The Development of a Partially Averaged Navier-Stokes KSKL Model

2021 ◽  
Author(s):  
Maarten Klapwijk ◽  
Thomas Lloyd ◽  
Guilherme Vaz
Keyword(s):  
Kinetic Energy ◽  
Boundary Conditions ◽  
Multiphase Flow ◽  
Eddy Viscosity ◽  
Navier Stokes ◽  
New Model ◽  
Cell Height ◽  
Sst Model ◽  
Energy Ratios ◽  
Model Derivation

Abstract A new partially averaged Navier-Stokes (PANS) closure is derived based on the KSKL model. The aim of this new model is to incorporate the desirable features of the KSKL model, compared to the SST model, into the PANS framework. These features include reduced eddy-viscosity levels, a lower dependency on the cell height at the wall, well-defined boundary conditions, and improved iterative convergence. As well as the new model derivation, the paper demonstrates that these desirable features are indeed maintained, for a range of modeled-to-total turbulence kinetic energy ratios (f_k), and even for multiphase flow.

Analytical Solution of Two Gradient-Diffusion Models Applied to Turbulent Couette Flow

1984 ◽  
Vol 106 (2) ◽  
pp. 211-216 ◽  
Author(s):  
F. S. Henry ◽  
A. J. Reynolds
Keyword(s):  
Kinetic Energy ◽  
Analytical Solution ◽  
Boundary Conditions ◽  
Couette Flow ◽  
Central Region ◽  
Eddy Viscosity ◽  
Diffusion Models ◽  
Gradient Diffusion ◽  
Wall Boundary Conditions ◽  
Model Equations

Two widely used gradient-diffusion models of turbulence, when applied to fully-developed Couette flow, are shown to reduce to a set of equations that can be solved analytically. The solutions reveal that both models predict the turbulence kinetic energy to be constant across the entire central region in which the modeling is applied. The implications for the prediction of velocity and eddy viscosity are explored. It is found that the point at which the model equations are matched to the near-wall boundary conditions is an important parameter of the solution.

scholarly journals On the over-production of turbulence beneath surface waves in Reynolds-averaged Navier–Stokes models

2018 ◽  
Vol 853 ◽  
pp. 419-460 ◽  
Author(s):  
Bjarke Eltard Larsen ◽  
David R. Fuhrman
Keyword(s):  
Kinetic Energy ◽  
Surface Waves ◽  
Turbulent Kinetic Energy ◽  
Exponential Growth ◽  
Potential Flow ◽  
Eddy Viscosity ◽  
Surf Zone ◽  
Breaking Waves ◽  
Navier Stokes ◽  
Closure Models

In previous computational fluid dynamics studies of breaking waves, there has been a marked tendency to severely over-estimate turbulence levels, both pre- and post-breaking. This problem is most likely related to the previously described (though not sufficiently well recognized) conditional instability of widely used turbulence models when used to close Reynolds-averaged Navier–Stokes (RANS) equations in regions of nearly potential flow with finite strain, resulting in exponential growth of the turbulent kinetic energy and eddy viscosity. While this problem has been known for nearly 20 years, a suitable and fundamentally sound solution has yet to be developed. In this work it is demonstrated that virtually all commonly used two-equation turbulence closure models are unconditionally, rather than conditionally, unstable in such regions. A new formulation of the $k$–$\unicode[STIX]{x1D714}$ closure is developed which elegantly stabilizes the model in nearly potential flow regions, with modifications remaining passive in sheared flow regions, thus solving this long-standing problem. Computed results involving non-breaking waves demonstrate that the new stabilized closure enables nearly constant form wave propagation over long durations, avoiding the exponential growth of the eddy viscosity and inevitable wave decay exhibited by standard closures. Additional applications on breaking waves demonstrate that the new stabilized model avoids the unphysical generation of pre-breaking turbulence which widely plagues existing closures. The new model is demonstrated to be capable of predicting accurate pre- and post-breaking surface elevations, as well as turbulence and undertow velocity profiles, especially during transition from pre-breaking to the outer surf zone. Results in the inner surf zone are similar to standard closures. Similar methods for formally stabilizing other widely used closure models ($k$–$\unicode[STIX]{x1D714}$ and $k$–$\unicode[STIX]{x1D700}$ variants) are likewise developed, and it is recommended that these be utilized in future RANS simulations of surface waves. (In the above $k$ is the turbulent kinetic energy density, $\unicode[STIX]{x1D714}$ is the specific dissipation rate, and $\unicode[STIX]{x1D700}$ is the dissipation.)

scholarly journals Error Analysis of a Subgrid Eddy Viscosity Multi-Scale Discretization of the Navier-Stokes Equations

SeMA Journal ◽  
2012 ◽  
Vol 60 (1) ◽  
pp. 51-74
Author(s):  
Christine Bernardi ◽  
Tomás Chacón Rebollo ◽  
Macarena Gómez Mármol
Keyword(s):  
Error Analysis ◽  
Eddy Viscosity ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Multi Scale

scholarly journals Asymptotic analysis of an optimal control problem for a viscous incompressible fluid with Navier slip boundary conditions

2021 ◽  
pp. 1-21
Author(s):  
Claudia Gariboldi ◽  
Takéo Takahashi
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Boundary Conditions ◽  
Control Problem ◽  
Stokes System ◽  
Navier Stokes ◽  
Slip Boundary Conditions ◽  
Navier Slip ◽  
Slip Boundary ◽  
Navier Slip Boundary Conditions

We consider an optimal control problem for the Navier–Stokes system with Navier slip boundary conditions. We denote by α the friction coefficient and we analyze the asymptotic behavior of such a problem as α → ∞. More precisely, we prove that if we take an optimal control for each α, then there exists a sequence of optimal controls converging to an optimal control of the same optimal control problem for the Navier–Stokes system with the Dirichlet boundary condition. We also show the convergence of the corresponding direct and adjoint states.

Comparison of LES of Steady Transitional Flow in an Idealized Stenosed Axisymmetric Artery Model With a RANS Transitional Model

2011 ◽  
Vol 133 (5) ◽  
Author(s):  
F. P. P. Tan ◽  
N. B. Wood ◽  
G. Tabor ◽  
X. Y. Xu
Keyword(s):  
Experimental Data ◽  
Turbulence Intensity ◽  
Eddy Viscosity ◽  
Flow Analysis ◽  
Wall Turbulence ◽  
Transitional Flow ◽  
Navier Stokes ◽  
Turbulence Structures ◽  
Eddy Simulation ◽  
Accurate Treatment

In this study, two different turbulence methodologies are investigated to predict transitional flow in a 75% stenosed axisymmetric experimental arterial model and in a slightly modified version of the model with an eccentric stenosis. Large eddy simulation (LES) and Reynolds-averaged Navier–Stokes (RANS) methods were applied; in the LES simulations eddy viscosity subgrid-scale models were employed (basic and dynamic Smagorinsky) while the RANS method involved the correlation-based transitional version of the hybrid k-ε/k-ω flow model. The RANS simulations used 410,000 and 820,000 element meshes for the axisymmetric and eccentric stenoses, respectively, with y+ less than 2 viscous wall units for the boundary elements, while the LES used 1,200,000 elements with y+ less than 1. Implicit filtering was used for LES, giving an overlap between the resolved and modeled eddies, ensuring accurate treatment of near wall turbulence structures. Flow analysis was carried out in terms of vorticity and eddy viscosity magnitudes, velocity, and turbulence intensity profiles and the results were compared both with established experimental data and with available direct numerical simulations (DNSs) from the literature. The simulation results demonstrated that the dynamic Smagorinsky LES and RANS transitional model predicted fairly comparable velocity and turbulence intensity profiles with the experimental data, although the dynamic Smagorinsky model gave the best overall agreement. The present study demonstrated the power of LES methods, although they were computationally more costly, and added further evidence of the promise of the RANS transition model used here, previously tested in pulsatile flow on a similar model. Both dynamic Smagorinsky LES and the RANS model captured the complex transition phenomena under physiological Reynolds numbers in steady flow, including separation and reattachment. In this respect, LES with dynamic Smagorinsky appeared more successful than DNS in replicating the axisymmetric experimental results, although inflow conditions, which are subject to caveats, may have differed. For the eccentric stenosis, LES with Smagorinsky coefficient of 0.13 gave the closest agreement with DNS despite the known shortcomings of fixed coefficients. The relaminarization as the flow escaped the influence of the stenosis was amply demonstrated in the simulations, graphically so in the case of LES.

Parallel iterative finite-element algorithms for the Navier–Stokes equations with nonlinear slip boundary conditions

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Kangrui Zhou ◽  
Yueqiang Shang
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Parallel Algorithms ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Slip Boundary Conditions ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Parallel Iterative ◽  
Nonlinear Slip Boundary Conditions

AbstractBased on full domain partition, three parallel iterative finite-element algorithms are proposed and analyzed for the Navier–Stokes equations with nonlinear slip boundary conditions. Since the nonlinear slip boundary conditions include the subdifferential property, the variational formulation of these equations is variational inequalities of the second kind. In these parallel algorithms, each subproblem is defined on a global composite mesh that is fine with size h on its subdomain and coarse with size H (H ≫ h) far away from the subdomain, and then we can solve it in parallel with other subproblems by using an existing sequential solver without extensive recoding. All of the subproblems are nonlinear and are independently solved by three kinds of iterative methods. Compared with the corresponding serial iterative finite-element algorithms, the parallel algorithms proposed in this paper can yield an approximate solution with a comparable accuracy and a substantial decrease in computational time. Contributions of this paper are as follows: (1) new parallel algorithms based on full domain partition are proposed for the Navier–Stokes equations with nonlinear slip boundary conditions; (2) nonlinear iterative methods are studied in the parallel algorithms; (3) new theoretical results about the stability, convergence and error estimates of the developed algorithms are obtained; (4) some numerical results are given to illustrate the promise of the developed algorithms.

Profiled End-Wall Design Using an Adjoint Navier-Stokes Solver

2006 ◽  
Author(s):  
Roque Corral ◽  
Fernando Gisbert
Keyword(s):  
Kinetic Energy ◽  
Cost Function ◽  
Unstructured Mesh ◽  
Low Pressure ◽  
Navier Stokes ◽  
Low Pressure Turbine ◽  
Gradient Based ◽  
Parallel Multigrid ◽  
End Wall ◽  
Discrete Formulation

A methodology to minimize blade secondary losses by modifying turbine end-walls is presented. The optimization is addressed using a gradient-based method, where the computation of the gradient is performed using an adjoint code and the secondary kinetic energy is used as a cost function. The adjoint code is implemented on the basis of the discrete formulation of a parallel multigrid unstructured mesh Navier-Stokes solver. The results of the optimization of two end-walls of a low pressure turbine row are shown.

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