Understanding Liquid Undercooling in Vapour Compression Systems

In a vapour compression refrigeration system (VCRS), liquid undercooling, also known as subcooling, is the process of cooling the liquid refrigerant below its saturation temperature at the condenser pressure. This typically happens after the condenser and before the expansion valve.

Let's consider the basic steps of the VCRS cycle:

1. Compression: Low-pressure vapour refrigerant is compressed to a high-pressure, high-temperature vapour.
2. Condensation: High-pressure vapour cools down and condenses into a high-pressure liquid.
3. Expansion: High-pressure liquid passes through an expansion valve, reducing its pressure and temperature, causing a portion to flash into vapour.
4. Evaporation: Low-pressure liquid/vapour mixture absorbs heat from the refrigerated space, evaporating completely into a low-pressure vapour before returning to the compressor.

Undercooling happens at the end of step 2, where the liquid is cooled further below its condensation temperature.

Effect of Undercooling on Refrigerating Effect and COP

The refrigerating effect is the amount of heat absorbed by the refrigerant in the evaporator. Per unit mass of refrigerant, it is the difference in enthalpy between the state leaving the evaporator ($\text{h}_1$) and the state entering the evaporator ($\text{h}_4$).

Refrigerating Effect ($\text{Q}_\text{e}$) = $\text{h}_1 - \text{h}_4$

In the expansion valve, the process is isenthalpic, meaning the enthalpy remains constant ($\text{h}_3 = \text{h}_4$), where $\text{h}_3$ is the enthalpy of the refrigerant entering the expansion valve.

When liquid refrigerant is undercooled before the expansion valve, its enthalpy ($\text{h}_3$) is reduced compared to saturated liquid enthalpy at the condenser pressure. Since $\text{h}_4 = \text{h}_3$, the enthalpy of the refrigerant entering the evaporator ($\text{h}_4$) is also reduced.

Assuming the state leaving the evaporator ($\text{h}_1$) remains the same (which is a common assumption, as the evaporator conditions are usually fixed by the application requirements), the refrigerating effect ($\text{h}_1 - \text{h}_4$) increases because $\text{h}_4$ is lower.

The compressor work input per unit mass of refrigerant is the difference in enthalpy between the state leaving the compressor ($\text{h}_2$) and the state entering the compressor ($\text{h}_1$).

Work Input ($\text{W}_\text{c}$) = $\text{h}_2 - \text{h}_1$

Undercooling primarily affects the liquid line and typically does not significantly change the conditions at the compressor inlet ($\text{h}_1$). The discharge state ($\text{h}_2$) might change slightly, but the change in work input is often smaller in magnitude compared to the increase in refrigerating effect.

The Coefficient of Performance (COP) of the refrigeration system is defined as the ratio of the refrigerating effect to the work input:

$\text{COP} = \frac{\text{Refrigerating Effect}}{\text{Work Input}} = \frac{\text{h}_1 - \text{h}_4}{\text{h}_2 - \text{h}_1}$

Since undercooling increases the refrigerating effect ($\text{h}_1 - \text{h}_4$) and the work input ($\text{h}_2 - \text{h}_1$) changes less significantly (or may even slightly decrease), the overall COP of the system increases.

Analyzing the Options

• Option 1: "increase the vapour superheat". Subcooling occurs in the liquid line, not the suction line entering the compressor. It does not directly increase the superheat leaving the evaporator (assuming constant evaporator conditions).
• Option 2: "reduce refrigerating effect". As explained above, undercooling increases the refrigerating effect.
• Option 3: "increase COP". By increasing the refrigerating effect with minimal change in work input, the COP increases. This aligns with our analysis.
• Option 4: "decrease COP". This is the opposite of the actual effect.

Therefore, the effect of liquid refrigerant undercooling is to increase the COP of the vapour compression refrigeration system.