Mathematic Model Of Deterministic Vortex Method With Its Application On The Wind Resistance Of Bridges

For the problem of high Reynolds number separated flows, the discrete vortex methodpresents the great advantage of being free from numerically dissipative truncation error due tothe adaptive characteristic of Lagrange. Random Vortex Method (RVM) is simple toimplement, but the disadvantage can't be ignored. First, for the long times, due to thedistortion of the vortex blobs, the error increases rapidly. Secondly, the resolution is lower byrandom vortex method to simulate the diffusion, and each random step can be considered as adisturbance to the flow. For the flow with boundary, due to the influence of the random walk, the strengths of the new vortex blobs on the boundary are random in a great degree. Thirdly, the no-slipping boundary condition is simulated by using nascent vortices, which results in ahigher numerical noise. In order to avoid the disadvantage of random walk and do not changethe advantage of the discrete vortex method as a Lagrange method, one of the deterministicvortex methods named particle strength exchange (PSE) was chosen to implement thesimulation of the flow around a bluff body. And the program is applied to analysis themicroscopic mechanics of the static load and the effects of the Reynolds number. The mainworks of this dissertation are concluded as follows,1. The theory of vortex methods is reviewed in detail. The deterministic vortex methodwith high resolution to treat with the diffusion is decided and the corresponding methodto deal with the boundary condition is chosen, which were deduced in detail and wereimplemented in the program. The parameters of the program are investigated and theprogram is validated. In order to avoid the distortion of the local vortices resulting insimulating inaccurately the Navier-Stokes equations, the redistribution of particlestrength is introduced in the program to guarantee the overlap of the particles in anytime step. To reduce the cost of the calculation and implement the long times and stablecalculation, even the redistribution with nonuniform resolution is introduced.2. The preliminary flow fields around bluff bodies are simulated by the program of PSE.The circlar sections with different Reynolds number, the square sections and therectangular sections with different wind attack angles are calculated. The main numericcharacteristics are shown in the paper, which are compared with the results of the windtunnel tests and the other references. The program is validated by these cases to simulatethe flow around bluff bodies.3. The aerostatic coefficients and the Strouhal numbers of various sections of the bridgesare calculated by using the program of PSE and the results are compared with the resultsof RVM and the tests. The stability of the program of PSE is verified.4. The simulation for two rectangular sections with different dimmesion ratios and thesection of Millau Bridge are conducted by the program of PSE. The distributions of thepressure are analyzed by proper orthogonal decomposition and the microscopicmechanics of the wind loading on the bluff body is investigated. The results arecompared with the results of the tests and the others. The region with great alteration ofthe pressure is determined. 5. The aerostatic coefficients and the Strouhal numbers theâ…¡shaped section, the section ofGreat Belt Bridge and the section of Sutong Bridge versus Reynolds numbers arestudied. And the results agree well with the results from wind tunnel tests. The pressurecoefficients on these three different sections versus Reynolds numbers are investigatedincluding the first and the second minimal pressure coefficients on the extrados and theintrados of these sections. The distributions of the pressure versus Reynolds numbers arecalculated, which explained the mechanics of the aerostatie coefficients and the StNumbers versus Reynolds numbers in microcosmic.6. The aerodynamic coefficients of the section of Sutong Bridge versus reduced windspeed are studied by PSE, which are compared with the results from experiments andRVM.