Numerical simulation of oscillating flows past a fixed circular cylinder

Tunghsing Ku, Purdue University

Abstract

This dissertation presents a numerical study of the flow field generated by an oscillatory stream past a fixed circular cylinder under the conditions of low Keulegan-Carpenter numbers (KC) and low Stokes numbers ($\beta$). The numerical models applied for the this study to solve the two-dimensional stream function-vorticity formulation of the Navier-Stokes equations are mixed spectral methods. A vector implementation of the mixed spectral-finite difference method on the CDC CYBER/205 is the back-bone of the numerical laboratory. In the numerical experiments, KC ranges from 0.2 to 5 and $\beta$ ranges from 52.8 to 196. Our study investigates the flow patterns, the steady streaming, the force coefficients, and the inception of asymmetrical flow. The results are presented mainly in graphical forms. The flow fields are described by means of absolute streamlines, viscous streamlines and vorticity fields. Moreover, the parallelization of the mixed spectral-direct radial integration method has been implemented on the nCUBE/2 and iPSC/860 hypercubes. The major efforts spent to parallelize the algorithm are devoted to calculating FFT's and the long range integrations. To minimize the communication overhead and to balance the load of the nodes so that higher efficiencies can be achieved, the Fourier domain (calculating domain) is divided into equal size subdomains and is mapped onto a ring-cube network connection between nodes. The optimal number of nodes is the largest possible number node obtained. Given a fixed number of nodes, the optimal decomposition is that the Fourier domain is decomposed by rows. The discrepancy in performance between optimal mapping and worst mapping is due to the fact that the communication overhead of the FFT's is one order higher than that of the radial integration scheme.

Degree

Ph.D.

Advisors

Giorgini, Purdue University.

Subject Area

Civil engineering

COinS