Manufactured Solutions for the Favre-Averaged Navier-Stokes Equations with Eddy-Viscosity Turbulence Models

AbstractIn this paper, we performed a comparison of four turbulence models using for numerical simulation of the hydrodynamic structure generated by a Rushton turbine in a cylindrical tank. The finite volume method was employed to solve the Navier-Stokes equations governing the transport of momentum. In this study four closure models tested were: k-ɛ standard, k-ɛ RNG, k-ɛ Realizable and RSM (Reynolds Stress Model). MRF (Multi Reference Frame) technique was used with FLUENT software package. The present work aimed to provide improved predictions of turbulent flow in a stirred vessel and in particular to assess the ability to predict the dissipation rate of turbulent kinetic energy (e) that constitutes a most stringent test of prediction capability due to the small scales at which dissipation takes place. The amplitude of local and overall dissipation rate is shown to be strongly dependent on the choice of turbulence model. The numerical predictions were compared with literature results for comparable configurations and with experimental data obtained using Particle Image Velocimetry (PIV). A very good agreement was found with regards to turbulence.

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Viscous Flow Calculations in Turbomachinery Channels

Volume 1: Turbomachinery ◽

10.1115/89-gt-5 ◽

1989 ◽

Author(s):

Francesco Martelli ◽

Vittorio Michelassi

Keyword(s):

Stokes Equations ◽

Turbulent Viscosity ◽

Axisymmetric Flow ◽

Turbulence Models ◽

Navier Stokes ◽

Algebraic Expression ◽

Two Dimensional ◽

Approximate Factorization ◽

Navier Stokes Equations ◽

Flow Configurations

An implicit procedure based on the artificial compressibility formulation is presented for the numerical solution of the two-dimensional incompressible steady Navier-Stokes equations in the presence of large separated regions. Turbulence effects are accounted for by the Chien low Reynolds number form of the K-ε turbulence model and the Baldwin-Lomax algebraic expression for turbulent viscosity. The governing equations are written in conservative form and implicitly solved in fully coupled form using the approximate factorization technique. Preliminary tests were carried out in a laminar flow regime to check the accuracy and stability of the method in two-dimensional and cylindrical axisymmetric flow configurations. After testing in laminar and turbulent flow regimes and comparing the two turbulence models, the code was successfully applied to an actual gas turbine diffuser at low Mach numbers.

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Enhanced Physics-Based Numerical Schemes for Two Classes of Turbulence Models

Advances in Numerical Analysis ◽

10.1155/2009/370289 ◽

2009 ◽

Vol 2009 ◽

pp. 1-13

Author(s):

Leo G. Rebholz

Keyword(s):

Finite Element ◽

Differential Operator ◽

Stokes Equations ◽

Turbulence Models ◽

Navier Stokes ◽

Numerical Schemes ◽

Discrete Laplacian ◽

Navier Stokes Equations ◽

Approximate Deconvolution ◽

Finite Element Schemes

We present enhanced physics-based finite element schemes for two families of turbulence models, the models and the Stolz-Adams approximate deconvolution models. These schemes are delicate extensions of a method created for the Navier-Stokes equations in Rebholz (2007), that achieve high physical fidelity by admitting balances of both energy and helicity that match the true physics. The schemes' development requires carefully chosen discrete curl, discrete Laplacian, and discrete filtering operators, in order to permit the necessary differential operator commutations.

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Multigrid Computation of Incompressible Flows Using Two-Equation Turbulence Models: Part II—Applications

Journal of Fluids Engineering ◽

10.1115/1.2819514 ◽

1997 ◽

Vol 119 (4) ◽

pp. 900-905 ◽

Cited By ~ 4

Author(s):

X. Zheng ◽

C. Liao ◽

C. Liu ◽

C. H. Sung ◽

T. T. Huang

Keyword(s):

Turbulent Flows ◽

Incompressible Flows ◽

Stokes Equations ◽

Three Dimensional ◽

Turbulence Models ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Time Stepping ◽

Grid Algorithm ◽

High Reynolds

In this paper, computational results are presented for three-dimensional high-Reynolds number turbulent flows over a simplified submarine model. The simulation is based on the solution of Reynolds-Averaged Navier-Stokes equations and two-equation turbulence models by using a preconditioned time-stepping approach. A multiblock method, in which the block loop is placed in the inner cycle of a multi-grid algorithm, is used to obtain versatility and efficiency. It was found that the calculated body drag, lift, side force coefficients and moments at various angles of attack or angles of drift are in excellent agreement with experimental data. Fast convergence has been achieved for all the cases with large angles of attack and with modest drift angles.

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Low-speed preconditioning for strongly coupled integration of Reynolds-averaged Navier–Stokes equations and two-equation turbulence models

Aerospace Science and Technology ◽

10.1016/j.ast.2018.03.015 ◽

2018 ◽

Vol 77 ◽

pp. 286-298 ◽

Cited By ~ 9

Author(s):

M.S. Campobasso ◽

M. Yan ◽

A. Bonfiglioli ◽

F.A. Gigante ◽

L. Ferrari ◽

...

Keyword(s):

Stokes Equations ◽

Turbulence Models ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Strongly Coupled ◽

Low Speed ◽

Reynolds Averaged Navier Stokes

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Computational Analysis of a Inverted Double-Element Airfoil in Ground Effect

Journal of Fluids Engineering ◽

10.1115/1.2353268 ◽

2006 ◽

Vol 128 (6) ◽

pp. 1172-1180 ◽

Cited By ~ 19

Author(s):

Stephen Mahon ◽

Xin Zhang

Keyword(s):

Flow Field ◽

Stokes Equations ◽

Near Field ◽

Turbulence Models ◽

Ground Effect ◽

Wake Flow ◽

Navier Stokes ◽

Main Element ◽

Ride Height ◽

Navier Stokes Equations

The flow around an inverted double-element airfoil in ground effect was studied numerically, by solving the Reynolds averaged Navier-Stokes equations. The predictive capabilities of six turbulence models with regards to the surface pressures, wake flow field, and sectional forces were quantified. The realizable k−ε model was found to offer improved predictions of the surface pressures and wake flow field. A number of ride heights were investigated, covering various force regions. The surface pressures, sectional forces, and wake flow field were all modeled accurately and offered improvements over previous numerical investigations. The sectional forces indicated that the main element generated the majority of the downforce, whereas the flap generated the majority of the drag. The near field and far field wake development was investigated and suggestions concerning reduction of the wake thickness were offered. The main element wake was found to greatly contribute to the overall wake thickness with the contribution increasing as the ride height decreased.

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Conical turbulent swirling vortex with variable eddy viscosity

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1986.0011 ◽

1986 ◽

Vol 403 (1825) ◽

pp. 235-268 ◽

Cited By ~ 3

Keyword(s):

Eddy Viscosity ◽

Stokes Equations ◽

Variable Viscosity ◽

Similarity Solutions ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Turbulent Vortex ◽

The Core ◽

Vortex Solutions ◽

Variable Eddy Viscosity

In the one hundred years since Rankine suggested his well known two-dimensional vortex model with finite core, no one has ever found any exact vortex solutions of the Navier-Stokes equations that can satisfy a complete set of physical boundary conditions. In this paper a variable viscosity is introduced and the existence of conical turbulent vortex solutions of the Navier-Stokes equations is examined. It is found that for a class of deliberately chosen eddy viscosity function a steady turbulent vortex can, for the first time, satisfy both the regularity condition at the core and the adherence condition at the surface, except for a singularity at the origin inherent in all conical similarity solutions. In its asymptotic form, if the eddy viscosity only varies in a boundary layer near the surface or the core, outside the layer the solution given would approach one of the laminar solutions of Yih et al . ( Physics Fluids 25, 2147 (1982)) or that of Serrin ( Phil. Trans. R. Soc. Lond. A 271, 325 (1972)) respectively. These results reveal some remarkable relations between the behaviour, and even the existence, of a vortex and turbulence.

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Strongly Coupled Fluid-Structure Interactions via a New Navier-Stokes Method for Prediction of Vortex-Induced Vibrations

24th International Conference on Offshore Mechanics and Arctic Engineering: Volume 3 ◽

10.1115/omae2005-67352 ◽

2005 ◽

Author(s):

Yannis Kallinderis ◽

Hyung Taek Ahn

Keyword(s):

Stokes Equations ◽

Computational Cost ◽

Three Dimensional ◽

Turbulence Models ◽

Design Tool ◽

Navier Stokes ◽

Time Step ◽

Navier Stokes Equations ◽

Vortex Induced Vibrations ◽

Offshore Industry

Numerical prediction of vortex-induced vibrations requires employment of the unsteady Navier-Stokes equations. Current Navier-Stokes solvers are quite expensive for three-dimensional flow-structure applications. Acceptance of Computational Fluid Dynamics as a design tool for the offshore industry requires improvements to current CFD methods in order to address the following important issues: (i) stability and computation cost of the numerical simulation process, (ii) restriction on the size of the allowable time-step due to the coupling of the flow and structure solution processes, (iii) excessive number of computational elements for 3-D applications, and (iv) accuracy and computational cost of turbulence models used for high Reynolds number flow. The above four problems are addressed via a new numerical method which employs strong coupling between the flow and the structure solutions. Special coupling is also employed between the Reynolds-averaged Navier-Stokes equations and the Spalart-Allmaras turbulence model. An element-type independent spatial discretization scheme is also presented which can handle general hybrid meshes consisting of hexahedra, prisms, pyramids, and tetrahedral.

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Validation of atmospheric boundary layer turbulence model by on-site measurements

Thermal Science ◽

10.2298/tsci1001199s ◽

2010 ◽

Vol 14 (1) ◽

pp. 199-207 ◽

Cited By ~ 1

Author(s):

Zarko Stevanovic ◽

Nikola Mirkov ◽

Zana Stevanovic ◽

Andrijana Stojanovic

Keyword(s):

Boundary Layer ◽

Atmospheric Boundary Layer ◽

Linear Models ◽

Stokes Equations ◽

Turbulence Models ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Boundary Layer Turbulence ◽

Askervein Hill ◽

Neutral Conditions

Modeling atmosperic boundary layer with standard linear models does not sufficiently reproduce wind conditions in complex terrain, especially on leeward sides of terrain slopes. More complex models, based on Reynolds averaged Navier-Stokes equations and two-equation k-? turbulence models for neutral conditions in atmospheric boundary layer, written in general curvilinear non-orthogonal co-ordinate system, have been evaluated. In order to quantify the differences and level of accuracy of different turbulence models, investigation has been performed using standard k-? model without additional production terms and k-? turbulence models with modified set of model coefficients. The sets of full conservation equations are numerically solved by computational fluid dynamics technique. Numerical calculations of turbulence models are compared to the reference experimental data of Askervein hill measurements.

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