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Capillary tube sizing charts for fluorine-based refrigerants.



ABSTRACT

This paper provides new selection charts for the sizing of adiabatic ad·i·a·bat·ic  
adj.
Of, relating to, or being a reversible thermodynamic process that occurs without gain or loss of heat and without a change in entropy.
 capillary capillary (kăp`əlĕr'ē), microscopic blood vessel, smallest unit of the circulatory system. Capillaries form a network of tiny tubes throughout the body, connecting arterioles (smallest arteries) and venules (smallest veins).  tubes operating with alternative refrigerants Chemical refrigerants are assigned an R number(sometimes the label replaces it with the word Freon) which is determined systematically according to molecular structure. The following is a list of refrigerants with their R numbers, IUPAC chemical name, molecular formula, and CAS number. . The mathematical model
Note: The term model has a different meaning in model theory, a branch of mathematical logic. An artifact which is used to illustrate a mathematical idea is also called a mathematical model and this usage is the reverse of the sense explained below.
 is based on conservation of mass, energy, and momentum of fluids in the capillary tube. After the developed model is validated val·i·date  
tr.v. val·i·dat·ed, val·i·dat·ing, val·i·dates
1. To declare or make legally valid.

2. To mark with an indication of official sanction.

3.
 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 re·frig·er·ate  
tr.v. re·frig·er·at·ed, re·frig·er·at·ing, re·frig·er·ates
1. To cool or chill (a substance).

2. To preserve (food) by chilling.
 and air-conditioning systems. It is used as an automatic flow rate controller for the refrigerant re·frig·er·ant
adj.
1. Cooling or freezing; refrigerating.

2. Reducing fever.

n.
1. A substance, such as air, ammonia, water, or carbon dioxide, used to provide cooling either as the working substance of
 when varying load conditions and varying condenser condenser

Device for reducing a gas or vapour to a liquid. Condensers are used in power plants to condense exhaust steam from turbines and in refrigeration plants to condense refrigerant vapours, such as ammonia and Freons.
 and evaporator evaporator

Industrial apparatus for converting liquid into gas or vapour. The single-effect evaporator consists of a container or surface and a heating unit; the multiple-effect evaporator uses the vapour produced in one unit to heat a succeeding unit.
 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 contraction, in physics
contraction, in physics: see expansion.
contraction, in grammar
contraction, in writing: see abbreviation.

contraction - reduction
, mixture effect, viscosity, and friction factor Friction factor can refer to:
  • Darcy friction factor
  • Fanning friction factor
  • Atkinson friction factor (ventilation of mines)
 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 con·dense  
v. con·densed, con·dens·ing, con·dens·es

v.tr.
1. To reduce the volume or compass of.

2. To make more concise; abridge or shorten.

3. Physics
a.
 temperature, and subcooling. Kim et al. (2002) presented a dimensionless correlation based on the Buckingham [pi] theorem theorem, in mathematics and logic, statement in words or symbols that can be established by means of deductive logic; it differs from an axiom in that a proof is required for its acceptance.  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 cum·ber·some  
adj.
1. Difficult to handle because of weight or bulk. See Synonyms at heavy.

2. Troublesome or onerous.



cum
 for practical applications. In an attempt to overcome this problem, selection charts for sizing or predicting refrigerant flow rate were developed (ASHRAE ASHRAE American Society of Heating, Refrigerating & Air Conditioning Engineers  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 thermodynamics, branch of science concerned with the nature of heat and its conversion to mechanical, electric, and chemical energy. Historically, it grew out of efforts to construct more efficient heat engines—devices for extracting useful work from expanding  and fluid mechanics fluid mechanics, branch of mechanics dealing with the properties and behavior of fluids, i.e., liquids and gases. Because of their ability to flow, liquids and gases have many properties in common not shared by solids.  (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 In fluid mechanics, two-phase flow occurs in a system containing gas and liquid with a meniscus separating the two phases.

Historically, probably the most commonly-studied cases of two-phase flow are in large-scale power systems.
 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 in·su·late  
tr.v. in·su·lat·ed, in·su·lat·ing, in·su·lates
1. To cause to be in a detached or isolated position. See Synonyms at isolate.

2.
 capillary tube,

* there is homogeneous The same. Contrast with heterogeneous.

homogeneous - (Or "homogenous") Of uniform nature, similar in kind.

1. In the context of distributed systems, middleware makes heterogeneous systems appear as a homogeneous entity. For example see: interoperable network.
 two-phase flow,

* there is negligible This article or section is written like a personal reflection or and may require .
Please [ improve this article] by rewriting this article or section in an .
 metastable met·a·sta·ble  
adj.
Of, relating to, or being an unstable and transient but relatively long-lived state of a chemical or physical system, as of a supersaturated solution or an excited atom.
 flow phenomenon,

* it is an oil-free refrigerant, and

* there is thermodynamic equilibrium In thermodynamics, a thermodynamic system is said to be in thermodynamic equilibrium when it is in thermal equilibrium, mechanical equilibrium, and chemical equilibrium. The local state of a system at thermodynamic equilibrium is determined by the values of its intensive  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 inlet /in·let/ (-let) a means or route of entrance.

pelvic inlet  the upper limit of the pelvic cavity.

thoracic inlet  the elliptical opening at the summit of the thorax.
 of the capillary and ends at the point where the pressure is dropped to the saturated saturated /sat·u·rat·ed/ (sach´ah-rat?ed)
1. denoting a chemical compound that has only single bonds and no double or triple bonds between atoms.

2. unable to hold in solution any more of a given substance.
 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 in·com·press·i·ble  
adj.
Impossible to compress; resisting compression: mounds of incompressible garbage.



in
 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 coefficient /co·ef·fi·cient/ (ko?ah-fish´int)
1. an expression of the change or effect produced by variation in certain factors, or of the ratio between two different quantities.

2.
 (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 up·si·lon or yp·si·lon
n.
Symbol The 20th letter of the Greek alphabet.
].sub.3] = [[V.sub.4]A]/[[upsilon].sub.4]. (7)

For steady-state adiabatic with no external work and neglecting the elevation elevation, vertical distance from a datum plane, usually mean sea level to a point above the earth. Often used synonymously with altitude, elevation is the height on the earth's surface and altitude, the height in space above the surface.  difference, the conservation of energy can be expressed as

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

where h and V are the enthalpy enthalpy (ĕn`thălpē), measure of the heat content of a chemical or physical system; it is a quantity derived from the heat and work relations studied in thermodynamics.  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 right-hand side nderecha

right-hand side right nrechte Seite f

right-hand side nlato destro 
, 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 entropy (ĕn`trəpē), quantity specifying the amount of disorder or randomness in a system bearing energy or information. Originally defined in thermodynamics in terms of heat and temperature, entropy indicates the degree to which a given  increases through the capillary due to the adiabatic irreversible process Noun 1. irreversible process - any process that is not reversible
physical process, process - a sustained phenomenon or one marked by gradual changes through a series of states; "events now in process"; "the process of calcification begins later for boys than for
 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 shear force

Force acting on a substance in a direction perpendicular to the extension of the substance, as for example the pressure of air along the front of an airplane wing. Shear forces often result in shear strain.
 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 shear stress
n.
See shear.



shear stress

A form of stress that subjects an object to which force is applied to skew, tending to cause shear strain.
 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 Reynolds number [for Osborne Reynolds], dimensionless quantity associated with the smoothness of flow of a fluid. It is an important quantity used in aerodynamics and hydraulics.  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 choke  
v. choked, chok·ing, chokes

v.tr.
1. To interfere with the respiration of by compression or obstruction of the larynx or trachea.

2.
a.
. 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 ther·mo·dy·nam·ic
adj.
1. Characteristic of or resulting from the conversion of heat into other forms of energy.

2. Of or relating to thermodynamics.
 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 val·i·date  
tr.v. val·i·dat·ed, val·i·dat·ing, val·i·dates
1. To declare or make legally valid.

2. To mark with an indication of official sanction.

3.
 the developed selection charts, the results from the chart are also compared with the experimental data.

Mathematical Model Verification

In order to validate To prove something to be sound or logical. Also to certify conformance to a standard. Contrast with "verify," which means to prove something to be correct.

For example, data entry validity checking determines whether the data make sense (numbers fall within a range, numeric data
 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 If the temperature of the liquid is lower than the saturation temperature for the existing pressure, it is called either a subcooled liquid (implying that the temperature is lower than the saturation temperature for the given pressure) or a compressed liquid (implying that the  region and a two-phase region. In the single-phase subcooled liquid region, due to the wall frictional frictional

pertaining to or emanating from friction.


frictional acanthosis
see acanthosis nigricans.
 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 vaporization, change of a liquid or solid substance to a gas or vapor. There is fundamentally no difference between the terms gas and vapor, but gas is used commonly to describe a substance that appears in the gaseous state under standard conditions of , 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 Adv. 1. in other words - otherwise stated; "in other words, we are broke"
put differently
, 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 (1) Any value passed to a program by the user or by another program in order to customize the program for a particular purpose. A parameter may be anything; for example, a file name, a coordinate, a range of values, a money amount or a code of some kind.  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 Choked flow

Fluid flow through a restricted area whose rate reaches a maximum when the fluid velocity reaches the sonic velocity at some point along the flow path.
 condition for any computation Computation is a general term for any type of information processing that can be represented mathematically. This includes phenomena ranging from simple calculations to human thinking. .

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 To perform mathematical operations or general computer processing. For an explanation of "The 3 C's," or how the computer processes data, see computer.  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 One repetition of a sequence of instructions or events. For example, in a program loop, one iteration is once through the instructions in the loop. See iterative development.

(programming) iteration - Repetition of a sequence of instructions.
 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 Other Dimensions is a collection of stories by author Clark Ashton Smith. It was released in 1970 and was the author's sixth collection of stories published by Arkham House. It was released in an edition of 3,144 copies.  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 o·ver·size  
n.
1. A size that is larger than usual.

2. An oversize article or object.

adj. o·ver·size also o·ver·sized
Larger in size than usual or necessary.
 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 starve  
v. starved, starv·ing, starves

v.intr.
1. To suffer or die from extreme or prolonged lack of food.

2. Informal To be hungry.

3. To suffer from deprivation.
, 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 acknowledgment, in law, formal declaration or admission by a person who executed an instrument (e.g., a will or a deed) that the instrument is his. The acknowledgment is made before a court, a notary public, or any other authorized person.  

The authors would like to express their appreciation to the Thailand Research Fund (TRF TRF

thyrotropin releasing factor.
) for providing financial support for this study.

NOMENCLATURE nomenclature /no·men·cla·ture/ (no´men-kla?cher) a classified system of names, as of anatomical structures, organisms, etc.

binomial 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 In physics, gravitational acceleration is the acceleration of an object caused by the force of gravity from another object. An interesting fact is that any object will accelerate towards a large object at the same rate, regardless of the mass of the object. , 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 Greek letters,
n.pl symbols based on the Greek alphabet that are used to represent phenomena and objects in science.
 

[mu] = dynamic viscosity dynamic viscosity
n.
Symbol A measure of the molecular frictional resistance of a fluid as calculated using Newton's law.
, 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 refrigeration, process for drawing heat from substances to lower their temperature, often for purposes of preservation. Refrigeration in its modern, portable form also depends on insulating materials that are thin yet effective.  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 Burnout

Depletion of a tax shelter's benefits. In the context of mortgage backed securities it refers to the percentage of the pool that has prepaid their mortgage.
 measurements. Energia Nucleare 7:407-25.

Dukler, A.E., M. Wicks, and R.G. Cleveland. 1964. Frictional pressure drop It has been suggested that , , , , , , , , , , , , , , and be merged into this article or section.  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 ASME - American Society of Mechanical Engineers  64:193.

McLinden, M.O., S.A. Klein, and E.W. Lemmon. 1998. REFPROP--Thermodynamic and Transport Properties of Refrigerants and Refrigerant Mixtures, NIST (National Institute of Standards & Technology, Washington, DC, www.nist.gov) The standards-defining agency of the U.S. government, formerly the National Bureau of Standards. It is one of three agencies that fall under the Technology Administration (www.technology.  Standard Reference Database, version 6.01. Gaithersburg, MD: National Institute of Standards and Technology National Institute of Standards and Technology, governmental agency within the U.S. Dept. of Commerce with the mission of "working with industry to develop and apply technology, measurements, and standards" in the national interest. .

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 air conditioning, mechanical process for controlling the humidity, temperature, cleanliness, and circulation of air in buildings and rooms. Indoor air is conditioned and regulated to maintain the temperature-humidity ratio that is most comfortable and healthful. , 2d ed. New York New York, state, United States
New York, Middle Atlantic state of the United States. It is bordered by Vermont, Massachusetts, Connecticut, and the Atlantic Ocean (E), New Jersey and Pennsylvania (S), Lakes Erie and Ontario and the Canadian province of
: 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 Purdue University (pərdy`, -d`), main campus at West Lafayette, Ind. , West Lafayette, Indiana West Lafayette (IPA: [wɛst ˈlɑ.fəˌjɛt]) is a city in Tippecanoe County, Indiana, United States, 65 miles (105km) northwest of Indianapolis. The population was 28,778 at the 2000 census. , 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
COPYRIGHT 2006 American Society of Heating, Refrigerating, and Air-Conditioning Engineers, Inc.
No portion of this article can be reproduced without the express written permission from the copyright holder.
Copyright 2006 Gale, Cengage Learning. All rights reserved.

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Author:Pirompugd, Worachest; Wongwises, Somchai
Publication:ASHRAE Transactions
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Date:Jul 1, 2006
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