Similarity solution

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

An exact solution of the Navier-Stokes equation which describes non-orthogonal stagnation-point flow in two dimensions

Abstract: A similarity solution is found which describes the flow impinging on a flat wall at an arbitrary angle of incidence. The technique is similar to a method used by Jeffery (1915) and discussed more recently by Peregrine (1981).

Stretching a Curved Surface in a Viscous Fluid

Abstract: This work is concerned with the viscous flow due to a curved stretching sheet. The similarity solution of the problem is obtained numerically by a shooting method using the Runge–Kutta algorithm. The physical quantities of interest like the fluid velocity and skin friction coefficient are obtained and discussed under the influence of dimensionless curvature. It is evident from the results that dimensionless curvature causes an increase in boundary layer thickness and a decrease in the skin friction coefficient.

Events before droplet splashing on a solid surface

Abstract: A high-velocity (≈1 m s ―1 ) impact between a liquid droplet (≈1 mm) and a solid surface produces a splash. Classical observations traced the origin of this splash to a thin sheet of fluid ejected near the impact point, though the fluid mechanical mechanism leading to the sheet is not known. Mechanisms of sheet formation have heretofore relied on initial contact of the droplet and the surface. In this paper, we theoretically and numerically study the events within the time scale of about 1 μs over which the coupled dynamics between the gas and the droplet becomes important. The droplet initially tries to contact the substrate by either draining gas out of a thin layer or compressing it, with the local behaviour described by a self-similar solution of the governing equations. This similarity solution is not asymptotically consistent: forces that were initially negligible become relevant and dramatically change the behaviour. Depending on the radius and impact velocity of the droplet, we show that the solution is overtaken by initially subdominant physical effects such as the surface tension of the liquid―gas interface or viscous forces in the liquid. At low impact velocities surface tension stops the droplet from impacting the surface, whereas at higher velocities viscous forces become important before surface tension. The ultimate dynamics of the interface once droplet viscosity cannot be neglected is not yet known.

Similarity Analysis for Turbulent Boundary Layer with Pressure Gradient: Outer Flow

Abstract: The equilibrium-type similarity analysis of George and Castillo for the outer part of zero pressure gradient boundary layers has been extended to include boundary layers with pressure gradient. The constancy of a single new pressure gradient parameter is all that is necessary to characterize these new equilibrium turbulent boundary layers. Three major results are obtained: First, most pressure gradient boundary experiments appear to be equilibrium flows (by the new definition), and nonequilibrium flows appear to be the exception. Second, there appear to be only three values of the pressure gradient parameter: one for adverse pressure gradients, one for favorable pressure gradients, and one for zero pressure gradients. Third, correspondingly, there appear to be only three normalized velocity deficit profiles, exactly as suggested by the theory