Research On Numerical Algorithm And Engineering Application Of Fuild Simulation Based On Smoothed Particle Hydrodynamics

Numerical simulation using computers has increasingly become a very important approach for solving problems in engineering and science. It plays a valuable role in providing tests and examinations for theories, offering insights to complex physics, and assisting in the interpretation and even the discovery of new phenomena.Despite grid-based numerical method has been widely used in many respects, there are still shortcomings, such as in large deformation of computational fluid dynamics, interfaces of movement material, free surface and so on, which limit their applications in many complex problems due to mesh distortion leading to too large calculation error or can not be carried out.In recent years, meshless method has been paid great attention, this method in many applications are superior to the traditional grid-based finite element method, finite difference method and the finite volume method and so on.This paper relies on Virtual Engineering Research Center of Shandong University and Centre for Advanced Computations in Engineering Science of NUS, makes a systematic study on corresponding technologies of a new generation meshless method-smooth particle hydrodynamics (SPH) method in the application process. This paper achieves the applications of SPH two-phase coupling and three-dimensional, and a numerical simulation of duct pneumatic conveying process, which extends engineering application fields of SPH method, creating the conditions for a real-assisted testing of SPH, has important theoretical and application value.The main contents in this thesis are as follows:A detailed analysis of basic ideas and solving problems process of the Smoothed Particle Hydrodynamics method is developed. Because there is no connection between particles of domain, the particles computed depend on the current local distribution of particles, so SPH method is meshless with adaptability attributes. In the thesis a systematical analysis of the Lagrange Navier-Stokes equations is studied, and the SPH expression with Navier-Stokes equations of the density, the momentum equations and the energy equations using SPH particle approximation is derived.The key technologies of fluid dynamics SPH numerical calculation are investigated. The algorithm should be handled specially in order to be suitable for simulating flow problem with different character. There are two approaches to evolve density in the conventional SPH method. The first approach is the summation density. Another approach of particle approximation for density is the continuity density. Although the density summation approach needs more computational effort, the summation density approach seems more popular in practical applications of SPH, partly because it well represents the essence of the SPH approximation. For simulating events with strong discontinuity, the continuity density approach is preferred. In the SPH method, the Dirac function is approximated with the smoothing function, two kinds of smoothing functions in the commonly used:Gaussian kernel function and the cubic spline kernel function are analysed.In SPH applications, the boundary condition is both advantage and weakness of this method nowadays. Two types of virtual particles used to deal with boundary condition are studied. The virtual particles of the first type are located right on the solid boundary. The virtual particles of the second type fill in the boundary region, which are usually used in the situation of boundary condition always changed. The virtual particles of the type II are constructed in the following way. For a certain real particle i, if it is located within the distance of kh, from the boundary, a virtual particle is placed symmetrically on the outside of the boundary. These virtual particles have the same density and pressure as the corresponding real particles but opposite velocity. In order to avoid the shock value and improve the stability of the algorithm to prevent the particles from non-physical penetration when they are close to each other, artificial viscosity is introduced to SPH momentum equation to amend. The discrete SPH equations are integrated with Leap-Frog algorithm in this thesis. The advantage of the Leap-Frog algorithm is low memory storage required in the computation and the efficiency for one force evaluation per step. Program structure of SPH algorithm is given. The basic SPH method and the accompanied other various algorithms of SPH are result in some special features in the SPH coding. These special features are generally involved under the main loop of time integration process. Shock tube problem and shear driven cavity problem are studied to test usefulness of SPH method in different fluid dynamics problems, SPH method can get satisfactory results in the above questions.Based on analyzing the basic principles of single-phase flow and discrete thought, SPH two-phase coupling simulation method is proposed. SPH method is a pure meshless method without background grid. The particles are of physical properties in the discretization process, so long as they can properly handle the interaction between particles with the same or different properties, the interface between different materials can be discriminated by the distribution of the whole movement of particles, so the movement of two-phase coupling flow can be described with different properties. In the SPH two-phase coupled flow simulation, solid phase or liquid phase is discreted the same SPH particles as gas phase particles, carrying the properties of solid phase or liquid phase.Technical improvement is studied to ensure the normal two-phase coupling flow numerical simulation. The density is normalized to solve boundary effect induced by too large difference near the interface between two phase fluids, to increase accuracy of interface between two phase fluids. The artificial state equation of SPH two phase coupling flow is studied. The problem of escape of smaller particles is solved by adding gas cohesion items in the state equation of particles with smaller density. Velocity correction of SPH two phase coupling is studied. The velocity correction method is introduced to prevent inter-penetration of the particles, so the interface of two-phase coupling is more clear and smooth. Bubbles numerical simulation problem and dam break numerical simulation problem are solved by using two phase coupling SPH method. The result is obtained and is verify that the proposed two-phase coupling SPH method is correct and feasible.Technical application of SPH in three-dimensional fluid flow is implemented. All-pair search algorithm, linked-list search algorithm are analyzed. And tree search optimization algorithm is introduced to the SPH method. With the program implemented, the computational efficiency is improved effectively. Because the pairwise interaction is based on the way of point to point, computational efficiency is improved and storage space is saved by using pairwise interaction in the SPH simulation and analysis. Thus the pairwise interaction is researched deeply, it is implemented by using the method of nearest neighboring particle searching, which store the necessary data for the coming SPH summation. Several methods for improving computational efficiency are researched. Based on the theoretical analysis of consistency of kernel approximation, the initial configuration method of particles is presented. Particles should be distributed as uniformly as possible, and all the qualities of the particles are the same or changing continuously. It is an effective solution to the problem of large errors of existing three dimensional SPH method in dealing with process of fluid flow. Using a simple and efficient variable smoothing length technology based on density transformation, the smoothing length is optimized and relaxed, and the steps and parameters of optimization and relaxation are given in this thesis.SPH method is used in duct pneumatic conveying simulation. Duct boundary implement method of pneumatic conveying process is researched. The method for solving viscous force is given using iterative approximation of strain rate and stress. The distribution of transportation materials and pressure in the duct is analyzed. Simulation method for duct boundary layer flow is proposed. The effect of boundary layer flow can be simulated by setting the viscosity parameter of boundary virtual particles and real particles, while central particles in the duct do not have a viscosity parameter, under the no-stick handling, the effect of boundary layer flow can be simulated. Wall heat will be produced when air encounters rigid wall during conveying process, wall heat energy conversion is researched, and SPH energy equation under the condition of artificial heat is given. SPH program prototype for duct conveying problem is implemented by simplifying impact factor reasonably, using related technologies mentioned above.VC++implementation technology for SPH numerical simulation method of duct pneumatic conveying is researched. Since Fortran is close to a natural description of mathematical formulas, is high calculation precision and implementation efficiency, is a popular process-oriented language, so Fortran is used to achieve the whole SPH process. But it is far from ideal in human-computer dialogue, interactive processing, and its interface is not enough beautiful, graphics processing functions are quite lacking. VC++is a popular object-oriented programming language in personal computer. VC++has powerful features, but it is more complicated in achieving scientific computing. So programming mix VC++and Fortran may get a good computing program with a friendly interface. In the thesis, SPH numerical simulation of pneumatic conveying process is implemented by using SPH basic principle and SPH two-phase coupling method. Based on maintaining computational efficiency, by adoption of VC++calling Fortran generates a dynamic link library (.D11) files, the interactive features of the SPH program are implemented.In summary, SPH two-phase coupling simulation method presented in the thesis extends SPH method, and completes existing smooth particle hydrodynamics applied theory. SPH method is employed in three-dimensional fluid flow, tree-search optimization algorithm is introduced to the SPH method, effectively improving the computational efficiency of smooth particle method. Especially in a large number of particles, the advantage of computational efficiency is more obvious. Several methods to improve the accuracy of calculated results are mentioned. SPH method is applied to the duct conveying simulation in the first time and extends the engineering applications, and calculation method is given in the condition of viscosity and wall heat conversion. The distribution of transportation materials and pressure in the duct is analyzed. Simulation method for duct boundary layer flow is proposed. Based on maintaining computational efficiency, by adoption of VC++calling Fortran generates a dynamic link library (.dll) files, the interactive features of the SPH program are implemented, creating the conditions for SPH really supporting test. These efforts have important theoretical and engineering application value.This paper has been supported by the 2007 China PhD abroad program for building high level university.