Numerical Predictions of Temporally Periodic Fluid Flow and Heat Transfer in Spatially Periodic Geometries

Some observations on numerical predictions of temporally periodic fluid flow and heat transfer in spatially periodic geometries, in both spatially developing and fully developed regions, are presented and discussed in this chapter. Special attention is given to several issues that have not been fully resolved in earlier publications. The key points and ideas are demonstrated in the context of computationally convenient finite volume solutions of the mathematical models of two-dimensional, laminar, constant-property Newtonian fluid flow and forced convection heat transfer in uniform arrays of staggered rectangular plates. A dimensionless plate length of 1, dimensionless plate thicknesses of 1/4, 1/8, 1/12, and 1/16, time-mean Reynolds number values ranging from 100 to 1000, and a Prandtl number of 0.7 were considered. The simulations of developing fluid flow and heat transfer were conducted with calculation domains consisting of one row of ten consecutive geometric modules, followed by a plate-free exit zone of suitable length. Calculation domains consisting of single and multiple geometric modules were considered in simulations of fluid flow and heat transfer in the temporally and spatially periodic region. Findings of particular interest include the following: (1) multiple-module simulations of temporally and spatially periodic fluid flow and heat transfer yielded multiple solutions, but the absolute percentage differences in the corresponding values of time-mean modular friction and Colburn factors were all less than 6.4% and 5.1%, respectively; (2) in simulations of unsteady temporally periodic flows, the values of fully developed time-mean modular friction factor obtained from the predictions of the developing flow and the flow in a single module in the spatially periodic region differed by up to 22%; and (3) the instantaneous spatial periodicity conditions imposed in simulations of temporally periodic flows in single or multiple modules in the spatially periodic region are less restrictive than the boundary conditions employed in the corresponding simulations of developing flows, so the former yielded unsteady fluid flow over a wider range of Reynolds number.