FLOW CHARACTERISTICS OF HFC-134a IN AN ADIABATIC HELICAL CAPILLARY TUBE

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1 E HEFAT7 5 th International Conerence on Heat Transer, Fluid Mechanics and Thermodynamics Sun City, South Arica Paper number: KM1 FLOW CHARACTERISTICS OF HFC-1a IN AN ADIABATIC HELICAL CAPILLARY TUBE Khan M. K., Sahoo P.K.* and Kumar R. *Author or correspondence P. Bag 61, Department o Mechanical Engineering, University o Botswana, Gaborone, Botswana sahoopk@mopipi.ub.bw ABSTRACT In this paper, an attempt is made to model the rerigerants low through helical adiabatic capillary tubes used in domestic rerigerators and small residential air conditioners. The present study, based on homogenous two-phase low model, predicts the perormance o the helical capillary tube under adiabatic low conditions. The variation o dierent physical parameters like pressure, temperature, quality, void raction, velocity, and entropy with the length o adiabatic capillary tube has been investigated. The eect o varying capillary tube diameter and the pitch on pressure variation along the length is carried out. The simulation results are validated with experimental indings o the previous researchers or straight capillary tube as the literature lacks experimental work on helical capillary tube. It is ound that when subjected to similar conditions, the helical capillary tubes are shorter than their straight counterparts. INTRODUCTION The capillary tube is a commonly used expansion device in small vapour-compression rerigeration system, where the load is airly constant. It is a long simple hollow drawn copper tube with internal diameter ranging rom.5. mm and length varies rom 6 m. It is simple in construction, has no moving part, and requires no maintenance. In an adiabatic capillary tube, the subcooled liquid rerigerant enters the capillary and as the low progresses the pressure drops linearly because o riction. As the pressure alls below its saturation value, a part o it lashes into vapour. Further downstream o the lashing point, more and more vapour starts generating that causes the luid velocity to increase, which in turn gives rise to acceleration pressure drop. adiabatic capillary tubes have been extensively investigated by dierent researchers and some o the works are highlighted here. Marcy [1] employed graphical integration method to evaluate the adiabatic capillary tube length using the Moody s riction actor. Mikol [] established through low visualization that the low through the capillary tube is a homogenous two-phase low. Koizumi et al. [] used the low visualization to observe the rerigerant low through glass capillary tube and developed a method or calculating the length o two-phase low region. Melo et al. [] investigated experimentally the eects o the condensing pressure, size o capillary tube, degree o subcooling at the capillary tube inlet and the rerigerant types (R1, R1a and R6a) on the length o capillary tube. NOMENCLATURE A [m ] cross sectional area o capillary tube d [m] capillary tube internal diameter D [m] coil diameter T sub [K] degree o subcooling e/d [-] relative roughness F [-] riction actor G [kg/m s] mass velocity (ρv) h [J/kg] enthalpy k [-] entrance loss coeicient L [m] capillary tube length m [kg/s] mass low rate P [Pa] pressure p [m] pitch Re [-] Reynolds number (Gd/µ) s [J/kgK] entropy T [K] temperature V [m/s] luid velocity v [m /kg] speciic volume x [-] vapour quality Special characters α [-] void raction

2 µ [kg/m-s] viscosity ρ [kg/m ] density θ [rad] angle τ w [N/m ] Wall shear Stress (ρv /8) Subscripts F g g I sp c s liquid phase vapour phase liquid-vapour mixture capillary tube inlet single-phase two-phase coil straight Flow through coiled tubes is ar more complex phenomena than the low inside straight tubes. In helical capillary tube, in addition to the riction and acceleration pressure drop, there exists another pressure drop acting in the radial direction due the presence o centriugal orces. These centriugal orces give rise to secondary lows as shown in Figure 1. Dean [5] was the irst to conduct a theoretical study o incompressible luids lowing through curved pipes. Ito [6] proposed empirical correlations or the various low regimes inside helical pipe. Ali [7] presented various correlations available or helical coils. straight capillary tube as the literature lacks the experimental data on helical capillary tube. The REFPROP 7 database [8], which is based on the Carnahan-Starling-DeSantis equation o state, has been used to determine the thermodynamic and transport properties o the rerigerants. MATHEMATICAL MODELING In Figure, section 1 represents pressure drop due to sudden contraction at capillary inlet, section single-phase subcooled low, and section liquid-vapour two-phase low region. Assumptions used or the purpose o analysis are as ollows: the low is one dimensional, steady, adiabatic and homogenous in two-phase region, capillary tube is assumed to have constant cross section and roughness, and metastabilty is ignored. The present mathematical model is based on the conservation mass, momentum, and energy equations and is discussed in the ollowing paragraphs. In a steady state the conservation o mass or capillary tube can be written as m G = & = ρv = constant (1) A Applying momentum balance across a dierential element gives the pressure drop as Coil Axis Figure 1 Secondary low in the cross section o a helical capillary tube capillary tubes are hardly used in practice while the helical capillary tubes are widely used in domestic rerigerators and room air conditioners. Thereore, an attempt is made to model the adiabatic helical capillary tube, based on the homogenous two-phase low model. To the best o authors knowledge no work has been reported or helical capillary tubes. Thus, or validation purpose a separate model based on the homogenous two-phase model is developed or adiabatic 1, Figure Computational domain o adiabatic helical capillary tube. dp = ρ V dl + ρvdv d Eqn. () reduces to ()

3 d = ρ dp dl + dρ () G ρ For low through a coil, the critical Reynolds number is higher than that o a strait tube and is given by Ito [6] correlation. d Recrit = () D The low is turbulent or the given input conditions. Ito [6] riction actor correlations or turbulent low (i.e., Re > Re crit ) is given by.5 D d c =.9 +. Re (5) d D The single phase liquid length is evaluated by integrating equation (), and considering entrance eects, d Lsp = ( P1 P ) k (6) sp ρv where the entrance loss coeicient k=1.5. The two-phase region o the tubes, i.e.,, is divided into n number o small section with a uniorm pressure dierential dp across each section as shown in Fig.. Applying continuity equation between sections and V A V A m = & = (7) ν ν Applying steady low energy equation, with no external work, heat transer and potential energy, between sections and one can get V G h + = h + xh g + ( ν + xν g ) (8) Equation (8) is quadratic in x, hence, the quality x can be expressed as ( G ν ν + h ) g g h g G ν ν g + G ν V G ν g h + h x = (9) G ν The two phase riction actor or straight capillary tube can be calculated rom any o the correlations provided with Re is replaced by Re g Vd Re = () µ ν where µ is the two-phase dynamic viscosity, given by two-phase viscosity correlation by Mc Adams [9] 1 x 1 x = + (11) µ µ g µ Speciic volume or homogenous two-phase mixture v = v + xv g (1) and the mixture velocity V = Gν (1) The pressure at any section i is given by P i = P i dp (1) where P is the saturation pressure corresponding to the rerigerant temperature at capillary tube inlet, i.e., T. With the pressure P i corresponding quality, x i, can be calculated rom equation (9), the entropy at the i-th section can be determined rom s i = s + xis g (15) The incremental length (dl) is calculated sequentially. For each section pressure, temperature, quality, riction actor and entropy are calculated. It is ound that the entropy keeps on increasing until a maximum and then decreases. The moment it starts decreasing, the low becomes supersonic and the second law o thermodynamic is violated with decreasing entropy and the calculation is stopped at the point o maximum entropy. Integrating equation (), 1 P s max ρ P s max dρ L = + d dp P (16) P G ρ The incremental length o each section is calculated using d ρ i P ρ Li = + (17), i G ρi The total length o two-phase region is n L = L i i= 1 (18) Equation (17) is used to determine the elemental length o adiabatic capillary tube in two-phase region. The total twophase length o the helical adiabatic capillary is the summation o these elemental lengths as given by equation (18). The total length o capillary tubes is the sum o single and two-phase lengths. L = L sp + L (19) RESULTS AND DISCUSSION The simulation results are validated with experimental indings o the previous researchers or straight capillary tube as the literature lacks experimental work on helical capillary tube. Hence, a separate mathematical model or adiabatic straight capillary tube has been developed, which employs Churchill s riction actor correlation [] in place o equation

4 (5) o the helical capillary tube model. Churchill s riction actor correlation is given by the ollowing equation: = Re ( ) A + B () s where, 16 1 A =.57 ln (1).9 ( 7 Re).7( / ) + e d and B = () Re The present model is validated with the experimental data o Wijaya et al. [11], shown in Figure. The results o the present model or straight adiabatic capillary tube are in good agreement with the experimental data. In Figure, it can be seen that or same mass low rate the length o helical capillary tube is shorter than that o straight capillary tube d and d respectively. Figures 5 to represent the variation o physical parameters with adiabatic capillary tube lengths. Pressure (bar) 8 6 R-1a P k = 9 bar T sub = o C d =.77mm e =.75 µm D c = d p = 5d p = 5d p = d 1 Figure Eect o varying pitch o helical capillary tube on the length o capillary tube. 9 Wijaya et al. data 8 Mass low rate (kg/h) 8 7 R1a T in = 1.1 o C T cond = 7.8 o C D =.8 mm e/d = (by deault) p= 5D D c = D Pressure (bar) Figure Comparison o the present model with Wijaya et al. [11] experimental data. 1 Figure 5 Pressure variation along the length o capillary tube Figure shows the eect o pitch on the length o helical capillary tube. It is observed that the length o capillary tube increases with the pitch. This is because the coil riction actor reduces with increasing the pitch o helix. A parametric study o the adiabatic capillary tubes, both helical and straight, are conducted using rerigerant R-1a as the working luid lowing in a capillary o.77 mm diameter. The upstream pressure is 9 bar, degree o subcooling is o C, mass low rate is kg/h, and the relative roughness (e) is.75µm. The pitch and coil diameter o the helical capillary are Figure 5 shows the variation o pressure o rerigerant along the length o capillary tube. In single-phase subcooled region, the pressure drops linearly due to rictional eects only. As soon as the lashing starts, pressure drops rapidly. In the two phase region, in addition to rictional pressure drop, there exists the acceleration pressure drop as well. It is ound that the slope o two-phase region or helical capillary tube is higher than that o the straight capillary tube. For helical capillary tube the pressure drop is higher than that or a straight capillary tube

5 because o the additional pressure drop due to secondary lows in radial direction. Figure 6 shows the variation o temperature o rerigerant along the capillary tube. As the low inside the capillary tube is considered to be adiabatic, the temperature o the rerigerant remains constant as long as it is in liquid state. In the two-phase region the saturation temperature is a unction o saturation pressure, the temperature alls according to the pressure inside the tube. As the pressure drops at a aster rate in a helical capillary tube than that o a straight tube, the corresponding pressure also drops at a aster rate. tube. It is evident rom the igure that or same length o tube, the helical capillary tube will have higher vapour quality and void raction than a straight capillary tube. Void raction Temperature ( o C) -. 1 Figure 8 Void raction variation along the length o capillary tube - 1 Figure 6 Temperature variation along the length o capillary tube Figure 9 shows the velocity variation with the length rom the inlet o capillary. In subcooled region the velocity is constant. With the generation o vapour, the density o the luid reduces resulting in acceleration o the luid, because the mass low is constant Vapour quality..15. Velocity (m/s).5. 1 Figure 7 Vapor quality variation along the length o capillary tube Figure 7 and Figure 8 show the variation o vapour quality and void raction, respectively, along the length o capillary 1 Figure 9 Velocity variation along the length o capillary tube. In Figure, it can be seen that there is a linear increase in entropy o the lowing rerigerant in the single-phase region o

6 the capillary tube. In two-phase region o the capillary tube, the entropy increases rapidly with the generation o vapour. Ater a certain distance, the incremental length or same pressure drop becomes negligibly small and the corresponding entropy shoots up. For the above mentioned inputs, it is ound that the helical capillary tube is 1 % shorter than the straight capillary tube. Entropy (kj/kg-k) Figure Entropy variation along the length o capillary tube. CONCLUSIONS In the present work, Ito s riction actor correlation or coiled tubes has been used to evaluate the helical capillary tube length and Churchill s riction actor correlation or straight capillary tube. The present model is used to evaluate the length o both helical and straight adiabatic capillary tubes. The two geometries when subjected to the similar conditions, it is ound that the length o helical capillary tube is 1% shorter than that o the straight capillary tube. Moreover, it is ound that the length the capillary tube increases with the pitch o the helix. REFERENCES [1] Marcy, G.P., Pressure drop with change o phase in a capillary tube, Rerigerating Engineering, vol. 57, 199, pp [] Mikol, E.P., Adiabatic single and two-phase low in small bore tubes, ASHRAE Journal,196, pp [] Koizumi, H. and Yokoyama, K., Characteristics o rerigerant low in a capillary tube, ASHRAE Trans., vol. 86, 198, pp [] Melo C., Ferreira, R.T.S., Neto, C.B., Goncalves, J.M., Mezavila, M.M., An experimental analysis o adiabatic capillary tube, Applied Thermal Engineering, vol.19,1999, pp [5] Dean, W. R., Note on the motion o luid in a curved pipe, Phil. Mag,, Vol., 197, pp. 8 [6] Ito, H., Friction actors or turbulent low in curved pipes, Journal o Basic Engineering, D81, 1959, pp. 1-1 [7] Ali, S., 1,Pressure drop correlations or low through regular helical coil tubes, Fluid Dynamics Research, vol. 8: p. 95- [8] McLinden, M.O., Klein, S.A., Lemmon E.W., REFPROPthermodynamic and transport properties o rerigerants and rerigerant mixtures, NIST Standard Reerence Database version 7,. [9] McAdams, W.H., Wood, W.K., Bryan, R.L., Vaporization inside horizontal tubes. II. Benzene-oil mixture, Trans. ASME, Vol. 6, 19, pp. 19 [] Churchill, S.W., Frictional equation spans all luid low regimes, Chemical Engineering, Vol. 8, 1977, pp [11] Wijaya, H. Adiabatic capillary tube test data or HFC- 1a. Proceedings o the IIR- Purdue Conerence, West Laayette, USA, vol.1, pp.6-71, 199.

Mathematical Modelling for Refrigerant Flow in Diabatic Capillary Tube

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