(Solved): A two-stage axial turbine operates at its design condition with axial absolute flow at the stage en ...

A two-stage axial turbine operates at its design condition with axial absolute flow at the stage entry and exit. The axial velocity is constant through both stages at 198.3 $\mathrm{m}/\mathrm{s}$. The gas $(\mathrm{Cp}=1.15\mathrm{kJ}/\mathrm{kg}?\mathrm{K};?=1.34)$ from the combustor is delivered at a stagnation temperature of $1450\mathrm{K}$. The rotor exit angle is given as $68.2^{?}$ (from the axial direction). The Mach number at the exit of the stator of the first stage is given as ${\mathrm{M}}_2=0.88$. It can be assumed that each stage does equal work. Determine: a) The mean-radius blade speed, U, the stator exit blade angle, the rotor inlet angle and the reaction ratio. b) The specific work done by each stage and the stage loading coefficient. c) Using Soderberg's relationships (neglect aspect ratio and Reynolds number corrections), estimate the total-to-static efficiency of each stage. d) Determine the static temperature, Mach number and pressure at the exit of the stator for the second stage if the pressure at the exit of the $1^{\text{st }}$ stage is given as $287.25\mathrm{kPa}$. e) Estimate the delivery stagnation pressure from the combustor, the static temperature at the exit of the $2^{\text{nd }}$ stage and the overall total-to-static efficiency of the turbine. f) What is the polytropic efficiency of this two-stage turbine?