On the scalar probability density function transport equation for binary mixing in isotropic turbulence at supercritical pressure

2001 ◽  
Vol 13 (11) ◽  
pp. 3386-3399 ◽  
Author(s):  
Hong Lou ◽  
Richard S. Miller
Keyword(s):  
Probability Density Function ◽  
Transport Equation ◽  
Probability Density ◽  
Density Function ◽  
Isotropic Turbulence ◽  
Supercritical Pressure ◽  
Binary Mixing

scholarly journals A Lagrangian probability-density-function model for collisional turbulent fluid–particle flows

2019 ◽  
Vol 862 ◽  
pp. 449-489 ◽  
Author(s):  
A. Innocenti ◽  
R. O. Fox ◽  
M. V. Salvetti ◽  
S. Chibbaro
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Turbulent Flows ◽  
Isotropic Turbulence ◽  
Fluid Phase ◽  
Stochastic Modelling ◽  
Inertial Particles ◽  
Particle Phase ◽  
Dense Particle

Inertial particles in turbulent flows are characterised by preferential concentration and segregation and, at sufficient mass loading, dense particle clusters may spontaneously arise due to momentum coupling between the phases. These clusters, in turn, can generate and sustain turbulence in the fluid phase, which we refer to as cluster-induced turbulence (CIT). In the present work, we tackle the problem of developing a framework for the stochastic modelling of moderately dense particle-laden flows, based on a Lagrangian probability-density-function formalism. This framework includes the Eulerian approach, and hence can be useful also for the development of two-fluid models. A rigorous formalism and a general model have been put forward focusing, in particular, on the two ingredients that are key in moderately dense flows, namely, two-way coupling in the carrier phase, and the decomposition of the particle-phase velocity into its spatially correlated and uncorrelated components. Specifically, this last contribution allows us to identify in the stochastic model the contributions due to the correlated fluctuating energy and to the granular temperature of the particle phase, which determine the time scale for particle–particle collisions. The model is then validated and assessed against direct-numerical-simulation data for homogeneous configurations of increasing difficulty: (i) homogeneous isotropic turbulence, (ii) decaying and shear turbulence and (iii) CIT.

Large Eddy Simulation/Eulerian Probability Density Function Approach for Simulating Hydrogen-Enriched Gas Turbine Combustors

2012 ◽  
Author(s):  
Christopher Lietz ◽  
Pratik Donde ◽  
Venkat Raman ◽  
Scott Martin
Keyword(s):  
Probability Density Function ◽  
Large Eddy Simulation ◽  
Transport Equation ◽  
Probability Density ◽  
Density Function ◽  
Eddy Simulation ◽  
Partially Premixed Combustion ◽  
Large Eddy ◽  
Probability Density Function Pdf ◽  
Combustion Regimes

To describe partially-premixed combustion inside hydrogen-rich combustors, a novel quadrature-based probability density function (PDF) approach is studied here. The PDF approach is comprehensive in describing multiple combustion regimes, and multiple inlet streams. The methodology is implemented in the context of the large eddy simulation (LES) approach. The main bottleneck in utilizing the PDF approach is that the PDF transport equation, which needs to be evolved along with the LES equations, is high-dimensional and intractable using conventional discretization techniques. In order to ensure that the PDF approach is easily transferred to existing industrial flow solvers, a quadrature-based Eulerian method for solving the PDF transport equation is considered here. The corresponding Eulerian equations are implemented in the open source OpenFOAM code using an unstructured grid system. Simulations of an experimental high-pressure combustor demonstrate that the PDF approach significantly changes the reaction structure compared to laminar chemistry assumption.

scholarly journals On the velocity distribution in homogeneous isotropic turbulence: correlations and deviations from Gaussianity

2011 ◽  
Vol 676 ◽  
pp. 191-217 ◽  
Author(s):  
MICHAEL WILCZEK ◽  
ANTON DAITCHE ◽  
RUDOLF FRIEDRICH
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Isotropic Turbulence ◽  
Single Point ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Homogeneous Isotropic Turbulence ◽  
Navier Stokes Equation ◽  
Conditional Averaging

We investigate the single-point probability density function of the velocity in three-dimensional stationary and decaying homogeneous isotropic turbulence. To this end, we apply the statistical framework of the Lundgren–Monin–Novikov hierarchy combined with conditional averaging, identifying the quantities that determine the shape of the probability density function. In this framework, the conditional averages of the rate of energy dissipation, the velocity diffusion and the pressure gradient with respect to velocity play a key role. Direct numerical simulations of the Navier–Stokes equation are used to complement the theoretical results and assess deviations from Gaussianity.

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