Similarity solution

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

Sink flows of a suspension of rigid rods : the failure of a similarity solution

Abstract: The flow of a suspension of rigid rods into a sink of finite size which may be either planar or axisymmetric is considered. For low rod concentrations the flow at large distances from the sink is well described by similarity solutions derived by Evans. For larger concentrations, however, these similarity solutions predict unrealistic flows with many regions of inflow and outflow. We show that the flow field far upstream of the sink is then dominated by an eigensolution involving zero net volume flux. This eigensolution is determined. The prediction is compared with the results of a full numerical solution for the flow of a suspension of rods from an infinite reservoir into a finite sink. It is also used to estimate the extent of the vortex enhancement generated by flow through a large but finite contraction. The results are compared with the numerical solutions and experiments of Lipscomb et al. This example shows that the parameter range for which a self-similar flow field is appropriate can be substantially smaller for a non-Newtonian fluid than is the corresponding range in the Newtonian case.

A similarity model in the surf zone

Abstract: In fluid mechanics, a powerful tool known as the similarity model has been applied successfully to describe velocity and pressure fields in steady boundary layer flows, jet flows and wake flows. These flows, with the exception of a few laminar cases, are quite complex and are usually not amenable to theoretical analysis. The similarity analysis offers an alternative and often provides useful engineering information on the mean flow characteristics. The present work explores the possibility of applying the similarity concept to describe the flow field of breaking waves in the surf zone. Before presenting the similarity solution, a non-dimensional surf zone parameter is examined. This parameter, in addition to its many implications of characterizing surf zone properties, is pertinent to defining the region of validity of the similarity solutions. Solutions on mean flow characteristics are then established based upon a similarity hypothesis which states that the profiles of flow properties such as velocity and wave form preserve geometrical similarity downstream from the source of the disturbance and, therefore, can be defined by a few local characteristic parameters. Conditions required to preserve similarity are examined. Finally, laboratory results from a number of studies (Flick, 1978; Svendsen et al., 1978; Sakai and Iwagaki, 1978) and those from the authors are used to test the validity of the proposed model.

Ignition and flame studies for an accelerating transonic mixing layer

Abstract: Numerical solutions have been obtained for a diffusion e ame in the two-dimensional, laminar, steady, viscous, multicomponent, compressible mixing layer in the presence of a pressure gradient by using the boundary-layer approximationsand solvingthe x-momentum,energy,and speciesconservation equations. Thenumericalsolutions have been validated against similarity solutions and then are extended to cases where no similarity solution exists. The numerical solutions are used to study the ignition process and the e ame structure in an accelerating transonic mixing layer. It is shown how ignition length depends on initial temperature, initial pressure, initial velocity, viscosity, and pressure gradient. Ignition is found to occur on the high-temperature-air side. Oxidation kinetics and transport are both controlling in the upstream ignition region. Farther downstream, transport is controlling in the fully established e ame. The boundary-layer approximation is found to be valid everywhere including the upstream ignition region.

Approximate solution for the temperature field of 1-D soil freezing process in a semi-infinite region

Abstract: Unfrozen liquid water always exists in the humid soil system below freezing point, and the amount of the unfrozen water decreases continuously with the temperature decreasing. This phenomenon is a special characteristic for the freezing of the humid soil system. The temperature field of 1-D soil freezing process in a semi-infinite region has been studied. The problem is a Stefan-like problem. After the continuous phase change process of soil water is divided into a finite number of substeps, the Stefan problem of a multi-phase material is obtained. A similarity solution is found and determined. In order to get the right solution of the nonlinear equations, a variable substitution technique is introduced. The approximate solution is verified by the numerical results of the continuous phase change model of soil freezing process. Finally, for practical purpose, the advancing factor of the freezing front and the mean squared error of the temperature caused by the measurement errors are defined. Computational examples concerning the effect of different parameters on the advancing factor of the freezing front and the effect of the measurement errors on the accuracy of the solution are presented and discussed.

Mixed convection row on vertical surface

Abstract: Mixed convective heat transfer on a vertical surface has been investigated for uniform free stream velocity and for several values of Prandtl number. An exact similarity solution is obtained for the case of a wall temperature that is inversely proportional to the distance from the leading edge. The non-dimensional temperature distribution suggests that over large η the boundary layer temperature is less than the free stream temperature.