On thick boundary layers over slender bodies with some effects of heat transfer, mass transfer and pressure gradient

Steiger, Martin H.; Bloom, Martin H.

doi:10.1016/0017-9310(62)90161-8

Cited by 7 publications

(2 citation statements)

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“…(13) and (14) have similarity solutions. This corresponds to the case of a slender body in hypersonic flow with the radius (r 0 ) and the boundary-layer thickness (d) varying as # 3/4 and the induced pressure (P e ) as x~1 12 . It should be noted that, from Eq.…”

Section: ?mentioning

confidence: 99%

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Asymptotic boundary-layer over a slender body of revolution in axial compressible flow

Wei

1965

AIAA Journal

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The singular perturbation method developed by S. Kaplun is used to solve the thick, compressible laminar boundary layer over a slender body of revolution. The transverse curvature effect is included and is found to be characterized by a dimensionless parameter, which is essentially a function of the ratio of the thickness of the boundary layer to the radius of the body of revolution. An asymptotic series solution is developed for the region where the thickness of the boundary layer is large compared with the radius of the slender body. The nondimensional skin-friction parameter \(2ir r G T w )/(cosa. U e v e )} is calculated as a function of the thickness parameter. Interpolations are then made with another known series solution, developed by Probstein and Elliott, which is valid where the boundary layer is thin compared with the radius of the slender body. Thus, interpolation is made to cover the range where the thickness of boundary layer is in the same order as the body radius. From these interpolations, good agreement is obtained between both series for the cone and cylinder. The asymptotic series solution also indicates that the skin friction and heat-transfer rate increase with the Mach number and fall off very slowly in the reciprocal-logarithmic manner with the thickness parameter. Nomenclature j8 -defined by 0 = S 0 c)U e /U e <)S 0 C = specific heat or, when not subscripted, Chapman-Rubesin constant / = defined by U/U. = ctf/dr? g = defined by g = h 8 /-[(h s ) e ] h = enthalpy k = coefficient of thermal conductivity of gas K = defined by Eq. (15) K 0 = defined by K Q = [2/3(1 + «o)]/(l -K) I = defined by Eq. (50c) M = Mach number P = static pressure Pr = Prandtl number C Ptl /k q = local rate of heat transfer from surface per unit area per unit time g = -fc(b!F/dY) r 0 = radius of body of revolution R = gas constant per gram 7 = ratio of specific heats, 7 = Cp/CV s = distance along the body surface, measured from forward stagnation point So = transformed coordinate along body surface defined by Eq. (6) T = absolution temperature u,v = components of velocity parallel and normal to surface x = distance along body axis y = distance normal to the body surface 6 = .boundary-layer thickness ?7 = nondimensional coordinate normal to body surface ri = defined by Eq. (19) ?7* = defined by Eq. (25) a. = angle between the tangent to the meridian profile and the x axis «o = defined by oo = [(r -l)/2]M e 2 n = absolute viscosity p = gas density £ = nondimensional thickness parameter, defined by Eq. (12) \I> = stream function defined by Eq. (8) T = shear stress r = i/,(dU/dy) e = gage function T(n) = gamma function Subscripts e = quantities outside the boundary layer W = quantities on the wall surface 0° = quantities in the freestream S = quantities at the stagnation point P = constant pressure V = constant volume T = gage function for g 1,2 = gage function for / Superscripts * = referring to the inner expansions ( ) = referring to the outer expansions ( )' = ordinary differentiation with respect to 77

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Section: ?mentioning

confidence: 99%

“…From Eqs. (9) and (10), it is seen that a new variable | can be defined so that the equations can be transformed into suitable forms with which a similarity solution can be examined: (12) Equations (9) and (10) expressed in a new coordinate system (£,77) will take the following forms:…”

Section: Equations Of the Boundary Layermentioning

confidence: 99%