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Abstract

For hypersonic flow intakes for determining the heat flux levels along the ramp various

correlations have been used and the results have been compared to experimental conclusions;

and it has been found that the two closely agree. The programs developed for calculating the heatflux assume that any complex phenomenon like separation, shock wave boundary layer

interaction or shock wave reflection isn’t happening or affecting the heat flux levels.

For hypersonic flow intakes, very high temperatures that the models face is quite a design

challenge. To aid in determining the temperatures, the models have to face, determination of heat

flux levels on various ramps has been done in present report. Although no pure research has beendone for this paper, but making use of the existing theory and data wisely, calculation of the heat

flux has been done using simple programs. Two different approaches have been opted, in one of

which heat flux has been calculated using correlation for coefficient of friction and in other

approach correlation for Stanton Number has been made use of; both of these correlations are afunction of local Reynolds Number, free stream and surface temperature and a constant relating

absolute viscosity of fluid to its temperature.



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List of Symbols, Abbreviations and Nomenclature

1. cf = friction coefficient

2. cp = specific heat at constant pressure

3. h = enthalpy

4. hc = convective heat transfer coefficient

5. k = conductivity

6. M = mach number

7. Nu = Nusselt number

8. Pr = Prandtl number

9. Qc = Convective heat flux

10. r = recovery factor

11. Re = Reynolds number

12. St = Stanton number

13. T’ = Reference temperature

14. ϒ = isentropic exponent

15. µ = Coefficient of viscosity

16. ρ = Density

Subscripts

1. aw = adiabatic wall

2. 0 = total

3. ∞ = free stream



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Contents Page No.

List of Figures………………………………………………………………………………4

List of tables………………………………………………………………………………..5

1. Introduction…………………………………………………………………………6

1.1 Background………………………………………………………………………6

1.2 Current work……………………………………………………………………..7

2. Aim of work………………………………………………………………………....8

3. Literature survey……………………………………………………………………9

4. Theory…………………………………………………………………………….....11

4.1 Heat flux through flat plate in Hypersonic flows………………………………..11

4.2 Heat flux determination using Stanton number Approach……………………....16

4.3 Criteria for determining Transition Reynolds number…………………………..19

4.4 Determination of heat flux from temperature history…………………………...20 4.5 Shock tunnel: Introduction and basic theory…………………………………....21

5. Methodology………………………………………………………………………..26

6. Experiment set-up and Experiment……………………………………………....27

6.1 Experiment set-up……………………………………………………………….27

6.2 Model description……………………………………………………………….27

6.3 Experimental procedure………………………………………………………....28

7. Flow charts………………………………………………………………………....29

7.1 Heat flux from temperature history……………………………………………..29

7.2 Heat flux from correlation based on Stanton number…………………………..30

7.3 Calculation of test section properties in shock tunnel………………………….31

7.4 Heat flux from correlation based on Coeff icient of friction…………………....32

8. Results and observation…………………………………………………………..33

9. Conclusion ……………………………………………………………………..….3 7

10. Appendix

11. Refrences



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List of Figures Page No.

1. Figure1: Comparison of different types of air breathing engines…………………………1

2. Figure2: Shock tunnel at VSSC…………………………………………………………...2

3. Figure3: 3D test model……………………………………………………………………. 8

4. Figure4: Co-axial thermocouple sketch…………………………………………………...20

5. Figure5: Shock tunnel schematic………………………………………………………….21

6. Figure6: Schematic of interaction of Shock in shock tunnel……………………………...22

7. Figure7 (a): Test Model image…………………………………………………………….27

Figure7 (b): Model description…. ………………………………………………………..27

Figure7 (c): Sensors used E Type…………………………………………………………27

8. Figure8: Sensor location in model………………………………………………………...28

9. Figure9: Plot comparison for experiment number 1055…………………………………..35

10. Figure10: Plot comparison for experiment number 1057……………………………….35

11. Figure11: Plot comparison for experiment number 1055………………………………..36

12. Figure12: Plot comparison between all the correlations and experimental

data for experiment number 1055…………………………………………….36



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List of Tables Page No.

1. Table1: Table for specifications of thermocouple used…………………………………..28

2. Table2: Table of comparison with cowl only at external ramp…………………………...33

3. Table3: Table of comparison for experiment 1055. ……………………………………...34

4. Table4: Table of comparison for experiment 1057 and 1060…………………………….34



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1.0 Introduction

1.1Background

A scramjet (supersonic combustion ramjet ) engine is an air-breathing jet engine in which

combustion takes place in supersonic

airflow. As in ramjets, a scramjet relies

on high vehicle speed to forcefully

compress and decelerate the incoming

air before combustion (hence ram jet).

Throughout the scramjet engine flow is

supersonic. This allows the scramjet to

efficiently operate at extremely highspeeds: theoretical projections place the

top speed of a scramjet

between Mach 12 and Mach 20, which

is near orbital velocity. The scramjet is

composed of three basic components: a converging inlet, where incoming air is compressed and

decelerated; a combustor, where gaseous fuel is burned with atmospheric oxygen to produce

heat; and a diverging nozzle, where the heated air is accelerated to produce thrust. No moving

parts are needed in a scramjet, which greatly simplifies both the design and operation of the

engine. In comparison, typical turbojet engines require inlet fans, multiple stages of

rotating compressor fans, and multiple rotating turbine stages, all of which add weight,

complexity, and a greater number of failure points to the engine. It is this simplicity that allows

scramjets to operate at such high velocities, as the conditions encountered in hypersonic flight

severely hamper the operation of conventional turbo machinery.

While scramjets are conceptually simple, actual implementation is limited by extreme technical

challenges. Hypersonic flight within the atmosphere generates immense drag, and temperatures

found on the aircraft and within the engine can be much greater than that of the surrounding air.

Maintaining combustion in the supersonic flow presents additional challenges. In present paper

the focus is on measuring the extreme thermal conditions encountered by a scramjet inlet in

hypersonic flow. Designing a scramjet poses design challenges due to high thermal and structural

Fig 1

http://en.wikipedia.org/wiki/Airbreathing_jet_engine

http://en.wikipedia.org/wiki/Supersonic

http://en.wikipedia.org/wiki/Mach_number

http://en.wikipedia.org/wiki/Oxygen

http://en.wikipedia.org/wiki/Thrust

http://en.wikipedia.org/wiki/Moving_parts


http://en.wikipedia.org/wiki/Axial-flow_compressor

http://en.wikipedia.org/wiki/Turbine

http://en.wikipedia.org/wiki/Hypersonic

http://en.wikipedia.org/wiki/Hypersonic

http://en.wikipedia.org/wiki/Turbine

http://en.wikipedia.org/wiki/Axial-flow_compressor



http://en.wikipedia.org/wiki/Thrust

http://en.wikipedia.org/wiki/Oxygen

http://en.wikipedia.org/wiki/Mach_number

http://en.wikipedia.org/wiki/Supersonic

http://en.wikipedia.org/wiki/Airbreathing_jet_engine



7

loads encountered by the inlet. So as a part of evaluation of a design, an estimate of the heat flux

levels in the scramjet is required; it could be done experimentally as well as using some

theoretical correlations.

1.2 Current work

ATFD (Aerothermal Test Facilty Department) of VSSC is doing research on Hyper

aerothermodynamics, which was very helpul, a short note about the test facility which has been

used ‘Shock Tunnel’ is given below.

Experiments are carried out in shock tunnel, which is an axisymmetric enclosed free jet tunnel

with a free jet diameter of 150mm to 300mm for different nozzles. The facility consists of a long

stainless steel tube (12.5 m), which is divided into two sections namely, the shorter section (2.5

m) known as the driver section where

nitrogen/Helium is used as the driver

gas and the longer section (10 m)

known as driven section, which is

separated by scored aluminum

diaphragm (nominal thickness 2 mm).

Similarly the driven section and the

test section are separated by Mylar

diaphragm. The driver and the test

sections are evacuated at the vacuum

levels. Fig 2

The property of the shock wave is that there is flow discontinuity i.e. there is abrupt change in

temperature and pressure and density across the shock wave. Since the phenomenon of heating

the air column is shock wave, very high heating rates and temperatures can be generated

depending on the shock strength. This wave in turn ruptures the Mylar diaphragm which

separates the test section and the driven section, a high enthalpy flow takes place over the model.

Typically the run times are in the range of 1 to 5 milliseconds for a conventional shock tunnel.

The enthalpy levels can be in the 1 to 3 MJ/Kg. The experiments are carried out on a wedge with

two ramp angles of 10.50

and 210, with a cowl and side plates to enclose whole body



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2.0 Aim of work

Measurement and comparison of heat flux generated in the hypersonic intake at Mach number in

the range of 6 experimentally and theoretically.

For this purpose coaxial thermocouples are placed on different positions. The thermocouples

records change in temperature on the surface and give the output in millivolts. Then this voltage

is converted into temperature, by this get the temperature history is obtained, using the

appropriate correlations the heat flux is found out by the temperature history. Again, just using

theoretical correlations for the heat flux over a flat plate in high speed flows the heat flux is

determined and then the two results are compared.

Fig 3

Model Details

The model is a wedge with two ramp angles of 10.500

and 210, with a cowl and side plates to

enclose whole set up is taken as shown in figure; the intake is rectangular pretending to be a 2Dflow.



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3.0 Literature Survey

Study of an Airframe integrated Scram jet ( 1977-1978)The Langley Research Center of NASA has been involved in a research program for the

development of airframe-integrated Scramjet concepts. These concepts use the entire

undersurface of the aircraft to process the engine airflow. The forebody of the aircraft serves as

an extension of the engine Inlet and the afterbody serves as an extension of the engine nozzle.

The NASA Hypersonic Research Engine (HRE) program was a major contributor to the

development of Scramjet technology. This program culminated in two major milestones:

(1) successful development of the first flight-weight, hydrogen-cooled engine structure,

including verification tests in the NASA Langley 8-Foot High-Temperature Structures Tunnel;

and (2) confirmation of dual-mode (subsonic/supersonic combustion) aero-thermodynamic

performance at Mach 5 to 7 in the NASA-Lewis facility at Plum Brook. This study was an

extension of the preliminary thermal-structural design of an airframe-integrated Scramjet

conducted by NASA. The thermal-structural design evolved in the study and the HRE

technologies form the basis for this effort. The aerodynamic lines were defined by NASA and

remained unchanged during the study.

Ronald G Veraar (TNO Defence, Security and Safety), Rijswijk (The Nethelands (May

2008)):-

Here are the correlations regarding the heat flux calculations over a flat plate in hypersonic

regime which are discussed in theory later. He has also proposed and analysed some scaling

techniques for wind tunnel models which were helpful and gave some idea about scaling the

models.

Hypersonic Aerothermodynamics; John J. Bertin ,( Visiting Professor at the United States

Air Force Academy, and Consultant to the United States Air Force)

About the environment faced by the aircraft at hypersonic velocities and the different flow

regimes. It also included the basic heat transfer equations and the experimental methods and

concepts regarding doing experiments in wind tunnels.



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Dr. Niklos J. Mourtos

His paper contained very basic concepts of hypersonic flow, equations, viscous interactions,

boundary layer. He actually simplified the clumsy heat flux equations to a very simple by taking

some approximations, e.g. very high mach numbers which lead to a simple equation which

stating that the heat flux is directly proportional to the cube of free stream velocity.

Flight Data Analysis of HyShot 2; Neal E. Hass*, Michael K. Smart ( NASA Langley

Research Center, Hampton), Virginia Allan Paull (University of Queensland, Brisbane,

Australia)

This helped to understand about the intake types, its real time test and validation, also from their

data an idea of the heat flux involved with given conditions could be obtained which could be

used to validate the correlations which have been used. HyShot was designed and flown above

Mach 7.5 to validate the use of short duration ground test facilities for scramjet development.

The scramjet payload was launched by an un-guided sounding rocket on a highly parabolic

trajectory to an altitude in excess 328 km. The scramjet experiment was conducted during re-

entry, and consisted of a double wedge intake with two back-to-back constant area combustion

chambers, one fueled with hydrogen at an equivalence ratio of 0.33, and the other un-fueled. The

useful experimental time window lasted approximately three seconds, commencing 537.5

seconds after launch when the payload was slightly above 35 km altitude. The data indicated that

hydrogen combustion generated a pressure ratio of approximately 1.78 for both windward

conditions (angle-of attack ~ 5 degrees, with Mach number ~ 2.6, temperature ~ 1330 K and

pressure > 39 kPa at the combustor entrance), and 1.37 for leeward conditions (angle-of-attack ~

-5 degrees, with Mach number ~ 3.4, temperature ~ 930 K and pressure > 25 kPa at the

combustor entrance).

Principles of Heat Transfer; by Frank Kreith-

From the above book the basic theory and equation governing the heat flux over flat plate in

hypervelocity flows was found and made use of. The theory is presented in a later section.



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Fundamental data obtained from Shock Tube Experiments; by A. Ferri –

From above book the fundamental functioning of the shock tunnel was understood and equations

derived to find out the conditions at the nozzle inlet necessary as inputs for determining the heat

flux on scramjet inlet.

4.0 Theory

As the scramjets operate at very high velocities, one might think that it will lead to very high

heat flux at the surface and it happens so. The aerothermodynamic environment of a vehicle,which will fly at hypersonic speeds, will include some, if not all, of the following phenomena:

boundary-layer transition and turbulence, viscous/ inviscid interactions, separated flows,

complex shock wave interactions, nonequillibrium chemistry and the effects of surface

catalyticity, ablation, and noncontinuum and real gas effects. The analysis is further complicated

if the vehicle contains an air-breathing, scramjet propulsion system.

Mainly only convective effects of the flow shall be considered as radiation and conduction heat

transfer from the constant temperature wall are being neglected.

4.1 Heat Flux through Flat Plate in Hypervelocity Flows[7]

–

To get a qualitative understanding of high speed flow in a continuum, let’s consider a laminar

boundary layer in high speed flow over an insulated plate. Although the velocity distribution is

quite similar to that observed at low Mach numbers but the temperature distribution is totally

different.

It is observed that the temperature increases in a direction towards the insulated surface and

reaches at the wall a value only slightly less than the total temperature of the free stream as a

result of viscous dissipation in the boundary layer. The shape of the temperature profile depends

on the relation between rate at which internal energy of the fluid increases in the boundary layer



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and rate at which heat is conducted towards the free stream and thus the Prandtl Number of the

flow.

Although the processes in a boundary layer aren’t adiabatic, it is general practice to relate them

to adiabatic processes. When a gas flows past an insulated surface, the temperature of the surface

will rise, but it won’t quite reach the stagnation temperature of the flow. The actual temperature

of an adiabatic wall is called the adiabatic wall temperature T as.

In practice the adiabatic and total temperatures could be related by the recovery factor which is

the fraction of the free stream dynamic temperature rise recovered at the wall. It is defined as –

Experiments with air in laminar flows have shown that for practical purposes

√

over wide range of velocities and temperatures, whereas for turbulent boundary layers recovery

could be approximated by,

√

When a surface isn’t insulated, the rate of heat flow between the gas and the solid surface is

governed by-

It is observed that at high speeds heat can flow from flow to surface even when the surface

temperature is higher than the free stream temperature owing to the boundary layer heating. To

calculate the heat transfer coefficients in high speed flow the analysis of the boundary layer for

low speed flows must be re-examined, taking into account the effects of viscous shear work and

heat conduction.

As for a laminar boundary layer –

… (4.1.A)



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if and are assumed constant and with the approximation that is introduced;

and,

with the aid of the above eq. in eq. 5.1.A

(

) … (4.1.B)

The above energy eq. could be used qualitatively to illustrate the effect of high velocities on heat

transfer and temperature distribution in a laminar-boundary layer. As high speed phenomenon is

of interest only in cases where Pr isn’t far from unity thus assuming Pr=1 further simplification

in eq. 5.1.B could be made as follows-

… (4.1.C)

for which one particular solution is –

Physically, the above eq. states that total temperature equals the free stream stagnation

temperature everywhere in the boundary layer. Thus the temperature at the wall is thus since

at . The rate of heat flow from the wall to the flow is therefore 0 from above

conclusion, since at y=0

This condition is true for adiabatic surfaces. However, in real flows the temperature gradient for

y>0 is finite, and the heat flows from fluid in the vicinity of the wall to the outer edge of the

boundary layer. This is only possible when the rate of heat conduction in the fluid across any

plane parallel to the wall is equal to the rate at which shear work crosses this plane in the

opposite direction, or



14

Dividing by and rearranging

. /

The above eq. shows that the stagnation temperature in boundary layer is constant when Pr=1

and the wall is insulated. The term represents the kinetic energy recovered in the boundary

layer where the viscous forces slow down the free stream to zero velocity at the wall, thus if the

Pr<1 the adiabatic wall temperature will be less than the free stream stagnation temperature. For

air where Pr 0.75 the results could be qualitatively applied.

For avoiding difficulties the surface (wall) temperature could be assumed to be constant . The

results obtained are applicable approximately to flow over curved surfaces as long as the

pressure gradient isn’t so large that it causes separation.

As for steady flow over flat plate-

… (4.1.D)

As eq. 5.1.C and 5.1.D are quite similar. They could be reduced to the same eq. if it is assumed

that total temperature is related to the velocity by the following relation-

Where a and b are constants. From boundary conditions -

At y=0, where u=0

At y=, where u=

Thus using these eq.



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or in terms of static temperature

This solution applies only to the constant temperature walls since at the walls where the velocity

is zero; the temperature must be constant to satisfy the boundary conditions. A physical

interpretation of this solution shows that the dimensionless temperature profile

and the

dimensionless velocity profile

are similar.

Thus the heat flux through the wall is now obtained by application of the conduction eq. at the

wall. With the aid of eq. -

But at y=0

so,

again as

thus,

The above eq. represents the heat flux from the surface to the flow but to determine the heat fluxflowing towards the wall a negative sign should be introduced;

The heat flux passing through the wall due to boundary layer heating in a high speed flow-



16

where,

here is the coefficient relating the viscosity to temperature. For air it is found to be around

0.67.

for high speed flows Stanton number ; if 1) the unit surface conductance is defined as

and if 2) the physical properties remain constant; which is quite unreasonable but

if the properties are calculated at a reference temperature such that

Although, the above analysis is applicable only to laminar flows; for wedges with sharp leading

edges and for flows with very high mach numbers and with very small free stream turbulence the

transition Reynolds number could be well beyond 1 million; thus the entire flow field could be

treated to be laminar. Still with the same governing eq. correlations for turbulent case have also

been included in program which produces results not very far from laminar case if transition

occurs.

Using these relations a matlab program ‘Heatf lux_again.m’ was developed which produces the

heat flux vs. distance along the ramp given free stream Mach number, dynamic pressure, free

stream stagnation temperature, property values like conduction coefficient, absolute viscosity

and model specifications as input. The property values for air are readily available at 1 atm.

Pressure and variety of temperatures. As and aren’t readily affected by pressure variation so

they are chosen as input parameters.

4.2 Heat flux determination using Stanton number approach[6]

Here another approach to determine the heat flux has been tried. The basic equation describing

convective heat transfer is:-

Qc = hc(Taw - Tw)------------------------------------------(4.2.A)



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In which Qc is convective heat flux to the wall, hc is the convective heat transfer coefficient, Taw

is the adiabatic wall temperature and Tw is the wall temperature. The adiabatic wall temperature

is the temperature assumed by a wall in a moving fluid stream when there is no heat transfer

between the wall and the stream. Here it is remarkable that heat flux is being affected by

adiabatic wall temperature rather than the free stream total temperature. The convective heat

transfer coefficient is dependent on the fluid properties and can be described by several

dimensionless numbers which are defined below. The heat flux of a calorific perfect gas is

parallel given by:-

Qc = ρVcp(Taw - Tw) --------------------------------------------------(4.2.B)

In which ‘ρ’ is the density of fluid, ‘V’ is the velocity and ‘cp‘ is the specific heat capacity at

constant pressure of gas.

The Stanton number is defined as the ratio of heat flux normal to wall to the heat flux parallel to

wall, hence:-

St =hc / (Vcp)

The relative importance of heat generated due to viscosity to heat conducted is given by Prandtl

number:-

Pr = cpµ/k here ‘µ’ is the dynamic viscosity and k is the thermal conductivity of the fluid.

Another very important dimensionless number is ‘Reynolds number’ which compares inertial

forces with respect to viscous forces and is given by:-

Re =

where L is the chosen reference length

Also ‘Nusselts number’ is defined as:-

Nu = hcL/k = St Re Pr

Hence combining all equations above, convective heat flux of a calorific perfect gas:-

Qc = St ρVcp(Taw - Tw)---------------------------------------------------(4.2.C)



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However to take into account of a calorific imperfect gas which is involved in high temperature

and high Mach number compressible flow, enthalpy is defined as:-

h = ∫ ----------------------------------------------------------------- (4.2.D)

so that the basic equation may be written as:-

Q = St ρV(haw - hw)-------------------------------------------------------(4.2.E)

Where hw is defined as:-

hw = h + r V2 /2

in which ‘r’ is known as compressibility factor defined as:-

r = Pra

; a = 0.5 for laminar boundary layer and a =0.3333 for turbulent boundary layer

Now taking into account the boundary layer heat transfer effects the above equations will be

rewritten and the ‘Stanton number’ could be written for a laminar boundary layer:-

St =

√ ( )

and for turbulent boundary layer:-

St = √

Where the ratio T’/T∞ are defined for laminar and turbulent boundary layer respectively as;-

= 1 + 0.032M

2+ 0.58(

= 1 + 0.035M2 + 0.45(

Hence in the heat transfer equation 4.2.E Stanton number and Reynolds no. are substituted as per

the above conditions.



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However if the equation number 4.2.C is carefully analysed to reduce this to a simple form

without getting in difficulty with so many dimensionless number.

For high Mach number laminar flow over a flat plate: Taw 0.88T0

So equation 4.2.C becomes: - Qc = St ρVCp(0.88T0 - Tw) ------------------(4.2.F)

Making approximation[5]

, again for high Mach number: haw h0

Where h0 = h∞ + V2/2, for hypersonic speeds ‘V’ is very large ,and high altitude ‘T’ is very less

h = CpT is relatively small h0 V2 /2

haw – hw h0 – hw V

2

/2Hence equation 4.2.E becomes: Qc = 0.5ρV3St----------------------------------- (4.2.G)

The equation 4.2.E, 4.2.F, and 4.2.C can be used to see the effect of Mach number on it for

which a matlab program has been prepared.

The rarefied gas nature and dissociation of gas has not been taken into account as the altitude for

testing has been chosen to be 25 km where gas is in continuum and the Mach number is not more

than 7.5 so the dissociation effects are marginal.

4.3 Criteria for Determining Transition Reynolds Number[2 ]

-

For Transition Reynolds Number for hypersonic flow over flat plates the following correlation

has been made use of

for 10<Reb /M2<1000 Retransition = 70000M

0.08Reb

0.46(+/- 30%)

and for Reb /M2>1000 Retransition = 6*10

6M

1.38Reb

-0.19(+/- 25%)

where Reb = Vb/ and b is the leading edge bluntness



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4.4 Determination of the heat flux from the temperature signal[1 ]

The determination of the heat flux from the temperature signal is based on the theory of one-

dimensional heat conduction into a semi-infinite body as it is described in many standard text

books. It is based on the assumption that during the measurement time the heat pulse penetrating

into the sensor for ideal conditions does not influence the temperature of the sensor at its rear

end. The formula given below holds good for the coaxial thermocouple as well as for the thin

film thermometer as long as the principle of a semi-infinite body is valid. From this, the

maximum-recommended measuring time for the thermocouple amounts to 20 ms, whereas the

thin film thermometer allows

100 ms. This only holds good if

the gauge is used to determine

the heat fluxes. For the

measurements of steady or very

slowly varying temperatures no

upper limit exists concerning

the measurement time.

The one-dimensional heat

conduction theory yields the

following relation between the

surface heat flux Qs and the surface temperature signal T (t):-

Qs(t) =√

√ *√

∫

+

For data evaluation this expression can be transformed to:-

Qs(tn) =

This expression is valid under the assumption that for t0

= 0 the temperature is set to T(t0) = 0,

i.e. the temperature in the formula given above represents the temperature difference of the

Fig 4



21

gauge registered during the measurement with respect to the initial temperature. The heat flux

signals shown above have been deduced by this formula.

4.5 Shock Tunnel: Introduction and Basic Theory[8]

–

Shock tunnel facility is one of the ultra short duration ground based facility used

to simulate flows of high enthalpies with very high velocities e.g. flows encountered by re-entry

bodies; so it could be used to measure various flow parameters that a proposed design will have

to encounter while facing very high enthalpy hypervelocity flows.

Basically shock tunnel composes of three sections driver, driven and test

section each separated by a diaphragm. The driver section contains a low molecular weight gas at

high pressure and the driven contains test gas at very low pressure as compared to driver. These

two are separated by a diaphragm designed to burst at a particular pressure difference. These two

together form the shock tube as shown in figure 4. In a shock tube as the diaphragm bursts shock

wave forms which travels towards the driven section end; at the same time an expansion wave

also forms which moves toward the driver end. Also the contact surface (driver- driven fluid

interface) precedes the shock wave; assuming no mixing of the driver and the driven fluids, the

flow states could be represented as shown in the figure 1.2.

The Shock Tunnel Facility

Fig 5



22

Representation of physical phenomenon in a shock tunnel w.r.t. time and position; further later

reflected shock- contact surface and other shock- shock interactions will take place.

Fig 6

Using ideal gas assumptions and fundamental conservation equations; across shock wave and

representing flow state upstream the shock by subscript 1 and that downstream the shock by

subscript 2 : –

ρ1v1 = ρ2v2 ... (4.5.A)

p1+ ρ1v12

= p2+ ρ2v22 … (4.5.B)

h1+ v1

2 = h2+ v2

2… (4.5.C)

p = ρRT … (4.5.D)

From equation 4.5.B & 4.5.D



23

ρ1(RT1+v12) = ρ2(RT2+v2

2)

From above equation

… (4.5.E)

Again from equation 4.5.C

√ … (4.5.F)

Negative sign has been chosen as and must have same signs.

Thus from eq. 4.5.E and 4.5.F

where,

w= Shock wave speed in inertial frame of reference =

a=2{(h2-h1)-R(T2-T1)};

b=4R(h2-h1)(T2-T1)-R2(T22-T1

2);

c= -2R2T12(h2-h1);

In present case as (speed of the shock wave itself) and where the

velocity is the flow gets in the direction of the movement of the shock wave after its encounter

with the shock wave.

Now, for the moving shock wave applying the Galilean Transformation and then the law of

conservation of mass

or,



24

}

where Ms is the mach no of the moving shock wave and

as across a normal shock wave,

and across the expansion fan

[2 / (4-1)]a+ u=constt.

[2 / (4-1)]a4 = [2 / (4-1)]a3+ u3

also

as & u3=u4

thus, ,

-

,

-

thus, should be very large to produce a very strong shock with given pressure ratio; this

could be achieved by either using a low molecular weight driver gas or by heating the driver gas



25

via a combustion reaction. The above eq. could be used for solving iteratively for shock wave

Mach number given the pressure ratio in driver and driven section; knowing Ms the conditions

downstream the shock could be calculated.

As soon as this shock reaches the other end of the driven section it gets reflected from

wall (diaphragm in case of shock tunnel) already heated fluid gets further heated from the

reflected shock wave; also behind reflected shock the flow stagnates which could be accelerated

through a C-D nozzle to get hypersonic flow in test section at high enthalpy. This addition to

shock tube makes up shock tunnel.

Now, for getting flow state behind reflected shock

Thus the above eq. could be solved iteratively for and knowing it all conditions

downstream the reflected shock could be calculated from normal shock relations.

The flow behind the reflected shock stagnates due to the presence of the wall, due to

its encounter with two shocks successively the fluid now present is at very high temperature and

pressure; it could be made use of by expanding that through a nozzle. For that purpose at the end

of the driven section wall another diaphragm is mounted and after that diaphragm a nozzle is

kept joining test section to driven tube. The diaphragm is weak enough that it ruptures with its

encounter with the shock and the test fluid expands through the nozzle to give the flow at

required Mach number.

To generate very strong shock waves the given driver fluid should be heated to high

temperatures for that purpose several means like using electric discharge, combustion, use of

electrical heaters are employed. Places where high enthalpy hypervelocity flows are to be

simulated shock tunnels are fundamental.



26

5.0 Methodology

Main aim is to determine the heat flux at the two external compression ramps of the intake of the

engine with specified angles of ramps and condition. As it is not possible to test a full scale

model, a model of the same geometry but of smaller size is prepared with particular Geometric

scaling factor (GSF).

The experiment for measuring the heat flux has been done on the external compression ramps

including the cowl and top plate and following it without including cowl (as it includes internal

effects like internal compressions, boundary layer interactions). For this with the thermocouples

fixed on the surface at specified location the whole set up is placed in shock tunnel with known

shock tunnel condition.

Using the basic equation and correlations, heat transfer by convection could be analytically

calculated on the mentioned surfaces in shock tunnel by solving those equations in Matlab

program. Using the available correlations the plots could be made as shown in the results and

compared with experimental data; to observe at what mach no. and conditions which correlations

gives results closer to experimental results. The comparison yielded that the results from

correlations matches the experimental observation closely with maximum error of 6 W/cm2.

Apart from that an effort has been made to calculate the test section stagnation condition and

other inputs like dynamic pressure in the shock tunnel from the relations derived from basic

theory, assuming that no real gas effects are present and gases behave perfectly, while the initial

conditions like temperature and pressure in the sections is known.

The steps involved in brief are as follows:-

1. Experimentally measuring the heat flux by temperature history one program

‘ temphistory.m’ involved and noting the tunnel conditions.

2. Calculating test section condition in the shock tunnel by a program ‘Shock_tunnel1.m’

which will serve the input conditions for theoretical calculation of heat flux.

3. Two programs ‘ Heat_flux_correlation.m’ and Heatflux_again.m’ used for heat flux

calculation with deferent correlations.

4. The values are checked with the experimental ones and results are shown.



27

6.0 Experiment set-up and Experiment

6.1.0 Experimental Set-up:-

The experiments have been carried out on aset up present in the shock tunnel facility at

ATFD-VSSC, at mach number 5.8 with

varying dynamic pressure and free stream

stagnation temperature, with the model as

shown in the figure. Fig 7(a)

6.2.0 Model description:

Fig 7(b)

The given profile is a two ramp side wall compression inlet. It has two ramp surfaces, the firstramp making an angle of 10.5 degrees with the freestream

and the second ramp making an angle of 21 degrees with

the freestream (making 10.5 degrees with first ramp), and

two expansion corners one making an angle of 12 degrees

with freestream and the other one making an angle of 7

degrees with freestream. Cowl lip is located at the starting

of the first expansion corner. Then there is a flat region

which is parallel to free stream which extends upto

245.2mm from the leading edge. Figure 7(c) denotes the Fig 7(c)

thermocouple used.



28

Table1: types of thermocouple used.

Below is the location for sensors on ramps:- Ramp 1and2 are compression ramps; Ramp 3and4

are expansion ramps; Ramp5 is flat region parallel to scramjet body axis

Fig 8

6.3.0 The experimental procedure :

First making a theoretical model for calculation of heat flux and developing a program for that

then validating the values with that of the experimental values.

The heat flux could be calculated experimentally by placing the thermocouples at the positions as

mentioned in the diagrams. The sensors give the output in form of milli-voltage, which isconverted into temperature which is time dependent and from this temperature history the heat

flux at that position is calculated, using the correlation mentioned as in the theory. Now that the

experimental value for the heat flux has been obtained; theoretical estimate of heat flux could

also be calculated at the points by the correlations mentioned in the theory. Finally, these

calculated heat fluxes are compared with the experimental one to observe the correctness of the

correlations.

Thermocouple Type Diameter Length Material

K Type (left) 1.2 mm 4 mm Chromel-Alumel

E Type (right) 1.9 mm 9 mm Chromel-Constanton



29

7.0 Flow charts

7.1.0 Flow chart for heat flux determination from temperature history, corresponding

matlab program: ‘temphistory.m’



30

7.2.0 Flow chart for heat flux determination from correlations, corresponding matlab

program: ‘heat_flux_correlation.m’



31

7.3.0 Flow chart for calculation of test section properties in shock tunnel, corresponding

matlab program: ‘Shock_ tunnel1.m’



32

7.4.0Flow chart for calculation of heat flux from different correlation, corresponding

matlab program: ‘Heatflux_again.m’



33

8.0 Results and observations

The table for comparisons is shown below; all the experiments are carried out at same Mach

number i.e. 5.8. It can be seen that the results are matching. With the cowl closed only the

external ramp comparison has been considered because their might be internal compression and

boundary layer interaction for which the theoretical calculation are quite tough, but with the cowl

removed test over whole surface was possible. The results might deviate from the experimental

ones a little bit because of ideal case assumption, but still calculated ones are close to the

experimental results, by which a qualitative idea of the heat fluxes involved before doing the

experiment can be gained.

The data obtained from the relations defining the shock wave speed in a shock tunnel have been

found to be in a close match with the originally observed values. The reasons for deviation could

be the very ideal assumptions, inaccurate inputs for initial temperatures, pressures, the actual

molecular weight and specific heat ratios of the driver and the test gas and insufficient account of

mixing taking place.

As close to leading edge in a flow at hypersonic Mach number all the approximations give same

results, but after 2nd compression as the Mach number is decreased to 3 equations give different

results. Again after the expansion due to increase in Mach number we have almost same value

from all 3 equations. This clearly shows that higher mach numbers i.e. above Mach 4.5 we can

very comfortably use equation 4(b) which is very simple instead of equation 5.

8.10 The results and table are as shown:-

8.1.1 with cowl – Table2

Experiment no. Heat flux calculated

(ramp1 15mm) in W/cm

2

Heat flux experimental (ramp1 15

mm) in W/cm

2

1049 20.06-20.09 20-23

1051 20-20.5 20-22



34

8.1.2 Without cowl and without side plate heat flux comparison in W/cm2-Table 3

8.1.3 Without cowl plate with side plate heat flux comparison in W/cm2- Table 4

Distance in from

leading edge in mm

Calculated for 1057 (W/cm2) Experimental for 1057 (W/cm

2)

61(ramp1) 10 12

100(ramp1) 7.8 9.5

123(ramp2) 12-14 10.5

140(ramp2) 11.5-13.2 7.5

168(ramp2) 10.5-12 10

Ramp 5 3.5 3.5

1052 20.6-20.8 22-26

Distance from

leading edge in mm

Calculated heat flux (W/cm2) Experimental heat flux (W/cm

2)

61(ramp1) 10.5 12

100(ramp1) 8.0-8.2 12

123(ramp2) 13-15 14

140(ramp2) 12-14 13

168(ramp2) 11-12 10

Ramp 5 3.5 3.5



35

Equations used for plots below:-

(A):- Qc = St ρVcp(Taw - Tw) (B):- Qc = St ρVCp(0.88T0 - Tw)

(C):- Qc = 0.5ρV3St (D):-

8.2.0 Plot comparison for 1055, triangles denote experimental values: - Fig 9

8.2.1 Plot comparison for 1057, triangles denote experimental values:- Fig10



36

8.2.3 Below is the plot comparisons by using another program Heatflux_again.m only for

1st

and 2nd

ramp, red circles denoting the experimental values. Y axis represents heat flux

in W/m2

and X axis distance from leading edge in m.Correlation:

1055- Fig 11

8.2.4 Comparison between all correlations and experimental data for 1055 - Fig 12



37

9.0 Conclusion

Concluding, as the Mach no. increase the increase in heat flux is observed and it is directly

proportional to cube of velocity over the surface. The heat flux decrease from leading edge and

after some length it becomes almost constant. A sudden jump is observed in heat flux soon after

compression which is obvious as there is more increase in density than decrease in velocity. For

higher Mach number, say after expansion on the ramps the heat flux does not vary much over

length, as mentioned earlier it is directly depending on cube of velocity and all correlations

converge to almost same value.

The Correlations A, Band C hold good for Mach no. above 3.5 (this was the Mach no. after

2nd

oblique shock), below this they do not give same value and in most cases only correlation C

is close to experimental one because it does not took the approximation of Cp to be constant

which is relevant also. Whereas, the correlation D is good for Mach no. below 4.5 (Mach no.

after 1st

oblique shock) and do not produce a good match with the experimental results above

Mach 4.5, i.e., after expansion on Ramp5.

The high heat flux is very close to leading edge, and as it is known that the hypersonic intakes

have a sharp leading edge so this might be a material challenge.

The complex phenomenon like flow separation, shock layer interactions were neither considered

in correlations nor in the programs, but it has produced well matching results with the

experiments.



References

1. Cook and Felderman equation

2. George A. Simeonides, Elias Kosmatopoulos, Laminar Turbulent Transition

Correlation in Supersonic/Hypersonic Flows.

3. John D. Anderson, Modern compressible flow, Second edition, Page 100-124.

4. John J. Bertin, Visiting Professor at the United States Air Force Academy and

Consultant to the United States Air Force, Hypersonic Aerothermodynamics, Page 87-

157.

5. Dr. Niklos J. Mourtos-A.E. 264, Hypersonic flow theory, AIAA education series, Page

21 -23.

6. Ronald G Veraar from TNO Defence, Security and Safety, Rijswijk, The Nethelands, Development of a scaling technique for duplication of in-flight Aerodynamic heat flux

distribution in ground test facilities, Page 1-5.

7. Frank Kreith , Principles of Heat transfer- Second Edition ,Publisher- International

Textbook Company

8. Fundamental data obtained from Shock Tube Experiments, Editor- A. Ferri,

Publisher- Pergamon Press

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