2.2 Heat Rejection Balance and Expansion Devices

The Heat Rejection Balance Equation

In any refrigeration system, energy cannot be created or destroyed (according to the First Law of Thermodynamics). This means that all energy entering the system must be balanced by an equal amount of energy leaving the system.

Energy enters the system in two primary locations:

1. The Evaporator: As heat absorbed from the product or refrigerated space (the cooling load).
2. The Compressor: As mechanical work input from the compressor motor, which is transferred into the refrigerant as heat (the heat of compression).

Energy leaves the system at the condenser, where it is rejected to the environment. The fundamental heat balance equation is:

$\text{Heat Rejected in Condenser} = \text{Heat Absorbed in Evaporator} + \text{Heat of Compression}$

$\text{Q}_{\text{condenser}} = \text{Q}_{\text{evaporator}} + \text{W}_{\text{compression}}$

The Heat Rejection Ratio (HRR)

The Heat Rejection Ratio (HRR) is the ratio of heat rejected at the condenser to the heat absorbed in the evaporator:

$\text{HRR} = \frac{\text{Q}_{\text{condenser}}}{\text{Q}_{\text{evaporator}}}$

Because the compressor always adds heat, the HRR is always greater than 1.0 (typically ranging from 1.15 to 1.50). The HRR depends heavily on the compression ratio of the system. When a system operates with a lower suction pressure or a higher discharge pressure, the compression ratio rises. This requires the compressor to perform more work per pound of refrigerant circulated, adding more heat of compression. Consequently, a system operating at lower suction pressures (like a freezer) will have a higher HRR and require a larger condenser to reject heat than a system operating at higher suction pressures (like a water chiller) with the same cooling capacity.

---

Worked Energy Balance Calculation

To perform a system heat balance, operators must convert electrical and mechanical power units into heat flow units. The standard conversions are:

• 1 Ton of Refrigeration (TR) = 12,000 BTU/hr (or 200 BTU/min)
• 1 Horsepower (HP) = 2,545 BTU/hr
• 1 Kilowatt (kW) = 3,412 BTU/hr

Scenario

An industrial ammonia refrigeration plant operates an evaporator with a cooling capacity of 150 TR. The high-stage compressor motor driving the system draws 180 kW of electrical power. Calculate the total heat rejection load that the condenser must handle in BTU/hr and TR, and find the system's Heat Rejection Ratio.

Step-by-Step Calculation

Step 1: Convert the evaporator cooling load ($Q_{\text{evaporator}}$) from TR to BTU/hr:

$\text{Q}_{\text{evaporator}} = 150\text{ TR} \times 12,000\text{ BTU/(hr} \cdot \text{TR)} = 1,800,000\text{ BTU/hr}$

Step 2: Convert the compressor power input ($W_{\text{compression}}$) from kW to BTU/hr:

$\text{W}_{\text{compression}} = 180\text{ kW} \times 3,412\text{ BTU/(hr} \cdot \text{kW)} = 614,160\text{ BTU/hr}$

Step 3: Calculate the total heat rejection required at the condenser ($Q_{\text{condenser}}$) using the heat balance equation:

$\text{Q}_{\text{condenser}} = 1,800,000\text{ BTU/hr} + 614,160\text{ BTU/hr} = 2,414,160\text{ BTU/hr}$

Step 4: Convert the condenser load back to Tons of Refrigeration (TR) of heat rejection:

$\text{Q}_{\text{condenser (TR)}} = \frac{2,414,160\text{ BTU/hr}}{12,000\text{ BTU/(hr} \cdot \text{TR)}} \approx 201.2\text{ TR}$

Step 5: Calculate the Heat Rejection Ratio (HRR):

$\text{HRR} = \frac{201.2\text{ TR}}{150\text{ TR}} \approx 1.34$

Result: The condenser must be sized to reject 2,414,160 BTU/hr (or 201.2 TR). The HRR is 1.34, indicating that the condenser must reject 34% more heat than the evaporator absorbs due to the heat of compression.

---

Expansion Devices and Flow Regulation

To maintain the heat balance, the rate of refrigerant flow into the evaporator must precisely match the rate of vaporization caused by the cooling load. If too little refrigerant is fed, the evaporator becomes starved, suction pressure drops, and cooling capacity is lost. If too much refrigerant is fed, the evaporator becomes flooded, leading to liquid carryover and compressor damage. Industrial ammonia systems use several types of expansion valves:

1. Hand Expansion Valve (HEV)

An HEV is a manually operated needle valve featuring a tapered stem, fine threads, and a micro-dial indicator.

• Operation: Unlike automatic valves, an HEV has a fixed orifice opening that acts as a constant throttle. It does not automatically adjust to changes in the cooling load.
• Application: HEVs are ideal for stable, continuous base loads (such as large cold storage rooms with constant product temperatures). They are also commonly installed in bypass lines around automatic valves to allow manual operation during maintenance.
• Limitations: If the evaporator load decreases, the HEV will feed too much refrigerant, causing flooding. If the load increases, the valve will starve the evaporator.

2. Thermostatic Expansion Valve (TXV)

A TXV is an automatic, self-regulating valve that controls refrigerant flow based on the superheat of the vapor leaving the evaporator. It balances three forces on a flexible diaphragm:

1. Bulb Pressure ($P_{\text{bulb}}$): Sensed by a remote bulb clamped to the evaporator outlet pipe. It acts on top of the diaphragm, pushing to open the valve as superheat rises.
2. Evaporator Pressure ($P_{\text{evap}}$): Sensed internally or via an equalizer line. It acts underneath the diaphragm, pushing to close the valve.
3. Spring Pressure ($P_{\text{spring}}$): An adjustable spring underneath the diaphragm. It acts as a closing force and determines the superheat setpoint.

• External Equalizer: If an evaporator has a significant pressure drop across its coil, the pressure at the coil inlet is higher than at the outlet. An internally equalized valve would sense the higher inlet pressure, causing the valve to close prematurely and starve the evaporator. To prevent this, an external equalizer line is connected from the evaporator outlet to the chamber beneath the TXV diaphragm, ensuring the valve senses the true outlet pressure.

3. Float Valves (Low-Side vs. High-Side)

Float valves regulate flow mechanically using a buoyant float ball that rides on the liquid refrigerant level.

• Low-Side Float Valve: Installed on the low-pressure side of the system (e.g., in a flooded evaporator or surge drum). The float senses the liquid level directly at suction pressure. If the liquid level falls (due to boiling), the float drops, opening the valve to feed more liquid from the high-pressure line. If the level rises, the float rises, closing the valve.
• High-Side Float Valve: Installed in a chamber on the high-pressure side (downstream of the condenser). As liquid drains from the condenser and fills the chamber, the float rises, opening the valve and draining the liquid immediately to the low-pressure evaporator. This prevents liquid from backing up into the condenser coils and is common in flooded package chillers.
• Float Switches: In modern plants, mechanical float valves are often replaced by electric float switches (or level transmitters) that signal a controller to open or close a liquid-line solenoid valve.

---

Troubleshooting Expansion Devices

• Valve Hunting: This occurs when a valve constantly cycles between overfeeding and underfeeding, causing swinging suction pressures. It is typically caused by an oversized valve orifice, an uninsulated or poorly located sensing bulb (such as mounting it on a vertical line or at the bottom of a pipe where oil accumulates), or a superheat setting that is too low.
• Evaporator Starving: Characterized by low suction pressure, high superheat, and frost melting off the evaporator coil. It is caused by a plugged orifice (often due to water moisture freezing in the valve or oil wax deposits), a lost charge in the TXV sensing bulb, or a valve adjusted too tight (spring pressure set too high).
• Evaporator Flooding: Characterized by high suction pressure, low or zero superheat, and heavy frosting extending down the suction line. It is caused by a valve stuck open (due to debris on the needle seat), a ruptured equalizer diaphragm, or a valve adjusted too loose.

---

Safety Precautions and Compressor Protection

The primary safety concern when managing expansion devices is preventing liquid carryover. Because liquid ammonia cannot compress, any liquid entering a reciprocating compressor cylinder will cause a hydrostatic lock. This results in blown head gaskets, cracked pistons, bent connecting rods, and broken valves. In screw compressors, liquid carryover can dilute the lubricating oil, washing it out of bearings and causing rotor-to-rotor galling.

To prevent this, industrial low-sides are equipped with suction accumulators (suction traps) that intercept liquid carryover. These vessels must have high-level safety float switches that automatically trip the compressor offline if the liquid level rises above a safe operating limit.