Investigation of some finite-difference techniques for solving the boundary layer equations

Blottner, F. G.

doi:10.1016/0045-7825(75)90012-2

Cited by 59 publications

(14 citation statements)

References 13 publications

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“…The formulation follows that described by Blottner. 16 A nonuniform grid spacing in the streamwise and normal directions is incorporated into the present formulation. The grid spacing is chosen so that the resulting solution is grid independent.…”

Section: Mean Flowmentioning

confidence: 99%

Effect of pressure gradient on the stability of compressible boundary layers

1992

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An investigation into the influence of pressure gradient (wall shaping) on the stability of compressible boundary layers is presented. The steady, compressible, nonsimilar boundary-layer equations are solved with a potential flow velocity distribution corresponding to a power law edge Mach number distribution. The stability of the mean flow is investigated using the small-disturbance compressible linear stability theory. The results indicate that two-dimensional second-mode (Mack) waves can be stabilized with pressure gradient. However, the effectiveness of the pressure gradient on the natural laminar flow control of two-dimensional second-mode waves decreases at hypersonic speeds. The maximum growth rate varies almost linearly with the pressure gradient level. The effect of pressure gradients on stabilizing three-dimensional first-mode waves is much larger than their effect on stabilizing two-dimensional first-mode waves.

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Section: Mean Flowmentioning

confidence: 99%

Effect of pressure gradient on the stability of compressible boundary layers

1992

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“…(16) and (17) (Tannehill 27 ; also see Ref. 28). The edge temperature T e and wall temperature T w are taken to be fixed.…”

Section: Validation Using High-mach-number Solutionsmentioning

confidence: 99%

Laminar Subsonic, Supersonic, and Transonic Boundary-Layer Flow past a Flat Plate

Otta

Rothmayer

2006

AIAA Journal

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A boundary-layer formulation is developed for the low-Mach-number limit. Self-similar low-Mach-number Falkner-Skan solutions are found for flow past a wedge. From computation of both this low-Mach-number-limit solution and the full compressible boundary-layer equations, it is shown that laminar transonic boundary-layer flow past a constant temperature flat plate may be accurately calculated using the simpler low-Mach-number-limit solution. Nomenclaturetemperatures with and without Mach number heating J = total enthalpy M ∞ = freestream Mach number m ∞ = parameter relating τ and M ∞ Pr = Prandtl number Re = Reynolds number T c= temperature within the boundary layer scaled using |T e − T w | for a flat plate T e , J e = temperature and total enthalpy at the edge of the boundary layer T * e = dimensional temperature at the edge of the boundary layer T w = nondimensional wall temperaturê T ,R = nondimensional perturbation temperature and density within the boundary layer U, V = streamwise and wall-normal velocities U e = velocity at the edge of the boundary layer β = pressure gradient parameter T * = dimensional temperature difference between the freestream and the wall ρ = density within the boundary layer ρ e , µ e = density and viscosity at the edge of the boundary layer ρ w = nondimensional wall density τ = freestream air temperature perturbation from wall temperature ψ, ,ˆ , f = stream functions Subscripts e = property at the edge of the boundary layer s, N = derivatives in boundary-layer equations w = property at the wall ξ, η = derivatives in boundary-layer equations in transformed coordinates

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“…[4], El-Amin and Sun [5], Ramteke and Kishore [6], Rhahimi and Jalali [7] and Zainuddin et al [8]. The finite difference based Kellerbox method is also reported by Blottner et al [9], Nayela et. al.…”

Section: Introductionmentioning

confidence: 96%

Free Convection Fluid Flow from a Spinning Sphere with TemperatureDependent Physical Properties

Makanda¹

2017

Proceedings of the 4th International Conference of Fluid Flow, Heat and Mass Transfer (FFHMT'17)

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-Natural convection from a spinning sphere with temperature dependent viscosity, thermal conductivity and viscous dissipation was studied. A unique system of non-similar partial differential equations was solved using the bivariate local-linearization method (BLLM). This method use Chebyshev spectral collocation method applied in both the η and ξ directions. Similar equations in the literature are normally solved by inaccurate time-consuming finite difference methods. This work introduces a robust method for solving partial differential equations arising in heat and mass transfer. The numerical method was validated by comparison to the results previously published in the literature. The method is fully described in this article and can be used as an alternative method in solving boundary value problems. This work also presents rarely reported results of the effect of selected parameters on spin-velocity profiles g(η).

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Investigation of some finite-difference techniques for solving the boundary layer equations

Cited by 59 publications

References 13 publications

Effect of pressure gradient on the stability of compressible boundary layers

Effect of pressure gradient on the stability of compressible boundary layers

Laminar Subsonic, Supersonic, and Transonic Boundary-Layer Flow past a Flat Plate

Free Convection Fluid Flow from a Spinning Sphere with TemperatureDependent Physical Properties

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