ES 202 Fluid and Thermal Systems Lecture 24 Power Cycles II 2 6 2003 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 Lecture 24 ES 202 Fluid Thermal Systems 2 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 Lecture 24 ES 202 Fluid Thermal Systems 3 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 Lecture 24 ES 202 Fluid Thermal Systems 4 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 W pump BWR W turbine 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 W turbine W pump thermal Q boiler Lecture 24 ES 202 Fluid Thermal Systems 5 Summary of Energy Analysis Rankine Cycle Q in W in reduced energy balance pump 0 0 W pump in m h2 h1 boiler 0 0 Q boiler in m h3 h2 turbine 0 0 W turbine out m h3 h4 0 0 Q condenser out m h4 h1 condenser Lecture 24 ES 202 Fluid Thermal Systems 6 How to find the h s Since the Rankine cycle operates around the twophase 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 Lecture 24 ES 202 Fluid Thermal Systems 7 Recall the States State 1 known pressure saturated liquid x 0 State 2 isentropic from State 1 to State 2 i e s2 s1 known pressure State 3 isobaric from State 2 to State 3 i e P3 P2 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 s4 s3 known pressure same as State 1 due to isobaric cooling from State 4 to State 1 Lecture 24 ES 202 Fluid Thermal Systems 8 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 h2 h1 u2 u1 P2v2 P1v1 assume incompressible assumed negligible Lecture 24 ES 202 Fluid Thermal Systems h2 h1 P2 P1 v 9 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 Lecture 24 T 3 2s ES 202 Fluid Thermal Systems 2a 1 4s 4a s 10 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 Lecture 24 ES 202 Fluid Thermal Systems 11