NASA NACA-TN-4363-1958 Simplified method for determination of critical height of distributed roughness particles for boundary-layer transition at Mach numbers from 0 to 5《当马赫数为0至5时.pdf

1、NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS TECHNICAL NOTE 4363 SIMPLIFIED METHOD FOR DETERMINATION OF CRITICAL HEIGHT OF DIXTRJBUTED ROUGHNESS PARTICLES FOR BOUNDARY-LAYER TRANSITION AT MACH NUMBERS FROM 0 TO 5 By Albert L. Braslow and Eugene C. Knox Langley Aeronautical Laboratory Langley Field, V

2、a. Washington September 1958 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NATIONAL ADVISORY COMMTTZEX FOR AERONAUTICS TECHNICAL NOTE 4363 SIMPLIFLED I“HOD FOR DETERMINATION OF CRITICAL J3EXGHT OF DISTRIIXTTED ROUGHNESS PARTICLES FOR BOUNDARY-LAYER

3、 TRANSITION AT MACH NUMBERS FROM 0 TO 5 By Albert L. Braslow and Eugene C. Khox SUMMARY A simplified method has been devised for determination of the critical height of three-dimensional roughness particles required to promote premature transition of a laminar boundary layer on models of airplanes o

4、r airplane components in a wind tunnel with zero heat trans- fer. A single equation is derived which relates the roughness height to a Reynolds number based on the roughness height and on local flow conditions at the height of the roughness, and charts are presented from which the critical roughness

5、 height can be easily obtained for Mach numbers from 0 to 5. A discussion of the use of these charts is presented with consideration of various model configurations. The method has been applied to various types of configurations in several wind-tunnel investigations conducted by the National Advisor

6、y Committee for Aeronautics at Mach numbers up to 4, and in all cases the calculated roughness height caused premature boundary-layer transi- tion for the range of test conditions. INTRODUCTION In wind-tunnel investigations with models of airplanes or airplane components, it is often desirable to lo

7、cate artificially the position of boundary-layer transition from laminar to turbulent flow by some method that will result in a negligible increase in drag other than that due to the change in the transition location. One satisfactory method of initiating transition is with the use of a strip of dis

8、tributed particles of roughness. A correlation of the minimum roughness size reqqired to initiate transition has been accomplished in references 1 and 2 at subsonic and supersonic speeds on the basis of a critical roughness Reynolds number formulated with the local flow conditions about the particle

9、s. Roughness particles smaller than the critical Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-2 NACA TlT 4363 size have been found to introduce no disturbances of sufficient magni- tude to influence transition, whereas roughness particles equal to

10、 the critical size initiate the formation of turbulent spots at the roughness that coalesce into a continuously turbulent flow somewhat downstream of the roughness. Only a small increase in roughness Reynolds number above the critical value is required to move the fully developed turbulent boundary

11、layer substantially up to the roughness particles. Determination of the critical roughness height for transition may be accomplished through a trial-and-error procedure with the use of the critical roughness Reynolds number and local variations of veloc- ity and temperature through the boundary laye

12、r. It is the purpose of this report, however, to present a direct approach, based on some simplifying assumptions, to the calculation of the size of roughness particles required for transition without the need for individual cal- culations of the velocity and temperature profiles. Charts required fo

13、r the application of this method are presented for Mach numbers from 0 to 5. SYMBOLS C To + s constant of proportionality, (Tw + s), in the assumed T viscosity relationship .k = C - c”0 - TO k height of roughness particles M Mach number Reynolds number based on roughness height and local flow condit

14、ions at top of roughness, ukk/vk Rk RX Reynolds number based on length of x from leading edge to roughness station and on conditions outside boundary layer, UXbO S Sutherlands constant, 216O R T local absolute temperature, % Provided by IHSNot for ResaleNo reproduction or networking permitted withou

15、t license from IHS-,-,-NACA TN 4363 3 TW U U X Y Y 7 qk c1 V P wall equilibrium temperature, To local streamwise component of velocity outside boundary layer local streamwise component of velocity inside boundary layer surface distance measured streamwise from leading edge to roughness station dista

16、nce normal to surface ratio of specific heat at constant pressure to specific heat at constant volume nondimensional height in boundary layer based on distance above surface, fi 2x nondimensional height in boundary layer based on roughness height, 2x coefficient of absolute viscosity coefficient of

17、kinematic viscosity local mass density Subscripts : k 0 conditions outside boundary layer t conditions at which transition occurs 2-D two-dimensional flat-plate surface 3-D three-dimensional cone surface conditions at top of roughness particle Provided by IHSNot for ResaleNo reproduction or networki

18、ng permitted without license from IHS-,-,-4 DEVELOPMENT OF METHOD NACA TN 4363 The method presented in this report for determining the critical roughness height required for premature boundary-layer transition at Mach numbers from 0 to 5 relates by means of charts the roughness height to the roughne

19、ss Reynolds number based on the local flow conditions at the top of the particle for a given Mach number and roughness loca- tion. The relations presented have been derived for zero pressure gradient and zero heat transfer at the surface by the following procedure. A given roughness particle may be

20、represented nondimensionally by the parameter qk, which is defined as The roughness Reynolds number, based on the particle height and the local flow conditions in the boundary layer at the top of the particle, is defined as ukk V k Rk = - The roughness Reynolds number, however, may be expressed as a

21、 function of station Reynolds number Rx based on the chordwise location of the roughness and local flow conditions outside the boundary layer: Rk = X Rx($)(?) Equation (3) may be rewritten in the form If the viscosity relationship (3) (4) Provided by IHSNot for ResaleNo reproduction or networking pe

22、rmitted without license from IHS-,-,-NACA TN 4363 5 is assumed, the kinemtic-viscosity ratio may be written as inasmuch as the pressure gradient normal to the surface in the boundary layer is negligible. assumption inherent in equation (3) is given in reference 3. A complete discussion of the validi

23、ty of the When equa- tion (6) is substituted into equation (4) and the factor $ therefore, the foregoing procedure for the estimation of the critical roughness height should be applied only for that particular case. The height of the roughness particles compared with the boundary-layer thickness at

24、the location of the roughness can be obtained with use of the nondimen- sional roughness height qk and the boundary-layer velocity profiles of figure 1. % J;liJ Minimization of Roughness Drag In order to minimize the drag contribution of the roughness parti- cles themselves, that is, the drag associ

25、ated with the roughness parti- cles other than the increment due to a forward movement in the location of transition, the roughness particles should be spread thinly in a Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-narrow band. Photographs of sat

26、isfactory strips of distributed granular- type roughness particles are shown in figure 5. Sometimes it is desir- able to use roughness particles larger than the critical height, because the critical height is too small to be manageable (0.001 inch) or because of reasons such as those discussed subse

27、quently; for example, the appli- cation of a single roughness size which will initiate transition through a Mach number and/or Reynolds number range. In these cases, roughness particles somewhat larger than the critical height can be used with no measurable roughness drag if the requirement of only

28、a narrow strip of thinly spread roughness is maintained. Limitat ions As previously mentioned, figures 1 to 4 apply to conditions of zero pressure gradient on surfaces at equilibrium temperature. For the case of heat transfer, therefore, the simplified procedure presented in this paper is inapplicab

29、le, and calculations of the boundary-layer velocity and temperature profiles for the specific conditions considered are required. For surfaces at equilibrium temperature, however, devia- tions from zero pressure gradient found on supersonic-airplane configu- rations for conditions where laminar flow

30、 is possible are most often small enough to permit successful application of the proposed method. Simplifying Considerat ions In applying this method to various types of configurations in several wind-tunnel investigations conducted by the National Advisory Committee for Aeronautics at subsonic spee

31、ds and at supersonic speeds up to a Mach number of 4, further simplifying considerations, which yielded successful results in all cases, were found to be expedient. A brief discussion of some of these considerations appears warranted. For tests of models through a range of Reynolds number and Mach n

32、um- ber, it was desirable to eliminate the need for changes in the rough- ness arrangement. This elimination was accomplished by using a rough- ness size determined for the combination of test Reynolds number and Mach number which required the largest roughness size - usually at the smallest Reynold

33、s number and largest Mach number condition. For tapered wings, roughness was applied at a constant percentage of the local chord (usually at about 5 percent); and in order to permit use of a single grain size across the span, the roughness was calculated for the largest chord. roughness was applied

34、to both wing surfaces in a size calculated by the use of the Mach number and unit Reynolds number based on the flow out- side the boundary layer on the upper surface at the maximum test angle of attack, which is the condition for which the critical roughness size was greatest. For a sharp subsonic l

35、eading-edge wing or for a round leading-edge wing, whether or not swept behind the Mach line, the free- For a wing with a sharp supersonic leading edge, Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-8 NACA TN 4363 stream Mach number and unit Reynol

36、ds number were used. that, with these simplifying procedures which permit use of a single grain size along the span of both wing surfaces, roughness particles larger than the minimum required to cause transition are used on many of the roughness strips for some of the test conditions; however, as po

37、inted out previously, careful application of a sparse distribution of roughness particles to a narrow strip will minimize the drag contri- bution of the roughness itself. It is obvious In order to initiate transition near the nose of slender fuselages, the charts of figure 4 were used. for boundary-

38、layer flow over a cone, deviations of the boundary-layer growth over the nose regions of slender fuselages from boundary-layer growth on a cone were usually small enough to permit application of these charts with reasonable accuracy. however, the calculations of reference 5 for hemispherical and fla

39、t noses appear to provide more accurate estimates of the critical rough- ness than the cone charts even though the methods of reference 5 were derived on the basis of incompressible flow. For supersonic Mach nun- bers, the flow behind the bowwave is, of course, subsonic and estimates of the critical

40、 roughness based on these subsonic conditions and on the methods of reference 5 seem reasonable. Although these charts were computed For fuselages with blunt noses, CONCLUDING REMAFX3 A simplified method has been presented for determination of the critical height of three-dimensional roughness parti

41、cles required to promote premature boundary-layer transition on models of airplanes or airplane components at equilibrium conditions (zero heat transfer) for Mach numbers from 0 to 5. Application of this method to various ty-pes of configurations in several wind-tunnel investigations conducted by th

42、e National Advisory Committee for Aeronautics at Mach numbers up to 4 has in all cases resulted in the successful initiation of transi- tion at the roughness strips. Langley Aeronautical Laboratory, National Advisory Comittee for Aeronautics, Langley Field, Va., August 21, 1958. Provided by IHSNot f

43、or ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TN 4363 REFERENCES 9 1. Von Doenhoff, Albert E., and Horton, Elmer A.: A Low-Speed Experi- mental Investigation of the Effect of a Sandpaper Type of Roughness on Boundary-Layer Transit ion. NACA Rep. 1349, 1958. (Supe

44、rsedes NACA TN 3858.) 2. Braslow, Albert L.: Effect of Distributed Granular-Type Roughness on Boundary-Layer Transition at Supersonic Speeds With and Without Surface Cooling. NACA RM 587, 1958. 3. Chapman, Dean R., and Rubesin, Morris W.: Temperature and Velocity Profiles in the Compressible Laminar

45、 Boundary Layer With Arbitrary Distribution of Surface Temperature. no. 9, Sept. 1949, pp. 547-565. Jour. Aero. Sci., vol. 16, 4. Schlichting, Hermann (J. Kestin, trans.): Boundary Layer Theory. McGraw-Hill Book Co., Inc . , 1955, p. 168. 5. Tetervin, Neal: Theoretical Distribution of Laminas-Bounda

46、ry-Layer Thickness, Boundary-Layer Reynolds Number and Stability Limit, and Roughness Reynolds Number for a Sphere and Disk in Incompress- ible Flow. NACA TN 4350, 1958. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-10 NACA TN 4363 Provided by IHSN

47、ot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TN 4363 P v (N a, -P cd i-i p1 -P cd i-i k k 0 k 8 rl k 11 k 0 k k 5 i-i $ a 0 P !3 i-i cd .rl m $ E -4 a Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-12 NACA T

48、N 4363 5 4 4 L 1 (a) 0 Mo = 2.75. Figure 3.- Variation of nondimensional height in boundary layer with ratio of roughness Reynolds number to square root of station Reynolds number for two-dimensional flat-plate bodies at Mach num- bers from 0 to 5. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TN 4363 13 9 8 7 6 5 37 2-D 4 3 2 1 0 Figure 3. - Concluded. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-14 NACA T