Topic
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, the generalized similarity solution of the governing momentum equations was used to obtain the solutions to the second order in respect of the inverse distance from the sphere center in a circular far-wake flow behind a sphere.
Abstract: The theory of hydrodynamic phenomenon of the axisymmetric circular far-wake flow behind a sphere is revisited in this study by the generalized similarity solution of the governing momentum equations to obtain the solutions to the second order in respect of the inverse distance from the sphere center. In case of a laminar wake, the nonlinear equation is derived from the Navier–Stokes equations; while in case of a turbulent wake, it is obtained from the Reynolds averaged Navier–Stokes (RANS) equations and the eddy viscosity concept. The first-order Oseen-type linearization yields solutions well known in the literature, but the second-order solutions obtained in this study are novel.
3 citations
01 Jan 1995
TL;DR: In this paper, a variation du regime auto-similaire avec le parametre fondamental is presented, which is a variation of the parametrization of the autoroute.
Abstract: On etudie l'existence de differents regimes auto-similaires pour une equation de reaction-diffusion intervenant dans la description des explosions turbulentes dans un fluide. On s'interesse specialement a la variation du regime auto-similaire avec le parametre fondamental
3 citations
TL;DR: In this article, the axisymmetric three-dimensional boundary layer equations are reduced into self-similar form with the help of new similarity transformation, and the resulting coupled nonlinear equations are solved numerically using shooting method coupled with Range-Kutta 6 (RK-6).
Abstract: The unsteady laminar flow of an incompressible viscous fluid over a nonlinearly stretching rotating disk is investigated. The axisymmetric three-dimensional boundary layer equations are reduced into self-similar form with the help of new similarity transformation. The resulting coupled nonlinear equations are solved numerically using shooting method coupled with Range-Kutta 6 (RK-6). An exact analytical solution for the large stretching parameter is also presented. Some interesting observations are made while interpreting the results physically. Dual solutions are obtained due to the presence of unsteadiness parameter for the nonlinear stretching of the rotating disk. The analytical results reveal that for large stretching parameter the azimuthal velocity becomes negligible and the flow behaviors turn into steady state, which is the most surprising observation of the paper. These results are also verified numerically by solving original self similar equations using shooting method.
3 citations
TL;DR: In this paper, a large eddy simulation of spatially evolving supersonic boundary layer transition over a flat-plate with freestream Mach number 4.5 is performed.
Abstract: The large eddy simulation (LES) of spatially evolving supersonic boundary layer transition over a flat-plate with freestream Mach number 4.5 is performed in the present work. The Favre-filtered Navier-Stokes equations are used to simulate large scales, while a dynamic mixed subgrid-scale (SGS) model is used to simulate subgrid stress. The convective terms are discretized with a fifth-order upwind compact difference scheme, while a sixth-order symmetric compact difference scheme is employed for the diffusive terms. The basic mean flow is obtained from the similarity solution of the compressible laminar boundary layer. In order to ensure the transition from the initial laminar flow to fully developed turbulence, a pair of oblique first-mode perturbation is imposed on the inflow boundary. The whole process of the spatial transition is obtained from the simulation. Through the space-time average, the variations of typical statistical quantities are analyzed. It is found that the distributions of turbulent Mac...
3 citations
01 Jan 2013
TL;DR: In this article, a B S T R A C T general group symmetry analysis is applied to analyze the free convective boundary-layer problem due to the motion of an elastic surface into an electrically conducting a class of non-Newtonian fluid.
Abstract: A B S T R A C T General group symmetry analysis so-called deductive group-theoretical method is applied to analyze the free convective boundary-layer problem due to the motion of an elastic surface into an electrically conducting a class of non-Newtonian fluid. The symmetry groups admitted by the corresponding boundary value problem are obtained. Particular attention is paid on the deductive group which provides the similarity solution of the problem. Also, the admissible form of the data, in order to be conformed to the obtained symmetries, is provided. Finally, with the use of the entailed similarity variables the problem is transformed into a boundary value problem of ODEs and is solved numerically for particular non-Newtonian fluid so-called powell-eyring fluid.
3 citations