scholarly journals SUBGRID MODELLING IN DEPTH INTEGRATED FLOWS

1988 ◽  
Vol 1 (21) ◽  
pp. 35 ◽  
Author(s):  
P.A. Madsen ◽  
M. Rugbjerg ◽  
I.R. Warren
Keyword(s):  
Shear Stress ◽  
Large Scale ◽  
Eddy Viscosity ◽  
Grid Size ◽  
Coastal Engineering ◽  
Shear Stresses ◽  
Two Dimensional ◽  
Bottom Shear Stress ◽  
Hydrodynamic Simulations ◽  
Engineering Studies

Hydrodynamic simulations in coastal engineering studies are still most commonly carried out using two-dimensional vertically integrated mathematical models. As yet, threedimensional models are too expensive to be put into general use. However, the tendency with 2-D models is to use finer and finer resolution so that it becomes necessary to include approximations to some 3-D phenomena. It has been shown by many authors that simulations of large scale eddies can be quite realistic in 2-D models (c.f. Abbott et al. 1985). Basically there exists two different mechanisms of circulation generation. The first one is based on a balance between horizontally and grid-resolved momentum transfers and the bed resistance - i.e. a balance between the convective momentum terms and the bottom shear stress. The second one is due to momentum transfers that are not resolved at the grid scale but appears instead as horizontally distributed shear stresses. In many practical situations the circulations will be governed by the first mechanism. This is the case if the diameter of the circulation and the grid size is much larger than the water depth. In this situation the eddies are friction dominated so that the effect of sub-grid eddy viscosity is limited. In this case 2-D models are known to produce very realistic results and several comparisons with measurements have been reported in the literature.

Large-scale modes of turbulent channel flow: transport and structure

2001 ◽  
Vol 448 ◽  
pp. 53-80 ◽  
Author(s):  
Z. LIU ◽  
R. J. ADRIAN ◽  
T. J. HANRATTY
Keyword(s):  
Shear Stress ◽  
Kinetic Energy ◽  
Shear Layer ◽  
Turbulent Kinetic Energy ◽  
Large Scale ◽  
Reynolds Shear Stress ◽  
Reynolds Numbers ◽  
Upstream Region ◽  
Two Dimensional ◽  
Normal Plane

Turbulent flow in a rectangular channel is investigated to determine the scale and pattern of the eddies that contribute most to the total turbulent kinetic energy and the Reynolds shear stress. Instantaneous, two-dimensional particle image velocimeter measurements in the streamwise-wall-normal plane at Reynolds numbers Reh = 5378 and 29 935 are used to form two-point spatial correlation functions, from which the proper orthogonal modes are determined. Large-scale motions – having length scales of the order of the channel width and represented by a small set of low-order eigenmodes – contain a large fraction of the kinetic energy of the streamwise velocity component and a small fraction of the kinetic energy of the wall-normal velocities. Surprisingly, the set of large-scale modes that contains half of the total turbulent kinetic energy in the channel, also contains two-thirds to three-quarters of the total Reynolds shear stress in the outer region. Thus, it is the large-scale motions, rather than the main turbulent motions, that dominate turbulent transport in all parts of the channel except the buffer layer. Samples of the large-scale structures associated with the dominant eigenfunctions are found by projecting individual realizations onto the dominant modes. In the streamwise wall-normal plane their patterns often consist of an inclined region of second quadrant vectors separated from an upstream region of fourth quadrant vectors by a stagnation point/shear layer. The inclined Q4/shear layer/Q2 region of the largest motions extends beyond the centreline of the channel and lies under a region of fluid that rotates about the spanwise direction. This pattern is very similar to the signature of a hairpin vortex. Reynolds number similarity of the large structures is demonstrated, approximately, by comparing the two-dimensional correlation coefficients and the eigenvalues of the different modes at the two Reynolds numbers.

scholarly journals FLOW DYNAMICS OF WAVES PROPAGATING OVER DIFFERENT PERMEABLE BEDS

2017 ◽  
pp. 35
Author(s):  
Sara Corvaro ◽  
Alessandro Mancinelli ◽  
Maurizio Brocchini
Keyword(s):  
Shear Stress ◽  
Flow Resistance ◽  
Single Layer ◽  
Coastal Engineering ◽  
Flow Dynamics ◽  
Bottom Shear Stress ◽  
Natural Stones ◽  
Wave Height Attenuation ◽  
Rough Beds ◽  
Good Agreement

The analysis of the hydrodynamics over porous media is of interest for many coastal engineering applications as the wave propagation over permeable structures or gravel beaches. The study of a boundary layer evolving over permeable beds is important to a better understanding of the interactions between the flow over and inside the porous medium. An experimental study has been performed to analyze the dynamics produced when waves propagate over two kinds of permeable beds: spheres (regular permeability) and natural stones. For comparative purposes the same analysis has been extended to two rough beds made, respectively, by a single layer of spheres and natural stones. We here focus on the correlation between the wave energy reduction induced by a porous bed and the flow resistance. An experimental law for the prediction of the friction factor is found by using the log-fit method in analogy to that reported in Dixen et al. (2008) for rough beds. Moreover, inspection of the turbulent velocity components allows one to evaluate the bottom shear stress. The latter analysis has been performed for different permeable beds (regular and irregular beds). A good agreement between the bottom shear stress behavior and the wave height attenuation over rough and permeable beds (Corvaro et al. 2010 and Corvaro et al. 2014a) has been observed.

Reynolds stress and eddy viscosity in direct numerical simulations of sheared two-dimensional turbulence

2010 ◽  
Vol 657 ◽  
pp. 394-412 ◽  
Author(s):  
PATRICK F. CUMMINS ◽  
GREG HOLLOWAY
Keyword(s):  
Reynolds Stress ◽  
Large Scale ◽  
Eddy Viscosity ◽  
Finite Domain ◽  
Spectral Space ◽  
Two Dimensional ◽  
Initial Value ◽  
Theoretical Predictions ◽  
Eddy Field ◽  
Scale Shear

The Reynolds stress associated with the adjustment of two-dimensional isotropic eddies subject to a large-scale shear flow is examined in a series of initial-value calculations in a periodic channel. Several stages in the temporal evolution of the stress can be identified. Initially, there is a brief period associated with quasi-passive straining of the eddy field in which the net Reynolds stress and the associated eddy viscosity remain essentially zero. In spectral space this is characterized by mutual cancellation of contributions to the Reynolds stress at high and low eddy wavenumbers. Subsequently, eddy–eddy interactions produce a tendency to restore isotropy at higher eddy wavenumbers, leading to an overall positive eddy viscosity associated with the dominant contribution to the Reynolds stress at low eddy wavenumbers. These results are consistent with theoretical predictions of positive eddy viscosity for initially isotropic homogeneous two-dimensional turbulence. Due to the inverse cascade, the accumulation with time of energy at the scale of the channel produces a competing tendency to negative eddy viscosity associated with linear shearing of the disturbances. This finite-domain effect may become dominant if the nonlinearity of the eddy field is relatively weak.

Grid-Induced Numerical Errors for Shear Stresses and Essential Flow Variables in a Ventricular Assist Device: Crucial for Blood Damage Prediction?

2018 ◽  
Vol 3 (4) ◽  
Author(s):  
Lucas Konnigk ◽  
Benjamin Torner ◽  
Sebastian Hallier ◽  
Matthias Witte ◽  
Frank-Hendrik Wurm
Keyword(s):  
Shear Stress ◽  
Prediction Models ◽  
Stokes Equations ◽  
Grid Size ◽  
Blood Pump ◽  
Navier Stokes ◽  
Shear Stresses ◽  
Damage Prediction ◽  
Blood Damage ◽  
Stress Calculation

Adverse events due to flow-induced blood damage remain a serious problem for blood pumps as cardiac support systems. The numerical prediction of blood damage via computational fluid dynamics (CFD) is a helpful tool for the design and optimization of reliable pumps. Blood damage prediction models primarily are based on the acting shear stresses, which are calculated by solving the Navier–Stokes equations on computational grids. The purpose of this paper is to analyze the influence of the spatial discretization and the associated discretization error on the shear stress calculation in a blood pump in comparison to other important flow quantities like the pressure head of the pump. Therefore, CFD analysis using seven unsteady Reynolds-averaged Navier–Stokes (URANS) simulations was performed. Two simple stress calculation indicators were applied to estimate the influence of the discretization on the results using an approach to calculate numerical uncertainties, which indicates discretization errors. For the finest grid with 19 × 106 elements, numerical uncertainties up to 20% for shear stresses were determined, while the pressure heads show smaller uncertainties with a maximum of 4.8%. No grid-independent solution for velocity gradient-dependent variables could be obtained on a grid size that is comparable to mesh sizes in state-of-the-art blood pump studies. It can be concluded that the grid size has a major influence on the shear stress calculation, and therefore, the potential blood damage prediction, and that the quantification of this error should always be taken into account.

Near Surface Velocity Distributions for Intermittent Separation of Turbulent Boundary Layers

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
V. A. Sandborn
Keyword(s):  
Shear Stress ◽  
Large Scale ◽  
Eddy Viscosity ◽  
Boundary Layer Separation ◽  
Surface Velocity ◽  
Surface Shear Stress ◽  
Mixing Length ◽  
Surface Shear ◽  
Near Surface ◽  
Stress Separation

At the location of intermittent turbulent boundary layer separation a finite positive mean surface shear stress still exists. It is demonstrated that viscous coordinates and a mixing length turbulent model may still be used at the location of intermittent separation. The large scale turbulent mixing in the separation region appears to require the universal mixing constant, K, increases with Reynolds number. Once true zero-mean-surface-shear-stress separation occurs, the mixing length model for the turbulent flow near the surface is no longer valid and a constant eddy viscosity is indicated.

Analysis of Shear Stress of Two Elasto-Plastic Random Surfaces

2011 ◽  
Vol 279 ◽  
pp. 224-229
Author(s):  
Lian Feng Lai ◽  
Cheng Hui Gao ◽  
Jian Meng Huang
Keyword(s):  
Shear Stress ◽  
Crack Initiation ◽  
Surface Crack ◽  
Wear Mechanisms ◽  
Shear Stresses ◽  
Two Dimensional ◽  
Crack Initiation And Propagation ◽  
Fea Model ◽  
Initiation And Propagation ◽  
Surface Crack Initiation

A FEA model of two-dimensional (2D) sliding between two interfering fractal rough solids was build, and the results was presented. The trends in shear stress between the rough solids were provided by the FEA. Combined with the delaminating theory of wear, the Maximum shear stresses and its distance are presented when loading and sliding. The result showed that the Maximum shear stresses was located in the subsurface which range about 2 to 8 um from the surface. In addition, with different plastic characteristics, the location of Maximum shear stresses were different. With modeling the contact and sliding between rough surfaces, the friction, sub-surface crack initiation and propagation and wear mechanisms can be understood deeply.

Large-scale vortex structures in turbulent wakes behind bluff bodies. Part 1. Vortex formation processes

1987 ◽  
Vol 174 ◽  
pp. 233-270 ◽  
Author(s):  
A. E. Perry ◽  
T. R. Steiner
Keyword(s):  
Large Scale ◽  
Vector Fields ◽  
Vortex Formation ◽  
Three Dimensional ◽  
Point Theory ◽  
Shear Stresses ◽  
Bluff Bodies ◽  
Two Dimensional ◽  
Mean Flow ◽  
Turbulent Wakes

An investigation of turbulent wakes was conducted and phase-averaged velocity vector fields are presented, as well as phase-averaged and global Reynolds normal and shear stresses. The topology of the phase-averaged velocity fields is discussed in terms of critical point theory. Here in Part 1, the vortex formation process in the cavity region of several nominally two-dimensional bluff bodies is investigated and described using phase-averaged streamlines where the measurements were made in a nominal plane of symmetry. It was found that the flows encountered were always three-dimensional and that the mean-flow patterns in the cavity region were quite different from those expected using classical two-dimensional assumptions.

Two-dimensional turbulent wakes

1967 ◽  
Vol 30 (3) ◽  
pp. 547-560 ◽  
Author(s):  
Ian S. Gartshore
Keyword(s):  
Shear Stress ◽  
Stress Reduction ◽  
Shear Stresses ◽  
Pressure Gradients ◽  
Two Dimensional ◽  
Stress Distributions ◽  
Mean Velocity ◽  
Lower Shear ◽  
Turbulent Wakes ◽  
Velocity Scale

The equations of mean motion indicate that two-dimensional turbulent wakes, when subjected to appropriately tailored adverse pressure gradients, can be self-preserving. An experimental examination of two nearly self-preserving wakes is reported here. Mean velocity, longitudinal and lateral turbulence intensity, inter-mittency and shear stress distributions have been measured and are compared with Townsend's data from the small-deficit undistorted wake. In comparison with the undistorted case, the present wakes have slightly lower turbulent intensities and significantly lower shear stresses, all quantities being non-dimensionalized by a local velocity scale taken as the maximum mean velocity deficit. A consideration of the reasons for the shear stress reduction leads to an expression from which the shear stresses in any symmetrical free equilibrium shear flow can be found. This relationship is used to calculate the rate of growth in the measured wakes, with reasonable success.

scholarly journals BEACH PROFILES AND ON-OFFSHORE SEDIMENT TRANSPORT

1980 ◽  
Vol 1 (17) ◽  
pp. 67 ◽  
Author(s):  
Akira Watanabe ◽  
Yoshihiko Riho ◽  
Kiyoshi Horikawa
Keyword(s):  
Shear Stress ◽  
Sediment Transport ◽  
Laboratory Test ◽  
Test Data ◽  
Critical Shear Stress ◽  
Two Dimensional ◽  
Bottom Shear Stress ◽  
Beach Profile ◽  
Profile Changes ◽  
Sloping Beach

The on-offshore sediment transport due to waves on a sloping beach is studied by analyzing the laboratory test data on two-dimensional beach deformation. The net rates of sediment transport both inside and outside the breaker zone are evaluated from beach profile changes and are related to the nondimensional bottom shear stress or the Shields parameter. The importance of the critical shear stress and of asymmetrical to-and-fro water partical motion near the bottom is pointed out.

scholarly journals MEASUREMENT AND MODELING OF SOLITARY WAVE INDUCED BED SHEAR STRESS OVER A ROUGH BED

2012 ◽  
Vol 1 (33) ◽  
pp. 21 ◽  
Author(s):  
Jaya Kumar Seelam ◽  
Tom E Baldock
Keyword(s):  
Shear Stress ◽  
Eddy Viscosity ◽  
Breaking Waves ◽  
Shear Stresses ◽  
Bed Shear Stress ◽  
Eddy Viscosity Model ◽  
Friction Factors ◽  
Convolution Model ◽  
Rough Bed ◽  
Bed Shear Stresses

Bed shear stresses generated by solitary waves were measured using a shear cell apparatus over a rough bed in laminar and transitional flow regimes (~7600 < Re < ~60200). Modeling of bed shear stress was carried out using analytical models employing convolution integration methods forced with the free stream velocity and three eddy viscosity models. The measured wave height to water depth (h/d) ratio varied between 0.13 and 0.65; maximum near- bed velocity varied between 0.16 and 0.47 m/s and the maximum total shear stress (sum of form drag and bed shear) varied between 0.565 and 3.29 Pa. Wave friction factors estimated from the bed shear stresses at the maximum bed shear stress using both maximum and instantaneous velocities showed that there is an increase in friction factors estimated using instantaneous velocities, for non-breaking waves. Maximum positive total stress was approximately 2.2 times larger than maximum negative total stress for non-breaking waves. Modeled and measured positive total stresses are well correlated using the convolution model with an eddy viscosity model analogous to steady flow conditions (nu_t=0.45u* z1; where nu_t is eddy viscosity, u* is shear velocity and z1 is the elevation parameter related to relative roughness). The bed shear stress leads the free stream fluid velocity by approximately 30° for non-breaking waves and by 48° for breaking waves, which is under-predicted by 27% by the convolution model with above mentioned eddy viscosity model.

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