Uncertainty Quantification of Spalart–Allmaras Turbulence Model Coefficients for Simplified Compressor Flow Features

2020 ◽  
Vol 142 (9) ◽  
Author(s):  
Xiao He ◽  
Fanzhou Zhao ◽  
Mehdi Vahdati
Keyword(s):  
Turbulence Model ◽  
Parametric Uncertainty ◽  
Navier Stokes ◽  
Stress Profile ◽  
Complex Flow ◽  
Flow Solver ◽  
Uniform Distributions ◽  
Flow Features ◽  
Artificial Neural Network Ann ◽  
Quantities Of Interest

Abstract Turbulence model in Reynolds-averaged Navier–Stokes (RANS) simulations has a crucial effect on predicting the compressor flows. In this paper, the parametric uncertainty of the Spalart–Allmaras (SA) turbulence model is studied in simplified two-dimensional (2D) flows, which includes some of the compressor tip flow features. The uncertainty is quantified by a metamodel-based Monte Carlo method. The model coefficients are represented by uniform distributions within intervals, and the quantities of interest include the velocity profile, the Reynolds stress profile, the shock front, and the separation size. An artificial neural network (ANN) is applied as the metamodel, which is tuned, trained, and tested using databases from the flow solver. The uncertainty of quantities of interest is determined by the range of the metamodel and the database samples from the flow solver. The sensitivity of the model coefficients is quantified by calculating the gradient of quantities of interest from the metamodel. Results show that the high-fidelity data of the quantities of interest cannot be fully enveloped by the uncertainty band in regions with separation and shock. Crucial model coefficients on the quantities of interest are identified. However, recalibration of these coefficients results in contradictory prediction of different quantities of interest across flow regimes, which indicates the need for a modified Spalart–Allmaras turbulence model form to improve the accuracy in predicting complex flow features.

Uncertainty Quantification of Spalart-Allmaras Turbulence Model Coefficients for Compressor Stall

2020 ◽  
Author(s):  
Xiao He ◽  
Fanzhou Zhao ◽  
Mehdi Vahdati
Keyword(s):  
Turbulence Model ◽  
Three Dimensional ◽  
Parametric Uncertainty ◽  
Sensitivity Analyses ◽  
Navier Stokes ◽  
Specific Flow ◽  
Stall Margin ◽  
Uncertainty Range ◽  
Uniform Distributions ◽  
Flow Features

Abstract The turbulence model in Reynolds-Averaged Navier-Stokes simulations is crucial in the prediction of the compressor stall margin. In this paper, parametric uncertainty of the Spalart-Allmaras turbulence model in predicting two-dimensional airfoil stall and three-dimensional compressor stall has been investigated using a metamodel-based Monte Carlo method. The model coefficients are represented by uniform distributions within physically acceptable ranges. The quantities of interest include characteristic curves, stall limit, blockage size and turbulence magnitude. Results show that the characteristics can be well predicted in the stable flow range, but the inaccuracy and the uncertainty increase when approaching stall. The stall point of the airfoil can be enveloped by the parametric uncertainty range, but that of the rotor cannot. Sensitivity analyses identified the crucial model coefficients to be source-related, where an increase in the predicted turbulence level will delay the onset of stall. Such results imply that implementing new turbulence production terms with respect to the rotor-specific flow features is likely to improve the model accuracy. The findings in this paper not only provide engineering rules of thumb for the model users, but also guide the future implementation of a data-driven turbulence model for the model developers.

Uncertainty Quantification of Spalart-Allmaras Turbulence Model Coefficients for Compressor Stall

2021 ◽  
pp. 1-36
Author(s):  
Xiao He ◽  
Fanzhou Zhao ◽  
Mehdi Vahdati
Keyword(s):  
Turbulence Model ◽  
Three Dimensional ◽  
Parametric Uncertainty ◽  
Sensitivity Analyses ◽  
Navier Stokes ◽  
Specific Flow ◽  
Stall Margin ◽  
Uncertainty Range ◽  
Uniform Distributions ◽  
Flow Features

Abstract The turbulence model in Reynolds-Averaged Navier-Stokes simulations is crucial in the prediction of the compressor stall margin. In this paper, parametric uncertainty of the Spalart-Allmaras turbulence model in predicting two-dimensional airfoil stall and three-dimensional compressor stall has been investigated using a metamodel-based Monte Carlo method. The model coefficients are represented by uniform distributions within physically acceptable ranges. The quantities of interest include characteristic curves, stall limit, blockage size and turbulence magnitude. Results show that the characteristics can be well predicted in the stable flow range, but the inaccuracy and the uncertainty increase when approaching stall. The stall point of the airfoil can be enveloped by the parametric uncertainty range, but that of the rotor cannot. Sensitivity analyses identified the crucial model coefficients to be source-related, where an increase in the predicted turbulence level will delay the onset of stall. Such results imply that implementing new turbulence production terms with respect to the rotor-specific flow features is likely to improve the model accuracy. The findings in this paper not only provide engineering rules of thumb for the model users, but also guide the future implementation of a data-driven turbulence model for the model developers.

Particle Trajectory Study in Submerged Flows With Baffles Using ν2¯−f and k−ε Turbulence Models

2010 ◽  
Vol 132 (5) ◽  
Author(s):  
A. Mehdizadeh ◽  
B. Firoozabadi ◽  
S. A. Sherif
Keyword(s):  
Turbulence Model ◽  
Turbulence Models ◽  
Navier Stokes ◽  
Test Case ◽  
Complex Flow ◽  
Two Phase ◽  
Erosion And Deposition ◽  
Flow Features ◽  
Elliptic Relaxation ◽  
Surface Jet

In this paper, the structure of a wall jet deflected by a baffle along with the trajectory of particles has been studied. This baffle is used to produce a stable deflected surface jet, thereby deflecting the high-velocity supercritical stream away from the bed to the surface. An elliptic relaxation turbulence model (ν2¯−f model) has been used to simulate this submerged flow. In recent years, the ν2¯−f turbulence model has become increasingly popular due to its ability to account for near-wall damping without use of damping functions. In addition, it has been proven that the ν2¯−f model is superior to other Reynolds-averaged Navier-Stokes (RANS) methods in many flows where complex flow features are present. In this study, we compare the results of the ν2¯−f model with available experimental data. Since erosion and deposition are coupled, the study of this problem should consider both of these phenomena using a proper approach. In addition to erosion over the bed, the trajectory of the particles is examined using a Lagrangian–Eulerian approach, the distribution of deposited particles over the bed is predicted for a two-phase test case based on a series of numerical simulations. Results show that the maximum erosion happens in a place in which no particle can be deposited, which causes the bed to deform very rapidly in that region. This should help prevent or reduce erosion over the bed. On the other hand, the study will help predict the trajectory of particles and the deposition rates at any section of the channel, and should thus provide useful information to control the erosion and deposition on the channel bed.

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.

scholarly journals Numerical Calculations of a Turbine Volute Using a 3-D Navier-Stokes Solver

1996 ◽  
Author(s):  
R. F. Martinez-Botas ◽  
K. R. Pullen ◽  
F. Shi
Keyword(s):  
Three Dimensional ◽  
Circular Cross Section ◽  
Staggered Grid ◽  
Navier Stokes ◽  
Complex Flow ◽  
Numerical Predictions ◽  
Flow Features ◽  
Simplec Algorithm ◽  
Complicated Geometry ◽  
High Reynolds

The turbine volute is a complex flow device, about which a few papers on both measurements and CFD predictions have appeared. The main reasons for the difficulties being the complicated geometry which hinders measurements to be taken by both intrusive and non-intrusive techniques, and makes the numerical predictions difficult. In this paper, the complex three-dimensional flow through a turbine volute with non-symmetric circular cross-section is studied by using a 3-D Navier-Stokes solver which has been developed by the authors. In this solver, the fully 3-D Reynolds averaged N-S equations coupled with high Reynolds number k-ε turbulence model together with the wall function under arbitrary curvilinear coordinate system are solved. The Semi-Implicit Method for Pressure-Linked Equations (SIMPLEC algorithm) with the non-staggered grid arrangement is used. In order to eliminate the decoupling between the velocity and pressure under non-staggered grid system, the physical covariant velocity component is selected as dependent variable in momentum equations and a momentum interpolation approach is employed. The validity of the free-vortex assumption is reviewed. The computation results are compared with a set of experiments performed previously by one of the authors. The flow features in the volute are discussed.

Investigation of Incompressible Flow Past Two Circular Cylinders of Different Diameters

2017 ◽  
Vol 67 (5) ◽  
pp. 487
Author(s):  
Yogesh Bhumkar ◽  
Priyank Kumar ◽  
Arnab Roy ◽  
Sudip Das ◽  
Jai Kumar Prasad
Keyword(s):  
Reynolds Number ◽  
Flow Field ◽  
Circular Cylinders ◽  
Navier Stokes ◽  
Complex Flow ◽  
Convective Boundary ◽  
Flow Past ◽  
Flow Features ◽  
Finite Volume Approach ◽  
Different Diameters

<p>A two - dimensional Navier-Stokes solver based on finite volume approach using a boundary-fitted curvilinear structured O-grid has been developed to obtain details of unconfined flow past cylinders at low Reynolds number of 100 and 200 based on diameter. Computations made on a single cylinder with smaller domain adopting the convective boundary conditions captured most of the flow features. This concept of a smaller domain, when used to capture the highly complex flow field around two cylinders of the same diameter placed in tandem at a Reynolds number of 200 showed reasonable results. The details of the flow field around two cylinders of different diameters placed at a typical distance of 3L and Reynolds number of 100 could be well captured adopting smaller domain concept. It is observed that the change in diameter of upstream cylinder strongly influences the overall flow field and the drag of the downstream cylinder.</p>

Assessment of the Reliability of Two-Equation URANS Models in Predicting a Precessing Flow

2019 ◽  
Vol 141 (7) ◽  
Author(s):  
Xiao Chen ◽  
Zhao F. Tian ◽  
G. J. Nathan
Keyword(s):  
Velocity Field ◽  
Navier Stokes ◽  
Field Energy ◽  
Complex Flow ◽  
Systematic Assessment ◽  
Sst Model ◽  
Flow Features ◽  
Velocity Decay ◽  
Flow Through ◽  
Good Agreement

A systematic assessment of unsteady Reynolds-averaged Navier–Stokes (URANS) models in predicting the complex flow through a suddenly expanding axisymmetric chamber is reported. Five types of URANS models assessed in the study comprise the standard k–ε model, the modified k–ε (1.6) model, the modified k–ε (1.3) model, the renormalization group (RNG) k–ε model, and the shear stress transport (SST) model. To assess the strengths and limitations of these models in predicting the velocity field of this precessing flow, the numerical results are assessed against available experimental results. Good agreement with the flow features and reasonable agreement with the measured phase-averaged velocity field, energy of total fluctuation and precession frequency can be achieved with both the standard k–ε and the SST models. The degree of accuracy in predicting the rate of both spreading and velocity decay of the jet was found to greatly influence the prediction of the precession motion.

scholarly journals Simulation of Film-Cooling Aerodynamics With a 2D Navier-Stokes Solver Using Unstructured Meshes

1995 ◽  
Author(s):  
Stefan Irmisch
Keyword(s):  
Film Cooling ◽  
Stokes Equations ◽  
Steady State Solution ◽  
Unstructured Meshes ◽  
Navier Stokes ◽  
Strong Interactions ◽  
Complex Flow ◽  
Navier Stokes Equations ◽  
Outer Flow ◽  
Flow Features

This paper describes the application of an unstructured mesh, solution-adaptive, 2D Navier-Stokes solver to the numerical simulation of the flow through film-cooled turbine cascades. The Navier-Stokes equations are solved using a cell-vertex explicit finite-volume method. Integration in time, to a steady-state solution, is performed by a five-stage Runge-Kutta algorithm. Turbulence effects are accounted for by a k-ε model. The use of unstructured meshes, based on Delaunay triangulation, allows to mesh the entire flow domain, including internal coolant passages, without any geometrical limitations. In combination with a solution-dependent mesh-adaption technique, the strong interactions between coolant and outer flow, leading to complex flow features, can be simulated in a realistic and efficient way. Solutions are presented for several test cases with and without film-cooling and are compared with experimental data, illustrating the capabilities of the presented flow solver.

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