Hybrid RANS/LES of flow in a rib-roughened channel with rotation

The aim of the present study is to verify the reliability of a k-ω based hybrid RANS/LES model in reproducing the flow in a rib-roughened rotating channel. The numerical results obtained with the hybrid RANS/LES model are compared to experimental data by Coletti and Arts (2011) and to the results obtained with the RANS k-ω model of Wilcox (2008). We demonstrate that the hybrid RANS/LES model gives realistic results for simulation of the rotating ribbed duct flow, without the necessity to add ad hoc corrections for system rotation to the underlying RANS mode

Degrees and distances in random and evolving Apollonian networks

This paper studies Random and Evolving Apollonian networks (RANs and EANs), in d dimension for any d>=2, i.e. dynamically evolving random d dimensional simplices looked as graphs inside an initial d-dimensional simplex. We determine the limiting degree distribution in RANs and show that it follows a power law tail with exponent tau=(2d-1)/(d-1). We further show that the degree distribution in EANs converges to the same degree distribution if the simplex-occupation parameter in the n-th step of the dynamics is q_n->0 and sum_{n=0}^infty q_n =infty. This result gives a rigorous proof for the conjecture of Zhang et al. that EANs tend to show similar behavior as RANs once the occupation parameter q->0. We also determine the asymptotic behavior of shortest paths in RANs and EANs for arbitrary d dimensions. For RANs we show that the shortest path between two uniformly chosen vertices (typical distance), the flooding time of a uniformly picked vertex and the diameter of the graph after n steps all scale as constant times log n. We determine the constants for all three cases and prove a central limit theorem for the typical distances. We prove a similar CLT for typical distances in EANs

RANS Equations with Explicit Data-Driven Reynolds Stress Closure Can Be Ill-Conditioned

Reynolds-averaged Navier--Stokes (RANS) simulations with turbulence closure models continue to play important roles in industrial flow simulations. However, the commonly used linear eddy viscosity models are intrinsically unable to handle flows with non-equilibrium turbulence. Reynolds stress models, on the other hand, are plagued by their lack of robustness. Recent studies in plane channel flows found that even substituting Reynolds stresses with errors below 0.5% from direct numerical simulation (DNS) databases into RANS equations leads to velocities with large errors (up to 35%). While such an observation may have only marginal relevance to traditional Reynolds stress models, it is disturbing for the recently emerging data-driven models that treat the Reynolds stress as an explicit source term in the RANS equations, as it suggests that the RANS equations with such models can be ill-conditioned. So far, a rigorous analysis of the condition of such models is still lacking. As such, in this work we propose a metric based on local condition number function for a priori evaluation of the conditioning of the RANS equations. We further show that the ill-conditioning cannot be explained by the global matrix condition number of the discretized RANS equations. Comprehensive numerical tests are performed on turbulent channel flows at various Reynolds numbers and additionally on two complex flows, i.e., flow over periodic hills and flow in a square duct. Results suggest that the proposed metric can adequately explain observations in previous studies, i.e., deteriorated model conditioning with increasing Reynolds number and better conditioning of the implicit treatment of Reynolds stress compared to the explicit treatment. This metric can play critical roles in the future development of data-driven turbulence models by enforcing the conditioning as a requirement on these models.Comment: 35 pages, 18 figure

Hybrid RANS/LES of plane impinging jets with k-omega based models

Plane impinging jets with nozzle-plate distances H/B=10 at Re=13500 and H/B=9.2 at Re=20000 are simulated with k-omega based hybrid RANS/LES models. Three ways of substitution of the turbulent length scale by the local grid size in the LES mode of the hybrid RANS/LES models are tested. The results show that the hybrid models give much better prediction of wall shear stress and heat transfer rate along the impingement plate than the RANS model. The good performance of the hybrid models is due to their ability to resolve the evolution and break-up of the vortices in the shear layer of the jet, which strongly affects the turbulent flow and convective heat transfer in the stagnation region and the developing wall-jet region