Comparison of Les and Rans Simulations of Turbulent Convection in a Structured Porous Media

Numerical simulations are performed of the turbulent flow and thermal field in a structured porous media. The geometry of interest is an open lattice structure that is made up of mutually orthogonal, millimeter-scale, thermally conductive cylindrical elements. A large-eddy simulation (LES) is performed and the results are used as reference data to evaluate the performance of three commonly used Reynolds Averaged Navier-Stokes (RANS) models: the Spalart-Allmaras model (SAM), the k-ω model (KWM) and the shear stress transport k-ω model (KWM/SST). Mean velocities, turbulent kinetic energy profiles, and turbulent viscosity predictions are compared as well as friction factor, wall shear stress and Stanton number. INTRODUCTION Structured porous media consisting of groupinterconnected, thermally conductive ligaments, can be configured to have wide ranging porosity, a large specific surface area, β, and effective thermal conductivity, ke, in a particular direction together with specified structural characteristics. When deployed as heat exchanger matrices, these structures produce high ntu-values (number of transfer units) because of the large specific surface area inherent to the media. Examples of structures with these characteristics are laminations of plain-weave screens Park et al. [7], and threedimensional woven mesh structures Wirtz et al. [11]. Xu and Wirtz [12, 13] have developed analytical models of porosity, εv, specific surface area, and the in-plane component of ke for orthogonal-weave and diamond-weave screen laminates. Their work shows that these laminates can be configured to have a relatively large specific surface area, with effective thermal conductivities of anisotropic screen laminates such as diamond weaves that could approach 78% of base material values. Wirtz and coworkers [11] employed a three-filament stacked weave configuration. These are very dense structures, with metal fractions, (1-εv) that can range from 0.59 to 0.785 and 2.36 ≤ βd ≤ 2π (d = filament diameter). A prototype aluminum stacked weave with one filament having twice the diameter of the other two has β = 4580 m and ke = 84 W/mK. Park et al. [7] (screen laminates) and Wirtz et al. [11] (3-filament weaves) found that these structures have friction factor and Stanton number characteristics that are comparable to other compact heat exchanger surfaces. Park et al. [7] have also shown that the performance of such structures, deployed as a heat exchanger surfaces is approximately proportional to ke β , so exchanger surfaces having both large specific surface area and effective thermal conductivity are expected to exhibit superior thermal performance. An open lattice structure heat exchanger matrix consisting of mutually orthogonal, thermally conductive, cylindrical filaments is considered in the present investigation. By varying the vertical and horizontal filament diameter, d, and pitch, p, Balantrapu and coworkers [1] have recently shown that the metal fraction, specific surface area and effective thermal conductivity can range as: 0 ≤ (1-εv) ≤ 0.94, 0.93 ≤ βdv ≤ πdv/ph and 0 < ke/ks ≤ π/4, where dv is the vertical filament diameter, ph is the horizontal pitch, and ks is the filament thermal conductivity. Consequently, these structures are very versatile. Gullbrand and coworkers [4] have recently reported on single-phase convection in mm-scale box lattices. They found that steady laminar flow persists up to a Reynolds number of 100, with transition to an unsteady flow at a Reynolds number of 300. The flow exhibits jet-like behavior, and at the highest Reynolds number considered, Re = 1000, they observed rms velocity fluctuations that were 26% of the mean velocity. Friction factor and Stanton number correlations were similar to those observed by Park et al. [7] and Wirtz et al. [11]. The Reynolds number is calculated by Re = ρVDh/μ, where ρ is the density of the fluid, V is the average pore velocity, Dh = 4εv/β is the hydraulic diameter, and μ is the molecular viscosity. In the literature, studies have been performed to evaluate the flow and thermal characteristics of porous media flows both numerically and experimentally. One porous media, which is