Improved Refrigerant Characteristics Flow Predictions in Adiabatic Capillary Tube

Transcription

1 Research Journal o Applied Sciences, Engineering and Technology 4(3: 9-97, 0 ISSN: Maxwell Scientiic Organization, 0 Submitted: February 6, 0 Accepted: March 08, 0 Published: July 0, 0 Improved Rerigerant Characteristics Flow Predictions in Adiabatic Capillary Tube, Shodiya Sulaimon, Azhar Abdulaziz and Amer N. Darus Department o Thermoluids, Faculty o Mechanical Engineering, Universiti Teknologi Malaysia (UTM, Skudai, Johor, Malaysia Department o Mechanical Engineering, Faculty o Engineering, University o Maiduguri (UNIMAID, Maiduguri, Borno, Nigeria Abstract: This study presents improved rerigerant characteristics low predictions using homogenous low model in adiabatic capillary tube, used in small vapor compression rerigeration system. The model is based on undamental equations o mass, momentum and energy. In order to improve the low predictions, the inception o vaporization in the capillary tube is determined by evaluating initial vapor quality using enthalpy equation o rerigerant at saturation point and the inlet entrance eect o the capillary tube is also accounted or. Comparing this model with experimental data rom open literature showed a reasonable agreement. Further comparison o this new model with earlier model o Bansal showed that the present model could be use to improve the perormance predictions o rerigerant low in adiabatic capillary tube. Key words: Compression, low, homogenous, model, rerigeration system, two-phase INTRODUCTION Capillary tube is a low capacity rerigeration equipment use exclusively in small vapor compression rerigeration and window air-conditioning system or expansion o rerigerant between outlet o condenser and inlet o evaporator. It is usually made rom hollow pipe o drawn copper with inner bore between to 0.00 m and length between.5 to 6 m. Capillary tube is simple in construction, cheap in cost, no maintenance required and the starting torque o the compressor is reduced. Though, the geometry o the tube is simple, but, the analysis o the rerigerant low is complex because o the change in phase rom liquid single-phase to two-phase liquid/vapor as the rerigerant lows along the tube. Literature showed that there are three common types o numerical models been used to study the behavior o rerigerant low in adiabatic capillary tube - two-phase homogenous low, two-phase separated low and twophase drit lux models. However, most o these researches used two-phase homogenous low model (Bansal and Rupasinghe, 998; Kritsadathikarn et al., 00; Liang and Wong, 00; Sami and Tribes, 998; Wongwises and Pirompak, 00; Wongwises and Suchatawut, 003. Bansal and Rupasinghe (998 developed a mathematical model using conservation equations o mass, momentum and energy. The equations were solved simultaneously using iterative step and Simpson s rule. A numerical model based on homogenous model was also proposed by Sami and Tribes (998. The model was tested under dierent input conditions using rerigerant R-, R- and its alternatives and result shows good agreement with measured data. Wongwises and Suchatawut (003 developed a model to study pressure distribution along the capillary tube with some conventional rerigerants and their alternatives. The equations were solved using Runge-kutta method. Even though, the slip velocity and drit lux velocity as it applies to separated and drit lux models reectively are not considered in homogenous model, Escanes et al. (995 and Bittle and Pate (996 regard it (homogenous model as a good numerical estimator or low o rerigerant in capillary tubes. As a result, up to date, many researchers (Fatouh, 007; Kim et al., 0; Shodiya et al., 0; Trisaksri and Wongwises, 003 use homogenous model or simulating rerigerant low in adiabatic capillary tubes. Since the model is widely accepted, there is need or improvement o the model in order to have better rerigerant low predictions. Most o the earlier models determined their inception o vaporization (two-phase by selecting their initial enthalpy directly rom the standard thermodynamic table (REFPROP, 007. The objective o this study is to improve upon the rerigerant low characteristics Correonding Author: Shodiya Sulaimon, Department o Thermoluids, Faculty o Mechanical Engineering, Universiti Teknologi Malaysia (UTM, Skudai, Johor, Malaysia 9

2 Res. J. Appl. Sci. Eng. Technol., 4(3: 9-97, 0 m V A V A VA (3 Fig. : Schematic diagram o capillary tube between condenser and evaporator predictions in adiabatic capillary tube by determining the vaporization inception at saturation point using enthalpy equation. The capillary tube entrance correction is also included. MATHEMATICAL MODELLING Figure shows capillary tube which is connected between outlet condenser and inlet evaporator. The low in the tube is modeled by dividing it into liquid single phase and two-phase liquid-vapor section. There is a linear pressure decrease in the single-phase while pressure drop per unit length increases as the length increases in the two-phase. The low in the tube is based on one dimensional two-phase homogenous low assumptions. The present model is also based on that o Wongwises and Chingulpitak (00 with modiications. The governing equations that were used to describe the single-phase and the two-phase are discussed in the ollowing subsection. Single-phase (liquid low region: The single phase liquid region is the region rom entrance o the capillary tube to where the pressure decreased to saturated pressure. Energy equation rom point to 3 (Fig. is given in Eq. (: p V p3 V3 Z g g g g Z 3 h IT 3 ( where, p and p 3 are pressures, V and V 3 are velocities, Z and Z 3 are horizontal height D and D 3 are densities at points and 3 reectively and g is the acceleration due to gravity. The total head loss (h IT is shown in Eq. (: h IT LV k V Dg g ( where is riction actor o single phase, L is singlephase length, D is inner diameter o capillary tube, k is coeicient o entrance loss and its value is.5 as given by Zhou and Zhang (006. The continuity equation or an incompressible luid is given in Eq. (3: where m is the mass low rate, A and A 3 are cross sectional area at points and 3 reectively. The pressure drop as a result o the sharp entrance o the rerigerant into the capillary tube is determined rom Eq. (4 (Chung, 998: P P G A g x C c A (4 where G is mass low per unit area, L and L g are eciic volumes o liquid and liquid/vapor phases reectively, x is the vapor quality and coeicient o contraction C c is a unction o the area ratio A /A given in Eq. (5: C c A A A (5 A A A 3 Since the tube is horizontal, Z = Z 3 and G =DV. Combining Eq. (, ( and (3, the length o single-phase, L is calculated rom Eq. (6: D L ( p p k 3 G (6 The saturated pressure at point 3, p 3, is determined by using the level o subcooling, T sub at tube inlet i.e., T 3 = T! T sub where T and T 3 are temperatures at points and 3, reectively. Friction actor o single-phase is determined using Colebrook equation, given below: where, log D Re Re VD (7 (8 g and : are wall roughness and rerigerant viscosity, reectively. Two-phase (liquid/vapor region: The low is treated as two-phase homogeneous low and the three conservation equations are applied. The conservation o mass equation can be expressed as: 93

3 Res. J. Appl. Sci. Eng. Technol., 4(3: 9-97, 0 VA 3 VA 4 m 3 4 (9 Considering the steady state adiabatic and ignoring the dierence in elevation, the equation o conservation o energy is written as: h V Constant (0 where, h is the enthalpy. As the rerigerant lows in the capillary tube the pressure drops and there is an increase in vapor quality, x. At any point: h = h (! x + h g x ( L = L (! x + L g x ( From Eq. (3: V m G A (3 By substituting Eq. (, ( and (3 into (0, expanding it and rearranging gives: V G 3 h3 h x( hg h x ( g G G ( g x (4 h 3 = u 3 + p 3 L 3 (6 The values o rerigerant properties including u 3 (internal energy and v 3 are taken rom REFPROP (007. Considering an elemental luid, the orce applied as a result o inner tube shear orce and dierence in pressure dierence on opposite ends on an element are equal to the time rate o change in linear momentum. The conservation o linear momentum is written as: PA ( P dp A DdL mdv w where, J w is the shear stress at the wall deined as: w tp V 8 (7 (8 Substituting Eq. (8 into (7 and assuming constant mass low rate, gives: D dp d dl tp G (9 The riction actor o the two-phase, tp is calculated using Lin et al.(99 ormulation as: tp tp where, Ø, the multiplier is given by: (0 The vapor quality, x, can now be expressed as: hg G g G V3 hg G g G g ( ( h h3 x G g (5 where, 8 Re tp ( Atp Btp 8 Re ( A B g x ( where, h g = h g h and L g = L g! L In this study, since a inite amount o superheat is required or the inception o vaporization (ormation o irst bubble, the irst vapor quality x, is evaluated by calculating enthalpy h 3 at saturated point using the enthalpy ormulation in Eq. (6 and substituting in Eq. (5, thus: 6 A. 457 ln Re md B ;Re Re A ( 94

4 Res. J. Appl. Sci. Eng. Technol., 4(3: 9-97, 0 L j D P tpj G j (6 Fig. : The grids o the numeric solution Total two-phase length is evaluated thus: L tp n L j j (7 A tp, B tp and Re tp is calculated in a similar way as Eq. (. The viscosity model used in calculating the twophase viscosity : tp is given by Cicchitti et al. (960 as ollow: : tp = x :g +(! x : (3 SOLUTION METHODOLOGY A computer program written in MATLAB (009b version 7.0 was used to solve the governing equations or the present two-phase homogenous low model. The capillary tube in the two-phase is divided into several sections as shown in Fig. (between points 3 and 4. To calculate the pressure P j, the vapor quality at that point must be known. The initial enthalpy h 3 is calculated using Eq. (6, which is substituted in Eq. (5 to evaluate the irst vapor quality, x. With the vapor quality known, the irst value o : tp, Re tp, A tp, B tp and tp are calculated. The pressure, P j in the capillary tube is now evaluated rom Eq. (4: P j = P 3 jp (4 Subsequent vapor qualities are calculated by evaluating the enthalpy h, using Eq. ( and substituting in Eq. (5. The entropies in these sections are express as: s j = s j (! x + s jg x (5 In each elemental point, P j, T j, x j, s j and tpj are computed. Entropy must increase as the rerigerant lows through the capillary tube. To make sure that the entropy increases, the computed entropy s j, is compared with the earlier one s j-. The evaluation is done element by element along the capillary tube until a region where the entropy reached maximum, that is, critical low condition achieved. The pressure, (P j max., where the entropy attained maximum, is compared with pressure o evaporator, P evap. I (P j max is greater than P evap., the pressure at point 4, P 4, is taken as (P j max and it is use or the computation. But, i pressure, (P j max, is lower than pressure, P evap., the pressure at point 4 is taken as P evap. To calculate the two-phase length, Eq. (9 was discretized so that each elemental length is calculated thus: Total capillary tube length, L, is evaluated thus: L = L + L tp (8 All thermophysical and thermodynamics properties are rom REFPROP (007 a computer program, version 8.0 which is created based on pressure unction. Mass low rate (Kg/s RESULTS AND DISCUSSION This section discusses the validity o the model with experimental data o Wijaya (99 and Fiorelli et al. (00. Figure 3 shows the comparison and relations between mass low rate and tube length or D = 0.84 mm and subcooling, T sub = 6.7 K, or dierent condensing temperatures. The Figure shows clearly that the mass low rate decreases with decrease in temperature o condenser and also decreases with increase in tube length. The decrease in mass low rate as the tube length is increasing could be attributed to increase in resistance to the rerigerant low. This suggests that increasing the capillary tube length will deinitely raise the pressure drop. In order to retain the pressure drop, the mass low rate must be brought down. The predicted results have an error within ±6% compare with measured data o Wijaya (99. Figure 4 shows the comparison o the mass low rate with the tube length or subcooling between 5.5 to 6.7 K and diameter o 0.84 mm. As it can be seen in the Figure, or the subcooling o 5.5 K, the new model result overpredicts the Wijaya (99 result having a percentage o about 8% and also, the subcooling o 6.7 K under-predict Tcond. = 30.8 K Tcond. = 36.3 K Tcond. = 3.9 K Tcond. = 37.4 K Capillary tube length (m Fig. 3: Mass low rate against capillary tube length with dierent condensing temperature 95

5 Res. J. Appl. Sci. Eng. Technol., 4(3: 9-97, 0 Mass low rate (Kg/s Mass low rate (Kg/s Subcooling = 5.5 Subcooling =. K Subcooling = 6.7 K Adiabatic capillary tube length (m Fig. 4: Mass low rate against capillary tube length with dierent subcooling D = 0.66 mm D = 0.79 mm D = 0.84 mm Adiabatic capillary tube length (m Fig. 5: Mass low rate against capillary tube length with dierent diameters Capillary tube pressure (Pa Experimental data o iorelli Bansal et al model Distribution rom Capillary inlet (m Fig. 6: Comparison o new model results and experimental data o Fiorelli with earlier model o Bansal the experimental results by about 7.5%. In general, there is an increase in mass low rate as the subcooling increases. This can be attributed to the act that the increased subcooling increases the length o the liquid phase rerigerant and this liquid rerigerant oers less resistance to rerigerant low compare to the two-phase liquid/vapor. Figure 5 shows the relationship between the new model result and the measured data o Wijaya (99 or mass low rate against capillary tube length with dierent diameters. For D = 0.66 mm the percentage error was between + and +5%. For D = 0.79 mm, the new model results predicts the experimental results between -5 and +% and D = 0.84 mm was between -4 and +%. In general, the mass low rate increases with increase in inner diameter o the capillary tube which can be attributed to increase in low capacity o the tube. This also leads to decrease in pressure drop as the diameter increases. For desired operating conditions, the rise in pressure drop needs relatively reduced mass low rate. Figure 6 shows the pressure distribution along the capillary tube and comparing the new model result with the experimental data o Fiorelli et al. (00 and also with the earlier model o Bansal and Rupasinghe (998. As can be seen in the Figure, the pressure decreases linearly rom 0 to 0.75 m (single-phase, thereater, the inception o the two-phase give rise to pressure drops to increase. The error between the new model result and experimental data o Fiorelli et al. (00 was about ±5%. The error between new model result and Bansal and Rupasinghe (998 model result was about - to +7%. CONCLUSION This study presents a modiied two-phase homogeneous low model used to improve the predictions o the eects o the design parameters o adiabatic capillary tube use in small vapor compression rerigerating and window air conditioning system. In an attempt to solving the problem o determining the position o inception o vaporization and evaluating the initial twophase riction actor, the enthalpy ormulation was used. When the new model was compared with the experimental data o Wijaya (99 and Fiorelli et al. (00, it was ound that the present modiied homogenous low model gave reasonable agreement. It was also compared with the previous homogeneous model o Bansal and Rupasinghe(998. With this present model, it can be concluded that the characteristics low predictions o rerigerants in adiabatic capillary tube can be enhanced, hence, improved design or capillary tube designers. ACKNOWLEDGMENT The present study was inancially supported by Research University Grant (RUG program: Tier Cost Centre Code:QJ J85, Universiti Teknologi, Malaysia. REFERENCES Bansal, P.K. and A.S. Rupasinghe, 998. An homogeneous model or adiabatic capillary tubes. Appl. Therm. Eng., 8(3-4: Bittle, R.R. and M.B. Pate, 996. A theoretical model or predicting adiabatic capillary tube perormance with alternative rerigerants. ASHRAE Trans., 0(:

6 Res. J. Appl. Sci. Eng. Technol., 4(3: 9-97, 0 Chung, M., 998. A Numerical Procedure or simulation o anno lows o rerigerants or rerigerant mixtures in capillary tubes. ASHRAE Trans., 04: Cicchitti, A., C. Lombardi, M. Silvestri, G. Saldaini and R. Zavattarelli, 960. Two-phase cooling experiment pressure drop, heat transer and burnout measurements. Energia Nucleare, 7: Escanes, F., C.D. Perez-Segarra and A. Oliva, 995. Numerical simulation o capillary-tube expansion devices. Int. J. Rerig., 8(: 3-. Fatouh, M., 007. Theoretical investigation o adiabatic capillary tubes working with propane/n-butane/isobutane blends. Energy Convers. Manage., 48: Fiorelli, F.A.S., A.A.S. Huerta and O.M. Silvares, 00. Experimental analysis o rerigerant mixtures low through adiabatic capillary tubes. Exp. Therm Fluid Sci., 6: Kim, L., K. Son, D. Sarker, J.H. Jeing and S.H. Lee, 0. An assessment o models or predicting rerigerant characteristics in adiabatic and nonadiabatic capillary tube. Heat Mass Transer, 47: Kritsadathikarn, P., T. Songnetichaovalit, N. Lokathada and S. Wongwises, 00. Pressure distribution o rerigerant low in an adiabatic capillary tube. ScienceAsia, 8: Liang, S.M. and T.N. Wong, 00. Numerical modeling o two-phase rerigerant low through adiabatic capillary tubes. Appl. Therm. Eng., : Lin, S., C.C.K. Kwok, R.Y. Li, Z.H. Chen and Z.Y. Chen, 99. Local rictional pressure drop during vaporisation o RI through capillary tubes. Int. J. Multiphase Flow, 7(: REFPROP, 007. Thermodynamic Properties o Rerigerants and Rerigerants Mixtures Version 8.0. Gathersburg, M.D. National Institute o Standards and Technology, USA. Sami, S. and C. Tribes, 998. Numerical prediction o capillary tube behaviour with pure and binary alternative rerigerants. Appl. Therm. Eng., 8(6: Shodiya, S., A.A. Azhar, N. Henry and A.N. Darus, 0. New empirical correlation or sizing adiabatic capillary tubes in rerigeration systems. Proceedings o the 4th International Meeting o Advances in Thermoluids, Melaka, Malaysia, Oct. 3-4, pp: Trisaksri, V. and S. Wongwises, 003. Correlations or sizing adiabatic capillary tubes. Int. J. Energ. Res., 7(3: Wijaya, H., 99. Adiabatic capillary tube test data or HCF-34a. Proceeding o IIR-Purdue Conerence, West Laayette, USA, : Wongwises, S. and W. Pirompak, 00. Flow characteristics o pure rerigerants and rerigerant mixtures in adiabatic capillary tubes. Appl. Therm. Eng., (8: Wongwises, S. and M. Suchatawut, 003. A simulation or predicting the rerigerant low characteristics including metastable region in adiabatic capillary tubes. Int. J. Energ. Res., 7: Wongwises, S. and S. Chingulpitak, 00. Eects o coil diameter and pitch on the low characteristics o alternative rerigerants lowing through adiabatic helical capillary tubes. Int Commun. Heat Mass Transer, 37(9: Zhou, G. and Y. Zhang, 006. Numerical and experimental investigations on the perormance o coiled adiabatic capillary tubes. Appl. Therm. Eng., 6(-: