In Part 2 we cover Section 9.5 of Potter & Somerton (The Regenerative Cycle). We continue with our example of the Reheat cycle developed in Part 1 and examine the performance effects of adding open and closed feedwater heaters. We do not consider Section 9.6 (The Supercritical Rankine Cycle) as a separate problem, and will use the Gavin Power Plant as an example of a supercritical system. We have previously covered Section 9.7 (Effect of Losses on Power Plant Efficiency) in Chapter 6, and the part describing Turbine Adiabatic Efficiency with the use of h-s (enthalpy-entropy) diagrams should be reviewed. Section 9.8 (The Combined Brayton-Rankine Cycle) is an optional part of this course - only if we find time to cover it.
We recommend that you attempt as many of the following Supplementary Problems as possible during this week:
All answers to the Supplementary Problems are given at the end of the chapter
We continue with our example of the Reheat cycle developed in Part 1, and examine the effect of adding a regenerative heat exchanger in the form of an Open Feedwater Heater, as shown below. We will find that this system does result in an increase in thermal efficiency by preheating the water before it enters the boiler, however at the expense of a reduced power output (why?) and the added complexity of adding a condensate pump to pump the saturated liquid to the mixture pressure of the open feedwater heater as shown.
For this example we have chosen the mixture pressure of the open feedwater heater as 100kPa. Notice that a portion of the steam is bled off from the LP turbine at a pressure of 100kPa, and then mixed with the compressed liquid (also at100kPa), ultimately resulting in saturated liquid at station (8). We first need to determine the mass flow fraction y of the bled steam requred bring the output of the open feedwater heater (8) to a saturated liquid state. From the energy equation applied to the 3 ports of the open feedwater heater (no heat supplied externally, no work done) we obtain:
Notice that the work output is reduced by having bled off a fraction y of the steam, and the boiler heat input is reduced by the increased temperature of the compressed liquid entering the boiler T9. Thus:
In our example below we are again extending the Reheat cycle developed in Part 1, and examine the effect of adding a regenerative heat exchanger in the form of a Closed Feedwater Heater, as shown below. We will find that this system does result in an increase in thermal efficiency by preheating the high pressure water before it enters the boiler, however at the expense of a reduced power output (again, why?).
Notice that a portion of the steam is bled off from the output of the HP turbine, and then used to heat the high pressure liquid, ultimately condensing to a saturated liquid at state (8). The condensed liquid is then passed through a throttling valve, or "Trap", before being returned to the condenser at state (9). As we have learned from our studies of refrigerators, a throttling valve is simply represented on the P-h diagram by a vertical line, since from the energy equation we find that h8 equals h9.
Consider first the evaluation of the mass flow fraction z, which is bled from the output of the HP turbine. Treating the closed feedwater heater as a heat exchanger, we have from the energy balance:
The question is how to determine the value of h7. In order for the steam being bled off from the HP turbine outlet to condense to a saturated liquid state, the temperature T7 may not be greater than the saturation temperature T8 (~180°C). The compressed liquid tables are extremely sparse and mainly unused, however in this particular case there is a table entry for 15MPa, 180°C, and we can use this example to compare the alternative approaches. One approach is to increase the enthalpy h8 by the equivalent amount of pump work required to raise the pressure of the saturated liquid to 15MPa, as follows:
where v is the specific volume of the saturated liquid at stage (8) and DP = P7 - P8.
In all the analysis that follows we have adopted the simpler and more conservative approach of assuming that h7 is equal to h8. This will always ensure that the temperature T7 is a few degrees less than T8. Thus:
Thus the net work output and total heat input (boiler + reheat) are given by:
Finally leading to the system thermal efficiency:
Please note that you may not get the exact same answers as those above. Various software and different property tables present slightly different values - this is ok, and as long as the approach is correct we will expect small variances in the numerical results.
In a practical power plant one may find various combinations of closed and open feedwater heaters. For example the Gavin Power Plant has one open and 7 closed feedwater heaters in each of the two sections of the plant (see photo below). In the following example we have chosen one open and one closed feedwater heaters in order to illustrate the method of analysis, however the same method will apply to any combination.
Once again we evaluate the mass flow fractions z and y (as above) in order to bring the respective bled streams to their saturated liquid states. An energy balance on both the closed and open feedwater heaters leads to the following values for z and y:
The reduced net work output and heat input now become:
And finally we obtain the thermal efficiency of the overall system as follows:
As always, you should check this result against the equivalent method of considering only heat in and heat rejected in the condenser.
The following photo shows one of the seven
Closed Feedwater Heaters used in each section of the Gavin
Power Plant.
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