Lecture No.3. The Ideal Reheat Rankine Cycle

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1 Lecture No.3 The Ideal Reheat Rankine Cycle 3.1 Introduction We noted in the last section that increasing the boiler pressure increases the thermal efficiency of the Rankine cycle, but it also increases the moisture content of the steam to unacceptable levels. Then it is natural to ask the following question: Two possibilities come to mind: 1. Superheat the steam to very high temperatures before it enters the turbine. This would be the desirable solution since the average temperature at which heat is added would also increase, thus increasing the cycle efficiency. This is not a viable solution, however, since it requires raising the steam temperature to metallurgically unsafe levels. 2. Expand the steam in the turbine in two stages, and reheat it in between. In other words, modify the simple ideal Rankine cycle with a reheat process. Reheating is a practical solution to the excessive moisture problem in turbines, and it is commonly used in modern steam power plants. The T-s diagram of the ideal reheat Rankine cycle and the schematic of the power plant operating on this cycle are shown in Fig The ideal reheat Rankine cycle differs from the simple ideal Rankine cycle in that the expansion process takes place in two stages. In the first stage (the high pressure turbine), steam is expanded isentropically to an intermediate pressure and sent back to the boiler where it is reheated at constant pressure, usually to the inlet temperature of the first turbine stage. Steam then expands isentropically in the second stage (low-pressure turbine) to the condenser pressure. Thus the total heat input and the total turbine work output for a reheat cycle become 46

2 The incorporation of the single reheat in a modern power plant improves the cycle efficiency by 4 to 5 percent by increasing the average temperature at which heat is transferred to the steam. FIGURE 3 1 The ideal reheat Rankine cycle. EXAMPLE 3.1 Steam is the working fluid in an ideal Rankine cycle with superheat and reheat. Steam enters the first-stage turbine at 8.0 MPa, 480ºC, and expands to 0.7 MPa. It is then reheated to 440ºC before entering the second-stage turbine, where it expands to the condenser pressure of MPa. The net power output is 100 MW. Determine (a) the thermal efficiency of the cycle, (b) the mass flow rate of steam, in kg/h, (c) the rate of heat transfer from the condensing steam as it passes through the condenser, in MW. Discuss the effects of reheat on the vapor power cycle. 47

3 SOLUTION FIGURE 3 2 Schematic and T-s diagram for Example 3 1. To begin, we fix each of the principal states. Starting at the inlet to the first turbine stage, the pressure is 8.0 MPa and the temperature is 480 o C, so the steam is a superheated vapor. h 1 = kj/kg and s 1 = kj/kg.k. State 2 is fixed by p 2 = 0.7 MPa and s 2 = s 1 for the isentropic expansion through the first-stage turbine. Using saturated liquid and saturated vapor data from table, the quality at state 2 is The specific enthalpy is then State 3 is superheated vapor with p 3 = 0.7 MPa and T 3 = 440 o C, so from table, h 3 = kj/kg and s 3 = kj/kg.k. 48

4 To fix state 4, use p 4 = MPa and s 4 = s 3 for the isentropic expansion through the second-stage turbine. With data from table, the quality at state 4 is The specific enthalpy is h 4 = (0.9382) = kj/kg State 5 is saturated liquid at MPa, so h kj/kg. Finally, the state at the pump exit h 6 = kj/kg. (a) The net power developed by the cycle is Mass and energy rate balances for the two turbine stages and the pump reduce to give, respectively where is the mass flow rate of the steam. The total rate of heat transfer to the working fluid as it passes through the boiler superheater and reheater is Using these expressions, the thermal efficiency is 49

5 (b) The mass flow rate of the steam can be obtained with the expression for net power given in part (a). (c)the rate of heat transfer from the condensing steam to the cooling water is H.W. 3.1 Find the cycle efficiency and specific steam consumption of a reheat cycle operating between pressures of 3 MPa and MPa, with superheat temp of 450ºC. Assume that the first expansion is carried out to the point where the steam is dry saturated and then the steam is reheated to the original superheat temp. The feed pump term may be neglected. H.W. 3.2 A smaller power plant produces steam at 3 MPa, 600 C, in the boiler. It keeps the condenser at 45 C by the transfer of 10MW out as heat transfer. The first 4:

6 turbine section expands to 500 kpa, and then flow is reheated followed by the expansion in the low-pressure turbine. Find the reheat temperature so that the turbine output is saturated vapor. For this reheat, find the total turbine power output and the boiler heat transfer. Answer. (Reheat temperature= 529 o C, total turbine power output= 6487 kw, the boiler heat transfer= kw) H.W. 3.3 A smaller power plant produces 25 kg/s steam at 3 MPa, 600 C, in the boiler. It cools the condenser with ocean water so that the condenser exit is at 45 C. A reheat is done at 500 kpa up to 400 C, and then expansion takes place in the lowpressure turbine. Find the net power output and the total heat transfer in the boiler. Answer. (Net power output= kw, the total heat transfer in the boiler= kw) EXAMPLE 3.2 Consider a steam power plant operating on the ideal reheat Rankine cycle. Steam enters the high-pressure turbine at 15 MPa and 600 C and is condensed in the condenser at a pressure of 10 kpa. If the moisture content of the steam at the exit of the low-pressure turbine is not to exceed 10.4 percent, determine (a) the pressure at which the steam should be reheated and (b) the thermal efficiency of the cycle. Assume the steam is reheated to the inlet temperature of the high-pressure turbine. Solution 4;

7 FIGURE 3 3 Schematic and T-s diagram for Example

8 53

9 H.W. 3.4 A steam power plant running on Rankine cycle has steam entering HP turbine at 20 MPa, 500ºC and leaving LP turbine at 90% dryness. Considering condenser pressure of MPa and reheating occurring up to the temperature of 500ºC determine, (a) the pressure at wich steam leaves HP turbine (b) the thermal efficiency Answer. (Pressure of steam leaving HP turbine = 1.40 MPa Thermal efficiency = 56.39%) EXAMPLE 3.3 Consider a steam power plant that operates on a reheat Rankine cycle and has a net power output of 80 MW. Steam enters the high-pressure turbine at 10 MPa and 500 C and the low-pressure turbine at 1 MPa and 500 C. Steam leaves the condenser as a saturated liquid at a pressure of 10 kpa. The isentropic efficiency of the turbine is 80 percent, and that of the pump is 95 percent. Show the cycle on a T-s diagram with respect to saturation lines, and determine (a) the quality (or temperature, if superheated) of the steam at the turbine exit, (b) the thermal efficiency of the cycle, and (c) the mass flow rate of the steam. 54

10 FIGURE 3 4 T-s diagram for Example

11 H.W. 3.5 A mass of steam under (70 bar) and (400 C) enters the first stage of a steam turbine with flow rate of (21600 kg/h) and leaves this stage at (7 bar) and drynessfraction of (0.98). The steam is then reheated under constant pressure to (400 C) before it expands in the second turbine stage down to the condenser pressure of (0.07 bar). Assume both the turbine stages have the same isentropic efficiency and calculate : 1. Thermal efficiency of the cycle. 2. Specific steam consumption. 3. Turbine power output in kilowatts. Answers: (1) 33.9%. (2) 2.993kg/(kW.h). (3) kW. H.W. 3.6 In a two stage steam turbine power plant. The steam supplied to the turbine at (100 bar) and 550 C. It is leaving the first stage turbine dry-saturated at pressure of (3 bar). The steam then reheat in the boiler at constant pressure to (450 C). It is then expanded in the second stage turbine to condenser pressure at (0.03 bar). The isentropic efficiency of the two stages are equal. Show the diagram sketch of the plant on the (T-S) diagram. Neglect the feed water pump work and calculate: 1. The thermal cycle efficiency. 2. The specific steam consumption. 56

12 3. The output power of the plant if the cooling water supplied to the condenser at (15 C) and leaves at (45 C) with flow rate of (708 kg/s). Answers: (1) 40%. (2) 2.212kg/(kW.h). (3) kw. H.W. 3.7 In a steam power plant develops an output power of (48MW) the steam enters the high pressure turbine at (70 bar) and (450 C) and leaves it at (10 bar) and (210 C). The steam is then reheated under constant pressure to (400 C) before it expands in the low pressure turbine to the condenser pressure of (0.07 bar)and dryness fraction of (0.93). Neglect the pump work and calculate: 1. The isentropic efficiency of each stage of turbine. 2. The cycle thermal efficiency. 3. The amount of cooling water having a temperature rise of (35 C) when circulated in the condenser. Answers: (1) 87.7%. (2) 36.6% (3) 565.3kg/s. References: 1- Thermal Engineering by R.K.Rajput 2- Power Plant Technology by El-Wakil M.M. 3- Power Plant Engineering and Economy by Dr. Rahim K. Jassim 4- Thermodynamic Fundamentals by Eistop 5- Thermodynamics by Yunus A. Cengel 57

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