FVM/BEM approach for the solution of nonlinear conjugate heat transfer problems

A general coupled algorithm is developed for the solution of the conjugate problem. A cooled turbine vane is considered and the fluid flow field and forced convection heat transfer external to vanes are resolved numerically by solving the Navier-Stokes equations using a cell centered finite volume method (FVM) on a non-skewed shifted periodic grid. The temperature within the vane is calculated by solving the conduction equation using the BEM. Conjugacy of external and internal temperature fields is accomplished by enforcing fluid/solid interfacial continuity of temperature and heat flux. An initial guess for the steady state external fluid flow and temperature is determined by subjecting the blade surface to an adiabatic condition. The blade surface temperatures are used as input to the BEM solver. Boundary fluxes are then computed and used as input for the now solver for the next time step. The iteration is continued until convergence of both solutions is achieved. Numerical results are presented and compare favorably to experimental results.