1、,/r/- 73ffz?337 OZ- NASA TECHNICAL MEMORANDUM NASA TM-76710 (PASA-Tl-76710) LPLUBlDCB OP THE EBlllsOLDS 1 82- 3 02 84 BiUElBBB OY EJOPHAL PORCBS OP SLEPDBR BODIES OF BBVOLCPTIOY (Yatioaal Aeronautics and Space Adainbtration) 31 p EC A03/1F A01 CSCL OlA Unclas 63/02 28653 INFLUENCE OF THE REYNOLDS NU
2、MBER ON TYY NORMAL FORCES OF SLENDER BODIES OF REVOLUTION Klaus Hartmann Translation of “Ueber den Einfluss der Reynoldszahl auf die Normalkraefte schlanker Flugkoerperruempfe“. Zeitschrift fur Flugwissenschaftm und Weltraumforschung., Vol. 2, No. 1, 1978, pp 22-35. I!ATIONAL kERONAUTIr.S AMD SPACE
3、ADFINISTRATICN dA3HINGTON D.C. 20546 MAY 1982 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-IMFLUSNCE OF THE REYNOLDS NUMSER ON - Klaus Hartmann Translation of “Ueber den Einfluss der Reynoldszahl auf die Normalkrzefte schlanker Plugkoerperruempfe“
4、. Zeitschrift fur Flugwissenschaften und Weltraumforschung, Vul. 2, No. 1, 1978, pp 22-35. Plow over slender bodies of revolution is strongly influenced by ihree-dimensional vortex separation. The influer.ce of the Reynolds number on nonlinear normal forcFs of slender bodies of revolution is investi
5、grchicht und ahl auf ahlbrrcrch Ma. = 0.5 bis 2.2 bo vanablc Rqnoldsrjhl im Transsomscben Wind4anal un; rm H-hgcschumgkcitswmdkarr.l der DFVLR/AVA mfmgrctcbe Krati und Momentcnmessungen. Dnrckrrtalungsmessung soure Expcmente zur Stromzazgmcbtbarmacbung liurchgefibrt. Dr expenmentellen Ergebnisse wus
6、td beschrezbt. Influence of the Reynolds number on the normal forces of slender bodies of molution Summary. The Jlou*ocr slender bodies of rervlutroir at high angles 01 attack IS strongly influenced by threedrmensional mrte separatron. Ai a result cf separatron the aerodynamic forces rncrease m a no
7、nlrnerrr uuy unth the angle ofdtack. The state ofth. boundary lqer at the separation lrnes bus a smkrng rnfluence on the aercdynamrc forces whrch therefore depend consrderabl. on the Reynolds number. The posrhon of thr separatron lrnes is not known a pnon but pr.011rs from the rnteractron kumr th, b
8、oundary layer and the outer separated flou: Duc to the complexrty of this flow. the theorenrol wlnJjrion of aedynami. forces for bodres of rclnlutron at hrgh angles of attack IS not yet posubk. It is therefore strll necessary to extend the WSLVI. knoudedge about the compltmted flow over bodes of rer
9、vlutron by systemahr wnd-tunnd mveshgahons. On the basrs 0, these inwcstrgations exrstrg computatronal methods have been impmrrd md new mhds have been mrked out. In thrs paper the rnfluence of the Rqnolds number Qn nonlrnear normal forces of slender bodies of revolution is mvestigated. For this purp
10、ose comprehensrue force-, moment- and pressure-drstnbution mersurimmts as uvll as flow msualrzatron expenments uee cumeu out m the Transonic Urnd Tuxnel and m the Hrgh-Speed Umi Titnnd ofthe DFVLR; AVA for bodies of revoluiru? at angles u; attack up ;i3* . /30 Figure 14 gives examples of normal forc
11、e distribution for var- iable Reynolds number which are given here without comment. intended to give the reader a complete overview of the experimental work. They are 14 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-I Figure 12. Normal force distri
12、butions for constant Reynolds number of incident flow. Figure 13. Normal force distributions for constant Reynolds number of incident flow. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-4. - Theoretical analysis of the exaerimental results 4.1 Theo
13、retical calculation methods and compaFison with measurements An exact treatment of the flow field around bodies with high argles of attack is not possible today. The approximate methods known from the literature are of the empirical or semi-empirical tyye and can be summarized with the term “transve
14、rse flow theory“. H. J. Allan and E. W. Perkins lO,ll make the assumption that the total norm1 force on the body consists of a frictionless part (potential transverse force) and a friction part (friction tratis- verse force). In order to determine the potential transverse force, Allan and Perkins us
15、e a simple method of M. M. Munk 1123 which is 3ascd on the momentum theorum. It applies for relatively slender odies in frictionless incompressible flow and, therefore, is res- t,r:i.cted to very small angles 01 attack. This method was developed In the analysis of balloon bodies. Methods for determi
16、ning the fric- tion lift for such closed bodies of revolution were given by H. Multhopp El, and X. Hafer 14. Projectile bodies differ from these body shapes because of a large ratio of length to diameter, the fact that the cross-section is for the most part constant, and because the tail is blunt. F
17、or such bodies, Allan and Perkins determined the friction transverse force by associating a clrcular cylinder with the transverse flov speed Up=U,sina to each body cross section, and a difference .a made between laminar and turbulent separation. L-. R. Kelly 15 further developed the method of Allan
18、and Perk,ns. Based on an analogy between the stationary, three-dimen- ronal flow around a projectile body and the unsteady two-dimensional low t.)f a circdlar cylinder which is suddenly set in motion fror rest, the Iionlinear, local normal force is set equal to the instant- aneoL: rag (per unit of l
19、ength) of a circular cylinder having the tmnsverse flow speed U The time coordinate of the unsteady case -3 associated with the space longitudinal coordinate of the body. 8 16 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Figure 14. Normal force di
20、stribution for constant Reynolds number of incident flow. The method of Kelly was expanded greatly by K. D. Thomson 16, especially by introducing a number of empirical corrections for various influences, for example, pressure gradients at the model head, various tail geometries, etc. Both Ke3y and T
21、homson use the assumption of Allan and Perkins tat the total normal force is the sum of the potential transverse force and the friction transverse force. The umteady drag coeffi- cients for determfning the distribution of the friction transverse force were taken from test results which were obtained
22、 first by V, Schwabe 17 and later on in improved form by T. Sarpkaya 18. The results of these experimental investigations for circular cylin- ders suddenly accelerated to a constant final speed are represented by the drag function shown in Figure 15. This drag function applies for laminar separation
23、 from the cylinder. For the more important practical case of turbulent separation, no experimental data is available. Kelly uses, therefore, a function for turbulent separa- tion which is obtained from the one for laminar separation multiplied 17 Provided by IHSNot for ResaleNo reproduction or netwo
24、rking permitted without license from IHS-,-,-a and the corresponding Reynolds number of the circular cylinder is ReD=2*1OS- . With increasing inci- dent Mach number and, thereforae, transverse flow Mach number, the For constant effective Reynolds number, a different transverse flow Mach number corre
25、sponds to each curve of Figures 17 and 18. each individual curve the transverse flow Mach number is not constant. It increases from the right to the left when passing through the curves, depending on angle of attack. For orientation, the curves have various marked angles of attack. The transverse fl
26、ow Mach num- ber takes on these values which extends from incompressible flow up to critical and even overcritical incident flow. In Figures 17 and 18, along the abscissa, we show the effective Reynolds number at which the individual curves reacb the critical transverse flow Mach number. The critica
27、l transverse flow Mach number was assumed to be (MaQ)knr. .L 0.5 , that is somewhat larger than the potential-theory critical value of the circular cylinder. On the right side of these m Yhis effective Rey- nolds number considers the pathle, * streamlines with its 26 Provided by IHSNot for ResaleNo
28、reproduction or networking permitted without license from IHS-,-,-characteristic lengbh and has been found to be a usable criterion for evaluatiyg whether or not separation over the body is lamfnar or turbulent. The nonlinear norim1 force parts can be represented by only one function in the form of
29、an analog drag coefficient of the circular cylinder as a function of effective Reynolds number. The normal forces and pitch moments calculated according to the transverse flow theory using this function give satisfactory results over the entire range of undercritical transverse flow Mach numbers. RE
30、FERENCES l K. Hartmann: Influence of Reynolds number on the normal forces of slender projectile bodies. extended version. Internal DFVLR AVA-Report 25176420 (1976). Dissertation TU Braunschweig 1976, 2 K. mrtmann: Aerodynamic investigations of projectiles in the transonic speed range. Part 11. Syste
31、matic pressure distribution measurements. Internal AVA Report 69A06 (1969). 3 W. Stahl, K. Nartmann, W. Schneider: Suggestions for research work on projectiles with small aspect ratio wings at the AVA, in collaboration with the Royal Aircraft Establishment, Farnborough, England. AVA Memorandum (1969
32、). 4 K. Hartmann: Three component measurements and pressure dis- tribution measurements including flow observations of a circular cylinder projectile body with various head shapes at Mach numbers of Ma, = 0.5 to 2.2 and various Reynolds numbers internal DFVLFt/ AVA report 25174A32 (1974). SI H. Ludw
33、ieg, W. Lorenz-Meyer, W. Schneider: The transonic wind tunnel of the aerodynamic test faciyity Goettingen year book 1966 of the WGLR pg. 145-155. C61 Th. Hottner and W. Lorenz-Meyer. The transonic wind tunnel of the aerodynamic test facility Goettingen (second development stage) yearbook 1968 of the
34、 DGLR, pg. 233-244. aerodynamic test facility Goettingen. 2. Flugwiss. 7 (19591, pg. 294-299. C71 H. Ludwieg and Th. Hottner: The high speed wind tunnel of the C81 H. Ludwieg and Th. Hottner: The supersonic test section (710 mm x 725 mm) of the high speed wind tunnel of the AVA. 2. Flugwiss. 11. 11
35、(1963), pg. 137-142. 27 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-g F. R. Grosche: Wind tunnel investigations of the vortex system of a body revalutlon with angle of attack with and with- out wing. 2. Flkgwiss. 18 (1970, p. 208-217. lo H. J. Al
36、len and E. W. Perkins: A study of effects of vis- cosity on flow over slender inclined bodies of revolution. NACA Rep- 1048 (1951). 11 H. J. Allen: Estimation of the forces and moments acting on inclined bodies of revolution of high fineness ratio. MACA RM A9126 (1949 1. 12 W. M.Munk: The aerodynami
37、c forces on airship hulls. NACA Rep. 184 (1924). Siehe auch M. M. Plunk: Aerodynamics of airships. In: W. F. Durand (Herausgeber): Aerodynamic Theory, Vol. VI. Julius Springer, Berlin 1936. Reprint Dover Publications, New York 1963. l3 H. Multhopp: The aerodynamics of a? aircraft body. Luft- fahrtfo
38、rsch. 18 (19411, p. 52-66. 14 X. Hafer: Investigations of the aerodynamics of wing body configurations. Dissertation TH Braunschweig 1957. Yearbook 1957 of the WGL, p. 191-207. 15 H. R. Kelly: The estlmation of normal force, drag and pitching moment coefficients for blunt based bodies of revolution
39、at large angles of attack. tT. Aeron. Sci. 21 (19541, p. 549-56. C161 K. D. Thomson: The estimation of viscous normal force, pitch- ing moment, side force and yawing moment on bodies of revolution at Incidences up tcj goo. WRE-Report 782, Salisbury, South Australia (1972). 17 M. Schwabe: Determining
40、 pressure in the nonsteady plane flow. Ing-Arch. 6 (19351, p. 34-50. English translation: Pressure distribution in nonunifcrm two-dimensional flow. NACA TM 1039 (1943) 18 T. Sarpkaya: Separated flow about lifting bodies and impulsive 19 E. Wedemeyer: Lift distribution of slet. er wing-body combina-
41、flow about cylinder. AIAA Courn. 4 (19651, p. 414-420. tion with separated flow. (1974). Internal DFVLRIAVA report 25173A32 20 F. J. Marshall and F. D. Deffenbaugh: Separated flow over a body of revolution, J. Aircraft 12 (1975), p. 78-85. 28 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-
