Interface Integral Boundary Element Method And Its Application In Aerodynamic Ablation Analysis Of Hypersonic Vehicles

Boundary Element Method(BEM)is a numerical method developed on the basis of foundamental solutions and conventional Boundary Integral Equations(BIEs)after absorbing the discretization technique from other numerical methods.Attributing to the advantage of boundary-only dicretization and semi-analytical feature,BEM has been developed to be a powerful technique in engineering and scientific computation.For solving moving-boundary problems,BEM has distinct advantage:adding the nodal displacements of moving boundaries to the original global coordinates naturally yields the information of nodes and elements of the new moving boundaries.No re-meshing process for the deformed body is needed,and no mesh distorsion problems occur.However,conventional BEM is built based on the foundamental solutions and boundary integral equations for single medium.Most engineering problems involve objects composed of different materials,therefore it is necessary to develop a BEM for multi-medium structures in order to utilize the advantage of BEM in solving practical engineering problems.The ablation of hypersonic aircrafts is a typical moving-bondary problem.During the flying of hypersonic vehicles equipped with Thermal Protection System(TPS),the ablative materials produce a series of chemical and physical reactions including melting,evaporating,pyrolysis and sublimating due to fricting with atmosphere,comsume some of their own masses to absorbe a quantity of aerodynamic heat,and protect the body of an aircraft.The research of ablation is important in engineering and science.However,the meshes of solid and fluid have to be re-constructed according to the motivation of ablation boundaries,if conventional domain-discretization based numerical methods such as Finite Difference Method(FDM),Finite Volume Method(FVM)and Finite Element Method(FEM)are used to solve such problems,which heavily influences the computational efficiency.BEM has the advantage of easily modelling complex geometry,which is very suitable for solving the ablation moving boundary problem.There is few report available concerning ablation analysis using BEM,and this thesis is a try in this area.The ablation TPS is always composed of multiple media,in order to make up for the short of BEM in solving multi-medium problems,a new BEM,named as Interface-integral BEM,is presented in this thesis,which is capable of solving general multi-mediuum mechanics and heat transfer problems in a single integral equaiton formulation.Meantime,deep research of hyper-singualr integrals involved in the interface integral equation for gradient variables(i.e.heat flux and stress)is conducted,in which high precise heat fluxes or stresses on the interfaces are computed through directly solving the hyper-singular integral equations.When conducting the aerodynamic ablating analysis,the aerodynamic thermal environment is computed using Panel Method(PM),and the thermal load for solid heat conduction is extracted from the computed aerodynamic thermal environment.The accordance of PM model and BEM model in geometry guarantees the efficiency of BEM in solving moving boundary problems.The detailed work is listed as follows:(1)Interface-integral BEM is proposed for solving varying coefficient and non-linear multi-medium problems.This method makes up for the deficiency of BEM in solving multi?medium problems,and can utilize the single integral equation to solve multi-medium problems.Firstly,for solving multi-medium varying coefficient heat conduction problems,the foundamental solution for Laplace equation is used to derive the boundary-domain integral equation for single medium.Based on a domain to interface degeneration technique,the infinite narrow domain integral is degenerated into an interface integral,and an interface integral equation is derived to solve multi-medium varying coefficient heat conduction problems.Secondly,for solving general solid mechanics problems,based on the general stress-strain constitutive relationship and the elastic Kelvin's foundamental solution,the general single medium mechanics boundary-domain integral equation is derived.Then considering the jump effect of material properties across the interface between different media,the general multi-medium mechanics interface integral equation is derived.Finally,the interface integral is introduced for elastoplasticity poblems,by regarding the elastic and plastic regions involved in the body under plastic deformation as different materials,and a new elasto-plastic boundary element formulation is derived,which involves no domain integrals concerning initial stresses or initial strains,and only displacements are taken as unknown variables appearently involved in the new integral equation.(2)In order to deal with the hyper-singular integrals in the interface integral equation for gradient variables such as heat flux or stress,deep research is conducted to study the hyper-singular integral properties,and then a direct method for evaluating arbitrary high order singular integrals is presented.Since the conventional "stress recovery method" and "rigid motion method" can not be used to calculate the heat fluxes or stresses on the interface,the only strategy to determine the interface gradient variables is directly solving the hyper-singlar interface integral equations.A new direct method for evaluating all kinds of singular integrals is presented.Finally,this direct method is applied to solve the hyper-singular interface integral equations.When the source point is located on the outer boundary or on the interface,a high order precise gradient variable results are obtained.(3)The interface integral equation for multi-medium transient heat conduction is developed for multi-medium composed ablation TPS structures.Based on the developed interface integral equation,a robust Fortran program is developed to do the transient analysis of multi-medium structures with variable thermal conductivities,in which,the analytically-integrated Radial Integration Method(RIM)is employed to transform the domain integral associated with the time derivative of tempertures into equivalent boundary integrals.As a result,not only a pure BEM without internal cell discretization can be developed,but also the computational efficiency is improved remarkably compared with conventional numerically-integrated RIM.(4)A coupled method based on the combination of BEM and aerodynamic Panel Method(PM)is built for solving the aerodynamic heating-ablation-heat conduction problems.For the heat conduction analysis in solid structures,an ablating moving boundaries condition is added to the transient BEM.The thermal load for the heat conduction in solids is gained by extracting the aero-heating fluxes from the computed results of the thermal environments.The aerodynamic thermal environment is computed based on the combination of compressible external inviscid flow and viscid boundary layer theory.The external inviscid flow is simplified to be a Laplace equation concerning the potential function of flow velocity.Green's theorm is used to transform the Laplace equation into a boundary integral equation,then PM is used to discretize the surface of the structure and to calculate the boundary integral equation.After the potential is calculated,the velocity field is obtained,then the velocity is applied into the viscid boundary layer equation as the outer boundary conditions.The aerodynamic heating results can be obtained through using visicid boundary layer theory.Since both the PM model for fluid and the BEM model for solid use the boundary-only discretization,they are accordant in geometry,and the modification to both fluid and solid regions are convinent,and the exchange of data between fluid and solid fields is easier,so that distinct advantage of BEM in solving moving boundary problems can be more efficiently employed.The developed Interface-integral BEM in this thesis,which utilizes a single integral equation to solve multi-meidum problems with varying coefficient or non-linear material properties,is innovative in theory of boundary integral equations.It is a promising numerical technique for solving practical engineering problems.Using the coupled BEM and PM technique for solving aeroheating ablation and heat conduction problems,which has fully taken the advantage of BEM for solving moving boundary problems,has significant real engineering application.