| In recent decades,hypersonic vehicles have become the focus of military research in many economic and political powers.Thermal protection technology plays a very important role in various studies of hypersonic vehicle.On the one hand,as the speed of the aircraft reaches Mach 5 or more,the outer surfaces of the hypersonic vehicles will be subjected to an extremely serious aerodynamic heating,which requires a more heat-resistant and reliable thermal protection system.On the other hand,to reach such high speed,vehicles need to be powered by scramjet engines that can provide sufficient thrust,which also generates extremely high temperatures during fuel combustion,and also requires the thermal protection system and seal structure to prevent the high temperatures from destroying the engine structure.Designing such systems and structures requires a lot of repeated experiments and is costly.However,it is economical and convenient to use simulate these thermal protection structures and systems on the computer.At the present stage,most popular numerical simulation softwares are based on finite element method or finite volume method.These methods are weak-form methods,which need to use virtual work principle or control volume to establish equations and require integrations during calculation.It is complicated to establish a unified solution format for multi-physical field coupled problems.In recent years,element differential method(EDM),as a new strong-form finite element method(FEM),has attracted wide attention.It has high computational efficiency,good robustness,and is convenient to establish discrete equations for various physical problems.In this dissertation,a series of studies about element differential method are conducted and element differential method is used to analyze multi-physical field coupled problems on various thermal protection structures of hypersonic vehicles.The main research contents are as follows:(1)The temperature and deformation distributions of some typical engine thermal protection structures are calculated by strong-form element differential method.Based on the shape functions of Lagrange element and the first and second derivatives of shape functions with respect to global coordinates,EDM discrete equations of element internal nodes and element boundary nodes are derived for heat conduction and thermoelastic problems.Then,the direct summation and weighted summation methods of element boundary nodes and their influence on the results are discussed.Finally,through the examples of 2D plate heat transfer and thermoelastic problems,engine joint and engine combustion chamber,comparing the EDM results with analytical solution or the Galerkin FEM results,the mesh independence,stability and accuracy of EDM are proved in the treatment of heat conduction and thermoelastic problems.(2)Based on the strong-form element differential method,the weak-form element differential method(WEDM)is proposed by replacing the element internal node equation with the weak-form equation.In this method,the second derivative of the form function does not appear in the element inner nodes,which makes it more accurate than the strong-form element differential method.It is proved that the strong-form element differential method and the weakform element differential method are more efficient than Galerkin finite element method by the calculation of the block model under a pression.At the same time,through the 2D ring with inner pression,three layer plate heat conduction problems and scramjet structure deformation analysis,the mesh independence,stability of solving large-scale problems can be verified for weak-form EDM.Meanwile,those examples proved that the weak-form EDM is accurate than strong-form EDM.(3)A coupled method of EDM and multi-domain boundary element method(MDBEM)is proposed to analyze the compression of fiber-reinforced thermal protection structures.The boundary element method(BEM)has a natural advantage in the analysis of ultra-thin and ultrafine structures due to the utilizing of singular basic solutions.However,the low efficiency of the boundary element method make it seldom be used in solving large-scale complicated mechanical problems.For fiber reinforced thermal protection structure,if using the boundary element method to simulate the fine fiber and its surrounding structures,using EDM to simulate the rest of the model and using displacement consistency,surface traction balance to couple two methods,the fiber can be accurately simulated and the efficiency of the algorithm can be improved.The accuracy and efficiency of the coupled method of EDM and MDBEM are verified by calculating mechanical behavior of fiber-reinforced thermal protection structure under pression.(4)A thermal-mechanical-seepage coupled model for the seal strctures on turbo based combined cylce engine(TBCC)was established and analyzed by EDM.The braided fiber seal strip is the core structure of the dynamic seal structure.The accurate model of the strip is quite complicated so that the thermal-mechanical-seepage coupled model is used to construct the mathematical model for the seal strip.Mechanical boundary conditions can be directly applied for rectangular section seal strip.However,for circular section seal strip and its surrounding structure,contact mechanics model should be analyzed because the contact surfaces are unsure.The calculation method of leakage to measure the performance of seal strip is given and some relative parameters of rectangular section seal strip are inverted with the leakage experimental data.The inversion results are in good agreement with the experiment,which verifies the rationality of the proposed mathematical model.Finally,the calculation examples of 3D rectangular section seal and 2D circular section seal are given and the leakages of the seal with different preloads and seepage pressure differences are obtained. |
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