Similarity solution

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

Analysis of Inclined Wall Plume by the k-ε Turbulence Model

Abstract: The similarity solution of inclined wall plume is obtained analytically. The mathematical model used herein consists of the continuity equation of flow, the momentum balance equation in the flow direction, the diffusion equation of concentration, the equation of kinetic energy of turbulence and the equation of viscous dissipation rate of turbulence. It is shown that this set of equations has the similarity solution which can be solved numerically for each angle of the inclined wall. This numerical model is applied to the wide range of the slope angle, which includes the vertical wall plume as the special case and the nearly horizontal wall plume. The velocity and concentration profiles of the inclined wall plume are explained well by the similarity solutions.

A similarity solution describing the collision of two planar premixed flames

Abstract: The problem of the head-on collision of two planar premixed flame fronts is considered using the idealized model of a single step reaction controlled by the deficient species and an Arrhenius reaction law. Density changes are neglected. It is shown that a similarity solution exists if the deficient species and temperature are equidiffusive (Lewis number unity). The similarity solution, derived using activation energy asymptotics, is valid in the intermediate region when the flames are close enough that their pre-heat zones overlap but their reaction zones may be considered to be well separated. A one–dimensional numerical simulation shows good agreement with the analytical solution.

Self-Similar Gravitational Collapse of Radiatively Cooling Spheres*

Abstract: A new self-similar solution describing spherical implosions of a gaseous sphere under both self-gravity and radiative diffusion is investigated in detail, where the diffusivity is modeled by a power law with respect to density and temperature. The reduced two-dimensional eigenvalue problem is solved to show that there is a unique quantitative relation between the two physical effects for the self-similar dynamics. The resultant spatial and temporal behaviors are also determined uniquely, once the opacity is specified. For a reference case of an inverse bremsstrahlung opacity in a fully ionized hydrogen plasma, the solution predicts that the system evolves within the applicable parameter ranges: 10-11 to 10-8 g cm -3 for the central density, a few to tens of 103 K for the central temperature, a few to tens of years for the collapse period, and a few to a dozen times the solar mass for the core mass. Persistent entropy emission via radiation plays an important role in the core formation with mass accretion, which is contrary to the predictions of implosion models under isothermal or adiabatic assumptions. The mass accretion rate is found to increase with time in a power-law form. The present solution turns out to be convectively stable.

Numerical method for elastic-plastic waves in cracked solids, Part 1: anti-plane shear problem

Abstract: The paper deals with a numerical method combining a characteristic-based scheme and Zwas' method in order to solve the hyperbolic PDE's of elastic and elastic-plastic anti-plane shear waves in two space dimensions. First, the need of new physically reasonable numerical methods for stress waves in solids is demonstrated by numerical applications to problems with impulsive loading, where defects of some standard methods are shown. Then, the new secon-dorder accurate method is derived. A suitable procedure to model the elastic-plastic behaviour of materials by simple waves is included. The capability of the methods is demonstrated by application to several examples. Additionally, for comparison with numerical results, a similarity solution for the semi-infinite crack undergoing an elastic-plastic shock loading is derived in the appendix.

A comparison between experimental measurements and numerical calculations of the structure of premixed rotating counterflow methane-air flames

Abstract: In this paper we investigate computationally the structure and extinction of rotating counterflow premixed methane-air flames. By seeking a similarity solution of the governing two-dimensional conservation equations, we reduce the problem to the solution of a two-point boundary value problem along the axial spatial coordinate. We apply arclength continuation methods to investigate the equivalence ratio at extinction versus the rotation rate for four flames with ejection velocities equivalent to the experimental conditions considered by Chen et al. The results of our study indicate that by counterrotating the gases from the burners the lean extinction limit can be lowered. This is due to the lowering of the value of the local strain rate in the neighborhood of the stagnation plane.