Evaluation of

Supersonic

Wind Tunnel

Submitted by:-

Siddharth Doshi

Roll No. : 07AE1022

Department of Aerospace Engineering

Indian Institute of Technology, Kharagpur

1. SUPERSONIC WIND TUNNELS

A supersonic wind tunnel is a wind tunnel that produces supersonic

speeds (1.2<M<5) The Mach number and flow are determined by the nozzle

geometry. The Reynolds number is varied changing the density level (pressure in

the settling chamber). Therefore a high pressure ratio is required (for a supersonic

regime at M=4, this ratio is of the order of 10). Apart from that, condensation or

liquefaction can occur. This means that a supersonic wind tunnel needs a drying

or a pre-heating facility. A supersonic wind tunnel has a large power demand

leading to only intermittent operation.

The power required to run a supersonic wind tunnel is enormous, of

the order of 50 MW per square meter of test section. For this reason most wind

tunnels operate intermittently using energy stored in high-pressure tanks. These

wind tunnels are also called intermittent supersonic blow down wind tunnels (of

which a schematic preview is given below). Another way of achieving the huge

power output is with the use of a vacuum storage tank.

1.1 Introduction:

Fig 1: Supersonic Wind Tunnel

The arrangement-namely, a convergent-divergent nozzle, a test

section, and a convergent-divergent diffuser- is a Supersonic Wind Tunnel (as

shown in the figure 1). A test model, (a cone, for example) is placed in the test

section, where aerodynamic measurements such as lift, drag, and pressure

distribution are made.

There are different types of wind tunnels; the kind of wind tunnel showed above

is an “Open circuit wind tunnel”. The different types are:

Closed circuit Wind tunnel

These have a return circuit and the air coming out of the exit is not allowed to

escape, rather it is made to go in a loop, it is compressed and sent back to the

settling chamber.

Open circuit Wind tunnel

These do not have a return circuit. The air is returned to the atmosphere. The

choice of such an arrangement might be dictated by the nature of power available

or lack of space for the return path.

Intermittent or Blow down pressure tunnels

They utilize an air supply from a storage plant. Flow is started by means of a quick

opening valve and lasts only until the pressure in the tank decreases to the value

that gives the minimum operating pressure ratio.

Intermittent vacuum tunnels

They use a vacuum sphere on the diffuser end, instead of a pressure tank on the

supply end. The supply in this tunnel is simply the atmosphere.

1.2 Component analysis:

The basic elements of a supersonic wind tunnel are:

Supersonic nozzle

The function of such a nozzle is to accelerate a stream from Mach

number unity to some desired final mach number. It is of the utmost importance,

in order that free flight is simulated, that the stream entering the test section be

uniform, parallel and shock free. Referring to fig 2, if the nozzle is symmetrical,

there must be a general divergence from the throat to the test section. Also

because of the symmetry, the center line is a stream line, and may be considered

a boundary of the flow for calculation purposes. Hence we need consider only

upper half of nozzle.

Fig 2: Supersonic nozzle

In order to have a net increase in area without any net change in the flow

direction, the wall contour must first curve out side from 7 to 3, and must then

curve in again until at the exit (point 1). Thus three separate zones may be

identified.

The expansion zone: 6-7-3-2-6, bounded by the throat 6-7, by characteristic 2-3

which on the center line symmetry attains the required test section Mach

number, and by the expansion portion of the nozzle wall 7-5-3. This a zone where

waves of both family are present

The test section: It is the region downstream of 1-2, where the flow is uniform and

parallel at test section Mach number ME. Because of the uniform, parallel flow,

the mach line 1-2 is straight, and is inclined a t the angle αE to the center line.

The straightening section 3-2-1: This is bounded by the Mach lines 3-2 and 2-1,

and by the straightening portion of the wall, 3-1. Since it is a general theorem that

only a zone of simple waves can be patched to a uniform, parallel flow it follows

that the zone 3-2-1 must have a simple wave flow such that all flow properties are

uniform on straight left running Mach waves in the zone.

Diffuser

In general one can define a diffuser as any duct designed to slow an

incoming gas flow to lower velocity at the exit of the diffuser. Needless to

mention that in case of a supersonic wind tunnel the incoming gas is supersonic.

However the shape of a diffuser is very different depending on whether the

incoming flow is subsonic or supersonic.

In any flow, the total pressure of the flowing gas is a measure of its

capability to perform useful work. On this basis, a loss of total pressure is always

an in-efficiency – a loss of the capability to do a certain amount of work. Hence

one could always expand the definition of a diffuser and say “a Diffuser is a duct

designed to slow an incoming gas flow to lower velocity at the exit of the

diffuser with as small a loss in total pressure as possible “. Consequently, an

ideal diffuser would be characterized by an isentropic compression to lower

velocities. Such a isentropic diffuser is shown in the figure below.

Fig 3: Diffuser

A supersonic flow enters the diffuser at M1, and is isentropically

compressed in a convergent duct to Mach 1 at the throat, where area of throat is

A*, and is further isentropically compressed in a divergent duct to a low subsonic

Mach number at the exit.

However, such an isentropic diffuser is extremely difficult to achieve

and to slow down a supersonic flow without generating shock waves is not

practically achievable. In the convergent portion the supersonic flow is turned

into itself and hence will inherently generate oblique shock waves which will

destroy the isentropic nature. Moreover in real life flow is viscous; and there will

be an entropy increase within the boundary layers on the walls of the diffuser. For

these reasons, an ideal isentropic diffuser can never be constructed.

1.3 Wind tunnel characteristics:

The energy of a closed circuit wind tunnel at steady state remains

constant. Thus the worked performed by the compressor is just equal to the heat

removed by the cooler,

W=Q

The above notion can be used to calculate an ideal value of the power

required for given pressure ratio and mass flow. In the wind tunnel circuit the

compressor and cooler are arranged as shown in fig 4.

Fig 4: Compressor-Cooler unit

Assuming that the heat transfer at cooler occurs reversibly, at constant

pressure the the relation between the heat per unit mass and the temperature is

q= cp (Tc – T0) = w

The temperature ratio Tc/T0 across the cooler is same as that across

the compressor. Assuming the compression to be reversible, Tc/T0 is related to the

pressure ratio by the isentropic relation:

Tc / T0 = (p0 / p’0) (γ-1)/ γ = λ (γ-1)/ γ

Thus the heat that must be removed, and the work that must be

supplied, per unit mass of fluid, is

w= γ R T0 (λ (γ-1)/ γ - 1 ) / (γ-1)

So the ideal wind tunnel power is then given by

P = mw = m γ R T0 ( λ (γ-1)/ γ - 1 ) / (γ-1)

Now the mass flow can be written using the throat as reference

section,

m = ρ*a*A* = ( 2 / (γ +1) )(1/2)( γ+1)/( γ-1)

Finally combining the above two equation, expression for the power

can be obtained as

P = ( γ / (γ-1) ) ( 2 / (γ +1) ) (1/2)( γ+1)/( γ-1) p0a0A*( λ (γ-1)/ γ - 1)

This shows that the power is proportional to the stagnation pressure,

the stagnation speed of sound, the throat area, and a function of the overall

pressure ratio. Since the work of the compressor is not actually done in the ideal,

reversible manner, the actual power required is higher than this ideal value .

2. EVALUATION OF SUPERSONIC WIND-TUNNEL IN THE DEARTMENT

The supersonic wind-tunnel present in the department aerodynamics

laboratory is blow-down type. Air is drawn from a tank containing air at high

pressure ( 5atm ) achieved using a compressor . The tank is 6ft. in diameter and

20 ft. in height. The test section is 5cm X 10cm. Air is blown into the tunnel,

where it is maintained at 25-28 psi at entry by a hand mechanism. Supersonic flow

at Mach number 2.2 is achieved. A diffuser is mounted at the end of the tunnel to

decrease the exit velocity to 3-10 m/s. Pressure gauges are fixed at various

positions to monitor pressure. The laboratory tunnel incorporates a supersonic

nozzle contour which has been designed using the method of characteristics

including an empirical correction for boundary layer growth which is an important

factor at high speeds in order to get shock-free inviscid supersonic nozzle. The

tunnel is equipped with a Schlieren system for shock observation. The installation

is suitable for the study of compressible fluid flow and the phenomenon of

normal shocks. Because of changes in temperature and compression in tank,

there is possibility of sum air changing into liquid state. To counter this 10000

small cylindrical cans are fixed in the tank which continuously removes moisture

from tank. Sometimes additional heating may be required. The supersonic wind

tunnel in our department is shown below:

Fig 5: The supersonic wind tunnel in

our department

Determination of Mach Number : Mach number (M) has been determined using four different techniques:

Schlieren Method is used to observe the shock wave over a wedge and then

, , M relation is used to calculate the Mach number.

Using Area- local Mach Number relationship.

Using static pressure measurement on the wall of test section.

Using Rayleigh-Pitot’s formula .

2.1 Using The Schlieren Method : The Schlieren apparatus for this experiment, shown schematically in

figure below, uses lenses, although for larger systems with long focal lengths

mirrors are customarily employed since these are less expensive than lenses for

comparable size and optical performance.

Fig 6: Schlieren Optical System

We have used schlieren system to determine the flow conditions

around a wedge. A shock wave is formed when supersonic flow passes over

the wedge.

Fig 7: Shock wave over the wedge From the experiment , the value of = 12.5o

the value of = 37o

The , , M relation, given below, can be used to determine the flow

Mach number .

where is the adiabatic index of air(= 1.4).

Putting the values of , in this relation , we get

2.2 Using Area- Local Mach Number Relationship: The areas of cross section at throat A* and any other cross section A of

nozzle are related to the mach number at the latter cross section as

We measure area of throat and area at exit and put them in the above

equation. Width is same all through out the nozzle. So we just measure heights. If

‘w’ is the width then

From experiment , A= 11.2 * w

A*=3.8 * w

Solving the equation using Matlab, we get the value of M to be

M=2.2213

M=2.6334

Fig 8: Solution obtained with Matlab .

2.3 Using Static Pressure Measurement on the Wall of Test Section : If P is the static pressure on the walls of test section and Po is the total pressure inside the test section then they are related by the following relation :

12

2

11

M

P

Po

=>

11

21

2

P

PM o

The static pressure P is recorded on a Hg – U tube and using

∆h = 47.8 cm and –ve sign should be taken in above equation. 1 cm of Hg = 1.3366 kNm-2 Therefore P = 37435.52 Nm-2 Total pressure as given by gauge pressure meter is 30 psi. Patm = 14.7psi. Therefore total pressure Po = 29 + 14.7 = 43.7 psi = 301355.5 Nm-2 Calculated Mach Number = 2.0173.

Manometer specifications: 100 divisions = 20 mb

1 division = 20 Nm-2 From experiment, the difference between the static pressure and total pressure at the exit of the diffuser was found to be 5 manometric divisions. So velocity at the end of diffuser:

Vexit= (5*20*2/1.225) ^ (1/2)

Therefore Vexit=12.65 ms-1, which is substantially lower than what we have inside

the test-section (around 700 m/sec)

2.4 Using Rayleigh – Pitot’s Formula : Because of the shock wave formation near the pitot tube , the flow

conditions differ on the side of pitot tube .

M= 2.0173

Fig 9: Pitot-tube in supersonic flow where P1 is static pressure at station 1 and P02 is total pressure at station 2 . Rayleigh – Pitot’s formula realtes these two quantities as

1

2

1

1

2

02

1

2

1

1

1

1

2

M

M

P

P

From experiment , P1 = [Patm + (1.3366 x 103 x ∆h1 )] Nm-2

P02 = [Patm + (1.3366 x 103 x ∆h2 )] Nm-2 ∆h1= -57.7 cm and ∆h2 =71.2 cm . Therefore P1 = 24203.18 Nm-2 and P02 = 196490.92 Nm-2 Putting up these values and =1.4, solving using Matlab, we get

M=2.4355

Fig 10: Solution obtained with Matlab

Conclusion: Thus the departmental supersonic wind tunnel has been evaluated. The Mach number of the flow calculated using all the four methods was around 2.2.

Report prepared under the guidance of

Prof. G. Bandyopadhyay (Department of Aerospace Engineering, IIT Kharagpur)