Generalized wall-functions for high-Reynolds-number turbulence models (original) (raw)
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Generalized wall-functions and their application for simulation of turbulent flows
Generalized wall functions in application to high-Reynolds-number turbulence models are derived. The wall functions are based on transfer of a boundary condition from a wall to some intermediate boundary near the wall (usually the ÿrst nearest to a wall mesh point but that is not obligatory). The boundary conditions on the intermediate boundary are of Robin-type and represented in a di erential form. The wall functions are obtained in an analytical easy-to-implement form, taking into account source terms such as pressure gradient, and do not include free parameters. The log-proÿle assumption is not used in this approach. Although the generalized wall functions are obtained for the k-model, generalization to other turbulence models is straightforward. The general approach suggested can be applied for studying high-temperature regimes with variable laminar viscosity and density.
The Method of Boundary Condition Transfer in Application to Modeling Near-Wall Turbulent Flows
Generalized wall functions in application to high-Reynolds-number turbulence models are derived. The wall functions are based on transfer of a boundary condition from a wall to some intermediate boundary near the wall (usually the first nearest to the wall mesh point but that is not obligatory). The boundary conditions on the intermediate boundary are of Robin-type and represented in a differential form. The wall functions are obtained in an analytical easy-to-implement form, can take into account source terms such as pressure gradient and buoyancy forces, and do not include free parameters. The log-profile assumption is not used in this approach. Both Dirichlet and Newman boundary-value problems are considered. A method for complementing solution near the wall is suggested. Although the generalized wall functions are obtained for the k-model, generalization to other turbulence models is straightforward. The general approach suggested is applicable to studying high-temperature regimes with variable laminar viscosity and density. A robust numerical algorithm is proposed for implementation of Robin-type wall functions. Test results made for a channel flow and axisymmetric impinging jet have showed reasonably good accuracy, reached without any case-dependent turning, and a weak dependence of the solution on the location of the intermediate boundary where the boundary conditions are set. It is demonstrated that the method of boundary condition transfer applied to low-Reynolds-number turbulence models can be used as a decomposition method.
To study and develop wall-functions for modeling of near-wall turbulent flows, a linear model equation is introduced. This equation simulates major mathematical peculiarities of the low-Reynolds-number model including a near wall sub-layer and transition region. Dirichlet and Newman boundary-value problems are considered. The standard and analytical wall-functions are investigated on different properties including the mesh sensitivity of a solution. A Robin-type interpretation of wall-functions as boundary conditions is suggested. It is shown that solution of a problem is mesh independent and more accurate in this case. General type analytical and numerical wall-functions are developed on the basis of a boundary condition transfer. An effective numerical method of decomposition is suggested. The method can be used in application to either high-Reynolds-number models with the numerical wall-functions or low-Reynolds-number models directly. Although a model equation is considered, the formulas, methods and conclusions are valid and can be directly used for the Reynolds Averaged Navier-Stokes (RANS) equations.
2005
The paper is devoted to the generalized wall functions of Robin-type and their application to near-wall turbulent flows. The wall functions are based on the transfer of a boundary condition from a wall to some intermediate boundary near the wall. The boundary conditions on the intermediate boundary are of Robin-type and represented in a differential form. The wall functions are formulated in an analytical easy-to-implement form, can take into account the source terms of the momentum equation, and do not include free parameters. The log-profile assumption is not used in this approach. A robust numerical algorithm is proposed for implementation of Robin-type wall functions to both finite-difference and finitevolume numerical schemes. The algorithm of implementation of the Robin-type wall functions to existing finite-volume codes is provided. The axisymmetric impinging jet problem is numerically investigated for different regimes on the base of the wall-functions implemented to the high-Reynolds-number k − ǫ model.
On some numerical methods in application to low-Reynolds-number turbulence models
2003
To study and develop wall-functions for low-Reynolds-number models, a model linear equation is introduced. This equation simulates major mathematical peculiarities of the low-Reynolds-number model including a near wall sub-layer and transition region. Dirichlet and Newman boundary-value problems are considered. The standard and analytical wall-functions are investigated on different properties including the mesh sensitivity of a solution. A Robintype interpretation of wall functions as boundary conditions is suggested. It is shown that solution of a problem is mesh independent and more accurate in this case. General type analytical and numerical wall-functions are developed on the basis of a boundary condition transfer. An effective numerical method of decomposition is suggested. The method can be used in application to either high-Reynolds-number models with the numerical wall-functions or low-Reynolds-number models directly. Although a model equation is considered, the formulas, methods and conclusions are valid and can be directly used for real low-Reynoldsnumber equations.
A new algorithm for the implementation of wall-functions in high Reynolds number simulations
Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2013
A new optimization algorithm based on a minimum residual technique is introduced to reduce the instability of numerical methods due to using wall functions to specify the boundary conditions for high Reynolds number flows. In the present article, four different models of the wall-function approximation are investigated for separated flow inside a two-dimensional asymmetric straight-walled diffuser. The equations of motion are closed with the j-e turbulent model. The spatial discretization of the computational domain is performed using a finite element method, whereas the temporal discretization is based on a semi-implicit sequential scheme of finite differences. The pressure-velocity coupling is solved through a variation of the algorithm of Uzawa. Numerical noise resulting from the symmetric treatment of the convective fluxes is treated via a balance dissipation method. The non-linearities resulting from the wall-function explicit calculation are dealt with by a minimal residual method.
Journal of Turbulence, 2019
Spalart-Allmaras (SA) model is a low Reynolds number (Re) model, which means that the first off-wall grid point should be placed in the viscous sub-layer with y + 1. This restriction of placing the first off-wall grid point so close to the wall leads to an increase in the mesh size, and thus the computation. The wall function approach is an alternative to this problem. The standard wall function method usually employed has a limitation for cases that involve high adverse pressure gradient and compressibility. This limits its use to the nonseparated flows only. The present work focuses on the formulation of the generalised wall function given by Shih et al. [A generalized wall function; 1999] and applies it to the SA turbulence model, with some modification. The proposed modification was found to remove the oscillation and inaccuracy found in the result when directly using the Shih et al. model. Several flows, with zero pressure gradient to those with adverse pressure gradient leading to flow separation, are solved with the proposed wall treatment, with relatively coarse grids involving y + beyond 50 and up to 100 for certain cases. It is concluded that the results in each case are close to those obtained by the low-Re SA model, despite the use of much coarser meshes.
CFD Modified Robin-type wall functions for turbulence industries
TIIMI, London 2010, 2010
CFD is the systematic analysis of computer based simulation to determine dynamic fluid flow, heat transfer and other fluid properties. Airbus researchers have found that commercial airliners commonly encounter physical problems with friction drag, 40% of which are caused by a turbulent boundary layer, which is a thin layer of air located just above the skin of a wing/airfoil and body of an aircraft. Drag habitually happens in various instances of fluid flow. It is sometime necessary; however, the disturbance caused by this friction should be optimized for the use of industrial requirement. This has resulted in constant challenge to find appropriate solutions to reduce and ultimately eliminate this effect altogether.
A new ODE-based turbulence wall model accounting for pressure gradient and Reynolds number effects
arXiv:2010.04097, 2020
In wall-modeled large-eddy simulations (WMLES), the near-wall model plays a significant role in predicting the skin friction, although the majority of the boundary layer is resolved by the outer large-eddy simulation (LES) solver. In this work, we aim at developing a new ordinary differential equation (ODE)-based wall model, which is as simple as the classical equilibrium model yet capable of capturing non-equilibrium effects and low Reynolds number effects. The proposed model reformulates the classical equilibrium model by introducing a new non-dimensional mixing-length function. The new mixing-length function is parameterized in terms of the boundary layer shape factor instead of the commonly used pressure-gradient parameters. As a result, the newly introduced mixing-length function exhibits great universality within the viscous sublayer, the buffer layer, and the log region (i.e., 0 < y < 0.1δ, where the wall model is typically deployed in a WMLES setup). The performance of the new model is validated by predicting a wide range of canonical flows with the friction Reynolds number between 200 and 5200, and the Clauser pressure-gradient parameter between-0.3 and 4. Compared to the classical equilibrium wall model, remarkable error reduction in terms of the skin friction prediction is obtained by the new model. Moreover, since the new model is ODE-based, it is straightforward to be deployed for predicting flows with complex geometries and therefore promising for a wide range of applications.
Robin-type wall functions and their numerical implementation
Applied Numerical Mathematics, 2008
The paper is devoted to numerical implementation of the wall functions of Robin-type for modeling near-wall turbulent flows. The wall functions are based on the transfer of a boundary condition from a wall to some intermediate boundary near the wall. The boundary conditions on the intermediate boundary are of Robin-type and represented in a differential form. The wall functions are formulated in an analytical easy-to-implement form, can take into account the source terms, and do not include free parameters. The relation between the wall functions of Robin type and the theory of Calderon-Ryaben'kii's potentials is demonstrated. A universal robust approach to the implementation of the Robin-type wall functions in finite-volume codes is provided. The example of an impinging jet is considered.