Three-dimensional viscous wakes

Steiger, Martin H.; Bloom, Martin H.

doi:10.1017/s0022112062001202

Cited by 9 publications

(2 citation statements)

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“…For example, in Ref. 2 Steiger and Bloom use an iteration method in which the nonlinear terms (that is, terms due to the compressibility) are assumed to be known functions of the coordinates, whereby the governing equation for the axial velocity becomes linear but nonhomogeneous and, therefore, amenable to solution by transform methods. The iteration then involves an evaluation of several integrals.…”

Section: F Approximate Compressible Solutions For the Axial Velocitymentioning

confidence: 99%

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Three - Dimensional Effects in Viscous Wakes

Steiger

Bloom

1963

AIAA Journal

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Three-dimensionality in wakelike or jetlike free mixing may stem from initial geometric configurations, nommiformities in flow variables over a cross section, or boundary conditions along the flow. These may be generated by bodies at angle of attack, nonaxisymmetric bodies, mixing of nonaxisymmetric jets with an outer flow, finite wings, or more artificial means. This paper is devoted to studies bearing on such configurations. The first section deals with the general mathematical model, in which the boundary layer approximations are used, and with methods of solution. Laminar and turbulent flow, compressibility, unsteadiness, and streamwise pressure gradients are admitted initially. The flux forms of the equations are given. Algebraic integrals of the energy equations and the diffusion (frozenflow) equations are obtained. A simplification of the convective terms, roughly corresponding to the Oseen approximation, is used in the asymptotic downstream region. The second section contains explicit solutions for specific configurations, in particular for flows whose initial isovels are of elliptic shape. These flows may be wakelike or jetlike. Compressibility is admitted; however, the flows must have uniform pressure and must be steady. The final section deals with interpretation and evaluation of the results. Nomenclature associated with dissociation and ionization energies eccentricity h = static enthalpy (h -H = stagnation enthalpy, H = h + ^2/2 £2 = [l + 4s]-1 K = pure constant of order 10 ~2 L = constant characteristic length [see Eq. (26)] Le = Lewis number m = non-negative integer, ra = 0,1,2 ... Pr = Prandtl number Mi = gram-mole weight of species i R Q = universal gas constant Q = see Eq. (14a) s^i = transformed axial coordinate t = time T = absolute temperature u = axial velocity component u = axial velocity defect (u = u e -u) v,w = crossflow velocity components (see Fig. 1) Wi = net rate of production of species i x = axial coordinate y,z = cross-plane coordinate components (see Fig. 1) on = mass friction of species i 8 = viscous layer thickness §j = viscous layer thickness in the plane z -0 5 2 = viscous layer thickness in the plane y = 0 dm = minimum transform viscous layer thickness e = measure of the initial eccentricity [see Eq. (23)] e v = turbulent eddy viscosity ,7^ = transformed normal coordinate tj s = value of rj when y = 8 A/ = vibrational energy of species j Pr cr,

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Section: F Approximate Compressible Solutions For the Axial Velocitymentioning

confidence: 99%

“…The incompressible solutions have been presented in Ref . 1 and are achieved in the following manner. At an initial station, let…”

Section: A Elliptic Wakelike or Jetlike Flows; Axial Velocitymentioning

confidence: 99%

Three - Dimensional Effects in Viscous Wakes

Steiger

Bloom

1963

AIAA Journal

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Wake Flow

Chang

1970

Separation of Flow

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Linearized viscous free mixing with streamwise pressure gradients

Bloom

Steiger

1964

AIAA Journal

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Sets of similar solutions applicable within a linearized approximation are derived for twodimensional compressible and axisymmetric incompressible viscous free mixing with streamwise pressure gradients Viewed as eigenfunctions these solutions can be superposed to represent arbitrary initial conditions However, it is observed that only one solution of the family possesses a net momentum defect (or excess) different from zero This mode decays exponentially in the normal direction and has a stronger streamwise persistence than any of the other solutions that have exponential normal decays; it is usually referred to as "the" similar solution

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Three-dimensional viscous wakes

Cited by 9 publications

References 1 publication

Three - Dimensional Effects in Viscous Wakes

Three - Dimensional Effects in Viscous Wakes

Wake Flow

Linearized viscous free mixing with streamwise pressure gradients

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