Vapor Compression Cycles

The vapor compression cycle forms the foundation of modern refrigeration and air conditioning systems. This thermodynamic cycle transfers thermal energy from a low-temperature region to a high-temperature region through the phase change and compression of a refrigerant working fluid.

Ideal Vapor Compression Cycle

The ideal vapor compression cycle consists of four reversible processes operating between two constant pressure levels:

Process Sequence

1. Isentropic Compression (1→2): Saturated vapor enters the compressor and undergoes reversible adiabatic compression to condenser pressure
2. Isobaric Heat Rejection (2→3): Superheated vapor flows through the condenser, desuperheating, condensing, and subcooling to saturated liquid
3. Isenthalpic Expansion (3→4): Saturated liquid expands through a throttling device to evaporator pressure
4. Isobaric Heat Absorption (4→1): Two-phase refrigerant evaporates completely to saturated vapor

Thermodynamic Analysis

For the ideal cycle operating between evaporator pressure P_evap and condenser pressure P_cond:

Refrigeration Effect:

q_e = h₁ - h₄ = h₁ - h₃  [kJ/kg]

Compression Work:

w_comp = h₂s - h₁  [kJ/kg]

Heat Rejection:

q_c = h₂s - h₃  [kJ/kg]

Coefficient of Performance (COP):

COP_ideal = q_e / w_comp = (h₁ - h₄) / (h₂s - h₁)

Where subscript ’s’ denotes isentropic compression.

Carnot Cycle Comparison

The Carnot refrigeration cycle represents the theoretical maximum efficiency between two temperature reservoirs. For refrigeration:

COP_Carnot = T_evap / (T_cond - T_evap)

The vapor compression cycle achieves 50-60% of Carnot COP due to:

• Irreversible throttling process (replacing isentropic expansion)
• Pressure drops in heat exchangers
• Non-isothermal heat transfer
• Compressor inefficiencies

Actual Vapor Compression Cycle

Real refrigeration systems deviate significantly from the ideal cycle due to irreversibilities and practical design constraints.

Key Deviations from Ideal Cycle

Compressor Isentropic Efficiency

Real compressor performance is characterized by isentropic efficiency:

η_isentropic = (h₂s - h₁) / (h₂a - h₁)

Where:

• h₂s = enthalpy after isentropic compression
• h₂a = actual discharge enthalpy

Typical isentropic efficiencies by compressor type:

Volumetric Efficiency

Volumetric efficiency accounts for re-expansion of clearance volume gas and suction valve pressure drop:

η_vol = (V_act / V_swept) = 1 - C(r^(1/n) - 1) - L_valve

Where:

• C = clearance volume ratio (0.02-0.06 for reciprocating)
• r = pressure ratio (P_discharge / P_suction)
• n = polytropic exponent (1.1-1.3)
• L_valve = valve loss factor (0.02-0.05)

Pressure-Enthalpy (P-h) Diagram Analysis

The P-h diagram provides essential visualization of refrigeration cycle performance and enables rapid cycle analysis.

Diagram Regions

Subcooled Liquid Region (left of saturated liquid line):

• Single-phase liquid below saturation temperature
• Subcooling degree = T_sat - T_actual at constant pressure
• Increases refrigeration effect, reduces flash gas

Two-Phase Region (between saturation lines):

• Liquid-vapor mixture at constant temperature and pressure
• Quality x = m_vapor / m_total
• Primary region for evaporation and condensation

Superheated Vapor Region (right of saturated vapor line):

• Single-phase vapor above saturation temperature
• Superheat degree = T_actual - T_sat at constant pressure
• Necessary for compressor protection

Critical State Points on P-h Diagram

For R-410A at standard rating conditions (ARI 550/590):

• Evaporating temperature: 45°F (410 psia)
• Condensing temperature: 130°F (2350 psia)

Performance metrics:

Refrigeration effect = h₁ - h₄ = 175.2 - 48.5 = 126.7 Btu/lb
Compression work = h₂ - h₁ = 196.8 - 175.2 = 21.6 Btu/lb
COP = 126.7 / 21.6 = 5.86

P-h Diagram Applications

Cycle modifications visualization:

• Quantify effect of subcooling and superheat
• Evaluate multi-stage compression benefits
• Analyze economizer cycle improvements
• Determine flash gas formation

Performance troubleshooting:

• Identify inefficient operating conditions
• Diagnose compressor issues (high superheat)
• Detect refrigerant charge problems
• Evaluate heat exchanger fouling

Coefficient of Performance Calculations

Basic COP Formulations

Refrigeration COP:

COP_R = Q_evap / W_comp = ṁ(h₁ - h₄) / ṁ(h₂ - h₁) = (h₁ - h₄) / (h₂ - h₁)

Heat Pump COP:

COP_HP = Q_cond / W_comp = (h₂ - h₃) / (h₂ - h₁)

Energy Balance Relationship:

COP_HP = COP_R + 1

COP Variation with Operating Conditions

For R-134a vapor compression cycle (ASHRAE Handbook - Fundamentals):

Key observations:

• COP decreases as condensing temperature increases (reduced Carnot efficiency)
• COP decreases as evaporating temperature decreases (increased lift)
• Compression ratio exponentially impacts discharge temperature
• High discharge temperatures limit compressor operation (typically 225-250°F max)

Actual COP Accounting for Component Inefficiencies

COP_actual = COP_ideal × η_compressor × η_motor / (1 + ΔP_fraction)

Where:

• η_compressor = combined isentropic and volumetric efficiency
• η_motor = motor efficiency (0.85-0.95)
• ΔP_fraction = pressure drop impact factor (1.02-1.08)

Example calculation for scroll compressor system:

COP_ideal = 5.86
η_isentropic = 0.70
η_volumetric = 0.95
η_motor = 0.90
ΔP_fraction = 1.05

COP_actual = 5.86 × 0.70 × 0.95 × 0.90 / 1.05 = 3.32

Effects of Subcooling and Superheat

Subcooling Analysis

Subcooling the refrigerant liquid below saturation temperature at condenser pressure increases system capacity and efficiency.

Benefits of subcooling:

1. Increased refrigeration effect: Lower enthalpy entering expansion valve
2. Reduced flash gas: Less vapor formed during throttling
3. Improved compressor efficiency: Higher mass flow for given displacement

Quantitative impact:

For R-410A at 130°F condensing, 45°F evaporating:

Rule of thumb: Each 1°F of subcooling increases capacity by approximately 0.5%.

Methods to achieve subcooling:

• Oversized condenser coil area
• Dedicated subcooler heat exchanger
• Suction-to-liquid heat exchanger (internal heat exchange)
• Mechanical subcooling (separate refrigeration circuit)

Superheat Analysis

Superheat serves protective and operational functions but impacts cycle performance differently at evaporator vs compressor inlet.

Evaporator superheat (useful superheat):

• Ensures complete evaporation before leaving coil
• Prevents liquid floodback to compressor
• Typical range: 5-10°F
• Minimal impact on capacity (slight decrease)

Suction line superheat (parasitic superheat):

• Heat gain from ambient environment
• Reduces refrigeration effect (higher h₁)
• Increases compression work (higher specific volume)
• Should be minimized through insulation

Compressor inlet superheat impact:

For R-134a at 40°F evaporating, 100°F condensing:

Rule of thumb: Each 10°F of superheat reduces capacity by approximately 2-3%.

Suction-to-Liquid Heat Exchanger (SLHX)

Internal heat exchange between cold suction gas and warm liquid refrigerant provides:

Advantages:

• Guaranteed liquid to expansion valve (prevents flash gas in receiver)
• Reduced compressor suction temperature variation
• Improved capacity for refrigerants with wet compression (e.g., R-134a, R-407C)

Disadvantages:

• Increased compressor discharge temperature
• Reduced COP for dry compression refrigerants (e.g., R-22, R-410A)
• Additional pressure drop

Effectiveness calculation:

ε = (T_liquid,in - T_liquid,out) / (T_liquid,in - T_suction,in)

Typical effectiveness: 0.40 - 0.70

Application guidelines:

Multi-Stage Compression Systems

Multi-stage compression divides the compression process into two or more steps with intercooling, reducing compression work and discharge temperature for high pressure ratio applications.

Two-Stage Compression with Intercooling

Application criteria:

• Compression ratio > 8:1 (typically T_evap < 0°F, T_cond > 100°F)
• Discharge temperature > 250°F in single-stage
• Large capacity systems (> 100 tons)

Optimal intermediate pressure:

For minimum total compression work, the optimal intermediate pressure is the geometric mean:

P_int,opt = √(P_evap × P_cond)

Or in terms of saturation temperatures (approximate):

T_int,opt = (T_evap + T_cond) / 2

Performance comparison (R-404A, -20°F evap, 100°F cond):

Work savings: 15-20% compared to single-stage at high compression ratios.

Intercooling Methods

Flash intercooling (flash gas removal):

• High-pressure liquid throttled to intermediate pressure
• Flash vapor separated and directed to second-stage suction
• Remaining liquid provides additional subcooling
• Most common method for refrigeration systems

Direct contact intercooling:

• Liquid refrigerant injected into discharge gas between stages
• Evaporation cools gas to saturation at intermediate pressure
• Simple, effective, minimal pressure drop
• Used in screw compressor systems

Indirect intercooling (water or air-cooled):

• External heat exchanger cools gas between stages
• Can achieve subcooled gas entering second stage
• Maximum thermodynamic benefit
• Added cost and complexity

Economizer Cycles

The economizer cycle combines flash intercooling with vapor injection to increase capacity and efficiency in single or two-stage compressor systems.

Flash Tank Economizer Configuration

System components:

1. Main expansion valve (high pressure to intermediate pressure)
2. Flash tank separator at intermediate pressure
3. Secondary expansion valve (intermediate to evaporator pressure)
4. Vapor injection port on compressor

Mass flow analysis:

ṁ_total = ṁ_evaporator + ṁ_economizer
ṁ_economizer = ṁ_total × (x_flash)

Where x_flash is flash gas quality at intermediate pressure.

Capacity increase:

Q_evap,econ = ṁ_evap(h₁ - h₄) = ṁ_total(1 - x_flash)(h₁ - h₄)
Q_evap,basic = ṁ_total(h₁ - h₃)

Capacity increase = [(1-x_flash)(h₁-h₄) - (h₁-h₃)] / (h₁-h₃) × 100%

Performance example (R-134a, 0°F evap, 120°F cond):

Subcooler Economizer Configuration

Alternative arrangement using dedicated subcooler heat exchanger instead of flash tank:

Advantages:

• Precise control of subcooling degree
• Can achieve greater subcooling than flash economizer
• Better for systems with variable loads

Disadvantages:

• Higher pressure drop than flash tank
• More complex piping and controls
• Requires additional heat exchanger

Economizer Selection Criteria

Cascade Refrigeration Systems

Cascade systems employ two separate refrigeration cycles operating in series to achieve very low evaporating temperatures (-100°F to -250°F) not practical with single-stage systems.

Cascade System Configuration

Low-temperature circuit:

• Evaporator at desired low temperature
• Condenser serving as cascade heat exchanger
• Refrigerant selected for low-temperature properties

High-temperature circuit:

• Evaporator is cascade heat exchanger
• Condenser rejecting heat to ambient
• Refrigerant selected for efficient heat rejection

Refrigerant Pair Selection

Optimum refrigerant combinations for cascade systems:

Selection criteria:

1. Normal boiling point of low-stage refrigerant below minimum evaporating temperature
2. Critical temperature of high-stage refrigerant well above condensing temperature
3. Compatible operating pressures (avoid excessive vacuum or pressure)
4. Minimal temperature difference at cascade heat exchanger (5-10°F)

Cascade Heat Exchanger Analysis

The cascade condenser/evaporator operates with:

Low-stage condensing temperature: T_cascade + ΔT_approach (typically 5-10°F) High-stage evaporating temperature: T_cascade

Heat balance:

Q_cascade = ṁ_low × (h₂,low - h₃,low) = ṁ_high × (h₁,high - h₄,high)

Optimal cascade temperature:

For minimum total compression work:

T_cascade,opt ≈ √(T_evap × T_cond)  [absolute temperatures]

More precisely, considering different refrigerants and efficiencies:

T_cascade,opt = (T_evap + α×T_cond) / (1 + α)

Where α accounts for refrigerant properties and compressor efficiencies (typically 1.2-1.5).

Cascade System Performance

Performance example: -100°F evaporator, 100°F condenser

Low stage: R-508B (-100°F to -45°F cascade) High stage: R-404A (-40°F cascade to 100°F)

Comparison to single-stage (theoretical):

• Single-stage R-508B would require compression ratio of 11.9
• Discharge temperature would exceed 250°F
• COP would be approximately 1.1
• Cascade provides 34% COP improvement plus reliable operation

Auto-Cascade Systems

Single refrigerant circuit using zeotropic mixture (e.g., R-508A, R-23/R-116) with rectifying column to separate components:

• High-boiling component condenses first (warm end)
• Low-boiling component evaporates last (cold end)
• Eliminates cascade heat exchanger
• Simplified design but less efficient than true cascade

Cycle Modifications and Advanced Configurations

Compound Compression Systems

Single refrigerant circuit with two compressor stages, but evaporators at both intermediate and low temperature levels.

Applications:

• Supermarket refrigeration (medium and low temp cases)
• Cold storage with multiple temperature zones
• Process cooling with varied temperature requirements

Advantages over separate systems:

• Reduced total compressor capacity (work shared)
• Lower condensing load
• Improved COP for medium-temp loads

Mass flow relationship:

ṁ_high-stage = ṁ_medium-temp + ṁ_low-temp

Hot Gas Bypass Capacity Control

Diverts high-pressure discharge gas directly to evaporator inlet or compressor suction for capacity reduction.

Methods:

1. Evaporator pressure regulator (EPR) bypass: Gas to evaporator inlet

   • Maintains minimum evaporator pressure
   • Prevents coil icing
   • Capacity reduction: 0-100%

2. Suction gas bypass: Gas to suction line

   • Prevents compressor surge
   • Less efficient than unloading
   • Used for minimum load situations

Efficiency impact:

Hot gas bypass is inefficient; use variable speed or digital scroll for better part-load performance.

Liquid Overfeed Systems

Circulate excess liquid refrigerant through evaporator (2-4 times required for heat absorption) with separation vessel.

Components:

• Liquid overfeed pump or gravity circulation
• Separation vessel (accumulator)
• Liquid recirculation line

Advantages:

• Higher heat transfer coefficient (wetted surface)
• More uniform coil temperature
• Better oil return
• Reduced superheat requirement

Applications:

• Large industrial refrigeration (ammonia)
• Ice rinks
• Food processing facilities
• Cold storage warehouses

Performance: 5-15% higher evaporator capacity vs direct expansion at same temperature.

Refrigerant Property Effects on Cycle Performance

Critical Refrigerant Selection Parameters

At 40°F saturated conditions (typical AC evaporator).

Temperature Glide in Zeotropic Mixtures

Zeotropic refrigerant blends (e.g., R-404A, R-407C, R-410A) exhibit temperature glide during phase change.

Temperature glide: Difference between bubble point and dew point at constant pressure.

Design implications:

• Use dew point for evaporator temperature (end of evaporation)
• Use bubble point for condenser temperature (start of condensation)
• Counterflow heat exchangers perform better (temperature matching)
• Charge critically important (composition shift with leaks)

Performance Optimization Strategies

Operating Condition Optimization

Maximize COP by:

1. Lower condensing temperature:

   • Use largest economical condenser
   • Clean condenser surfaces regularly
   • Reduce condenser air/water temperature
   • Effect: 2-3% COP increase per 1°F reduction

2. Higher evaporating temperature:

   • Optimize air/water flow across evaporator
   • Minimize fouling and defrost frequency
   • Use lowest practical supply air/fluid temperature
   • Effect: 2-4% COP increase per 1°F increase

3. Optimize superheat and subcooling:

   • 5-10°F evaporator superheat (thermostatic expansion valve)
   • 10-15°F condenser subcooling
   • Minimize suction line heat gain
   • Effect: 3-5% COP improvement

4. Reduce pressure drops:

   • Properly size suction lines (ΔP < 2 psi, Δ < 1°F)
   • Clean filters and strainers
   • Minimize line length and fittings
   • Effect: 1-2% COP improvement per psi reduction

Capacity Control Methods

Ranked by part-load efficiency (best to worst):

1. Variable speed drive (VFD):

   • Power ∝ Speed³ (affinity laws for centrifugal)
   • Power ∝ Speed for positive displacement (approximately)
   • 20-50% energy savings at part load

2. Digital scroll modulation:

   • 10-100% capacity in 10% steps
   • Maintains high efficiency at part load
   • No hot gas bypass losses

3. Cylinder unloading (reciprocating):

   • 25%, 50%, 75%, 100% capacity steps
   • Moderate efficiency degradation
   • Simple, reliable

4. Slide valve (screw compressor):

   • 10-100% continuous modulation
   • Efficiency decreases linearly with capacity
   • Good for most applications

5. Hot gas bypass:

   • Continuous capacity control
   • Poor part-load efficiency
   • Use only for minimum load protection

References and Standards

ASHRAE Handbook - Fundamentals (2021):

• Chapter 1: Psychrometrics
• Chapter 2: Thermodynamics and Refrigeration Cycles
• Chapter 30: Thermophysical Properties of Refrigerants

ASHRAE Handbook - Refrigeration (2022):

• Chapter 1: Halocarbon Refrigeration Systems
• Chapter 2: Ammonia Refrigeration Systems
• Chapter 3: Carbon Dioxide Refrigeration Systems

Industry Standards:

• ANSI/ASHRAE Standard 15: Safety Standard for Refrigeration Systems
• ANSI/ASHRAE Standard 34: Designation and Safety Classification of Refrigerants
• ANSI/AHRI Standard 540: Performance Rating of Positive Displacement Refrigerant Compressors
• ISO 917: Testing of Refrigerant Compressors

Design Tools:

• NIST REFPROP: Reference Fluid Thermodynamic and Transport Properties Database
• Solkane (Honeywell): Refrigerant property calculator and cycle analysis
• ASHRAE Refrigerant Pressure-Temperature Charts (I-P and SI units)

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