Hypersonic Laminar Wakes and Transition Studies

Pallone, A.; Erdos, John; Eckerman, J.; MCKAY, W.

doi:10.2514/6.1963-171

Cited by 18 publications

(5 citation statements)

References 5 publications

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“…The transition criteria given by Zeiberg 8 was employed in determining the transition point. The procedure given by Pallone, et al 4 for calculating the transition point could have been used as an alternative method. The pressure gradient in the wake was determined (with a slight modification) from the blast-wave theory of Sakurai.…”

Section: Discussionmentioning

confidence: 99%

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Pressure gradient effects on nonequilibrium far wakes

Fanucci

Ness

1964

AIAA Journal

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To summarize, the following conclusions are noteworthy: 1) The azimuthal component of velocity is nonzero in contrast to nonrotating case in which v$> = 0.2) The rotating effect generates vorticity in that, for large distances, the flow pattern is irrotational in the nonrotating case. In the rotating case, the azimuthal component of velocity is responsible for vorticity for large R.3) The wave-like terms f n (hR) (corresponding to a boundary layer) appearing in the solution, effective in a small distance from the surface of the sphere, and behaving like exp[-(1 + i)(R e /2) lf2 (R -1)] are essentially similar in nature in rotating and nonrotating cases.4) The drag on the sphere remains unchanged (due to rotation) to the order 6, since v x , v r , and p remain unchanged to that order.In a forthcoming paper, the preceding discussion will be extended to a compressible fluid in the presence of a magnetic field.T HE purpose of this note is to present some results of recent calculations 1 pertaining to the far wake of re-entry vehicles. In these calculations, the effect of pressure gradient on a laminar-turbulent nonequilibrium mixture is assessed. The far wake problem has attracted many investigators, for example, Refs. 2-4; however, to the authors' knowledge, the quantitative effect of pressure gradient on a dissociatedionized fluid medium undergoing nonequilibrium chemical kinetics has not appeared in the literature. AnalysisAn integral method of solution is employed similar to that of Ref . 5. The chemical model consists of 22 chemical reactions involving the 8 species 0, N, 0 2 , N 2 , NO, NO+, e~, 0 2~. The O 2~ species appears in an attachment reaction and a mutual neutralization reaction. The back rate constants for these reactions are taken from Ref. 6.The Sutherland relation is used to compute the viscosity in the laminar region. In the turbulent region, the turbulent diffusivity model given bywas used. This expression is attributed to Lees and Hromas 2 and Ting and Libby. 7 Here 5 m is a transformed wake thickness, p e and u e refer to the density and velocity at the edge of the wake, and U Q refers to the velocity at the centerline of symmetry. The transition criteria given by Zeiberg 8 was employed in determining the transition point. The procedure given by Pallone, et al. 4 for calculating the transition point could have been used as an alternative method. The pressure gradient in the wake was determined (with a slight modification) from the blast-wave theory of Sakurai. 9

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Section: Discussionmentioning

confidence: 99%

“…It may be of interest that Pian's result can also be represented respectively, then F aa~l = K aa -K ab K b r l K ba (4) this being a well-known relation much used for eliminating coordinates from stiffness matrices. It should be noted that Pian's matrix K inverts into M~lG-l M~l T and that (5) hence F aa -BG~1B T , which gives Eq.…”

Section: Technical Commentsmentioning

confidence: 97%

Pressure gradient effects on nonequilibrium far wakes

Fanucci

Ness

1964

AIAA Journal

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“…In these calculations, a value of K = 0.04 was used for all diffusivity models.^ Additionally, a laminar-turbulent transition calculation was performed. The transition criterion is that presented by Pallone, et al 13 ; it is given in terms of a Reynolds number based on axis velocity defect and wake radius, and a Mach number based on axis velocity defect. ** The diffusivity used in the turbulent portion of this calculation is model 1.…”

Section: Turbulent Wake Calculationsmentioning

confidence: 99%

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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“…With the 41-in. 3 arc chamber and a 0.2-in.-diam throat, the decay rate of stagnation pressure is approximately 3%/msec. …”

Section: Introductionmentioning

confidence: 98%