Similarity solution

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

Time-dependent simulations of point explosions with heat conduction

Abstract: A hydrodynamic-diffusion code is used to simulate a point explosion. The gas motion is governed by both hydrodynamics and nonlinear heat conduction and is a combination of the well-known, self-similar Taylor–Sedov spherically expanding shock wave and the spherically expanding thermal wave. Two problems are discussed. In the first problem, a similarity solution exists if the diffusion coefficient is given in terms of powers of density and temperature which also define the ambient spatial density profile. If the initial explosion energy is small, the diffusive effect is limited to a region behind the shock. However, if the explosion energy is large, the thermal front precedes the hydrodynamic front, which is then an isothermal shock. In the second problem, the initial density is constant and the diffusion coefficient depends on only a power of the temperature. In this case, the solution is not self-similar; in early times, heat conduction dominates; in late times—hydrodynamics. The problems were previously ...

Mixed convection heat transfer from a vertical heated plate embedded in a sparsely packed porous medium

Abstract: An improved numerical study on mixed convection from a heated vertical plate embedded in a Newtonian fluid saturated sparsely packed porous medium is undertaken by considering the variation of permeability, porosity and thermal conductivity. The boundary layer flow in the porous medium is governed by the LapwoodForchheimer-Brinkman extended Darcy model. Similarity transformations are employed and the resulting ordinary differential equations are solved numerically by using a shooting algorithm with the Runge-KuttaFehlberg integration scheme to obtain velocity and temperature distributions. Besides, the skin friction and Nusselt number are also computed for various physical parameters governing the problem under consideration. It is found that the inertial parameter has a significant influence on decreasing the flow field, whereas its influence is reversed on the rate of heat transfer for all values of permeability parameter considered. Further, the results under the limiting conditions were found to be in good agreement with the existing ones.

A numerical model for the jet flow generated by water impact

Abstract: In this paper a numerical model is developed aimed at describing the jet flow caused by water impact. The study, carried out in the framework of a potential-flow assumption, exploits the shallowness of the jet region to significantly simplify the local representation of the velocity field. This numerical model is incorporated into a fully nonlinear boundary-element solver that describes the flow generated by the water entry of two-dimensional bodies. Attention is focused on the evaluation of the capability of the model to provide accurate free-surface shape and pressure distribution along the wetted part of the body contour, with particular regard to the jet region. After a careful verification, the proposed model is validated through comparisons with the similarity solution of the wedge impact with constant entry velocity. This similarity solution is derived with the help of an iterative procedure which solves the governing boundary-value problem written in self-similar variables.

Mixed Convective Burning of a Fuel Surface With Arbitrary Inclination

Abstract: An analysis is developed for mixed, forced, and free convective combustion on a flat fuel surface of arbitrary inclination that makes use of the laminar boundary layer approximation to describe the gas flow and of the flame-sheet approximation to describe the gas-phase reactions. A mixed-convection parameter (Re/sub x//sup n/+Gr/sub x//sup m/)/sup 1/2n/ that properly scales the dependent and independent variable fields and a mixed convection ratio (Gr/sub x//sup m//Re/sub x//sup n/)/sup 1/2/ that plays the role of the downstream local similarity coordinate are introduced in the nondimensionalization of the equations. It is shown that these two parameters, rather than the standard Reynolds, Re/sub x/, and Grashof, Gr/sub x/, numbers are the optimum choice of governing nondimensional groups for this problem. The values of m and n are selected to obtain a similarity solution of the governing equations in the pure free convection limit for a vertical (m = 2, n = 4) and a horizontal (m = 2, n = 5) surface, which are the cases solved in this work. With this formulation, the solution of the problem provides for both cases smooth transition of all physical variables from one convective limit to the other. Results are obtained from numericalmore » integration of the governing equations and from application of the local similarity approximation. It is shown that the range of validity of local similarity is extended beyond that obtained with alternate formulations and that the proper limits are approached. For use in practical applications, the results suggest that explicit expressions for the mass burning rate and for the fraction of unburnt pyrolyzate can be found that will suffice over the whole range of mixed-flow intensity.« less