Vance F. Dippold, III

Glenn Research Center, Cleveland, Ohio

Computational Analyses of the 

LIMX TBCC Inlet High-Speed Flowpath

NASA/TM—2012-217219

January 2012
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Vance F. Dippold, III

Glenn Research Center, Cleveland, Ohio

Computational Analyses of the 

LIMX TBCC Inlet High-Speed Flowpath

NASA/TM—2012-217219

January 2012

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared for the

58th Joint Army-Navy-NASA-Air Force (JANNAF) Propulsion Meeting 

sponsored by the JANNAF Interagency Propulsion Committee

Arlington, Virginia, April 18–22, 2011
Acknowledgments

This work was supported by the Fundamental Aeronautics Hypersonics Project. 

The author is grateful for the help of J. Dave Saunders, John Slater, Bobby Sanders, and Lois Weir.

Available from

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7115 Standard Drive

Hanover, MD 21076–1320

National Technical Information Service

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Available electronically at http://www.sti.nasa.gov

Trade names and trademarks are used in this report for identification 

only. Their usage does not constitute an official endorsement, 

either expressed or implied, by the National Aeronautics and 

Space Administration.

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. 
NASA/TM—2012-217219 1

Computational Analyses of the 

LIMX TBCC Inlet High-Speed Flowpath

Vance F. Dippold, III

National Aeronautics and Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Abstract

Reynolds-Averaged Navier-Stokes (RANS) simulations were performed for the high-speed flowpath

and isolator of a dual-flowpath Turbine-Based Combined-Cycle (TBCC) inlet using the Wind-US code. 

The RANS simulations were performed in preparation for the Large-scale Inlet for Mode Transition

(LIMX) model tests in the NASA Glenn Research Center (GRC) 10- by 10-ft Supersonic Wind Tunnel. 

The LIMX inlet has a low-speed flowpath that is coupled to a turbine engine and a high-speed flowpath 

designed to be coupled to a Dual-Mode Scramjet (DMSJ) combustor. These RANS simulations were 

conducted at a simulated freestream Mach number of 4.0, which is the nominal Mach number for the 

planned wind tunnel testing with the LIMX model. For the simulation results presented in this paper, the 

back pressure, cowl angles, and freestream Mach number were each varied to assess the performance and 

robustness of the high-speed inlet and isolator. Under simulated wind tunnel conditions at maximum inlet 

mass flow rates, the high-speed flowpath pressure rise was found to be greater than a factor of four. 

Furthermore, at a simulated freestream Mach number of 4.0, the high-speed flowpath and isolator showed 

stability for freestream Mach number that drops 0.1 Mach below the design point. The RANS simulations 

indicate the yet-untested high-speed inlet and isolator flowpath should operate as designed. The RANS 

simulation results also provided important insight to researchers as they developed test plans for the 

LIMX experiment in GRC’s 10- by 10-ft Supersonic Wind Tunnel.

Nomenclature

D flowpath cross-section diameter; in.

M Mach number

p static pressure; psi

Rex Reynolds number per foot

T static temperature; °R

u streamwise velocity; ft/s

x streamwise distance from leading edge of trapezoidal plate; in.

y

+ non-dimensional wall distance

Subscripts

AIP Aerodynamic Interface Plane

CFD from computational fluid dynamics (CFD) simulations

COR corrected to account for first turn shock loss in true Mach 4 freestream flow

eq equivalent

iso isolator entrance

ref reference condition, no-back pressure

t throat of convergent-divergent section

0 total condition

∞ freestream condition
NASA/TM—2012-217219 2

Introduction

Air-breathing hypersonic flight has been a focus of aeronautics research for the past half century

(Refs. 1 and 2). NASA has invested in air-breathing hypersonic flight because it is an intriguing 

alternative method for reaching low earth orbit and access to space rather than using conventional rocket 

propulsion systems (Refs. 1 and 3). The advantage of air-breathing hypersonic propulsion systems over 

rocket systems is that the air-breathing systems carry only their fuel and use the oxygen present in the 

atmosphere as the oxidizer, thus reducing the total take-off weight and the cost.

A focal point for air-breathing hypersonic propulsion is a Dual Mode Scramjet (DMSJ) combustor

(Ref. 4). However, unlike conventional turbine engines, DMSJ-based propulsion systems require forward 

velocity to produce thrust. Thus, systems have been developed to accelerate these vehicles from take-off 

to speeds in which the DMSJ propulsion system can operate effectively (typically upwards of Mach 3 to 

4). Rocket-Based Combined-Cycle (RBCC) systems use rockets engines to boost the vehicle to the Mach 

3 to 4 range, at which time the ramjet and scramjet engine can begin operating (Ref. 5). Turbine-Based 

Combined-Cycle (TBCC) systems use turbine engines to accelerate the vehicle to the ramjet transition 

velocity (Ref. 6).

While ramjet- and scramjet-enabling technologies have been developed over many decades, few 

studies have focused on how to effectively transition from the turbine stage to DMSJ stage—this critical 

event is referred to as Mode Transition. The NASA Fundamental Aeronautics Program is conducting 

experiments with a Large-scale Inlet for Mode Transition (LIMX) (Refs. 7 and 8) to map out and 

demonstrate the process of transitioning from the turbine to the DMSJ stages of a TBCC system. These 

tests will be conducted in NASA Glenn Research Center’s (GRC) 10- by 10-ft Supersonic Wind Tunnel

(Ref. 9). The LIMX inlet is an over-under inlet that consists of a low-speed flowpath for a turbine engine 

and a high-speed flowpath with an isolator that could be coupled to a DMSJ engine. Moving ramps and 

cowls vary the shape of the inlet so it can operate over a range of freestream conditions (Ref. 10). The 

low-speed flowpath includes bleed regions to help control and optimize the flow entering the engine face.

During the initial phases of testing, mass-flow plugs will be used to back-pressure each flowpath, 

simulating an actual engine; in later phases of testing, an actual turbine engine will be coupled to the lowspeed flowpath. A rotating cowl between the low-speed and high-speed flowpaths is used to split the inlet 

flow into two directions—low-speed and high-speed flowpaths. This rotating cowl is also referred to as

the inlet splitter. The splitter can be positioned to close off flow through the low-speed flowpath and 

direct flow into the high-speed flowpath. The high-speed flowpath consists of a rectangular inlet and a 

rectangular-to-round isolator upstream from where a DMSJ combustor would be located. The isolator has 

an area increase of 20 percent and length-to-diameter of 7.2, in which the diameter is based on the 

diameter of a circle equivalent in area to the throat of the high-speed flowpath. The high-speed flowpath 

was designed to be coupled to an actual DMSJ combustor. However, for economical reasons, current test 

plans will only use a cold-pipe and massflow plug assembly to back-pressure this flowpath.

Small-scale experimental tests were performed in GRC’s 1- by 1-ft Supersonic Wind Tunnel to 

validate the design of the low-speed flowpath (Ref. 7). The massflow and back pressure performance of 

the low-speed flowpath was assessed and optimized by adjusting the bleed rates and region sizes for a 

range of cowl angles and back pressure conditions. While the small-scale Inlet for Mode Transition 

(IMX) model did include a high-speed flowpath, this flowpath did not include the rectangular-to-round 

isolator or a means to back-pressure the high-speed flowpath. Therefore, no data is available from the 

IMX experiments to validate computational fluid dynamics (CFD) results for the high-speed flowpath. 

These two shortcomings are not true for the LIMX model. Therefore, CFD simulations were performed 

for the LIMX high-speed flowpath to computationally predict the flow characteristics through the highspeed flowpath, especially the back pressure performance of the yet-untested rectangular-to-round 

isolator. Additionally, the CFD simulations were performed in order to predict the stability of the inlet in 

the event the high-speed Mach number decreased.

The rectangular-to-round isolator experiments associated with the LIMX hardware will also provide a 

new data set. Due to the geometry of the LIMX inlet, which was designed to model an actual installed 
NASA/TM—2012-217219 3

TBCC inlet, the isolator in the LIMX test will see asymmetric inflow. For example, the boundary layer on 

the ramp side is expected to be much thicker than the boundary layer on the cowl side due to the far 

greater distance the flow travels over the ramp to the isolator. While a number of past studies have looked 

at isolators with asymmetric inflows, most used two-dimensional isolators (Ref. 11). Few past efforts 

have considered rectangular-to-round isolators with asymmetric inflows (Ref. 12), and the LIMX 

experiments and CFD simulations will help broaden the range of available data.

The CFD simulations will help researchers understand and interpret the experimental results once 

experimental data becomes available.

Modeling

LIMX Experimental Model

The LIMX inlet model is a dual-stream inlet system with a low-speed flowpath designed to be 

coupled to a turbine engine and a high-speed flowpath designed to be coupled to a DMSJ combustor

(Ref. 10). A computer automated design (CAD)-generated image of the LIMX design, as it will be 

installed in GRC 10- by 10-ft Supersonic Wind Tunnel, is illustrated in Figure 1. The overall length of the 

model, from tip to tail, is nearly 30 ft, and the width of the inlet flowpaths is 12 in. The two flowpaths are 

arranged in an over-under configuration, separated by a rotating splitter. Figure 2 shows the dual-flowpath 

inlet system with the splitter positioned to allow flow into both flowpaths. The low-speed flowpath is a 

Mach 4 design—the upper limit of the target mode-transition window—while the high-speed flowpath is 

a Mach 7 design. During the inlet mode transition, the splitter rotates toward the low-speed flowpath ramp 

surface to fully close off the low-speed flowpath. Since this work focuses on the high-speed flowpath, the 

reader is directed to References 7, 8, and 10 for more details concerning the low-speed flowpath.

The LIMX model is supported from the top by a strut in the wind tunnel, as shown in Figure 1. A 

schematic of the LIMX high-speed flowpath is shown in Figure 3. Freestream air first encounters the 

model at the tip of a large trapezoidal precompression forebody plate, which has a ramp angle of 6.5°. In 

addition to the trapezoidal plate, the ramp turns another 6°, 77.95 in. downstream of the leading edge. At 

this turn, the sidewall begins, with a 20° leading edge angle. Using the leading edge of the trapezoidal 

plate as the reference point, x=0 in., the flow for the high-speed flowpath compresses again on the back of 

the splitter another 7° at x=111.72 in. Before encountering the high-speed cowl tip, the high-speed flow 

undergoes 19.5° of total compression. Inside the inlet, at x=156.70 in., the flow along the ramp 

experiences an 8.5° expansion turn. This results in 11° of combined compression. The two-dimensional, 

rectangular high-speed flowpath entrance is nominally 141.56 in. downstream from the leading edge and 

it has a nominal capture height of 32.957 in. The high-speed inlet cowl can rotate from +2° (away from 

the ramp) to –11° (towards the ramp). The high-speed flowpath throat is located at station x=181.0 in. and 

has a height of 2.50 in. The isolator is positioned downstream of the inlet throat. The rectangular-to-round 

isolator has a 20 percent area increase. Using the diameter of a circle of equivalent area as the isolator 

entrance (Deq,iso), the length of the isolator was designed to be 7.2*Deq,iso. The aerodynamic interface plane

(AIP) is located at the end of the isolator, at x=225.43, and has a diameter of 6.60 in. The AIP represents 

the entrance to a DMSJ combustor. However, the current experimental test plans do not include testing 

with a DMSJ combustor. Instead, a cold pipe with a conical massflow plug will be connected downstream

of the isolator to impose back pressure upon the high-speed flowpath.

The high-speed flowpath was designed for Mach 7 freestream conditions; however most of the inlet 

mode-transition testing will be conducted at Mach 4, which is near the low-speed flowpath design point 

and the mode-transition freestream Mach number. While the LIMX model’s mode-transition Mach 

number is Mach 4, the 10- by-10-ft Supersonic Wind Tunnel is limited to Mach 3.5101 with proper 

temperature and pressure conditions. To overcome this limitation, the LIMX model will be rotated to a –

6.856° angle-of-attack such that the throat Mach numbers will be representative of what would be 

expected if Mach 4 conditions were available to the model (Ref. 13). Therefore, while the actual wind 
NASA/TM—2012-217219 4

tunnel Mach number is 3.5101. This configuration is referred to as simulated Mach 4. Tunnel conditions 

will be set to a total pressure of 35.970 psi and a Reynolds number of Rex=2.55 million.

Computational Model

The Wind-US code, version 2.0 (Refs. 14 and 15), was used to run the CFD simulations of the LIMX 

high-speed flowpath. The Wind-US code is a general-purpose, Reynolds-Averaged Navier-Stokes 

(RANS) CFD solver for both structured and unstructured grids. The code is developed and managed by 

the NPARC Alliance, a partnership between GRC, U.S. Air Force Arnold Engineering Development 

Center, and The Boeing Company. The Wind-US code offers several numerical schemes, as well as 

several zero-, one-, and two-equation turbulence models. The Wind-US code includes the second-order 

Roe numerical scheme and the Menter Shear Stress Transport (SST) turbulence model (Ref. 16) which 

were used for this study. The CFD simulations were performed on various multi-node Linux (Linus 

Torvalds) clusters, typically using eight to 20 processor cores. Even so, the simulations took four to 

seven days of wall-clock time to converge.

Structured grids were created for the LIMX high-speed flowpath. It should be noted that the 

computational grids were constructed for the LIMX model in an upside-down configuration, like Figure 2. 

These grids took advantage of several assumptions to simplify the simulation in an effort to reduce the 

computational expense. First, horizontally symmetric flow was assumed since the inlet model is horizontally 

symmetric. The grid was created for only half the inlet, using an inviscid wall boundary condition along the 

symmetry plane. Second, the low-speed flowpath was assumed to have no effect on the high-speed flow 

when the splitter is positioned to fully close-off the low-speed flowpath. Therefore, only the high-speed 

flowpath was modeled. Third, it was assumed that spillage over the inlet sidewalls would be nearly zero

since the sidewalls are designed to be well forward of the oblique shock location. Under this assumption, 

only the flow immediately upstream of the inlet and sidewalls was modeled—the full trapezoidal plate of 

the experimental model was not simulated—and inviscid wall boundary conditions were imposed along the 

grid surfaces upstream of the inlet sidewall. Lastly, it was assumed that the cold pipe and mass flow plug 

downstream of the high-speed isolator could be simulated by a convergent-divergent section as a way to 

impose back pressure. The throat area of the convergent-divergent section would be variable to create a 

desired back pressure. Modeling a convergent-divergent section would be significantly simpler than creating 

a grid for the mass flow plug. The convergent-divergent section was placed two AIP diameters downstream 

of the AIP. The throat area of this convergent-divergent section was reduced to increase back pressure 

through the high-speed flowpath. For the cases presented here, the convergent-divergent throat areas ranged 

from 100 to 73 percent of the AIP area.

In the streamwise direction, the grid had 481 points along the ramp, 161 points spaced through the 

high-speed inlet, and 201 points spaced through the isolator. The maximum streamwise spacing through 

each of these sections was 0.59 in. inside the inlet and isolator, and 1.46 in. overall. There were 81 points 

placed vertically across the flowpath and 45 points placed horizontally across the flowpath. The grid was 

packed to viscous walls, such that the grid spacing at the wall was nominally set to a non-dimensional 

wall spacing of y

+

=0.5. It has been shown that the non-dimensional wall spacing, y

+

, of the first grid point 

off the wall needs to be on the order of 1.0 (Refs. 17 and 18). Each grid had 4.5 million grid points. The 

typical grid is shown in Figure 4.

The inflow into the computation uses the frozen inflow boundary condition, which fixes the Mach 

number, static pressure, static temperature, and flow angle at the inflow and is applicable to supersonic 

inflows because changes in the flow properties downstream do no propagate upstream (Ref. 19). The 

wind tunnel test section conditions were specified at the inflow: M∞=3.5101, p∞=0.46446 psi, and 

T∞=222.506 °R. The flow angle was set to 6.856°, as previously mentioned, to simulate a Mach 4 

freestream flow. (The angle-of-attack was positive in the RANS simulations, since the model was upsidedown compared to the experiment.) At the outflows, since the flow there would likely be supersonic, no 

pressure boundary condition was imposed. Instead, the flow properties were extrapolated on the 

boundary.
NASA/TM—2012-217219 5

To speed up convergence of each solution, each grid was run using every fourth grid point, and then 

every second grid point, before finally converging the solution using every grid point. Solving on the 

coarser grids first allowed the overall flowfield to set up rather quickly before solving the turbulence 

details in the finest grid. This approach is standard practice for structured RANS calculations and is 

commonly referred to as grid sequencing. Furthermore, converging the solution on multiple grid sequence 

levels helped ensure that the finest grid solution was not dependent on the grid (i.e., the solution would 

not change significantly if minor changes to the grid were made). Table 1 shows the massflow and massaveraged total pressure at the AIP for the coarse (every fourth grid point), medium (every second grid 

point), and fine grid solutions. The mass-averaged total pressure is defined as:

Mass-averaged total pressure ( )

( ) ∫

∫ ⋅

⋅ ⋅

=

A

A

u dA

p u dA

ρ

0 ρ

in which p0 is the local total pressure, u is the local streamwise velocity, ρ is the local density, and A is the 

cross-section area. Table 1 also shows the percent difference in the massflow and mass-averaged total 

pressure between the three grid sequence solutions. Between the coarse and medium grid solutions, the 

massflow differs by 1.15 percent and the total pressure differs by 2.56 percent. Between the medium and 

fine solutions, the differences are 0.55 and 0.63 percent, respectively. This large reduction in percent 

difference shows that the solution is reaching grid-independence for the fine grid.

Lastly, each solution was started from the default, freestream-flow initialization by Wind-US. While 

the grid topologies were identical and solutions could be restarted from solutions of different cowl angles

and back pressure configurations, comparisons during early simulations indicated that hysteresis existed. 

For the same back-pressured configuration, the RANS solver converged to different solutions for 

increasing back pressure cases (restarting from a solution with a larger convergent-divergent throat area) 

and decreasing back pressure cases (restarting from a solution with a smaller convergent-divergent throat 

area). Therefore, it was decided to begin all simulations from the same solution initialization—freestream 

conditions, the Wind-US default initialization.

Results

No Back Pressure Applied

The first set of simulated LIMX high-speed flowpath cases that was run varied the high-speed cowl 

angle and did not back-pressure the inlet, i.e., the convergent-divergent throat area was 100 percent of the 

AIP area. For these cases, the high-speed cowl was rotated from –11° to +2° (fully open). The computed 

massflow rate at the AIP is plotted with respect to high-speed cowl rotation angle in Figure 5. As the cowl 

angle increases from –11° to –5°, the massflow rate increases and eventually peaks. However, after the 

massflow rate peak at –5° cowl angle, it is decreased at the –4° cowl angle. From –4° cowl angle to 0° 

cowl angle, the massflow rate further decreases. From 0° to +2° cowl angle, the massflow into the highspeed AIP sharply decreases, and it is believed that the inlet is unstarted in this configuration. While the 

high-speed inlet was designed to achieve maximum massflow with a 0° cowl angle at the Mach 7 design 

point (Ref. 10), the numerical simulations indicate that the massflow peaks at a –5° cowl angle for the 

Mach 4 mode transition point. This prediction will help test planners to concentrate measurements at the 

–5° cowl angle to maximize inlet performance during mode.

The CFD simulations predict that a massflow rate maximum exists at –5° cowl rotation. It is 

important to understand how the inlet behaves at larger cowl angles, especially if it does experience 

unstart. In Figure 6, signed Mach number (sign(u)*M) contours are plotted at the high-speed flowpath

entrance, x=141.56. A negative Mach number indicates that the flow direction is upstream. At the smaller 

cowl angles (–11°, –9°, –6°, and –5°), the flow into the high-speed inlet remains attached, though the 

boundary layer is noticeably thicker along the ramp surface than along the cowl surface, especially at the 
NASA/TM—2012-217219 6

corners. However, at cowl angles of –4° and larger, large regions of separated flow exist along the ramp 

corners. In Figure 7, Mach number contours are plotted at cross sections spaced 2 in. apart along the highspeed flowpath. Looking at the solutions for cowl angles of 0° to –4°, the large regions of separated flow 

(denoted by the dark blue iso-surfaces) in the corners extend up to 10 in. into the high-speed flowpath. 

While separated flow is observed along the ramp and the ramp corners in the 

–5° to –9° cowl angle solutions, it does not encompass nearly as large a percentage of the cross sectional 

area as for 0° to –4° cowl angle solutions. These regions of large separated flow impose a blockage on the 

inlet, reducing the aerodynamic capture area, and thereby causing the reduction in massflow observed in 

Figure 6 for cowl angles of 0° to –4° (Ref. 13).

Similar to Figure 7, Figure 8 shows the Mach number contours at cross sections, equally spaced every

4 in., along the compression ramp forward of the high-speed cowl tip (x<141 in.), at the inlet entrance, 

and aft of the cowl tip (x> 141 in.) of the high-speed flowpath for each cowl angle. The plots also include 

streamlines extending forward from the cowl leading edge that loosely depict the stream tube flowing into 

the high-speed flowpath. For the cowl angles of –5° and less, the stream tube is mostly flat in the vertical 

direction (i.e., the stream traces have constant y-values at each cross section) far upstream of the flowpath

entrance. For the cowl angles of –4° and greater, the stream tube curls down in the vertical direction near 

the inlet sidewall. This further illustrates the reduced upstream capture area flowing into the high-speed 

flowpath. This inlet does not appear to be unstarted in the traditional definition, in which the pressure rise 

moves upstream of the inlet entrance. However, this inlet is considered to be unstarted because the

captured massflow is reduced due to aerodynamic blockage at the entrance, caused by the massive corner 

separations (Ref. 11). The non-back-pressured inlet analyses predict that maximum massflow 

configuration of the high-speed flowpath is with the high-speed cowl angle set within the following 

range: –4° to –6°.

Back Pressure Applied

Upon determining the range of high-speed flowpath cowl rotation angles that maximized massflow

(–4° to –6°), the high-speed flowpath was back-pressured to simulate the presence of a DMSJ combustor. 

In the LIMX tunnel experiment, a cold-pipe and massflow plug assembly will be used to vary back

pressure. Following the convention used by Slater and Saunders (Ref. 20), in an effort to reduce 

computational complexity and solution time, a converging-diverging nozzle section with a variable throat 

area downstream of the AIP was used to vary back pressure. The throat areas ranged from 75 to 90

percent of the AIP cross section area.

The maximum massflow into the LIMX high-speed flowpath, without back pressure, was achieved 

with the simulation configured with a cowl rotation angle of –5°. Next, this configuration was simulated 

again with a back pressure that varied within the range from pAIP/piso,ref=0.781 to pAIP/piso,ref=2.86. The 

reference pressure condition, piso,ref, is the mass-averaged static pressure at the isolator entrance for the 

non-back-pressured condition; the AIP pressure, pAIP, is the mass-averaged static pressure at the AIP. 

Figure 9 shows six simulation results with axial distributions of ramp and cowl surface pressures plots 

and numerical-schlieren plots through the isolator. Each simulation pertained to a unique back pressure 

state. Immediately noticeable is the waviness of the cowl surface pressure plots compared to the relatively 

smooth ramp surface pressure plots. Along the cowl surface, shock and expansion waves are clearly 

observed; whereas along the ramp surface only a smooth pressure rise is observed after an initial shock. 

While this difference in pressure rise along the isolator surfaces may initially be puzzling, it is quite 

understandable when put into the context of an asymmetric flowpath: due to a greater ramp length than 

cowl length, a thick boundary layer forms along the ramp surface. The shock and expansion waves easily 

penetrate the thin boundary layer on the cowl, but they do not fully transmit through the thick boundary 

layer along the ramp (Ref. 8). This is observed in the numerical-schlieren images in Figure 9, especially 

for pAIP/piso,ref=1.62, 2.28, and 2.72, in which the dark regions depicting the shock waves do not fully 

extend to the lower ramp surface. Therefore, only a smooth pressure rise is observed along the ramp 

surface.
NASA/TM—2012-217219 7

Another interesting feature observed in the pressure plots of Figure 9 is that it is quite feasible to 

back-pressure the flowpath upstream of the isolator. While convention typically limits back-pressuring 

the flowpath to only the isolator, the simulations show that the downstream region of the inlet section can 

be back-pressured, too, and remain stable. During the experimental testing of this inlet, while the isolator 

is fully back-pressured (in the range of pAIP/piso,ref=2.72), the CFD simulations predict that the high-speed 

flowpath can withstand at least an additional 14 percent increase in back pressure (with respect to the 

reference isolator entrance pressure) without unstarting. This is quite important to the safety of the model, 

the safety of the wind tunnel facility, and the efficiency of the test program. If a similar inlet and isolator 

design were to be used in a flight vehicle, this additional unstart margin would help increase mission 

safety as well.

The LIMX high-speed flowpath was also back-pressured for cowl angles of –4° and –6°. For these 

simulations, the isolator pressure had the following ranges:

• For the –4° cowl angle, pAIP/piso,ref = 0.728 to 2.27.

• For the –6° cowl angle, pAIP/piso,ref = 0.841 to 3.46.

Figures 10 and 11 show the surface pressure and numerical-schlieren plots for the back-pressured –4° and 

–6° cowl angle inlets. As with the –5° cowl angle configuration that had results plotted in Figure 9, the 

boundary layer along the ramp surface is significantly thicker than that along the cowl surface. Again, this 

causes a smooth pressure rise on the ramp surface, whereas the shock and expansion waves are clearly 

observed in the pressure plots along the cowl surface. The CFD simulations predict that the –4° cowl 

configuration with a fully back-pressured isolator (pAIP/piso,ref=2.18) can withstand at least a nine percent 

increase in pressure (with respect to the isolator reference pressure) before the inlet unstarts. Similarly, 

the –6° cowl configuration with a fully back-pressured isolator (pAIP/piso,ref=3.17) can experience at least a 

29 percent increase in pressure before the inlet unstarts. These results show that the high-speed inlet and 

isolator can be stably back-pressured through the –4° to –6° range of cowl angles.

Another way to quantify the isolator performance is to compare the pressure rise through the isolator 

to the normal shock pressure rise for the same inflow (Ref. 18). Tables 2 to 4 list the pressure rise through 

the isolator as a percentage of the normal shock pressure rise for each of the three back-pressured 

configuration of the LIMX high-speed flowpath, using the corresponding non-back-pressured 

configuration (high-speed cowl angle) as the reference. The table also lists the AIP total pressure as a 

percentage of the normal shock total pressure. For the fully back-pressured, –4° cowl angle configuration 

(pAIP/piso,ref=2.18), the isolator attains 96.6 percent of the static pressure rise of the normal shock and 

maintains 89.7 percent of the normal shock total pressure. For –5° (pAIP/piso,ref=2.72) and –6°

(pAIP/piso,ref=3.17) cowl angles, the isolator attains 90.0 and 89.6 percent of the normal shock pressure rise, 

and maintains 82.9 and 84.0 percent of the normal shock total pressure.

In addition to observing the calculated surface pressure and numerical-schlieren plots for the backpressured high-speed flowpath, it was helpful to look at Mach number contours through the isolator. 

Figure 12 shows Mach number cross section contour plots equally spaced every 2 in. through the isolator 

for the fully back-pressured isolator and for each high-speed cowl angle. These plots show that the flow in 

the high-speed flowpath separates from the ramp surface (indicated by the blue iso-surface) upstream of 

the isolator but reattaches in the upstream half of the isolator—far upstream of the AIP. The plots also 

show that a thick boundary layer develops along the ramp surface. While the flow decelerates 

considerably from the beginning of the isolator to the AIP, from near Mach 2 local flow to barely sonic 

local flow, the flow is not uniform as it passes the AIP, primarily due the difference in boundary layer 

thickness between the ramp and cowl surfaces. The non-uniformity of the flow at the AIP is further 

observed in contour plots of Mach number in Figures 13 to 15. Without back pressure, the core flow 

through the isolator exceeds Mach 1.8 (for the –4° cowl angle) to Mach 2.2 (for the –6° cowl angle). In 

the thick boundary layer along the ramp, the flow reduces to Mach 1.2 to Mach 1.4 above the wall. When 

the isolator is fully back-pressured, the AIP sees a core Mach number between 0.8 and 1.0 while the flow 

is Mach 0.2 to 0.3 near the bottom of the thick boundary layer. Pressure, normalized by the freestream 
NASA/TM—2012-217219 8

static pressure, is similarly plotted in Figures 16 to 18. The AIP pressure contour plots show that the 

pressure is also non-uniform across the AIP, as one might expect. In most configurations, the static 

pressure is greater on the cowl side of the high-speed flowpath at the AIP than on the ramp side. For 

turbine flowpaths, this non-uniform pressure distribution is quantified as the static pressure distortion:

(pmax – pmin)/pavg (Ref. 8). The static pressure distortion at the AIP is listed in Tables 2 to 4. For the fully 

back-pressured isolator, the static pressure distortion at the AIP ranges from 8.9 percent for cowl angles 

of 5° and 6° to 10.1 percent for a cowl angle of 4°. While the static pressure distortion is a useful figure of 

merit for turbine-based inlets, it is unclear how useful it is for a DMSJ combustor, in which there are no 

moving parts to stall or fatigue.

Inflow Mach Number Stability

The –6° cowl angle configuration was further tested for freestream Mach number stability. Using the 

back-pressured case pAIP/piso,ref=3.17, the simulated freestream Mach number was reduced from Mach 4 to 

3.9. (This corresponded to a reduction of actual tunnel Mach number from Mach 3.5101 to 3.4293). A 

plot of the surface pressure is shown in Figure 19. Due to the lower freestream total pressure, the pressure 

rise in the high-speed flowpath moves forward from the beginning of the isolator (black trace) to about 

6 in. upstream of the isolator (red trace). Since the CFD simulation predicted that the high-speed flowpath 

would remain stable at Mach 3.9, the freestream simulated Mach number was further reduced, to Mach 

3.8 (Mach 3.3458, actual). In this case, the CFD simulation did not converge, as the high-speed flowpath

lost back pressure and unstarted. These two simulations predict that the high-speed flowpath had a 

simulated freestream Mach number margin of 0.1 Mach, agreeing with the inlet design (Ref. 8).

Future Work

In the future, after data from the first phases of the LIMX tests are available, the experimental data 

will be compared to the simulation results reported here. The experimental data will be used to validate 

and improve the computer code and the methods for computational analysis of hypersonic inlets and 

isolators. Lastly, upon successfully validating the computational results with the experimental data, 

validated simulation results will also be used to help clarify the experimental results—fill in the gaps in 

regions of the high-speed flowpath where experimental data isn’t available. In this way, both the 

numerical prediction of high-speed flow paths and understanding of mode transition are improved.

Conclusions

In preparation of the Large-scale Inlet for Mode Transition (LIMX) tests in the NASA Glenn 

Research Center’s 10- by 10-ft Supersonic Wind Tunnel, high-fidelity, numerical simulations were 

performed for the LIMX high-speed flowpath using the Wind-US computational fluid dynamics (CFD) 

code. The high-speed flowpath is part of an over-under, dual-flowpath turbine-based combined cycle 

inlet, designed to feed a Dual-Mode Scramjet (DMSJ) combustor. While the performance of the lowspeed flowpath was extensively tested in a small-scale series of experiments, the full performance of the 

high-speed flowpath had not yet been assessed. Therefore, numerical simulations were completed for the 

high-speed flowpath with and without back pressure at the mode-transition freestream Mach number, 

Mach 4. The simulation results show that massflow is maximized for a high-speed cowl angle of –5°. 

This gives researchers a range of high-speed cowl angles in which to concentrate their efforts: –4° to –6°.

The simulations also showed that cowl angles of –4° and larger will have large corner separations along 

the ramp surface. Simulations were also completed for cowl angles positioned at –4°, –5°, and –6° with 

back pressure. For each cowl rotation angle, the high-speed isolator was fully back-pressure and showed 

excellent stability. In fact, the simulations showed that the high-speed flowpath stability margin is 

increased with further back-pressuring, such that the pressure rise moved upstream of the isolator and into 

the inlet without unstarting the inlet. Between six and eight back-pressured simulations were completed 
NASA/TM—2012-217219 9

for each cowl angle; these simulations fully characterized the high-speed flowpath under back pressure. 

Simulations also showed that the high-speed flowpath with a fully back-pressured isolator could 

withstand a 0.1 reduction in freestream Mach number. The data helped researchers plan for LIMX 

experiments, providing insight into the operable limits of the high-speed flowpath.

References

1. Mansour, N. N., Pittmann, J. L., and Olson, L. E., “Fundamental Aeronautics Hypersonics Project: 

Overview,” AIAA Paper 2007-4263, June 2007.

2. Beckel, S. A., Garrett, J. L., and Gettinger, C. G., “Technologies for Robust and Affordable Scramjet 

Propulsion,” AIAA Paper 2006-7980, Nov. 2006.

3. Auslender, A. H., Suder, K. L., Thomas, S. R., “An Overview of the NASA FAP Hypersonics 

Project Airbreathing Propulsion Research,” AIAA Paper 2009-7277, Oct. 2009.

4. Curran, E. T., and Stull, F. D., U.S. Patent 3,667,233, “Dual Mode Supersonic Combustion Ramjet 

Engine,” June 1972.

5. Foster, R. W., Escher, W. J. D., and Robinson, J. W., “Studies of an Extensively Axisymmetric 

Rocket Based Combined Cycle (RBCC) Engine Powered SSTO Vehicle,” AIAA Paper 89-2294, 

July 1989.

6. Walker, S., Tang, M., and Mamplata, C., “TBCC Propulsion for a Mach 6 Hypersonic Airplane,” 

AIAA Paper 2009-7238, July 2009.

7. 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

Propulsion Meeting, Boston, Massachusetts, May 2008.

8. Saunders, J. D., Slater, J. W., Dippold, V., Sanders, B. W., and Weir, L. J., “Inlet Research Status for 

a Large-Scale Turbine-Based Combined-Cycle Engine Testbed,” JANNAF Propulsion Meeting, San 

Diego, California, Dec. 2009.

9. Soeder, R. H., Roeder, J. W., Linne, A. A., and Panek, J. W., “User Manual for NASA Glenn 10- by 

10-Foot Supersonic Wind Tunnel,” NASA/TM-2004-212697, May 2004.

10. 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, May 2008.

11. Emami, S., Trexler, C. S., Auslender, A. H., Weidner, J. P., “Experimental Investigation of InletCombustor Isolators for a Dual-Mode Scramjet at a Mach Number of 4,” NASA/TP-3502, May 1995.

12. Smart, M. K., and Trexler C. A., “Mach 4 Performance of Hypersonic Inlet with Rectangular-to-Elliptical 

Shape Transition,” Journal of Propulsion and Power, Vol. 20, No. 2, pp. 288-293, Mar. 2004.

13. Weir, L. J. and Sanders, B. W., “Investigation of a Two-Dimensional, Mixed-Compression Mach 5.0

Inlet,” NASA/CR-2004-213122, July 2004.

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

15. Georgiadis, N. J., Yoder, D. A., Towne, C. S., Engblom, W. A., Bhagwandin, V. A., Power, G. D., 

Lankford, D. W., Nelson, C. C., “Wind-US Code Physical Modeling Improvements to Complement 

Hypersonic Testing and Evaluation,” AIAA Paper 2009-193, Jan. 2009.

16. Menter, F. R., “Two-Equation Eddy Viscosity Turbulence Models for Engineering Applications,” 

AIAA Journal, Vol. 32, No. 8, pp. 1598-1605, Jan. 1994.

17. Georgiadis, N. J., Dudek, J. C., and Tierney, T., “Grid Resolution and Turbulent Inflow Boundary 

Conditions for NPARC Calculations,” AIAA Paper 95-2613, July 1995.

18. Dudek, J. C., Georgiadis, N. J., and Yoder, D. A., “Calculation of turbulent subsonic diffuser flows 

using the NPARC Navier-Stokes code,” AIAA Paper 96-0497, Jan. 1996.

19. Slater, J. W., “Verification Assessment of Flow Boundary Conditions for CFD Analysis of 

Supersonic Inlet Flows,” AIAA Paper 2001-3882, July 2001.

20. Slater, J. W. and Saunders, J. D., “CFD Simulation of Hypersonic TBCC Inlet Mode Transition,” 

AIAA Paper 2009-7349, Oct. 2009.
NASA/TM—2012-217219 10

TABLE 1.—GRID CONVERGENCE: MASSFLOW AND MASS-AVERAGED TOTAL PRESSURE AT AIP

Grid Level

Solution

Coarse Medium Fine

Actual Delta

(%) Actual Delta

(%) Actual Delta

(%)

Mass flow (lbm/s) 3.525 -- 3.566 1.15 3.585 0.55

p0 (psi) 13.897 -- 14.253 2.56 14.163 –0.63

TABLE 2.—AIP PRESSURE, PRESSURE DISTORTION, AND PERCENT CHANGE WITH RESPECT TO 

THE NORMAL SHOCK PRESSURE RISE FOR –4° HIGH-SPEED COWL ANGLE

AND VARIABLE CONVERGING-DIVERGING NOZZLE SECTION

pAIP/piso,ref 0.728 1.57 1.78 1.94 2.18 2.27

C-D nozzle throat area (%) 100 90 88 86 83 81

Max pressure (psi) 3.4502 7.1533 8.0874 8.7311 9.4053 9.8949

Min pressure (psi) 2.7995 6.188 7.078 7.677 8.5074 9.1144

Mass-average static pressure (psi) 3.0278 6.5727 7.4383 8.0889 8.8636 9.4224

AIP static pressure distortion (%) 21.49 14.69 13.57 13.03 10.13 8.28

p, normal shock (%) 33.0 71.3 80.8 87.98 96.6 102.9

p0, normal shock (%) 89.4 86.0 86.3 89.1 89.7 86.7

TABLE 3.—AIP PRESSURE, PRESSURE DISTORTION, AND PERCENT CHANGE WITH RESPECT TO

THE NORMAL SHOCK PRESSURE RISE FOR –5° HIGH-SPEED COWL ANGLE

AND VARIABLE CONVERGING-DIVERGING NOZZLE SECTION

pAIP/piso,ref 0.781 0.782 1.62 2.28 2.72 2.86

C-D nozzle throat area (%) 100 88 86 83 80 78

Max pressure (psi) 3.6053 3.6571 7.0401 9.8321 11.3896 12.0577

Min pressure (psi) 2.8991 2.884 5.7892 8.4448 10.4172 11.0837

Mass-average static pressure (psi) 3.1696 3.1821 6.611 9.1899 10.956 11.5224

AIP static pressure distortion (%) 22.28 24.30 18.92 15.10 8.88 8.45

p, normal shock (%) 25.8 25.8 53.3 75.3 90.0 94.6

p0, normal shock (%) 93.6 95.2 88.1 83.8 82.9 84.5

TABLE 4.—AIP PRESSURE, PRESSURE DISTORTION, AND PERCENT CHANGE WITH RESPECT TO

THE NORMAL SHOCK PRESSURE RISE FOR –6° HIGH-SPEED COWL ANGLE

AND VARIABLE CONVERGING-DIVERGING NOZZLE SECTION

pAIP/piso,ref 0.841 0.833 1.45 1.96 2.38 2.92 3.17 3.46

C-D nozzle throat area (%) 100 88 86 85 83 80 78 75

Max pressure (psi) 3.1143 3.1179 5.7533 7.1458 8.6306 10.2293 11.1612 11.9976

Min pressure (psi) 2.6195 2.5438 3.9895 5.7379 7.3762 9.3824 10.223 11.2154

Mass-average static pressure (psi) 2.7764 2.7729 4.9655 6.4834 7.9968 9.766 10.5917 11.5116

AIP static pressure distortion (%) 17.82 20.70 35.52 21.72 15.69 8.67 8.86 6.79

p, normal shock (%) 23.57 23.4 43.8 55.0 67.7 82.7 89.6 97.5

p0, normal shock (%) 97.65 98.3 92.1 90.1 87.5 83.9 84.0 85.2
NASA/TM—2012-217219 11

Figure 1.—CAD-generated image of the LIMX inlet model mounted in the wind tunnel.

Figure 2.—Inverted LIMX dual-flowpath inlet with the splitter positioned to allow airflow into both flowpaths.

Figure 3.—Schematic of simplified LIMX inlet high-speed flowpath used for CFD (–6° high-speed cowl, 

80 percent At/AAIP).
NASA/TM—2012-217219 12

Figure 4.—LIMX high-speed inlet grid (–6° high-speed cowl, 80 percent At/AAIP).

Figure 5.—LIMX high-speed flowpath massflow at the 

AIP with no back pressure.
NASA/TM—2012-217219 13

Figure 6.—Signed Mach number contours at LIMX high-speed flowpath entrance with the high-speed cowl set at 

different angles and no back pressure.
NASA/TM—2012-217219 14

Figure 7.—Mach number contours through LIMX high-speed flowpath without back pressure.
NASA/TM—2012-217219 15

Figure 8.—Mach number contours and stagnation streamlines over ramp of LIMX high-speed

flowpath without back pressure.
NASA/TM—2012-217219 16

Figure 9.—Simulated LIMX isolator surface pressure and 

schlieren images with the high-speed cowl positioned at –5°.
NASA/TM—2012-217219 17

Figure 10.—Simulated LIMX isolator surface pressure and 

schlieren images with the high-speed cowl positioned at –4°.
NASA/TM—2012-217219 18

Figure 11.—Simulated LIMX isolator surface pressure and 

schlieren images with the high-speed cowl positioned at –6°.
NASA/TM—2012-217219 19

Figure 12.—Mach number contours through LIMX isolator.
NASA/TM—2012-217219 20

Figure 13.—Mach number contours at AIP of LIMX high-speed flowpath with –4° cowl 

angle and back pressure.
NASA/TM—2012-217219 21

Figure 14.—Mach number contours at AIP of LIMX high-speed flowpath with –5° cowl 

angle and back pressure.
NASA/TM—2012-217219 22

Figure 15.—Mach number contours at AIP of LIMX high-speed flowpath with 

–6° cowl angle and back pressure.
NASA/TM—2012-217219 23

Figure 16.—Static pressure contours at AIP of LIMX high-speed flowpath with 

–4° cowl angle and back pressure.
NASA/TM—2012-217219 24

Figure 17.—Static pressure contours at AIP of LIMX high-speed flowpath with –5° cowl 

angle and back pressure.
NASA/TM—2012-217219 25

Figure 18.—Static pressure contours at AIP of LIMX high-speed flowpath

with –6° cowl angle and back pressure.
NASA/TM—2012-217219 26

Figure 19.—LIMX isolator surface pressure for –6° cowl angle 

and varying freestream Mach number.

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14. ABSTRACT

Reynolds-Averaged Navier-Stokes (RANS) simulations were performed for the high-speed flowpath and isolator of a dual-flowpath 

Turbine-Based Combined-Cycle (TBCC) inlet using the Wind-US code. The RANS simulations were performed in preparation for the 

Large-scale Inlet for Mode Transition (LIMX) model tests in the NASA Glenn Research Center (GRC) 10- by 10-ft Supersonic Wind 

Tunnel. The LIMX inlet has a low-speed flowpath that is coupled to a turbine engine and a high-speed flowpath designed to be coupled to a 

Dual-Mode Scramjet (DMSJ) combustor. These RANS simulations were conducted at a simulated freestream Mach number of 4.0, which is 

the nominal Mach number for the planned wind tunnel testing with the LIMX model. For the simulation results presented in this paper, the 

back pressure, cowl angles, and freestream Mach number were each varied to assess the performance and robustness of the high-speed inlet 

and isolator. Under simulated wind tunnel conditions at maximum inlet mass flow rates, the high-speed flowpath pressure rise was found to 

be greater than a factor of four. Furthermore, at a simulated freestream Mach number of 4.0, the high-speed flowpath and isolator showed 

stability for freestream Mach number that drops 0.1 Mach below the design point. The RANS simulations indicate the yet-untested highspeed inlet and isolator flowpath should operate as designed. The RANS simulation results also provided important insight to researchers as 

they developed test plans for the LIMX experiment in GRC’s 10- by 10-ft Supersonic Wind Tunnel.

15. SUBJECT TERMS

Turbine-based combined-cycle; Hypersonic; Inlet; Isolator; Inlet mode transition; CFD 

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