Modeling of a One-Equation LES for Plant Canopy Flows

2011 ◽  
Author(s):  
Hisashi Hiraoka
Keyword(s):  
Kinetic Energy ◽  
Energy Equation ◽  
Navier Stokes ◽  
Plant Canopy ◽  
Production Term ◽  
Eddy Simulation ◽  
Dissipation Term ◽  
Wake Production ◽  
Canopy Flows ◽  
Basic Equations

A one-equation-type subgrid-scale (SGS) model was proposed in order to enable the large eddy simulation (LES) of plant canopy flows. The SGS kinetic energy equation was derived from the equations of continuity and Navier-Stokes. This equation was closed by modeling the unknown terms according to the physical meaning of each term in the equation. The wake production term in the SGS kinetic equation could be derived analytically. However, the wake dissipation term did not appear when the SGS kinetic energy equation was derived from the basic equations.

Note on Turbulent Kinetic Energy Production for Reynolds-Averaged Navier–Stokes Models

2016 ◽  
Vol 138 (11) ◽  
Author(s):  
Solkeun Jee ◽  
Gorazd Medic ◽  
Georgi Kalitzin
Keyword(s):  
Kinetic Energy ◽  
Strain Rate ◽  
Turbulent Kinetic Energy ◽  
Energy Equation ◽  
Boussinesq Approximation ◽  
Navier Stokes ◽  
Mean Flow ◽  
Production Term ◽  
The Mean ◽  
Reynolds Averaged Navier Stokes

Linear eddy-viscosity Reynolds-Averaged Navier–Stokes (RANS) turbulence models are based on the Boussinesq approximation that asserts the Reynolds stresses to be linearly dependent on the mean strain rate. Using the Boussinesq approximation for the Reynolds stress yields a production term in the turbulent kinetic energy equation that is proportional to the square of the magnitude of the strain rate tensor. For some flows, this relation to the strain causes overproduction of turbulence. Widely used ad hoc modifications of the production term using vorticity lead to an inconsistent energy balance in the mean flow kinetic energy equation, violating the energy conservation. In this note, how to obtain a consistent RANS framework for a given production term modification is shown.

A k-ε Model for Particle-Laden Turbulent Flows

2009 ◽  
Author(s):  
J. D. Schwarzkopf ◽  
C. T. Crowe ◽  
P. Dutta
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Turbulent Flows ◽  
Carrier Phase ◽  
Critical Role ◽  
New Production ◽  
Mean Velocity ◽  
Production Term ◽  
Dissipation Term ◽  
Velocity Gradients

A dissipation transport equation for the carrier phase of particle-laden turbulent flows was recently developed. This equation shows a new production of dissipation term due to the presence of particles that is related to the velocity difference between the particle and the surrounding fluid. In the development, it was assumed that each coefficient was the sum of the coefficient for single phase flow and a coefficient quantifying the contribution of the particulate phase. The coefficient for the new production term (due to the presence of particles) was found from homogeneous turbulence generation by particles and the coefficient for the dissipation of dissipation term was analyzed using DNS. A numerical model was developed and applied to particles falling in a channel of downward turbulent air flow. Boundary conditions were also developed to ensure that the production of turbulent kinetic energy due to mean velocity gradients and particle surfaces balanced with the turbulent dissipation near the wall. The turbulent kinetic energy is compared with experimental data. The results show attenuation of turbulent kinetic energy with increased particle loading; however the model does under predict the turbulent kinetic energy near the center of the channel. To understand the effect of this additional production of dissipation term (due to particles), the coefficients associated with the production of dissipation due to mean velocity gradients and particle surfaces are varied to assess the effects of the dispersed phase on the carrier phase turbulent kinetic energy across the channel. The results show that this additional term plays a significant role in predicting the turbulent kinetic energy and a reason for under predicting the turbulent kinetic energy near the center of the channel is discussed. It is concluded that the dissipation coefficients play a critical role in predicting the turbulent kinetic energy in particle-laden turbulent flows.

Study of unsteady cavitating flow around Clark-Y hydrofoil using nonlinear PANS model with near-wall correction

2021 ◽  
Author(s):  
Benqing Liu ◽  
Wei Yang ◽  
Sien Li ◽  
Jie Chen ◽  
Biao Huang ◽  
...  
Keyword(s):  
Turbulent Transport ◽  
Cavitating Flow ◽  
Navier Stokes ◽  
Cloud Cavitation ◽  
Production Term ◽  
Dissipation Term ◽  
Lift And Drag ◽  
Lift And Drag Coefficient ◽  
Drag Ratio ◽  
Near Wall

In this paper, we describe the use of a new nonlinear partially-averaged Navier–Stokes (PANS) model with near-wall correction for simulating the cavitating flow around a Clark-Y hydrofoil. For comparison, the standard [Formula: see text]–[Formula: see text] PANS model is also used. The results demonstrate that compared to [Formula: see text]–[Formula: see text] PANS and experiment, the new PANS model shows better performance for cavitation flow, including time-averaged velocity, root mean square (rms) velocity and cavity shedding processing. Through the calculation of the lift and drag coefficient at [Formula: see text] and [Formula: see text], it can be concluded that the cavitation will decrease the lift and increase the drag of the hydrofoil, resulting in a decrease of the lift-to-drag ratio. From the analysis of different terms in both the turbulent kinetic energy (TKE) and dissipation rate transport equations of the cloud cavitation, it is found that the production term and the dissipation term are dominant in the turbulent transport, and they are mainly distributed in the vapor–liquid interface and the trailing edge of the hydrofoil.

scholarly journals Large Eddy Simulation of Laminar and Turbulent Flow on Collocated and Staggered Grids

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
M. J. Ketabdari ◽  
H. Saghi
Keyword(s):  
Stokes Equations ◽  
Solution Procedure ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Staggered Grids ◽  
Driven Cavity ◽  
Eddy Simulation ◽  
Laminar And Turbulent Flow ◽  
Basic Equations ◽  
Collocated Grids

Momentum and Continuity are the basic equations for fluid flow modeling. The momentum equations in their final form are known as Navier-Stokes equations and can be solved using different numerical methods. There are several approaches such as SIMPLE, PISO, and Fractional Step for solving these equations. In solution procedure, it needs to decide where to store the velocity components. Staggered and Collocated grids can be used to evaluate this problem. On Staggered grids, the velocity components are stored at the cell face, and the scalar variables such as pressure are stored at the central nodes. However, on Collocated grids, all parameters are defined at the same location at the central nodes. The Staggered grids method gives more accurate pressure gradient estimation. However, Collocated grids method is simpler for solving the equations. In this paper, for solving Navier-Stokes equations, Collocated and Staggered grids are employed. Comparison of horizontal and vertical velocities and stream lines at various Reynolds numbers was performed. The results were validated using standard tests such as lid-driven cavity, channel and backward facing step. Discussion is made on accuracy of these methods to estimate horizontal and vertical velocity profiles.

scholarly journals Evaluation of mean velocity and mean speed for test ventilated room from RANS and LES CFD modeling

2019 ◽  
Vol 85 ◽  
pp. 02004 ◽  
Author(s):  
Nikolay Ivanov ◽  
Marina Zasimova ◽  
Evgueni Smirnov ◽  
Detelin Markov
Keyword(s):  
Kinetic Energy ◽  
Cfd Modeling ◽  
Navier Stokes ◽  
Velocity Data ◽  
Mean Velocity ◽  
Energy Field ◽  
Eddy Simulation ◽  
Large Eddy ◽  
The Mean ◽  
The Difference

The paper presents and discusses data for the ventilation airflow in an isothermal room corresponding to the Nielsen et al. (1978) test computed with Large Eddy Simulation (LES) and Reynolds-Averaged Navier-Stokes (RANS) approaches. As LES computations provide directly both the speed and velocity components data, the difference between the mean speed and mean velocity values is computed and discussed. For the RANS computations that give the mean velocity data only, application of the velocity-to-speed conversion procedure based on the turbulence kinetic energy field provided by a turbulence model resulted in accurate mean speed evaluation.

Roughness effects on the Reynolds stress budgets in near-wall turbulence

2014 ◽  
Vol 760 ◽  
Author(s):  
Junlin Yuan ◽  
Ugo Piomelli
Keyword(s):  
Kinetic Energy ◽  
Outer Layer ◽  
Reynolds Shear Stress ◽  
Wall Turbulence ◽  
Roughness Sublayer ◽  
Spatial Inhomogeneity ◽  
Mean Flow ◽  
Production Term ◽  
Turbulent Fluctuations ◽  
Wake Production

AbstractThe physics of the roughness sublayer are studied by direct numerical simulations (DNS) of an open-channel flow with sandgrain roughness. A double-averaging (DA) approach is used to separate the spatial variations of the time-averaged quantities and the turbulent fluctuations. The spatial inhomogeneity of velocity and Reynolds stresses results in an additional production term for the turbulent kinetic energy (TKE) – the ‘wake production’; it is the excess wake kinetic energy (WKE), generated from the work of mean flow against the form drag, that is not directly dissipated into heat, but instead converted into turbulence. The wake production promotes wall-normal turbulent fluctuations and increases the pressure work, which ultimately leads to more homogeneous turbulence in the roughness sublayer, and to the increase of Reynolds shear stress and the drag on the rough wall. In the fully rough regime, roughness directly affects the generation of the wall-normal fluctuations, while in the transitionally rough regime, the region affected by roughness is separated from the region of intense generation of these fluctuations. The budget of the WKE and the connection between the wake and the turbulence suggest strong interactions between the roughness sublayer and the outer layer that are insensitive to the variation of the outer-layer conditions. Furthermore, the present results may have implications for the relationship between the roughness geometry and the flow dynamics in the region directly affected by roughness.

scholarly journals Large-eddy simulation of plant canopy flows using plant-scale representation

2007 ◽  
Vol 124 (2) ◽  
pp. 183-203 ◽  
Author(s):  
Wusi Yue ◽  
Marc B. Parlange ◽  
Charles Meneveau ◽  
Weihong Zhu ◽  
René van Hout ◽  
...  
Keyword(s):  
Large Eddy Simulation ◽  
Plant Canopy ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Canopy Flows

Spectra and Cospectra Over Flat Uniform Terrain

1994 ◽  
Author(s):  
J. C. Kaimal ◽  
J. J. Finnigan
Keyword(s):  
Boundary Layer ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Turbulent Flows ◽  
Energy Equation ◽  
Spatial Scales ◽  
Random Forcing ◽  
Dissipation Term ◽  
Turbulent Kinetic Energy Equation

Turbulent flows like those in the atmospheric boundary layer can be thought of as a superposition of eddies—coherent patterns of velocity, vorticity, and pressure— spread over a wide range of sizes. These eddies interact continuously with the mean flow, from which they derive their energy, and also with each other. The large “energy-containing” eddies, which contain most of the kinetic energy and are responsible for most of the transport in the turbulence, arise through instabilities in the background flow. The random forcing that provokes these instabilities is provided by the existing turbulence. This is the process represented in the production terms of the turbulent kinetic energy equation (1.59) in Chapter 1. The energy-containing eddies themselves are also subject to instabilities, which in their case are provoked by other eddies. This imposes upon them a finite lifetime before they too break up into yet smaller eddies. This process is repeated at all scales until the eddies become sufficiently small that viscosity can affect them directly and convert their kinetic energy to internal energy (heat). The action of viscosity is captured in the dissipation term of the turbulent kinetic energy equation. The second-moment budget equations presented in Chapter 1, of which (1.59) is one example, describe the summed behavior of all the eddies in the turbulent flow. To understand the conversion of mean kinetic energy into turbulent kinetic energy in the large eddies, the handing down of this energy to eddies of smaller and smaller scale in an “eddy cascade” process, and its ultimate conversion to heat by viscosity, we must isolate the different scales of turbulent motion and separately observe their behavior. Taking Fourier spectra and cospectra of the turbulence offers a convenient way of doing this. The spectral representation associates with each scale of motion the amount of kinetic energy, variance, or eddy flux it contributes to the whole and provides a new and invaluable perspective on boundary layer structure. The spectrum of boundary layer fluctuations covers a range of more than five decades: millimeters to kilometers in spatial scales and fractions of a second to hours in temporal scales.

Dynamic -equation model for large-eddy simulation of compressible flows

2012 ◽  
Vol 699 ◽  
pp. 385-413 ◽  
Author(s):  
Xiaochuan Chai ◽  
Krishnan Mahesh
Keyword(s):  
Kinetic Energy ◽  
Total Energy ◽  
Compressible Flows ◽  
Eddy Viscosity ◽  
Energy Equation ◽  
Isotropic Turbulence ◽  
Equation Model ◽  
Eddy Simulation ◽  
Eddy Viscosity Model ◽  
Large Eddy

AbstractThis paper presents a dynamic one-equation eddy viscosity model for large-eddy simulation (LES) of compressible flows. The transport equation for subgrid-scale (SGS) kinetic energy is introduced to predict SGS kinetic energy. The exact SGS kinetic energy transport equation for compressible flows is derived formally. Each of the unclosed terms in the SGS kinetic energy equation is modelled separately and dynamically closed, instead of being grouped into production and dissipation terms, as in the Reynolds averaged Navier–Stokes equations. All of the SGS terms in the filtered total energy equation are found to reappear in the SGS kinetic energy equation. Therefore, these terms can be included in the total energy equation without adding extra computational cost. A priori tests using direct numerical simulation (DNS) of decaying isotropic turbulence show that, for a Smagorinsky-type eddy viscosity model, the correlation between the SGS stress and the model is comparable to that from the original model. Also, the suggested model for the pressure dilatation term in the SGS kinetic energy equation is found to have a high correlation with its actual value. In a posteriori tests, the proposed dynamic $k$-equation model is applied to decaying isotropic turbulence and normal shock–isotropic turbulence interaction, and yields good agreement with available experimental and DNS data. Compared with the results of the dynamic Smagorinsky model (DSM), the $k$-equation model predicts better energy spectra at high wavenumbers, similar kinetic energy decay and fluctuations of thermodynamic quantities for decaying isotropic turbulence. For shock–turbulence interaction, the $k$-equation model and the DSM predict similar evolutions of turbulent intensities across shocks, owing to the dominant effect of linear interaction. The proposed $k$-equation model is more robust in that local averaging over neighbouring control volumes is sufficient to regularize the dynamic procedure. The behaviour of pressure dilatation and dilatational dissipation is discussed through the budgets of the SGS kinetic energy equation, and the importance of the dilatational dissipation term is addressed.

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