A class of subgrid-scale models preserving the symmetry group of Navier–Stokes equations

2007 ◽  
Vol 12 (3) ◽  
pp. 243-253 ◽  
Author(s):  
Dina Razafindralandy ◽  
Aziz Hamdouni ◽  
Claudine Béghein
Keyword(s):  
Symmetry Group ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Subgrid Scale ◽  
Navier Stokes Equations ◽  
Scale Models

LES of Compressible Turbulent Annular Pipe Flow With a Rotating Wall

2003 ◽  
Author(s):  
Joon Sang Lee ◽  
Xiaofeng Xu ◽  
R. H. Pletcher
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Stokes Equations ◽  
Outer Wall ◽  
Navier Stokes ◽  
Subgrid Scale ◽  
Turbulent Structures ◽  
Navier Stokes Equations ◽  
Rotating Wall ◽  
Annular Pipe

Flow in an annular pipe with and without a wall rotating about its axis was investigated at moderate Reynolds numbers. The compressible filtered Navier-Stokes equations were solved using a second order accurate finite volume method. Low Mach number preconditioning was used to enable the compressible code to work efficiently at low Mach numbers. A dynamic subgrid-scale stress model accounted for the subgrid-scale turbulence. When the outer wall rotated, a significant reduction of turbulent kinetic energy was realized near the rotating wall and the intensity of bursting effects appeared to decrease. This modification of the turbulent structures was related to the vortical structure changes near the rotating wall. It has been observed that the wall vortices were pushed in the direction of rotation and their intensity increased near the non-rotating wall. The consequent effect was to enhance the turbulent kinetic energy and increased the intensity of the heat transfer rate there.

scholarly journals Dynamic Modeling of α in the Isotropic Lagrangian Averaged Navier-Stokes-α Equations

2004 ◽  
Author(s):  
Hongwu Zhao ◽  
Kamran Mohseni ◽  
Jerrold E. Marsden
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Future Research ◽  
Computational Domain ◽  
Subgrid Scale ◽  
Navier Stokes Equations ◽  
Test Filter ◽  
Decaying Turbulence ◽  
Turn Over ◽  
Spatially Varying

A dynamic procedure for the Lagrangian Averaged Navier-Stokes-α (LANS-α) equations is developed where the variation in the parameter α in the direction of anisotropy is determined in a self-consistent way from data contained in the simulation itself. In order to derive this model, the incompressible Navier-Stokes equations are Helmholtz-filtered at the grid and a test filter levels. A Germano type identity is derived by comparing the filtered subgrid scale stress terms with those given in the LANS-α equations. Assuming constant α in homogenous directions of the flow and averaging in these directions, results in a nonlinear equation for the parameter α, which determines the variation of α in the non-homogeneous directions or in time. Consequently, the parameter α is calculated during the simulation instead of a pre-defined value. As an initial test, the dynamic LANS-α model is used to compute isotropic homogenous forced and decaying turbulence, where α is constant over the computational domain, but is allowed to vary in time. The resulting simulations are compared with direct numerical simulations and with the LANS-α simulations using fixed value of α. As expected, α is found to change rapidly during the first eddy turn-over time during the simulations. It is also observed that by using the dynamic LANS-α procedure a more accurate simulation of the isotropic homogeneous turbulence is achieved. The energy spectra and the total kinetic energy decay are captured more accurately as compared with the LANS-α simulations using a fixed α. The current results suggest some promising applications of this dynamic LANS-α model, such as to a spatially varying turbulent flow, which we hope to undertake in future research.

scholarly journals Assessment of Solution Algorithms for LES of Turbulent Flows Using OpenFOAM

Fluids ◽  
2019 ◽  
Vol 4 (3) ◽  
pp. 171 ◽  
Author(s):  
Santiago López Castaño ◽  
Andrea Petronio ◽  
Giovanni Petris and Vincenzo Armenio 
Keyword(s):  
Turbulent Flows ◽  
Mixed Model ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Subgrid Scale ◽  
Reynolds Analogy ◽  
Navier Stokes Equations ◽  
Hexahedral Meshes ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

We validate and test two algorithms for the time integration of the Boussinesq form of the Navier—Stokes equations within the Large Eddy Simulation (LES) methodology for turbulent flows. The algorithms are implemented in the OpenFOAM framework. From one side, we have implemented an energy-conserving incremental-pressure Runge–Kutta (RK4) projection method for the solution of the Navier–Stokes equations together with a dynamic Lagrangian mixed model for momentum and scalar subgrid-scale (SGS) fluxes; from the other side we revisit the PISO algorithm present in OpenFOAM (pisoFoam) in conjunction with the dynamic eddy-viscosity model for SGS momentum fluxes and a Reynolds Analogy for the scalar SGS fluxes, and used for the study of turbulent channel flows and buoyancy-driven flows. In both cases the validity of the anisotropic filter function, suited for non-homogeneous hexahedral meshes, has been studied and proven to be useful for industrial LES. Preliminary tests on energy-conservation properties of the algorithms studied (without the inclusion of the subgrid-scale models) show the superiority of RK4 over pisoFoam, which exhibits dissipative features. We carried out additional tests for wall-bounded channel flow and for Rayleigh–Bènard convection in the turbulent regime, by running LES using both algorithms. Results show the RK4 algorithm together with the dynamic Lagrangian mixed model gives better results in the cases analyzed for both first- and second-order statistics. On the other hand, the dissipative features of pisoFoam detected in the previous tests reflect in a less accurate evaluation of the statistics of the turbulent field, although the presence of the subgrid-scale model improves the quality of the results compared to a correspondent coarse direct numerical simulation. In case of Rayleigh–Bénard convection, the results of pisoFoam improve with increasing values of Rayleigh number, and this may be attributed to the Reynolds Analogy used for the subgrid-scale temperature fluxes. Finally, we point out that the present analysis holds for hexahedral meshes. More research is need for extension of the methods proposed to general unstructured grids.

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.

Reconsideration of the Fan Scaling Laws: Part II — Applications

2003 ◽  
Author(s):  
Asad M. Sardar ◽  
William K. George
Keyword(s):  
Scaling Laws ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Pressure Coefficient ◽  
Navier Stokes ◽  
Flow Measurements ◽  
Navier Stokes Equations ◽  
Fan Performance ◽  
Flow Rate Coefficient ◽  
Scale Models

The entire approach to the scaling of fan performance was reconsidered in Part I from first principles using the Navier-Stokes equations appropriate to rotating and swirling (incompressible) flows. Generalized fan scaling laws (GFSL) were derived, consistent with the fact that both Strouhal and Reynolds number must be maintained constant for full dynamical similarity to be possible. As a consequence, dynamic similarity is only possible if ΩD2/ν = const. (in addition to U/ΩD = constant, or equivalently, Q/ΩD3 = constant). This can be contrasted with the classical fan laws (CFSL) which for the same flow rate coefficient would imply that Q/ΩD3 = const. The differences in fan scaling laws between GFSL and CFSL lead to very different fan pressure and fan power scaling criteria. For example, using the GFSL, the pressure coefficient (or Euler number), similarity between the model and prototype fan results in ΔPm/ΔPp = 1/(Lm/Lp)2 (for constant kinematic viscosity), whereas the CFSL pressure scaling criteria lead to ΔPm/ΔPp = (Ωm/Ωp)2 (Lm/Lp)2. Clearly these are very different scaling results and affect the scaling of all the relevant fan performance parameters. In this paper, several applications will be described of experimental programs which utilized these GFSL to design dynamically similar scale models of automotive fans, and these designs are contrasted with what might have been done had the classical laws been used. Three of the facilities were built, and each allowed detailed flow measurements, which would not otherwise have been possible. In addition, the implications and advantages of making tests in a high-pressure facility are explored. Some suggestions will also be made as to how the generalized scaling laws can be applied in design practice.

scholarly journals Finite-scale equations for compressible fluid flow

2009 ◽  
Vol 367 (1899) ◽  
pp. 2861-2871 ◽  
Author(s):  
L.G. Margolin
Keyword(s):  
Numerical Simulation ◽  
Turbulent Flows ◽  
Compressible Fluid ◽  
High Speed ◽  
Energy Transport ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
One Dimensional ◽  
Scale Models

Finite-scale equations (FSE) describe the evolution of finite volumes of fluid over time. We discuss the FSE for a one-dimensional compressible fluid, whose every point is governed by the Navier–Stokes equations. The FSE contain new momentum and internal energy transport terms. These are similar to terms added in numerical simulation for high-speed flows (e.g. artificial viscosity) and for turbulent flows (e.g. subgrid scale models). These similarities suggest that the FSE may provide new insight as a basis for computational fluid dynamics. Our analysis of the FS continuity equation leads to a physical interpretation of the new transport terms, and indicates the need to carefully distinguish between volume-averaged and mass-averaged velocities in numerical simulation. We make preliminary connections to the other recent work reformulating Navier–Stokes equations.

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