Higher-order-compact simulation of unsteady flow past a rotating cylinder at moderate Reynolds numbers
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Higher-order-compact simulation of unsteady flow past a rotating cylinder at moderate Reynolds numbers Rajendra K. Ray · Jiten C. Kalita
Received: 4 June 2014 / Revised: 23 September 2014 / Accepted: 5 October 2014 © SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2014
Abstract A recently developed transformation-free higher-order compact finite difference scheme, in non-uniform cylindrical polar grids, is extended and applied to study the temporal development of two-dimensional viscous incompressible flow past a circular cylinder which starts translating and rotating impulsively from rest, for two moderate Reynolds numbers (Re) for the rotational parameter α lying between 0.5 and 3. This scheme does not require transformation from the actual flow domain to the computational domain. The scheme is at least third-order accurate in space and second-order accurate in time. To compute the flow, streamfunction–vorticity (ψ–ω) formulation for the two-dimensional Navier–Stokes equations in polar coordinates is used. The drag and lift coefficients along with various other properties related to stream function and vorticity behavior are investigated. The computed results using present scheme for two (Re = 500, Re = 1,000) Reynolds numbers with different rotational parameters are compared with existing experimental and numerical results. Excellent agreement is obtained in all the cases, and in most of the cases, our numerical results are closer to the experimental ones than previously published numerical results. Keywords
Transient · HOC · Navier–Stokes · Rotating cylinder · Non-uniform polar grids
Mathematics Subject Classification
65N06 · 65Z05 · 65Y99
1 Introduction The problem of the flow past a rotating cylinder represents an ideal case for the study of unsteady flow separation. It also has significant practical importance in the boundary-layer
Communicated by Paul Milewski. R. K. Ray (B) Indian Institute of Technology, Mandi, India e-mail: [email protected]; [email protected] J. C. Kalita Indian Institute of Technology, Guwahati, India e-mail: [email protected]
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R. K. Ray, J. C. Kalita
control of bluff bodies such as airfoils and other related structures. Interestingly, while the flow becomes asymmetric only at higher Reynolds numbers and larger time for the flow past a translating circular cylinder, for the rotating cylinder, asymmetry sets in due to the impulsive rotation of the body even for small Reynolds numbers and also for times just after the start. One can see different complex behaviors in the fluid flow which is largely triggered by this asymmetry. Because of this intriguing nature of the flow, this problem continues to hold attention among the computational fluid dynamics community over a long period of time. Recent experimental, theoretical and numerical investigations on this problem (Badr et al. 1990; Chen et al. 1993; Chew et al. 1995; Chou 2000; Kang et al. 1999; Mittal and Kumar 2003; Padrino and Joseph 2006; Sanyasiraju and Manjula 2007; Stojkovi´c et al.
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