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NASA/TM-2001-210568 AIAA-2001-Q226 

Wind Code Application to External Forebody 

Flowfields With Comparisons to 

Experimental Results 

EC Frate 

Dynacs Engineering Company, Inc., Brook Park, Ohio 

H.D. Kim 

Glenn Research Center, Cleveland, Ohio 

May 2001 

https://ntrs.nasa.gov/search.jsp?R=20010050983 2018-05-14T14:46:51+00:00Z
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NASA/TM-2001-210568 AIAA-2001-0226 

Wind Code Application to External Forebody 

Flowfields With Comparisons to 

Experimental Results 

F.C Frate 

Dynacs Engineering Company, Inc., Brook Park, Ohio 

H.D. Kim 

Glenn Research Center, Cleveland, Ohio 

Prepared for the 

39th Aerospace Sciences Meeting and Exhibit 

sponsored by the American Institute of Aeronautics and Astronautics 

Reno, Nevada, January 8-11, 2001 

National Aeronautics and 

Space Administration 

Glenn Research Center 

May 2001 
Acknowledgments 

The authors would like to thank J. Slater for assembling the grids for this study. T. Bencic is also 

acknowledged for working with the TSP system and supplying the relevant data. 

NASA Center for Aerospace Information 

7121 Standard Drive 

Hanover, MD 21076 

Available from 

National Technical Information Service 

5285 Port Royal Road 

Springfield, VA 22100 

Available electronically at http: //gltrs.grc.nasa.gov IGLTRS 
WIND CODE APPLICATION TO EXTERNAL FOREBODY FLOWFIELDS WITH 

COMPARISONS TO EXPERIMENTAL RESULTS 

F.e. Frate 

Dynacs Engineering Company, Inc. 

Brook Park, Ohio 44142 

H.D. Kim 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 441 35 

Abstract 

The WIND Code, a general purpose Navier-Stokes 

solver, has been utilized to obtain supersonic external 

flowfield CFD solutions over an axisymmetric, parabolic forebody with comparisons made to wind tunnel 

experimental results. Various cases have been investigated at supersonic freestream conditions ranging from 

Mach 2.0 to 3.5, at 0° and 3° angles-of-attack, and with 

either a shatp-nose or blunt-nose forebody configuration. Both a turbulent (Baldwin-Lomax algebraic turbulence model) and a laminar model have been 

implemented in the CFD. Obtaining the solutions 

involved utilizing either the parabolized- or full-NavierStokes analyses supplied in WIND. Comparisons have 

been made with static pressure measurements, with 

boundary-layer rake and flowfield rake pitot pressure 

measurements, and with temperature-sensitive paint 

experimental results. Using WIND's parabolized NavierStokes capability, grid sequencing, and the BaldwinLomax algebraic turbulence model allowed for 

significant reductions in computational time while still 

providing good agreement with experiment. Given that 

CFD and experiment compare well, WIND is found to 

be a good computational platform for solving this type of 

forebody problem, and the grids developed in 

conjunction with it will be used in the future to 

investigate varying freestream conditions not tested 

experimentally. 

Introduction 

A reusable, Rocket Based Combined Cycle 

(RBCC), single-stage-to-orbit launch vehicle concept 

called GTX (formerly known as Trailblazer)1 is one that 

will use air-breathing propulsion to aid in reducing the 

required propellant mass fraction and, therefore, cost of 

access to space. Figure l ea) shows a scaled-down 

model of the vehicle concept that was tested in NASA 

Glenn's lO-by-IO foot Supersonic Wind Tunnel (SWT) 

with Mach numbers ranging from 2.0 to 3.5 and at 

various angles-of-attack to experimentally evaluate the 

external aerodynamics and mass capture characteristics. 2 It was desired to model the experimental set-up 

(as far as the forebody is concerned) and compute the 

external flowfield to a reasonably accurate extent with 

CFD. This was done in order to develop a capability 

NASAffM-200l-210568 1 

that could supply any additional external flowfield 

information (which may eventually affect the inlets) not 

suppli ed by the experiment. As part of the project 

scope, the use of grid sequencing and a parabolized 

Navier-Stokes

3 (PNS) analysis was investigated in 

order to save computational time and yet still obtain 

high fidelity CFD results. A "simultaneous" integration 

between experimental and CFD efforts was made 

possible because of these capabilities. 

Methods And Procedures 

Experiment 

The forebody hardware had the following parabolic 

contour: r=-0.001l6105x2+O.223959x, where r=radius 

and x=axial distance. Either a sharp-nose tip or a 

0.464 in. radius blunt-nose tip was used during each test. 

This parabolic geometry transitioned smoothly into a 

constant radius cylindrical section from x=96.45 in. and 

aft (referenced from the sharp-nose forebody tip). The 

conditions investigated for the sharp- and blunt-nose 

forebodies included Mach 2.0, 2.5, 3.0 and 3.5, with a 

unit Reynolds Number (Re#/ft) of -3.3Xl06

, 2.7X106

, 

2.5Xl06 and 2.5X106, respectively. Angles-of-attack (a) 

equal to 0°, ±3°, ±6° and ±9° were investigated at each 

freestream condition, though only 0° and 3° are focused 

on in this paper. All angles are with respect to the 

model's installation in the 10- by 10-foot SWT. 

During several sharp-nose experimental tests for 

0.=0°, a grit was applied at x=3.0 in. in order to trip the 

boundary-layer to turbulent. Sharp-nose forebody 

experimental results with and without application of the 

grit will be presented and compared to the turbulent and 

laminar CFD solutions. 

For the sharp-nose configuration, the CFD results 

can be directly compared with the following 

experimental data: 

1) Static pressure measurements along the forebody, 

2) Boundary-layer rake and flowfield rake measurements (both measuring pitot pressures) at 

various axial and circumferential forebody 

locations, and 

3) Temperature-sensitive paint (TSP) results. 
For the blunt-nose forebody, only the boundary-layer 

rake pitot pressure measurements were available and 

could be compared with the CFD solutions. 

Computational Model 

Coordinates for the forebody were supplied and 

incorporated into the gridding process. A rough 

schematic and general description of what was modeled 

in the CFD is shown in Fig. l(b). The expelimental data 

to be used in comparison with the CFD data is relevant 

up to a point just in front of the three propuJ ion pods' 

centerbody tips at x=93.33 in. (which are visible in 

Fig. l (a)). The pods were not modeled in the CFD 

process. However, the grid did model the constant 

cylindrical section up to x=150 in. Therefore, expelimental data obtained circumferentially between the pod 

positions is only valid (in comparisons with the CFD) at 

locations where the first effects from each centerbody's 

conical shock would still not be disturbing the forebody 

f1owfield. 

In modeling the sharp-nose forebody configuration, 

a 3-D 1800 single zone, structured grid with two levels 

of sequencing was created (modeling x=-25 to 150 in.) 

using ICEM CFD Mulcad.4 The grid is shown in 

Fig. 2(a). The grid contains 161 grid points axially in 

the i-direction, 149 radially in the j-direction, and 

61 circumferentially in the k-direction. Because of the 

way the sharp-nose grid was assembled, the PNS 

capability (for space marching in the axial direction) 

could be used in the WIND solution process. The wall 

spacing at the body was 0.0002 in. (based on y+ 

criteria), with 0.1 in. axial spacing at the nose and 

1.0 in. axial spacing along the forebody surface. The 

sharp-nose grid i=l boundary condition (B.c.) was set 

to a frozen B.C., as was the j=jmax B.C. An outflow B.C. 

was used for i==imax. The j=1 B.C. consisted of a 

singular axis B.C. ahead of the forebody and a viscous 

wall B.c. along the forebody. For this 1800 grid, k=1 

and k=kmax were reflection B.C.'s. 

A separate 3-D 1800 grid was created for the bluntnose forebody configuration, with a 0.464 in. radius 

nose-tip. The grid created for this blunt-nose forebody 

can be seen in Fig. 2(b). To accurately grid the 

forebody in the nose-tip region, a somewhat "polar 

grid" was created, with the i=1 location corresponding 

to the singular axis boundary condition. The grid wraps 

around the nose while traveling in the i-direction. The 

grid dimensioning corresponds to 141x 149x61 (for two 

levels of sequencing). The wall spacing was equal to 

0.0002 in., with 0.06 in. axial spacing at the nose, and 

1.0 in. axial spacing along the body. An FNS analysis 

instead of a PNS analysis was the solution method used 

for the blunt-nose grid because of the singular axis at 

i=l. Depending on processor availability, for certain 

runs the grid could be split into two zones and run using 

WIND's parallel processor capability. 

NASAffM-2001-210568 2 

The WIND Code's capabilities and documentation 

are described in detail in Ref. 5. WIND Version 3.0 was 

used in all CFD calculations. The viscous equations 

were solved during each run of WIND using either a 

turbulent (Baldwin-Lomax algebraic model) or a 

laminar model. WIND was run in standard mode, using 

the ideal gas model along with the Sutherland law for 

the transport properties. An adiabatic wall condition 

was utili zed. The paranleters specified within the 

WIND input file included total free stream conditions, a 

downstream keyword of pressure extrapolate always, 

specification of the turbulenc e or laminar model, 

sequencing specification, and PNS- or FNS-specific 

commands. WIND was run mainly in single processor 

mode using either RI0000 (225 MHz) or R1 2000 

(400MHz) SGI processors, depending on availability. 

The sharp-nose grid solutions involved running the 

PNS capability to convergence. In addition to 

accurately resolving the boundary-layer, the L2 norm of 

the residuals was seen to drop -3 orders of magnitude 

(except at the nose-tip) to a value usually below 10-4. 

The blunt-nose grid (with FNS capability) was 

investigated for convergence by monitoring the 

integrated pressure and viscous forces, the boundarylayer profile, the flowfield , and usually a drop of 

-3 orders of magnitude in the L2 norm of the residuals. 

The primary grid sequencing used corresponded to 

every other grid point from the grid dimensions quoted 

above (both for sharp- and blunt-nose cases). This 

approach was selected based on a grid sequencing/ 

convergence study (per the methods of Ref. 6) 

described in the Appendix. 

Results And Discussion 

Results from the grid convergence study (see 

Tables 1 and 2) showed the following general trends 

with respect to CPU time. The PNS cases (for sharpnose grids) ran 5 to 10 times faster than the FNS cases 

(blunt-nose grid). Using the Medium grids (every other 

grid point) instead of the Fine grids reduced the run 

time by approximately a factor of 25. Use of the PNS 

capability where possible, use of the coarser (Medium 

grid spacing) grids, and use of an algebraic turbulence 

model (instead of a one- or two-equation model) helped 

greatly reduce the computational time, given that most 

of the cases were run on a single processor. This 

allowed for a greater number of comparisons that could 

be made with experimental results. These comparisons 

will now be discussed. 

Sharp-nose Results 

Normalized Surface Static Pressure Distributions. 

Fig. 3(a) displays the normalized static pressure (PSlati! 

Ptunnel static) plotted versus the axial distance from the 

nose-tip for the Mach 2.5, a=O° test case. Turbulent 

CFD results are plotted with the corresponding experimental (without grit-applied) static pressure data. The 
CFD results are seen to compare well with the 

experimental data. At a =O°, it is expected that all static 

pressures at a given axial station along the circumferential (8-direction) should be equal (i.e., no pitch or 

yaw). The figure shows that, in general, this is the case 

here . 8 is measured, looking upstream, traveling 

counter-clockwise (or clockwise because of symmetry) 

from the top of the model's forebody to the bottom (see 

Fig. 1(b». The static pressure is highest at the nose-tip, 

after which it steadily decreases as the flow expands 

over the parabolic forebody surface. The slight 

waviness in the CFD solution near the nose-tip region 

may be due to the way the PNS solution method 

handles the coarser grid at this "discontinuity." 

For Mach 2.5 (a=3°), Fig. 3(b) shows CFD and 

experimental results coincide fairly well. When at 

angle-of-attack, higher static pressures are expected on 

the windward side (8=180° line) of the forebody as 

compared to the 120°/240° lines, the 90°/270° lines and 

the leeward side (0° line). The 0° line along the 

forebody surface experiences the lowest pressures. The 

experimental 90° and 270° values, as well as the 120° 

and 240° values again line up fairly well. Note that the 

static pressure distribution for the a=O° case (Fig. 3(a» 

would lie approximately centered in between the a =3° 

distributions presented for the 0° to 180° circumferential range in Fig. 3(b). 

In general, the trends at the other Mach numbers 

investigated are the same as for Mach 2.5, though the 

Mach 3.0 and 3.5 cases both showed several 

discrepancies. As is seen in Fig. 4(a), the Mach 3.0 

solution showed the experimental normalized static 

pressure distribution consistently offset below the CFD 

solution. As is seen in Fig. 4(b), the Mach 3.5 static 

pressure distributions showed good agreement at the 

front of the fore body, but the experimental static 

pressures were found to be lower than the CFD static 

pressure distribution line further downstream. The 

source of the discrepancies could be attributed to 

increases in velocities in the SWT not accounted for in 

the CFD. Axial (in addition to planar) wind tunnel 

gradients on the order of 6Mach-0.04 spanning over 

the volume occupied by the model were found in the 

Mach 3.0 and 3.5 calibration curves (at high Re#/ft). 

This is important since all CFD cases were run exactly 

at 2.00, 2.50, 3.00 and 3.50. As will be discussed in the 

boundary-layer rake section, even the small Mach 

changes mentioned above could help account for the 

discrepancies found in the results. 

Normalized Flowfield Rake Pitot Pressure Contour 

Plots at x- 98.95 in. (8=SO to 35°,175° to 145°) 

A comparison of CFD and experimental flowfield 

rake data obtained at x=98.95 in. is now made. Located 

near a plane slightly aft of the centerbody tips, flowfield 

rakes were used to measure the variation of the pitot 

pressure circumferentially on the leeward and windward sides of the forebody. It should be noted that 

NASAlTM-2001-210568 3 

experimentally there were only four rakes (8=5°, 15°, 

25° and 35°) used for each run, but the model was run 

at both positive and negati ve angles-of-attack. This 

allowed the data to be compiled as shown in Fig. 5 

using data from eight rakes (adding data at 8=145°, 

155°, 165° and 175°). Figure 1(b) gives a general idea 

of where these eight rakes (at x=98.95 in.) are located. 

The variable plotted in Fig. 5 is the normalized pitot 

pressure (Ppilo/PtunneIIOtal)' The CFD solution used in the 

comparison is that obtained assuming a turbulent 

boundary-layer over the entire forebod y. The two lefthand side contour quadrants (top and bottom) represent 

the experimental data, and they can be directly compared with the CFD results that have been placed to the 

right-hand side. Refer to the visual aids to the right of 

the quadrant plots to better understand the data being 

presented. The surface of the forebody has been 

depicted in each quadrant figure with a dashed line. 

The particular cases shown in Fig. 5 are the 

Mach 2.5 comparison for a=3 ° (Fig. 5(a» and the 

Mach 3.5 comparison for a=3° (Fig. 5(b» . Overall, 

comparing CFD to experiment, the agreement is very 

good for all the conditions tested. The bottom 

(windward) rakes show higher gradients closer to the 

forebody surface as compared to the top (leeward) 

rakes, as may be expected when at an angle-of-attack. 

WIND's PNS capability is seen to be capturing the 

general features of the flowfield quite well. The trends 

at the other Mach numbers are very similar to those just 

discussed. Generally, the windward side experienced 

slightly higher pitot pressures than the leeward in the 

outer "freestream" region of the external forebody flow. 

Temperature-Sensitive Paint (TSP) Data 

Figure 6(a) shows experimental TSP data for each 

of the four Mach number cases at a =O° (without grit 

application). The equilibrium surface temperature can 

be inferred by the TSP surface profile distributions. 

This plot can help characterize the transition from a 

laminar to a turbulent boundary-layer occurring along 

the forebody . For Mach 2.0, 2.5 and 3.0, similar 

temperature distributions are found where the 

minimum-maximum-minimum peaks are occurring at 

the same axial locations along the forebody. The 

general location for this "transition" region is thus 

occurring from x-20 to -35 in. The sudden increase in 

temperature is known to correspond to the beginning of 

transition. 7 Though the Mach 3.5 curve differs from the 

other three, it appears the peak occurs slightly aft of the 

peak for the other Mach numbers. Taken as a whole, 

however, this data shows transition is occurring at 

roughly the same location, which may be expected 

since the Re#/ft is approxi-mately the same for all four 

cases. 

Figure 6(b) shows the same four flow conditions, 

but now the grit has been applied at x=3.0 in. This is 

evident from the "blip" in the temperature distribution 

seen at this location. Comparing with and without grit 
application, the temperature distributions have changed. 

Both Mach 2.0 and 2.5 (with grit applied) show 

approximately a constant temperature level that is near 

that seen on the aft portion of the forebody in the no grit 

applied case (indicating the grit has tripped the 

boundary-layer to turbulent further upstream). Though 

Mach 3.0 and 3.5 with grit differ, transition to turbulent 

is seen to have occurred further upstream than in the no 

grit cases. This experimental TSP data (along with the 

experimental boundary-layer rake data) will be compared with the turbulent and laminar CFD results in the 

next section to investigate this transition further. 

Normalized Boundary-Laver Rake Pitot Pressure Profiles 

In the experiment, four boundary-layer rakes were 

placed in various positions axially and circumferentially 

along the forebody surface. For each test condition, the 

model was run at both a positive and negative angle-ofattack. Therefore, experimental data can be reduced to 

eight rake locations using symmetry considerations and 

positi ve/negative angle-of-attack information (see 

Fig. l (b». The rake locations through symmetry 

considerations reduce to the following: (x=32.5 in., 

8=58°, 122°), (x=53.94 in. , 8=9°, 171 °), (x=75.38 in., 

8=87°,93°), and (x=100.33 in. , 8=10°,170°). The 

distance normal to the surface versus the normalized 

pitot pressure (PpitotlPrunnel rora~ will be plotted. Turbulent 

and laminar sharp-nose grid CFD solutions have been 

obtained for all the cases investigated and are compared 

with experimental results in this ection. Plotting both 

CFD solutions together with the experimental data 

allows for a "first order" estimate of the type of 

boundary-layer (laminar, transitional, or turbulent) over 

the entire forebody. Though this is not quite accurate 

(since the downstream boundary-layer is dependent on 

what the boundary-layer characteristic has been 

upstream), the comparison will be shown to be good 

enough for the purposes of this study and provides 

"bounds" on the type of flow. 

Figure 7 shows the four boundary-layer rakes for 

the Mach 2.0 case at 0.=0°, with additional experimental data included for the case where grit was 

applied to the sharp-nose forebody configuration to trip 

the boundary-layer to turbulent. Over the forebod y, the 

experimental boundary-layer data without grit applied 

shows good agreement with the turbulent CFD data at 

the three downstream rake locations. However, the 

boundary-layer rake located at x=32.5 in. shows the 

data does not entirely lie on the turbulent solution 

profile, but rather has a slightly thinner profile. This 

agrees with the no grit TSP results presented 

previously, which showed that the turbulent boundarylayer was not obtained until omewhere near this rake 

position. 

The assumption made in the flowfield rake section 

discussed previously (in regards to presenting the 

experimental flowfield rake data at x=98.95 in. with 

only the turbulent CFD data) is quite sufficient for 

NASAfTM-2001-210568 4 

sharp-nose forebody comparisons. Note that laminar 

and turbulent CFD static pressure distributions were 

very identical. Hence, this wa the reason for only 

plotting experimental stati c pressure data with the 

turbulent CFD data. 

Comparing the Mach 2.0 results with the gritapplied experimental data, it can be seen in Figs. 7(a-d) 

that the profiles lie almost on top of the turbulent CFD 

solution profiles. The profiles are seen to be slightly 

thicker than profiles without grit. Transition ha 

occuned further upstream than the case without grit. 

Therefore, agreement with the turbulent CFD profile is 

much better for the case with grit. 

It should also be noted, though not presented here, 

that all eight experimental rake profiles for the 0.=3° 

case (without grit) lie on top of their respective 

turbulent CFD profiles. This is the case for all cases 

tested with the sharp-nose grid. Therefore, there is very 

good experimental and CFD agreement at angle-ofattack for the sharp-nose forebody , and WIND (with all 

the assumptions made) has done a good job of capturing the pertinent flow phenomenon. This suggests that 

transition from laminar to turbulent occurs further 

upstream when at angle-of-attack than is seen for the 

0.=0°. As would be expected at an angle-of-attack, the 

leeward side rakes, especially those closest to the top of 

the forebody (x=53.94 and 100.33 in.), display a thicker 

boundary-layer profile than the windward side rakes at 

the same axial locations. In addition, as the flow 

proceeds downstream over the forebody, the effects of 

expansion can be seen to be taking place, with 

"freestream" pitot pressures continually decreasing. 

Also note that the pitot pressure does not reach a 

constant value outside the "boundary-layer" in these 

plots because of the "conical" nature of the flow. 

Mach 2.5 and 3.0 sharp-nose forebody experimental data showed very similar trends to the Mach 2.0, 

0.=0° and 3° results just discussed (i.e., experiment and 

turbulent CFD pitot pressure profiles don 't line up 

exactly until after x=32.5 in. for 0.=0°, and they line up 

at all locations measured for 0.=3°). However, Mach 3.5 

actually showed that the experimental boundary-layer 

data without grit does not line up with the turbulent 

CFD profile until somewhere after x=53.94 in. Transition appears to have occurred further back as compared 

to the other Mach number cases (as might be 

ascertained from the TSP data in Fig. 6(a). 

Mach 3.5 pitot pressures in the "freestream" (for 

the experiment and CFD) were offset from one another 

at various axial stations. Higher "free stream" pitot 

pressures were obtained for the experimental data as 

compared to the CFD data at upstream locations, while 

lower "freestrearn" experi-mental pitot pressures were 

obtained at the downstream locations. The trend agreed 

with 10- by lO-foot SWT data showing an increasing 

freestream Mach number with axial travel downstream 

in the tunnel for certain conditions (and therefore a 

decreasing "freestream" pitot pressure). Several Mach 
• 

number perturbation CFD runs (on the order b.Mach 

-0.04) showed the discrep-ancies between experimental 

and CFD boundary-layer rake "freestream" values 

could be explained by these slight Mach number 

gradients. 

Blunt-nose Results 

Numerous FNS runs of the WIND code have been 

completed for the blunt-nose Medium grid (every other 

grid point) at a=0° and at a=3° (M == 2.0, 2.5, 3.0, and 

3.5). A summary of the results for these cases follows. 

Comparing boundary-layer profiles, trends at Mach 

2.0 and Mach 2.5 (for a=00) are somewhat similar to 

the sharp-nose Mach 2.0, 2.5 and 3.0 (0,=0°) forebody 

trends. Figures 8(a-d) shows the Mach 2.5, a=0°, bluntnose boundary-layer rake profile comparisons (all 

without grit) over the forebody length. At x=32.5 in., 

the experimental data actually is seen to lie closer to a 

laminar boundary-layer profile than a turbulent one. 

However, further downstream at x=53.94 in., the 

experimental profiles are lying on top of the turbulent 

CFD solution profiles. Generally speaking for these 

cases just mentioned, the thickness for both the sharpand blunt-nose profiles, as well as the normalized 

"freestream" pitot pressure values, agree quite well with 

each other (station-to-station) over the forebody 

surface. 

Mach 3.0 and 3.5 boundary-layer rake results, 

however, show that the experimental data (no grit was 

applied in any of the blunt-nose cases) do not lie 

directly on the turbulent CFD solution until further 

downstream than had been seen in the sharp-nose 

forebody solutions. For the Mach 3.5, 0,=0° solution, 

the experimental profile lies atop the laminar CFD 

profile even up to x=53.94 in. Therefore, transition is 

occurring downstream of this station for the blunt-nose 

condition, whereas this type of definjtive statement 

could not be made for the corresponding sharp-nose 

cases (where the upstream experiment profiles were 

found only slightly offset from the turbulent CFD 

solutions). 

For a=3°, the trends are actually slightly different 

for several of the blunt-nose cases as compared to the 

sharp-nose cases. As before for the sharp-nose cases at 

Mach 2.0 and 2.5, the experimental profiles lay nearly 

atop the turbulent CFD profiles at all the rake locations. 

However, the Mach 3.0 and 3.5 experimental profiles 

(up to and including x=53.94 in. on the windward side) 

lie either somewhere in between turbulent and laminar 

CFD profiles or directly on top of the laminar profile 

(see Fig. 9 for Mach 3.0). This was not seen in the 

sharp-nose cases at any Mach number when the 

forebody was at any angle-of-attack. 

In summary, it may be deduced that, in general, 

transition has occurred at arial locations ahead of where 

the experimental profile finally matches the turbulent 

solution. When taking all boundary-layer rakes as a 

whole, this overall view of the data can be compared to 

NASA/fM-2001-210568 5 

the experimental TSP data (as was shown in Fig. 6). 

The conclusions drawn from the CFD-combined expelimental normalized pitot pressure plots show good 

general agreement with the TSP data conclusions, and 

provide some general idea of boundary-layer transition 

location and characteristics. Overall, the PNS capability 

is seen to have done a good job in returning worthwhile 

results that agree well with experiment. 

Summary And Conclusion 

In comparisons involving NASA Glenn 's 10- by 

lO-foot Supersonic Wind Tunnel experimental results, 

very good agreement between WIND Code CFD and 

experiment has been found . Using WIND's PNS capability where possible, the coarser grids, and the 

Baldwin-Lomax algebraic turbulence model allowed 

for great reductions in the computational time while 

still maintaining good agreement with the experimental 

results. Running CFD concurrently with experimental 

testing allowed for one's information to feed directly 

into the planning for the other. Future use of the CFD 

models to obtain reasonably accurate information that 

was not obtained with the experiment is now an option. 

The WIND code has been found to be a good solver for 

the applications set forth in this study. 

Appendix 

Grid Convergence Study 

A grid convergence study for the sharp-nose and 

blunt-nose grids has been performed based on the 

procedures outlined in Ref. 6. The total drag coefficient 

(pressure plus viscous drag coefficient) was the 

parameter used for comparison in these studies. 

First, for the sharp-nose grid, the Mach 2.5 (0,=0°) 

flowfield was computed on three grids, each with twice 

the number of grid points in the i-, j-, and k- directions 

as the previous grid (i.e., Coarse, Meruum and Fine grid 

spacing). The Fine grid was chosen as the reference 

grid and is referred to as grid 1, the Medium grid is 

referred to as grid 2, and the Coarse as grid 3. 

The Grid Convergence Index (GCl), similar to the 

Richardson error estimator and based on the 

generalized theory of Richardson Extrapolation, 

provides a calculated error band on the solution 

functionals (total drag coefficient in this case). It also 

provides a measure of uncertainty for grid convergence. 

Though two levels of sequencing (three grids) were 

utilized with a constant grid refinement ratio of 2, the 

GCI was calculated using a Factor of safety (Fs) equal 

to 3 in order to be conservative. Table 1 presents the 

sharp-nose grid's relevant information for the grid 

convergence study. Defining "p" (the order of 

convergence) per Ref. 6, it is calculated by using the 

solution functionals obtained from the three grids and 

the grid refinement ratio. For the sharp-nose grid, using 

Table I values, p was calculated as -1.74. This shows 

the solution is not quite at a second-order level of 

convergence. This may be expected since, with the PNS 
capability, WIND automatically changes to a first-order 

explicit operator in the i-direction (marching direction) 

only, while keeping second-order operators in the other 

direction . The Fine glid GCI (GCI 12) was calculated as 

0.05 percent, while the Medium grid GCI (GCl z3) was 

calculated as 0.17 percent. The solutions were found to 

be in the asymptotic range [GClzi(GCI 12*2P) '" 1.00]. 

These value were deemed good enough for the 

purposes of this study. The Medium grid has been used 

throughout this paper for the sharp-nose forebody cases. 

For the blunt-nose grid, the Mach 2.5 (a=OO) 

flowfield was also computed on three grids, each with 

twice the number of grid points in the i-, j-, and 

k-directions as the previous grid (i.e., Coarse, Medium 

and Fine grid spacing). Using the same procedure as 

described above, Table 2 presents the relevant bluntnose grid information for the grid convergence study. 

The order of convergence p was calculated as -1.52. 

This shows that the solution is not at a second-order 

level of convergence, where FNS calculations for the 

blunt-nose case use second-order explicit operators in 

all directions. The difference between theoretical and 

calculated order of convergence may be due to grid 

stretching, grid quality, nonlinearities in the solutions 

(such as the presence of shocks) and possibly other 

factors. 6 The Fine grid GCI (GCI12) was calculated as 

0.38 percent, while the Medium grid GCI (GCI23) was 

calculated as 1.09 percent. The solutions were found to 

be in the asymptotic range [(GClzi(GCI 12*2P» '" 1.00]. 

These values were deemed good enough for the 

purposes of this study. The Medium grid has been used 

throughout this paper for the blunt-nose forebody cases. 

References 

'Trefuy, C.J., An Air-Breathing Launch Vehicle Concept 

for Single-Stage-to-Orbit, NASA TM-1 999-209089, 1999. 

2Kim, H.D., and Frate, F.C., "Experimental Evaluation of 

the Effect of Angle-of-Attack on the External Aerodynamics and Mas Capture of a Symmetric, Three-Engine 

Air-Breathin g Launch Vehicle Configuration at 

Supersonic Speeds," 37th JANNAF Combustion Subcommittee, 25th Airbreathing Propulsion Sub-committee, 

and 19th Propulsion Systems Hazards Subcommittee Joint 

Meeting, Nov 13-17, 2000. 

3Seddon , J., and Gold smith , E.L. , Practical Intake 

Aerodynamic Design, Anderson, B.H. and Towne, C.E., 

Application of Computational Fluid Dynamics to Inlets, 

AIAA Education Series, 1993. 

4Akdag, V. and Wulf, A., "Integrated Geometry and Grid 

Generation System fo r Complex Configurations," 

Software Systems for Surface Modeling and Grid 

Generation, NASA CP-3143, Apr. 1992. 

5WIND D oc um en t a ti o n H ome Page , 

http://www .grc.nasa.gov/www/winddocs/index.html, The 

WIND Code, WWW page created by Charles Towne, 

Version 3.0, Accessed Jan.- Dec. 2000. 

6Roache, PJ., Verification and Validation in Computational Science and Engineering, Hennosa Publishers, 

Albuquerque, New Mexico, 1998. 

7Schlichting, H. , Boundary-Layer Theory, Sixth Edition, 

McGraw-Hill, New York, 1968. 

T a bl e1.-Sh larp-nose F ore b d oly Gn ·d C on vergence S d R tu Iy esu ts - M ac h2 .5, a= 

Grid Number Grid Spacing Total CPU time Total Drag Calculated order 

(Nonnalized by (Corrected for Coefficient of convergence 

finest grid spacing) machine use) (P) 

Fine (1) - 000 sequencing in WIND 1 -75,500 sec 0.108639 

Medium (2) - III sequencing in WIND 2 -3,000 sec 0.108596 1.74 

Coarse (3) - 222 seguencing in WIND 4 -200 sec 0.108452 

T a e bl 2 - BI unt-nose F b d ore o ly Grid C on vergence S d R tu Iy es ul ts - M ac h25 . ,a= 

Grid Number Grid Spacing Total CPU time Total Drag Calculated order 

(Nonnalized by (Corrected for Coefficient of convergence 

finest lQid spacing) machine use) (p) 

Fine (1) - 000 sequencing in WIND 1 -446,500 sec 0.107664 

Medium (2) - III sequencing in WIND 2 -17,000 sec 0.107411 1.52 

Coarse (3) - 222 sequencing in WIND 4 -2,000 sec 0.106686 

NASAITM-2001-210568 6 

--.--------
x=32.S in x=7S.38 in 

TWO POSSIDLE NOSE 

CONFIGURA TrONS 

~ 

~arp-n ose 'k~ 

x=98.9S in 

~,. ji~ Blunt-nose k 

W M 

Figure 1 - (a) Scaled-down GTX Model, (b) Schematic and general description of forebody used for CFD. 

W M 

Figure 2 - Isometric views, (a) Sharp-nose forebody grid, (b) Blunt-nose forebody grid. 

(Every grid point for the finest grid is shown.) 

NASAfTM- 2001 -21 0568 7 
1.8 

u i 1.6 

~ .3 1.4 

~ 

~ 1.2 -1--------- ;;;: 

- CFO 

o Experiment - 90 deg 

- Experiment - 210 deg 

a Experiment · 180 deg 

A Experiment - 120 deg 

() Expenment - 240 deg 

1.8 

.. - CFO - 180 

a Experiment . 180 deg 

CFO · 12O 

A Experiment - 120 deg 

o Experiment - 240 deg 

- CFD-90 

o Experiment - 90 deg 

- Experiment - 270 deg 

- CFD-O 

0.8 +---~--_-~--_----_-~--_---___i 8+-- -----~-----------------~ 

o 10 20 30 40 50 60 70 80 90 100 10 20 30 40 50 60 70 

x -(distance from nose tip) x -(distance from nose tip) 

(a) (b) 

Figure 3 - Sharp-nose Forebody Normalized Static Pressure Distribution, (a) Mach 2.5, cx=oo, 

(b) Mach 2.5, cx=3 °. 

80 90 100 

2.2 

- CFO 

2.6 .........••••.•.....••.•..•.........•..•.....•....•••• ··r····cc··= ·"' ····"' ····cc····cc·····;:::····"'····"'· ···"' ····cc. ;;;;;;;;' 

1.8 u 

~ 1.6 

~ .a 1.4 

;;;: 

o Experiment - 90 deg 

- Experiment - 210 deg 

,2 +-----------~~I ----------------~ ! 

C. 

0.8 .......................................................................................... . 

2.4 

22 

E 2 

~ ~ 1.8 

E. 1.6 

e, 

g l.4 !l £ 12 

0.8 

- CFO 

C Experiment - 90 deg 

- Experiment - 270 deg 

0.6 +---~-__ - _ - __ --__ -_-__ --__ -_--< 0.6 +-- __ _--~ __ - __ --- __ --__ - __ - -1 

10 20 30 40 50 60 70 80 90 100 10 20 30 40 50 80 70 

x -(distance from nose tip) x -(distance from nose tip) 

(a) (b) 

Figure 4 - Sharp-nose Forebody Normalized Static Pressure Distribution, (a) Mach 3.0, cx=oo, 

(b) Mach 3.5, cx=oo. 

- - -------- - ---- 

. ------ ----. 

80 90 100 
Experiment CFD 

" 

'0 

-6 _7 -6 -5 ...... -3 - 2 _ , 

-02 

-,. 

..a _7 -6 -5 -" -3 _2 _1 

Distance from vehicle centerline (inch) 

(a) 

Experiment CFD 

'0 

-6 -7 -6 -5 ....A -3 -2 _I 

-a 7 -6 -5 -" -3 _2 _, 

Distance from vehicle centerline (inch) 

(b) 

Leeward 

Windward 

Leeward 

Windward 

Symmetry 

Plane 

Experiment -I CFD .. . . 25 155 5 15 25 

3 35 

Synwletry 

Plane 

-

Figure 5 - Sharp-nose Flowfield Rake Nonnalized Pitot Pressure Contour Plots for a =3° at x=98.95 inches 

(experiment vs. turbulent CFD), 

(a) Mach 2.5, a=3°, 

(b) Mach 3.5, a=3°. 

NASA/fM-2001-210568 9 
Hot 1.5 

1.4 

~ 

~ 1.3 

.. 

a. 

~ 1.2 

" ~ 1.1 

co 

E 

(; 1 z 

- M=2.0 

M=2.5 

Mach 3.5 -M=3.0 

' 

Mach 2.0 

j :;,;, 2.5:-' ------~--

1.4 

~ - ~ 1.3 

.. 

a. 

~ 1.2 f-

" 

~ 1.1 

co 

E 

(; 1 z 

0.9 

~ Mach 2.5 

- M=2.0 

M=2.5 

-M=3.0 

- M=3.5 

0.9 +--~----r---'-----r---~-----r----.---~ 

0.8 Cold 0 

(a) 

Cold 

o 10 20 30 40 50 60 

Distance (Inches) 

10 20 30 40 50 60 70 80 

Distance (Inches) 

(a) (b) 

Figure 6 - Sharp-nose normalized temperature distribution over part of forebody for a=0° cases, 

(a) No grit applied, (b) With grit applied at x=3.0 inches. 

~2~-----------------r---------t---, _ CFD· Turbulorll .......•...... . ......... ~ 

, . '" CFD · Laminar • .•••. .f.- •.••. ..j. •• ~ 

" 1.6 o Exp!Himerll · Nogrit 1 

.£ 1.4 A Experiment . Grit at b3.0' i'.2 1'------------------'············,···· .... . + .......... ~ 

i ', ...................................... , .............. ··············!·············· .. ···········+·······I 

so .• +·········r·········,··············:·············· .. ··· ...... ! ............. , ............. : ......... \V 

0.6 1---:----------------;---,---~-G 

0.4 

0.2 

0.1 0.2 0.3 0.4 0.5 

0 .• + ....... ; ............ , ........... j ............. : ............ : ........... ..,. .... _ 

0.4 -1-........... , .......... ; ............. ; .......... . 

0.2 

(b) 

(c) 

(d) 

w ·······.·········· i·······, .......... , ... . 

0 .. ................................... ., ............ i ............ ; 

0 .• + ..................... : .......... + ........ , .......... . , ......... pc ....... + ... _ ..... , .... ..... j 

0.4 + ......................... , ........................... , ....... "IiY ................ + ............. 'j' ......... j 

0.2 ........... .j. ••••• 

°0~--~0~,-- ~~~0~4~~0.5~~0~ .• --~0C7--0~ .• ~~0 .• 

P(pitotyP(tunnei total) 

70 

Figure 7 (a-d) - Sharp-nose Boundary-Layer Rake Normalized Pitot Pressure Profiles along the forebody at various 

axial stations (turbulent and laminar CFD VS, experimental (with and without grit)), 

Mach 2,0, a=O°, 

(a) x=32.S inches, (b) x=S3,94 inches, (c) x=7S.38 inches, (d) x=lOO.33 inches. 

NASAffM-2001-210S68 10 

80 
, - -

" 

(a) 

2.2 r.=========;-------;---t, - eFD -Turbulent 

1.8 ••• CFD - Laminar 

~ 1.6 0 Experiment 

£:1.4 

--'---~- -i 

W, ·2 

i' 8 

........ 1. .. 

0 0.6 

0.4 

0.2L:::= ........ ~ ....• ~._ ... ~ .. _. ~ .... ~ , ........... ~ 

0.1 0.2 0.3 0.4 0.5 0.6 

(b) 

.... f.... . ....... { 

:~ t ~ •.• ~~.: :::: .. ::: .. ~:;;:---.------i:) .... ~0.1 

(c) 

0.2 

0.6 

0.4 

0.2 

0.3 0.4 

0.1 

0.5 0.6 .............. : .................. 1 

...... ·· .. i .. · .. · .... ·1·· 

0.2 

(d) 

0.6 

0.4 

0.2 

··············i 

0.1 0 .2 0.3 0 .4 

p{pitotyP(tunnel total) 

0.5 0.6 

Figure 8 (a-d) - Blunt-nose Boundary-Layer Rake Normalized Pitot Pressure Profiles along the forebody at various 

axial stations (turbulent and laminar CFD vs. experimental (all without grit», Mach 2.5, a=0°, 

(a) x=32.5 inches, (b) x=53.94 inches, (c) x=75.38 inches, (d) x=IOO.33 inches. 

u 

u 

, 

0.' 

.. 

02 

'" V 

..c: 

() 

.9 

Q 

~ v 

u 

§ 

..... 

'" CS 22 

U 

U 

, 

o • 

.. 

02 

22 ,---'---;--'-~-~r--~~ 

2 

... 

1.6 ······i-

-... ~ ... +.-.. ~ 

; i 

. ........... ;. .. . 

0 .15 0.2 0..25 0.3 0.35 0 .. OA5 0 0,15 0.2 0..25 0.3 0.3$ 0." 0.45 0 0 .05 0.1 0.15 0.2 0.25 0.3 0.35 0 .• 

I =-_~W----:::-:::ih,t----jr~x=;.lOO.33 in - CFO - T urbulenl 

. - - CFO - laminar 

o Experiment 

, ...... ·· ... • ......... • .. •• .... · .. , ...... ,· ...... ' .... ·1 ........ • ....... ·• 

P pito/P tunnel total 

Figure 9 - Blunt-nose Boundary-Layer Rake Normalized Pitot Pressure Profiles along the forebody at various axial 

stations, Mach 3.0, a =3°. 

NASAffM- 2001-210568 11 
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REPORT TYPE AND DATES COVERED 

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4. TITLE AND SUBTITLE 5. FUNDING NUMBERS 

Wind Code Application to External Forebody Rowfields 

With Comparison to Experimental Results 

6. AUTHOR(S) VVU-708-73-20-00 

F.e. Frate and H.D. Kim 

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION 

REPORT NUMBER 

National Aeronautics and Space Administration 

John H. Glenn Re earch Center at Lewis Field E-12532 

Cleveland, Ohio 44135 - 3191 

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AGENCY REPORT NUMBER 

ational Aeronautics and Space Administration 

Washington, DC 20546-0001 NASA TM-2001-210568 

AlAA-2001-0226 

11. SUPPLEMENTARY NOTES 

Prepared for the 39th Aerospace Sciences Meeting and Exhibit sponsored by the American Institute of Aeronautics and 

Astronautics, Reno, Nevada, January 8-11, 2001. F.e. Frate, Dynacs Engineering Company, Inc. , 2001 Aerospace 

Parkway, Brook Park, Ohio 44142; and HD. Kim, NASA Glenn Research Center. Responsible person, Hyun Dae Kim, 

organization code 5850,216-433-8344. 

12a. DISTRIBUTION/AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE 

Unclassified - Unlimited 

Subject Category: 02 Distribution: Nonstandard 

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

This publication is available from the NASA Center for AeroSpace Infonnation, 301-621-0390. 

13. ABSTRACT (Maximum 200 words) 

The WIND Code, a general purpose Navier-Stokes solver, has been utilized to obtain supersonic external flowfield CFD 

solutions over an axisymmetric, parabolic forebody with comparisons made to wind tunnel experimental results. Various 

cases have been investigated at supersonic freestream conditions ranging from Mach 2.0 to 3.5, at 0° and 3° angles-ofattack, and with either a sharp-nose or blunt-nose forebody configuration. Both a turbulent (Baldwin-Lomax algebraic 

turbulence model) and a laminar model have been implemented in the CFD. Obtaining the solutions involved utilizing 

either the parabolized- or full-Navier-Stokes analyses supplied in WIND. Comparisons have been made with static 

pressure measurements, with boundary-layer rake and flowfield rake pitot pressure measurements, and with temperaturesensitive paint experimental results. Using WIND's parabolized Navier-Stokes capability, grid sequencing, and the 

Baldwin-Lomax algebraic turbulence model allowed for significant reductions in computational time while still providing 

good agreement with experiment. Given that CFD and experiment compare well, WIND is fou nd to be a good computational platform for solving this type of forebody problem, and the grids developed in conjunction with it will be used in 

the future to investigate varying freestream conditions not tested experimentally. 

14. SUBJECT TERMS 15. NUMBER OF PAGES 

Computational fluid dynamics; Supersonic boundary layers; 17 

Forebodies; Boundary layer transition 16. PRICE CODE 

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