Prediction of Heat Flux in a Scramjet Combustor with Kerosene Fuel
through CFD
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
Nonreacting and reacting flow simulations are carried out for a scramjet combustor to predict the heat transfer
characteristics on the walls. 3-D RANS equations are solved along with SST-k ω turbulence model and fast
chemistry using commercial software. The validation exercise for a nonreacting flow in a convergent-divergent
nozzle shows a good match of computed heat flux with experimental data. Grid independence of the heat flux on
the scramjet combustor walls has been demonstrated using various grids and found that a minimum of 1st grid
spacing of 10 micron is required to accurately predict the wall heat flux. Heat transfer coefficient is found to be
almost independent with various isothermal wall. It is demonstrated that well resolved CFD simulation is
required to generate input for thermo-structural design of high speed propulsion system.
Keywrods: Scramjet, heat flux, heat transfer coefficient, CFD, reacting flow
1. Introduction
The development of a scramjet engine leading to the building of an efficient hypersonic air breathing vehicle for
civil and military applications has started in early 1960s [1, 2]. In order to fulfil the requirement of fuel for the
scramjet engine, both hydrogen and kerosene were studied extensively [3]. In many applications, hydrocarbon
fuels are preferred due to their greater density and ease of handling [4], especially for the lower hypersonic (M <
8) flight regimes. Computational Fluid Dynamics (CFD) is being utilized to model accurately the flow field
during design phase of scramjet engine by resolving several complex physical processes including three
dimensionality shock boundary interaction, atomization and vaporization of liquid fuel, turbulent mixing, slow
chemical reactions, heat load on scramjet engine walls etc. Numerical studies for scramjet combustor with liquid
hydrocarbon (i.e., kerosene fuel) are not many in the reported literature. Bouchez and Dufour [5,6] reported
numerical studies on strut-based kerosene fuelled scramjet combustor using MSD-2.2.2 CFD code developed at
ONERA and obtained reasonably good match between the computational and experimental wall static pressure.
Manna et al. [7] have numerically explored the effect of the combustor inlet Mach number and total pressure on
the flow development in a scramjet combustor. It was shown that higher combustor entry Mach number and
distributed fuel injection are required to obtain predominant supersonic flow and avoid thermal choking. The
presence of fuel injection struts makes the flow fully three-dimensional, causes significant flow blockage and
affects the mixing and combustion pattern in the scramjet combustor. Manna et al. [8] have numerically
investigated an optimized flight sized scramjet combustor performance in terms of thrust and combustion
efficiency using CFD tools. Combustor performance was improved significantly by redistributing the fuel,
relocating the strut and proper drop size distribution. Effect of middle wall on the combustor performance was
evaluated by comparing simulation results. Improved mixing and combustor performance were reported due to
the presence of the middle wall.
The major problem faced in the design of the scramjet airframe is high thermal load caused due to
burning of fuel inside the engine and also external aerodynamic heating at the outside surface. Measurement of
wall heat flux and temperature pose formidable challenge due to high value of heat flux and oxidising
environment. Local hot spot, critical in the design of scramjet engine airframe, cannot be located correctly by
theoretical/experimental studies. Advances in numerical methods and computer hardware have made CFD a
viable tool to predict heat transfer characteristics on the complete wall surface along with the 3-D fluid flow
calculations.
1
In the present work, a scramjet combustor flow field is numerically analysed along with proper wall
boundary conditions to determine wall heat flux (qw) and heat transfer coefficient (hc) using CFX software [9].
The code is first validated against published literature of nonreacting supersonic convergent-divergent flow [10]
and subsequently used for the present scramjet combustor.
2. Computational methodology
Three-dimensional Reynolds Averaged Navier Stokes (RANS) equations are solved using CFX software [9],
which is an integrated software system capable of solving diverse and complex multidimensional fluid flow
problems. The code is fully implicit, finite volume method with finite element based discretization of geometry.
The method retains much of the geometric flexibility of finite element methods as well as the important
conservation properties of the finite volume method. It utilizes numerical upwind schemes to ensure global
convergence of mass, momentum, energy and species. It implements a general non-orthogonal, structured,
boundary fitted grids. To circumvent the initial numerical transient, the discretization of the convective terms are
done by first order upwind difference scheme till few time steps initially and subsequently, the convective terms
are discretized through 2nd order scheme to capture the flow features more accurately. SST-k turbulence model
[11] with scalable wall function was used to predict capability on heat flux distribution in reacting flow
simulations.
2.1 Combustion model
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. When reactants mix at the
molecular level, they instantaneously form the products. The model assumes that the reaction rate may be related
directly to the time required to mix reactants at molecular level. In turbulent flows, this mixing time is dictated
by the eddy properties and therefore the burning rate in proportional to the rate at which turbulent kinetic energy
is dissipated, i.e., reaction rate is proportional to ε/k, where, k is the turbulent kinetic energy and ε is its
dissipation rate. The chemistry of the kerosene (C12H23) reaction is represented on a molar basis by,
𝐶12 𝐻23 + 17.75(𝑂2 + 0.6𝐻2 𝑂 + 2.64𝑁2 ) → 12𝐶𝑂2 + 22.15𝐻2 𝑂 + 46.86𝑁2
The mixing rate determined from the Eddy Dissipation Model (EDM) is given as.
Rk   Aebu 

Yp 

Y
min Y f , o , Bebu

k
1  s 
 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.
2.2 Heat flux modelling near the wall
The heat flux at the wall is modelled using the thermal law-of-the-wall function approach of Kader [12] in CFX
software. The heat flux distribution near-wall follows a non-dimensional temperature profile through the viscous
sub-layer and the logarithmic region. The heat flux ( q w ), is defined as:
𝑞𝑤 =
where,
𝜌 𝐶𝑝 𝑢𝜏
𝑇+
(𝑇𝑤 − 𝑇𝑓 )
𝑇 + = Pr∗ 𝑦 + ∗ 𝑒 (−Γ) + [2.12 ∗ 𝑙𝑛(𝑦 + ) + 𝛽] ∗ 𝑒 (−Γ)
𝛽 = (3.85 𝑃𝑟 1/3 − 1.3) 2 + 2.12 ∗ 𝑙𝑛(𝑃𝑟)
𝛤=
0.01∗(𝑃𝑟∗𝑦 + )4
1+5∗𝑃𝑟 5 ∗ 𝑦 +
and
𝑦+ =
𝑃𝑟 =
𝜇∗𝐶𝑝
𝜆
𝜏
1/2
, 𝑢𝜏 = ( 𝜔 )
𝜌
𝜌∗∆𝑛∗𝑢𝑡
𝜇
3. Validation case: Convergent-Divergent (CD) Nozzle
Convective heat transfer rate measurements in a convergent-divergent nozzle by Back et al [10] are taken as the
test case for validation. Tests were carried out for a wide range of stagnation pressures (from 2 to 30 bar) and
stagnation temperatures (from 600 to 1200 K). Compressed air was heated by internal combustion of methanol
2
and then passed through a long chamber to obtain uniformity of flow before it entered the nozzle. The ratio of
methanol-to-air weight flow rate was small enough (even for the highest stagnation temperature) and the
products of the combustion could be treated approximately as air. The nozzle is having a throat diameter of
0.0458 m with the contraction ratio of 7.75 to 1.0 and expansion ratio of 2.68 to 1.0. Further details of the
geometry and test conditions are available in Ref. 10.
Simulated region considered for the present study is shown in Fig.1. Since, nozzle geometry is
axisymmetric, a 900 sector (i.e., 1/4th geometry) is considered for computational domain, which is shown in
Fig.2. Multi-block structured grids (hexahedral) with 0.83 million cells are made using ICEM-CFD software
[13]. The grids are fine near the nozzle wall, while relatively coarser grids are provided in the remaining portion
of the nozzle. Average y+ ~ 2 is obtained for nozzle walls. The stagnation pressure of 10.38 bar and stagnation
temperature of 824 K (same as done in test) are imposed at the nozzle entry. Fluid is taken as pure air in present
simulations. The nozzle walls are specified isothermal wall (Tw = 467 K) conditions. The supersonic outflow
boundary condition is applied at the exit of the nozzle. Log-normalized maximum residue of four order less for
various flow variables and global mass, momentum, and energy imbalance less than 0.1% between outlet and
inlet of the computational domain are considered as the convergence criteria.
Fig.1: Experimental setup with simulated region for CFD
Numerical simulations are carried out using the commercial CFD code CFX software [9] by solving
RANS equation along with SST-k turbulent model [11] with automatic wall function to predict wall heat flux
on nozzle wall for nonreacting flow. The comparison of computed heat flux distribution with test data along the
flow direction is shown in Fig.3, which shows a good match with experimental data.
Fig.2: Computational domain of C-D Nozzle
Fig.3: Comparison of heat flux with test data [10]
4. Heat flux estimation in scramjet combustor
A typical cruise hypersonic air-breathing mission is explained in Ref. [14] for the demonstration of 20 seconds
duration flight. The operating Mach number and altitudes are 6.5 and 32.5 km respectively. A supersonic
combustor ramjet (scramjet) is considered to generate the thrust for the vehicle. Due to the limitation of the
connected pipe mode test facility, the development and testing of the scramjet combustor was focused on the half
scale module. This scramjet combustor with fuel injector struts was directly connected to a blow-down type high
enthalpy test facility. A vitiated air heater (hydrogen burner with make-up oxygen supply) was used to obtain
high enthalpy airflow equivalent to flight total temperature and total enthalpy of 1650-1750 K and 1.55-1.65
3
MJ/kg respectively. Test gas was accelerated through a contoured convergent-divergent nozzle to Mach ~2.0 at
the combustor entry.
The combustor dimensions were non-dimensionalised with the combustor entry height (h). Total length
of the combustor including facility nozzle is 26 h. The facility nozzle entry and combustor exit cross section
areas are 5.2h2 and 9h2 respectively. The width of the combustor is kept constant throughout the length.
However, the height of the combustor is varied (bottom wall is flat while top wall is divergent) while
ascertaining that the combustor can be fitted in the overall vehicle envelope without much drag penalty. The
schematic of the scramjet combustor is shown in Fig. 4. The combustor has four sections. The 1 st section has a
constant area with a length h (1st section), followed by 10 (2nd section), 40 (3rd section) and 7.50 (4th section)
divergent at top wall for 2.3h, 8.1h and 10h length respectively. The left wall has a half-wedge of 0.007h
thickness inside facing the free stream flow placed at a distance of 2.9h from the combustor inlet.
Fig.4: Schematic picture of scramjet combustor
The computational domain along with the facility nozzle and the combustor is shown in Fig.5. In the
simulation, X-axis is taken along the flow direction (length of combustor), while, Y and Z-axis are chosen along
the height and width of the combustor respectively, with the origin being placed at the intersect point between
left wall and bottom wall at combustor entry. Liquid kerosene (C12H23) is injected through 104 injection points
provided in the 4 struts. Each strut contains 13 injection holes on either side. 1st strut is placed upstream and near
the left wall while the last strut (4th strut) is put in the downstream and adjacent to the right wall. All the injection
holes have approximately of the same size with a diameter of 0.5 mm. The schematic picture of strut-4 (zoomed
view) showing the location of injection holes is also presented in Fig.5. The inlet conditions as achieved in
ground test facility at nozzle entry plane correspond to the flight condition of Mach 6.5 at 32.5 km altitude.
Liquid kerosene fuel is injected at an equivalence ratio () of 0.9 with a Rosin-Rammler particle distribution of
diameter D = 37.32 m and dispersion spread parameter of 1.5.
Fig.5: Computational domain of scramjet combustor along with strut details
Multi-block structured hexahedral grids (with grid sizes 2.04 million to 3.12 million cells) are made
using ICEM-CFD software [13] for the entire computational domain. (Results with different grids are compared
subsequently). The typical grid distribution for computational domain in X-Y plane at Z/h = 1.6 and in X-Z plane
at Y/h = 0.5 are shown in Fig.6. The grids are fine near the leading edge and trailing regions of the struts and
near-wall regions, while relatively coarser grids are provided in the remaining portion of the nozzle and
combustor. Average y+ ~ 5 is obtained (for fine grid) for nozzle, combustor and struts walls. Stagnation enthalpy
4
of 1.62 MJ/kg, and mass fraction of O2, H2O and N2 of 24%, 18% and 58% respectively are applied at facility
nozzle entry. All the flow properties are kept constant in the entry plane of facility nozzle and fuel injector
respectively. All walls are specified as isothermal wall (Tw) conditions. The supersonic outflow boundary
condition is applied at the exit of the combustor. The same convergence criterion in the previous case is also
considered here.
Fig.6: Grid distribution on various planes in computational domain
5. Results and discussion
Both nonreacting and reacting flow simulations are carried out to estimate the heat flux distribution on the
combustor wall. Reacting flow simulations are carried out with transverse injection of liquid kerosene fuel into
the main flow through the struts at an equivalence ratio () of 0.9.
5.1 Baseline case: Reacting flow with Tw = 600 K, Grid sensitivity study
To find the grid independence of heat flux, reacting flow simulations with wall temperature (Tw) of 600 K are
carried out taking the minimum grid size (n) from 80 m to 5 m (grid distribution is changed mostly adjacent
to the wall regions) with three intermediate values of n = 40 m, 15 m and 10 m. Accordingly, total grid size
for computational domain has been changed from 2.04 million to 3.12 million cells. The maximum heat flux
(qwmax) is observed at the leading edge of 1st strut. Comparison of non-dimensionalised local wall heat flux
(defined as qw/qwmax) along the flow direction at Z/h = 1.6 is shown in Fig.7 for various grid distributions. It is
observed that the results are almost same for n = 10 m and 5 m, which depicts that minimum grid spacing of
n =10 m is required to predict the heat flux values adjacent to the wall.
Fig.7: Comparison of heat flux distribution
with various grid size at Z/h = 1.6
Fig.8: Contour of heat flux on combustor wall
Contour plot of the heat flux distribution for top wall and left side wall is shown in Figs.8(a) & (b)
respectively. Clearly higher heat flux zones are observed behind the struts [Fig.8(a)] which is due to the reaction
of kerosene fuel with supersonic air. For the left wall, higher heat flux values are found towards the top and
bottom wall corners. Axial distribution of wall heat flux is compared in Fig.9 for all four walls. In general, high
heat flux values are obtained adjacent to the reaction intense zone (in the middle of the combustor). High heat
5
flux is observed at the leading region of the left wall. Top, bottom and left side walls are showing almost similar
values of heat flux whereas, right side wall has shown comparatively less value which is due to the fact that the
right side wall has been faced less combustion zone compared to the other walls.
5.2 Comparison nonreacting and reacting flow heat flux at Tw = 600 K
Nonreacting flow simulation is carried out with isothermal wall (Tw = 600 K) to calculate heat flux values on the
combustor walls. Nonreacting and reacting flow heat flux comparison is shown in Figs. 10 along an axial line
generator for top wall. It has been observed that, heat flux increased due to heat release in case of reacting flow
compared to nonreacting flow case. Larger heat flux values are observed in Section-III regions of the combustor,
which is due to the more reaction subsequent to vaporization of kerosene fuel.
Fig.9 : Comparison of heat flux distribution
Fig.10: Comparison of heat flux
5.3 Effect of wall temperature on combustor walls
A separate simulation is carried out with isothermal wall of Tw = 900 K to see the effect of wall temperature on
heat transfer characteristics in wall. Fig.11 shows the comparison of axial (local) heat flux distribution for top
wall. Higher heat flux values are obtained for lower isothermal wall temperature which is due to the fact that the
thermal gradient of temperature is more in case of lower wall temperature causing more amount of heat to flow.
Fig.12 shows the local heat transfer coefficient distribution along the axial length for top wall. Heat
transfer coefficient, hc is defined as follows:
qw
hc 
(Taw  Tw )
Where, Taw is the adiabatic wall temperature and Tw is the isothermal wall temperature. Though there
are differences in the heat flux values as seen earlier, heat transfer coefficient has been found almost same for
two isothermal conditions. This shows that the heat transfer coefficient is independent of the wall temperature.
Conclusions
Numerical simulations are carried out to predict the heat flux for scramjet combustor analysis. Three
dimensional RANS equations are solved along with SST- k ω turbulence model and species transport equations
using commercial CFD software CFX. Single step chemical reaction with Lagrangian Particle Tracking Method
is used for combustion of kerosene fuel. The code is first validated by comparing computational and
experimental heat flux data for nonreacting supersonic convergent-divergent flow and a good agreement is
observed. The validated methodology is applied to predict the heat transfer characteristics for scramjet
combustor walls for reacting and nonreacting cases for different wall temperatures. Grid independence of the
results revealed that first grid size of 10 micron (minimum) adjacent to the wall is required to accurately predict
the wall heat flux. Heat flux values are found to be more in the third section of the combustor where maximum
reaction takes place after fuel vapourization. It is observed that although the heat flux varying with different wall
temperature, heat transfer coefficient distribution remained almost invariant. The computed heat flux provides
important design input for thermo-structural design of scramjet combustor.
6
Fig. 11: Comparison of heat flux distribution
Fig.12: Comparison of hc distribution
References
1. Feri, A., 1964, “Review of problems in application of supersonic combustion,” Journal of Royal
Aeronautical Society, 68(645), 1964, pp. 575–597.
2. Waltrup, P.J., 1987, “Liquid-fueled supersonic combustion ramjet: A research perspective,” Journal of
Propulsion and Power, 3(6), pp. 515–524.
3. Curran, E.T., 2001, “Scramjet engines: The first forty years,” Journal of Propulsion and Power, 17(6), pp.
1138–1148.
4. Edwards, T., 2003, “Liquid Fuels and Propellants for Aerospace Propulsion: 1903–2003,” Journal of
Propulsion and Power, 19(6), pp. 1089-1107.
5. Bouchez, M., Dufour, E., Montazel, X., 1998, “Hydrocarbon Fueled Scramjet for Hypersonic Vehicles,”
AIAA Paper No. 1998-1589.
6. Dufour, E., and Bouchez, M., 2001, “Computational Analysis of a Kerosene Fueled Scramjet,” AIAA
Paper No. 2001-1817.
7. Manna, P., Behera, R., and Chakraborty, D., 2008, “Liquid fueled strut based scramjet combustor design –
a computational fluid dynamics approach,” Journal of Propulsion and Power, 24(2), pp. 274–281.
8. Manna, P., Dharavath, M., Sinha, P.K., Chakraborty, D., 2013, “Optimization of a flight-worthy scramjet
combustor through CFD,” Aerospace Science and Technology, 27(1), pp. 138–146.
9. ANSYS CFX software, Release 11.0: Installation and Overview, January 7th, 2007.
10. Back, L. H., Massier, P. F., and Gier, H. L., 1965, “Convective Heat Transfer in a Convergent–Divergent
Nozzle,” Technical report 32-415, Jet Propulsion Laboratory, California Institute of Technology, Pasadena
CA.
11. Menter, F.R., 1994, “Two-equation eddy-viscosity turbulence models for engineering applications,” AIAAJournal, 32(8), pp.1598-1605.
12. Kader, B.A., 1981, “Temperature and concentration profiles in fully turbulent boundary layers,”
International Journal of Heat and Mass Transfer, 24(9), pp.1541-1544.
13. ICEM-CFD software, Release 11.0: Installation and Overview, January 7th, 2007.
14. Pannerselvam, S., Thiagarajan, V., Ganesh, A.T.K., Geetha, J.J., Ramanujachari, V., Prahlada, 2005,
“Airframe integrated scramjet design and performance analysis,” ISABE Paper No. 2005-1280.
7