ME3280 Turbines and Centrifugal Machinery Fall 2017
Dr. T. J. Barber
Problem 9: Turbine Meanline Analysis
In class, we designed a 7-stage compressor for a moderate size gas-turbine engine. We assumed for this design:
• Overall Pressure Ratio = 4.15
• Air-mass flow = 20 kg/s
• Turbine inlet stagnation temperature = 1100 K
When we went through the design, we determined:
• N = 250 rev/sec or 15,000 RPM
• p02 exiting the compressor was 4.15 p01 = 4.15 (1.01bar) = 4.19 bar
• p2 exiting the compressor was 3.838 bar
• DT0 compressor = T073-T011=164.5 0K
Now design a turbine to drive this compressor with the following assumptions:
· The burning and mixing in the combustor is very efficient and can be assumed to be an isentropic, constant pressure process [p0, p].
· The flow into the turbine has zero swirl. The flow leaving the turbine also should have zero swirl to maximize the engine thrust.
· The turbine work is the same as for the compressor
· A growth in the mean radius over the combustor occurs such that the turbine blade speed at the mean radius is U = 340 m/s.
· There was no bleed of flow from the compressor necessary to cool the turbine and compressor disks (i.e. no change in mass flow).
• Assume constant CX along the mean radius that will also be held constant
• This will be a single stage (stator/rotor) design in order to minimize weight
• Overall turbine adiabatic efficiency ha= 0.9 & polytropic efficiency hp= 0.9
• Assume that there is no relative total pressure loss across the stator, Y = 0.0.
• Ratio of specific heats, g =1.333, Rair = 287 m2/(s2 K) [Assume for simplicity g=1.4]
• Other conversions:
• multiply bar by 1.02 x 104 to get kgf/m2
• multiply kgforce by 9.8146 to get kgmass
Find the following for this turbine design:
1. overall turbine temperature and pressure ratio
2. mean radius velocity triangles (all velocity components and angles) at stations: (1) - inlet to stator, (2) - exit of stator, inlet to rotor, and (3) - exit of rotor
3. sketch the velocity triangles
4. ps, Ts, r, po, To, poR, ToR and annulus area at each station along mean radius
a) Work coefficient, Reaction, and Flow coefficient
b) Comment about the Reaction. What could be done to improve it?
c) Use a free vortex strategy to determine the velocity triangles of the stator and rotor at the tip and hub.
Hint: Solve for station 1, 3 and then 2. Make sure you check all units!!!!!