48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition
4 - 7 January 2010, Orlando, Florida
AIAA 2010-942
Parametric Investigation of Racetrack-to-Circular CrossSection Transition of a Dual-mode Ramjet Isolator
Nadir T. Bagaveyev1 and William A. Engblom2
Embry-Riddle Aeronautical University, Daytona Beach, FL, 32114
and
Vishal A. Bhagwandin3
U.S. Army Research Laboratory, Aberdeen Proving Ground, MD, 21005
Reynolds Averaged Navier Stokes (RANS) simulation is used to parametrically evaluate the performance
of a matrix of 3-D isolator configurations which transition from a racetrack entrance cross-section to a
circular exit cross-section. The matrix includes isolators with length-to-height ratios of 6 to 16, divergence
angles of 0 to 2 degrees, and different cross section shape transition functions. Generic isolator entrance flow
conditions for a dual-mode ramjet (DMR) were provided by Pratt & Whitney Rocketdyne, and are used to
impose a spatially-varying isolator inflow profile, and a mass-averaged uniform inflow profile, in two
separate sets of matrix computations. Isolator performance is characterized by maximum allowable static
pressure rise (without unstart), and related stagnation pressure recovery, exit flow distortion, and shock train
onset sensitivity. The implications of the results for selecting a racetrack-to-circular, transitional isolator
geometry are discussed.
Nomenclature
AR
a
b
H
L
M
p
po
T
u
x
y
θ
= aspect ratio (= a/b)
= racetrack semi-width
= racetrack semi-height
= height of isolator racetrack inlet (= 2b)
= length of isolator
= Mach number
= static pressure
= stagnation (or total) pressure
= static temperature
= velocity in axial or x- direction
= axial distance from isolator inlet plane (normalized by L)
= transition multiplier function
= divergence angle
= ratio of specific heats
I. Introduction
S
ignificant efforts to develop air breathing propulsion systems which enable hypersonic flight are currently
ongoing. For example, the USAF, NASA, DARPA, Boeing and Pratt & Whitney Rocketdyne have partnered
on the X-51A, a waverider-type scramjet-powered hypersonic vehicle, managed by Air Force Research Laboratory
(AFRL) [1]. Another example is the Falcon Combined-Cycle Engine Technology (FaCET) program, managed by
DARPA, for which a dual-mode ramjet engine has recently been developed and tested by Pratt & Whitney
Rocketdyne [2]. Educational institutions like the University of Virginia (UVa) are also leading efforts in hypersonic
vehicle research with the Hy-V program [3].
1
Undergraduate Student, Member AIAA.
Associate Professor, Mechanical Engineering Department, Associate Fellow AIAA.
3
Aerospace Engineer, Aerodynamics Branch, Member AIAA.
1
American Institute of Aeronautics and Astronautics
2
Copyright © 2010 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.
Computational fluid dynamics (CFD) can be used to complement the scramjet flowpath design process.
Parametric studies of various design configurations using CFD can provide important insight into complex flow
phenomena and identify and estimate the sensitivity of flowpath performance to various design features. The focus
of the current study is the parametric evaluation of a family of isolator configurations for a generic dual-mode ramjet
(DMR) using CFD.
The primary role of the isolator component in a dual-mode ramjet is to contain the precombustion shock train.
This shock train is most difficult to contain within the isolator length during the ramjet mode of operation (i.e.,
subsonic combustion), which takes place around a relatively low flight Mach of 3 to 6 [4]. Shock boundary layer
interaction is strong and results in large regions of boundary layer separation.
Figure 1 summarizes the key
features of the ramjet mode.
Figure 1: Features of dual-mode ramjet mode [4]
Based on an experimental investigation, Penzin [5] terms this mode of isolator operation as separation shock
and characterizes the mode as containing non-symmetric flow with large three dimensional separated regions in the
duct corners, long ducts required to achieve a given pressure rise, and a significant variation in the cross-sectional
pressure distribution at a given axial station. The flow in this mode is also found to be very sensitive to inflow
profiles and large pressure fluctuations are observed. Studies conducted on rectangular cross-section isolators, such
as the numerical investigation of Nedungadi and Wie [6], have showed that complex corner flow separation exists
for wide range of inflow Mach numbers and cross-section aspect ratios. The separation shock mode clearly poses
significant challenges for development of an efficient, light-weight, and robust engine design.
From a vehicle performance point-of-view, it is desirable that the isolator flowpath (i) maximizes the static
pressure rise across isolator without inlet unstart (i.e., highest throttle level), (ii) maximizes stagnation pressure
recovery, and (iii) minimizes flow distortion. The pressure recovery directly affects thrust level. Flow distortion
tends to reduce the uniformity of mixing in the combustor, and in turn, combustion efficiency and thrust.
Elliptical and racetrack isolator cross-sections have the advantage of not imposing corner flow separation
regions. Rectangular isolator cross-sections also impose mechanical and thermal stress concentration areas, and
may deform in a non-uniform manner. Circular combustor cross-sections are desirable for same reason of
mitigating mechanical and thermal stress concentrations. An isolator which transitions between a racetrack and
circular cross section appears to have advantages over the well-studied rectangular cross-section. Consequently, the
main objective of this work is to numerically evaluate the performance of racetrack-to-circular cross section
configurations using a generic isolator inlet flow condition, in order to identify the optimal geometric transition.
II. Methodology
The transitional isolator flowpath is decoupled from the inlet and combustor sections to facilitate rapid matrix
evaluations. The matrix of racetrack-to-circular cross-section isolator configurations, and a generic Mach 5 flight
condition, was provided for this study by Pratt&Whitney Rocketdyne (PWR) [7].
Flowpath Geometry
The racetrack isolator entrance (or inlet throat) geometry is the same for all simulations, as shown in Figure 2.
Cross-sectional area of the throat is ~30 sq. in. and has AR=1.6. The isolator exit cross-section is always circular
(AR=1.0) but the area changes from depending on the divergence angle, θ, which is a constant along a given isolator.
2
American Institute of Aeronautics and Astronautics
The cross-sectional area at any axial location corresponds to that of a conical nozzle with the same divergence angle.
Consequently, the area increases quadratically with x. This smooth change in area is necessary to minimize losses
associated with compression and expansion processes.
Figure 2: Racetrack isolator entrance [7]
The aspect ratio transition functions alter the aspect ratio between the isolator entrance (x=0) and exit (x=L) from 1.6
to 1.0. Transition functions are based on the normalized multiplier functions, y(x), shown in Figure 3. These
multiplier functions were established using a combination of hyperbolic sine and cosine functions. Aspect ratio
changes according to Equation 1, where the multiplier is set based on the aggressiveness of the geometric transition.
Figure 3: Transition
functions [7]
AR ( x)
( AR x
L
AR x
0
) * Y ( x)
AR x
0
(1)
The matrix of transitional isolator geometries evaluated includes three independent parameters: length-to-height
ratio (L/H = 6, 8, 10, 12, 14 and 16); divergence angle (θ = 0.0, 0.5, 1.0, 1.5 and 2.0 degrees), and aspect ratio
transition function (y(x) = forward aggressive, front moderate, linear, aft moderate and aft aggressive). Note that
this matrix is 6 x 5 x 5 or 150 cases.
Grid Generation
MATLAB-generated Gridgen Glyph scripts were used to produce a consistent set of grids for the 150 different
isolator geometries in the matrix. The grids contain 2.85M cells in a 24-block structured mesh. Each block contains
120K cells to promote efficient use of parallel processing. Figures 4a and 4b show two examples of the grids
generated. The isolator geometry is symmetric in XY-plane. A grid-to-the-wall strategy is employed resulting in a to
a y+ value of less than 5 for all wall surfaces.
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Figure 4a: L/H = 6, θ = 0 , front aggressive transition geometry (every 4th grid point shown)
Figure 4b: L/H = 16, θ = 2 , aft aggressive transition geometry (every 4th grid point shown)
The blocking topology was optimized for parallel computing on 24 3.2-GHz Intel Xeon processors. Solution
advancement utilized Wind-US’s multi-grid sequencing capability where successive solutions were obtained on a
coarse (55K cells), medium (357K cells) and for some select cases, fine grid (2.85M cells). Since there was minimal
effect of precision between sample medium and fine grid solutions, the medium grid result was used for the bulk of
the simulations.
Flow Conditions
Isolator entrance (or inlet throat) flow profile data was numerically generated by PWR for a generic inlet
operating at Mach 5 flight conditions using a Reynolds-Averaged Navier Stokes (RANS) solver. Figures 5a and 5b
illustrate the variation in pressure and Mach number. This data is used to specify spatially-varying inflow
conditions for one complete matrix of computations. That is, flow states are interpolated for each grid point along
the inflow boundary for use by the Wind-US flow solver. This data is also used to create a mass-averaged flow
state (summarized in Table 1), which is used to specify uniform inflow conditions for another complete matrix of
computations. A constant wall temperature of 1143R was applied for all computations.
Figure 5a: Inlet throat pressure profile
[7]
Figure 5b: Inlet throat Mach profile
[7]
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m
P
po
T
M
U
Racetrack
Inlet
Throat
Flow
Conditions
21.75 lbm/s
14.93 psi
78.73 psi
852.13 R
1.72
2429.25 ft/s
Table 1: Mass-averaged inlet throat (isolator entrance) conditions
Numerical Model
The numerical simulations were conducted using the Wind-US flow solver. Wind-US is a CFD platform
developed by the NPARC Alliance, a partnership between NASA Glenn Research Center (GRC), USAF Arnold
Engineering & Development Center (AEDC), and Boeing Phantom Works. Wind-US is a general-purpose flow
solver that supports equation sets governing turbulence and chemically reacting, compressible flows [8].
Wind-US was utilized here as a RANS solver. The inviscid flux function was chosen as Roe’s second-order,
upwind-biased, flux-difference splitting algorithm. The default implicit time-advancement scheme, a spatially-split
approximate factorization scheme, was chosen. Local time-stepping was used to advance the solution towards
steady-state, based on a chosen Courant-Friedrichs-Lewy (CFL) number of 1. Menter’s Shear Stress Transport [9],
two-equation, eddy-viscosity turbulence model was employed. After an initial investigation of equilibrium gas
effects, it was determined that these effects are small enough to be neglected and a perfect gas model with constant
γ=1.4 was used.
Numerical Procedure
Two sets of results were computed using the aforementioned matrix of isolator geometries, using (i) spatiallyuniform inflow and (ii) spatially-varying inflow, as described earlier. In all cases the back pressure which results in
near unstart is to be determined iteratively.
In the uniform inflow cases, the stagnation pressure and temperature is maintained at the inflow boundary, and
the flow velocity is permitted to float. The back pressure is adjusted until the shock train is ~1H from the inlet
throat. In the spatially-varying cases inflow profile was frozen to maintain the given profile, and so, no unstart was
permitted to occur numerically. A Linux script was established to use the wall pressure profiles to monitor
separation and shock progression. The backpressure is automatically adjusted until the shock train induced flow
separation reached ~1.5H from the inlet throat. This distance was chosen to be able to differentiate this type of flow
separation from that induced by the inflow itself. Once the 1H location is obtained to within 0.25H, and the
solution is converged, this matrix case is deemed completed.
Three metrics (see Equation 2) are used to evaluate isolator performance, including static pressure ratio,
stagnation pressure recovery factor, and an exit flow distortion. The first two conventional metrics involve
quantities which are simply mass flow rate averaged at the exit plane. The flow distortion is introduced here as a
measure of the degree to which the axial flow momentum varies across the exit plane. A uniform momentum profile
at the exit plane would result in zero distortion. Here the mass flow rate averaged axial momentum is used to
calculate the sum of the variation in the axial momentum over each cell face along the exit plane, weighted by the
cell face area. This value is normalized by the total mass flow rate.
Static Pressure Ratio = pexit/pinlet
Stagnation Pressure Recovery = po,exit/po,inlet
N
Distortion Index =
i 1
i
ui
(2)
N
u Ai
m
where
u
i
i
u i m i
m
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Grid Convergence
Figure 6 shows Mach contours along the symmetry plane for a typical isolator geometry using the spatiallyuniform inflow conditions. Converged solutions are obtained at three grid levels (i.e., coarse, medium, and fine) for
the same back pressure of 52 psi. The medium grid omits every other grid point used in the fine grid. The coarse
grid omits every other grid point used in the medium grid. The isolator is nearly unstarted in each case with lead
shock at a distance H from the inlet. The isolator is not drawn to scale for illustrative purposes. Although this
geometry is perfectly symmetric across the isolator height direction (as can be observed here), the flow separation is
strongly asymmetric for the medium and fine grid results. The stagnation pressure recovery for the coarse and
medium grids differ from the fine grids by 1.0% and 0.3%, respectively, indicating that a sufficient level of grid
independence has been demonstrated. The medium grid level is used for all spatially-uniform inflow computations
presented in Results section.
Static
Pressure
Ratio
Total
Pressure
Recovery
Exit Mach
number
Coarse
3.4647
Medium
3.4593
Fine
3.4635
0.8129
0.8109
0.8048
0.4749
0.4774
0.4751
Table 2: Performance results vs. grid level
for uniform inflow case
Figure 6: Mach contours along symmetry plane
when using spatially-uniform inflow vs. grid level
Figure 7 shows Mach contours along the symmetry plane for a typical isolator geometry using the spatiallyvarying inflow conditions. Converged solutions are again obtained at three grid levels (i.e., coarse, medium, and
fine) at the same back pressure. Table 2 provides the performance results applicable to each grid level, which show
agreement with fine grid result to within 1% for coarse and 0.3% for medium. The contour plots in Figure 7 indicate
illustrate how little difference occurs between the medium and fine grid results. A sufficient level of grid
independence has been demonstrated. The medium grid level is used for all spatially-varying inflow computations
presented in Results section.
Static
Pressure
Ratio
Total
Pressure
Recovery
Exit Mach
number
Coarse
2.6029
Medium
2.6053
Fine
2.6063
0.6937
0.6901
0.6891
0.5722
0.5646
0.5668
Table 3: Performance results vs. grid level for
spatially-varying inflow case
Figure 7: Mach contours along symmetry plane
when using spatially-varying inflow vs. grid level
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III. Results
Spatially-Uniform Inflow Matrix
The matrix of transitional isolator geometries evaluated using the spatially-uniform inflow condition includes
three independent parameters: length-to-height ratio (L/H = 6, 10 and 16); divergence angle (θ = 0, 1, and 2
degrees), and aspect ratio transition function (y(x) = forward aggressive, linear, aft aggressive). We consider the
results for each of the three performance metrics (i.e., static pressure ratio, stagnation pressure recovery, and exit
flow distortion), which are mass-flux averaged at the isolator exit plane.
a) L/H = 6
b) L/H = 10
c) L/H = 16
Figure 8: Static pressure ratio vs. divergence angle and transition function for
a) L/H=6, b) L/H=10, c) L/H=16
The maximum static pressure rise permitted by each transitional isolator is shown in Figure 8. The isolator
shock train reaches to a distance of 1H from the isolator entrance for all cases (i.e., “nearly unstarted”). For a given
isolator length, the static pressure rise is negligibly sensitive to divergence angle and transition function. There is
less than 2% variation in this metric for L/H=6 and 16 cases. It is unclear why the L/H=10 case results in a larger
variation of 5%. The peak static pressure ratio occurs for θ=1 and a linear transition for all three L/H values. The
allowable static pressure ratio increases with isolator length, as expected, from 3.1 at L/D=6 to 3.5 at L/D=16.
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a) L/H = 6
b) L/H = 10
c) L/H = 16
Figure 9: Stagnation pressure recovery vs. divergence angle and transition function for
a) L/H=6, b) L/H=10, c) L/H=16
The stagnation pressure recovery at the isolator exit, for the static pressure ratio resulting in near unstart, is
provided in Figure 9. Note that these performance values are obtained from the same CFD simulation results used
to form Figure 8. For a given isolator length, the stagnation pressure recovery is negligibly sensitive to the
transition function (i.e., less than 1% variation). However, pressure recovery is strongly affected by the divergence
angle, increasing by 10% from θ=2 to 0 . There is negligible change in the strength of the leading normal shock.
This pressure recovery increase is apparently related to reduced viscous boundary layer losses in a less adverse
pressure gradient. The pressure recovery also decreases slowly as isolator length increases, due to the increased
viscous boundary layer losses (i.e., 1-2%).
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a) L/H = 6
b) L/H = 10
c) L/H = 16
Figure 10: Flow distortion vs. divergence angle and transition function for
a) L/H=6, b) L/H=10, c) L/H=16
The flow distortion at the isolator exit, for the static pressure ratio resulting in near unstart, is depicted in Figure
10. Note that these performance values are obtained from the same CFD simulation results used to form Figures 8
and 9. The effect of divergence angle is the most evident, consistently reaching the largest distortion levels at θ=2
for all isolator lengths. As isolator length increases, the distortion decreases significantly. Presumably, viscous
effects diffuse the velocity gradients within the shock train more effectively over the long region of subsonic isolator
flow.
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Spatially-Varying Inflow Matrix
The full matrix of 150 transitional isolator geometries are evaluated using a realistic spatially-varying inflow
condition. The isolator geometry is varied using three independent parameters: length-to-height ratio (L/H = 6, 8,
10, 12, 14, and 16); divergence angle (θ = 0, 0.5, 1, 1.5, and 2 degrees), and aspect ratio transition function (y(x) =
forward aggressive, front moderate, linear, aft moderate, aft aggressive). We consider the results for each of the
three performance metrics (i.e., static pressure ratio, stagnation pressure recovery, and exit flow distortion), which
are mass-flux averaged at the isolator exit plane.
d) L/H = 12
a) L/H = 6
b) L/H = 8
e) L/H = 14
c) L/H = 10
f) L/H = 16
Figure 11: Static pressure ratio vs. divergence angle and transition function for
a) L/H=6, b) L/H=8, c) L/H=10, d) L/H=12, e) L/H=14, f) L/H=16
The maximum static pressure rise permitted by each transitional isolator is shown in Figure 11. The isolator
shock train reaches to a distance of 1H from the isolator entrance for all cases (i.e., “nearly unstarted”). For a given
isolator length, the static pressure rise is modestly affected by the transition function. The linear transition
consistently holds the maximum pressure ratio for any choice of isolator length and divergence angle, except for
L/H=6 and low divergence angle. The front aggressive transition function consistently holds the lowest pressure
ratio. Rapid changes in the geometry in the forward section have a significant effect on the developing shock train,
and apparently reduce isolator performance. These results also indicate that a θ=0.5 provides the maximum
allowable static pressure ratio for isolator lengths, except for L/H=6. These trends are in contrast to those presented
for the spatially-uniform inflow matrix. The allowable static pressure ratio increases significantly with isolator
length, from 2.1 at L/D=6 to 3.0 at L/D=16. These values are significantly lower than those found using spatiallyuniform inflow, illustrating the importance of accounting for realistic spatial variations reaching the isolator
entrance.
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a) L/H = 6
d) L/H = 12
b) L/H = 8
e) L/H = 14
c) L/H = 10
f) L/H = 16
Figure 12: Total pressure recovery vs. divergence angle and transition function for
a) L/H=6, b) L/H=8, c) L/H=10, d) L/H=12, e) L/H=14, f) L/H=16
The stagnation (or total) pressure recovery at the isolator exit, for the static pressure ratio resulting in near
unstart, is provided in Figure 12. Note that these performance values are obtained from the same CFD simulation
results used to form Figure 11. For a given isolator length, the stagnation pressure recovery is minimally sensitive
to the transition function (i.e., less than 2% variation). The pressure recovery is very strongly affected by the
divergence angle, increasing by 25% from θ=2 to 0 . Also, the optimal pressure recovery is roughly 10% lower
than that found from the spatially-uniform inflow study (Figure 9). The separated shock train losses are apparently
more strongly affected by non-uniform inflow, as suggested by Penzin [5]. The pressure recovery also decreases
slowly as isolator length increases, due to the increased viscous boundary layer losses (i.e., 2%).
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a) L/H = 6
d) L/H = 12
b) L/H = 8
e) L/H = 14
c) L/H = 10
f) L/H = 16
Figure 13: Flow distortion vs. divergence angle and transition function for
a) L/H=6, b) L/H=8, c) L/H=10, d) L/H=12, e) L/H=14, f) L/H=16
The flow distortion at the isolator exit, for the static pressure ratio resulting in near unstart, is depicted in Figure
13. Note that these performance values are obtained from the same CFD simulation results used to form Figures 11
and 12. The effect of divergence angle is most pronounced, reaching the largest levels for a θ=2 . As isolator
length increases, the distortion decreases significantly. Presumably, viscous effects diffuse the velocity gradients
within the shock train more effectively over the long region of subsonic isolator flow. These trends are similar to
those demonstrated in Figure 10 for the spatially-uniform inflow cases.
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Figure 14 illustrates effects of the divergence angle on isolator performance. Note that the initial region of low
speed flow (blue) near the isolator entrance is shock-induced flow separation which is caused by the asymmetric
spatially-varying inflow that is being enforced. The large low speed region, that reaches the exit, extends forward as
back pressure is increased and eventually merges with the upstream separated flow region to form one separated
flow region, and may be considered the verge of isolator unstart. The plots in Figure 14 are all taken at the same
back pressure, but the θ=0.5 case is slightly further from unstart since the flow is attached (see magenta oval)
further downstream than the other cases.
Figure 14 also depicts the flow distortion at the isolator exit plane. Although significant distortion in evident for
θ=0.0 case, the distortion is observed to be getting somewhat worse as divergence angle increases. These
illustrations are consistent with the trend observed in Figure 13.
Figure 14: Mach contours for L/H = 10, linear transition function at same back pressure (37 psi),
for various divergence angles
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Shock Train Position Sensitivity
Figure 15a and 15b illustrate the sensitivity of the shock train onset to increasing back pressure for both
spatially-varying and uniform inflow conditions for the same, representative isolator geometry (i.e., L/H = 16, θ=2
linear transition). This sensitivity is important to quantify since combustion instabilities will cause variations in the
effective back pressure on the isolator. The movement of the shock train is approximated by the movement of the
leading edge of the large separated flow region created by the lambda-shock. For back pressures of 55 psi and 44
psi , the isolator is on the verge of unstart for the uniform inflow and spatially-varying inflow cases, respectively.
Figure 15a: Shock progression using uniform inflow Figure 15b: Shock progression using spatially-varying inflow
(L/H = 16, θ=2 linear transition function)
(L/H = 16, θ=2 linear transition function)
Static
Pressure
Ratio
Total
Pressure
Recovery
Exit Flow
Distortion
35 psi
2.329
45 psi
2.994
55 psi
3.659
0.564
0.658
0.772
0.6336
0.4807
0.3380
Table 4a: Metrics for uniform inflow (L/H = 16,
θ=2 linear transition function)
Static
Pressure
Ratio
Total
Pressure
Recovery
Exit Flow
Distortion
35 psi
2.342
40 psi
2.677
44 psi
2.942
0.543
0.591
0.635
0.6170
0.5913
0.5767
Table 4b: Metrics for spatially-varying inflow
(L/H = 16, θ=2 linear transition function)
Table 4a and 4b summarize isolator performance for the shock train progression cases discussed above, using
uniform inflow and spatially-varying inflow conditions, respectively. This is relevant when considering off-design
performance. The total pressure recovery is severely reduced when isolator is operated as lower than maximum
back pressure. This is due to increased viscous losses in supersonic flow entry region. The exit flow distortion is
also dramatically increased as back pressure is reduced. This is apparently due to the reduced distance over which
viscous forces act to eliminate velocity gradients after the shock train terminates.
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A series of simulations were conducted to quantify the sensitivity of shock train onset to isolator back pressure. To
reduce the matrix size the L/H is fixed to an intermediate value of 10. Figures 16a and 16b describes shock train
onset sensitivity, in terms of shock train movement divided by back pressure change, in vicinity of maximum back
pressure using spatially-varying and uniform inflow conditions, respectively. Specifically, the maximum back
pressure (i.e., for which shock train reaches ~1H from the inlet throat) for each isolator configuration is reduced by 5
psi to measure the movement of the shock train leading edge. Shock train movement depends strongly on
divergence angle, especially for the uniform inflow cases, but also depends on the transition function describing the
geometry change. Shock position is greatest at lower divergence angles, as expected. The front aggressive
geometry transition also increases sensitivity, presumably via a stronger affect on the development of the shock train
itself.
Figure 16a: Shock sensitivity dependence on
geometry and divergence at near-unstart
pressures for L/H = 10 spatially-varying cases.
Figure 16b: Shock sensitivity dependence on
geometry and divergence at near-unstart
pressures for L/H = 10 uniform cases.
IV. Conclusions
The performance of a matrix of 150 isolator geometries which transition from racetrack-to-circular cross-section
have been evaluated using the Wind-US RANS flow solver and the Shear Stress Transport turbulence model using i)
spatially-uniform inflow conditions, and ii) realistic spatially-varying inflow conditions. Spatial non-uniformity in
the inflow is shown to have a pronounced affect on isolator performance in the ramjet-mode, and should be utilized
when optimizing an isolator flowpath design.
The linear transition function (i.e., linear change in cross-sectional area) produces the optimal allowable static
pressure ratio before unstart, regardless of isolator length or divergence angle. The divergence angle to maximize
the allowable static pressure ratio is found to be θ=0.5 (spatially-varying inflow) and 1.0 (uniform inflow), for the
Mach 5 flight condition assumed herein.
Stagnation pressure recovery is strongly affected by divergence angle, and an optimal recovery occurs for θ=0 ,
regardless of geometric transition, isolator length, or inflow conditions, which all have minor effect. However, the
sensitivity of the shock train position to back pressure variations is the most significant for the lowest divergence
angles and a front aggressive geometric transition. The latter is deemed an important consideration, considering the
potential variations in back pressure during flight (e.g., due to combustion instabilities).
Exit flow distortion, as defined herein, is found to be optimal at low divergence angles and for long isolators,
regardless of geometric transition function. Stagnation pressure recovery and exit flow distortion metrics degrade
rapidly when operating at less than maximum isolator back pressure conditions due to increased viscous losses along
turbulent boundary layer during supersonic entry.
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Acknowledgments
This work was partially funded by the Florida Center for the Advancement of Aero-Propulsion (FCAAP),
directed by Dr. Ray Mankbadi at Embry-Riddle Aeronautical University. The authors would like to thank Pratt and
Whitney Rocketdyne for providing the technical data and study constraints necessary to conduct this effort, with
special thanks to Dean Andreadis, AIAA Fellow in Hypersonic Systems, for offering his expertise and guidance.
Finally, we would like to thanks Embry-Riddle Aeronautical University for providing the necessary supercomputer
resources on the Zeus Beowulf Linux Cluster.
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Andreadis, D., Patrick, G., Hawkins, R., Patel, J., Van Dyke, K., “Transitional Isolator Optimization Study”
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8
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