Similarity solution

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

Water surge impingement onto a vertical wall: A new self-similarity solution for impact pressure

Abstract: The impingement process of water surge onto a vertical wall and the impact pressure are studied analytically in this work. We propose a new initial-boundary value problem particularly for the fluid motion near the corner of the horizontal bed and the vertical wall. The explicit solutions of the velocity and the pressure fields are analytically obtained using the self-similarity method under some verifiable physical assumptions. The impact pressure is found to be proportional to the product of the squared incident surge front velocity and the density of water, with a constant coefficient of around 0.867. We compare the analytical solution of the impact pressure with some existing laboratory data. The analytical solution agrees with the median value of the stochastic data of impact pressure from laboratory experiments. Subsequently, the velocity and the pressure fields from the analytical model are compared to the numerical simulation results based on OpenFOAM. The comparisons validate the physical assumptions made in the analytical derivation, demonstrating fair consistency. The analytical model successfully describes the early stage of the contact process between the surge front and the wall and provides a theoretical basis for the physics of water surge impingement.

Effect of boundary conditions on turbulence characteristics in two-phase jet flows with phase transitions

Abstract: It is shown that there are no self-similarity and similarity of transverse fields of correlation moments of fluctuating parameters of phases in two-phase jets, in contrast to one-phase jets. The influence of the initial values of a number of parameters of a two-phase jet (gas temperature, volume concentration of droplets in the initial cross section, and radius of the initial cross section of the jet) on turbulence characteristics is analyzed on the basis of numerical simulations.

Similarity Solutions for Unsteady Hydromagnetic Free Convection Boundary Layer Flow over Flat Plates with Thermophoresis

Abstract: This paper is focused on the analysis of thermophoresis on an unsteady two dimensional free convective boundary layer flow along a permeable inclined flat plate in the presence of magnetic field and thermophoresis. Governing time dependent partial differential equations are non- dimensionalzed and transformed into a system of nonlinear ordinary differential equations by applying similarity transformations. These are solved numerically by using the shooting method along with Runge-Kutta sixth order integration scheme. Numerical results for the dimensionless velocity, temperature and concentration profiles have been obtained and displayed graphically. The skin-friction coefficient, wall heat transfer coefficient and wall deposition flux rate have also been obtained and are presented in tabular form. The obtained numerical results also show that increased unsteadiness parameter significantly controls the thermophoretic particle.

Simple solutions of an opening in elastic-brittle plastic rock mass by total strain and incremental approaches

Abstract: This study deals with simple solutions for a spherical or circular opening excavated in elastic-brittle plastic rock mass compatible with a linear Mohr-Coulomb (M-C) or a nonlinear Hoek-Brown (H-B) yield criterion. Based on total strain approach, the closed-form solutions of stresses and displacement are derived simultaneously for circular and spherical openings using original H-B and M-C yield criteria. Two simple numerical procedures are proposed for the solution of generalized H-B and M-C yield criteria. Based on incremental approach, the similarity solution is derived for circular and spherical openings using generalized H-B and M-C yield criteria. The classical Runge-Kutta method is used to integrate the first-order ordinary differential equations. Using three data sets for M-C and H-B models, the results of the radial displacements, the spreading of the plastic radius with decreasing pressure, and the radial and circumferential stresses in the plastic region are compared. Excellent agreement among the solutions is obtained for all cases of spherical and circular openings. The importance of the use of proper initial values in the similarity solution is discussed.