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Similarity solution

About: Similarity solution is a research topic. Over the lifetime, 2074 publications have been published within this topic receiving 59790 citations.


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TL;DR: In this article, an infinite non-slender flat delta wing with leading edge separation modeled by symmetrical conical vortex sheets is considered and a similarity solution for the three dimensional steady velocity potential is sought with boundary conditions to be satisfied on the line which is the intersection of the wing sheet surface with the surface of the unit sphere.
Abstract: We consider inviscid incompressible flow about an infinite non-slender flat delta wing with leading-edge separation modeled by symmetrical conical vortex sheets. A similarity solution for the three dimensional steady velocity potential Φ is sought with boundary conditions to be satisfied on the line which is the intersection of the wing sheet surface with the surface of the unit sphere. A numerical approach is developed based on the construction of a special boundary element or ‘winglet’ which is effectively a Green function for the projection of ∇2Φ = 0 onto the spherical surface under the similarity ansatz. When the wing semi-apex angle γo is fixed satisfaction of the boundary conditions of zero normal velocity on the wing and zero normal velocity and pressure continuity across the vortex sheet then leads to a nonlinear eigenvalue problem. A method of ensuring a condition of zero lateral force on a lumped model of the inner part of the rolled-up vortex sheet gives a closed set of a equations which is solved numerically by Newton's method. We present and discuss the properties of solutions for γ0 in the range 1.30 < γ <89.50. The dependencies of these solutions on γ0 differs qualitatively from predictions of slender-body theory. In particular the velocity field is in general not conical and the similarity exponent must be calculated as part of the global eigenvalue problem. This exponent, together with the detailed flow field including the position and structure of the separated vortx sheet, depend only on γ0. In the limit of small γ0, a comparison with slender-body theory is made on the basis of an effective angle of incidence.

11 citations

Journal ArticleDOI
TL;DR: In this article, the stability properties of a mixed convection boundary layer developing over a heated horizontal plate is studied under linear and quasi-parallel flow assumption. But the main aim of the present work is to find out if there is a critical buoyancy parameter that would indicate the importance of heat transfer in destabilizing mixed convective boundary layers, when the buoyancy effect is given by Boussinesq approximation.
Abstract: The spatial stability properties of a mixed convection boundary layer developing over a heated horizontal plate is studied here under linear and quasi-parallel flow assumption. The main aim of the present work is to find out if there is a critical buoyancy parameter that would indicate the importance of heat transfer in destabilizing mixed convection boundary layers, when the buoyancy effect is given by Boussinesq approximation. The undisturbed flow used here is that given by the similarity solution of [1] that implies the wall temperature to vary as the inverse square root of the distance from the leading edge of the plate. The stability of this flow has been investigated by using the compound matrix method (CMM)—that allows finding all the modes in the chosen range in the complex wave number plane for spatial stability analysis. Presented neutral curves for mixed convection boundary layer show the existence of two types of disturbances present simultaneously, for large buoyancy parameter. One notices very unstable high-frequency mode when the buoyancy parameter exceeds the above-mentioned critical value. This unstable thermal mode is in addition to the hydrodynamic mode of isothermal flow given by corresponding similarity profile. The calculated critical buoyancy parameter is shown to qualitatively match with experimental results.

11 citations

Journal ArticleDOI
TL;DR: In this article, the authors describe a two parameter family of solutions for the local asymptotic behavior of UCM fluids at reentrant corners, where the natural stress basis is used to re- derive the equations in the core flow and boundary layers, with full description of the scalings and matching being given.
Abstract: This paper continues the description of a two parameter family of solutions for the local asymptotic behaviour of UCM fluids at re-entrant corners. Here, the natural stress basis is used to re-derive the equations in the core flow and boundary layers, with full description of the scalings and matching being given. The parametric solution dependence is completed with numerical deteremination of the coefficient of the downstream wall shear rate. The flow structure implicitly assumes the absence of a separating streamline in the upstream region.

11 citations

Journal ArticleDOI
TL;DR: In this article, an analytical solution of the boundary layer fluid flow and heat transfer of a quiescent viscous fluid over a non-linearly stretching surface is presented, where thermal radiation effects are included in the energy governing equation.
Abstract: In this article, an analytical solution of the boundary layer fluid flow and heat transfer of a quiescent viscous fluid over a non-linearly stretching surface is presented. The thermal radiation effects are included in the energy governing equation. Surface velocity and temperature conditions are assumed to be of the power-law form with an exponent of 1/3 for velocity and arbitrary exponent m for surface temperature or heat flux conditions. The system of nonlinear differential equations is solved by Homotopy Analysis Method (HAM) for two cases of Prescribed Surface Temperature (PST) and Prescribed Heat Flux (PHF). The results of this method appear in the form of series expansions, the convergence of which is analyzed carefully. Graphical results are finally presented in order to investigate the influence of Prandtl number (Pr) and thermal radiation on heat transfer phenomena.

11 citations

Journal ArticleDOI
TL;DR: Self convergence of the fully implicit radiation hydrodynamics code in the planar geometry agrees well with the scaling law for radiation driven strong shock propagation in aluminium and shows that the asymptotic convergence rate of the code is realized properly.

11 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202313
202238
202141
202045
201947
201850