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Abstract
In this article, the influence of different mean void fraction correlations on a shell-and-tube evaporator dynamic model performance has been evaluated. The model proposed is based on the moving-boundary approach and includes expansion valve modeling. Several transient tests, using R134a as working fluid, have been carried out varying refrigerant mass flow, inlet enthalpy, and secondary fluid flow. Then model performance, using different mean void fractions, is analyzed from the system model outputs (evaporating pressure, refrigerant outlet temperature, and condensing water outlet temperature). The slip ratio expressions selected are a homogenous and momentum flux model and Zivi, Chisholm, and Smith correlations. The results of the comparison between experimental and model predictions depend on the transient characteristics, and there is not a single slip ratio correlation that provides the best performance in all the cases analyzed.
Nomenclature
| A | = | area (m2) |
| AK | = | expansion valve parameter (m2) |
| BK | = | expansion valve parameter (m2 K−1) |
| cp | = | specific heat capacity (J kg−1 K−1) |
| D | = | diameter (m) |
| f | = | friction coefficient |
| F | = | Chen's forced convection correction factor |
| h | = | specific enthalpy (J kg−1) |
| k | = | thermal conductivity (W m−1 K−1) |
| kA | = | expansion valve parameter (m2) |
| L | = | evaporator zone length (m) |
| m | = | mass (kg) |
| = | refrigerant mass flow rate (kg s−1) | |
| n | = | summation upper bound |
| N | = | compressor speed (rpm) |
| P | = | pressure (Pa) |
| Pr | = | Prandtl number |
| = | cooling power (W) | |
| Re | = | Reynolds number |
| S | = | slip ratio |
| sf | = | Chen's suppression factor |
| T | = | temperature (K) |
| t | = | time (s) |
| u | = | dynamic viscosity (μPa s) |
| = | volumetric flow rate (m3 s−1) | |
| x | = | vapor quality |
| Xtt | = | Martinelli parameter |
Greek symbols
| α | = | heat transfer coefficient (W m−2 K−1) |
| γ | = | mean void fraction |
| ΔT | = | degree of superheating (K) |
| ΔTstatic | = | static degree of superheating (K) |
| μ | = | density ratio |
| ρ | = | density (kg/m3) |
| σ | = | vapor–liquid surface tension (N m−1) |
| υ | = | specific volume (m3 kg−1) |
Subscripts
| 1e | = | evaporation zone |
| 2e | = | superheating zone |
| actual | = | experimental value |
| bf | = | two-phase |
| c | = | condensing |
| cat | = | catalog |
| Ch | = | Chisholm's correlation |
| conv | = | convective |
| cs | = | cross-section |
| e | = | evaporator |
| ex | = | external |
| g | = | glycol–water mixture |
| h | = | homogenous model |
| i | = | inlet |
| in | = | internal |
| k | = | k-value of a dataset |
| L | = | saturated liquid |
| LV | = | liquid to vapor |
| M | = | metal surface |
| max | = | maximum |
| min | = | minimum |
| MF | = | momentum flux model |
| nb | = | nucleate boiling |
| r | = | refrigerant |
| s | = | shell |
| Sm | = | Smith's correlation |
| t | = | tube |
| Te | = | total evaporator length |
| o | = | outlet |
| V | = | saturated vapor |
| VS | = | vapor to superheating |
| Z | = | Zivi's correlation |
Acronyms
| FV | = | finite-volume distributed-parameter model |
| MB | = | moving-boundary model |
| MVF | = | mean void fraction |
| PID | = | proportional integral derivative |
| RMS | = | root mean square value |