Assessment on the use of common correlations to predict the mass-flow rate of carbon dioxide through capillary tubes in transcritical cycles

Capillary tubes are extensively used in small refrigeration and air-conditioning systems with synthetic refrigerants and hydrocarbons. For CO₂ transcritical applications, it has been shown that the capillary tube demonstrates an intrinsic capability of adjusting the upper pressure close to the optimal value in response to changes of gas-cooler heat sink temperature. The CO₂ flow rate through four capillary tubes of various lengths, diameters and materials was measured in a test rig. Each capillary tube was tested with inlet pressure varying from 7.5 MPa to 11 MPa and inlet temperature from 20 °C to 40 °C. Outlet pressure varied from 1.5 MPa to 3 MPa. The experimental results were validated against different numerical and approximate analytical solutions of the capillary tube equations. These models give good predictions only if the friction factor of the capillary tube is calculated accounting for its dependence on the tube roughness.