Revenge of the Fridge: Vapor Compression Strikes Back

DOFPro Team

Between the time the narrator finished recording the narration and the final editing of the video, we came across the CoolProp property package in DWSIM. Its main purpose is to provide accurate calculation of refrigerant properties in refrigeration cycles. The narration states that no such method exists in DWSIM. We were unable to re-record the narration, but we were able to rerun the calculations using CoolProp. The displayed values are the CoolProp values, but they do not agree with the narration. We point out visually whenever we had to make these corrections.

This video explains

• The coefficient of performance
  • For a refrigerator
  • For a heat pump
• The vapor compression cycle calculations

\(T_\mathrm{hot}\)

\(T_\mathrm{cold}\)

\(|Q_\mathrm{hot}|\)

\(|W|\)

\(|Q_\mathrm{cold}|\)

In a heat engine you want to generate work. You do so by converting as much of the high-temperature heat as possible into work. The efficiency of any heat engine operating between two heat reservoirs is defined as:

\[\eta \equiv \frac{|W|}{|Q_\mathrm{hot}|}\]

Again, it’s what you want divided by what you pay for. The efficiency of a Carnot engine is:

\[\eta \equiv \frac{|W|}{|Q_\mathrm{hot}|} = 1 - \frac{T_\mathrm{cold}}{T_\mathrm{hot}}\]

\(T_\mathrm{hot}\)

\(T_\mathrm{cold}\)

\(|Q_\mathrm{hot}|\)

\(|Q_\mathrm{cold}|\)

\(|W|\)

In a refrigerator, we want to remove heat at a cold temperature. We do so by putting in work. The coefficient of performance for a refrigerator is the heat removed at the low temperature divided by the work that you have to put in,

\[\dfrac{|Q_\mathrm{cold}|}{|W|} = \omega = \text{C.O.P.}\]

Again, it’s what you want divided by what you pay for. The coefficient of performance for a Carnot refrigerator is

\[\dfrac{|Q_\mathrm{cold}|}{|W|} = \dfrac{T_\mathrm{cold}}{T_\mathrm{hot} - T_\mathrm{cold}}\]

\(T_\mathrm{hot}\)

\(T_\mathrm{cold}\)

\(|Q_\mathrm{hot}|\)

\(|Q_\mathrm{cold}|\)

\(|W|\)

In a heat pump, we want to supply heat at a warm temperature. We do so by putting in work. The coefficient of performance for a heat pump is the heat supplied at the warm temperature divided by the work that you have to put in,

\[\dfrac{|Q_\mathrm{hot}|}{|W|} = \omega = \text{C.O.P.}\]

Again, it’s what you want divided by what you pay for. The coefficient of performance for a Carnot heat pump is

\[\dfrac{|Q_\mathrm{hot}|}{|W|} = \dfrac{T_\mathrm{hot}}{T_\mathrm{hot} - T_\mathrm{cold}}\]

Vapor Compression Cycle

Vapor Compression Cycle

\(|\dot{Q}_\mathrm{hot}|\ \uparrow\)

\(|\dot{Q}_\mathrm{cold}| \uparrow\)

\(|\dot{W}_s|\)

Evaporator

\(\ \ \ \ \ \ \dot{Q}_\mathrm{cold} = \dot{m} \Delta \hat{H} = \dot{m} \left(\hat{H}_\mathbf{b} -\hat{H}_\mathbf{a} \right)\)

Inlet enthalpy comes from isenthalpic valve.

Outlet enthalpy is saturated vapor at \(T_\mathrm{evap}\), \(P_\mathrm{evap}\).

Compressor

\(\ \ \ \ \ \ \dot{W}_s = \dot{m} \Delta \hat{H} = \dot{m} \left(\hat{H}_\mathbf{c} -\hat{H}_\mathbf{b} \right)\)

Inlet enthalpy, entropy are from saturated vapor at \(T_\mathrm{evap}\), \(P_\mathrm{evap}\).

Outlet enthalpy comes from property table at \(P_\mathrm{comp}\), \(\hat{S}_\mathbf{c}\).

For isentropic, \(\hat{S}_\mathbf{c} = \hat{S}_\mathbf{b}\)

\(|\dot{Q}_\mathrm{hot}|\ \uparrow\)

\(|\dot{Q}_\mathrm{cold}| \uparrow\)

\(|\dot{W}_s|\)

Condenser

\(\ \ \ \ \ \ \dot{Q}_\mathrm{hot} = \dot{m} \Delta \hat{H} = \dot{m} \left(\hat{H}_\mathbf{d} -\hat{H}_\mathbf{c} \right)\)

Inlet enthalpy comes from compressor.

Outlet enthalpy is saturated liquid at \(T_\mathrm{cond}\), \(P_\mathrm{cond}\).

Throttling Valve

\(\ \ \ \ \ \ \Delta \dot{H}_s = 0 \implies \hat{H}_\mathbf{a} = \hat{H}_\mathbf{d}\)

Outlet quality comes from property table at \(T_\mathrm{evap}\), \(P_\mathrm{evap}\).

Vapor Compression Cycle

Rankine Cycle

Pressure-Enthalpy Diagram

Vapor Compression DWSIM

The Takeaways

1. The purpose of a refrigerator is to remove heat at a low temperature and reject it at a high temperature. Its coefficient of performance is the magnitude of the heat removed over the magnitude of the work required.
2. The purpose of a heat pump is to take heat at a low temperature and supply it at a high temperature. Its coefficient of performance is the magnitude of the heat supplied over the magnitude of the work required.
3. Carnot refrigerators and heat pumps are modeled as Carnot engines running backwards.
4. The most common refrigeration cycle is the vapor compression cycle, essentially a Rankine cycle running in reverse.

Thanks for watching!
The previous video in the series is in the link in the upper left. The next video in the series is in the upper right. To learn more about Chemical and Thermal Processes, visit the website linked in the description.

The DOFPro Team