2. Performance & Scaling of Turbomachines

Question 1

what is the formula for the relative inlet mach number, M(1,rel)

Answer 1

• M(1,rel) = sqrt(M_1^2 + U^2/γRT)

Question 2

why is the isentropic efficiency of a turbomachine important

Answer 2

• because it determines the overall work input or output of a machine
• which is a key indicator of performance

Question 3

what is the worded formula for the isentropic efficiency of a turbine and compressor

Answer 3

• turbine isentropic efficiency = actual work / ideal work
• compressor isentropic efficiency = ideal work / actual work

Question 4

what is total to total efficiency referring to

Answer 4

• the measure of the internal losses within the machine
• the formulas only use stagnation values

Question 5

what is the formula for the total to total efficiency of a turbine, n(tt)

Answer 5

• turbine n(tt) = (h(01) - h(02)) / (h(01) - h(02s))

Question 6

what is the formula for the total to total efficiency of a compressor, n(tt)

Answer 6

• compressor n(tt) = (h(02s) - h(01)) / (h(02) - h(01))

Question 7

what is total to static efficiency

Answer 7

• the measure of the of the internal losses within the machine
• including wasted energy
• the formulas use stagnation and static values

Question 8

what is the formula for the total to static efficiency of a turbine, n(ts)

Answer 8

• turbine n(ts) = (h(01) - h(02)) / (h(01) - h(2s))

Question 9

what is the formula for the total to static efficiency of a compressor, n(ts)

Answer 9

• compressor n(ts) = (h(2s) - h(01)) / (h(02) - h(01))

Question 10

between n(tt) and n(ts), which one is always greater for a turbine or compressor

Answer 10

• n(tt)

Question 11

what is the polytropic efficiency, n(p)

Answer 11

• the measure of the internal efficiency of one stage of a multistage machine

Question 12

what is the formula for stagnation temperature ratios for a turbine using the polytropic efficiency

Answer 12

• T(02)/T(01) = (p(02)/p(01))^(n(p)*γ-1/γ)

Question 13

what is the formula for the stagnation temperature ratios for a compressor using the polytropic efficiency

Answer 13

• T(02)/T(01) = (p(02)/p(01))^(γ-1/γn(p))

Question 14

how does the isentropic and polytropic efficiency compare for high pressure ratio turbines and compressors

Answer 14

• for high pressure ratio turbines, n(is) > n(p)
• for high pressure ratio compressors, n(p) > n(is)