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Abstract
This work presents a dynamic model for a CO2 heat pump gas cooler. The gas cooler model is based on the conservation equations of energy, mass, and momentum. Due to the importance of an expansion device and a compressor for heat exchanger modeling, detailed mathematical treatment is also given to those devices. The spatial variations of temperature, pressure, specific volume, and mass flow rate are predicted at each time step. The model is validated by comparing simulation results and experimental data for transient and steady conditions. It observes a reasonably good agreement between these results, with a maximum deviation of 2°C (3.6°F) between the mathematical model and experimental data, with the test data exhibiting a fairly similar trend. The developed model is therefore presented as a useful tool for analyzing the dynamic behavior for the gas cooler of a heat pump operating with CO2.
Nomenclature
| A | = | heat transfer area (m2) |
| cp | = | specific heat (J kg−1 K−1) |
| d | = | tube diameter (m) |
| dh | = | hydraulic diameter (m) |
| f | = | friction factor |
| g | = | acceleration of gravity (m s−2) |
| G | = | mass velocity (kg s−1m−2) |
| h | = | specific enthalpy (kJ kg−1) |
| H | = | heat transfer coefficient (W m−2K−1) |
| K | = | conductivity (W m−1K−1) |
| = | mass flow rate (kg s−1) | |
| N | = | rotational speed (rpm) |
| P | = | pressure (pa) |
| pe | = | perimeter (m) |
| Pr | = | Prandtl number |
| Re | = | Reynolds number |
| t | = | time (s) |
| T | = | temperature (K) |
| v | = | specific volume (m3 kg−1) |
| V | = | piston volumetric displacement (m3 h−1) |
| x | = | quality |
| z | = | heat exchanger length (m) |
Greek symbol
| α | = | void fraction |
| η | = | efficiency |
| θ | = | flow inclination |
| ρ | = | specific mass (kg m−3) |
Subscripts
| 1 | = | input |
| 2 | = | output |
| c | = | critical |
| comp | = | compressor |
| e | = | external |
| eq | = | equivalent |
| f | = | primary fluid |
| i | = | internal |
| is | = | isentropic |
| nv | = | needle valve |
| t | = | wall tube |
| v | = | vapor |
| vol | = | volumetric |
| w | = | water |
Superscripts
| 0 | = | initial value |