FLOW CHARACTERISTICS = OF - R-407C IN ADIABATIC AND DIABATIC COILED CAPILLARY TUBES

Abstract

Present research work has been carried out to investigate the flow characteristics of refrigerant R-407C flowing through straight, helical and spiral capillary tubes under adiabatic and diabatic flow conditions. The parametric study was conducted by varying operating conditions and geometrical parameters of the capillary tubes. The experimental data obtained from the present work have been used to develop separate non-dimensional empirical correlations for the prediction of refrigerant mass flow rate of R-407C flowing through straight, helical and spiral capillary tubes under adiabatic and diabatic flow conditions. The empirical correlations have been validated with the experimental data of previous researchers. The mathematical models have also been developed for each capillary tube geometry under adiabatic and diabatic flow conditions. These models have been validated with the present and previous experimental results available in the literature. Further, these mathematical models have been used to develop capillary tube selection charts for refrigerant R-407C. The capillary specifications and experimental conditions used in the present study are given in Table I and 2 for adiabatic and diabatic flow conditions respectively. Table 1 Range of parameters for adiabatic flow conditions parameters straight capillary tube helical capillary tube spiral capillary tube capillary tube diameter, d,, mm 1.02, 1.27, 1.52 1.02, 1.27, 1.52 1.02, 1.27, 1.52 capillary tube length, L, m 1.0, 1.5, 2.0 1.0, 1.5, 2.0 1.0, 1.5, 2.0 helical coil diameter, D, mm -- 60, 100, 140 -- spiral coil pitch, p, mm -- -- 20, 60, 100 capillary inlet subcooling,1T,ub,°C 3 - 12 3 - 12 3 - 12 capillary inlet pressure, P;,,, kPa 1470, 1640, 1860 1470, 1640, 1860 1470, 1640, 1860 Table 2 Range of parameters for diabatic flow conditions parameters straight capillary tube helical capillary tube spiral capillary tube capillary tube diameter, d,, mm 1.02, 1.27, 1.52 1.02, 1.27, 1.52 1.02, 1.27, 1.52 capillary tube length, L, m 1.0 1.5 2.0 1.0 1.5 2.0 1.0 1.5 2.0 *heat exchange length, Lhx, m 0.2 0.7 1.2 0.2 0.7 1.2 0.2 0.7 1.2 adiabatic inlet length Li, m 0.2 0.2 0.2 helical coil diameter, D, mm -- 60, 100, 140 -- spiral coil pitch, p, mm -- -- 20, 60, 100 capillary inlet subcooling, OTSUb,°C 3 - 12 3 - 12 3 - 12 capillary inlet pressure, P,,, kPa 1470, 1640, 1860 1470, 1640, 1860 1470, 1.640, 1860 suction line inlet temp., TS,;,°C -2, 4 -2, 4 -2, 4 * For each capillary length, the initial 0.2 m and last 0.6 m lengths of capillary tube were not soldered with the suction line of compressor. Therefore, = (L — 0.8) m. 111 The analysis of experimental results of adiabatic capillary tube reveals the following facts. 1. The refrigerant mass flow rate increases with the increase of tube diameter, inlet subcooling and capillary inlet pressure, whereas the same decreases with the increase of tube length. 2. The refrigerant mass flow rate is highly sensitive to tube diameter, i.e., the increase of tube diameter results in the rise of refrigerant mass flow rate in a significant manner. 3. The mass flow rate variation with respect to subcooling in both straight and coiled capillary tubes of a given diameter is independent of capillary tube length. 4. The variation of refrigerant mass flow rate with subcooling is observed to be a function of capillary tube diameter, i.e., the slope of mass flow rate variation with subcooling increases as the capillary tube diameter increases. 5. As compared to the mass flow rate of R-407C in straight capillary tube, the mass flow rate in helical capillary with coil diameters of 60 mm, 100 mm and 140 mm is reduced by an average of 10 percent, 7 percent and 5 percent respectively. 6. As compared to the mass flow rate of R-407C in straight capillary tube, the mass flow rate in spiral capillary with coil pitches of 20 mm, 60 mm and 100 mm is reduced by an average of 17 percent, 13 percent and 10 percent respectively. 7. The difference between the temperature profiles of the straight and coiled capillary tube is not significant, thus, can not be quantified. However, it is observed that the exit temperature for coiled tubes is lower than that for straight tubes operating under similar conditions. Based on the experimental data of present investigation, the non-dimensional correlations have been developed to predict the mass flow rate of R-407C flowing in straight, helical and spiral capillary tubes. Buckingham pr-theorem has been used to evolve non-dimensional groups and finally the correlations have been developed using multiple variable regression technique. The correlations developed for adiabatic capillary tubes are as follows: 7f1 =24.425(7[2)1.675(83 1-0.373/ir4)-0.015(5 1-1.498(it6 10.777 (it-,) .031/it8)0.121 _ straight )TI " O.0087(ir2)1.5381(i3 )-0.3511/x4 )0.003 (i5 1/-0.463 (it) -0.965 (~7 1-0.5071 (if) 1-1.235 (it)°°98 . - helical 7t l = 1. 165(712 )1.481 (it 3 1-/0.348 (1t4 f°°°5 (if 1/-1.133 /,6 )0.473 (i7 )-/0.807 (t )-/0.299 /i9 10%053 - spiral / / I 12 2/ m d,PfP„ L d2P2C OT„un ddPJhfg d..p16 where, 7r, _ ; ~2 = 2 > ~3 —; ~4 = 2 )r5 = 2 7r6 = 2 d<[1 d` of Alf ,uI 2t7- '°—g ; 7x8 = ~L ; ir9 = D (helical); ir9 = p (spiral) Pt The developed correlations predict the experimental data of present study in an error band of ±8 percent. The predictions from proposed correlations also find good agreement with the experimental data measured by previous investigators. iv Similarly, the analysis of experimental results of .diabatic capillary tube reveals the following facts. 1. The mass flow rate in diabatic capillary tube is always higher than that in adiabatic capillary tube at the same operating conditions. However, as inlet subcooling increases at a given capillary inlet pressure, the difference of mass flow rate between diabatic and adiabatic capillary tube reduces. 2. As the suction line inlet temperature is increased from -2 °C to 4 °C, the average reduction of mass flow rate in diabatic capillary tube is about 4 percent. 3. For inlet subcooling range of 3-12 °C, the relative difference of mass flow rates between diabatic capillary tube with suction line inlet temperature of -2 °C and adiabatic capillary tube are 7-20 percent, 5-15 percent and 3-9 percent for heat exchange length parameter of 0.6, 0.47 and 0.2 respectively. 4. As compared to the mass flow rates of R-407C in straight capillary tube of heat exchange length parameter of 0.2, 0.47 and 0.6, the mass flow rates in corresponding helical, capillary with coil diameters of 60-140 mm is reduced by an average of 4-9 percent, 3-7 percent and 2-5 percent respectively. 5. As compared to the mass flow rates of R-407C in straight capillary tube of heat exchange length parameter of 0.2, 0.47 and 0.6, the mass flow rates in corresponding spiral. capillary . tube with coil pitches of 20-100 mm is reduced by an average of 8-15 percent, 6-12 percent 6. There is a significant difference between the temperature profiles of the adiabatic and diabatic capillary tubes. There was no visible effect of coil diameter/coil pitch on the temperature profiles of diabatic helical/spiral capillary tubes. The non-dimensional correlations developed for diabatic capillary tubes are as follows: Jr, =0.0256(1I2j-0.396(irj)0038(sr4)1.351()-0.158(/()-0.0I6(if7 1-0.019(8 1-0.218(89)-0.696(10)-0.617011 1-0.399 - straight $, = 0.003(7r2)-0.359(,r3 1004(,r4)1.386(,r5)-0.134(,r6)0.005(n7)-0./016(,78)-0./121(n9 )-0.754(,r10 1-0.5830,,)-0./361(x12 0.054 - helical $, = 0.002(112)-II'336(x3/)0.043(,r4 11.213(x5)-0.135(76)0.017(,7}-0.016(,T8)-0.068 x(7r 1 0.7I4(/.10) 0.555(ifll)-0.271(/12 10.04) -spiral m L / L d, P1 P„ . d, PrP,.o, ./ d Prcar1 T,~,6 . d// Prc,,1 7 ,P . where, TI = , 'T2 = 7 , )r3 - hr 9 )r4 = 2 , = = 2 , )77 = 2 , d,Nf d~ d, Pf Pf l~r ,uf d~Pfhrx d~PfQ _ P8 P P 2 , ,r9 2 , ',o , ~r„ , ~r12_ d' (helical); ,r2 =f . (spiral) Pf F9f Pf f'f , The proposed correlations for diabatic straight, helical and spiral capillary tubes predict the experimental data of present study in an error band of ±5 percent, ±8 percent and -5 to +10 percent respectively. v In addition, the numerical models based on homogenous two phase flow, are also developed to predict the flow characteristics of a refrigerant in straight, helical and spiral capillary tubes for adiabatic and diabatic flow conditions. A set of differential equations is obtained by applying the law of conservation of mass, momentum and energy. These differential equations are solved using finite difference method. The most reliable and frequently used correlations for friction factor and heat transfer coefficient available in the literature are used in the model, thus the numerical models do not have dependency on the experimental results obtained from the present work. This makes the models versatile and offers flexibility to design engineers to assess the design and comparative performance aspects of capillary tube with a number of alternative refrigerants and their mixtures working under different operating conditions. The developed models for straight, helical and spiral capillary tube geometries are validated with the experimental data of previous studies as well as that of the present study. vi