Unconfined Flow Over Square Cylinder

Problem Definition:

This problem considers the laminar flow over a heated 2D square shape body. Since the solver can handle only 3D grids, therefore in order to simulate 2D problems we specify symmetry boundary conditions in the z-direction. The schematic diagram is shown in Fig 4.1 where the channel height has been taken as unity and the Reynolds number for the flow is 100. Other parameters like specific heat (Cp) and density (ρ) are taken as unity. The values of thermal conductivity (k) and dynamic viscosity (μ) are calculated from the following relation:

Where Pr is the Prandtl Number

Results:

Instantaneous streamlines and isotherms are shown in Fig. 4.2 for Re=100. The time evolution of drag & lift coefficient and space-averaged Nusselt number are shown in Fig. 4.3. The values of time averaged drag coefficient and Nusselt number are 1.54 (1.41 in Breuer et al. [1]) and 4.12 (4.03 in Sharma and Eswaran [2]) respectively. The values are found to be in good comparison with the published results.

(a)


(b)
Figure 4.2: Instantaneous snapshots of (a) Streamlines (b) Isotherms


(a)


(b)
Figure 4.3: Time evolution of (a) drag and lift coefficients,
(b) space-averaged Nusselt number

References:

[1] M. Breuer J. Bernsdorf T.Z. and Durst F. (2000) ‘Accurate Computations of the Laminar Flow Past a Square Cylinder Based on Two Different Methods: Lattice-Boltzmann and Finite-Volume’, International Journal of Heat and Fluid Flow, Vol. 21, pp. 186–196.
[2] M. Breuer J. Bernsdorf T.Z. and Durst F. (2004) ‘Heat and Fluid Flow Across a Square Cylinder in the Two-Dimensional Laminar Flow Regime’, Numerical Heat Transfer Part A, Vol. 45, pp. 247–269.