Actual Rankine Cycle
and Actual Rankine
Engine
Dexter Lyndon Sabusap
Instructor
ME411A Thermodynamics 2
Outline
• Deviations from Ideal Rankine Cycle
• Analysis of an Actual Rankine Cycle
• Analysis of an Actual Rankine Engine
2
Deviations from Ideal Rankine Cycle
• Pressure drop in the steam generator.
• Pressure drop in the steam line (pts. 1 to 1’).
• Pressure drop in the condenser.
• Pressure drop in the feedwater line (pts. 4 to 4’).
• Heat losses in the steam line (pts. 1 to 1’).
• Heat losses in the turbine/engine.
• Irreversible adiabatic expansion in the turbine.
• Inefficient pump.
• Subcooled condensate.
3
Deviations from Ideal Rankine Cycle
• IMPORTANT NOTE: Not all of the listed deviations
appear in an Actual Rankine Cycle, but the presence of
at least (1) deviation makes the entire cycle no longer
ideal.
4
Analysis of an Actual Rankine Cycle
Schematic Diagram
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’
’
’
5
Analysis of an Actual Rankine Cycle
• Heat Added in the Boiler
𝑸′𝑨 = 𝒉𝟏 − 𝒉𝟒′
• Heat Rejected in the Condenser
𝑸′𝑹 = 𝒉𝟐′ − 𝒉𝟑′
• Net Heat Transfer to the Cycle
𝑸′𝑵𝑬𝑻 = 𝑸′𝑨 − 𝑸′𝑹
• Engine Work, a.k.a. Turbine Work
❖ If work is Irreversible Adiabatic Expansion
𝑾′𝑻 = 𝒉𝟏′ − 𝒉𝟐′
❖If work is Polytropic Expansion with QT,loss
𝑾′𝑻 = 𝒉𝟏′ − 𝒉𝟐′ − 𝑸𝑻,𝒍𝒐𝒔𝒔
6
Analysis of an Actual Rankine Cycle
• Pump Work
𝑾′𝑷 = 𝒉𝟒 − 𝒉𝟑′
Alternatively:
𝑾𝑷
𝑾′𝑷 =
𝜼𝒎,𝑷
where
𝜼𝒎,𝑷
This is the “isentropic
efficiency of compression”
that you learned from
previous lecture on vapor
processes.
pump mechanical efficiency
• Back-Work Ratio
𝑩𝑾𝑹 = 𝑾𝑷′ Τ𝑾𝑻′
7
Analysis of an Actual Rankine Cycle
• Cycle Thermal Efficiency
𝑾′𝑵𝑬𝑻
𝒆′𝒄 =
× 𝟏𝟎𝟎%
𝑸′𝑨
8
Analysis of an Actual Rankine Cycle
NOTE: We put an “over-dot” on a variable when its unit
includes the time unit. Examples:
𝑘𝑔
𝑘𝐽
𝑊ሶ 𝑇 𝑘𝐽
=
𝑚
ሶ
×
𝑊
𝑇 𝑘𝑔
𝑠
𝑠
𝑘𝐽
𝑘𝑔
𝑘𝐽
ሶ
𝑊𝑃 𝑠 = 𝑚ሶ 𝑠 × 𝑊𝑃 𝑘𝑔
𝑘𝑔
𝑘𝐽
𝑄ሶ 𝐴 𝑘𝐽
=
𝑚
ሶ
×
𝑄
𝐴 𝑘𝑔
𝑠
𝑠
9
Analysis of an Actual Rankine Cycle
T-s Diagram of an Actual Rankine Cycle
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Analysis of an Actual Rankine Cycle
Effect of Pump and Turbine Irreversibilities
Here, subscript “s” refers to ideal
Rankine cycle, while “a” refers to
actual Rankine cycle.
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Analysis of an Actual Rankine Engine
Schematic Diagram
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Actual Rankine
Engine
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’
’
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Analysis of an Actual Rankine Engine
Energy Chargeable to the Engine
Still, the energy chargeable to the turbine (or the engine)
is the maximum amount of energy that could be
extracted from the steam supplied to the turbine.
𝑬′𝑪 = 𝒉𝟏′ − 𝒉𝒇𝟑′
13
Analysis of an Actual Rankine Engine
Definition of Terms
• Turbogenerator is a generator driven by a turbine.
• Ideal Work (W or WT) is equivalent to work done in a
reversible adiabatic expansion process (S = C).
• Indicated or Actual Fluid Work (WI or W’T) is equivalent
to work done in an irreversible adiabatic expansion or
in a polytropic expansion process.
• Brake Work (WB) is the useful work available at the
engine/turbine shaft.
• Combined Work (WK) is the electrical energy at
generator outlet.
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Analysis of an Actual Rankine Engine
Rate of Brake Work, a.k.a. Brake Power (BP)
Brake Work (or Brake Power if expressed in per unit
time) is calculated as the rotational kinetic energy of a
shaft. For the torque (T) and angular speed (ω), the
Brake Power (BP) can be calculated as:
𝑩𝑷 = 𝑻𝝎
BP may have units of W or lbf-ft/s or horsepower (hp).
T may have units of N-m or lbf-ft.
ω may have units of radians per second.
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Analysis of an Actual Rankine Engine
• Schematic Symbol of a Turbogenerator
STEAM TURBINE
SHAFT COUPLING
A.C. GENERATOR
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Analysis of an Actual Rankine Engine
Schematic Diagram of Actual Rankine Cycle with
Generator
𝒎ሶ is the mass
flow rate of
circulating
steam
𝒎ሶ
’
’
’
’
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Analysis of an Actual Rankine Engine
Thermal Efficiencies
• Ideal Thermal Efficiency
𝑾𝑻
𝒆𝒆 𝒐𝒓 𝒆𝑻 =
𝑬′𝑪
• Indicated Thermal Efficiency
𝑾𝑰 𝑾′𝑻
𝒆𝑰 =
=
𝑬′𝑪
𝑬′𝑪
• Brake Thermal Efficiency
𝑾𝑩
𝒆𝑩 =
𝑬′𝑪
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Analysis of an Actual Rankine Engine
Thermal Efficiencies
• Combined Thermal Efficiency
𝑾𝑲
𝒆𝑲 =
𝑬′𝑪
19
Analysis of an Actual Rankine Engine
Steam Rates
• Ideal Steam Rate
𝟑𝟔𝟎𝟎
𝒎𝑻 𝒐𝒓 𝑻𝑺𝑹 =
𝑾𝑻
• Indicated Steam Rate
𝟑𝟔𝟎𝟎 𝟑𝟔𝟎𝟎
𝒎𝑰 𝒐𝒓 𝑰𝑺𝑹 =
=
𝑾𝑰
𝑾′𝑻
• Brake Steam Rate
𝟑𝟔𝟎𝟎
𝒎𝑩 𝒐𝒓 𝑩𝑺𝑹 =
𝑾𝑩
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Analysis of an Actual Rankine Engine
Steam Rates
• Combined Steam Rate
𝟑𝟔𝟎𝟎
𝒎𝑲 𝒐𝒓 𝑪𝑺𝑹 =
𝑾𝑲
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Analysis of an Actual Rankine Engine
Engine Efficiencies
• Indicated Engine Efficiency
𝑾𝑰 𝑾′𝑻
𝜼𝑰 =
=
𝑾𝑻 𝑾𝑻
• Brake Engine Efficiency
𝑾𝑩
𝜼𝑩 =
𝑾𝑻
This is the “isentropic
efficiency of expansion”
that you learned from
previous lecture on
vapor processes.
• Combined Engine Efficiency
𝑾𝑲
𝜼𝑲 =
𝑾𝑻
22
Analysis of an Actual Rankine Engine
Engine Efficiencies
• Turbine or Engine Mechanical Efficiency
𝑾𝑩 𝑾𝑩
𝜼𝒎,𝒆 =
=
𝑾𝑰 𝑾′𝑻
• Generator Efficiency
𝑾𝑲
𝜼𝒈𝒆𝒏 =
𝑾𝑩
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Analysis of an Actual Rankine Engine
Heat Rates
• Ideal Heat Rate
𝑯𝑹𝑻 𝒐𝒓 𝑯𝑹 = 𝒎𝑻 × 𝑬′𝑪
• Indicated Heat Rate
𝑯𝑹𝑰 𝒐𝒓 𝑰𝑯𝑹 = 𝒎𝑰 × 𝑬′𝑪
• Brake Heat Rate
𝑯𝑹𝑩 𝒐𝒓 𝑩𝑯𝑹 = 𝒎𝑩 × 𝑬′𝑪
• Combined Heat Rate
𝑯𝑹𝑻 𝒐𝒓 𝑪𝑯𝑹 = 𝒎𝑲 × 𝑬′𝑪
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Example 1
A turbogenerator has a combined steam rate of 5.35
kg/kWh at its rated output of 20,000 kW. The steam is at
1.8 MPa, 300°C, and the exhaust is at 0.01 MPa. Calculate
(a) the combined heat rate, (b) the combined thermal
efficiency, and (c) the combined engine efficiency.
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Example 2
Steam at 5.2 MPa, 400°C expands in a turbine to 0.036
MPa. The circulating steam is 140 kg/s. Determine for the
ideal Rankine cycle: (a) the work, (b) the thermal
efficiency, and (c) the steam rate. For the ideal Rankine
turbine, determine as well the (d) the work, (e) the
thermal efficiency, and (f) the steam rate. For an actual
Rankine turbine with same specifications, its BSR is 4.80
kg/kWh, engine mechanical efficiency of 98%, and the
driven electric generator has an efficiency of 93%. Find
(g) brake thermal efficiency, (h) brake engine efficiency,
(i) combined work, and (j) quality and temperature of
actual exhaust steam.
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