Topology Optimization Of Underwater Body Shape For Drag Reduction In Low Reynolds Number Based On Variable Density Method

Drag reduction has long been noticed and studied as a significant way to achieve long voyage goals and energy saving requirements in marine strategies.The optimal design of hydrodynamic body shape is an important antecedent in the drag reduction step of underwater vehicles,and a good streamlined body shape contributes a very large percentage in drag reduction.Current research on underwater shape optimization is focused on using intelligent algorithms to optimize the shape and size parameters of bionic simplified models or surrogate models constructed by mathematical methods,which cannot change the topological information of the structure during the optimization process.However,topology optimization,which is covering information on topology,shape and dimensions,has greater design freedom.It is essentially a structural design method that achieves from nothing to something by determining the structural configuration in the design domain,requires less definition of the initial structural priori,and also ensures the manufacturability of the generated structure by using additional constraints.Therefore,we propose an approach for topology optimization based on the variable density method,and use the approach for the topology optimization design of the optimal drag-reducing body shape.The details of the study are as follows:This paper uses the proposed variable density topology optimization approach to numerically investigate the optimal shape of drag reduction for objects in two-and three-dimensional flows under steady incompressible external flow conditions,and detail the implementation steps and operational details of the topology optimization.The topology optimization approach based on the variable density method is implemented by filling the design domain with the porous medium,and adding artificial Darcy friction to the Navier-Stokes equation characterizing the effect of the material on the fluid.Material density,which will be used to implement material interpolation,is regularized by filtering and projection techniques.By transforming the boundary integral form of the viscous stress expression of the drag force into the volume integral form of artificial Darcy friction and the convective term,we finish the drag expression corresponding to the implicit interface on the structure.The continuous adjoint analysis method is used to obtain the concomitant sensitivities of objective function and volume fraction,and thus the gradient information.Method of Moving Asymptotes is used to iteratively solve the topological optimization problem with the partial differential equation constraints.In the two-dimensional topology optimization problem,the flow field is controlled by the dimensionless incompressible steady Navier-Stokes equation,and the optimal settings of key parameters such as filter radius,grid density,penalty factor,projection slope and the influence of variables such as Reynolds number,volume fraction and constraint accuracy are investigated in the topology optimization process.It is these good parameter settings avoid common problems in the variable density method such as mesh dependence and gray cells.Thus,the robust topology optimization structure and its good convergence effect and evolution history are obtained.And the topology optimization results obtained using different objective functions are compared,and the similarities and differences of the results in terms of the variation of body shape and drag with Reynolds number are summarized.The effect of lift on drag is also introduced,and the range of variation of lift and the constraint effect of lift-to-drag ratio on drag are discussed.In the three-dimensional topology optimization problem,some parameter settings in two-dimensional problem are changed to compare the similarities and differences between three-dimensional and two-dimensional topology optimization results.And for structured meshes,the effects and computational speed of different meshing strategies are compared.The similarities and differences of shape,drag and convergence performance with Reynolds number of the three-dimensional topology corresponding to the two objective functions are focused on to explore the influence of convection terms in them.By comparing the variation of the flow field with Reynolds number for the structures corresponding to different objective functions,the correlation between the structure body shape and the distribution and variation characteristics of the velocity,pressure and pressure gradient fields in the basin is discussed.The relationship between drag and body shape is also explored.And it is demonstrated that the resulting threedimensional structures at different Reynolds numbers are nearly streamlined rotating bodies,which do not experience flow separation at low Reynolds numbers.