1、, NASA CONTRACTOR REPORT 168428 NEW CONSIDERATIONS ON SCALE EXTRAPOLATION OF WING PRESSURE DISTRIBUTIONS AFf:=ECTED BY TRANSONIC . SHOCK-INDUCED SEPARATION Mohammad M. S. Khan Jones F. Cahill Contract NAS2-10855 October 1984 NlSI National Aeronautics and Space Adnlinistration 00111111111111111111111
2、11111111111111111111 1 NF02367 NASA-CR-166426 19830023326 -lrBR A.RV COpy AUG 1 118. LANGLEY RESEARC CirHER LIBRARY NASA. .;P70N. VA. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NASA CONTRACTOR REPORT 166426 NEW CONSIDERATIONS ON SCALE EXTRAPOLAT
3、ION OF WING PRESSURE DISTRIBUTIONS AFFECTED BY TRANSONIC SHOCK-INDUCED SEPARATION Mohammad M. S. Khan Jones F. Cahill Lockheed-Georgia Co. Contract NAS2-1085S NIS/ NatIonal AeronautIcs and Space Administration AMES RESEARCH CENTER Moffett Field, California 94035 Provided by IHSNot for ResaleNo repro
4、duction or networking permitted without license from IHS-,-,-rj NASA CONTRACTOR REPORT 166426 NEW CONSIDERATIONS ON SCALE EXTRAPOLATION OF WING PRESSURE DISTRIBUTIONS AFFECTED BY TRANSONIC SHOCK-INDUCED SEPARATIONS Part I. Part II. ANALYTICAL CONSIDERATIONS OF SHOCK-BOUNDARY LAYER CORRELATIONS - MOH
5、AMMAD M. S. KHAN REFINED EXTRAPOLATION OF WING LOAD DISTRI BUTIONS WITH TRANSONIC SHOCK-INDUCED SEPARATION - JONES F. CAHILL PREPARED FOR: NASA-AMES RESEARCH CENTER BY THE LOCKHEED-GEORGIA COMPANY PREFACE NASA Contractor Report 3178 (published in 1979) presented a method for predicting the effects o
6、f change in Reynolds number on wing pressure distributions which are affected by transonic shock induced separations. That prediction was made possible by the discovery that the variation of trailing-edge pressure recovery with angle of attack and Mach number could be collapsed into a Single curve t
7、hrough use of an empirically derived correlation parameter. The information presented in this report consists of the results of studies identified as Tasks 2.1 and 2.2 of Contract NAS2-10855. These studies are concerned respectively with the derivation of an analytical parameter to replace the empir
8、ical parameter of CR3178 t and with the refinement of the correlation process by use of the analytical parameter and other considerations. This report is also identified as Lockheed Report LG83ER005. 1 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-
9、, 2 PART I. ANALYTICAL CONSIDERATIONS OF SHOCK BOUNDARY LAYER CORRELATIONS Mohammad H. S. Khan SUMMARY Wing trailing-edge separations that occur at transonic speeds as a result of shock-boundary layer interactions are known to pr.oduce large adverse effects on aircraft aerodynamic characteristics. L
10、arge losses in lift and changes in wing torsional loads have been shown to result from such separations. Infor mation on this subject for aircraft design must rely on wind tunnel test results. In currently existing wind tunnels, however, data can be obtained only at Reynolds numbers an order of magn
11、itude less than flight values. A procedure for extrapolating low Reynolds number pressure distribution data to flight conditions has been published in a previous NASA Contractor Report by Cahill and Connor. The correlation of trailing-edge separation data, which is vi tal to that extrapolation proce
12、dure, was developed purely from an empirical analysis of experimental data. This report presents the results of a study that examines the basic fluid dynamic principles underlying shock-boundary layer interactions and develops an analytical parameter that should describe conditions leading to traili
13、ng-edge separation. The essential features of the interaction region are defined by using a triple-layer conceptualization of the controlling fluid dynamic phenomena. By matching conditions at the boundaries of the three layers, a parameter is derived that defines flow similarity in terms of suscept
14、ibility to separation downstream of the shock. It is concluded that a successful cor relation of the separation data should include this similiarity parameter and a shape factor of the incoming boundary layer. Comparisons show a linear relationship between the similarity parameter developed here and
15、 the correlating parameter that successfully collapsed data on the development of trailing-edge separation in the previous work of Cahill and Connor. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-T-B1/2 = C Cf Cp k K = L M P Re til u uT x y “I 0 0+
16、 Jl P Tw NOMENCLATURE (P/Ps)-A y“ -X/C empirical correlation parameter obtained by Cahill and Connor Airfoll Chord Wall friction coefficient Pressure cQefficient vonKarman constant (Me2-n (Y+n M 2 e Similarity parameter Reference length Mach number Pressure Reynolds number Velocity parallel to the w
17、all Friction velocity Coordinate in streamwise direction Coordinate normal to the wall Ratio of specific heats of air Boundary layer thickness Wall layer thickness Small perturbation parameter Viscosity Density Shear stress at wall 3 Provided by IHSNot for ResaleNo reproduction or networking permitt
18、ed without license from IHS-,-,-4 Superscripts * Dimensional quantities Subscripts o Quantties related to incoming profile e Boundary layer edge quantities s Quantities at shock location INTRODUCTION The interaction of shock waves with boundary layers in transonic flows over wings is known to produc
19、e significant effects on the aerodynamics of high-speed aircraft. Local effects of the interaction include an increase in the displacement and momentum thickness, and a decrease in skin friction for some considerable distance, causing a possible separation of the boundary layer. Of greater importanc
20、e is the modification introduced by the interaction to the boundary layer approaching the airfoil trailing edge that may change conditions for separation at the trailing edge. In such cases, the shock-wave boundary-layer interaction produces local as well as global effects represented by a loss in l
21、ift, increase in drag, and other adverse effects of separated flows, such as buffeting. Therefore. accurate prediction of shock boundary layer interaction and its effects on trailing-edge separation at flight conditions are critical for improved aircraft design. Since the flow structure in shock-ind
22、uced separation at transonic speeds is complex, the solution to the full Navier-Stokes equations must be considered for accurate prediction. Significant progress has been achieved in the development of methods for the direct numerical solution of the full Reynolds equation of turbulent flows. Althou
23、gh these methods hod the promise of offering the most complete and accurate solution for viscous flow, they have been limited in practice because of their large computing requirements. Experimental data obtained from wind tunnel testing are of great help to a designer in establ1shing a criterion for
24、 shock-induced trailing-edge separation. However, due to size limitations, much of the data are obtained at Reynolds numbers that are lower than flight condition Reynolds numbers. An effort to extrapolate wind tunnel data to flight conditions (Reynolds number and Mach number) has been Provided by IH
25、SNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-undertaken by Cahill and Conner (Ref. 1). Their correlation is based purely on an empirical analysis of experimental data. An extrapolation derived from consideration of fluid mechanics principles could be applied wi
26、th much greater confidence. The purpose of the present study is to develop analytical parameters that characterize the shock-wave boundary-layer interaction at transonic speeds. The intent is to illuminate the Cahill-Connor correlation and/or point to a more fundamental paramete for the interaction.
27、 Here we adopt an asymptotic analysis of the governing equations under conditions of incipient separation. This is because asymptotic solutions include the essential physics of the phenomenon of interaction as was demonstrated by Melnik and Grossman (refs. 2, 3) and Adamson, Liou, and Messiter (ref
28、4). In this report, we briefly describe the analyses and findings of these authors and then relate the basic parameters derived to those due to Cahill and Connor (ref. 1). PROBLEM FORMULATION Asymptotic Theory of Interaction Several interrelated flow characteristics of the shock boundary-layer inter
29、action region are shown in Figure 1. The incoming turbulent boundary-layer flow is slightly supersonic, except in a thin region near the wall where the flow is subsonic. The shock wave weakens as it penetrates into the boundary layer and terminates at the sonic line. Thus, the shock pressure-rise at
30、tenuates in the subsonic region beneath the shock, resulting in a smooth pressure distribution on the wall. It is clear that the pressure gradient normal to the wall in the interaction region is not small; hence, the classical boundary-layer formulation is inappropriate. Melnik and Grossman (refs. 2
31、, 3) considered a simplified model of a weak normal shock wave interaction with a fully developed turbulent boundary layer over a flat plate, as shown in Figure 2. location is defined by Re = U P L IIJ. e e e The Reynolds number at the shock 5 Provided by IHSNot for ResaleNo reproduction or networki
32、ng permitted without license from IHS-,-,-6 C P SHOCK EWPTIC LEAKAGE PRE-SHOCK I BENEATH SHOCK - COMPRESSION I VIRTUAL SHOCK r-THICKNESS , SURFACE PRESSURE DISTRIBUTION FlOW UNSTEADY INTERACTION COMPLEX UPSTREAM INFLUENCE SHOCK WEAKENS AS IT PEN ETRA TES VELOCITY PROFILE NOTE: o P B. L. APPROX. I) *
33、 CONCEPT _ ft. 0 -INVAUD _ r INVAUD oy Figure-l :-Ffow -StructUre-tn the Shock/Boundary-layer Interaction Region Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-. i NORMAL SHOCK WAVE * u .-_ “t * -po. 1-; M 11-“1 I * 1-. ,. * * * R.=P utiI -1 e = 0 (
34、In R. 2 M -lte-O; (M -l)/e CONSTANT. Figure 2. Melnik-Grossman-Model of Weak Shock/Boundary Layer Interaction where U e P and Jl are the undisturbed free-stream values of velocity, e e_ density, and viscosity, and L 1s the distance from the plate leading edge to the shock location. The wall shear st
35、ress and friction coefficient of the in coming boundary layer are related by A small parameter, defined by = ( C f /2) 1/2 , o (1) 7 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-is introduced, and we notethat 1. -1 = 0 ( nHe) (2) thus -o as He-oo
36、* The friction velocity is also given by uT = U e. Let Me denote the un-disturbed Mach number. The analysis of Melnik and Grossman is based on a formal asymptotic expansion of the full Reynolds averaged Navier-Stokes equations in the double - limi t M -1 and -0 (which implies Re-oo) while X = (M 2 -
37、 1) I is e - e held fixed. The parameter X can be interpreted as a normalized shock strength because (M 2 - 1) is the proportional to the shock strength and characterizes e the “fullness“ of the incoming velocity profile. The value of X controls the relative rates at which the two basic parameters M
38、e and approach their respec tive limits. If the fixed value assigned to X is 0(1), then this limit is called “weak“ shock limit. Undisturbed Boundary Layer Before considering the analysis in the interaction region, we review first the basic features of the asymptotic solution of the undisturbed comp
39、ressible boundary layer over a flat plate in limit R-oo. The turbulent boundary layer at high Reynolds number develops a two-layer structure, as illustrated in Figure 3. In the outer region there is a balance between turbulent stress and convec tion of momentum. This region comprises most of the bou
40、ndary layer, and the velocity profile is well represented by the small defect form of the law of the wake U = 1 +E Uo (x,y/o) where 0 is the boundary layer thickness and x and yare cartesian axes, x is parallel, and y is normal to the plate. (Lengths and velooities are made * * dimensionless by usin
41、g Land U , respectively). As a consequence of the e 8 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-U-e .-/ J / O( /-e) 7 INVISCID FLOW VELOCITY DEFECT LAYER MOMENTUM + PRESSURE + TURBULENT STRESS WAll LAYER VISCOUS STRESS + TURBULENT STRESS -1 e =
42、 0 (In RJ 6 = 0 ( e ) 6+= 0 e -1 EXP (- Figure 3. Schemati c of the Undisturbed Boundary Layer 9 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-balance between the turbulent stress term and the convective terms in the x-momentum equation, we obtain
43、the estimate 0= o(E) (4 ) In the inner region, in a very thin layer near the wall, there is a balance between turbulent and viscous stress while the convective terms are of smaller order of magnitude. , The velocity profile takes on a law-of-the-wall form (5 ) where 0+ is the thickness of the wall l
44、ayer, and it is related to 0 and Re by (6) In the overlap region, y 10 1 y 10+, the velocity profiles in the outer and inner regions should match, and it follows from the matching that and -1 0= aCE) = a (lnRe) r+ -1 -1 u = a E exp (- E ) (7) (8) Equation (8) shows that, for high Reynolds number flo
45、ws (E-O) , the wall layer is exponentially thin compared with the overall thickness of the boundary layer. From the matching of the velocity profiles it is also established that the profile has a logarithmic form in the overlap region, U-1 + k-1E ln (y/o) + , as (y/o)-o and + , as (y/o )_00 10 Provi
46、ded by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-with k = 0.41, the von Karman constant and c = 5.0. Therefore, the velocity profile in the defect layer does not satisfy the no-slip condition on the r surface. -r . Finally, we notice that the pressure grad
47、ient, dp/dx, does not affect the wall layer unless it is 03 Exp (-1 ). This follows from equating the order of dp/dx to that of the viscous stress term in the x-momentum equation. Interaction Region Upstream of the interaction region, the boundary layer has a two-layer, law of the wake/law of the wa
48、ll, form. Outside the boundary layer there is an inviScid, irrotational flow that contains a weak normal shock wave. In the in teraction region, sketched in Figure 4, the boundary layer develops a three-layer structure. The extent of the interaction region in the streamwise direction is 0(3/2), and it is the same for the three layers. The main deck has a thickness O() and thus extends over most of the bound
