Mathematical modeling on gas turbine blades/vanes under variable convective and radiative heat flux with tentative different laws of cooling

In the last twenty years the modeling of heat transfer on gas turbine cascades has been based on computational fluid dynamic and turbulence modeling at sonic transition. The method is called Conjugate Flow and Heat Transfer (CHT). The quest for higher Turbine Inlet Temperature (TIT) to increase electrical efficiency makes radiative transfer the more and more effective in the leading edge and suction/ pressure sides. Calculation of its amount and transfer towards surface are therefore needed. In this paper we decouple convection and radiation load, the first assumed from convective heat transfer data and the second by means of emissivity charts and analytical fits of heteropolar species as CO2 and H2O. Then we propose to solve the temperature profile in the blade through a quasi-two-dimensional power balance in the form of a second order partial differential equation which includes radiation and convection. Real cascades are cooled internally trough cool compressed air, so that we include in the power balance the effect of a heat sink or law of cooling that is up to the designer to test in order to reduce the thermal gradients and material temperature. The problem is numerically solved by means of the Finite Element Method (FEM) and, subsequently, some numerical simulations are also presented.