The entire chapter is required reading however we will be take a somewhat different approach to describing and analyzing the various systems. Potter & Somerton (together with all other Thermo texts that I have seen) uses T-s (temperature-entropy) diagrams exclusively to describe vapor power cycles. We find this approach cumbersome, non-intuitive and even incorrect in the description of feedwater pumps. We will make exclusive use of P-h (pressure-enthalpy) diagrams to describe the various vapor power systems which we inroduced in M321 in Chapter 4.
In Part 1 we cover Sections 9.1 through 9.4 of Potter & Somerton which include the Ideal Rankine Cycle and the Reheat Cycle. Throughout Parts 1 and 2 we will use a single example of a high pressure pressure (15MPa) power cycle to evaluate the comparitive effects of the various modifications and extensions of the basic Rankine cycle.
This chapter covers the use of Steam Tables,
and at this stage we have found three typos in the Steam tables,
as follows:
1. Page 356, first row group, third column (0.10 MPa - replace
h at 500°C (3483.1 kJ/kg) with 3488.1 kJ/kg.
2. Page 357, second row group, third column - replace the header
[P = 1.80 MPa (207.15°C)] with [P = 2.00 MPa (212.4°C)].
3. Page 358, third row group - replace the temperature T = 406°C
with 400°C.
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
In this chapter we will make extensive use of P-h (pressure-enthalpy) diagrams, which we find to be much more intuitive than the T-s (temperature-entropy) diagrams used by Potter & Somerton. A typical P-h diagram for steam is shown below. Make as many copies of this diagram as you need since we will require that all problems to be solved shold first be drawn on the P-h diagram. An introductory example showing the use of the P-h diagram to do a qualitative analysis of a vapor power system was presented in ME321 in Steam Power Plants. Review this example before continuing.
This is shown below as an ideal Rankine cycle, which is the simplest of the vapor power cycles (refer: Potter Section 9.2). We have specifically split the turbine into a High Pressure (HP) turbine and a Low Pressure (LP) turbine since we will find that having a single turbine to expand from 15MPa to 10kPa results in a totally impractical system. As an example the Gavin Power Plant is a supercritical system having a high pressure of 24MPa. It has a turbine set consisting of 6 turbines - a High Pressure Turbine, Reheat turbine, and 4 large Low Pressure turbines operating in parallel.
As stated above, our approach is that prior to doing any analysis we will always first sketch the complete cycle on a P-h diagram based exclusively on the pressure and temperature data presented, as follows:
Notice that since both turbines are considered ideal, they follow the isentropic curve (1)-(2). From the P-h diagram we see that the LP turbine output (station (2)) has a quality of 80%. This is unacceptable. The condensed water will cause erosion of the turbine blades, and we should always try to maintain a quality of above 90%. One example of the effects of this erosion can be seen on the blade tips of the final stage of the Gavin LP turbine. During 2000, all four LP turbines needed to be replaced because of the reduced performance resulting from this erosion.
Thus we would like to extend this example to the more practical Reheat cycle as shown below (refer: Potter Section 9.4). The HP turbine expands the steam from 15 MPa to 1 MPa, and the steam is subsequently reheated back to 600°C before being expanded in the LP turbine to 10 kPa.
Again we plot this cycle on the P-h diagram and compare it to the previous situation of no reheat, as shown below:
We notice that reheating the output of the HP turbine back to 600°C (process (2)-(3)) allows both significantly more power output as well as increasing the quality at the LP turbine output (4) to 98%.
The above reheat cycle performance is determined as follows (be sure that you understand this process) :
Notice that we could have also determined the thermal efficiency by the simpler method of evaluating the condenser heat transferred, thus:
where qcondenser = h4-h5
This is an excellent check and should always be done to validate your answer. The reason why we have preferred to evaluate the output power is that it is the primary purpose of a steam power plant, thus we are always interested in its value. Thermal efficiency is important in its own right, however only on condition that we can satisfy the output power requirements of the steam power plant.
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