Study On The Data Interpolation Methods Of Fluid-structure-thermal Interaction Problems

When Hypersonic vehicles fly in the atmosphere for a long time, the interactionbetween shock wave and viscosity will lead to a dramatic increase in the temperature ofthe gas around the vehicles(may reach several thousand degrees Celsius), generating aintense aerodynamic heating environment. At hypersonic speeds these temperatures areso high that it will not only affect the working of cabin instruments but also cause thechange of structure mechanic property, and then reduce the structure strength, causeaerothermoelastic behaviors and disastrous consequences to hypersonic vehicles. Inorder to design the thermal protection structure of hypersonic vehicles and evaluate itsreliability in more detail, make clear the thermal environment of the thermal protectionstructure and its heat transfer, dissipation, distribution mechanism and the resultingdeformation and damage characteristics, the coupled fluid-thermal-structure interactionmust be considered in numerical simulations.The present study on fluid-thermal-structure coupling is on the first step. As aresult of many years study, we have developed many well-proved CFD and CSD solversthat are now regularly used within the design cycle. When considering the coupledproblem of FS（IFluid Structure Interaction）, in order to reuse these well-proved solverswe favor the coupling of existing structural and fluid solvers (the partitioned approach).The partitioned approach, so called―loose coupling‖solves FSI problems in an iterativeway. It allows the use of existing software and grids, but couple the structure and fluidat each time level by data transfer on the fluid-structure interface. Since each solver hasdifferent characteristics, it will use a different mesh. For an instance, the fluid mesh andthe structure mesh often have different emphases when they are generated. Meanwhile,the thermal protection structures will always astrict the mesh. As a result, these mesheswill not generally coincide at the fluid-structure interface. How to transfer informationbetween two non-matching meshes in an accurate and simple way has become abottleneck problem to the fluid-thermal-structure coupling development. In order toovercome this problem, a study on the fluid-structure data transfer is presented in thisthesis.This thesis is composed of five chapters.In the preface of this thesis, we illustrated the background of coupledfluid-thermal-structure interactive data transfer and had a review on differentinterpolation schemes research status. A brief discussion focused on the local and globalinterpolation methods was made. Then, a description was given about the work in thethesis. In the second chapter, we analyzed the variables needed to be transferred in thefluid-thermal-structure coupling procedure. Then we introduced the fundamentals ofdata transfer. Based on the different interpolation schemes review in the preface, sixselections were made: Mapping point interpolation, Constant VolumeTetrahedron(CVT),Thin-Plate Splines(TPS), Multiquadric-Biharmonic(MQ),InverseMultiquadric-Biharmonic (IMQ), Compact Support C2.The first two are local methods,the others are global methods, also called RBF(Radial Basis Functions). Finally, wepresented the full technical descriptions of each method.In Chapter three, Analytical tests were performed to examine the accuracy andefficiency of the methods in3D half circle case. We generated two meshes which havedifferent grid types and refinement levels, assumed the accurate variable distribution ofone mesh by giving a mathematical expression, and then applied six methods toaccomplish the data transfer from one mesh to the other. Interpolation error wasachieved by comparing the accurate data given by mathematical expression andinterpolation result. This section described the results of the applications test cases,which include the variable contour of interpolated mesh, the distribution of theinterpolation error, the average and maximum interpolation error statistical summary,the interpolation efficiency, etc. In addition, how did the mesh density and artificialparameters impact on the interpolation accuracy was also studied in this section.The local interpolation methods like Mapping point interpolation and ConstantVolume Tetrahedron have a common restriction that the data transfer often depends onthe connectivity relationship between the two meshes, this is explicit sometimes andhard to achieve in complex configuration applications. The Radial Basis Functions, alsocategorized as global methods need only arbitrary sets of point clouds, in any form, sothat it can overcome the local interpolation methods’s restriction. In Chapter four, wefocused on TPS, MQ and Compact Support C2three radial basis functions. Since theCompact Support C2generates a sparse matrix while TPS and MQ make a full matrix,the former is more applicable for large scale numerical analysis in engineeringapplications. But the Compact Support C2function’s interpolation accuracy is worsethan TPS and MQ. So how to reduce the computing resource and storage in keeping theinterpolation accuracy condition is an issue that needs to be addressed urgently. In orderto improve the accuracy of the Compact Support C2function, this thesis proposed animprovement scheme based on scaling the mesh by geometry size in three dimensions.This thesis chose the airfoil and wing-body two different cases to exam theimprovement. The test results indicate that these three radial basis function especiallythe Compact Support C2function achieved big improving precision after adopted thescheme. It shows that the improved Compact Support C2function achieves a goodbalance between the accuracy and efficiency and has a greater application prospect for fluid-thermal-structure data transfer.At the last chapter, a review about the work in the thesis was made, the shortage ofthe work and the direction about the future work are presented.