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[해외논문] Upstream influence in boundary layers 45 years ago

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences, v.358 no.1777, 2000년, pp.3047 - 3061  

Duck, P. W. (Department of Mathematics, University College, Gower Street, London WC1E 6BT, UK) ,  Ruban, A. I. ,  Lighthill, Sir James

Abstract

My two-part paper 'Boundary layers and upstream influence', published in 1953, surveyed a wide range of experimental evidence on how a disturbance in supersonic flow, which in inviscid theory would affect only downstream conditions, is able to exercise an upstream influence through the agency of a boundary layer, either laminar or turbulent. Then, by systematically comparing the data with existing attempts to account for the phenomenon theoretically, it concluded that, essentially, two mechanisms of upstream influence exist. Mechanism (i), first suggested by Oswatitsch & Wieghardt in 1941, depended on a particular property of supersonic flow over a wall: that either wall curvature on inviscid theory, or (for a flat wall) curvature $d^2\delta_1/dx^2$ of the displacement-thickness contour on boundary-layer theory, generates a proportional pressure gradient; which, in the latter case, is $A_2d^2\delta_1/dx^2, A_2$ being a known positive function of Mach number. Also, this positive pressure gradient might be expected to thicken the layer at a spatial rate $d\delta_1d/dx = A_1 (A_2d^2\delta 1/dx^2)$, where $A_l$, although far from precisely known, must be less for a turbulent than for a laminar layer; so that, finally, the e-folding distance of upstream influence would be $A_1A_2$. Mechanism (i) was compared, in part II of my paper, with a different proposal (see the work of Howarth in 1948) for a theoretical programme concerned with 'propagation up the subsonic layer', in which only the undisturbed boundary-layer distribution (including its subsonic part) would be taken, as influenced by viscosity, while disturbances to it would be treated inviscidly. The reason why attempts to carry out this programme had failed was explained in terms of earlier theories of boundary-layer instability, in which time-dependent disturbances had been found to be influenced by viscosity in two layers: a wall layer and a critical layer. For disturbances independent of time these would coincide into a single wall layer in which, however, the influence of viscosity still needed to be taken into account; in which case, the analysis could be satisfactorily completed but became in essence merely an expression of mechanism (i) with a relatively precise determination of $A_1$. Mechanism (ii), identified in work by Lees in 1949 at Princeton and by Liepmann, Roshko & Dhawan in 1949 at Caltech, depended on the upstream spreading of a separation bubble till it became sufficiently slender to cause no further separation ahead of it. Part I of my paper was concerned to point out that, although mechanism (i) can work only when a well-defined coefficient $A_2$ exists (that is, for supersonic flow), mechanism (ii) is effective in both subsonic and supersonic flow. This was illustrated by analysing data on flow up a step at various Mach numbers (with various locations for transition to turbulence) in terms of boundary-layer separation studies. Those instructive examples, which may today be somewhat less known, and which included several interesting cases of both steady and also unsteady separated flows, can appropriately be recalled in a colloquium devoted to such phenomena.

참고문헌 (22)

  1. Ackeret J. Feldmann F. & Rott N. 1946 Mitt. Inst. Aerodyn. Zurich no.10. Or Tech. Memo. Nat. Adv. Comm. Aero. Wash. no.1113 (1947). 

  2. Bardsley, O., Mair, W.A.. III. The interaction between an oblique shock-wave and a turbulent boundary-layer. The philosophical magazine, vol.42, no.324, 29-36.

    상세보기 crossref

  3. BARRY, F. W., SHAPIRO, A. H., NEUMANN, E. P.. The Interaction of Shock Waves with Boundary Layers on a Flat Surface. Journal of the aeronautical sciences, vol.18, no.4, 229-238.

    상세보기 crossref

  4. Bogdono® S. M. & Solarski A. H. 1951 Aero. Engng Lab. Report no. 184 (Princeton NJ). 

  5. Ferri A. 1939 Atti Guidonia no. 17 (Rome). 

  6. Gadd G. E. & Holder D. W. 1952 The interaction of an oblique shock wave with the boundary layer on a at plate. Part I. Results for M = 2. Aero. Res. Council Report no. 14848. 

  7. Goldstein S. 1938 Modern developments in uid dynamics. Oxford University Press. 

  8. Holder D. W. & North R. J. 1950 Observations of the interaction between the shock waves and boundary layers at the trailing edges of airfoils in supersonic ow. Aero. Res. Council Report no. 13621. 

  9. 10.1098/rspa.1938.0037 Howarth L. 1938 On the solution of the laminar boundary layer equations. Proc. R. Soc. Lond. A 164 547{579. 

    상세보기 crossref

  10. Howarth, L.. The propagation of steady disturbances in a supersonic stream bounded on one side by a parallel subsonic stream. Proceedings of the Cambridge Philosophical Society. Mathematical and physical sciences, vol.44, no.3, 380-390.

    상세보기 crossref

  11. Johannesen, N.H.. "LII. Experiments on two-dimensional supersonic flow in corners and over concave surfaces." The philosophical magazine, v.43 no.340 (1952), pp. 568-580, doi:10.1080/14786440508520212.

    crossref

  12. Kuo Y. H. 1951 On the re ection of a weak shock wave from a boundary layer along a at plate. Ithaca NY: Cornell University. 

  13. Lees L. 1949 Aero. Engng Lab. Report no. 143 (Princeton NJ). 

  14. Lees L. & Crocco L. 1952 Aero. Engng Lab. Report no. 195 (Princeton NJ). 

  15. Liepmann H. W. Roshko A. & Dhawan S. 1949 On the re° ection of shock waves from boundary layers. Galcit Report (Pasadena CA). Or Tech. Memo. Nat. Adv. Comm. Aero. Wash. no. 2334 (1951). 

  16. 10.1098/rspa.1953.0067 Lighthill M. J. 1953a On boundary layers and upstream in° uence. I. A comparison between subsonic and supersonic ows. Proc. R. Soc. Lond. A 217 344{357. 

    상세보기 crossref

  17. 10.1098/rspa.1953.0075 Lighthill M. J. 1953b On boundary layers and upstream in° uence. II. Supersonic ows without separation. Proc. R. Soc. Lond. A 217 478{507. 

    상세보기 crossref

  18. Mair, W.A.. "LXVIII. Experiments on separation of boundary layers on probes in front of blunt-nosed bodies in a supersonic air stream." The philosophical magazine, v.43 no.342 (1952), pp. 695-716, doi:10.1080/14786440708520987.

    crossref

  19. Oswatitsch K & Wieghardt K. 1941 German wartime report. Reprinted as Tech. Memo. Nat. Adv. Comm. Aero. Wash. no. 1189 (1948). 

  20. Schlichting H. 1933 Zur Entstehung der Turbulenz bei der Plattenstromung. Nachr. Ges. Wiss. Gottingen Math.-Phys Kl. 181{208. 

  21. Stewartson, K.. On the interaction between shock waves and boundary layers. Proceedings of the Cambridge Philosophical Society. Mathematical and physical sciences, vol.47, no.3, 545-553.

    상세보기 crossref

  22. 10.1007/978-3-662-33791-2_4 Tollmien W. 1929 Uber die Entstehung der Turbulenz. Nachr. Ges. Wiss. Gottingen 21{44. Translated as `The production of turbulence' Tech. Memo. Nat. adv. Comm. Aero. Wash. no. 609. 

    crossref

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