This work presents a numerical model to simulate refrigerant flow through capillary tubes, commonly used as expansion devices in refrigeration systems. The flow is divided in a single-phase region, where the refrigerant is in the subcooled liquid state, and a region of two-phase flow. Due to compressibility of the flow in the two-phase region, critical or choked flow condition is generally found in capillary tubes.

For the present model the capillary tube is considered straight and horizontal. The flow is taken as one-dimensional and adiabatic. Steady state condition is also assumed and the metastable flow phenomena are neglected. In the single phase region, the refrigerant pressure and temperature are calculated by solving the mass and momentum conservation equations.

The two-fluid model, considering the hydrodynamic and thermal non-equilibrium between the liquid and vapor phases, is applied to the two-phase flow region. In this region, the conservation equations for the mass of the mixture, momentum of the liquid phase, momentxun of the vapor phase, energy of the mixture and energy for the vapor phase, are solved for the liquid velocity, vapor velocity, pressure, void fraction and liquid temperature.

Closure of the governing equations is performed with the friction factor correlation for the single-phase region and constitutive equations for the terms related with the transport of mass, momentum and energy between the phases

The system of differential equations is solved using a 4th order Runge-Kutta method. Choked flow is assumed at the tube exit where dp/dz is taken as minus infinity. Numerically this conditions is implemented by evaluating dp/dz at each location along the tube until it becomes positive indicating that the maximum absolute value has been reached.

The solution of the system of differential equations is performed along the tube until the flow is choked, or until the evaporation pressure is reached, if the flow is not choked. From the model the length of capillary tube can be obtained, from known mass flow rate and operating.

In the latter case, the numerical procedure is iterative, wherein the mass flow is adjusted so that the flow blocking section coincides with the end of the tube.

 The model was validated by comparing the results with experimental data in dispomVeis Research Center Refrigeration, Ventilation and Air Conditioning Department of Mechanical Engineering, Federal University of Santa Catarina. The mass flow and pressure distributions along two capillaries operating with HFC-134a at different operating conditions were used in this comparison. It also presents a detailed analysis of the influence of the constitutive equations and some empirical parameters of the model results. The mean absolute error obtained between the calculated critical mass flow rates and measures was 2.4% and among the values ​​of the lengths of the capillary tube calculated and measured was 4.5%.

The two-fluid model enables a more realistic two-phase flow within the capillary tube. However, this sophistication requires the use of a greater number of constitutive equations in relation to the homogeneous model. Some computational results for the title, void fraction, velocity and temperature of each phase are presented and discussed. The model is also used to show the relationship between the mass flow rate, tube length and diameter, degree of subresfiiamento and condensing pressure.