# Capillary tube sizing charts for fluorine-based refrigerants.

ABSTRACT

This paper provides new selection charts for the sizing of adiabatic capillary tubes operating with alternative refrigerants. The mathematical model is based on conservation of mass, energy, and momentum of fluids in the capillary tube. After the developed model is validated by comparison with the experimental data reported in literature, selection charts that contain the relevant parameters are proposed for sizing adiabatic capillary tubes. The selection charts are presented for some alternative refrigerants and a wide range of operations. These newly developed selection charts can be practically used to select capillary tube size from the flow rate and flow condition or to determine mass flow rate directly from a given capillary tube size and flow condition.

INTRODUCTION

The capillary tube is one type of expansion device used in small vapor-compression refrigerating and air-conditioning systems. It is used as an automatic flow rate controller for the refrigerant when varying load conditions and varying condenser and evaporator temperatures are to be encountered. Its simplicity, low initial cost, and low starting torque of compressors are the main reasons for its use. To meet the demands of the environment and also to improve the performance of the equipment, reevaluation of the individual components, in particular the use of alternative ozone-safe substances in the capillary tube, is necessary. The proper size of the capillary tube used with a new refrigerant is one of the important factors for the optimum performance of refrigerating and air-conditioning systems.

The design and analysis of adiabatic capillary tubes have been studied extensively. Some researchers have developed correlations for selecting the adiabatic capillary tube size operating with some alternative refrigerants. Bansal and Rupasinghe (1996) presented an empirical approach to develop a simple correlation for sizing capillary tubes used for R-134a. The correlation was based on the assumption that the capillary tube length depended on the capillary tube inner diameter, mass flow rate of refrigerant in the tube, pressure difference between high side and low side, degree of subcooling, and relative roughness of the capillary tube material. Jung et al. (1999) developed a method to predict the size of capillary tubes for R-22 and its alternatives. Stoecker and Jones's (1982) basic model was modified with the consideration of subcooling, area contraction, mixture effect, viscosity, and friction factor equations. McAdams et al.'s (1942) equation was used for the two-phase viscosity and Stoecker and Jones's equation for the friction factor. Simple correlating equations were provided to determine the dependence of mass flow rate on the length and diameter of the capillary tube, the condensing temperature, and subcooling. Kim et al. (2002) presented a dimensionless correlation based on the Buckingham [pi] theorem to predict the mass flow rate through adiabatic capillary tubes for R-22, R-407C, and R-410A. The correlation was developed on the basis of the experimental data, and the values of refrigerant properties used in the correlation were obtained from the REFPROP (McLendon et al. 1998) database. Trisaksri and Wongwises (2003) presented new correlations for 25 refrigerants; R-12, R-22, R-134a, R-401A, R-401B, R-401C, R-404A, R-402B, R-404A, R-407A, R-407B, R-407C, R-407E, R-408A, R-409A, R-409B, R-410A, R-410B, R-411A, R-411B, R-414B, R-500, R-501, R-502A, and R-507A. The correlations can be used for the practical sizing of adiabatic capillary tubes.

In all these methods, however, the calculations are cumbersome for practical applications. In an attempt to overcome this problem, selection charts for sizing or predicting refrigerant flow rate were developed (ASHRAE 1988; Wong-wises and Pirompak 2001; Choi et al. 2004). These charts, however, are limited due to the range of operating conditions and types of refrigerants. Therefore, there is need for charts for selecting capillary tubes for an extensive number of refrigerants and operating conditions. In the present study, the main concern is to develop a selection chart for several refrigerants that have expansive operating conditions. This chart can be used practically to predict the refrigerant mass flow rate or determine the capillary tube size from the flow rate and flow condition. It is practical, simple to use, and based on input parameters known to the designer.

MATHEMATICAL MODELING

For the study of the flow characteristics of refrigerants, a computer program developed at our laboratory was used. In this model, the study of the physical behavior and parameters is developed based on the fundamental principle of thermodynamics and fluid mechanics (Wongwises and Pirompak 2001; Trisaksri and Wongwises, 2003). As shown in Figure1, a capillary tube is connected between a condenser and evaporator. The flow characteristics of refrigerant in a capillary tube may generally be divided into a single-phase flow region and a two-phase flow region.

The theoretical flow model of refrigerant through the capillary tube is based on the following assumptions:

* it is a straight, horizontal capillary tube with constant inner diameter and roughness,

* there is one-dimensional and steady turbulent flow through the capillary tube,

* it is a fully insulated capillary tube,

* there is homogeneous two-phase flow,

* there is negligible metastable flow phenomenon,

* it is an oil-free refrigerant, and

* there is thermodynamic equilibrium through the capillary tube.

[FIGURE 1 OMITTED]

In this model, various design parameters that influence the size of the capillary tube as well as the tube diameter, roughness, degree of subcooling, refrigerant mass flow rate, and condenser and evaporator temperatures and pressure are included. The governing equations used to describe the flow behavior in the single-phase and two-phase flow regions are presented below.

Single-Phase Flow Region

The single-phase flow region begins at the inlet of the capillary and ends at the point where the pressure is dropped to the saturated pressure.

The steady flow energy equation between points 1 and 3 in Figure 1 can be written as

[[P.sub.1]/[[[rho].sub.1]g]] + [[V.sub.1.sup.2]/2g] + [Z.sub.1] = [[P.sub.3]/[[[rho].sub.3]g]] + [[V.sub.3.sup.2]/2g] + [Z.sub.3] + [h.sub.L]. (1)

For an incompressible fluid, and from the continuity equation,

m = [[rho].sub.2][V.sub.2]A = [[rho].sub.3][V.sub.3]A = [rho]VA. (2)

The total head loss can be determined from

[h.sub.L] = [f.sub.sp] [[L.sub.sp]/D] [[V.sup.2]/2g] + k[[V.sup.2]/2g], (3)

where [f.sub.sp] is the single-phase friction factor and k is the entrance loss coefficient (for square edged, k = 0.5).

For a horizontal tube, [Z.sub.2] = [Z.sub.3], and from the mass flow rate of refrigerant per unit the cross-section area (G) is [rho]V; therefore, the single-phase length, [L.sub.sp], of the capillary tube can be determined from

[L.sub.sp] = [([P.sub.1] - [P.sub.3]) x [2[rho]/[G.sup.2]] - k - 1] x [D/[f.sub.sp]]. (4)

The pressure at point 3 is assumed to be saturated and can be determined by knowing the subcooling temperature at the capillary tube entrance. The single-phase friction factor, [f.sub.sp], can be calculated from the Colebrook formula as follows:

1/[square root of [f.sub.sp]] = 1.14 - 2log[(e/D) + [9.3/[Re x [square root of [f.sub.sp]]]]], (5)

where

Re = [rho]VD/[mu]. (6)

Two-Phase Flow Region

The flow in this region is modeled as homogeneous flow. The fundamental equations applicable to this section are conservation of mass, energy, and momentum.

Consider a control volume in the two-phase region as shown in Figure 1.

The conservation of mass can be expressed as

m = [[V.sub.3]A]/[[upsilon].sub.3] = [[V.sub.4]A]/[[upsilon].sub.4]. (7)

For steady-state adiabatic with no external work and neglecting the elevation difference, the conservation of energy can be expressed as

h + [[V.sup.2]/2] = constant, (8)

where h and V are the enthalpy and velocity at any point in the two-phase region.

As the refrigerant flows through the capillary tube, its pressure gradually drops and the vapor fraction continuously increases. At any point,

h = [h.sub.f](1 - x) + [h.sub.g]x and (9)

[upsilon] = [[upsilon].sub.f](1 - x) + [[upsilon].sub.g]x. (10)

For continuity, m = [rho]VA = constant,

V = m/[rho]A = G/[rho]. (11)

Substituting Equations 9-11 into Equation 8, expanding the right-hand side, and rearranging gives

[h.sub.3] + [[V.sub.3.sup.2]/2] = [h.sub.f] + x([h.sub.g] - [h.sub.f] + [[[G.sup.2][[upsilon].sub.f.sup.2]]/2] + [x.sup.2]([[upsilon].sub.g] - [[upsilon].sub.f])[.sup.2][[G.sup.2]/2] + [G.sup.2][[upsilon].sub.f]([[upsilon].sub.g] - [[upsilon].sub.f])x. (12)

Thus, the quality, x, can be expressed as

x = {-[h.sub.fg] - [G.sup.2][[upsilon].sub.f][[upsilon].sub.fg] + [square root of (([h.sub.fg] + [G.sup.2][[upsilon].sub.f][[upsilon].sub.fg])[.sup.2] - (2[G.sup.2][[upsilon].sub.fg.sup.2])([h.sub.f] + 0.5 [G.sup.2][[upsilon].sub.f.sup.2] - [h.sub.3] - 0.5[V.sub.3.sup.2]))]}/[[G.sup.2][[upsilon].sub.fg.sup.2]] (13)

where [h.sub.fg] = [h.sub.g] - [h.sub.f] and [[upsilon].sub.fg] = [[upsilon].sub.g] - [[upsilon].sub.f].

The entropy increases through the capillary due to the adiabatic irreversible process and also notes that

s = [s.sub.f](1 - x) + [s.sub.g]x. (14)

The conservation of momentum can be expressed by again considering the element of fluid. The different forces applied to the element due to shear force acting on the inner pipe wall and the pressure difference on opposite ends are equal to the time rate of change in linear momentum of the system. Therefore,

(P[[[pi][D.sup.2]]/4]) (P + dP)[[[pi][D.sup.2]]/4] - [[tau].sub.w][pi]DdL = mdV, (15)

where [[tau].sub.w] is the wall shear stress defined as

[[tau].sub.w] = [f.sub.tp][rho][V.sup.2]/8. (16)

For constant mass flow rate, substituting Equation 16 into Equation 15 and rearranging gives

dL = [2D/[f.sub.tp]][[-[rho]dP/[G.sup.2]] + d[rho]/[rho]]. (17)

The homogeneous two-phase friction factor, [f.sub.tp], can be determined from Colebrook's equation with the Reynolds number defined as

Re = GD/[[upsilon].sub.tp]. (18)

SOLUTION METHODOLOGY

The capillary tube in the two-phase region (between points 3 and 4) can be divided into numerous sections. Since [P.sub.3] is known (saturated liquid), then the pressure at any section i is calculated from

[P.sub.i] = [P.sub.3] - i[DELTA]P. (19)

With the pressure [P.sub.i] known, the quality, [x.sub.i], can be calculated from Equation 13. The entropy of the section can be expressed as

[s.sub.i] = [s.sub.if](1 - x) + [s.sub.ig]x. (20)

For each section, [P.sub.i], [T.sub.i], [x.sub.i], [s.sub.i], and [f.sub.i] are calculated. The calculation is done section by section along the capillary tube up to the point where the entropy is maximum. At this point, the fluid velocity is equal to the local speed of sound and the flow is choked. Its pressure, [P.sub.i,smax], is compared to the evaporator pressure, [P.sub.evap]. If the pressure where the entropy is maximum, [P.sub.i,smax], is greater than the evaporator pressure, [P.sub.evap], the pressure at point 4, [P.sub.4], is taken as [P.sub.i,smax] and the pressure [P.sub.i,smax] is used for the calculation. If the pressure where the entropy is maximum, [P.sub.i,smax], is less than the evaporator pressure, [P.sub.evap], the pressure at point 4 is taken as [P.sub.evap].

From Equation 17, the two-phase length, [L.sup.tp], can be determined from

[L.sub.tp] = D[[-2/[G.sup.2]][[P.sub.s,max].[integral].[P.sub.3]][[rho]dP/[f.sub.tp]] + 2 [[P.sub.s,max].[integral].[P.sub.3]][dP/[[rho][f.sub.tp]]], (21)

where the two-phase friction factor, [f.sub.tp], can be calculated from Colebrook's equation.

Therefore, the total length of the capillary tube, L, can be written as

L = [L.sub.sp] + [L.sub.tp]. (22)

From the above calculation, the viscosity models used to calculate the two-phase viscosity, [[mu].sub.tp], are as follows:

Cicchitti et al. (1960)

[[mu].sub.tp] = x[[mu].sub.g] + (1 - x)[[mu].sub.f] (23)

Dukler et al. (1964)

[[mu].sub.tp] = [x[[upsilon].sub.g][[mu].sub.g] + (1-x)[[upsilon].sub.f][[mu].sub.f]]/[x[[upsilon].sub.g] + (1-x)[[upsilon].sub.f]] (24)

McAdams et al. (1942)

1/[[mu].sub.tp] = [x/[[mu].sub.g]] + [[1-x]/[[mu].sub.f]] (25)

All thermodynamic and thermophysical refrigerant properties are taken from the REFPROP computer program, version 6.01 (McLendon et al. 1998), and are developed in the function of pressure.

RESULTS AND DISCUSSION

The viscosity model used in the present work varied developing on the refrigerant and was based on the recommendations of past research (Wongwises and Pirompak 2001), in particular Bittle and Pate (1994). The Dukler et al. (1964) model was used for simulations with R-12 and R-22, and the Cicchitti et al. (1960) model was used for R-134a, while the McAdams et al. (1942) model, as the best all-round predictor, was used for the remaining refrigerants. After verification of the present numerical simulation is done by comparison with the experimental data, the charts used to predict the refrigerant mass flow rate or the capillary tube size are developed. In the final step, validating the developed selection charts, the results from the chart are also compared with the experimental data.

Mathematical Model Verification

In order to validate the present model, comparisons were made with the limited available experimental data reported in the literature.

Figure 2 shows a comparison of the pressure distribution along the capillary tube obtained from the model and that obtained from the experiment of Mikol (1963) for R-12. The conditions for the numerical calculation to obtain the curve correspond to the experimental condition of Mikol (1963) for R-12. As described, the flow of refrigerant through the capillary tube from the outlet of the condenser to the inlet of the evaporator can be divided into two regions: a single-phase subcooled liquid region and a two-phase region. In the single-phase subcooled liquid region, due to the wall frictional effects in fully developed flow in a constant-area tube, the pressure of refrigerant drops linearly while the temperature remains constant along the capillary tube. After the inception of vaporization, due to the frictional and acceleration effects, the pressure and temperature of refrigerant drops relatively fast--this is more rapid as the flow approaches the critical flow condition. The comparison shows an average error in length of 8.61%. The temperature distribution data of Sami and Maltais (2001) for R-410B is compared with the simulation result. Sami and Maltais (2001) did not specify the roughness of the capillary tube in their paper. The roughnesses used for the present simulations were obtained and averaged from their experimental data. There is good agreement between the experimental data and the numerical results. The agreement of the model with the experimental data is satisfactory. It should be noted that the temperature distribution shown in Figure 2 looks similar to the pressure distribution; this is because the single-phase length for this experimental condition is very short. In other words, the constant temperature region disappears in this figure.

Comparisons were also made with the R-410A experimental data of Fiorelli et al. (2002) for the pressure distribution and the temperature distribution along the capillary tube. It was found that the present numerical results from the McAdams et al. (1942) viscosity model are in good agreement.

[FIGURE 2 OMITTED]

Development of Practical Selection Chart

The results show that the developed model can be considered an effective tool for capillary tube design. The present mathematical model can be used to develop the charts for selecting appropriate capillary tubes for specific applications. The first step in developing a selection chart is to select parameters that have an influence on the length of the capillary tube. These parameters are focused on the input parameter to keep the selection chart simple and practical. The selected parameters used in the present correlation are: condensing temperature [T.sub.cond], subcooling temperature [T.sub.sub], capillary tube diameter D, and refrigerant mass flow rate m. The subcooling temperature is used to specify the phase inlet of the capillary tube. The evaporator pressure is not included in the selection chart, but the lengths of capillary tube correspond to the choked flow condition for any computation.

The steps of the development of the charts are as follows.

1. Select the capillary tube diameter (D) as 1.63 mm.

2. Select the degree of subcooling ([T.sub.sub]) as 0[degrees]C.

3. Select the condenser temperature ([T.sub.cond]) as 30[degrees]C.

4. Assume the mass flow rate of refrigerant (m).

5. Calculate the capillary tube length of the single-phase flow ([L.sub.sp]) as

[L.sub.sp] = [D/[f.sub.sp]][([P.sub.1] - [P.sub.3])[2[rho]/[G.sup.2]] - k - 1].

6. Compute the quality of refrigerant (x) and the capillary tube length of the two-phase flow ([L.sub.tp]) as

x = {-[h.sub.fg] - [G.sup.2][[upsilon].sub.f][[upsilon].sub.fg] + [square root of (([G.sup.2][[upsilon].sub.f][[upsilon].sub.fg] + [h.sub.fg])[.sup.2] - 2[G.sup.2][[upsilon].sub.fg.sup.2][[[[G.sup.2][[upsilon].sub.f.sup.2]]/2] + [h.sub.f] - [h.sub.3] - [[V.sub.3.sup.2]/2])]}]/[[G.sup.2][[upsilon].sub.fg.sup.2]] and [L.sub.tp] = D[[-2/[G.sup.2]][[P.sub.s,max][p.sub.evap].[integral].[P.sub.3]][[rho]/[f,sub.tp]]dP + 2[[P.sub.s,max],[P.sub.evap].[integral].[P.sub.3]][d[rho]/[[rho][f.sub.tp]]]].

7. If the total capillary tube length is not equal to 2,030 mm, calculation steps 4-6 are repeated until the total capillary tube length is equal to 2,030 mm.

8. Vary the condenser temperature (30[degrees]C-60[degrees]C). Calculation steps 4-7 are repeated.

9. Vary the degree of subcooling (0[degrees]C-35[degrees]C). Calculation steps 3-8 are repeated.

10. The selection charts, in which the x-axis is the condenser temperature and the y-axis is the refrigerant mass flow rate, are created at various degrees of subcooling.

Figure 3 shows an example of the preliminary selection chart for refrigerant R-134a flowing through a capillary tube having an internal diameter of 1.63 mm and a length of 2.03 m. The chart is developed in the style of ASHRAE (1988). The chart is valid only for steady adiabatic capillary tube flow. For a capillary tube having an internal diameter of 1.63 mm and a length of 2.03 m, the required mass flow rate can be easily determined from this chart by knowing the condenser pressure and the degree of subcooling. However, for a capillary tube having internal diameter and length other than these, the flow correction factor is required.

The steps of the development of the correction factor chart are as follows.

1. Start with [T.sub.cond] = 45[degrees]C, [T.sub.sub] = 0[degrees]C.

2. Select D as 0.5 mm.

3. Select L as 250 mm.

4. Assume the mass flow rate of refrigerant.

5. Calculate the capillary tube length of the single-phase flow.

6. Calculate the quality of refrigerant and the capillary tube length of the two-phase flow.

7. If the total capillary tube length is not equal to that assigned in step 3, calculation steps 4-6 are repeated until the total capillary tube length is equal to that assigned in step 3.

8. Calculate the correction factor by dividing the mass flow rate obtained from the last iteration by that obtained from the selection chart at 45[degrees]C for the condenser temperature and 0[degrees]C for the degree of subcooling.

[FIGURE 3 OMITTED]

9. Vary the capillary tube length between 250 and 10,000 mm. Then, calculation steps 4-8 are repeated.

10. Vary the internal diameter between 0.5 and 5 mm. Then, calculation steps 3-9 are repeated.

11. The correction chart in which the x-axis is the capillary tube length and the y-axis is the correction factor of mass flow rate of refrigerant is created at various internal diameters.

The correction factor chart to be applied to Figure 3 for other dimensions and lengths of capillary tubes is shown in Figure 4. It is interesting to note that ASHRAE (1988) uses the same chart for both R-12 and R-22. However, as expected, the R-12 and R-22 charts developed from the present mathematical model give different values of various parameters. With the same method, the selection charts and corresponding correction factor charts in the same style for the other alternative refrigerants as shown in Figures 5-12 can also be developed. It should be noted that a capillary tube correctly selected for a given condensing temperature may not be oversized for a higher condensing temperature if the refrigerant charge is limited.

To validate the selection chart, comparisons were made with the experimental data of Wijaya (1992) and Melo et al. (1999). Wijaya (1992) measured mass flow rates through a range of adiabatic capillary tubes with different inner diameters and condensing and subcooling temperatures for R-134a. Comparison of mass flow rates obtained from the present selection chart with the measured mass flow rates for four condensing temperatures of 37.8[degrees]C, 43.3[degrees]C, 48.9[degrees]C, and 54.4[degrees]C; 0.84 mm capillary tube inner diameter; and 16.7[degrees]C subcooling temperature shows that the measured mass flow rates fall within [+ or -]15% of the proposed selection chart (see Table 1).

[FIGURE 4 OMITTED]

Comparison of the results from the selection chart with the R-134a measured data of Melo et al. (1999) for the capillary tube diameter of 0.77 mm, capillary tube length of 2.009 m, condenser pressure of 14 bar, and roughness of 0.75 [micro]m shows that the selection chart underpredicts the mass flow rate for various given levels of subcooling with an average error of 15.0% (See Table 2).

However, because of the potential for floodback, evaporator starving, and other ills, capillary tube selections should always be confirmed by actual testing over the range of applicable temperatures.

CONCLUSIONS

This paper presents new selection charts for selecting the capillary tube size from the refrigerant mass flow rate and flow condition or for predicting the refrigerant mass flow rate through adiabatic capillary tubes from a given capillary tube size and flow condition. The mathematical model is developed from the homogeneous flow model. The governing equations are based on the basis of conservation of mass, energy, and momentum. The model is validated by comparing it with the measured data reported in the literature. The development of the selection charts, which can be used to size capillary tubes, is described. The selection charts and flow correction factors are proposed for practical use. The developed selection charts are verified by comparing them with the limited available experimental data. The comparison results are in good agreement.

ACKNOWLEDGMENT

The authors would like to express their appreciation to the Thailand Research Fund (TRF) for providing financial support for this study.

NOMENCLATURE

A = capillary cross-sectional area, [m.sup.2]

D = inner diameter, m

f = friction factor

G = mass flow rate per unit area, kg/s x [m.sup.2]

g = gravitational acceleration, m/[s.sup.2]

h = specific enthalpy, J/kg

k = entrance loss coefficient

L = length, m

m = mass flow rate, kg/s

P = pressure, Pa

Re = Reynolds number

s = specific entropy, J/kg x K

T = temperature, [degrees]C

e = roughness, m

V = velocity, m/s

x = quality

Greek Letters

[mu] = dynamic viscosity, kg/m s

[upsilon] = specific volume, [m.sup.3]/kg

[rho] = density, kg/[m.sup.3]

Subscripts

cond = condenser

evap = evaporator

f = liquid phase

g = gas phase

sp = single phase

tp = two phase

sub = subcooling

[FIGURE 5 OMITTED]

[FIGURE 6 OMITTED]

[FIGURE 7 OMITTED]

[FIGURE 8 OMITTED]

[FIGURE 9 OMITTED]

[FIGURE 10 OMITTED]

[FIGURE 11 OMITTED]

[FIGURE 12 OMITTED]

REFERENCES

ASHRAE. 1988. 1988 ASHRAE Handbook--Equipment, chapter 19. Atlanta: American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc.

Bansal, P.K, A.S. Rupasinghe. 1996. An empirical model for sizing capillary tubes. International Journal of Refrigeration 19:497-505.

Bittle, R.R., and M.B. Pate. 1994. A theoretical model for predicting adiabatic capillary tube performance with alternative refrigerants. ASHRAE Transactions 102(2):52-64.

Choi, J., Y. Kim, and J.T. Chung. 2004. An empirical correlation and rating charts for the performance of adiabatic capillary tubes with alternative refrigerants. Applied Thermal Engineering 24:29-41.

Cicchitti, A., C. Lombardi, M. Silvestri, G. Soldaini, and R. Zavattarelli. 1960. Two-phase cooling experiments--Pressure drop, heat transfer and burnout measurements. Energia Nucleare 7:407-25.

Dukler, A.E., M. Wicks, and R.G. Cleveland. 1964. Frictional pressure drop in two-phase flow, Parts A and B. AIChE Journal 10:38-51.

Fiorelli, F.A.S., A.A.S. Huerta, and O.M. Silvares. 2002. Experimental analysis of refrigerant mixtures flow through adiabatic capillary tubes. Experimental Thermal and Fluid Science 26:499-512.

Jung, D., C. Park, and B. Park. 1999. Capillary tube selection for HCFC-22 alternatives. International Journal of Refrigeration 22:604-14.

Kim, S.G., M.S. Kim, and S.T. Ro. 2002. Experimental investigation of the performance of R22, R407C and R410A in several capillary tubes for air-conditioners. International Journal of Refrigeration 25:521-31.

McAdams, W.H., W.K. Wood, and R.L. Bryan. 1942. Vaporization inside horizontal tubes, II--Benzene-oil mixture. Transactions of ASME 64:193.

McLinden, M.O., S.A. Klein, and E.W. Lemmon. 1998. REFPROP--Thermodynamic and Transport Properties of Refrigerants and Refrigerant Mixtures, NIST Standard Reference Database, version 6.01. Gaithersburg, MD: National Institute of Standards and Technology.

Melo, C., R.T.S. Ferreira, N.C. Boabaid, J.M. Goncalves, and M.M. Mezavi. 1999. An experimental analysis of adiabatic capillary tubes. Applied Thermal Engineering 19:669-84.

Mikol, E.P. 1963. Adiabatic single- and two-phase flow in small bore tubes. ASHRAE Journal 5:75-86.

Sami, S.M., and H. Maltais. 2001. Experimental analysis of capillary tubes behavior with some HCFC-22 alternative refrigerants. International Journal of Energy Research 25:1233-1247.

Stoecker, W.F., and J.W. Jones. 1982. Refrigeration and Air Conditioning, 2d ed. New York: McGraw-Hill.

Trisaksri, V., and S. Wongwises. 2003. Correlations for sizing adiabatic capillary tubes. International Journal of Energy Research 27:1145-64.

Wijaya, H. 1992. Adiabatic capillary tube test data for HFC-134a. Proceedings of the International Refrigeration Conference on Energy Efficiency and New Refrigerants, Purdue University, West Lafayette, Indiana, pp. 63-71.

Wongwises, S., and W. Pirompak. 2001. Flow characteristics of pure refrigerants and refrigerant mixtures in adiabatic capillary tubes. Applied Thermal Engineering 21:845-61.

This paper provides new selection charts for the sizing of adiabatic capillary tubes operating with alternative refrigerants. The mathematical model is based on conservation of mass, energy, and momentum of fluids in the capillary tube. After the developed model is validated by comparison with the experimental data reported in literature, selection charts that contain the relevant parameters are proposed for sizing adiabatic capillary tubes. The selection charts are presented for some alternative refrigerants and a wide range of operations. These newly developed selection charts can be practically used to select capillary tube size from the flow rate and flow condition or to determine mass flow rate directly from a given capillary tube size and flow condition.

INTRODUCTION

The capillary tube is one type of expansion device used in small vapor-compression refrigerating and air-conditioning systems. It is used as an automatic flow rate controller for the refrigerant when varying load conditions and varying condenser and evaporator temperatures are to be encountered. Its simplicity, low initial cost, and low starting torque of compressors are the main reasons for its use. To meet the demands of the environment and also to improve the performance of the equipment, reevaluation of the individual components, in particular the use of alternative ozone-safe substances in the capillary tube, is necessary. The proper size of the capillary tube used with a new refrigerant is one of the important factors for the optimum performance of refrigerating and air-conditioning systems.

The design and analysis of adiabatic capillary tubes have been studied extensively. Some researchers have developed correlations for selecting the adiabatic capillary tube size operating with some alternative refrigerants. Bansal and Rupasinghe (1996) presented an empirical approach to develop a simple correlation for sizing capillary tubes used for R-134a. The correlation was based on the assumption that the capillary tube length depended on the capillary tube inner diameter, mass flow rate of refrigerant in the tube, pressure difference between high side and low side, degree of subcooling, and relative roughness of the capillary tube material. Jung et al. (1999) developed a method to predict the size of capillary tubes for R-22 and its alternatives. Stoecker and Jones's (1982) basic model was modified with the consideration of subcooling, area contraction, mixture effect, viscosity, and friction factor equations. McAdams et al.'s (1942) equation was used for the two-phase viscosity and Stoecker and Jones's equation for the friction factor. Simple correlating equations were provided to determine the dependence of mass flow rate on the length and diameter of the capillary tube, the condensing temperature, and subcooling. Kim et al. (2002) presented a dimensionless correlation based on the Buckingham [pi] theorem to predict the mass flow rate through adiabatic capillary tubes for R-22, R-407C, and R-410A. The correlation was developed on the basis of the experimental data, and the values of refrigerant properties used in the correlation were obtained from the REFPROP (McLendon et al. 1998) database. Trisaksri and Wongwises (2003) presented new correlations for 25 refrigerants; R-12, R-22, R-134a, R-401A, R-401B, R-401C, R-404A, R-402B, R-404A, R-407A, R-407B, R-407C, R-407E, R-408A, R-409A, R-409B, R-410A, R-410B, R-411A, R-411B, R-414B, R-500, R-501, R-502A, and R-507A. The correlations can be used for the practical sizing of adiabatic capillary tubes.

In all these methods, however, the calculations are cumbersome for practical applications. In an attempt to overcome this problem, selection charts for sizing or predicting refrigerant flow rate were developed (ASHRAE 1988; Wong-wises and Pirompak 2001; Choi et al. 2004). These charts, however, are limited due to the range of operating conditions and types of refrigerants. Therefore, there is need for charts for selecting capillary tubes for an extensive number of refrigerants and operating conditions. In the present study, the main concern is to develop a selection chart for several refrigerants that have expansive operating conditions. This chart can be used practically to predict the refrigerant mass flow rate or determine the capillary tube size from the flow rate and flow condition. It is practical, simple to use, and based on input parameters known to the designer.

MATHEMATICAL MODELING

For the study of the flow characteristics of refrigerants, a computer program developed at our laboratory was used. In this model, the study of the physical behavior and parameters is developed based on the fundamental principle of thermodynamics and fluid mechanics (Wongwises and Pirompak 2001; Trisaksri and Wongwises, 2003). As shown in Figure1, a capillary tube is connected between a condenser and evaporator. The flow characteristics of refrigerant in a capillary tube may generally be divided into a single-phase flow region and a two-phase flow region.

The theoretical flow model of refrigerant through the capillary tube is based on the following assumptions:

* it is a straight, horizontal capillary tube with constant inner diameter and roughness,

* there is one-dimensional and steady turbulent flow through the capillary tube,

* it is a fully insulated capillary tube,

* there is homogeneous two-phase flow,

* there is negligible metastable flow phenomenon,

* it is an oil-free refrigerant, and

* there is thermodynamic equilibrium through the capillary tube.

[FIGURE 1 OMITTED]

In this model, various design parameters that influence the size of the capillary tube as well as the tube diameter, roughness, degree of subcooling, refrigerant mass flow rate, and condenser and evaporator temperatures and pressure are included. The governing equations used to describe the flow behavior in the single-phase and two-phase flow regions are presented below.

Single-Phase Flow Region

The single-phase flow region begins at the inlet of the capillary and ends at the point where the pressure is dropped to the saturated pressure.

The steady flow energy equation between points 1 and 3 in Figure 1 can be written as

[[P.sub.1]/[[[rho].sub.1]g]] + [[V.sub.1.sup.2]/2g] + [Z.sub.1] = [[P.sub.3]/[[[rho].sub.3]g]] + [[V.sub.3.sup.2]/2g] + [Z.sub.3] + [h.sub.L]. (1)

For an incompressible fluid, and from the continuity equation,

m = [[rho].sub.2][V.sub.2]A = [[rho].sub.3][V.sub.3]A = [rho]VA. (2)

The total head loss can be determined from

[h.sub.L] = [f.sub.sp] [[L.sub.sp]/D] [[V.sup.2]/2g] + k[[V.sup.2]/2g], (3)

where [f.sub.sp] is the single-phase friction factor and k is the entrance loss coefficient (for square edged, k = 0.5).

For a horizontal tube, [Z.sub.2] = [Z.sub.3], and from the mass flow rate of refrigerant per unit the cross-section area (G) is [rho]V; therefore, the single-phase length, [L.sub.sp], of the capillary tube can be determined from

[L.sub.sp] = [([P.sub.1] - [P.sub.3]) x [2[rho]/[G.sup.2]] - k - 1] x [D/[f.sub.sp]]. (4)

The pressure at point 3 is assumed to be saturated and can be determined by knowing the subcooling temperature at the capillary tube entrance. The single-phase friction factor, [f.sub.sp], can be calculated from the Colebrook formula as follows:

1/[square root of [f.sub.sp]] = 1.14 - 2log[(e/D) + [9.3/[Re x [square root of [f.sub.sp]]]]], (5)

where

Re = [rho]VD/[mu]. (6)

Two-Phase Flow Region

The flow in this region is modeled as homogeneous flow. The fundamental equations applicable to this section are conservation of mass, energy, and momentum.

Consider a control volume in the two-phase region as shown in Figure 1.

The conservation of mass can be expressed as

m = [[V.sub.3]A]/[[upsilon].sub.3] = [[V.sub.4]A]/[[upsilon].sub.4]. (7)

For steady-state adiabatic with no external work and neglecting the elevation difference, the conservation of energy can be expressed as

h + [[V.sup.2]/2] = constant, (8)

where h and V are the enthalpy and velocity at any point in the two-phase region.

As the refrigerant flows through the capillary tube, its pressure gradually drops and the vapor fraction continuously increases. At any point,

h = [h.sub.f](1 - x) + [h.sub.g]x and (9)

[upsilon] = [[upsilon].sub.f](1 - x) + [[upsilon].sub.g]x. (10)

For continuity, m = [rho]VA = constant,

V = m/[rho]A = G/[rho]. (11)

Substituting Equations 9-11 into Equation 8, expanding the right-hand side, and rearranging gives

[h.sub.3] + [[V.sub.3.sup.2]/2] = [h.sub.f] + x([h.sub.g] - [h.sub.f] + [[[G.sup.2][[upsilon].sub.f.sup.2]]/2] + [x.sup.2]([[upsilon].sub.g] - [[upsilon].sub.f])[.sup.2][[G.sup.2]/2] + [G.sup.2][[upsilon].sub.f]([[upsilon].sub.g] - [[upsilon].sub.f])x. (12)

Thus, the quality, x, can be expressed as

x = {-[h.sub.fg] - [G.sup.2][[upsilon].sub.f][[upsilon].sub.fg] + [square root of (([h.sub.fg] + [G.sup.2][[upsilon].sub.f][[upsilon].sub.fg])[.sup.2] - (2[G.sup.2][[upsilon].sub.fg.sup.2])([h.sub.f] + 0.5 [G.sup.2][[upsilon].sub.f.sup.2] - [h.sub.3] - 0.5[V.sub.3.sup.2]))]}/[[G.sup.2][[upsilon].sub.fg.sup.2]] (13)

where [h.sub.fg] = [h.sub.g] - [h.sub.f] and [[upsilon].sub.fg] = [[upsilon].sub.g] - [[upsilon].sub.f].

The entropy increases through the capillary due to the adiabatic irreversible process and also notes that

s = [s.sub.f](1 - x) + [s.sub.g]x. (14)

The conservation of momentum can be expressed by again considering the element of fluid. The different forces applied to the element due to shear force acting on the inner pipe wall and the pressure difference on opposite ends are equal to the time rate of change in linear momentum of the system. Therefore,

(P[[[pi][D.sup.2]]/4]) (P + dP)[[[pi][D.sup.2]]/4] - [[tau].sub.w][pi]DdL = mdV, (15)

where [[tau].sub.w] is the wall shear stress defined as

[[tau].sub.w] = [f.sub.tp][rho][V.sup.2]/8. (16)

For constant mass flow rate, substituting Equation 16 into Equation 15 and rearranging gives

dL = [2D/[f.sub.tp]][[-[rho]dP/[G.sup.2]] + d[rho]/[rho]]. (17)

The homogeneous two-phase friction factor, [f.sub.tp], can be determined from Colebrook's equation with the Reynolds number defined as

Re = GD/[[upsilon].sub.tp]. (18)

SOLUTION METHODOLOGY

The capillary tube in the two-phase region (between points 3 and 4) can be divided into numerous sections. Since [P.sub.3] is known (saturated liquid), then the pressure at any section i is calculated from

[P.sub.i] = [P.sub.3] - i[DELTA]P. (19)

With the pressure [P.sub.i] known, the quality, [x.sub.i], can be calculated from Equation 13. The entropy of the section can be expressed as

[s.sub.i] = [s.sub.if](1 - x) + [s.sub.ig]x. (20)

For each section, [P.sub.i], [T.sub.i], [x.sub.i], [s.sub.i], and [f.sub.i] are calculated. The calculation is done section by section along the capillary tube up to the point where the entropy is maximum. At this point, the fluid velocity is equal to the local speed of sound and the flow is choked. Its pressure, [P.sub.i,smax], is compared to the evaporator pressure, [P.sub.evap]. If the pressure where the entropy is maximum, [P.sub.i,smax], is greater than the evaporator pressure, [P.sub.evap], the pressure at point 4, [P.sub.4], is taken as [P.sub.i,smax] and the pressure [P.sub.i,smax] is used for the calculation. If the pressure where the entropy is maximum, [P.sub.i,smax], is less than the evaporator pressure, [P.sub.evap], the pressure at point 4 is taken as [P.sub.evap].

From Equation 17, the two-phase length, [L.sup.tp], can be determined from

[L.sub.tp] = D[[-2/[G.sup.2]][[P.sub.s,max].[integral].[P.sub.3]][[rho]dP/[f.sub.tp]] + 2 [[P.sub.s,max].[integral].[P.sub.3]][dP/[[rho][f.sub.tp]]], (21)

where the two-phase friction factor, [f.sub.tp], can be calculated from Colebrook's equation.

Therefore, the total length of the capillary tube, L, can be written as

L = [L.sub.sp] + [L.sub.tp]. (22)

From the above calculation, the viscosity models used to calculate the two-phase viscosity, [[mu].sub.tp], are as follows:

Cicchitti et al. (1960)

[[mu].sub.tp] = x[[mu].sub.g] + (1 - x)[[mu].sub.f] (23)

Dukler et al. (1964)

[[mu].sub.tp] = [x[[upsilon].sub.g][[mu].sub.g] + (1-x)[[upsilon].sub.f][[mu].sub.f]]/[x[[upsilon].sub.g] + (1-x)[[upsilon].sub.f]] (24)

McAdams et al. (1942)

1/[[mu].sub.tp] = [x/[[mu].sub.g]] + [[1-x]/[[mu].sub.f]] (25)

All thermodynamic and thermophysical refrigerant properties are taken from the REFPROP computer program, version 6.01 (McLendon et al. 1998), and are developed in the function of pressure.

RESULTS AND DISCUSSION

The viscosity model used in the present work varied developing on the refrigerant and was based on the recommendations of past research (Wongwises and Pirompak 2001), in particular Bittle and Pate (1994). The Dukler et al. (1964) model was used for simulations with R-12 and R-22, and the Cicchitti et al. (1960) model was used for R-134a, while the McAdams et al. (1942) model, as the best all-round predictor, was used for the remaining refrigerants. After verification of the present numerical simulation is done by comparison with the experimental data, the charts used to predict the refrigerant mass flow rate or the capillary tube size are developed. In the final step, validating the developed selection charts, the results from the chart are also compared with the experimental data.

Mathematical Model Verification

In order to validate the present model, comparisons were made with the limited available experimental data reported in the literature.

Figure 2 shows a comparison of the pressure distribution along the capillary tube obtained from the model and that obtained from the experiment of Mikol (1963) for R-12. The conditions for the numerical calculation to obtain the curve correspond to the experimental condition of Mikol (1963) for R-12. As described, the flow of refrigerant through the capillary tube from the outlet of the condenser to the inlet of the evaporator can be divided into two regions: a single-phase subcooled liquid region and a two-phase region. In the single-phase subcooled liquid region, due to the wall frictional effects in fully developed flow in a constant-area tube, the pressure of refrigerant drops linearly while the temperature remains constant along the capillary tube. After the inception of vaporization, due to the frictional and acceleration effects, the pressure and temperature of refrigerant drops relatively fast--this is more rapid as the flow approaches the critical flow condition. The comparison shows an average error in length of 8.61%. The temperature distribution data of Sami and Maltais (2001) for R-410B is compared with the simulation result. Sami and Maltais (2001) did not specify the roughness of the capillary tube in their paper. The roughnesses used for the present simulations were obtained and averaged from their experimental data. There is good agreement between the experimental data and the numerical results. The agreement of the model with the experimental data is satisfactory. It should be noted that the temperature distribution shown in Figure 2 looks similar to the pressure distribution; this is because the single-phase length for this experimental condition is very short. In other words, the constant temperature region disappears in this figure.

Comparisons were also made with the R-410A experimental data of Fiorelli et al. (2002) for the pressure distribution and the temperature distribution along the capillary tube. It was found that the present numerical results from the McAdams et al. (1942) viscosity model are in good agreement.

[FIGURE 2 OMITTED]

Development of Practical Selection Chart

The results show that the developed model can be considered an effective tool for capillary tube design. The present mathematical model can be used to develop the charts for selecting appropriate capillary tubes for specific applications. The first step in developing a selection chart is to select parameters that have an influence on the length of the capillary tube. These parameters are focused on the input parameter to keep the selection chart simple and practical. The selected parameters used in the present correlation are: condensing temperature [T.sub.cond], subcooling temperature [T.sub.sub], capillary tube diameter D, and refrigerant mass flow rate m. The subcooling temperature is used to specify the phase inlet of the capillary tube. The evaporator pressure is not included in the selection chart, but the lengths of capillary tube correspond to the choked flow condition for any computation.

The steps of the development of the charts are as follows.

1. Select the capillary tube diameter (D) as 1.63 mm.

2. Select the degree of subcooling ([T.sub.sub]) as 0[degrees]C.

3. Select the condenser temperature ([T.sub.cond]) as 30[degrees]C.

4. Assume the mass flow rate of refrigerant (m).

5. Calculate the capillary tube length of the single-phase flow ([L.sub.sp]) as

[L.sub.sp] = [D/[f.sub.sp]][([P.sub.1] - [P.sub.3])[2[rho]/[G.sup.2]] - k - 1].

6. Compute the quality of refrigerant (x) and the capillary tube length of the two-phase flow ([L.sub.tp]) as

x = {-[h.sub.fg] - [G.sup.2][[upsilon].sub.f][[upsilon].sub.fg] + [square root of (([G.sup.2][[upsilon].sub.f][[upsilon].sub.fg] + [h.sub.fg])[.sup.2] - 2[G.sup.2][[upsilon].sub.fg.sup.2][[[[G.sup.2][[upsilon].sub.f.sup.2]]/2] + [h.sub.f] - [h.sub.3] - [[V.sub.3.sup.2]/2])]}]/[[G.sup.2][[upsilon].sub.fg.sup.2]] and [L.sub.tp] = D[[-2/[G.sup.2]][[P.sub.s,max][p.sub.evap].[integral].[P.sub.3]][[rho]/[f,sub.tp]]dP + 2[[P.sub.s,max],[P.sub.evap].[integral].[P.sub.3]][d[rho]/[[rho][f.sub.tp]]]].

7. If the total capillary tube length is not equal to 2,030 mm, calculation steps 4-6 are repeated until the total capillary tube length is equal to 2,030 mm.

8. Vary the condenser temperature (30[degrees]C-60[degrees]C). Calculation steps 4-7 are repeated.

9. Vary the degree of subcooling (0[degrees]C-35[degrees]C). Calculation steps 3-8 are repeated.

10. The selection charts, in which the x-axis is the condenser temperature and the y-axis is the refrigerant mass flow rate, are created at various degrees of subcooling.

Figure 3 shows an example of the preliminary selection chart for refrigerant R-134a flowing through a capillary tube having an internal diameter of 1.63 mm and a length of 2.03 m. The chart is developed in the style of ASHRAE (1988). The chart is valid only for steady adiabatic capillary tube flow. For a capillary tube having an internal diameter of 1.63 mm and a length of 2.03 m, the required mass flow rate can be easily determined from this chart by knowing the condenser pressure and the degree of subcooling. However, for a capillary tube having internal diameter and length other than these, the flow correction factor is required.

The steps of the development of the correction factor chart are as follows.

1. Start with [T.sub.cond] = 45[degrees]C, [T.sub.sub] = 0[degrees]C.

2. Select D as 0.5 mm.

3. Select L as 250 mm.

4. Assume the mass flow rate of refrigerant.

5. Calculate the capillary tube length of the single-phase flow.

6. Calculate the quality of refrigerant and the capillary tube length of the two-phase flow.

7. If the total capillary tube length is not equal to that assigned in step 3, calculation steps 4-6 are repeated until the total capillary tube length is equal to that assigned in step 3.

8. Calculate the correction factor by dividing the mass flow rate obtained from the last iteration by that obtained from the selection chart at 45[degrees]C for the condenser temperature and 0[degrees]C for the degree of subcooling.

[FIGURE 3 OMITTED]

9. Vary the capillary tube length between 250 and 10,000 mm. Then, calculation steps 4-8 are repeated.

10. Vary the internal diameter between 0.5 and 5 mm. Then, calculation steps 3-9 are repeated.

11. The correction chart in which the x-axis is the capillary tube length and the y-axis is the correction factor of mass flow rate of refrigerant is created at various internal diameters.

The correction factor chart to be applied to Figure 3 for other dimensions and lengths of capillary tubes is shown in Figure 4. It is interesting to note that ASHRAE (1988) uses the same chart for both R-12 and R-22. However, as expected, the R-12 and R-22 charts developed from the present mathematical model give different values of various parameters. With the same method, the selection charts and corresponding correction factor charts in the same style for the other alternative refrigerants as shown in Figures 5-12 can also be developed. It should be noted that a capillary tube correctly selected for a given condensing temperature may not be oversized for a higher condensing temperature if the refrigerant charge is limited.

To validate the selection chart, comparisons were made with the experimental data of Wijaya (1992) and Melo et al. (1999). Wijaya (1992) measured mass flow rates through a range of adiabatic capillary tubes with different inner diameters and condensing and subcooling temperatures for R-134a. Comparison of mass flow rates obtained from the present selection chart with the measured mass flow rates for four condensing temperatures of 37.8[degrees]C, 43.3[degrees]C, 48.9[degrees]C, and 54.4[degrees]C; 0.84 mm capillary tube inner diameter; and 16.7[degrees]C subcooling temperature shows that the measured mass flow rates fall within [+ or -]15% of the proposed selection chart (see Table 1).

[FIGURE 4 OMITTED]

Comparison of the results from the selection chart with the R-134a measured data of Melo et al. (1999) for the capillary tube diameter of 0.77 mm, capillary tube length of 2.009 m, condenser pressure of 14 bar, and roughness of 0.75 [micro]m shows that the selection chart underpredicts the mass flow rate for various given levels of subcooling with an average error of 15.0% (See Table 2).

However, because of the potential for floodback, evaporator starving, and other ills, capillary tube selections should always be confirmed by actual testing over the range of applicable temperatures.

CONCLUSIONS

This paper presents new selection charts for selecting the capillary tube size from the refrigerant mass flow rate and flow condition or for predicting the refrigerant mass flow rate through adiabatic capillary tubes from a given capillary tube size and flow condition. The mathematical model is developed from the homogeneous flow model. The governing equations are based on the basis of conservation of mass, energy, and momentum. The model is validated by comparing it with the measured data reported in the literature. The development of the selection charts, which can be used to size capillary tubes, is described. The selection charts and flow correction factors are proposed for practical use. The developed selection charts are verified by comparing them with the limited available experimental data. The comparison results are in good agreement.

ACKNOWLEDGMENT

The authors would like to express their appreciation to the Thailand Research Fund (TRF) for providing financial support for this study.

NOMENCLATURE

A = capillary cross-sectional area, [m.sup.2]

D = inner diameter, m

f = friction factor

G = mass flow rate per unit area, kg/s x [m.sup.2]

g = gravitational acceleration, m/[s.sup.2]

h = specific enthalpy, J/kg

k = entrance loss coefficient

L = length, m

m = mass flow rate, kg/s

P = pressure, Pa

Re = Reynolds number

s = specific entropy, J/kg x K

T = temperature, [degrees]C

e = roughness, m

V = velocity, m/s

x = quality

Greek Letters

[mu] = dynamic viscosity, kg/m s

[upsilon] = specific volume, [m.sup.3]/kg

[rho] = density, kg/[m.sup.3]

Subscripts

cond = condenser

evap = evaporator

f = liquid phase

g = gas phase

sp = single phase

tp = two phase

sub = subcooling

[FIGURE 5 OMITTED]

[FIGURE 6 OMITTED]

[FIGURE 7 OMITTED]

[FIGURE 8 OMITTED]

[FIGURE 9 OMITTED]

[FIGURE 10 OMITTED]

[FIGURE 11 OMITTED]

[FIGURE 12 OMITTED]

REFERENCES

ASHRAE. 1988. 1988 ASHRAE Handbook--Equipment, chapter 19. Atlanta: American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc.

Bansal, P.K, A.S. Rupasinghe. 1996. An empirical model for sizing capillary tubes. International Journal of Refrigeration 19:497-505.

Bittle, R.R., and M.B. Pate. 1994. A theoretical model for predicting adiabatic capillary tube performance with alternative refrigerants. ASHRAE Transactions 102(2):52-64.

Choi, J., Y. Kim, and J.T. Chung. 2004. An empirical correlation and rating charts for the performance of adiabatic capillary tubes with alternative refrigerants. Applied Thermal Engineering 24:29-41.

Cicchitti, A., C. Lombardi, M. Silvestri, G. Soldaini, and R. Zavattarelli. 1960. Two-phase cooling experiments--Pressure drop, heat transfer and burnout measurements. Energia Nucleare 7:407-25.

Dukler, A.E., M. Wicks, and R.G. Cleveland. 1964. Frictional pressure drop in two-phase flow, Parts A and B. AIChE Journal 10:38-51.

Fiorelli, F.A.S., A.A.S. Huerta, and O.M. Silvares. 2002. Experimental analysis of refrigerant mixtures flow through adiabatic capillary tubes. Experimental Thermal and Fluid Science 26:499-512.

Jung, D., C. Park, and B. Park. 1999. Capillary tube selection for HCFC-22 alternatives. International Journal of Refrigeration 22:604-14.

Kim, S.G., M.S. Kim, and S.T. Ro. 2002. Experimental investigation of the performance of R22, R407C and R410A in several capillary tubes for air-conditioners. International Journal of Refrigeration 25:521-31.

McAdams, W.H., W.K. Wood, and R.L. Bryan. 1942. Vaporization inside horizontal tubes, II--Benzene-oil mixture. Transactions of ASME 64:193.

McLinden, M.O., S.A. Klein, and E.W. Lemmon. 1998. REFPROP--Thermodynamic and Transport Properties of Refrigerants and Refrigerant Mixtures, NIST Standard Reference Database, version 6.01. Gaithersburg, MD: National Institute of Standards and Technology.

Melo, C., R.T.S. Ferreira, N.C. Boabaid, J.M. Goncalves, and M.M. Mezavi. 1999. An experimental analysis of adiabatic capillary tubes. Applied Thermal Engineering 19:669-84.

Mikol, E.P. 1963. Adiabatic single- and two-phase flow in small bore tubes. ASHRAE Journal 5:75-86.

Sami, S.M., and H. Maltais. 2001. Experimental analysis of capillary tubes behavior with some HCFC-22 alternative refrigerants. International Journal of Energy Research 25:1233-1247.

Stoecker, W.F., and J.W. Jones. 1982. Refrigeration and Air Conditioning, 2d ed. New York: McGraw-Hill.

Trisaksri, V., and S. Wongwises. 2003. Correlations for sizing adiabatic capillary tubes. International Journal of Energy Research 27:1145-64.

Wijaya, H. 1992. Adiabatic capillary tube test data for HFC-134a. Proceedings of the International Refrigeration Conference on Energy Efficiency and New Refrigerants, Purdue University, West Lafayette, Indiana, pp. 63-71.

Wongwises, S., and W. Pirompak. 2001. Flow characteristics of pure refrigerants and refrigerant mixtures in adiabatic capillary tubes. Applied Thermal Engineering 21:845-61.

Table 1. Comparison Between Data from Selection Chart and Experimental Data From Wijaya (1992) (R-134a, D = 0.84 mm, [T.sub.sub] = 16.7[degrees]C) [T.sub.cond] = [T.sub.cond] = 37.8[degrees]C 43.3[degrees]C m (kg/h) m (kg/h) Selection Error Selection Error L (m) Experiment Chart (%) Experiment Chart (%) 1.52 9.24 8.28 -10.38 10.06 8.64 -14.14 1.83 8.24 8.10 -1.70 9.17 8.45 -7.85 2.13 7.70 7.91 2.76 8.42 8.26 -1.90 2.44 7.13 7.73 8.44 7.84 8.06 2.82 2.75 6.84 7.54 10.30 7.63 7.87 3.20 3.04 6.45 7.36 14.18 7.16 7.68 7.23 [T.sub.cond] = [T.sub.cond] = 48.9[degrees]C 54.4[degrees]C m (kg/h) m (kg/h) Selection Error Selection Error L (m) Experiment Chart (%) Experiment Chart (%) 1.52 10.85 9.45 -12.91 11.64 10.26 -11.84 1.83 10.13 9.24 -8.83 10.96 10.03 -8.45 2.13 9.10 9.03 -0.72 9.81 9.80 -0.08 2.44 8.59 8.82 2.62 9.31 9.58 2.85 2.75 8.38 8.61 2.75 9.13 9.35 2.37 3.04 7.88 8.40 6.62 8.56 9.12 6.56 Table 2. Comparison Between Data from Selection Chart and Experimental Data from Melo et al. (1999) (R-134a, [P.sub.in] = 14 bar, L = 2.009 m, D = 0.77 mm) [T.sub.sub] m (kg/h) ([degrees]C) Experiment Selection Chart Error (%) 2.81 5.00 4.74 -5.20 3.56 5.23 4.85 -7.23 3.41 5.38 4.83 -10.30 3.70 5.40 4.88 -9.79 4.59 5.23 5.01 -4.22 5.19 5.73 5.10 -11.01 6.07 5.50 5.21 -5.33 7.41 5.65 5.37 -5.06 8.15 6.35 5.46 -14.01 8.44 6.00 5.49 -8.46 9.19 5.85 5.58 -4.52 9.78 5.92 5.65 -4.56 10.67 6.04 5.76 -4.61 10.81 6.08 5.78 -4.85 10.96 6.12 5.80 -5.09 11.26 6.35 5.85 -7.85 12.00 6.69 5.96 -10.97 12.44 6.38 6.02 -5.65 13.19 6.50 6.13 -5.63 13.78 6.54 6.22 -4.84 14.07 6.85 6.27 -8.47 14.67 6.88 6.35 -7.71 15.11 6.69 6.42 -4.07

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Author: | Pirompugd, Worachest; Wongwises, Somchai |
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Publication: | ASHRAE Transactions |

Geographic Code: | 1USA |

Date: | Jul 1, 2006 |

Words: | 4959 |

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