Anisotropy Properties of Turbulence in Flow Over Seepage Bed

2021 ◽  
Author(s):  
Anurag Sharma ◽  
Bimlesh Kumar
Keyword(s):  
Reynolds Stress ◽  
Isotropic Turbulence ◽  
Outer Region ◽  
Seepage Flow ◽  
Invariant Function ◽  
Data Sets ◽  
Flow Depth ◽  
Seepage Flows ◽  
Two Component ◽  
Anisotropy Tensor

Abstract The present study analyses the Reynolds stress anisotropy in the non-uniform sediment beds under the condition of no seepage and downward seepage flow. The results show the estimation of the deviation measure from the isotropic turbulence in view of Reynolds stress tensor for turbulent flow in the presence of seepage through the channel bed. The investigation presents the Lumley triangle for flow turbulence, Eigen values, and the invariant functions for the whole flow depth subjected to no seepage and seepage beds. The longitudinal profile of anisotropy tensor within the near-bed zone for seepage flow provides the higher anisotropic stream than those of no seepage flow, while the remaining (transverse and vertical) profiles of anisotropy tensor in the vicinity of bed for seepage flows provides lower anisotropic stream. The anisotropic invariant maps show the near bed anisotropy inclining to be a two-component isotropy subjected to no seepage and seepage flow. With the increase in vertical distance from bed surface that is close to the water surface, the data sets of anisotropic invariant maps for no seepage and seepage flows show a trend of one-component isotropy, while it has an affinity to develop a three-component isotropy in the vicinity of mid zone of the flow depth. Invariant function data sets present a well two-component isotropy in the near bed region of flow and a quasi-three component isotropy in the outer region of flow for seepage flows as compared to no seepage flow.

scholarly journals Reynolds averaged turbulence modelling using deep neural networks with embedded invariance

2016 ◽  
Vol 807 ◽  
pp. 155-166 ◽  
Author(s):  
Julia Ling ◽  
Andrew Kurzawski ◽  
Jeremy Templeton
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Reynolds Stress ◽  
Network Architecture ◽  
Eddy Viscosity ◽  
Deep Neural Networks ◽  
Test Cases ◽  
Neural Network Architecture ◽  
Stress Anisotropy ◽  
Anisotropy Tensor

There exists significant demand for improved Reynolds-averaged Navier–Stokes (RANS) turbulence models that are informed by and can represent a richer set of turbulence physics. This paper presents a method of using deep neural networks to learn a model for the Reynolds stress anisotropy tensor from high-fidelity simulation data. A novel neural network architecture is proposed which uses a multiplicative layer with an invariant tensor basis to embed Galilean invariance into the predicted anisotropy tensor. It is demonstrated that this neural network architecture provides improved prediction accuracy compared with a generic neural network architecture that does not embed this invariance property. The Reynolds stress anisotropy predictions of this invariant neural network are propagated through to the velocity field for two test cases. For both test cases, significant improvement versus baseline RANS linear eddy viscosity and nonlinear eddy viscosity models is demonstrated.

Visual Simulation of Soil-Structure Destruction with Seepage Flows

2021 ◽  
Vol 4 (3) ◽  
pp. 1-18
Author(s):  
Xu Wang ◽  
Makoto Fujisawa ◽  
Masahiko Mikawa
Keyword(s):  
Soil Structure ◽  
Water Saturation ◽  
Seepage Flow ◽  
Momentum Exchange ◽  
Visual Effects ◽  
Seepage Rate ◽  
Capillary Model ◽  
Seepage Flows ◽  
Dam Breaking ◽  
Soil And Water

This paper introduces a method for simulating soil-structure coupling with water, which involves a series of visual effects, including wet granular materials, seepage flows, capillary action between grains, and dam breaking simulation. We develop a seepage flow based SPH-DEM framework to handle soil and water particles interactions through a momentum exchange term. In this framework, water is seen as a seepage flow through porous media by Darcy's law; the seepage rate and the soil permeability are manipulated according to drag coefficient and soil porosity. A water saturation-based capillary model is used to capture various soil behaviors such as sandy soil and clay soil. Furthermore, the capillary model can dynamically adjust liquid bridge forces induced by surface tension between soil particles. The adhesion model describes the attraction ability between soil surfaces and water particles to achieve various visual effects for soil and water. Lastly, this framework can capture the complicated dam-breaking scenarios caused by overtopping flow or internal seepage erosion that are challenging to simulate.

Turbulence Anisotropy Investigations in an Internal Combustion Engine

2021 ◽  
Author(s):  
James R MacDonald ◽  
Claudia Fajardo
Keyword(s):  
Internal Combustion Engine ◽  
Isotropic Turbulence ◽  
Combustion Engine ◽  
Internal Combustion ◽  
Two Dimensional ◽  
Velocity Data ◽  
Compression Stroke ◽  
Turbulence Anisotropy ◽  
Anisotropy Tensor ◽  
Component Velocity

Abstract The assumption of isotropic turbulence is commonly incorporated into models of internal combustion engine (ICE) in-cylinder flows. While preliminary analysis with two-dimensional velocity data indicates that the turbulence may tend to isotropy as the piston approaches TDC, the validity of this assumption has not been fully investigated, partially due to lack of three-component velocity data in ICEs. In this work, the velocity was measured using two-dimensional, three-component (2D-3C) particle image velocimetry in a single-cylinder, motored, research engine to investigate the evolution of turbulence anisotropy throughout the compression stroke. Invariants of the Reynolds stress anisotropy tensor were calculated and visualized, through the Lumley triangle, to investigate turbulence states. Results showed the turbulence to be mostly anisotropic, with preferential tendency toward 2D axisymmetry at the beginning of the compression stroke and approaching isotropy near top-dead-center. Findings provide new insights into turbulence in dynamic, bounded flows to assist with the development of physics-based, quantitative models.

Modelling of rapid pressure—strain in Reynolds-stress closures

1994 ◽  
Vol 269 ◽  
pp. 143-168 ◽  
Author(s):  
Arne V. Johansson ◽  
Magnus Hallbäck
Keyword(s):  
Strain Rate ◽  
Reynolds Stress ◽  
Sudden Change ◽  
Model Parameters ◽  
Rapid Distortion Theory ◽  
Flow Parameters ◽  
Turbulent Reynolds Number ◽  
Principal Axes ◽  
Anisotropy Tensor ◽  
Rapid Pressure

The most general form for the rapid pressure—strain rate, within the context of classical Reynolds-stress transport (RST) closures for homogeneous flows, is derived, and truncated forms are obtained with the aid of rapid distortion theory. By a classical RST-closure we here denote a model with transport equations for the Reynolds stress tensor and the total dissipation rate. It is demonstrated that all earlier models for the rapid pressure—strain rate within the class of classical Reynolds-stress closures can be formulated as subsets of the general form derived here. Direct numerical simulations were used to show that the dependence on flow parameters, such as the turbulent Reynolds number, is small, allowing rapid distortion theory to be used for the determination of model parameters. It was shown that such a nonlinear description, of fourth order in the Reynolds-stress anisotropy tensor, is quite sufficient to very accurately model the rapid pressure—strain in all cases of irrotational mean flows, but also to get reasonable predictions in, for example, a rapid homogeneous shear flow. Also, the response of a sudden change in the orientation of the principal axes of a plane strain is investigated for the present model and models proposed in the literature. Inherent restrictions on the predictive capability of Reynolds-stress closures for rotational effects are identified.

Anisotropy Invariants of Reynolds Stress Tensor in a Duct Flow and Turbulent Boundary Layer

1998 ◽  
Vol 120 (2) ◽  
pp. 280-284 ◽  
Author(s):  
A. Mazouz ◽  
L. Labraga ◽  
C. Tournier
Keyword(s):  
Surface Roughness ◽  
Turbulent Flow ◽  
Stress Tensor ◽  
Reynolds Stress ◽  
Pipe Flow ◽  
Duct Flow ◽  
Reynolds Stress Tensor ◽  
Entire Thickness ◽  
Anisotropy Tensor ◽  
Flow Turbulence

The present study shows that the Reynolds stress anisotropy tensor for turbulent flow depends both on the nature of the surface and the boundary conditions of the flow. Contrary to the case of turbulent boundary layers with k-type surface roughness, the measured anisotropy invariants of the Reynolds stress tensor over a series of spanwise square bars separated by rectangular cavities (k-type) in duct flows show that roughness increases the anisotropy. There is a similarity between the effect of roughness on channel flow turbulence and that on pipe flow turbulence. The present data show that the effect of introducing a surface roughness significantly perturbs the entire thickness of the turbulent flow.

Turbulence anisotropy with higher-order moments in flow through passive grid under rigid boundary influence

2020 ◽  
pp. 095440622096973
Author(s):  
Pankaj Kumar Raushan ◽  
Santosh Kumar Singh ◽  
Koustuv Debnath
Keyword(s):  
Reynolds Stress ◽  
Isotropic Turbulence ◽  
Near Field ◽  
Far Field ◽  
Field Region ◽  
Rigid Boundary ◽  
Third Order ◽  
Solidity Ratio ◽  
Eigen Values ◽  
Flow Through

The investigation presents the estimate of the degree of deviation from the isotropic turbulence in terms of Reynolds stress tensor for grid generated turbulence under the influence of bottom boundary. The turbulence triangle, Eigen values, and the invariant functions are presented at near and far field regions of the grids with different solidity ratio. In addition, the work also deals with the analysis based on third-order moments of the velocity fluctuations and the ratio of momentum flux to the turbulent kinetic energy in the frequency domain. The Reynolds stress anisotropy exposes that the anisotropic invariant maps possess a closed looping trend in the near field region and an open looping trend in the far-field region of the grid. Further, to describe the physical behaviour of the velocity time-series of random fluctuating components in the stream-wise directions, the probability distribution function are estimated and interpreted.

A Priori Analysis of Explicit Algebraic Stress Models for a Turbulent Flow Through a Straight Square Duct

2004 ◽  
Author(s):  
H. Naji ◽  
O. El Yahyaoui ◽  
G. Mompean
Keyword(s):  
Turbulent Flow ◽  
Reynolds Stress ◽  
Stokes Equations ◽  
A Priori ◽  
Proximity Effects ◽  
Navier Stokes ◽  
Wall Region ◽  
Square Duct ◽  
Anisotropy Tensor ◽  
Stress Models

The ability of two explicit algebraic Reynolds stress models (EARSMs) to accurately predict the problem of fully turbulent flow in a straight square duct is studied. The first model is devised by Gatski and Rumsey (2001) and the second is the one derived by Wallin and Johansson (2000). These models are studied using a priori procedure based on data resulting from direct numerical simulation (DNS) of the Navier-Stokes equations, which is available for this problem. For this case, we show that the equilibrium assumption for the anisotropy tensor is found to be correct. The analysis leans on the maps of the second and third invariants of the Reynolds stress tensor. In order to handle wall-proximity effects in the near-wall region, damping functions are implemented in the two models. The predictions and DNS obtained for a Reynolds number of 4800 both agree well and show that these models are able to predict such flows.

Large-scale characteristics of a stably stratified turbulent shear layer

2021 ◽  
Vol 927 ◽  
Author(s):  
Tomoaki Watanabe ◽  
Koji Nagata
Keyword(s):  
Shear Layer ◽  
Reynolds Stress ◽  
Large Scale ◽  
Outer Region ◽  
Turbulent Shear ◽  
Wall Region ◽  
Late Time ◽  
Turbulent Shear Layer ◽  
Small Scales ◽  
Scale Characteristics

Implicit large eddy simulation is performed to investigate large-scale characteristics of a temporally evolving, stably stratified turbulent shear layer arising from the Kelvin–Helmholtz instability. The shear layer at late time has two energy-containing length scales: the scale of the shear layer thickness, which characterizes large-scale motions (LSM) of the shear layer; and the larger streamwise scale of elongated large-scale structures (ELSS), which increases with time. The ELSS forms in the middle of the shear layer when the Richardson number is sufficiently large. The contribution of the ELSS to velocity and density variances becomes relatively important with time although the LSM dominate the momentum and density transport. The ELSS have a highly anisotropic Reynolds stress, to a degree similar to the near-wall region of turbulent boundary layers, while the Reynolds stress of the LSM is as anisotropic as in the outer region. Peaks in the spectral energy density associated with the ELSS emerge because of the slow decay of turbulence at very large scales. A forward interscale energy transfer from large to small scales occurs even at a small buoyancy Reynolds number. However, an inverse transfer also occurs for the energy of spanwise velocity. Negative production of streamwise velocity and density spectra, i.e. counter-gradient transport of momentum and density, is found at small scales. These behaviours are consistent with channel flows, indicating similar flow dynamics in the stratified shear layer and wall-bounded shear flows. The structure function exhibits a logarithmic law at large scales, implying a $k^{-1}$ scaling of energy spectra.

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