1、, ,; I i- 5 / Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-REPORT 1150 CONSIDERATIONS ON THE EFFECT OF WIND-TUNNEL WALLS ON OSCILLATING AIR FORCES FOR TWO-DIMENSIONAL SUBSONIC COMPRESSIBLE FLOW By HARRY L. RUNYAN and CHARLES E. WATKINS Langley Aer
2、onautical Laboratory Langley Field, Va. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-National Advisory Committee for Aeronautics Headquarters, 1724 F Street NW., Washington 25, D. C. Created by act of Congress approved March 3, 1915, for the super
3、vision and direction of the scientific study of the problems of flight (U. S. Code, title 50, sec. 151). Its membership was increased from 12 to 15 by act approved March 2,1929, and to 17 by act approved May 25,194s. The members are appointed by the President, and serve as such without compensation.
4、 JEROME C. HUNSAKER, SC. D., Massachusetts Institute of Technology, Chairman DETLEV W. BRONK, PH. D., President, Rockefeller Institute for Medical Research, Vice Chairman HON. JOSEPH P. ADAMS, member, Civil Aeronautics Board. ALLEN V. ASTIN, PH. D., Director, National Bureau of Standards. LEONARD CA
5、RMICHAEL, PH. D., Secretary, Smithsonian Institu- tion. LAURENCE C. CRAIGIE, Lieutenant General, United States Air Force, Deputy Chief of Staff (Development). JAMES H. DOOLITTLE, SC. D., Vice President, Shell Oil Co. LLOYD HARRISON, Rear Admiral, United States Navy, Deputy and Assistant Chief of the
6、 Bureau of Aeronautics. R. M. HAZEN, B. S., Director of Engineering, Allison Division, General Motors Corp. WILLIAM LITTLEWOOD, M. E., Vice President-Engineering, American Airlines, Inc. HON. ROBERT B. MURRAY, JR., Under Secretary of Commerce for Transport,ation. RALPH A. OFSTIE, Vice Admiral, Unite
7、d States Navy, Deputy Chief of Naval Operations (Air). DONALD L. PUTT, Lieutenant General, United States Air Force, Commander, Air Research and Development Command. ARTHUR E. RAYMOND, SC. D., Vice President-Engineering, Douglas Aircraft Co., Inc. FRANCIS W. R.EICHEI.DERFBR, SC. D., Chief, United Sta
8、tes Weather Bureau. THEODORE P. WRIGHT, SC. D., Vice President for Research, Cornell University. HUQH L. DRYDEN, PH. D., Director JOHN F. VICTORY, LL. D., Executive Secretary JOKN IV. CROWLEY, JR., B. S., Associate Director for Research E. H. CHAMBERLIN, Executive Oficer HENRY J. E. REID, D. Eng., D
9、irector, Langley Aeronautical Laboratory, Langley Field, Vn. SMITH J. DIGFRANCE, D. Eng., Director, Ames Aeronautical Laboratory Moffett Field, Calif EDWARD R. SHARP, SC. D., Director, Lewis Flight Propulsion Laboratory, Cleveland Airport, Cleveland, Ohio LANQLEY AERONAUTICAL LABORATORY, AMES AERONA
10、UTICAL LABORATORY, LEWIS Fr.8 :HT IROPULSION LABORATORY, Langley Field, Va. Moffett Field, Calif. Clevel:,tld Airport, Cleveland, Ohio Conduct, under unified control, for all agencies, of scientific research on the fundamental prollems of flight II Provided by IHSNot for ResaleNo reproduction or net
11、working permitted without license from IHS-,-,-I, :.A:- ; , REPORT 1150 CONSIDERATIONS ON THE EFFECT OF WIND-TUNNEL WALLS ON OSCILLATING AIR FORCES FOR; TWO-DIMENSIONAL SUBSONIC COMPRESSIBLE FLOW By HARRY L. RUNYAN and CHARLES E. WATKINS SUMMARY This report treats the e$ect of wind-tunnel walls on t
12、he oscillating two-dimensional air forces in a compressible medium. The walls are simulated by the usual method of placing images at appropriate distances above and below the wing. An im- portant result shown is that, for certain conditions of wing -frequency, tunnel height, and Mach number, the tun
13、nel and wing may form a resona,nt system so that the-forces on the wing are greatly changed from the condition qf no tunnel walls. It is pointed out that similar conditions exist.for three-dimensional flow in circular and rectangu.lar tu.nnels and apparently, within certain Mach number ranges, in tu
14、,lne/s of notzuniform cross section or even in open tun.nels or jets. INTRODUCTION The understancling of flutter and ot,her nonsteady phe- nomena requires a knowledge of the associated unsteady flow. In the underlying theories of unsteady flow, such assumptions as small displacements, linearizations
15、, and an inviscid fluid are made in order to obt,ain workable ancl usable results. When it is necessary to investigate the cflect of these assump- tions on analytical results by measurements of the forces ancl moments on an oscillating wing in a wind tunnel or to treat cases that do not conform to t
16、heory, the question of the effect of the tunnel walls naturally arises. In the case of steady flow the problem of t,he effect of turlnel walls is more or less classic and has been treatecl by many investigators. In general, these investigators have been able to obtain relatively simple factors which
17、 can be used to modify measurements of the air forces on a wing in a tunnel to cor- respond to free-air conditions. The extension of t,he results to compressible flow presents no difficulties since the results for incompressible flow can be corrected according to Prancltl- Glauert correction factors
18、. In the case of unsteady flow, Reissner, reference 1, and W. P. Jones, reference 2, have published papers showing the effect of wind-tunnel walls for the incompressible case. In both papers, the influence of the tunnel walls is found to be comparative1.y small for most cases, although indications a
19、re given that, for some ranges of a reduced-frequency param- eter, the effect may be quite large. In the unsteady case, unlike the steady case, the transition from results for incom- pressible flow to those for compressible flow cannot be accom- plished by simple transformations. This difficulty is
20、a result of the fact that, in an incompressible fluid, the velocity of propagation of a disturbance is infinite and no time lag occurs between the initiat,ion of a disturbance and its effect at another position in the field, but, in a compressible fluid, a definite time is required for a signal to r
21、each a distant field point so that both a phase lag and a change in magnitude result. Under certain conditions this phase lag can result in a resonant condition which would involve large corrections. The purpose of this report is to consider the effect of wind- tunnel walls on the forces on an oscil
22、lating airfoil of infinit.e span with considerations of the compressibility of the fluid. The usual method of images is employed in order to satisfy the condition of no normal velocity at the tunnel walls. First, the effect of tunnel walls on the incluced vertical velocity, hereinafter referred to a
23、s clownwash, of an oscil- lating doublet is determined and this result is used to for- mulate the integral equation for the clownwash of an oscil- lat,ing airfoil in a tunnel. This report is not intended to give numerical values or any detailed calculations of final t,unnel-wa.11 correction factors
24、but mainly to show the csist- ing need for such calculations ancl to present. equations for calculating corrections for the two-climcnsional case. SYMBOLS constant semichord velocity of sound tunnel height Hankel functions Mach number local pressure cliff erence time velocity clownwash or vertical i
25、nduced veloci t,y Cartesian coordinates Eulers constant angular frequency wave length acceleration potential velocity potentia,l fluid density I Supersedes NACA TN 2552, “Considerations on the Effect of IVind-Tunnel Valls on Oscillatiw! Air Forces for Two-Dimensionnl Subsmic Compressible Flow” by IS
26、arry L. Runynn alld Chnrles E. Watkins, 1951. 280466-54 1 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-2 REPORT 115-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS ANALYSIS EFFECT OF TUNNEL WALLS ON THE DOWNWASH OF A SINGLE DOUBLET The differential eq
27、uation that governs flow due to small nonsteady perturbations imposed on a steady, uniform flow field is the wave equation. Referred to rectan,;ular coordinates, fixed relative to the undisturbed stre:m at, infinity, this equation is In this equation the independent variable J ,_ ,., i ,. .*:. _ _,
28、a _., ;- L _ EFFECT OF WIN e”w(-$) lim f% a2 s - - 1 V z-0 -m gl(-W v ac2) $Ji2+82(-nH)2dt (10) represents the additional downwash due to the presence of tunnel walls. Thus the relative value of w. a,s compared with wo+wl is the main it,em of interest here. The integrals appearing in equations (9) a
29、nd (10) can be reduced to simpler form for evaluation but since the steps required to reduce one of the integrals are the same as required to reduce the other, only the integral appearing in ,equation (9) will be treated in detail. The reduced form of the other integral can then be obtained by simpl
30、e comparison. The Hankel function in equation (9) satisfies the following identity: . HOLY bY2 ( $2”pw) G -p2 however, with damping present, resonant frequencies yielding values of wH/V in the neighbor- hood of those given in equation (20) would exist and it is not likely that quantitative agreement
31、 or even possibly qualita- tive agreement. between calculated and measured downwash (or forces) can be realized when t.he value of wH/T7 is in the neighborhood of these critical values. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-II-1.111111.11.1
32、11 -. 7 .- ,+$ Ii li -;:, +-* _, j ;,y ,. ., ,:, _ .: . 7: .I ,:- 1 ; ,(I I -:- :. ._ ;i EFFECT OF WIND-TUNNEL iVALLS ON OSCILLATItiG AIR FORCES. FOR TJKO-DTMENSIONAL COMPRESSIBLE FLOW 5 It is interesting to note that the effect of boundary condi- tions such as section geometry, tunnel-wall flexibil
33、ity, and so forth is to change the value of the critical frequency but not to do away wit*h the possibility of resonance. Also, by treat- ments similar to those employed herein, it can be shown that under idealized conditions resonance can occur in three- dimensional flow in both round and rectangul
34、ar tunnels or apparently, within certain Mach number ranges, in tunnels of nonuniform cross section .(expanding or contracting sec- tion) or even in open tunnels or jets. which may be derived from equation (20) is shown plotted, for m= 1, as a function of Mach number in figure 3. Equa- tions (21) an
35、d figure 3 show that finite values of the critical frequency exist for the conditions M=O, V=O, and c# m. These conditions correspond to a compressible fluid at zero velocity in the tunnel. For these conditions equations (21) and the corresponding wave lengths The fundamental or smallest critical va
36、lues of wH/V, cor- responding to m=l in equation (20), are shown plotted as functions of Mach number M in figure 2. This figure indi- cates that there is no finite critical value of wH/Vfor the con- ditions M=O, VSO, and c= 0, which correspond to a flow of incompressiblei fluid in the tunnel. This r
37、esult agrees with those found in references 1 and 2. The frequency parameter cf=(2m - l)ap (m=l,2,3,. . .) (21) IE 12 IO wH r8 6 I I u I I I I I I I .2 .4 .6 .8 1.0 M FIGURE 2.-Fundamental critical values of frequency parameter wH/V FIGURE 3.-Fundamental critical values of frequency parameter wH/c p
38、lotted as a. function of Mach number 111. plotted as a function of Mach number M. x2”c- 2H w 2m-1 (m=l, 2,3, . . .) (22) agree, respectively, with results found in the literature for the characteristic frequencies and wave lengths associated with transverse acoustic vibrations in rectangular chamber
39、s when the location of the source of disturbance is excluded as a nodal point. See, for example, reference 6. It may be of interest to note that equation (21) can be derived from the principle of standing waves as follows: The condition for resonance for the type of disturbance considered implies th
40、at the standing transverse waves have a maximum velocity at the midsection of the tunnel and zero velocity at 3.2 2.8 2.4 .8 .4 .6 M Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-6 REPORT 115O-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS the boundar
41、ies. A half-sine wave of wave length X=2H or any odd divisor of this length, namely, xr, may be expressed simply as (compare with eq. (6): iw t+s = -2pi l$f A(xo)e ( cy; JI,” -c- :_ EFFECG?F ,I , -. .; . - SIR FORCES FOR TWO-DIMENSIONAL COMPRESSIBLE FLOW 7 CONCLUDING REMARKS The important result sho
42、wn is that, in a tunnel of infinite length containing a flowing fluid, a resonant condition involving a transverse oscillation of the fluid across the tunnel is possible and measured air forces at or near this condition of resonance might be greatly modified from those measured in free air. This res
43、onant condition is a (simple) function of-Mach number,.trmnel height, and wing frequency and brings to attention a new type of tunnel-wall interference. REFERENCES 1. Reissner, Eric: Wind Tunnel Corrections for the Two-Dimensional Theory of Oscillating .Airfoils. Rep. No. SB-318-S-3, Cornell Aero. L
44、ab., Inc., Apr. 22, 1947. 2. Jones, W. Prichard: Wind Tunnel Interference Effect on the Values of Experimentally Determined Derivative Coefficients for Oscil- lating Airfoils. R. & M. No. 1912, British A.R.C., 1943. 3. Watson, G. N.: A Treatise on the Theory of Bessel Functions. Sec- ond ed., The Ma
45、cmillan Co., 1944. 4. Ilarp, S. N., Shu, S. S., and Weil, H.: Aerodynamicsof the Oscil- lating Airfoil in Comnressible Flow. Tech. Ren. No. F-TR- I 1167IND. Air Materiel Command. U. S. Air Force. Oct. 1947. LANGLEY AERONAUTICAL LABORATORY, NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS, LANGLEY FIELD,
46、VA., September 24, 1951. 5. Infeld, L., Smith, V. G., and Chien, W. Z.: On Some Series of Bessel Functions. Jour. Math. and Phys., vol. XXVI, no. 1, Apr. 1947. 6. Morse, Philip M.: Vibration and Sound. Second ed., McGraw-Hill Book Co., Inc., 1948. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-
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