The role of solid obstacle surface roughness in turbulent convection in porous media is not well understood, even though it is frequently used for heat transfer enhancement in many applications. The focus of this paper is to systematically study the influence of solid obstacle surface roughness in porous media on the microscale flow physics and report its effect on macroscale drag and Nusselt number. The Reynolds-averaged flow field is numerically simulated using the realizable k-ε model for a flow through a periodic porous medium consisting of an in-line arrangement of square cylinders with square roughness particles on the cylinder surface. Two flow regimes are identified with respect to the surface roughness particle height—fine and coarse roughness regimes. The effect of the roughness particles in the fine roughness regime is limited to the near-wall boundary layer around the solid obstacle surface. In the coarse roughness regime, the roughness particles modify the microscale flow field in the entire pore space of the porous medium. In the fine roughness regime, the heat transfer from the rough solid obstacles to the fluid inside the porous medium is less than that from a smooth solid obstacle. In the coarse roughness regime, there is an enhancement in the heat transfer from the rough solid obstacle to the fluid inside the porous medium. Total drag reduction is also observed in the fine roughness regime for the smallest roughness particle height. The surface roughness particle spacing determines the fractional area of the solid obstacle surface covered by recirculating, reattached, and stagnating flow. As the roughness particle spacing increases, there are two competing factors for the heat transfer rate—increase due to more surface area covered by reattached flow and decrease due to fewer roughness particles on the solid obstacle surface. Decreasing the porosity and increasing the Reynolds number amplify the effect of the surface roughness on the microscale flow. The results suggest that heat transfer in porous media can be enhanced, if the increase in drag can be overcome. The results also show that the fine roughness regime, which is frequently encountered due to corrosion, is detrimental to the heat transfer performance of porous media.
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Drag enhancement by the addition of weak waves to a wave-current boundary layer over bumpy walls
We present direct numerical simulation results of a wave-current boundary layer in a current-dominated flow regime (wave driven to steady current ratio of 0.34) over bumpy walls for hydraulically smooth flow conditions (wave orbital excursion to roughness ratio of 10). The turbulent, wave-current channel flow has a friction Reynolds number of $350$ and a wave Reynolds number of $351$ . At the lower boundary, a bumpy wall is introduced with a direct forcing immersed boundary method, while the top wall has a free-slip boundary condition. Despite the hydraulically smooth nature of the wave-driven flow, the phase variations of the turbulent statistics for the bumpy wall case were found to vary substantially when compared with the flat wall case. Results show that the addition of weak waves to a steady current over flat walls has a negligible effect on the turbulence or bottom drag. However, the addition of weak waves to a steady current over bumpy walls has a significant effect through enhancement of the Reynolds stress (RS) accompanied by a drag coefficient increase of $11\,\%$ relative to the steady current case. This enhancement occurs just below the top of the roughness elements during the acceleration portion of the wave cycle: Turbulent kinetic energy (TKE) is subsequently transported above the roughness elements to a maximum height of roughly twice the turbulent Stokes length. We analyse the TKE and RS budgets to understand the mechanisms behind the alterations in the turbulence properties due to the bumpy wall. The results provide a mechanistic picture of the differences between bumpy and flat walls in wave-current turbulent boundary layers and illustrate the importance of bumpy features even in weakly energetic wave conditions.
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- Award ID(s):
- 1736668
- NSF-PAR ID:
- 10389917
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 947
- ISSN:
- 0022-1120
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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In the coastal ocean, interactions of waves and currents with large roughness elements, similar in size to wave orbital excursions, generate drag and dissipate energy. These boundary layer dynamics differ significantly from well-studied small-scale roughness. To address this problem, we derived spatially and phase-averaged momentum equations for combined wave–current flows over rough bottoms, including the canopy layer containing obstacles. These equations were decomposed into steady and oscillatory parts to investigate the effects of waves on currents, and currents on waves. We applied this framework to analyse large-eddy simulations of combined oscillatory and steady flows over hemisphere arrays (diameter $D$ ), in which current ( $U_c$ ), wave velocity ( $U_w$ ) and period ( $T$ ) were varied. In the steady momentum budget, waves increase drag on the current, and this is balanced by the total stress at the canopy top. Dispersive stresses from oscillatory flow around obstacles are increasingly important as $U_w/U_c$ increases. In the oscillatory momentum budget, acceleration in the canopy is balanced by pressure gradient, added-mass and form drag forces; stress gradients are small compared to other terms. Form drag is increasingly important as the Keulegan–Carpenter number $KC=U_wT/D$ and $U_c/U_w$ increase. Decomposing the drag term illustrates that a quadratic relationship predicts the observed dependences of steady and oscillatory drag on $U_c/U_w$ and $KC$ . For large roughness elements, bottom friction is well represented by a friction factor ( $f_w$ ) defined using combined wave and current velocities in the canopy layer, which is proportional to drag coefficient and frontal area per unit plan area, and increases with $KC$ and $U_c/U_w$ .more » « less
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Abstract Air–sea momentum and scalar fluxes are strongly influenced by the coupling dynamics between turbulent winds and a spectrum of waves. Because direct field observations are difficult, particularly in high winds, many modeling and laboratory studies have aimed to elucidate the impacts of the sea state and other surface wave features on momentum and energy fluxes between wind and waves as well as on the mean wind profile and drag coefficient. Opposing wind is common under transient winds, for example, under tropical cyclones, but few studies have examined its impacts on air–sea fluxes. In this study, we employ a large-eddy simulation for wind blowing over steep sinusoidal waves of varying phase speeds, both following and opposing wind, to investigate impacts on the mean wind profile, drag coefficient, and wave growth/decay rates. The airflow dynamics and impacts rapidly change as the wave age increases for waves following wind. However, there is a rather smooth transition from the slowest waves following wind to the fastest waves opposing wind, with gradual enhancement of a flow perturbation identified by a strong vorticity layer detached from the crest despite the absence of apparent airflow separation. The vorticity layer appears to increase the effective surface roughness and wave form drag (wave attenuation rate) substantially for faster waves opposing wind.
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$Re_K=2.56$ $Re_K$
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2022.628
