Similarity solution

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

A free-convection boundary-layer model for the centrifugal etching of an axisymmetric cavity

Abstract: The etching of an axisymmetric cavity under the influence of an artificial acceleration field generated inside a centrifuge is considered. It is shown that the etching process is governed by a thin convective-diffusive boundary layer along the curved cavity wall. To describe this boundary layer, local coordinates are introduced near the wall, with arc length s being one of these.

Semianalytical self-similar solution of bent-over jet in cross-flow

Abstract: The flow and scalar field in the cross section of a bent-over momentum jet in cross-flow has been investigated via a 2D numerical solution of the governing equations with similarity transformation. The semianalytical model employs a free shear layer model for turbulent closure and the assumption of a constant velocity in the direction of the cross-flow; the entire solution depends solely on a dimensionless turbulent mixing parameter λ that measures the relative importance of advection and diffusion. The computed streamlines and vorticity field clearly indicate a vortex-pair flow for all λ. The shape of the scalar distribution, however, grows from a circular cell to a kidney-shaped double peak structure. Using a value of λ = 55, the computed jet trajectory and spreading and the cross-sectional shape are in good agreement with the experiments, although the dilution is somewhat overpredicted. The results suggest a free shear layer model of e = 0.0272Wml*, where e, Wm, and l* are the eddy viscosity, maximum v...

Transpired Turbulent Boundary Layers Subject to Forced Convection and External Pressure Gradients

Abstract: The problem of forced convection transpired turbulent boundary layers with external pressure gradient has been studied by using different scalings proposed by various researchers. Three major results were obtained: First, for adverse pressure gradient boundary layers with suction, the mean deficit profiles collapse with the free stream velocity, U‘ , but into different curves depending on the strength of the blowing parameter and the upstream conditions. Second, the dependencies on the blowing parameter, the Reynolds number, and the strength of pressure gradient are removed from the outer flow when the mean deficit profiles are normalized by the Zagarola/Smits [Zagarola, M. V., and Smits, A. J., 1998, ‘‘Mean-Flow Scaling of Turbulent Pipe Flow,’’ J. Fluid Mech., 373 ,3 3‐79] scaling, U‘d * /d. Third, the temperature profiles collapse into a single curve using the new inner and outer scalings proposed by Wang and Castillo [Wang, X., and Castillo, L., 2003, ‘‘Asymptotic Solutions in Forced Convection Turbulent Boundary Layers,’’ J. Turbulence, 4(006)], which produce the true asymptotic profiles even at finite Pe

Similarity solution for a two-phase one-dimensional Stefan problem with a convective boundary condition and a mushy zone model

Abstract: A two-phase solidification process for a one-dimensional semi-infinite material is considered. It is assumed that it is ensued from a constant bulk temperature present in the vicinity of the fixed boundary, which it is modelled through a convective condition (Robin condition). The interface between the two phases is idealized as a mushy region and it is represented following the model of Solomon, Wilson, and Alexiades. An exact similarity solution is obtained when a restriction on data is verified, and it is analysed the relation between the problem considered here and the problem with a temperature condition at the fixed boundary. Moreover, it is proved that the solution to the problem with the convective boundary condition converges to the solution to a problem with a temperature condition when the heat transfer coefficient at the fixed boundary goes to infinity, and it is given an estimation of the difference between these two solutions. Results in this article complete and improve the ones obtained in Tarzia (Comput Appl Math 9:201–211, 1990).

The Generalized Riemann Problem for First Order Quasilinear Hyperbolic Systems of Conservation Laws II

Abstract: In this paper, we are concerned with the existence and uniqueness of the local solution to the generalized Riemann problem for first order quasi-linear hyperbolic systems of conservation laws in the presence of the shock wave with large amplitude and the centered wave. Apart from some exceptions, we prove the problem admits a unique piecewise smooth solution u=u(t,x), and this solution has a structure similar to the similarity solution u=u(x/t) of the corresponding Riemann problem in the neighborhood of the origin, provided that the coefficients of the system and the initial conditions are sufficiently smooth. The application of our results in rich system is also given.