1、NATIONALADVISORYCOMMITTEE. FOR AERONAUTICSTECHNICAL NOTE 3176WALL INTERFERENCE IN WIND TUNNELS WITH SLOTTED ANDPOROUS BOUNDARIES AT SUBSONIC SPEEDSBy Barrett S. Baldwin, Jr. , John B. Turner,and Earl D. KnechtelAmes Aeronautical LaboratoryMoffett Field, Calif.WASHINGTONMay 1954z-=Provided by IHSNot
2、for ResaleNo reproduction or networking permitted without license from IHS-,-,-TECH LIBRARYKAFB,NM.V9Illlllllll!llllllll!llu(luNATIONAL ADVISORY COMMITIEEFOR AERONAUTICS onb5izqTECHNICALWIT 3176uWALL INTERFERENCE IN WIND TLJNTiELsWITH sLom ANDsumARYLinearized compressible-flowanalysiswind-tunnel-wal
3、l interference for subsonicSPEEDSB. Turner,is applied to the study offlow in ei,ther”two-POROUS BOUNDARIES AT SUBSONICBy Barrett S. Baldwin, Jr., Johnand Earl D. fiechteldimensional or circular test sections having slotted or porous walls.Expressions are developed for evaluatingblockage and lift int
4、erference.INTRODUCTIONa71In solid-wall wind tunnels the effects of blockage severely limitmodel sizes that can be tested at high subsonic speeds; in fact, the*model must become vanishingly small as sonic speed is approached. Ithas been demonstrated that if the walls are ventilated (e.g., slottedor p
5、orous) then blockage is reduced and much larger models can betested. However, wall-interference effects, although reduced, stillexist and must be evaluated in order to correct the wind-tunnel data tofree-air conditions.It is the objective of the present investigation to analyze two ofthe principal w
6、all-interference effects, blockage and lift interference,for two- and three-dimensional subsonic flows in ventilated testsections, where blockage refers to the mean incremental velocity inducedin the vicinity of the model by wall interference and lift interferenceis the mean upwash so induced. In th
7、e three-dimensional case it isconvenient to perform the analysis for a circular test section. Theresults obtained for the circular test section may be applied to a squaretest section of equal cross-sectional area since the wall interferenceat the center of the tunnel should be relatively insensitive
8、 to such achange in the shape of the wall.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-2 NACflTN 3176SYMBOLSAabcGgh10IIK.K=K1LMme?nrn!lRr,e,xufactor in Fourier integral transform of q*slot width of slotted wall (see fig. 1)wing span of model wingc
9、onstant factor in nonlinear term of boundary equationFourier integral transform with respect to x of dummy variable of Fourier transformhalf tunnel height modified-Bessel function of the first kind and order zeromodified Bessel function of -thefirst kind and order onemodified Bessel function of the
10、second kind and order zeromodified Bessel function of the second kind and order oneslot constant,- slot separation oflift on the modelnsin()lslotted wall (see fig. 1)free-streamlsli qj dqsinh (q)(20)is obtained for the additional stream velocfiy at the position ofthe model due to the walls. -.Solid
11、wall.- Letting K m or l/R- m in equation (20) esme V3flu J e-% X me= dq=K 2fi2h2o sinh (q) 24 2h2E wIdeal porous wall.- At K= O equation_ becomesw cosh (q) -Au = 1K=o q11(q)2”+ ,(:)J4Kl(q)Io(q)+(q) Io(q)+ q(q)Il(q)- qroo(q2+$)KddIdd 10($ .( the shape of the curvethe ends and interpolated in the midd
12、le. A graph ofin figure showing the variation of blockage factorfor the cylindrical, ideal slotted tunnel.(39)the values for thevalues of K/r.was calculated nearequation (38) appearswith slot parameterAgain, letting +.0 has the same effect on the blockage cor-rection as letting (1/R)-0,so that near
13、sonic speed the ideal porouswall should act like an open jet and the slotted wall should act likean ideal slotted wall.Lift Interference in a Circular TunnelThe upwash correction will be calculated using the infinitesimalmodel size approximation and the approximate boundary condition ofequation (6).
14、s Let x be the coordinate in the free-stream direction, z thecoordinate in the direction of lift on the model, and y the remaining.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-18 NACA TN 3176*Cartesian coordinate. The cylindrical coordbiates r and
15、 6 are related -to the Cartesian coordinatesby “r= fia.d=be seen from reference 1 that the appropriate free air%rb(r 1+ )h i;er sin e. It can “solution is(40) which is the potential of a horseshoe vortex having infinitesimal span.The ftictthat the actual span is finite introduces higher-order termsw
16、hich are negligible at distances large compared to the size of the .:=+model. Here rb is related to the lift on the model hy.- The Fourier transformAn arbitrary parameter athe Fourier transform of afunction be/L= purkl . (41)with respect-to x of 91 cannot be found. _will be introduced into the poten
17、tial so that “” -”related function can be.found. Let thisP= = (Je-a%+p=a -CJ-ic-ii= sineh-r - e -aax ) rso that .Then a will be eliminatedwith a at zero.From reference 4 it islim ql = Q1aofrom the resulting by taking thefound that the Fotiier transform of(42) .limit e-a is r K= (r) . By the use of a
18、n inversion,fl “-”differentiation, and reinversion, as in the derivation of eQuatiOn (33),b -ah iS it is found that the transform of eaxs.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TN 3176 19igarKl(f3r,/O(4+(:)pq) -qo(q7 1I, . * * . rProvid
19、ed by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-$Reacing 11 (qr/ro) by its power serie expanston, differentiating with respect to z,which is equal to r sin e, and setting r = O yields()L(q) Io(q)+ %(!) ll(q)l qs COS (:)l(q) - q +KJq) NJ ()2-K.= 0 q2112(q)
20、+ “ II=(q) - qIo(q)12roIdeal “slotted.wall.- When l/R is set equal to zero in equa-tion (48), a limiting process is required to.obtainthe correct result _ ;at (/R) = O. The result of this process is ,Aw =-fi“E=oOpen jet.- LettingThe value of Aw inthe values for the.closed1734nro2()Kl-r.K +1ro :K = O
21、 in equation (50) yieldsrbAw =- -P 4flro2:=0rK -o(50)the general case of equation (48) lies betweenwall “andthe open jet.CONCLUDING REMARKSA method of evaluatingwall interference of yartly open walls inolv- _ing mixed potential and viscous flows has been presented. EWressions forblockage and lift in
22、terference for both slotted and porous walls have beenderived. Some new details of the method may prove useful in other theo-retical treatments of this type of problem.The results of the analysis indicate that near sonic speed, the*-P -.blockage correction for an ideal porous Wall.approaches that of
23、 OPen ._. -,jet. Similarly, any linear viscous or taper_$fectof a 810tted wall issuppressed near sonic speed, so that the blo_ckagecorrection approaches- -that of an ideal slotted wall.Ames Aeronautical LaboratoryNational Advisory CommitteeMoffett Field, Calif.,.- .for AeronauticsY29, 1953Provided b
24、y IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-lUiCATN 3176 23.APPENDIX ADERIVATION OF THE BOUNDARY EQUATION .In this appendix an approximate smoothed or average boundary equa-tion for a slotted wall will be derived.An ideal slotted wall has zero perturbation
25、 pressure at the slotsand zero normal flow at the strips. These conditions can be expressed6.8a(p=o at the slotsz*.O at the stripsan I(Al)When the slot spacing and model dimensions are small ccmpared totunnel dimensions, the perturbation flow can be separated into a rapidlyvarying and a relatively u
26、niform part so that the two parts can beinvestigated separately. It till be shown that the effect of the rapidlyvarying part can be replaced by a condition on the relatively uniformpart.-Let q, , ?, amd = represent the rapidly varpng part of the flowfield and , u, v, and w the remaining part of the
27、perturbation flow.For a plane wall at z = h equations (Al) require thatwU+u= o at the slots1(A2);+W=O at the stripsIn additionc= -F.w.o far from the wall (M)In order to solve for , use canbe made of the fact that u, v,and w are nearly constant at the wall compared to ti,%, and %, sothat u and w canb
28、e considered constant in equations (A2).Since the slots lie along the x direction, iS nearly cotantin the x direction, so that atifix csnbe neglected compared toa?jayWd a%z. As in slender airplane theory, this leads to a two-dimensional crossflow for whichProvided by IHSNot for ResaleNo reproduction
29、 or networking permitted without license from IHS-,-,-24 MICA TN 3176(A4) - .Then can be of the form Q(x) f(y,z) where Q(x) is a slowlyvarng fction of x, and f(y,z) satisfies the two-dimensionalLaplace equation. Then,?.!. f(y,z);=ax axand since ; is equal to -u, a constant, at the slots, f(y,z) must
30、 beconstant at the slots or=Qaf=oh byat the slotsThis equation-canbe used to replace the first of equations (A2),and altogether there results-V=o at the slotsassuming thatEquations$= -w = constant at the strips1(A5)? =7= 3.0 far from the wallEl (A7)transforms the region under consideration in the El
31、 plane to the entireright half of the .52 plane, as can be seen by following the procedureoutlined for the first transformation. It is found that in the =plane, the slot lies along the imaginary axis from -i sin (fia/2Z)to+i sin (ma/2Z) and the solid boundary including the two half strips liesalong
32、the imaginary axis outside of *i sin (fia/2Z)0The transformationE= ,2+- (M)Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-26 IfACATN 3176The neglected termszero at infinity if+: (h-X) w(hx) AZn e1A(h-X) +W (h-X) -r.transforms the region under consid
33、eration to tlepos.itie real half ofthe nFi”()lj at hem”and melds(All)for a plane wa.In considering a curved cylindrical wall, ft appears that the aboveresults are not altered appreciably if the radius of curvature of thewall is everywhere large compared to the slot spacing.2 Hence, it can beassumed
34、that equations (All) are applicable to any slotted wall.2For a circular cylindrical slotted wall, solution of the boundary valueproblema: o=)%2 (u+:) uin addition to the usual requirements for linearization. This addi-tional requirement can be reasonably relaxed to(w + 3)2 c2uU at the wall (A13)Equa
35、tion (AIO) indicates singularities,in at the edges of.theslots. Experience with wing leading edges indicates that this.dis-crepancy can be reasonably ignored. Howeverfi_equation(A13) should atleast be satisfied at the center of the slots. The effect of thiscondition on u and v will now be determined
36、. Differentiatingequation (AIO) yieldscosh.1: (h-X)dOw =WaxJsid2 + h-x)+ in (=)-w. .Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-MC m 3176ThenCOBI()Tw =Wz =hi in (!)”:” (?) w=;” hand(w+;) = wIz =h()sin Y 21so that equation (A13) becomes()sin= z2-1or29(a4)This result places a lower limit on the ratio of open to total area(a/Z) for which the results of this analysis can be expected to applyto slotted sections.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-
