Conjugate Heat Transfer of SCHOLAR Scramjet Combustor – A CFD
Validation Study
Anand Bhandarkar, Malsur Dharavath, P. Manna and Debasis Chakraborty*
Defence Research and Development Laboratory,
Kanchanbagh, Hyderabad-500058, India
Tel: +91-40-24583310, Fax: +91-40-24340037, Email*: debasis_cfd@drdl.drdo.in
ABSTRACT
Numerical investigations were carried out for SCHOLAR scramjet combustor to explore the conjugate heat
transfer (CHT) capability of CFD software ANSYS-CFX in nonreacting and reacting flow. Hydrogen fuel which
is injected at 300 angle to the vitiated air flow in the combustion duct consisting of copper and steel wall outside,
is considered for present numerical studies. Both fluid flow and solid conduction are solved together. 3-D RANS
equations are solved along with k-  turbulence model and species transport equations for fluid domain while 3D
heat conduction equations are solved to calculate solid transient temperature distribution. Single step chemical
reaction with fast chemistry i.e., eddy dissipation combustion model (EDM) is used for combustion of hydrogen
fuel. Simulations are carried out with facility nozzle to get realistic boundary profiles at the combustor entry.
Computed facility nozzle exit pitot pressure profiles match well with experimental data. Good match is observed
between computed bottom wall pressure distribution and experimental data except the injection regions, where
CFD predicts higher values because of more heat release due to fast chemistry assumption. Solid interface
temperatures for both copper and steel wall are predicted well in nonreacting (t=1.0 sec – 6.4 sec) flow.
However, in reacting flow (6.4 sec – 24.0 sec), present CFD results overpredict (within 10%) the experimental
values near the injection zones and underpredict (within 12%) away from the injection zones. Interface
temperature is found to change very little with the change of exterior wall boundary conditions and variable
material property data. Higher heat flux has been predicted adjacent to the fuel injection region compared to the
downstream regions.
Keywords: Conjugate heat transfer, SCHOLAR combustor, reacting flow, hydrogen fuel, skin temperature
1. Introduction
The goal of heat transfer studies is the accurate prediction of temperature and heat flux distribution in time and
space in a body and on its boundaries. When there is an interaction between heat conduction in the solid with
convective heat transfer in the fluid, is often called the Conjugate Heat Transfer (CHT) problem in literature. If
we want to obtain more realistic and accurate calculations of the temperature fields, which are very important for
evaluating thermal stresses and proper choice of the material to use, we have to fully take this coupling effect
into account. With the great increase in speed and memory storage of modern computers, improved
computational schemes as well as grid generation algorithms; this problem is amenable to numerical simulation.
Computational Fluid Dynamics (CFD) codes are extensively employed in the design of high-speed air-breathing
engines. CFD analysis based on the Reynolds Averaged Navier-Stokes (RANS) equations uses models for the
turbulent fluxes that employ many assumptions and empirically determined coefficients for turbulent viscousfluxes and chemical specie-production source-terms. Therefore, these models need to be validated with
experimental data before being applied to the similar class of problems. A supersonic-combustion scramjet
model known as SCHOLAR scramjet combustor has been tested at NASA Langley’s Direct-Connect Supersonic
Combustion Test Facility (DCSCTF) [1-3]. Experiments were carried out to provide a relatively simple case for
validation of CFD codes involving supersonic injection, mixing and combustion with supersonic air flow in a
duct. The enthalpy of the test gas (vitiated air) is equivalent to Mach 7.0 flight. Few numerical simulations of
this experiment have already been reported in literature [4-6]. Murty [7] has solved SCHOLAR scramjet
combustor flow field and thermal response of solid walls separately. Two methods were used for the prediction
of transient wall temperature. In the first method, heat transfer coefficient values obtained from CFD simulations
at different wall temperatures are used for the thermal analysis of combustor wall. While in second method,
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engineering correlation (Eckert’s reference temperature method) is used to obtain the heat transfer coefficient
using CFD flow field data, which is used for the thermal analysis of combustor walls.
In the present work, conjugate heat transfer analysis for the SCHOLAR scramjet combustor is carried out
using a commercial CFD code [8]. The purpose of the present simulations is to predict the solid skin temperature
in CHT mode and compare with experimental data to validate the code.
2. Description of the experiment
The combustor test model along with the facility nozzle is shown in Fig.1. The combustor consists of two main
sections; the upstream copper section and the downstream carbon steel section. Stainless steel flanges and carbon
gaskets separate the sections from each other and the nozzle. The facility nozzle provides a nominal Mach
number of 2.0 at the entry of the combustor. Proceeding from left to right, there is a constant area segment, a
small outward step at the top wall, a second short constant area segment followed by a constant 3° divergence of
the top wall. The bottom wall is flat and horizontal. The span is constant at 87.88 mm. The height (H) of the
combustor at entry is 38.86 mm while at the exit is 112 mm. Hydrogen fuel is injected at a pressure of 3.44 MPa,
temperature of 302 K, equivalence ratio of 1.0 at an angle of 30° to the flow direction. The injector nozzle is
designed by the method of characteristics to produce Mach 2.5 flow at the injector exit. The duct is uncooled.
The wall thickness of the copper duct is greater than 32 mm and the carbon steel duct is 19 mm.
Fig.1 Scholar scramjet combustor model [1]: (a) Facility nozzle, copper and steel duct sections (b) Zoomed view
in the vicinity of fuel injector and pilots.
3. Computational methodology
Three-dimensional RANS equations are solved using CFX-code [8], which is an integrated software system
capable of solving diverse and complex multidimensional fluid flow problems. The turbulence was solved using
k- [9] model along with wall function. For combustion, the eddy dissipation combustion model is used for its
simplicity and robustness in predicting the performance of reactive flows in many engineering applications. The
eddy dissipation model is based on the concept that chemical reaction is fast compared to the transport process in
the flow. The fast chemistry of the hydrogen reaction is represented on a molar basis by,
𝐻2 + 0.5(𝑂2 + 0.879𝐻2 𝑂 + 2.429𝑁2 ) → 1.439𝐻2 𝑂 + 1.214𝑁2
The mixing rate determined from the Eddy Dissipation Model (EDM) is given as.
Rk   Aebu 

Yp 

Y
min Y f , o , Bebu

k
s
1  s 

Where, Yf,, Yo and Yp are the mass fractions of fuel, oxidizer and products respectively, Aebu and Bebu are
the model constants and vs is the stiochiometric ratio.
3.1 Gas-Solid Interface Boundary Condition
For CHT approach, in general, at the gas-solid and solid-solid interface, the energy balance is done using FFTB
method (Flux Forward, Temperature Backward). At the interface of two different regions, the heat flux and the
temperature must be conserved.
T
T
T1 |12  T2 | 21 k1 n1 |12  k2 n2 |21
,
This is achieved using an inner iterative loop. The boundary heat flux at the common interface in the
second domain is prescribed equal to the calculated heat flux in the first domain (Flux Forward). With this
Neumann boundary condition, the temperature distribution on the second domain can be computed. The
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temperature profile obtained in the second domain at the common interface is prescribed back to the first domain
as a Dirichlet boundary condition (Temperature Back). The temperature distribution and the heat flux are then
computed in the first domain and the loop is iterated till the temperature and heat flux differences at the domain
interface are below the desired numerical error. When the convergence is reached, the physical time step is
incremented and iteration for the next time step starts. The time step for the numerical simulation is calculated
based on the method that the thermal pulse within the solid materials should not cross more than one
computational cell within a prescribed time step. This is calculated as follows;
t 
 x2
2
Where, δt is the time step, δx is the smallest cell characteristic length in the solid domain and α is thermal
diffusivity of the solid materials.
3.2 Computational domain and boundary details
The computational domain is shown in Fig.2. It consists of two parts, namely, facility nozzle and combustor with
fuel injection system. Both the parts are simulated together to predict correctly the boundary layer growth at the
entrance of the combustor. Due to the symmetry along the width of the combustor, only half of the geometry is
considered for the simulation to reduce computational time. The origin is taken at the centre of the nozzle exit
(or combustor inlet). X-axis is considered along the length of the combustor, while Y and Z-axes are taken along
the height and width of the combustor respectively. A structured grid of 3.6 million cells is generated using
ICEM-CFD [10]. The typical grid structure of the nozzle and in the neighbourhood of the injector is shown in
Fig 3. The grids are made sufficiently fine to capture all the flow features. To enable accurate prediction of wall
heat flux, grids are taken very fine near the wall (y+ ~ 1) and relatively coarser in the core.
Uniform inflow condition is provided at vitiated air and fuel entry conditions. The details of boundary
conditions at respective boundaries are provided in Fig.2. Supersonic outflow boundary is specified at the
combustor outlet. The water cooled walls of the facility nozzle are considered isothermal at 500 K [4]
temperature along with no slip wall condition. Both adiabatic and natural convection boundary conditions are
applied at the outer walls of copper and steel blocks in separate simulations to see the effect of exterior wall
boundary condition. Transient CHT case; non-reacting simulation is carried out for initial 5.4 seconds (from 1
sec to 6.4 sec instance), while reacting CHT simulation is carried out for rest 17.6 sec (from 6.4 to 24 sec
instance).
Fig. 2: Computational domain with boundary details
Fig. 3: Grid distribution at injector region
4. Results and discussion
The nozzle and combustor flow field are simulated together, so that the solution at the exit plane of the facility
nozzle provides accurate values of various flow variables at combustor entry plane. The calculated nozzle-exit
pitot pressure profiles are presented in Fig.4a and Fig.4b for the vertical center plane and the horizontal center
plane respectively. Both show very good agreement with the experimental data. Average values of Mach
number, static pressure and static temperature are found to about 1.95, 1.05 bar and 1200 K respectively.
4.1 Reacting flow simulation without solid wall
A reference reacting flow simulation without solid walls is carried out to understand complex mixing,
combustion and heat transfer process in the combustor. The comparison of temperature and O2 mass fraction
contours at different axial locations are shown in Figs.5a and 5b respectively. It is to be noted that VULCAN
used Drummond’s 9 species and 18-reactions [6] H2-air kinetic mechanisms, whereas an infinitely fast chemistry
is used in the present computation. Because of fast chemistry assumption, reactions are comparatively fast. The
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experimental (CARS) measurement samples indicate that heat-release occurs after 0.4 m, while the temperature
contour of present simulation show the heat release at this location. Although, oxygen is seen to be burnt
completely at the core of the combustor, significant amount of unburnt oxygen is seen to be present near the
sidewalls. Fig.6 shows the comparison of bottom wall surface pressures between present computation,
experimental data [1] and VULCAN [6]. The instantaneous high heat release due to fast chemistry model in the
present simulation is responsible for high pressure in the near injection zone. In the downstream region of
combustor (X > 0.6 m), the present computations match better with the experimental result.
Fig.4: Comparison of computed pitot pressure with experimental data
a)
b)
Fig.5 Comparison of a) temperature b) O2 mass fraction distribution at various cross sections
Fig.6 Comparison of centreline bottom-wall pressure distribution
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4.2 CHT simulation with constant material properties
The conjugate heat transfer analysis is performed using constant material properties for the copper and steel
block as mentioned in Table-1. To avoid the initial disturbances, reliable experimental data are used from 1 sec
instance. Hence, the CHT numerical simulation has been started from 1 sec. Solid temperatures were initialized
corresponding to the reported measured data at 1 sec which are 335 K and 365 K for copper and steel blocks
respectively. Non-reacting CHT simulation has been carried out for 1.0 - 6.4 sec (total 5.4 seconds) before fuel
injection while reacting flow CHT simulation has been carried out for next 17.6 seconds with fuel injection, i.e.
from 6.4 to 24.0 sec instance. Outside wall was assumed adiabatic in the simulation. The transient wall
temperature is monitored at locations, 2.8 mm from the interface for copper block and adjacent to interface for
steel block. Comparison of temperature history with time at three locations on top wall is shown in Figs. 7(a)-(c).
Results show that the present CFD results over predict the experimental results near the fuel injection zone at
copper block (at X=0.197 m i.e. very close to the injection zone the maximum difference is 10% and at X=0.426
m the maximum difference is within 6%) whereas, in the downstream location in steel block, CFD under predicts
(at X=0.978 m the maximum difference is 12%) the experimental results. More heat release due to infinitely fast
chemistry assumptions may be the cause for the over prediction of the results adjacent to the injection zone.
Table 1: Material properties of materials
Material
Density, 
(kg/m3)
Specific heat,
Cp (J/kg-K)
Thermal conductivity,
k (W/m-K)
Copper
8933
385
401
Steel
7854
434
60.5
Fig.7: Comparison of transient wall temperature at three different locations
Fig.8: Comparison of transient wall temperature at X = 0.426 m
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Separate simulation is carried out with natural convection heat transfer exterior boundary condition for
copper and steel block and the transient wall temperature at X=0.426 m is compared with experimental results
and adiabatic wall boundary condition in Fig.8. Almost identical results of both the simulations show minimal
effect of wall exterior boundary condition.
4.3 CHT simulation with variable material properties
The effect of variable material properties on the solid temperature distribution is studied through numerical
simulations. The density of material which does not vary much with temperature is taken as constant (values
mentioned in Table-1), while the variations of specific heat (Cp) and thermal conductivity (k) are taken as a
function of temperature [11] and shown in Fig.9. The values of specific heat (Cp) and thermal conductivity (k)
for copper vary less than 5.6% and 5.0% respectively in the temperature range of 300 K to 600 K, whereas, the
same parameters vary about 82% and 48% respectively for carbon steel in the temperature range of 300 K to 900
K. These property values are directly used in the simulation as a function of temperature. Fig.10 shows the
transient wall surface temperature comparison between constant and variable material properties at X = 0.978 m.
From the plots, it is evident that there is almost negligible effect of temperature dependent material properties on
interface wall temperature prediction. The temperature distribution inside the copper and steel block along the
thickness (from inner wall surface to outer wall surface) at t= 24 sec are shown in Figs.11(a) and (b)
respectively. The effect of variable properties is almost negligible for copper section (variation in temperature is
less than 1%) because the material property variation is minimal in this section. While it is significant for the
steel section due to the large property variation for the corresponding temperature limits. Predicted outer wall
temperature in case of variable property is about 10.0% less compared to constant wall property case.
Fig.9: Variable material properties distribution
Fig.10: Comparison of surface temperature
Fig. 11: Comparison of temperature distribution in solid
Fig.12 gives the interface temperature along the combustor bottom wall at different time instants. The
temperature for copper section is 335 K and for steel section it is 365 K initially (at t=1 sec), which increases
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after wards with time. For reacting flow, i.e., t=6.4 sec onwards, the rate of temperature increase is more initially
which decreases gradually with time towards the end of the experiment.
Fig.12: Centreline bottom wall temperature at different time instants
5. Conclusions
Numerical simulations were carried out for SCHOLAR scramjet combustor to explore the CHT capability of
CFX code in reacting flow. The CHT analysis is performed for 23 seconds to predict the transient wall
temperature. The facility nozzle was modeled along with combustor to provide realistic inflow conditions for the
combustor. Results of the simulation show that the wall temperature is over predicted (maximum 10%) for the
locations X=0.197 m and 0.426 m near to the combustion zone while it is under predicted (~12%) for the
location X=0.978 m away from the reaction zone. This is because of the high heat release near the injector due to
fast chemistry (EDM) combustion model. The wall pressure in the bottom wall is high near the injection region,
while it matches well with experiment in downstream regions. The variable material properties and the free
convection boundary condition for the copper and steel block have negligible effect on interface wall
temperature prediction. But it affects the temperature distribution inside solid region significantly. Though the
various parameters are predicted within acceptable accuracy, the results can further be improved by using finite
rate chemistry model.
References
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a Supersonic Combustor for CFD Code Validation,” AIAA Paper 2002-0743.
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Experiments for Propelled Hypersonic Flight,” AIAA Paper 2002-3879.
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Supersonic Confined Flow,” MS Thesis.
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