Document
NASA/TM-2001-210390
Wind-Tunnel Investigations of
Blunt-Body Drag Reduction Using
Forebody Surface Roughness
Stephen A. Whitmore NASA Dryden Flight Research Center Edwards, California Stephanie Sprague University of Kansas Lawrence, Kansas Jonathan W. Naughton University of Wyoming Laramie, Wyoming January 2001 The NASA STI Program Office...in Profile CONFERENCE PUBLICATION.
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NAS A/TM-2001-210390
Wind-Tunnel Investigations of
Blunt-Body Drag Reduction Using
Forebody Surface Roughness
Stephen A. Whitmore NASA Dryden Flight Research Center Edwards, California Stephanie Sprague University of Kansas Lawrence, Kansas Jonathan W. Naughton Universi_' of Wyoming Laramie Wyoming National Aeronautics and Space Administration Dryden Flight Research Center Edwards, California 93523-0273 January 2001
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WIND-TUNNEL INVESTIGATIONS OF BLUNT-BODY
DRAG REDUCTION USING FOREBODY SURFACE ROUGHNESS
Stephen A. Whitmore* NASA Dryden Flight Research Center Edwards, California Stephanie Sprague t University of Kansas Lawrence, Kansas Jonathan W. Naughton ¢ University of Wyoming Laramie, Wyoming reduction of approximately 15 percent when the drag Abstract optimum is reached. When this drag reduction is scaled to the X-33 base area, drag savings approaching This paper presents results of wind-tunnel tests that 45,000 N (10,000 lbf) can be realized.
demonstrate a novel drag reduction technique for blunt- based vehicles. For these tests, the forebody roughness Nomenclature of a blunt-based mcxlel was modified using micromachined surface overlays. As forebody Acronyms roughness increases, txmndary layer at the model aft CFD thickens and reduces the shearing effect of external flow computational fluid dynamics on the separated flow behind the base region, resulting LASRE Linear Aerospike SR-71 Experiment in reduced base drag. For vehicle configurations with large base drag, existing data predict that a small Symbols increment in foreN_dy friction drag will result in a A slope parameter relatively large decrease in base drag. If the added increment in forebody skin drag is optimized with forebody pressure distribution curve-fit ao, al,a2, a3 respect to base drag. reducing the total drag of the coefficients configuration is i:x_ssible. The wind-tunnel tests results B law-of-the-wake bias parameter conclusively demtmstrate the existence of a forebody drag-base drag t_plimal point. The data demonstrate that b model span, cm the base drag coefficient corresponding to the drag minimum lies betv, een 0225 and 0.275, referenced to base pressure distribution curve-fit b O, b 2. b 4 coefficients the base area. Most importantly, the data show a drag C intercept parameter _Aerospace Engineer. As_,oclate Fellow. AIAA.
drag coefficient CD 'Student Intern. Department of Aerospace Engineering, Student Member. AIAA.
base pressure drag coefficient C D t,,,,,, :IProfessor. Department of Mechanical Engineering. Senior Member. AIAA forebody pressure drag coefficient COl,,, rl,¢,,l_ Copyright © 2001 bv the American Institute of Aeronautics and zero-lift free-stream total drag coefficient Astronautics. Inc. No copyright is asserted in the United Stales under CD o Title 17. tIS Code The [IS Government has a royalty-free license "viscous" forebody drag coefficient CF to exercise all rights under the copyright claimed herein for Governmental purposcs All other rights are reserved by the copyright local skin-friction coefficient owner.
c f, American Institute of Aeronautics and Astronautics axial location within wind tunnel, cm x pressure coefficient Cp ith scalar component of independent average base pressure coefficient x i variable vector average forebody pressure coefficient C P fl, rebt, d_ lateral coordinate (for wake, boundary Y D' section drag, N/m layer, or base area), cm dP e + longitudinal pressure gradient on dx nondimensional boundary-layer Y model, kPa/m coordinate dO longitudinal gradient of the boundary- Z dx output vector layer momentum thickness z( meas ) measurement vector E[.]
expectation operator ith scalar component of measurement z i H wake or boundary-layer shape parameter, vector H = 8/0
ff Clauser pressure gradient parameter
base height, cm h base F friction velocity i measurement index local curve-fit error for velocity L model length, cm k--_ J distribution number of repeated pressure scans N trial_ A0 first variation of momentum I! thickness, cm number of data points local static pressure, kPa gradient with respect to 8 P V 6 free-stream static pressure ratio in wind wake half-width, local boundary-layer p,, ......(x) tunnel thickness, cm free-stream static pressure ahead of initial estimate of wake half-width or P_ wind-tunnel model, kPa boundary-layer thickness dynamic pressure, kPa 8* boundary-layer displacement thickness, cm dynamic pressure ratio in wind tunnel _] ratio( X ) wake displacement thickness, cm free-stream dynamic pressure ahead of wind-tunnel model, kPa dummy integration variable Reynolds number based on model Re L forebody surface incidence angle, deg length L wake momentum thickness, cm Reynolds number based on local axial Re_ free-stream momentum thickness, cm coordinate x K law-of-the-wake slope parameter t" leading-edge radius, cm equivalent sand-grain roughness of Ks velocity at the edge of the wake or U_, surface, cm boundary layer, m/sec K-E energy dissipation free-stream velocity ahead of the Uoo wind-tunnel model, m/see A Dirac delta function minimum velocity in wake velocity Ilmm Z roughness overlay "land" thickness, cm profile, m/see sample mean g local velocity distribution (in wake or .(>9 dummy integration variable boundary layer), m/see + F1 wake parameter II nondimensional boundary-layer velocity air density, kglcm 3 X P independent variable vector '9 American Institute of Aeronautics and Astronautics Z and make the autonomous reentry and landing task less roughness overlay slot thickness, cm difficult.
curve-fit squared error for base ports abase An early body of experimental work conducted in the curve-fit squared error for side ports aside late 1950"s and early 1960's by Hoerner 2 offers a sample variance for pressure port _0 potential solution to the reusable launch vehicle (RLV) incidence angle 0 base drag problem. For blunt-based objects with heavily separated base areas, a correlation between the base T, roughness overlay shim thickness, cm 9 pressure drag and the "viscous" forebody drag has been mean-square error in base drag demonstrated. This paper presents the results of a series _lt'C Dm.e coefficient estimate of wind-tunnel experiments that exploit this forebody- to-base drag relationship to reduce the overall drag of a mean-square error in forebody pressure _2CDforebod) simple blunt-based configuration by adding precise coefficient levels of roughness to the forebody.
mean-square error in viscous forebody tIJ2C D 0 drag coefficient estimate Background mean-square error in viscous forebody q_ 2 Cr For blunt-based objects whose base areas are heavily drag coefficient estimate separated, a clear relationship between base drag and _2A0 mean-square error in momentum the viscous forebody drag has been demonstrated by thickness estimate, cm 2 Hoerner. 2 In this paper, the viscous forebody drag is defined as the axial projection of the integral of all mean-square error in velocity profile L_I AII / U e curve fit, cm 2 viscous forces acting on the vehicle forebody. These viscous forces include surface skin friction, frictional Superscripts, Subscripts, and Mathematical Operators effects of forebody flow separation, and parasite drag.
Axial forces resulting from the forebody pressure i measurement index distribution are considered separately from the viscous j pressure port index forebody drag in this paper.
(k) iteration index Figure 1 shows subsonic drag data taken from ^ Hoerner for two- and three-dimensional projectiles. The estimated parameter three-dimensional curve fit of the data was originally A variational operator published by Hoerner. 2 The two-dimensional curve fit is a new fit of Hoerner's original data. The authors of this T vector transpose paper believe that this new fit is a better representation Introduction of the base drag data.
An important feature is the trend for decreasing base Designs advocated for the current generation of drag as the viscous forebody drag increases (fig. 1). This reusable launch or space-access vehicles are derived from variations of the original lifting-body concept. 1 base drag reduction is a result of boundary-layer effects at the vehicle base. The surface boundary layer acts as For many reasons, these designs all have large base an insulator between the external flow and the separated areas compared with those of conventional aircraft. For air behind the base. As the forebody drag increases, the example, the large base areas of the X-33 and Venture boundary-layer thickness at the forebody aft also Star configurations are required to accommodate the increases. This increase reduces the effectiveness of the aerospike rocket engines. The base area is highly "jet pump" caused by the shearing of the external flow separated, resulting in large negative base pressure coefficients. Because of the large base-to-wetted-area on the separated flow behind the base region.
ratios of these vehicles, the base drag comprises the Vehicle configurations with large base drag majority of the overall vehicle drag. The resulting low coefficients lie on the steep portion of Hoerner's curve, lift-to-drag ratios result in very steep approach glide where a small increment in the forebody friction drag slopes. These steep approach angles present difficult should result in a relatively large decrease in the base energy management tasks for autonomous reentry drag. Conceptually, if the added increment in viscous systems. Any decrease in base drag potentially can significantly improve the overall vehicle performance forebody drag is optimized with respect to the base American Institute of Aeronautics and Astronautics drag, then reducing the overall drag of the configuration The Linear Aerospike SR-71 Experiment may be possible. Figure 2 shows this drag optimization, based on curve fits of Hoerner's data. These data clearly Flight test results from the LASRE drag reduction experiment 6 provide some incomplete validation of the illustrate the concept of the "drag bucket."
above hypothesis. The LASRE was a flight test of an approximately 20-percent half-span model of an X-33 Another important feature of the data shown in figures forebody model mounted on top of the NASA SR-71 1 and 2 is that for the same viscous forebody drag, two- aircraft. The LASRE sought to reduce base drag by dimensional objects tend to have a significantly larger adding a small amount of surface roughness to the base drag than three-dimensional objects. These drag model forebody. The model was instrumented with load differences result from periodic shedding in the base cells that allowed a six-degree-of-freedom measurement region where avon Karman vortex street structure 3' 4 of of forces and moments, and with surface pressure ports evenly spaced vortices of alternating strengths sets up that allowed the model forebody pressure and base drag within the wake. In general, the base flow around to be numerically integrated.
three-dimensional objects is characterized by very- broadband (frequency) flow disturbances; the periodic The LASRE verified that the base drag was reduced flow phenomenon is far less pronounced than for two- by as much as 15 percent; unfortunately, the overall drag of the configuration was not reduced. The methods for dimensional objects. The base pressure under applying the forebody sand-grain roughness were nonperiodic (three-dimensional) flow conditions is believed to be too crude to achieve an overall drag considerably higher (equating to lower base drag) than reduction. Further tests under a more controlled flow under similar conditions in a periodic (two-dimensional) environment were clearly required.
flow.
Wind-Tunnel Tests The ramifications of this two-dimensional-three- dimensional base drag difference become A series of low-speed, two-dimensional, wind-tunnel extremely important when one considers full-scale, tests was conducted to study the potential for high-Reynolds number flight vehicles. Saltzman, et al. 5 minimizing the total configuration drag using surface have compiled subsonic drag data from vehicles roughness increments. In these tests, a leading-edge configured for hypersonic flight. This compendium cylinder with a blunt afterbody was tested. The full- includes flight data for the X-15, M2-F1, M2-F3, scale flight data (figs. 3-4) demonstrate that the results X-24A, and X-24B vehicles; the Space Shuttle; and the of the two-dimensional tests should be generally Linear Aerospike SR-71 Experiment (LASRE). These applicable to large-scale, three-dimensional vehicles. In data are compared to the two- and three-dimensional fact, with regard to the comparisons shown in figure 3, mathematical models derived from Hoerner's data tests performed using two-dimensional models were believed to be more representative of the large-scale (fig. 3). The full-scale flight data clearly agree more flight vehicles than those performed with three- closely with the two-dimensional curve than the three- dimensional models. The series of tests had two primary dimensional one. For full-scale configurations, the flow objectives: appears to be locally two-dimensional and allows the trailing vortex street to become well-established.
1.
Test the hypothesis regarding forebody roughness Figure 4 shows direct visual proof of this assertion, as a in a systematic manner to conclusively periodic vortex structure is clearly visible trailing demonstrate existence of a viscous forebody drag- behind the M2-FI vehicle.
base drag optimum (the "drag bucket").
2, Establish a criterion for when tbrebody drag is The data shown in figures 1-3 imply that large-scale, suboptimal (that is. at what point does increasing blunt-based vehicles are quasi-two-dimensional, and forebody drag result in an overall drag reduction).
configurations with a base drag coefficient greater than approximately 0.30 (referenced to the base area) will lie Wind-Tunnel Model De_;cription on the left side of Hoerner's curve. These configurations may be considered to be suboptimal with respect to the Figure 5 shows a three-view drawing of the wind-tunnel model. The machined-aluminum model viscous forebody drag coefficient. Incrementally increasing the viscous forebody drag theoretically consists of a 2.54-cm-diameter (l-in.) cylindrical should lower the overall drag of the configuration. leading edge with a flat-sided afterbody 11.43-cm American Institute of Aeronautics and Astronautics (4.5-in.) long. Removable aluminum plates on the sides local total and static pressure ratios--referenced to the of the model allow various levels of surface roughness dynamic and static pressure ahead of the model--as a to be tested by interchanging the plates. The base-to- function of the axial position in the tunnel. Figure 8 wetted area of the model is approximately 10.7 percent. shows this calibration plot. At each pressure Figure 6 shows the model mounted in the wind tunnel. measurement location, the derived dynamic pressure was used to compute the local pressure coefficient.
The forebody roughness of the model was increased by bonding micromachined brass overlays to the side plates. Figure 5 shows a sample of this roughness p(x) - Psratio(x)p_] "screen" overlaid on the top view of the model. These Cp(x) = Zlr,,ti,,(x)Zioo (1) "screens" consist of a series of transverse bars with the shim (z), slot (E), and "land" (k) dimensions With the model mounted in the wind tunnel, a determining the roughness of the surface. Figure 7 maximum free-stream airspeed of approximately shows the geometric layout for these bar grid overlays.
28.0 m/sec (92 ft/sec) was achieved. Based on the model A single overlay geometry using lands and slots aligned length, this free-stream velocity translates to a Reynolds parallel to the direction of flow was also tested. Table 1 number (Re L ) of approximately 2.25 × 105. Tests were shows the geometries tested, and the equivalent surface also performed at airspeeds of approximately roughness (Ks) derived from empirical-fit formulae 14.6 m/sec (48 ft/sec). The corresponding Re L for these presented in Mills. 7 lower-speed tests was approximately 1.25 x 10 . The wind-tunnel turbulence intensity levels were sufficiently Table 1. Screen overlay roughness dimensions.
large that the model flow was turbulent beginning at the leading edge.
Configuration number _., cm Y. cm 7:. cm K_, cm Instrumentation 1 0.0000 0.0000 0.0000 0.0000" 2 0.0051 0.0051 0.0051 0.0163"* All test measurements were performed using only 3 0.0254 0.0381 0.0254 0.1143 pressure instrumentation. The methods used to interpret 4 0.0508 0.1016 0.0508 0.2896 the measurements are presented in the "Analysis Methods" section. The tunnel itself was instrumented 5 0,0508 0.2032 0,0508 0.4854 with series of static pressure taps along the side of the 6 @1016 0.2540 0.1016 0.6911 tunnel. Total (reference) pressure levels were sensed * Smooth model with a pitot probe placed five model lengths ahead of the ** Parallel bars model. A total of 16 pressure taps was distributed around the centerline of the model: 5 ports on the model forebody, 8 ports placed along the sides of the model, Wind-Tunnel Description and 3 ports placed on the model base. These port The model was tested in a low-speed wind tunnel at locations allowed body pressure forces to be accurately the NASA Dryden Flight Research Center (Edwards, integrated. Figure 5 shows the locations of the 16 model California). The ambient, open-cycle tunnel has a test pressure ports. Several leading-edge ports can be seen section approximately 10 by 25 cm (4 by 10 in.). An on the model mounted in the tunnel (fig. 6).
alternating current (A/C) motor uses a squirrel-cage fan located at the downstream end to pull air through the The total model drag coefficient was measured by tunnel. When the model was mounted in the tunnel test wake velocity profiles sensed using a traversing pitot- section, the total blockage was 10 percent. This level of static probe. Both local total and static pressures were blockage is considered high for traditional wind-tunnel sensed by this probe. The probe tip was placed 12.7 cm testing.
(5 in.) ali of the model base area. The wake probe tip diameter was approximately 0.025 cm. Similar momentum-defect measurements for skin friction were The primary effect of the blockage was to accelerate the flow around the model forebody, causing a rise in the performed at the model aft using a traversing dynamic pressure and a drop in the static pressure along boundary-layer pitot probe. For the boundary-layer the sides of the tunnel wall (outside of the tunnel wall profiles, only local total pressure was measured by the boundary layer). The dynamic pressure rise (static traversing probe. Local static pressure was assumed pressure drop) was taken into account by calibrating constant across the depth of the boundary layer.
American Instilule of Aeronautics and Aslronautics port was addressed a total of 100 times and these data Free-stream static pressure at the model base was sensed samples were averaged to minimize the effects of by a side port on the tunnel wail. The boundary-layer random sensor errors. The resulting zero readings were probe tip diameter was approximately 0.02 cm. Figure 6 written to an archival file for later use by postprocessing shows the wake and boundary-layer probes mounted in analysis algorithms.
the tunnel. The probe positions relative to the centerline of the model were measured using a digital micrometer.
Surface Pressure Scans The estimated accuracy of the digital positioning sensor was approximately 0.0025 cm (0.001 in.).
The pressure scans read data from the 16 model pressure ports as well as the total and static pressure All of the model, tunnel wall, and traversing probe levels in the tunnel. For each configuration tested--that pressure data were sensed with a highly accurate set of is, each different grid pattern or airspeed--the pressure digital (RS-422) scanning pressure modules. These data scans were repeated ten times. For each of the ten were recorded by a laptop computer using the serial port measurement sequences, the zeroing procedure was to perform individual channel addressing. Full-scale performed and the tunnel was activated and allowed to span of these differential pressure modules was stabilize. Typically, 100 individual data samples were ±2.490 kPa (__.52.0 Ibf/ft2). The manufacturer's accuracy averaged for each data run to minimize the effects of specifications for the differential pressure measurements random measurement errors and tunnel turbulence.
is _+0.05 percent of full scale, or approximately After ten pressure scans were taken for each ±0.00125 kPa (±0.026 Ibf/ft2). The differential pressure confguration, the data were converted to pressure transducers were referenced to the pitot probe placed coefficients by postprocessing algorithms and the approximately 64 cm (25 in.) ahead of the model. The pressure coefficients data were averaged. The standard reference pitot pressure was sensed with a highly deviation of the ten measurement sequences data was accurate absolute pressure manometer. The estimated used as a representation of the end-to-end accuracy of accuracy for the absolute reference pressure the measurement system. Typically the end-to-end measurement is approximately ±0.010 kPa pressure coefficient error varied between ±0.003 (±0.16 Ibf/ft2). The reference temperature was sensed and _+0.005.
externally to the tunnel using a type "'T'" thermocouple with an estimated accuracy of approximately Wake and Boundary-Layer Surveys ±0.5 °C (±0.9 °FL For the wake surveys, each data point consists of a Test Procedures pitot and a static-pressure measurement taken at a single lateral offset (y) from the model centerline. For the boundary-layer surveys, each data point consists of a The low dynamic pressure levels--less than 0.4788kPa (10 Ibf/ftz/--during this series of wind- pitot measurement taken at a lateral offset and a wall static pressure measurement. For each data point, 100 tunnel tests required that data be taken with great data samples were averaged to minimize the effects of consistency to minimize the effects of experimental random measurement errors and tunnel turbulence. To procedure on the overall errors. For all test conditions completely define the wake profile, approximately 200 and configurations, the transducers were zeroed prior to y-position data points were required. For early tests in testing, and the model angle of attack was set to zero by the tunnel, the entire wake profile was measured. These comparison of the left and right surface m_xtel data were so symmetrically distributed that as a time- pressures. To set the zero angle-of-attack position, the saving measure, later tests only surveyed one-half of the model position _a.', perturbed until the left and right wake profile.
surface pressure cur_es lay directly on top of each other.
Because of the large number of data samples Transducer Zer_ing (approximately 20,000) required to define the wake for each measurement configuration, completing each of Although the electronically scanned pressure transducers have a built-in feature that allows the the wake surveys ten times as was done with the pressure survey data was considered impractical.
transducers to be zeroed on-line, experimentation Instead, each wake survey was performed twice and the determined that a superior level of bias correction was resulting data were interleaved to form a single local achieved when the transducers were manually zeroed before each data run. Transducer biases were evaluated velocity distribution profile. At the beginning of each of the two wake surveys, the probe sensor zero readings by taking readings with the tunnel in the "off" position were taken and written to an archival file for use by the (zero airspeed). In this zeroing process, each pressure American Institute of Aeronautics and Astronautics postprocessing routines. Whencomputed, transducer suboptimal sideof Hoerner's dragcurve. Thus,by
biases were assumed constant fortheduration of each
adding roughness to the forebody, the overalldrag
coefficient should bereduced.
wake survey.
Analysis Methods Wake Profile Analysis This section derives the analysis methods used in this This analysis method fits the wind-tunnel wake data series of wind-tunnel tests. A baseline set of two- with a symmetric "cosine law" velocity distribution dimensional, incompressible, computational fluid profile of the form dynamics (CFD) calculations will be presented first.
Next, the viscous calculations used to convert the measured wind-tunnel pressures data into the various u(Y)-_r--,l+cosl'n_)]+[l-cos(rt_ (2) components of the drag coefficient will be presented.
Ue L Ue - ' For each analysis method presented in this section, an error analysis is also presented in the appendix.
In equation (2), Umi n iS the minimum velocity in the wake, 3' is the lateral distance outwards from the center Computational Fluid Dynamics Analysis of the wake, U e is the velocity at the edge of the wake, u(y) is the local velocity within the wake, and 8 is the The CFD calculations were performed to give pretest wake half-width. A least-squares method was used to drag predictions to verify that the smooth model curve-fit the measured velocity distribution data to the configuration lay on the suboptimal portion of Hoerner's base drag curve. profile assumed in equation (2). In this method, equation (2) is rewritten as a linear system of the form Only the CFD estimates of forebody pressure and base drag coefficients were used for the pretest drag Z (meas)= AX (k) + C (3) predictions. Not enough computational cells were embedded within the boundary layer to allow the where skin-friction coefficient to be accurately computed.
using the CFD data. The integrated skin drag coefficient was predicted using the two-dimensional Hoerner drag model.
The CFD flow calculations were performed using a commercially available code. 8 The core solver for this code features a finite-volume, cell-centered discretization, and uses a time-accurate, "PISO" (pressure-implicit with splitting of operators) solution z( meas )= • , X(k)= algorithm to solve the integral form of the • I Navier-Stokes equations. Although the code has compressibility and transient solution capabilities, only "(Y,,)J the incompressible steady-state solution was used in this cos(try,,/8 {_)) analysis. The analysis was set up to force turbulence at • Uel the leading edge of the model. For this analysis, a simple _<-g (energy-dissipation) turbulence model was used.
Figure 9 shows the predicted CFD model flow field. and The CFD solutions clearly show a periodic vortex structure trailing the model. When the pressure forces are summed along the surface of the model and A=_ UU _LW+I projected perpendicular to the longitudinal axis, the integrated forebody pressure coefficient is approximately -0.018 and the integrated base drag A simple least-squirms method is used to solve for coefficient is approximately 0.035. Based on data shown estimates of the slope and intercept parameters, A and C: in figure 2, the smooth model should lie on the American Institute of Aeronautics and Astronautics
^ (k) and the cosine velocity distribution law gives a
u.,#, = ;_(k) + _(k) reasonable curve fit. Note that the center of the wake (4) Ue appears to contain a significant amount of turbulence that significantly decreases near the edge of the wake.
Using a first-order perturbation, equation (4) can be "updated" using nonlinear regression to get a refined When the velocity profile has been curve-fit, value for 5 : equation (1) is substituted into the equations for the wake displacement and momentum thickness and analytically evaluated to give (5) Z('neas)_ 2(k)= _(k)V_X(k)[_(k+ l)__(k)] where (8) and rt-----_ sm _:_
P "(")rl "(")l
(9)
o,,, =
VsX (k) = (6) dy = 1 + , Ue Ue rt Y" sin r_ y" In equations (8) and (9), u(y) is the local velocity in the wake at lateral offset location y, and U e is the local velocity at the edge of the wake. The free-stream momentum thickness is calculated from the local After extensive algebra, the least-squares solution to momentum thickness using the well-known Squire- equations (5) and (6) can be written as Young formula: 10
_(k + I) = _(k)
_ _/[H+51
Ooo = o, |Ue] z
(10)
" [[ n,,, rrtv?l_
'LU_J
X ' }
,:,[L[_(_)] L j J (7)
Equation (10) corrects for the effects of the wind + tunnel blockage described earlier in this paper. In equation (10), H is the wake shape parameter defined by t=l (_ * 1,t' H - (11) Ow Assuming that a starting value for the wake half-width, 8 (°). is known beforehand (from visual The free-stream drag coefficient is computed from the normalized section drag inspection of the wake data), equations (4)-(7) are solved iteratively until convergence. Convergence O' 0_ typically takes less than ten iterations.
- - _-- (12) CDo 1 2 - h ha., __PUo_ hba._e Figure 10 shows an example wake curve fit compared with the wind-tunnel data. These data were obtained from the smooth model configuration tested at An approximate accounting of overall error in the Re L = 2.25 × 105. The turbulent wake extends beyond wake drag coefficient can be performed using a linear the lateral boundaries of the wind-tunnel model by perturbation analysis. The appendix shows this approximately 3 cm. The wake structure is symmetric linearized error analysis.
American Institute of Aeronautics and Astronautics Boundary-Layer Profile Analysis dPe/dx is the longitudinal pressure gradient at the edge of the boundary layer. Based on the correlation of The forebody skin friction coefficient is evaluated equation (17), the numerical value of I1 corresponding using the boundary-layer velocity profiles in a similar to a zero pressure gradient flow is approximately 0.426.
manner as the wake analysis presented earlier. In this Earlier authors have placed this zero gradient value at case, however, Coles' "law of the wake," approximately 0.5 l° and 0.55. 7 For this analysis, the more modern value recommended by Das is used. A value for II greater than the zero gradient value (0.426)
[ . 2frt v-17 ,,+ = lnly+] +2rlsm L_,jj + 8 (13)
corresponds to an adverse pressure gradient• A value for 1-I less than the zero gradient value (0.426) corresponds is curve-fit to the local velocity profile data. The law of to a favorable pressure gradient.l° the wake is a very general experimental correlation for turbulent boundary layers, and relates the Following the procedure used earlier with the wake nondimensional velocity integral analysis, equation (16) is rewritten as a linear system of the form + u(y) u - (14) =1 Xl to the nondimensionalized boundary-layer coordinate (18) • ' ] Zn . -l'n J y = ._Re x (15,_ where In equations (13)-(15), 5 is local boundary-layer thickness, K is the law-of-the-wake slope parameter, B is the law-of-the-wake bias parameter, II is the wake pressure gradient parameter, and c f_ is the local
[ -"<!7 Q'
z,.= 1 Ue j F = _ 2 skin-friction coefficient. The accepted "best value" for (19) currently is 0.41.1° The bias parameter, B, varies with the level of surface roughness and for a smooth plate has a numerical value of approximately 5.0. Re x is the Reynolds number based on the local axial coordinate, x.
In equations (18)-(19), the subscript i is the The roughness dependent bias term can be eliminated measurement, and the superscript (k) is the iteration from equation (13) by expressing the law of the wake in index. After some extensive algebra, the least-squares terms of the local "velocity defect": solution to equation (19) can be written as _2 l-u(Y)] = _ 1 , rzv v U,.3 - _[21q cos2[_] - In[_]] (16' c),.x = 2 xi 2' i i The wake parameter, I-I, is proportional to the local longitudinal pressure gradient. Das l°" 12 has established (20) an empirical correlation that relates the wake parameter to the more familiar "Clauser parameter, ''13 [3, where =2 n 1 21 _ -I 211 :os I a--'-In
,.) -
2 8* dPe i- - 0 .J 0.42F1" + 0.7611 - 0.4 = 13 = (17) 1 9 dx c.t, 5.PUe" Using a first-order perturbation with respect to 8, In equation (17), 8" is the local displacement equation (20) can be updated using nonlinear regression to get a refined value for 8 : thickness, c.f, is the local skin-friction coefficient, and American Institute of Aeronautics and Astronautics 17=1.032; and a l/7th-power-curve exponential curve fit. Analysis of equation (17) presented in White 1°
I*)-- + (21)
shows that FI-- 1.032 corresponds to a weak adverse pressure gradient. The model data presented in the where the ith component of the Z vector is "Results and Discussion" section support this conclusion. Clearly, the curve fit using FI = 1.032 gives overall fit consistency.
2F :,l .Fy, ll
., : 4 L2,,cos L j_InL jj (22)
The estimated values for 8, Cfx, and FI are used to calculate the local momentum and displacement thickness by integrating the law of the wake across the The resulting updated equation for 8 is depth of the boundary layer. As derived in White, 10 the resulting expressions for the displacement and &(k + t) momentum thickness are 8* _ ,1@,1 +FI (24) 8 _z K and (23) = 8(_) 0 I /G[( H)_I /_fx(2+3.2ii+l.SF12)] (25) I_7 1_.7,_1 It --3'i F YJ ll[- (",_a')
J
4- For simplicity, the effect of the local laminar sublayer +rt[I-- sin _ = _(k) _(k) L 8 LU is ignored in equations (24) and (25). For the Reynolds numbers tested, earlier analysis estimates that ignoring the laminar sublayer introduces integral errors of less When the variational algorithm of equations than 0.2 percent. 12 When the local momentum and (21)-(23) is modified to allow direct estimation of FI displacement thickness have been evaluated, then the along with 8 and c f,, the equations rapidly diverge. To integrated viscous forebody drag coefficient can be circumvent this numerical problem, FI was selected for evaluated using the "Clauser" form of the von Karman this analysis to give the best overall fit consistency. This momentum equation, 1° procedure typically consisted of selecting a starting value for I1 and then computing c f, and 8 by iteratively solving equations (21 )-(23) until dO (2 + _cf, cf, dx H)H 2 - 2 (26) convergence. At this ix)int, the value for FI was varied by a small amount and the iterative algorithm was repeated. If the total fit error improved, then FI was In equation (26), H = 8*/0 is the boundary-layer again varied in the same direction; if not, then the value shape parameter. The Clauser parameter, 13, is related to was varied in the opposite direction. Using this ad hoc the local pressure gradient, the displacement thickness, and the local skin-friction coefficient as procedure, a minimum fit error is typically reached after less than ten trials.
cf, 8* dPe Figure 11 shows an example boundary-layer curve fit ._ - (27) 1 "_ dx compared with the wind-tunnel data. The normalized 7DUe" velocity distribution is plotted against the normalized position within the boundary layer. These data were Solving equations (26) and (27) for the local skin- obtained from the smooth model configuration tested at friction coefficient gives Re L = 2.25 x 105. Three fit curves are plotted here: a law-of-the-wake curve fit with FI = 0.426 (zero pressure gradient); a law-of-the-wake curve fit with the wake = 9d0 H (28) cf, "dxlH + (2 + H)I31 parameter adjusted to give the minimum fit error, American Institute of Aeronautics and Astronautics for the taper of the base pressure near the outer edges of
Asdemonstrated byClauser, 13 forsmall-to-moderate
the model. In this curve-fitting scheme, ports 7 and 11
pressure gradients, the termson the right sideof
were weighted one-half as much as the three base area H ports (ports 8, 9, and 10). This weighting scheme was equation (28), [H + (2 + H)IB] ' are approximately selected to give a base drag taper correction factor of constant. Integrating equation (28) along the forebody approximately 0.925. This correction factor is suggested length, L, gives by Saltzman, et al. 5 for full-scale flight vehicles.
The base pressure drag coefficient is given l fL,_dO H dr analytically by the evaluating the surface integral CF = LJo-d-_XlH + (2 + H)I3] (29) =,_0 H - LIH +(2 + H)_] CDb .... = -."05 Cp[y] dy = 0.5" biY dy (31) As with the earlier wake analysis, an approximate = b 0 + 0.0833 b 2 + 0.0125 b 4 accounting of overall error in the wake drag coefficient can be performed using a linear perturbation analysis.
Figure 13 shows a sample base pressure distribution The appendix show's this linearized error analysis.
curve fit. These data were measured on the smooth model with the wind tunnel operating at an approximate Forebody Pressure Analysis Reynolds number of 2 25 × 105, based on model length The forebody pressure coefficient was evaluated by Results and Discussion curve-fitting the pressure distributions as a function of local incidence angle. 0. For the forebody data, seven The wind-tunnel data clearly support the earlier CFD forebody pressures--ports I, 2, 3, 4, 14, 15, and 16 predictions that the smooth model will lie on the (fig. 5)--are curve-fit with a third-order polynomial.
suboptimal side of Hoerner's curve. The suboptimal The forebody pressure drag coefficient is analytically hypothesis is most clearly demonstrated by examining given by the surface integral the base area pressure distributions. Figure 14 shows these results. The base pressure coefficients are plotted here as a function of y for various surface grid patterns.
CDt,,,,4_,,I, = _ CplOlcos[OldO o Figure 14(a) shows the pressure distributions for Re L = 2.25 × 105, and figure 14(b) shows the pressure = %0 cos[0l dO
f distributions for Re L = 1.25 × 105. Interestingly, the
1 ,30, 0 i = 0 surface pattern with fine-mesh parallel slots and lands causes the base drag to dramatically rise (and have a 0 + 0.570S a I + 0.4674 a-, + 0.4510 a 3 lower base pressure coefficients) when compared with the smooth surface model. Conversely, the surface Figure 12 sht,v,s a plot of a sample forebody curve fit.
pattern with transverse slots and lands causes the base These smooth m¢_del data were measured with the wind drag to gradually lower (and have higher base pressure = _.,_ × 105 . The forebody tunnel operatm_ at Re/. _ _" coefficients) when compared to the smooth surface pressure coeflicient data is plotted as a function of the model.
local incidence angle. The upper and lower surface pressure data lie nearly superimposed on each other, so A similar behavior was observed by Krishnan, et al., ]4 not surprisingl,_, the third-order curve-fit closely when the authors added rib[et 15 structures to the matches the pressure cocflicient data.
forebody of an axisymmetric wind-tunnel model with a blunt base. The authors" intents were that the riblets Base Pressure Analysi_ would lower base drag; however, the results were opposite of expectations. When Krishnan's results and The base pressure coefficient was evaluated by the data presented in figure 14 are interpreted curve-fitting the base pressure distributions as a function considering Hoerner's curve (fig. 3), the rising base drag of the lateral offset coordinate, v. For the base pressure is completely reasonable. The grid pattern with parallel data, five base area pressure ports--ports 7, 8, 9. 10, and slots and lands has the effect of acting like riblets on the 11 (fig. 5)--were curve-fit with a fourth-order model forebody. The riblet structures have the effect of polynomial. The pressure ports on the sides of the model lowering the forebody drag coefficient. Because the (ports 7 and 11 ) were included in the curve fit to account American Institute of Aeronautics and Astronautics elusive "drag bucket" is clearly defined and the primary forebody skin drag coefficient is lowered, the base drag hypothesis of this paper is conclusively proven. The is expected to correspondingly increase. Clearly, riblets drag reduction from the smooth model configuration to should not be used in conjunction with "suboptimal" the optimum point is approximately 15 percent. Also, configurations that have highly separated base regions; comparison of figure 15 with figure 16 shows that the their effect will cause the base drag to rise.
base drag coefficient corresponding to the total drag coefficient minimum lies somewhere between 0.225 and Figure 15 shows results from the wind-tunnel tests 0.275. This value is a bit lower than the 0.25-0.30 range that further illustrate this concept. The measured base predicted by analysis of Hoerner's original data (figs. 2 drag coefficient is plotted with the viscous forebody and 3).
drag coefficient calculated from the boundary-layer survey data. These data are compared to the curve fit of Hoerner's two-dimensional data from figure 1. The open Summary and Concluding Remarks symbols represent data for Re L = 2.25 x 105 and the closed symbols represent data for Re L = 1.25 x 105.
Current designs of transatmospheric crew return and The error bars show the expected "l-c" standard reusable launch vehicles have extremely large base-to- deviations based on the error analyses presented earlier.
wetted area ratios when compared to conventional The agreement with the curve fit of Hoerner's data is vehicle designs. These truncated base areas are highly reasonably good. separated, resulting in large, negative, base pressure coefficients. Because of the large base-to-wetted-area Figure 16 shows the model total drag coefficient data ratio, base drag makes up the majority of overall vehicle (as calculated from the wake survey data) plotted with drag. Any reduction in base drag directly improves the viscous forebody drag coefficient. The error bars vehicle performance, resulting in an enhanced lift-to- show the expected "1-o" standard deviations based on drag ratio, extended range, and a less-severe approach the error analyses presented earlier. Figure 16 also glide slope.
shows the predicted drag curve defined using Hoerner's two-dimensional curve from figure 1, the viscous Early work performed on blunt-based bodies offers a forebody drag measurement, and the model forebody potential solution. For blunt-based bodies, a direct drag coefficient predicted (-0.018) by the CFD correlation exists between base and "viscous" forebody solutions. Note that, with the exception of the data for drag. As the forebody drag coefficient increases, the the parallel grid (riblets) overlay, the agreement with the base drag of the projectile generally tends to decrease.
predicted drag curve is very good.
This base drag reduction results from boundary-layer effects at the vehicle base. Conceptually, if the added The disagreement for the parallel grid test points is increment in forebody skin drag is optimized with caused by a sharp rise in the forebody pressure respect to the base drag reduction, then reducing the coefficients. Figure 17 shows these data. The forebody overall drag of the configuration may be possible.
pressure distributions for all of the grids are plotted here In order to test the above concept, a series of as a function of the local incidence angle. Figure 17(a) small-scale wind-tunnel tests was conducted. In these shows the higher Reynolds number data (2.25 × 105), tests, a two-dimensional cylinder with a blunt afterbody and figure 17(b) shows lower Reynolds number data was tested. The series of tests had two primary (1.25 × 105). The transverse grid patterns do not objectives: to test the forebody roughness hypothesis in a systematic manner to conclusively demonstrate significantly alter the forebody pressure distribution; existence of a "'drag bucket"; and to establish a criterion however, the forebody pressure data are considerably for when forebody drag is suboptimal (that is. when will higher for the parallel grid pattern. The parallel grid data increasing forebody drag result in an overall drag are clearly an anomaly. The reasons for this pressure reduction).
anomaly are not clear at this point, but the parallel grid possibly caused relaminarization of the flow and This paper presents the wind-tunnel test results. Both induced a localized separation. This anomaly requires primary objectives were satisfied. These wind-tunnel results conclusively demonstrate existence of a further investigation.
forebody drag optimum. Also, the wind-tunnel data demonstrate that the base drag coefficient corresponding Most importantly, the data shown in figure 16 to the total drag minimum lies somewhere between demonstrate the existence of a drag minimum with 0.225 and 0.275. This optimality point is slightly lower regard to the viscous forebody drag coefficient. The American Institute of Aeronautics and Astronautics than the 0.25-0.30 range predicted by analysis of implementation methods that allow for on-line adaptive modification of the forebody drag coefficient to seek the Hoerner's original data. The use of parallel grid lines that emulate the effects of riblet structures on bodies optimal point should be explored and developed. The with highly separated base regions will likely cause the limits of practical applicability for this technology are total drag of the configuration to rise. Most importantly, unknown at this point. This drag reduction technology is the data show a peak drag reduction was approximately still in its infancy; however, a wide spectra of potential users exist, including the aerospace, automotive, ground 15 percent. When this 15-percent drag reduction is transport, and shipping industries. Use of this drag scaled to the size of the X-33 vehicle, the drag savings reduction technique offers the potential for decreased approaches approximately 45,000 N (10,000 Ibf).
operating costs resulting from decreased overall fuel consumption.
Clearly, this experiment should be repeated for different ranges of Reynolds number and aspect ratios to determine if the lower optimality point indicated by the data is real. The methods should also be demonstrated as being effective in the presence of induced drag. Practical o Two-dimensional data (from Hoerner) Two-dimensional curve fit D Three-dimensional data (from Hoerner) ----- Three-dimensional curve fit .8 .5 CDbase .4 0 .3 .2 .1 0 0.5 1.0 1.5 2.0 CF 000636 Figure 1. The effect of the viscous forebody drag on the base drag of a blunt-based projectile.
American Institute of Aeronautics and Astronautics 1 Two-dimensional drag optimization -- -- -- Three-dimensional drag optimization .8 _//, .6 ............. / / C F + .4 CDbase _ / / .2 I,- i "L Drag bucket 0 .2 .4 .6 .8 1.0 CF oo0637 Figure 2. Schematic depiction of the predicted "drag bucket."
Drag coefficients Base (two-dimensional model) .... Total (two-dimensional model) n__ Base (three-dimensional model) .... Total (three-dimensional model) [] Base (flight data) Total (flight data) .8 .7 / - M2-F3 -_ .. //' .6 I l/
Shu.l, X24-B- \ H,-tO
.5 X-33 Enterprise--,_ \ \ ..L / _: .,., X-151 _\___1"/: X24"A C D .4 X-33 "_,.,. .... 4 1 , .3 - _1_.15 Shuttk_- _- M2-F1 ] _-,_, _ Enterprise I
. .2.F I
.2 "" - _ " _ X24-B_X24-A I .1 .01 .10 1.00 CF 000638 Figure 3. Comparison of flight data to two- and three-dimensional drag models.
American Institute of Aeronautics and Astronautics 2.90 m Figure 4. Von Karman "vortex street" formation trailing the M2-F 1 vehicle.
American Institute of Aeronautics and Astronautics 2.54 cm 10.16 cm (1.0 in.)
(4.0 in.)
Mount " Tunnel walls I Front view 10.033 cm (3.95 in.) i Tunnel walls Pivot pin Y 000640 (a) Three-view drav,'ing.
Figure 5. Schematic of wind-tunnel model.
American Institute of Aeronautics and Astronautics Model top view, looking down 15 14 13 12 11 ,10 1 _-9 2 8 3 4 5 6 7 000641 (b) Pressure port numbering scheme.
Figure 5. Schematic of wind-tunnel model. Concluded.
Figure 6. Base drag model mounted in wind tunnel.
American Institute of Aeronautics and Astronautics Direction of flow 0.75 in.
4.5 in.
CenterUne - Inset of bar grid pattern Z Etched surface 000643 Figure 7. Bar grid surface overlay screen pattern.
American Institute of Aeronautics and Astronautics 1.0002 1.0000 L .9998 Wake probe location .9996 O Dynamic pressure ratio Boundary-layer P/Poo [] Static pressure ratio probe location .9994 Re L ~ 2.25 x 105 /% Static pressure ratio Re L ~ 1.25 x 105 .9992 .9990
I t
.9988 20 30 40 0 10 Axial position in tunnel, cm o00644 Figure 8. Dynamic pressure calibration to account for tunnel blockage.
000645 Figure 9. Two-dimensional, incompressible CFD solutions of wind-tunnel model flow field (smooth configuration).
American Institute of Aeronautics and Astronautics Cosine curve fit O Measured data 1.02 1.00 Smooth mod_ = 2.25 x 105 .98 u(y) .g6 Ue .94 .92 .90 -7.5 -5.0 -2.5 0 2.5 5.0 7.5 y, cm oo0646 Figure 10. Example wind-tunnel wake data.
Curve fit, rl = 1.032 .... Curve fit, R = 0.426 m_ _ 1/Tth power law fit Wind-tunnel test data 1.1 r Smooth model Re L = 2.25 x 105 1.0 .9 u(y) U e .8 .7
/ I
.6 .001 .01 .10 1.00 y/8 ooo_r Figure l 1, Example wind-tunnel boundary-layer curve fit.
American Institute of Aeronautics and Astronautics Third-order polynomial curve fit 0 Wind-tunnel data points 1.5 i 5 _.._mooth model, Re L = 2.25 x 10 1 • 0 _ ...... ! " Cpforebody 05 " -2.0 0 20 40 60 80 1O0 O, deg oo0_e Figure 12. Example forebody pressure coefficient curve fit.
Fourth-order polynomial curve fit 0 Wind-tunnel data points 1.5 Smooth model, Re L = 2.25 x 105 1.0 .5 Cpbase -.5 -1.0 -1.5 -2.0 -1.0 -.5 0 .5 1.0 1.5 -1.5 y, cm 0oo_9 Figure 13. Example base pressure coefficient curve fit.
American Institute of Aeronautics and Astronautics O Smooth model [] Transverse grid 2, Ks ~ 0.1143 cm Transverse grid 4, K s - 0.4854 cm A Parallel grid 1, Ks ~ 0.0163 cm IX Transverse grid 3, K s ~ 0.2896 cm I_ Transverse grid 5, K s - 0.6911 cm -.15 [ ,_ Increasing levels of roughness / -.20 _ -.25 I" ( -.30 Cpbase -.35 / -.40 -.45 -.50 -.55 -1.25 0 1.25 2.50 -2.50 y, cm 00065_ (a) Re L = _..5 x 105.
O Smooth model [] Transverse grid 2, K s - 0.1143 cm <_ Transverse grid 4, Ks ~ 0.4854 cm A Parallel grid 1, Ks ~ 0.0163 cm IN. Transverse grid 3, Ks - 0.2896 cm I_ Transverse grid 5, K s - 0.6911 cm -.15 [ 1",, -.20 '_ _X A /_ _ Increasing levels of roughnessA_ -.25 [ ] [_,"'_'_ _ _ _/_ "] -.30 Cpbase Z _, -.35 (' _() Parallel grid -.40 -.45 -.50 -2.50 -1.25 0 1.25 2.50 y, cm 000651 (b) Re/. = 1.25x105 .
Figure 14, Base pressure distributions for various grid patterns.
American Institute of Aeronautics and Astronautics • Re L- 1.225x 105 a ReL ~ 2.250 x 105 .50 -"_--.Parallel grid (riblets) ....
.45 \//-Smooth model CDbase .40 (from .35 " _/Hoerner, scurvs .....
pressure survey) .30 _ [nc;eaoSi;_s .25 .20 0 .05 .10 .15 .20 C F (from boundary-layer survey) 000652 Figure 15. Comparison of wind-tunnel base drag data as a function of Hoerner's curve.
• Re L~1.225x105 a Re L ~ 2.250 x 105 .60 _Parallel grid (rlblets) .55 r- Smooth model .
CD .50 \ _ /- Prediction from (from .45 wake \//' / Hoerner's curve _r.// / Increasing levels survey) .40 / " ' of roughness .35 .30 .05 .10 .15 .20 C F (from boundary-layer survey) 000653 Figure 16. Comparison of wind-tunnel wake survey data as a function of the predicted "drag bucket."
American lnstitule of Aeronautics and Astronautics O Smooth model [] Transverse grid 2, K s ~ 0.1143 cm Transverse grid 4, K s ~ 0.4854 cm Z_ Parallel grid 1, K s ~ 0.0163 cm IX Transverse grid 3, Ks ~ 0.2896 cm [_ Transverse grid 5, Ks ~ 0.6911 cm /-- Parallel Cpforebody -1 -2 0 20 40 60 80 100 O, deg 000654 (a) Re L = 2.25 x 105 .
O Smooth model [] Transverse grid 2, K s ~ 0.1143 cm Transverse grid 4, K s ~ 0.4854 cm Z_ Parallel grid 1, K s ~ 0.0163 cm IX Transverse grid 3, K s ~ 0.2896 cm I_ Transverse grid 5, Ks ~ 0.6911 cm 1t Cpforebody 0 ,-- Parallel / -1 Smooth I _1_ -- model and _. / transverse grids _u -2 0 20 40 60 80 100 0, deg 000655 (b) Re L = 1.25x 105 .
Figure 17. Forebody pressure distributions for various grid patterns.
American Institute of Aeronautics and Astronautics APPENDIX tlJ2A0 w ERROR ANALYSIS METHODS = E[A0 2] Introduction = 82E[I-_lAh_rl-2[/_(_)ll}dP'[ U_L LUeJJ An approximate accounting of overall error in the wind tunnel-derived drag coefficient estimates is (A-2) derived herein. The wake error analysis is presented
x !it I --DTL
first; the boundary-layer skin-friction error analysis is presented next. The estimated errors in the forebody and
base pressure drag coefficients are presented last. The f'f 1 E[A_(_)A_(_)II[I_ 2p(_)ll l
[ < < JL[ L ,Jjj
error equations derived in this appendix were used to calculate the data point error bounds plotted in figures 15 and 16.
X{[ l-2Ffi(_,lltL UeJJ ] d_d_ Estimating the Wake Drag Coefficient Errors An approximate accounting of overall error in the Assuming that random local errors in the velocity wake drag coefficient can be performed using a linear profile curve fit are uncorrelated, the expectation perturbation analysis. Using the fundamental definition operation in equation (A-2) becomes for momentum thickness, linear perturbations can be expressed in terms of the velocity profile curve-fit error E[Ah(_)Ah(_)] A[_(_')I L U,, U e J L--_e'J by taking the first variation of the forebody surface incidence angle, 0, with respect to u(y)/U e : 0 when _ _ _ l (A-3) au/u, when _ =
l
AO=A.O,)/U" _ UeJ _j (A-I) = _2au/u,[A_. _] In equation (A-3), A_, r_ is the Dirac delta function 16 The mean-square error in momentum thickness ns velocity and _2Au/U" is the mean-square error in the evaluated by taking the expectation of the square of equation (A- 1).
distribution curve fit. Substituting equation (A-3) into equation (A-2), the interior integral reduces to the following:
f Ill
(A-4) 2[h(_)]] 2 = VmA"/ufIL - L UCJJ Substituting equation (A-4) into equation (A-2), and using the wake cosine law (eq. (2)) to evaluate the outer American Institute of Aeronautics and Astronautics these differences in mind, the mean-squared error integral, the approximate mean-square error in the momentum thickness reduces to the following: formula for the momentum thickness becomes
' s= ,e-' F_F"""I = -,F""#'l+ _,](A-5)
W'a°" = a"IV, L L--u-TJ - "L--_ ] qJ'A0,, A first-order perturbation of equation (A-5) gives the error equation for the free-stream momentum thickness = EIA021 estimate (assuming that errors in the velocity ratio and = a2 (A-8) shape parameter are negligible when compared to the momentum thickness errors):
}<,4' t,@r, _ r,,ql l
LJo / U e L L u e Jd "o t _e '- L V e JJ / _2[1 2 AO_ A0.
x _I J Au/Ue[l 2[a(_)]12 d_ "J O - Ue -- H+S]
= 52 v: fu"l I
(A-6) Substituting the law-of-the-wake velocity distribution "3 (eq. (16)) into equation (A-8) and integrating gives the Hmi n mean-square error in momentum thickness:
r",,,,,,n +,]
Finally, the approximate mean square error in total tIO2AO drag coefficient is 2 2 (A-9) _K W-co O +4of 1x+5.48304 H+xI121] x [XK2- 2_Ix + 4FllK '-X /l ba._ e _ The corresponding mean-square error in the viscous (A-7) +51 forebody drag coefficient estimate is = 4 52 ufl2A,;,U,,FUet I#1 /_b_., .- LU_J qJ-cr "_ H 2
+,]
- [_,,, +<r+,,)_,]
":' 2 (A-IO) In equation (20), H is the shape parameter defined by x 8"tlJ Au/U,, RK equation (10), 6 is the boundary-layer thickness, and velocity gK--- W2_,,/_, is the mean-square error in the x 2 2c. Ix+ +548304 rl+ xll2]] profile curve fit.
Estimating the Forebody Drag Coefficient EstimatinR the Forebody Viscous Drag Coefficient Errors Errors The boundary-layer error analysis follows a nearly For each configuration, the forebody pressure drag identical process when compared to the wake error coefficient errors are approximated using the pressure analysis. The main exceptions are that the integrals are coefficient standard deviations from the ten individual performed from {0,6} instead of {-8.8}, and the trials. For each pressure port location, 0j, the mean and velocity distribution is given by the law of the wake instead of the cosine law velocity distribution. Keeping variance in pressure coefficients are computed as American Institute of Aeronautics and Astronautics /_lriah h v2 = y, [o'0cos02] (A-13)
_, cp,(o)
CDforeb°d) i = I i= I (A-I 1) _0 = Ntrial s Estimating the Base Drag Coefficient Errors and The base drag coefficient errors are computed in a similar manner as the forebody drag coefficient errors.
N rrials However, instead of weighting the Cp standard
[ Cp,(O) - _ol2
deviations using cos[0], the weighting procedure 2 i=1 follows the scheme used to establish the base area a 0 = (A-12) N trials - I curve fits (that is, the Cp variances in the two ports along the sides of the model are weighted one-half as Based on equation (30), which is a pressure integral much as the Cp variances in the three base-area ports): weighted by the cosine of the local incidence angle, 2 3 mean-square error in forebody drag coefficient is ! 2 computed as the sum-square of individual forebody =1 i=1 pressure coefficient errors, weighted by the cosine of the = (A-14) local incidence angle.
American Institute of Aeronautics and Astronautics 9Rade, Lennart and Bertil Westergren, Beta References Mathematics Handbook: Concepts, Theorems, Methods, 1Wong, Thomas J., Charles A. Hermach, John O.
Algorithms, Formulas, Graphs, Tables, 2nd ed., CRC Relier, Jr., and Bruce E. Tinling, "Preliminary Studies of Press, Boca Raton, FL, 1990.
Manned Satellites--Wingless Configurations: Lifting Body," NACA Conference on High-Speed I°White, Frank M, Viscous Fluid Flow, 2nd ed., Aerodynanlics: A Compilation of the Papers Presented, McGraw-Hill, New York, 1991.
NASA TM-X-67369, 1958, pp. 35--44.
I IColes, Donald, "The Law of the Wake in the 2Hoerner, Sighard E, Fluid-Dynamic Drag: Practical Information on Aerodynamic Drag and Hydrodynamic Turbulent Boundary Layer," Journal of Fluid Resistance, Self-published work, Library of Congress Mechanics, vol. 1, 1955, pp. 191-226.
Card Number 64-19666, Washington, D.C., 1965.
12Whitmore, Stephen A., Marco Hurtado, Jose 3Tanner, M., "'Theories for Base Pressure in Rivera, and Jonathan W. Naughton, "A Real-Time Incompressible Steady Base Flow," Progress in Aerospace Sciences, vol. 34, 1998, pp. 423--480. Method for Estimating Viscous Forebody Drag Coefficients," AIAA-2000-0781, Jan. 2000 (also 4Rathakrishnan, E., "Effect of Splitter Plate on Bluff available as NASA TM-2000-209015).
Body Drag," AIAA Jourl_al, vo]. 37, no. 9, Sept. 1999, pp. 1125-1126.
13Clauser, Francis H., "Turbulent Boundary Layers in Adverse Pressure Gradients," Journal of Aeronautical 5Saltzman, Edwin J., K. Charles Wang, and Kenneth Sciences, vol. 21, no. 2, Jan. 1954, pp. 91-108.
W. Iliff, "Flight-Determined Subsonic Lift and Drag Characteristics of Seven Lifting-Body and Wing-Body Reentry Vehicle Configurations With Truncated Bases," 14Krishnan, V., E R. Viswanath, and S. Rudrakumar, AIAA-99-0383, Jan. 1999.
"Effects of Riblets on Axisymmetric Base Pressure," Journal of Spacecraft and Rockets, vol. 34, no. 2, 6Whitmore, Stephen A. and Timothy R. Moes, "A March-April 1997, pp. 256-258.
Base Drag Reduction Experiment on the X-33 Linear Aerospike SR-71 Experiment (LASRE) Flight 15Walsh, Michael J., "Riblets as a Viscous Drag Program:' AIAA-99-0277, Jan. 1999.
Reduction Technique," AIAA Journal, vol. 21, no. 4, 7Mills, Anthony E, Heat and Mass Transfer, Irwin Apr. 1983, pp. 485-486.
Publishing Co., Burr Ridge, IL, 1995.
16Freiberger, W. F., ed., The International Dictionary 8Adaptive Research, CFD 2000: Computational of Applied Mathematics, Van Nostrand Company, Inc., Fluid Dynamics System Version 2.2 User's Mamtal, Princeton, N J, 1960.
Pacific-Sierra Research Corporation, 1995.
American Instituteof Aeronautics and Astronautics REPORT DOCUMENTATION PAGE Form Approved OMB No. 0704-0188 Public reporting burden for this collection of inlormation is estimated to average 1 hour per response, including the time for reviewing instructions, searching exisling data sources, gathering and maintaining the data needed, and comp,)eting and reviewing the collection oI information Send comments regarding this burden estimate or any other aspect of this collection ol information including suggestions for re0ucing this burden, to Washington Headquarters Services, Directorate lot Information Operations and Re )orts, t215 Jefferson Davis Highway, Suite 1204, Arlington, VA 222024302. and to the Offee ol Management and Budget, Paperwork ReDuction Pro_ect (0704-01B8), Washington, DC 20503 1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORTTYPE AND DATES COVERED January 2001 Technical Memorandum 4.TFFLE AND SUBTITLE 5. FUNDING NUMBERS Wind-Tunnel Investigations of Blunt-Body Drag Reduction Using Forebody Surface Roughness 718-20-00-E8-53-00-b52 6. AUTHOR(S) Stephen A. Whitmore, Stephanie Sprague, and Jonathan W. Naughton 8. PERFORMING ORGANIZATION 7. PERFORMING ORGANIZATION NAME(S) ANDADDRESS(ES) REPORT NUMBER NASA Dryden Flight Research Center P.O. Box 273 H-2439 Edwards, California 93523-0273 10. SPONSORING/MONITORING 9.SPONSORING/MONITORING AGENCY NAME(S) ANDADDRESS(ES) AGENCY REPORT NUMBER National Aeronautics and Space Administration NASA/TM-2001-210390 Washington, DC 20546-0001 11. SUPPLEMENTARY NOTES Presented at 39th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, January 8-11, 2001, AIAA-2001-0252. Stephanie Sprague, University of Kansas. Jonathan W. Naughton, University of Wyoming.
12a. DISTRIBUTION/AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE Unclassified--Unlimited Subject Category 05 This report is available at http://www.dfrc.nasa.gov/DTRS/ 13. ABSTRACT (Maximum 200 words) This paper presents results of wind-tunnel tests that demonstrate a novel drag reduction technique for blunt-based vehicles. For these tests, the forebody roughness of a blunt-based model was modified using micomachined surface overlays. As forebody roughness increases, boundary layer at the model aft thickens and reduces the shearing effect of external flow on the separated flow behind the base region, resulting in reduced base drag. For vehicle configurations with large base drag, existing data predict that a small increment in forebody friction drag will result in a relatively large decrease in base drag. If the added increment in forebody skin drag is optimized with respect to base drag, reducing the total drag of the configuration is possible. The wind-tunnel tests results conclusively demonstrate the existence of a forebody drag- base drag optimal point. The data demonstrate that the base drag coefficient corresponding to the drag minimum lies between 0.225 and 0.275, referenced to the base area. Most importantly, the data show a drag reduction of approximately 15 percent when the drag optimum is reached. When this drag reduction is scaled to the X-33 base area, drag savings approaching 45,000 N (10,000 lbf) can be realized.
14. SUBJ ECT TERMS 15. NUMBER OF PAGES Base drag, Drag reduction, Reusable launch vehicle, Skin friction, Wind tunnel 16. PRICE CODE A03 17. SECURITY CLASSIFICATION 18. SECURITY CLASSIFICATION 19. SECURITY CLASSIFICATION 20. LIMITATION OF ABSTRACT OF REPORT OF THIS PAGE OF ABSTRACT Unclassified Unclassified Unclassified Unlimited NSN 7540-01-280-5500 Standard Form 298 (Rev, 2-89) Pre_ribed by A_ISI SlCl Z39-18 298-102 National Aeronautics and SPECIAL FOURTH-CLASS RATE POSTAGE AND FEES PAID Space Administration NASA Code YVI" PERMIT No G27 Washington, D.C. 20546-0001 USA official Business Penalty for Private Use, $300 POSTMASTER: If Undeliverable (Section 158 Postal manual) Do Not Return