9.2 Condensers: Air-Cooled, Water-Cooled & Evaporative Condensers

9.2 Condensers: Air-Cooled, Water-Cooled & Evaporative Condensers

The condenser is the primary heat-rejection heat exchanger in a vapor-compression refrigeration system. Its thermodynamic function is to receive high-pressure, superheated discharge vapor from the compressor, desuperheat the vapor, condense it into saturated liquid, and subcool the liquid before delivering it to the liquid line and expansion device. Understanding condenser heat transfer mechanisms, water-flow rates, fouling resistances, and head-pressure regulation is a core competency tested on the PE Mechanical HVAC exam.

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1. Total Heat of Rejection (THR) & Energy Balance

By the First Law of Thermodynamics, for an open steady-flow refrigeration system, the rate of heat rejected at the condenser ($\dot{Q}_{\text{cond}}$) must equal the thermal energy absorbed at the evaporator plus the work added to the refrigerant by the compressor:

$\dot{Q}_{\text{cond}} = \dot{Q}_{\text{evap}} + \dot{W}_{\text{comp}}$

  +-------------------------+                 +--------------------------+
  |  Evaporator Cooling     |                 |  Compressor Electrical   |
  |  Load (Q_evap)          |                 |  Power / Work (W_comp)   |
  |  1.0 Ton = 12,000 Btu/hr|                 |  ~0.5 to 1.2 kW/ton      |
  +------------+------------+                 +------------+-------------+
               |                                           |
               +--------------------+----------------------+
                                    |
                                    V
                     +------------------------------+
                     |  TOTAL HEAT OF REJECTION     |
                     |  (THR = Q_evap + W_comp)     |
                     |  ~14,000 to 16,000 Btu/hr/ton|
                     +------------------------------+

Total Heat Rejection Factor ($F_{\text{THR}}$)

$\text{THR} = \dot{Q}_{\text{evap}} \times F_{\text{THR}}$

$F_{\text{THR}} = 1 + \frac{\dot{W}_{\text{comp}}}{\dot{Q}_{\text{evap}}} = 1 + \frac{1}{\text{COP}_R} = 1 + \frac{\text{kW/ton} \times 3,412.14}{12,000} = 1 + \frac{\text{kW/ton}}{3.51685}$

• Open-Drive Chillers: Motor losses stay in the ambient mechanical room; fluid work is $w_a = \dot{m}(h_2 - h_1)$.
• Hermetic & Semi-Hermetic Compressors: The motor is cooled directly by suction gas. Therefore, 100% of motor electrical losses are added to the refrigerant, increasing $\text{THR}$ to:

$\dot{Q}_{\text{cond, hermetic}} = \dot{Q}_{\text{evap}} + \dot{W}_{\text{electrical, in}}$

For typical air-conditioning applications ($\text{COP} \approx 3.0$ to $4.0$), $\text{THR}$ ranges from $14,400$ to $15,600\text{ Btu/(hr}\cdot\text{ton)}$ ($1.20$ to $1.30\text{ tons of heat rejection per ton of cooling}$). In low-temperature refrigeration ($\text{COP} \approx 1.5$), $\text{THR}$ can reach $20,000\text{ Btu/(hr}\cdot\text{ton)}$ ($F_{\text{THR}} \approx 1.67$).

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2. Three Internal Condenser Thermal Zones

Refrigerant flows through three distinct thermodynamic regimes inside the condenser:

Enthalpy / Phase Progression:

[ Superheated Vapor ] ===> [ Two-Phase Vapor/Liquid Mixture ] ===> [ Subcooled Liquid ]
(1. Desuperheating Zone)   (2. Condensing Zone / Latent)          (3. Subcooling Zone)
  ~10% to 15% Area           ~80% to 85% Area                       ~5% Area
  Single-phase vapor gas     Constant Temp & Pressure               Single-phase liquid
  h_discharge -> h_g         h_g -> h_f (h_fg rejected)             h_f -> h_out

1. Desuperheating Zone (10% to 15% of total heat duty): Single-phase gas cooling from discharge temperature ($140^\circ\text{F}$ to $220^\circ\text{F}$) down to the Saturated Condensing Temperature ($T_{\text{sat}}$). Convective heat transfer coefficient is relatively low ($h \approx 30-80\text{ Btu/(hr}\cdot\text{ft}^2\cdot^\circ\text{F)}$).
2. Condensing Zone (80% to 85% of total heat duty): Two-phase condensation at constant saturation temperature ($T_{\text{sat}}$) and constant saturation pressure ($P_{\text{cond}}$). Latent heat of condensation ($h_{fg}$) is released. Two-phase film boiling/condensation produces extremely high heat transfer coefficients ($h \approx 300-1,200\text{ Btu/(hr}\cdot\text{ft}^2\cdot^\circ\text{F)}$).
3. Subcooling Zone (5% of total heat duty): Single-phase liquid cooling from $T_{\text{sat}}$ down to leaving liquid temperature ($T_{\text{liquid}}$). Essential for bubble-free liquid feed to the expansion valve.

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3. Comparison of Condenser Types

+---------------------------------------------------------------------------------------------------------+
|                                    CONDENSER ARCHITECTURE COMPARISON                                    |
+-----------------------+---------------------------------+-----------------------------------------------+
| Condenser Type        | Heat Sink Fluid                 | Typical Saturated Condensing Temp (SCT)       |
+-----------------------+---------------------------------+-----------------------------------------------+
| **Air-Cooled**        | Ambient Air (Dry-BulB Temp)     | SCT = Ambient DBT + 20°F to 30°F (115°F to 125°F)|
| **Water-Cooled**      | Condenser Water (Cooling Tower) | SCT = Tower Water LWT + 5°F to 10°F (95°F-105°F)|
| **Evaporative**       | Air + Evaporating Water Spray   | SCT = Ambient WBT + 12°F to 18°F (90°F-96°F)  |
+-----------------------+---------------------------------+-----------------------------------------------+

Detailed Engineering Analysis of Each Type

A. Air-Cooled Condensers

• Mechanics: Hot refrigerant vapor flows inside finned copper or aluminum tubes while propeller fans draw ambient air across external fins. Microchannel coils utilize multi-port extruded aluminum tubes with folded louvered fins, reducing refrigerant charge by 40% to 70%.
• Design Temperature Difference (TD or CTOA): Defined as Saturated Condensing Temperature minus Entering Air Dry-Bulb Temperature: $\text{TD} = T_{\text{cond, sat}} - T_{\text{ambient, DB}}$ Typical commercial design: $\text{TD} = 20^\circ\text{F}$ to $30^\circ\text{F}$. On a $95^\circ\text{F}$ summer day, $T_{\text{cond}} = 115^\circ\text{F}$ to $125^\circ\text{F}$.
• Advantages: Zero water consumption, zero water treatment chemicals, zero risk of Legionella, simple maintenance.
• Disadvantages: High condensing pressure reduces compressor COP ($1.0$ to $1.3\text{ kW/ton}$ vs $0.5$ to $0.6\text{ kW/ton}$ for water-cooled), high fan acoustic noise, large rooftop footprint.

B. Water-Cooled Condensers

• Mechanics: Shell-and-tube or brazed plate heat exchangers. In a shell-and-tube condenser, high-pressure refrigerant condenses on the shell side over enhanced copper tubes while cooling tower water circulates through multiple tube passes.
• Standard Rating Conditions (AHRI 550/590):
  • Entering Condenser Water Temp (ECWT): $85.0^\circ\text{F}$
  • Leaving Condenser Water Temp (LCWT): $95.0^\circ\text{F}$ (Standard $\Delta T = 10.0^\circ\text{F}$ at $3.0\text{ GPM/ton}$)
  • Low-flow Design: $85.0^\circ\text{F}$ in, $94.0^\circ\text{F}$ out ($\Delta T = 9.0^\circ\text{F}$ at $3.33\text{ GPM/ton}$) or $85.0^\circ\text{F} \to 97.5^\circ\text{F}$ ($\Delta T = 12.5^\circ\text{F}$ at $2.4\text{ GPM/ton}$).
• Condenser Water Flow Formula: $\dot{Q}_{\text{cond}}\text{ (Btu/hr)} = 500 \times \text{GPM}_{\text{CW}} \times (T_{\text{LCWT}} - T_{\text{ECWT}})$ $\text{GPM}_{\text{CW}} = \frac{\text{THR (Btu/hr)}}{500 \times \Delta T_{\text{CW}}} = \frac{\text{Tons} \times 15,000}{500 \times 10^\circ\text{F}} = 3.0\text{ GPM/ton}$
• Waterside Fouling Factor ($R_f$): Mineral scale, biological slime, and silt increase thermal resistance. AHRI 550/590 standard rating fouling allowance is $R_f = 0.00025\text{ hr}\cdot\text{ft}^2\cdot^\circ\text{F/Btu}$. Waterside tube cleaning is performed mechanically with nylon brushes or chemically via acid circulation.

C. Evaporative Condensers

• Mechanics: Combines a condensing coil bundle and an open cooling tower inside a single enclosure. Water is pumped from a lower basin to spray nozzles that cascade water over bare serpentine refrigerant coils. Axial fans draw air upward counterflow to falling water.
• Thermodynamic Advantage: Latent evaporation of water directly from the coil surface transfers heat against the ambient wet-bulb temperature (WBT) rather than the dry-bulb temperature.
• Performance: On a $95^\circ\text{F}\text{ DB} / 75^\circ\text{F}\text{ WB}$ design day, an evaporative condenser achieves $T_{\text{cond}} \approx 90^\circ\text{F}$ to $95^\circ\text{F}$ (compared to $120^\circ\text{F}$ for air-cooled), slashing compressor power by 25% to 35%.
• Application: Industrial ammonia (R-717) cold storage, food processing plants, and large supermarket central rack systems.

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4. Condenser Log Mean Temperature Difference (LMTD)

Heat transfer across the condenser is calculated using the overall heat transfer equation:

$\dot{Q}_{\text{cond}} = U \cdot A \cdot \text{LMTD}$

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

For a water-cooled condenser with constant refrigerant condensing temperature ($T_{\text{cond}}$):

• $\Delta T_1 = T_{\text{cond}} - T_{\text{LCWT}}$ (at refrigerant inlet / water exit)
• $\Delta T_2 = T_{\text{cond}} - T_{\text{ECWT}}$ (at refrigerant liquid exit / water inlet)

Temperature Profile (Water-Cooled Shell & Tube):

Refrigerant:  T_cond ========================================> Saturated Condensing Temp (T_cond)
                                                    |
              ^                                     |  Approach = T_cond - T_LCWT
              |                                     V
Water Stream: |-------------------------------------> T_LCWT (95°F)
              |      Water Temperature Rise (10°F)  ^
              +-------------------------------------+ T_ECWT (85°F)

$\text{Condenser Approach Temperature} = T_{\text{cond, sat}} - T_{\text{LCWT}}$

Typical approach temperatures for clean water-cooled condensers range from $3^\circ\text{F}$ to $8^\circ\text{F}$.

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5. Low-Ambient Head Pressure Control

In air-cooled systems operating during winter or cold shoulder months, cold ambient air dramatically increases condenser heat rejection capacity, causing condensing pressure to plummet. Insufficient head pressure results in:

1. Inadequate pressure differential across the thermal expansion valve (TXV), causing starving of the evaporator.
2. Inadequate oil return from DX coils due to low refrigerant velocity.
3. Nuisance low-pressure cut-out tripping.

Low-Ambient Control Strategies

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6. Worked Example: Water-Cooled vs. Air-Cooled Condenser Sizing

Problem: A water-cooled water chiller produces $350\text{ tons}$ of cooling capacity with an operating efficiency of $0.58\text{ kW/ton}$. The condenser operates with entering condenser water at $85.0^\circ\text{F}$ and leaving condenser water at $95.0^\circ\text{F}$. Saturated condensing temperature is $101.0^\circ\text{F}$.

Find:

1. The Total Heat of Rejection ($\text{THR}$) in $\text{Btu/hr}$ and the heat rejection factor ($F_{\text{THR}}$).
2. The required condenser water flow rate ($\text{GPM}_{\text{CW}}$).
3. The Condenser Log Mean Temperature Difference ($\text{LMTD}$) and Condenser Approach Temperature.
4. If the chiller were replaced with an air-cooled unit operating at $1.15\text{ kW/ton}$ on a $95^\circ\text{F}$ ambient day, compute the new $\text{THR}$ in $\text{Btu/hr}$.

Step-by-Step Solution:

Step 1: Compute THR and Rejection Factor for the water-cooled chiller. $\dot{Q}_{\text{evap}} = 350\text{ tons} \times 12,000\text{ Btu/(hr}\cdot\text{ton)} = 4,200,000\text{ Btu/hr}$

$\text{Compressor Electrical Power: } \dot{W}_{\text{comp}} = 350\text{ tons} \times 0.58\text{ kW/ton} = 203.0\text{ kW}$ $\dot{W}_{\text{comp}} = 203.0\text{ kW} \times 3,412.14\text{ Btu/(hr}\cdot\text{kW)} = 692,664\text{ Btu/hr}$

$\text{THR}_{\text{water}} = \dot{Q}_{\text{evap}} + \dot{W}_{\text{comp}} = 4,200,000 + 692,664 = 4,892,664\text{ Btu/hr}$

$F_{\text{THR}} = \frac{4,892,664}{4,200,000} = 1.1649$

Step 2: Compute Condenser Water Flow Rate ($\text{GPM}$). $\Delta T_{\text{CW}} = 95.0^\circ\text{F} - 85.0^\circ\text{F} = 10.0^\circ\text{F}$

$\text{GPM}_{\text{CW}} = \frac{\text{THR}}{500 \times \Delta T_{\text{CW}}} = \frac{4,892,664\text{ Btu/hr}}{500 \times 10.0^\circ\text{F}} = 978.53\text{ GPM}$ $\text{Flow per ton: } \frac{978.53\text{ GPM}}{350\text{ tons}} = 2.80\text{ GPM/ton}$

Step 3: Compute LMTD and Approach Temperature. $\Delta T_1 = T_{\text{cond}} - T_{\text{LCWT}} = 101.0^\circ\text{F} - 95.0^\circ\text{F} = 6.0^\circ\text{F}$ $\Delta T_2 = T_{\text{cond}} - T_{\text{ECWT}} = 101.0^\circ\text{F} - 85.0^\circ\text{F} = 16.0^\circ\text{F}$

$\text{LMTD} = \frac{\Delta T_2 - \Delta T_1}{\ln(\Delta T_2 / \Delta T_1)} = \frac{16.0 - 6.0}{\ln(16.0 / 6.0)} = \frac{10.0}{\ln(2.6667)} = \frac{10.0}{0.98083} = 10.20^\circ\text{F}$

$\text{Approach} = T_{\text{cond}} - T_{\text{LCWT}} = 101.0^\circ\text{F} - 95.0^\circ\text{F} = 6.0^\circ\text{F}$

Step 4: Compute Air-Cooled Chiller THR. $\dot{W}_{\text{comp, air}} = 350\text{ tons} \times 1.15\text{ kW/ton} = 402.5\text{ kW}$ $\dot{W}_{\text{comp, air}} = 402.5\text{ kW} \times 3,412.14\text{ Btu/hr/kW} = 1,373,386\text{ Btu/hr}$ $\text{THR}_{\text{air}} = 4,200,000 + 1,373,386 = 5,573,386\text{ Btu/hr}$ $F_{\text{THR, air}} = \frac{5,573,386}{4,200,000} = 1.3270$ (Notice that the air-cooled condenser must reject $13.9%$ more heat than the water-cooled condenser due to higher compressor electrical power!)

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7. NCEES Reference Handbook Navigation & Exam Traps

• Heat Transfer Section: LMTD formula $\Delta T_{lm} = \frac{\Delta T_1 - \Delta T_2}{\ln(\Delta T_1 / \Delta T_2)}$ and overall heat exchanger relation $q = U A \Delta T_{lm}$.
• Hydronics Equation: $q = 500 \times \text{GPM} \times \Delta T$. The 500 constant is valid only for pure water at standard density ($\rho = 8.33\text{ lbm/gal}$, $c_p = 1.0\text{ Btu/lbm}\cdot^\circ\text{F}$). If glycol is used, $C = 500 \times \text{SG} \times c_p$.
• THR Trap: Never assume $\text{THR} = \dot{Q}_{\text{evap}}$ ($12,000\text{ Btu/ton}$). Condensers must ALWAYS reject both evaporator heat and compressor work ($14,000$ to $16,000+\text{ Btu/ton}$).