Engineering Transactions, 45, 3-4, pp. 349-362, 1997

Numerical Solution of the Viscous Flow Past a Circular Cylinder Under the Influence of a Magnetic Field

M. Morzyński
Poznań University of Technology, Poznań

E. Gürgey
Hermann-Föttinger-Institut Für Strömungsmechanik, TU-Berlin

F. Thiele
Hermann-Föttinger-Institut Für Strömungsmechanik, TU-Berlin

The steady laminar incompressible viscous flow over an insulated circular cylinder is investigated. The flow is subjected to an external uniform magnetic field. Besides the familiar Reynolds number, the flow structure also depends on the Hartmann number. A fully implicit finite difference method based on the stream function formulation of the Navier-Stokes equations is used to solve the problem numerically. The magnetic field has a significant influence on the flow, it can delay or even completely cancel the development of the wake and the separation. The flow tends to be more stable since the convection process is suppressed by the magnetic field. Furthermore the drag is increased although the separation is absent.

Full Text: PDF
Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).


J. JOSSERAND, P. MARTY P and A. ALEMANY, Pressure and drag measurements on a cylinder in a liquid metal flow with an aligned magnetic field, Fluid Dynamics Research, 11, 107-117, 1993.

Y. MOCHIMARU, Numerical simulation of the flow past a circular cylinder under a magnetic field, Computers and Fluids, 21, 2, 177-184, 1992.

G. GERBETH, A. THESS and P. MARTY, Theoretical study of the flow around a cylinder in crossed electric and magnetic fields, Eur. J. Mech., B/Fluids, 9, 3, 239-257, 1990.

H. SCHÜTZ, Ein direktes Lösungsverfahren der Navier-Stokes Gleichungen in reiner Strömfunktionsformulierung zur Simulation instationärer inkompressibler Strömungen in zweidimensionalen Geometrien, Ph.D. Thesis, TU-Berlin 1990.

M. MORZYŃSKI and F. THIELE, Numerical stability analysis of the flow about a cylinder, Z. Angew. Math. Mech., 71, 5, T424-428, 1991.

E. GÜRGEY and F. THIELE, Numerical simulation of the viscous flow over an oscillating airfoil, experimental and numerical flow visualisation, ASME FED - Vol. 128, B. KHALIGHI et al. [Eds.], presented at the Winter Annual Meeting of ASME, Atlanta, Georgia, December 1-6, 1991.

A. TIMME, Über die Geschwindigkeitsverteilung in Wirbeln, Ing. Arch., 25, 205-225, 1957.

A.S. GROVE, F.H. SHAIR, E.E. PETERSEN and A. ACRIVOS, An experimental investigation of the steady separated flow past a circular cylinder. Part 1, J. Fluid Mech., 19, 60-79, 1964.

M. COUTANCEAU and R. BOUARD, Experimental determination of the main features of the viscous flow in the wake of a circular cylinder in uniform translation. Part 1. Steady flow, J. Fluid Mech., 79, 231-256, 1977.

W.M. COLLINS and S.C.R. DENNIS, Flow past an impulsively started circular cylinder, J. Fluid Mech., 60, 105-127, 1973.

B. FORNBERG, A numerical study of steady viscous flow past a circular cylinder, J. Fluid Mech., 98, 819-855, 1980.

R. FRANKE and B. SCHÖNUNG, Die numerische Simulation der laminaren Wirbelablösung an Zylindern mit quadratischen oder kreisförmigen Querschnitten, SFB 210/T/39, 1988.