Nonequilibrium Wakes With Laminar and Turbulent Transport

Lien, Hwaachii; Erdos, John; Pallone, A.

doi:10.2514/6.1963-447

Cited by 10 publications

(4 citation statements)

References 9 publications

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“…Also, some indications of the effect of laminar-turbulent transitions are shown; the transition criterion is based upon the correlations presented by Pallone etal. 18 The turbulent viscosity models considered herein are the following: 1 case, is within § Although it is not obvious from Fig. 4, the curvature parameter for «NO is identical to all others at X/CoA 12 = 0; for X > 0, the OINO develops an off-axis peak due to off-axis chemistry.…”

Section: Turbulent Wake Calculationsmentioning

confidence: 98%

Finite-difference calculation of hypersonic wakes

Bleich

Zeiberg

1964

AIAA Journal

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A finite-difference method is used to solve the system of equations governing the hypersonic air wake with nonequilibrium chemistry; both laminar and turbulent transports are considered. Numerical results for laminar flow are compared with results of an integral method. Additional calculations for turbulent flow are presented to show some effects of the oxygen-electron attachment process in the far wake, and of the choice of the model of turbulent diffusivity. Nomenclature Cp = specific heat D = vehicle base diameter L = Lewis number h = enthalpy h° = enthalpy of formation P = pressure Rt, = vehicle base radius T = temperature U = X component of velocity U = velocity defect V = Y component of velocity Wi = net rate of generation of species i X = stream wise coordinate Y -radial coordinate a = mass fraction du -velocity radius rj -density transformed radial coordinate a = Prandtl number n = viscosity p = densitŷ = stream function Subscripts 0 = evaluated on wake axis Y = ^ = 0 e = evaluated at edge of wake, or freestream i -refers to species i Superscript ( ) = mass-averaged quantity

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Section: Turbulent Wake Calculationsmentioning

confidence: 98%

Finite-difference calculation of hypersonic wakes

Bleich

Zeiberg

1964

AIAA Journal

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“…3a-3d, it is quite clear that extreme care must be exercised in the selection of functional forms for the analytical profiles to be employed in any laminar diffusion calculation using the integral method. 13 " 15 In the case of turbulent flow, the existence of such complicated external profiles may also be expected to contribute significantly to the difficulty in any two-dimensional treatment of the wake.…”

Section: A Mapping Of the Chemically-reacting Inviscid Flow Fieldmentioning

confidence: 99%

“…More recently, various authors 13 " 15 have proposed to use the integral method 4 for simultaneous treatment of diffusion and chemical relaxation in turbulent as well as laminar wakes behind objects of arbitrary (but axisymmetric) shape. The terms for production (or depletion) of chemical species in the species conservation equations in these treatments are considered identical in form for both the laminar and the turbulent cases, and the reaction rate constants employed in subsequent numerical calculations are often those published in the literature for homogeneous gas mixtures.…”

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confidence: 99%

A quasi-one-dimensional treatment of chemical reactions in turbulent wakes of hypersonic objects

Hayes

Lin

1964

AIAA Journal

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25 Langmuir, I., "The effect of space charge and initial velocities on the potential distribution and thermionic current between parallel plane electrodes," Phys.The effects of different mixing models on the chemical reaction histories in the turbulent wakes of hypersonic objects are investigated in a quasi-one-dimensional approximation. The radial propagation of the turbulent front is represented as a prescribed entrainment boundary and the chemical composition of the initial flow entering the boundary is calculated according to existing approximate methods for tracing chemical reactions in laminar flows. In the absence of a suitable chemical kinetics theory for turbulent flows, only the limiting cases of extremely slow and extremely fast viscous dissipation are considered for the subsequent turbulent mixing process. Specific examples are presented for the flow behind hypersonic spheres in air. In the slow-dissipation case, the high-entropy gas in the wake remains hot, and may even be reheated strongly by three-body atomic recombination. This gives rise to large amplitude fluctuations of the chemical species. In the fast dissipation case, the temperature generally falls off rapidly with distance behind the sphere, but moderately strong reheating may still take place due to sudden enhancement of the exothermic exchange reaction N + O2-*• NO -j-O. The mean electron density in the far wake is found to be extremely sensitive to the mixing model.

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“…(4)(5)(6)(7)(8)(9)(10)(11) to the dynamical properties of the turbulence field, it is now necessary to establish a functional relationship between the local mean-square fluctuation intensity and the diffusive smearing rate. By invoking restriction 2, Sec.…”

Section: Governing Equation For \F/mentioning

confidence: 99%

A bimodal approximation for reacting turbulent flows. I - Description of the model.

Lin

1966

AIAA Journal

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Nonequilibrium Wakes With Laminar and Turbulent Transport

Cited by 10 publications

References 9 publications

Finite-difference calculation of hypersonic wakes

Finite-difference calculation of hypersonic wakes

A quasi-one-dimensional treatment of chemical reactions in turbulent wakes of hypersonic objects

A bimodal approximation for reacting turbulent flows. I - Description of the model.

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