Inlet aerodynamics plays a key role in the successful operation of hypersonic airbreathing systems for flexible and economical access-to-space and atmospheric flight. Flow separation, however, can critically deteriorate the engine performance particularly for internal-compression scramjets with high contraction, where the boundary layer is susceptible to adverse pressure gradients. The flow physics of an axisymmetric scramjet inlet is investigated by means of the design optimisation of transition trip wires

Boyce, Russell R.

Ogawa, H.

University of Queensland eSpace

Numerical Investigation of Turbulence Effects on Boundary Layer Separation 
in Axisymmetric Scramjet Inlets via Design Optimisation 
 
H. Ogawa and Russell R. Boyce 
Centre for Hypersonics, School of Mechanical and Mining Engineering 
The University of Queensland, St. Lucia, Brisbane, QLD 4072, Australia 
h.ogawa@uq.edu.au 
 
ABSTRACT 
Inlet aerodynamics plays a key role in the successful operation of hypersonic airbreathing systems for flexible and economical 
access-to-space and atmospheric flight. Flow separation, however, can critically deteriorate the engine performance particularly 
for internal-compression scramjets with high contraction, where the boundary layer is susceptible to adverse pressure gradients. 
The flow physics of an axisymmetric scramjet inlet is investigated by means of the design optimisation of transition trip wires. 
 
1. Introduction 
Scramjet propulsion is a promising hypersonic 
airbreathing technology that offers the potential for 
reliable and economical access to space and high-speed 
atmospheric cruise. Axisymmetric scramjets featuring 
innovative concepts such as inlet fuel injection and 
radical-farming shock-induced separation are being 
developed in the SCRAMSPACE program, which is 
now underway as an international collaboration led by 
The University of Queensland (UQ). 
Scramjet engines typically consist of an inlet, 
combustor and nozzle, where airflow capture, 
compression, fuel mixing, combustion, and expansion 
occur in a sequential manner. The inlet, in particular, 
plays a crucial role for reliable operation of scramjets. 
Extensive numerical investigation recently conducted at 
UQ has indicated considerable influence of viscosity on 
the inlet flow physics, suggesting a critical importance 
of boundary layer modelling. Fig.1, for instance, shows 
a prominent difference in the inlet flowfields computed 
by different two-equation RANS turbulence models, i.e., 
cubic k-ε and k-ω SST. The boundary layer shape factor 
H (= δ
*
/θ) at the first compression corner (x = 0.232m) 
plotted in Fig.2. subsequently shows a large value of the 
k-ε model comparable to the laminar boundary layer (the 
smaller the H value, the ‘healthier’ the boundary layer). 
 
Fig.1. Inlet flowfields with k-ε / k-ω (SST) turbulence model 
0 
5 
10 
15 
20 
25 
30 
Laminar B.L. Spalart-Allmaras k-ε k-ω
H
1
 
(SST)  
Fig.2. B.L. shape factor at the first compression corner 
with various turbulence models 
The present research is undertaken to investigate the 
key mechanism responsible for inlet flow physics in a 
state-of-the-art design optimisation approach so as to 
allow appropriate measures to be taken against boundary 
layer separation which can crucially affect the engine 
performance in ground tests and flights, where both 
laminar and turbulent flows can occur in practice. 
 
2. Methods 
1. Freestream conditions and inlet configuration 
The freestream conditions are M∞ = 8.0, p∞ = 1197Pa 
and T∞ = 226.5K, assuming scramjet operation on a 
constant dynamic pressure trajectory of 53.6kPa at an 
altitude of 30km. The Reynolds number based on the 
inlet radius (0.075m) is Re∞ = 2.26×10
5
. k∞ = 3.45×10
3
 
m
2
/s
2
 and ε∞ = 3.45×10
3
 m
2
/s
3
 or ω∞ = 4.30×10
5
/s for the 
turbulence properties. The inlet has a contraction ratio of 
4.8, comprising three ramps (as seen in Fig.1) and a 
leading-edge tip radius of 0.5mm. 
2. Computational fluid dynamics 
The flowfields are assumed to be thermally perfect 
and computed by utilising a commercial high-fidelity 
code CFD++. The Navier-Stokes equations are solved 
by an implicit algorithm with second order spatial 
accuracy and multigrid convergence acceleration. Two 
cylindrical trip wires with the same radius rt are 
implemented as virtual turbulence source to induce 
boundary layer transition added to the cubic k-ε model. 
0 
5 
10 
15 
20 
k-ε =0.1mm =0.2mm =0.5mm =1mm 
H
1
 
fine 
coarse 
r t r t r t r t  
Fig.3. Mesh dependency of B.L. shape factor 
A two-dimensional structured mesh comprising 
21,582 cells (219×100 nodes) with y
+
 = 0.32 at the 
surface is used to represent the axisymmetric flow 
domain. This resolution is chosen, based on a 
preliminary mesh sensitivity study, where the same 
effectiveness of the trip wires located at xt = 0.1m and 
0.15m in preventing separation is observed between the 
fine (438×200 nodes) and coarse grids, as seen in Fig.3, 
where separation is suppressed when rt ≥ 0.2mm. 
 3. Optimisation algorithms 
The multi-objective design optimisation capability 
based on evolutionary algorithms developed at the 
University of New South Wales campus at the 
Australian Defence Force Academy [1] is employed to 
investigate the effects of transition trip wires and wall 
temperature, coupled with the CFD solver in the 
optimisation chain. Optimisation has been performed 
with 32 individuals in the population pool for the 
double-objective problem stated as: 
 minimise:  (1) trip wire radius rt 
  (2) B.L. shape factor H1 
 subject to:  H1 < 5 for attached boundary layer 
 for: trip wire radius 0 ≤ rt ≤ 0.25mm 
  trip wire positions 0 ≤ xt1,2 ≤ 0.238m 
  wall temperature 200 ≤ Tw ≤ 400K 
 
3. Results and Observations 
Design optimisation has been performed over 20 
generations. No distinct Pareto front has been observed 
with respect to the two objective functions, i.e. rt and H1, 
nor has notable influence of the wall temperature Tw 
(results are not shown here). The majority of the 
evaluated trip wire settings have led to attached 
boundary layers (thus feasible solutions), whereas only 
8 individuals among 640 solutions have failed to 
suppress boundary layer separation (infeasible solutions), 
as plotted in Fig.4, out of which 3 representative 
solutions I1,2,3 are selected for detailed flowfield analysis, 
along with 3 adjacent feasible individuals F1,2,3. 
0 
0.05 
0.1 
0.15 
0.2 
0.25 
0 0.05 0.1 0.15 0.2 
r
t [
m
m
] 
x
t
 [m] 
feasible 
infeasible 
I
1
F
1
F
2
I
2
F
3
I
3
 
Fig.4. Mean trip wire position 
tx  vs trip wire radius rt 
Compared in Fig.5 are the distributions of the shape 
factor of the boundary layer from the inlet leading edge 
to the second ramp. The individuals F1,2,3 with attached 
boundary layers are characterised by relatively low and 
flat distributions comparable to the k-ω SST case, 
whereas a local rise of the shape factor is observed for 
the infeasible individuals I1,2,3 as well as the k-ε case, 
indicative of the occurrence of flow separation. It is 
noteworthy that the local cluster of infeasible solutions 
around xt = 0.15m in Fig.4 is present near the streamwise 
station of the H rise, where the onset of flow separation 
persists for a long period during steady computations
1
. 
                                                 
1 Note that the H values are plotted for the fully converged 
flowfields for the k-ε and k-ω cases, while used for the other 
cases are the solutions after 2000 iterations, which is found to 
be adequate to judge separation for optimisation, though more 
than 20,000 iteration steps are required for full convergence. 
0 0.05 0.1 0.15 0.2 0.25 
H
 
x [m] 
k-ε 
feasible F
1
 
feasible F
2
 
feasible F
3
 
infeasible I
1
 
infeasible I
2
 
infeasible I
3 
k-ω (SST)
 
Fig.5. B.L. shape factor distributions 
The distributions of the turbulent kinetic energy are 
plotted in Fig.6. It is noticeable that the turbulence 
added in the vicinity of the leading edge (x ≈ 0.02m near 
the initial H peak in Fig.5) has rapidly vanished for the 
infeasible I1 case, while it is damped once shortly after 
addition and regenerated downstream (x ≥ 0.15m) in the 
case of the feasible F1 for the similar trip wire positions 
and radius to I1. The turbulence intensified by local 
transition trips are found to endure and grow to a fully 
turbulent level for F2 and F3, whereas it dissipates 
quickly and reduces to a near laminar state for I2 and I3. 
0
2
4
6
x 104
0
0.05
0.1
0.15
0.2
0.25
0
0.005
0.01
0.015
k [m2/s2]
x [m]
n
 
[m
]
k−ε
feasible F1
feasible F2
feasible F3
infeasible I1
infeasible I2
infeasible I3
k−ω (SST)
 
Fig.6. Turbulent kinetic energy distributions 
4. Concluding remarks 
The effects of turbulence on the boundary layer 
separation have been investigated numerically for an 
axisymmetric scramjet inlet by means of design 
optimisation using trip wires to augment the turbulence 
predicted by the k-ε model. The results have revealed 
remarkable sensitivity of the boundary layer to transition 
trip, whose subtle difference can critically affect the fate 
of the inlet flowfield. The underlying mechanism is yet 
to be scrutinised, with particular attention to the reported 
tendency of the k-ε model to underestimate turbulence in 
adverse pressure gradients [2] and sensitivity of the k-ω 
model to the freestream turbulence property values [3]. 
References 
[1] T. Ray and W. Smith, “A Surrogate Assisted Parallel 
Multiobjective Evolutionary Algorithm for Robust 
Engineering”, Engineering Optimization, 38 (8), 2006. 
[2] J.E. Bardina, P.G. Huang and T.J. Coakley, “Turbulence 
Modeling Validation, Testing and Development”, NASA 
TM-110446, 1997. 
[3] D.C. Wilcox, Turbulence Modeling for CFD, DCW 
Industries, Inc., 2006. 


Numerical investigation of turbulence effects on boundary layer separation in axisymmetric scramjet inlets via design optimisation

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Numerical investigation of turbulence effects on boundary layer separation in axisymmetric scramjet inlets via design optimisation

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