scholarly journals Development and Use of Machine-Learnt Algebraic Reynolds Stress Models for Enhanced Prediction of Wake Mixing in Low-Pressure Turbines

2019 ◽  
Vol 141 (4) ◽  
Author(s):  
H. D. Akolekar ◽  
J. Weatheritt ◽  
N. Hutchins ◽  
R. D. Sandberg ◽  
G. Laskowski ◽  
...  
Keyword(s):  
Reynolds Stress ◽  
Gene Expression Programming ◽  
A Priori ◽  
Low Pressure ◽  
Navier Stokes ◽  
Flow Features ◽  
Turbulence Closures ◽  
Rans Models ◽  
Development Analysis ◽  
Stress Models

Nonlinear turbulence closures were developed that improve the prediction accuracy of wake mixing in low-pressure turbine (LPT) flows. First, Reynolds-averaged Navier–Stokes (RANS) calculations using five linear turbulence closures were performed for the T106A LPT profile at isentropic exit Reynolds numbers 60,000 and 100,000. None of these RANS models were able to accurately reproduce wake loss profiles, a crucial parameter in LPT design, from direct numerical simulation (DNS) reference data. However, the recently proposed kv2¯ω transition model was found to produce the best agreement with DNS data in terms of blade loading and boundary layer behavior and thus was selected as baseline model for turbulence closure development. Analysis of the DNS data revealed that the linear stress–strain coupling constitutes one of the main model form errors. Hence, a gene-expression programming (GEP) based machine-learning technique was applied to the high-fidelity DNS data to train nonlinear explicit algebraic Reynolds stress models (EARSM), using different training regions. The trained models were first assessed in an a priori sense (without running any RANS calculations) and showed much improved alignment of the trained models in the region of training. Additional RANS calculations were then performed using the trained models. Importantly, to assess their robustness, the trained models were tested both on the cases they were trained for and on testing, i.e., previously not seen, cases with different flow features. The developed models improved prediction of the Reynolds stress, turbulent kinetic energy (TKE) production, wake-loss profiles, and wake maturity, across all cases.

scholarly journals Development and Use of Machine-Learnt Algebraic Reynolds Stress Models for Enhanced Prediction of Wake Mixing in LPTs

2018 ◽  
Author(s):  
Harshal D. Akolekar ◽  
Jack Weatheritt ◽  
Nicholas Hutchins ◽  
Richard D. Sandberg ◽  
Gregory Laskowski ◽  
...  
Keyword(s):  
Reynolds Stress ◽  
Gene Expression Programming ◽  
A Priori ◽  
Navier Stokes ◽  
Non Linear ◽  
Flow Features ◽  
Turbulence Closures ◽  
Rans Models ◽  
Exit Mach Number ◽  
Stress Models

Non-linear turbulence closures were developed that improve the prediction accuracy of wake mixing in low-pressure turbine (LPT) flows. First, Reynolds-averaged Navier–Stokes (RANS) calculations using five linear turbulence closures were performed for the T106A LPT profile at exit Mach number 0.4 and isentropic exit Reynolds numbers 60,000 and 100,000. None of these RANS models were able to accurately reproduce wake loss profiles, a crucial parameter in LPT design, from direct numerical simulation (DNS) reference data. However, the recently proposed kv2¯ω transition model was found to produce the best agreement with DNS data in terms of blade loading and boundary layer behavior and thus was selected as baseline model for turbulence closure development. Analysis of the DNS data revealed that the linear stress-strain coupling constitutes one of the main model form errors. Hence, a gene-expression programming (GEP) based machine-learning technique was applied to the high-fidelity DNS data to train non-linear explicit algebraic Reynolds stress models (EARSM). In particular, the GEP algorithm was tasked to minimize the weighted difference between the DNS and RANS anisotropy tensors, using different training regions. The trained models were first assessed in an a priori sense (without running any CFD) and showed much improved alignment of the trained models in the region of training. Additional RANS calculations were then performed using the trained models. Importantly, to assess their robustness, the trained models were tested both on the cases they were trained for and on testing, i.e. previously not seen, cases with different flow features. The developed models improved prediction of the Reynolds stress, TKE production, wake-loss profiles and wake maturity, across all cases, in particular those trained on just the wake region.

A Priori Analysis of Explicit Algebraic Stress Models for a Turbulent Flow Through a Straight Square Duct

2004 ◽  
Author(s):  
H. Naji ◽  
O. El Yahyaoui ◽  
G. Mompean
Keyword(s):  
Turbulent Flow ◽  
Reynolds Stress ◽  
Stokes Equations ◽  
A Priori ◽  
Proximity Effects ◽  
Navier Stokes ◽  
Wall Region ◽  
Square Duct ◽  
Anisotropy Tensor ◽  
Stress Models

The ability of two explicit algebraic Reynolds stress models (EARSMs) to accurately predict the problem of fully turbulent flow in a straight square duct is studied. The first model is devised by Gatski and Rumsey (2001) and the second is the one derived by Wallin and Johansson (2000). These models are studied using a priori procedure based on data resulting from direct numerical simulation (DNS) of the Navier-Stokes equations, which is available for this problem. For this case, we show that the equilibrium assumption for the anisotropy tensor is found to be correct. The analysis leans on the maps of the second and third invariants of the Reynolds stress tensor. In order to handle wall-proximity effects in the near-wall region, damping functions are implemented in the two models. The predictions and DNS obtained for a Reynolds number of 4800 both agree well and show that these models are able to predict such flows.

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.

Investigation of the Accuracy of RANS Models to Predict the Flow Through a Low-Pressure Turbine

2016 ◽  
Vol 138 (12) ◽  
Author(s):  
R. Pichler ◽  
R. D. Sandberg ◽  
V. Michelassi ◽  
R. Bhaskaran
Keyword(s):  
Linear Models ◽  
Turbulence Modeling ◽  
A Priori ◽  
Flow Characteristics ◽  
Turbulence Models ◽  
Low Pressure ◽  
Transport Equations ◽  
Compressible Turbulence ◽  
Low Pressure Turbine ◽  
Rans Models

In the present paper, direct numerical simulation (DNS) data of a low-pressure turbine (LPT) are investigated in light of turbulence modeling. Many compressible turbulence models use Favre-averaged transport equations of the conservative variables and turbulent kinetic energy (TKE) along with other modeling equations. First, a general discussion on the turbulence modeling error propagation prescribed by transport equations is presented, leading to the terms that are considered to be of interest for turbulence model improvement. In order to give turbulence modelers means of validating their models, the terms appearing in the Favre-averaged momentum equations are presented along pitchwise profiles at three axial positions. These three positions have been chosen such that they represent regions with different flow characteristics. General trends indicate that terms related with thermodynamic fluctuations and Favre fluctuations are small and can be neglected for most of the flow field. The largest errors arise close to the trailing edge (TE) region where vortex shedding occurs. Finally, linear models and the scope for their improvement are discussed in terms of a priori testing. Using locally optimized turbulence viscosities, the improvement potential of widely used models is shown. On the other hand, this study also highlights the danger of pure local optimization.

scholarly journals Reynolds Stress Perturbation for Epistemic Uncertainty Quantification of RANS Models Implemented in OpenFOAM

Fluids ◽  
2019 ◽  
Vol 4 (2) ◽  
pp. 113 ◽  
Author(s):  
Luis F. Cremades Rey ◽  
Denis F. Hinz ◽  
Mahdi Abkar
Keyword(s):  
Experimental Data ◽  
Numerical Simulation ◽  
Reynolds Stress ◽  
Epistemic Uncertainty ◽  
Turbulent Viscosity ◽  
Navier Stokes ◽  
Simulation Data ◽  
Direct Numerical Simulation Data ◽  
Engineering Problems ◽  
Rans Models

Reynolds-averaged Navier-Stokes (RANS) models are widely used for the simulation of engineering problems. The turbulent-viscosity hypothesis is a central assumption to achieve closures in this class of models. This assumption introduces structural or so-called epistemic uncertainty. Estimating that epistemic uncertainty is a promising approach towards improving the reliability of RANS simulations. In this study, we adopt a methodology to estimate the epistemic uncertainty by perturbing the Reynolds stress tensor. We focus on the perturbation of the turbulent kinetic energy and the eigenvalues separately. We first implement this methodology in the open source package OpenFOAM. Then, we apply this framework to the backward-facing step benchmark case and compare the results with the unperturbed RANS model, available direct numerical simulation data and available experimental data. It is shown that the perturbation of both parameters successfully estimate the region bounding the most accurate results.

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.

Modeling Of Turbulent Transport Equations

1996 ◽  
Author(s):  
Charles G. Speziale
Keyword(s):  
Turbulent Flows ◽  
Reynolds Stress ◽  
Time Scales ◽  
Eddy Viscosity ◽  
Ad Hoc ◽  
Stokes Equations ◽  
Transport Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Stress Models

The high-Reynolds-number turbulent flows of technological importance contain such a wide range of excited length and time scales that the application of direct or large-eddy simulations is all but impossible for the foreseeable future. Reynolds stress models remain the only viable means for the solution of these complex turbulent flows. It is widely believed that Reynolds stress models are completely ad hoc, having no formal connection with solutions of the full Navier-Stokes equations for turbulent flows. While this belief is largely warranted for the older eddy viscosity models of turbulence, it constitutes a far too pessimistic assessment of the current generation of Reynolds stress closures. It will be shown how secondorder closure models and two-equation models with an anisotropic eddy viscosity can be systematically derived from the Navier-Stokes equations when one overriding assumption is made: the turbulence is locally homogeneous and in equilibrium. A brief review of zero equation models and one equation models based on the Boussinesq eddy viscosity hypothesis will first be provided in order to gain a perspective on the earlier approaches to Reynolds stress modeling. It will, however, be argued that since turbulent flows contain length and time scales that change dramatically from one flow configuration to the next, two-equation models constitute the minimum level of closure that is physically acceptable. Typically, modeled transport equations are solved for the turbulent kinetic energy and dissipation rate from which the turbulent length and time scales are built up; this obviates the need to specify these scales in an ad hoc fashion. While two-equation models represent the minimum acceptable closure, second-order closure models constitute the most complex level of closure that is currently feasible from a computational standpoint. It will be shown how the former models follow from the latter in the equilibrium limit of homogeneous turbulence. However, the two-equation models that are formally consistent with second-order closures have an anisotropic eddy viscosity with strain-dependent coefficients - a feature that most of the commonly used models do not possess.

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.

How Turbulence Models Perform in Simulating Pipeflow Response to Targeted Wall-Shapes?

2021 ◽  
Author(s):  
Mehran Masoumifar ◽  
Suyash Verma ◽  
Arman Hemmati
Keyword(s):  
Three Dimensional ◽  
Turbulence Models ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Flow Response ◽  
High Reynolds Numbers ◽  
Flow Features ◽  
Rans Models ◽  
Response And Recovery ◽  
High Reynolds

Abstract This study evaluates how Reynolds-Averaged-Navier-Stokes (RANS) models perform in simulating the characteristics of mean three-dimensional perturbed flows in pipes with targeted wall-shapes. Capturing such flow features using turbulence models is still challenging at high Reynolds numbers. The principal objective of this investigation is to evaluate which of the well-established RANS models can best predict the flow response and recovery characteristics in perturbed pipes at moderate and high Reynolds numbers (10000-158000). First, the flow profiles at various axial locations are compared between simulations and experiments. This is followed by assessing the well-known mean pipeflow scaling relations. The good agreement between our computationally predicted data using Standard k-epsilon model and those of experiments indicated that this model can accurately capture the pipeflow characteristics in response to introduced perturbation with smooth sinusoidal axial variations.

RANS Modelling of Accelerating Boundary Layers

2013 ◽  
Author(s):  
Ugochukwu R. Oriji ◽  
Paul G. Tucker
Keyword(s):  
Boundary Layers ◽  
Eddy Viscosity ◽  
Navier Stokes ◽  
Viscosity Models ◽  
Cubic Model ◽  
Rans Models ◽  
The One ◽  
Stress Models ◽  
Reynolds Average ◽  
Laminar State

A numerical investigation of accelerated boundary layers (BL) has been performed using linear and non-linear eddy viscosity models (EVM). The acceleration parameters (KS) investigated range between 1.5×10−6 and 3.0×10−6. The one equation (k-l), Spalart Allmaras (SA) and the two-equation Menter SST and Chien models in their standard forms are found to be insensitive to acceleration. Nevertheless, proposed modifications for the SA, Chien and the k-l models significantly improved predictions. The major improvement was achieved by modifying the damping functions in these models and also an analogous source term, E, for the Chien model. Encouraging agreement with measurements is found using the Launder Sharma (LS), Cubic and Explicit Algebraic Stress Models (EASM) in their standard forms. The cubic model best predicted the turbulence quantities. Investigations confirm that it is practical for Reynolds Average Navier-Stokes (RANS) models to capture reversion from the turbulent to laminar state albeit for equilibrium sink type flows.

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