Dias et al. 314 / Vol. XXXIII, No. 3, July-September 2011 ABCM João Paulo Dias jpdias@polo.ufsc.br Federal University of Santa Catarina Department of Mechanical Engineering 88040-900 Florianópolis, SC, Brazil José Luiz Gasche gasche@dem.feis.unesp.br São Paulo State University – College of Ilha Solteira Department of Mechanical Engineering 15385-000 Ilha Solteira, SP, Brazil André Luiz Seixlack andre@dem.feis.unesp.br São Paulo State University – College of Ilha Solteira Department of Mechanical Engineering 15385-000 Ilha Solteira, SP, Brazil Mathematical Modeling of the Ester Oil-Refrigerant R134a Mixture Two- Phase Flow with Foam Formation Through a Small Diameter Tube This work presents a mathematical modeling to study the ester oil ISO VG-10- refrigerant R134a mixture two-phase flow with foam formation through a 3.22 mm ID tube. Based on experimental visualization results, the flow is divided into three regions: a single phase flow at the inlet of the tube; an intermediary bubbly flow region; and a foam flow region at the end of the tube. Numerical results for mass flow rate, pressure and temperature distributions along the flow were compared with experimental data available in literature, showing good agreement. The major discrepancy between the mass flow rate data was about 21%. These results show that the mathematical modeling worked well for predicting the overall characteristics of the flow and can be generically used to other oil-refrigerant mixtures. Keywords: oil, refrigerant, mixture, compressor, foam Introduction 1 The vapor compression refrigeration system is the most widely used method of producing cooling effects for both air conditioning and food refrigeration industries. This type of system is composed basically of four mechanical components: compressor, evaporator, condenser, and expansion device. Two important fluids complete the system: the refrigerant, which is responsible for the heat exchanges that occur in the condenser and evaporator, and the lubricant oil, whose main purpose is to reduce the friction among the compressor sliding parts. These two fluids are in constant physical interaction inside the components of the system, producing the formation of a mixture consisting of lubricant oil and refrigerant. The formation of this mixture brings advantages and disadvantages. It is well known that a good miscibility between refrigerant and lubricant oil is required to allow easy return of circulating oil to the compressor, which benefits evaporators, condensers, and expansion devices. In addition, high refrigerant absorption rates in the oil are desirable to diminish the equalizing pressure, which reduces torque and power required for compressor start-up (Prata and Barbosa, 2007). On the other hand, this miscibility can modify the lubrication of sliding parts, the performance of journal bearings, and the leakage of refrigerant gas through the compressor clearances. For example, reduction in load capacity of compressor journal bearings has been observed when oil-refrigerant mixture flow model is used rather than pure oil flow model (Grando, Priest and Prata, 2005). Two types of mixture can be found in the system. In the evaporator, condenser, and expansion device, where a large amount of refrigerant circulates, a refrigerant-rich mixture is found. The concentration of oil in this type of mixture is small, usually less than 10%. However, the oil can affect the heat exchangers performance taking into account that, at high vapor quality, the amount of oil in the liquid phase can achieve values much higher than 10%. Otherwise, inside the compressor, where lubricant oil is the predominant fluid, an oil-rich mixture prevails. In this case, the oil concentration ratio is commonly larger than 70%. A literature review on oil-refrigerant mixture studies shows that more emphasis has been given to refrigerant-rich mixtures: Schlager, Pate and Bergles (1987), Eckels and Pate (1991), Hambraues (1995), Cho and Tae (2000), Cho and Tae (2001), Bassi Paper received 28 July 2009. Paper accepted 10 June 2010. Technical Editor: José Parise and Bansal (2003), Chen, Won and Wang (2005), and Bandarra Filho, Cheng and Thome (2009). The purpose of these works has been mainly to analyze the oil influence in pressure drop and heat transfer coefficient in condensers and evaporators. Nomenclature a = constant of Equation 9, dimensionless b = constant of Equation 9, dimensionless c = constant of Equation 9, dimensionless d = constant of Equation 9, dimensionless f = Darcy friction factor, dimensionless G = mass flux, kg m -2 s -1 m & = mass flow rate, kg s -1 n = foam behavior index, dimensionless p = pressure, Pa R = tube internal radius, m r = radial coordinate, m T = temperature, o C u = longitudinal flow velocity, m s -1 u s = foam slip velocity at the tube wall, m s -1 u 0 = foam velocity in the plug flow region, m s -1 x = mass quality, dimensionless z = tube longitudinal coordinate, m w = refrigerant mass fraction, kg refrig kg mixt -1 w sat = solubility of refrigerant in oil, kg refrig kg mixt -1 Greek Symbols α = void fraction, dimensionless δ s = liquid layer thickness, m ε = tube internal roughness, m φ = metastability factor, dimensionless κ = foam solidity index, Pa s n μ = absolute viscosity, Pa s ρ = density, kg m -3 σ = standard deviation τ e = foam yield stress, Pa τ rz = shear stress, Pa Subscripts lr = relative to liquid refrigerant l = relative to liquid phase in = relative to inlet