Wall Function Boundary Conditions Research Articles

Computational Fluid Dynamics Modeling of Steam Condensation in the Presence of Noncondensable Gas in Inclined Tubes

In this paper, film condensation of steam in inclined tubes in the presence of noncondensable gases is modeled using numerical method. A single-phase fluid model incorporating a wall-function boundary condition is proposed to simulate the heat and mass transfer interaction between the liquid condensate and the gas-vapor mixture region. A user defined function is implemented to impose the proposed boundary to the governing equations for steady state incompressible flow. The performance of applying this boundary condition and subsequent treatment of the heat transfer at the liquid-mixture interface is validated against published experimental results. The calculated profiles of local and average Nusselt number for various inlet conditions compares favorably to the previous published experimental results and correlations. For all simulated cases, increases in inlet and bulk concentrations of noncondensable gases resulted in a decrease in the thermal performance of the condensing tube. Additionally, it is found that the inclination angle of the condensing tube can impact the local distribution of the heat transfer coefficient and Nusselt number, while there is only small effect on the average along the length of the entire tube.

Generalized wall function and its application to compressible turbulent boundary layer over a flat plate

Wall function boundary conditions including the effects of compressibility and heat transfer are improved for compressible turbulent boundary flows. Generalized wall function formulation at zero-pressure gradient is proposed based on coupled velocity and temperature profiles in the entire near-wall region. The parameters in the generalized wall function are well revised. The proposed boundary conditions are integrated into Navier-Stokes computational fluid dynamics code that includes the shear stress transport turbulence model. Numerical results are presented for a compressible boundary layer over a flat plate at zero-pressure gradient. Compared with experimental data, the computational results show that the generalized wall function reduces the first grid spacing in the directed normal to the wall and proves the feasibility and effectivity of the generalized wall function method.

A new wall function boundary condition including heat release effect for supersonic combustion flows

A new wall function boundary condition considering combustion heat release effect (denoted as CWFBC) is proposed, for efficient predictions of skin friction and heat transfer in supersonic combustion flows. Based on a standard flow model including boundary-layer combustion, the Shvab–Zeldovich coupling parameters are introduced to derive a new velocity law-of-the-wall including the influence of combustion. For the temperature law-of-the-wall, it is proposed to use the enthalpy–velocity relation, instead of the Crocco–Busemann equation, to eliminate explicit influence of chemical reactions. The obtained velocity and temperature law-of-the-walls constitute the CWFBC, which is a unified form simultaneously holding for single-species, multi-species mixing and multi-species reactive flows. The subsequent numerical simulations using this CWFBC on an experimental case indicate that the CWFBC could accurately reflect the influences on the skin friction and heat transfer by the chemical reactions and heat release, and show large improvements compared to previous WFBC. Moreover, the CWFBC can give accurate skin friction and heat flux for a coarse mesh with y+ up to 200 for the experimental case, except for slightly larger discrepancy of the wall heat flux around ignition position.

Improvement and application of wall function boundary condition for high-speed compressible flows

In order to develop a wall function boundary condition for high-speed flows so as to reduce the grid-dependence of the simulation for the skin friction and heat flux, a research was performed to improve the compressible wall function boundary condition proposed by Nichols. Values of parameters in the velocity law-of-the-wall were revised according to numerical experiments and the expression of temperature law-of-the-wall was modified based on theoretical analysis and numerical simulation. Besides, the formula of the heat conduction term in near-wall region was derived so that the coupling between the wall function boundary condition and CFD code was realized more accurately. Whereafter, the application study of the modified wall function was carried out. The numerical case of supersonic turbulent boundary layer on a flat plate illustrated that the modified wall function produces reasonable results of skin friction and heat flux, and profiles of velocity, temperature and turbulent eddy viscosity for coarse grids with the initial wall spacing of y+<400, and that the modifications to the original wall function can obviously improve the simulation precision. As for the application of separation flows, it was found from the numerical cases of supersonic cavity flow and hypersonic axisymmetric compression corner that the compressible velocity law-of-the-wall originally established based on the fully-developed attached turbulent boundary layer approximately holds in the near-wall region inside the separation flows, which ensures that reliable skin friction and heat flux can be given by the wall function inside the separation flows, while for the region near separation and reattachment points, the wall function gives results with a relatively large error, because the velocity law-of-the-wall used in the wall function takes on obvious deviation from the real velocity profiles near the separation and reattachment points.

Computational fluid dynamics analysis of multi-element, high-lift aerofoil sections at transonic manoeuvre conditions

The application of a previously developed computational method to the prediction of high-lift performance for multi-element aerofoil sections operating at transonic flow conditions is described. The flows are computed by solving the Reynolds-averaged Navier–Stokes equations, using a full differential Reynolds-stress turbulence model to evaluate the various Reynolds-stress components appearing in the governing mean-flow equations. Algebraic wall functions are used to bridge the molecular viscosity-dominated region immediately adjacent to the aerofoil surfaces. An unstructured grid-based computational fluid dynamics (CFD) methodology is used to deal with the geometric complexity of the multi-element aerofoil configurations. Initial results are presented for the viscous, transonic flow development around the SKF 1.1 supercritical aerofoil section, equipped with either a trailing-edge flap or a leading-edge slat. Predicted surface pressure distributions generally compare well with experimental data for the two high-lift aerofoil geometries considered, at a free-stream Mach number of 0.6 and over a range of incidence angles. There are some discrepancies in the regions immediately downstream of shock wave/boundary layer interactions, possibly resulting from the use of wall-function boundary conditions in the computations. Predicted Mach number contours indicate the complexity of the transonic flow fields for high-lift configurations, with the slat wake passing through an extensive supersonic-flow region, terminated by a normal shock wave, on the main aerofoil upper surface, for example.

Analysis of wind flow around a parabolic collector (2) heat transfer from receiver tube

Parabolic collectors of commercial solar thermal power plants are subject to variable convection heat transfer from the receiver tube. In the present study heat transfer from a receiver tube of the parabolic trough collector of the 250 kW solar power plants in Shiraz, Iran, is studied taking into account the effects of variation of collector angel of attack, wind velocity and its distribution with respect to height from the ground. The governing equations for the two-dimensional steady state wind flow include continuity, momentum and energy equations and RNG-based k– ε model for turbulence scheme. Finite volume discretization method is used to solve the governing equations with wall function boundary condition and the SIMPLE approach is employed to iterate for the pressure correction and convergence of the velocity field. The momentum equation contains buoyancy force when the buoyancy effect is high and force convection effect is low. Computation is carried out for various wind velocities and different collector orientations with respect to wind direction. For solution of the energy equation, temperature of the receiver tube is taken as 350 K and ambient temperature is assumed to be 300 K. Various recirculation and temperature fields were observed around the receiver tube for different flow conditions. Effect of collector orientation on the average Nu number for the receiver tube was found negligible when the wind speed is low ( Re⩽4.5×10 5 based on the collector aperture). But when the wind velocity is high ( Re>4.5×10 5), the collector effect on the variation of Nu around the glass cover of the absorber tube is considerable.

Numerical modeling of flow and scour below a pipeline in currents: Part I. Flow simulation

The performance of the standard k– ε, Wilcox high-Reynolds-number k– ω, Wilcox low-Reynolds-number k– ω and Smagorinsky's subgrid scale (SGS) turbulence models is examined against the flow around a circular cylinder 0.37 diameter above a rigid wall. The governing equations are solved using finite difference method in a non-orthogonal boundary-fitted curvilinear coordinate system. A mesh dependence study for the four turbulence models is carried out on computational meshes with different densities. In addition, the performance of the k– ω models with either wall function or no-slip boundary condition on the cylinder surface is examined on the finest mesh. It is found that the SGS model over-predicts the shedding of vortices from the cylinder and is sensitive to the computational mesh and the model constant C s used. The standard k– ε and the Wilcox k– ω models predict the mean velocity field quite well but generally under-predict the velocity and hydrodynamic force oscillations using wall functions on the cylinder surface. It is also found that the Wilcox k– ω models with the no-slip boundary condition on the cylinder surface give better predictions on the shedding of vortices than their counterparts using the wall function boundary condition.

Wall Function Boundary Conditions Including Heat Transfer and Compressibility

Wall function boundary conditions that include the effects of compressibility and heat transfer are developed for transport-type turbulence models. The wall functions are based on coupled velocity and temperature profiles valid in both the viscous sublayer and the log layer. The wall function boundary conditions are developed within a rigid set of assumptions so that a consistent set of relationships are derived for the wall shear stress, the wall heat transfer, and the turbulence quantities at the first point off the wall. The new boundary conditions are incorporated into a Navier‐Stokes computational fluid dynamics code that includes the Spalart‐Allmaras and shear stress transport turbulence models. The wall function boundary conditions produce reasonable engineering solutions for the test cases presented for initial wall spacings of y + < 100.

７．流体力学 ２方程式モデルによるトレンチ付開水路落差工流れの数値解析

Complex flows over a drop with a trench in which supercritical and subcritical flow coexist, have b en computed by a low Reynolds number k-ω turbulence model and the standard k-ω model. The k-ω model predicts the free-surface shape, separation area and the turbulent kinetic energy and shear stress distributions in both test cases consistently well, while k-ω model fails to reproduce the case of supercritical flow over and past the trench. The calculation results imply that complex flow over the drop and trench cannot be represented properly by the method that relies on the wall function boundary condition.

Modelling turbulent thermofluid flow in stationary gas tungsten arc weld pools

The effects of turbulence in stationary gas tungsten arc (GTA) welds in AISI 304 stainless steel were examined using a finite element thermofluids model. The model includes buoyancy, Lorentz and Marangoni driven fluid flow, a large deformation model of the free surface, and a k–ε turbulence model. To facilitate implementation of the wall function boundary conditions for the k–ε turbulence model, a dynamic numerical grid remapping technique was used to clearly separate elements in the liquid from those in the solid. The influences of sulphur content of AISI 304 stainless steels on the turbulent viscosity, fluid flow, and weld pool dimensions were simulated. Good correlation between experimentally observed and predicted weld pool shapes and dimensions was obtained. Also, the effect of sulphur concentration on AISI 304 weld pool dimensions was correctly predicted. The simulations indicate that the flow in such stationary GTA weld pools in AISI 304 stainless steel is not laminar and that quantitatively accurate predictions of weld pool fluid flow and weld shapes and dimensions will only be possible if the effects of turbulence in GTA weld pools are modelled correctly.

Unstructured Mesh Navier-Stokes Calculations of the Flow Field of a Helicopter Rotor in Hover

Three-dimensional viscous flow field around a lifting helicopter rotor in hover is calculated by using an unstructured mesh methodology. The flow solver utilizes a cell-centered finite-volume scheme that is based on the Roe’s flux-difference splitting and an implicit Jacobi/Gauss-Seidel time integration. The effect of turbulence is estimated by the Spalart-Allmaras one-equation model coupled with a wall function boundary condition. A solution-adaptive mesh refinement technique is used for efficient capturing of the tip vortex. Calculations are performed at two operating conditions with varying tip Mach number and collective pitch setting. Formation of the tip vortex is well captured through a series of adaptive mesh refinement procedure starting from a coarse initial mesh. Good agreements are obtained between the numerical result and the experiment for both the blade loading and the tip vortex behavior. It is demonstrated that the rotor performance and the flow field are significantly affected by viscosity. The process of tip vortex formation around the blade tip is also qualitatively investigated.

Prediction of Turbulent Separated Flow in a Turnaround Duct Using Wall Functions and Adaptivity

This paper presents an application of adaptive remeshing to the prediction of turbulent separated flows. The paper shows that the κ - ϵ model with wall functions can predict separated flows along smooth curved surfaces. Success is achieved if the wall functions exhibit values of y+ close to 30, and if meshes are fine enough to guarantee that wall function boundary conditions are grid converged. Adaptive remeshing proves to be a very cost effective tool in this context. The methodology is demonstrated on a problem possessing a closed form solution to establish the performance and reliability of the proposed approach. The method is then applied to prediction of turbulent flow in an annular, axisymmetric turnaround duct (TAD). Predictions from two computational models of the TAD are compared with experimental measurements. The importance of appropriate meshes to achieve grid independent solutions is demonstrated in both cases. Better agreement with measurements is obtained when partially developed profiles of u, κ, and ϵ are specified at the TAD inlet.

Streamwise Curvature Effect on the Incompressible Turbulent Mean Velocity Over Curved Surfaces

A curvature law of the wall, which determines the mean velocity profile, is analytically derived for near-wall turbulent flows to include strong curved-channel wall curvature effects through a perturbation analysis. The new law allows improved analysis of such flows, and it provides the basis for improved wall function boundary conditions for their computation (CFD), even for strong curvature cases. The improved law is based on the algebraic eddy viscosity and curvature-corrected mixing length concepts, the latter of which is a linear function of the gradient Richardson number. To include the complete Richardson number effects, the local streamline curvature effects in the gradient Richardson number are kept. To overcome the mathematical difficulty of keeping all of these local streamline curvature terms, an innovative nonconstant-parameter perturbation solution technique is successfully applied. [S0098-2202(00)00903-2]

An experimental/numerical study of the turbulent boundary layer development along a surface with a sudden change in roughness

A theory for the description of turbulent boundary layer flows over surfaces with a sudden change in roughness is considered. The theory resorts to the concept of displacement in origin to specify a wall function boundary condition for a k-e model. An approximate algebraic expression for the displacement in origin is obtained from the experimental data by using the chart method of Perry and Joubert(J.F.M., vol. 17, pp. 193-122, 1963). This expression is subsequently included in the near wall logarithmic velocity profile, which is then adopted as a boundary condition for a k-e modelling of the external flow. The results are compared with the lower atmospheric observations made by Bradley(Q. J. Roy. Meteo. Soc., vol. 94, pp. 361-379, 1968) as well as with velocity profiles extracted from a set of wind tunnel experiments carried out by Avelino et al.( 7th ENCIT, 1998). The measurements are found to be in good agreement with the theoretical computations. The skin-friction coefficient was calculated according to the chart method of Perry and Joubert(J.F.M., vol. 17, pp. 193-122, 1963) and to a balance of the integral momentum equation. In particular, the growth of the internal boundary layer thickness obtained from the numerical simulation is compared with predictions of the experimental data calculated by two methods, the knee point method and the merge point method.

Wall-function treatment in pdf methods for turbulent flows

A wall-function boundary condition is developed for the pdf/Monte Carlo method. Like traditional wall functions, this reproduces the logarithmic velocity profile and shear stress in equilibrium flow conditions. A constant-stress analysis for the pdf, and a linear-stress analysis for the first two moments of the pdf are developed as the basis for this wall-function approach. Stable and accurate boundary conditions are derived and demonstrated with fully-developed channel flow.

Application of roughness-dependent boundary conditions to turbulent oscillatory flows

Abstract The purpose of this paper is to model wave-induced oscillatory flows traversing rough beds using high-Reynolds number turbulence models based on boundary conditions that are sensitized to the local state of bed roughness (be it hydraulically smooth, transitional, or fully rough). Such boundary conditions replace more traditional approaches (based on a no-slip velocity condition), which are, hitherto, most commonly applied to the majority of oceanographic and estuarine calculations. Both eddy-viscosity and differential second-moment (DSM) closures are implemented and compared with experimental data. It is shown that the linear length scale used in the eddy-viscosity k- l model will lead to serious errors. This paper should, therefore, convey the message to coastal and marine engineers that, eddy-viscosity models, such as the k- l model, that are still employed in the vast majority of coastal engineering simulations and are used to calculate parameterized flow coefficients used in large-scale three-dimensional hydrodynamic codes, such as those for predicting internal tides and sediment transport, should be replaced by advanced turbulence transport models. The other aim of this paper is to show how near-bed predictions of turbulent kinetic energy profiles on rough boundary layers, whose roughness is related to Nikuradse sand grains, can be improved. It is demonstrated that when wall-function boundary conditions (sensitized to the bed roughness) are used, in favour of a more traditional non-slip velocity strategy, a better agreement with experimental data is achieved.

Simulation of three-dimensional turbulent flows on unstructured meshes

A three-dimensional Navier-Stokes flow solver is developed on unstructured tetrahedral meshes. For a turbulence closure, a standard high-Reynolds-number k-e model with a wall function boundary condition is used. The seven equations of motion are discretized and integrated in a tightly coupled manner. The time integration is achieved using an explicit Runge-Kutta time-stepping scheme. The inviscid flux terms are discretized based on a cell-centered finite volume formulation with Roe's flux-difference splitting. The numerical method is applied for flows on a two-dimensional backward-facing step and a three-dimensional turbomachinery geometry. The results are compared with analytical and experimental data for validations.

Shock/turbulent boundary-layer interaction with wall function boundary conditions

Shock/turbulent boundary-layer interaction with wall function boundary conditions