Calibration of an extended Eddy Viscosity Turbulence Model using Uncertainty Quantification

This paper is concerned with the propagation of uncertainties in the values of turbulence model coefficients and parameters in turbulent flows. These coefficients and parameters are determined from experiments performed on elementary flows and they are subject to uncertainty. The widely used k–ε turbulence model is considered. It consists of model transport equations for the turbulence kinetic energy and rate of turbulent dissipation. Both equations involve various model coefficients about which adequate knowledge is assumed known in the form of probability density functions. The study is carried out for the flow over a 2D backward-facing step configuration. The Latin Hypercube Sampling method is employed for the uncertainty quantification purposes as it requires a smaller number of samples compared to the conventional Monte-Carlo method. The mean values are reported for the flow output parameters of interest along with their associated uncertainties. The results show that model coefficient variability has significant effects on the streamwise velocity component in the recirculation region near the reattachment point and turbulence intensity along the free shear layer. The reattachment point location, pressure, and wall shear are also significantly affected.

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Temperature Corrected Turbulence Model for High Temperature Jet Flow

Journal of Fluids Engineering ◽

10.1115/1.1792266 ◽

2004 ◽

Vol 126 (5) ◽

pp. 844-850 ◽

Cited By ~ 35

Author(s):

Khaled S. Abdol-Hamid ◽

S. Paul Pao ◽

Steven J. Massey ◽

Alaa Elmiligui

Keyword(s):

High Temperature ◽

Turbulence Model ◽

Room Temperature ◽

Eddy Viscosity ◽

Mixing Layer ◽

Supersonic Jet ◽

Turbulence Models ◽

Jet Flows ◽

Viscosity Term ◽

Mixing Layer Flows

It is well known that the two-equation turbulence models under-predict mixing in the shear layer for high temperature jet flows. These turbulence models were developed and calibrated for room temperature, low Mach number, and plane mixing layer flows. In the present study, four existing modifications to the two-equation turbulence model are implemented in PAB3D and their effect is assessed for high temperature jet flows. In addition, a new temperature gradient correction to the eddy viscosity term is tested and calibrated. The new model was found to be in the best agreement with experimental data for subsonic and supersonic jet flows at both low and high temperatures.

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Modeling Reichardt’s Formula for Eddy-Viscosity in the Fluid Film of Tilting Pad Thrust Bearings

Volume 7: Fluids Engineering ◽

10.1115/imece2017-71749 ◽

2017 ◽

Author(s):

Xin Deng ◽

Brian Weaver ◽

Cori Watson ◽

Michael Branagan ◽

Houston Wood ◽

...

Keyword(s):

Shear Stress ◽

Wall Shear Stress ◽

Turbulence Model ◽

High Speed ◽

Eddy Viscosity ◽

The Other ◽

Fluid Film ◽

Suitable Model ◽

Velocity Gradients ◽

Wall Shear

Oil-lubricated bearings are widely used in high speed rotating machines such as those used in the aerospace and automotive industries that often require this type of lubrication. However, environmental issues and risk-adverse operations have made water lubricated bearings increasingly popular. Due to different viscosity properties between oil and water, the low viscosity of water increases Reynolds numbers drastically and therefore makes water-lubricated bearings prone to turbulence effects. The turbulence model is affected by eddy-viscosity, while eddy-viscosity depends on wall shear stress. Therefore, effective wall shear stress modeling is necessary in producing an accurate turbulence model. Improving the accuracy and efficiency of methodologies of modeling eddy-viscosity in the turbulence model is important, especially considering the increasingly popular application of water-lubricated bearings and also the traditional oil-lubricated bearings in high speed machinery. This purpose of this paper is to study the sensitivity of using different methodologies of solving eddy-viscosity for turbulence modeling. Eddy-viscosity together with flow viscosity form the effective viscosity, which is the coefficient of the shear stress in the film. The turbulence model and Reynolds equation are bound together to solve when hydrodynamic analysis is performed, therefore improving the accuracy of the turbulence model is also vital to improving a bearing model’s ability to predict film pressure values, which will determine the velocity and velocity gradients in the film. The velocity gradients in the film are the other term determining the shear stress. In this paper, three approaches applying Reichardt’s formula were used to model eddy-viscosity in the fluid film. These methods are for determining where one wall’s effects begin and the other wall’s effects end. Trying to find a suitable model to capture the wall’s effects of these bearings, with aim to improve the accuracy of the turbulence model, would be of high value to the bearing industry. The results of this study could aid in improving future designs and models of both oil and water lubricated bearings.

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Development and Initial Validation of a Two-Equation Transition Sensitive Turbulence Model for CFD Simulations

Fluids Engineering ◽

10.1115/imece2006-14956 ◽

2006 ◽

Author(s):

J. M. Jones ◽

D. K. Walters

Keyword(s):

Boundary Layer ◽

Turbulence Model ◽

Eddy Viscosity ◽

Flow Behavior ◽

Boundary Layer Separation ◽

Transitional Flow ◽

Model Framework ◽

Modeling Framework ◽

Initial Development ◽

New Model

This paper presents the initial development and validation of a modified two-equation eddy-viscosity turbulence model for computational fluid dynamics (CFD) prediction of transitional and turbulent flow. The new model is based on a k-ω model framework, making it more easily implemented into existing general-purpose CFD solvers than other recently proposed model forms. The model incorporates inviscid and viscous damping functions for the eddy viscosity, as well as a production damping term, in order to reproduce the appropriate effects of laminar, transitional, and turbulent boundary layer flow. It has been implemented into a commercially available flow solver (FLUENT) and evaluated for simple attached and separated flow conditions, including 2-D flow over a flat plate and a circular cylinder. The results presented show that the new model is able to yield reasonable predictions of transitional flow behavior using a very simple modeling framework, including an appropriate response to freestream turbulence and boundary layer separation.

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Uncertainty Quantification of Turbulence Model Coefficients via Latin Hypercube Sampling Method

Journal of Fluids Engineering ◽

10.1115/1.4003762 ◽

2011 ◽

Vol 133 (4) ◽

Cited By ~ 20

Author(s):

Matthew C. Dunn ◽

Babak Shotorban ◽

Abdelkader Frendi

Keyword(s):

Uncertainty Quantification ◽

Turbulent Flows ◽

Turbulence Model ◽

Sampling Method ◽

Latin Hypercube Sampling ◽

Recirculation Region ◽

Free Shear Layer ◽

Latin Hypercube ◽

Reattachment Point ◽

Mean Velocity

The article is concerned with the propagation of uncertainties in the values of turbulence model coefficients and parameters in turbulent flows. These coefficients and parameters are obtained through experiments performed on elementary flows, and they are subject to uncertainty. In this work, the widely used k-ɛ turbulence model is considered. It consists of model transport equations for the turbulence kinetic energy and the rate of turbulent dissipation. Both equations involve various model coefficients about which adequate knowledge is assumed known in the form of probability density functions. The study is carried out for a flow over a 2D backward-facing step configuration. The Latin Hypercube Sampling method is employed for the uncertainty quantification purposes as it requires a smaller number of samples compared to the conventional Monte Carlo method. The mean values are reported for the flow output parameters of interest along with their associated uncertainties. The results show that model coefficient variability has significant effects on the streamwise mean velocity in the recirculation region near the reattachment point and turbulence intensity along the free shear layer. The reattachment point location, pressure, and wall shear are also significantly influenced by the uncertainties of the coefficients.

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Flow Analyses in a Single-Stage Propulsion Pump

Journal of Turbomachinery ◽

10.1115/1.2836631 ◽

1996 ◽

Vol 118 (2) ◽

pp. 240-248 ◽

Cited By ~ 8

Author(s):

Y. T. Lee ◽

C. Hah ◽

J. Loellbach

Keyword(s):

Boundary Layer ◽

Numerical Method ◽

Turbulence Model ◽

Eddy Viscosity ◽

Single Stage ◽

Acoustic Properties ◽

Turbulent Eddy ◽

Trailing Edge ◽

Local Flow ◽

Blade Row

Steady-state analyses of the incompressible flow past a single-stage stator/rotor propulsion pump are presented and compared to experimental data. The purpose of the current study is to validate a numerical method for the design application of a typical propulsion pump and for the acoustic analysis based on predicted flowfields. A steady multiple-blade-row approach is used to calculate the flowfields of the stator and the rotor. The numerical method is based on a fully conservative control-volume technique. The Reynolds-averaged Navier–Stokes equations are solved along with the standard two-equation k–ε turbulence model. Numerical results for both mean flow and acoustic properties compare well with measurements in the wake of each blade row. The rotor blade has a thick boundary layer in the last quarter of the chord and the flow separates near the trailing edge. These features invalidate many Euler prediction results. Due to the dramatic reduction of the turbulent eddy viscosity in the thick boundary layer, the standard k–ε model cannot predict the correct local flow characteristics near the rotor trailing edge and in its near wake. Thus, a modification of the turbulence length scale in the turbulence model is applied in the thick boundary layer in response to the reduction of the turbulent eddy viscosity.

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