United Technologies Research Center Turbomachinery in Propulsion Engines -- Problems 10-13 -- Rensselaer – Hartford Campus Dr. William T. Cousins United Technologies Research Center Text: S. Larry Dixon and C. Hall, “Fluid Mechanics and Thermodynamics”, 7th ed, Elsevier Inc., 2014 ISBN-10: 0124159540 ISBN-13: 978-0124159549

Information for Problems 10, 11, 12 and 13 If needed, use: For the Turbine: Cp = 1.157 kJ/kg K, R = 0.287 kJ/kg K, γ = 1.33 For the Compressor: Cp = 1.005 kJ/kg K, R = 0.287 kJ/kg K, γ = 1.4 Engine Inlet conditions are standard day inlet conditions. The single stage turbine in the J-30 was designed to drive the 10-stage axial compressor. The design point specifications for the compressor are mdot = 30 lbm/sec and P02/P01 = 3.8, at an operating speed of 17,000 rpm, with an efficiency of 0.90. The average mean radius of the compressor is 0.1835 m. The measured hub radius, tip radius, the mean radius values of angles α2 , β2 and β3 of the turbine, the mean radius spacing sm , and the axial chord bZ of the blades, was measured as shown in the two following figures, and the values obtained. rh = 0.152 m rt = 0.216 m α2 = 60° β2 = 30° β3 = -57° sm = 0.02 m bZ = 0.025 m

Problem 10 Estimate (be sure to list any assumptions you might make) the density of the combustion products in the turbine. Assume a 5% loss of total pressure in the burner, and a combustion temperature of 1100 K.

Problem 11 (page 1) Using the data provided, calculate CX/Um for the turbine. Assume that mdot fuel = 3% of the mass flow rate of the air. Also, while you have the measured turbine hub and tip radius, assume there is a 5% area blockage (reduction) due to the fact that there are turbine blades in the flow path.

Problem 12 Using the turbine design spreadsheet presented in class, find Δh0/Um2 and α3 . Find the turbine efficiency ηtt from the Smith chart. Sketch the velocity triangles.

Problem 13 Using Z = 0.8, predict the blade spacing s, and compare the prediction with the measurements.