A Transform Free Higher Order Compact Finite Difference Scheme for Simulating the Flow behind a Rotationally Oscillating Circular Cylinder at Reynolds number 500 H. V. R. Mittal 1, a , Rajendra K. Ray 2,b 1 Research Scholar, School of Basic Sciences, Indian Institute of Technology Mandi, Himachal Pradesh, India 2 Asst. Prof., School of Basic Sciences, Indian Institute of Technology Mandi, Himachal Pradesh, India a mittal2988@gmail.com, b rajendra@iitmandi.ac.in Keywords: HOC, Navier-Stokes, non-uniform polar grids, rotationally oscillating cylinder. Abstract. Two-dimensional incompressible, viscous fluid flow around a rotationally oscillating circular cylinder is studied numerically by using a recently developed higher order compact finite difference scheme (HOC) at Reynolds number Re = 500. The stream function vorticity formulation of Navier Stokes equations in cylindrical polar coordinates are considered as the governing equations. Different values of peak rotation rate α m and forced oscillation frequency f e are considered. The simulated results are in a good agreement both qualitatively and quantitatively with the previously published results. Introduction During last one decade Higher Order Compact (HOC) finite difference schemes are gradually gaining popularity because of their high accuracy and advantages associated with compact difference stencils. A compact finite difference stencil is one that utilizes grid points only directly adjacent to the node about which the differences are taken. In addition, if the scheme has an order of accuracy greater than two, it is termed as HOC method. The higher order accuracy of HOC methods combined with the compactness of the difference stencils yields highly accurate numerical solutions on relatively coarser grids with greater computational efficiency. Kalita et al. [1] first developed this type of HOC scheme on rectangular non-uniform grids for the steady 2D convection diffusion equation with variable coefficients without any transformation. Later on, Ray and Kalita [2] have extended the scheme for non-uniform polar grids which can be easily extended for curvilinear coordinates. The robustness of this scheme has already been tested successfully in the case of a non-oscillating cylinder flow [3], [4]. Though much of the prior work has already been done in the case of rotationally oscillating cylinder too, but still there are many aspects that need to be clarified in this regard. We have employed our scheme to this general complex flow situation to examine its accuracy and robustness. In this present work, we extend the applicability of our newly developed scheme in reference [2] to capture the very complex flow phenomena of unsteady flow past a rotationally oscillating circular cylinder for the Reynolds numbers Re = 500 with different forced oscillating frequencies (fe) and a fixed peak rotation rate (αm). We compute the flow for very long duration of time to investigate the influence of Se and αm on vortex shedding phenomenon as well as lift and drag coefficients. We compare the computed results, both qualitatively and quantitatively, with the experimental flow visualizations and numerical results that are available in the literature. In all the cases, our numerical results are in excellent agreement with the existing results. The paper is arranged in the following sequence. Initially, we discuss about the governing equations and discretization procedure, next section deals with our numerical results and comparisons with existing experimental and numerical results. Finally, in last section we summarize our observations in the conclusions. Applied Mechanics and Materials Vol. 367 (2013) pp 126-131 © (2013) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/AMM.367.126 All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of TTP, www.ttp.net. (ID: 14.139.34.2-20/06/13,10:54:01)