John W. Slater and John D. Saunders

Glenn Research Center, Cleveland, Ohio

Computational Fluid Dynamics (CFD) 

Simulation of Hypersonic Turbine-Based 

Combined-Cycle (TBCC) Inlet Mode Transition

NASA/TM—2010-216362

May 2010

AIAA–2009–7349
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John W. Slater and John D. Saunders

Glenn Research Center, Cleveland, Ohio

Computational Fluid Dynamics (CFD) 

Simulation of Hypersonic Turbine-Based 

Combined-Cycle (TBCC) Inlet Mode Transition

NASA/TM—2010-216362

May 2010

AIAA–2009–7349

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared for the

16th International Space Planes and Hypersonic Systems and Technologies Conference

cosponsored by the AIAA, DLR, and DGLR

Bremen, Germany, October 19–22, 2009
Acknowledgments

This work was performed as part of the Hypersonics Project of the NASA Fundamental Aerodynamics Program, Dr. James L. 

Pittman, Principal Investigator. Within the Hypersonics Project, this work was performed as part of the Propulsion Technology 

Integration task lead by Dr. Kenneth L. Suder as the Associate Principal Investigator. The second author serves as Manager for the 

Inlet Mode Transition experiment. The authors would also like to acknowledge the technical input of Mr. Vance Dippold III and 

Dr. Jinho Lee of the NASA Glenn Research Center and Mr. Bobby W. Sanders and Ms. Lois J. Weir of Techland Research, Inc.

Available from

NASA Center for Aerospace Information

7115 Standard Drive

Hanover, MD 21076–1320

National Technical Information Service

5301 Shawnee Road

Alexandria, VA 22312

Available electronically at http://gltrs.grc.nasa.gov

This work was sponsored by the Fundamental Aeronautics Program 

at the NASA Glenn Research Center.

Level of Review: This material has been technically reviewed by technical management. 
Computational Fluid Dynamics (CFD) Simulation of Hypersonic 

Turbine-Based Combined-Cycle (TBCC) Inlet Mode Transition 

John W. Slater and John D. Saunders 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Abstract 

Methods of computational fluid dynamics were applied to simulate the aerodynamics within the 

turbine flowpath of a turbine-based combined-cycle propulsion system during inlet mode transition at 

Mach 4. Inlet mode transition involved the rotation of a splitter cowl to close the turbine flowpath to 

allow the full operation of a parallel dual-mode ramjet/scramjet flowpath. Steady-state simulations were 

performed at splitter cowl positions of 0°, –2°, –4°, and –5.7°, at which the turbine flowpath was closed 

half way. The simulations satisfied one objective of providing a greater understanding of the flow during 

inlet mode transition. Comparisons of the simulation results with wind-tunnel test data addressed another 

objective of assessing the applicability of the simulation methods for simulating inlet mode transition. 

The simulations showed that inlet mode transition could occur in a stable manner and that accurate 

modeling of the interactions among the shock waves, boundary layers, and porous bleed regions was 

critical for evaluating the inlet static and total pressures, bleed flow rates, and bleed plenum pressures. 

The simulations compared well with some of the wind-tunnel data, but uncertainties in both the windtunnel data and simulations prevented a formal evaluation of the accuracy of the simulation methods. 

Nomenclature 

R Gas constant 

REC Total-pressure recovery at the engine face (REC = pt2/pt0) 

pt0 Total pressure of the flow in the freestream ahead of the inlet (158.8 psi) 

pt2 Average total pressure at the engine face 

W2 Flow rate at the engine face 

WHS Reference capture flow rate of the ramjet/scramjet flowpath 

WLS Reference capture flow rate of the turbine flowpath 

αhole Angle of bleed hole axis with respect to surface 

Δ Normalized difference in value 

γ Ratio of specific heats 

1.0 Introduction 

One concept for access to space involves a two-stage vehicle in which an air-breathing propulsion 

system is used for the first stage with staging occurring at hypersonic speeds (Refs. 1 and 2). The airbreathing propulsion system integrates a turbine engine flowpath within the flowpath of a dual-mode 

ramjet/scramjet engine to form a turbine-based combined-cycle (TBCC) propulsion system. The turbine 

flowpath provides thrust for take-off and acceleration to supersonic speeds. The ramjet/scramjet flowpath 

provides thrust to accelerate the vehicle to the hypersonic staging speed. Figure 1 shows a schematic of 

the first-stage vehicle with a TBCC propulsion system. The turbine and ramjet/scramjet flowpaths are in 

parallel in an over/under configuration. A splitter cowl divides the inlet flow between the turbine and 

ramjet/scramjet flowpaths. Both flowpaths also share a nozzle. At some supersonic speed, the turbine 

flowpath ceases operation to allow full operation of the ramjet/scramjet. Inlet mode transition is the 

NASA/TM—2010-216362 1 
Turbine Flowpath

Ramjet / Scramjet Flowpath

Splitter Cowl (closed)

Nozzle

Turbine Engine

Figure 1.—A schematic of the first-stage with a turbine-based combined-cycle airbreathing propulsion system with the 

turbine flowpath open (top) and closed (bottom). 

process by which the inlet flow is diverted from the turbine flowpath to the ramjet/scramjet flowpath. The 

schematic of Figure 1 shows a rotating splitter cowl that can rotate to shut off flow to the turbine flowpath 

as part of the inlet mode transition. 

One challenge for this concept is the establishment of stable and efficient aerodynamic processes for 

the flow through both flowpaths and during the inlet mode transition. The inlet flow is characterized by 

shock waves, turbulent boundary layers, shock/boundary layer interactions, and internal supersonic 

compression. Within the turbine flowpath, a terminal shock in the throat decelerates the flow to subsonic 

speeds for intake by the turbine engine. Stability requires that the inlet remain started with the terminal 

shock in the throat. Efficiency requires that the total-pressure recovery be maximized. A less efficient 

inlet would require a larger propulsion system to generate the required thrust, which would increase the 

weight of the propulsion system and vehicle. The vehicle should accelerate during inlet mode transition 

and disruptions to the thrust would degrade the system. 

The aerodynamics of inlet flow for TBCC propulsion systems and inlet mode transition has been 

studied by a relatively small number of studies (Refs. 3 to 5). Reference 3 discussed a small-scale windtunnel test of a rectangular inlet that examined the stability and operation of a ramjet/scramjet flowpath as 

the inlet flow was diverted for a turbine flowpath. However, the focus of Reference 3 was on the 

ramjet/scramjet flowpath rather than the turbine flowpath. References 4 and 5 focused on the 

aerodynamics of the turbine flowpath. Reference 4 discussed the design of a rectangular inlet based on the 

schematic of Figure 1 and that inlet has become known as the inlet mode transition (IMX) inlet. The IMX 

inlet was studied with methods of computational fluid dynamics (CFD) and with a series of small-scale 

wind-tunnel tests. Some results of the CFD simulations and wind-tunnel tests were reported in Ref. 5. The 

CFD simulations provided some understanding of the flow features and performance of the inlet and the 

effects of the variation of some of the design parameters of the IMX inlet. The wind-tunnel tests were 

primarily intended to demonstrate the proof-of-concept of the IMX inlet and screen the parameters of the 

inlet design and operation space. The wind-tunnel tests did obtain data on the performance of the inlet and 

other flow properties during the inlet mode transition. However, a formal assessment of the uncertainties 

in the wind-tunnel data was not performed given the screening nature of the wind-tunnel tests. 

The present paper discusses further CFD simulations of the IMX inlet. One objective was to better 

understand the flow features and aerodynamics within the turbine flowpath during the inlet mode 

transition. Another objective was to assess the applicability of the CFD methods for simulating inlet mode 

transition through comparison with the wind-tunnel test data. Ideally, one would like to make a statement 

on the accuracy of the CFD methods; however, the lack of an uncertainty assessment of the wind-tunnel 

data and lack of clear methods for determining uncertainty in CFD methods prevented a formal accuracy 

assessment of the CFD methods. 

The next section discusses further details on the IMX inlet and the wind-tunnel tests. Section 3.0 

discusses the CFD methods for modeling the inlet flow and geometry and establishing the flow domain, 

boundary conditions, initial flow solution, and computational grid. Included is a discussion on the 

NASA/TM—2010-216362 2 
modeling of the porous bleed boundary condition needed to simulate the bleed regions within the turbine 

flowpath. Section 4.0 presents the results of the CFD study and includes visualizations of the flow 

features and streamwise variations of the Mach number, static pressure, and total pressure during inlet 

mode transition. The details of the flow in the bleed regions are discussed and includes the variation of 

bleed rates and plenum static pressures during inlet mode transition. The performance of the inlet is 

examined through an evaluation of the total-pressure recovery and distortion at the engine face. 

Conclusions are then stated as to the applicability of CFD methods for simulating inlet mode transition. 

2.0 Inlet Mode Transition (IMX) Inlet 

Some details on the design of the IMX inlet and the small-scale wind-tunnel tests are now provided as 

background for the CFD simulations. Figure 2 shows a cut-away image of the IMX inlet as tested in the 

wind-tunnel. The view is flipped from Figure 1 so that the turbine flowpath is now below the 

ramjet/scramjet flowpath. The IMX inlet has a rectangular cross-section for most of the turbine and 

ramjet/scramjet flowpaths. This simplified the mechanics of the splitter cowl rotation and other variable 

geometry required for the operation of a mixed-compression inlet at subsonic, transonic, and supersonic 

speeds. Flat sidewalls bounded the rectangular portions of inlet flowpaths. Within the turbine flowpath, 

the cross-section transitions from a rectangular to a circular shape just ahead of the engine face. The 

cross-sectional area was kept constant through the shape transition. The ramjet/scramjet flowpath 

remained rectangular since the flow was intended to remain supersonic through the flowpath and not of 

interest for study in the wind-tunnel tests. 

The ramps and forward portions of the ramjet/scramjet flowpath of the IMX inlet were designed for a 

Mach 7 staging. This created relatively long surfaces on which boundary layers developed that were 

ingested by the turbine flowpath. As seen in Figure 1, the splitter cowl rotates such that its leading edge 

rests on the ramp surface to fully close off the turbine flowpath as part of the inlet mode transition. Thus, 

the turbine flowpath is integrated into the ramjet/scramjet flowpath. The top surface of the splitter cowl is 

part of the ramp for the ramjet/scramjet flowpath while the bottom surface is a portion of the cowl of the 

turbine flowpath. Compression must occur efficiently on both surfaces during inlet mode transition. 

The model for the small-scale wind-tunnel tests had an engine face diameter of 1.821 in., which was 

also the width of the rectangular cross-sections of the flowpaths. The leading edge of the ramp was at 

(x,y) = (0,0) in. where x is the horizontal Cartesian coordinate and y is the vertical coordinate. The leading 

edge of the splitter cowl for the turbine flowpath at the 0° position was at (x,y) = (16.46, 3.78) in. The 

leading edge of the cowl for the ramjet/scramjet flowpath was at (x,y) = (21.23, 5.00) in. 

Sidewall

Engine Face

Ramjet / Scramjet Flowpath

Flow Plug

Ramp 

Leading 

Edge

Turbine Flowpath

Splitter Cowl 

Leading Edge

Ramjet / Scramjet Cowl

Figure 2.—The IMX inlet model for the small-scale wind-tunnel tests. 

NASA/TM—2010-216362 3 
The turbine flowpath contained nine porous bleed regions: four on the ramp, two on the cowl, and 

three on each sidewall. The bleed regions on the ramp and cowl each had a plenum into which the bleed 

flow was extracted. The flow exited the plenums through plenum exits that led to the external flow. The 

areas of the exits were sized so that the exiting flow was choked. This prevented external disturbances 

from entering the plenum and affecting the inlet flow through the bleed holes. Static pressure taps in the 

bleed plenums recorded the plenum static pressure. The sidewall bleed regions did not have plenums and 

the bleed holes extracted the flow directly to the external flow. 

The throat of the turbine flowpath was located in a region from approximately x = 23 to 25 in. Vortex 

generators were positioned within the turbine flowpath downstream of the throat at station at x = 26.5 in. 

The vortex generator array consisted of six vortex generators arrayed with two on the ramp, two on the 

cowl and one on each of the sidewalls. The vortex generators had an incidence of 16° in an alternating 

pattern. 

The engine face was located at x = 32.9 in. A total-pressure rake consisting of nine probes recorded 

the total pressure at the engine face. A “cold pipe” consisting of a straight section of pipe with a flow plug 

at the outflow was attached to the engine face of the turbine flowpath. The flow through the plug was 

choked and the level of back pressure (average static pressure at the engine face) was adjusted by 

translating the plug along the axis of the duct. Other data collected included the static pressures along the 

surfaces of the turbine flowpath at the plane of symmetry and about the circumference of the engine face. 

The CFD simulations were performed to match the conditions of the tests of the wind-tunnel 

experiment for which the Mach number of the freestream flow ahead of the inlet was at Mach 3.974, 

which was close to the Mach 4 at which inlet mode transition was expected to occur. The total pressure 

and total temperature of the freestream flow was pt0 = 158.8 psi and 547.2 °R, respectively. The model 

was oriented at a zero angle-of-attack with respect to the freestream flow. The CFD simulations were 

performed at splitter cowl positions of 0°, –2°, –4°, and –5.7° for which wind-tunnel test data was 

available. 

3.0 CFD Methods 

The methods used to perform the CFD simulations of the IMX inlet are now described to provide 

background for understanding the results and assess the applicability of the CFD methods for simulating 

inlet mode transition. The methods include those for modeling the flow, turbulence, geometry, flow 

domain, porous bleed regions, and other boundary conditions. The procedures for generating the grid and 

the initial flow solution are also described. 

3.1 Flow Equations 

The aerodynamics of the flow through the inlet was assumed to be described by the ReynoldsAveraged Navier-Stokes (RANS) equations. The RANS equations were discretized upon a structured, 

multi-block grid and solved using the Wind-US CFD solver (Ref. 6). The temperatures were assumed to 

be within the limits to allow the use of the ideally-perfect air model. The inviscid fluxes of the RANS 

equations were modeled using a second-order, upwind Roe flux-difference splitting method. The flow 

was assumed to be turbulent with the turbulent eddy viscosity calculated through a turbulence model. The 

two models used in the simulations were the one-equation Spalart-Allmaras model and the two-equation 

Menter shear-stress transport (SST) model. The simulation results presented in this paper were computed 

using the SST turbulence model. The Spalart-Allmaras turbulence model yielded similar results as the 

SST model; however, the SST model was used since it was more likely to improve the modeling of flows 

with significant boundary layer separation. The use of turbulence models for mixed-compression inlet 

simulations was discussed in earlier papers (Refs. 7 to 9). The equations were solved using a timemarching method with a first-order, implicit Euler method using local time-stepping. An initial solution 

was specified and the time-marching iterations were performed to obtain iterative convergence to a 

steady-state solution. The use of steady-state simulations for the inlet mode transition was based on the 

NASA/TM—2010-216362 4 
observation that the rotation of the splitter cowl occurred at much slower rate than the fluid velocities. It 

was assumed that the splitter cowl would require about 2 seconds to rotate from its design position of 0° 

through a rotation of 11.8° to close the turbine flowpath. The time scale of the fluid particles flowing 

along the length of the inlet was much smaller than the time scale of the splitter cowl rotation. Thus, it 

was assumed that the flow during inlet mode transition could be simulated with steady-state CFD 

simulations at each of the four splitter cowl positions of 0°, –2°, –4°, and –5.7°. 

3.2 Porous Bleed Boundary Condition 

The porous bleed regions within the turbine flowpath were critical for limiting the adverse effects of 

shock/boundary layer interactions by removing low-momentum flow within the boundary layer and 

enhancing the velocity profile to better withstand the high pressure gradients of the shock/boundary layer 

interactions. Within the throat of the turbine flowpath, the bleed regions helped keep the inlet started with 

the terminal shock in the throat by extracting flow downstream of the terminal shock. References 8 and 9 

describe the porous bleed models and provide simulations that demonstrate the application of the models. 

The models are outlined below. 

The bleed model is applied as a boundary condition imposed for surface grid points located within a 

bleed region. The bleed model assumes the region is continuously porous, and so, the flow through 

individual holes is not resolved nor are individual holes recognized. The bleed model affects the flow 

solution through a boundary condition on the component of the fluid velocity normal to the surface, vN, 

which is computed in the manner of 

BB

bleed

N A

W

v

ρ = (1) 

where AB is the surface area of the grid cell face at the boundary and ρB is the fluid static density at the 

boundary. The subscript “B” denotes flow properties evaluated at the boundary grid point. One form of 

the bleed model simply involves specifying Wbleed and assuming it remains constant through the 

simulation. This is the constant-bleed boundary condition model. 

It should be intuitive that the bleed rate should vary according to local flow conditions across the bleed 

region. One approach is to compute Wbleed using the equation 

bleed = − WQW −BsonicBsonic (2) 

The Wsonic-B is a reference flow rate defined as 

2/1 ( ) ( 12/1 )

2

1 −γ+γ−

− ⎟

⎠

⎞ ⎜

⎝

⎛ +γ

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ γ Φ=

B

BBBsonic TR

W Ap (3) 

The calculation of Wsonic-B assumes isentropic conditions through the bleed holes with choked flow 

(M = 1) within the bleed holes. The static pressure pB and temperature TB are evaluated at the boundary 

grid point and are both easily computed from the CFD flow field. The porosity of the bleed region Φ is 

computed as the ratio 

region

bleed

A

A =Φ (4) 

where Ableed is the cross-sectional area of the bleed holes and Aregion is the surface area of the bleed region. 

NASA/TM—2010-216362 5 
The surface sonic flow coefficient Qsonic-B is evaluated using the curve fit of Ref. 9. The curve fit is 

based on a scaling of wind-tunnel test data for circular bleed holes oriented at αhole = 90° to the surface. 

The curve fit has the form of 

59361420.0 03069346.0 59799735.0

2

+⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ − −= B

plenum

B

plenum

Bsonic

p

p

p

p Q (5) 

The pplenum is the average static pressure of the bleed plenum. A basic assumption of the model is that the 

volume of the bleed plenum is relatively large such that the Mach number of the flow within the plenum 

is very low, and so, much of the plenum is at the plenum static pressure, pplenum. The ratio (pplenum/pB) is the 

static plenum pressure ratio. The coefficient Qsonic-B is positive for bleed flow and negative for flow 

injection. As discussed in Reference 9, this allows the bleed model to simulate local injection or blowing 

of flow within the bleed region that might be present during shock/boundary layer interactions. 

The bleed model is complete once the plenum pressure pplenum is known. One option for evaluating 

pplenum is to simply specify pplenum and assume that it remains constant throughout the simulation. This is 

known as the constant-pressure bleed boundary condition model. This implies that the inlet has a control 

system that maintains pplenum at the specified value. 

An alternative option is to impose a constraint on pplenum involving the flow through the bleed plenum 

exit. The flow out of the plenum exit is modeled as a nozzle flow of the form 

( )( ) 12/1

2

2/1

2

1 1

−γ+γ−

⎟

⎠

⎞ ⎜

⎝

⎛ −γ + ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ γ = exit

B

exitDexit plenum M

TR pACW (6) 

The Aexit is the cross-sectional area of the bleed plenum exit. The CD is the discharge coefficient of the 

flow through the exit. The Mexit is the Mach number of the flow through the exit. The bleed exit is 

typically operated such that the flow through the exit is choked with Mexit = 1. This ensures that the 

exterior flow does not propagate into the bleed plenum and inlet flow. Subsonic values of Mexit can be 

calculated from the ratio of the plenum pressure and the external static pressure with the assumption of 

isentropic flow through the exit. Equation 6 also assumes that the total temperature within the plenum is 

approximately equal to the surface static temperature TB. The plenum pressure is computed from the 

condition that the amount of flow through the exit must equal the total bleed flow through the porous 

bleed region. Reference 8 provides further discussion on modeling the plenum exit. Simpler bleed 

systems, such as those on the IMX inlet, have fixed exit areas. When the exit areas are fixed, the model is 

known as the fixed-exit bleed boundary condition model. 

3.3 Flow Domain, Geometry Modeling, and Boundary Conditions 

The flow domain is the control volume within which the flow equations are solved. The boundaries of 

the flow domain for the IMX inlet adhered to the shape of the inlet surfaces or were shaped as inflow or 

outflow boundaries. The equations required boundary conditions to be imposed on the boundaries of the 

flow domain. Figure 3 shows the outline and boundaries of the flow domain used for the CFD 

simulations. The geometric and flow symmetry of the inlet allowed the flow domain to only represent 

one-half of the inlet, which in this case was the left-hand side as one looked down the inlet from the 

leading edge of the splitter cowl to the engine face. Thus, the entire boundary on the right-hand side of the 

flow domain was on the plane-of-symmetry and symmetry boundary conditions were applied, which were 

equivalent to inviscid, slip-wall boundary conditions. 

NASA/TM—2010-216362 6 
Nozzle

Throat

Inflow

Ramp

Outflow, 

Ramjet / Scramjet 

Flowpath

Turbine Engine Face

Outflow, 

Turbine 

Flowpath

Ramp Leading Edge

Outflow, 

Exterior

Ramjet / Scramjet 

Cowl

Splitter Cowl 

Leading Edge

Turbine Flowpath Throat

Symmetry plane is on the 

right side of the geometry

Figure 3.—Flow domain for the CFD simulations. 

The surfaces of the ramps and cowls of the turbine and ramjet/scramjet flowpaths had twodimensional profiles whose coordinates were listed in Reference 4. The sidewalls were flat with swept 

leading edges that aligned closely to the ramp shock angles at the Mach 7 design point. Downstream of 

the throat of the turbine flowpath, the subsonic diffuser increased in cross-sectional area. Just ahead of the 

engine face of the turbine flowpath, the inlet cross-section transitioned from a rectangular to circular 

shape. The surfaces of the inlet, except for the bleed regions, were specified with adiabatic, no-slip wall 

boundary conditions. 

Bleed boundary conditions were imposed within the bleed regions of the turbine flowpath. Figure 4 

shows the portion of the flow domain from the leading edge of the splitter cowl to just downstream of the 

throat of the turbine flowpath. The nine porous bleed regions are shown as the dark blue regions. Table 1 

lists the nine bleed regions and the porosity and bleed hole angle αhole for each bleed region. There were 

no bleed regions in the ramjet/scramjet flowpath. 

TABLE 1.—BLEED PROPERTIES AT SUPERCRITICAL CONDITIONS FOR THE SPLITTER COWL POSITION OF 0° 

Bleed 

Region Φ αhole 

(deg)

Wbleed/WLS

(EXP) 

Wbleed/WLS

(CFD) 

pplenum/pt0

(EXP)

pplenum/pt0

(CFD) 

CD * Aexit

(in.2

) 

R1 0.40 90 2.10% 2.10% 0.01828 0.00145 4.0996 

R2 0.20 90 1.34% 1.33% 0.01465 0.01974 0.1725 

R3 0.20 90 1.74% 1.74% 0.05683 0.04962 0.0880 

R4 0.20 90 1.48% 1.49% 0.24200 0.23275 0.0159 

C1 0.20 90 0.72% 0.72% 0.06522 0.05945 0.0298 

C2 0.20 90 0.92% 0.94% 0.23643 0.22179 0.0105 

SW1 0.20 30 3.77% 3.76% ---------- ---------- --------- 

SW2 0.20 30 0.81% 0.79% ---------- ---------- --------- 

SW3 0.20 30 1.01% 0.97% ---------- ---------- --------- 

Total ----- -- 13.89% 13.66% ---------- ---------- --------- 

NASA/TM—2010-216362 7 
R1 (2.10%) 2.10% 

R2 (1.34%) 1.33% 

R3 (1.74%) 1.74% 

R4 (1.48%) 1.49% 

SW3 (1.01%) 0.97% C2 (0.92%) 0.94% 

C1 (0.72%) 0.72%

SW2 (0.81%) 0.79% 

SW1 (3.77%) 3.76% 

Bleed rates are a percentage of

the theoretical capture of the

low-speed duct, WLS.

Total Bleed

(13.89%) 13.66%

(Experiment) CFD

Vortex Generators 

Turbine

Flowpath

Ramjet / Scramjet Flowpath

Figure 4.—Flow domain about the throat showing bleed regions and supercritical bleed rates with the 

splitter cowl at 0°. 

Figure 5.—Geometry of the vortex generators modeled 

as flat plates. 

The position of the vortex generators in the turbine flowpath can be seen in Figure 4. The vortex 

generators were modeled as rectangular flat plates with equivalent planform area as the actual airfoilshaped vortex generators. Reference 7 provides justification of this approach for modeling the vortex 

generators. Figure 5 shows the three vortex generators modeled for the flow domain. The surfaces of the 

vortex generators were specified with adiabatic, no-slip wall boundary conditions. There were no vortex 

generators in the ramjet/scramjet flowpath. 

The forward inflow boundary was established at x = –0.76 in. The relatively short distance between 

the inflow and the leading edge of the ramp was possible due to the supersonic nature of the freestream 

inflow just ahead of the inlet. A freestream inflow boundary was also established approximately parallel 

to and above the oblique shock originating from the leading edge of the ramp. 

 The external outflow boundary was established downstream of the leading edge of the cowl lip for 

the ramjet/scramjet flowpath such that all external oblique shocks exited at this external outflow 

boundary. A supersonic outflow boundary condition was imposed at this external outflow boundary and it 

involved first-order extrapolation of the conservative variables. 

NASA/TM—2010-216362 8 
The flow through the ramjet/scramjet flowpath remained supersonic and was not of interest in the 

simulations. The outflow boundary of the ramjet/scramjet flowpath was established at x = 27.50 in. and 

was specified with a supersonic outflow boundary condition with first-order extrapolation. 

On the vertical boundary above the sidewall, the flow was assumed to be parallel to the freestream 

flow. While some cross-spillage over the leading edge of the sidewall was possible, it was assumed that 

the amount of spillage was small enough to be ignored. Thus, this boundary was simulated with an 

inviscid wall boundary condition, which precluded any sidewall spillage. 

The outflow boundary of the turbine flowpath was placed approximately six engine face diameters 

downstream of the engine face. This was assumed sufficient to ensure that the outflow boundary 

condition did not bias the flow conditions at the engine face, which were of interest in evaluating the 

performance of the inlet. The flow domain downstream of the engine face consisted of a constant-area 

duct of three engine face diameters in length and a converging-diverging nozzle of three engine face 

diameters in length. Both can be seen in Figure 3. The converging-diverging nozzle simulated the effect 

of the flow plug used in the wind-tunnel test when the nozzle throat was choked. The engine-face static 

pressure, which is also known as the back pressure of the turbine flowpath was increased by reducing the 

area of the nozzle throat. With choked flow in the nozzle throat, the flow was supersonic downstream of 

the nozzle throat in the diverging portion of the nozzle. A supersonic extrapolation boundary condition 

was used at the outflow boundary. 

3.4 Grid Generation and Grid Resolution 

A multi-block, structured grid consisting of H-grids was generated for the flow domain. The grid was 

clustered near the no-slip boundaries to resolve the turbulent boundary layer such that the first grid point 

off the wall was at a non-dimensional distance of about y

+ ≈ 1. Away from the walls, the grid points were 

distributed so as to keep the maximum grid stretching (ratio of distances between grid points) below 

15 percent and the maximum grid resolution below a grid resolution limit. In the throat, the streamwise 

and cross-stream grid resolution was kept approximately uniform and below the specified grid resolution 

limit. 

To determine the appropriate grid resolution limit, a grid resolution study was performed on a planar 

(2D) grid of the forward portion of the IMX inlet. Simulations were performed on four grids for which the 

grid resolution limit was specified at 0.0364, 0.0228, 0.0152, and 0.0079 in. The effect of the grid 

resolution was determined by examining the bleed rate for the R1 bleed region and the total-pressure 

recovery (ratio of the average total pressure to the freestream total pressure) of the flow at the flow plane 

at the ramp shoulder, which was just downstream of the R1 bleed region. The results of the grid 

resolution study are listed in Table 2. It can be seen that the variation in the bleed rate was much greater 

than the variation in the total-pressure recovery. Thus, the grid resolution was based on resolving the 

bleed rate. The greater sensitivity of the bleed rates to grid resolution likely reflects the importance of 

resolving the interaction of the shock waves with the bleed regions in properly obtaining the bleed rates. 

Between grid resolutions of 0.0152 and 0.0079 in. the bleed rate changed by 0.08 percent. It was decided 

that a grid resolution limit of 0.0152 in. was sufficient to adequately resolve the bleed rates, as well as, the 

total pressure recovery. This grid resolution limit was a fraction 0.12 of the bleed hole diameter (1/8th in.). 

This is less than an earlier study which suggested a resolution of 0.4 of the bleed hole diameter to resolve 

the bleed rates (Ref. 8). 

TABLE 2.—RESULTS OF THE GRID RESOLUTION STUDY 

Grid Resolution 

Δs, in. 

Wbleed/WLS 

(R1) 

Δ

(%) 

REC Δ

(%)

0.0364 1.605% 6.940 0.835302 –0.071 

0.0228 1.533% 2.112 0.835297 –0.071 

0.0152 1.502% 0.080 0.838188 –0.275 

0.0079 1.501% ------ 0.835894 ------ 

 

NASA/TM—2010-216362 9 
The resulting grid contained 28 blocks and over 11.7 million grid points. Six of the blocks that 

contained about 3.2 million grid points were used to resolve the external flow field and ramjet/scramjet 

flowpath. The remaining blocks and grid points resolved the internal flow of the turbine flowpath. There 

were 541 grid points in the streamwise direction between the leading edge of the splitter cowl and the 

throat. In the cross-stream direction between the ramp and cowl, there were 181 grid point in the blocks 

between the leading edge of the splitter cowl and the ramp shoulder. Between the ramp shoulder and 

throat, 121 grid points were used between the ramp and cowl. Downstream of the throat, 61 grid points 

were used between the ramp and cowl. This created some block interfaces with abutting block boundaries 

with non-contiguous grid lines. In the cross-stream direction between the sidewall and symmetry plane, 

61 grid points were used. Figure 6 shows a vertical grid plane near the entrances to the turbine and 

ramjet/scramjet flowpaths. To display the grid with some clarity, every other grid point was removed 

from the plot. Figure 6 shows the various grid blocks with the number of grid points varying between 

blocks so as to keep maximum grid resolution below the grid resolution limit. This ensured that the 

shocks were resolved consistently through the internal flowpaths. Figure 7 shows the grid in the crossstream plane at the leading edge of the splitter cowl and at the engine face. The H-grid grid topology was 

maintained through to the circular engine face. 

Turbine Flowpath

Figure 6.—The grid in the region of the entrances to the turbine and ramjet/ 

scramjet flowpaths (every other grid point is shown for clarity). 

Figure 7.—The cross-stream grids at the splitter cowl 

lip for the turbine flowpath (left) and the turbine 

engine face (right). 

NASA/TM—2010-216362 10 
3.5 Initial Flow Solution and Iterative Convergence 

The time-marching solution to the RANS equations required an initial solution for the flow field from 

which to iterate to the steady-state solution. For these simulations, the initial solution was set to the 

supersonic conditions of the freestream ahead of the inlet. A series of iteration sets were performed to 

handle the complexities of establishing the mixed-compression flow field within the turbine flowpath. 

The first set involved several hundred iterations to establish a realistic supersonic flow through the turbine 

flowpath. The outflow nozzle was set with a diameter just slightly smaller than the diameter of the engine 

face so as not to choke. The vortex generators were not included within the flow domain. First-order 

inviscid flux terms were used and viscous flux terms were not included. A coarser grid was used through 

the use of the grid sequencing in which every other grid point was bypassed. This approach allowed the 

large transients to be damped or propagate out of the flow domain. The resulting flow field contained the 

primary oblique shocks through the inlet. 

The next set of several hundred iterations included the viscous terms to begin developing the 

boundary layers. The bleed regions were included to provide some control of the shock/boundary layer 

interactions. At first, the bleed rates for each bleed region were specified using the constant-bleed model. 

As the bleed flows develop, the bleed boundary conditions were changed to the constant-pressure bleed 

boundary condition. The bleed plenum pressures were adjusted during the iteration sets to obtain the 

desired bleed flow rate for each bleed region. 

The iteration sets continued with gradual introduction of the second-order flux methods and finer 

grids. During the process, the flow rates through the bleed regions and engine face were monitored to 

check on the iterative convergence. The flow rates were the primary measure of iterative convergence. It 

was possible to reach a level of iterative convergence of the bleed rates to levels of variation of Wbleed/WLS

≈ 0.01 percent. Similar converge was observed for the engine-face flow rate W2/WHS. Another measure of 

iterative convergence was the variation of the total-pressure recovery. The solutions were typically able to 

converge to a variation of less than 0.001 (1/10th of a count). 

The terminal shock and subsonic flow were established within the turbine flowpath by reducing the 

outflow nozzle throat area until choking was achieved. Further reductions in the nozzle throat increased 

the back pressure in the subsonic diffuser and pushed the terminal shock forward toward the inlet throat. 

Once the terminal shock was in the proximity of the throat, the vortex generators were added to the flow 

domain. 

The turbine flowpath was considered supercritical when the terminal shock was established 

downstream of the bleed regions in the throat (R4/C2/SW3). With supersonic flow over all of the bleed 

regions, the bleed rates were at their supercritical levels. The wind-tunnel test data listed the supercritical 

bleed rates at each position of the splitter cowl. As the iterations were continued, the plenum static 

pressures were then adjusted until the supercritical bleed rates approached those of the wind-tunnel test. 

Table 1 lists the supercritical bleed rates from the wind-tunnel test and the CFD solution for the splitter 

cowl in the 0° position. The values of the resulting plenum pressures are also listed. The bleed rates are 

also shown in Figure 4. 

With the bleed rates and plenum pressure known, Equation (6) was used to calculate the product of 

CD Aexit, which are listed in Table 1. These values were used to model the fixed-exit bleed system for the 

remaining inlet mode transition simulations at the other splitter cowl positions. The SW1, SW2, and SW3 

bleed regions did not have plenums and exhausted directly to the external flow. It was assumed the flow 

through these bleed regions was choked. Thus, the plenum pressures for these three bleed regions were 

held fixed during the inlet mode transition simulations at the plenum pressure that produced the match 

with the supercritical bleed rate. 

4.0 CFD Results 

Some results of the CFD simulations are presented to illustrate the flow features and quantify the flow 

properties and inlet performance. These include variations of the Mach number, static pressure, bleed 

NASA/TM—2010-216362 11 
rates, bleed plenum pressures, total-pressure recovery, and total-pressure distortion. The applicability of 

the CFD methods for simulating inlet mode transition was evaluated through comparison of the CFD 

results to wind-tunnel test data. 

4.1 Flow Features 

The CFD simulations provided an illustration of the shock waves, Mach numbers, static pressures, 

boundary layers and other flow features that allowed a greater understanding of the aerodynamics of the 

inlet flow during inlet mode transition. Figure 8 illustrates the changes in the flow field as the splitter 

cowl was rotated toward the closed position. Shown are the Mach number contours on the symmetry 

plane of the turbine flowpath from the leading edge of the splitter cowl to the throat for the four splitter 

cowl positions simulated (0°, –2°, –4°, and –5.7°). The four simulations were all performed at the same 

corrected flow rate for the turbine flowpath. For the flow field with the 0° splitter cowl position, an 

oblique shock started at the leading edge of the splitter cowl and propagated downward and intersected 

the ramp at the end of the R1 bleed region. An oblique shock reflected from the ramp and intersected the 

cowl just upstream of the C1 bleed region. There were several other reflected oblique shocks that formed, 

but they were too weak to show up clearly on the plot. The terminal shock was downstream of the R4 and 

C2 throat bleed regions and the flow was supercritical. The Mach number decelerated through the 

flowpath and decreased to about Mach 1.5 prior to the terminal shock. Downstream of the terminal shock, 

the Mach numbers were high subsonic values. 

The blue arrows show the bleed momentum vectors across the bleed regions. The lengths of the 

arrows represent the relative magnitude of the local bleed momentum. Each arrow represents a single 

boundary grid point at which the porous bleed boundary condition was applied. One can see that the bleed 

model indicated a variation of bleed rates across the bleed region due to variations in the local pressures. 

As the splitter cowl was rotated toward the closed position, the oblique shock changed angle and 

position such that the point of interaction with the ramp moved forward into the R1 bleed region. 

Downstream of the shock, the static pressures increased, which increased the bleed rate in the aft portion 

of the R1 bleed region. The oblique shock also became weaker as the splitter cowl angle became more 

aligned with the incoming ramp flow. The closing of the splitter cowl reduced the compression within the 

turbine flowpath which increased the Mach numbers in the throat. The higher Mach numbers resulted in 

stronger shock/boundary layer interactions which increased the boundary-layer separation downstream of 

the terminal shock. 

Figure 8 includes the flow rates through the engine face of the turbine flowpath W2 as normalized by 

the reference captured flow rate of the ramjet/scramjet cowl WHS, which was computed as the rate of 

freestream flow through the capture area of the frontal projection of the leading edge of the cowl of the 

ramjet/scramjet flowpath. Figure 8 also includes the total bleed rates WBleed as normalized by the reference 

capture flow rate of the splitter cowl WLS. As can be seen, both W2 and WBleed decreased as the splitter 

cowl was rotated toward the closed position. The W2 decreased because the smaller opening captured less 

flow. The WBleed decreased due to higher Mach numbers and lower pressures within the turbine flowpath. 

The flow through the turbine flowpath was quite three-dimensional despite the two-dimensional 

nature of the geometry. The sidewall boundary layer resulted in low-momentum corner flows. Figure 9 

shows the Mach number contours for a horizontal slice through the duct or “top view”. Only a section in 

the throat region from x = 19.56 to 24.87 in. is shown. The flow is from the left to right and the sidewall 

is shown at the top and symmetry plane is shown at the bottom. The R4 and C2 bleed regions are shown 

as the vertical darker bands in the middle of the plot. The inset numbers indicate the Mach numbers at the 

respective locations. The terminal shock is indicated by the dark clustering of contours. Toward the 

symmetry plane, the terminal shock formed an approximately normal shock. However, toward the 

sidewall, the terminal shock interacted significantly with the sidewall boundary layer and a low-speed 

region formed along the sidewall downstream of the throat bleed regions. 

NASA/TM—2010-216362 12 
Cowl 

Rotation 

Angle

- 2.0o

- 4.0o

- 5.7o

W2/WHS = 0.4696 WBLEED/WLS = 0.1380

W2/WHS = 0.3628 WBLEED/WLS = 0.1297

W2/WHS = 0.2620 WBLEED/WLS = 0.1220

W2/WHS = 0.1855 WBLEED/WLS = 0.1014

Mach Number Contours

0.0o

3.5

2.6

1.8

0.9

0.0

Mach

R1 R2 R3 R4

C2 C1 Splitter Cowl Leading Edge

Ramp

Throat

Figure 8.—Mach number contours at symmetry plane and flow rates for the supercritical 

flow at each of the cowl positions. 

1.0

0.5

1.1

1.2

1.47

1.53

1.94

1.64 2.11

C2 

(23.81-24.17)

R4 

(23.56-24.10)

Flow

Symmetry Plane

Sidewall

Top View

x = 19.56 in 24.87 in

Terminal Shock

Mach

2.35

1.61

0.87

0.14

-0.60

Figure 9.—Top view of the flow in the throat of the turbine flowpath. 

Figure 10 shows an isotropic view of this region with Mach number contours at horizontal and 

vertical slices and at a number of axial slices. The low-speed region downstream of the throat reveals 

itself as a reversed flow region in the upper corner of the duct. The reversed flow region constricted the 

flow area downstream of the throat and limited the ability of the flow to decelerate to subsonic Mach 

numbers. Thus downstream of the terminal shock, the Mach numbers are still approximately sonic. 

Another observation of the flow field is that the Mach numbers in the throat approached Mach 1.5, as 

shown in Figure 11. Typically, values of Mach 1.3 are desired for a mixed-compression inlet. The higher 

throat Mach number leads to a stronger terminal shock, which leads to greater losses in total-pressure and 

more severe interactions with the boundary layers. 

NASA/TM—2010-216362 13 
R4

C2

SW3

Terminal Shock

Reversed Flow

Mach

2.35

1.61

0.87

0.14

-0.60

Figure 10.—Isometric views of the flow in the throat of the turbine flowpath. 

Axial Cut (x=23.98)

1.39

1.51 1.12 1.43

1.6

1.2

0.8

0.3

-0.1

-0.5

Mach

Figure 11.—Mach number contours at an axial cut 

just downstream of the throat bleed regions. 

The bleed regions and the bleed modeling were significant to the flow field and the CFD simulation. 

Figure 12 illustrates the behavior of the flow within the bleed regions of the throat. The three plots show 

the outline of a short section of the throat containing the R4, C2, and SW3 bleed regions. The flow is 

from the left to right. The arrows represent the magnitudes of the local bleed flow momentum vectors 

distributed on the boundary grid points in the bleed regions. The arrows are colored by the local Mach 

number. The Mach number scale is different between each bleed region to better show the bleed variation. 

The C2 bleed region shows the bleed flow leaving the flow domain. The maximum Mach number reaches 

about 0.04 with a total bleed rate of 1.015 percent. The local bleed flow was greater near the sidewall. As 

seen in Figure 10, this was where the terminal shock interacted with the sidewall boundary layer. The 

interaction allowed the higher static pressures downstream of the terminal shock to feed forward into the 

boundary layer. The vectors for the SW3 bleed region also indicated flow out of the flow domain for a 

total bleed rate of 1.151 percent. The Mach numbers approached 0.24. The flow rate through the SW3 

bleed region was slightly greater than the rate through the C2 bleed region, but the area of the SW3 bleed 

region was smaller, which explains the higher Mach numbers than the C2 bleed region. The plots of the 

R4 bleed region show most of the flow leaving the flow domain with the highest Mach numbers near the 

sidewall. The plots of the R4 bleed region indicate that there is a small portion adjacent to the SW3 for 

NASA/TM—2010-216362 14 
R4

Mach

WR4/WLS = 1.483%

Note the change in the scale of Mach

number between R4, C2, and SW1.

C2

x = 23.24 in

x = 24.87 in

Flow

WC2/WLS = 1.015%

SW3

WSW3/WLS = 1.151%

0.24

0.18

0.12

0.06

0.00

0.04

0.03

0.02

0.01

0.00

Mach

0.04

0.03

0.02

0.01

0.00

Mach

Grid block in the Turbine 

Flowpath Throat

Figure 12.—Momentum vectors of flow through the bleed regions in the throat. 

which flow was injected from the R4 bleed plenum into the flow domain. One likely cause of this is that 

the high flow rate of SW3 reduced the local static pressure to values below the value of the plenum 

pressure of R4. Equation (5) indicates that for static plenum pressure ratios greater than one, the sonic 

flow coefficient is negative. The ability to model local injection or recirculation is a unique capability of 

the bleed model. Reference 9 further explains and provides some validation of this capability of the bleed 

model. 

4.2 Mach Numbers 

The variation of the average Mach number through the turbine flowpath illustrates the pattern of 

deceleration of the flow as the cross-sectional area changes. The change in area between the leading edge 

of the splitter cowl and the throat of the turbine flowpath is shown in Figure 13. The area is normalized by 

the area at the leading edge of the splitter cowl. The contraction ratio is the ratio of the cross-sectional 

area at the leading edge of the splitter cowl to the cross-sectional area at the throat. The contraction ratio 

for each cowl position can be read as the value of the curves at approximately x =25 in. As can be seen, as 

the splitter cowl was rotated toward the closed position, the contraction ratio decreased because the area 

at the leading edge of the splitter cowl decreased while the throat area remained the same. This can also 

be observed in Figure 8. 

The lower contraction ratios resulted in less compression, and so, the Mach number did not decelerate 

as fast through the duct. This is shown in Figure 14 with the variation of the average Mach number 

through the turbine flowpath from the leading edge of the splitter cowl to just downstream of the throat. 

The Mach numbers were area-averaged at each grid plane, which was approximately perpendicular to the 

flow direction. At the leading edge of the splitter cowl, the Mach number decreased slightly as the splitter 

cowl closed since the boundary layer became a greater proportion of the flow. The Mach number 

decreased through the duct as oblique shocks and increased contraction reduced the Mach number. As the 

splitter cowl was rotated toward the closed position and the contraction ratio decreased, the rate of 

decrease of the Mach numbers between x = 19 in. and the terminal shock became less. This resulted in 

higher Mach numbers ahead of the terminal shock. 

NASA/TM—2010-216362 15 
0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

15 17 19 21 23 25

Contraction Ratio

x, inches

0.0 deg

-2.0 deg

-4.0 deg

-5.7 deg

Figure 13.—Area contraction ratio through the turbine flowpath. 

0.0

0.5

1.0

1.5

2.0

2.5

3.0

16 18 20 22 24 26 28 30 32 34 36

Mach Number

x, inches

0.0 deg

-2.0 deg

-4.0 deg

-5.7 deg

Figure 14.—Area-averaged Mach number through the turbine flowpath. 

The variation of the Mach numbers show an averaged position of the terminal shock as the location at 

which the Mach number decreased below the sonic value. One observation is that the position of the 

terminal shock did not vary greatly as the splitter cowl was rotated toward the closed position. This is a 

desirable property in that it suggests that the rotation of the splitter cowl will not cause unstart by forcing 

the terminal shock forward. Downstream of the terminal shock the Mach number variations were similar 

and resulted in the approximately equal values of the Mach number at the engine-face. This is expected 

since the four simulations were performed at the same corrected flow rate, which is only a function of 

Mach number. 

4.3 Static Pressures 

The distribution of the static pressures through the turbine flowpath illustrated the compression of the 

flow through the turbine flowpath as the flow was decelerated. Figure 15 shows the variation of the static 

pressures along the ramp at the plane of symmetry through the turbine flowpath at the supercritical 

condition. The compression at the throat decreased as the splitter cowl was rotated toward the closed 

NASA/TM—2010-216362 16 
0.0

0.1

0.2

0.3

0.4

0.5

0.6

16 18 20 22 24 26 28 30 32

p / pt0

x, inches

EXP: 0.0 deg

EXP: - 2.0 deg

EXP: - 4.0 deg

EXP: - 5.7 deg

CFD: 0.0 deg

CFD: - 2.0 deg

CFD: - 4.0 deg

CFD: - 5.7 deg

Figure 15.—Static pressures on the ramp through the turbine flowpath. 

position and the contraction ratio decreased. The pressures from the surface static pressure taps in the 

wind tunnel test are also plotted in Figure 15. The comparisons suggest that the CFD indicated lower 

engine-face pressures for similar pressures in the throat. This also suggests that for similar engine-face 

pressures, the CFD indicated the terminal shock would be more forward in the throat. The differences are 

likely due to differences in the development of the boundary layers and their interaction with the bleed 

regions between the wind-tunnel test and the CFD simulations. 

4.4 Bleed Rates and Plenum Pressures 

The operation and performance of the bleed regions were evaluated through the examination of the 

bleed rates and bleed plenum pressures of each bleed region as the splitter cowl was rotated toward the 

closed position. These properties were measured or calculated as part of the wind-tunnel test. Figure 16 

compares the bleed rates and bleed plenum pressures from both the CFD simulations and the wind-tunnel 

test for supercritical conditions. The left plots show the bleed rates and the right plots show the bleed 

plenum pressures. The top two plots illustrate the forward bleed regions (R1, R2, and SW1). The middle 

two plots illustrate the middle bleed regions (R3, C1, and SW2). The bottom two plots illustrate the throat 

bleed regions (R4, C2, and SW3). 

The bleed rates at the 0° cowl position matched closely with the wind-tunnel data because this was 

the matching condition used in setting the bleed region exit areas. Of interest is how the bleed rates varied 

as the splitter cowl was rotated toward the closed position. The variations for R1, R2, R4, and C2 showed 

remarkable agreement with the wind-tunnel test data. The variations for C1, SW2, and SW3 showed some 

deviation from the wind-tunnel test data. The variations for SW1 and R3 showed the most deviation. The 

CFD simulation results suggest that the bleed rate of SW1 increased as the splitter cowl was rotated 

toward the closed position. This was similar to the increase in the bleed rate of R1. The increase is 

plausible because as the splitter cowl was rotated toward the closed position, the oblique shock from the 

splitter cowl leading edge, moved forward along the bleed regions R1 and SW1, as observed in Figure 8. 

More of those bleed regions were behind the shock and encountered increased pressures, which increased 

the bleed rate. One explanation is that the calculations of the bleed rates for SW1 for the wind-tunnel tests 

were in error. The sidewall bleed regions did not bleed into plenums, and so, assumptions of choked flow 

were imposed to calculate the bleed rates from the wind-tunnel test. Estimates of the uncertainty in the 

bleed rates calculated from the wind-tunnel tests were not performed. While the bleed rates of R1 

compared well between the CFD simulations and the wind-tunnel tests, the plenum pressures did not 

compare well. The CFD simulations indicated that bleed region R1 did not have a choked exit and the 

NASA/TM—2010-216362 17 
plenum pressure was set to the minimum value allowed in the simulation. An inconsistency was that the 

wind-tunnel data showed that the plenum pressures of R1 were greater than R2, which is not likely a 

possibility since the flow over R1 is at a lower surface pressure than the flow over R2. The plenum 

pressures of R2, R3, and C1 showed differences between the CFD and wind-tunnel test. These differences 

highlight the continuing challenges of bleed modeling for CFD. The bleed plenum pressures are important 

because they are proportional to the bleed drag. Higher levels of plenum pressure result in lower bleed 

drag. It is rather remarkable that the plenum pressures of R4 and C2 showed a very good match between 

the CFD simulations and the wind-tunnel data. While encouraging, the matches may just be a fortunate 

coincidence and more study is needed before the bleed models can be considered fully validated for 

indicating bleed plenum pressures. 

0.0%

1.0%

2.0%

3.0%

4.0%

5.0%

6.0%

0.0 2.0 4.0 6.0

Wbleed / WLS

Cowl Rotation, deg

EXP: R1

EXP: R2

EXP: SW1

CFD: R1

CFD: R2

CFD: SW1

0.00

0.01

0.02

0.03

0.0 2.0 4.0 6.0

pplenum / pt0

Cowl Rotation, deg

EXP: R1

EXP: R2

CFD: R1

CFD: R2

0.0%

0.5%

1.0%

1.5%

2.0%

0.0 2.0 4.0 6.0

Wbleed / WLS

Cowl Rotation, deg

EXP: R3

EXP: C1

EXP: SW2

CFD: R3

CFD: C1

CFD: SW2

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.0 2.0 4.0 6.0

pplenum / pt0

Cowl Rotation, deg

EXP: R3

EXP: C1

CFD: R3

CFD: C1

0.0%

0.5%

1.0%

1.5%

2.0%

0.0 2.0 4.0 6.0

Wbleed / WLS

Cowl Rotation, deg

EXP: R4

EXP: C2

EXP: SW3

CFD: R4

CFD: C2

CFD: SW3

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.0 2.0 4.0 6.0

pplenum / pt0

Cowl Rotation, deg

EXP: R4

EXP: C2

CFD: R4

CFD: C2

Figure 16.—Bleed flow rates (left) and bleed plenum static pressures (right) for each bleed region with respect to the 

cowl position for supercritical inlet flow. 

NASA/TM—2010-216362 18 
4.5 Engine-Face Total-Pressure Recovery 

The performance of an inlet is represented in part by the total-pressure recovery (ratio of the average 

total pressure at the engine face to the freestream total pressure, REC = pt2/pt0). Figure 17 shows the 

variation of the area-averaged total pressure through the turbine flowpath for the four splitter cowl 

positions. The average total pressure at the leading edge of the splitter cowl decreased as the splitter cowl 

was rotated toward the closed position because the lower total pressure of the boundary layer was a 

greater proportion of the flow. The total pressure increased within the bleed region as some of the lower 

total-pressure portions of the boundary layer were extracted from the inlet flow. The total-pressure 

recovery dropped sharply across the terminal shock. As the splitter cowl was rotated toward the closed 

position, the terminal shock became stronger due to higher Mach numbers ahead of the terminal shock 

and the losses in the total pressure increased. 

When the total-pressure recovery is plotted with respect to the normalized engine-face flow rate 

(W2/WHS), the plot is commonly referred to as the “characteristic cane curve”. Figure 18 shows the cane 

curves as obtained from the wind-tunnel tests and the CFD simulations for the four positions of the 

splitter cowl. The open symbols indicate the data from the wind-tunnel test. The solid symbols indicate 

the results of the CFD simulations. 

A cane curve is created by varying the engine-face static pressure or back pressure. A typical 

sequence is to start with the inlet operating supercritical with the terminal shock downstream of the throat 

bleed regions. The back pressure is then increased. In the wind-tunnel test, the back-pressure was 

increased by translating the flow plug to reduce the area of the choked exit of the plug of the cold-pipe. In 

the CFD simulation, the back pressure was increased by reducing the area of the choked nozzle. With 

increased back pressure, the terminal shock was pushed forward into the throat where the Mach numbers 

were lower and the losses in the total-pressure across the terminal shock were lower. This increased the 

total-pressure recovery. As the terminal shock encountered the throat bleed regions, the bleed flow 

increased and the engine-face flow rate decreased. This caused the cane curve to bend over as the engineface flow rate decreased greater than the increase in the total-pressure recovery. The start of this bend in 

the cane curve is noted as the “knee” of the cane curve and is the desired operating point of the inlet. 

0.0

0.2

0.4

0.6

0.8

1.0

16 18 20 22 24 26 28 30 32

Total Pressure Recovery

x , inches

0.0 deg

- 2.0 deg

- 4.0 deg

- 5.7 deg

Figure 17.—Area-averaged total pressure recovery through the turbine flowpath. 

NASA/TM—2010-216362 19 
0.1

0.2

0.3

0.4

0.5

0.6

0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

Total Pressure Recovery

W2 / WHS

EXP: 0.0 deg

EXP: - 2.0 deg

EXP: - 4.0 deg

EXP: - 5.7 deg

Const Pplenum

CFD: 0.0 deg

CFD: - 2.0 deg

CFD: - 4.0 deg

CFD: - 5.7 deg

Constant Corrected Flow

Figure 18.—Characteristic “cane” curves of the turbine flowpath during inlet mode 

transition. 

The cane curves of Figure 18 indicated some unique behavior of fixed-exit bleed systems and the 

IMX inlet. At 0°, the cane curve from the wind-tunnel test did not bend over. The inlet unstarted when the 

back pressure was increased above the highest point shown. In an inlet unstart, the terminal shock is 

pushed ahead of the throat and is expelled out of the inlet and ahead of the leading edge of the splitter 

cowl. The behavior of the cane curve suggested that the terminal shock was not able to sit within the 

R4/C2/SW3 throat bleed regions in a stable manner. The cross-sectional area in this region of the inlet has 

little variation, which reduces the inlets natural ability to stabilize the shock. The CFD simulation 

indicated similar behavior. The CFD simulation indicated a slightly higher flow rate, but the totalpressure recoveries were reasonably close to those of the wind-tunnel test. The maximum total-pressure 

recovery achieved prior to unstart was essentially the same as for the wind-tunnel test. 

At the –2.0° splitter cowl position, the wind-tunnel test data indicated that the cane curve changed to 

a lower flow rate and recovery rather than directly unstarting the inlet. Reference 5 referred to this as 

“popping” in which the terminal shock jumped forward of the R4/C2/SW3 bleed regions and stopped at 

the downstream edge of the R3/C1/SW2 bleed regions. Further increase of the back pressure in the windtunnel test continued the creation of the cane curve at the new terminal shock location. This is seen 

toward the top of the cane curve. The CFD simulation did capture the initial portion of the cane curve, but 

was not able to simulate the popping. The CFD simulation indicated that the inlet unstarted rather than 

stopping the terminal shock at the R3/C1/SW2 bleed regions. One explanation is that the back pressure 

was varied in a smoother manner in the wind-tunnel tests than in the CFD simulations. 

The wind-tunnel test data for the –4.0° splitter cowl position indicated the popping behavior; 

however, the data for the –5.7° position indicated a defined knee and reduced engine-face flow rates 

beyond the knee. The CFD simulations at the –4.0° and –5.7° splitter cowl positions indicated only the 

lower portions of the cane curve. At higher levels of back pressure, the CFD simulations exhibited 

iterative non-convergence and eventual unstart of the inlet. The reasons for the deficiencies of the CFD 

methods for these two splitter cowl positions are not understood at this time. 

Figure 18 includes a trace of the constant corrected flow line that connects the four CFD simulations 

performed with the same exit flow nozzle throat area. The matching of the four simulation points with the 

constant corrected flow line enhances the applicability of the CFD methods for the simulation of inlet 

mode transition. A turbine engine typically operates with constant corrected flow (Ref. 10) and inlet mode 

transition strategies anticipate that the inlet mode transition will closely follow a constant corrected flow 

line (Ref. 5). 

NASA/TM—2010-216362 20 
It is possible to incorporate a control system for the bleed region so as to control the level of plenum 

static pressure. Reference 11 demonstrated that by maintaining a near constant plenum pressure, the bleed 

systems of a supersonic inlet were able to enhance the stability of the terminal shock by removing greater 

amounts of bleed flow. With the fixed bleed plenum exits, the plenum pressure will increase as the 

terminal shock moves into the bleed region. This limits the amount of bleed flow the bleed region can 

extract, which limits the ability of the bleed region to stabilize the terminal shock. The control system can 

act by varying the bleed plenum exit area by either fluidic or mechanical means. Figure 18 includes a 

cane curve generated at the 0° splitter cowl position for a constant-pressure bleed boundary condition. 

The cane curve bends over due to greater amounts of bleed flow being extracted and achieves slightly 

higher levels of total-pressure recovery than for the fixed-exit bleed boundary condition. This increases 

the stability margin of the IMX inlet to withstand inlet unstart. Reference 8 presents another CFD 

application demonstrating the differences between the fixed-exit and constant-pressure bleed models. 

4.6 Engine-Face Total-Pressure Distortion 

The distortion of the total pressure at the engine face can affect the performance and stability of the 

turbine engine. Severe distortion can result in the stalling of the turbine engine (Refs. 10 and 12). In this 

section we evaluate the ability of the CFD simulation to indicate total-pressure distortion. Figure 19 

shows the contours of the Mach number and total-pressure recovery at the engine face of the turbine 

flowpath with the splitter cowl at the 0° position and flow rate at the top point on the cane curve just prior 

to inlet unstart. The distinct feature of the flow is that a sizable reversed flow region existed at the engine 

face in the upper left position. The Mach numbers reached a maximum of about 0.5 near the bottom of the 

engine face. The mass-averaged Mach number of the engine face is 0.1744. The total-pressure recoveries 

range from 0.55 in the reversed flow region to upwards of 0.65 at the bottom of the engine-face. The 

mass-averaged, total-pressure recovery at the engine face is 0.5664. These mass-averaged quantities are 

based on integration over the CFD grid and flow field. 

0.0

0.1

-0.1

0.2

0.3

0.4

Mavg = 0.1744 0.5

0.5

0.4

0.3

0.2

0.1

0.0

-0.1

Mach

0.55

0.56

• 0.58

• 0.62

• 0.60

• 0.64

• 0.65 REC = 0.5664

0.65

0.63

0.61

0.59

0.57

0.55

REC

Figure 19.—Mach number and total-pressure recovery contours at the engine face. 

NASA/TM—2010-216362 21 
Due to the small scale of the wind-tunnel test article, a standard 40-probe engine-face rake (Ref. 13) 

could not be used. The engine-face properties are determined on a total-pressure rake array consisting of 

nine total-pressure probes arranged on four rakes and two rings arranged in a polar manner. Ring 1 is 

located at a radius of 0.5257 and ring 2 is located at a radius of 0.8030. Rake 4 is located at the top of the 

engine-face and extends to the center of the engine-face to include a total-pressure probe at the center of 

the engine-face. 

The CFD flowfield was interpolated onto the rake probe locations to allow a comparison between the 

engine-face properties of the CFD flow field and the wind-tunnel test. Figure 20 shows this comparison 

for each ring. Rake 5 is simply a repeat of rake 1 to provide a complete 360° representation of the rake 

properties. Since the CFD flowfield is symmetric about the plane-of-symmetry, the values at rakes 1, 3, 

and 5 are all the same. The CFD simulation indicates a higher Mach number and total-pressure recovery 

at rake 2 than for the wind-tunnel test. The wind-tunnel test indicates that the low speed flow is located 

about rake 2. 

The average total-pressure recovery and Mach number at the engine face are plotted with respect to 

the level of back-pressure in Figure 21. As the inlet is back-pressured, the total-pressure recovery 

increases and the Mach number decreases. Shown are two plots for the CFD: one calculated for massaveraged values on the CFD grid and one for the area-averaged values on the rake. While the variation of 

the mass-averaged recovery compares well with the wind-tunnel test, the values from the rake indicates 

that the CFD simulation has a higher recovery of about 0.01. The variation of the average Mach numbers 

for the CFD simulation bracket the wind-tunnel test values. 

0.50

0.55

0.60

0.65

12345

Total Pressure Recovery

Rake Arm

EXP: Ring 1

EXP: Ring 2

CFD: Ring 1

CFD: Ring 2

0.0

0.1

0.2

0.3

0.4

0.5

1234

Mach Number

Rake Arm

5

EXP: Ring 1

EXP: Ring 2

CFD: Ring 1

CFD: Ring 2

Figure 20.—Total pressure recovery and Mach number at the engine-face rake probes for the 

flow fields at the “top” of the cane curves. 

0.40

0.45

0.50

0.55

0.60

0.40 0.45 0.50 0.55 0.60

Total Pressure Recovery

Average Static Pressure, p2 / pt0

EXP

CFD: Grid

CFD: Rake

0.16

0.18

0.20

0.22

0.24

0.40 0.45 0.50 0.55 0.60

Average Mach Number, M2

Average Static Pressure, p2 / pt0

EXP

CFD: Grid

CFD: Rake

Figure 21.—Average total pressure recovery and Mach number at the engine face as the 

turbine flowpath is back-pressured. 

NASA/TM—2010-216362 22 
0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.40 0.45 0.50 0.55 0.60

Distortion

Average Static Pressure, p2 / pt0

EXP

CFD: Grid

CFD: Rake

Figure 22.—Distortion at the engine face. 

The level of total-pressure distortion can be represented by a wide variety of distortion indices 

(Ref. 12). A simple distortion index is obtained by the formula 

( )

AVG

MAX MIN

REC

REC REC DIST − = (7) 

where RECMAX, RECMIN, and RECAVG are the maximum, minimum, and average total-pressure recoveries 

observed at the engine face. The variation of the distortion as calculated using Equation (7) with respect 

to the inlet back pressure is shown in Figure 22. As inlet back pressure increases, the distortion decreases. 

This is consistent with the terminal shock moving forward in the throat and shock interactions becoming 

less severe. The CFD simulations indicate significantly greater distortion than the wind-tunnel test. This 

can be realized from Figure 20 that shows a significantly greater range of total pressure in the CFD results 

than for the wind-tunnel test. The reasons for the differences in distortion between the CFD and windtunnel test are not well understood. A puzzling aspect is that the CFD methods seem to be capable of 

determining the correct average total pressure at the engine face as shown in the comparisons of the totalpressure recovery. It may be that the CFD methods are not correctly capturing or resolving the spatial 

development of vortical or turbulent structures as they propagate downstream within the subsonic duct to 

the engine face. 

5.0 Conclusion 

The CFD simulations satisfied one objective of providing a greater understanding of the 

aerodynamics of the inlet mode transition process through the illustration of the flow features and 

quantification of the flow properties and inlet performance measures. Comparison of the results of the 

CFD simulations with data from wind-tunnel tests addressed another objective of assessing the 

applicability of the CFD methods for simulating inlet mode transition. Uncertainties in both the windtunnel test data and CFD methods prevented a formal evaluation of the accuracy of the CFD methods. 

Some of the CFD results agreed with the values and trends of the wind-tunnel test data and provided 

encouragement that the CFD methods can be applied to simulate inlet mode transition. Inconsistencies in 

the agreement between CFD results and test data provide insight for improving the CFD methods. Some 

specific conclusions include: 

• The CFD simulations demonstrated that inlet mode transition could occur in a stable manner in 

which the terminal shock remained in the throat as the splitter cowl was rotated toward the closed 

position. 

NASA/TM—2010-216362 23 
• The CFD simulations were able to indicate the performance of the turbine flowpath during the 

inlet mode transition as measured by the total-pressure recovery and illustrated by the 

characteristic cane curves. At splitter cowl positions of 0° and –2°, the peak levels of totalpressure recovery matched closely to the data of the wind-tunnel tests with a slight offset in the 

engine-face flow rate. 

• At the splitter cowl position of –2°, the CFD simulations were not able to simulate the “popping” 

phenomena observed in the wind-tunnel tests. This may be a reflection of the instability of the 

shock system at these conditions. 

• At splitter cowl positions of –4° and –5.7°, the results of the CFD simulations agreed with the 

lower parts of the cane curves, but the CFD methods indicated inlet unstart at much lower levels 

of engine-face back pressure and total-pressure recoveries than observed in the wind-tunnel tests. 

• The CFD simulations were able to follow the constant corrected flow line through the inlet mode 

transition. This is important because the inlet mode transition will likely follow a constant 

corrected flow path. 

• The results of the CFD simulations agreed closely with the surface static pressures through the 

turbine flowpath; however, the pressures at the engine-face were lower than indicated by the 

wind-tunnel tests. This could be alternatively stated that the CFD simulations indicated a more 

forward terminal shock position than observed in the wind-tunnel tests for equivalent engine-face 

static pressures. 

• The CFD methods were able to simulate realistic bleed flows with variations of bleed rates over 

the bleed regions due to shocks and localized injection of flow. Comparisons with the windtunnel test data showed some remarkable agreement for bleed rates and bleed plenum static 

pressures through the inlet mode transition for some of the bleed regions and considerable 

differences for others. The lack of consistency of the comparisons is of concern and warrants 

further work in the development of bleed models. 

• While the CFD simulations were able to match closely with some of the total-pressure recoveries 

at the engine face, the distribution of total pressure at the engine face seemed considerably 

different than observed in the wind-tunnel tests. The CFD simulations indicated a much higher 

level of total-pressure distortion than observed in the wind-tunnel tests. Further study regarding 

the CFD methods is needed to understand this inconsistency. 

References 

1. Bradley, M., Bowcutt, K., McComb, J., Bartolotta, P., and McNelis, N., “Revolutionary Turbine 

Accelerator (RTA) Two-Stage-to-Orbit (TSTO) Vehicle Study,” AIAA–2002–3902, July 2002. 

2. Bartolotta, P.A., McNelis, N.B., and Shafer, D.G., “High Speed Turbines: Development of a Turbine 

Accelerator (RTA) for Space Access,” AIAA–2003–6943, December 2003. 

3. Albertson, C.W., Emani, S., and Trexler, C.A., “Mach 4 Test Results of a Dual-Flowpath, Turbine 

Based Combined Cycle Inlet,” AIAA–2002–8138, November 2006. 

4. Sanders, B.W., and Weir, L.J., “Aerodynamic Design of a Dual-Flow Mach 7 Hypersonic Inlet 

System for a Turbine-Based Combined-Cycle Hypersonic Propulsion System,” NASA/CR—2008-

215214, 2008. 

5. Saunders, J.D., Slater, J.W., Dippold, V., Lee, J., Sanders, B.W., and Weir, L.J., “Inlet Mode 

Transition Screening Test for a Turbine-Based Combined-Cycle Propulsion System,” JANNAF, May 

2008. 

6. Mani, M., Cary, A., and Ramakrishnan, S., “A Structured and Hybrid-Unstructured Grid Euler and 

Navier-Stokes Solver for General Geometry,” AIAA–2004–0524, January 2004. 

7. Slater, J.W., “CFD Methods for Computing the Performance of Supersonic Inlets,” AIAA–2004–

3404, July 2004. 

NASA/TM—2010-216362 24 
NASA/TM—2010-216362 25 

8. Slater, J.W. and Saunders, J.D, “Modeling of Fixed-Exit Porous Bleed Systems,” AIAA–2008–0094, 

January 2008. 

9. Slater, J.W., “Improvements in Modeling 90-degree Bleed Holes for Supersonic Inlets,” AIAA–

2009–0710, January 2009. 

10. Mattingly, J.D., Heiser, W.H., and Daley, D.H., Aircraft Engine Design, AIAA, Inc., New York, 

1987. 

11. Sanders, B. W. and Mitchell, G. A., “Increasing the Stable Operating Range of a Mach 2.5 Inlet,” 

AIAA–1970–0686, June 1970; Also NASA TM X–52799, June 1970. 

12. Goldsmith, E.L., and Seddon, J. ed., Practical Intake Aerodynamic Design, AIAA, Inc., New York, 

1993, ch. 2. 

13. Society of Automotive Engineers, “Gas Turbine Engine Inlet Flow Distortion Guidelines,” SAE 

ARP-1420, February 2002. 
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Computational Fluid Dynamics (CFD) Simulation of Hypersonic Turbine-Based CombinedCycle (TBCC) Inlet Mode Transition 

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14. ABSTRACT

Methods of computational fluid dynamics were applied to simulate the aerodynamics within the turbine flowpath of a turbine-based 

combined-cycle propulsion system during inlet mode transition at Mach 4. Inlet mode transition involved the rotation of a splitter cowl to 

close the turbine flowpath to allow the full operation of a parallel dual-mode ramjet/scramjet flowpath. Steady-state simulations were 

performed at splitter cowl positions of 0°, -2°, -4°, and -5.7°, at which the turbine flowpath was closed half way. The simulations satisfied 

one objective of providing a greater understanding of the flow during inlet mode transition. Comparisons of the simulation results with 

wind-tunnel test data addressed another objective of assessing the applicability of the simulation methods for simulating inlet mode 

transition. The simulations showed that inlet mode transition could occur in a stable manner and that accurate modeling of the interactions 

among the shock waves, boundary layers, and porous bleed regions was critical for evaluating the inlet static and total pressures, bleed flow 

rates, and bleed plenum pressures. The simulations compared well with some of the wind-tunnel data, but uncertainties in both the windtunnel data and simulations prevented a formal evaluation of the accuracy of the simulation methods. 

15. SUBJECT TERMS

Supersonic inlets; Hypersonic inlets 

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