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.

Development and Application of a Transported Probability Density Function Method on Unstructured Three-Dimensional Grids for the Prediction of Nitric Oxides

2013 ◽  
Vol 136 (3) ◽  
Author(s):  
Andreas Fiolitakis ◽  
Peter Ess ◽  
Peter Gerlinger ◽  
Manfred Aigner
Keyword(s):  
Nitric Oxide ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Flame Structure ◽  
Hybrid Approach ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Nitric Oxides ◽  
German Aerospace

The present work explores the capability of the transported probability density function (PDF) method to predict nitric oxide (NO) formation in turbulent combustion. To this end a hybrid finite-volume/Lagrangian Monte Carlo method is implemented into the THETA code of the German Aerospace Center (DLR). In this hybrid approach the transported PDF method governs the evolution of the thermochemical variables, whereas the flow field evolution is computed with a Reynolds-averaged Navier–Stokes (RANS) method. The method is used to compute a turbulent hydrogen-air flame and a methane-air flame and computational results are compared to experimental data. In order to assess the advantages of the transported PDF method, the flame computations are repeated with the “laminar chemistry” approach as well as with an “assumed PDF” method, which are both computationally less expensive. The present study reveals that the transported PDF method provides the highest accuracy in predicting the overall flame structure and nitric oxide formation.

scholarly journals Derivation of Equations for a Size Distribution of Spherical Particles in Non-Transparent Materials

2021 ◽  
Vol 5 (4) ◽  
pp. 53-60
Author(s):  
Daniel Gurgul ◽  
Andriy Burbelko ◽  
Tomasz Wiktor
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Size Distribution ◽  
Density Function ◽  
Cross Section ◽  
Three Dimensional ◽  
Spherical Particles ◽  
Two Dimensional ◽  
Mathematical Formulas ◽  
Transparent Materials

This paper presents a new proposition on how to derive mathematical formulas that describe an unknown Probability Density Function (PDF3) of the spherical radii (r3) of particles randomly placed in non-transparent materials. We have presented two attempts here, both of which are based on data collected from a random planar cross-section passed through space containing three-dimensional nodules. The first attempt uses a Probability Density Function (PDF2) the form of which is experimentally obtained on the basis of a set containing two-dimensional radii (r2). These radii are produced by an intersection of the space by a random plane. In turn, the second solution also uses an experimentally obtained Probability Density Function (PDF1). But the form of PDF1 has been created on the basis of a set containing chord lengths collected from a cross-section.The most important finding presented in this paper is the conclusion that if the PDF1 has proportional scopes, the PDF3 must have a constant value in these scopes. This fact allows stating that there are no nodules in the sample space that have particular radii belonging to the proportional ranges the PDF1.

scholarly journals Assessment of a three-dimensional line-of-response probability density function system matrix for PET

2012 ◽  
Vol 57 (21) ◽  
pp. 6827-6848 ◽  
Author(s):  
Rutao Yao ◽  
Ranjith M Ramachandra ◽  
Neeraj Mahajan ◽  
Vinay Rathod ◽  
Noel Gunasekar ◽  
...  
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Three Dimensional ◽  
Response Probability ◽  
Function System ◽  
System Matrix

A probability density function method for turbulent mixing and combustion on three-dimensional unstructured deforming meshes

2000 ◽  
Vol 1 (2) ◽  
pp. 171-190 ◽  
Author(s):  
S Subramaniam ◽  
D. C. Haworth
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Turbulent Mixing ◽  
Three Dimensional ◽  
Quantitative Agreement ◽  
Particle Number Density ◽  
Time Dependent ◽  
Ic Engine ◽  
Density Control

A hybrid Lagrangian-Eulerian methodology is developed for numerical simulation of turbulent mixing and combustion in arbitrary three-dimensional time-dependent geometric configurations. The context is a probability density function (PDF) based approach intended for modelling in cylinder processes in reciprocating piston internal combustion (IC) engines. Issues addressed include mean estimation, particle tracking and particle number-density control on three-dimensional unstructured deforming meshes. The suitability of the methodology for statistically time-dependent three-dimensional turbulent flow with large density variations is demonstrated via simulations of turbulent freon vapour/air mixing on an unstructured deforming mesh representing an idealized IC engine [13]. Computed profiles of mean and r.m.s. freon mole fractions show good quantitative agreement with measurements. Moreover, inherent advantages of the Lagrangian-Eulerian PDF approach are demonstrated, compared to Eulerian finite volume solutions of an (approximately) equivalent set of moment equations. The new approach is, by design, compatible with existing computational fluid dynamics codes that are used for multidimensional modelling of in-cylinder thermal fluids processes. This work broadens the accessibility of PDF methods for practical turbulent combustion systems.

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.

A two-fluid model for gas-particle turbulent flows based on the probability density function approach

2019 ◽  
Vol 30 (01) ◽  
pp. 1950008
Author(s):  
Lu Wang ◽  
Jiangrong Xu
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Turbulent Flows ◽  
Present Model ◽  
Fluid Model ◽  
Navier Stokes ◽  
Turbulence Modulation ◽  
Two Fluid Model ◽  
Two Fluid

According to experimental observations, laden particles in turbulence may attenuate or augment the carrier phase turbulence. But until now, there are no widely recognized models for estimating the so-called turbulence modulation phenomenon. In this paper, a novel two-fluid model is proposed based on the probability density function (PDF) approach. The Reynolds stress equation of the present model contains both production and dissipation terms due to the presence of particles, the turbulence modulation phenomenon can be well explained with the new model. To further explore the two-fluid model, a comparative study on PDF and Reynolds-averaged approaches is carried on, the differences and relations between the present model and the classical two-fluid Reynolds averaged Navier–Stokes (RANS) model are analyzed in the paper. Theoretical and numerical analysis indicates that the proposed model shows particular promise for predicting particle-laden turbulent flows.

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