POWER STATIONS
Prof. Farouk Okasha
Department of Mechanical Power Engineering -Mansoura University
2- STEAM CYCLE
• The Ideal Rankine
• Rankine is widely accepted as the standard for steam powerplants.
Flow diagram of a Rankine cycle T-s Diagram
Analysis of Ideal Rankine Cycle:
Heat added : 𝒒𝑨 = 𝒉𝟏 − 𝒉𝟒
Turbine work: 𝒘𝑻 = 𝒉𝟏 − 𝒉𝟐
Heat rejected: 𝒒𝑹 = 𝒉𝟐 − 𝒉𝟑
Pump work : 𝒘𝒑 = 𝒉𝟒 − 𝒉𝟑
Net work : ∆𝒘𝒏𝒆𝒕 = (𝒉𝟏 −𝒉𝟐 ) − (𝒉𝟒 − 𝒉𝟑 )
Thermal efficiency
𝒘𝒏𝒆𝒕 (𝒉𝟏 −𝒉𝟐 )−(𝒉𝟒 −𝒉𝟑 )
𝜼𝒕𝒉 = =
𝒒𝑨 𝒉𝟏 −𝒉𝟒
Work ratio
𝒘𝒏𝒆𝒕 (𝒉𝟏 −𝒉𝟐 )−(𝒉𝟒 −𝒉𝟑 )
𝑾𝑹 = =
𝒘𝑻 𝒉𝟏 −𝒉𝟐
T-s Diagram
Important notes
- For small units the pump work may be negligible compared
with the turbine work.
- This simplification is not true for modern steam powerplant
as p4 is 70 bar or higher while p3 is about 0.07 bar.
- An acceptable approximation for the pump work may be
calculated as the change in flow work.
𝒘𝒑 = 𝒗𝟑 (𝑷𝟒 − 𝑷𝟑 ) (2-2)
2.2 External Irreversibility of Rankine Cycle
The external irreversibility is primarily due to the
temperature differences between:
- primary heat source (the flue gases) and working fluid
- condensing working fluid and condenser cooling water.
External irreversibility with Rankine cycle.
Pinch Point: is the minimum approach point between the two lines representing
the temperatures of the heat source and the working fluid.
counter flow
parallel flow
Important notes:
- Too small a pinch-point results in low overall temperature difference and, hence, lower irreversibilites,
but in a large and costly steam generator.
- Too large a pinch point leads to a small, inexpensive steam generator but large overall temperature
differences and irreversibities and, hence, reduction in plant efficiency.
- The most economical pinch-point is obtained by optimization that takes into account both fixed charges
(based on capital costs) and operating costs (based on efficiency and fuel costs).
Important notes:
- Generally counter flow is favored over parallel flow from both thermodynamic and heat
transfer considerations.
- Considering the lower temperature limit of the cycle in the condenser there is little that
can be done to improve things. Optimization the design of the condenser to obtain the
lowest temperature difference between the two lines taking into consideration the
condenser overall cost. However, it is worth to indicate that the lower the temperature of
the cooling water at c, the lower the condenser steam temperature and the higher the
cycle efficiency.
Steam Superheating
- Superheat enables heat addition at an
average temperature higher than using
saturated steam only and according to the
Carnot principle, this should yield higher
cycle efficiency.
- Superheat appears have another extra
beneficial effect. It leads to drier steam
turbine exhaust for saturated steam. A
turbine operating with less moisture is more
efficient and less prone to blade damage.
Effect of Superheat on external irreversibility
Reheat T-s diagram
𝑞𝐴 = (ℎ1 − ℎ6 )
+ (ℎ3 − ℎ2 (
𝑤𝑇 = (ℎ1 −ℎ2 )
+ (ℎ3 −ℎ4 (
Reheat leads to an increase in the average
temperature at which heat is added and
Modern fossil-fueled powerplants utilize superheat
maintains the boiler-superheat-reheat portion
and at least one stage of reheat. Some powerplants
closer to the flue gases line ae, which improves
use two stages of reheat, however more than two
the cycle efficiency. Reheat has an additional
stages results in cycle complication and increased
advantage as it results in drier steam at the
capital costs that are not justified by improvements
turbine exhaust which is beneficial for the
in efficiency.
operation of the real cycles
Effect of reheat pressure
The cycle efficiency is dependent on the pressure at
which the steam is reheated.
A reheat pressure very close to the initial pressure
results in little improvement in cycle efficiency because
only a small portion of additional heat is added at high
temperature.
A further reduction in reheat pressure causes the
temperature differences between the primary and the
working fluids to increase and start to offset the addition
of heat at high temperature, hence causing the efficiency
to decrease again.
It is also worth to note that the reheat results in drier
exhaust steam; see x4 values. A very low pressure ratio Effect of reheat-to-initial pressure ratio on efficiency,
may even yield superheated exhaust steam, an un-flavored high-pressure turbine exit temperature and low-pressure
situation for condenser operation. turbine exit quality. Data of cycle (172/538/552)
A superheat-reheat powerplant is usually assigned The optimum efficiency holds at a
P1/T1/T3 in bar absolute-degree Celsius. For instance, the
case in the presented Fig. is 172/538/552, whereas a pressure ratio of 0.2-0.25 for the most
double-reheat plant may be assigned 165/538/552/566. modern power plant.
