Aero-thermodynamic analysis of a cylindrical leading edge placed in a hypersonic stream is carried out using an in-house developed conjugate heat transfer (CHT) solver. Isotropic and functionally graded materials (FGM) are tested as heat shields to understand the effects of the material property on the flow structure and aerodynamic heating associated with the mutual coupling of fluid flow and heat transfer. A simplified partitioned approach is employed to couple the independently developed fluid flow and heat transfer solvers to perform conjugate heat transfer studies. This framework employs a cell-centred finite volume formulation with an edge-based algorithm. Both strong and loose coupling algorithms are implemented for the data transfer across the fluid–solid interface. A test case of hypersonic flow over a cylindrical leading edge composed of an isotropic material is considered to validate the accuracy and correctness of numerical formulation adopted in the in-house solver. The significance of solid domain materials on the conjugate heat transfer has been studied by considering both isotropic material and FGM. The loosely coupled CHT solver required 10 times less simulation time when compared with the strongly coupled CHT solver. The interface heat flux evolution over time showed a decreasing trend, whereas an increasing trend was for the interface temperature. The current study strongly recommends CHT analysis for the design of thermal protection system of space vehicles. The thermal performance of FGMs composed of various volume fractions of Zirconia and Titanium alloy (Ti6Al4V) is assessed. The temperature distributions obtained from the CHT analysis shows that FGM with a power index of unity is a good material choice for thermal protection systems.

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Abstract. When simulating a wind turbine, the lowest eigenmodes of the rotor blades are usually used to describe their elastic deformation in the frame of a multi-body system. In this paper, a finite element beam model for the rotor blades is proposed which is based on the transfer matrix method. Both static and kinetic field matrices for the 3-D Timoshenko beam element are derived by the numerical integration of the differential equations of motion using a Runge–Kutta fourth-order procedure. In the general case, the beam reference axis is at an arbitrary location in the cross section. The inertia term in the motion differential equation is expressed using appropriate shape functions for the Timoshenko beam. The kinetic field matrix is built by numerical integration applied on the approximated inertia term. The beam element stiffness and mass matrices are calculated by simple matrix operations from both field matrices. The system stiffness and mass matrices of the rotor blade model are assembled in the usual finite element manner in a global coordinate system accounting for the structural twist angle and possible pre-bending. The program developed for the above-mentioned calculations and the final solution of the eigenvalue problem is accomplished using MuPAD, a symbolic math toolbox in MATLAB®. The natural frequencies calculated using generic rotor blade data are compared with the results proposed from the FAST and ADAMS software.

Abstract. In the simulation of a wind turbine, the lowest eigenmodes of the rotor blades are usually used to describe their elastic deformation in the frame of a multibody system. In this paper, a finite element beam model for the rotor blades based on the transfer matrix method is proposed. Both static and kinetic field matrices for the 3D Timoshenko beam element are derived by numerical integration of the differential equations of motion using RUNGE KUTTA 4th order procedure. The beam reference axis in the general case is at an arbitrary location in the cross section. The inertia term in the motion differential equation is expressed using appropriate shape functions for the Timoshenko beam. The kinetic field matrix is built by numerical integration applied on the approximated inertia term. The beam element stiffness and mass matrices are calculated by simple matrix operations from both field matrices. The system stiffness and mass matrices of the rotor blade model are assembled in the usual finite element manner in a global coordinate system with the accounting for structural twist angle and possibly pre-bending. The program developed for the above calculations and the final solution of the eigenvalue problem is accomplished using MuPAD, a symbolic math toolbox of MATLAB®. The calculated natural frequencies using generic rotor blade data are compared with the results proposed from FAST and ADAMS software.