ES 202 Fluid and Thermal Systems Lecture 22 Isentropic Efficiencies Simple Power Cycles 2 3 2003 Assignments Homework 8 103 8 104 in Cengel Turner Reading assignment 8 14 8 16 to 8 18 in Cengel Turner ES 201 notes Section 7 9 and 8 4 Lecture 22 ES 202 Fluid Thermal Systems 2 Announcements Lab 3 this week in DL 205 Energy Lab 4 lab groups over 3 periods 6 students per group group formation let me know by the end of today schedule sign up EES program for property lookup download from course web I am available for discussion during evenings this week in preparation for Exam 2 next Monday email me in advance to set up a meeting time Propose Review for Exam 2 on this Saturday from 3 pm to 5 pm let me know if you have major conflicts before I make room reservation Convo schedule tomorrow 2 50 to 3 30 pm 8th period 3 35 to 4 15 pm 9th period Lecture 22 ES 202 Fluid Thermal Systems 3 Road Map of Lecture 22 Quiz on Week 7 materials Comments on Lab 2 overall better write up than Lab 1 some impressive write ups very encouraging Comments on constant specific heat for argon a deeper look at variable specific heats Representation of isentropic and non isentropic processes on h s diagram introduce the limit of best performance notion of isentropic efficiency T s diagram for compressor and turbine Power cycles Lecture 22 ES 202 Fluid Thermal Systems 4 My Lab 2 Water Wall experiment 5 points The Pendulum demonstration the key difference is the change in momentum on a concave versus a flat surface The Torricelli like demonstration depth rather than base area is the controlling factor The Four tube demonstration recognition of static and stagnation pressure measurements difference between stagnation pressure and static pressure is the dynamic pressure flow velocity increases from large to small tube difference between stagnation and static measurements increases from large to small tube as a result pressure drops from large to small tube higher static pressure in first tube relative to third tube stagnation pressure stays almost constant from large to small tube with a slight drop due to losses small difference between second and fourth tube The Three coil demonstration Lecture 22 learn to think in non dimensional world e g D L D same pressure difference across coil in all cases loss is smaller in shorter and wider coil apart from major loss there is also minor loss due to continuous change in flow direction ES 202 Fluid Thermal Systems 5 My Lab 2 Cont d Pipe friction experiment 5 points comparison between measured and predicted values on the same plot explanation for the difference question on zero surface roughness assumption try out non zero values for surface roughness gives equivalent surface roughness for PVC pipe discussion of sources of error manometer reading timing Torricelli s experiment 5 points mean and variation in results discharge velocity and contraction coefficients must be smaller than unity if not give explanation for the non physical values discussion of sources of error unsteadiness extent of valve opening measurement of shooting range Lecture 22 ES 202 Fluid Thermal Systems 6 A Deeper Look at Variable Specific Heats In classical statistical mechanics the specific heat at constant specific volume cv can be expressed as nf cv R 2 where nf is the number of degrees of freedom of the molecular model In ideal gases the difference between the two specific heats cp cv is the specific gas constant nf 2 c p cv R cp R 2 Some examples of molecular models are smooth sphere model for monatomic gases like helium argon etc rigid or flexible dumb bell model for diatomic gases like oxygen nitrogen etc flexible rigid Lecture 22 ES 202 Fluid Thermal Systems 7 A Deeper Look at Variable Specific Heats II For the smooth sphere model nf 3 which stands for translational motion in 3 spatial coordinates This model holds true for monatomic gases over a very wide range of temperatures Hence a constant specific heat assumption is excellent for monatomic gases For rigid dumb bell model nf 5 which includes translational motion in 3 spatial coordinates and rotational motion along 2 major axes At high temperatures the rigid dumb bell model becomes flexible to take into account of possible vibrational motion 2 additional degrees of freedom KE PE nf 7 Lecture 22 ES 202 Fluid Thermal Systems 8 A Deeper Look at Variable Specific Heats III The transition from the rigid dumb bell model to the flexible dumb bell model for diatomic gases occurs gradually over a temperature range specific heat ratio Figure F 1 in Compressible Fluid Dynamics by Thompson For monatomic gases k 5 3 at all temperatures temperature K The molecular model for more complex molecules tri atomic or higher are more sophisticated and their dependency of modal excitation on temperature is much more complicated But the crude picture has been sketched here Lecture 22 ES 202 Fluid Thermal Systems 9 Adiabatic Devices Energy Analysis For most steady state devices for examples compressors turbines nozzles diffusers the flow process between the inlet and outlet state is often modeled as adiabatic because heat transfer is not the primary function of these devices not true for heat exchangers flow process at design condition is often fast compared with the heat transfer process For these devices the energy balance can be reduced to a simple form 2 2 dE v v Qin Win m in h gz m out h gz dt 2 2 in out steady state m in due to mass conservation adiabatic W in m Lecture 22 2 2 v v h gz h gz 2 2 out in ES 202 Fluid Thermal Systems 10 Adiabatic Devices Energy Analysis II If the changes in kinetic energy and potential energy can be further neglected commonly assumed in compressor and turbine analyses NOT in nozzle and diffuser the rate of work input will be directly related to the mass flow rate change in enthalpy W in m hout hin Based on the above result the change in enthalpy between the inlet and outlet state in a compressor or a turbine can be interpreted as directly related to the work input per mass flow W in Win hout hin m Lecture 22 ES 202 Fluid Thermal Systems 11 Adiabatic Devices Entropy Analysis For these adiabatic devices the entropy balance can also be reduced to a simple form dS Q in m in sin m out sout S gen dt T steady state m in due to mass conservation adiabatic S gen m sout sin Based on the above result the change in entropy between the inlet and outlet states can be interpreted as the entropy generation per mass flow Sgen S gen m sout sin For