On asymptotic theory of plane separated flows. (English) Zbl 1502.35128
Summary: A review of investigations of plane steady external flows of incompressible fluid with developed separation zones at high Reynolds numbers is presented.
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 76D10 | Boundary-layer theory, separation and reattachment, higher-order effects |
| 76M45 | Asymptotic methods, singular perturbations applied to problems in fluid mechanics |
| 35B40 | Asymptotic behavior of solutions to PDEs |
References:
| [1] | Helmholtz H (1868) Über discontinuirliche Flüssigkeits-Bewegungen. Monatsbericht Akad Wiss Berlin April: 215-228 · JFM 01.0341.03 |
| [2] | Kirchhoff, G., Zur Theorie freier Flüssigkeitsstrahlen, J Reine Angew Math, 70, 4, 289-298 (1869) · JFM 02.0730.02 |
| [3] | Kirchhoff G (1876) Vorlesungen über mathematische Physik: Mechanik, 21Vor. Teubner, Leipzig · JFM 08.0542.01 |
| [4] | Lord Reyleigh (1876) On the resistance of fluids. Philos Mag Ser 5 2:1150-1160 |
| [5] | Joukowsky, NE, A modification of Kirchhoff’s method of determining a two-dimensional motion of a fluid given a constant velocity along an unknown streamline, Mat Sb, 15, 1, 121-276 (1890) |
| [6] | Michell, JH, On the theory of free stream lines, Philos Trans R Soc Lond A, 181, 389-431 (1890) · JFM 22.0947.01 · doi:10.1098/rsta.1890.0006 |
| [7] | Planck, M., Zur Theorie der Flüssigkeitsstrahlen, Ann Phys Chem NF, 21, 3, 499-509 (1884) · JFM 16.0829.02 · doi:10.1002/andp.18842570311 |
| [8] | Levi-Civita, T., Scie e leggi di resistenza, Rend Circ Matem Palermo, 23, 1-37 (1907) · JFM 38.0753.04 · doi:10.1007/BF03013504 |
| [9] | Prandtl, L., Proceedings of 3rd international congress in applied mechanics, Stockholm 1930, 41-42 (1931), Stockholm: Ab Sveriges Litogr Tryckerier, Stockholm |
| [10] | Squire, HB, On the laminar flow of a viscous fluid with vanishing viscosity, Philos Mag Ser 7, 17, 1150-1160 (1934) · JFM 60.1384.05 · doi:10.1080/14786443409462468 |
| [11] | Imai, I., Discontinuous potential flow as the limiting form of the viscous flow for vanishing viscosity, J Phys Soc Jpn, 8, 3, 399-402 (1953) · doi:10.1143/JPSJ.8.399 |
| [12] | Ackerberg, RC, Boundary-layer separation at a free streamline, Part 1. Two-dimensional flow, J Fluid Mech, 44, 2, 211-225 (1970) · Zbl 0216.52503 · doi:10.1017/S0022112070001799 |
| [13] | Brillouin M (1911) Les surfaces de glissement d’Helmholtz et la résistance des fluides. Ann Chim Phys 8ser 23:145-230 · JFM 42.0793.02 |
| [14] | Villat H (1914) Sur la validité des solutions de certains problèmes d’Hydrodynamique. J Math Pures Appl 6ser 10(3):231-290 · JFM 45.1064.01 |
| [15] | Wu, TY; Holt, M., Inviscid cavity and wake flows, Basic developments in fluid dynamics, 1-116 (1968), New York: Academic Press, New York |
| [16] | Brodetsky, S., Discontinuous fluid motion past circular and elliptic cylinders, Proc R Soc Lond A, 102, 542-553 (1923) · JFM 49.0746.03 · doi:10.1098/rspa.1923.0014 |
| [17] | Sychev VicV (2010) To the theory of Kirchhoff-type potential flow around a body. TsAGI Sci J 41(5):531-533 |
| [18] | Scheichl, B., A note on the far-asymptotics of Helmholtz-Kirchhoff flows, Theor Compat Fluid Dyn, 28, 3, 377-384 (2014) · doi:10.1007/s00162-014-0322-9 |
| [19] | Cisotti, U., Idromeccanica piana. Parte seconda (1922), Milano: Libreria Editrice Politecnica, Milano |
| [20] | Birkhoff, G.; Zarantonello, EH, Jets, wakes, and cavities (1957), New York: Academic Press, New York · Zbl 0077.18703 |
| [21] | Gurevich, MI, The theory of jets in an ideal fluid (1979), Moscow: Nauka, Moscow |
| [22] | Wu, TY, Cavity and wake flows, Ann Rev Fluid Mech, 4, 243-284 (1972) · doi:10.1146/annurev.fl.04.010172.001331 |
| [23] | Prandtl L (1905) Über Flüssigkeitsbewegung bei sehz kleiner Reibung. Verh III Intern Math-Kongr, Heidelberg, 1904. Teubner, Leipzig, S 484-491 · JFM 36.0800.02 |
| [24] | Howarth, L., On the solution of the laminar boundary layer equations, Proc R Soc Lond A, 164, 547-579 (1938) · JFM 64.1452.01 |
| [25] | Hartree DR (1939) A solution of the laminar boundar-layer equation for retarded flow. Aero Res Coun Rep Memo 2426 (issued 1949) |
| [26] | Goldstein, S., On laminar boundary-layer flow near a position of separation, Q J Mech Appl Math, 1, 1, 43-69 (1948) · Zbl 0033.31701 · doi:10.1093/qjmam/1.1.43 |
| [27] | Stewartson, K., Is the singularity at separation removable?, J Fluid Mech, 44, 2, 347-364 (1970) · Zbl 0219.76033 · doi:10.1017/S0022112070001866 |
| [28] | Terrill, RM, Laminar boundary-layer flow near separation with and without suction, Philos Trans R Soc Lond A, 253, 55-100 (1960) · Zbl 0098.17303 · doi:10.1098/rsta.1960.0018 |
| [29] | Rosenhead, L., Laminar boundary layers (1963), Oxford: Clarendon Press, Oxford · Zbl 0115.20705 |
| [30] | Van Dyke, M., Perturbation methods in fluid mechanics (1975), Stanford: Prabolic Press, Stanford · Zbl 0329.76002 |
| [31] | Brown, SN; Stewartson, K., Laminar separation, Ann Rev Fluid Mech, 1, 45-72 (1969) · doi:10.1146/annurev.fl.01.010169.000401 |
| [32] | Sychev, VV, Laminar separation, Fluid Dyn, 7, 3, 407-417 (1972) · Zbl 0313.76017 · doi:10.1007/BF01209044 |
| [33] | Messiter AF (1975) Laminar separation-a local asymptotic flow description for constant pressure downstream. AGARD CP 168, Flow Separation, paper No 4 |
| [34] | Neiland VYa (1969) Theory of laminar boundary layer separation in supersonic flow. Fluid Dyn 4(4):33-35 · Zbl 0256.76041 |
| [35] | Stewartson, K.; Williams, PG, Self-induced separation, Proc R Soc Lond A, 312, 181-206 (1969) · Zbl 0184.52903 · doi:10.1098/rspa.1969.0148 |
| [36] | Stewartson, K., On the flow near the trailing edge of a flat plate II, Mathematika, 16, 1, 106-121 (1969) · Zbl 0191.25006 · doi:10.1112/S0025579300004678 |
| [37] | Messiter, AF, Boundary-layer flow near the trailing edge of a flat plate, SIAM J Appl Math, 18, 1, 241-257 (1970) · Zbl 0195.27701 · doi:10.1137/0118020 |
| [38] | Smith, FT, The laminar separation of an incompressible fluid streaming past a smooth surface, Proc R Soc Lond A, 356, 443-463 (1977) · Zbl 0376.76024 · doi:10.1098/rspa.1977.0144 |
| [39] | Korolev, GL, Numerical solution of the asymptotic problem of laminar boundary-layer separation from a smooth surface, TsAGI Sci J, 11, 2, 27-36 (1980) |
| [40] | van Dommelen, LL; Shen, SF; Cebeci, T., Interactive separation from a fixed wall, Numerrical and physical aspects of aerodynamic flows II, 393-402 (1984), New York: Springer, New York · Zbl 0581.76047 · doi:10.1007/978-3-662-09014-5_24 |
| [41] | Ruban, AI, Fluid dynamics: part 3 boundary layers (2018), Oxford: Oxford University Press, Oxford · Zbl 1395.76001 · doi:10.1093/oso/9780199681754.001.0001 |
| [42] | Smith, FT, Laminar flow of an incompressible fluid past a bluff body: the separation, reattachment, eddy properties and drag, J Fluid Mech, 92, 1, 171-205 (1979) · Zbl 0413.76003 · doi:10.1017/S0022112079000574 |
| [43] | Ruban, AI, On laminar separation from a corner point on a solid surface, TsAGI Sci J, 5, 2, 44-54 (1974) |
| [44] | Ruban, AI, A numerical method for solving the free-interaction problem, TsAGI Sci J, 7, 2, 45-51 (1976) |
| [45] | Sychev VV, Ruban AI, Sychev VicV, Korolev GL (1998) Asymptotic theory of separated flows. Cambridge University Press, Cambridge · Zbl 0944.76003 |
| [46] | Kravtsova, MA, Numerical solution of the asymptotic problem of incompressible boundary-layer separation ahead of a body corner point, Comput Math Math Phys, 33, 3, 397-406 (1993) · Zbl 0798.76017 |
| [47] | Sychev VV (1967) On steady laminar flow of a fluid around a bluff body at high Reynolds number. In: Proceedings of 8th symposium on current problems of the mechanics of liquids and gases, Tarda, Poland (See TsAGI Sci J (2018) 49 (4): 373-384) |
| [48] | Keulegan, GH, Laminar flow at the interface of two liquids, J Res Nat Bur Stand, 32, 6, 303-327 (1944) · Zbl 0061.45202 · doi:10.6028/jres.032.016 |
| [49] | Lock, RC, The velocity distribution in the laminar boundary layer between parallel streams, Q J Mech Appl Math, 4, 1, 42-63 (1951) · Zbl 0042.43002 · doi:10.1093/qjmam/4.1.42 |
| [50] | Diesperov, VN, On the flow in a Chapman mixing layer, Dokl Akad Nayk SSSR, 284, 2, 305-309 (1985) · Zbl 0644.76115 |
| [51] | Imai I (1957) Theory of bluff bodies. Tech Note BN-104, Inst Fluid Dyn Appl Math, University of Maryland |
| [52] | Van Dyke MD (1956) Second-order subsonic airfoil theory including edge effects. NACA Rep 1274 |
| [53] | Sychev VicV (2010) On asymptotic theory of separated flows past bodies. Fluid Dyn 45(3):441-457 · Zbl 1215.76023 |
| [54] | Sychev, VV, Asymptotic theory of separated flows, Fluid Dyn, 17, 2, 179-188 (1982) · doi:10.1007/BF01314493 |
| [55] | Ruban, AI, Asymptotic theory of flow attachment for viscous incompressible fluid, Fluid Dyn, 15, 6, 844-851 (1980) · Zbl 0467.76037 · doi:10.1007/BF01096634 |
| [56] | Sychev VicV (2001) High Reynolds number flow past a plate mounted at a small angle of attack. Fluid Dyn 36(2):244-261 · Zbl 1101.76321 |
| [57] | Kármán Th V (1921) Über laminare und turbulente Reibung. ZAMM 1(4):233-252 · JFM 48.0968.01 |
| [58] | Pohlhausen, K., Zur näherungsweisen Integration der Differentialgleichung der laminaren Grenzschicht, ZAMM, 1, 4, 252-290 (1921) · JFM 48.0968.02 · doi:10.1002/zamm.19210010402 |
| [59] | Roshko, A., A review of concepts in separated flows, Proc Can Congr Appl Mech, 3, 81-115 (1967) |
| [60] | Riabouchinsky DP (1920) On steady fluid motions with free surfaces. Proc Lond Math Soc Ser 2 19(3):206-215 · JFM 47.0756.04 |
| [61] | Yudovich, VI, On the loss of smoothness of solutions of the Euler equations with time, Dyn Contin Medium, 16, 71-78 (1974) |
| [62] | Yudovich, VI, On gradual loss of smoothness and instability inherent to ideal fluid flows, Dokl Ross Akad Nauk, 370, 6, 760-763 (2000) |
| [63] | Sychev VicV (2011) On regions of turbulence in separated flows. TsAGI Sci J 42(5):555-563 |
| [64] | Schlichting, H., Über das ebene Windschattenproblem., Ing-Arch, 1, 5, 533-571 (1930) · JFM 56.1261.06 · doi:10.1007/BF02079870 |
| [65] | Roshko A (1954) On the development of turbulent wakes from vortex streets. NACA Rep 1191 |
| [66] | Arie, M.; Rouse, H., Experiments on two-dimensional flow over a normal wall, J Fluid Mech, 1, 2, 129-141 (1956) · doi:10.1017/S0022112056000093 |
| [67] | Roshko, A., Transition in incompressible near-wakes, Phys Fluids Suppl, 10 pt II, 9, 181-183 (1967) · doi:10.1063/1.1762441 |
| [68] | Roshko, A.; Fiszdon, W., On the persistence of transition in the near-wake, Problems of hydrodynamics and continuum mechanics, 431-438 (1969), Moscow: Nauka, Moscow |
| [69] | Sychev, VV, Boundary-layer separation from a flat surface, TsAGI Sci J, 9, 3, 20-29 (1978) |
| [70] | Zubtsov, AV, Separation of a laminar boundary layer from a plane surface, TsAGI Sci J, 16, 5, 108-110 (1985) |
| [71] | Smith, FT; Merkin, JH, Triple-deck solutions for subsonic flow past humps, steps, concave or convex corners and wedged trailing edges, Comput Fluids, 10, 1, 7-25 (1982) · Zbl 0516.76043 · doi:10.1016/0045-7930(82)90018-4 |
| [72] | Sychev VicV (2013) On the theory of the flow around bodies of revolution at high Reynolds numbers. TsAGI Sci J 44(6):727-747 |
| [73] | Sychev VicV (1993) Asymptotic theory of vortex breakdown. Fluid Dyn 28(3):356-364 · Zbl 0792.76015 |
| [74] | Sychev VicV (2005) On asymptotic theory of vortex breakdown. TsAGI Sci J 36(3-4):13-20 |
| [75] | Cheng, HK; Smith, FT, The influence of airfoil thickness and Reynolds number on separation, ZAMP, 33, 2, 151-180 (1982) · Zbl 0504.76042 |
| [76] | Rothmayer, AP; Smith, FT, Large-scale separation and hysteresis in cascades, Proc R Soc Lond A, 402, 83-108 (1985) · doi:10.1098/rspa.1985.0109 |
| [77] | Barnett, M., Analysis of crossover between local and massive separation on airfoils, AIAA J, 26, 5, 513-521 (1988) · Zbl 0664.76061 · doi:10.2514/3.9927 |
| [78] | Timoshin, SN, Separated flow around a thin profile with parabolic leading edge at high Reynolds number, TsAGI Sci J, 16, 2, 24-32 (1985) |
| [79] | Sychev VicV (2004) On a separated flow around an arc at high Reynolds numbers. TsAGI Sci J 35(3-4):3-12 |
| [80] | Sychev VicV (2006) On the flow around an arc at high Reynolds numbers with formation of local separation regions. TsAGI Sci J 37(1-2):26-33 |
| [81] | Cheng HK (1984) Laminar separation from airfoils beyond trailing-edge stall. AIAA Paper 84-1612 |
| [82] | Khrabrov, AN, Nonuiqueness of laminar separated flow over an airfoil at angle of attack according to the Kirchhoff model, TsAGI Sci J, 16, 5, 1-9 (1985) |
| [83] | Cheng, HK; Lee, CJ; Cebeci, T., Laminar separation studied as an airfoil problem, Numerical and physical aspects of aerodynamic flows III, 102-125 (1986), New York: Springer, New York · Zbl 0604.76046 · doi:10.1007/978-1-4612-4926-9_6 |
| [84] | Lee, CJ; Cheng, HK, An airfoil theory of bifurcating laminar separation from thin obstacles, J Fluid Mech, 216, 255-284 (1990) · Zbl 0699.76045 · doi:10.1017/S0022112090000428 |
| [85] | Chaplygin, SA, On the problem of jets in an incompressible fluid, Proc Phys Sect Soc Nat Sci, 10, 1, 35-40 (1899) |
| [86] | Messiter AF (1979) Boundary-layer separation. In: Proceedings of 8th U.S. Natational Congress in applied mechanics, pp. 157-179. Western Periodicals, North Hollywood |
| [87] | Sychev VicV (2007) Separation zones in the flow near a small-angle convex corner. Fluid Dyn 42(2):221-235 · Zbl 1200.76045 |
| [88] | Tulin, MP, Supercavitating flows-small perturbation theory, J Ship Res, 7, 3, 16-37 (1964) · doi:10.5957/jsr.1964.8.1.16 |
| [89] | Korolev GL, Sychev VicV (2017) On a boundary layer in a separated flow region. TsAGI Sci J 48(6):493-504 |
| [90] | Sychev VicV (2018) Marginal separation into reverse-flow region. TsAGI Sci J 49(7):683-700 |
| [91] | Rothmayer, AP; Smith, FT; Johnson, RW, High Reynolds number asymptotic theories, Handbook of fluid dynamics, Part III (1998), Boca Raton: CRC Press, Boca Raton · Zbl 0978.76001 |
| [92] | Stewartson, K., Multistruetured boundary layers on flat plates and related bodies, Adv Appl Mech, 14, 145-239 (1974) · doi:10.1016/S0065-2156(08)70032-2 |
| [93] | Stewartson, K., D’Aembert’s paradox, SIAM Rev, 23, 3, 308-343 (1981) · Zbl 0484.76002 · doi:10.1137/1023063 |
| [94] | Smith, FT, On the high Reynolds number theory of laminar flows, IMA J Appl Math, 28, 3, 207-281 (1982) · Zbl 0494.76042 · doi:10.1093/imamat/28.3.207 |
| [95] | Smith, FT, Steady and unsteady boundary-layer separation, Ann Rev Fluid Mech, 18, 197-220 (1986) · Zbl 0615.76048 · doi:10.1146/annurev.fl.18.010186.001213 |
| [96] | Kluwick, A.; Kluwick, A., Interacting laminar and turbulent boundary layers, Recent advances in boundary layer theory, 231-330 (1998), Wien: Springer, Wien · Zbl 0909.76023 · doi:10.1007/978-3-7091-2518-2_7 |
| [97] | Cowley, SJ; Aref, H.; Philips, JW, Laminar boundary-layer theory: a 20th century paradox?, Mechanics for a new millennium, 389-412 (2001), Alphen aan den Rijn: Kluwer, Alphen aan den Rijn |
| [98] | Neiland, VYa; Bogolepov, VV; Dudin, GN; Lipatov, II, Asymptotic theory of supersonic viscous gas flows (2008), Oxford: Elsevier, Oxford |
| [99] | Adamson, TC Jr; Messiter, AF, Analysis of two-dimensional interactions between shock waves and boundary layers, Ann Rev Fluid Mech, 12, 103-138 (1980) · Zbl 0498.76062 · doi:10.1146/annurev.fl.12.010180.000535 |
| [100] | Smith, FT, On internal fluid dynamics, Bull Math Sci, 2, 1, 125-180 (2012) · Zbl 1246.00022 · doi:10.1007/s13373-012-0019-6 |
| [101] | Smith, FT, On the non-parallel flow stability of the Blasius boundary layer, Proc R Soc Lond A, 366, 91-109 (1979) · Zbl 0411.76042 · doi:10.1098/rspa.1979.0041 |
| [102] | Zhuk, VI, Tollmien-Schlichting waves and solitons (2001), Moscow: Nauka, Moscow |
| [103] | Cowley SJ, Wu X (1994) Asymptotic approaches to transition modeling. In: Progress in transition modeling, AGARD Rep 793. Chap. 3, pp 1-38 |
| [104] | Ruban, AI, Asymptotic theory of short separation regions on the leading edge of a slender airfoil, Fluid Dyn, 17, 1, 33-41 (1982) · Zbl 0528.76043 · doi:10.1007/BF01090696 |
| [105] | Stewartson, K.; Smith, FT; Kaups, K., Marginal separation., Stud Appl Math, 67, 1, 45-61 (1982) · Zbl 0514.76039 · doi:10.1002/sapm198267145 |
| [106] | Ruban, AI, A singular solution of the boundary layer equations which can be extended continuously through the point of zero surface friction, Fluid Dyn, 16, 6, 835-843 (1981) · Zbl 0504.76041 · doi:10.1007/BF01089710 |
| [107] | Brown, SN; Stewartson, K., On an integral equation of marginal separation, SIAM J Appl Math, 43, 5, 1119-1126 (1983) · Zbl 0531.76045 · doi:10.1137/0143072 |
| [108] | Zametaev, VB, Marginal separation in three-dimensional flows, Theor Comput Fluid Dyn, 8, 3, 183-200 (1996) · Zbl 0865.76017 · doi:10.1007/BF00418057 |
| [109] | Braun S, Scheichl S (2014) On recent developments in marginal separation theory. Philos Trans R Soc Lond A 372:20130343 · Zbl 1353.76040 |
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