Raymond S. Castner

Glenn Research Center, Cleveland, Ohio

Alaa Elmiligui

Langley Research Center, Hampton, Virginia 

Susan Cliff

Ames Research Center, Moffett Field, California 

Exhaust Nozzle Plume and Shock Wave Interaction

NASA/TM—2013-217838

February 2013

AIAA–2013–0012
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Raymond S. Castner

Glenn Research Center, Cleveland, Ohio

Alaa Elmiligui

Langley Research Center, Hampton, Virginia 

Susan Cliff

Ames Research Center, Moffett Field, California 

Exhaust Nozzle Plume and Shock Wave Interaction

NASA/TM—2013-217838

February 2013

AIAA–2013–0012

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

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NASA/TM—2013-217838 1

Exhaust Nozzle Plume and Shock Wave Interaction

Raymond S. Castner

National Aeronautics and Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Alaa Elmiligui

National Aeronautics and Space Administration

Langley Research Center

Hampton, Virginia 23681

Susan Cliff

National Aeronautics and Space Administration

Ames Research Center

Moffett Field, California 94035

Abstract

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 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 to 15 percent) changes in 

shock amplitude.

Nomenclature

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.
NASA/TM—2013-217838 2

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 Nwave 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.

Recent studies to develop aircraft with acceptable sonic boom noise include programs such as the 

Quiet Spike (Ref. 1) and the Shaped Sonic Boom Demonstrator (SSBD) (Ref. 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 Putnam

(Ref. 3), who performed an experimental study of exhaust nozzles and the effects of the exhaust plume.

Tests were done in a 4- by 4-ft 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 (Refs. 4 and 5), to slot nozzles (Ref. 6) and engine-wing-body models

(Refs. 7 and 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 plumes were studied: one created by a twodimensional (2-D) 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 59° 

delta wing-body model. CFD codes and geometry models are listed in Table I. The Mach number 

contours and pressure profiles from these configurations are presented.

Computational Modeling

WIND-US

Two- and three-dimensional (3-D) exhaust nozzles were modeled with WIND-US (Table I). WINDUS is a general purpose fluid flow solver that is used to numerically solve various sets of equations 

governing physical phenomena (Ref. 9). 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 multicore 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.

PAB3D

In this study, PAB3D (Ref. 10) was used in conjunction with two-equation k–ε turbulence closure and 

nonlinear algebraic Reynolds stress models to simulate the 2-D CD supersonic nozzle (Table I). 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, 
NASA/TM—2013-217838 3

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 analysis

(Ref. 11). 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.

TABLE I.—SUMMARY OF CFD CODES AND GEOMETRY MODELS

CFD Code Geometry

2-D Models 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”

Cart3D

Cart3D was used to evaluate 3-D effects for a 59° delta wing-body model with a fuselage embedded

CD nozzle and a wedge shock located above the nozzle plume (Table I). Cart3D (Refs. 12 and 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 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 module (Refs. 14 to 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 (Ref. 17) and others with and without adaptation (Refs. 18 to 21). The 

adaptation module allows greatly reduced mesh generation and analysis time and offers effective use of 

computational resources for an accurate solution.

USM3D

The 59° delta wing-body model with the embedded fuselage CD nozzle was also studied using 

USM3D (Table I). 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 equations (Refs. 22 and 23). For the current study, Roe’s flux 

difference splitting scheme was used 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 SpalartAllmaras 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 2nd order significantly improves the chance of convergence with the code, but 
NASA/TM—2013-217838 4

it is sometimes not necessary. USM3D has been used for propulsion simulation and plume induced flow 

separation studies (Refs. 24 and 25). The present study implements a simplified approach to generate a 

nozzle exhaust plume. The CD solid nozzle shape developed by Putnam was modeled within the aft 

fuselage of the 59° delta wing-body configuration. The boundary condition at the nozzle plenum face 

was set to a cold air jet temperature of 590 °R, 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.

Geometry Modeling

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

For the 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 (Figure 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 5° wedge. Critical dimensions for the nozzle were a 2.05 in. throat height and a 3.88 in.

exit height; the boat-tail angle was 5°, with a 2.6 in. long boat-tail bevel (Figure 1(a)). The computational 

domain extended 152 in. downstream of the nozzle exit, 22.86 in. above, and 45.7 in. below the nozzle

(Figure 1(b)). 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 in. below the centerline of the nozzle. External flow conditions were run at Mach 2.2, an angle of 

attack of 0° for a 50,000 ft flight altitude. 

Figure 1.—(a) 2-D CD supersonic slot nozzle geometry, (b) computational domain for the 2-D CD supersonic slot 

nozzle with a 2.5° wedge angle, and (c) details of grid at nozzle exit.

2.052 3.879 4.109 4.57

18.0

15.36

5°

Nozzle

Wedge

Computational Domain

Wedge

(a)

(b) (c)

x = 58 x = 119 x = 271.4

y = –47.1

y = 0

y = 47.1
NASA/TM—2013-217838 5

The wedge shock generator (wedge) used in this study had both a 2.5° and 5° half-angle leading edge. 

The wedge was located 22.86 in. 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.

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

Figure 2(a) displays the seven variations of the axisymmetric CD supersonic exhaust nozzle, as tested 

by Putnam (Ref. 5). For this study, a scale replica of the sixth design, “Nozzle 6”, was selected, as this 

nozzle is consistent with previous work (Ref. 4). 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 in. throat diameter and a 13.42 in. exit diameter; the boat tail angle was 5°. The computational 

domain (Figure 2(b) and (c)) extended 271 in. downstream of the nozzle exit, and 57.1 in. 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 (Figure 3) was unswept with 2.5° 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 in. above the nozzle centerline, and the leading edge of the wedge was located in a plane 13.14 in. 

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 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.

59° Wing-Body Model with “Nozzle 6”: Cart3D

The Cart3D model surface (Figure 4(a)) was developed from the baseline “Nozzle 6” paired with the 

59° delta-wing body model (Ref. 9). 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 2.5° half angle leading and 

trailing edges. The wedge was located 57.1 in. above the nozzle centerline, and the leading edge of the 

wedge was located in a plane 13.14 in. upstream of the nozzle exit. External flow conditions were run at 

Mach 2.2 and an angle of attack of zero. 
NASA/TM—2013-217838 6

(a)

(b)

Figure 2.—(a) Three-dimensional axisymmetric CD supersonic “Nozzle 6” from Putnam (Ref. 3), (b) computational 

domain (centerline cut) for 3-D axisymmetric CD supersonic ‘Nozzle 6’ with the 2.5° wedge angle, (c) grid at nozzle 

exit (centerline cut).

x = –20.6 x = 61 x = 332

y = –57.1

y = 57.1

Wedge Nozzle

Computational Domain
NASA/TM—2013-217838 7

Figure 3.—Three-dimensional axisymmetric CD supersonic “Nozzle 6” with the 2.5° wedge.

Front Side

Isometric Top
NASA/TM—2013-217838 8

Figure 4.—(a) Cart3D and USM3D model surface of the 59° wing-body model with 'Nozzle 6' (Ref. 9). (b) USM3D 

grid of the 59° wing-body model with “Nozzle 6”. Color contours are for the maximum included angle of each 

tetrahedral cell (low = 71°; high = 179°).

59° Wing-body model Nozzle 6 Wedge

Front Side

Top

Isometric

(a)

(b)

Forward Grid 

Boundary

Symmetry Plane

Plume 

‘Baffle’ Grid
NASA/TM—2013-217838 9

59° Wing-Body Model with “Nozzle 6”: USM3D

A USM3D model was created for the 59° 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 4(b) 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° 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 in.) 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 59° 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 in. to provide y+ values around 1.0. The anisotropic 

spacing of the baffle was set to 0.01 in. 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).

Results

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

Two-dimensional solutions with WIND-US are shown with Mach contours in Figure 5 and Figure 6, 

and detailed pressure distributions are shown in Figure 7. Two-dimensional solutions with PAB3D are 

shown with Mach contours in Figure 8. Figure 9 compares the results of the two codes.

Figure 5(a) shows the Mach number contours for the 2.5° wedge simulation in the absence of the 

nozzle plume, and displays the entire computational domain. Figure 5(b) 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 2.5° down for the length of the wedge, and 

then deflected 2.5° back to the axial direction. Figure 5(c) is a close-up view of the plume interaction in 

Figure 5(b). At the top of the contour plot (Figure 5(c)), 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 Figure 6(a) for the 5° wedge-only, and Figure 6(b) for the 2-D 

CD supersonic slot nozzle with the 5° wedge, where the nozzle plume was deflected down 5°. A closeup

of the plume and shock interaction is provided. Figure 6(c) shows the Euler solution, using the same 

geometry and flow conditions for the 5° wedge. These figures also demonstrate how the wedge shock is 

displaced by a thickening of the nozzle plume (Figure 6(b)) when compared to the Euler nozzle plume 

(Figure 6(c)).

Both Figure 5 and Figure 5 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 through the plume.

The near field pressure signature coefficient, ∆P/P, is compared in Figure 7(a) along a line located

12.5 in. below the nozzle centerline for five cases: (1) 5° wedge with cold jet, (2) 2.5° wedge with cold 

jet, (3) 5° wedge with 1900 °R jet (4) 5° wedge only, and (5) 2.5° wedge only. For the 2.5° wedge shock, 

the maximum ΔP/P of 0.179 was at x=181 in. The magnitude for the 2.5° wedge shock with the nozzle 

plume was 8.2 percent higher than the magnitude without the nozzle plume. For the 5° wedge shock the 

maximum ΔP/P of 0.381 was at x=177 in. The maximum value of ΔP/P was the same for both a cold and 
NASA/TM—2013-217838 10

hot (1900 °R) jet. The difference between the 5° wedge shock with and without the jet was 5.5 percent. 

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 in. are caused by the reflection of the nozzle lip shock off the “freestream” boundary, which are

not present for the wedge-only case. 

Figure 5.—WIND-US Mach contours for 2.5° 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 in.

2.5° Wedge

Cut-Plane

Plume

Mach 2.2

Nozzle

2.5° Wedge

(a)

(c)

Mach 2.2

2.5°

Shock formed off the lower 

nozzle plume boundary

(b)

2.5° Wedge

Mach 2.2
NASA/TM—2013-217838 11

Figure 6.—WIND-US Mach contours for 5° wedge angle, (a) wedge-only, (b) 2-D CD supersonic slot 

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

Figure 7(b) compares pressure signatures for the 2.5° wedge simulation, at a location of 12.5 in.

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 wedgeonly. The pressure profile for the Euler solution is indistinguishable from the 2.5° 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 

(a)

Cut-Plane

Nozzle

Mach 2.2

5° Wedge

(c)

Mach 2.2

Mach 2.2

Nozzle

Cut-Plane

5° Wedge

Shock formed off the lower 

nozzle plume boundary

5°

Shock movement due to 

thicker nozzle plume

No shock movement 

with Euler nozzle plume

(b)
NASA/TM—2013-217838 12

turning caused a change in wedge shock location. Figure 7(c) shows the same comparison of (1) 

turbulent, (2) Euler, and (3) wedge-only pressure signatures for the 5° wedge. The Euler case resembles 

the 5° 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.

(a)

(b)

Figure 7.—(a)WIND-US ∆P/P at 12.5 in. below nozzle centerline for 2.5° and 5° wedge angle. 

Wedge-only, and 2-D CD supersonic slot nozzle NPR = 8. (b) WIND-US ∆P/P at 12.5 in. 

below nozzle centerline for 2.5° wedge angle. Wedge-only, and 2-D CD supersonic slot 

nozzle at NPR = 8, both viscous and Euler solutions. (c). WIND-US ∆P/P at 12.5 in. below 

nozzle for 5° wedge angle. Wedge-only, and 2-D CD supersonic slot nozzle at NPR = 8, 

both viscous and Euler solutions.

-0.300

-0.200

-0.100

0.000

0.100

0.200

0.300

0.400

0.500

50 100 150 200 250 300

∆P/P

x, in

dP/P slot nozzle with 5 degree

wedge 530 R

dP/P - slot nozzle w 2.5 degree

wedge

dP/P slot nozzle with 5 deg wedge

1900R

5 deg wedge only

2.5 deg wedge only

Nozzle Lip Shock

Wedge 

bow

shock Lip Shock Reflection

530 R

8.2%

5.5%

Boat-tail 

Expansion

Nozzle with 5° wedge 

(530 °R)

Nozzle with 2.5° wedge 

(530 °R)

Nozzle with 5 ̊ wedge 

(1900 °R)

5° wedge-only

2.5° wedge-only

-0.300

-0.250

-0.200

-0.150

-0.100

-0.050

0.000

0.050

0.100

0.150

0.200

0.250

50 100 150 200 250 300

∆P/P

x, in

dP/P - slot nozzle w 2.5 degree

wedge

2.5 deg wedge only

Slot nozzle w 2.5 degree wedge

Euler soln

Nozzle with 2.5° wedge

2.5° wedge-only

Nozzle with 2.5° wedge, 

Euler

Lip shock reflection

Nozzle Exit 

Plane x=119 in.
NASA/TM—2013-217838 13

Figure 7.—Concluded.

Figure 8.—PAB3D Mach contours for 5° wedge angle, (a) wedge-only, (b) with 2-D CD supersonic 

slot nozzle at NPR = 8

Figure 8(a) shows the PAB3D Mach number contours for the 5° wedge simulation in the absence of 

the nozzle plume, and Figure 8(b) shows the contours with the 5° 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 5° down for the length of the generator, and then turned back 5° to

-0.300

-0.200

-0.100

0.000

0.100

0.200

0.300

0.400

0.500

50 100 150 200 250 300

∆P/P

x, in

dP/P slot nozzle with 5

degree wedge 530 R

dP/P slot nozzle with 5

deg wedge 1900R

5 deg wedge only

Nozzle with 5° wedge 

(530 °R)

Nozzle with 5° wedge 

(1900 °R) 5° wedgeonly

Nozzle with 5° wedge 

(530 °R), Euler

Lip shock reflection

Nozzle exit

plane x=119 in.

5° Wedge

Mach 2.2

5° Wedge

Nozzle Plume

(a)

(b)
NASA/TM—2013-217838 14

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 in. below the nozzle 

centerline. This comparison demonstrates (1) that WIND-US and PAB3D obtain the same peak pressure 

signature for the 5° wedge-only case, and (2) obtain the same peak pressure signature for the 2-D CD 

supersonic slot nozzle and 5° wedge shock interaction. Discepancies between the WIND-US and PAB3D 

pressure profiles occur downstream of the interaction at x= 213 in. for both the wedge-only case and the 

nozzle plume with the 5° 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.

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 2.5° wedge are displayed in Figure 10. This was a fully 3-D Euler simulation. The nozzle 

plume was first deflected down 2.5° , then deflected up 2.5° , and finally deflected back to the axial 

direction. Figure 11 shows the ΔP/P for the “Nozzle 6” and wedge interaction for a location one diameter 

(15.24 in.) 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 in. The wedge bow shock interaction can be seen at 

x=175 in., 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 percent greater than the wedge-only. The minimum ΔP/P was –0.286, 

8.3 percent less than the wedge-only.

Figure 9.—Comparison between WIND-US and PAB3D ∆P/P at 

12.5 in. below nozzle centerline for 5° wedge angle. Wedge-only 

and 2-D CD supersonic slot nozzle at NPR = 8.
NASA/TM—2013-217838 15

Figure 10.—Centerline cut side view of WIND-US Mach contours for 2.5° wedge angle, with 3-D 

axisymmetric CD supersonic “Nozzle 6” at NPR = 8.

Figure 11.—ΔP/P at 15.24 in. below WIND-US solution for 2.5° wedge angle, 

with 3-D axisymmetric CD supersonic “Nozzle 6” at NPR = 8.

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

Δ

0 100 200 300 400

P/P

X, in

wing and plume

shock

wing shock

Wedge and plume

Wedge only

Boat

Tail

Expansion

Nozzle Lip 

Shock

Wedge

bow

shock

Wedge

tail

shock

15.6%

8.3 %

Mach 2.2

Cut

Plane

Nozzle

2.5° Wedge

Plume
NASA/TM—2013-217838 16

59° Wing-Body Model with “Nozzle 6”: Cart3D

Figure 12(a) shows Mach number contours for the 59° 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 Figure 12(b). 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. Figure 13 shows the ΔP/P signature at an h/L=1.0, a location 

much farther away than the previous simulations (256.6 in. versus 12.5 in.). 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 59° wing-body model signature is 

present between values of x=50 and 320 in. and the wedge bow shock starts at x=350 in. The peak 

overpressure for the 59° wing-body model with “Nozzle 6” case was 0.10, which is 10.3 percent greater 

than the wedge-only. The minimum ΔP/P was –0.08, 11.3 percent more than the wedge shock. These farfield differences in ΔP/P between the 59° 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 (Figure 11).

Figure 12.—(a) Cart3D Mach Contours for the 59° wing-body model with “Nozzle 6” and the 2.5° wedge; 

NPR = 8, (b) adapted computational mesh.

2.5° Wedge

59° Wing-body Model Plume

Mach 2.2

Line sensor at h/L = 1 

(a) (256.66 in. below nose)

(b)
NASA/TM—2013-217838 17

Figure 13.—Cart3D ΔP/P at h/L=1.0 for the 59° wing-body model with “Nozzle 6”

and the 2.5° wedge; NPR = 8.

59° Wing-Body Model with “Nozzle 6”: USM3D

A USM3D computational result of the 59° wing-body model with 'Nozzle 6' and the 2.5° wedge is 

shown in Figure 14(a). 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 (Figure 14(b)) 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° 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 in.

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° 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 59° 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 Figure 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 (Figure 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 16(a) and (b) 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.

-0.10

-0.05

0.00

0.05

0.10

0.15

0 100 200 300 400 500 600

ΔP/P

X, in

Vehicle and

wedge shock

Wedge shock

Vehicle only

Vehicle

nose

shock Wing

expansion

Wedge

tail shock

10.3%

11.3%

Wedge

bow

shock
NASA/TM—2013-217838 18

Figure 14.—(a) USM3D Mach Contours for the 59° wing-body model with “Nozzle 6” and the 2.5° 

wedge; NPR = 8, (b) USM3D computational mesh.

(a)

(b)

h/L = 1

Mach cone aligned prism cells

Baffle grid cells
NASA/TM—2013-217838 19

Figure 15.—USM3D ΔP/P at h/L=1.0 for the 59° wing-body model with “Nozzle 

6”and the 2.5° wedge; NPR = 8.

Figure 16.—USM3D 59° 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) 59° wing-body model with “Nozzle 6” and the 2.5° wedge.

Conclusions

Both 2-D and 3-D simulations were performed on exhaust nozzles with interaction from shock waves 

generated by a 2.5° and a 5° 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 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 versus Euler cases, where the ΔP/P profile changed by 5.5

to 8 percent with viscous plume modeling. The 2-D inviscid case showed little difference in pressure 

signature with or without the presence of the nozzle plume.

-0.10

-0.05

0.00

0.05

0.10

0.15

0.00 100.00 200.00 300.00 400.00 500.00 600.00

ΔP/P

X, in

Vehicle and

wedge shock

Wedge shock

Vehicle only

15.1%

11.3%

Vehicle

nose

shock

Vehicle

wing

expansion

Wedge

bow

shock

Wedge

tail

shock

(a) (b)

Wedge

bow

shock

Wedge

tail

shock

Bow shock 

movement

Tail shock 

movement
NASA/TM—2013-217838 20

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 2-D 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 percent increase in ΔP/P overpressure 

with the modeling of the nozzle plume (Figure 11), where the 2-D Euler results showed almost no 

difference with the configuration and nozzle plume (Figure 7(b)). 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 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- by 1-ft supersonic wind 

tunnel at the NASA Glenn Research Center.

References

1. Freund, D., Howe, D., Simmons, F., and Schuester, L., “Quiet Spike Prototype Aerodynamic 

Characteristics From Flight Test,” AIAA 2008−125, Jan. 2005.

2. Graham, D., Dahlin, J., Meredith, K., and Vadnais, J., “Aerodynamic Design of Shaped Sonic Boom 

Demonstration Aircraft,” AIAA 2005−8, Jan. 2005.

3. Putnam, L. and Capone, F., “Experimental Determination of Equivalent Solid Bodies to Represent 

Jets Exhausting into a Mach 2.20 External Stream,” NASA TN-D-5553, 1969.

4. Castner, R. S., “Analysis of Plume Effects on Sonic Boom Signature for Isolated Nozzle 

Configurations,” NASA/TM—2008-215414 (AIAA-2008-3729), June 2008.

5. Bui, T., “CFD Analysis of the Nozzle Jet Plume Effects on Sonic Boom Signature,” AIAA-2009-

1054, Jan. 2009.

6. Castner, R. S., “Slot Nozzle Effects for Reduced Sonic Boom on a Generic Supersonic Wing 

Section,” AIAA-2010-1386, Jan. 2010.

7. Castner, R. S., “Analysis of Exhaust Plume Effects on Sonic Boom for a 59-Degree Wing Body 

Model,” AIAA-2011-917, Jan. 2011.

8. Castner, R. S., “Exhaust Plume Effects on Sonic Boom for a Delta Wing and Swept Wing-Body 

Model,” AIAA-2012-1033, Jan. 2012.

9. Towne, C. E., “Wind-US Users Guide, Version 2.0,” NASA/TM—2009-215804, Oct. 2009.

10. Abdol-Hamid, K., Pao, S. P., Hunter, C., Deere, K. A., Massey, S. J., and Elmiligui, A. “ PAB3D: Its 

History in the Use of Turbulence Models in the Simulation of Jet and Nozzle Flows,” AIAA-2006-

489, Jan. 2006.

11. Massey, S. J., POST Code Manual, URL: http://www.asm-usa.com/PAB3D/doc/post/ [cited 5 Oct. 

2012].

12. 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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Refined Cartesian Grids with Embedded Boundaries,” AIAA Paper 2000-0808, 38th Aerospace 

Sciences Meeting and Exhibit, Reno, NV, Jan. 2000.
NASA/TM—2013-217838 21

14. Aftosmis, M. J.; and Berger, M. J., “Multilevel Error Estimation and Adaptive H-Refinement for 

Cartesian Meshes with Embedded Boundaries,” AIAA Paper 2002-0863, 40th AIAA Aerospace 

Sciences Meeting and Exhibit, Reno, NV, Jan. 2002.

15. 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, Jun. 2007.

16. Nemec, M., Aftosmis, M. J., and Wintzer, M., “Adjoint-Based Adaptive Mesh Refinement for 

Complex Geometries,” AIAA Paper 2008-0725, Jan. 2008.

17. Wintzer, M., Nemec, M., and Aftosmis, M., “Adjoint-Based Adaptive Mesh Refinement for Sonic

Boom Prediction,” AIAA-2008-6593, Aug. 2008.

18. 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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CART3D (Invited), AIAA-2011-3500, 29th AIAA Applied Aerodynamics Conference, HI, Jun.

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and Bangert, Linda, “Sonic Boom Computations for a Mach 1.6 Cruise Low Boom Configuration 

and Comparisons with Wind Tunnel Data (Invited), AIAA-2011-3496, 29th AIAA Applied 

Aerodynamics Conference, HI, Jun. 2011.

21. Elmiligui, A., Cliff, S., Wilcox, F., and Thomas, S. “Numerical Predictions of Sonic Boom 

Signatures for Straight Line Segmented Leading Edge Model”, Seventh International Conference on 

Computational Fluid Dynamics, ICCFD7-2004, Big Island, HI, Jul. 9-13, 2012.

22. Frink, N. T., Pirzadeh, S. Z., Parikh, P. C., Pandya, M. J., and Bhat, M. K., “The NASA Tetrahedral 

Unstructured Software System,” The Aeronautical Journal, Vol. 104, No. 1040, Oct. 2000, pp. 491-

499.

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Flows,” AIAA Paper-96-0292, Jan. 1996.

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Advanced Turbulence Models with the Unstructured-Grid CFD Tool, TetrUSS,” AIAA 2004-0714, 

Jan. 2004.

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Separation” AIAA-2011-1055, Jan. 2011.
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Exhaust Nozzle Plume and Shock Wave Interaction 

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13. SUPPLEMENTARY NOTES

14. ABSTRACT

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 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 to 15 percent) changes in shock amplitude. 

15. SUBJECT TERMS

Exhaust nozzles; Plumes; Shock wave interaction 

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