THE UNIVERSITY OF QUEENSLAND

Bachelor of Engineering Thesis

Cooling Analysis for Hydrogen-Fuelled Scramjet Combustors Using CFD

Student Name: Thomas lade

Course Code: MECH4501

Supervisor: Anand Veeraragavan

Submission Date: 2 June 2017

A thesis submitted in partial fulfilment of the requirements of theBachelor of Engineering Degree in Mechanical & Aerospace Engineering

UQ Engineering

Faculty of Engineering, Architecture and Information Technology

Abstract

Scramjet combustors are home to some of the highest temperatures seen in aerospace

vehicles, requiring significant active cooling if sustainable flight is to be achieved. De-

spite being in development for over 50 years, little research has been conducted in this

area which will need to change if scramjets are to become a fully functional vehicle.

This thesis studies the capability of hydrogen fuel to act as a regenerative coolant in

a simplified scramjet combustor model with a concentric counterflow heat exchanger.

Using CFD, the conjugate heat transfer system was solved repetitively, changing the

significant variables, combustor wall thickness, hydrogen channel thickness, hydrogen in-

let pressure and hydrogen mass flow rate with each iteration. While all parameters were

capable of sufficiently cooling the combustor wall, reducing the hydrogen channel thick-

ness resulted in much greater cooling ability, with a 1 mm channel thickness resulting

in a maximum wall temperature recorded as just over 1800 K, compared to the 2000 K

typical of other parameters.

Acknowledgements

My thanks goes to my supervisor, Anand V., without your guidance and ability to an-

swer all of my stupid questions without any sign of frustration, this thesis surely would

not have seen the light of day.

2

Contents

1 Introduction 3

1.1 Scramjets Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2 Aim & Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.3 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2 Literature Review 5

2.1 Scramjet Wall Heat Flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2 Fuel Combustion Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.3 Combustor Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.4 Hydrogen Storage & Cooling Properties . . . . . . . . . . . . . . . . . . . . 7

2.5 Turbulent Effects on Heat Transfer . . . . . . . . . . . . . . . . . . . . . . 9

2.6 Previous Scramjet Cooling Analysis . . . . . . . . . . . . . . . . . . . . . . 10

2.7 Conjugate Heat Transfer in CFD . . . . . . . . . . . . . . . . . . . . . . . 11

3 System Description 12

3.1 Model Scramjet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.2 Heat Flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.3 Fuel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.4 Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.5 Geometry & Geometry Simplification . . . . . . . . . . . . . . . . . . . . . 15

3.6 Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.6.1 Standard System Parameters . . . . . . . . . . . . . . . . . . . . . 18

3.7 Alternate Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

4 CFD Case 20

4.1 Software and Solver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

4.2 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

4.3 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

4.3.1 Heat Flux Boundary Condition . . . . . . . . . . . . . . . . . . . . 23

4.4 Thermophysical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

4.4.1 Hydrogen Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

4.4.2 Carbon-Carbon Composite Model . . . . . . . . . . . . . . . . . . . 26

4.5 Turbulence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4.6 Interpolation Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

4.7 Mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

4.8 Convergence and Mesh Independence . . . . . . . . . . . . . . . . . . . . . 30

5 Results 32

5.1 General Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

5.1.1 Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

5.2 Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

5.3 Fluid Channel Thickness . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

5.4 Solid Wall Thickness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

5.5 H2 Inlet Mass Flow Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

5.6 H2 Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

6 Conclusion 41

7 Recommendations 42

Appendices 43

A Residual Plots 43

B Solid - Fluid Interface Temperature Profiles 46

C Lower Wall Temperature Profiles 48

List of Figures

1 Flight Regime of Various Aerospace Engines [Razzaqi and Smart, 2011] . . 3

2 Typical pressure distribution within a Scramjet engine [Suraweera et al.,

2009] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

3 Fuel jet penetration increase with temperature normalised at 300 K [Barth,

2014] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

4 Carbon-Carbon composite brake pads on an aircraft [Korte, 2006] . . . . . 7

5 Measured convective heat transfer coefficients, Reynolds numbers and

Nusselt numbers [Slaby and Mattson, 1968] . . . . . . . . . . . . . . . . . . 8

6 Nusselt number of pipe flow with different inlet designs [Meyer and Olivier,

2002] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

7 Model scramjet combustor cross section [F.Zander and R.G.Morgan, 2007] 10

8 Time accurate temperature results [F.Zander and R.G.Morgan, 2007] . . . 11

9 Heat flux along the half-scale REST scramjet combustor section [Barth,

2014] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

10 Model heat flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

11 Original geometry of the half-scale M12 REST engine [Barth, 2014] . . . . 15

12 Constant area combustor section geometry . . . . . . . . . . . . . . . . . . 16

13 Generalised cylindrical geometry . . . . . . . . . . . . . . . . . . . . . . . . 16

14 Geometry of CFD representation (Fluid region in light grey, Solid in dark) 21

15 Boundary labels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

16 Convective coefficient values for the combustor heat flux . . . . . . . . . . 24

17 Comparison between selected hydrogen density model and actual density . 25

18 Enlarged mesh at inlet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

19 Enlarged mesh at outlet . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

20 Enlarged mesh at interface . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

21 Residual plot of simulation convergence . . . . . . . . . . . . . . . . . . . . 31

22 Velocity near inlet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

23 Velocity near outlet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

24 Temperature near inlet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

25 Temperature near outlet . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

26 Temperature profiles along Z axis . . . . . . . . . . . . . . . . . . . . . . . 34

27 Varying fuel channel thickness results . . . . . . . . . . . . . . . . . . . . . 35

28 Velocity Profiles at Outlet . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

29 Temperature profile at outlet . . . . . . . . . . . . . . . . . . . . . . . . . 37

30 Varying wall thickness results . . . . . . . . . . . . . . . . . . . . . . . . . 38

31 Varying mass flow rate results . . . . . . . . . . . . . . . . . . . . . . . . . 39

32 Velocity profile at outlet . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

33 Varying hydrogen pressure results . . . . . . . . . . . . . . . . . . . . . . . 40

34 Comparison of Specific Heat and Absorbed Heat . . . . . . . . . . . . . . . 41

1

Nomenclature

CFD Computational Fluid Dynamics

ρ Density

µ Dynamic Viscosity

t Thickness or time

SF Safety Factor

P Pressure

Pc Critical Pressure

T Temperature

Tc Critical Temperature

σ Stress

L Length

W Width

Q Heat Energy

h Convective Heat Transfer Coefficient

k Conductive Heat Transfer Coefficient

R Universal Gas Constant

V Volume

Vm Molar Volume

ω Acentric Factor

Cv Constant Volume Specific Heat

q Heat Flux

kf Forward Reaction Rate

E Activation Energy

Re Reynolds Number

Nu Nusselt Number

D Pipe Diameter

A Surface Area

2

1 Introduction

Engines designed to produce thrust at hypersonic speeds, also known as scramjets,

have been a hot topic for researchers across the globe since the early 1960’s [Dharavath

et al., N.D.] . So far most firing tests last for less than a milisecond, where the wall

temperature of the engine remains a constant 300 kelvin despite the massive heat flux

imposed on it from the combustion of its fuel. However, in order to reach the next stage

of testing where the firing of the engine lasts for a much longer amount of time, this

heat energy will need to be absorbed by coolant. This coolant can be sourced as the

fuel for the scramjet, which after being used as a coolant, will have a much larger com-

bustion rate.

The following report will deal with the CFD analysis of a coolant system for the walls

of a REST (Rectangular to Elliptical Shape Transitioning) scramjet engine.

1.1 Scramjets Overview

All air-breathing jet-type engines designs occupy a space within the efficiency-velocity

curve. Although still in development, scramjets are theorised to occupy this curve be-

tween Mach 6 and 12 [Razzaqi and Smart, 2011].

Figure 1: Flight Regime of Various Aerospace Engines [Razzaqi and Smart, 2011]

Where typical air-breathing engines require some sort of mechanical compression to in-

crease the pressure of incoming air, scramjets along with ramjets are unique in that all

3

inlet compression is achieved by shockwaves formed at high mach numbers, which al-

lows for an engine completely void of mechanical components. What separates scram-

jets from ramjets is the velocity within the combustor, for a ramjet incoming air is

slowed to subsonic conditions before combustion where as a scramjet contains super-

sonic flow throughout the engine.

Currently, rockets are used for hypersonic vehicles but are much less efficient than air-

breathing engines, mostly owing to rockets having to carry their own oxidiser instead

of utilising the atmosphere like the scramjet engine. This opens up the potential use

for scramjets to be used as an in-atmosphere stage for a cheap access to space vehicles.

However, the low thrust-to-weight ratio of these engines compared to rockets decreases

their acceleration substantially, meaning in order to reach required speeds they must

spend much more time within the atmosphere compared to rockets.

1.2 Aim & Objectives

The overall aim of this investigation is to analyse a simple coolant system for scram-

jet combustors using CFD, varying critical constants in order to provide parameters in

which it can be adequately cooled for long duration flights.

In order to achieve this aim, several objectives were planned and accomplished. These

are as follows in chronological order:

1. Review literature to understand the problem and previous attempts at solving it.

2. Select a scramjet engine to model geometry and heat flux from.

3. Generalise and simplify model to fit inside a CFD package.

4. Construct CFD model and select variables to investigate during analysis.

5. Iteratively run CFD simulations, varying previously selected variables.

6. Analyse and report results.

4

1.3 Scope

In Scope

• Modelling of Hydrogen fuel channel

• Analysis of Hydrogen fuel cooling

ability

Out of Scope

• Structural design of hypersonic vehi-

cle to allow design of fuel channel

• Modelling of interior combusting flow

flow

• Planum design and modelling

• Hydrogen storage design

• CFD code development

2 Literature Review

2.1 Scramjet Wall Heat Flux

A scramjet is made up of 4 sections, an inlet, an isolator a combustor, and a nozzle.

Due to the combustion of the air-fuel mixture, the combustor sees the highest heat flux.

This heat flux can reach up to 5 MW/m2 [Barth, 2014] due to the massive tempera-

tures and concentrated shockwaves as seen in figure 2, which interact with the bound-

ary layer and drastically increase heat transfer [Delery and Bur, 2000].

Figure 2: Typical pressure distribution within a Scramjet engine [Suraweera et al.,2009]

Due to the low thrust-to-weight ratio of scramjets, they require a fairly large amount of

time within the atmosphere to reach desired speeds. This gives the engine time to heat

up to a maximum, which is theorised to be over 2500 K [Barth, 2014]. At these temper-

atures very few materials can survive, let alone with any kind of structural strength.

5

2.2 Fuel Combustion Efficiency

One of the greatest engineering obstacles to overcome in scramjet design is obtaining

high combustion efficiency within the combustor. This can be achieved in many ways

such as mixing, injection jet penetration and increasing combustion rate. The latter can

be improved by increasing the temperature of the combusting gasses, according to the

Jachimowski Hydrogen Air-Reaction Model [Jachimowski and C.J., 1992].

kf = ATBe−E/RT

Where A and B are coefficients for each non-global reaction. This equation shows strong

correlation between temperature and reaction rate but no solid increase in combustion

rate can be stated here as the specifics of the combustion are not known. However it

can be said that when the hydrogen fuel is used as a coolant, its injection tempera-

ture will increase which will increase the combustion efficiency of the scramjet engine at

least a modest amount.

On top of this, increasing the temperature of injected fuel will also increase the pene-

tration of the injected fuel into the incoming airflow, ”Which would allow for a modest

increase in the mixing and combustion of the jet” [Barth, 2014]. It can be seen from

figure 3 that a fuel temperature increase to 1000K will increase penetration depth by

13.8%.

Figure 3: Fuel jet penetration increase with temperature normalised at 300 K [Barth,2014]

6

2.3 Combustor Materials

The combustor cans in modern jet engines can be related very closely to that of scram-

jet combustion regions. In a jet engine combustor, temperatures can reach up to 2100oC

[Milne, 2014] which is close to a REST scramjet’s maximum temperature of roughly

2500 oC [Barth, 2014]. These extremely high temperatures prevents the use of the vast

majority of engineering materials and calls for the use of advanced aerospace materials.

Typically jet combustor cans are made from a superalloy containing materials with ”un-

usually high resistance to heat, corrosion, and wear such as tungsten, molybdenum, nio-

bium, tantalum, and rhenium” [Storm, 2014] then the metal is coated in a roughly 250

micrometer thick layer of ceramic, which results in a reduction of temperature that the

superalloy sees of 300oC.

Figure 4: Carbon-Carbon composite brake pads on an aircraft [Korte, 2006]

As an alternative to titanium, scramjets are proposed to use a carbon carbon compos-

ite as their combustor wall material. This advanced composite consists of carbon fiber

within a matrix of graphite, and has the capability to withstand temperatures over

2000oC [Eberle et al., N.D.]. It is currently used in other super high temperature appli-

cations such as the leading edges on the space shuttle [Rodriguez and Snapp, 2003] and

aircraft brake disks [Korte, 2006]. Carbon carbon composites are highly anisotropic ma-

terials, consisting of layers of material sandwiched together to form the complete struc-

ture. This leads to the heat conduction of the material to also be highly anisotropic

with conduction normal to the plies at 8 W/(m K) and 30 parallel to the ply [Ohlhorst

et al., N.D.].

2.4 Hydrogen Storage & Cooling Properties

Scramjet engines typically utilise Hydrogen as fuel owing to its incredibly fast combus-

tion rate. Luckily Hydrogen is also an effective coolant as it has an extremely high spe-

cific heat of 14.32 kJ/(kg K) [Smidth, N.D.] at 20o C. In comparison, Helium is also

7

regarded to have a high specific heat with a value of 5.19 kJ/(kg K) [Smidth, N.D.]. On

the other hand hydrogen has very low density, which leads to very inefficient (in terms

of volume per kg of hydrogen) storage solutions. Much research has been put into this

topic to enhance the storage density of hydrogen, particularly in the automotive indus-

try, where recent breakthroughs have allowed gas storage at pressures between 30 to 70

MPa [Eberle et al., 2012] which increases the density from 0.0813 kg/m3 at atmospheric

pressure to 20.537 kg/m3 at 30 MPa and 30.811 kg/m3 at 50 MPa [National Institute of

Standards and Technology].

A paper published by NASA in 1968 experimentally obtained convective heat transfer

coefficients of high velocity (Mach 0.9) laminar Hydrogen flow in a hexagonal tube ar-

ray [Slaby and Mattson, 1968]. The experiment yielded the results in figure 5.

Figure 5: Measured convective heat transfer coefficients, Reynolds numbers and Nusseltnumbers [Slaby and Mattson, 1968]

It is worth noting that the hydrogen in this experiment was at room pressures and tem-

peratures, meaning density will be lower than in the proposed scramjet cooling regime.

As a consequence heat transfer coefficients will likely be understated and cannot be di-

rectly used for the problem.

The paper then goes on to use the results to formulate an empirical Nusselt number

formulation. This correlation is stated below. This formula may be used for ’back of the

hand’ calculations when estimating expected values.

Nub = 0.023Re0.8b Pr0.4

b

[(TsTb

)exp

(1.59

x/De

− 0.57

)](1)

Where the subscripts b and s stand for bulk and surface respectively.

8

2.5 Turbulent Effects on Heat Transfer

It is well known that turbulent flows tend to have a much greater heat transfer than

its laminar counterpart. Shown in figure 6 are the results of an experiment whereby

water’s heat transfer ability in a pipe was studied over a range of mass flow rates with

different inlet geometries [Meyer and Olivier, 2002]. This data is presented as Nusselt

Number vs Reynolds number, where Nusselt number is calculated by the equation 2.

Nu =hD

k(2)

Figure 6: Nusselt number of pipe flow with different inlet designs [Meyer and Olivier,2002]

The paper goes on to state that the flow transitions from laminar to turbulent over the

range Re = 2100 and 3000. It was also stated that within this regime it is very diffi-

cult to predict where turbulent effects will appear, and when engineers design heat ex-

changers they try to avoid transitional flow for this reason [Meyer and Olivier, 2002]. It

can be seen that at approximately Re= 2600, Nusselt number shows a much sharper in-

crease, a telling sign of the onset of turbulent flow features.

It is also worth noting that of the four different inlets tested (not shown as their design

is irrelevant) there was known discernible difference in the onset of turbulence. Leading

to the conclusion that the inlet design should not be a factor in heat transfer analysis.

9

2.6 Previous Scramjet Cooling Analysis

Although scramjet combustor cooling is a relatively under-studied field, there have

been previous studies conducted in this area. In a study by F.Zander and R.G.Morgan

[2007], a proposed scramjet combustor section was analysed for the purpose of deter-

mining the applicability of carbon-carbon composite for the wall. They accomplished

this by selecting a flight path at Mach 8 and 27 km altitude, and designed a simple re-

generative cooling system consisting of 1mm carbon-carbon coposite at the wall, 1mm

of graphite insulation then a 3mm thick inconel fuel manifold. The fuel manifold was

placed only on the bodyside of the scramjet combustor, with radiative cooling acting as

the cooling mechanism on the cowlside. The fuel was chosen as a hydrocarbon, and was

run through the fuel manifold to act as a regenerative coolant. A diagram of this model

can be seen in figure 7.

Figure 7: Model scramjet combustor cross section [F.Zander and R.G.Morgan, 2007]

This model was then solved using numerical techniques with analytical models for con-

vective heat transfer, which allowed the temperature at the seven points outlined in fig-

ure 7 to be calculated in a time accurate regime. It was found that the highest tem-

perature of the combustor wall was 1950 K, within the allowable limits for the carbon-

carbon composite material. The conclusion was then reached that for this particularly

flight path, sustained flight is possible with the proposed design. The full results can be

seen in figure 8.

10

Figure 8: Time accurate temperature results [F.Zander and R.G.Morgan, 2007]

From figure 8 it can be seen that temperature reaches equilibrium after roughly 12.5

seconds, this is useful information for estimating the time a CFD simulation may take.

2.7 Conjugate Heat Transfer in CFD

Simulating conjugate heat transfer within CFD is a much more complex task than sim-

ulating a fluid only mesh. This is due to two regions (solid and fluid), with vastly differ-

ent dynamics being coupled within the same simulation. There are two distinct meth-

ods to solve these simulations described by Duchaine et al. [2009], one solution involves

directly coupling the solid and fluid regions with a large quantity of simultaneous equa-

tions, and the other involves indirectly coupling two separate solvers (one for the solid

region and one for the fluid) with a boundary condition. Because the latter method was

used in this report, it will be briefly described here.

The coupling of the two separate solvers for the solid and fluid regions is described by

Veeraragavan et al. [2016]. In physical conjugate heat transfer systems the heat flux

and temperature at the interface between the two regions is equal. Using this piece of

information a shared boundary condition is implemented such that initially either the

solid or fluid region is solved with initial conditions, which then imposes the tempera-

ture and heat flux at the region interface as a boundary condition to the other region

where the process is repeated until the end of the simulation. Because of this conjugate

11

heat transfer solvers of this type have two iterations per time step.

3 System Description

To properly analyse a regeneratively cooled combustor in CFD, the system must first be

formulated. In the following sections a description of the parts of the system and how

they were formulated is presented.

3.1 Model Scramjet

The analysis will use heat flux values and geometrical bounds based on a half scale ver-

sion of the M12 REST (Rectangular to Elliptical Shape Transition) Scramjet Engine

of Suraweera et al. [2009] travelling at Mach 10. This decision is based on access to

the simulations and experimental results of this engine as well as the full scale version,

making scalability assessment of the cooling system easier and more accurate compared

to estimating the heat flux of larger scaler engines.

3.2 Heat Flux

The wall heat flux readings along the Bodyside (top) and Cowlside (bottom) combus-

tion section of the half-scale Scramjet engine across two tests can be seen below. The

flow was estimated to have an adiabatic wall temperature of 2540 K, and walls were as-

sumed to be at a uniform 300 K [Barth, 2014].

12

Figure 9: Heat flux along the half-scale REST scramjet combustor section [Barth, 2014]

The above figure shows impressive repeatability between tests (shots), and can therefore

be confidently used in the cooling analysis. It was assumed that in general scramjets

show roughly this trend of heat transfer within the combustor, with heat flux increasing

at the start of the section, then trailing off near the end.

In order to not overload the hydrogen fuel coolant the heat flux into the model was not

modelled after the bodyside nor the cowlside values shown above. Instead the average

of the two values was used, with missing data in the cowlside at around x = 1050 filled

in using the value at x = 1075. This is not too unrealistic as the heat flux within the

circumference of the combustor wall will be spread out within the material. The actual

heat flux values can be seen below in figure 10. Note that the x axis begins at 0 rep-

resenting the start of the combustor section instead of the entire vehicle like in figure 9.

13

Figure 10: Model heat flux

3.3 Fuel

By choice, the selected model scramjet is a hydrogen-fueled design, with a low equiv-

alence ratio of 0.7 corresponding to a mass flow rate of roughly 3.6 g/s [Barth, 2014].

This fuel was kept at a pressure of 1.1 MPa in the plenum before being injected into

the flow stream at room temperature. While this pressure works well for shock tunnel

testing, the hydrogen will need to be stored at much higher pressures up to 70 MPa as

discussed in section 2.4. The mass flow rate might also be increased in full flight designs

in order to achieve net thrust. Both of these parameters will most likely have an impact

on the heat flux imposed on the combustor walls, however modelling this is well outside

the scope of this investigation. Therefore it is assumed that the heat flux is independent

of the hydrogen fuel mass flow rate and pressure.

3.4 Material

The materials used for the scramjet walls are largely dictated by their ability to with-

stand high temperatures. Although some tricks can be used to increase the heat resis-

tance of the material such as using a ceramic coating on the combustor walls to reduce

the temperature seen by the bulk material. As described in section 2.3, carbon-carbon

composite materials make an excellent high temperature material for scramjet combus-

tors and as such are used for the combustor wall material. Given that a definite max-

imum temperature of these materials is difficult to obtain a general rule of thumb of

2300 K [Eberle et al., N.D.] maximum temperature is employed.

14

3.5 Geometry & Geometry Simplification

As previously stated, the model scramjet is that of the half-scale M12 REST engine, a

diagram of its geometry is seen in figure 11.

Figure 11: Original geometry of the half-scale M12 REST engine [Barth, 2014]

Label Name Label NameC Inlet D IsolatorE Constant Area Combustor F Diverging CombustorG Nozzle H Inlet Leading EdgeI Side Wall Leading Edge J Side-Cowl CornerK Inlet Injectors L Cowl Leading EdgeM Cowl Notch O ThroatP Combustor Step

Table 1: Table of dimensions

As can be seen in figure 11 the combustor section is 282mm long and consists of a con-

stant area and a diverging area section, which doubles the cross-sectional area of the

combustor by the end of its length. In order to generalise the combustor geometry, the

diverging section was removed, and the constant area section lengthened to 282 mm.

Furthermore the non-circular shape is unique to the REST engine, and it restricts CFD

15

meshes to 3-dimensions only, vastly increasing the simulation running time. Hence the

combustor was also approximated as a cylindrical section, seen in figure 13 allowing for

2-dimensional simulations to be conducted.

Figure 12: Constant area combustor section geometry

Figure 13: Generalised cylindrical geometry

The coolant channel itself was designed as a simple annular pipe surrounding the com-

bustor wall. This decision was made based on the simplicity of its geometry allowing it

to be modelled in a CFD package easily, and its relatively low cooling ability, which will

yield conservative results.

The wall thickness was based on a conservative calculation for structural strength using

a simple thin-walled pressure vessel stress calculation as seen by equation 3.

t = SFPr

σ(3)

Where SF is the safety factor (set as 1.5), P is the pressure (set as 30 MPa explained

in section 3.6.1), r is the radius of the combustor, σ is the yield strength of the selected

carbon-carbon composite (200 MPa [Eberle et al., N.D.]) and t is the thickness. This

16

results in a thickness of roughly 2.8 mm which was rounded up to 3 mm to be conserva-

tive.

To ensure equal heat transfer through the combustor wall, both inner circumferences,

labelled ’C’ in both diagrams were set as equal. A table of dimensions can be seen in

table 2.

Dimension Value (mm)a 15.5b 8.8r 12.4

t0 (inner wall thickness) 3 (variable)t1 (fuel channel thickness) 3 (variable)

L 282

Table 2: Table of dimensions

Both the inner wall and fuel channel thicknesses were initially set as 3 mm but were

variable in simulations.

3.6 Variables

Due to the simplicity of the proposed design, there are a fairly limited number of vari-

ables that can be analysed during the solving process. However variables associated

with the geometry of the model scramjet such as the inner radius of the combustor

and its length are not selected as variables since it would mean the heat flux values are

invalid. Listed in table 3 are the variables chosen for analysis and a justification as to

why they were selected.

17

Variable Values Justification

Wall Thickness 1.5, 3, 4, 6 mm

By varying the wall thickness thethermal resistance of the wall can bealtered, showcasing the system’s sensi-tivity to this parameter. 1.5 mm wascalculated to be the thinnest wall thatcould maintain structural strength,and 6 mm was chosen as it was doublethe standard thickness.

Hydrogen ChannelThickness

1, 2, 3, 4 mm

The convective heat transfer of thehydrogen should be heavily depen-dant on the geometry of its channel.1 mm was assumed to be the small-est thickness able to be manufactured,and 4 mm was found to be where heattransfer began to asymptote.

Hydrogen Pressure1, 5, 20, 30, 50,70 MPa

Hydrogen can be stored at a range ofpressures, knowing the cooling abil-ity of the hydrogen at these pressureis useful. the storage pressure of hy-drogen fuel in scramjets can be be-tween 1 MPa [Barth, 2014] and 70MPa [Eberle et al., 2012], more reso-lution is needed around 1 MPa thoughdue to greater changes in specific heatin this range.

Hydrogen Mass FlowRate

2.4, 3.6, 4.8 g/s

Scramjets often have different equiv-alence ratios, as such it is importantto know if the combustor will be suf-ficiently cooled at different fuel flowrates. 3.6 g/s is the flow rate of themodel scramjet at nomindal equiv-alence ratios, both lower and higherflow rates may be used depending onthe system.

Table 3: Selected variables

3.6.1 Standard System Parameters

In order to compare each variable properly a standard system must be selected. For

example the fluid pressure when varying channel thickness must be equal to the fluid

pressure when varying flow rate, so a fair comparison can be made. The standard sys-

tem and the justification behind these choices can be seen in table 4.

18

Variable Value Justification

Fluid ChannelThickness

3 mm

A thin coolant channel must be used to en-sure sufficient fluid velocity and heat trans-fer, but it must be thick enough to be man-ufactured, 3 mm was found to be a goodmiddle ground through experimentation.

Solid WallThickness

3 mm

By making the standard wall thicknessequal to the standard fluid channel thick-ness a fair comparison to the effect of eachvariable can be carried out, furthermore itwas shown through quick calculations thatthinner walls might not be able to hold upstructurally to the large fluid pressures.

Fluid Pressure 30 MPa

30 MPa was chosen as it was the lowestpressure used in high pressure Hydrogenstorage and was roughly a half-way pointbetween current pressures in scramjet tests(1MPa [Barth, 2014]) and the typical maxi-mum storage pressure of 70 MPa.

Mass Flow Rate 3.6 g/sThis mass flow rate corresponds to thatused in the model scramjet experiments.

Table 4: Standard system

3.7 Alternate Approaches

Although a model scramjet has been presented in the previous sections, it is highly sim-

plified and it is worth summarising some alternative approaches and why they were not

used here.

1. Flowing hydrogen fuel coolant in the positive Z direction, not the negative:

While the heat flux is higher at the front of the combustor section, and therefore

having the low temperature hydrogen inlet at this part of the section may be ad-

vantageous, the packaging solution for this solution is more complex, with the hy-

drogen flow having to enter the coolant channel right next to the injector, run

through the coolant channel then be rerouted back into the injector. Hence the

simpler solution was used.

2. Using the original combustor geometry instead of the simplified constant area

model:

Although using the original geometry will give more accurate results for the spe-

cific scramjet considered, it then only becomes valid for that geometry and us-

ing a constant area combustor section gives the most general solution possible.

Furthermore the replaced diverging area section is located where the heat flux

19

drops considerably, hence changes to this area are unlikely to greatly affect re-

sults.

3. Using a full-scale model:

In order to quantify the assumptions made and understand the reasons for heat

flux trends access to simulations and the people who conducted the research is

useful, which is the case with this particular model.

4. Simulating a full 3-dimensional mesh:

Access to large computational resources was available to be able to run large sim-

ulations, however if this was used it would have been difficult to iteratively run

simulations with different variables. Furthermore it would require significant time

investment in order to set up properly and validate, risking the failure of the project.

4 CFD Case

4.1 Software and Solver

A conjugate heat transfer solver with a fluid and solid domain is required to solve the

proposed heat transfer problem. Originally the still-in-development Eilmer 4 CFD pack-

age was used, however it was quickly realised that it was inadequate in its current state.

In its place the open source CFD code, OpenFOAM version 4.1, was used.

The solver used within the OPENFOAM framework was chosen as the conjugate heat

transfer implicit solver chtMultiRegionSimpleFoam. The implicit version of the solver

was required due to the large amount of time heat transfer problems take to converge.

This solver uses the separate solver coupling method described in section 2.7 to simu-

late conjugate heat transfer between a solid and fluid region.

4.2 Geometry

The geometry of the CFD case was constructed by taking a slice of the geometry shown

in figure 13 and has the same dimensions as stated in table 2. While this is techni-

cally a two dimensional shape within the cfd solver, the geometry has width because

in OpenFOAM, a two-dimensional geometry is constructed with a single cell in the 3rd

dimension (width), which allows cylindrical geometry to be modelled with the correct

cell volumes.

20

Figure 14: Geometry of CFD representation (Fluid region in light grey, Solid in dark)

The simplicity of this geometry allows it to be modelled within a CFD solver very eas-

ily, with a single block representing the solid region below another single block repre-

senting the fluid region.

4.3 Boundary Conditions

A case for a CFD simulation is set up by constructing a mesh, then applying bound-

ary conditions to that mesh’s outside walls. The boundary conditions are used to ’close’

the problem and make it a self-sufficient system. For example an inlet boundary condi-

tion would mean a fluid flow across that wall of the mesh, then an outlet would essen-

tially allow the flow to leave the mesh. Figure 15 deconstructs the geometry shown in

figure 14 into boundaries and table 5 explains each boundary condition. Note that the

actual names for the boundary conditions within OpenFOAM are not used as they are

too specific to make much sense out of.

21

Figure 15: Boundary labels

LabelBoundaryCondition

Explanation

1 Adiabatic Wall

The top surface of the geometry is the outsidewall of the geometry (where the scramjet is con-nected to the main body of the craft), and it wasassumed that at steady state there is no heattransfer across this boundary. This boundarycondition also applies a no-slip condition on thefluid to correctly model flow close to a wall.

2 Inlet

The Hydrogen fuel enters the system across thisboundary in a negative Z direction, at a specifiedtemperature and pressure using a constant massflux condition.

3 Fluid-Solid InterfaceAt this boundary the solid and fluid regions arecoupled, in that the temperature solution foreach region is shared to the other.

4 Zero-Gradient Outlet

Here the Hydrogen flow exits the system, mod-elled with the use of a zero-gradient condition,which extends the variables profile through theoutlet.

5 Adiabatic WallMuch like boundary 1, this wall was assumed tonot have any heat transfer at steady state.

6Non-Uniform HeatFlux

Here the imposed heat flux from the combustoris applied to the system. This is a more complexboundary condition which will be explained inmore detail in section 4.3.1.

7 Fluid SymmetryThis boundary condition is essentially a wall con-dition without the no-slip condition, which cor-rectly models a slice of an axi-symmetric model.

8 Solid SymmetryMuch like 7 this condition is needed to correctlymodel the axi-symmetric geometry.

Table 5: Boundary condition explanation

22

4.3.1 Heat Flux Boundary Condition

In the scramjet combustor model heat is transferred to the combustor wall from the in-

ner flow according to equation 4. This equation simplifies the complex heat conduction

within moving fluids using the constant ’h’.

Q = hA∆T (4)

Where ∆T is the temperature differential between the simulation temperature and the

set boundary temperature. However, CFD codes calculate heat transfer according to

the more fundamental discretised conduction equation for one-dimensional flux, equa-

tion 5.

Q =kA∆T

∆x(5)

Where k is the heat conduction coefficient of the medium, and ∆T∆x

is the temperature

gradient in the required direction.

In order for a convection boundary condition to be constructed the CFD code must be

’tricked’ into it by making the heat convection equal to the heat conduction computed

by the CFD code. This is accomplished by varying the applied boundary temperature

at each point on the boundary, and at each time step, according to equation 6.

Tboundary =1

1 + k∆xh

+ Tsim (6)

Now all that is needed is to sub in the correct constants, h and k to calculate the right

boundary temperature and in turn the right heat flux. For k this is simple, it is sim-

ply the heat conduction coefficient of the solid wall, explained in section 4.4.2. However

the heat convection coefficient h is more complex as it varies along the length of the

combustor with heat flux shown in figure 9. h is able to be calculated at each of these

points by equation 7.

h =q

∆T(7)

Where q is the average heat flux between the body and cowlside heat flux shown in fig-

ure 9 and ∆T is 2240 K, the difference between the bulk inner flow temperature and

the 300 K walls in the experiment [Barth, 2014]. h is then calculated at each cell posi-

tion using linear interpolation where necessary and applied to the boundary condition.

These h values are shown below in figure 16.

23

Figure 16: Convective coefficient values for the combustor heat flux

Linear interpolation was used to fill out the plot between data points as the use of more

complex functions such as splines and polynomials were found to return unrealistic be-

haviour, with exaggerated peaks and troughs.

4.4 Thermophysical Model

The large temperature variations expected within the simulation calls for attention to

detail when it comes to the thermodynamic models used for both the fluid and solid

regions.

4.4.1 Hydrogen Model

Density

The extremely high pressure of the hydrogen pushes its density outside of the regime of

a perfect gas. Instead the Peng-Robinson Equation of State, seen below, was used in its

place.

P =RT

Vm − b− αa

V 2m + 2bVm − b2

a =0.45724R2T 2

c

Pc

b =0.0778RTc

Pc

α = (1 + k(1−(T

Tc

)0.5

))

24

k = 0.37464 + 1.54226ω − 0.26992ω2

Using the values Tc = 33, Pc = 1.3MPa [Hoge and Lassiter, N.D.] and the acentric fac-

tor, ω = -0.22 [Reid et al., N.D.]. The equation of state for the hydrogen fuel can accu-

rately be modelled.

To add confidence in this density model, the density of the hydrogen was calculated at

all simulated pressures, 1 through 70 MPa, at 300 K and compared to data obtained

from the National Institute of Standards and Technology as seen in figure 17.

Figure 17: Comparison between selected hydrogen density model and actual density

Their is some notable difference between actual and model density at high pressures,

particularly at 70 MPa. However, the model is still far superior to using the perfect gas

equation, and a significant density difference is only seen in one simulation at 70 MPa.

As such the Peng-Robinson gas model was deemed accurate enough for these purposes.

Viscosity The viscosity was calculated using OpenFOAM’s sutherland model, where

the usual three variables are simplified to two, As and Ts.

µ =As√T

1 + Ts/T

Where As and Ts were set as 6.71×10−7 and 83 respectively [Saxena, 1973].

Heat Conduction

Because heat conduction within a fluid is a complex phenomena, simple solutions can-

not be used for its model. In its place Euckland’s approximation is used, which is pack-

aged within the Sutherland Viscosity approximation. Equation 8 states Euckan’s ap-

25

proximation and its inputs.

k = µCv

(1.32 + 1.77

R

Cv

)(8)

Specific Heat

The specific heat of the hydrogen was set as a constant 14.8 kJ/(kg K) based on data

from the National Institute of Standards and Technology [National Institute of Stan-

dards and Technology]. It was aparent from this data that above 0oc hydrogen shows

no drastic changes in its specific heat, hence a constant value could be confidently used.

Unfortunately hydrogen’s specific heat does change depending on its pressure, which

becomes an issue when investigating the effects of hydrogen pressure on the heat trans-

fer of the system. To combat this the specific heat was changed for each pressure value

presented in table 3.

Pressure (MPa) Specific Heat (kJ/(kg K))1 14.55 14.5420 14.6830 14.850 14.970 14.95

Table 6: Hydrogen specific heat at set pressures [National Institute of Standards andTechnology]

4.4.2 Carbon-Carbon Composite Model

As the wall material is a solid, the thermodynamic model can be simplified to contain

only density, heat conduction and specific heat.

Density

Due to the extremely low coefficient of thermal expansion for carbon, its density is con-

stant at approximately 1600 kg/m3, taken as the average between several carbon-carbon

composite materials [Ohlhorst et al., N.D.].

Heat Conduction

Carbon-Carbon is a highly anisotropic material, with heat conduction in plane signifi-

cantly larger than out of plane. Typically in-plane heat conduction coefficient is approx-

imately 30 W/(m K) and out-of-plane is 7 W/(m K) [Ohlhorst et al., N.D.]. The latter

value does vary down to approximately 5.5 at room temperature but remains relatively

constant at temperatures above 600 K, well below what will occur within the combustor

26

wall.

Due to the lack of a working anisotropic solver within OpenFOAM, the lower, out-of-

plane heat conduction coefficient was chosen and kept constant at all temperatures, this

will lead to a less smooth temperature distribution along the length of the combustor,

resulting in a higher maximum temperature, although this is a conservative result and

will be fine for the purposes of this study.

Specific Heat

Unlike the heat conduction coefficient, specific heat of Carbon-Carbon composites does

vary greatly with temperature. However, specific heat only alters time accurate mod-

els, since this is an implicit solver, it’s use is mostly a place holder, as such its value was

chosen to be constant at an expected temperature within the wall, 1200 K, correlating

to a heat capacity of 1800 J/(kg K).

4.5 Turbulence

As shown in section 2.5 turbulence plays a massive role in the heat transfer process. As

such determining whether turbulence is present in the system will need to be carefully

analysed. To achieve this the Reynolds number of each simulation was calculated and

compared to the data shown in figure 6. It has been shown in experiments that for an-

nular concentric channels, the flow is laminar below a Reynolds number of 3600, and

turbulent above 21600 [Jaafar1 et al., N.D.] when calculated using equation 9. Given

that in figure 6 transition occurred at 50 % the way through the transitional regime, it

was assumed that if the Reynolds number of the system was above roughly 12600, that

a turbulence model would be applied to the simulation.

Re =2ρV t

µ(9)

Where t is the thickness of the fluid channel. The Reynolds number for all simulations

was calculated and compared to the turbulent criteria set out.

27

Variable ValueReynoldsNumber

Channel Thickness 1 mm 7180Channel Thickness 2 mm 6960Channel Thickness 3 mm 6732Channel Thickness 4 mm 6554Wall Thickness 1.5 mm 7344Wall Thickness 3 mm 6732Wall Thickness 4 mm 6114Wall Thickness 6 mm 5667Pressure 1 MPa 7030Pressure 5 MPa 6891Pressure 20 MPa 6790Pressure 30 MPa 6732Pressure 50 MPa 6701Pressure 70 MPa 6678Mass Flow Rate 40 mg/s 4488Mass Flow Rate 60 mg/s 6732Mass Flow Rate 80 mg/s 8988

Table 7: Simulation Reynolds numbers

Note that here fuel mass flow rate has been changed to the simulated mass flow rate,

or 1/60th of the total fuel mass flow rate of the scramjet. As can be seen in table 7 the

maximum Reynolds number across all simulations was 8988, below the critical value of

12600. Hence the turbulence model used in all simulations was laminar.

4.6 Interpolation Scheme

One of the main drawbacks of CFD is the approximations that must be made to solve

the field. In that vein the interpolation scheme is required, as the name suggests, to in-

terpolate values within the mesh accurately in order for the simulation to be solved.

There are countless schemes available in CFD packages, each with their own specific

use. Because of this researching and selecting the correct interpolation scheme for the

specific CFD case is a monumental task in itself. Hence it is typical practise to simply

find a case similar to the case in question, and use the same scheme. This method was

employed here.

Due to the simple nature of the conjugate heat transfer problem solved in this investi-

gation, multiple comparable conjugate heat transfer examples were found within Open-

FOAM. The most common interpolation scheme used in these cases were the Bounded

Gauss Upwind scheme for the fluid region and Gauss Linear Corrected for the solid re-

gion.

28

4.7 Mesh

As the geometry of the CFD case is relatively simple, so to is the mesh. The only no-

table features are that of the cell clustering towards the inlet and each north and south

wall of the mesh, including the interface. This clustering can be seen in the below fig-

ures 18, 19 and 20. Figures 18 and 19 represent roughly the same portion of the overall

mesh to show the clustering differences between each end.

Figure 18: Enlarged mesh at inlet Figure 19: Enlarged mesh at outlet

Through these figures it can be seen that that the horizontal cell size is much larger

at the outlet than the inlet, this was done as at the inlet, the boundary layer develops

rapidly, causing large gradients between cells. Without clustering, the cells would have

had to be the same small size seen in figure 18 the entire length, greatly increasing the

total number of cells and therefore computational time. By clustering cells near the in-

let, this can be avoided.

Figure 20: Enlarged mesh at interface

It can be seen that it figure 20 that the cell size becomes smaller then enlarges seam-

29

lessly. This occurs at the interface between solid and fluid regions. On the fluid side

clustering is required to resolve the boundary layer of the fluid flow accurately, this is

particularly important in this analysis as the boundary layer profile greatly affects heat

transfer. The clustering on the solid side is required to match the cell size on the fluid

side, if clustering were not present there would be computational error in the simulation

due to the way CFD is constructed.

4.8 Convergence and Mesh Independence

The most critical factor when running CFD simulations is to ensure that the mesh is

dense enough to accurately represent the system, and in implicit schemes, that the sim-

ulation converges to a solution. The former is accomplished by repetitively running sim-

ulations, increasing cell density each time and checking important results until there is

a sufficiently low change to prove the mesh is dense enough. This was accomplished by

checking the heat absorbed by the Hydrogen fuel in the standard system configuration

while increasing cell numbers in the fluid and solid regions, first in the Y direction, then

in the Z. These results can be seen in table 8.

No. Cells YFluid

No. Cells YSolid

No. Cells ZHeat Absorbed(W)

60 60 100 226.490 90 100 230.590 90 125 232.190 90 150 232.5

Table 8: Mesh independence analysis

Fortunately the initial mesh density was close to the final converged values so the mesh

validation study was a relatively quick process. Considering there was only a 2.6 % dif-

ference between the initial and final cell density results there is a case to be made that

the original cell density should be used to save computation time. However, simulation

times were not large to begin with and considering that variables will be changed in

some simulations a higher mesh density should prevent any deviations in the simula-

tions.

To accommodate the change in variables shown in table 3, each extremity of each vari-

able was tested for mesh independence by increasing the cell density by 50% and ob-

serving results. This can be seen in table 9. Furthermore the geometric variables, chan-

nel thickness and wall thickness, had their cell numbers altered to maintain their orig-

inal cell density. For example the 1 mm channel thickness mesh had 30 cells instead of

90 in the Y direction, as it is one third of the original 3 mm geometry.

30

Variable Value Absorbed Heat (W)Channel Thickness 1 mm 233Channel Thickness 4 mm 232.5Wall Thickness 1.5 mm 232.5Wall Thickness 6 mm 232.5Pressure 70 MPa 232.5Pressure 1 MPa 232.5Mass Flow Rate 80 mg/s 233.7

Table 9: 50% Cell density increase results for extreme variables

The maximum mass flow rate of 80 mg/s showed the greatest divergence from the stan-

dard absorbed heat of 232.5 W, but this change was still well within reasonable limits,

hence the original cell density was used for all simulations.

To ensure each simulation was run to convergance without the need to analyse each

simulation a conservative implicit run time of 110 000 s was used for all simulations.

Convergence was then checked by plotting the residuals of each simulation. A reduction

in residuals by five orders of magnitude is sufficient to confidently prove convergence

has occurred. The residual plot for the standard system is seen in figure 21.

Figure 21: Residual plot of simulation convergence

As can be seen, the simulation’s enthalpy (analogous to temperature) converges much

31

slower than the other variables but does reduce by more than five orders of magnitude,

proving convergence. However it can be seen that the pressure residuals converge to a

value one order of magnitude greater than the other variables. Usually this would be

a concern, however the simulation is actually at constant pressure, so convergence of

this value is meaningless. Residual plots for all simulations can be seen in appendix A.

The reason for the much thicker enthalpy line is due to the fact that two regions exist

with enthalpy solutions in the simulation and OpenFOAM does not differentiate be-

tween them, meaning each of the two enthalpy solutions at each time step are logged

within the same list, so the thick line is actually a single small line jumping up and

down each iteration. Also note that although simulations were run for 110 000 seconds,

there were double that amount of iterations as described in section 2.7.

The slow nature of enthalpy convergence is explained by the slow and asymptotic na-

ture of heat transfer in solids, as the heat transfer rate decreases as the temperature

differential between two areas decreases.

5 Results

By running the CFD simulation repetitively, solutions for the modified variables were

able to be found, along with results such as absorbed heat by the hydrogen, maximum

temperature, temperature profiles and fluid profiles. By comparing the results within

the same variable, some justification of the results can be found, strengthening the trust

in the accuracy of answers.

Note that where the maximum wall temperature is stated, this is also the maximum

temperature of the entire simulation, and is slightly exaggerated compared to reality

due to the isotropic nature of the simulations.

5.1 General Simulation

To give confidence that the simulations were indeed run and resolved the flow and tem-

perature fields correctly, direct simulation results from the standard parameter model

(described in section 3.6.1) is presented.

32

5.1.1 Velocity

Figure 22: Velocity near inlet Figure 23: Velocity near outlet

The development of the boundary layer near the walls of the hydrogen fluid channel is

apparent in figures 23 and 22, with flow near the wall at either end of the simulation

approaching zero. Furthermore it can be seen at the outlet that the flow near the centre

of the challenge accelerates to approximately double that of the inlet. This is in part

due to the decrease in density of the fluid as it is heated and due to the thickening of

the boundary layer slowing a larger chunk of the flow near the wall.

5.2 Temperature

Figure 24: Temperature near inlet Figure 25: Temperature near outlet

Presented in figures 24 and 25 is the temperature solution near the inlet and outlet of

the simulation containing both the solid and fluid regions. The interface between the re-

gions can be seen easily in figure 24 halfway down the image. It can be seen that at this

point there is no sharp change in temperature, as should be the case in conjugate heat

transfer cases as theoretically the temperature at the wall on the solid side should be

exactly equal to that on the fluid side. This being said on the very left edge of figure 24

some temperature mismatch can be seen, however this is due to a limitation of the inlet

boundary condition.

33

Figure 26: Temperature profiles along Z axis

In order to confirm the temperature solution in the solid region the temperature profiles

along the lower wall and interface are plotted in figure 26. It can be seen that the tem-

perature along the interface is simply the temperature seen at the lower wall but shifted

down and smoothed slightly. The smoothing can clearly be seen near the Z value of

0.23, where sharp jumps in temperature in the solid black line are not present to the

same extent in the dashed. This provides confidence in the solution as it shows that

the heat conduction within the solid is operating in both the Z and Y directions. Once

again, due to the limitations of the CFD package used, this smoothing of the temper-

ature was understated compared to reality where the solid would have a much higher

conduction coefficient in the Z direction.

34

5.3 Fluid Channel Thickness

Figure 27: Varying fuel channel thickness results

As seen in figure 27, the maximum temperature drops significantly at thin fuel channel

thickness to almost 1800 K. This is significant because it shows that at small channel

thicknesses this coolant system is quite effective, and achieves a significant safety gap

between the maximum wall temperature and the maximum temperature of the mate-

rial. It can also be seen that the absorbed heat and maximum temperature asymptote

at larger channel thicknesses, due to the slower velocity of the hydrogen changing the

heat transfer mechanism to mainly conduction like a solid, not convection.

The reasons behind the high absorbed heat at low channel thicknesses can be seen clearly

when the velocity profiles at the outlet are plotted.

35

Figure 28: Velocity Profiles at Outlet

Figure 28 shows how the velocity increases proportional to the inverse of channel thick-

ness squared, increasing the mass flow rate at the boundary layer drastically at lower

channel thicknesses and therefore increasing the heat transfer at the wall interface.

36

Figure 29: Temperature profile at outlet

As seen in figure 29, there are areas of the hydrogen fuel that do not see any increase

in temperature, essentially wasting cooling potential. However in the 1 mm and, to a

lesser degree, channel thickness simulation the far edge of the hydrogen flow does see an

increase in temperature. At these low channel thickness the coolant system is able to

take advantage of the entirety of the fluid flow, although not to its full capacity, mean-

ing there is still room for increased cooling ability.

37

5.4 Solid Wall Thickness

Figure 30: Varying wall thickness results

The effect of wall thickness is much less than that of channel thickness, with only an

approximate 13 K difference in maximum temperature over a 400 % increase in thick-

ness. This leads to the conclusion that the heat conduction resistance presented by

the wall is not the limiting factor in the design of this cooling system. There is some

anomalous behaviour of the trend line around the 3 mm wall thickness region, however

the deviation is not significant and is highly unlikely to mean there is something wrong

with the simulations.

38

5.5 H2 Inlet Mass Flow Rate

Figure 31: Varying mass flow rate results

Note that the mass flow rates shown in the plot correspond to the simulated mass flow

rates, not the total mass flow rate. The results in figure 31 are rather surprising in that

there is little change despite a 33 % increase in mass flow rate. At first glance there

should theoretically be a quite substantial increase in heat transfer due to the larger

mass flux at the wall interface.

Figure 32: Velocity profile at outlet

39

The answer for the unexpected results comes from the velocity profiles in figure 32. It

can be seen at the wall interface (Y value = 0.0151), the fluid’s boundary layer is actu-

ally slower and takes more distance to speed up compared to the outer wall boundary

layer. Furthermore the fluid’s peak velocity is seen much closer to the interface wall.

The cause for these two points is most likely due to the viscosity of the hydrogen being

much greater at higher temperatures, which pushes the path of least resistance closer

to the outer wall, taking the flow direction with it. This essentially causes a lower mass

flow rate close to the wall interface and therefore lower heat transfer.

5.6 H2 Pressure

Figure 33: Varying hydrogen pressure results

Once again the absorbed heat and maximum temperature showed little difference across

the range of simulations. Any difference that was present was most likely a result of the

higher specific heat of hydrogen at higher pressures. Although at lower pressures den-

sity does decrease dramatically, meaning higher velocities throughout the fluid channel,

there was no change in the mass flow in that channel. In other words, the boundary

layer at the combustor wall interface had a higher velocity but equal cooling capacity,

meaning no distinct change in heat transfer.

40

Figure 34: Comparison of Specific Heat and Absorbed Heat

As seen in figure 34 the absorbed heat follows roughly the same trend as the specific

heat of the hydrogen across all pressures, although some deviation is seen at 30 MPa.

This gives strong evidence that the only variable influencing the absorbed heat by the

hydrogen coolant was its specific heat. Reaffirming that Hydrogen is an excellent coolant

due to its high specific heat compared to other fuels.

6 Conclusion

A CFD analysis on cooling characteristics of hydrogen for a simple scramjet combus-

tor wall heat flux case is presented. It has shown that the only variable of significant

importance to the success of an annular channel coolant system for hydrogen-fuelled

scramjet combustors is the thickness of the coolant channel, and it is therefore the lim-

iting factor for this coolant system. The maximum temperature seen by the combustor

wall was below the maximum usable temperature of Carbon-Carbon composites of 2300

K across all presented parameters, and was able to be reduced to approximately 1800 K

with a channel thickness of 1 mm. Therefore it can be confidently stated that using this

coolant system, a scramjet combustor will be sufficiently cooled to prevent damage.

41

7 Recommendations

Due to the fact that there was such a large advantage to using a thin fluid channel,

more analysis in the effect of pressure and flow rate should be conducted to determine

the effect of these variables at lower channel thicknesses than the 3 mm conducted in

this study. Furthermore fuel may be able to be stored in cryogenic or at least cooler

conditions than the room temperature 300 K that was used here, hence analysis to the

effect of the hydrogen’s inlet temperature may be of use.

Due to the higher heat fluxes at the beginning of the combustor section, it may be ad-

vantageous to flow the hydrogen fuel in the opposite direction, i.e. in the positive Z di-

rection instead of the negative direction used here. This will mean the cooler hydrogen

at the inlet will be sent directly onto the hottest part of the section, potentially reduc-

ing the maximum temperature in the combustor wall, however this could cause prob-

lems with packaging.

42

Appendices

A Residual Plots

1mm Channel Thickness Residuals 2mm Channel Thickness Residuals

3mm Channel Thickness Residuals 4mm Channel Thickness Residuals

40 mg/s Flow Rate Residuals 80 mg/s Flow Rate Residuals

43

1.5mm Wall Thickness Residuals 3mm Wall Thickness Residuals

4mm Wall Thickness Residuals 6mm Wall Thickness Residuals

1 MPa Inlet Pressure Residuals 5 MPa Inlet Pressure Residuals

44

20 MPa Inlet Pressure Residuals 30 MPa Inlet Pressure Residuals

50 MPa Inlet Pressure Residuals 70 MPa Inlet Pressure Residuals

45

B Solid - Fluid Interface Temperature Profiles

Varying Channel Thickness Interface Temperature Profile

Varying Mass Flow Rate Interface Temperature Profile

46

Varying Wall Thickness Interface Temperature Profile

Varying Pressure Interface Temperature Profile

47

C Lower Wall Temperature Profiles

Varying Channel Thickness Lower Wall Temperature Profile

Varying Mass Flow Rate Lower Wall Temperature Profile

48

Varying Wall Thickness Lower Wall Temperature Profile

Varying Pressure Lower Wall Temperature Profile

49

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