scholarly journals The continuous eddy simulation capability of velocity and scalar probability density function equations for turbulent flows

2021 ◽  
Vol 33 (2) ◽  
pp. 025107
Author(s):  
Stefan Heinz
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Turbulent Flows ◽  
Eddy Simulation

Detection of turbulent error by helicity in an ultrasonic flowmeter

2018 ◽  
Vol 41 (4) ◽  
pp. 1110-1122 ◽  
Author(s):  
Geng Jie ◽  
Li Dong ◽  
Du Guang-sheng ◽  
Liu Zheng-gang ◽  
Hu De-cai
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Large Scale ◽  
Ultrasonic Flowmeter ◽  
Propagation Path ◽  
Eddy Simulation ◽  
Turbulent Spectrum ◽  
Large Eddy ◽  
Ultrasonic Propagation

Turbulence generated by invading structures in pipes introduces uncertainties into measurements using ultrasonic flowmeters. A numerical model based on large eddy simulation (LES) is developed here to study the features of turbulent errors in a typical U-shaped ultrasonic flowmeter. According to the flow structures obtained by LES, a one-dimensional turbulent spectrum and probability density function of helicity along the effective ultrasonic propagation path are calculated. It can be seen that the turbulent error is dominated by the large-scale anisotropic vortices in a specific range on the sampling line, and the anisotropic vortices have the common largest fluctuating scales in the error-dominated area in which the Reynolds number ( Re) exceeds 15,000. The results provide possibilities for reducing the turbulent error by limiting the largest fluctuating scale through structure optimization. The probability density function of streamwise helicity is first introduced to unveil the continuous turbulent development in an ultrasonic flowmeter, which has the potential to contribute to turbulent analyses.

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.

On the one-point probability density function for the wind velocity in the neutral atmospheric surface layer

1998 ◽  
Vol 366 ◽  
pp. 351-365
Author(s):  
A. WENZEL ◽  
M. BALDAUF
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Turbulent Flows ◽  
Wind Velocity ◽  
Joint Probability ◽  
Second Moments ◽  
New Equation ◽  
The One ◽  
Strain Interaction

The differential equation describing the one-point joint probability density function for the wind velocity given by Lundgren (1967) in neutral turbulent flows is extended by a term which also takes into consideration the pressure–mean strain interaction. For the new equation a solution is given describing the one-point probability density function for the wind velocity fluctuations if the profile of the mean wind velocity is logarithmic. The properties of this solution are discussed to identify the differences to a Gaussian having the same first and second moments.

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.

Sign in / Sign up

Export Citation Format

Share Document