Subject :- Engineering Thermodynamics ( ) Prepared by : THAKOR AKASHKUMAR GANESHBHAI TRIVEDI MURALIDHAR MAHENDRABHAI CHARAN UDIT YUVRAJ VAISHNANI NIRAV KAMLESHBHAI VARMA MALIK DEVENDRAKUMAR Topic :- Ideal Referegrartion Guided by :- Krishna Gupta

Objective The objective of ideal regenerative feed heating cycle is to achieve the efficiency equal to the efficiency of a carnot cycle by supplying the feed water to the boiler at saturation temperature T1 corresponding to boiler pressure p1.

Ideal Regenerative Feed Heating Cycle :- Second concept :- In this concept, hollow turbine casing is used as shown in figure. In this arrangement the condensate after leaving the pump circulates around the turbine casing so that heat is transferred from the steam expanding in the turbine to the condensate circulating around it.

The feed water is gradually heated along the path 3-4 and the steam is gradually losing the same amount of heat during expansion process, resulting in a decrease in entropy. The process 1-2’ thus represents reversible expansion of steam in the turbine with reversible heat rejection to the surrounding liquid heated reversibly in the process 3-4. Considering the casing as a part of the system, the heat added along the process 3-4 cancels with heat rejected along process 1-2’, so line 1-2’ is parallel to 3-4. By this way the ideal regenerative cycle is equal to that of carnot.

Calculation Heat supplied, q S = T 1 (s 1 – s 4 ) Heat rejected, q R = T 2 (s 2 ’ – s 3 ) Net work done, w net = q S – q R = T 1 (s 1 – s 4 ) – T 2 (s 2 ’-s 3 ) Since (s 1 = s 4 ) = (s 2 ’ – s 3 ), w net = (T 1 – T 2 )(s 1 – s 4 ) Efficiency of ideal regenerative cycle, η Reg = From this equation, the efficiency of ideal regenerative feed heating is equal to the carnot cycle.

Limitations :- It is not feasible to put an infinite number of heaters or to pass feed water through hollow turbine casing. Reversible heat transfer cannot be achieved in infinite time. The dryness fraction of steam decreases due to the feed heating process, it leads to excessive erosion of turbine blades.

Actual Regenerative Cycle

In figure, the turbine condensate is increasingly heated as it passes through successive feed heaters where bled steam is introduced to heat up the condensate in the process of indirect heat transfer. The bled steam condensate is added to the feed line by the drain pump. The main disadvantage of this method is, the feed pump and the feed pump and the drain pump have to handle a hot feed water.

Calculations Consider 1 kg of steam entering the turbine. According to enthalpy balance equation with control volume approach. Heat entering = Heat leaving For heater No. 1, m 1 h 1 + (1-m 1 )h f2 = h f1 m 1 = For heater No. 2, m 2 h 2 + (1 – m 1 –m 2 )h f3 = (1 – m 1 )h f2 m 2 =

For heater No. 3, m 3 h 3 + (1 – m 1 – m 2 – m 3 )h f4 = (1 – m 1 – m 2 )h f3 m 3 = For heater No.4, m 4 h 4 + (1 – m 1 – m 2 – m 3 – m 4 )h f5 = (1 – m 1 – m 2 – m 3 )h f4 m 4 = Neglecting pump work :- Heat supplied to boiler, q s = (h 0 – h f1 ) Heat rejected from the cycle, q r = (1 – m 1 – m 2 – m 3 – m 4 )(h 5 – h f5 ) = (1 - ∑m)(h 5 – h f5 ) Work done in the cycle = q s – q r w T = w net = (h 0 – h f1 )(1 - ∑m)(h 5 – h f5 )

The thermal efficiency of the regenerative cycle is given by η Reg = = η Reg = 1 – The thermal efficiency of the regenerative cycle is given by η Rank = 1 – In regenerative feed heating process, more is the number of heaters, more is the total temperature rise of feed water, less becomes the heat addition to the water in the boiler, more becomes the mean temperature of heat addition, and more is the cycle efficiency.

h-s diagram and T-s diagram :-

Advantages It is significantly the cycle efficiency because most of the extraction of steam is at low pressure stages of the turbine where the steam expands with relatively low efficiency. Feed water heating process reduces irreversibility, thus heating process in the boiler tends to become reversible. Due to feed water heating average temperature of heat addition to the cycle is increased, thus thermal efficiency of the cycle increases. It reduces the heat rate, and hence reduces operating cost.

It reduces the steam flow to the condenser which requires smaller condenser. It reduces temperature ranges in the boiler, thus less thermal stresses are set-up in the boiler. It improves turbine drainage due to many extractions, hence it reduces erosion due to moisture.

Disadvantages It requires more steam flow rate, which needs a larger boiler capacity for a given power. If there is no change of boiler output, the turbine output drops due to extraction of steam. It increases the complication of the plant. The addition of heaters, require greater maintenance. The piping and high pressure heaters are much more expensive.

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