The Pros and Cons of Wall Functions

2015 ◽  
Author(s):  
Luís Eça ◽  
Gonçalo Saraiva ◽  
Guilherme Vaz ◽  
Hugo Abreu
Keyword(s):  
Shear Stress ◽  
Boundary Conditions ◽  
Daily Basis ◽  
Wall Layer ◽  
Direct Application ◽  
Slip Condition ◽  
Wall Function ◽  
Friction Forces ◽  
Wall Functions ◽  
Advantages And Disadvantages

Simulations of viscous flows based on the Reynolds-Averaged Navier-Stokes (RANS) equations have become an engineering tool used on a daily basis. One of the main goals of such calculations is to determine friction forces, which are a consequence of the shear-stress at solid walls. In RANS (and other more sophisticated mathematical models), there are two main approaches for the determination of the shear-stress at a wall: direct application of the no-slip condition, i.e. the velocity gradient is determined directly at the surface; wall functions which determine the shear-stress at the wall from semi-empirical equations applicable up to the outer edge of the so-called “wall layer/log layer”. Although the first option is physically preferable, its numerical requirements may lead to iterative convergence problems and/or excessive calculation times. Therefore, especially at high Reynolds numbers, it is not unusual to use the latter approach. In this paper we discuss the advantages and disadvantages of wall-function boundary conditions. To this end we have calculated the flow around a flat plate, conventional and laminar airfoils and a circular cylinder. The influence of the location where wall functions are applied (distance to the wall) and the effect of the Reynolds number (ranging from model to full scale applications) are discussed. Griding requirements for wall-function boundary conditions are also addressed. The results obtained with wall functions are compared with those obtained from the direct application of the no slip at the wall. The results obtained in this study show that the use of wall functions in viscous flow calculations may be justifiable or completely unacceptable depending on the flow conditions. Furthermore, it is also shown that wall-function boundary conditions also require clustering of grid nodes close to the wall, but obviously less demanding than the direct application of no slip condition.

On the modelling of turbulent flow over low-angle sand dunes

2019 ◽  
Author(s):  
И.И. Потапов ◽  
К.С. Снигур ◽  
Г.И. Цой
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Shear Stress ◽  
Turbulent Flow ◽  
River Flow ◽  
Numerical Solutions ◽  
Control Volume ◽  
Sand Dunes ◽  
Wall Function ◽  
Wall Functions

Предложена математическая модель задачи о движении двумерного турбулентного потока жидкости в напорном канале с волнистым дном. Математическая модель включает уравнения Рейнольдса, уравнения переноса кинетической энергии и диссипации турбулентности, приведенные к квазигидродинамическому виду. Предложен алгоритм решения задачи с помощью метода контрольных объемов и метода конечных элементов. Численно решена задача о движении турбулентного потока над неподвижными пологими песчаными дюнами. Выполнено сравнение полученных расчетов с экспериментальными данными. Purpose. The aim of the paper is the development of mathematical models describing a turbulent river flow along gently sloping dunes and allowing estimation of the contribution of gently sloping dunes on the flow hydraulic resistance. Methodology. A quasi-hydrodynamic form of the classical RANS equations are used for describing the hydrodynamic flow. The standard k model is used for the turbulence viscosity while the equations have been transformed to the quasi-hydrodynamic form. A wall functions method is used for describing the flow near solid channel wall. Results. A new mathematical model for the problem of turbulent flow in a pressure channel with low-angle dunes is proposed. An algorithm for solving the problem is proposed. It is based on the control volume method and the finite element method. The problem of the turbulent flow over 6 fixed low-angle sand dunes is solved numerically. Numerical solutions are obtained with four different wall functions. A comparative analysis of the obtained solutions with the experimental data is carried out. Findings. It is shown that the proposed mathematical model describes the turbulent flow over low-angle dunes qualitatively and quantitatively. The solution obtained with the Volkov wall function provides the best agreement with the experiment. It is found out that the bed shear stress obtained in the near-wall computational cell by the wall functions method does not qualitatively agree with the experimental data for all considered wall functions. At the same time, the shear stress obtained in the next calculation cell agrees with the experimental data qualitatively and quantitatively. The average relative error of the shear stress obtained with the Volkov wall function is 6.84.

Public-Private Partnership for the Development of Space Sector in the United States and Great Britain

2022 ◽  
pp. 76-87
Author(s):  
V. P. Zavarukhin ◽  
N. D. Frolova ◽  
D. V. Baibulatova
Keyword(s):  
Great Britain ◽  
Space Exploration ◽  
The United States ◽  
Public Private Partnership ◽  
Direct Application ◽  
High Tech ◽  
Private Partnership ◽  
Advantages And Disadvantages ◽  
Space Industry ◽  
Space Activities

The article provides an analysis of modern trends in building public-private partnership (PPP), gives an overview of key studies devoted to this subject in general and PPPs in the field of space activities in particular. The authors analyze the practice of public-private partnerships in the U. S. and Great Britain on the examples of specific mechanisms, their key features, advantages and disadvantages that determine the possibility of their application in different areas of government-business cooperation in the field of space exploration. In order to find possible ways for direct application or adaptation of this experience in Russia for organizing space exploration PPPs the researchers concluded that the level of high-tech production in this country is insufficient and significant administrative barriers for attracting private sector into the space industry are still present.

MEMS-Scale Turbomachinery Based Vacuum Roughing Pump

2014 ◽  
Vol 136 (10) ◽  
Author(s):  
Anthony J. Gannon ◽  
Garth V. Hobson ◽  
Michael J. Shea ◽  
Christopher S. Clay ◽  
Knox T. Millsaps
Keyword(s):  
Boundary Condition ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Boundary Conditions ◽  
Knudsen Number ◽  
Slip Flow ◽  
Slip Boundary Condition ◽  
3D Simulations ◽  
Slip Boundary ◽  
Wall Shear

This study forms part of a program to develop a micro-electro-mechanical systems (MEMS) scale turbomachinery based vacuum pump and investigates the roughing portion of such a system. Such a machine would have many radial stages with the exhaust stages operating near atmospheric conditions while the inlet stages operate at near vacuum conditions. In low vacuum such as those to the inlet of a roughing pump, the flow can still be treated as a continuum; however, the no-slip boundary condition is not accurate. The Knudsen number becomes a dominant nondimensional parameter in these machines due to their small size and low pressures. As the Knudsen number increases, slip-flow becomes present at the walls. The study begins with a basic overview on implementing the slip wall boundary condition in a commercial code by specifying the wall shear stress based on the mean-free-path of the gas molecules. This is validated against an available micro-Poiseuille classical solution at Knudsen numbers between 0.001 and 0.1 with reasonable agreement found. The method of specifying the wall shear stress is then applied to a generic MEMS scale roughing pump stage that consists of two stators and a rotor operating at a nominal absolute pressure of 500 Pa. The zero flow case was simulated in all cases as the pump down time for these machines is small due to the small volume being evacuated. Initial transient two-dimensional (2D) simulations are used to evaluate three boundary conditions, classical no-slip, specified-shear, and slip-flow. It is found that the stage pressure rise increased as the flow began to slip at the walls. In addition, it was found that at lower pressures the pure slip boundary condition resulted in very similar predictions to the specified-shear simulations. As the specified-shear simulations are computationally expensive it is reasonable to use slip-flow boundary conditions. This approach was used to perform three-dimensional (3D) simulations of the stage. Again the stage pressure increased when slip-flow was present compared with the classical no-slip boundaries. A characteristic of MEMS scale turbomachinery are the large relative tip gaps requiring 3D simulations. A tip gap sensitivity study was performed and it was found that when no-slip boundaries were present the pressure ratio increased significantly with decreasing tip gap. When slip-flow boundaries were present, this relationship was far weaker.

A Method of Measuring Turbulent Flow Structures With Particle Image Velocimetry and Incorporating Into Boundary Conditions of Large Eddy Simulations

2018 ◽  
Vol 140 (7) ◽  
Author(s):  
Puxuan Li ◽  
Steve J. Eckels ◽  
Garrett W. Mann ◽  
Ning Zhang
Keyword(s):  
Particle Image Velocimetry ◽  
Large Eddy Simulation ◽  
Boundary Conditions ◽  
Particle Image ◽  
Advantages And Disadvantages ◽  
Eddy Simulation ◽  
Piv Measurement ◽  
Image Velocimetry ◽  
Large Eddy ◽  
Inlet Conditions

The setup of inlet conditions for a large eddy simulation (LES) is a complex and important problem. Normally, there are two methods to generate the inlet conditions for LES, i.e., synthesized turbulence methods and precursor simulation methods. This study presents a new method for determining inlet boundary conditions of LES using particle image velocimetry (PIV). LES shows sensitivity to inlet boundary conditions in the developing region, and this effect can even extend into the fully developed region of the flow. Two kinds of boundary conditions generated from PIV data, i.e., steady spatial distributed inlet (SSDI) and unsteady spatial distributed inlet (USDI), are studied. PIV provides valuable field measurement, but special care is needed to estimate turbulent kinetic energy and turbulent dissipation rate for SSDI. Correlation coefficients are used to analyze the autocorrelation of the PIV data. Different boundary conditions have different influences on LES, and their advantages and disadvantages for turbulence prediction and static pressure prediction are discussed in the paper. Two kinds of LES with different subgrid turbulence models are evaluated: namely dynamic Smagorinsky–Lilly model (Lilly model) and wall modeled large eddy simulation (WMLES model). The performances of these models for flow prediction in a square duct are presented. Furthermore, the LES results are compared with PIV measurement results and Reynolds-stress model (RSM) results at a downstream location for validation.

scholarly journals Experimental study of wall boundary conditions for large-eddy simulation

2001 ◽  
Vol 446 ◽  
pp. 309-320 ◽  
Author(s):  
IVAN MARUSIC ◽  
GARY J. KUNKEL ◽  
FERNANDO PORTÉ-AGEL
Keyword(s):  
Boundary Layer ◽  
Boundary Condition ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Large Eddy Simulation ◽  
Boundary Conditions ◽  
Streamwise Velocity ◽  
New Model ◽  
Eddy Simulation ◽  
Large Eddy

An experimental investigation was conducted to study the wall boundary condition for large-eddy simulation (LES) of a turbulent boundary layer at Rθ = 3500. Most boundary condition formulations for LES require the specification of the instantaneous filtered wall shear stress field based upon the filtered velocity field at the closest grid point above the wall. Three conventional boundary conditions are tested using simultaneously obtained filtered wall shear stress and streamwise and wall-normal velocities, at locations nominally within the log region of the flow. This was done using arrays of hot-film sensors and X-wire probes. The results indicate that models based on streamwise velocity perform better than those using the wall-normal velocity, but overall significant discrepancies were found for all three models. A new model is proposed which gives better agreement with the shear stress measured at the wall. The new model is also based on the streamwise velocity but is formulated so as to be consistent with ‘outer-flow’ scaling similarity of the streamwise velocity spectra. It is therefore expected to be more generally applicable over a larger range of Reynolds numbers at any first-grid position within the log region of the boundary layer.

Extension of classical stability theory to viscous planar wall-bounded shear flows

2019 ◽  
Vol 877 ◽  
pp. 1134-1162 ◽  
Author(s):  
Harry Lee ◽  
Shixiao Wang
Keyword(s):  
Boundary Conditions ◽  
Shear Flows ◽  
Early Stage ◽  
Linear Instability ◽  
Slip Condition ◽  
Translation Invariant ◽  
Alternative Derivation ◽  
Wall Boundary ◽  
Wall Boundary Conditions ◽  
Parallel Shear Flows

A viscous extension of Arnold’s inviscid theory for planar parallel non-inflectional shear flows is developed and a viscous Arnold’s identity is obtained. Special forms of the viscous Arnold’s identity have been revealed that are closely related to the perturbation’s enstrophy identity derived by Synge (Proceedings of the Fifth International Congress for Applied Mechanics, 1938, pp. 326–332, John Wiley) (see also Fraternale et al., Phys. Rev. E, vol. 97, 2018, 063102). Firstly, an alternative derivation of the perturbation’s enstrophy identity for strictly parallel shear flows is acquired based on the viscous Arnold’s identity. The alternative derivation induces a weight function. Thereby, a novel weighted perturbation’s enstrophy identity is established, which extends the previously known enstrophy identity to include general streamwise translation-invariant shear flows. Finally, the validity of the enstrophy identity for parallel shear flows is rigorously examined and established under global nonlinear dynamics imposed with two classes of wall boundary conditions. As an application of the enstrophy identity, we quantitatively investigate the mechanism of linear instability/stability within the normal modal framework. The investigation reveals a subtle interaction between a critical layer and its adjacent boundary layer, which determines the stability nature of the disturbance. As an implementation of the relaxed wall boundary conditions imposed for the enstrophy identity, a control scheme is proposed that transitions the wall settings from the no-slip condition to the free-slip condition, through which a flow is stabilized quickly in an early stage of the transition.

Reconstruction Effectiveness of Locally Supported Flat Slabs to Increase in Shear Resistance

2020 ◽  
Vol 309 ◽  
pp. 246-251
Author(s):  
Mária Bolešová ◽  
Katarína Gajdošová ◽  
Marek Čuhák
Keyword(s):  
Shear Stress ◽  
Numerical Models ◽  
Shear Resistance ◽  
Reconstruction Method ◽  
Detailed Calculation ◽  
Shear Reinforcement ◽  
Flat Slab ◽  
Advantages And Disadvantages ◽  
Flat Slabs ◽  
Eurocode 2

The most used horizontal load-bearing systems in concrete buildings are flat slabs. The effective and economic reconstruction of a locally supported flat slab of an existing building creates a complex task. Shear stress arises near the column and it becomes critical in design with increasing slab slenderness and requires a more detailed calculation. Increasing in the shear resistance of the flat slab can be achieved in various ways. Each method brings different effectiveness, advantages and disadvantages. The most widely used methods of the reconstruction are the increase in the size of the column (therein increasing the control perimeter for displaying the shear stress), the increase in the thickness of the flat slab or reinforcing the slab with shear reinforcement. Bolts and screw anchors (using different mounting angles) can be used as shear reinforcement. Each mentioned reconstruction method should be subjected to numerical calculations and verification of its efficiency. The parametric study presented in this paper is focused on the reconstruction techniques and their verification according to various numerical models. The results from Eurocode 2, fib Model Code 2010 and the new generation of Eurocode 2 are compared to show the differences between them. The aim of this paper is to bring a demonstration of the reconstruction methods that will increase in the shear resistance of the locally supported flat slabs and trying to choose the most effective one.

scholarly journals Numerical investigation of the impact of branching vessel boundary conditions on aortic hemodynamics

2017 ◽  
Vol 3 (2) ◽  
pp. 321-324 ◽  
Author(s):  
Pavlo Yevtushenko ◽  
Florian Hellmeier ◽  
Jan Bruening ◽  
Titus Kuehne ◽  
Leonid Goubergrits
Keyword(s):  
Shear Stress ◽  
Pressure Drop ◽  
Boundary Conditions ◽  
Reference Method ◽  
Patient Specific ◽  
Simplified Method ◽  
The Mean ◽  
The Impact ◽  
Significant Attention ◽  
Aortic Hemodynamics

AbstractCFD has gained significant attention as a tool to model aortic hemodynamics. However, obtaining accurate patient-specific boundary conditions still poses a major challenge and represents a major source of uncertainties, which are difficult to quantify. This study presents an attempt to quantify these uncertainties by comparing 14 patient-specific simulations of the aorta (reference method), each exhibiting stenosis, against simulations using the same geometries without the branching vessels of the aortic arch (simplified method).Results were evaluated by comparing pressure drop along the aorta, secondary flow degree (SFD) and surface-averaged wall shear stress (WSS) for each patient. The comparison shows little difference in pressure drop between the two methods (simplified-reference) with the mean difference being 1.2 mmHg (standard deviation: 3.0 mmHg). SFD and WSS, however, show striking differences between the methods: SFD downstream of the stenosis is on average 61 % higher in the simplified cases, while WSS is on average 3.0 Pa lower in the simplified cases.Although unphysiological, the comparison of both methods gives an upper bound for the error introduced by uncertainties in branching vessel boundary conditions. For the pressure drop this error appears to be remarkably low, while being unacceptably high for SFD and WSS.

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