制冷与低温原理

κ −1 κ
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§1.2 Refrigeration of gas adiabatic expansion
在实际膨胀过程中，由于过程的不可逆，理想 气体的积分等熵效应由下式确定
m −1 ⎤ ⎡ m ⎛ p2 ⎞ ⎥ ⎢ ⎟ ΔT = T1 − T2 = T1 1 − ⎜ ⎜ ⎥ ⎢ ⎝ p1 ⎟ ⎠ ⎥ ⎢ ⎦ ⎣
p1
p2 ⎛ ∂T ⎞ ⎜ ⎜ ∂p ⎟ ⎟ dp = ∫p1 ah dp ⎝ ⎠h
•节流效应转化曲线
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§1.2 Refrigeration of gas adiabatic expansion
•Isothermal throttling effect (等温节流效应)
•节流制冷（液化）循环
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§1.1 Phase Transformation Refrigeration
•P-h diagram （压焓图）
•Isobar (等压线） •Isenthalpic (等焓线） •Isentropic (等熵线） •Isochore (等容线) •Critical point (临界点）
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• Throttling evaporation（闪发、节流气化） • Refrigeration effect （制冷量、制冷效应）
q0 = r (1 − χ )
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§1.1 Phase Transformation Refrigeration
• Thaw(融化) & sublimation(升华) of solid substances
§1.3 Refrigeration cycles
•Reversed Carnot’s cycle (逆卡诺循环)
制冷剂向高温热源放出的热量：
q = T ( s1 − s4 )
制冷量：
q0 = T ( s1 − s4 )
' 0
循环消耗的功：
w0 = T − T0' (s1 − s4 )
(
)
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§1.3 Refrigeration cycles
表1-1冰的升华压力和对应的升华温度
温度／℃ 升华压力／kPa 0 0.61 -25 63×10-3 -50 3.87×10-3 -75 0.116×10-3
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§1.1 Phase Transformation Refrigeration
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§1.1 Phase Transformation Refrigeration
Principles of Refrigeration & Cryogenics
制冷与低温原理
王 立 Phone：62334425 Email：Liwang@me.ustb.edu.cn
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Content
• Exordium（绪论） • Chapter 1: Thermodynamic foundations of refrigeration(制冷) & cryogenics(低温) 制冷与低温的热力学基础 • Chapter 2: Refrigerants 制冷工质 • Chapter 3: Vapor refrigeration cycles 蒸汽制冷循环
r : Latent Heat (潜热) h: Enthalpy (焓) s: Entropy (熵)
•The higher the boiling point the larger the LH •R717-NH3；R744-CO2；R22-CHF2Cl（二氟一氯甲烷）
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§1.1 Phase Transformation Refrigeration
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Applications of R&C Tech.
• Air conditioning (building, domestic, vehicles & industries) • Environment simulation • Food refrigeration, freeze & delivery • Medical and biological applications • Nature gas, hydrogen … liquefaction • Aviation & Spaceflight • ……
•Reversed Carnot’s cycle
制冷系数 (Coefficient of performance COP)：
COP R
q0 T 0' = ε0 = = w0 T − T 0'
Fra Baidu bibliotek
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§1.3 Refrigeration cycles
•具有传热温差(外部不可逆)的循环
T0 ε= Tk − T0
•Integral isentropic effect(积分等熵效应):
ΔT = ∫ as dp
p1 p2
for an ideal gas
⎡ Δ T = T1 − T 2 = T1 ⎢1 − ⎢ ⎢ ⎣ ⎛ P2 ⎞ ⎜ ⎜ P ⎟ ⎟ ⎝ 1 ⎠
κ −1 κ
⎤ ⎥ ⎥ ⎥ ⎦
T2 ⎛ p2 ⎞ ⎟ =⎜ ⎜ T1 ⎝ p1 ⎟ ⎠
•热能驱动制冷循环
按热力学第一定律：
qk = qH + q0
对于可逆制冷机，按热力学第二定律， 在一个循环中熵增为零：
qk qH q0 = + Ta TH T0
热力系数
ζ0 =
q0 ⎛ T0 ⎞⎛ TH − Ta ⎞ ⎟ ⎜ ⎟ = COPH =⎜ ⎜ ⎟ ⎜ ⎟ qH ⎝ Ta − T0 ⎠⎝ TH ⎠
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Applications of R&C Tech.
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Refrigerants
• Halocarbon compounds (卤化碳制冷剂：甲、 乙、丙烷的衍生物) • Hydrocarbons (甲、乙、丙烷等） • Inorganic compounds (无机化合物：水、氨、 CO2等) • Mixed refrigerant (混合制冷剂) • Cryogenic working fluids (低温工质：CH4, air, fluorin, argon, nitrogen, neon等)
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Content
• Chapter 4: Gas refrigeration & Liquefaction (液化) cycles 气体制冷与液化循环 • Chapter 5: Principles air/gas separation 气体分离原理 • Chapter 6: Entropy & exergy analysis 熵与“火用”分析
• For a refrigeration cycle
Qo + W = Qh
Q0: Heat absorbed from low temp. reservoir W: Work from outside Qh: Heat released (rejected) to high temp. reservoir
式中，m为多变指数 （补充内容：向心式透平膨胀机）
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§1.2 Refrigeration of gas adiabatic expansion
•Adiabatic gas discharge process (绝热放气过程)
（例：Simon expansion) 对容器内的气体运用热力学第一定律
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§1.2 Refrigeration of gas adiabatic expansion
•Differential isentropic expansion effect:
⎛ ∂T ⎞ T ⎛ ∂v ⎞ as = ⎜ ⎜ ∂p ⎟ ⎟ = c ⎜ ∂T ⎟ ⎠p ⎝ ⎠s p ⎝
for an ideal gas
R ⎛ ∂v ⎞ ⎜ ⎟ = ⎝ ∂T ⎠ p p
as ,id
κ −1 T = κ p
•Integral isentropic expansion effect(积分等熵效应):
ΔT = ∫ as dp
p1
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p2
§1.2 Refrigeration of gas adiabatic expansion
⎛ ∂T ⎞ ah = ⎜ ⎟ ⎜ ∂p ⎟ ⎠h ⎝
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§1.2 Refrigeration of gas adiabatic expansion
•Throttling expansion process (节流膨胀过程)
•实际气体节流膨胀时的积分节流效应
ΔT = T2 − T1 = ∫
，，
p2
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Homework & References
Homework • Read the textbook beforeafter/ the classes word by word carefully and thoughtfully. References • 吴业正，制冷与低温技术原理，高等教育出版社，
热力完善度
ε η = ≤1 ε0
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§1.3 Refrigeration cycles
•变温热源时的逆向可逆循环——洛伦兹循环
T0 m εi = Tm − T0 m
式中，T0m和Tm分别为制冷 剂吸热时低温热源的平均温 度和放热时高温热源的平均 温度
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§1.3 Refrigeration cycles
The equation obeys the 1st law and the 2nd law of thermodynamics simultaneously
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§1.1 Phase Transformation Refrigeration
• Liquid evaporation
r = h"− h' = T ( s"− s' )
hdm = dU
式中，U为容器内气体总内能。
dU = d (mu ) = mdu + udm
经推导变换
T2 ⎛ p2 ⎞ ⎟ =⎜ ⎜ T1 ⎝ p1 ⎟ ⎠
κ −1 κ
结果与有外功输出的可逆绝热(等熵)膨胀过程相同。
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§1.2 Refrigeration of gas adiabatic expansion
北京，2004 • 吴业正，制冷原理与设备，西安交通大学出版社， 西安，1987 • Thomas M. Flynn, Cryogenic engineering (Second edition), Marcel Dekker, Inc. , New York, NY, 2005
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Chapter 1. Thermodynamic Foundations of R&C
•Throttling expansion process (节流膨胀过程)
•节流过程是一降温而不制冷的过程。节流时有摩擦损失，是一 个不可逆过程，其结果将导致熵的增加。 •理想气体的内能和焓仅是温度的函数。因此，理想气体节流时
，，
Δu = 0
Δh = 0
ΔT = 0
•实际气体节流膨胀时的微分节流效应 (Joule-Thomson effect)
§1.2 Refrigeration of gas adiabatic expansion
•Isentropic (等熵) expansion = reversible adiabatic expansion 可逆绝热膨胀 •Gas expansion through an expander(膨胀机)
with work down to the surroundings（例：布雷
顿循环、布雷顿制冷机）
•Differential isentropic expansion effect (微分等 熵效应)::
⎛ ∂T ⎞ T ⎛ ∂v ⎞ as = ⎜ ⎜ ∂p ⎟ ⎟ = c ⎜ ∂T ⎟ ⎠p ⎝ ⎠s p ⎝
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Exordium（绪论） • Refrigeration & cryogenic technology The tech. to get a temperature artificially below the temperature of circumstance and to keep it. • Temperature range of refrigeration >120k/-153℃ • Temperature range of cryogenics <120k/-153℃
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§1.3 Refrigeration cycles
•Absorption refrigeration (吸收式制冷) •Adsorption refrigeration（吸附是制冷）
吸附过程和脱附过程