Implementation and analysis of numerical solution of the population balance equation in CFD packages

Simulation of polydisperse flows must include the effects of particle–particle interaction, as breakage and aggregation, coupling the population balance equation (PBE) with the multiphase modelling. In fact, the implementation of efficient and accurate new numerical techniques to solve the PBE is necessary. The direct quadrature method of moments, known as DQMOM, is a moment-based method that uses an optimal adaptive quadrature closure and came into view as a promising choice for this implementation. In the present work, DQMOM was implemented in two CFD packages: the commercial ANSYS CFX, through FORTRAN subroutines, and the open-source OpenFOAM, by directly coding the PBE solution. Transient zero-dimensional and steady one-dimensional simulations were performed in order to explore the PBE solution accuracy using several interpolation schemes. Simulation cases with dominant breakage, dominant aggregation and invariant solution (equivalent breakage and aggregation) were simulated and validated against an analytical solution. The solution of the population balance equation was then coupled to the two-fluid model, considering that all particles classes share the same velocity field. Momentum exchange terms were evaluated using the local instantaneous Sauter mean diameter of the size distribution function. The two-dimensional tests were performed in a backward facing step geometry where the vortex zones traps the particles and provides high rates of breakage and aggregation.     

A first‐order hyperbolic framework for large strain computational solid dynamics: An upwind cell centred Total Lagrangian scheme

This paper builds on recent work developed by the authors for the numerical analysis of large strain solid dynamics, by introducing an upwind cell centred hexahedral finite volume framework implemented within the open source code OpenFOAM [ http://www.openfoam.com/ ]. In Lee, Gil and Bonet (2013), a first‐order hyperbolic system of conservation laws was introduced in terms of the linear momentum and the deformation gradient tensor of the system, leading to excellent behaviour in two‐dimensional bending dominated nearly incompressible scenarios. The main aim of this paper is the extension of this algorithm into three dimensions, its tailor‐made implementation into OpenFOAM and the enhancement of the formulation with three key novelties. First, the introduction of two different strategies in order to ensure the satisfaction of the underlying involutions of the system, that is, that the deformation gradient tensor must be curl‐free throughout the deformation process. Second, the use of a discrete angular momentum projection algorithm and a monolithic Total Variation Diminishing Runge–Kutta time integrator combined in order to guarantee the conservation of angular momentum. Third, and for comparison purposes, an adapted Total Lagrangian version of the hyperelastic‐GLACE nodal scheme of Kluth and Després (2010) is presented. A series of challenging numerical examples are examined in order to assess the robustness and accuracy of the proposed algorithm, benchmarking it against an ample spectrum of alternative numerical strategies developed by the authors in recent publications. Copyright © 2016 John Wiley & Sons, Ltd.     

Five-equation and robust three-equation methods for solution verification of large eddy simulation

This study evaluates the recently developed general framework for solution verification methods for large eddy simulation(LES) using implicitly filtered LES of periodic channel flows at friction Reynolds number of 395 on eight systematically refined grids.The seven-equation method shows that the coupling error based on Hypothesis I is much smaller as compared with the numerical and modeling errors and therefore can be neglected. The authors recommend five-equation method based on Hypothesis II, which shows a monotonic convergence behavior of the predicted numerical benchmark(S_C), and provides realistic error estimates without the need of fixing the orders of accuracy for either numerical or modeling errors. Based on the results from seven-equation and five-equation methods, less expensive three and four-equation methods for practical LES applications were derived. It was found that the new three-equation method is robust as it can be applied to any convergence types and reasonably predict the error trends. It was also observed that the numerical and modeling errors usually have opposite signs, which suggests error cancellation play an essential role in LES. When Reynolds averaged Navier-Stokes(RANS) based error estimation method is applied, it shows significant error in the prediction of S_C on coarse meshes. However, it predicts reasonable S_C when the grids resolve at least 80% of the total turbulent kinetic energy.     

Numerical modelling of vented lean hydrogen deflagations in an ISO container

Hydrogen process equipment are often housed in 20-foot or 40-foot container either be at refueling stations or at the portable standalone power generation units. Shipping Container provide an easy to install, cost effective, all weather protective containment. Hydrogen has unique physical properties, it can quickly form an ignitable cloud for any accidental release or leakages in air, due to its wide flammability limits. Identifying the hazards associated with these kind of container applications are very crucial for design and safe operation of the container hydrogen installations. Recently both numerical studies and experiment have been performed to ascertain the level of hazards and its possible mitigation methods for hydrogen applications. This paper presents the numerical modelling and the simulations performed using the HyFOAM CFD solver for vented deflagrations processes. HyFOAM solver is developed in-house using the opensource CFD toolkit OpenFOAM libraries. The turbulent flame deflagrations are modelled using the flame wrinkling combustion model. This combustion model is further improved to account for flame instabilities dominant role in vented lean hydrogen-air mixtures deflagrations. The 20-foot ISO containers of dimensions 20′ × 8′ × 8′.6″ filled with homogeneous mixture of hydrogen-air at different concentration, with and without model obstacles are considered for numerical simulations. The numerical predictions are first validated against the recent experiments carried out by Gexcon as part of the HySEA project supported by the Fuel Cells and Hydrogen 2 Joint Undertaking (FCH 2 JU) under the Horizon 2020 Framework Programme for Research and Innovation. The effects of congestion within the containers on the generated overpressures are investigated. The preliminary CFD predictions indicated that the container walls deflections are having considerable effect on the trends of generated overpressures, especially the peak negative pressure generated within the container is overestimated. Hence to account for the container wall deflections, the fluid structure interactions (FSI) are also included in the numerical modelling. The final numerical predictions are presented with and without the FSI. The FSI modelling considerably improved the numerical prediction and resulted in better match of overpressure trends with the experimental results.     

基于OpenFOAM的5×5棒束流动数值模拟

为验证OpenFOAM燃料组件子通道单相棒束流动的有效性,利用在OpenFOAM中实现的SST k-ω模型对MATIS-H基准题进行了模拟。基于OpenFOAM求解子通道速度场和压力场。将OpenFOAM的模拟数据与MATIS-H基准试验的数据进行了对比。结果表明,在网格划分精度为3级时,OpenFOAM模拟CFD子通道单相流动数据与MATIS-H基准题数据吻合度较好。由于格架和搅混翼的存在,冷却剂向中心流道靠拢,高低压区分布明显,趋于中心对称。子通道内产生涡旋,加强了燃料棒表面换热。OpenFOAM在子通道CFD模拟上具有应用前景。     

Study on Two-phase Flow in Fluid Channel of Lead-based Fast Reactor Based on OpenFOAM

In order to study the thermal-hydraulic characteristics of two-phase flow caused by the special thermal properties of lead/lead-bismuth in lead-based fast reactors, the influence of bubble in fluid channel on the heat transfer capacity and safety of the core was simulated. In this paper the open source CFD calculation software OpenFOAM was adopted, and the numerical simulation was applied based on VOF method to construct a common triangular channel model in lead-based fast reactor. By simulating the two-phase flow of the coolant channel, it is found that as the flow rate increases, the outlet temperature of the coolant decreases. In the flow process of the gas-liquid two-phase flow in the channel, it can be found that the gas phase basically flows inside the channel. In the simulation of the fuel assembly, the corner channel is an area with a large amount of bubbles, which will cause the local heat transfer to deteriorate and cause the fuel assembly to burn out.     

基于OpenFOAM的离心压气机流场数值研究

基于开源平台OpenFOAM建立离心压气机数值计算程序,分别使用SSTk-ω和Spalart-Allmaras两种湍流模型对带无叶扩压器的离心压气机进行了全流道数值模拟,从压力、速度、熵产等多个角度分析了离心压气机内部流场特性,探究了不同湍流模型对数值模拟结果的影响。结果表明:SST k-ω能更好地反映二次流、涡流、流动分离等现象,Spalart-Allmaras湍流模型中叶轮射流-尾流影响较大;由间隙泄漏流引起的低速区从叶顶前缘逐步发展到叶顶尾缘,最后进入无叶扩压器进行增压降速,形成了流动损失,降低了离心压气机效率;离心压气机内部高熵区主要集中在轮盖侧,轮盘侧相对于轮盖侧熵值较小,离心压气机流道内部熵值随叶高增加而增加。     

Implementation of the eddy dissipation model of turbulent non-premixed combustion in OpenFOAM

This work discusses the implementation of eddy dissipation model in OpenFOAM CFD toolbox. The code was validated in modeling of confined non-premixed Methane jet flame. The model predictions were extensively compared against published experimental results as well as ANSYS Fluent® predictions. The differences between the implemented model in OpenFOAM and Fluent were demonstrated.