Differential quadrature method to stability analysis of pipes conveying fluid with spring support

It is a new attempt to extend the differential quadrature method (DQM) to stability analysis of the straight and curved centerline pipes conveying fluid. Emphasis is placed on the study of the influences of several parameters on the critical flow velocity. Compared to other methods, this method can more easily deal with the pipe with spring support at its boundaries and asks for much less computing effort while giving aceptable precision in the numerical results. Supported by National Key Project of China (No. PD9521907) and the National Science Foundation of China (No. 19872025).     

A numerical investigation of wall effects in three‐dimensional,laminar flow over a backward facing step with a constant aspect and expansion ratio

The wall effects are investigated in the three‐dimensional laminar flow over a backward‐facing step. For this purpose, a numerical experiment is designed under actual laboratory conditions. The aspect ratio of the computational domain is 1:40 and the expansion ratio is 1:2. The Reynolds number ranges from 100 to 950. The governing equations are the steady state, isothermal and incompressible Navier–Stokes equations for Newtonian fluids. They are solved with a homemade Galerkin finite element code. The computations are validated with data from available laboratory and numerical experiments. The results focus on the variation of both velocity profiles and lengths of eddies along the lower and upper wall in the spanwise direction. Calculated streamlines in the streamwise and transverse direction show how the flow is distorted near the lateral wall and how it develops up to the plane of symmetry. The study of skin friction lines along the top and bottom wall of the domain reveals a flow that takes place in the spanwise direction. This spanwise component of the flow becomes more dominant with increasing Reynolds number and is impossible to be sustained at steady state for Reynolds numbers higher than 950 for this particular geometry. Copyright © 2012 John Wiley & Sons, Ltd.