination is proportional to the density gradient into the

flow field. The arrangement adopted in schlieren technique is shown in the below figure.

A beam of light is sent through the test section from the light source by a properly

oriented concave mirror M1. The beam coming from the test section is reflected on to thescreen or a photographic plate through two suitably located concave mirrors M2.and M3.

A sharp knife edge is inserted at the focal point of the mirror M2.to intercept half the

light. Thus in the absence of the flow through the test section the screen is illuminated

uniformly by the light escaping the knife edge. But in the presence of flow the rays oflight are differently deflected (as in a prism) on account of the variable density and the

refractive index in the flow field. Therefore grater or lesser part of the light beam will

now escape the knife edge. This gives a varying intensity of the illumination on thescreen.

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Gun Tunnels

The conventional high Mach number supersonic tunnels suffer from serious

disadvantages of low temperature in the test section; this is overcome in the shock tube

by accelerating the flow by a shock wave. The same principle in a slightly different wayis employed in the gun tunnels. Here very strong shock waves are generated by a moving

piston.

In a typical gun tunnel a multistage compressor raises the pressure of nitrogen to about10,000 bar in a strong reservoir. One or more 5mm thick diaphragms are punctured insuccession which forces the flow in a thick walled cylinder provided with piston. The

movement of the piston and the resulting strong shock waves downstream generate very

high Mach numbers (~ 10) in the test section. If the downstream pressure in the duct isreduced to a very small value still higher Mach number (~20) can be obtained. Such

tunnels are used for studying hypersonic and non-equilibrium flows and meteorological

problems.

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Schematic drawings of the 3.5-foot hypersonic wind tunnel

Schematic drawing of the 3.5-foot tunnel pebble-bed heater

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The pebble-bed heater, though serving perhaps for Mach numbers from 5to 10, could not, it was clear, provide the heat required for representing theconditions encountered by reentry bodies. There was yet, however, a

possibility of accomplishing this objective in a tunnel capable of operating forreasonably long periods of time. This possibility lay in the use of an electric arc toheat the air as it passed through the tunnel. The initial investigation of arc-heated

jets was made in 1956 by Jeff Buck, R. W. Eglington, A. Kamiya, Merrill Nourse,and others. Later the work was continued by William Carlson and Carl Sorenson.First investigated were some arc-jet ideas, which had originated in Germany.This study, however, was just the beginning of work. Aside from keeping thetunnel walls and electrodes from melting, one of the problems in the design of anarc-jet facility arose from the contamination of the air by vaporized material fromthe electrodes. The problems in the development of a practical arc-jet tunnelwere obviously great, but the need for such a facility was also great and the

project was pushed with ever increasing vigor.\

Sketch of hypersonic wind

NASA JPL's Hypersonic Wind Tunnel

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Illustration of the 8'x6'/9'x15' Wind Tunnel Complex

Description

The 8- by 6-Foot Supersonic Wind Tunnel (8x6 SWT) is an atmospheric tunnel with

perforated stainless steel walls that provide boundary layer control during transonic

operations. It is the only transonic propulsion wind tunnel at NASA. Aircraft such as theAdvanced Turboprop, the National Aerospace Plane, the Advanced Tactical Fighter, the

Joint Strike Fighter and the High Speed Civil Transport have been tested in this facility.

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Schematic of a supersonic wind tunnel

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ISENTROPIC FLOW OF A CALORICALLY PERFECT GAS

THROUGH VARIABLE AREA DUCTS

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We have,

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Supersonic Wind Tunnel Design Let us go through a small thought experiment.

Assume that we want to design a supersonicwind tunnel with a test section Mach number of 3(see Fig. 5.6). Some immediate information aboutthe nozzle is obtained from Gas Table A.I;

at M = 3, Ae/A* = 4.23 and po/pe = 36.7.

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A second alternative is to exhaust the nozzle into aconstant area duct which serves as the test section,and to exhaust this duct into the atmosphere, assketched in Fig. 5.15.

In this case, because the testing area is inside theduct, shock waves from the duct exit will not affectthe test section. Therefore, assume a normal shockstands at the duct exit.

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The static pressure behind the normal shock is p2, and because theflow is subsonic behind the shock, p2 = p = 1 atm. In this case, thereservoir pressure p0 is obtained from where p2/pe is the staticpressure ratio across a normal shock at Mach 3, is obtained fromTable A.2.

Note that, by the simple addition of a constant-area ductwith a normal shock at the end, the reservoir pressure

required to drive the tunnel has markedly dropped from36.7 to 3.55 atm.

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Normal shock properties

Find out the reservoir pressure required to drive the tunnel at M=4.5 at test section

Now, as a third alternative, add a divergent duct behind the normalshock in Fig. 5.15 in order to slow the already subsonic flow to alower velocity before exhausting to the atmosphere.

This is sketched in Fig. 5.16. At the duct exit, the Mach number is avery low subsonic value, and for all practical purposes the localtotal and static pressure are the same.

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Moreover, assuming an isentropic flow in the divergent duct behindthe shock, the total pressure at the duct exit is equal to the total

This is even better yetthe total pressure required to drivethe wind tunnel has been further reduced to 3.04 atm.

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The normal shock and divergent exhaust duct in Fig. 5.16 are actingas specific mechanism to slow the air to low subsonic speeds beforeexhausting the atmosphere. Such mechanisms are called diffusers,and their function is slow the flow with as small a loss of totalpressure as possible.

The ideal diffuser would compress the flow isentropically, hence with

no loss of total pressure. For example, consider the wind tunnelsketched in Fig. 5 6.

After isentropically expanding through the supersonic nozzle andpassing through the test section, conceptually the supersonic flowcould be isentropically compressed by the convergent part of thediffuser to sonic velocity at the second throat, and then furtherisentropically compressed to low velocity in the divergent sectiondownstream of the throat.

This would take place with no loss in total pressure, and hence thepressure ratio required to drive the tunnel would be unity aperpetual motion machine! Obviously, something is wrong. Theproblem can be seen by reflecting on the results of Chap. 4.!

When the convergent part of the diffuser changes the direction ofthe supersonic flow at the wall, it is extremely difficult to preventoblique shock waves from occurring inside the duct. Moreover, even

without shocks, the real-life effects of friction between the flow andthe diffuser surfaces cause a loss of total pressure. Therefore, thedesign of a perfect entropic diffuser is physically impossible.

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Supersonic Flow

.Airspeed measurements in supersonic flow, that is, forM >1, are qualitatively different from those for subsonic flow. Insupersonic flow, a shock wave will form ahead of the Pitottube, as shown in Fig. 4.21. Shock waves are very thinregions of the flow (for example, 10~

4cm), across which

some very severe changes in the flow properties takeplace. Specifically, as a fluid element flows through ashock wave,

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Shock wave

Figure 4.22 Changes across a shock wave in front of a Pitot tube in supersonic flow.

1. The Mach number decreases.2. The static pressure increases.3. The static temperature increases.4. The flow velocity decreases.5. The total pressurepo decreases. 6. The total temperature Tostays the same for a perfect gas.

These changes across a shock wave are shown in Fig. 4.22.

How and why does a shock wave form in supersonic flow? These are variousanswers with various degrees of sophistication. However, the essence is as follows.Refer to Fig. 4.16, which shows a Pitot tube in subsonic flow. The gas molecules thatcollide with the probe set up a disturbance in the flow. This disturbance is

communicated to other regions of the flow, away from the probe, by means of weakpressure waves (essentially sound waves) propagating at the local. speed of sound. Ifthe flow velocity V1 is less than the speed of sound, as in Fig. 4.16, then thepressure disturbances (which are traveling at the speed of sound) will work their wayupstream and eventually will be felt in all regions of the flow. On the other hand, referto Fig. 4.21, which shows a Pitot tube in supersonic flow. Here V1is greater than thespeed of sound. Thus, pressure disturbances that are created at the probe surface andthat propagate away at the speed of sound cannot work their way upstream. Instead,these disturbances coalesce (unite) at a finite distance from the probe and form anatural phenomenon called a shock wave, as shown in Figs. 4.21 and 4.22. The flowupstream of the shock wave (to the left of the shock) does not feel the pressuredisturbance; that is, the presence of the Pitot tube is not communicated to theflow upstream of the shock. The presence of the Pitot tube is felt only in the

regions of flow behind the shock wave.Thus, the shock wave is a thin boundary in asupersonic flow, across which major changes in flow properties take place and whichdivides the region of undisturbed flow upstream from the region of disturbed flowdownstream.

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