1. ES 202 Fluid and Thermal Systems Lecture 24: Power Cycles (II) (2/6/2003)

2. Lecture 24ES 202 Fluid & Thermal Systems2 Assignments Homework: –8-132, 8-133 in Cengel & Turner (try them but don’t need to hand them in on Monday) Study for Exam 2

3. Lecture 24ES 202 Fluid & Thermal Systems3 Announcements Problem session this evening at 7 pm Review for Exam 2 on Saturday from 3 to 5 pm in GM Room What can you expect? –3 problems: one property table lookup (similar to in-class exercises) two problems (require analysis and calculations) What can you bring to the exam? –textbook –1 equation sheet (cannot consist of worked out problems) –computer (cannot use EES) My advice to you on exam –always work out logic in symbols and substitute numbers at the end

4. Lecture 24ES 202 Fluid & Thermal Systems4 Road Map of Lecture 24 Finish up power cycle –property table supplies enthalpy values at various states –approximation on pump work –non-ideal cases Caution with property tables/computer programs –absolute versus relative Address common questions/concerns Refrigeration cycles

5. Lecture 24ES 202 Fluid & Thermal Systems5 Energy Conversion With reference to the T-s diagram on previous slide, a few observations are noteworthy: –the divergence of constant pressure lines at high temperatures implies that the mechanical power extracted from the turbine outweighs that required by the pump –in most situations, a fraction of the turbine work output is used to drive the pump and this fraction is called the back work ratio: –the Rankine cycle can be viewed as an energy conversion process from thermal energy to mechanical energy –the ratio between the net power output (turbine power – pump power) and the heat addition at the boiler is termed the thermal efficiency:

6. Lecture 24ES 202 Fluid & Thermal Systems6 Summary of Energy Analysis (Rankine Cycle)

7. Lecture 24ES 202 Fluid & Thermal Systems7 How to find the h’s? Since the Rankine cycle operates around the two- phase region, the ideal gas and incompressible substance models are not applicable in general. The values of enthalpy can be acquired from property tables or computer programs. –recall the information you know about each state –needs two independent, intensive properties to specify the enthalpy (State Principle)

8. Lecture 24ES 202 Fluid & Thermal Systems8 Recall the States State 1: known pressure, saturated liquid (x = 0). State 2: isentropic from State 1 to State 2 (i.e. s 2 = s 1 ), known pressure State 3: isobaric from State 2 to State 3 (i.e. P 3 = P 2 ), exact location depends on total heat transfer during heating process (specific enthalpy obtained from energy balance) State 4: isentropic from State 3 to State 4 (i.e. s 4 = s 3 ), known pressure (same as State 1 due to isobaric cooling from State 4 to State 1

9. Lecture 24ES 202 Fluid & Thermal Systems9 Approximation on Pump Work The isentropic compression from State 1 to State 2 occurs in the compressed liquid region. In case the values of enthalpy is not available, approximation is commonly done as follows: –due to the divergence of constant pressure lines at high temperatures, the temperature difference between State 1 and State 2 is usually very small in the compressed liquid region (it is exaggerated on the process diagram for identification) –the enthalpy difference can be simplified using incompressible assumption: assume incompressible

10. Lecture 24ES 202 Fluid & Thermal Systems10 Non-Ideal Turbine/Pump For non-ideal cases, there are irreversibilities in the pump and turbine: –separate isentropic efficiencies for turbine and pump –relate actual work to ideal work through isentropic efficiency –important points to remember: pressure is the same for both ideal and actual states temperature is different between ideal and actual states entropy at actual state is always larger than ideal states be careful when you can use the isentropic relationships T s 1 3 2s 4s 4a 2a

11. Lecture 24ES 202 Fluid & Thermal Systems11 Absolute Versus Relative In doing cycle analysis, using computer programs (i.e. EES) is a common practice. But you need to be aware of the facts that –presure, temperature and specific volume are absolute measures –specific internal energy, specific enthalpy and specific entropy depend on the reference state (don’t pull their values from one table and use them with another table or computer program, they may have different reference states) Usually in energy balance and entropy balance, the changes in specific enthalpy, specific internal energy and specific entropy are quantities of interests, not their absolute values.