6. Thermodynamic Cycles Objective Classification of Thermodynamics Cycles Analysis & Calculation of Power Cycles Carnot Vapor Cycle, Rankie Cycle, Regeneration Rankie Cycle,Reheat Rankie Cycle Cogeneration Gas Refrigeration Cycle Vapor-Compression Refrigeration Cycle Refrigerant Other Refrigeration Cycles

6.1 Classification of Thermodynamics Cycles Power Cycle (+) Heat Energy Mechanical Energy Heat Pump Cycle (－) Refrigeration Cycle: keep low temperature of heat source with low temperature Heat Pump Cycle: keep high temperature of heat source with high temperature Working Fluid Gas Cycle: no phase-change of working fluid during cycle Vapor Cycle: phase-change of working fluid during cycle Combustion form Inner Combustion Outer Combustion Combustion occurs in system Combustion occurs out of system Gas is also the working fluid. The heat is transferred to working fluid through heat exchanger.

6.2 Carnot Vapor Cycle Several impracticalities are associated with this cycle: 1. It is impractical to design a compressor that will handle two phases for isentropic compression process(4-1). 2. The quality of steam decrease during isentropic expansion process(2-3) which do harm to turbine blades.

6.2 Carnot Vapor Cycle 3. The critical point limits the maximum temperature used in the cycle which also limits the thermal efficiency. 4. The specific volume of steam is much higher than that of water which needs big equipments and large amount of work input.

6.2 Carnot Vapor Cycle

6.3 Rankine Vapor Cycle Principle S 4-6 Constant pressure heat 1 2 3 4-6 Constant pressure heat addition in a boiler 6-1 to Superheat Vapor 1-2 Isentropic expansion in a turbine 2-3 Constant pressure heat rejection in a condenser 3-4 Isentropic compression in a pump

6.3 Rankine Vapor Cycle

6.3 Rankine Vapor Cycle S p v 1 6 5 4 3 2 p1 p2 4 6 1 2 3 T s 1 6 5 4

6.3 Rankine Vapor Cycle Efficiency 4-5-6-1 Constant pressure heat addition in a boiler 1-2 Isentropic expansion in a turbine 2-3 Constant pressure heat rejection in a condenser 3-4 Isentropic compression in a pump

6.3 Rankine Vapor Cycle Because of uncompressibility of water

6.3 Rankine Vapor Cycle Definition: d — the steam required to generate work of

6.3 Rankine Vapor Cycle Influencing factors

6.3 Rankine Vapor Cycle 1. － Pressure of Steam, Turbine Inlet 4 5 5’ 1’ 1 2 2’ －Unchange Two Cycles: ① 3-4-5-1-2-3 ② 3-4-5’-1’-2’-3

6.3 Rankine Vapor Cycle Disadvantages: 1. 2. 3 4 5 5’ 1’ 1 2 2’ decrease the turbine efficiency and erodes the turbine blades. Increase of requirements on pressure vessels and equipment investment. 2.

6.3 Rankine Vapor Cycle 2. － Temperature of Steam, Turbine Inlet 4 5 1 1’ 2’ 2 6 －Unchange Two Cycles: ① 3-4-5-6-1-2-3 ② 3-4-5-6-1’-2’-3

6.3 Rankine Vapor Cycle Advantages: i ii Disadvantages: 4 5 1 1’ 2’ 2 6 i ii it decreases the moisture content of the steam at the turbine exit. Disadvantages: Superheating temperature is limited by metallurgical considerations.

6.3 Rankine Vapor Cycle 3. － Condenser Pressure, Turbine Exit 4 5 1 3’ 2’ 2 6 4’ －Unchange Two Cycles: ① 1-2-3-4-5-6-1 ② 1-2’-3’-4’-5-6-1

6.3 Rankine Vapor Cycle i Disadvantages: ii 4 5 1 3’ 2’ 2 6 4’ i Disadvantages: ii i Condense pressure is limited by the sink temperature. ii It increases the moisture content which is highly undesirable.

6.3 Rankine Vapor Cycle Example Consider a steam power plant operating on the ideal Rankine cycle. The steam enters the turbine at 2.5MPa and 350℃ and is condensed in the condenser at pressure of 70kPa. Determine The thermal efficiency of this power plant The thermal efficiency if steam is condensed at 10kPa The thermal efficiency if steam is superheated to 600 ℃ The thermal efficiency if the boiler pressure is raised to 15MPa while the turbine inlet temperature is maintain at 600 ℃

State 1: State 2: Ideal Rankine Cycle

State 3: State 4:

6.3 Rankine Vapor Cycle Actual cycle Irreversibility Flow friction Heat transfer under temperature difference Heat loss to the surroundings

6.3 Rankine Vapor Cycle Actual Rankine Vapor Cycle Turbine Efficiency 2’ 3(4) 2 1 5 6 Turbine Efficiency Ideal Cycle Consumed Steam kg/h Actual Cycle

6.3 Rankine Vapor Cycle Mechanical Efficiency Relative Effective Efficiency Effective Power Boiler Efficiency Equipment Efficiency

6.4 Improvement to Rankine Cycle 预热锅炉给水，使其温度升高后再进入锅炉，可提高水在锅炉内的平均吸热温度，减小水与高温热源的温差，对提高循环效率有利。 利用汽轮机中的蒸汽预热锅炉给水，称为回热。 Transfer heat to the feedwater from the expanding steam in a heat exchanger built into the turbine ,called Regeneration. 3(4) e 2 7 1 d 5 6 T s Disadvantages: It is difficult to control the temperature The dryness is small

6.4 Improvement to Rankine Cycle Ideal Regenerative Cycle 3(4) e 2 7 1 d 5 6 T s Regenerative Cycle: 1-7-d-3-4-5-6-1 General Carnot Cycle:3-4-5-7-d-3 Ideal Carnot Cycle: 5-7-2-e-5 Same Efficiency

Ideal Regenerative Cycle Extracting Regeneration Boiler Turbine Regenerator Condenser Mixing Chamber Pump II Pump I 1 2 7 3 4 5 6

Ideal Regenerative Cycle 3(4) 2 7 1 6 5 1kg akg (1-a)kg T s >0

Ideal Regenerative Cycle 1 3 2 7 1 6 5 T s 4 8 9 Turbine Boiler Regenerator 7 Mixing Chamber 2 8 Cond- enser 9 4 6 5 3 Pump II Pump I

6.3.2 Ideal Reheat Cycle 蒸汽经汽轮机绝热膨胀至某一中间压力时全部引出，进入锅炉中特设的再加热器中再加热。温度升高后再全部引入汽轮机绝热膨胀做功。称为再热循环。

Ideal Reheat Cycle 3 c 2 a 1 5 4 6 b intermediate pressure

6.4 Improvement to Rankine Cycle Extracting Regeneration Boiler Turbine Regenerator Condenser Mixing Chamber Pump II Pump I 1 2 7 3 4 5 6

6.4 Improvement to Rankine Cycle Cogeneration Definition Cogeneration is the production of more than one useful form of energy from the same energy source. electric power heat in low quality

6.5 Gas Refrigeration Cycle Ideal Reversed Carnot Cycle T1 — Temperature of heat source with high temperature, surrounding temperature T2 — Temperature of heat source with low temperature, cold source q1 — Heat rejected to the surroundings q2 — Heat absorbed from cold source w0 — Work input

6.5 Gas Refrigeration Cycle Turbine Compressor Condenser Cold Source 1 2 3 4 1-2 Isotropic Compress 2-3 Isotonic Heat Rejection to Surrounding 3-4 Isotropic Expansion 4-1 Isotonic Heat Absorption

6.5 Gas Refrigeration Cycle p v 1 2 3 4 Cp— Constant, Ideal Gas Heat Absorbed from Cold Source Heat Rejected to the condenser 1 T s 2 3 4 T1 T3 Work of Compressor Work of Turbine

6.5 Gas Refrigeration Cycle 1 T s 2 3 4 T1 T3 2’ 3’ 4’

6.5 Gas Refrigeration Cycle Turbine Condenser Cold Source Compre- ssor 1 2 3 4 5 6 T 3’ 3 4 5’ 2 5 1 6 g k m n s

Vapor-Compression Refrigeration Cycle Shortcomings of Gas-Compression Refrigeration Cycle 1.small Refrigeration-Coefficient because heat absorption and rejection are not isothermal process; 2.Lower refrigeration capability of refrigerant (gas) So…refrigerant is changed to Vapor The highest efficiency is that of Vapor Carnot Reverse Cycle Impracticalities: 1.Large moisture content is highly undesirable for compressor and turbine. 2.Work output is limited by liquid expansion in the turbine.

Vapor-Compression Refrigeration Cycle So…practical vapor-compression refrigeration cycle is: 2 2 3 4 3 4 1 1 6 5

Vapor-Compression Refrigeration Cycle 1-2 Isotropic compress to superheated vapor 2-3-4 Isotonic condensed to saturated liquid 4-5 Isentropic expansion in a turbine 4-6 Isotropic expansion through throttle to humidity vapor 5-1 Constant pressure heat absorption in a cool source to dry saturate vapor 1 2 3 4 5 6

Work difference between Turbine and throttle Vapor-Compression Refrigeration Cycle 1 2 3 4 5 6 Throttle: ① fluid with low quality is difficult to be compressed. ② work loss is relatively small ③ easily adjust pressure of fluid and temperature of cold source Work difference between Turbine and throttle

Vapor-Compression Refrigeration Cycle Regeneration — more realistic cycle Advantages: 1. 2. 3.Superheated vapor is desirable T 2 Super- cooled Liquid 3 4 4’ Superheated Vapor 1’ 5’ 5 1 s

Vapor-Compression Refrigeration Cycle Compressor Condenser Cold Source 1’ 2 4 4’ Regenerator Throttle Valve 5’ 1 Conditions:

Isotropic Compress Efficiency Vapor-Compression Refrigeration Cycle 1 2 2’ 4 5 3 Irreversibility 1-2’ Isotropic Compress Efficiency 制冷机的制冷能力是随 工作条件不同而变化的， 因此，给出制冷能力时， 必须指明相应的工作条件。

6.7 Refrigerant Definition The work fluid cycling flowing in refrigeration system while transferring energy with surrounding in order to refrigerate. Thermodynamic Request Critical temperature should be much higher than temperature of surroundings. ① steam easier be condensed; ② larger range of latent heat; ③ heat absorption and heat rejection closer to isothermal process

6.7 Refrigerant Thermodynamic Request Solidification temperature should be lower than evaporation temperature to prevent blocking the pipes. Larger latent heat is more desirable. appropriate saturate pressure small being nontoxic ,non-corrosive, nonflammable, chemically steady; low cost Environment & Safety Request Ammonia 氨 ， Feron 氟利昂

Water — lithium bromide 6.8 Absorption Refrigeration System Definition The form of refrigeration that inexpensive thermal energy instead of mechanical energy or electric power is consumed to transfer heat form low temperature to high temperature is absorption refrigeration. Geothermal Energy Solar Energy Absorption refrigeration system involves the absorption of a refrigerant by a transport medium . Ammonia — Water NH3－ H2O Water — lithium bromide H2O － LiBr

6.8 Absorption Refrigeration System Principle Condenser Evaporation Q－Solar Energy Expansion Valve Adjust Valve NH3-H2O Absorber Generator pump rectifier Cooling Water Q1 Q2 Q3 Q4 NH3 Weak Rich NH3

6.8 Absorption Refrigeration System Thermodynamic Analysis Thermal Efficiency Advantage: A liquid is compressed instead of a vapor , and thus the work input for absorption refrigeration system is very small.

6.9 Vapor-Jet Refrigeration System Principle Mixture Condenser Evaporation Expansion Valve pump Q1 Q2 Boiler Diffuser Nozzle

6.9 Vapor-Jet Refrigeration System Condenser Evaporation Expansion Valve pump Q1 Q2 Boiler 1’ 1 2 3 4 5’ 5 2’ Q3 T 1’ 5’ 3 4 1 5 2’ 2 s

6.9 Vapor-Jet Refrigeration System Thermodynamic Analysis Thermal Efficiency Disadvantage: Irreversibility such as mixture process and heat transfer with temperature difference; Large exergy loss

6.10 Liquefaction of Gases 气体液化循环中的工质，在循环中即作为冷却剂使用， 同时本身又被液化并输出液态产品。 The liquefaction of gases has always been an important area of refrigeration since many important scientific and engineering process at cryogenic temperature depend on liquefied gas. Example: separation of oxygen and nitrogen from air preparation of liquid propellants for rockets the study of material properties at low temperature the study of exciting phenomenon such as superconductivity 气体液化循环中的工质，在循环中即作为冷却剂使用， 同时本身又被液化并输出液态产品。

6.10.1 Min. Work in Liquefaction of Gases 2 8 6 4 5 Gas-Liquid Coefficient Quality at State 4

6.10.2 Linde Cycle Principle Condenser Expansion Valve Heat Exchanger Separator Liquid Removed Compressor 1 2 3 4 5 6 P2 T s 1 2 6 4 5 3 7 P1

6.10.2 Linde Cycle Thermodynamic Analysis Take the Heat Exchanger, Expansion Valve, Separator as system. Liquid: y kg ; gas: (1-y) kg T s 1 2 6 4 5 3 7 P1 P2 Heat of liquefaction y kg:

6.10.2 Linde Cycle Irreversibility in liquefaction Thermodynamic Analysis Irreversibility in liquefaction of gas: ① heat loss in heat exchanger q’ ② non-adiabatic, heat addition from surrounding q’’ T s 1 2 6 4 5 3 7 P1 P2

cannot be treated as Ideal Gas 6.10.2 Linde Cycle Irreversibility in compression of gas: ① isothermal compression 1-2 ② isothermal efficiency (0.59) Thermodynamic Analysis T s 1 2 6 4 5 3 7 P1 P2 Actual work consumption cannot be treated as Ideal Gas

6.10.3 Claude Cycle Thermodynamic Analysis a-y y Condenser Compressor Liquid Removed 2 Compressor HE1 HE2 HE3 Turbine Expansion Valve Separator 1 3 4 4’ 6 7 8 9 y a-y Thermodynamic Analysis

Piston expander： Turbine： Considering mechanical efficiency