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Reflection and Refraction of Waves Across an Interface of two-phase Flow

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Acta Mathematicae Applicatae Sinica 2021年第1期37卷 137-147页

作者： Kai HU Hui KAN Chun-lei TANG Xiao-zhou YANG School of Mathematics and Statistics Southwest UniversityChongqing 400715China Wuhan Institute of Physics and Mathematics Chinese Academy of SciencesWuhan 430071China

We investigate a hyperbolic system of one-dimensional isothermal fluid with liquid-vapor phase *** refraction-reflection phenomena are intensively analyzed when elementary waves travel across the two-phase *** apply the characteristic method and hodograph transform of Riemann to reduce the nonlinear PDEs to a concise *** for the case of incident rarefaction wave,reduced linear equations are convenient to solve by Laplace *** an integral formula in wave interaction region is derived in this paper,instead of the hypergeometric functions solutions for non-isothermal polytropic *** is also observed that when incident waves travel from the vapor phase to the liquid phase,the refracted waves must be accelerated and move forward.

关键词： p-system two-phase fluid Hodograph transform Volterra equation

RESEARCH ON METHOD TO CALCULATE VELOCITIES OF SOLID phase AND LIQUID phase IN DEBRIS FLOW

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Applied Mathematics and Mechanics(English Edition) 2006年第3期27卷 399-408页

作者：陈洪凯唐红梅陈野鹰 Institute of Geotechnical Engineering Chongqing Jiaotong University Chongqing 400074P. R. China Key Laboratory for the Exploitation of Southwestern Resources and the Environmental Disaster Control Engineering Ministry of EducationChongqing UniversityChongqing 400044P. R. China

Velocities of solid phase and liquid phase in debris flow are one key problem to research on impact and abrasion mechanism of banks and control structures under action of debris flow. Debris flow was simplified as two-phase liquid composed of solid phase with the same diameter particles and liquid phase with the same mechanical features. Assume debris flow was one-dimension two-phase liquid moving to one direction, then general equations of velocities of solid phase and liquid phase were founded in two-phase theory. Methods to calculate average pressures, volume forces and surface forces of debris flow control volume were established. Specially, surface forces were ascertained using Bingham＇s rheology equation of liquid phase and Bagnold＇s testing results about interaction between particles of solid phase. Proportional coefficient of velocities between liquid phase and solid phase was put forward, meanwhile, divergent coefficient between theoretical velocity and real velocity of solid phase was provided too. To state succinctly before, method to calculate velocities of solid phase and liquid phase was obtained through solution to general equations. The method is suitable for both viscous debris flow and thin debris flow. Additionally, velocities every phase can be identified through analyzing deposits in-situ after occurring of debris flow. It is obvious from engineering case the result in the method is consistent to that in real-time field observation.

关键词： debris flow two-phase fluid velocities of solid phase and liquid phase calculation method verification

Experimental and Theoretical Analysis of the Drag Torque in Wet Clutches

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fluid Dynamics & Materials Processing 2019年第4期15卷 403-417页

作者： Haojie Pan Xiaojun Zhou School of Mechanical Engineering Zhejiang UniversityHangzhou310000China

Traditional mathematical models cannot predict and explain the phenomenon by which the drag torque(DT)in wet clutches rises in the high-speed *** order to evaluate the DT in such conditions,a two-phase air-fluid mathematical model for a DT with grooves was *** mathematical model was based on the theory of viscous fluid flow.A two-phase volume of fluid model was also used to investigate the distribution and volume fraction of air and *** on three friction plates with different grooves were conducted to validate the resulting mathematical *** was found that the gap between plates decreased in the high-speed zone,thereby producing an increase of the DT in the high-speed *** results support the understanding of the physical phenomena relating to disengaged wet clutches,and provide a theoretical basis for the future improvement of drive systems.

关键词： Wet clutch drag torque two-phase fluid groove form

Simulation of Droplet Impact onto Horizontal and Inclined Solid Surfaces with Lattice-Boltzmann Method

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Journal of Harbin Institute of Technology(New Series) 2013年第6期20卷 97-105页

作者： Sheng-Lin Quan Wei-Zhong Li Sheng-Qiang Shen Ya-Li Guo Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education Dalian University of Technology

In this paper, the lattice-Bohzmann method is used to investigate the droplet dynamics after impact on horizontal and inclined solid surface. The two-phase interparticle potential model is employed. The model is found to possess a linear relation between the macroscopic properties （ surface tension σ and contact angle α） and microscopic parameters （ G, G, ）. The flow state of the droplet on the surface is analyzed in detail, and the effects of surface characteristic, impact velocity, impact angle, the viscosity and surface tension of the liquid are investigated, respectively. It is shown that the lattice-Bohzmann method can not only track exactly and automatically the interface, but also the simulation results have a good qualitative agreement with ones of the previous experimental and numerical studies.

关键词： Lattice-Boltzmann method interpartiele potential model droplet impact two-phase fluid numerical simulation