The Study Of Smoothed Particle Hydrodynamics And Its Application On Water Turbine

Smoothed particle hydrodynamics (SPH) method, as one of the earliestmeshfree methods, is a kind of full meshfree and Lagrangian algorithm,which scatters the computational area with discretizing particles. Theseparticles carry the basic information of the particle position, such as velocity,density, pressure and temperature and so on. With the help of kernelapproximation and particle approximation, SPH method firstly discretizesthe domain by which partial differential equations (PDE) are defined.Furthermore, the method provides an approximation for the values of thefield functions and their derivatives at any points. The functionapproximation is then applied to the PDEs to produce a set of ordinarydifferential equations (ODE) in a discretized form with respect only to time.By solving the ODEs one could obtain the information of the problemdomain.This paper is concerned with the exploration of SPH method,particularly the searching methods of the smoothed particle hydrodynamics.Firstly, based on fully analyzing the exploration of the normal searchingmethods using in the SPH method, the algorithm named Geohash which isused in the map searching is introduced into the nearest particle searching inthe SPH method. The Geohash method utilizes a new coding strategy bytransferring the two coordinates into one character string. And bycomparing the string one could get the nearest particles for the computingparticle quickly. Comparing with the normal searching method likeall-paired method and linked-list method, the Geohash method is more efficient.Based on the exploration of SPH method and definition of the openingboundary condition, this paper simulates the normal free surface model, oneis the free fall of one droplet into the water tank, the other is thetwo-dimension dam break. We gave the velocity and pressure of these twomodels, respectively, and analyzed the numerical result. Particularly, webuild up the two-dimensions and three-dimension of water tank andsimulate the linear ocean waves. By analyzing the wave height and waveshape, it is clear that the SPH method could obtain the result which could becompared with theoretical resolution.Finally, the paper introduces the inlet velocity boundary and outletpressure boundary into the SPH method and uses the flow around thecircular cylinder as the testing model, which proves that the tow boundariescould be successfully used to simulate the open system model. Then weutilize the SPH method to simulate the movement of water turbine in theopen system and compare the result with the consequence of moving gridutilized in another paper. It is shown that the SPH method could quickly andprecisely simulate the movement of water turbine, especially the openingand closing of the blade. The result of the simulation could preciselyresponse to the test.