ME 11b
Thermal Sciences
Winter 2023 Week 2 Lecture 2
P RO F ESSO R M E L A NY HU N T
2 6 5 G AT ES- THO MAS L A B
HU N T @ C A LTEC H.EDU
1
Today
HW 1:
◦ I will have an extra office hour today at 4-5 in 265 Gates-Thomas.
◦ The solution (with numbers) for the gas turbine problem that we were doing
in class is posted on CANVAS.
◦ Understanding how we did this problem will help with homework.
Topics for Today:
• How to increase power output and improve efficiency
• Nozzles and diffusers
• Start on propulsion
2
Mars 100 Gas Turbine Engine
Stage: stator blade
followed by a rotor
Exhaust
Turbine
Compressor
Combustion
chamber
15 stage axial
compressor
Turbine:
4 stages (2 stages on
shaft for
compressor; 2 stages
for power output)
3
Rotor and stator
blades
Compressor rotor blades: https://www.etradeasia.com/
Turbine stator blades:https://www.exportersindia.com/aster-spacetechnologies-pvt-ltd/gas-turbine-blades-hyderabad-india-1912636.htm
Maximum blade temperature:
standard blades 1200 K
cooled blades 1800 K
Cooled turbine blades
4
Gas turbine cycles
Power in Watts = 𝑊𝑊̇ 𝑛𝑛𝑛𝑛𝑛𝑛 = 𝑚𝑚̇ wnet
Mass flow rate in kg/sec, 𝑚𝑚̇
How do we increase the specific net work of the cycle?
Standard Brayton cycle, wnet = wt - wc
5
Reheat and intercooling
Increase net
work output
P2=P3
P1’=P3’
3
3’’
qh1
3’
Temperature, T
P1=P4
qh2
4
1’
2
ql2
1’’
ql1
1
Compressors:1 to 1’ and 1” to 2
Add heat qh1 and qh2
Turbines: 3 to 3’ and 3” to 4
Reject heat ql1 and ql2
Entropy, s
6
Closed-loop Brayton with reheat and
intercooling
ql1
1’’
ql2
1
1’
4
wc2
wc1
wt1
wt2
c2
c1
t1
t2
2
wnet= wt1+wt2-wc1-wc2
qh= qh1 + qh2
ql = ql1 + ql2
qh1
3
3’
3’’
qh2
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Gas turbine cycles
How do we increase thermodynamic efficiency?
Standard Brayton cycle, wnet = wt – wc = qh – ql and
ηth = wnet/ qh
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Closed Brayton with regeneration
– increase efficiency
ql
4’
Regenerator
Heat addition,
qh
heat
qregen
1
2
2’
4
3
T
C
wc
wt
Energy balance on regenerator?
9
Regenerator; heat exchanger
Increase thermal
efficiency of
cycle by using
waste heat
10
Energy balance
Use general equation of the first flow for problems
involve flow and cross out terms that are not important
dE


Qcv = Wcv +
dt
+ ∑ m e (he + Ve / 2 + gze ) −
2
cv
exits
2

m
(
h
V
+
∑ i i i / 2 + gzi )
entrances
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Brayton cycle with regenerator
Energy balance on regenerator: ∑ 𝑚𝑚̇ ehe=∑ 𝑚𝑚̇ ihi
What would make an “ideal” regenerator?
Regenerator efficiency, ηreg= qactual/qideal
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Closed-loop Brayton with regeneration,
reheat and intercooling
ql2
ql1
1’
1’’
1
4’
4
c1
wc1
c2
Regenerator
2
wc2
wt2
wt1
qregen
2’
t2
t1
qh1
3
3’
3’’
qh2
wnet= wt1+wt2 – wc1 – wc2
qh=qh1+qh2; ql=ql1+ql2
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Turbojet
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Nozzles and diffusers -- steady
Purpose
State 1
State 2
◦ Accelerate (nozzle) or decelerate (diffuser)
◦ Change in cross-sectional area (A1≠A2)
First Law on mass basis:
2
qcv = wcv + (he + Ve / 2 + gze )
2
− (hi + Vi / 2 + gzi )
Or, h1+V12/2=h2+V22/2
And, from mass balance, 𝑚𝑚̇ 1 =ρ1V1A1 = 𝑚𝑚̇ 2 =ρ2V2A2
ρ=density; V=speed; A=cross-sectional area
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Nozzle and diffusers
Mass balance: ρ1V1A1 = ρ2V2A2
Energy equation: h1+V12/2 = h2 + V22/2
For an ideal nozzle or diffuser, isentropic flow: s1 = s2
Ideal gas + isentropic: T2 /T1 =
𝑃𝑃2
𝑃𝑃1
(𝑘𝑘−1)/𝑘𝑘
ηnozzle=V2jet/V2jet,isentropic
What is different about a turbojet, as compared to a gas turbine
cycle for power?
16
Turbojet
Draw a T-s diagram for
the turbojet
a=ambient
1
2
3
4
5
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Westinghouse J32-WE-2 (9.5A) Turbojet Engine
From Smithsonian National Air and Space Museum website
Development of the 9.5A (military designation J32-WE-2) began in late 1942,
and Westinghouse delivered the first engine to the U.S. Navy in mid-1944. The
Navy selected the 9.5A to power the Gorgon II-B and III-B air-to-air missiles,
but these applications did not materialize.
An improved version, the 9.5B, powered the Martin TD2N-1 high-speed target
drone, which successfully flew in 1945. The engine's high cost and continuing
development delays led to the cancellation of the TD2N-1 program in 1946.
Westinghouse manufactured 24 of the 9.5A and 20 of the 9.5B engines.
Despite their limited use, they constituted the first family of small turbojet
engines successfully developed and produced in the United States.
https://airandspace.si.edu/collection-objects/westinghouse-j32-we-2-95a-turbojet-engine-cutaway-motorized
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