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11. Power & Refrigeration Systems 11.1 Introduction to Power Systems Recall the basic formula for the power cycles: Wout ,net η th = QH The cycles can be categorizes depending on the working fluid: • Gas cycles: gaseous phase alone • Vapor cycles: both liquid and vapor phases The cycles can be also categorized as • Closed cycles: the working fluid returns to the initial state. • Open cycles: the working fluid is renewed. 11.2 The Rankine Cycle The Rankine cycle is the model for the simple “steam power plant”. It consists of four-steady-state processes: 1-2 : Reversible adiabatic pumping process 2-3 : Constant-pressure boiling process 3-4 : Reversible adiabatic expansion 4-1 : Constant-pressure condesing process Note: • State 3 could be saturated vapor or superheated vapor. • If State 3 is saturated vapor, we have Wnet area 1 − 2 − 2′ − 3 − 4 − 1 η th = = Q H area a − 2 − 2′ − 3 − b − a • The Carnot cycle (1′ − 2′ − 3 − 4 − 1′ ) is difficult to achieve because the two-phase mixture enters the pump. • The superheated-vapor state is often preferable due to the “pure” vapor entering the turbine. 11.3 Effect of Pressure and Temperature on Rankine Cycle • Effect of the condensing pressure If P4 decreases, Wnet and ηth increase (pros), but x4 decreases (cons). • Effect of the superheating steam If T3 increases, Wnet and ηth increase (pros), and x4 increases (pros). • Effect of the maximum pressure If P4 decreases, Wnet tends to be the same, ηth increases (pros), but x4 decreases (cons). 11.4 Reheat Cycle When the reheat cycle is utilized, • The boiling pressure can be raised. • The moisture content in turbine can be avoided. Note: If the material we use can withstand the temperature at 3′, there is no need for the reheat cycle because the simple Rankine cycle would be more efficient. 11.5 The Regenerative Cycle Liquid water enters the boiler at relatively low temperature, causing a low efficiency. A practical solution is to use a regenerator or a feedwater heater, which has two types: 11.5.1 Open feedwater heater An open (or direct-contact) feedwater heater is a mixing chamber between the extracted stream and the liquid water. 11.5.2 Closed feedwater heater In a closed feedwater heater, the steam and the feedwater do not mixed. It can be used with a drip pump or a trap. For an actually steam power plant, the processes are more complex 11.6 Deviation of Actual Cycles from Ideal Cycles The most important losses are • Turbine losses from non-isentropic expansion and heat transfer • Pump losses from non-isentropic expansion and heat transfer • Piping losses from pressure drop and heat transfer • Condensing losses from heat transfer 11.7 Cogeneration The cogeneration is designed for supplying a source of both electricity and the process steam. 11.8 Air-Standard Power Cycles An air-standard power cycle is an ideal cycle based on these assumptions: • Air has a fixed mass (or mass flow). • Air is an ideal gas. • Air has a constant CPo. • The combustion process is replaced by a heat-transfer process from a source. • The cycle is completed by heat transfer to the surroundings. • All processes are internally reversible. Examples for air-standard power cycles: • Gas turbine engines (Brayton cycle) • Spark-ignition internal combustion engines (Otto cycles) • Compression-ignition internal combustion engines (Diesel cycles) 11.9 The Brayton Cycle The Brayton cycle involves • two isentropic processes • one (or two) isobaric process(es). The working fluid is gas, and the Brayton cycle is an ideal cycle for a simple gas turbine engine. A simple open Brayton cycle A simple closed Brayton cycle Note: for an ideal/simple Brayton cycle T1 T4 1 η th = 1 − = 1 − = 1− T2 T3 (P2 / P1 )( k −1) / k P2/P1 is named the pressure ratio of the Brayton cycle. Thus, as the pressure ratio increases, ηth is increased as well. However, P2 is limited by T3 (the highest temperature in the cycle). The actual Brayton cycle Irreversibilities are caused by • pressure drop in pipes (friction) • efficiencies of the compressor and turbine h 2 s − h 1 T2 s − T1 ηcomp = = h 2 − h1 T2 − T1 h3 − h4 T3 − T4 η turb = = h 3 − h 4 s T3 − T4 s Generally, if ηcomp and ηturb is below 60%, all work from the turbine is required to drive the compressor. Thus, ηth reduced to zero. 11.10 The Simple Gas Turbine Cycle with a Regenerator The efficiency of the cycle is improved by introducing a regenerator, which is a counter-flow heat exchanger. Note: the regenerator is useless if the pressure ratio is increased from state 2 to state 2′. It can be shown that for an ideal regenerative Brayton cycle: ( k −1) / k T1 P2 η th = 1 − T3 P1 Thus, ηth depends not only on the pressure ratio, but the ratio of the maximum to the minimum temperature. The effectiveness or efficiency of the regenerator is given by hx − h2 h x − h 2 Tx − T2 η regen = = = h x′ − h 2 h 4 − h 2 T4 − T2 11.11 Gas Turbine Power Cycle Configuration It is found that the reversible isothermal compressor or turbine would be preferable to the isentropic one if the pressure ratio is the same. Thus, for a cycle, which has • two isothermal processes • two isobaric processes This is called the Ericsson cycle. However, the work-related devices are not practical to transfer heat. The processes; therefore, become adiabatic. To modify the Brayton cycle closer to the Ericsson cycle, we introduce • multistage compressions with intercooling. • multistage expansion with reheat. For many stages of compression and expansion, it approaches the isothermal process. Some arrangements of components in the gas turbine cycle. 11.13 Reciprocating Engine Power Cycles Define Compression ratio (rv) [-], Vmax rv = Vmin Mean effective pressure (Pmeff) [Pa], Wnett = Pmeff (Vmax − Vmin ) 11.14 The Otto Cycle The air-standard Otto cycle is an ideal cycle to approximate a spark-ignition internal combustion engine. The four processes are composed of • two isentropic processes • two isochoric processes Recall that rv is the compression ratio: Vmax V1 v1 v 4 rv = = = = Vmin V2 v 2 v 3 From the derivation, T1 T4 1 η th = 1 − = 1 − = 1 − k −1 T2 T3 rv Thus, increasing rv leads to a higher thermal efficiency of the Otto cycle. 11.15 The Diesel Cycle The air-standard Diesel cycle is an ideal cycle to approximate a compression- ignition internal combustion engine. The four processes are composed of • two isentropic processes • one isobaric process • one isochoric process The compression ratio is Vmax V1 v1 rv = = = Vmin V2 v 2 Define the cutoff ratio (rc) [-] V3 v 3 rc = = V2 v 2 From the derivation, T1 (T4 / T1 − 1) η th = 1 − kT2 (T3 / T2 − 1) We can rewrite in terms of rv and rc: 1 rc − 1 k η th k (r − 1) = 1 − k −1 rv c The term in the brackets is always greater than unity. We conclude that η th ,otto > η th ,diesel if both engines have the same rv. Note: • ηth,diesel increases with decreasing rc. • At rc = 1, ηth,diesel = ηth,otto. • However, Diesel cycles operated at much higher rv, resulting in the typical higher value of ηth. 11.16 The Stirling Cycle The Stirling cycle is composed of • two isothermal processes • two isochoric processes This engine has been developed as an external combustion engine with regeneration. 11.17 Introduction to Refrigeration Systems For the basic ideal refrigeration system, the cycle is the same as the Rankine power system: • two isentropic processes • two isobaric processes except that the processes are reversed. 11.18 The Vapor-Compression Refrigeration Cycle Consider the reversed Rankine cycle: However, the isentropic expansion from state 3 to state 4′ (mostly liquid) provides only little work. Thus it is not worth to place a turbine here. As a result, we replace the isentropic expansion with the throttling process (state 3 to state 4). Note that the two- phase mixture entering the compressor (state 1′ to state 2′) should be avoided. Thus the vapor-compression refrigeration cycle becomes Note: • For the throttling process across the expansion valve, h = constant. • The analysis of a refrigerator and a heat pump is the same. • Recall the COP of a refrigerator and a heat pump: QL β = Wcomp QH β′ = Wcomp 11.19 Working Fluids for Vapor- Compression Refrigeration Systems There are many different working fluids (refrigerants) for the vapor-compression refrigeration systems: • Ammonia was used in the early days and is still used in industrial refrigeration. It is toxic, but cheap. It has favorable transport properties to get higher COP. No effect on O3. • CFCs, such as R11, R12, or R22, are good for many applications. R11 is for water chillers. R12 is for house- hold refrigerators. R22 is for air conditioners. All of them cause ozone crisis. • R134a, which has no effect on the ozone layer, is presently replacing R12. 11.20 Deviation of the Actual Vapor- Compression Refrigeration Cycle from the Ideal Cycle • Non-quasi-equilibrium compression and heat transfer in the compressor • Pressure drop in pipes, condenser, and evaporator • Heat transfer through pipes 11.21 The Absorption Refrigeration Cycle In this type of refrigerator, the refrigerant is transported by a “transport” medium. Ammonia-Water is the most favorite one where Ammonia is the refrigerant, and water is the transport medium. QL Note: β = Wpump + Q′H Advantage (compared with the vapor- compression refrigeration system) • a liquid is compressed rather than a vapor. Thus, it requires less work. • good for inexpensive heat source such as geothermal or solar energy. Disadvantage • more expensive • more complexity and require more space • less COP (COP < 1) 11.22 The Air-Standard Refrigeration Cycle This refrigeration system uses a gas as a working fluid. The cycle is the reversed Brayton cycle. Its applications are • liquefaction of air and other gases. • aircraft cooling (lighter components). Closed cycle Open cycle The analysis of the air-standard refrigeration cycle is similar to the Brayton cycle. 11.23 Combined-Cycle Power and Refrigeration Systems