51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition AIAA 2013-0012

07 - 10 January 2013, Grapevine (Dallas/Ft. Worth Region), Texas

Exhaust Nozzle Plume and Shock Wave Interaction

Raymond Castner1,
NASA Glenn Research Center, Cleveland, Ohio, 44135
Alaa Elmiligui2,
NASA Langley Research Center, Hampton, Virginia, 23681
Susan Cliff3,
NASA Ames Research Center, Moffett Field, California, 94035

Fundamental research for sonic boom reduction is needed to quantify the interaction of shock waves
generated from the aircraft wing or tail surfaces with the exhaust plume. Both the nozzle exhaust plume
shape and the tail shock shape may be affected by an interaction that may alter the vehicle sonic boom
signature. The plume and shock interaction was studied using Computational Fluid Dynamics simulation on
two types of convergent-divergent nozzles and a simple wedge shock generator. The nozzle plume effects on
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the lower wedge compression region are evaluated for two- and three-dimensional nozzle plumes. Results
show that the compression from the wedge deflects the nozzle plume and shocks form on the deflected lower
plume boundary. The sonic boom pressure signature of the wedge is modified by the presence of the plume,
and the computational predictions show significant (8-15%) changes in shock amplitude.

AOA = Angle of attack, degrees

β = Nozzle boat-tail angle, degrees
D = Test nozzle diameter, in
h = Distance below vehicle, in
L = Vehicle length, in
M∞= Free-stream Mach number
NPR = Nozzle pressure ratio = Pt / P∞
P = Local static pressure, psia
Pt = Total pressure in nozzle, psia
P∞ = Free-stream static pressure, psia
ΔP = P - P∞
ΔP/P = (P - P∞)/ P∞
To= Nozzle total temperature, R
T∞= Free-stream total temperature, R
t = Time, seconds
x = Distance along abscissa of pressure signature, in
y = Vertical distance from nozzle centerline, in

I. Introduction

The reduction of sonic boom overpressures of supersonic aircraft may enable high speed travel over
populated areas. The impact of the sonic boom on populated areas is so large that the FAA has prohibited
supersonic flight over land by civil aircraft in the United States. Most supersonic aircraft produce an N-wave
pressure signature on the ground; a rise in pressure from the bow shock of the vehicle followed by an expansion to a
negative pressure and then the return to atmospheric pressure. The bow and tail shocks create the “double boom”
often heard on the ground. The aircraft pressure signature near the vehicle has multiple shocks and expansions that
attenuate and coalesce to the N-wave form on the ground.

_______________________________
Aerospace Engineer, Inlet and Nozzle Branch, 21000 Brookpark Road, AIAA Associate Fellow
2
Research Aerospace Engineer, Configurations Aerodynamics Branch, NASA Langley, AIAA Senior Member
3
Aerospace Engineer, Applied Modeling and Simulations Branch, Moffett Field, AIAA Associate Fellow

This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States.
 Recent studies to develop aircraft with acceptable sonic boom noise include programs such as the Quiet
Spike1 and the Shaped Sonic Boom Demonstrator (SSBD)2 that achieved reduced intensity of the forward portion of
the pressure signature. Research was also done to reduce the loudness contribution from aft components including
the nozzle exhaust. One example was the work of Putnam3, who performed an experimental study of exhaust
nozzles and the effects of the exhaust plume. Tests were done in a 4-foot by 4-foot supersonic wind tunnel with
pressure measurements taken one diameter away from the nozzle. Study of exhaust nozzle plume effect on sonic
boom has progressed from analysis and testing of an isolated nozzle 4,5, to slot nozzles6 and engine-wing-body
models7,8. These studies demonstrated how the nozzle lip shock from an under-expanded nozzle plume could
suppress the nozzle boat-tail expansion and reduce the trailing shock.
The previous studies did not examine the exhaust nozzle plume interaction with shocks generated by the
wing and tail, which may affect the plume shape and the sonic boom signature. The subject of this report is the
study of simplified exhaust nozzle plume interaction with a tail shock, generated by a simple wedge shock generator
(wedge). The intent is to provide a baseline analysis of a generic nozzle and wedge configuration, and demonstrate
the effect of the nozzle exhaust plume on the wedge pressure signature. The WIND-US, PAB3D, Cart3D, and
USM3D computational fluid dynamic (CFD) codes were used for this analysis,. Two types of supersonic nozzle
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plumes were studied: one created by a two-dimensional convergent-divergent (CD) slot nozzle and one created by
an axisymmetric CD nozzle (Putnam‟s “Nozzle 6”). The axisymmetric CD nozzle was also studied within the aft
fuselage of a 59⁰ delta wing-body model. CFD codes and geometry models are listed in Table 1. The Mach number
contours and pressure profiles from these configurations are presented.

II. Computational Modeling

II.A. WIND-US
Two- and three-dimensional exhaust nozzles were modeled with WIND-US (Table 1). WIND-US is a
general purpose fluid flow solver that is used to numerically solve various sets of equations governing physical
phenomena9. WIND-US was used to take advantage of the established capability to correctly compute nozzle
plumes with viscous and turbulence effects. The code supports the solution of the Euler and Navier-Stokes
equations, along with supporting equation sets governing turbulent and chemically-reacting flows. The flow solver
is parallelized and can take advantage of multi-core and multi-CPU hardware. The version used was WIND-US 4.6.
WIND-US was used with the modified second-order Roe upwind scheme for stretched grids, implicit time stepping
with a Courant–Friedrichs–Lewy (CFL) number of 1.0, and the Menter Shear Stress Transport (SST) turbulence
model.

II.B. PAB3D
In this study, PAB3D10 was used in conjunction with two-equation k–ε turbulence closure and nonlinear
algebraic Reynolds stress models to simulate the two-dimensional convergent-divergent supersonic nozzle (Table 1).
PAB3D has been tested and documented for the simulation of aero-propulsive and aerodynamic flows involving
separation, mixing, and other complicated phenomena. PAB3D has been ported to a number of platforms, and offers
a combination of good performance and low memory requirements. In addition to its advanced preprocessor, which
can handle complex geometries through multi-block general patching, PAB3D has a runtime module capable of
calculating aerodynamic performance and a postprocessor for data analysis11. PAB3D solves the simplified
Reynolds-averaged Navier–Stokes equations in conservative form by neglecting streamwise derivatives of the
viscous terms. Viscous models include coupled and uncoupled simplified Navier–Stokes and thin-layer Navier–
Stokes solver options. Roe‟s upwind scheme is used to evaluate the explicit part of the governing equations, and van
Leer‟s scheme is used for the implicit part. Diffusion terms are centrally differenced, inviscid terms are upwind
differenced, and two finite volume flux-splitting schemes are used to construct the convective flux terms. PAB3D is
third order accurate in space and second-order accurate in time.

II.C. Cart3D
Cart3D was used to evaluate three-dimensional effects for a 59⁰ delta wing-body model with a fuselage
embedded convergent-divergent nozzle and a wedge shock located above the nozzle plume (Table 1). Cart3D12,13 is
a high-fidelity analysis package for conceptual and preliminary aerodynamic design that provides solution to the
Euler equations. It allows users to perform automated CFD analysis on complex geometry. Geometry for Cart3D is
represented by surface triangulations. These may be generated from within a Computer-Aided Design (CAD)
system, from legacy surface triangulations or from diagonalized (diagonal added to each quadrilateral face)
structured surface grids. Cart3D uses an embedded multilevel Cartesian mesh to discretize the space surrounding the

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 geometry and determines the surface geometry out of the set of "cut-cells" which intersect the surface triangulation.
The flow solver is parallelized via OPENMP and can take advantage of multi-core and multi-CPU hardware.
Solutions were obtained using the adjoint-based mesh adaptation module14-16. This module uses adjoint-weighted
residual error-estimates to drive mesh adaptation. Once a user specifies the output function of interest, such as lift,
drag, or off-body pressures along a line with a corresponding error tolerance; the module automatically refines the
mesh to drive the remaining numerical errors below the requested tolerance. This module combined with domain
rotation to nearly align the mesh with the Mach angle has been validated for sonic boom prediction by Wintzer 17 and
others with and without adaptation18-21. The adaptation module allows greatly reduced mesh generation and analysis
time and offers effective use of computational resources for an accurate solution.

II.D. USM3D
The 59⁰ delta wing-body model with the embedded fuselage convergent-divergent nozzle was also studied
using USM3D (Table 1). USM3D is a tetrahedral cell-centered, finite volume Euler and Navier-Stokes (N-S)
method. The USM3D flow solver has a variety of options for solving the flow equations and several turbulence
models for closure of the N-S equations22,23. For the current study, Roe‟s flux difference splitting scheme was used
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and the CFL was set to 20. Flux limiters are used within the code to preclude oscillations due to shocks and
discontinuities by limiting the values of the spatial derivatives. For the present study, at the start of a new solution,
the USM3D code was computed using the Spalart-Allmaras turbulence model with first order spatial accuracy for
10000 iterations, and then the code automatically switched to second order spatial accuracy. Obtaining a well-
converged first order accurate solution before switching to 2 nd order significantly improves the chance of
convergence with the code, but it is sometimes not necessary. USM3D has been used for propulsion simulation and
plume induced flow separation studies. 24,25 The present study implements a simplified approach to generate a
nozzle exhaust plume. The convergent-divergent solid nozzle shape developed by Putnam was modeled within the
aft fuselage of the 59⁰ delta wing-body configuration. The boundary condition at the nozzle plenum face was set
to a cold air jet temperature of 590 degrees Rankine, and a pressure of 8 times atmospheric conditions at 50,000 ft.
The ratio of specific heats was assumed 1.4 within the nozzle as well as in the free-stream flowfield.

III. Geometry Modeling

III.A. 2-D CD Supersonic Slot Nozzle: WIND-US and PAB3D

For the two-dimensional (2-D) supersonic slot nozzle, both WIND-US and PAB3D utilized the same grid.
A structured computational domain consisting of 13 zones and 461,496 grid points was used (Fig. 1). This nozzle
geometry simulates a high aspect ratio slot nozzle with infinite span. Simulations were run at the design nozzle
pressure ratio (NPR) of 8.0. Temperature for the nozzle plume was 530 R, with one case run at 1900 R for the 5⁰
wedge. Critical dimensions for the nozzle were a 2.05 inch throat height and a 3.88 inch exit height; the boat-tail
angle was 5⁰, with a 2.6 inch long boat-tail bevel (Fig. 1a). The computational domain extended 152 inches
downstream of the nozzle exit, 22.86 inches above, and 45.7 inches below the nozzle (Fig 1b). Multi-block wall-
packed grids, with the initial grid spacing producing y+ values near 1.0, were generated for use on parallel processor
systems. Viscous wall boundaries were used for all nozzle surfaces. Convergence was assessed by monitoring the
nozzle mass flow and the off-body pressure profile at 12.5 inches below the centerline of the nozzle. External flow
conditions were run at Mach 2.2, an angle of attack of zero degrees for a 50,000 ft flight altitude.
The wedge shock generator (wedge) used in this study had both a 2.5⁰ and 5⁰ half-angle leading edge. The
wedge was located 22.86 inches above the nozzle centerline, and the leading edge of the wedge was located at the
same axial station as the nozzle exit. The upper boundary of the mesh contains the profile of the lower wedge
surface where the boundary conditions were a solid wall with no slip. Boundary conditions upstream and
downstream of the wedge were „freestream‟ boundaries, as were boundaries at the front, bottom, and aft portion of
the computational domain. In WIND-US, „freestream‟ boundaries create partial shock reflections, which can only
be avoided by moving the boundary farther away from the model, and increasing computational grid size. In this
case, the modeling approach was acceptable because the partial shock reflections from the „freestream‟ boundaries
affected the flow field aft of the shock/nozzle plume interaction at the supersonic flow conditions.
CFD grids were also constructed with a 2.5˚ and a 5.0˚ wedge-only components. These solutions were
compared to solutions with the wedge and the 2-D CD supersonic slot nozzle.

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 III.B. 3-D Axisymmetric CD Supersonic “Nozzle 6”: WIND-US
Figure 2a displays the seven variations of the axisymmetric CD supersonic exhaust nozzle, as tested by
Putnam5. For this study, a scale replica of the sixth design,“Nozzle 6”, was selected, as this nozzle is consistent with
previous work4. This simulation was run as half of the nozzle with a vertical symmetry plane and consisted of 19
zones with 11,061,540 grid points. This nozzle had a design pressure ratio of 8.12 and simulations were performed
at NPR=8. Critical dimensions for the nozzle were a 10.22 inch throat diameter and a 13.42 inch exit diameter; the
boat tail angle was 5⁰. The computational domain (Figs. 2b and 2c) extended 271 inches downstream of the nozzle
exit, and 57.1 inches above and below the nozzle. Multi-block wall-packed grids with the initial grid spacing
selected to produce y+=1.0 were generated for use on parallel processor systems. To reduce computational time on a
large 3-D grid, inviscid wall boundaries were used for all nozzle surfaces. External flow conditions were run at
Mach 2.2, an angle of attack of zero, and an Euler solution was generated.
The wedge (Fig. 3) was unswept with 2.5⁰ half angle leading and trailing edges. This wedge permitted
study of shock and expansion regions passing through a nozzle plume. The wedge was located at 57.1 inches above
the nozzle centerline, and the leading edge of the wedge was located in a plane 13.14 inches upstream of the nozzle
exit. In this case, the axial station for the leading edge of the wedge was close to the nozzle throat, not the nozzle
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exit. The upper boundary of the mesh contained the profile of the lower wedge surface where the boundary
conditions were inviscid wall boundaries. All other boundary conditions were again set to the WIND-US
„freestream‟ boundary condition.

III.C. 59⁰ Wing-Body Model with “Nozzle 6”: Cart3D

The Cart3D model surface (Fig. 4a) was developed from the baseline “Nozzle 6” paired with the 59⁰ delta-
wing body model9. The nozzle flowfield was simulated with a pressure boundary at the nozzle plenum, and Cart3D
computations of the nozzle plume were obtained at a nozzle pressure ratio of 8. The computational domain
extended 10 body lengths in all directions, and line sensors at both one and two body lengths below the vehicle were
used to drive the mesh adaptation.
The wedge used in this test case had a diamond wedge profile with 2.5⁰ half angle leading and trailing
edges. The wedge was located 57.1 inches above the nozzle centerline, and the leading edge of the wedge was
located in a plane 13.14 inches upstream of the nozzle exit. External flow conditions were run at Mach 2.2 and an
angle of attack of zero.

III.D. 59⁰ Wing-Body Model with “Nozzle 6”: USM3D

A USM3D model was created for the 59⁰ wing-body model with “Nozzle 6”. Near-body grids suitable for
viscous compuatations were generated for USM3D using commercial software. These near body grids were
cylindrical in shape. Figure 4b shows grid with features such as the forward grid boundary, the symmetry plane and
the nozzle plume baffle grid. The grid is highly refined near the body and a Mach cone aligned prism grid is
appended to the inner cylindrical grid allow for accurate sonic boom computations at greater distances from the
model.
Two cuts through the volume mesh are displayed, colored by the maximum included angle of each
tetrahedral cell. The plume baffle surface grid possesses no thickness and allows for refined anisotropic cells off
both sides of its surface. The baffle is cone shaped and increases in diameter by 0.5 degree to simulate a nozzle with
an expanding jet or plume. A nozzle pressure ratio of 8.0 was used for the computations and the model length
(256.66 inches) was computed in feet with a Reynolds number of 2.16 per foot, at an altitude of 50,000 ft to simulate
a realistic sized supersonic vehicle in flight. The boundary conditions were set to no slip for all surface boundaries
on the 59⁰ wing-body model and the wedge, except for the nozzle lip which was set to an inviscid boundary. The
nozzle plenum face was set to jet exhaust flow. The initial spacing off the solid surfaces was 0.0001 inches to
provide y+ values around 1.0. The anisotropic spacing of the baffle was set to 0.01 inches and the baffle “surface”
average-edge length was a factor of three smaller than the surrounding mesh. Most of the configuration had y+
values less than 1.0 except a very small region at the wing-body intersection and the leading edge (near 2.0).

IV. Results

IV.A. 2-D CD Supersonic Slot Nozzle: WIND-US and PAB3D

Two-dimensional solutions with WIND-US are shown with Mach contours in Figs. 5 and 6, and detailed
pressure distributions are shown in Fig. 7. Two-dimensional solutions with PAB3D are shown with Mach contours
in Fig. 8. Figure 9 compares the results of the two codes.

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 Figure 5a shows the Mach number contours for the 2.5⁰ wedge simulation in the absence of the nozzle
plume, and displays the entire computational domain. Figure 5b shows the contours for the wedge and the 2-D CD
supersonic slot nozzle plume interaction, and also displays the entire computational domain. The nozzle plume was
deflected 2.5⁰ down for the length of the wedge, and then deflected 2.5⁰ back to the axial direction. Figure 5c is a
close-up view of the plume interaction in Fig. 5b. At the top of the contour plot (Fig. 5c), the shocks created by the
nozzle lip interact with shocks from the wedge and a reflection from the WIND-US “freestream” boundary. This
reflected shock intersects the nozzle plume.
A similar situation was observed in Fig. 6a for the 5⁰ wedge-only, and 6b for the 2-D CD supersonic slot
nozzle with the 5⁰ wedge, where the nozzle plume was deflected down 5⁰. A closeup of the plume and shock
interaction is provided. Fig. 6c shows the Euler solution, using the same geometry and flow conditions for the 5⁰
wedge. These figures also demonstrate how the wedge shock is displaced by a thickening of the nozzle plume (Fig.
6b) when compared to the Euler nozzle plume (Fig. 6c).
Both Figs. 5 and 6 demonstrate how the nozzle plume boundary is turned or deflected by the wedge shock.
As the lower boundary turns, shocks form off the lower nozzle plume boundary and the wedge shock appears to pass
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through the plume.

The near field pressure signature coefficient, ∆P/P, is compared in Fig. 7a along a line located 12.5 inches
below the nozzle centerline for five cases: (1) 5⁰ wedge with cold jet, (2) 2.5⁰ wedge with cold jet, (3) 5⁰ wedge
with 1900 degrees Rankine jet (4) 5⁰ wedge only, and (5) 2.5⁰ wedge only. For the 2.5⁰ wedge shock, the maximum
ΔP/P of 0.179 was at x=181 inches. The magnitude for the 2.5⁰ wedge shock with the nozzle plume was 8.2%
higher than the magnitude without the nozzle plume. For the 5⁰ wedge shock the maximum ΔP/P of 0.381 was at
x=177 inches. The maximum value of ΔP/P was the same for both a cold and hot (1900 R) jet. The difference
between the 5⁰ wedge shock with and without the jet was 5.5%. For both cases, the presence of a viscous nozzle
plume slightly increases the peak over-pressure, due to the increased turning angle caused by the thickened viscous
nozzle plume. The small shocks seen at x=220 inches are caused by the reflection of the nozzle lip shock off the
“freestream” boundary, which are not present for the wedge-only case.
Figure 7b compares pressure signatures for the 2.5⁰ wedge simulation, at a location of 12.5 inches below
the nozzle centerline. WIND-US simulations were conducted with (1) a viscous boundary layer using the SST
turbulence model, (2) an inviscid (Euler) solution, and (3) a viscous solution of the wedge-only. The pressure
profile for the Euler solution is indistinguishable from the 2.5⁰ wedge-only case, except for the expected differences
due to reflection of the nozzle lip shocks. For the turbulent case, the wedge shock moved slightly upstream due to
the thicker viscous nozzle plume. The additional flow turning caused a change in wedge shock location. Figure 7c
shows the same comparison of (1) turbulent, (2) Euler, and (3) wedge-only pressure signatures for the 5⁰ wedge.
The Euler case resembles the 5⁰ wedge only case, based on agreement in the plateau between x=180 and x=190.
However, the Euler case more closely resembles the turbulent cases based on the the peak value and the shock
location.
Fig. 8a shows the PAB3D Mach number contours for the 5⁰ wedge simulation in the absence of the nozzle
plume, and Fig. 8b shows the contours with the 5⁰ wedge and the 2-D CD supersonic slot nozzle interaction.
Similar to the WIND-US computations, the shocks created by the nozzle lip were reflected off the “freestream”
boundary behind the wedge and back to the nozzle plume centerline. The PAB3D nozzle plume was deflected 5⁰
down for the length of the generator, and then turned back 5⁰ to exhaust in the axial direction. The nozzle plume was
shifted down from its source due to the presence of the wedge shock. PAB3D Mach contours showed good
qualitative comparison with WIND-US Mach contours.
Figure 9 shows comparisons between PAB3D pressure signatures with the k-ε turbulence model, and
WIND-US pressure signatures with the SST turbulence model, at a location of 12.5 inches below the nozzle
centerline. This comparison demonstrates (1) that WIND-US and PAB3D obtain the same peak pressure signature
for the 5⁰ wedge-only case, and (2) obtain the same peak pressure signature for the 2-D CD supersonic slot
nozzle and 5⁰ wedge shock interaction. Discepancies between the WIND-US and PAB3D pressure profiles occur
downstream of the interaction at x= 213 inches for both the wedge-only case and the nozzle plume with the 5⁰
wedge shock. This discrepancy could be due do the difference in turbulence models (not studied), but also
demonstrates the need for a comparison to experimental data.

IV.B. 3-D Axisymmetric CD Supersonic “Nozzle 6”: WIND-US

WIND-US Mach contours on the symmetry plane for the 3-D axisymmetric CD supersonic “Nozzle 6” and
the 2.5⁰ wedge are displayed in Fig. 10. This was a fully three-dimensional (3-D) Euler simulation. The nozzle
plume was first deflected down 2.5⁰, then deflected up 2.5⁰, and finally deflected back to the axial direction. Fig. 11

5
 shows the ΔP/P for the “Nozzle 6” and wedge interaction for a location one diameter (15.24 inches) below the
nozzle centerline. A comparison is made between the wedge-only and “Nozzle 6” with the wedge. The nozzle boat
tail expansion, lip shock and the secondary expansion/shock around the nozzle plume can be seen for values of x=70
to 100 inches. The wedge bow shock interaction can be seen at x=175 inches, and comparisons can be made to the
wedge-only. The peak ΔP/P for the nozzle plume and wedge case was 0.31, which is 15.6% greater than the wedge-
only. The minimum ΔP/P was -0.286, 8.3% less than the wedge-only.

IV.C. 59⁰ Wing-Body Model with “Nozzle 6”: Cart3D

Figure 12a shows Mach number contours for the 59⁰ wing-body model with “Nozzle 6” installed in the aft
fuselage. The nozzle plume deflects downward through the compression region of the wedge and then upwards
through the expansion region of the wedge before returning straight behind the vehicle. The Cart3d mesh,
developed through adjoint-based mesh adaptation, is displayed in Fig. 12b. The mesh adaptation strategy included a
line sensor downstream of the nozzle to generate a high density grid for the nozzle plume, in addition to both the
high density grid generated around the vehicle and high density mesh aligned with vehicle shock waves. Fig. 13
Shows the ΔP/P signature at an h/L=1.0, a location much farther away than the previous simulations (256.6 inches
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versus 12.5 inches). The pressure profile was required at a larger distance from the vehicle to obtain a profile that
was not affected by large changes in grid density, casued by the grid adaptation near the vehicle. The 59⁰ wing-
body model signature is present between values of x=50 and 320 inches and the wedge bow shock starts at x=350
inches. The peak overpressure for the 59⁰ wing-body model with “Nozzle 6” case was 0.10, which is 10.3% greater
than the wedge-only. The minimum ΔP/P was -0.08, 11.3% more than the wedge shock. These far-field differences
in ΔP/P between the 59⁰ wing-body model with “Nozzle 6” and the wedge-only case are similar to the near-field
ΔP/P results presented in the WIND-US solution (Fig. 11).

IV.D. 59⁰ Wing-Body Model with “Nozzle 6”: USM3D

A USM3D computational result of the 59⁰ wing-body model with 'Nozzle 6' and the 2.5⁰ wedge is shown
in Figure 14a. The plume boundary is well defined from the use of the baffle grid. The influence of the
compression region of the wedge results in downward plume deflection, and upward deflection in the expansion
region. The grid lines are overlaid with a view of the plume (Fig. 14b) where the Mach cone aligned prism cells are
displayed in the lower portion of the image. The cells maintain axial spacing and stretch in the Mach wave direction
to reduce dissipation and attenuate the pressure signatures to greater distances. The 0.5 degree cone angle of the
baffle does not follow the plume boundaries, but it is sufficiently close to allow for the solution of the plume
boundary. The baffle grid was placed 5 inches downstream of the nozzle, but the anisotropic mesh is coarser than
desired between the nozzle and initiation of the baffle clustering. The leading and trailing edges of the baffle are
problematic because the anisotropic cells must make a 360 degree turn around the baffle, which results in stretched
and enlarged cells. This was not expected to affect the pressure signature. The authors are investigating other
meshing techniques to improve the mesh in this region.
Computations of the wedge-only were performed with clustering of the same baffle grid to eliminate any
possible effects from different grids used in the computations. A solution of the 59⁰ wing-body model alone was
also performed with the same baffle as used with the wedge. The pressure signatures at one body length below the
model nose are compared for these combinations of components in Fig. 15. The wedge pressure signature was
modified by the presence of the nozzle plume in a similar manner that was shown for the Cart3D Euler results (Fig.
13). The wedge bow and tail shock strengths, compared to the wedge-only computation, have increased and
decreased in magnitude by 15.1 and 11.3 percent, respectively, from the influence of the nozzle plume. The
increased bow strength appears to be due to the downward deflection of the nozzle plume from influence of the
wedge, indicating that the nozzle plume influences pressures in a similar way as a solid surface. The bow shock
bends as a result of the plume and is forward of the wedge-only computation. The forward movement is due to the
downward movement of the lower nozzle plume boundary. Figure 16a and 16b superimpose lines aligned with the
bow and tail shocks from the diamond-profile computation on the symmetry plane Mach contours for solutions with
and without the model and plume. The shock position deviates from linear near the center of the plume for both
bow and tail shocks.

V. Conclusions
Both 2-D and 3-D simulations were performed on exhaust nozzles with interaction from shock waves
generated by a 2.5⁰ and a 5⁰ wedge. For 2-D nozzles, the upper nozzle plume boundary is turned or deflected by the
wedge shock, and the lower boundary is also deflected through the same turning angle. As the lower plume
boundary turns, shocks form off the lower boundary, parallel and co-planar to those above the boundary. Shock

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 strength was increased by the presence of the nozzle plume at both cold and elevated nozzle plume temperatures, but
increased temperature did not increase the shock strength. Results were different for turbulent CFD cases vs. Euler
cases, where the ΔP/P profile changed by 5.5% to 8% with viscous plume modeling. The 2-D inviscid case showed
little difference in pressure signature with or without the presence of the nozzle plume.
The changes in the viscous computations were due to a thickened viscous nozzle plume, which increased
turning of the shock, and shock strength, formed off the lower plume boundary. For design of supersonic aircraft,
the effect of viscosity in the ΔP/P profile is not likely to affect the overall aircraft signature, when based on the
results of the two-dimensional simulations. Accurate analysis of the plume and possible tailoring of the aircraft
surfaces to reduce unwanted plume effects could be performed prior to closing a design. It appears reasonable to
perform design studies with Euler analysis and then perform viscous CFD computations, to make high fidelity
vehicle changes, before finalizing the design.
Results obtained for the 3-D simulations displayed up to a 15% increase in ΔP/P overpressure with the
modeling of the nozzle plume (Fig 11), where the 2-D Euler results showed almost no difference with the
configuration and nozzle plume (Fig 7b). The wedge pressure signature was modified by the presence of the plume
and the plume path was modified by the pressure disturbance from the wedge. This implies that detailed
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computations of the nozzle plume should be modeled during design of modern low boom supersonic transport
configurations. It is not clear whether these effects require viscous modeling since the trends appear to be captured
with inviscid computations. It seems prudent to accurately model the plume to determine the extent of pressure
signature changes during vehicle design as it is expected that different shaped vehicles could have either favorable
or detrimental effects from the influence of nozzle plumes. Further study and comparison to experimental data is
warranted, but at the time of publishing, no known experimental validation data exists for this shock and plume
interaction. At this time, a nozzle plume and shock interaction experiment is planned for the 1-foot by 1-foot
supersonic wind tunnel at the NASA Glenn Research Center.

VI. Acknowledgements

This work was funded by the NASA Fundamental Aeronautics Program, High Speed Project.

VII. References
1
Freund, D., Howe, D., Simmons, F., and Schuester, L., "Quiet Spike Prototype Aerodynamic Characteristics From
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2010-1386, Jan. 2010.
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Castner, R. S., "Analysis of Exhaust Plume Effects on Sonic Boom for a 59-Degree Wing Body Model," AIAA-
2011-917, Jan. 2011.
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Castner, R. S., "Exhaust Plume Effects on Sonic Boom for a Delta Wing and Swept Wing-Body Model," AIAA-
2012-1033, Jan. 2012.
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the Use of Turbulence Models in the Simulation of Jet and Nozzle Flows", AIAA-2006-489, Jan. 2006.
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5 Oct. 2012].
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Aftosmis, M. J., Berger, M. J., and Melton, J. E., “Robust and Efficient Cartesian Mesh Generation for
Component-Based Geometry,” AIAA Journal, Vol. 36, No. 6, 1998, pp. 952-960.
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Aftosmis, M. J., Berger, M. J., and Adomavicius, G., “A Parallel Multilevel Method for Adaptively Refined
Cartesian Grids with Embedded Boundaries,” AIAA Paper 2000-0808, 38th Aerospace Sciences Meeting and
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Aftosmis, M. J.; and Berger, M. J., “Multilevel Error Estimation and Adaptive H-Refinement for Cartesian

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Exhibit, Reno, Nev., Jan. 2002.
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Nemec, M., and Aftosmis, M. J., “Adjoint Error-Estimation and Adaptive Refinement for Embedded-Boundary
Cartesian Meshes,” AIAA Paper 2007-4187, 18th AIAA CFD Conf., Miami, FL, June 2007.
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Nemec, M., Aftosmis, M. J., and Wintzer, M., “Adjoint-Based Adaptive Mesh Refinement for Complex
Geometries,” AIAA Paper 2008-0725, Jan. 2008.
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Wintzer, M., Nemec, M., and Aftosmis, M., "Adjoint-Based Adaptive Mesh Refinement for Sonic Boom
Prediction," AIAA-2008-6593, Aug. 2008.
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Cliff, S. E., Thomas, S. D., McMullen, M. S., Melton, J.E., and Durston, D. A., “Assessment of Unstructured
Euler Methods for Sonic Boom Pressure Signatures Using Grid Refinement and Domain Rotation Methods,” NASA
TM-2008-214568, Sept. 2008.
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AIAA-2011-3500, 29th AIAA Applied Aerodynamics Conference, Hawaii, June, 2011.
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Linda, “Sonic Boom Computations for a Mach 1.6 Cruise Low Boom Configuration and Comparisons with Wind
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AIAA-2011-1055, Jan. 2011.

Table 1. Summary of CFD codes and geometry models.

CFD Code Geometry
Two-dimensional (2-D) Models Three-dimensional (3-D) Models

WIND-US 2-D CD Supersonic Slot Nozzle 3-D Axisymmetric CD “Nozzle 6”

PAB3D 2-D CD Supersonic Slot Nozzle --
Cart3D -- 59˚ Wing-body Model with “Nozzle 6”
USM3D -- 59˚ Wing-body Model with “Nozzle 6”

8
 5˚

2.052 3.879 4.109 4.57

15.36
(a)
18.0

Wedge
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Wedge

y= 47.1
Computational Domain
y= 0

Nozzle
y= - 47.1

x=58 x=119 x=271.4

(b) (c)

Fig. 1. (a) 2-D CD supersonic slot nozzle geometry, (b) computational domain for the 2-D CD supersonic slot nozzle
with a 2.5⁰ wedge angle, (c) details of grid at nozzle exit.

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(a)

Nozzle
Wedge

y= 57.1
Computational Domain

y= - 57.1

x= -20.6 x=61 x=332

Fig. 2. (a) 3-D axisymmetric CD supersonic “Nozzle 6” from Putnam3, (b) computational domain (centerline cut) for
3-D axisymmetric CD supersonic „Nozzle 6‟ with the 2.5⁰ wedge angle,
(c) grid at nozzle exit (centerline cut).

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Isometric
Front

11
Top
Side

Fig. 3. 3-D axisymmetric CD supersonic “Nozzle 6” with the 2.5⁰ wedge.

 59˚ Wing-body model Nozzle 6 Wedge
(a)

Front Side

Top
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Isometric

(b)

Symmetry Plane

Forward
Grid
Boundary

Plume
‘Baffle’
Grid

Fig. 4. (a) Cart3D and USM3D model surface of the 59⁰ wing-body model with 'Nozzle 6' 9
(b) USM3D grid of the 59⁰ wing-body model with “Nozzle 6”.
Color contours are for the maximum included angle of each tetrahedral cell
(low = 71˚ ; high = 179˚)

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 2.5⁰ Wedge

Mach 2.2
(a)

2.5⁰ Wedge
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Mach 2.2
(b)

2.5˚

2.5⁰ Wedge

Cut-Plane
Nozzle Shock formed off the
Plume
lower nozzle plume
boundary
Mach 2.2
(c)

Fig. 5. WIND-US Mach contours for 2.5⁰ wedge angle, (a) wedge-only,
(b) full computational domain of the 2-D CD supersonic slot nozzle at NPR = 8,
(c) close-up of the 2-D CD supersonic slot nozzle at NPR = 8.
Shows the location of the cut plane for ΔP/P data at y=-12.5 inches.

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 5⁰ Wedge

Mach 2.2

(a)
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5˚
5⁰ Wedge

Cut-Plane
Nozzle Shock formed off the
lower nozzle plume
boundary
Mach 2.2
Shock movement due to
(b) thicker nozzle plume

Cut-Plane
Nozzle

Mach 2.2 No shock movement with

(c) Euler nozzle plume

Fig. 6. WIND-US Mach contours for 5⁰ wedge angle,

(a) wedge-only, (b) 2-D CD supersonic slot nozzle at NPR = 8,
(c) 2-D CD supersonic slot nozzle Euler solution.

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 dP/P slot with
Nozzle nozzle
5˚with 5
degree
wedge wedge 530 R
(530 R)
0.500 Nozzle with 2.5˚
dP/P - slot nozzle w 2.5
wedge
degree (530 R)530 R
wedge
5.5% Nozzle with 5˚
0.400 dP/P slot nozzle with 5
wedge (1900 R)
deg wedge 1900R
5 deg wedge only
5˚ wedge-only
0.300
2.52.5˚
degwedge-only
wedge only
0.200 Wedge
bow
∆P/P

0.100 shock Lip Shock Reflection

8.2%

0.000
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50 100 150 200 250 300

-0.100 Boat-tail
Expansion Nozzle Lip Shock
-0.200

-0.300
x, in

Fig. 7(a). WIND-US ∆P/P at 12.5 inches below nozzle centerline for 2.5 ⁰ and 5⁰ wedge angle.
Wedge-only, and 2-D CD supersonic slot nozzle NPR = 8.

0.250
0.200
0.150
Lip shock reflection
Nozzle Exit
0.100
Plane x=119 in.
0.050
0.000
∆P/P

50 100 150 200 250 300

-0.050
-0.100
dP/P - slotwith
Nozzle nozzle
2.5˚wwedge
2.5
-0.150 degree wedge

-0.200 2.52.5˚
degwedge-only
wedge only

-0.250
Slot nozzle
Nozzle w 2.5
with 2.5˚degree
wedge,
-0.300 wedge
x, in Euler Euler soln

Fig. 7(b). WIND-US ∆P/P at 12.5 inches below nozzle centerline for 2.5 ⁰ wedge angle.
Wedge-only, and 2-D CD supersonic slot nozzle at NPR = 8, both viscous and Euler solutions.

15
 dP/P slotwith
Nozzle nozzle
5˚ with
0.500 5 degree wedge
wedge (530 R) 530 R
dP/P slotwith
Nozzle nozzle
5˚ with
0.400 5 deg
wedgewedge 1900R
(1900 R)
5˚ wedge-only
5 deg wedge only
0.300
Nozzle
slot with
nozzle w 55˚deg
wedge
wedge (530soln
Euler R),
0.200 Euler
Nozzle exit
∆P/P

plane x=119 inches

0.100
Lip shock reflection

0.000
50 100 150 200 250 300
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-0.100

-0.200

-0.300
x, in
Fig. 7(c). WIND-US ∆P/P at 12.5 inches below nozzle for 5 ⁰ wedge angle.
Wedge-only, and 2-D CD supersonic slot nozzle at NPR = 8, both viscous and Euler solutions.

5⁰ Wedge
(a)

(b)
5⁰ Wedge

Nozzle Plume

Mach 2.2

Fig. 8. PAB3D Mach contours for 5⁰ wedge angle,

(a) wedge-only, (b) with 2-D CD supersonic slot nozzle at NPR = 8

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Downloaded by CARLETON UNIVERSITY on November 28, 2015 | http://arc.aiaa.org | DOI: 10.2514/6.2013-12

Fig. 9. Comparison between WIND-US and PAB3D ∆P/P at 12.5 inches below nozzle centerline for 5⁰ wedge
angle. Wedge-only and 2-D CD supersonic slot nozzle at NPR = 8.

2.5⁰ Wedge

Nozzle

Cut
Plane

Plume
Mach 2.2

Fig. 10. Centerline cut side view of WIND-US Mach contours for 2.5 ⁰ wedge angle,
with 3-D axisymmetric CD supersonic “Nozzle 6” at NPR = 8.

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 0.4
15.6%
wing and
Wedge andplume
plume
0.3 shock
Wedge
Wedge only
bow wing shock
0.2
shock
0.1
ΔP/P

0.0
0 100 200 300 400
-0.1
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Wedge
Nozzle Lip
-0.2 tail
Boat Shock
shock
-0.3
Tail
Expansion
8.3 %
-0.4
X, in
Fig. 11. ΔP/P at 15.24 inches below WIND-US solution for 2.5 ⁰ wedge angle,
with 3-D axisymmetric CD supersonic “Nozzle 6” at NPR = 8.

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 2.5⁰ Wedge

Plume
59⁰ Wing-body Model

Line sensor at h/L = 1

(a) Mach 2.2 (256.66 inches below nose)
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(b)

Fig. 12. (a) Cart3D Mach Contours for the 59⁰ wing-body model with “Nozzle 6” and the 2.5⁰ wedge; NPR = 8,
(b) adapted computational mesh.

0.15
Vehicle and
wedge shock
Wedge Wedge shock
0.10
bow 10.3%
shock Vehicle only

0.05
ΔP/P

0.00
Vehicle Wedge
nose tail shock
-0.05 Wing
shock
expansion
11.3%
-0.10
0 100 200300 400 500 600
X, in
Fig 13. Cart3D ΔP/P at h/L=1.0 for the 59⁰ wing-body model with “Nozzle 6” and the 2.5⁰ wedge; NPR = 8.

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 (a)
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h/L = 1

(b)

Baffle grid cells

Mach cone aligned prism cells

Fig. 14. (a) USM3D Mach Contours for the 59⁰ wing-body model with “Nozzle 6” and the 2.5⁰ wedge; NPR = 8,
(b) USM3D computational mesh.

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 0.15
Vehicle and
Wedge wedge shock
0.10 bow Wedge shock
shock 15.1%
Vehicle only
ΔP/P 0.05

0.00
Wedge
Vehicle Vehicle tail
nose wing shock
-0.05 shock expansion
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11.3%
-0.10
0.00 100.00 200.00 300.00 400.00 500.00 600.00
X, in
Fig 15. USM3D ΔP/P at h/L=1.0 for the 59⁰ wing-body model with “Nozzle 6'”and the 2.5⁰ wedge; NPR = 8.

Wedge
tail Tail shock
shock movement
Wedge
bow
shock

Bow shock
movement

(a) (b)

Fig 16. USM3D 59⁰ wing-body model with “Nozzle 6”: superimposed lines aligned with the bow and tail shocks
from the wedge (computation on the symmetry plane). Mach contours for solutions (a) wedge-only (b) 59⁰ wing-
body model with “Nozzle 6” and the 2.5⁰ wedge.

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