A Rankine cycle with regeneration has one open and one closed feedwater heat. St

Question

A Rankine cycle with regeneration has one open and one closed feedwater heat. Steam leaves the
boiler at 1400psi, 1000°F and expands to 500 psi where a portion of the steam is extracted to the closed
feedwater heater. Condensate exits the closed feedwater heater saturated at 500 psi and is trapped
into the open feedwater heater operating at 120 psi. The feedwater leaves the closed feedwater heater
at 1400 psi at a temperature equal to the saturation temperature at 500psi. The remaining steam
expands through the second stage turbine to 120 psi where some of the steam is extracted to the open
feedwater heater. Saturated liquid exits the open feedwater heater. The remaining steam expands
through the third state turbine to the condenser which is operating at a pressure of 2 psi. Consider the
pumps and turbines to operate adiabatically and to all have isentropic efficiencies of 85%. The net
power output of the cycle is 1 x 10
9
Btu/hr. Calculate:
a) the mass flow rate of steam through the first turbine
b) the rate of heat transfer in Btu/hr to the into the steam generator
c) the thermal efficienc

Explanation / Answer

Steam power plants generate most of the electric power in the world. To save fuel, efforts are constantly made to improve the efficiency of the cycle on which steam power plants operate. The general idea is to increase the fluid average temperature during heat addition and decrease the fluid temperature during heat rejection. This section will introduce one such cycle - the ideal regenerative Rankine cycle, which increases the fluid average temperature during the heat addition process. Regeneration T-s Diagram of Lowering the Condenser Pressure In a simple Rankine cycle, heat is added to the cycle during process 2-2'-3 (see the T-s diagram on the left). During this first stage (process 2-2'), the temperature of the water is low. That reduces the average temperature during heat addition (process 2-2'-3). To remedy this shortcoming, increasing the temperature of the feedwater (water leaving the pump and entering the boiler) can be considered. This is accomplished by extracting stream from the turbine to heat the feedwater. This process is called regeneration and the heat exchanger where heat is transferred from steam to feedwater is called a regenerator, or a feedwater heater. There are actually two main types of feedwater heaters. If the steam mixes with the compressed water from the pump, it is an open feedwater heater. If the steam does not mix with the compressed water from the pump, it is a closed feedwater heater. Open Feedwater Heaters An Open Feedwater Heater Click to View Movie (44.0 kB) Schematic of a Power Plant Running an Ideal Regenerative Rankine Cycle with One Open Feedwater Heater T-S Diagram of an Ideal Regenerative Rankine Cycle with One Open Feedwater Heater An open feedwater heater is basically a mixing chamber, where the steam extracted from the turbine mixes with the water exiting the pump. In an ideal condition, the water leaves the heater as a saturated liquid at the heater pressure. The schematic of a steam power plant with one open feedwater heater is shown on the left. In an ideal regenerative Rankine cycle with an open feedwater heater, steam from the boiler (state 5) expands in the turbine to an intermediate pressure (state 6). At this state, some of the steam is extracted and sent to the feedwater heater, while the remaining steam in the turbine continues to expand to the condenser pressure (state 7). Saturated water from the condenser (state 1) is pumped to the feedwater pressure and send to the feedwater heater (state 2). At the feedwater heater, the compressed water is mixed with the steam extracted from the turbine (state 6) and exits the feedwater heater as saturated water at the heater pressure (state 3). Then the saturated water is pumped to the boiler pressure by a second pump (state 4). The water is heated to a higher temperature in the boiler (state 5) and the cycle repeats again. The T-s diagram of this cycle is shown on the left. Note that the mass flow rate at each component is different. If 1 kg steam enters the turbine, y kg is extracted to the feedwater heater and (1-y) kg continues to expand to the condenser pressure. So if the mass flow rate at the boiler is , then the mass flow rate from other components are: Condenser: (1-y) Pump : (1-y) Feedwater Heater: y+(1-y) = Pump : For convenience, heat and work interactions for regenerative Rankine cycle is expressed per unit mass of steam flowing through the boiler. They are: Heat Input: qin = h5 - h4 Heat Output: qout = (1 - y)(h1 - h7) Work Output: Wturb,out = (h5 - h6) + (1 - y)(h6 - h7) Work input: Wpump,in = (1 - y)(h2 - h1) + (h4 - h3) Open feedwater heaters are simple and inexpensive, and can also bring the feedwater to saturated state. However, each feedwater needs a separate pump which adds to the cost.

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