Formulation and Numerical Methodology for Three-Dimensional Wake of Heated Circular Cylinder

Abstract

ABSTRACT A time-dependent three-dimensional wake of a heated circular cylinder is formulated. Its numerical methodology is presented, and computed results in an isothermal and a buoyant wakes are validated as follows. First, a wake with buoyancy from a heated circular cylinder with infinite spanwise length is formulated as a three-dimensional and time-dependent thermal flow with body force and varying density and properties. Second, a numerical methodology for the above formulations is obtained by employing grid generation using elliptic partial differential equations and by extending the highly simplified marker-and-cell (HSMAC) method to the flow with varying density and properties. At an isothermal condition, the present formulation and methodology become those for an isothermal fluid flow. Third, for the isothermal wake at Reynolds numbers of 100 and 300, the Strouhal numbers, time-averaged drag coefficients, and root-mean-squared (RMS) amplitudes of the lift coefficient, vorticity distribution, and streaklines are computed and presented. Fourth, in the air buoyant wake, the time-averaged mean Nusselt numbers at the Grashof numbers 0 and 490 and the Reynolds number 70 agree well with the previous results. Last, the buoyant wake at Reynolds number 300 and Richardson number 0.3 of air is computed and presented.