Powered, Aerodynamic Simulations of An Airbreathing, Hypersonic Vehicle
Powered, Aerodynamic Simulations of An Airbreathing, Hypersonic Vehicle
Powered, Aerodynamic Simulations of An Airbreathing, Hypersonic Vehicle
Powered, Aerodynamic
Simulations of an Airbreathing,
Hypersonic Vehicle
Alexander D. T. Ward1 and Michael K. Smart2
alexander.ward1@uq.net.au
1PhD Candidate, 2Professor
A key parameter for thrust production is the exit area of the scramjet nozzle. In this
work, the nozzle expansion area was varied by increasing the frontal area around the
engine modules. The increased expansion was observed to create additional thrust,
however the detrimental effects of reduced angle of attack on engine performance
and trim drag resulted in reduced overall net thrust.
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NOMENCLATURE
α Angle of attack, °
Elevon deflection angle, °, positive down
Estimated discretisation error
Trajectory angle, °
Mesh refinement functional
, Nozzle exit area, m
, Combustor exit area, m
Drag coefficient
Lift coefficient
Moment coefficient about centre of gravity
Mach number
Dynamic pressure, kPa
Thrust, N
Velocity, m/s
Weight, N
1.0 INTRODUCTION
If reliable and reusable vehicles for the launch of small satellites are developed, an
increase in launches is expected, potentially with a commensurate decrease in cost [1, 2].
A technology shift to hypersonic accelerators equipped with airbreathing propulsion can
fundamentally change access-to-space. The primary benefit is in their improved
operability, which mimics a modern-day airliner compared to traditional, expendable
rockets [3]. This stems from fundamental design differences, relatively high fuel
efficiency (specific impulse), improved reusability and responsiveness. In particular, the
supersonic combustion ramjet, or scramjet, is an attractive engine choice for the
hypersonic portion of a staged launch system [4].
The benefits of reusability are beginning to be explored with the propulsive boost-back
and vertical landing of the SpaceX Falcon 9 [5]. In 2019, SpaceX have reused the same
orbital booster three times and have a goal of flying that same booster twice more before
the end of the year [6]. Although revolutionary, further advancement in rocket
performance is difficult because modern rockets operate close to theoretical limits [7].
Further improvement of airbreathing engines is expected given their technological
infancy.
There have been numerous, notable efforts to develop a reusable, airbreathing launcher.
For example the National Aero-Space Plane (NASP, USA, 1986-1995, [1, 2]), HOrizontal
Take Off and Landing (HOTOL, England, 1982-1989, [9]), Sänger II (Germany, [3, 4])
and SKYLON (England, [12]). For various technical, economic and political reasons
however, an airbreathing launch vehicle has not yet been realised [13].
1.1 Airframe Integration
One such impediment to their development is the unique need for the careful, synergistic
integration of the airbreathing engine into the airframe. As flight Mach number increases,
the relative size of the inlet and nozzle must increase to extract a given fraction of
available thrust from the propulsive stream [14]. At hypersonic speeds, the vehicle must
effectively become a flying engine. The forebody forms part of the inlet, capturing and
compressing the freestream and the high pressure exhaust is further expanded over the
aftbody.
WARD & SMART 24429 3
This complicates the analysis and design through tightly coupling the aerodynamic and
propulsive components and hence disciplines. The high pressure exhaust gases in
particular mean small changes to nozzle design can have a large effect on overall system
performance (acceleration capability). This is because the thrust margin of a hypersonic
accelerator tends to be the small difference between the two relatively large forces, thrust
and drag [11, 12]. The exhaust also contributes strongly to lift and pitching moment.
Much work has been done on scramjet nozzle integration to various classes of vehicles.
For example, Edwards (1988) highlighted the importance of cowl geometry on vehicle
performance for a planar scramjet engine module and concluded 3D simulations were
required because of the complex interactions between separate exhaust flows and the
vehicle geometry [17]. Nozzle integration on accelerating waveriders was studied by
O’Neill and Lewis [18] while Weidner et al. and Henry et al. explored the same but for
winged accelerators with planar scramjet flowpaths [19, 20].
This paper presents a methodology and preliminary results for powered, aerodynamic
simulations of a scramjet-powered accelerator for the purposes of evaluating nozzle
design and integration problems. This vehicle was proposed by Smart and Tetlow in [4]
and subsequently the subject of vehicle and trajectory optimisation studies [20, 21]. It
therefore provides an established candidate geometry. Furthermore, as a conical vehicle,
it provides unique geometry which has not been studied in this way or for these purposes
before.
1.2 Objectives
Our objectives were 1) to present a methodology for the simulation of realistic hypersonic
vehicles suitable to the preliminary design stage and 2) to demonstrate this methodology
in evaluating a design change to the external shroud of the vehicle’s scramjet modules.
This evaluation is the first step in determining a desirable shape for the nozzle exit.
1.3 Approach
The general approach is as follows.
1. Generate the geometry parametrically in individual, logical components using
the Python library of the CAD package, Rhinocerous (Section 2.0).
2. Intersect each of these individually watertight components to obtain a single,
watertight surface mesh of the entire vehicle.
3. Simulate the inviscid, 3D flowfield around the powered vehicle using Cart3D
and correct for viscous drag with a boundary layer code (Section 3.1).
4. Simulate the internal scramjet isolator and combustor using a quasi-1D cycle
analysis code to obtain combustor exit conditions (Section 3.3).
5. Perform simulations at a given Mach number and a trimmed, lift equals weight
condition. The trim forces are approximated externally (Section 3.2 and 3.4).
Scripting the generation of the geometry with Python has several benefits. It allows
precise variation of a specific parameter with the ability to include logical rules for how
to generate dependent geometry. This allows a robust parametric model. Practically, the
Python script becomes a record of that specific vehicle and other information such as key
parameters (e.g. exit area) can be calculated and written to a logfile.
The CFD solver used (Cart3D, introduced in Section 3.1), requires a single watertight
mesh. The robust mesh intersection tools included with Cart3D [27] were used to create
the final geometry from the individual components. This retains the definitions of the
component surfaces and allows a straightforward breakdown of forces. Figure 1 shows
the baseline vehicle examined in this work coloured by the 24 individual vehicle
components.
The centreline shroud geometry was designed to cant inwards at 2°, the vehicle’s nominal
angle of attack. This was chosen to minimise the frontal area. However, the rear of each
engine module does come out of aerodynamic shadow when they are integrated
circumferentially around the axisymmetric vehicle and it is at some angle of attack. This
is shown in the bottom row of images in Figure 3.
WARD & SMART 24429 5
Figure 2 The radius of the shroud ( ) in between the engine modules was varied in the current study.
These results and further details may be found in [33]. For the slender bodies investigated,
the viscous drag was 15‐25% of the total drag. By computing the viscous drag and adding
it to the Cart3D value, the total drag predictions were within 6% of the experimental
values on average. Lift and pitching moment are generally predicted well by Cart3D and
within 5% of experimental values [36, 37].
The propulsive boundary conditions developed in [38] were used to model the flow
conditions at the combustor exit. Previous work has shown that 3D, inviscid computations
are adequate to predict core flow features. However, depending on wake structure, the
inviscid Euler equations cannot accurately predict the flowfield around the base with
strong interactions between the inviscid and viscous flow regimes [41, 42, 43].
3.2 Deflected Elevon Aerodynamics
The vehicle elevons were used to trim the pitching moment created by the airframe and
engines. They were placed such that the undeflected trailing edge was coincident with the
wing trailing edge. The elevons were originally sized in [22] based on the experimental
work of [42] to have an area and chord of 15% of the wing planform area and chord
respectively. Following later vehicle and trajectory analyses using the methodology
developed in [22], the elevon area was reduced slightly to 10% (1.66 m ). The elevon
chord was kept at 15% (1.38 m) giving a span of 1.20 m.
The aerodynamic forces on the deflected elevons are approximated using classical shock-
expansion theory and assuming 1.4 [43]. This approximation was made to avoid
modifying the vehicle geometry during a simulation. The swept wing and deflected
elevon are modelled in 2D and in isolation. That is, the flow seen by the wing leading
edge is the freestream and interaction effects with the forebody and fuselage and edge
effects of the finite elevon span are neglected. A schematic of this model is shown in
Figure 4a.
For compression faces, the weak oblique shock angle caused by flow turning by , is
found by solving the oblique shock ‐ ‐ equation (Eq. 1) using the secant root-finding
method.
2 sin 1
tan …( 1 )
tan cos 2 2
The downstream Mach number , and pressure , are calculated from the oblique
shock relations given in Eq. 2 and 3.
1 1 sin 1 /2 …( 2 )
sin sin 1 /2
2
1 sin 1 …( 3 )
1
For expansion through a turning angle of , the Mach number downstream , of the
expansion fan is calculated from the Prandtl-Meyer function either side of the fan:
…( 4 )
1 1 …( 5 )
arctan 1 arctan 1
1 1
WARD & SMART 24429 7
1 1 /2 …( 6 )
1 1 /2
The resultant aerodynamic loads were assumed to act at the centroid of the deflected
elevon. Care was taken to remove the forces of the undeflected elevon from the Cart3D
solution. No viscous forces were included at this stage but viscous drag was calculated
on the entire wing (i.e. including undeflected elevon) and included in the vehicle forces.
The predicted aerodynamics of the deflected elevons for 15° 15° at 8 and
2° are shown in Figure 4.
3.3 Propulsion
The scramjet isolator, injector block and combustor were modelled using quasi-1D, cycle
analysis [44]. This code solves the differential equations for conservation of mass,
momentum and energy. The properties of the air flowing into the duct and therefore the
inflow to the 1D code were calculated a priori with 3D CFD simulations. The different
capture and pre-compression of the inboard and outboard inlets was accounted for by
running separate cases. An average skin friction coefficient of 0.002 was assumed and
gaseous hydrogen was injected at an equivalence ratio of 1.00.
The cycle code provided the flow properties of the real exhaust gases at the combustor
exit ( , , , . This flow is a hot, combusting mixture of air, fuel and combustion
products ( 1.4). The method of Pindzola [45] was followed to simulate this flow with
cold air in Cart3D (perfect gas, 1.4).
This requires that the initial expansion angle, jet to freestream pressure ratio ( / ) and
a similarity parameter (Eq. 7) be preserved. The similarity parameter (derived from
conserving the thrust coefficient) scales the exit Mach number [45]:
…( 7 )
This scaling was used in powered Cart3D simulations of Skylon and computed
aerodynamic loads compared well with independent results obtained with engineering
methods [13].
The combustor exit boundary condition was deliberately placed normal to the engine
centreline and at combustor exit, away from the nozzle exit [46]. This assumes there is
no further combustion in the nozzle and the flow exiting the divergent combustor may be
modelled as one dimensional – both limitations on the current methodology.
Figure 5 A cut through the vehicle at the engine centreline showing the throat and combustor
the vehicle geometry (black) and exit boundary conditions (BC) (red). Note the flowpath
(grey) is shown only for reference and was not part of the simulated geometry. The vehicle is
scaled by 0.75 longitudinally in this figure.
Figure 6 The general process for the trimmed, powered simulations at lift equals weight.
(b) Driven by pressure signals on downstream line sensors (48.9 million cells) for plume
visualisation. The aerodynamic forces were within 8% of those calculated on the mesh in (a).
Figure 7 Two representative examples of the adaptively refined meshes 8.0, 2.7° . The
cell edges are coloured by cell volume.
(a) Convergence with mesh resolution of the functional 0.1 0.8 . The final value is
within 0.9% of the Richard extrapolation (dashed line).
(b) Aerodynamic coefficients with mesh (c) Aerodynamic coefficients with solver
resolution. iterations on the final three meshes.
Figure 8 Representative convergence history at Mach 8, 2.7° for the baseline geometry. The
final mesh was 30.0 million cells. The aerodynamic coefficients have been normalised by their final
values, 0.0413, 0.0310, 0.0034.
5.1 Mach 8, . °
The net thrust (normalised by reference area and dynamic pressure) is plotted for the five
vehicle geometries in Figure 9. The error bars on the – plot come from the adjoint
error estimate in the functional (Figure 8a). Because is also a function of lift, this gives
a conservative estimate of the remaining discretisation error in the net thrust.
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Noting the vertical scale, it is interesting that even with such a seemingly large change to
the vehicle geometry, the actual performance doesn’t change. The increased drag of the
shroud appears to be largely balanced by the increased thrust of the internal nozzle.
Unlike the thrust margin, the lift and pitching moment coefficient increase substantially
as the shroud gets larger (Figure 10). The larger shroud has a large compression surface
which generates a large amount of lift. Furthermore, the shroud creates a shock that
pressurises the fluid under the wings (see Figure 13a versus Figure 13c).
The increase in pitching moment may be attributed to an increase in the shroud’s nose up
pitching moment and a decrease in the restoring moment from the boat tail.
Figure 10 Lift coefficient and moment coefficient about the centre of gravity (
8.0, 2.03°
WARD & SMART 24429 13
All vehicles produced a positive, nose-up pitching moment requiring a positive, elevon
down deflection. The deflected elevons increase the L/D of the wings. This partially
offsets the drag penalty of the elevons because the vehicle now flies at a lower angle of
attack. As the pitching moment increases, the required elevon deflection and lift increase.
This decreases the required angle of attack and consequently decreases the airframe drag
but also engine thrust. The elevon drag further decreases performance; ,
0.00002 for , 0.519 m and , 0.0023 for , 0.861 m .
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Figure 13 Pressure fields on plane at 0 and vehicle underside for 8.0, 0.0413
and 0.0 (pressure shown in Pa).
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,
a) Minimum expansion nozzle, , 0.519 m , 9.4
,
b) Maximum expansion nozzle, , 0.861 m , 4.3
Figure 15 Mach number contours through the inboard engine centreline 8.0,
0.0413 and 0.0.
6.0 CONCLUSIONS
A scramjet powered, hypersonic accelerator has the potential to decrease the cost of
access-to-space, primarily through operability and reusability benefits. For adequate
acceleration performance, these vehicles require relatively large engines which must be
integrated within the airframe. Inviscid simulations were performed using adjoint-driven
mesh refinement to obtain verified results.
By varying the size of the external scramjet shroud, a trade-off between thrust-producing,
expansion area and extra frontal area was investigated. At constant angle of attack, the
difference in net thrust between designs was small but commensurate changes in lift and
pitching moment coefficient complicate comparisons. However, the difference became
more pronounced when simulations were performed at the more realistic condition of
pitch-trimmed at a specified lift coefficient. The benefits of increased expansion were
primarily offset by the detrimental effects of trim drag and reduced angle of attack on
engine performance.
These results emphasise the importance of accounting for the coupling between
aerodynamic and propulsive components in the analysis of airframe-integrated vehicles.
Future work includes investigating this geometry change at different Mach numbers on
the accelerator’s trajectory (different freestream to combustor exit pressure ratios).
Finally, the applicability of the inviscid solver in the base region and the effects of this
region on aerodynamic forces and moments must be considered.
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ACKNOWLEDGMENTS
A. Ward gratefully acknowledges the financial support of an Australian Government
Research Training Program (RTP) Scholarship. The authors are greatly appreciative of
the contributions of C. Pierens and R. Palmer for the mass modelling of SPARTAN; D.
Curran for the CFD simulations of the CREST forebody and inlet and cycle analyses of
the CREST scramjet flowpath; and finally, R. Jones for the CREST inlet geometry post-
processing tools.
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