Application of Reynolds-Stress Transport Models to Stern and Wake Flows

1995 ◽  
Vol 39 (04) ◽  
pp. 263-283 ◽  
Author(s):  
F. Sotiropoulos ◽  
V. C. Patel
Keyword(s):  
Reynolds Stress ◽  
Turbulence Model ◽  
Stokes Equations ◽  
Reynolds Stress Model ◽  
Equation Model ◽  
Navier Stokes ◽  
Tensor Model ◽  
Stress Model ◽  
Wake Flows ◽  
Flow Features

ABSTRACT The Reynolds-averaged Navier-Stokes equations are solved to assess the importance of the turbulence model in the prediction of ship stern and wake flows. Solutions are obtained with a two-equation scalar turbulence model and a seven-equation Reynolds-stress tensor model, both of which resolve the flow up to the wall, holding invariant all aspects of the numerical method, including solution domain, initial and boundary conditions, and grid topology and density. Calculations are carried out for two tanker forms used as test cases at recent workshops, and solutions are compared with each other and with experimental data. The comparisons reveal that the Reynolds-stress model accurately predicts most of the experimentally observed flow features in the stern and near-wake regions whereas the two-equation model predicts only the overall qualitative trends. In particular, solutions with the Reynolds-stress model clarify the origin of the stern vortex.

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]

Development and Application of an Anisotropic Two-Equation Model for Flows With Swirl and Curvature

2003 ◽  
Author(s):  
Xiaohua Wang ◽  
Siva Thangam
Keyword(s):  
Energy Spectrum ◽  
Turbulent Flows ◽  
Reynolds Stress ◽  
Scaling Laws ◽  
Reynolds Stress Model ◽  
Equation Model ◽  
Stress Model ◽  
Generalized Model

An anisotropic two-equation Reynolds-stress model is developed by modeling the energy spectrum and through invariance based scaling. In this approach the effect of rotation is used to modify the energy spectrum, while the influence of swirl is modeled based on scaling laws. The resulting generalized model is validated for benchmark turbulent flows with swirl and curvature.

Development and Application of a Two-Scale Non-Linear Reynolds Stress Turbulence Model

2007 ◽  
Author(s):  
S. Y. Jaw ◽  
R. R. Hwang
Keyword(s):  
Turbulent Flows ◽  
Reynolds Stress ◽  
Turbulence Model ◽  
Dissipation Rate ◽  
Reynolds Stress Model ◽  
Stress Model ◽  
Turbulence Scale ◽  
Non Linear ◽  
Algebraic Reynolds Stress Model ◽  
Near Wall

To improve the prediction of turbulent flows, a two-scale, non-linear Reynolds stress turbulence model is proposed in this study. It is known that for the near-wall low-Reynolds number turbulent flows, the Kolmogorov turbulence scale, based on the fluid kinematic viscosity and dissipation rate of turbulent kinetic energy (ν,ε), is the dominant turbulence scale, hence it is adopted to address the viscous effects and the rapid increase of dissipation rate in the near wall region. As a wall is approached, the turbulence scale transits smoothly from turbulent kinetic energy based (k, ε) scale to (ν,ε) scale. The damping functions of the low-Reynolds number models can thus be simplified and the near-wall turbulence characteristics, such as the ε distribution, are correctly reproduced. Furthermore, to improve the prediction of the anisotropic Reynolds stresses for complex flows, a nonlinear algebraic Reynolds stress model is incorporated. The same turbulence scales are adopted in the nonlinear algebraic Reynolds stress model. The developed two-scale non-linear Reynolds stress model is first calibrated with the DNS budgets of two-dimensional channel flows, and then applied to predict the separation flow behind a backward facing step. It is found that the proposed two-scale nonlinear Reynolds stress turbulence model is capable of providing satisfactory results without increasing much computation efforts or causing numerical stability problems.

Modeling of Cube Array Roughness: RANS, LES, and DNS

2021 ◽  
Author(s):  
Samuel Altland ◽  
Haosen H. A. Xu ◽  
Xiang I. A. Yang ◽  
Robert Kunz
Keyword(s):  
Reynolds Stress ◽  
Significant Degree ◽  
Reynolds Stress Model ◽  
Stress Model ◽  
Mean Velocity ◽  
Flow Features ◽  
Drag Partition ◽  
Flow Phenomena ◽  
Rans Models ◽  
Packing Densities

Abstract Flow over arrays of cubes is an extensively studied model problem for rough wall turbulent boundary layers. While considerable research has been performed in computationally investigating these topologies using DNS and LES, the ability of sublayer-resolved RANS to predict the bulk flow phenomena of these systems is relatively unexplored, especially at low and high packing densities. Here, RANS simulations are conducted on six different packing densities of cubes in aligned and staggered configurations. The packing densities investigated span from what would classically be defined as isolated, up to those in the d-type roughness regime, filling in the gap in the present literature. Three different sublayer-resolved turbulence closure models were tested for each case; a low Reynolds number k-ε model, the Menter k-ω SST model, and a full Reynolds stress model. Comparisons of the velocity fields, secondary flow features, and drag coefficients are made between the RANS results and existing LES and DNS results. There is a significant degree of variability in the performance of the various RANS models across all comparison metrics. However, the Reynolds stress model demonstrated the best accuracy in terms of the mean velocity profile as well as drag partition across the range of packing densities.

Prediction of Heat Transfer in a Ribbed Channel: Evaluation of Unsteady RANS Methodology

2005 ◽  
Author(s):  
William D. York ◽  
D. Scott Holloway ◽  
James H. Leylek
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Reynolds Stress ◽  
Flow Direction ◽  
Reynolds Stress Model ◽  
Navier Stokes ◽  
Stress Model ◽  
Clemson University ◽  
Ribbed Channel ◽  
Closure Models

Heat transfer in a straight channel with rib turbulators on one wall is predicted numerically with an unsteady Reynolds-averaged Navier-Stokes (URANS) methodology and compared to code-validation quality experimental data from the literature. Additionally, for comparison, steady simulations of the problem are conducted using two popular turbulence closure models, a Realizable k-ε model and a differential Reynolds-stress model. Closure in the URANS simulation is provided by a new eddy-viscosity-based model that was developed in the Advanced Computational Research Laboratory at Clemson University. This new model consists of three transport equations, and it is designed specifically to promote natural unsteadiness in the flow without the need for artificial forcing. In all cases, the Reynolds number, based on hydraulic diameter, is equal to 24,000. Eight square ribs, orthogonal to the flow direction, are equally spaced on the bottom wall of the channel. For the URANS simulation, after the flow becomes fully-developed in the streamwise direction, the predicted Nusselt number on the ribbed wall follows the trend of measured data from the modeled experimental study. However, the unsteady simulation slightly overpredicts the distance to the peak heat transfer aft of each rib. Also, the heat transfer prediction is very dependent on the grid resolution aft of the ribs. Therefore, efficient refinement of the unstructured mesh and grid-independence issues are discussed. Results of both steady simulations show a significant underprediction of Nusselt number over the entire ribbed wall, with the Reynolds-stress model giving the better result of the two steady closure models. The results of this study clearly show that unsteady vortex shedding off of the ribs is important in the physics of this problem, and a systematic, unsteady methodology is necessary to accurately predict ribbed-channel heat transfer.

scholarly journals Assessment of turbulence model predictions for a centrifugal compressor simulation

2017 ◽  
Vol 1 ◽  
pp. 2II890 ◽  
Author(s):  
Lee Gibson ◽  
Lee Galloway ◽  
Sung in Kim ◽  
Stephen Spence
Keyword(s):  
Reynolds Stress ◽  
Turbulence Model ◽  
Centrifugal Compressor ◽  
Pressure Ratio ◽  
Reynolds Stress Model ◽  
Operating Conditions ◽  
Stress Model ◽  
Local Flow ◽  
Sst Model ◽  
Model Predictions

Abstract Steady-state computational fluid dynamics (CFD) simulations are an essential tool in the design process of centrifugal compressors. Whilst global parameters, such as pressure ratio and efficiency, can be predicted with reasonable accuracy, the accurate prediction of detailed compressor flow fields is a much more significant challenge. Much of the inaccuracy is associated with the incorrect selection of turbulence model. The need for a quick turnaround in simulations during the design optimisation process also demands that the turbulence model selected be robust and numerically stable with short simulation times. In order to assess the accuracy of a number of turbulence model predictions, the current study used an exemplar open test case, the centrifugal compressor “Radiver”, to compare the results of three eddy-viscosity models and two Reynolds stress type models. The turbulence models investigated in this study were: (i) Spalart-Allmaras (SA), (ii) Shear Stress Transport (SST), (iii) a modification to the SST model denoted the SST-curvature correction (SST-CC), (iv) Reynolds stress model of Speziale, Sarkar and Gatski (RSM-SSG), and (v) the turbulence frequency formulated Reynolds stress model (RSM-ω). Each was found to be in good agreement with the experiments (below 2% discrepancy), with respect to total-to-total parameters at three different operating conditions. However, for the near surge operating point P1, local flow field differences were observed between the models, with the SA model showing particularly poor prediction of local flow structures. The SST-CC showed better prediction of curved rotating flows in the impeller. The RSM-ω was better for the wake and separated flow in the diffuser. The SST model showed reasonably stable, robust and time efficient capability to predict global performance and local flow features.

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