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北京大学, . EFFECT OF TRANSVERSE CURVATURE ON AXISYMMETRIC COMPRESSIBLE LAMINAR BOUNDARY LAYER[J]. Chinese Journal of Theoretical and Applied Mechanics, 1966, 9(2): 150-172. DOI: 10.6052/0459-1879-1966-2-1966-003
Citation: 北京大学, . EFFECT OF TRANSVERSE CURVATURE ON AXISYMMETRIC COMPRESSIBLE LAMINAR BOUNDARY LAYER[J]. Chinese Journal of Theoretical and Applied Mechanics, 1966, 9(2): 150-172. DOI: 10.6052/0459-1879-1966-2-1966-003
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EFFECT OF TRANSVERSE CURVATURE ON AXISYMMETRIC COMPRESSIBLE LAMINAR BOUNDARY LAYER

  • Peking University

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    • Abstract
  • The thickness of the boundary layer over an axisymmetric slender body may be comparable to, or even of several times the local radius of the transverse curvature of the body. The practice of replacing distance of a point in the boundary layer from the axis by the local body radius, as in classical Prandtl boundary layer equatiions,is then no longer applicable.The present work discusses the effcet of the transverse curvature on the axisymmetric compressiboe laminar boundary layer flow,analogous to the work of Lighthill and Glauert for the incompressible case.The first part of the paper deals with the strong effect region, i.e., the region where the boundary layer thickness is much larger than the local body radius.The usual assumptions of perfect gas, Prandtl number equal to one and linear viscosity-temperature relation are made.Neglecting the pressure gradient,one may find a small parameter ε to characterize the transverse curvature effect.The reduced stream function is then expressed as a power series of ε and the asymptotic solutions for skin friction and heat transfer rate are found.It is shown that the singularity of the second approximation(the third term in series)near the wall may be removed by using the PLK method and the solution is then uniformly valid.For power-lawed bodies,rw~xn,the skin friction coefficient Cf and the Stanton number St in the strong effect region may be expressed as Cf=4Ce/Rex Tw/Te x/rw cosφ{θ+[0.577-In(1+2n)]θ2}+O(θ3,St=1/2Cf In the second part, the transverse curvature effect in the entire flow field is investigated by means of momentum integral method where the Crocco's independent variables x,μ are used.With a suitable choice of a relation between shearing stress τ and velocity μ,approximate solutions for Cf and St of the circular cylinder and circular cone, valid for the entire range of transverse curvature paameters Ω and Φ,are found Coparison of the results with the Probstein and Elliott's serics solution for the weak effect region and the solution for the strong effect region found in the first part is made.
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    • References (13)
  • Probstein, R, F, and Elliott, D., The transverse curvature effect in eompressi6le axially symmetric laminar boundary Payer flow, jour.Aero. Sci,23, 3, 1956, 208-224.
    Seban, R. A. and Bond, R., Skin-friction and heat transfer characteristics of a laminar boundary layer on“cylinder in axial incomfsressihle flaw, Jour. Aero. Sci,18, 10, 1951, 671-675.
    Kelly, H. R., A note an the laminar boundary layer on a circular cylinder in axial incompressible flow, Jour. Aero. Sci,21, 9, 1954, 534.
    Glauerr, M. B. and Z.igtrthill, M. J., The axisymmetric boundary layer on a long thin cylinder, Proc.Ray. Sac., 5rries A, 230, 1955, 188-203.
    Stewartson, K,The asymptotic boundary layer an a circular cylinder in axial incompressible flow, Quart. Appl, Math., 13, 2, 1955, 113-122.
    Bourne, D. E. and Ltavies, D. R., Heat transfer through the laminar boundary layer an“circular cylinder in axial incompressible flaw, Quart. Jour, of Mech. and Appl. Math., 11, 1, 1958, 52-66.
    Yasuhara, M., Axisymmetric viscous flaw past very slender bodies of revolution, jour. Aero. Sci,29, 5. 1962. 667-679.
    Rant, J.. Skin friction of slender cones in hypersonic flow, AIAA Jour., 2, 4, 1964, 755-756.
    Stewartson, K,Viscous hypersonic flow past a slender cone, Phys. of Fluids, 7, 5, 1964, 667-675.
    Wei, M. H., Asymptotic boundary layer over a slender body of revolution in axial compressible flow. AIAA Jour.. 3. 5. 1965. 809-816.
    Гиневский,А.С.,Солодкин,Е.Е.,Влияние поперечной кривизны поверхности на характеристики осесимметричного турбулентного пограничного слоя,ПММ,22,6,1958,819-825.
    Гиневский,А.С.,Солодкин,Е.Е.,Влияние поперечной кривизны поверхности на характеристики неизотермического осесимметричного турбулентного пограничного слоя сжимаемого чаза,Изб,АН СССР,ОТН,Мех.ц Мащ.,1,1963,66-110.
    钱学森(Tsien, H. S),The Poincaré-Lighthill-Kuo Method, in "Advances in Appl.Mech.", Vol. IV. Academic Press. New York.1956,281-349.
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