HIGH SPEED FLOW EXPERIMENTS

LABORATORY MANUAL

DEPARTMENT OF AEROSPACE ENGINEERING

INDIAN INSTITUTE OF TECHNOLOGY MADRAS
Tamil Nadu - 600036

July 29, 2015

 Contents

1 Nozzle Flow and Critical Pressure Ratio 3

2 Pressure curve in the Laval Nozzle 6

3 Shock Location in CD Nozzle using Compressible Flow unit 9

4 Pitot measurement in Supersonic Wind-tunnel 11

5 Shock Tube 13

6 Schlieren and Shadowgraph Optical Flow Visualization Techniques 16

7 Supersonic Flow past Diamond Wedge Airfoil 18

8 Flow past NACA 0012 airfoil in Transonic Wind tunnel 20

1
 List of Figures

1 Mass flow rate of a CD nozzle at various back pressures . . . . . . . . . . . . . . 4

2 Experiment setup of the converging diverging nozzle with pressure ports (not to
scale). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3 Pressure variation through converging-diverging nozzle. . . . . . . . . . . . . . . 6
4 Nozzle with gradual expansion (not to scale) . . . . . . . . . . . . . . . . . . . . 7
5 Pitot-tube in a supersonic flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
6 Schematic diagram of the shock tube facility (not to scale) . . . . . . . . . . . . . 13
7 Schematic diagram of the Z-folded Schlieren flow visualization technique using
mirrors (not to scale) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
8 Examples of optical flow visualization. . . . . . . . . . . . . . . . . . . . . . . . . 17
9 Diamond wedge airfoil in supersonic flow . . . . . . . . . . . . . . . . . . . . . . . 18

2
 1 Nozzle Flow and Critical Pressure Ratio

Objective

• Find the critical pressure ratio and compare it with the theoretical value.

• Obtain the mass flow rate through the nozzle and compare the results with theoretically
calculated mass flow rate.

Theory

Flow is induced by the pressure difference across the nozzle. As the reservoir pressure is equal
to the atmospheric pressure the reduction of receiver pressure from this value drives the flow
through the nozzle. Correspondingly the flow velocity increases at the throat. The flow rate
through a nozzle depends on the velocity in the smallest cross-section(throat) and can reach at
maximum sound velocity. The maximum possible flow rate (also called as choked flow) through
a nozzle is therefore limited and is not related to the pressure ratio. The critical pressure ratio,
pcr
p0 , is the point at which the sound velocity is reached in the smallest cross-section. It depends
solely on the type of medium and its isentropic exponent γ.

  γ
pcr 2 γ−1
= = 0.53 for air
p0 γ+1

The mass flow rate through the nozzle can be calculated as,

 γ+1
γ − 1 2 − 2(γ−1)  γ 1/2 p0

ṁ
=M 1+ M √
A 2 R T0

where,
pcr = Critical pressure
p0 = Total pressure
T0 = Total temperature
ṁ = Mass flow rate
A = Area of cross-section
M = Mach number
R = characteristic gas constant
γ = ratio of specific heats
And therfore the maximum mass flow rate (ie., at M = 1) is,

3
 Figure 1: Mass flow rate of a CD nozzle at various back pressures

"   γ+1 #1/2

ṁ γ 2 γ−1 p
∗
= √0
A R γ+1 T0

Once critical pressure is achieved at the throat section, further reduction in the back pressure
(or increase in the fan rpm) does not change the pressure or velocity at the converging section
of the nozzle, and the mass flow rate remains constant thereafter [1].

Procedure

• Attach Laval nozzle and measuring nozzle to the intake connection using union nuts.

• Connect the pressure measurement point p1 to the negative connection of the manometer
0-1 bar at the smallest cross-section.

• Connect the pressure measurement point for the measuring nozzle to the negative con-
nection of the velocity display.

• Switch on compressor and adjust gradually.

• Record velocity c at the measuring nozzle, rotational speed n and pressure p1 at the Laval
nozzle.

• Repeat measurements until the fan reaches the maximum speed.

Figure 2: Experiment setup of the converging diverging nozzle with pressure ports (not to scale).

4
Observations

Atmospheric pressure, p0 = ..........

Table 1: Experimental observations

Si No. RPM p1 ṁ v

Apparatus

• Nozzle with a gradual expansion

• Compressible flow unit

• Pitot probe

Results

• Obtain the value of critical pressure.

• Calculate the maximum mass flow rate through the nozzle.

• Plot mass flow rate and throat pressure ratio as a function of back pressure or fan rpm.

Discussion

• Discuss the reason for the variation between experimental and theoretical obtained results.

Conclusion...

5
 2 Pressure curve in the Laval Nozzle

Objective

• Understand the flow characteristics of a convergent-divergent nozzle with respect to the

change in back pressure.

Theory

One-dimensional steady flow is assumed with a hypothetically large reservoir and receiver.
Atmosphere is acting as the reservoir and therefore, p0 = atmospheric pressure. Before starting
the experiment both the receiver and the reservoir are having the same pressure and therefore
there won’t be any flow through the nozzle. As the fan rpm increases the receiver pressure
reduces and flow begins.
At a particular back pressure termed as ”First critical Pressure” flow becomes ’choked’ and
sonic condition is achieved at the throat, and the flow through the diverging section remains
isentropic and subsonic corresponding to a pure venturi case where back pressure will be equal to
the exit pressure of the nozzle. As the back pressure reduces from first critical pressure, a normal
shock appears in the diverging section of the nozzle. This normal shock moves downstream with
a reduction in back pressure.

Figure 3: Pressure variation through converging-diverging nozzle.

”Second critical pressure refers to a case where the normal shock stands at the exit of the

6
nozzle. Between first and second critical pressures the diverging section acts as a nozzle until it
experience the normal shock and thereafter acts as a diffuser. In all these cases back pressure
will be equal to the exit pressure of the nozzle. When the back pressure reaches ”Third critical
pressure”, fully isentropic supersonic flow is achieved in the diverging nozzle. This condition
is known as the fully expanded case or design condition for the particular nozzle. As the
receiver condition is between second and third critical pressures the nozzle exit pressure will
be lesser than the back pressure and oblique shocks are present at the exit, this is termed as
over-expansion. A further reduction of back pressure below third critical pressure results in a
higher nozzle exit pressure and there will be expansion fans at the exit of the nozzle, which is
referred as under-expansion.

Procedure

The experiment is set up in the same way as the previous experiment.

• Switch on compressor and set to 25000 rpm.

• Connect the manometer 0-1 bar in sequence to the pressure measurement points p1 to p5 .

• Record velocity c at the measuring nozzle, rotational speed and pressure p1 to p5 at the
Laval nozzle.

Repeat measurements at maximum speed (approx. 34000 rpm).

Figure 4: Nozzle with gradual expansion (not to scale)

Observations

Atmospheric pressure, p0 = ..........

Table 2: Experimental observations

Si No. RPM p1 p2 p3 p4 p5

7
Apparatus

• Nozzle with a gradual expansion

• Compressible flow unit

• Pitot probe

Results

• Plot the pressure distribution along the axis of the nozzle for different values of back
pressures.

Discussion

• In case of jet aircraft, the nozzle usually operates in under-expanded condition. Discuss
the correctness of the statement.

Conclusion...

8
3 Shock Location in CD Nozzle using Compressible Flow unit

Objective

• Obtain the shock location in a CD nozzle using compressible flow unit and compare the
result with theoretically obtained shock location.

Theory

Shock location from experiment

For a fully expanded nozzle the pressure sensors readings on the diverging section of the nozzle
continuously decreases. If the continuously decreasing readings shows a sudden increase in the
measurement from one pressure sensor to the other it represents the presence of standing normal
shock between those two sensors.

Shock location from theory

The mass flow rate across the nozzle remains constant once the nozzle is chocked, and the value
can be calculated as,

"  γ+1 #1/2

p0 A∗

γ 2 γ−1
ṁ = √
R γ+1 T0

Therefore at the exit of the nozzle,

s  
γ γ−1 2
ṁ = ρe Ae ve = pe Ae Me 1+ Me
R 2

This can be re-written as a quadratic equation in terms of Me2 as,

s !
γ−1 ṁ R
(Me2 )2 + (Me2 ) − =0
2 p e Ae γ

and can be solved to obtain the exit mach number (Me ). The total pressure behind the
p02
shock is calculated from isentropic table for the pressure ratio pe corresponding to Me . As
the reservoir pressure (p01 ) is already known, the Mach number of the flow ahead of the shock
p02
tube can be obtained from the normal shock table corresponding to the total pressure ratio p01 .

Therefore the area ratio at the shock location is,

!− γ+1
γ−1 2 2(γ−1)
A 1 1+ 2 M1
=
A∗ M1 γ+1
2

9
Procedure

• Adjust the fan rpm such a way that the back pressure is in between first and second
critical pressures.

• take reading for different rpm.

Observations

Mass flow rate through the nozzle = .......

Table 3: Experimental observations

Si No. RPM p1 p2 p3 p4 p5

Apparatus

• Nozzle with a gradual expansion

• Compressible flow unit

• Pitot probe

Results

• Plot the shock location along the axis of the nozzle for different back pressures, mark the
approximate location obtained from experiment.

Discussion...

Conclusion...

10
 4 Pitot measurement in Supersonic Wind-tunnel

Objective

• Measurement of flow Mach number using a pitot-tube in a supersonic wind tunnel.

Theory

The pitot-tube in a supersonic flow will act as a obstruction to the flow and create a detached
bow shock ahead of the mouth of it. Supersonic flow crosses the normal portion of the shock.
Therefore the stagnation pressure ahead of the shock is not the same as it is sensed by the
pitot-tube (i.e. behind the normal shock).

Figure 5: Pitot-tube in a supersonic flow

p02 can be obtained from the pitot-tube reading, as p01 is known for a friction-less nozzle as
the settling chamber pressure. Therefore from the total pressure ratio across the nozzle ( pp02
01
),
the Mach number ahead of the nozzle can be obtained from the normal shock table for the
corresponding total pressure ratio. Static pressure at the test section is also measured which
can be used to calculate the Mach number using isentropic table corresponding to the pressure
p01
ratio p1 .

Procedure

• Start the wind tunnel and allow flow to come in a steady state.

• Note down settling chamber pressure (p01 ), pitot-tube pressure (p02 ) and static pressure
in the test section (p1 ).

• Repeat for different fan rpm.

Observations

Atmospheric pressure (reference) = .......

11
 Table 4: Experimental observations
p01 p02
Si No. RPM p1 p01 p1 Misen p02 p01 Mpitot

Apparatus

• Supersonic wind tunnel

• Pitot-tube

• U-tube manometer

• Multi-tube manometer

Results

• Plot the Mach number values obtained from pitot-tube measurement and static pressure
measurement for different fan rpm.

Discussion...

Conclusion...

12
 5 Shock Tube

Objective

• To understand the operation of a shock tube facility.

• Obtain the shock Mach number of the moving normal shock in a shock tube theoretically
and experimentally.

Theory

Shock tubes are facilities used to generate high pressure, high temperature gases, by utilizing
the propagation of shock wave through the gas. Shock tube consists of a high pressure driver
section and a low pressure driven section separated by a diaphragm. The diaphragm bursts
due to the pressure difference between the two sections and a shock wave propagates through
the driven section while an expansion fan propagates through the driver section. This facility
is widely used to carryout studies on propagating shock waves.

Figure 6: Schematic diagram of the shock tube facility (not to scale)

Shock Mach number from experiment

Method 1 :- As the incident shock pass through the driven section, the pressure jump
across the shock will be clearly visible on the sensor readings. The sensors are placed at a
known distance and the time delay between the pressure jumps can be obtained from the sensor
readings. therefore shock velocity,

dx
S=
dt

and the corresponding shock Mach number is

S
Ms =
a1
√
where a1 = γ1 R1 T1 , sound velocity at the driven section.

13
 Method 2 :- The pressure ratio across the nozzle can be obtained from a single sensor
reading., i.e. p1 upstream of the shock and p2 downstream of the shock. Therefor the shock
Mack number is,

r
γ1 − 1 γ1 + 1 p 2
Ms = +
2γ1 2γ1 p1

Shock Mach number from theory

The initial condition in the shock tube are known, therefore for the corresponding driven pres-
sure (p1 ) and rupture pressure (p4 ), shock Mach number can be obtained from the equation
given below,

  2γ4
  γ4 −1
p4 2γ1 1
= 1+ (Ms2 − 1)   
p1 γ1 + 1 1− γ4 −1 a1
Ms − 1
γ1 +1 a4 Ms

This equation can be solved using bi-section method.

Procedure

• Set the initial pressure in the driven section.

• Release the high pressure gas to the driver section.

• Take all the pressure sensor reading by setting sufficient pre-trigger and post-trigger tim-
ings.

• Repeat the experiment with different initial pressures and diaphragm characteristics.

Observations

Distance between driven section pressure sensors, dx = .....

Table 5: Experimental observations

p2
Si No. p1 p4 Mst p2 p1 Mse2 dt Mse1

Apparatus

• Shock tube facility

• Pressure transducers

14
 • DAQ

Results

• Compare the theoretically and experimentally calculated shock Mach numbers for different
initial conditions in the shock tube.

Discussion

• Check whether the results are within the uncertainty limit.

Conclusion...

15
 6 Schlieren and Shadowgraph Optical Flow Visualization
Techniques

Objective

• To understand the basics of Schlieren and Shadowgraph flow visualization techniques.

Theory

Optical flow visualization techniques are based on the fact that the speed of light and therefore
the refractive index changes with density.

Schlieren flow visualization

The basic principle of the Schlieren technique is the combination of the optical projection of an
object with an indication of its light deflection. Schlieren photography relies on the fact that
light rays are bent whenever they encounter changes in density of a fluid. These are used to
visualize the flow away from the surface of an object. The Schlieren system shown in figure [7]
uses two concave mirrors on either side of the test section. The light source is placed such that
the reflected light from the mirror forms parallel rays that pass through the test section. On
the other side, the parallel rays are collected by another mirror and focused to a point at the
knife edge. The diverging beam of light is again reflected using another mirror and then focused
using a convex lens into a recording device like a video camera. A minimum distance between
the field mirrors of about 2f, where f is the mirror focal length, is required to provide space for
the test area.

Figure 7: Schematic diagram of the Z-folded Schlieren flow visualization technique using mirrors
(not to scale)

16
 (a) Schlieren image (b) Shadowgraph

Figure 8: Examples of optical flow visualization.

Now if the parallel rays of light encounter a density gradient in the test section, the light
is bent, or refracted. This light deviation can produce localized brightening, or darkening in
an image, depending on which way the ray deviates. The index gradient is directly related to
flow density gradient. The deflected light is compared to undeflected light at a viewing screen.
The undisturbed light is partially blocked by a knife edge. The light that is deflected toward or
away from the knife edge produces a shadow pattern depending upon whether it was previously
blocked or unblocked. This shadow pattern is a light-intensity representation of the expansions
(low density regions) and compressions (high density regions) which characterize the flow. In
simple words density gradient perpendicular to the knife edge is detected using this visualization
technique.

Shadowgraph flow visualization

This method is similar to Schlieren without a knife edge. A Shadowgram is not a focused image
rather it is a mere shadow. In Shadowgram the differences in light intensity are proportional
to the second derivative of the refractive index field in the transparent medium.

Apparatus

• Schlieren and Shadowgraph experimental setup

Results...

Discussion...

Conclusion...

17
 7 Supersonic Flow past Diamond Wedge Airfoil

Objective

• Calculate cl and cd of a diamond wedge airfoil at different angles of attack and compare
the result with theoretically calculated lift and drag coefficients.

Theory

Consider a symmetrical diamond wedge airfoil with a half angle of  placed at an angle of attack
α with respect to the free stream flow [9].

(a) angle of attack (α) = 0 (b) angle of attack (α) 6= 0

Figure 9: Diamond wedge airfoil in supersonic flow

Experimental calculation of lift and drag coefficients

Pressure ports are provided on the wedge surface to measure p2 , p3 , p4 , and p5 . Now,

 
1 p4 − p3 p5 − p2
cl = cos (α + ) + cos (α − ) (1)
γM12 cos  p1 p1
 
1 p4 − p3 p5 − p2
cd = sin (α + ) + sin (α − ) (2)
γM12 cos  p1 p1

Theoretical calculation of lift and drag coefficients

The lift and drag coefficients are calculated using equations [1] and [2]. For this the pressure
values p2 , p3 , p4 , and p5 are calculated by considering the free stream condition along with
angle of attack and half angle of the diamond wedge airfoil. The presence of an oblique shock
has to be considered when the flow turns towards itself and an expansion fan when the flow
turns away.

18
Procedure

• Operate the wind tunnel in steady supersonic conditions.

• Take readings for a fixed free stream condition at different angles of attack.

• Repeat the experiment by changing the free stream condition.

Observations

Half angle of the diamond wedge airfoil,  = .....

Free stream Mach number, M1 = .....

Table 6: Experimental observations-1

Si No. Angle of p1 p2 p3 p4 p5 cl cd
attack
(α)

Angle of attack, α = .....

Table 7: Experimental observations-2

Si No. M1 p1 p2 p3 p4 p5 cl cd

Apparatus

• Supersonic wind tunnel

• Diamond wedge airfoil

• pitot probes

Results

• Plot cl vs α and cd vs α obtained from both experiment and theory.

Discussion

• Discuss the reason for the deviation of the experimental data from the theory.

Conclusion...

19
 8 Flow past NACA 0012 airfoil in Transonic Wind tunnel

Objective

• To get the pressure distribution on a NACA 0012 airfoil in transonic flow (at α = 0) and
hence calculate the equivalent error in α.

Theory

For an incompressible flow, the lift over a thin airfoil (camber = 0) is given by cl = clα α,
where clα = 2π/rad. In case of compressible flow, linearized perturbation theory suggests a
Prandtl-Glauert compressibility correction for this lift slope given by,

clα
clα(M∞ ) = p
1 − M∞2

where M∞ is the free stream Mach number.

2π
clα(M∞ ) = p
2
1 − M∞

The normal and axial coefficient for an aerodynamic body can be obtained by integrating
the pressure and skin friction coefficients over the body surface from LE to TE. For a 2D body,

cl = cn cos α − ca sin α

For small α
Z c
1
cl = cn = (cp,l − cp,u )dx
c 0

where
p − p∞
cp = 1 2
2 ρv∞

If the discrete values of p are known then discrete summation of the above equation gives
the value of the lift coefficient.

Procedure

• Start the experiment by switching on the injector to a given pressure and note down the
corresponding port pressures.

• Repeat the experiment for different injector pressures at the same angle of attack.

20
Observations

Injector pressure = .....

Table 8: Experimental observations

Port loca- Remark pg pa cp cp .δx
tion (x/c) or −δcl

Apparatus

• Self-correcting induction type transonic wind tunnel

• NACA 0012 airfoil

• Scanni-valve pressure transducer

Results

• Plot pg vs x/c.

• Plot cp vs x/c.

• Plot cp .dx vs x/c.

Discussion...

Conclusion...

21