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.

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.

scholarly journals An analytical verification test for numerically simulated convective flow above a thermally heterogeneous surface

2015 ◽  
Vol 8 (6) ◽  
pp. 1809-1819 ◽  
Author(s):  
A. Shapiro ◽  
E. Fedorovich ◽  
J. A. Gibbs
Keyword(s):  
Analytical Solution ◽  
Boundary Conditions ◽  
Numerical Algorithms ◽  
Boussinesq Equations ◽  
Thermal Forcing ◽  
Pressure Poisson Equation ◽  
Wall Boundary ◽  
Wall Boundary Conditions ◽  
Buoyancy Driven Flows ◽  
Boussinesq Fluid

Abstract. An analytical solution of the Boussinesq equations for the motion of a viscous stably stratified fluid driven by a surface thermal forcing with large horizontal gradients (step changes) is obtained. This analytical solution is one of the few available for wall-bounded buoyancy-driven flows. The solution can be used to verify that computer codes for Boussinesq fluid system simulations are free of errors in formulation of wall boundary conditions and to evaluate the relative performances of competing numerical algorithms. Because the solution pertains to flows driven by a surface thermal forcing, one of its main applications may be for testing the no-slip, impermeable wall boundary conditions for the pressure Poisson equation. Examples of such tests are presented.

scholarly journals Effect of Wall Boundary Conditions on a Wall-Modeled Large-Eddy Simulation in a Finite-Difference Framework

Fluids ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 112
Author(s):  
H. Jane Bae ◽  
Adrián Lozano-Durán
Keyword(s):  
Boundary Condition ◽  
Large Eddy Simulation ◽  
Boundary Conditions ◽  
Eddy Viscosity ◽  
Grid Point ◽  
Eddy Simulation ◽  
Wall Boundary ◽  
Wall Boundary Conditions ◽  
Wide Range ◽  
Large Eddy

We studied the effect of wall boundary conditions on the statistics in a wall-modeled large-eddy simulation (WMLES) of turbulent channel flows. Three different forms of the boundary condition based on the mean stress-balance equations were used to supply the correct mean wall shear stress for a wide range of Reynolds numbers and grid resolutions applicable to WMLES. In addition to the widely used Neumann boundary condition at the wall, we considered a case with a no-slip condition at the wall in which the wall stress was imposed by adjusting the value of the eddy viscosity at the wall. The results showed that the type of boundary condition utilized had an impact on the statistics (e.g., mean velocity profile and turbulence intensities) in the vicinity of the wall, especially at the first off-wall grid point. Augmenting the eddy viscosity at the wall resulted in improved predictions of statistics in the near-wall region, which should allow the use of information from the first off-wall grid point for wall models without additional spatial or temporal filtering. This boundary condition is easy to implement and provides a simple solution to the well-known log-layer mismatch in WMLES.

scholarly journals Dirichlet absorbing boundary conditions for classical and peridynamic diffusion-type models

2020 ◽  
Vol 66 (4) ◽  
pp. 773-793 ◽  
Author(s):  
Arman Shojaei ◽  
Alexander Hermann ◽  
Pablo Seleson ◽  
Christian J. Cyron
Keyword(s):  
Boundary Conditions ◽  
Materials Science ◽  
Unbounded Domains ◽  
Diffusion Models ◽  
Absorbing Boundary Conditions ◽  
The Finite Element Method ◽  
Absorbing Boundary ◽  
Diffusion Type ◽  
2D And 3D ◽  
Accuracy And Stability

Abstract Diffusion-type problems in (nearly) unbounded domains play important roles in various fields of fluid dynamics, biology, and materials science. The aim of this paper is to construct accurate absorbing boundary conditions (ABCs) suitable for classical (local) as well as nonlocal peridynamic (PD) diffusion models. The main focus of the present study is on the PD diffusion formulation. The majority of the PD diffusion models proposed so far are applied to bounded domains only. In this study, we propose an effective way to handle unbounded domains both with PD and classical diffusion models. For the former, we employ a meshfree discretization, whereas for the latter the finite element method (FEM) is employed. The proposed ABCs are time-dependent and Dirichlet-type, making the approach easy to implement in the available models. The performance of the approach, in terms of accuracy and stability, is illustrated by numerical examples in 1D, 2D, and 3D.

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