Numerical Computation of Flow Reattachment Lengthovera Backward-Facing Step at High Reynolds Number

Investigation of flow separation and reattachment length over a backward facing step are such as the subjects of fundamental fluid dynamics research. The purpose this study is measurement of reattachment length on backward facing step. For this purpose, unsteady flow over a step was simulated in a 2-D by using Computational Fluid Dynamic. Then, secondary flow was added to the 1/3 height of step. In order to, the effect of angles of 15°, 30°, 45° and 90°, expansion ratios of 1.5, 2, 3 and 4, pressure coefficient and Reynolds number with 75000 over backward facing stepwere investigated. To verify the numerical model, the velocity profile using different turbulence models was compared with experimental values in a sudden expansion. The results showed that RNG k-ε turbulent model was selected as the most suitable model to predict recirculation flow over backward facing step. The results of numerical analysis indicated that the reattachment length increase with increasing step angle, expansion ratio and Reynolds number. Also with increasing Reynolds number, when secondary flow is added to 1/3 height of step, the eddy diameters and the length of recirculation flow zone decrease. Moreover, increasing pressure coefficient led to increasing the reattachment length

Numerical Computation of Flow Reattachment Lengthovera Backward-Facing Step at High Reynolds Number

Investigation of flow separation and reattachment length over a backward facing step are such as the subjects of fundamental fluid dynamics research. The purpose this study is measurement of reattachment length on backward facing step. For this purpose, unsteady flow over a step was simulated in a 2-D by using Computational Fluid Dynamic. Then, secondary flow was added to the 1/3 height of step. In order to, the effect of angles of 15°, 30°, 45° and 90°, expansion ratios of 1.5, 2, 3 and 4, pressure coefficient and Reynolds number with 20000<Re<75000 over backward facing stepwere investigated. To verify the numerical model, the velocity profile using different turbulence models was compared with experimental values in a sudden expansion. The results showed that RNG k-ε turbulent model was selected as the most suitable model to predict recirculation flow over backward facing step. The results of numerical analysis indicated that the reattachment length increase with increasing step angle, expansion ratio and Reynolds number. Also with increasing Reynolds number, when secondary flow is added to 1/3 height of step, the eddy diameters and the length of recirculation flow zone decrease. Moreover, increasing pressure coefficient led to increasing the reattachment length

On integral equations with Weakly Singular kernel by using Taylor series and Legendre polynomials

This paper is concerned with the numerical solution for a class of weakly singular Fredholm integral equations of the second kind. The Taylor series of the unknown function, is used to remove the singularity and the truncated Taylor series to second order of k(x, y) about the point (x0, y0) is used. The integrals that appear in this method are computed exactly and some of these integrals are computed with the Cauchy principal value without using numerical quadratures. The solution in the Legendre polynomial form generates a system of linear algebraic equations, this system is solved numerically. Through numerical examples, performance of the present method is discussed concerning the accuracy of the method