Numerical Prediction of Poly-Dispersed Condensation Using Quadrature Method of Moments and Multi-Fluid Model

2017 ◽  
Author(s):  
Anjaneyulu Lankadasu ◽  
Laurent Krumenacker ◽  
Anil Kumar ◽  
Amita Tripathi
Keyword(s):  
Method Of Moments ◽  
Laval Nozzle ◽  
High Efficiency ◽  
Fluid Model ◽  
Computational Cost ◽  
Droplet Size Distribution ◽  
General Purpose ◽  
Navier Stokes ◽  
Quadrature Method ◽  
Quadrature Method Of Moments

Accurate prediction of condensation plays an important role in the development of high efficiency turbo-machines working on condensable fluid. Therefore it demands modeling of poly-disperse characteristic of number distribution function while modeling condensation. Two such kind of models are considered in this work and they are namely, quadrature method of moments (QMOM) and multi-fluid method (MFM) models. The vital difference between these two models lies in the method of discretisation of the droplet size distribution. Further, their numerical aspects like ease of implementation in general purpose computational fluid dynamics solvers, accuracy and associated computational cost are discussed. In order to obtain accurate thermodynamic properties, the real gas formulations defined in IAPWS-IF97 are used. These algorithms are applied to the compressible Navier-Stokes solver of Fluidyn MP and tests are carried on Laval nozzle and compared with the experimental measurements.

CFD Modelling of Bubbly Flow in Adiabatic Upward Pipe Using a Solver Based on OpenFOAM® With the Quadrature Method of Moments

2014 ◽  
Author(s):  
Carlos Peña-Monferrer ◽  
Alberto Passalacqua ◽  
Sergio Chiva ◽  
José L. Muñoz-Cobo
Keyword(s):  
Method Of Moments ◽  
Two Phase Flow ◽  
Fluid Model ◽  
Bubbly Flow ◽  
Phase Flow ◽  
Computational Results ◽  
Quadrature Method ◽  
Cfd Modelling ◽  
Two Phase ◽  
Quadrature Method Of Moments

An Eulerian-Eulerian approach was used to model adiabatic bubbly flow with CFD techniques. The OpenFOAM® solver twoPhaseEulerFoam was modified to predict upward bubbly flow in vertical pipes. Interfacial force and bubble induced turbulence models are studied and implemented. The population balance equation included in the two-fluid model is solved to simulate a polydisperse flow with the quadrature method of moments approximation. Two-phase flow experiments with different superficial velocities of gas and water at different temperatures are used to validate the solver. Radial distributions of void fraction, air and water velocities, Sauter mean diameter and turbulence intensity are compared with the computational results. The computational results agree well with the experiments showing the capability of the solver to predict two-phase flow characteristics.

Representing Polydispersed Droplet Behavior in Nucleating Steam Flow With the Quadrature-Method-of-Moments

2006 ◽  
Author(s):  
A. Mousavi ◽  
A. G. Gerber ◽  
M. J. Kermani
Keyword(s):  
Phase Transition ◽  
Method Of Moments ◽  
Supersonic Nozzle ◽  
Droplet Size Distribution ◽  
Quadrature Method ◽  
Steam Turbines ◽  
Two Phase ◽  
Wide Range ◽  
Quadrature Method Of Moments ◽  
Droplet Behavior

This paper applies the Quadrature-Method-of-Moments (QMOM) to the polydispersed droplets spectrum typical in low pressure steam turbines. Various modes of nonequilibrium phase transition are present in steam turbines, starting with primary and secondary homogeneous nucleation as the main source of moisture followed by heterogeneous nucleation and surface entrainment sources. The range of phase transition possibilities leads to a wide range of droplet sizes, which are present under various combinations of inertial and thermal nonequilibrium. Given the extensive prevalence of CFD in turbomachinery design, it is of interest to develop an efficient modeling approach for polydispersed droplet flows that avoids solving an excessive number of equations to represent the droplet size distribution. Methods based on QMOM have shown promise in this regard in other applications areas of two-phase flow, and this paper attempts to quantify its potential for steam turbine applications by applying the method to supersonic nozzle studies with homogeneous and heterogeneous phase transitions.

Numerical Methods for the Solution of Population Balance Equations Coupled with Computational Fluid Dynamics

2020 ◽  
Vol 11 (1) ◽  
pp. 339-366 ◽  
Author(s):  
Mohsen Shiea ◽  
Antonio Buffo ◽  
Marco Vanni ◽  
Daniele Marchisio
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Method Of Moments ◽  
Fluid Model ◽  
Population Balance ◽  
Quadrature Method ◽  
Balance Equations ◽  
Flow Models ◽  
Population Balance Equations ◽  
Quadrature Method Of Moments

This review article discusses the solution of population balance equations, for the simulation of disperse multiphase systems, tightly coupled with computational fluid dynamics. Although several methods are discussed, the focus is on quadrature-based moment methods (QBMMs) with particular attention to the quadrature method of moments, the conditional quadrature method of moments, and the direct quadrature method of moments. The relationship between the population balance equation, in its generalized form, and the Euler-Euler multiphase flow models, notably the two-fluid model, is thoroughly discussed. Then the closure problem and the use of Gaussian quadratures to overcome it are analyzed. The review concludes with the presentation of numerical issues and guidelines for users of these modeling approaches.

scholarly journals CFD-PBM Coupled Simulation of Liquid-Liquid Dispersions in Spray Fluidized Bed Extractor: Comparison of Three Numerical Methods

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Dan Zheng ◽  
Wei Zou ◽  
Chuanfeng Peng ◽  
Yuhang Fu ◽  
Jie Yan ◽  
...  
Keyword(s):  
Fluidized Bed ◽  
Method Of Moments ◽  
Chemical Engineering ◽  
High Reliability ◽  
Scale Up ◽  
Population Balance ◽  
Numerical Code ◽  
Balance Model ◽  
Quadrature Method ◽  
Quadrature Method Of Moments

A coupled numerical code of the Euler-Euler model and the population balance model (PBM) of the liquid-liquid dispersions in a spray fluidized bed extractor (SFBE) has been performed to investigate the hydrodynamic behavior. A classes method (CM) and two representatively numerical moment-based methods, namely, a quadrature method of moments (QMOM) and a direct quadrature method of moments (DQMOM), are used to solve the PBE for evaluating the effect of the numerical method. The purpose of this article is to compare the results achieved by three methods for solving population balance during liquid-liquid two-phase mixing in a SFBE. The predicted results reveal that the CM has the advantage of computing the droplet size distribution (DSD) directly, but it is computationally expensive if a large number of intervals are needed. The MOMs (QMOM and DQMOM) are preferable to coupling the PBE solution with CFD codes for liquid-liquid dispersions simulations due to their easy application, reasonable accuracy, and high reliability. Comparative results demonstrated the suitability of the DQMOM for modeling the spray fluidized bed extractor with simultaneous droplet breakage and aggregation. This work increases the understanding of the chemical engineering characteristics of multiphase systems and provides a theoretical basis for the quantitative design, scale-up, and optimization of multiphase devices.

Sign in / Sign up

Export Citation Format

Share Document