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.

Rayleigh-Bénard Convection in Open and Closed Rotating Cavities

2005 ◽  
Vol 129 (2) ◽  
pp. 305-311 ◽  
Author(s):  
Martin P. King ◽  
Michael Wilson ◽  
J. Michael Owen
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Nusselt Numbers ◽  
Bénard Convection ◽  
Published Evidence ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Numbers ◽  
Rayleigh Benard

Buoyancy effects can be significant in the rotating annular cavities found between compressor discs in gas-turbine engines, where Rayleigh numbers above 1012 are common. In some engines, the cavity is “closed” so that the air is confined between four rotating surfaces: two discs and inner and outer cylinders. In most engines, however, the cavity is “open” and there is an axial throughflow of cooling air at the center. For open rotating cavities, a review of the published evidence suggests a Rayleigh–Bénard type of flow structure, in which, at the larger radii, there are pairs of cyclonic and anti-cyclonic vortices. The toroidal circulation created by the axial throughflow is usually restricted to the smaller radii in the cavity. For a closed rotating annulus, solution of the unsteady Navier–Stokes equations, for Rayleigh numbers up to 109, show Rayleigh–Bénard convection similar to that found in stationary enclosures. The computed streamlines in the r-θ plane show pairs of cyclonic and anti-cyclonic vortices; but, at the larger Rayleigh numbers, the computed isotherms suggest that the flow in the annulus is thermally mixed. At the higher Rayleigh numbers, the computed instantaneous Nusselt numbers are unsteady and tend to oscillate with time. The computed time-averaged Nusselt numbers are in good agreement with the correlations for Rayleigh–Bénard convection in a stationary enclosure, but they are significantly higher than the published empirical correlations for a closed rotating annulus.

On Direct Numerical Simulation of Turbulent Flows

2011 ◽  
Vol 64 (2) ◽  
Author(s):  
Giancarlo Alfonsi
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
High Performance Computing ◽  
Turbulent Flows ◽  
High Performance ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Turbulent Shear ◽  
Navier Stokes Equations ◽  
Performance Computing

The direct numerical simulation of turbulence (DNS) has become a method of outmost importance for the investigation of turbulence physics, and its relevance is constantly growing due to the increasing popularity of high-performance-computing techniques. In the present work, the DNS approach is discussed mainly with regard to turbulent shear flows of incompressible fluids with constant properties. A body of literature is reviewed, dealing with the numerical integration of the Navier-Stokes equations, results obtained from the simulations, and appropriate use of the numerical databases for a better understanding of turbulence physics. Overall, it appears that high-performance computing is the only way to advance in turbulence research through the front of the direct numerical simulation.

Numerical Modelling of Hydrodynamic Instabilities in Supercritical Fluids

2021 ◽  
pp. 32-54
Author(s):  
Sakir Amiroudine
Keyword(s):  
Boundary Layer ◽  
Thermal Boundary Layer ◽  
Stokes Equations ◽  
Gravitational Instability ◽  
Heat Diffusion ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Stability Diagrams ◽  
The Stability ◽  
Rayleigh Benard

The case of a supercritical fluid heated from below (Rayleigh-Bénard) in a rectangular cavity is first presented. The stability of the two boundary layers (hot and cold) is analyzed by numerically solving the Navier-Stokes equations with a van der Waals gas and stability diagrams are derived. The very large compressibility and the very low heat diffusivity of near critical pure fluids induce very large density gradients which lead to a Rayleigh–Taylor-like gravitational instability of the heat diffusion layer and results in terms of growth rates and wave numbers are presented. Depending on the relative direction of the interface or the boundary layer with respect to vibration, vibrational forces can destabilize a thermal boundary layer, resulting in parametric/Rayleigh vibrational instabilities. This has recently been achieved by using a numerical model which does not require any equation of state and directly calculates properties from NIST data base, for instance.

scholarly journals The emergence of localized vortex–wave interaction states in plane Couette flow

2013 ◽  
Vol 721 ◽  
pp. 58-85 ◽  
Author(s):  
Kengo Deguchi ◽  
Philip Hall ◽  
Andrew Walton
Keyword(s):  
Reynolds Number ◽  
Turbulent Flows ◽  
High Reynolds Number ◽  
Stokes Equations ◽  
Wave Interaction ◽  
Critical Layer ◽  
Navier Stokes ◽  
Turbulent Spots ◽  
Navier Stokes Equations ◽  
High Reynolds

AbstractThe recently understood relationship between high-Reynolds-number vortex–wave interaction theory and computationally generated self-sustaining processes provides a possible route to an understanding of some of the underlying structures of fully turbulent flows. Here vortex–wave interaction (VWI) theory is used in the long streamwise wavelength limit to continue the development found at order-one wavelengths by Hall & Sherwin (J. Fluid Mech., vol. 661, 2010, pp. 178–205). The asymptotic description given reduces the Navier–Stokes equations to the so-called boundary-region equations, for which we find equilibrium states describing the change in the VWI as the wavelength of the wave increases from $O(h)$ to $O(Rh)$, where $R$ is the Reynolds number and $2h$ is the depth of the channel. The reduced equations do not include the streamwise pressure gradient of the perturbation or the effect of streamwise diffusion of the wave–vortex states. The solutions we calculate have an asymptotic error proportional to ${R}^{- 2} $ when compared to the full Navier–Stokes equations. The results found correspond to the minimum drag configuration for VWI states and might therefore be of relevance to the control of turbulent flows. The key feature of the new states discussed here is the thickening of the critical layer structure associated with the wave part of the flow to completely fill the channel, so that the roll part of the flow is driven throughout the flow rather than as in Hall & Sherwin as a stress discontinuity across the critical layer. We identify a critical streamwise wavenumber scaling, which, when approached, causes the flow to localize and take on similarities with computationally generated or experimentally observed turbulent spots. In effect, the identification of this critical wavenumber for a given value of the assumed high Reynolds number fixes a minimum box length necessary for the emergence of localized structures. Whereas nonlinear equilibrium states of the Navier–Stokes equations are thought to form a backbone on which turbulent flows hang, our results suggest that the localized states found here might play a related role for turbulent spots.

Approximation of attractors, large eddy simulations and multiscale methods

1991 ◽  
Vol 434 (1890) ◽  
pp. 23-39 ◽  
Keyword(s):  
Turbulent Flows ◽  
Mathematical Theory ◽  
Stokes Equations ◽  
Multiscale Methods ◽  
Large Eddy Simulations ◽  
Navier Stokes ◽  
Theory Approach ◽  
Navier Stokes Equations ◽  
Approximate Inertial Manifolds ◽  
Large Eddy

Recent advances in the mathematical theory of the Navier-Stokes equations have produced new insight in the mathematical theory of turbulence. In particular, the study of the attractor for the Navier-Stokes equations produced the first connection between two approaches to turbulence that seemed far apart, namely the conventional approach of Kolmogorov and the dynamical systems theory approach. Similarly the study of the approximation of the attractor in connection with the newly introduced concept of approximate inertial manifolds has produced a new approach to large eddy simulations and the study of the interaction of small and large eddies in turbulent flows. Our aim in this article is to survey and describe some of the new results concerning the functional properties of the Navier-Stokes equations and to discuss their relevance to turbulence.

Probability Density Functions of Vorticities in Turbulent Channels with Effects of Blowing and Suction

2016 ◽  
Vol 17 (2) ◽  
pp. 127-135
Author(s):  
Can Liu ◽  
Xi Chen
Keyword(s):  
New York ◽  
Probability Density ◽  
Turbulent Flows ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Generalized Hyperbolic Distribution ◽  
Mean Velocity ◽  
Navier Stokes Equations ◽  
Turbulent Channel Flows ◽  
Probability Density Function Pdf

AbstractThis paper presents direct numerical simulation (DNS) result of the Navier–Stokes equations for turbulent channel flows with blowing and suction effects. The friction Reynolds number is ${\rm{R}}{{\rm{e}}_\tau} = 394$ and a range of blowing and suction conditions is covered with different perturbation strengths, i. e. $A = 0.05, $ 0.1, 0.2. While the mean velocity profile has been severely altered, the probability density function (PDF) for (spanwise) vorticity – depending on wall distance $({y^ +})$ and blowing/suction strength (A) – satisfies the generalized hyperbolic distribution (GHD) of Birnir [The Kolmogorov-Obukhov statistical theory of turbulence, J. Nonlinear Sci. (2013a), doi: 10.1007/s00332-012-9164–z; The Kolmogorov-Obukhov theory of turbulence, Springer, New York, 2013b] in the bulk of the flow. The latter leads to accurate descriptions of all PDFs (at ${y^ +} = 40, $ 200, 390 and $A = 0.05, $ 0.2, for instance) with only four parameters. The result indicates that GHD is a general tool to quantify PDF for turbulent flows under various wall surface conditions.

scholarly journals Effects of baffle length on turbulent flows generated in stirred vessels

2011 ◽  
Vol 1 (4) ◽  
Author(s):  
Meriem Ammar ◽  
Zied Driss ◽  
Wajdi Chtourou ◽  
Mohamed Abid
Keyword(s):  
Turbulent Flows ◽  
Stokes Equations ◽  
Control Volume ◽  
Numerical Results ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Rushton Turbine ◽  
Stirred Vessels ◽  
Hydrodynamic Behaviour ◽  
Effective System

AbstractThe aim of this paper is to study the effect of baffles length on the turbulent flows in stirred tanks. The hydrodynamic behaviour induced by a Rushton turbine (RT6) is numerically predicted by solving the Navier-Stokes equations in conjunction with the Renormalization Group (RNG) of the k-ɛ turbulence model. These equations are solved by a control volume discretization method. The numerical results from the application of the computational fluid dynamics (CFD) code Fluent with the multi-reference frame (MRF) model are presented in the vertical and horizontal planes in the impeller stream region. Our studies were carried out on three different systems. The most effective system was selected based on its calculated power consumption figure. All numerical results showed good agreement with experimental data.

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