A methodology to devise consistent probability density function models for particle dynamics in turbulent dispersed two-phase flows

2021 ◽  
Vol 33 (2) ◽  
pp. 023312
Author(s):  
Jean-Pierre Minier
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Particle Dynamics ◽  
Two Phase Flows ◽  
Two Phase ◽  
Function Models

scholarly journals A comprehensive probability density function formalism for multiphase flows

2009 ◽  
Vol 628 ◽  
pp. 181-228 ◽  
Author(s):  
MADHUSUDAN G. PAI ◽  
SHANKAR SUBRAMANIAM
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Multiphase Flows ◽  
Transport Equations ◽  
Governing Equations ◽  
Two Phase Flows ◽  
Two Phase ◽  
Spatial Homogeneity ◽  
Statistical Representation

A theoretical foundation for two widely used statistical representations of multiphase flows, namely the Eulerian–Eulerian (EE) and Lagrangian–Eulerian (LE) representations, is established in the framework of the probability density function (p.d.f.) formalism. Consistency relationships between fundamental statistical quantities in the EE and LE representations are rigorously established. It is shown that fundamental quantities in the two statistical representations bear an exact relationship to each other only under conditions of spatial homogeneity. Transport equations for the probability densities in each statistical representation are derived. Exact governing equations for the mean mass, mean momentum and second moment of velocity corresponding to the two statistical representations are derived from these transport equations. In particular, for the EE representation, the p.d.f. formalism is shown to naturally lead to the widely used ensemble-averaged equations for two-phase flows. Galilean-invariant combinations of unclosed terms in the governing equations that need to be modelled are clearly identified. The correspondence between unclosed terms in each statistical representation is established. Hybrid EE–LE computations can benefit from this correspondence, which serves in consistently transferring information from one representation to the other. Advantages and limitations of each statistical representation are identified. The results of this work can also serve as a guiding framework for direct numerical simulations of two-phase flows, which can now be exploited to precisely quantify unclosed terms in the governing equations in the two statistical representations.

scholarly journals Flow Pattern and Resistance Characteristics of Gas–Liquid Two-Phase Flow with Foam under Low Gas–Liquid Flow Rate

Energies ◽  
2021 ◽  
Vol 14 (13) ◽  
pp. 3722
Author(s):  
Bin Wang ◽  
Jianguo Hu ◽  
Weixiong Chen ◽  
Zhongzhao Cheng ◽  
Fei Gao
Keyword(s):  
Stainless Steel ◽  
Probability Density Function ◽  
Probability Density ◽  
Flow Pattern ◽  
Density Function ◽  
Two Phase Flow ◽  
Phase Flow ◽  
Liquid Ratio ◽  
Two Phase ◽  
Foam Flooding

To reduce the cost of arranging air foam flooding equipment at each wellhead, a method of establishing centralized air foam flooding injection stations is proposed. The flow pattern and resistance characteristics of air foam flooding mixtures in different initial conditions are studied. Experimental results indicate that the probability density function of stratified flow is obtained by comparing stainless steel and transparent pipes. If the gas–liquid ratio is kept constant, then the shape of the probability density function remains unchanged in both stainless steel and transparent tubes. Meanwhile, the flow pattern under the gas–liquid ratio is determined by comparing the image recognition results with the probability density function, and a formula for calculating the resistance and pressure drop of the gas and liquid two-phase flow in the horizontal and upward pipes is established. Compared with the experiments, the error results of the calculation are small. Thus, the proposed equations can be used to predict the flow resistance of real air foam flooding.

scholarly journals Deep learning for presumed probability density function models

2019 ◽  
Vol 208 ◽  
pp. 436-450 ◽  
Author(s):  
Marc T. Henry de Frahan ◽  
Shashank Yellapantula ◽  
Ryan King ◽  
Marc S. Day ◽  
Ray W. Grout
Keyword(s):  
Deep Learning ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Function Models

Experimental Investigation for Flow Regime Identification Using Probability Density Function of Void Fraction Signals

2020 ◽  
Vol 142 (6) ◽  
Author(s):  
Min-Song Lin ◽  
Shao-Wen Chen ◽  
Feng-Jiun Kuo ◽  
Yen-Shih Cheng ◽  
Pei-Syuan Ruan ◽  
...  
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Flow Regime ◽  
Void Fraction ◽  
Flow Conditions ◽  
Two Phase ◽  
Specific Flow ◽  
Wide Range ◽  
Flow Regime Identification

Abstract In this study, upward air–water two-phase flow tests were carried out in a 3 cm diameter pipe under atmospheric pressure, and over 3000 data points were collected from a wide range of superficial gas and liquid velocities (⟨jg⟩ ≈ 0.02–30 m/s and ⟨jf⟩ ≈ 0.02–2 m/s) for the investigation of flow regime identification. The probability density function (PDF) of transient void fraction signals and its full-width at half-maximum (FWHM) were obtained and used for analysis and data classification. Considering the features of PDF profiles, the flow conditions can be classified into four regions, which show a fair agreement with the existing flow regime maps in general trends. Furthermore, by examining the FWHM distributions, two more regions with high-FWHM (HF) values were identified as the transitions of higher-flow bubbly-to-slug and slug-to-churn flows as well as most portion of churn flow, and a valley region next to the HF regions can express the transition of churn-to-annular flows. Overall, six groups of flow conditions can be classified based on the present methodology, and each group can be corresponding to specific flow regimes or transition regions. This study can provide a simple and efficient way for flow regime identification.

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