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Cheatsheet: Refrigeration Cycles
1. Vapor-Compression Refrigeration Cycle
1.1 Ideal Cycle Components and Processes
| Process | Description |
|---|---|
| 1-2: Isentropic Compression | Compressor increases pressure and temperature of refrigerant vapor; s₁ = s₂ |
| 2-3: Constant Pressure Condensation | Refrigerant rejects heat to surroundings in condenser; exits as saturated liquid |
| 3-4: Throttling (Isenthalpic) | Expansion valve reduces pressure; h₃ = h₄; quality increases |
| 4-1: Constant Pressure Evaporation | Refrigerant absorbs heat from cold space in evaporator; exits as saturated vapor |
1.2 Performance Parameters
| Parameter | Formula |
|---|---|
| Coefficient of Performance (COP) | COP = QL/Wnet = (h₁ - h₄)/(h₂ - h₁) |
| Refrigeration Effect | QL = ṁ(h₁ - h₄) |
| Compressor Work | Wcomp = ṁ(h₂ - h₁) |
| Heat Rejected | QH = ṁ(h₂ - h₃) |
| Refrigeration Capacity | Expressed in tons (1 ton = 12,000 Btu/hr = 3.517 kW) |
1.3 Actual Cycle Deviations
- Compression: Non-isentropic due to irreversibilities; isentropic efficiency ηc = (h₂s - h₁)/(h₂a - h₁)
- Pressure drops in evaporator and condenser due to friction
- Heat transfer to/from surroundings in connecting pipes
- Subcooling of liquid leaving condenser increases COP
- Superheating of vapor entering compressor protects compressor from liquid droplets
2. Refrigerant Properties and Selection
2.1 Common Refrigerants
| Refrigerant | Key Characteristics |
|---|---|
| R-134a | Automotive and residential AC; replaced R-12; GWP = 1430; non-toxic, non-flammable |
| R-410A | Residential/commercial AC; replaced R-22; zeotropic blend; higher pressure than R-22 |
| R-22 | Being phased out (HCFC); ODP = 0.055; formerly common in AC |
| R-717 (Ammonia) | Industrial refrigeration; excellent thermodynamic properties; toxic but natural refrigerant |
| R-744 (CO₂) | Natural refrigerant; low GWP; requires high operating pressures; transcritical cycles |
2.2 Selection Criteria
- Thermodynamic performance: high latent heat, suitable pressure range
- Environmental impact: Ozone Depletion Potential (ODP), Global Warming Potential (GWP)
- Safety: toxicity, flammability classification (ASHRAE 34)
- Chemical stability and compatibility with materials
- Cost and availability
3. Absorption Refrigeration Systems
3.1 Basic Absorption Cycle
| Component | Function |
|---|---|
| Absorber | Refrigerant vapor absorbed by solution; heat rejected QA |
| Pump | Pumps rich solution to high pressure; work input minimal (Wpump ≪ Wcomp) |
| Generator | Heat input QG drives refrigerant from solution; produces weak solution |
| Condenser | Refrigerant vapor condenses; heat rejected QC |
| Expansion Valve | Throttles liquid refrigerant to low pressure |
| Evaporator | Refrigerant evaporates; absorbs heat QE from cold space |
3.2 Performance and Working Pairs
| Parameter | Definition/Value |
|---|---|
| COPabsorption | COP = QE/QG (heat-driven; range 0.6-0.8) |
| H₂O-LiBr System | Water is refrigerant, lithium bromide is absorbent; used for AC; limited to T > 0°C |
| NH₃-H₂O System | Ammonia is refrigerant, water is absorbent; industrial refrigeration; rectifier needed |
3.3 Advantages and Applications
- Heat source can be waste heat, solar, or natural gas
- Fewer moving parts than vapor-compression systems
- Quiet operation
- Used in applications where electricity is expensive or heat is available
4. Multistage and Cascade Refrigeration
4.1 Multistage Compression
| Feature | Description |
|---|---|
| Purpose | Reduces compressor work and discharge temperature for large pressure ratios |
| Optimal Interstage Pressure | Pint = √(Plow × Phigh) for two-stage |
| Flash Chamber | Separates liquid and vapor between stages; improves efficiency |
| Intercooling | Cools refrigerant between compression stages; approaches isothermal compression |
4.2 Cascade Refrigeration
- Two or more separate refrigeration cycles in series
- Evaporator of higher-temperature cycle cools condenser of lower-temperature cycle
- Different refrigerants in each cycle optimized for temperature range
- Used for very low temperatures (T <>
- COPcascade = COP₁ × COP₂/(COP₁ + COP₂ + 1)
5. Modified Vapor-Compression Cycles
5.1 Cycle Enhancements
| Modification | Benefit |
|---|---|
| Liquid Subcooling | Increases refrigeration effect; reduces quality entering evaporator |
| Vapor Superheating | Prevents liquid carryover to compressor; may decrease COP if excessive |
| Suction Line Heat Exchanger | Subcools liquid with cold suction vapor; increases h₁, decreases h₄ |
5.2 Heat Pump Operation
| Parameter | Formula/Description |
|---|---|
| COPHP | COPHP = QH/Wnet = (h₂ - h₃)/(h₂ - h₁) |
| Relationship | COPHP = COPR + 1 |
| Application | Space heating; reversible operation for heating/cooling |
6. Air-Conditioning Systems
6.1 Psychrometric Properties
| Property | Definition |
|---|---|
| Dry Bulb Temperature (DBT) | Temperature measured by standard thermometer |
| Wet Bulb Temperature (WBT) | Temperature with evaporative cooling; constant enthalpy lines on chart |
| Dew Point Temperature | Temperature at which condensation begins at constant humidity ratio |
| Relative Humidity (φ) | φ = Pv/Pg where Pv is vapor pressure, Pg is saturation pressure |
| Humidity Ratio (ω) | ω = 0.622 × Pv/(P - Pv) in lbv/lbda or kgv/kgda |
| Specific Enthalpy | h = cpT + ωhfg where cp ≈ 1.005 kJ/kg·K for dry air |
6.2 Air-Conditioning Processes
| Process | Characteristics |
|---|---|
| Sensible Heating/Cooling | Constant humidity ratio (horizontal line on chart); changes temperature only |
| Humidification | Increases moisture content; steam injection (constant DBT) or evaporative (constant WBT) |
| Dehumidification | Cooling below dew point; condensate removed; decreases both T and ω |
| Adiabatic Mixing | h₃ = (ṁ₁h₁ + ṁ₂h₂)/(ṁ₁ + ṁ₂); ω₃ = (ṁ₁ω₁ + ṁ₂ω₂)/(ṁ₁ + ṁ₂) |
6.3 Load Calculations
- Sensible Heat Ratio (SHR) = Qsensible/Qtotal
- Cooling load: Qsensible = ṁacp(T₁ - T₂); Qlatent = ṁahfg(ω₁ - ω₂)
- Bypass Factor (BF) = (T₂ - Tcoil)/(T₁ - Tcoil); indicates coil effectiveness
- Apparatus Dew Point (ADP): effective surface temperature of cooling coil
7. Gas Refrigeration Cycles
7.1 Reversed Brayton Cycle
| Process | Description |
|---|---|
| 1-2: Isentropic Compression | Compressor increases gas pressure and temperature |
| 2-3: Constant Pressure Cooling | Heat exchanger rejects heat to surroundings |
| 3-4: Isentropic Expansion | Expander (turbine) reduces temperature below T₁ |
| 4-1: Constant Pressure Heating | Refrigerated space adds heat to gas |
7.2 Performance
- COP = 1/(rp(γ-1)/γ - 1) where rp = P₂/P₁ is pressure ratio
- Uses air or helium as working fluid
- Lower COP than vapor-compression but operates at very low temperatures
- No phase change; continuous gas operation
- Applications: aircraft AC, cryogenic systems, liquefaction processes
8. Thermodynamic Analysis
8.1 First Law Analysis
| Component | Energy Balance |
|---|---|
| Compressor | Wcomp = ṁ(h₂ - h₁); for isentropic: ηc = (h₂s - h₁)/(h₂a - h₁) |
| Condenser | Qout = ṁ(h₂ - h₃) |
| Expansion Valve | h₃ = h₄ (isenthalpic throttling) |
| Evaporator | Qin = ṁ(h₁ - h₄) |
8.2 Second Law Analysis
- Carnot COPR = TL/(TH - TL); maximum theoretical efficiency
- Carnot COPHP = TH/(TH - TL)
- Exergy destruction identifies irreversibilities in each component
- Throttling valve: major source of irreversibility (Δs > 0, Δh = 0)
- Second law efficiency: ηII = COPactual/COPCarnot
8.3 Key Performance Metrics
| Metric | Expression |
|---|---|
| Energy Efficiency Ratio (EER) | EER = Qcooling (Btu/hr) / Winput (W) |
| Seasonal EER (SEER) | Cooling output over season / Total electrical input; accounts for part-load |
| Heating Seasonal Performance Factor | HSPF = Total heating output (Btu) / Total electrical input (W·hr) |
9. Refrigeration System Components
9.1 Compressor Types
| Type | Characteristics |
|---|---|
| Reciprocating | Positive displacement; piston-cylinder; 1-1500 tons; capacity control via cylinder unloading |
| Rotary (Scroll) | Positive displacement; two spiral scrolls; 2-20 tons; smooth operation, high efficiency |
| Screw | Positive displacement; helical rotors; 20-750 tons; continuous compression, oil-cooled |
| Centrifugal | Dynamic; impeller accelerates refrigerant; >100 tons; high flow, low pressure ratio per stage |
9.2 Heat Exchangers
- Evaporator types: direct expansion (DX), flooded, shell-and-tube
- Condenser types: air-cooled (finned tube), water-cooled (shell-and-tube), evaporative
- Effectiveness-NTU method: ε = (actual heat transfer)/(maximum possible heat transfer)
- Log Mean Temperature Difference: LMTD = (ΔT₁ - ΔT₂)/ln(ΔT₁/ΔT₂)
- Heat transfer: Q = UA × LMTD where U is overall heat transfer coefficient
9.3 Expansion Devices
| Device | Application |
|---|---|
| Thermostatic Expansion Valve | Modulates flow based on superheat at evaporator exit; maintains constant superheat |
| Capillary Tube | Fixed restriction; simple, no moving parts; limited to small systems with constant load |
| Electronic Expansion Valve | Precise control via sensors and controller; optimal for variable load applications |
| Float Valve | Maintains liquid level in evaporator; used in flooded evaporators |
10. Special Applications and Considerations
10.1 Low-Temperature Refrigeration
- Cascade systems required for T <>
- Auto-refrigerating cascade uses mixed refrigerants
- Cryogenic systems: T < -150°c;="" use="" gas="" cycles="" or="" joule-thomson="">
- Liquefaction: Linde cycle (simple throttling), Claude cycle (expander)
10.2 Capacity Control Methods
| Method | Description |
|---|---|
| On-Off Control | Simple cycling; large temperature swings; low cost |
| Hot Gas Bypass | Redirects discharge gas to evaporator inlet; reduces capacity without cycling |
| Variable Speed Drive | Varies compressor speed; excellent efficiency at part-load; higher cost |
| Cylinder Unloading | Deactivates cylinders in reciprocating compressors; stepped capacity reduction |
10.3 Refrigeration Safety
- ASHRAE 34: refrigerant safety classification (toxicity: A/B; flammability: 1/2L/2/3)
- Pressure relief devices required on all pressure vessels
- Refrigerant leak detection and monitoring systems
- Maximum discharge temperature limits to prevent oil breakdown (~150°C for mineral oil)
- Evacuation and charging procedures per EPA regulations
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