Subgrid-Scale Modeling of Turbulent Convection Using Truncated Navier-Stokes Dynamics

2002 ◽  
Vol 124 (4) ◽  
pp. 823-828 ◽  
Author(s):  
J. A. Domaradzki ◽  
S. Radhakrishnan
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Small Scale ◽  
Subgrid Scale ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Scale Modeling ◽  
Large Eddy ◽  
Mesh Resolution ◽  
Subgrid Scale Modeling

Using concepts from the subgrid-scale estimation modeling we develop a procedure for large-eddy simulations which employs Navier-Stokes equations truncated to an available mesh resolution. Operationally the procedure consists of numerically solving the truncated Navier-Stokes equation and a periodic processing of the small scale component of its solution. The modeling procedure is applied to simulate turbulent Rayleigh-Be´nard convection.

Large Eddy Simulation of Turbulent-Cavitation Interactions in a Venturi Nozzle

2010 ◽  
Vol 132 (12) ◽  
Author(s):  
Nagendra Dittakavi ◽  
Aditya Chunekar ◽  
Steven Frankel
Keyword(s):  
Large Eddy Simulation ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Small Scale ◽  
Navier Stokes Equations ◽  
Vapor Cavity ◽  
Eddy Simulation ◽  
Downstream Region ◽  
Large Eddy ◽  
Venturi Nozzle

Large eddy simulation of turbulent cavitating flow in a venturi nozzle is conducted. The fully compressible Favre-filtered Navier–Stokes equations are coupled with a homogeneous equilibrium cavitation model. The dynamic Smagorinsky subgrid-scale turbulence model is employed to close the filtered nonlinear convection terms. The equations are numerically integrated in the context of a generalized curvilinear coordinate system to facilitate geometric complexities. A sixth-order compact finite difference scheme is employed for the Navier–Stokes equations with the AUSM+-up scheme to handle convective terms in the presence of large density gradients. The stiffness of the system due to the incompressibility of the liquid phase is addressed through an artificial increase in the Mach number. The simulation predicts the formation of a vapor cavity at the venturi throat with an irregular shedding of the small scale vapor structures near the turbulent cavity closure region. The vapor formation at the throat is observed to suppress the velocity fluctuations due to turbulence. The collapse of the vapor structures in the downstream region is a major source of vorticity production, resulting into formation of hair-pin vortices. A detailed analysis of the vorticity transport equation shows a decrease in the vortex-stretching term due to cavitation. A substantial increase in the baroclinic torque is observed in the regions where the vapor structures collapse. A spectra of the pressure fluctuations in the far-field downstream region show an increase in the acoustic noise at high frequencies due to cavitation.

MATHEMATICAL ANALYSIS FOR THE RATIONAL LARGE EDDY SIMULATION MODEL

2002 ◽  
Vol 12 (08) ◽  
pp. 1131-1152 ◽  
Author(s):  
LUIGI C. BERSELLI ◽  
GIOVANNI P. GALDI ◽  
TRAIAN ILIESCU ◽  
WILLIAM J. LAYTON
Keyword(s):  
Large Eddy Simulation ◽  
Simulation Model ◽  
Stokes Equations ◽  
Strong Solutions ◽  
Navier Stokes ◽  
Subgrid Scale ◽  
Navier Stokes Equations ◽  
Large Eddy Simulation Model ◽  
Eddy Simulation ◽  
Large Eddy

In this paper we consider the Rational Large Eddy Simulation model recently introduced by Galdi and Layton. We briefly present this model, which (in principle) is similar to others commonly used, and we prove the existence and uniqueness of a class of strong solutions. Contrary to the gradient model, the main feature of this model is that it allows a better control of the kinetic energy. Consequently, to prove existence of strong solutions, we do not need subgrid-scale regularization operators, as proposed by Smagorinsky. We also introduce some breakdown criteria that are related to the Euler and Navier–Stokes equations.

Large eddy simulation of the atmosphere on various scales

2009 ◽  
Vol 367 (1899) ◽  
pp. 2947-2956 ◽  
Author(s):  
M.J.P. Cullen ◽  
A.R. Brown
Keyword(s):  
Large Eddy Simulation ◽  
Stokes Equations ◽  
Lower Boundary ◽  
Navier Stokes ◽  
Small Scale ◽  
Navier Stokes Equations ◽  
Weather Forecasts ◽  
Eddy Simulation ◽  
Scale Models ◽  
Large Eddy

Numerical simulations of the atmosphere are routinely carried out on various scales for purposes ranging from weather forecasts for local areas a few hours ahead to forecasts of climate change over periods of hundreds of years. Almost without exception, these forecasts are made with space/time-averaged versions of the governing Navier–Stokes equations and laws of thermodynamics, together with additional terms representing internal and boundary forcing. The calculations are a form of large eddy modelling, because the subgrid-scale processes have to be modelled. In the global atmospheric models used for long-term predictions, the primary method is implicit large eddy modelling, using discretization to perform the averaging, supplemented by specialized subgrid models, where there is organized small-scale activity, such as in the lower boundary layer and near active convection. Smaller scale models used for local or short-range forecasts can use a much smaller averaging scale. This allows some of the specialized subgrid models to be dropped in favour of direct simulations. In research mode, the same models can be run as a conventional large eddy simulation only a few orders of magnitude away from a direct simulation. These simulations can then be used in the development of the subgrid models for coarser resolution models.

scholarly journals Generalized Navier–Stokes Equations and Dynamics of Plane Molecular Media

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 288
Author(s):  
Alexei Kushner ◽  
Valentin Lychagin
Keyword(s):  
Carbon Dioxide ◽  
Internal Structure ◽  
Stokes Equation ◽  
Hydrogen Cyanide ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations

The first analysis of media with internal structure were done by the Cosserat brothers. Birkhoff noted that the classical Navier–Stokes equation does not fully describe the motion of water. In this article, we propose an approach to the dynamics of media formed by chiral, planar and rigid molecules and propose some kind of Navier–Stokes equations for their description. Examples of such media are water, ozone, carbon dioxide and hydrogen cyanide.

A note on the solution of the Navier-Stokes equations for a spherically symmetric expansion into a very low pressure

1973 ◽  
Vol 59 (2) ◽  
pp. 391-396 ◽  
Author(s):  
N. C. Freeman ◽  
S. Kumar
Keyword(s):  
Shock Wave ◽  
Reynolds Number ◽  
Stokes Equation ◽  
Stokes Equations ◽  
Low Pressure ◽  
Navier Stokes ◽  
Spherically Symmetric ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Type Flow

It is shown that, for a spherically symmetric expansion of a gas into a low pressure, the shock wave with area change region discussed earlier (Freeman & Kumar 1972) can be further divided into two parts. For the Navier–Stokes equation, these are a region in which the asymptotic zero-pressure behaviour predicted by Ladyzhenskii is achieved followed further downstream by a transition to subsonic-type flow. The distance of this final region downstream is of order (pressure)−2/3 × (Reynolds number)−1/3.

The Onset of Turbulence: Insights Into the Navier-Stokes Equations

2017 ◽  
Author(s):  
Carl E. Rathmann
Keyword(s):  
Stokes Equations ◽  
Direct Consequence ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Fluid Behavior ◽  
Onset Of Turbulence ◽  
And Mathematics ◽  
High Reynolds

For well over 150 years now, theoreticians and practitioners have been developing and teaching students easily visualized models of fluid behavior that distinguish between the laminar and turbulent fluid regimes. Because of an emphasis on applications, perhaps insufficient attention has been paid to actually understanding the mechanisms by which fluids transition between these regimes. Summarized in this paper is the product of four decades of research into the sources of these mechanisms, at least one of which is a direct consequence of the non-linear terms of the Navier-Stokes equation. A scheme utilizing chaotic dynamic effects that become dominant only for sufficiently high Reynolds numbers is explored. This paper is designed to be of interest to faculty in the engineering, chemistry, physics, biology and mathematics disciplines as well as to practitioners in these and related applications.

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