ES 202 Fluid and Thermal Systems

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1 ES Fluid and Thermal Systems Lecture : Power Cycles (/4/) Power cycle Road Map of Lecture use Rankine cycle as an example the ideal Rankine cycle representation on a T-s diagram divergence of constant pressure lines analysis of individual components (energy balance) effects of irreversibility in and compressor Comments on Quiz 4 Lecture ES Fluid & Thermal Systems

2 Power Cycles The integration of s, compressors, heat exchangers and combustors can generate power. For example, the gas engine: identify the different components The process path of any thermodynamic cycles form a closed loop on any phase/property diagram. The direction of process path determines what kind of cycle it is (extracting power versus refrigeration, etc.) Lecture ES Fluid & Thermal Systems Rankine Cycle Schematic of a typical Rankine cycle: heat exchanger (heat addition) /compressor 4 heat exchanger (heat removal) For an ideal Rankine cycle: from State to State : isentropic compression () from State to State : isobaric heating (boiler) from State to State 4: isentropic expansion () from State 4 to State : isobaric cooling (condenser) Lecture ES Fluid & Thermal Systems 4

3 Questions of Interests Representation on a T-s diagram How do we get a net work output from the cycle? Effects of irreversibilities on cycle performance (graphical representation) Analysis of individual components definition of thermal efficiency back work ratio Lecture ES Fluid & Thermal Systems 5 The T-s Diagram Advice on problem solving: start with a process diagram on a T-s plane: T isobaric heating through boiler P = P isentropic expansion through isentropic compression through isobaric cooling through condenser Lecture ES Fluid & Thermal Systems 6 4 s P 4 = P

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 outweighs that required by the in most situations, a fraction of the work output is used to drive the and this fraction is called the back work ratio: BWR = the Rankine cycle can be viewed as an energy conversion process from thermal energy to mechanical energy the ratio between the net power output ( power power) and the heat addition at the boiler is termed the thermal efficiency: ηthermal = boiler Lecture ES Fluid & Thermal Systems 7 Effects of Irreversibilities Irreversibilities in the and for non-ideal processes result in higher entropy at the exit of (a) and (4a). T s a 4s 4a s higher temperature at exit implies more work higher temperature at exit implies less work Lecture ES Fluid & Thermal Systems 8

5 Energy Analysis Adopt a divide and conquer approach to analyze the Rankine cycle. Apply energy balance to the four individual components in the cycle. Depending on the particular component, different terms in the energy balance are active while others are suppressed. Typical assumptions common to all four components are: steady state operation negligible changes in kinetic and potential energy Caution: changes in kinetic energy are not negligible for nozzle and diffusers For these components, the energy balance can be reduced to a simple form: de v v = in + in + m& in h + + gz m& { out h + + gz dt in out steady state = m& in (due to mass conservation) Lecture ES Fluid & Thermal Systems 9 Summary of Energy Analysis Q & in W & in reduced energy balance >, in = m& h boiler > boiler, in = m& h <, out = m& h4 condenser < condenser, out = m& 4 h Lecture ES Fluid & Thermal Systems

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