Stefanie M. Hirt and Bernhard H. Anderson

Glenn Research Center, Cleveland, Ohio

Experimental Investigation of the Application

of Microramp Flow Control to an Oblique

Shock Interaction

NASA/TM—2009-215630

November 2009

AIAA–2009–919
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Stefanie M. Hirt and Bernhard H. Anderson

Glenn Research Center, Cleveland, Ohio

Experimental Investigation of the Application

of Microramp Flow Control to an Oblique

Shock Interaction

NASA/TM—2009-215630

November 2009

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared for the

47th Aerospace Sciences Meeting

sponsored by the American Institute of Aeronautics and Astronautics

Orlando, Florida, January 5–8, 2009

AIAA–2009–919
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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. 
NASA/TM—2009-215630 1 

Experimental Investigation of the Application of Microramp 

Flow Control to an Oblique Shock Interaction 

Stefanie M. Hirt and Bernhard H. Anderson 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Abstract 

The effectiveness of microramp flow control devices in controlling an oblique shock interaction was 

tested in the 15- by 15-Centimeter Supersonic Wind Tunnel at NASA Glenn Research Center. Fifteen 

microramp geometries were tested varying the height, chord length, and spacing between ramps. 

Measurements of the boundary layer properties downstream of the shock reflection were analyzed using 

design of experiments methods. Results from main effects, D-optimal, full factorial, and central 

composite designs were compared. The designs provided consistent results for a single variable 

optimization. 

Nomenclature 

Ap microramp half angle 

a response equation coefficient 

c microramp chord length 

H incompressible shape factor 

h microramp height 

M Mach number 

Mb Mach number for the shock only baseline case 

s microramp spacing 

U streamwise velocity 

U∞ freestream streamwise velocity 

xp microramp centerline position 

 boundary layer thickness 

* boundary layer displacement thickness 

 boundary layer momentum thickness 

I. Introduction 

A supersonic inlet is used to decelerate and compress the flow before it enters the engine. In mixed 

compression inlets, a series of reflected oblique shocks decelerate the flow to around Mach 1.3 before a 

normal shock brings the flow to subsonic conditions. Where these shocks impact the wall shock boundary 

layer interactions (SBLIs) thicken and possibly separate the boundary layer. 

Bleed has become the standard means of reducing the effects of the boundary layer. Part of the low 

velocity flow in the boundary layer is removed, leaving a higher average flow velocity in the inlet. 

However, since air is being removed from the system, the inlet must be larger to provide the same total 

mass flow to the engine, and the bleed flow is typically dumped overboard, which adds significant drag. 

Microramp flow control devices (refs. 1 and 2) are another potential means of controlling boundary layers 
NASA/TM—2009-215630 2 

through SBLIs that are of interest as an alternative to bleed due to their low weight and mechanical 

simplicity. 

Microramp flow control devices have the potential to improve the flow downstream of an oblique 

shock by increasing the velocity near the wall. The counter-rotating vortices generated by the microramp 

flow control devices mix the higher momentum flow from the outer portion of the boundary layer—and 

for larger microramps the edge of the core flow—with the flow near the wall. This creates an increase in 

the near-wall velocity at the cost of creating a deficit farther from the wall. 

Vortex generators have been used in subsonic diffusers to avoid separation due to flow turning 

angles. In this test, the vortex generators were located in the supersonic flow upstream of the shock 

interaction to condition the flow prior to the interaction. Microramps also differ from traditional vortex 

generators in their size. While traditional vortex generators typically have heights on the order of the 

boundary layer thickness, microramp heights are on the order of 20 to 50 percent of the boundary layer 

thickness. 

A test was conducted in the 15- by 15-Centimeter Supersonic Wind Tunnel at NASA Glenn Research 

Center to test the effectiveness of microramp flow control devices on an oblique shock interaction. Fifteen 

microramp geometries were tested using design of experiment (DOE) techniques (ref. 3). The variables 

studied were the height, h; chord length, c; and spacing between ramps, s. 

Data was also taken for three baseline cases for comparison to the microramp performance. The 

baseline cases included the tunnel with no microramps and no shock, the tunnel with microramps and no 

shock, and the tunnel with a shock and no microramps. For all cases, boundary layer pitot pressure 

surveys were taken at 10 spanwise positions to examine the three-dimensional influence of the ramps. 

This paper discusses the results from the DOE analysis examining how the incompressible shape 

factor and boundary layer thickness vary throughout the test space and comparing various orders of 

modeling. The measured flowfields downstream of the oblique shock reflection are also examined to gain 

insight into the effects revealed by the DOE analysis. 

II. Test Setup 

A. 15- by 15-Centimeter Supersonic Wind Tunnel 

The 15- by 15-Centimeter Supersonic Wind Tunnel, shown in figure 1, is a continuous flow facility in 

the Engine Research Building at NASA Glenn Research Center. The inflow is connected to the central air 

supply which provides 40 psig (280 kPa) pressure at ambient temperature. This supply air is regulated by 

an upstream valve that is controlled to maintain a constant test section total pressure. The exhaust exits to 

the central altitude exhaust system, which can sustain pressures less than 2.0 psia (14 kPa). 

The test section has a constant area of 5.91 by 5.91 in. (15.0 by 15.0 cm) and has configurable insert 

sections on each of the four walls. Downstream of the test section the flow encounters a rearward facing 

step where the tunnel area expands to a 9.25 by 9.25 in. (23.5 by 23.5 cm) section. 

The tunnel Mach 2.0 nozzle block was used for this test. The inlet total pressure was set to give a 

Reynolds number of 4.00E6/ft (13.1E6/m). During the test the Reynolds number was monitored so that 

the measured value was held within 0.02E6/ft (0.07E6/m). A shock generator plate was mounted on the 

removable sidewalls to provide an oblique shock at a nominal incidence angle of 8.5°. An actuation 

system in the downstream expanded section allowed the tunnel to be started with the plate at a lower 

angle. Because of error in the positioning system for the shock generator plate, the angle was measured 

with an inclinometer after each run. Based on the measurements, the mean shock incidence angle during 

the testing was 8.46° with a standard deviation of 0.03°. 

The layout of the oblique shock in the tunnel can be seen in figure 2. The tunnel centerline was 

defined as z = 0 cm, and the inviscid shock impingement was selected as x = 0 cm. The microramps were 

inserted onto the tunnel wall in the supersonic flow upstream of the shock. The microramp centerline was 

positioned at x = –13 cm. 
NASA/TM—2009-215630 3 

B. Microramps 

The microramps were positioned with their centerline at xp = –13 cm. Figure 3 shows the microramps 

geometry variables. The height, h; the spacing, s; and the chord length, c, were varied. The microramp 

half-angle, Ap, was held constant at 24°. The heights studied were 3, 4, and 5 mm. The spacings were 

25, 30, and 35 mm, and the chord lengths were 12, 18, and 24 mm. Within these ranges DOE 

methodology was used to select the specific microramp geometry configurations to test. Fifteen 

configurations were built and tested as shown in figure 4. To reduce the effects of corner interactions on 

the measurements, an array of three microramps was centered in the tunnel with measurements taken 

from z = –s/2 to s/2 across the center microramp. A picture of three of the microramp inserts that were 

tested is shown in figure 5. 

C. Instrumentation and Data Systems 

The primary measurement plane was located x = 4 cm for all cases tested in which the oblique shock 

was present. This location was chosen to avoid influence of the expansion fan from the back of the shock 

generator plate on the measurements. A remotely actuated instrumentation arm capable of translation in 

the y- and z-directions was used to translate a pitot probe to collect boundary layer profiles over 

10 spanwise (z) locations and 30 transverse (y) locations. The pitot probe tip was flattened to allow 

measurements near the wall. The probing pattern is shown in figure 6 with each intersection representing 

a measurement point. Since symmetry is expected about z = 0 cm (in line with the microramp tip), six 

equally spaced profiles were taken at positive z-values, one at z = 0 cm, and only three at negative 

z-values to confirm symmetry. A total of 25 static pressure taps were arrayed on the tunnel wall as shown 

in figure 7. Steady state pressure values were supplied to ESCORT, the NASA Glenn steady state data 

acquisition system, as acquired by the pressure measurement system. 

III. Design of Experiments 

The outcome of a DOE analysis is a predicted response surface. For this experiment the response 

variables chosen were the boundary layer thickness and the incompressible shape factor. The predicted 

response surface is defined by an equation that describes how the response variable changes as a function 

of the factor variables (in this case, s, h, and c) within the design space. The response surface equation can 

be used to estimate the value of the response variable at configurations that were not tested. 

The boundary layer thickness, , was selected as a response parameter because it provides 

information on the extent to which the vortex impacts the core flow. The incompressible shape factor, H, 

was chosen primarily because it has been used to quantify improvements in boundary layer health for 

bleed flows (ref. 4). The incompressible shape factor is typically used instead of the compressible form 

even in compressible flow because it is independent of Mach number. A flat plate turbulent boundary 

layer has an incompressible shape factor of approximately 1.3 at all Mach numbers, and a boundary layer 

near separation has an incompressible shape factor of about 2.7 (ref. 5). 

The values of the factor variable that were held constant were determined through a DOE screening 

study. The purpose of the screening study was to determine the best size, geometry, location and 

orientation of the micro-ramp actuactors and to set the range of the factor variables which should be 

studied in the DOE itself. In the screening DOE study, there were actually 5 independent factor (design) 

variables considered. Using a Main Effects DOE strategy, there were 6 CFD cases run in the screening 

process. The results of the screening study led to the selection of three factor variables to be included in 

the current effort and provided the best overall ranges for the selected factor variables. 

To test every combination of the three factor variables at the three selected levels, 27 geometries 

would be needed. DOE techniques were used to select 15 of those cases comprising a face-centered 

central composite design, which provides the first- and second-order effects of each variable and the firstorder interactions. Within these 15 configurations, three other levels of DOE designs are contained (main 

effects, D-optimal, and full factorial). 
NASA/TM—2009-215630 4 

A. Main Effects Design 

A main effects design for three factor variables contains only four configurations and allows the 

estimation of the first-order variable effects. The design is termed saturated because all of the data points 

are used to calculate the response surface coefficients with none left over for error estimation. For the 

main effects design, the response equation for the incompressible shape factor is 

H a a s a h a c  0  1  2  3 (1) 

where a0, a1, a2, and a3 are coefficients calculated to fit the measured data points. The equation for the 

boundary layer thickness has the same form. Main effects designs are useful when very few test cases can 

be run, only linear responses to the variable are expected with no interaction between variable, or for 

screening many variables with minimal test cases. 

B. D-optimal Design 

The next higher order design is a D-optimal design, which allows for estimation of the first-order 

effects and chosen first-order variable interactions. Choosing which interactions to include requires some 

foresight, which in this case was gained by prior CFD calculations. The s-h and h-c interactions were 

selected, requiring a total of 6 configurations: the four main effects configurations plus two additional 

ones. A D-optimal design may or may not be saturated depending on which interactions are found to be 

significant during analysis. If any of the selected interactions proves to not be statistically significant, 

those terms can be excluded from the model and an error estimate can be made. For the selected 

D-optimal design, the response equation for the incompressible shape factor is 

H a a s a h a c a sh a hc  0  1  2  3  12  23 (2) 

The equation for the boundary layer thickness has the same form. D-optimal designs are useful to limit 

the required number of test cases when some information or insight is available to guide the selection of 

interactions to include in the analysis. 

C. Full Factorial Design 

A full factorial design allows for estimation of the first-order effects and all first-order interactions. A 

full factorial design is not saturated because there are 8 configurations tested and only 7 coefficients to 

calculate. Even if all interactions are found to be statistically significant, at least one data point remains 

for error estimation. For the full factorial design, the response equation for the incompressible shape 

factor is 

H a a s a h a c a sh a hc a sc  0  1  2  3  12  23  13 (3) 

The equation for the boundary layer thickness has the same form. 

D. Central Composite Design 

All of the 15 configurations taken together comprise a face centered central composite design. This 

design allows for estimation of first- and second-order effects and all first-order interactions, requiring the 

estimation of 9 coefficients. For the central composite design, the response equation for the 

incompressible shape factor is 

2

33

2

22

2

0 1 2 3 12 23 13 11 H  a  a s  a h  a c  a sh  a hc  a sc  a s  a h  a c (4) 

The equation for the boundary layer thickness has the same form. 
NASA/TM—2009-215630 5 

IV. Results 

A. Baseline Cases 

Three baseline configurations were tested as part of this effort (1) the tunnel with no microramps and 

no shock, (2) the tunnel with microramps and no shock, and (3) the tunnel with a shock and no 

microramps. At each measured x-position for the baseline cases, table 1 gives the span-averaged 

boundary layer parameters: the boundary layer thickness, ; the compressible displacement thickness, *; 

the compressible momentum thickness, ; and the incompressible shape factor, H. 

The empty tunnel configuration provides information regarding the boundary layer where the 

microramps were inserted. Figure 8 shows contour plots of the Mach number, M, at the microramp 

insertion plane (x = –13 cm) and the measurement plane (x = 4 cm). With the Mach 2.0 nozzle block 

installed in the tunnel, the measured Mach number at the boundary layer edge was M = 1.96. A row of 

11 spanwise static pressure taps was located at x = 4 cm. For measurements at that position, the wall static 

pressure used in the Mach number calculation was an average of the nearest taps for points taken when 

the probe was away from the wall. For profiles at other positions, a single static pressure tap on the tunnel 

centerline was available at each position for the Mach number calculation. 

Figure 9 shows profiles at x = –13 cm and x = 4 cm of the velocity ratio, U/U∞, where U∞ is the 

velocity at the edge of the boundary layer. The data at x = –13 cm shows a boundary layer thickness of 

1.14 cm with the edge of the boundary layer defined at U/U∞ = 0.95. This gives a microramp height 26.3, 

35.0, and 43.7 percent of the boundary layer thickness for the 3, 4, and 5 mm microramps, respectively. 

The incompressible shape factor, H = 1.32, for both positions indicates a typical flat plate turbulent 

boundary layer. Figure 10 shows how the boundary layer thickness varies in the spanwise direction. The 

data from the negative z locations is plotted as the absolute value of the z coordinate and indicated by the 

red crosses. This was done to make any asymmetries in the flow easier to identify. 

For the configuration with microramps and no shock the microramp insert with microramps of 

s = 25 mm, h = 3 mm, and c = 12 mm was tested. This configuration provides insight into the 

development of the vortices. Figure 11 shows contour plots of the Mach number, M, at planes 

x = –8, –4, 0, and 4 cm. Moving downstream, the region of influence of the vortex rises. Figure 12 shows 

the velocity ratio profile at z = 0 cm for the same four x-planes downstream of the microramps. Figure 13 

shows how the boundary layer thickness varies in the spanwise direction. As the vortex develops, the 

boundary layer is thicker in line with the microramp tip (z = 0 cm) and thins in the region between the 

ramps. 

The Mach number contours for the configuration with the oblique shock and no microramps are 

shown in figure 14 and provide a direct comparison to the results that will be shown in the following 

section. Downstream of the reflected shock the edge Mach number is reduced to M = 1.43. The velocity 

ratio profile at z = 0 cm is shown in figure 15. At the x = 4 cm measurement plane the shock increases the 

boundary layer thickness to 1.40 cm compared to 1.30 cm for the baseline with no shock. Also, the 

incompressible shape factor increases to H = 1.75 compared to H = 1.32 for the no shock case. Figure 16 

shows how the boundary layer thickness varies in the spanwise direction for the oblique shock case. 

B. DOE Response 

Response surfaces were created to model the variation of the boundary layer thickness and 

incompressible shape factor within the design space. The span-averaged boundary layer parameters for all 

configurations used in the analysis are shown in table 2. Coefficients were calculated based on each of the 

four orders of design described in section III. The resulting coefficients are shown in tables 3 and 4 for the 

boundary layer thickness and incompressible shape factor, respectively. Any coefficients not listed in the 

table were zero for all designs. 
NASA/TM—2009-215630 6 

Figures 17 to 24 show contours for these equations on planes at the edge of the design space. The 

results for the main effects (figs. 17 and 18) and D-optimal (figs. 19 and 20) designs are very similar. The 

effects of the interactions and second-order terms can be seen in the full factorial (figs. 21 and 22) and 

central composite (figs. 23 and 24), respectively. The second-order effects are particularly evident in the 

curved boundary layer thickness contours in figure 23. Comparing the boundary layer thickness and 

incompressible shape factor, the quantities minimize in opposite corners of the design space. 

The result of using each of the design orders to compute an optimal microramp configuration based 

on minimizing the incompressible shape factor is shown in table 5. For each of the cases, the minimum 

occurs at or near s = 25 mm, h = 5 mm, c = 24 mm. The minimum values for incompressible shape factor 

agree for all orders of design. Note that the value for the main effects experiment is exactly the measured 

value at that point. This is expected, since four points are used to calculate four coefficients. The last two 

columns of the table show the range of the 95 percent confidence interval, which indicates the range in 

which the true value of the incompressible shape factor is expected to fall. For the main effects design, no 

calculation on the confidence interval can be made because the design is saturated. Increasing the number 

of available data points decreases the range of the confidence interval indicating a more accurate 

estimation of the value. 

C. Microramp Configurations 

For each of the 15 microramp configurations tested, the Mach number contours downstream of the 

shock reflection are shown in figure 25. Increasing the height or chord length creates a stronger vortex 

that has influence extending farther into the core flow. This agrees with the DOE response surface 

showing increased boundary layer thickness for microramps with a large height and chord compared to 

smaller microramps. Figure 26 shows the contours of M-Mb, where Mb is Mach number for the baseline 

oblique shock only case, similar to figures shown for previous microramp research (ref. 6). This 

emphasizes the changes in the flow caused by the microramps. The M-Mb = 0 contours are marked in the 

figure. In these plots the velocity deficit caused by the microramp is apparent. The magnitude of the 

deficit increases with increasing height and chord, as the stronger vortices carry more of the higher 

momentum fluid near the wall. This increased mixing accounts for the improvements in incompressible 

shape factor for large microramps. Even though the velocity deficit increases, the corresponding increases 

in the near wall velocity outweigh this effect in the calculation of the shape factor. Figure 27 shows how 

the boundary layer thickness varies in the spanwise direction. As was true for the microramp 

configuration without the shock, for these cases the boundary layer is thicker in line with the microramp 

tip and thins in the region between the ramps. Comparing the points for positive and negative z-positions, 

the symmetry was generally quite good. 

Conclusion 

Design of experiments techniques are well suited to evaluating the effectiveness of microramps. The 

response surface equation for microramps is expected to be continuous. DOE also allows the many 

potential variables to study to be dealt with efficiently in a controlled manner. Different orders of DOE 

designs provide different benefits for microramp evaluation. The main effects design allows very few data 

points to be used to estimate the response surface, but no error estimate is available. Using a main effects 

design, the optimal configuration based on a single variable optimization will always occur in the corner 

of the design space due to the form of the response equation. For the variables and ranges in the current 

study, the main effects design was found to provide a reasonable estimate of the response variable trends. 

The D-optimal design still requires very few configurations and can have points for error estimation if not 

all chosen interactions are statistically significant. The range of the confidence interval is fairly large for 

the D-optimal design, but may be sufficient for some purposes. The factorial design required twice the 

points of a main effects design, but greatly improves the confidence interval. For evaluation of microramp 

configurations, the factorial design provides a balance of accuracy and test efficiency that makes it a 
NASA/TM—2009-215630 7 

promising model for configuration specific design. The central composite design requires a significantly 

larger test matrix for minimal improvement of the estimates of the response variables in this study. For 

other variables or ranges where second order effects are important, moving to a central composite design 

may be necessary in order to accurately predict the effects of the factor variables. 

The optimum value for shape factor according to each of the orders of DOE designs occurs for ramps 

with a large height and chord length and a close spacing relative to the design space. The minimum 

boundary layer thickness occurs at the opposite of all three geometric parameters. Looking at the 

flowfield measured downstream of the oblique shock reflection, microramps with small heights and chord 

lengths generate relatively weak vortices. Most of the mixing in this case occurs within the boundary 

layer, allowing minimal increase in boundary layer thickness, but providing little benefit to the near wall 

flow. For larger microramps with stronger vortices, more flow is pulled into the near wall region, 

including part of the core flow. This provides a greater benefit to the near wall flow leading to 

improvements in incompressible shape factor. For an inlet system, a combination of these and potentially 

additional parameters such as wall shear stress will likely need to be considered together to determine the 

optimal configuration of microramps for a given system. Work is currently planned that will look at the 

effects of microramps in a system with shocks and a subsonic diffuser to help answer the question at a 

system level. 

References 

1. Anderson B.H., Tinapple, J., Surber, L., “Optimal Control of Shock Wave Turbulent Boundary Layer 

Interactions Using Micro-Array Actuation,” AIAA–2006–3197, June 2006. 

2. Lin J.C., “Review of Research on Low-Profile Vortex Generators to Control Boundary-Layer 

Separation,” Progress in Aerospace Sciences, 2002. 

3. Box, G.E.P., Hunter, W.G., and Hunter, J.S., “Statistics for Experimenters,” John Wiley, New York. 

4. Fukuda, M.K., Hingst, W.G., Reshotko, E., “Control of Shock Wave-Boundary Layer Interactions by 

Bleed in Supersonic Mixed Compression Inlets,” NASA CR-2595, 1975. 

5. Castillo, L., Wang, X., George, W.K., “Separation Criterion for Turbulent Boundary Layers Via 

Similarity Analysis,” Journal of Fluids Engineering, vol. 126, p. 297, 2004. 

6. Ford, C.W.P., Babinsky, H., “Micro-Ramp Control for Oblique Shock Wave/Boundary Layer 

Interactions,” AIAA–2007–4115, June 2007. 

TABLE 1.—SPAN-AVERAGED BOUNDARY LAYER PARAMETERS 

FOR BASELINE CONFIGURATIONS 

 , 

cm 

*, 

cm 

, 

cm 

H 

x = –13 cm none 1.142 0.283 0.100 1.316 

x = –8 cm 

none 1.196 0.292 0.104 1.314 

microramps 1.188 0.291 0.117 1.338 

x = –4 cm 

none 1.217 0.301 0.106 1.321 

microramps 1.325 0.324 0.108 1.303 

x = 0 cm 

none 1.350 0.342 0.116 1.303 

microramps 1.358 0.347 0.120 1.297 

x = 4 cm 

none 1.297 0.326 0.118 1.322 

microramps 1.333 0.337 0.124 1.322 

shock 1.402 0.516 0.190 1.746 
NASA/TM—2009-215630 8 

TABLE 2.—SPAN-AVERAGED BOUNDARY LAYER PARAMETERS 

AT x = 4 cm FOR ALL CONFIGURATIONS 

s, 

mm 

h, 

mm 

c, 

mm 

, 

cm 

*, 

cm 

, 

cm 

H 

25 3 12 1.438 0.527 0.197 1.724 

35 3 12 1.448 0.530 0.196 1.731 

25 5 12 1.651 0.552 0.213 1.666 

35 5 12 1.587 0.538 0.206 1.679 

25 3 24 1.522 0.537 0.205 1.690 

35 3 24 1.498 0.531 0.201 1.701 

25 5 24 1.726 0.556 0.226 1.617 

35 5 24 1.665 0.545 0.217 1.631 

25 4 18 1.602 0.538 0.210 1.639 

35 4 18 1.538 0.526 0.202 1.663 

30 3 18 1.452 0.530 0.198 1.720 

30 5 18 1.548 0.509 0.204 1.627 

30 4 12 1.511 0.527 0.200 1.678 

30 4 24 1.590 0.535 0.209 1.644 

30 4 18 1.571 0.528 0.204 1.653 

TABLE 3.—DOE MODEL COEFFICIENTS FOR BOUNDARY LAYER THICKNESS, 

a0 a1 a2 a3 a12 a11

Main effects 1.156E+00 –4.010E-03 9.440E-02 8.275E-03 ------------- ------------- 

D-optimal 1.201E+00 –3.298E-03 8.549E-02 6.790E-03 0.000E+00 ------------- 

Factorial 8.696E-01 7.603E-03 1.736E-01 5.965E-03 –2.773E-03 ------------- 

Central composite 2.412E+00 –8.358E-02 8.187E-02 6.087E-03 0.000E+00 1.325E-03 

TABLE 4.—DOE MODEL COEFFICIENTS FOR INCOMPRESSIBLE SHAPE FACTOR, H

a0 a1 a2 a3 a23 a22

Main effects 1.815E+00 1.935E-03 –3.223E-02 –3.538E-03 ------------- ------------- 

D-optimal 1.819E+00 1.500E-03 –3.129E-02 –3.381E-03 0.000E+00 ------------- 

Factorial 1.784E+00 1.128E-03 –1.948E-02 –6.396E-04 –6.729E-04 ------------- 

Central composite 2.179E+00 1.384E-03 –2.187E-01 –3.240E-03 0.000E+00 2.301E-02 

TABLE 5.—OPTIMIZATION RESULTS FOR THE FOUR LEVELS OF DOE DESIGNS 

s, 

mm 

h, 

mm 

c, 

mm 

Hmin 95 percent

CI low 

95 percent 

CI high 

Main effects 25 5 24 1.617 ----- ----- 

D-optimal 25 5 24 1.61888 1.59 1.64 

Factorial 25 5 24 1.61856 1.61 1.62 

Central composite 25.51 4.72 23.99 1.61688 1.61 1.63 
NASA/TM—2009-215630 9 

Figure 1.—The 15- by 15-Centimeter Supersonic Wind Tunnel 

at NASA Glenn Research Center. 

Figure 2.—Layout of the test in the tunnel. Microramp centerline was positioned at x = –13 cm. 
NASA/TM—2009-215630 10 

Figure 3.—Microramp geometry parameters shown in views. (a) A top view. (b) A side view. 

Figure 4.—Face-centered central composite DOE 

design. The circles indicate variable combinations 

that were tested. 

Figure 5.—Picture of three microramp inserts. 
NASA/TM—2009-215630 11 

Figure 6.—Representation of the measurement plane. Each intersection represents 

a measurement point. 

Figure 7.—Static pressure tap distribution with tap locations marked by “x”. 

Figure 8.—Contour plots of Mach number, M, for the case with no shock and no microramps. 

(a) x = –13 cm. (b) x = 4 cm. 
NASA/TM—2009-215630 12 

Figure 9.—Profiles of the velocity ratio, U/U∞, on the tunnel centerline for the case with no shock and 

no microramps. (a) x = –13 cm. (b) x = 4 cm. 

Figure 10.—Spanwise boundary layer thickness, , variation with negative z values mirrored 

across the y-axis for the case with no shock and no microramps. (a) x = –13 cm. (b) x = 4 cm. 
NASA/TM—2009-215630 13 

Figure 11.—Contour plots of Mach number, M, for the case with no shock and 

baseline microramps. (a) x = –8 cm. (b) x = –4 cm. (c) x = 0 cm. (d) x = 4 cm. 
NASA/TM—2009-215630 14 

Figure 12.—Profiles of the velocity ratio, U/U∞, on the tunnel centerline for the case with no shock and 

baseline microramps. (a) x = –8 cm. (b) x = –4 cm. (c) x = 0 cm. (d) x = 4 cm. 
NASA/TM—2009-215630 15 

Figure 13.—Spanwise boundary layer thickness, , variation with negative 

z values mirrored across the y-axis for the case with no shock and baseline microramps. (a) x = –8 cm. (b) x = –4 cm. (c) x = 0 cm. (d) x = 4 cm. 

Figure 14.—Contour plots of Mach number, M, for the 

case with an oblique shock and no microramps at 

x = 4 cm. 
NASA/TM—2009-215630 16 

Figure 15.—Profiles of the velocity ratio, U/U∞, on the 

tunnel centerline for the case with an oblique shock 

and no microramps at x = 4 cm. 

Figure 16.—Spanwise boundary layer thickness, , 

variation with negative z values mirrored across 

the y-axis for the case with an oblique shock 

and no microramps at x = 4 cm. 

Figure 17.—Main effects DOE model for boundary layer thickness, . Levels of  are shown as 

contours. (a) s = 35 mm, h = 3 mm, and c = 12 mm surfaces. (b) s = 25 mm, h = 5 mm, 

and c = 24 mm surfaces. 
NASA/TM—2009-215630 17 

 

Figure 18.—Main effects DOE model for incompressible shape factor, H. Levels of H are shown as 

contours. (a) s = 35 mm, h = 3 mm, and c = 12 mm surfaces. (b) s = 25 mm, h = 5 mm, 

and c = 24 mm surfaces. 

Figure 19.—D-optimal DOE model for boundary layer thickness, . Levels of  are shown as contours. 

(a) s = 35 mm, h = 3 mm, and c = 12 mm surfaces. (b) s = 25 mm, h = 5 mm, and c = 24 mm surfaces. 

Figure 20.—D-optimal DOE model for incompressible shape factor, H. Levels of H are shown as contours. 

(a) s = 35 mm, h = 3 mm, and c = 12 mm surfaces. (b) s = 25 mm, h = 5 mm, and c = 24 mm surfaces. 
NASA/TM—2009-215630 18 

Figure 21.—Full Factorial DOE model for boundary layer thickness, . Levels of  are shown as contours. 

(a) s = 35 mm, h = 3 mm, and c = 12 mm surfaces. (b) s = 25 mm, h = 5 mm, and c = 24 mm surfaces. 

 

Figure 22.—Full factorial DOE model for incompressible shape factor, H. Levels of H are shown as 

contours. (a) s = 35 mm, h = 3 mm, and c = 12 mm surfaces. (b) s = 25 mm, h = 5 mm, and 

c = 24 mm surfaces. 

Figure 23.—Central composite DOE model for boundary layer thickness, . Levels of  are shown as 

contours. (a) s = 35 mm, h = 3 mm, and c = 12 mm surfaces. (b) s = 25 mm, h = 5 mm, and 

c = 24 mm surfaces. 

 
NASA/TM—2009-215630 19 

Figure 24.—Central composite DOE model for incompressible shape factor, H. Levels of H are shown as contours. 

(a) s = 35 mm, h = 3 mm, and c = 12 mm surfaces. (b) s = 25 mm, h = 5 mm, and c = 24 mm surfaces. 

Figure 25.—Contour plots of Mach number, M, at x = 4 cm for microramp spacing. (a) s = 25 mm. (b) s = 30 mm. 

(c) s = 35 mm. 
NASA/TM—2009-215630 20 

Figure 25.—Continued. 
NASA/TM—2009-215630 21 

Figure 25.—Concluded. 
NASA/TM—2009-215630 22 

Figure 26.—Contour plots of relative Mach number, M-Mb, at x = 4 cm for microramp spacing. (a) s = 25 mm. 

(b) s = 30 mm. (c) s = 35 mm. Contour lines at the M-Mb = 0 level are marked with “0”. 
NASA/TM—2009-215630 23 

Figure 26.—Continued. 

 
NASA/TM—2009-215630 24 

Figure 26.—Concluded. 
NASA/TM—2009-215630 25 

Figure 27.—Spanwise boundary layer thickness, , variation with negative z values mirrored across the y-axis for 

microramp spacing. (a) s = 25 mm. (b) s = 30 mm. (c) s = 35 mm. 
NASA/TM—2009-215630 26 

Figure 27.—Continued. 
NASA/TM—2009-215630 27 

Figure 27.—Concluded.
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1. REPORT DATE (DD-MM-YYYY)

01-11-2009 

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Technical Memorandum 

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4. TITLE AND SUBTITLE

Experimental Investigation of the Application of Microramp Flow Control to an Oblique 

Shock Interaction 

5a. CONTRACT NUMBER

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5c. PROGRAM ELEMENT NUMBER

6. AUTHOR(S)

Hirt, Stefanie, M.; Anderson, Bernhard, H. 

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WBS 984754.02.07.03.13.02 

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National Aeronautics and Space Administration 

John H. Glenn Research Center at Lewis Field 

Cleveland, Ohio 44135-3191 

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NASA 

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This publication is available from the NASA Center for AeroSpace Information, 443-757-5802

13. SUPPLEMENTARY NOTES

14. ABSTRACT

The effectiveness of microramp flow control devices in controlling an oblique shock interaction was tested in the 15- by 15-Centimeter 

Supersonic Wind Tunnel at NASA Glenn Research Center. Fifteen microramp geometries were tested varying the height, chord length, and 

spacing between ramps. Measurements of the boundary layer properties downstream of the shock reflection were analyzed using design of 

experiments methods. Results from main effects, D-optimal, full factorial, and central composite designs were compared. The designs 

provided consistent results for a single variable optimization.

15. SUBJECT TERMS

Compressible boundary layers; Boundary layer control; Vortex generators; Oblique shock waves 

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