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The capillary tube is the simplest form of control for refrigerant flow in a refrigeration system. Capillary tubes are extremely fine inner diameter round tubes, in the range of 0.5 -2 mm. Since capillary tubes are simple, have no moving parts, are inexpensive, and allow the pressures in the system to equalize during the off cycle, the capillary tube is used in almost all small refrigeration systems, such as household refrigerators, dehumidifiers, and room air-conditioners.

Figure 1 shows the typical pressure distribution of refrigerant 22 flowing through a capillary tube. The ordinate on the right is a saturated temperature scale corresponding to the pressure scale along the left axis. The flow can be divided into four regions: a subcooled liquid region, a metastable liquid region, a metastable two-phase region and an equilibrium two-phase region. The flow enters the capillary tube in a subcooled liquid condition. Once the pressure drops down to the saturated condition, a metastable (superheated) liquid flow occurs for a short distance until the onset of vaporization (Mikol 1963, Li et al. 1990, Lin et al. 1991, ASHRAE 1994). The prcssure drop is linear and the temperature is constant in these liquid regions (al-b-c2). At point c2, the vapor bubbles form first. The superheated liquid releases heat to the saturated bubble which produces a saturated liquid state. In this metastable two-phase region, the evaporating flow can be characterized by three different fluids: superheated liquid, saturated liquid and saturated vapor (Feburie et al. 1993). When all of the superheated liquid changes to saturated liquid, the flow becomes a thermodynamic equilibrium two-phase flow. The pressure drop is then exponential (c2-d-e) due to acceleration and two-phase friction effects. The flow is usually choked at the tube exit.

There have been several theoretical studies of adiabatic capillary tube flows. The models developed in very early years (Marcy 1949, Hopkins 1950, Prosek 1953, Whitesel 1957, Cooper et al. 1957, Niaz and Davis 1969, Erth 1969, Rezk and Awn 1979, Koizumi and Yokoyama 1980, Goldstein 1981, Rizza 1982) do not consider the metastable flow. It is well established that the metastable condition has to be accounted for in analytical studies to avoid a significant underestimation of the mass flow rate of refrigerant. More recent studies by Maczek et al. (1983) and Kuijpers and Janssen (1983) have been made on the effects of nonequilibrium metastable flow on capillary tube flow. The two-phase flow model was assumed to be homogenous. The liquid superheat and flashing delays were accounted for in the model. In 1990 Kuehl and Gold- Schmidt (1990) conducted a series of experiments using R-22 as the refrigerant and developed empirical equations. Later, Kuehl and Goldschmidt (1 991) proposed a steady-state capillary flow model and found that the metastable region must bc considered to obtain good agreement with experimental data. Escanes et al. (1995) developed a capillary flow model for both transient and steady situations. However, the metastable region was neglected in this formulation.

In this paper, a theoretical model is developed that allows a realistic simulation of adiabatic capillary flow. Empirical data, such as transport coefficients and the underpressure in the metastable region, are needed in order to apply this model. The calculated results are compared with the empirical equations for R-22 proposed by Kuehl and Goldschmidt (1990) and with the ASHRAE design charts. Rating correlations for R-134a flowing through adiabatic capillary tubes are also developed using the model.