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

2021 ◽  
pp. 1-36
Author(s):  
Xiao He ◽  
Fanzhou Zhao ◽  
Mehdi Vahdati

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.

Author(s):  
Xiao He ◽  
Fanzhou Zhao ◽  
Mehdi Vahdati

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.


2020 ◽  
Vol 142 (9) ◽  
Author(s):  
Xiao He ◽  
Fanzhou Zhao ◽  
Mehdi Vahdati

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.


2013 ◽  
Vol 37 (3) ◽  
pp. 283-292 ◽  
Author(s):  
Dae-Woong Kim ◽  
Jin-Hyuk Kim ◽  
Kwang-Yong Kim

Aerodynamic performance of a transonic axial compressor with a casing groove combined with injection has been investigated in this work. Three-dimensional Reynolds-averaged Navier–Stokes equations with k-ε turbulence model are discretized by finite volume approximations and solved on hexahedral grids for the flow analyses. For parametric study, the front and rear lengths and height of the casing groove are selected as the geometric parameters and are changed with constant injection to investigate their effects on the stall margin and peak adiabatic efficiency. As a result of the parametric study, the maximum stall margin and peak adiabatic efficiency are found to be obtained in the axial compressor having 70% height of the reference groove. The results show that the application of the casing groove combined with injection to an axial compressor is effective for the simultaneous improvement of both the stall margin and peak adiabatic efficiency of the compressor.


Author(s):  
R. C. Schlaps ◽  
S. Shahpar ◽  
V. Gümmer

In order to increase the performance of a modern gas turbine, compressors are required to provide higher pressure ratio and avoid incurring higher losses. The tandem aerofoil has the potential to achieve a higher blade loading in combination with lower losses compared to single vanes. The main reason for this is due to the fact that a new boundary layer is generated on the second blade surface and the turning can be achieved with smaller separation occurring. The lift split between the two vanes with respect to the overall turning is an important design choice. In this paper an automated three-dimensional optimisation of a highly loaded compressor stator is presented. For optimisation a novel methodology based on the Multipoint Approximation Method (MAM) is used. MAM makes use of an automatic design of experiments, response surface modelling and a trust region to represent the design space. The CFD solutions are obtained with the high-fidelity 3D Navier-Stokes solver HYDRA. In order to increase the stage performance the 3D shape of the tandem vane is modified changing both the front and rear aerofoils. Moreover the relative location of the two aerofoils is controlled modifying the axial and tangential relative positions. It is shown that the novel optimisation methodology is able to cope with a large number of design parameters and produce designs which performs better than its single vane counterpart in terms of efficiency and numerical stall margin. One of the key challenges in producing an automatic optimisation process has been the automatic generation of high-fidelity computational meshes. The multi block-structured, high-fidelity meshing tool PADRAM is enhanced to cope with the tandem blade topologies. The wakes of each aerofoil is properly resolved and the interaction and the mixing of the front aerofoil wake and the second tandem vane are adequately resolved.


2014 ◽  
Vol 136 (6) ◽  
Author(s):  
B. A. Younis ◽  
A. Abrishamchi

The paper reports on the prediction of the turbulent flow field around a three-dimensional, surface mounted, square-sectioned cylinder at Reynolds numbers in the range 104–105. The effects of turbulence are accounted for in two different ways: by performing large-eddy simulations (LES) with a Smagorinsky model for the subgrid-scale motions and by solving the unsteady form of the Reynolds-averaged Navier–Stokes equations (URANS) together with a turbulence model to determine the resulting Reynolds stresses. The turbulence model used is a two-equation, eddy-viscosity closure that incorporates a term designed to account for the interactions between the organized mean-flow periodicity and the random turbulent motions. Comparisons with experimental data show that the two approaches yield results that are generally comparable and in good accord with the experimental data. The main conclusion of this work is that the URANS approach, which is considerably less demanding in terms of computer resources than LES, can reliably be used for the prediction of unsteady separated flows provided that the effects of organized mean-flow unsteadiness on the turbulence are properly accounted for in the turbulence model.


Author(s):  
Fahua Gu ◽  
Mark R. Anderson

The design of turbomachinery has been focusing on the improvement of the machine efficiency and the reduction of the design cost. This paper presents an integrated design system to create the machine geometry and to predict the machine performance at different levels of approximation, including one-dimensional design and analysis, quasi-three-dimensional-(blade-to-blade, throughflow) and full-three-dimensional-steady-state CFD analysis. One of the most important components, the Reynolds-averaged Navier-Stokes solver, is described in detail. It originated from the Dawes solver with numerous enhancements. They include the use of the low speed pre-conditioned full Navier-Stokes equations, the addition of the Spalart-Allmaras turbulence model and an improvement of wall functions related with the turbulence model. The latest upwind scheme, AUSM, has been implemented too. The Dawes code has been rewritten into a multi-block solver for O, C, and H grids. This paper provides some examples to evaluate the effect of grid topology on the machine performance prediction.


Author(s):  
Robert P. Dring ◽  
William D. Sprout ◽  
Harris D. Weingold

A three-dimensional Navier-Stokes calculation was used to analyze the impact of rotor tip clearance on the stall margin of a multi-stage axial compressor. This paper presents a summary of: (1) a study of the sensitivity of the results to grid refinement, (2) an assessment of the calculation’s ability to predict stall margin when the stalling row was the first rotor in a multi-stage rig environment, (3) an analysis of the impact of including the effects of the downstream stator through body force effects on the upstream rotor, and (4) the ability of the calculation to predict the impact of tip clearance on stall margin through a calculation of the rear seven airfoil rows of an eleven stage high pressure compressor rig. The result of these studies was that a practical tool is available which can predict stall margin, and the impact of tip clearance, with reasonable accuracy.


1992 ◽  
Vol 114 (3) ◽  
pp. 627-642 ◽  
Author(s):  
R. F. Kunz ◽  
B. Lakshminarayana

An explicit, three-dimensional, coupled Navier–Stokes/k–ε technique has been developed and successfully applied to complex internal flow calculations. Several features of the procedure, which enable convergent and accurate calculation of high Reynolds number two-dimensional cascade flows, have been extended to three dimensions, including a low Reynolds number compressible form of the k–ε turbulence model, local time-step specification based on hyperbolic and parabolic stability requirements, and eigenvalue and local velocity scaling of artificial dissipation operators. A flux evaluation procedure, which eliminates the finite difference metric singularity at leading and trailing edges on H- and C-grids, is presented. The code is used to predict the pressure distribution, primary velocity, and secondary flows in an incompressible, turbulent curved duct flow for which CFD validation quality data are available. Also, a subsonic compressor rotor passage, for which detailed laser, rotating hot-wire, and five-hole pressure probe measurements have been made is computed. Detailed comparisons between predicted and measured core flow and near-wall velocity profiles, wake profiles, and spanwise mixing effects downstream of the rotor passage are presented for this case. It is found that the technique provides accurate and convergent engineering simulation of these complex turbulent flows.


1995 ◽  
Vol 39 (04) ◽  
pp. 263-283 ◽  
Author(s):  
F. Sotiropoulos ◽  
V. C. Patel

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.


Author(s):  
Mehran Masoumifar ◽  
Suyash Verma ◽  
Arman Hemmati

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.


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