Ideal cycles III

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Lecture 4

• Ideal cycles III
• Reheat cycle
• Intercool cycle
• The WR21 engine
• Polytropic efficiencies
• Exercise
• Problem 2.1, 2.3 and 2.9

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Reheat cycle/Reheat with heat exchanger

• Split expansion into a high pressure and a low
  pressure step and reheat in between

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Selection of pressure ratio reheat cycle
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Theory 4.1 - Selection of optimal pressure ratio
reheat cycle
Introduce auxiliary variable ß according to
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Theory 4.1 - Selection of optimal pressure ratio
reheat cycle
Insert result into power formula
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Efficiency for reheat cycle (at pressure division
for max. power output)
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Cycle changes due to reheat
Figure 2.5 or better from Cengel
You introduce an additional cycle operating at
lower pressure ratio. We have already derived
what we want to know!!! Decreasing pressure
ratio in simple cycle gt efficiency decreases.
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Reheat/reheat with heat exchange compared to
single cycle

• Simple reheat
• Power output increases
• Decrease in efficiency (added cycle is worse than
  underlying cycle, since simple cycle efficiency
  decreases with pressure ratio)
• Reheat with heat exchange
• Power output increases
• Increase in efficiency. Heat is added at a higher
  average temperature and removed at a lower
  temperature than in simple cycle. See figure to
  the right.

Simple cycle
Reheat with heat exchange
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Intercooling

• Bulky and requires large amounts of cooling water
• Compactness and self-containedness of gas turbine
  is lost
• What about efficiency and power output of cycle
  ?....
• Try to draw a T-S diagram and make some
  arguments. Check with CRS.

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The WR 21

• ICR cycle - Intercooled Recuperated Cycle
• Improved part load performance gt 30 reduction
  in fuel burn for a typical operating profile
• 25 MW output
• Fits in footprint of current naval engines of
  similar power.
• LM2500 ?th37. ICR ?th43.
• Starts in two minutes instead of 4 hours for
  comparable steam engine.
• Greater power for given space when compared with
  steam/diesel.

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The WR 21
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Polytropic efficiencies - motivation

• If we study multistage designs the isentropic
  efficiency for high pressure compressors tend to
  be lower than for low pressure compressors. Why?

• Assume ?s (stage efficiency) constant, the
  overall temperature rise ?T is obtained by

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Polytropic efficiency - motivation
Thus, the total efficiency is always less than
the stage efficiency.

• But

Preheat effect as you go through the stages you
move to the right in the T-s diagram. Isobars
diverge in that direction!
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Polytropic efficiency preheat independence

• Define the polytropic efficiency (differential
  stage efficiency) as

We have (second revision question lecture 1
before integrating)
(1) (2) produces
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Polytropic efficiency preheat independence
Similarly for a turbine
First guess for preliminary design work
Polytropic efficiencies are useful for
preliminary design, when many compressor concepts
with different pressure ratios may be evaluated
for a given application.
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Recommendation to get started with the course

• Work through Example 2.1 and 2.2 at home (page
  74-78).
• Derive the optimal pressure ratio (for maximum
  power) for the simple cycle gas turbine (Theory
  2.1)
• Derive the efficiency for the heat-exchange cycle
  (Theory 3.1)
• Read very important sections as stated in
  course PM (so far section 2.1, 2.2 and 2.3)
• Start with Design Task 1 !!!
• If you have time
• Read all important sections as well.
• Work through example 2.3 and attempt to solve
  problem 2.5.

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Learning goals

• Know how to show (by arguments or T-S diagrams)
  how the efficiency of the reheat cycle with and
  without heat exchange changes in comparison with
  the simple cycle (ideal case)
• Be able to derive the optimal pressure division
  in ideal reheat cycles
• Be familiar with the polytropic efficiency
  concept and state reasonable loss levels for
  turbine and compressors