The present research aims to assess the capability of a comprehensive Euler/Lagrange approach for predicting gas-solid flows and the associated solid particle erosion.The open-source code OpenFOAM®4.1 was used to...The present research aims to assess the capability of a comprehensive Euler/Lagrange approach for predicting gas-solid flows and the associated solid particle erosion.The open-source code OpenFOAM®4.1 was used to carry out the numerical simulations,where the standard Lagrangian libraries were substantially extended to account for all necessary models.Particles are tracked considering both translational and rotational motion as well as all relevant forces,such as gravity/buoyancy,drag and transverse lift due to shear and particle rotation.The tracking time step was dynamically adapted ac-cording to the locally relevant time scales,which drastically reduces computational times.Stochastic approaches are adopted to model particle turbulent dispersion,particle collisions with rough walls and particle-particle interactions.Five solid particle erosion models,available in the literature,were considered to estimate pipe bend erosion.Three study cases are provided to validate the adopted nu-merical approach and erosion models extensively.The first case intends to evaluate the ability of the extended CFD code to predict the behaviour of gas-solid flows in pneumatic conveying systems.This goal is achieved by comparing the numerical results with the experimental data obtained by Huber(1997)and Huber and Sommerfeld(1994,1998)in a pneumatic conveying system.Here,the importance of considering inter-particle collisions and surface roughness for predicting particle velocity,mass flux and mean diameter distributions in gas-solid flows is highlighted.The second and third case intend to evaluate the ability of the erosion models in estimating bend erosion in diluted gas-solid flows.The erosion data obtained experimentally by Mazumder et al.(2008)and Solnordal et al.(2015)in very dilut pneumatic conveying systems is used for validating the numerical results,neglecting now inter-particle collisions and two-way coupling.Besides a comprehensive analysis of the different influential properties on erosion,the innovation of the present study is as follows.For the first time also a temporal modifi-cation of the surface roughness due to the erosion was considered in the simulations obtained from previous measurements(Novelletto Ricardo&Sommerfeld,2020).As the surface roughness is increased due to erosion,eventually erosion rate becomes lower.This is the result of diminishing wall collision frequency.Simulations for several degrees of surface roughness showed that larger roughness is coupled with a drastic reduction of erosion.Hence,numerical simulations neglecting wall surface roughness are not realistic.The consideration of a particle size distribution instead of mono-sized computations showed a possible reduction of erosion rate.The detailed analysis of the different single-particle erosion models revealed that the model proposed by Oka et al.(2005)and Oka and Yoshida(2005)yields the best agreement with the measurements,however particle and wall properties are needed.展开更多
In this paper, a modified version of the Classical Lagrange Multiplier method is developed for convex quadratic optimization problems. The method, which is evolved from the first order derivative test for optimality o...In this paper, a modified version of the Classical Lagrange Multiplier method is developed for convex quadratic optimization problems. The method, which is evolved from the first order derivative test for optimality of the Lagrangian function with respect to the primary variables of the problem, decomposes the solution process into two independent ones, in which the primary variables are solved for independently, and then the secondary variables, which are the Lagrange multipliers, are solved for, afterward. This is an innovation that leads to solving independently two simpler systems of equations involving the primary variables only, on one hand, and the secondary ones on the other. Solutions obtained for small sized problems (as preliminary test of the method) demonstrate that the new method is generally effective in producing the required solutions.展开更多
介绍了1种把Eulerian计算过程和Lagrangian计算过程耦合起来的数值技术,编写了计算程序,把爆炸流场作用过程和结构动力学响应过程的计算结合起来,实现了爆炸流场对结构加载和结构动力响应及对爆炸流场反作用过程的模拟。利用Eulerian过...介绍了1种把Eulerian计算过程和Lagrangian计算过程耦合起来的数值技术,编写了计算程序,把爆炸流场作用过程和结构动力学响应过程的计算结合起来,实现了爆炸流场对结构加载和结构动力响应及对爆炸流场反作用过程的模拟。利用Eulerian过程的流体弹塑性有限差分计算程序MMIC(multi-materials in cell)模拟爆炸流场发展过程,利用Lagrangian过程的结构动力学有限元计算程序模拟结构响应。应用Euler-Lagrange耦合技术分析了爆炸作用下飞片的变形、破坏和对靶体的侵彻过程,计算结果表明,本文的方法可以较好地反映流场与结构各自的运动发展及相互间作用过程。展开更多
文摘The present research aims to assess the capability of a comprehensive Euler/Lagrange approach for predicting gas-solid flows and the associated solid particle erosion.The open-source code OpenFOAM®4.1 was used to carry out the numerical simulations,where the standard Lagrangian libraries were substantially extended to account for all necessary models.Particles are tracked considering both translational and rotational motion as well as all relevant forces,such as gravity/buoyancy,drag and transverse lift due to shear and particle rotation.The tracking time step was dynamically adapted ac-cording to the locally relevant time scales,which drastically reduces computational times.Stochastic approaches are adopted to model particle turbulent dispersion,particle collisions with rough walls and particle-particle interactions.Five solid particle erosion models,available in the literature,were considered to estimate pipe bend erosion.Three study cases are provided to validate the adopted nu-merical approach and erosion models extensively.The first case intends to evaluate the ability of the extended CFD code to predict the behaviour of gas-solid flows in pneumatic conveying systems.This goal is achieved by comparing the numerical results with the experimental data obtained by Huber(1997)and Huber and Sommerfeld(1994,1998)in a pneumatic conveying system.Here,the importance of considering inter-particle collisions and surface roughness for predicting particle velocity,mass flux and mean diameter distributions in gas-solid flows is highlighted.The second and third case intend to evaluate the ability of the erosion models in estimating bend erosion in diluted gas-solid flows.The erosion data obtained experimentally by Mazumder et al.(2008)and Solnordal et al.(2015)in very dilut pneumatic conveying systems is used for validating the numerical results,neglecting now inter-particle collisions and two-way coupling.Besides a comprehensive analysis of the different influential properties on erosion,the innovation of the present study is as follows.For the first time also a temporal modifi-cation of the surface roughness due to the erosion was considered in the simulations obtained from previous measurements(Novelletto Ricardo&Sommerfeld,2020).As the surface roughness is increased due to erosion,eventually erosion rate becomes lower.This is the result of diminishing wall collision frequency.Simulations for several degrees of surface roughness showed that larger roughness is coupled with a drastic reduction of erosion.Hence,numerical simulations neglecting wall surface roughness are not realistic.The consideration of a particle size distribution instead of mono-sized computations showed a possible reduction of erosion rate.The detailed analysis of the different single-particle erosion models revealed that the model proposed by Oka et al.(2005)and Oka and Yoshida(2005)yields the best agreement with the measurements,however particle and wall properties are needed.
文摘In this paper, a modified version of the Classical Lagrange Multiplier method is developed for convex quadratic optimization problems. The method, which is evolved from the first order derivative test for optimality of the Lagrangian function with respect to the primary variables of the problem, decomposes the solution process into two independent ones, in which the primary variables are solved for independently, and then the secondary variables, which are the Lagrange multipliers, are solved for, afterward. This is an innovation that leads to solving independently two simpler systems of equations involving the primary variables only, on one hand, and the secondary ones on the other. Solutions obtained for small sized problems (as preliminary test of the method) demonstrate that the new method is generally effective in producing the required solutions.
文摘介绍了1种把Eulerian计算过程和Lagrangian计算过程耦合起来的数值技术,编写了计算程序,把爆炸流场作用过程和结构动力学响应过程的计算结合起来,实现了爆炸流场对结构加载和结构动力响应及对爆炸流场反作用过程的模拟。利用Eulerian过程的流体弹塑性有限差分计算程序MMIC(multi-materials in cell)模拟爆炸流场发展过程,利用Lagrangian过程的结构动力学有限元计算程序模拟结构响应。应用Euler-Lagrange耦合技术分析了爆炸作用下飞片的变形、破坏和对靶体的侵彻过程,计算结果表明,本文的方法可以较好地反映流场与结构各自的运动发展及相互间作用过程。
