Study of the integration of wind tunnel and computational methods for aerodynamic configurations

APPENDIX A. SOLUTION OF THE DOUBLET CONTRIBUTION TO THE INDUCED APPENDIX B. SOLUTION OF THE SOURCE CONTRIBU_ON TO THE INDUCED iv LIST OF SYMBOLS Vector from a panel corner point to a velocity scan point A Magnitude of vector Area Area of a panel f, Vector from a panel corner point on the same side as vector _ to a velocity scan point B Magnitude of vector Velocity potential influence coefficient at point J due to a uniform source distribution over BjK panel K Coefficient of drag C D Velocity potential influence coefficient at point J due to a uniform doublet distribution over CjK panel K Lift coefficient C L Pitching moment coefficient CM Pressure coefficient

cp

dS Differential surface area element Panel unit vectors in local coordinate system Total number of surface panels N S P An arbitrary point in space Corrected dynamic pressure qc Measured dynamic pressure qm Vector between a point P and an element dS S Configuration surface Imaginary surface at infinity Velocity vector v V Velocity vector magnitude Velocity influence coefficient at point P due to a uniform doublet distribution on panel K

V pK

due to a uniform source distribution on panel K Velocity influence coefficient at point P VOVK W Wake surface @ Total velocity potential Perturbation velocity potential Free-stream velocity potential Doublet singularity strength per unit area Source singularity strength per unit area Subscripts: i Interior region J Refers to panel J K Refers to panel K L Lower surface of a panel P Refers to a velocity scan point P U Upper surface of a panel W Refers to the presence of the wind tunnel walls in a PMARC model Refers to the absence of the wind tunnel walls in a PMARC model nw vi SUMMARY A study was conducted to determine the effectiveness of using a low-order panel code to estimate wind tunnel wall corrections. The corrections were found by two computations. The first computation included the test model and the surrounding wind tunnel walls, while in the second computation the wind tunnel walls were removed. The difference between the force and moment coefficients obtained by comparing these two cases allowed the determination of the wall correctionsl The technique was verified by matching the test-section, wall-pressure signature from a wind tunnel test with the signature predicted by the panel code (Panel Method Ames Research Center (PMARC)). To prove the viability of the tech- nique, two cases were considered. The first was a two-dimensional high-lift wing with flap that was tested in the 7- by 10-Foot Wind Tunnel at NASA Ames Research Center. The second was a 1/32-scale model of the F/A-18 aircraft which was tested in the low-speed wind tunnel at San Diego State Univer- sity. Results of this study indicate that the proposed wind tunnel wall correction method is comparable to other methods and that it also inherently includes the corrections resulting from model blockage and wing lift.

1. INTRODUCTION Wind tunnels provide a well-controlled environment which is free of atmospheric hazards for aero- dynamic measurements. One of the typical problems associated with a wind tunnel test is the error intro- duced into the measurements by the presence of the wind tunnel walls. Since the flow in a wind tunnel is constrained by the walls, it must accelerate around the model in order to satisfy the continuity equation.

As a result, the model behaves inside the wind tunnel as if it were at a slightly greater speed than the nominal wind tunnel velocity (ref. 1).

The increased velocity or dynamic pressure, caused by the solid blockage of the model, results in an increase in all the forces and moments acting on the model. Because the velocity in the viscous wake is slower than the velocity in the free stream, an additional blockage, known as wake blockage, is created.

As the wake grows, the free-stream velocity must increase, again as defined by the continuity equation.

The increase in velocity around the model and its wakes causes a pressure gradient to develop (accord- ing to the Bernoulli equation) which creates an apparent increase in drag on the model. A blockage cor- rection is needed to be able to determine the incremental velocity that, when added to the free stream, accounts for the extra forces and moments. Once the velocity increment is found, the aerodynamic data can be "corrected" to obtain the desired free-air results.

The angle of attack of the model is also affected by the wind tunnel boundaries. The presence of the wind tunnel walls alters the normal curvature of the flow around the test body, creating an apparent increase in the angle of attack (ref. 1). To complete the wind tunnel wall corrections, the geometric angle of attack needs to be corrected for this apparent increase. In this study, however, only the dynamic pres- sure correction was calculated, although the angle-of-attack correction can be determined using the same numerical technique.

Most methodsfor determiningthedynamicpressure correctiontakea mathematical approach based

on aerodynamic potentialtheory.Using a potentialflow model,a solid bodycanbe simulatedwith a source-sink systemwhile the wakeis simulatedwith doublets.Early methods,suchasHerriot's (ref. 2), attemptto represent the solid blockageby usingimages. Herriot simulatesthemodel with a source-sink distributionandthewalls with aninfinite distributionof source-sink images.The correctionis foundby summingup the effect of theimagesalone.Maskell (ref. 3) usesa similar methodologyto determinethe increase in drag.In this method,the wakeblockage is replacedby a sourcewhich,because of continuity, is matchedby a downstream sink of the samestrength. Imagesin this modelarecomposed of adoubly infinite source-sinksystemwhich is spaced onetunnelheightapartvertically andonetunnelwidth apart horizontally(ref. 4). The incrementalincrease in velocity dueto the imagesis the sourcestrength divided by twice the width of thejet multiplied by the heightof the tunnel.The increased dragcanthen beeasilyfoundfrom the incremental velocity.

Anotherapproach to theproblemis the wall-pressure signature methoddevelopedby Hackett

(ref. 5).Hackett usesaninversemethodto determinethestrengths of a seriesof sources andsinksthat,

whenacteduponby an appropriate wall-imagesystem, will producethe samepressure signature

observed during the test.In this method,the solid andwakeblockages arehandledseparately. The wake blockageis foundby matchingthe actualwakepressure signature with a signaturegenerated by a poten- tial sourceimagesystem.The correctionis derivedby finding theinfluenceof the imagesystemalone.

The surfaceblockageis handledin the samemanner.

Similarly, it is possibleto determinethecorrectionby usingpanelmethods. Low-orderpanelcodes modelthe geometryof a bodywith a seriesof panels.A flow field is generated by distributingsource and/ordoubletsingularitiesover thepanels.Oncea problemis modeledcorrectly,the panelcodescan determinetheforces,moments, andpressures actingon thebody.To determinethe wall correctionsby this method,two computations arenecessary. Thefirst computation modelsthe geometryof thetest

bodyandthe wind tunnelwalls,while the second computationmodelsonly the geometryof thetest

body.Thevalidity of the first computationis evaluated by comparingthe wall-pressure signature obtainedin the wind tunneltestat thecenterlineof the testsectionwith the signaturecalculatedby the panelcode.If the signatures match,thenthetunnelwalls aremathematically removedfrom the com- putermodelandthe forces,moments, andpressures arerecalculated. The differencebetweenthe two cases is thecorrection.

Two cases werestudiedto demonstrate themethod.The first casewasa two-dimensional, high-lift

wing with a singleflap which wastestedin the7- by 10-FootWind Tunnel atNASA AmesResearch

Center(ARC) (ref. 6). The second casewasa 1/32-scale modelof anF/A-i8 aircraft which wastestedin

thelow-speedwind tunnelat SanDiego StateUniversity (SDSU).A low-orderpanelcode,Panel

MethodAmesResearch Center(PMARC) (ref. 7), which is beingdevelopedatARC, wasusedfor the

computations. The cases werechosen to showtheversatilityof thecodeto handlearelatively simple

geometry,thetwo-dimensional wing andflap, anda complexgeometryconsistingof a three-

dimensional fighter. After a reviewof the mathematical modelin chapter2, the resultsfrom thetest cases arepresented in chapter3.

2. THEORY 2.1 The Mathematical Model In this chapter a brief description of the important principles of panel methods will be provided.

These methods, as well as the current low-order panel code (PMARC) are based on potential-flow theory. The steady-state flow is considered to be irrotational, incompressible, and inviscid, and must therefore satisfy Laplace's equation V2_ = 0 (1) applied over a control volume. The closed surface of a body divides the flow field into two regions--an inner region and an outer region--as shown in figure 1, where both flows satisfy equation (1). For most applications, the flow field outside the body is the region of interest. The boundary conditions for equa- tion (1) are 1. The normal velocities across the body's solid boundaries must be equal to zero or a prescribed value.

2. The flow disturbance due to the model must diminish far from the aircraft.

3. The flow field must satisfy the Kutta condition along sharp trailing edges to fix the circulation.

Equation (1) is solved by applying Green's Identity to the volume encompassed by both flow regions. The resulting surface integral defines the potential at any point in the region such that (ref. 8)

(2)

Op = _ (_- _i)_. V dS 4r_ r _" (Vt_- Vt_i)dS S+W+S** S+W+S,_ In the integral, r is the distance from a point in a region, P, to an area element, dS, on the surface of a body or a wake. The variable fi is the unit normal vector of the surface or wake element pointing into the flow and the subscript i represents the internal flow region. The first integral of equation (2) is the contribution from a distribution of doublets on the surface and wake per unit area. The second integral is the contribution from a similar distribution of sources per unit area. This equation is reduced by applying the second boundary condition and by assuming that the upper and lower wake surfaces are infinitesi- mally close to each other. This thin-wake assumption allows the entrainment in the wake to be neglected; therefore, the jump in the normal velocity is zero, which causes the source term to disappear from the integral (ref. 9). The simplified equation becomes

s S w

where000is thefree-stream potentialof the boundarysurfaceat infinity.

If point P lies on the bodysurface, the integralsbecome singular.The singularityis avoidedby assuminga hemispherical deformationof thebody's surfacecentered at P (ref. 8).In thelimit wherethe

radiusof thedeformationgoesto zero,theresultingtotal potentialatpoint P is

1 1 1 1

¢Yi_p = -._ If (_ - _i)_l "V(1)dS -_(_-_i)p-'-_ f f rfi "(V_ - V_i)dS

S-P S (4) w where 1/2(qr--@i) p is the contribution from the hemispherical deformation only. The subscript S-P denotes that the point P is excluded from the integral. Equation (4) is solved by applying the internal Dirichlet boundary condition, which assumes that the internal potential equals the onset potential. As a result, the surface singularities have to provide only the perturbation potential instead of the total poten- tial (ref. 8). Looking at P inside the surface, equation (4) reduces to (5)

1 . • + _ =

4n _,, ,, ,, 4re J Jr (V_-VO_o)dS _-_--fflf(rbu _L)fi.VI1)dS 0 S-P S W The doublet density on the surface exterior is defined as the perturbation potential (ref. 9) (6) 4rqa = • - ¢0,, = and the source density is defined as (ref. 9) (7) 4nor = -fi-(V¢ - V_) The source strength of each singularity is found by applying the first boundary condition to equa- tion (7). The doublet strengths are found by reducing equation (5) into a single integral which contains only the unknown singularities. This is accomplished by substituting equation (6) into equation (5).

After solving for the doublet and source strengths, the potential at any point P is found by substituting and I.t into equation (5) and solving for 4)0, which results in (8) $ S W In the equation, K = 0 if the point P is not on the body's surface, K = 2n if P is on a smooth part of the outer surface of the body, K = -2n if P is on a smooth part of the inner surface of the body, or if P is at a crease in the surface, then K = the solid angle contained at that crease (ref. 8).

The external velocity field is found by Vp = VCI_p (9) P, the velocity is At any point (10) Vp=-II BVp[n" VK(1)]dS - II _VK(-lr)dS - II_tVp[ _ "VK(1)ldW + V¢¢ S S W where Vp is taken with respect to the coordinates of point P and VK is taken with respect to the cen- troid of panel K.

By breaking up the surface of a body and its wake into panels, the integrals of equations (8) and (10) can be rewritten in a discrete form. This is done by assuming that constant-strength doublets and sources are distributed on the panels and that the potential and induced velocity at a point is the sum of the influ- ences from each panel. The unknown doublet strengths can then be found by using a set of simultaneous equations that are defined as the sum of the surface integrals of each panel. Because the source strengths are known, they are moved to the right-hand side (RHS) of the resulting matrix equation. The discrete forms of equations (8) and (10) are (ref. 9) Ns NW NS J = 1,N S (11) E (I-I-KCJK) + E (I-tWLCJL) + E (IKBJK =0; K=I L=I K=I Ns NW NS (12) _"p= V_ - E (.kVtlpK) - E (.LVBLK) - E 05k V.pK) K=I L=I K=I where the potential influence coefficients are found by evaluating the gradients from equation (10). The influence coefficient for the source is BjK = (13)

lds

Panel K and (14) CjK = Panel K for the doublet.

The velocity-influence coefficients for the source and doublet are, respectively (ref. 9), (15) Panel K and (16) Q_JK =- ff Vj[RK" VK(1)] dS Panel K In PMARC, either the Dirichlet or Neumann boundary conditions can be applied to the surface panels, and a combination of the two can be applied to a given geometry. Equation (11) is applied if the designated patch (a group of panels) is part of a thick boundary enclosing an inner volume. This type of patch is called a Dirichlet patch. A form of equation (12), where only the induced normal velocities are considered, is used if the patch is part of an open surface. This type of patch is called a Neumann patch (ref. 9).

The remaining discussion will focus on the solution of the velocity equation (12). The solution technique involves finding the velocity contribution from the doublet and source of each panel. The total contribution is the sum of all the panels. The induced velocity at a point P by a constant unit strength doublet distribution over a panel is given by equation (16). Using the vector identity

= x x e+ e)

equation (16) becomes (17) Panel K Noting that and remembering that potential flow satisfies Laplace's equation, equation (17) further reduces to (18) Panel K or (19) P_elK By applying the identity _f (fi x V)dS = _d_ C S equation (19) can be rewritten as (20) but (21) due to constant doublet distribution over a panel is given by Finally, the velocity at any point P (22) Wl.tjK -" --_ r X-r d_ This is the Biot-Savartequationfor thevelocity inducedata point by a line vortex.

The line integralof equation(22) is solvedby considering only onesideof a panelat a time.The total contributionfrom thepanelis the sumof thecontributionsof thefour sides.The solutionof equa-

tion (22) for onesideof a panelis

(23) VlajK= A(B)[(A)(B) - _. b] where A and B are the magnitudes of _ and b defined by figure 2.

If the point in question is far enough away from a panel, a far-field approximation can be made without significantly affecting the solution's accuracy. The approximation assumes that a doublet can be treated as a point doublet instead of a distributed doublet. This allows the integral to be replaced with the multiplication of the integrand and the panel area whose contribution is being evaluated. The same argument holds for the treatment of the source contribution. Assuming a unit doublet is used, the far- field expression is (24) or (25) Vi.tjK = -VJ(_)areaK ,- j where r is the distance from the centroid of panel K to the influenced point.

The solution of this equation is -3(PN)? + r2fi (26) VgjK = -area K r 5 The completed proofs of equations (23) and (26) and the definition of PN are given in Appendix A.

The contribution to the induced velocity of a constant unit strength source distribution over a panel is given by equation (15)i After substituting equation (21) into equation (i5), it becomes

(27)

Panel K

The solutionis

(28)

VcrjK= GL[(SM)(I')- (SL)(lVl)]+ CJKn

SeeAppendixB for thedefinitionsof the nomenclature.

The far-field equationfor thesourceof unit strengthis simply

(29)

Vo :area ( )

For the completed proofs see Appendix B.

It should be pointed out that although the doublet solution, equation (23), is valid for a twisted panel (a panel that is nonplanar), the source solution, equation (28) is not. This problem should not usually affect a particular geometry that may have a limited number of twisted panels because the far-field approximation is used about 90% of the time for most configurations. In some cases, however, a twisted panel may cause the doublet solution to converge slowly. This phenomenon is investigated in Appendix C.

Since the singularities are known from the doublet solution, the velocities on each control point can be evaluated (ref. 8). The tangential velocities are found by differentiating the doublet strengths in the appropriate directions, while the normal velocity is either zero or a user-defined value. From the result- ing velocity at each control point the corresponding pressure coefficient is found by the equation _:

(30)

CPK=I V 2 Finally, the lift and drag forces can be calculated by numerically integrating the pressure distribution, and the moment coefficients can be determined around a user-defined reference line.

2.1.1 Shortcomings of Potential Flow-Based Computer Codes- Because potential flow-based codes exclude viscous effects, they cannot predict friction drag. By assuming that a thin wake exists, the viscous wake blockage is reduced. This results in a decrease of the calculated drag on the computer model. Also, older panel codes could not accurately predict the shape of free wakes. PMARC improves this by taking into account the unsteady nature of the wake by using a time-stepping technique (ref. 10).

Although the wake is still assumed to be thin, the new wake modeling will allow a more realistic wake roll-up calculationandimprovethe computational capability.Modeling of separated flow is alsoa prob- lem for panelcodes.Onepossiblemethodfor modelingthe separation is for the userto attacha wakeat a guessed separation line on the bodyandto enclosethe endof the wakewith the endof thetrailing-

edgewake.This modelcanhelp incorporatetheeffectof wakeblockageinto thecomputations. This

technique, however,needs further study.

2.1.2 Method of Removing the Wind Tunnel Walls- Wind tunnel walls are removed by moving them far enough away from the tested body so they have little or no influence on it. Because it is impor- tant to retain the same matrix for the two computations, the integrity of the RHS of the doublet matrix equation is maintained by not removing the wind tunnel walls. Elimination of the tunnel walls from the model would result in a slight difference to the RHS which would result in a slightly different solution.

The extent of the difference would depend on the individual case.

2.1.3 Calculation of the Wall Correction Factor- The correction factor is found by taking the ratio of the lift coefficients of the two computer model cases and applying it to the dynamic pressure such that (ref. 11) (31) q m , nw JCalculated To find the "corrected" dynamic pressure, qc, the lift-coefficient ratio is simply multiplied by the mea- sured dynamic pressure from the wind tunnel test, qm- The corrected dynamic pressure can then be applied to the aerodynamic coefficient calculations to find the corrected force and moment coefficients.

3. DISCUSSION OF RESULTS 3.1 Case One: The Two-Dimensional High-Lift Wing The two-dimensional test case was modeled after a wind tunnel test of a high-lift NACA 4412 airfoil equipped with a NACA 4415 single-slotted flap at the ARC 7- by 10-Foot Wind Tunnel (ref. 6). For the wind tunnel test, the chord length of the wing was 35 in. and 14 in. for the flap. The angle of attack was 8.2 ° and the flap deflection was 21.8 ° .

The two-dimensional characteristics of the wing and flap were modeled by extending their span to 1000 times the chord length of the wing. The upper and lower walls of the wind tunnel were modeled in the same manner. The side walls were not included in the computer model because they were not neces- sary because of the two-dimensionality of the problem. The pressures and forces on the walls and the airfoils were taken only from the center of the configuration to assure that they would not be skewed by tip effects. Figure 3 shows a section of the PMARC model.

3.1.1 Verification of the Computer Model-The first step was to estimate the distortion in the free stream resulting from the model blockage effects in the wind tunnel. This was done by examining the predicted velocity profile at the centerline of the test section near the location of the wind tunnel pitot tube. The velocity profile is presented in figure 4. The velocity profile does show a dynamic pressure increase which, as stated earlier, is caused by the blockage effects. Since no data from the experiment were available, this procedure was used only to validate that blockage effects were predicted by the computer model.

The next step was to compare the wall-pressure signature resulting from the model blockage effects in the test section. The comparison of the wall-pressure signatures from the wind tunnel test and the computations are shown in figure 5. The peak from the wall-pressure signature matched very well, thus giving confidence to the technique. The lower wall-pressure signatures, however, did not. One possible explanation (keeping in mind that the wind tunnel test was of a high-lift nature) is that a separation bubble occurred at the floor of the wind tunnel during the test. It would have resulted from the circula- tion caused by the wakes from the airfoils interacting with the boundary-layer separation from the floor, which the panel code would not have been able to predict. Another possible explanation is that the highly deflected flap wake interacted with the floor boundary layer, which, also, could not be modeled by PMARC. In either case, it is impossible to be certain because neither effect was observed during the experiment.

Another means of checking the validity of the panel model was to compare the pressure distributions over the wing and flap airfoils, as shown in figures 6 and 7, respectively. Included in the figures are the pressure distributions from the PMARC test case that did not include the tunnel walls. PMARC accu- rately predicted the pressure distribution over the wing. The discrepancy between the wind tunnel test data and the PMARC test data for the flap was attributed to the separation from the wing disrupting the flow over the flap. The large pressure peak at the leading edge of the flap was due to the high accelera- tion of the flow predicted by the code through the flap gap. This occurred because the panel code could not predict the viscous flow in the gap region. The wind tunnel test data also showed a separated wake coming off the last 30% of the flap, which PMARC did not predict.

Anotherapproachtakento showthatthe panelcodepredictedthe solid blockageeffect wasto move

thewind tunnelwalls awayfrom thewing andflap to determinewhetherthe solutionof thelift and

momentcoefficientsconverged as theheightbetweentheairfoils andthetunnelwalls increased.

Figures8 and9 showtheresultsfrom the investigation. As expected, the lift coefficientdecreased for boththe wing andthe flap. This wasa resultof thedecrease of the dynamicpressure over theconfigura- tion andit is anexcellentexampleof the effectof solid blockage.The momentcoefficientof the wing decreased asthe walls weremoved,but increased for theflap. The decrease in lift caused a decrease in thepitching momentandresultedin a lowering of theCM of the wing. Theeffect on the flap would be explainedby a broaddistributionof the lift. In otherwords,the lift wasnot concentrated nearthequarter chordbecause of a shift of the centerof pressure. Theresultwasthat thelift wasevenlydistributedover theentireflap. Therefore,althoughthe total lift coefficientdecreased, the pitchingmomentcoefficient

increased asthe tunnelwalls weremovedfartherfrom themodel.Again,a combinedsinglecorrection

for the solid andwakeblockages is foundby takingthepercentage differencebetweenthe two eases, with andwithoutthe influenceof the tunnelwalls.

Othermethods,however,calculatethe solid blockageandwakeblockagecorrectionsseparately.

Keepingthis in mind, matchingthewing pressure distributionwith thewind tunneltestgivescredibility to the solid blockageeffectbeingpredictedcorrectlyby PMARC. The interactionof the flow over the wing with the wind tunnelwalls wasresponsible for theincrease in dynamicpressure which is the solid blockage.The disparityof the pressure distributionoverthe flap betweenthe PMARC testcaseandthe

wind tunneltestshowthatthe PMARC modeldid not predictthewakeblockageasaccurately. This was

dueto a separated wakecomingoff theflap, which could not bemodeled.It is difficult to determine whetherthis differencewas appreciable because the corrections obtainedfrom PMARC weresimilar to thecorrectionsobtainedusingothermethods(ref. 6).

3.1.2 Wall Correction Computed by PMARC- The total section lift data and the corresponding corrections from PMARC are tabulated in table 1. The data are taken from the five spanwise sections of the configuration. The coefficients were lower on the last section because of tip effects and because this was a three-dimensional effect, they were omitted from the correction calculations. Slight tip effects also caused minor increases in the coefficients farther out in the spanwise direction. The PMARC lift data compared favorably with the wind tunnel test lift data. The test measured a CL of 3.2 (ref. 6) for the main wing, a 14% change compared with the PMARC test case. The difference can be attributed to the overprediction of the leading-edge pressure peak by PMARC. The overprediction is a characteristic of panel codes because they cannot predict the viscous flow that occurs at the leading edge of an airfoil.

TABLE 1.- COEFFICIENT OF LIFT CALCULATED BY PMARC Section With Tunnel Wall Without Tunnel Walls qc]qm 5.055 1.071 5.413 5.055 1.071 5.413 1.071 5.413 5.055 1.071 5.053 5.413 1.078 5.412 5.019 3.1.3 Wall Correction Comparison- The wall corrections were computed by four other methods and axe tabulated in table 2. The six methods from reference 4 were of the same magnitude (the methods of Pope, Allen and Maskell and PMARC were almost identical). The methods of Allen and Maskell, Pope, and Thorn were based on the classical approach outlined in the introduction. The equation used by Thorn was a simplified form of Herriot's equations which predicted a higher correction than the others.

Merker's was lower, but his method was originally developed for automotive wind tunnel testing.

TABLE 2.- WALL CORRECTION FACTORS BY VARIOUS METHODS Method qc/qm 1.072 Allen and Maskell 1.046 Merker PMARC 1.071 1.070 Pope 1.090 Thom 3.2 Case Two: The F/A-18 Aircraft Model 3.2.1 Model Fabrication and Wind Tunnel Apparatus- The F/A-18 aircraft test was conducted in the low-speed 32- by 45-in. closed-circuit wind tunnel at SDSU. The 1/32-scale model was manufac- tured by the Hasegawa Model Company of Japan and was reinforced internally with a steel frame, sev- eral balsa wood ribs, fiberglass, and epoxy so it would be structurally sound at high angles of attack. The model was 23.5 in. long with a wingspan of 14 in. and a mean aerodynamic chord of 4.32 in. The test was conducted with a 2.5-in. radar boom attached at the nose (without the wingtip missiles). Diagrams of the model and the test section are shown in figures 10 and 1 l, respectively. The model was connected to two fixed struts that were attached to the wings and an adjustable hinged jackscrew that was attached to the arresting hook underneath the tail section. The force and moment data were acquired using a six- component load balance in conjunction with a Hewlett-Packard Data Acquisition System. The static upper wall pressures were taken along the centerline of the tunnel using a differential water manometer board. The signature measurements extended from the plane of the pitot-static ports to downstream from the model but they were still within the test section as shown in figure 12.

3.2.2 Validation of the Wind Tunnel Test- The wind tunnel tests were conducted at varying dynamic pressures and angles which ranged from 16.4 to 36.9 lb/ft 2 and 1° to 56 °, respectively. The dynamic pressures represented a range of velocities from 117 to 176 ft/sec, which resulted in Reynolds numbers between 242,000 and 364,000, based on the mean aerodynamic chord. The test angle range was chosen to serve a dual purpose. The first and foremost reason was to show the viability of the panel code wall correction method. The second was to determine the tunnel wall corrections that would be needed for a full-scale test at high angles of attack in the 40- by 80-Foot Wind tunnel at the National Full-Scale Aerodynamic Complex at ARC. The 1/32 model size was chosen because it allowed the opportunity to geometrically simulate such a test in the SDSU wind tunnel because the plane/wind tunnel test section area ratios were the same. Since a large amount of separation would most certainly occur at high angles of attack, the PMARC calculated wall corrections would only be a guideline for that wind tunnel test.

To determinewhethertheSDSUwind tunneltestdatawereaccurate, the measured aerodynamic

characteristics werecompared with theresultsfrom reference 12.The comparison is presented in figure 13.The CL andCDdatashowa very goodcorrelationbetweenthetwo tests. From this compari- sonit wasdetermined thatthe dataobtainedfrom the wind tunneltestwerereasonably accurate such thatvalid wall correctionscould becalculated.

3._.2.3 Verification of the Computer Model- The PMARC F/A- 18 computer model was modified from an existing data file generated by McDonnell Douglas which is presented in figure 14. The changes involved modifying the panel density of the wings and both stabilizers and eliminating the sharp edge created by the intersection of the ventral nacelles. The changes were made to eliminate solution conver- gence problems of the original McDonnell Douglas model. By smoothing out the sharp edges on the body and by eliminating the inconsistent paneling, a "cleaner" computer model was produced that did not have the convergence problems. The repaneled model is shown in figure 15. The finished model was not as detailed as the original, but because the only concern was the blockage effects, it was considered an acceptable tradeoff.

The geometry went through three derivations before the final configuration of 1336 panels was settled upon. Problems occurred at the intersection of the the wing and the horizontal and vertical tails which resulted in a couple of slightly twisted panels on the main fuselage near the trailing edge of the wing which caused the solution to converge slowly. The upper wall-pressure distribution was used to validate the computer solution. The comparisons of the wind tunnel and PMARC signatures are pre- sented in figure 16. They do not compare as favorably as the two-dimensional airfoil. The trends were the same; however, the magnitudes were not. The wind tunnel test pressure coefficient peaks were about 20% larger for the 46 ° and 20 ° cases and as much as 80% larger between the 0 ° (the PMARC model) and the 1° (the wind tunnel test) case. These results indicate that the computer model was not creating as much blockage as the wind tunnel model.

The CL of the F/A-18 computer model was affected by the placement of the wakes. Originally, the wakes extended from the trailing edges of the wing and the horizontal and vertical tails and were allowed to follow the path of the free stream. At low angles of attack, however, the CL was higher with- out the influence of the wind tunnel walls than with the walls' influence. It was obvious that the com- puter model was in error. After remodeling the aircraft it was discovered that the problem was with the placement of the wakes. By allowing the wing wake to follow the free stream, it cut through the vertical tail and caused an excessive amount of drag on the aircraft. The problem was solved by manually forc- ing the wing wake around the vertical tail. Also, instead of the wakes immediately following the path of the free stream, they were forced to follow the aircraft's angle of attack for a distance half the length of the plane before they turned in the direction of the free stream. The distance the wake followed the air- craft's angle of attack was determined after manipulating many different test cases. It was discovered during this time that an endless variety of lift data within a 10% margin could be generated depending on the placement of the wake. The best course was to place the wake where it would be expected during a wind tunnel test. It must be pointed out that the wake must be placed in the same location for both com- puter calculations. After the adjustments to the wakes were made, the CL data and the wall corrections at all angles of attack were more believable. The predicted aerodynamic characteristics are presented in figure 13.

3.2.4 Wall Corrections Computed by PMARC- Before discovering that the wake placement was causing most of the problems with the computer model, a study was conducted to determine whether the wing of the F/A-18 model, figure 17, followed the same CL trend as the full configuration. The wing was found to follow the expected trend, which led the troubleshooting in the direction of the wake prob- lem. The correction data for the wing and the full configuration are presented, with other correction techniques, in figure 18. It can be seen from figure 18 that the panel code correction method predicted wall corrections similar to the classical methods. The conclusion, therefore, is that the technique was successful in adequately predicting the wall corrections for the F/A-18.

4. CONCLUSIONS

A studywasconducted to determinethe viability of usinga low-orderpanelcodeto calculatewind

tunnelwall corrections. Resultsof theinvestigationwerepromising. Thepanelcode,PMARC, pre-

dictedthedynamicpressure wall correctionfor a two-dimensional airfoil to be 1.071,which wassimilar to thewall correctionpredictionmadeby othertechniques. Although theflow separation thatoccurred during thewind tunneltestcould not bemodeledby PMARC, the wall correctionwasnot significantly affected.The predictionof theF/A-18 aircraftwall corrections posedotherchallenges andproblems,of

which the geometrydevelopment andwakeplacementwerethe mostserious.The geometrygeneration

wasa challengebecause of its complexity,andthevariety of the wakeplacementwasa problembecause it severelyaffectedthe wall correction.Eventually,theproblemsweresatisfactorilyresolvedsothatthe final resultscompared favorablywith othermethods.

Although manyproblemsoccurredduring this study,muchinsight wasgainedinto the useof panel

codesasa means of predictingwind tunnelwall corrections.It wasevidentthatto usethis technique

effectively,caremustbetakenduringthe generation of complexgeometries andwhenchoosingthe

properwakeplacements.In thefuture,it is hopedthatimprovedseparation andboundary-layer model- ing techniques will bedeveloped. Whenthis is accomplished, theaccuracyof wind tunnel wall correc- tionsfor complexgeometries determined by panelcodeswill greatlyimprove.

PRECEDING PAGE BLANK NOT FILMED

APPENDIX A SOLUTION OF THE DOUBLET CONTRIBUTION TO THE INDUCED VELOCITY An introductory phase of this research project was to study the structure of first-order panel codes.

For this study the influence coefficients were analyzed first and then the formulation was numerically investigated. In Appendices A and B the mathematical formulations are provided, and in Appendix C the numerical influence of these elements will be investigated.

Starting with the Biot-Savart equation, VILI'JK = ___ _ X dg (A1) . r 3 By considering only one side of a panel, the line integral can be changed to a single-element integral.

Now, let _ represent the direction formed by _ x d_ such that × d_ = -_r sin 0 ds (A2) From figure 19 h (A3) r=_ and h (A4) tan 0 which results in (A5) Substituting in equation (A2) and equation (A5), equation (A 1) becomes BLANK NOT FILMED P_ECEDiNG PAGE (A6) VI.tjK =- _(h/sin0)sin0(h/sin20)d0 O2 e r ,-,102 = _h[COS01 _ c0s02] = --ff sin0 dO = -_-t-cosuJ01 f (h3/sin30) 01 01 From figure 19 (A7) COS01 = (A8) Substituting equations (A7) and (A8) into equation (A6) (A9) g= unit vector between _ and _-

(_x(_-_)) (_x_-_×_) _-_

(A10)

i_×(___) I-I_×___×_1I_×_1

The perpendicular distance h is (A11)

_____ ___i _I._-_ I_

Substituting equations (A9), (A10), and (A11) into equation (A6) yields (A12)

(_×_)l_:__]_+sFA*_-- __ (_×_---))_A+S>[ A,B

_ [A*B-_.b]

I_×_ll_×_J_-r_L A,_ i_×_1 _

And finally, (_x b)(A+B) (A13) VgjK = A,B,(A*B- ft. _ ) The point doublet is simply the integrand from the general solution multiplied by the panel area.

Vi.tjK = _VjIfi. V(1)], areaK = -areaK, Vj(_) (A14) Letting results in n._'-- n r 3 = (12 + m 2 + n2) 3/2 thus V j( ) = Vj 3/2 12 + m 2 + n 2) 3 2 In _ - _ 5/2 J - _ m2 )5/2 [( 2"]'-" 3I( 2mn 1-:" 3I( 2n2 1_ =-_ 12+m2+n2)5i 12+m2+n 2) 12+ +n 2 = _ 1 2 5/2 _- 3 (12_+ m2 + n2)5)2 + 2 + m2 + n215/2/h ] [ n(l_+m]+nl¢]7 [ 12+m2+n 2 ]_

(12+m2+n) ] [( J[(1 ] j

-3* PN* Y+ r 2. fi (A15) - r 5 where, from figure 20, PN = Finally, 3* PN* ? + r 2.

(A16) VIXjK = area k r 5

APPENDIX B SOLUTION OF THE SOURCE CONTRIBUTION TO THE INDUCED VELOCITY The source potential is solved by the technique presented by Hess (ref. 13). From the potential (B1) BjK= _I }dS Panel,K where r = _/R 2 + Z 2 R = (x - e) 2 + (y - rl) 2 dS = R,dR*d0 Rewriting equation 031), R dO

RdR

BjK = 5]R2 + Z 2 But r = _]R 2 + Z 2 RdR dr= 4R 2 + Z 2 The integral now becomes (B2) BjK= dr dO= (r-lZl)dO= rdO-lZlAO Jlflzl j Realizing that R and Z represent the parallel and normal planes, where Z = 0 and x = y = 0, respectively, the integral from equation (B2) can be written _rdO = _RdO+ _ZdO If the integrals are solved for just one side of the panel, the line integral disappears and (B3) frdO = fRdO+ fZdO To solve the integrals it is necessary to define the following quantities. The directional unit vectors for the problem are, from figure 21 ffa y-ri 4R 2 + Z 2 Z fi= 4R 2 + Z 2 From figure 22,

Idl= 4(e2 - El) + (1"12 - I"11)

(E2 - El) COS0_ = d (I'12- rl]) sin t_ - d where _d (cosot, sin o_,0) R = (e-x,rl-y,0) RI = (el- x,rll- y,0) R2 = (E2- x,1"12- y,0 )

and

S= (e - x)costz + (11 - y)sin (x

S 1 = (e 1 - x)cos0t +(111- y)sinct $2 = (e2- x)costz + (1"12- y)sin ct The perpendicular distance from the vector d to the point defined by (x,y,0) is d× R = (X-el)sintz- (y rll)COSC_ = (x- e2)sin (x - (y - rl2)cosct R12 = _ The solution for the first term of equation (B4) is, noting that R 2 = S 2 + R22 S 2 = R 2 _ R22 cos0 = R12 R sin 0 = -- = R R and differentiating (R2_ R22)1/2 (1 / 2)_-_l/2]dR R 2 d0(cos0) = I'

R'2LR2(R2-R /"2J --

thus

fRd0 = fRR2 R*RI2dR = R(R2- R122)1/2 R12_RR2 dR

but

Finally, IR2+S 2 This equation can be rewritten as (B4) f Rd0= RI+ R2 +--_[ R12 log The second term solution is simply ZdO = Z dO = Z(02- 01)

S

from the 1 and m plane to the normal plane Translating 0 Thus Zfd0 = . -1(" S2Z tan _,RI_2 )- tan-I(RSI@R1 ) But from the trigonometry identity,

1 tan-l(Al- tan-l(1)= tan (B--DT

(B5) Zld0= tan-l( Z* R12(R1 $2-- R-- 2sl) ) z, The induced velocities are found by differentiating the potential, which yields for one side of a panel (ref. 13) OBJK IR-R-_ + R2+ I (B6a) Vx = Ox = c°s°t*R121°g + R2 _BjK IRI+R2+dl (B6b) Vy = _yy = sin or* R12 log R1 + R2 _ d -1( Z* R12(RIS2- R2S 1) 1 (B6c) _BJK = Z, tan - .....

The total velocity influence is found by summing the contributions from the four sides of the panel.

PMARC uses the nomenclature developed for the panel code VSAREO (ref. 9) which is different from the Hess nomenclature. The method of solving the problem in the VSAERO nomenclature was not clear until the Hess solution was developed. The conversion from Hess to VSAERO follows.

Nomenclature from VSAERO:

. -1[" RNUM-]

CJk : tan [ D--_--_J RNUM = SM* PN* (B* PA - A* PB) DNOM = PA* PB + pN2A*B* SM 2 PN = PJK" n

A-I I

B--I I

s=FI

PA = pN2SL + AI*AM PB = PA - AI*SM SM = g. ff'l SL = g* 1" AM= _.rTa AL = _.1 A1 = AM*SL-AI'_SM GL = g log N + B-

TABLE 3.- CONVERSIONFROM THE HESS

TO THE VSAERONOMENCLATURE

HESS VSAERO

1,m ,n

l, m, n

A = I(AL, AM)I a

Rl

B

R2

,S = (SL, SM) a

= (sinoc*R12,cosoc*R12 )

d×R AM*SL - AL*SM

PB

Z*S2

PA

Z*S1

RNUM

Z, R12(R 1* S2- R2* S1)

DNOM

Z* SI* $2+R22" RI*R2

aThe components are in the panel plane.

The final VSAERO form is (B7) VcrjK = GL(SM* 1 - SL* r_) + CjKn The point solution is (B8) WffjK = area K -'_ r J

APPENDIX C PANEL ANALYSIS For this panel analysis, the program PANEL.ANY (see the following section) was developed. The program was designed to find the induced velocity at an arbitrary point in space due to the influence of a uniform distribution of doublets and sources over a given panel. The investigation was done in three parts. The fin'st part was to determine at what point the far-field approximation, based on the panel chord length, could be implemented. This was important because the computer time needed to calculate the far-field approximation was 40 times faster than the full integration technique. Considering that most problems consist of thousands of panels, and that the contribution from each panel must be calculated, it was evident that the approximation was important to the overall efficiency of the panel code. The second and third parts of the analysis were performed to determine the magnitude of the induced velocity at dif- ferent locations from a uniform doublet and source distribution over a planar and twisted (nonplanar) panel, respectively. This analysis was important in understanding how the integration solution differed from the far-field point solution from different locations.

The first task was accomplished by using the program to choose an arbitrary point in space. The pro- gram calculated the induced velocity at that point by both the integral and the point methods. The pro- gram then formed a line between the chosen point and the center of the panel. The line was divided into 15 separate points and the program calculated the induced velocities at each point. A far-field radius was found by comparing the divergence between the point calculation and the more accurate integral formu- lation. The radius was the distance where the difference between the two methods was not appreciable.

Many different initial point locations were tested during the analysis. After some trial and error, it was determined that a good starting radius was six panel chord lengths away from the center of the rectangu- lar panel, with the chord length of the panel equaling unity. Three of the test cases are presented here.

The first case was a point directly above the center of the panel. For the second case the point was located over the median of the panel (fig. 23), where DW = 45 °. For the last case the point was over the horizontal of the panel (fig. 24), where DW = 20 °. The magnitude of the vector R, as stated earlier, was six panel chord lengths away from the center of the panel. Figures 25, 26, and 27 show the results from the three cases, respectively. The divergence of the first case occurred at the point farthest away from the panel at a radius of 2. The other two cases began their divergence closer to a radius of 1.6. From the other test cases not presented here, the worst divergence also occurred near a radius of 2. Allowing for some margin of safety, the far-field radius for the point solutions was finally determined to be 2.5.

The next task was the evaluation of the induced velocity as a line traversed over the panel. The user chose an initial point to begin the traverse either over the median, the horizontal, or a distance off the median of the panel (figs. 28 and 29). As before, the line was divided into 15 separate points. Except, in this case, the height above the panel remained constant. From figures 30 and 31, it is seen that the induced velocity of a line of points over the median and the horizontal of the panel were exactly the same for both the integral and point source methods. For this case the line was at a height of one panel chord length. The off-median case showed the same behavior. For this particular comparison the far- PRECEW,_G PAGE BLANK NOT FILMED field factor was not important because only the difference made by the location of the line of points was studied.

The last task was to investigate the effect of a twisted panel on the induced velocities. As stated earlier, the doublet integral solution was not affected by a twisted panel because it treated the sides of a panel as line vortices. For this reason it was not studied. Thus, only the source solutions are presented here. Figure 32 shows the geometry of the twisted panel. For the test cases the height was one radius measured from the panel center and the line of points traversed the up diagonal of the panel. Results from twist angles ('I_) of 0 °, 10 °, and 20 ° are shown in figures 33, 34, and 35, respectively. The inte- gral solution was affected by the twisted panel; however, the point solution was not. At this time, no explanation can be found for the behavior of the integral solution.

The study was concluded by examining the influence of points of an off-median line over a twisted panel in which TW = 10% Two cases were considered. The first was an off-median line that fell directly over the panel at DM = 0.25. The results are shown in figure 36. The only significant difference between the point and integral solutions was a slight phase shift. The second case considered a line that did not fall over the panel at DM = 3. The interesting results of this case are shown in figure 37. Again, no explanation can be offered. A further thorough analysis of the mathematics involved with the source integral solution will be necessary to answer the questions that resulted from this study.

C.I The PANEL.ANY Program C PROGRAM PANEL.ANY DIMENSION X(5),Y(5),Z(5) PI=3.14159 EPS=I.E-06 THE45=SQRT (2.)/2.

DUB= 1.0 SIG=I.0 T=0.0 CINC=0.0 OPEN (2, FILE=' INDIV' ,STATUS= 'NEW' ) 1 CONTINUE C ************************************************** C CASE ONE: MEDIAN *** C CASE TWO: OVER CORNER *** C CASE THREE: STRAIGHT LINE OVER MEDIAN *** C CASE FOUR: STRAIGHT LINE OVER HORIZONTAL *** C CASE FIVE: CHOOSE INITIAL POINT *** WRITE (6,*) 'ENTER CASE AND TWIST(DEG) : ' READ(5,*) LLL, TW TW=TW*PI/180.

X(1)=-.5 X(2)=.5 X(3)=.5 X(4) =-.5 Y(I)=-.5 Y(2) =-.5 Y(3)=.5 Y(4)=.5 DZ=TAN (TW) IF (DZ.GT. 0.0) THEN Z (1) =DZ Z (2)=-DZ Z (3) =DZ Z (4)=-DZ ELSE DO 5 I=i,4 z (I)=0.0 CONTINUE ENDIF X (5) =X (1) Y (5) =Y (i) z (5) =z (i) IF (LLL. LE. 2) THEN WRITE(6,*) 'ENTER ANGLE:' READ(5,*) THETA THETA=THETA*P I / 18 0 .

WRITE (6,*) 'ENTER INCREMENT:' READ (5, *) TTT ELSE IF (LLL.EQ. 5) THEN WRITE (6,*) 'ENTER THE POINT LOCATION OF INTEREST:' *) PXI PYI PZI READ (5, , , WRITE (6,*) 'ENTER INCREMENT:' READ (5, *) TTT GO TO 7 ENDIF WRITE(6,*) 'ENTER OFF CENTERLINE INCREMENT: ' READ (5, *) CINC ENDIF CALL CASE(LLL, PI,THETA, THE45,DI,PXI,PYI,PZI) TIXY=SQRT(PXI*PXI+PYI*PYI) /15.

7 CONTINUE DO i00 NT=I,31 T=T+I.

TT=T*TTT IF (LLL. LE. 2 .OR. LLL.EQ. 5) THEN pX=PXI*TT PY=PYI*TT pZ=PZI*TT ELSE IF (LLL.EQ. 3) THEN PX=PXI-(T-I.)* (PXI/15.)

PY=PYI + CINC PZ=PZI END I F IF (LLL.EQ. 4) THEN PX=(PXI-((T-I.)*TIXY/SQRT(2-) )) + (CINC*THE45) PY=(PYI-((T-I.)*TIXY/SQRT(2-))) + (CINC*THE45) PZ=PZI ENDIF ENDIF RDI ST=SQRT (PX*PX+PY*PY+PZ*PZ) VX=0.0 VY=0.0 VZ=0.0 VXS=0.0 VYS=0.0 VZS=0.0 VXD=0.0 VYD= 0.0 VZD=0.0 PVXS=0.0 PVYS=0.0 PVZS=0.0 PVXD=0.0 PVYD=0.0 PVZD=0.0 PNLX=. 25" (X (i) +X (2) +X (3) +X (4)) PNLY=.25* (Y (1) +Y (2) +Y (3) +Y (4) ) PNLZ=.25* (Z (1) +Z (2) +Z (3) +Z (4) ) PNX=PX-PNLX PNY=PY-PNLY PNZ:PZ-PNLZ PNS=SQRT(PNX*PNX+PNY*PNY+PNZ*PNZ) DIX=X (3) -X (i) DIY=Y (3) -Y (I) DIZ=Z (3)-Z(1) m2x=x (4) -X (2) D2Y=Y (4) -Y (2) m2z=z (4)-Z(2) CRX=DIY*D2Z-D2Y*DIZ CRY=D2X*DIZ-DIX*D2Z CRZ=DIX*D2Y-D2X*DIY CRSQ=SQRT(CRX*CRX+CRY*CRY+CRZ*CRZ) AREA=CRSQ/2.

CNX=CRX/CRSQ CNY=CRY/CRSQ CNZ=CRZ/CRSQ PNN=CNX*PNX+CNY*PNY+CNZ*PNZ TCMX= (X (3) +X (4) ) /2. - PNLX TCMY= (Y (3) +Y (4) ) /2. - PNLY TCMZ=(Z (3) +Z(4)) /2. - PNLZ TMS=SQRT(TCMX*TCMX+TCMY*TCMY+TCMZ*TCMZ) CMX=((X(3)+X(4))/2. - PNLX)/TMS

CMY = ( (Y (3) +Y (4) ) /2. - PNLY)/TMS

CMZ= ( (Z (3) +Z (4) ) /2. - PNLZ)/TMS C LX= CMY* CNZ -CNY * CMZ CLY =CNX* CMZ -CMX * CNZ CLZ=CMX* CNY-CNX*CMY PVXD=AREA* (3. *PNN*PNX-PNS* PNS*CNX) / (PNS * *5 ) PVYD=AREA * (3. *PNN*PNY-PNS*PNS *CNY) / (PNS * *5 ) PVZD=AREA* (3. *PNN*PNZ-PNS*PNS*CNZ) / (PNS* *5) PVXS =AREA* PNX/ (PNS * * 3 ) PVYS=AREA* PNY / (PNS * * 3 ) PVZ S=AREA* PNZ / (PNS* * 3 ) DO 20 J=l, 4 K=J+I AX=PX-X (J) AY=PY-Y (J) AZ=PZ-Z (J) BX=PX-X (K) BY=PY-Y (K) BZ=PZ-Z (K) sx=x (K) -X(J) SX=X (K) -Y (J) SZ=Z (K) -Z (J) + AZ*AZ) A=SQRT(AX*AX + AY*AY + BZ*BZ) B=SQRT(BX*BX + BY*BY + SZ*SZ) S=SQRT(SX*SX + SY*SY C SOURCE CONTRIBUTION SM=SX*CMX+SY*CMY+SZ*CMZ SL=SX*CLX+SY*CLY+SZ*CLZ AM=AX*CMX+AY*CMY+AZ*CMZ AL=AX*CLX+AY*CLY+AZ*CLZ BM=BX*CMX+BY*CMY+BZ*CMZ ALL=AM*SL-AL*SM RJ3=alog((A+B+S)/(A+B-S))/S PA=PNZ*PNZ*SL + ALL*AM PB=PA - ALL*SM RNUM=SM*PNZ*(B*PA - A*PB) DNOM=PA*PB + PNZ*PNZ*A*B*SM*SM DE=ATAN2(RNUM, DNOM) VXS=VXS+RJ3*(SM*CLX-SL*CMX)+DE*CNX VYS=VYS-(RJ3*(SM*CLY-SL*CMY)+DE*CNY) VZS=VZS+RJ3*(SM*CLZ-SL*CMZ)+DE*CNZ DOUBLET CONTRIBUTION C - AZ*BY AVBX=AY*BZ - AX*BZ AVBY=AZ*BX - AY*BX AVBZ=AX*BY ADB=AX*BX + AY*BY + AZ*BZ VMOD=(A+B)/(A*B*(A*B + ADB)) VXD=VXD + DUB*VMOD*AVBX DUB*VMOD*AVBY VYD=VYD + VZD=VZD + DUB*VMOD*AVBZ C TOTAL VX=VXD+VXS VY=VYD+VYS VZ=VZD+VZS 20 CONTINUE TVS=SQRT(VXS*VXS+VYS*VYS+VZS*VZS) TPVS=SQRT(PVXS*PVXS+PVYS*PVYS+PVZS*PVZS) TVD=SQRT(VXD*VXD+VYD*VYD+VZD*VZD) TPV]9=SQRT(PVXD*PVXD+PVYD*PVYD+PVZD*PVZD) TV= _Q_T (VX*VX+VY*VY+VZ *VZ ) IF (LLL.EQ. 4) THEN IF (PX.LE. 0.0) THEN PDI=-SQRT (PX*PX+PY*PY) ELSE PDI=SQRT(PX*PX+PY*PY) ENDIF ENDIF IF (LLL.LE. 2) WRITE (6, *) fRADIUS=', RDIST 4O IF (LLL.EQ. 3) WRITE (6, *) 'X-AXIS =' , PX IF (LLL.EQ. 4) WRITE (6, *) 'XY-PLANE=',PDI WRITE (6, *) CASE = ' , LLL SOURCE ONLY: ' WRITE (6, *) TOTAL= ' , TVS WRITE (6, *) POINT SOURCE ONLY:' WRITE (6, *) TOTAL=' , TPVS WRITE (6, *) DOUBLET ONLY: ' WRITE (6, *) WRITE (6, *) 'TOTAL =' , TVD ONLY:' WRITE (6,*) 'POINT DOUBLET WRITE (6, *) 'TOTAL =' ,TPVD WRITE (6, *) 'VX=' ,VX WRITE (6, *) 'VY=' ,VY WRITE (6,*) 'VZ =',vz WRITE (6, *) 'TOTAL=' , TV RDIST, TVS, TPVS, TVD, TPVD IF (LLL.LE. 2) WRITE (2, *) PX, TVS, TPVS, TVD, TPVD IF (LLL.EQ. 3) WRITE (2, *) IF (LLL.EQ. 4)WRITE (2, *) PDI, TVS, TPVS, TVD, TPVD WRITE (6,*) ' WRITE (6,*) ' 100 CONTINUE CALL EXIT END 4]

SUBROUTINE CASE(LLL, PI,THETA, THE45,DI,PXI,PYI,PZI)

WRITE(6,*) 'INPUT LINE INITIAL RADIUS:'

READ(5,*) DI

IF (LLL. GE. 3) THETA=45. *PI/180.

IF (LLL.EQ. 1.0R. LLL.EQ. 3) THEN

PXI=DI*COS (THETA)

PYI=0.0

PZI=DI*SIN (THETA)

ELSE

PXI=DI*COS (THETA) *THE45

PYI=DI*COS (THETA) *THE45

PZI=DI*SIN (THETA)

ENDIF

RE TURN

END

REFERENCES 1. Rogers, E. W.: Blockage Effects in a Closed or Open Tunnels. AGARDograph No. 109, October 1966.

2. Herriot, J. G.: Blockage Corrections for Three Dimensional-Flow Closed-Throat Wind Tunnels with Consideration of the Effect of Compressibility. NACA TR-995, 1950.

3. Maskell, E. C.: A Theory of the Blockage Effects on Bluff Bodies and Stalled Wings in a Closed Wind Tunnel. Air Research Committee R&M 3400, 1965.

4. Pope, A.; and Rae, W.: Low Speed Wind Tunnel Testing. Second ed. John Wiley and Sons, Inc., 1984, pp. 344-444.

, Hackett, J.E.; Sampath, S.; and Phillips, C. G.: Determination of Wind Tunnel Constraint Effects by a Unified Pressure Signature Method. Part 1: Applications to Winged Configurations.

NASA CR-166186, 1981.

6. Adair, D.; and Horne, W. C.: Characteristics of a Separating Confluent Boundary Layer and the Downstream Wake. NASA TM-100046, 1987.

7. Ashby, D.; Dudley, M.; and Iguchi, S.: Development and Validation of an Advanced Low-Order Panel Method. NASA TM-101024, 1988.

8. Ashby, D.; and Sandlin, D.: Application of a Low Order Panel Method to Complex Three Dimen- sional Internal Flow Problems. NASA CR-177424, 1986.

9. Maskew, B.: Program VSAERO, A Computer Program for Calculating the Non-Linear Aero- dynamic Characteristics of Arbitrary Configurations. NASA CR-4023, 1987.

10. Katz, J.; and Maskew, B.: Unsteady Low-Speed Aerodynamics Model for Complete Aircraft Configurations. AIAA Paper 86-2180-CP, August 1986.

11. Katz, J.: Integration of Computational Methods in Automotive Wind Tunnel Testing. SAE Paper 89-0601, February 1989.

12. Peters, G.E.: F/A-18 Basic Aerodynamic Data. McDonnell Douglas Report MDC-A8575 Revision A, August 1985, pp. 3.5-3.6.

13. Hess, J. L.;and Smith, A. M.: Calculation of Potential Flow About Arbitrary Bodies. Progress in Aeronautical Sciences, Volume 8. Pergamon Press, 1967, pp. 1-t38.

P U W L Figure 1.- Section through the idealized flow field.

PNECEUiNG PAGE B',.A_qK NOT FILMED P p = VortexLineStrength Panel k ds Figure 2.- Line vortex geometry.

Figure3.- Sectionof the two-dimensional PMARC model.

Pitot Tube D .5 [] [] I":1 .3 [] [] [] .1 [] [] .I- [] H [] -.1 [] [] [] [] ".3 [] _o [] -.5 --_' .99 1.00 V/V oo Figure 4.- Computed velocity profile at the test section centerline.

O Cp, PMARC Re=l.8 x 10 6 O Cp, exper A" .u 0 , I , I , I i I , I , I -1 -4.0 -2.5 -1.0 .5 2.0 3.5 5.0 X Figure 5.- Pressure distribution, tunnel.

Re=l.8 x 106 [] Cpnw, PMARC <> Cpw, PMARC P -, O Cp, exper ¢0 > _10 0 0 0 .2 .4 .6 .8 1.0 1.2 X Figure 6.- Pressure distribution, wing.

<_ ..... 6 n Cpnw, PMARC _]_ He=I.U X 1U _ Cpw, PMARC

i3

"5 "5 -1 .95 1.05 1.15 1.25 × Figure 7.- Pressure distribution, flap.

1.15 [] CI, wing O CI, flap o CI, total 1.10 5 1.o5 1.00 ._ ,,, j r_ 0 5 10 15 delta H/c Figure 8.- Lift decrease as a function of tunnel height.

1.20 [] CI, wing E_ <_ CI, flap 1.15 1.10 O_1.05 1.00 .95 5 10 15 delta H/c Figure 9.- Pitching moment increase as a function of tunnel height.

..#_=,= ;1

Not.: o,.gr.,.w,,hou,,h, radarboom.,,a J

All Dimensions in Inches _ _ y

l

8.1

Ii

= 15.2 --" I "J ;-= 14.1 -, _'_3.8 ---_ Figure 10.- McDonnell Douglas F/A-18 model.

,n,no.

I 5-1/2 Figure 11.- Test section geometry.

< 28 I I I I I I | | I 1 I I I I I I I I I Pressure . vF13.19 vr_9.22 I Ports All Dimensions in Inches 1-13 1 13-19 1-1/2 19-22 2 22-23 1-1/2 32 16 Wing AdJustable Strut I Strut r "41--2-1/2

J

L

..... i 68 Figure 12.- Wind tunnel cross section.

3.5 • PMARC 4 PMARC(wingonly) [] SDSU _ 2.5 =.1 0 Langley _1.5 :t= Q,I 8 .S '4 -.5 t -5 5 15 25 35 45 55 C_ • PMARC [] SDSU _ ra O Langley _ [] C_ [] "6 oj "6 O L) .5 5 15 25 35 45 55 c_ Figure 13.-Aerodynamic characteristics of the F/A-18.

Figure 14.-F/A-18 paneled modelfrom McDonnellDouglas.

Figure 15.- F/A-18 paneled modelafterrework.

-O(x= 0 <>_=1 -m (x = 20 0_ = 20 -m(_ = 46 0c¢= 46 -.2 El[] [] [] rnrn []l'q[] _111 rn _ E] rn m u [] 1 mm " Z^__k; _ ".

---I I 0 4O 10 20 30 X, Tunnel Centerline in Inches Figure 16.- Pressure distribution, tunnel upper wail.

/

/ / Figure 17.- F/A-18, wing only.

1.08 [] Pope • Herr&Mask 1.06 III Thorn if E o" 1.04 b 0" 1.02 1.00 0 10 20 30 40 50 20 1.04 [] Pope • PMARC, Wing only _._ 1.03 E O" "0 1.02 0" 1.01 1.00 _-_._[ J_.l-J I t-J_, ! J l___l t. [_* I__ • L_ J_tJ 0 10 20 30 40 50 20 (X Figure 18.- Wall correction comparison.

Figure 19.- Vector orientation.

• ?. _= PN n Figure 20.- Panel orientation.

P sm I si Figure 21.- Vector orientation in the panel plane.

(e2' Ti2) $2 R12 (X,Y) Figure 22.- Source derivation geometry.

Figure23.- Point orientation,overmedian.

__S------ J

Figure 24.- Point orientation, over horizontal.

30- [] Int Source 4, Pt Source • Int Source - OPt Doublet

=1o

r,

'

1 2 3 4 5 6 Radius Figure 25.- Over median, DW -- 90 °, 30- o Int Source • Pt Source • Int Source O Pt Doublet o 10 _1 0 1 2 3 4 5 6 Radius Figure 26.- Over median, DW = 45 °.

[] Int Source [IJ • Pt Source J _ • Int Source _> Pt Doublet o 20 "ID _=10 0 1 2 3 4 5 6 Radius Figure 27.- Over horizontal, DW = 20 °.

Z MD y J C X

.Soy,-

Figure 28.- Panel transverse, over horizontal (HZ) and over median (MD).

Z OMD J ,,. I " I I" / I f "_ '% / I I J f % ¢- • ,s" __x____V,

/

f

/I"

/

Figure 29.- Panel transverse, over off-median.

1.45 D Source (MD) • PT Source (MD) • Source (HZ) 0 PT Source .45 0 1 -1 X Figure 30.- Panel transverse, source contribution.

O Doublet (MD) • PT Doublet (MD) 3 • Doublet (HZ) • _ 0 PT Doublet (HZ) O --1 -1 0 1 Figure 31.- Panel transverse, doublet contribution.

Z UP t_ Top View The Up Diagonal D,,- Panel Edge Front View Figure 32.- Twisted panel orientation, UP = over the Up diagonal.

.2O [] Int Source • Pt Source u .16 > "o -= .12 .08 -3 -2 -1 0 1 2 Radius Figure 33.- Twisted panel, TW = 0% .20 [3 Int Source • Pt Source _.16 I .08 -2 -1 0 1 2 3 -3 Radlus Figure 34.- Twisted panel, TW = 10 °.

.2O [] Int Source • Pt Source "o_ .16 "_ .12 .08 -2 -1 0 1 2 3 -3 Radius Figure 35.-Twisted panel, TW = 20 °.

.O7 [] Int Source • PI Source .06 =>, U .05 _.04 "ID c:: .03 , I x i _ I J .02 ___ , t -4 -2 0 2 4 6 -6 Radius Figure 36.- Off median, DM = 0.25, TW = 10 °.

.07 [] Int Source , • PI Source .06 _.05 "_.04 .03 .02 , I , , , t • I , I -6 -4 -2 0 2 4 Radius Figure 37.- Off median, DM = 3, TW = 10°.

N/" SA Report Documentation Page

N alonal Ae_on aulJc$ end Space Adminis_'etlc*n 2. Government Accession No.

3. Recipient's Catalog No.

1. Report No.

NASA TM- 102196 5. Report Date 4. Title and Subtitle October 1989 Study of the Integration of Wind Tunnel and Computational Methods for Aerodynamic Configurations 6. Performing Organization Code 8. Performing Organization Report No.

7. Author(s) A-89148 Lindsey E. Browne and Dale L. Ashby 10. Work Unit No.

505-68-71 9. Performing Organization Name and Address 11. Contract or Grant No.

Ames Research Center Moffett Field, CA 94035 13. Type of Report and Period Covered Technical Memorandum 12. Sponsoring Agency Name and Address National Aeronautics and Space Administration 14. Sponsoring Agency Code Washington, DC 20546-0001 15. Supplementary Notes Point of Contact: Dale L. Ashby, Ames Research Center, MS 247-2, Moffett Field, CA 94035 (415) 694-5047 or FTS 464-5047 16. Abstract A study was conducted to determine the effectiveness of using a low-order panel code to estimate wind tunnel wall corrections. The corrections were found by two computations. The first computation included the test model and the surrounding wind tunnel walls, while in the second computation the wind tunnel walls were removed. The difference between the force and moment coefficients obtained by comparing these two cases allowed the determination of the wall corrections. The technique was verified by matching the test-section, wall-pressure signature from a wind tunnel test with the signature predicted by the panel code. To prove the viability of the technique, two cases were considered. The first was a two-dimensional high-lift wing with flap that was tested in the 7- by 10-Foot Wind Tunnel at NASAAmes Research Center.

The second was a 1/32-scale model of the F/A- 18 aircraft which was tested in the low-speed wind tunnel at San Diego State University. The panel code used was PMARC (Panel Method Ames Research Center).

Results of this study indicate that the proposed wind tunnel wall correction method is comparable to other methods and that it also inherently includes the corrections due to model blockage and wing lift.

18. Distribution Statement 17. Key Words (Suggested by Author(s)) Unclassified-Unlimited Wind tunnel Computational Subject Category - 02 Aerodynamic 22. Price 20. Security Classif. (of this page) 21. No. of Pages 19. Security Classif. (of this report) A04 Unclassified Unclassified IASA FORM 1626 OCT86 For sale by the Nationai Technical Information Service, Springfield, Virginia 22161