Question

A major objective in advancing gas turbine engine technologies is to increase the temperature limit associated with operation of the gas turbine blades. This limit determines the permissible turbine gas inlet temperature, which, in turn. strongly influences overall system performance. In addition to fabricating turbine blades from special, high-temperature, high-strength superalloys, it is common to use internal cooling by machining flow channels within the blades and routing air through the channels. We wish to assess the effect of such a scheme by approximating the blade as a rectangular solid in which rectangular channels are machined. The blade, which has a thermal conductivity of k-25 W/m. K, s 6 mm thick, and each channel has a 2 mm * 6 mm rectangular cross section, with a 4-mm spacing between adjoining channels. Under operating conditions for which ho 1000 W/m2. K, T1700 K, h 200 W/m2. K, and T400 K, determine the temperature field in the turbine blade. At what location is the temperature a maximum? Air channel gases 4 mm To Turbine blade, k gases 2 3 4 6 Ay 1 mm 10 11 12 Symmetry adiabat Symmetry 15 16 171 i 181 adiabat hi 1920 2 Ar- l mm Symmetry adiabat Using Matlab, plot the 2D temperature distribution in the blade, around the channel for nodes 1 to 21 To do so Find the boundary condition for each node and the corresponding finite differences equation Justify each boundary condition. In particular, explain why adiabatic boundary conditions may be used on the left, bottom and right boundaries of the system shown above Write the finite difference equation for each node. Justify every single one Solve the linear system of equations (for example using Matlab and the function inv) Plot the 2-D temperature distribution (For example using Matlab in colorscale using the function imagesc. Choose an appropriate scale) Where are the isotherms? How are they oriented? -

Answer 1