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Description
INTRODUCTION
The capillary tube is a commonly used expansion device for low-capacity vapor-compression refrigeration systems where the cooling load is fairly constant. It is a long, simple, hollow, drawn copper tube with internal diameter ranging from 0.5 to 2.0 mm and length varying from 2 to 5 m. In a refrigeration system, the refrigerant often enters the capillary in the subcooled condition. As the liquid refrigerant enters the capillary, the pressure of the refrigerant drops linearly due to friction, and as the pressure falls below the saturation pressure, part of the refrigerant flashes from liquid phase to to vapor phase. The inception of vaporization onsets two-phase flow in the capillary tube. This causes an increase in fluid velocity as well, which causes more friction and acceleration of the pressure drop, resulting in flashing of more liquid from liquid phase to to vapor phase.
Owing to its simplicity and low cost, the capillary tube as an expansion device in a vapor compression system has been widely explored. To facilitate system designers, Staeblar (1948) developed a capacity balance chart for various combinations of compressor displacement and capillary resistance. Mikol (1963) experimentally studied the two-phase flows of refrigerants R-12 and R-22 inside an adiabatic capillary tube. Melo et al. (1999) conducted experiments to study the effects of condensing pressure, capillary tube size, and degree of subcooling at capillary inlet for different refrigerants (R-12, R-134a, and R-600a). Bansal and Rupasinghe (1998) developed a numerical model, CAPIL, to compute the length of an adiabatic straight capillary tube using finite difference methods. Wongwises and Pirompak (2001) presented a model to predict the flow of refrigerants and zeotropes in a straight adiabatic capillary tube. It has been noted that curved capillary tubes have drawn very little attention from researchers and the studies are mainly confined to straight adiabatic capillary tubes only. An attempt to study the flow of refrigerant R-22 through an adiabatic coiled capillary tube was made by Kuehl and Goldschmidt (1990); it was concluded that irrespective of the percentage of the overall length coiled or the phase of refrigerant (liquid or two-phase mixture), the resistance to the flow is increased due to the coiling. They found that the mass flow rate of the coiled capillary was about 5% lower than that of a straight capillary tube. It is a known fact that flow through a coiled tube is a comparatively far more complex phenomenon than that through a straight tube. In fact, the pressure loss during flow through a curved tube is larger than that during flow through a straight tube under similar conditions. In addition to the frictional pressure drop, the radial pressure drop is also present, which exists in a spiral capillary tube due to the presence of the centrifugal force in such tubes. Dean (1927) was the first to conduct a theoretical study of incompressible fluids flowing through curved pipes; he proposed a nondimensional number, [Re(d/D).sup.0.5], known as the Dean number (De) to signify the secondary flow in the cross section of the coiled tube. A comprehensive review of the work on flow through curved pipes and tubes has been done by Ali (2001).
Due to the scarcity of a reliable and comprehensive model of an adiabatic spiral capillary tube to compute the length and predict the flow characteristics of refrigerants for a given set of input parameters, the present study was undertaken.
MATHEMATICAL MODELING
The flow of refrigerant through an adiabatic spiral capillary tube has been divided into two distinct regions, the single-phase subcooled liquid region and the two-phase liquid-vapor region. A schematic diagram of a spiral capillary tube is shown in Figure 1a. The section 1,2 represents the pressure drop due to the sudden contraction at capillary inlet; in section 2--3, single-phase subcooled flow takes place; and section 3--4 represents the liquid-vapor two-phase flow region.
[FIGURE 1 OMITTED]
During the analyses of the adiabatic capillary tubes, it is assumed that the capillary tube is of uniform cross section and surface roughness. Further, the flow through the capillary tube is considered one dimensional, steady, and adiabatic homogeneous two-phase flow, and the phenomenon of metastability is ignored. It is also assumed that a pure refrigerant is flowing through the capillary tube and there exists thermodynamic equilibrium inside the capillary tube.
In Figure 1b an infinitesimal fluid element of length dL inside a capillary tube is shown. Applying the momentum conservation equation on the fluid element and assuming constant mass velocity of refrigerant, Equation 1 is evolved (Wongwises and Pirompak 2001):
P*A - (P + dP)*A - [[tau].sub.w]([pi]d)dL = GAdV (1)
Equation 1 reduces to
- dP = [f/[2d]][rho][V.sup.2]dL + [rho]VdV. (2)... |
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