| To improve the thrust-weight ratio and thermal cycle efficiency, the gas temperature at turbine inlet has been increased, and it has greatly exceeded the yielding limit of the metal material. Thus an effect cooling system is required to maintain the blade operation. It is a key problem for improving the cooling efficiency that the thermal load and the thermal stress in the blade should be accurately predicted. And the thermal-flow-elastic coupling technique has shown its great potential in solving the problem mentioned above. The purpose of the paper is to investigate the key problems of applying finite difference method to thermal-flow-elastic coupling simulations, and to study the thermal-flow-elastic problems in the air-cooled turbines.Firstly the physical model of the thermal-flow-elastic coupling problems is studied, and the controlling equations are deduced. Such equations consist of three parts: (1) the dimensionless time-averaged N-S equation systems in both the cylindrical coordinates and body-fitted coordinates, (2) the thermal transport controlling equation taking account of the effects of thermal conduction, thermal radiation and thermal deformation on the thermal dissipation in the Cartesian coordinates and its expanded form in the arbitrary curvilinear coordinates, (3) elastic stress equilibrium differential equations with displacement the solving variable both considering and not considering the effects of thermal deformation in the Cartesian coordinates and their expansion in the arbitrary curvilinear coordinates. Then the posing methods of coupling boundary conditions, including coupled heat transfer, flow-elastic, thermal-elastic, and thermal-flow-elastic coupling conditions, are analyzed. The numerical models for the multi-field coupling problems are constructed based on the controlling equations and the coupling boundary conditions. Since the multi-block structured grids are employed to discretize the computational field, the data transfer methods for such four kinds of coupling simulations are also provided.Secondly the discretizing schemes and numerical methods for solving the flow, thermal and elastic controlling equations are studied because of quite the importance of such problem for the thermal-flow-elastic simulations employing finite difference method. For the 3-D viscous flow controlling equations the third-order accurate TVD difference scheme with Godunov characteristic is employed. For the thermal field controlling equation there are two kinds of numerical methods, viz. an implicit ADI method for the steady thermal controlling equation and another kind of ADI method combining a kind of high-order accurate scheme for the unsteady one. The latter method uses a compact scheme to discretize the first- and the second-order cross partial differential terms, and the method is with first-order accuracy in time and forth-order accuracy in space, which is higher than those of the explicit method and the C-N method. For the 2-D elastic stress controlling equations the displacement method is utilized, since the Dirichlet problem is easier constructed with the displacement method than that with the stress method. And projecting beam is selected as the validation case. The comparison between the predicted stress distribution and the analytic one show that the accuracy of the Neumann problems greatly affects the final numerical results, and that there are slight deviation between the numerical result and the analytic one with a second-order scheme for the equilibrium equation but large deviation with a first-order scheme. The dimensionless 3-D solid elastic stress controlling equations are deduced, and the orders of magnitude of the variables and their coefficients are obtained. For the sake of convenience in constructing solving method, the elliptic elastostatics equations are selected as the controlling equations. And ADI method is deduced on the basis of Possion modeling equation, and two kinds of difference scheme, a three-node one and a five-node one, are constructed. The variable-separating solving method and the coupling solving method are utilized in the simulations separately, and the results show that the former one is with less computational load and converging speed than the latter one, but the latter one is with quite nice stability. For the equilibrium equation containing Neumann problem, its computational stability is crucial to that of the whole iteration. For the equilibrium equation at the boundary nodes and the equilibrium differential equation at the inner nodes, the coupling method is with fairly good computational stability, but the separating method is with simpler algorithm. In addition the latter one could be easily programmed, and it is also with simple formula for the data transfer between multi-block grids. To improve the stability of computation, the principle diagonal elements of discretized linear equations system matrixes are modified, which unfortunately reduces the computational speed. The simulation with the methods mentioned above is carried out. And the numerical results, especially those at the inner nodes, agree rather well with the analytic ones.Thirdly the thermal-flow-elastic coupling solver employing finite difference method is developed, and the thermal-flow-elastic coupling simulations by the solver are carried out, with the test case as MARKII guide vane. The simulations by use of CFX10 with several turbulence models andγ?θtransition model show that the laminar flow exists at the whole leading edge of the vane, and that because of the strong shock wave at the suction midst and the strengthened instable flow at the pressure trailing edge the turbulent flow occurs at the aft suction side and the pressure trailing edge. Coupled heat transfer simulation utilizing HIT-3D (a CHT solver developed by Harbin Institute of Technology) with B-L and q ?ωturbulence models and B-L&AGS transition model are accomplished. The predicted flow fields in the main flow field agree well with the measured one, otherwise the predicted boundary layer flows and vane thermal loads differ from the employed models. The B-L algebraic turbulence model, not able to model transition process, over-predicts the temperature and heat transfer coefficient (HTC). q ?ωlow-Re turbulence model, able to model the effects of transition on the flow and heat transfer, predicts temperature and HTC distributions with less deviations from the measured ones than the B-L model does. And the B-L&AGS transition model, able to model the transition process, predicts thermal load agreeing best to the measured one, otherwise it under-predicts the HTC at several part of the vane surface since such model neglects the transport of the intermittency along the outer normal direction of the wall.Finally the flow-elastic coupling and thermal-elastic coupling simulations of the MARKII vane, on the basis of CHT results, are carried out. Compared to the strain and stress caused by thermal load induced acting force, those caused by aerodynamic load induced acting force is rather small. The thermal-elastic results reveal that the thermal deformation and thermal stress of the vane are influenced by the thermal field, temperature gradient, vane geometry and the constraint on the vane, high temperature and temperature gradient leading to large vane deformation and vane stress separately. The results also reveal that the thermal stress cause by the thermal load predicted by different turbulence and transition models differ from the model selected. That with B-L model is higher than those with the other models, and that with B-L&AGS transition model is with the smallest value. For the sake of comparison, there is thermal-elastic simulation utilizing ANSYS, a finite element solver. And the differences of the predicted thermal-elastic results by the different solvers are quite slight, which proves the ability of the developed solver in thermal-elastic analysis.
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