Mathematical Modeling for Adiabatic Flow of Refrigerant in Helical Capillary Tube

Abstract

Present work has been carried out to investigate the flow characteristics of refrigerants R-407 C, R-134a, R-410 A, R-12 and R-404 A flowing through helical capillary tube under adiabatic flow conditions. The parametric study was conducted by varying operating conditions and geometrical parameters of the capillary tube. A mathematical model has been developed to predict the performance of a refrigerant in helical capillary tube under adiabatic flow conditions. The proposed model can predict the length of the adiabatic helical capillary tube for a given mass flow rate or the mass flow rate through a given length of capillary tube. A computer program coded in MATLAB has been developed to compute either length or mass flow rate by fixing some of parameter. This model also includes the effect of various design parameters, like capillary tube diameter, capillary tube coil diameter, degree of sub-cooling, evaporator pressure, inlet pressure, mass flow rate. Thermodynamic and transport property can derived from advanced property data base such as REFPROP. The mathematical model based on homogenous two phase flow without considering metastable length has been developed to predict the flow characteristics of a refrigerant in helical capillary tube for adiabatic flow conditions. A set of differential equations is obtained by applying the law of conservation of mass, momentum and energy. These differential equations are solved using finite difference method. Different correlations for friction factor and viscosity available in the literature are used in the model. Performance of conventional and non conventional refrigerants can be compared under different operating conditions. The developed model can be considered as an effective tool for designing and optimizing capillary tubes working with newer alternative refrigerants. The model is validated by comparison with the experimental data of Kim et al. (2002) for R-22, R-407C and R-410A, Zhou and Zhang (2006) for R-22 and Khan et al (2009) for R-134a. The results obtained from the present model show reasonable agreement with the experimental data. The proposed model can be used to design helical capillary tubes working with various refrigerants.