scholarly journals A semi-implicit discrepancy model of Reynolds stress in a higher-order tensor basis framework for Reynolds-averaged Navier–Stokes simulations

AIP Advances ◽  
2021 ◽  
Vol 11 (4) ◽  
pp. 045025
Author(s):  
Zhen Zhang ◽  
Shuran Ye ◽  
Bo Yin ◽  
Xudong Song ◽  
Yiwei Wang ◽  
...  
Keyword(s):  
Reynolds Stress ◽  
Higher Order ◽  
Navier Stokes ◽  
Order Tensor ◽  
Discrepancy Model ◽  
Tensor Basis ◽  
Reynolds Averaged Navier Stokes

Output-Based Adaptive Reynolds-Averaged Navier–Stokes Higher-Order Finite Element Solutions on a Multielement Airfoil

AIAA Journal ◽  
2021 ◽  
pp. 1-14
Author(s):  
Carmen-Ioana Ursachi ◽  
Marshall C. Galbraith ◽  
Steven R. Allmaras ◽  
David L. Darmofal
Keyword(s):  
Finite Element ◽  
Higher Order ◽  
Navier Stokes ◽  
Reynolds Averaged Navier Stokes

scholarly journals Reynolds-averaged Navier–Stokes equations with explicit data-driven Reynolds stress closure can be ill-conditioned

2019 ◽  
Vol 869 ◽  
pp. 553-586 ◽  
Author(s):  
Jinlong Wu ◽  
Heng Xiao ◽  
Rui Sun ◽  
Qiqi Wang
Keyword(s):  
Reynolds Stress ◽  
Condition Number ◽  
Stokes Equations ◽  
Plane Channel ◽  
Channel Flows ◽  
Data Driven ◽  
Navier Stokes ◽  
Rans Equations ◽  
Reynolds Averaged Navier Stokes ◽  
Stress Models

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 (e.g. flows with massive separation). 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 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 the 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.

scholarly journals On the Reynolds-Averaged Navier-Stokes Equations

2019 ◽  
Author(s):  
Bohua Sun
Keyword(s):  
Stress Tensor ◽  
Reynolds Stress ◽  
Current Literature ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Closure Problem ◽  
Navier Stokes Equations ◽  
Fluctuation Velocity ◽  
Reynolds Stress Tensor ◽  
Reynolds Averaged Navier Stokes

This paper attempts to clarify an long-standing issue about the number of unknowns in the Reynolds-Averaged Navier-Stokes equations (RANS). This study shows that all perspectives regarding the numbers of unknowns in the RANS stem from the misinterpretation of the Reynolds stress tensor. The current literature consider that the Reynolds stress tensor has six unknown components; however, this study shows that the Reynolds stress tensor actually has only three unknown components, namely the three components of fluctuation velocity. This understanding might shed a light to understand the well-known closure problem of turbulence.

Application of Higher-Order Adaptive Method to Reynolds-Averaged Navier–Stokes Test Cases

AIAA Journal ◽  
2016 ◽  
Vol 54 (9) ◽  
pp. 2626-2644 ◽  
Author(s):  
Yixuan Hu ◽  
Carlee Wagner ◽  
Steven R. Allmaras ◽  
Marshall C. Galbraith ◽  
David L. Darmofal
Keyword(s):  
Adaptive Method ◽  
Higher Order ◽  
Navier Stokes ◽  
Test Cases ◽  
Reynolds Averaged Navier Stokes

scholarly journals Revisiting the Reynolds-averaged Navier–Stokes equations

Open Physics ◽  
2021 ◽  
Vol 19 (1) ◽  
pp. 853-862
Author(s):  
Bohua Sun
Keyword(s):  
Stress Tensor ◽  
Reynolds Stress ◽  
Velocity Fluctuation ◽  
Stokes Equations ◽  
Symmetric Tensor ◽  
Navier Stokes ◽  
Difficult Situation ◽  
Velocity Fluctuations ◽  
Reynolds Stress Tensor ◽  
Reynolds Averaged Navier Stokes

Abstract This study revisits the Reynolds-averaged Navier–Stokes (RANS) equations and finds that the existing literature is erroneous regarding the primary unknowns and the number of independent unknowns in the RANS. The literature claims that the Reynolds stress tensor has six independent unknowns, but in fact the six unknowns can be reduced to three that are functions of the three velocity fluctuation components, because the Reynolds stress tensor is simply an integration of a second-order dyadic tensor of flow velocity fluctuations rather than a general symmetric tensor. This difficult situation is resolved by returning to the time of Reynolds in 1895 and revisiting Reynolds’ averaging formulation of turbulence. The study of turbulence modeling could focus on the velocity fluctuations instead of the Reynolds stress. An advantage of modeling the velocity fluctuations is, from both physical and experimental perspectives, that the velocity fluctuation components are observable whereas the Reynolds stress tensor is not.

Computational simulation of turbulent flows around a marine propeller by solving the partially averaged Navier–Stokes equation

2019 ◽  
Vol 233 (18) ◽  
pp. 6357-6366
Author(s):  
Woochan Seok ◽  
Sang Bong Lee ◽  
Shin Hyung Rhee
Keyword(s):  
Turbulent Flow ◽  
Reynolds Stress ◽  
Stokes Equation ◽  
Leading Edge ◽  
Reynolds Stress Model ◽  
Navier Stokes ◽  
Stress Model ◽  
Navier Stokes Equation ◽  
Local Flow ◽  
Reynolds Averaged Navier Stokes

This study concerns the characteristics of the partially averaged Navier–Stokes method for local flow analysis around a rotating propeller. Partially averaged Navier–Stokes, resolving crucial large-scale structures of turbulent flow at a given computational grid resolution, is a bridging turbulence closure model between the Reynolds-averaged Navier–Stokes equation and the direct numerical simulation. A detailed comparison between partially averaged Navier–Stokes and Reynolds-averaged Navier–Stokes models is made to achieve a better understanding of partially averaged Navier–Stokes characteristics for predicting the coherent structures in turbulent flow. The two-equation k-ω shear stress transport model and the seven-equation Reynolds stress model are selected for Reynolds-averaged Navier–Stokes computations. The problem of interest is the flow around a rotating KP505 propeller in open water conditions at an advance ratio of 0.7. Near the leading edge, the partially averaged Navier–Stokes results are similar to those of Reynolds stress model in terms of the vortical structures. Vorticity predicted by different turbulence models, however, shows significant differences. For a more detailed analysis, the velocity gradient constituting the vorticity is identified at the leading edge. It is proven that partially averaged Navier–Stokes is able to capture the anisotropic characteristics of the flow at the leading edge, where both the geometric and flow characteristics change abruptly.

scholarly journals Performance of turbulence and cavitation models in prediction of incipient and developed cavitation

2016 ◽  
Vol 18 (4) ◽  
pp. 333-350 ◽  
Author(s):  
Phoevos Koukouvinis ◽  
Homa Naseri ◽  
Manolis Gavaises
Keyword(s):  
Large Eddy Simulation ◽  
Simulation Model ◽  
Reynolds Stress ◽  
Eddy Viscosity ◽  
Navier Stokes ◽  
Large Eddy Simulation Model ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Reynolds Averaged Navier Stokes ◽  
The Impact

The aim of this article is to assess the impact of turbulence and cavitation models on the prediction of diesel injector nozzle flow. Two nozzles are examined, an enlarged one, operating at incipient cavitation, and an industrial injector tip, operating at developed cavitation. The turbulence model employed includes the re-normalization group k–ε, realizable k–ε and k–ω shear stress transport Reynolds-averaged Navier–Stokes models; linear pressure–strain Reynolds stress model and the wall adapting local eddy viscosity large eddy simulation model. The results indicate that all Reynolds-averaged Navier–Stokes and the Reynolds stress turbulence models have failed to predict cavitation inception due to their limitation to resolve adequately the low pressure existing inside vortex cores, which is responsible for cavitation development in this particular flow configuration. Moreover, Reynolds-averaged Navier–Stokes models failed to predict unsteady cavitation phenomena in the industrial injector. However, the wall adapting local eddy viscosity large eddy simulation model was able to predict incipient and developed cavitation, while also capturing the shear layer instability, vortex shedding and cavitating vortex formation. Furthermore, the performance of two cavitation methodologies is discussed within the large eddy simulation framework. In particular, a barotropic model and a mixture model based on the asymptotic Rayleigh–Plesset equation of bubble dynamics have been tested. The results indicate that although the solved equations and phase change formulation are different in these models, the predicted cavitation and flow field were very similar at incipient cavitation conditions. At developed cavitation conditions, standard cavitation models may predict unrealistically high liquid tension, so modifications may be essential. It is also concluded that accurate turbulence representation is crucial for cavitation in nozzle flows.

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