Vapor Compression Chillers: Design & Performance

Vapor compression chillers constitute the dominant technology for commercial and industrial cooling applications, leveraging the thermodynamic properties of refrigerants to transfer heat from chilled water to a heat rejection medium. Understanding the underlying physics, component design, and performance metrics enables proper selection, operation, and optimization of these systems.

Vapor Compression Refrigeration Cycle

The vapor compression cycle operates through four fundamental thermodynamic processes that exploit the phase-change properties of refrigerants to move thermal energy against its natural gradient.

Thermodynamic Process Analysis

The refrigeration cycle consists of:

1. Isentropic Compression: Low-pressure vapor enters the compressor and undergoes compression, increasing both temperature and pressure. The work input is:

$$W_{comp} = \dot{m} (h_2 - h_1)$$

where $\dot{m}$ is refrigerant mass flow rate, $h_2$ is discharge enthalpy, and $h_1$ is suction enthalpy.

2. Isobaric Condensation: High-pressure superheated vapor releases heat to the cooling medium (water or air) in the condenser, transitioning through desuperheating, condensation, and subcooling:

$$Q_{cond} = \dot{m} (h_2 - h_3)$$

3. Isenthalpic Expansion: Subcooled liquid passes through the expansion device, experiencing a pressure drop with constant enthalpy ($h_3 = h_4$), resulting in a two-phase mixture at evaporator pressure.

4. Isobaric Evaporation: The refrigerant absorbs heat from chilled water, evaporating completely and potentially superheating:

$$Q_{evap} = \dot{m} (h_1 - h_4)$$

The coefficient of performance quantifies thermodynamic efficiency:

$$\text{COP}{ref} = \frac{Q{evap}}{W_{comp}} = \frac{h_1 - h_4}{h_2 - h_1}$$

graph TD
    A[Evaporator<br/>Low P, Low T<br/>Refrigerant Evaporates] -->|Low Pressure Vapor<br/>h1| B[Compressor<br/>Work Input<br/>Pressure & Temp Rise]
    B -->|High Pressure Vapor<br/>h2| C[Condenser<br/>High P, High T<br/>Heat Rejection]
    C -->|High Pressure Liquid<br/>h3| D[Expansion Device<br/>Isenthalpic Process<br/>Pressure Drop]
    D -->|Low Pressure Mixture<br/>h4| A

    E[Chilled Water In<br/>12°C] -.->|Heat Absorption| A
    A -.->|Cooling Effect| F[Chilled Water Out<br/>7°C]

    G[Condenser Water In<br/>29°C] -.->|Heat Absorption| C
    C -.->|Heat Rejection| H[Condenser Water Out<br/>35°C]

Refrigerant Selection Criteria

Refrigerant selection significantly impacts performance and environmental compliance. Key properties include:

ASHRAE Standard 34 classifies refrigerant safety, while ASHRAE Standard 15 governs system design and installation practices.

Compressor Technologies

The compressor type fundamentally determines chiller capacity range, efficiency characteristics, and maintenance requirements.

Centrifugal Compressors

Centrifugal compressors dominate large-capacity applications (150-10,000+ tons) through dynamic compression. The impeller imparts kinetic energy to refrigerant vapor, which converts to pressure energy in the diffuser.

Performance characteristics:

• Pressure ratio per stage: 2.5-4.0:1
• Isentropic efficiency: 75-85%
• Capacity modulation via inlet guide vanes or variable speed
• Surge limitation at low loads (typically 10-15% minimum)

Pressure ratio relationship:

$$\frac{P_2}{P_1} = \left(1 + \frac{\eta_c}{\eta_{pol}} \left[\left(\frac{U}{\sqrt{C_p T_1}}\right)^2 - 1\right]\right)^{\frac{\gamma}{\gamma-1}}$$

where $U$ is impeller tip speed, $C_p$ is specific heat, and $\eta_{pol}$ is polytropic efficiency.

Screw Compressors

Twin-screw compressors provide positive displacement compression for medium capacities (50-750 tons) through meshing helical rotors.

Performance characteristics:

• Built-in volume ratio determines optimal pressure ratio
• Isentropic efficiency: 65-75%
• Stepless capacity control via slide valve
• Oil injection for sealing, cooling, and lubrication
• Economizer ports enhance efficiency at part-load

Scroll Compressors

Scroll compressors utilize orbiting and fixed scrolls for small to medium capacities (up to 200 tons, larger in modular configurations).

Performance characteristics:

• Inherently high volumetric efficiency (>95%)
• Isentropic efficiency: 60-70%
• Fewer moving parts than reciprocating designs
• Reduced vibration and noise
• Digital or inverter-driven capacity modulation

Comparison Matrix

Heat Exchanger Design

Evaporators and condensers constitute the heat transfer interfaces where refrigerant phase change facilitates thermal energy movement.

Evaporator Configuration

Shell-and-tube evaporators predominate in large chillers, with refrigerant typically on the shell side and chilled water inside tubes.

Heat transfer governing equation:

$$Q = UA \cdot \text{LMTD}$$

where $U$ is overall heat transfer coefficient, $A$ is heat transfer area, and LMTD is log mean temperature difference:

$$\text{LMTD} = \frac{\Delta T_1 - \Delta T_2}{\ln(\Delta T_1 / \Delta T_2)}$$

For evaporators with phase change, the evaporating coefficient dominates:

$$\frac{1}{U} = \frac{1}{h_{evap}} + \frac{t_{tube}}{k_{tube}} + \frac{1}{h_{water}} + R_{fouling}$$

Enhanced tube surfaces (rifled, microfin, or turbulated) increase $h_{evap}$ by 200-400% through increased surface area and improved nucleate boiling.

Condenser Design

Water-cooled condensers similarly employ shell-and-tube construction, with design considerations for:

• Desuperheating zone (typically 10-15% of heat rejection)
• Condensing zone (70-80% of heat rejection)
• Subcooling zone (5-15% of heat rejection)

The condensing coefficient depends on film condensation physics:

$$h_{cond} = 0.725 \left[\frac{g \rho_l (\rho_l - \rho_v) k_l^3 h_{fg}}{\mu_l \Delta T D}\right]^{0.25}$$

where $\rho$ is density, $k$ is thermal conductivity, $h_{fg}$ is latent heat, $\mu$ is viscosity, and $D$ is tube diameter.

Efficiency Metrics and Ratings

Chiller efficiency quantification employs multiple metrics across various operating conditions.

Power Consumption: kW/ton

The industry-standard efficiency metric expresses electrical power input per ton of cooling capacity:

$$\text{kW/ton} = \frac{P_{input} \text{ (kW)}}{Q_{cooling} \text{ (tons)}}$$

Lower kW/ton values indicate higher efficiency. The relationship to COP:

$$\text{COP} = \frac{3.517}{\text{kW/ton}}$$

Typical performance ranges at ARI Standard 550/590 conditions:

AHRI Certification and IPLV

AHRI Standard 550/590 establishes rating conditions and the Integrated Part Load Value (IPLV), which weights performance at multiple load points:

$$\text{IPLV} = 0.01A + 0.42B + 0.45C + 0.12D$$

where A, B, C, D represent efficiency at 100%, 75%, 50%, and 25% load respectively.

This metric better represents annual performance since chillers operate predominantly at part-load conditions. IPLV improvements of 30-40% relative to full-load ratings are common with variable-speed drives and optimized control strategies.

Thermodynamic Limits

The Carnot COP establishes theoretical maximum efficiency:

$$\text{COP}{Carnot} = \frac{T{evap}}{T_{cond} - T_{evap}}$$

For standard conditions (7°C chilled water, 35°C condenser water):

$$\text{COP}_{Carnot} = \frac{280.15}{308.15 - 280.15} = 10.01$$

Actual chillers achieve 40-60% of Carnot efficiency, with losses from:

• Non-isentropic compression (70-85% efficiency)
• Heat exchanger temperature differences (3-8°C approach)
• Pressure drops in piping and heat exchangers
• Motor and transmission losses (90-97% efficiency)

Understanding these fundamentals enables engineers to specify appropriate equipment, optimize operating parameters, and troubleshoot performance issues systematically based on physical principles rather than empirical observation alone.

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