Similarity solution

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

Lubricated axisymmetric gravity currents of power-law fluids

Abstract: The motion of glaciers over their bedrock or drops of fluid along a solid surface can become unstable when these substrates are lubricated. Previous studies modeled such systems as coupled gravity currents (GCs) consisting of one fluid that lubricates the flow of another fluid, and having two propagating fronts. When both fluid are Newtonian and discharged at constant flux, global similarity solutions were found. However, when the top fluid is strain-rate softening experiments have shown that each fluid front evolved with a different exponent. Here we explore theoretically and numerically such lubricated GCs in a model that describes the axisymmetric spreading of a power-law fluid on top of a Newtonian fluid, where the discharge of both fluids is power law in time. We find that the model admits similarity solutions only in specific cases, including the purely Newtonian case, for a certain discharge exponent, at asymptotic limits of the fluids viscosity ratio, and at the vicinity of the fluid fronts. Generally, each fluid front has a power-law time evolution with a similar exponent as a non-lubricated GC of the corresponding fluid, and intercepts that depend on both fluid properties. Consequently, we identify two mechanisms by which the inner lubricating fluid front outstrips the outer fluid front. Many aspects of our theory are found consistent with recent laboratory experiments. Discrepancies suggest that hydrofracturing or wall slip may be important near the fronts. This theory may help to understand the dynamics of various systems, including surges and ice streams.

An extension result on similarity solutions arising during mixed convection

Abstract: In this paper, we are interested in the boundary value problem involving a third order autonomous ordinary nonlinear differential equation. Its solutions are the similarity solutions of a problem of boundary-layer theory dealing with mixed convection phenomena in a porous medium. We confirm our results by numerical illustrations using a shooting algorithm of Mathematica.

Solid/liquid density differences and the initial stages of phase change in the presence of natural convection

Abstract: The solidification of a pure liquid phase- change material in the presence of natural convection is a commonly recurring problem in natural science and tech- nology. The numerical solution of this Stefan problem is made difficult by the fact that there is initially no solid phase; hence, the classical 1D Neumann similarity solution is often used for the purposes of initiating a computation. However, if the solid and liquid phases have different den- sities at the solidification temperature, this solution is not valid. This paper considers the limit of the coupled heat and momentum equations for small times, and finds that it is not possible to solve the corresponding problem, when the densities are different, without introducing a singular- ity into the liquid velocity and pressure. The solution to a non-classical Stefan problem, where cooling is due to a constant heat flux, is also considered, and is found to be free from such singularities.

Numeric Investigation of an Axi-Symmetric Turbulent Jet

Abstract: This work is focused on a numerical investigation of a turbulent axi-symmetric round jet in order to incorporate the knowledge of turbulence. Flow field analysis of a turbulent jet is one of the major research areas in recent years as turbulent jet dictates the interaction between fluid and other physical phenomena. Heat transfer, natural convection, frame propagation all depend on the behavior of turbulent jet. The mass and momentum transfer phenomena governs the flow field of the jet. A two dimensional pressure based Navier-stock solver is used to resolve the flow parameter of a turbulent round jet. Around One hundred twenty five thousand quadratic mesh elements are used for the simulation. A Mesh independency test has been done before resolving results. Characteristic flow parameters such as mean axial velocity, mean radial velocity distribution, turbulent kinetic energy, turbulent intensity, the turbulent dissipation rate are determined and presented. Similarity solution for mean axial velocity distribution and mean radial velocity distribution at different axial location are calculated and compared with experimental data. The result shows good agreement with experimental data.Copyright © 2014 by ASME

The symmetric turbulent plane wake downstream of a sharp trailing edge

Abstract: The analysis and modeling of the symmetric turbulent plane wake downstream of a sharp trailing edge is addressed. A compact description of the flow near the trailing edge is formulated using the results of a previous asymptotic analysis. The new description retains the two-layered structure identified in the previous work, and it clarifies the principal dynamics of the flow in the near-wake outer layer, away from the wake centerline. For zero-pressure-gradient flow, the near-wake outer layer is shown to be represented to leading order by the similarity solution that governs the outer region of the surface boundary layer. The leading perturbation in the outer layer due to the developing near-wake inner-layer flow is identified, and this is shown to be asymptotically smaller than undetermined higher-order terms associated with the surface boundary-layer flow. Results of the new near-wake analysis are used to formulate an algebraic eddy viscosity model for wake flow predictions at arbitrary distances from the trailing edge. The model is used in a numerical solution of the boundary layer equations, and computed velocity and Reynolds stress profiles are shown to compare well with experimental data.