scholarly journals Theoretical modeling of convection II. Reynolds Stress Model

2006 ◽  
Vol 2 (S239) ◽  
pp. 19-34 ◽  
Author(s):  
V. M. Canuto
Keyword(s):  
Reynolds Stress ◽  
Reynolds Stress Model ◽  
Heat Fluxes ◽  
Time Dependent ◽  
Dynamic Equations ◽  
Stress Model ◽  
Buoyant Flows ◽  
Non Local ◽  
The Mean ◽  
General Time

AbstractThe Reynolds Stress Model (RSM) yields the dynamic equations for the second-order moments (e.g., heat fluxes) needed in the equations for the mean variables (e.g., mean temperature). The RSM equations are in general time dependent and non-local. We first discuss the “buoyancy only” case and the tests of the non-local model against a variety of data. We also “plumenize” the model in order to exhibit the up-down flows that characterize convection so as to show that a non-local RSM is fully equipped to account for the “plume aspect” of buoyant flows. Next, we extend the RSM to account for stable and/or unstable stratification and shear, a formalism that is needed to describe the overshooting region contributed by differentail rotation. We conclude by discussing the equation for the dissipation of turbulent kinetic energy which plays a key role in any RSM.

A Numerical Study of Vortex Breakdown in Turbulent Swirling Flows

1999 ◽  
Vol 122 (1) ◽  
pp. 179-183 ◽  
Author(s):  
Robert E. Spall ◽  
Blake M. Ashby
Keyword(s):  
Reynolds Stress ◽  
Stokes Equations ◽  
Vortex Breakdown ◽  
Numerical Study ◽  
Reynolds Stress Model ◽  
Navier Stokes ◽  
Stress Model ◽  
Mean Flow ◽  
Navier Stokes Equations ◽  
The Mean

Solutions to the incompressible Reynolds-averaged Navier–Stokes equations have been obtained for turbulent vortex breakdown within a slightly diverging tube. Inlet boundary conditions were derived from available experimental data for the mean flow and turbulence kinetic energy. The performance of both two-equation and full differential Reynolds stress models was evaluated. Axisymmetric results revealed that the initiation of vortex breakdown was reasonably well predicted by the differential Reynolds stress model. However, the standard K-ε model failed to predict the occurrence of breakdown. The differential Reynolds stress model also predicted satisfactorily the mean azimuthal and axial velocity profiles downstream of the breakdown, whereas results using the K-ε model were unsatisfactory. [S0098-2202(00)01601-1]

Application of a Reynolds Stress Model to Engine-Like Flow Calculations

1985 ◽  
Vol 107 (4) ◽  
pp. 444-450 ◽  
Author(s):  
Sherif El Tahry
Keyword(s):  
Reynolds Stress ◽  
Combustion Engine ◽  
Reynolds Stress Model ◽  
Unknown Boundary ◽  
Stress Model ◽  
Mean Flow ◽  
Numerical Accuracy ◽  
Piston Cylinder ◽  
The Mean ◽  
Unknown Boundary Conditions

A version of a Reynolds stress turbulence model was adopted and applied for calculating turbulence in internal combustion engine flows. Simultaneously, to improve the numerical accuracy of the computations, a skew-upwind differencing scheme was introduced, thereby replacing the less accurate upwind differencing scheme originally present in the computations. With these modifications applied to an existing code, comparisons were made with measured mean and turbulent velocities of a flow field in an axisymmetric piston-cylinder assembly. The results of the computations were generally encouraging particularly for the mean flow. However, discrepancies were observed which are attributed to either (or both) unknown boundary conditions or shortcomings in the Reynolds stress model.

Testing Reynolds stress model in solar interior

2006 ◽  
Vol 2 (S239) ◽  
pp. 373-375
Author(s):  
J. Y. Yang ◽  
Y. Li
Keyword(s):  
Reynolds Stress ◽  
Convection Zone ◽  
Reynolds Stress Model ◽  
Solar Interior ◽  
Stress Model ◽  
Solar Convection Zone ◽  
Solar Convection ◽  
Mode Oscillation ◽  
Non Local ◽  
Oscillation Frequencies

AbstractThe Reynolds stress model (RSM) for turbulent convection motion is compared to the MLT in solar model. The free parameters involved in the RSM are also tested with the aid of helioseismology. It is found that, the structure of solar convection zone is differ from the MLT when using the RSM, especially for the Reynolds correlations and the temperature gradient. Both the local and non-local RSM can improve the calculated solar p-mode oscillation frequencies with the appropriate choice of the parameters' value.

scholarly journals Three-Dimensional Navier-Stokes Computation of Turbine Nozzle Flow With Advanced Turbulence Models

1995 ◽  
Author(s):  
J. Luo ◽  
B. Lakshminarayana
Keyword(s):  
Reynolds Stress ◽  
Three Dimensional ◽  
Turbulence Models ◽  
Reynolds Stress Model ◽  
Navier Stokes ◽  
Nozzle Flow ◽  
Stress Model ◽  
Mean Flow ◽  
The Mean ◽  
Algebraic Reynolds Stress Model

A three-dimensional Navier-Stokes procedure has been used to compute the three-dimensional viscous flow through the turbine nozzle passage of a single stage turbine. A low Reynolds number k-ε model and a zonal k-ε/ARSM (algebraic Reynolds stress model) are utilized for turbulence closure. The algebraic Reynolds stress model is used only in the endwall region to represent the anisotropy of turbulence. A four-stage Runge-Kutta scheme is used for time-integration of both the mean-flow and the turbulence transport equations. For the turbine nozzle flow, comprehensive comparisons between the predictions and the experimental data obtained at Penn State show that most features of the vortex-dominated endwall flow, as well as nozzle wake structure, have been captured well by the numerical procedure. An assessment of the performance of the turbulence models has been carried out The two models are found to provide similar predictions for the mean flow parameters, although slight improvement in the prediction of some secondary flow quantities has been obtained by the ARSM model.

Three-Dimensional Navier–Stokes Computation of Turbine Nozzle Flow With Advanced Turbulence Models

1997 ◽  
Vol 119 (3) ◽  
pp. 516-530 ◽  
Author(s):  
J. Luo ◽  
B. Lakshminarayana
Keyword(s):  
Reynolds Stress ◽  
Three Dimensional ◽  
Turbulence Models ◽  
Reynolds Stress Model ◽  
Navier Stokes ◽  
Nozzle Flow ◽  
Stress Model ◽  
Mean Flow ◽  
The Mean ◽  
Algebraic Reynolds Stress Model

A three-dimensional Navier–Stokes procedure has been used to compute the three-dimensional viscous flow through the turbine nozzle passage of a single-stage turbine. A low-Reynolds-number k–ε model and a zonal k-ε/ARSM (algebraic Reynolds stress model) are utilized for turbulence closure. The algebraic Reynolds stress model is used only in the endwall region to represent the anisotropy of turbulence. A four-stage Runge–Kutta scheme is used for time integration of both the mean-flow and the turbulence transport equations. For the turbine nozzle flow, comprehensive comparisons between the predictions and the experimental data obtained at Penn State show that most features of the vortex-dominated endwall flow, as well as nozzle wake structure, have been captured well by the numerical procedure. An assessment of the performance of the turbulence models has been carried out. The two models are found to provide similar predictions for the mean flow parameters, although slight improvement in the prediction of some secondary flow quantities has been obtained by the ARSM model.

Prediction of strongly curved turbulent duct flows with Reynolds stress model

AIAA Journal ◽  
1997 ◽  
Vol 35 ◽  
pp. 91-98
Author(s):  
Jiang Luo ◽  
Budugur Lakshminarayana
Keyword(s):  
Reynolds Stress ◽  
Reynolds Stress Model ◽  
Stress Model

A Robust Implementation of a Reynolds Stress Model for Turbomachinery Applications in a Coupled Solver Environment

2020 ◽  
Author(s):  
David Roos Launchbury ◽  
Luca Mangani ◽  
Ernesto Casartelli ◽  
Francesco Del Citto
Keyword(s):  
Reynolds Stress ◽  
Turbulence Modeling ◽  
Computational Cost ◽  
Reynolds Stress Model ◽  
Tip Vortex ◽  
Stability And Convergence ◽  
Stress Model ◽  
Robust Implementation ◽  
Flow Phenomena ◽  
The Stability

Abstract In the industrial simulation of flow phenomena, turbulence modeling is of prime importance. Due to their low computational cost, Reynolds-averaged methods (RANS) are predominantly used for this purpose. However, eddy viscosity RANS models are often unable to adequately capture important flow physics, specifically when strongly anisotropic turbulence and vortex structures are present. In such cases the more costly 7-equation Reynolds stress models often lead to significantly better results. Unfortunately, these models are not widely used in the industry. The reason for this is not mainly the increased computational cost, but the stability and convergence issues such models usually exhibit. In this paper we present a robust implementation of a Reynolds stress model that is solved in a coupled manner, increasing stability and convergence speed significantly compared to segregated implementations. In addition, the decoupling of the velocity and Reynolds stress fields is addressed for the coupled equation formulation. A special wall function is presented that conserves the anisotropic properties of the model near the walls on coarser meshes. The presented Reynolds stress model is validated on a series of semi-academic test cases and then applied to two industrially relevant situations, namely the tip vortex of a NACA0012 profile and the Aachen Radiver radial compressor case.

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