This paper focuses on the development and application of a threedimensional gas-kinetic Bhatnagar-Gross-Krook(BGK)method for the viscous flows in rotating machinery.For such flows,a rotating frame of reference is usually used in formulating the Navier-Stokes(N-S)equations,and there are two major concerns in constructing the corresponding BGK model.One is the change of the convective velocities in the N-S equations,which can be reflected through modification of the gas streaming velocity.The other one is the necessity to account for the effect of the additional Coriolis and centrifugal forces.Here,a specifically-designed acceleration term is added into the modified Boltzmann equation so that the source effects can be naturally included into the gas evolution process and the resulted fluxes.Under the finitevolume framework,the constructed BGK model is locally solved at each cell interface and then the numerical fluxes can be evaluated.When employing the BGK scheme,it is sometimes found that the calculated spatial derivatives of the initial and equilibrium distribution functions are sensitive to the mesh quality especially in complex rotating flow applications,which may significantly influence flux evaluation.Therefore,an improved approach for computing these slopes is adopted,through which the modeling capability for viscous flows is enhanced.For validation,several numerical examples are presented.The computed results show that the present method can be well applied to a wide range of flows in rotating machinery with favorable accuracy.
Aiming at a complex multi-block structured grid,an efficient dynamic mesh generation method is presented in this paper,which is based on radial basis functions(RBFs)and transfinite interpolation(TFI).When the object is moving,the multi-block structured grid would be changed.The fast mesh deformation is critical for numerical simulation.In this work,the dynamic mesh deformation is completed in two steps.At first,we select all block vertexes with known deformation as center points,and apply RBFs interpolation to get the grid deformation on block edges.Then,an arc-lengthbased TFI is employed to efficiently calculate the grid deformation on block faces and inside each block.The present approach can be well applied to both two-dimensional(2D)and three-dimensional(3D)problems.Numerical results show that the dynamic meshes for all test cases can be generated in an accurate and efficient manner.
An unsteady load calculation method for the support configuration of a monopile-supported offshore wind turbine is developed based on the Fluent software platform.Firstly,the water wave is generated by imposing the inlet boundary conditions according to the exact potential flow solution.Then the wave evolution is simulated by solving the unsteady incompressible Navier-Stokes(N-S)equations coupled with the volume of fluid method.For the small amplitude wave with reasonable wave parameters,the numerical wave result agrees well with that of the given wave model.Finally,a monopile support configuration is introduced and a CFD-based load calculation method is established to accurately calculate the unsteady load under the combined action of wave and wind.The computed unsteady wave load on a small-size monopile support located in the small amplitude wave flow coincides with that of the Morison formula.The load calculations are also performed on a large-size monopile support and a monopile-supported offshore wind turbine under the combined action of small amplitude wave and wind.
