5.1. Gas heat pump and refrigeration cycle

Gas heat pumps and gas regrigerators are basically following the reverse Brayton cycle (or Joule cycle).

_images/BraytonReverse.png

Figure 5.1: Reverse Brayton cycle for gas refrigeration.

As for any heat pump or refrigerator, (Eq.2.11, and Eq.2.10) the coefficients of performance of Reverse Brayton cycle are:

COP_{R,Joule} = \frac{1}{\frac{|q_{23}|}{|q_{41}|}-1} \qquad \text{and} \qquad COP_{HP,Joule} = \frac{1}{1-\frac{|q_{41}|}{|q_{23}|}}

Considering the working fluid as an ideal gas, and because no machine is working in transformations 2-3 and 4-1, application of the balance energy equation reads:

|q_{23}| = \dot{m} c_p (T_2-T_3) \qquad \text{ and } \qquad |q_{41}| = \dot{m} c_p (T_1-T_4)

such that the COPs of Reverse Brayton cycle become:

COP_{R,Joule} = \frac{1}{\frac{T_2-T_3}{T_1-T_4}-1} \qquad \text{and} \qquad COP_{HP,Joule} = \frac{1}{1-\frac{T_1-T_4}{T_2-T_3}}

As for gas turbine, it is possible to determine gas temperatures after the compressor and the turbine thanks to isentropic relations for ideal gases:

\frac{T_1}{T_2} = \frac{p_2}{p_1}^{\frac{1-\gamma}{\gamma}} = \frac{p_3}{p_4}^{\frac{1 - \gamma}{\gamma}} = \frac{T_4}{T_3}

we finally obtain:

(5.1)COP_{R,Joule} = \frac{1}{r_p^{\frac{\gamma-1}{\gamma}}-1} \qquad \text{and} \qquad COP_{HP,Joule} = \frac{1}{1-r_p^{\frac{1-\gamma}{\gamma}}}

where r_p=\frac{p_2}{p_1} is the pressure ratio.

_images/COPJoule.png

Figure 5.2: COP for reverse Brayton cycle (Joule cycle) for heat pump or refrigerators as a function of the pressure ratio for IG with \gamma=1.4.

Figure 5.2: reveals that the performance of such machine is good for low pressure ratio.

Remarks

  • As for gas turbine, it is possible to easily account for the adiabatic compressor and adiabatic turbine irreversibilities by using the isentropic efficiency of both components (see Section 4.2.3: ).

  • It is also possible to improve the cycle using regeneration (see Section 4.2.4: )

  • Heat pumps and Refrigerators using the reverse Brayton cycle have low performances and are used only for specific applications.