Second Moment Closure Modeling and DNS of Stratified Shear Layers

Buoyant shear layers encountered in many engineering and environmental applications have been studied by researchers for decades. Often, these flows have high Reynolds and Richardson numbers, which leads to significant/intractable space-time resolution requirements for DNS or LES. On the other hand, many of the important physical mechanisms, such as stress anisotropy, wake stabilization, and regime transition, inherently render eddy viscosity-based RANS modeling inappropriate. Accordingly, we pursue second-moment closure (SMC), i.e., full Reynolds stress/flux/variance modeling, for moderate Reynolds number non-stratified, and stratified shear layers for which DNS is possible. A range of sub-model complexity is pursued for the diffusion of stresses, density fluxes and variance, pressure strain and scrambling, and dissipation. These sub-models are evaluated in terms of how well they are represented by DNS in comparison to the exact Reynolds averaged terms, and how well they impact the accuracy of full RANS closure. For the non-stratified case, SMC model predicts the shear layer growth rate and Reynolds shear stress profiles accurately. Stress anisotropy and budgets are captured only qualitatively. Comparing DNS of exact and modeled terms, inconsistencies in model performance and assumptions are observed, including inaccurate prediction of individual statistics, non-negligible pressure diffusion, and dissipation anisotropy. For the stratified case, shear layer and gradient Richardson number growth rates, and stress, flux and variance decay rates, are captured with less accuracy than corresponding flow parameters in the non-stratified case. These studies lead to several recommendations for model improvement.

Second Moment Closure Modeling and DNS of Stratified Shear Layers

Buoyant shear layers are encountered in many engineering and environmental applications, and have been studied by researchers in the context of experiments and modeling for decades. Often, these flows have high Reynolds and Richardson numbers, and this leads to significant/intractable space-time resolution requirements for DNS or LES modeling. On the other hand, many of the important physical mechanisms in these systems, such as stress anisotropy, wake stabilization, and regime transition, inherently render eddy viscosity-based RANS modeling inappropriate. Accordingly, we pursue second-moment closure (SMC), i.e., full Reynolds stress/flux/variance modeling, for moderate Reynolds number non-stratified, and stratified shear layers for which DNS is possible. A range of sub-model complexity is pursued for the diffusion of stresses, density fluxes and variance, pressure strain and scrambling, and dissipation. These sub-models are evaluated in terms of how well they are represented by DNS in comparison to the exact Reynolds averaged terms, and how well they impact the accuracy of the full RANS closure. For the non-stratified case, the SMC model predicts the shear layer growth rate and Reynolds shear stress profiles accurately. Stress anisotropy and budgets are captured only qualitatively. Comparing DNS of exact and modeled terms, inconsistencies in model performance and assumptions are observed, including inaccurate prediction of individual statistics, non-negligible pressure diffusion, and dissipation anisotropy. For the stratified case, shear layer and gradient Richardson number growth rates, and stress, flux and variance decay rates, are captured with less accuracy than corresponding flow parameters in the non-stratified case. These studies lead to several recommendations for model improvement.

Comparative assessment of SAS, IDDES and hybrid filtering RANS/LES models based on second-moment closure

The question of which turbulence model is better for a given class of applications is always confusing for the CFD researchers and users. Comparative assessments of scale-adaptive simulation (SAS), improved delay detached-eddy simulation (IDDES) and other hybrid RANS/LES models based on eddy-viscosity models (EVMs) are thoroughly investigated. But how well they perform based on a second-moment closure needs to be answered. In this paper, a widely acclaimed Reynolds-stress model (RSM) in aeronautical engineering, SSG/LRR-[Formula: see text] model, is carried out. The relevant test cases include the NACA0012 airfoil stalled flows and turret separated flow. In order to make a more reasonable comparison, a seventh-order scheme WCNS-E8T7 is adopted to reduce the influence of the numerical dissipation and a symmetrical conservative metric method is used to ensure the robustness. By comparing with the relevant experimental data and the solutions by original SSG/LRR-[Formula: see text] model (etc. URANS), it shows that all of the three hybrid methods (SAS, IDDES and hybrid filtering methods) based on the SSG/LRR-[Formula: see text] model have a good ability to simulate unsteady turbulence. Among them, the IDDES correction has the most potential.

Numerical Simulation of the Effect of Channel Orientation on Fluid Flow and Heat Transfer at High Buoyancy Number in a Rotating Two-Pass Channel With Angled Ribs

Convective heat transfer in a rotating two-pass square channel with 45 deg ribs is numerically investigated to simulate turbine blade cooling operation under extreme design cooling conditions (high rotation number, high density ratio, and high buoyancy number). Two channel orientations are examined β = 0 deg and β = 45 deg in order to determine the effects of passage orientation on flow and heat transfer. For a reference pressure of 10-atm and a Reynolds number of 25,000, the results show that at low buoyancy number and for both channel orientations, the combined effect of Coriolis and centrifugal buoyancy forces generates an important thermal gradient between low- and high-pressure surfaces of the first passage, while the second passage remains almost unchanged compared to the stationary cases. At high buoyancy number, and unlike low buoyancy number, the interaction of Coriolis-driven cells, rib-induced vortices, and buoyancy-driven cells are destructive, which degrade the heat transfer rate on trailing and leading surfaces in the first passage for β = 0 deg. In contrast, for β = 45 deg, this interaction is constructive, which enhances the heat transfer rate on co-trailing and co-leading surfaces. In the second passage, the interaction of rib-induced vortices and buoyancy-driven cells deteriorates significantly the heat transfer rate in case of β = 0 deg than in case of β = 45 deg compared to low buoyancy number. The computations are performed using the second-moment closure turbulence model and the numerical results are in fair agreement with available experimental data.

Wind-Wave Effects on Estuarine Turbulence: A Comparison of Observations and Second-Moment Closure Predictions

Observations of turbulent kinetic energy, dissipation, and turbulent stress were collected in the middle reaches of Chesapeake Bay and were used to assess second-moment closure predictions of turbulence generated beneath breaking waves. Dissipation scaling indicates that the turbulent flow structure observed during a 10-day wind event was dominated by a three-layer response that consisted of 1) a wave transport layer, 2) a surface log layer, and 3) a tidal, bottom boundary layer limited by stable stratification. Below the wave transport layer, turbulent mixing was limited by stable stratification. Within the wave transport layer, where dissipation was balanced by a divergence in the vertical turbulent kinetic energy flux, the eddy viscosity was significantly underestimated by second-moment turbulence closure models, suggesting that breaking waves homogenized the mixed surface layer to a greater extent than the simple model of TKE diffusing away from a source at the surface. While the turbulent transport of TKE occurred largely downgradient, the intermittent downward sweeps of momentum generated by breaking waves occurred largely independent of the mean shear. The underprediction of stress in the wave transport layer by second-moment closures was likely due to the inability of the eddy viscosity model to capture the nonlocal turbulent transport of the momentum flux beneath breaking waves. Finally, the authors hypothesize that large-scale coherent turbulent eddies played a significant role in transporting momentum generated near the surface to depth.