Study of the performance of a vapor compression refrigeration system using conically coiled tube-in-tube evaporator and condenser

Accepted Manuscript

Study of the performance of a vapor compression refrigeration system using conically coiled tube-in-tube evaporator and condenser M.R. Salem , H.A. El-Gammal , A.A. Abd-Elaziz , K.M. Elshazly PII: DOI: Reference:

S0140-7007(18)30498-5 https://doi.org/10.1016/j.ijrefrig.2018.12.006 JIJR 4205

To appear in:

International Journal of Refrigeration

Received date: Revised date: Accepted date:

28 August 2018 3 December 2018 5 December 2018

Please cite this article as: M.R. Salem , H.A. El-Gammal , A.A. Abd-Elaziz , K.M. Elshazly , Study of the performance of a vapor compression refrigeration system using conically coiled tube-in-tube evaporator and condenser, International Journal of Refrigeration (2018), doi: https://doi.org/10.1016/j.ijrefrig.2018.12.006

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Highlights The performance of a vapor compression refrigeration system is investigated.



Effects of conical evaporator/condenser torsions and taper angles are tested.

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Effects of the evaporator/condenser annuli Dean numbers are investigated.

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Correlations for the COP and evaporator/condenser effectiveness are proposed.

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Study of the performance of a vapor compression refrigeration system using conically coiled tube-in-tube evaporator and condenser M.R. Salem(*), H.A. El-Gammal, A.A. Abd-Elaziz and K.M. Elshazly Mechanical Engineering Department, Faculty of Engineering at Shoubra, Benha University,

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108 Shoubra St., 11629, Cairo, Egypt (*)

Corresponding author (M.R. Salem)

Email: [email protected] , [email protected]

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Abstract

This study experimentally investigates the effect of the geometrical parameters of a vertical conically coiled tube-in-tube (CCTIT) evaporator/condenser and their operating conditions on their effectiveness and on the coefficient of performance (COP) of a vapor compression

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refrigeration system (VCRS). Twelve CCTIT evaporator/condenser of different taper angles

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(0-135) and torsions (0.0777-0.1311) are tested for different water Dean numbers in their annuli, while R134a flows in their internal tube in a counter flow configuration. The results

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show that increasing the evaporator/condenser taper angles and torsions in addition to decreasing their water Dean numbers augment the evaporator/condenser effectiveness and the

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COP of the VCRS. However, the coils taper angles have the more dominant effect than the

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other studied parameters. Finally, experimental correlations are developed to predict the COP of the VCRS in addition to the effectiveness of both the evaporator and condenser as functions of the investigated parameters. Keywords: Conically coiled tube; Coefficient of performance; Vapor compression refrigeration system; Taper angle; Torsion. Nomenclatures

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ACCEPTED MANUSCRIPT Specific heat at constant pressure, J kg-1 C-1

h

Specific enthalpy, kJ kg-1

I

Electrical current, A

L

Length, m

̇

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Diameter, m

Mass flow rate, kg s-1

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Number of the turns of the HCT Pressure, Pa

p

Pitch, m

Q

Heat transfer rate, W

q

Amount of heat energy per unit mass, kJ kg-1

S

Spacing, m

T

Temperature,

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PT

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P

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Voltage drop, V Power, W

w

Specific work, kJ kg-1

Dimensionless Groups Dean Number Reynolds Number -3-

ACCEPTED MANUSCRIPT Greek Letters Cone angle, degree Differential

Power factor Effectiveness

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Coil torsion (dimensionless pitch ratio) Dynamic viscosity, kg m-1 s-1

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Density, kg m-3

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Uncertainty

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Superscripts and Subscripts Average

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Condenser/compressor/coil ev

Evaporator Inner/inlet/internal Out/outer

ref

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Coil curvature ratio

Refrigerant

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ACCEPTED MANUSCRIPT s

Surface

sub

Subcooled/subcooling

sup

Superheated/superheating

w

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Tube Water

Acronyms and Abbreviations Alternate Current

CCTIT

Conically Coiled Tube-In-Tube

COP

Coefficient of Performance

HCT

Helically Coiled Tube

HCTIT

Helically Coiled Tube-In-Tube

RE

Refrigeration Effect

VCRS

Vapor Compression Refrigeration System

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1 Introduction

Enhancing the thermal performance of the refrigeration systems affects directly on the energy, material and cost savings. The VCRS is one of the refrigeration systems, which is used in most domestic refrigerators in addition to in numerous large industrial and commercial refrigeration systems [1]. There are numerous methods that were employed in the VCRS to improve its COP. One of the proposed methods for improving the heat exchange is the helically coiled tubes (HCTs). They are widely used as heat exchangers and have many -5-

ACCEPTED MANUSCRIPT applications. This wide application of the HCTs is due to their compactness and the geometry promotes good mixing of the fluids, which leads to increasing the heat transfer coefficients [2, 3]. Due to the extensive use of the HCTs in these applications, knowledge about heat transfer and pressure drop characteristics is very important. A schematic representation of HCT characteristics with main geometrical parameters is shown in Fig. 1. Considering any

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cross-section of the HCT created by a plane passing through the coil axis, the side of tube wall nearest to the coil axis is termed inner side of the coil, while the farthest side is labeled as the outer side of the coil.

There are also dimensionless parameters that were commonly used to explain the effects of

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the coil curvature and coil torsion. They are defined as follows [4]:

( )

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( )

Where

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Coil curvature ratio; it is the ratio of the inner diameter of the coiled tube ( .

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mean diameter of the coil curvature,

) to the

Coil torsion (pitch ratio); it is the ratio of the coil pitch ( ) to the established length of

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one turn of the coil (

).

There are numerous studies, which were carried out to enhance the COP of the VCRS. Some

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of them investigated the effect of employing liquid-suction heat exchanger into the VCRS [5, 6]. Other studies were devoted to investigating the effect of geometrical parameters of the capillary tube on the VCRS performance [79]. In other investigations, the effect of adding nanoparticles to the cycle refrigerant or compressor oil was examined [1012]. In addition, the performance ejector refrigeration cycle was examined by other researchers [1315]. Furthermore, the effect of the VCRS evaporation and condensations temperatures and -6-

ACCEPTED MANUSCRIPT pressure were presented by [16, 17]. Moreover, there are many investigations on the thermal performance in the HCTs. Garimella et al. [18] experimentally examined the thermal attributes in the annulus-side of coiled tubes. In the experiments, two coil curvature ratios and two annuli diameter ratios were tested. Compared with the straight tubes, the authors indicated that the coiled ducts resulted in better heat transfer coefficients. Kang et al. [19]

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experimentally investigated the frictional loss and condensation characteristics of refrigerant R134a flowing in an HCT. The researchers demonstrated that the condensation coefficients of the refrigerant were reduced with increasing the Reynolds number of the water in the

curved annulus. Murai et al. [20] used the backlight imaging tomography to examine the

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centrifugal acceleration of phase distribution and interfacial pattern for gas-liquid flow in an HCT. The experiments showed that the centrifugal force caused due to the coil curvature, which generates a wall-clingy liquid film against gravity. Naess [21] presented experimental

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data on the average heat transfer attributes for four annular-coil geometries, covering the laminar, transition and turbulent flow regimes. The experiments confirmed that the convected

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heat in the transition and laminar regions significantly enhanced with increasing the HCT

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curvature. Salem et al. [2225] conducted a series of experimental investigations on the thermal performance characteristics of a shell and coil heat exchanger with/without

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Al2O3/water nanofluid in the HCT at different operating conditions of the two sides of the heat exchangers and at different geometrical parameters of the HCT. The main result was that

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the HCT provided a significant enhancement in the hydrothermal performance of the heat exchanger. The authors proposed numerous correlations to predict the average Nusselt numbers and the friction factor at for the studied parameters. From the literature survey, it is clear that there are numerous techniques that were conducted to enhance the COP of the VCRSs. However, there is still a need for the COP improvement. One of the proposed techniques is the HCT, which enhanced the thermal performance of the

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ACCEPTED MANUSCRIPT heat exchangers examined by other researchers. As indicated, the geometrical parameter of the coiled tubes and the operating conditions of the VCRS affect its COP. It was demonstrated that decreasing the coil curvature increased the rate of heat transfer rate in addition to the pressure drop. Therefore, in the present study, it is aimed to investigate the effect of the geometrical parameters of coiled tubes with different taper angles and coil

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torsions on the performance attributes of the refrigeration cycle at different operating conditions.

2 Experimental apparatus

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The apparatus used in the present investigation comprises heating and cooling water loops along with the refrigerant circuit. The hot water (supplied to the annulus side of the VCRS evaporator) circuit consists of a heating unit with a thermostat, pump, valves, water flow

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meter, and the connecting pipes. While the cooling water supplied to the annulus side of the VCRS condenser from the domestic water supply is passed through the connecting pipes and

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is controlled by a valve and water flow meter through an open loop. In addition, the

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refrigerant circuit consists of a compressor, valves, CCTIT condenser, filter drier, sight glass, capillary tube, CCTIT evaporator, temperature sensors, pressure/pressure difference

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transducers, and the connecting pipes. Fig. 2 is a schematic representation of the experimental facility in which the heating water from the heating unit to/from the evaporator annulus, and

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the cooling water to/from the condenser annulus is revealed as red lines, while the refrigerant (R134a) in the VCRS is illustrated with blue lines. Thirteen CCTIT evaporators/condensers of counter-flow configuration are constructed with different taper angles and coil torsions. The characteristic dimensions of the tested coils are revealed in Table 1. The experimental runs are divided into two parts; in the first part, twelve of them (coils no. 1 to 12) are used as evaporators while the coil no. 13 is used as the

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ACCEPTED MANUSCRIPT condenser. In the second part of the experiments, the coils no. 1 to 12 are used as condensers while the coil no. 13 is used as the evaporator. The CCTITs are formed from straight soft copper tubes of the same length; 5000 mm. The internal tube is of inner (dt,i) and outer (dt,o) diameters of 8.31 mm and 9.52 mm, respectively, while the outer tube is of inner (dan,i) and outer (dan,o) diameters of 17.65 mm and 19.05 mm, respectively. In addition, the coils are

(

)

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formed with four different taper angles (); 0° (helical), 45°, 90°, and 135°, using Eq. (3). ( )

It should be noted that a mild steel sheet was formed with the required cone angle and used

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for coiling the copper tubes. The first (top) turn of all coils is of an inner coil diameter of 100 mm, while the final (base) turn is of a different diameter according to the coil taper angle. It ought to be noticed that for CCTITs of  = 0°, the pitch between the coil turns is the same,

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while for other angles, the pitch increments as the coil turn diameter increase to provide the same torsion for all turns as indicated in Eq. (2). In addition, expanding the cone angle leads

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to decreasing the total number of coil-turns due to the fixed length of the tube as illustrated in Table 1.

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Additionally, to prevent any flattening to the CCTITs during coiling process, the tubes are

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filled with fine sand before bending to safeguard the smoothness of the inward surface and this is washed with high hot water flow after the process. Furthermore, care is taken to locate

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the inner tube into the centre of the outer tube by using a circular ring that has the dimension of the annulus with a clearance of 0.5 mm amid the filling progression. As the annulus is filled with fine sand, the ring is moved systematically until it exits from the other end of the tube after the annulus is completely loaded with the fine sand. Additionally, two copper pipes of inner diameters of 17.65 mm are welded at the outer tube to permit the water to enter/exit to/from the annular passage. Moreover, the outer surface of the CCTIT evaporators/condensers is thermally isolated with a rubber insulation material -9-

ACCEPTED MANUSCRIPT (12.4 mm thickness). Fig. 3 reveals a schematic representation of the CCTIT evaporator/condenser. In the present VCRS, a 1 hp centrifugal compressor model (KCG498HAG-C221H) is used. Additionally, a narrow copper tube of 1.62 mm internal diameter and 1500 mm effective length is conducted as a capillary device. Two digital pressure/differential pressure

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transducers are employed for measuring the pressure and pressure difference of the

refrigerant at the evaporator/condenser inlets and exits. One of them is of a high scale

(installed at the inlet and exit of the condenser) with a differential pressure range of 0206.8 kPa, with a maximum pressure of 17.24 bar. While the other transducer of a lower scale

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(installed at the inlet and exit of the evaporator) with a differential pressure range of 0103.4 kPa, with a maximum pressure of 3.45 bar. Both transducers are liquid and gas pressure measurement and of an accuracy of

of full scale. Four temperature sensors of digital

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readers with a resolution of 0.1C are utilized to measure the temperatures of the refrigerant incoming or leaving the condenser and the evaporator. The sensors are conducted on the

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refrigerant copper tube. Disregarding the conduction resistance of the tube wall, the readings

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are presumed to equal the refrigerant temperatures at these locations. The used filter drier and sight glass are Danfoss Type. The size of their inlet and outlet tubes is 3/8 inch.

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For the heating unit, it is comprised of a stainless-steel slab (2 mm thickness), which is formed to produce a cabinet with dimensions of 300 mm * 300 mm * 600 mm. Three ports

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are conducted to the cabinet; one is at the tank base, which represents the departure pipe to the pump. Whilst the others are on the cover of the tank, which represent the inlet ports from the evaporator and from the by-pass line. Two electric heaters (have a maximum power of 6 kW) are installed horizontally at the bottommost of the heating cabinet to heat the water to the wanted temperature. The operation of the electric heaters is based on a pre-adjusted digital thermostat, which is used to keep a constant temperature of the water directed to the - 10 -

ACCEPTED MANUSCRIPT evaporator. Moreover, the outer sides of the tank are thermally isolated utilizing a layer of each of ceramic fiber and glass wool. The heating water is given from the heating unit and circulated through the annular passage of the evaporator, flow meter-1 and is backed to the heating tank. The water is delivered by a 0.5 hp power rating centrifugal pump with a maximum capacity of 30 l/min. Two identical variable area flow meters of a range from 1.8 of reading), are used to estimate the rate of the heating/cooling

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to 18 l/min (accuracy of

water flow required for the evaporator/condenser. Four digital sensors, with a resolution of 0.1C, are directly embedded into the flow streams, at approximately 50 mm from inlet and exit ports of the annulus of the evaporator and condenser, to measure the water temperatures.

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While for the cooling loop, the cooling water circuit is an open loop. It is provided from the domestic water source and supplied to the annular passage of the condenser then to the drain.

3 Experimental procedures

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The rate of water flow is specified by a valve and flow meter-2.

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To initiate the experiments, the following parts are assembled: the evaporator, compressor,

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condenser, filter drier, sight glass, capillary tube, heating tank, pump, piping, flow meters, valves, and the pressure transducers. These parts are connected together using either nuts or

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welding the pipes with silver solder. Then, the temperature sensors are attached on the refrigeration piping at evaporator/condenser inlets and outlets, in addition to four temperature

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sensors are inserted in evaporator/condenser water inlets and outlets to measure the heating and cooling water inlet and outlet temperatures. After attaching the temperature sensors on the refrigerant tubes, they are well isolated from the surroundings. After assembling the VCRS components, it is charged with R134a. The first step to collect the data from the system is to fill the heating tank with water from the domestic water supply, and then the electric heaters, the compressor, and the pump are turned

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ACCEPTED MANUSCRIPT on. The temperature of the heating water in the tank is adjusted at 200.5C by regulating the temperature of the heating tank through its thermostat. While the condenser annulus is linked to the tap of the domestic water supply through a flexible hose. The water from the heating tank is circulated in the main line to the evaporator annulus at different flow rates in each experiment. The remainder from the pumped flow is returned to the tank through a bypass

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line. The ranges of the operating conditions are revealed in Tables 2 and 3.

In addition, all experiments are conducted with cooling water entering the condenser annulus at 281C inlet temperature. While its flow rate is adjusted through the faucet handle and the

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flow meter 2. A series of 144 experiments are carried out on the twelve evaporator/condenser geometries shown in Table 1. During the test operation, the steady-state condition is conducted when a maximum variation of

for each temperature sensor reading within 20

minutes is recorded. Moreover, it is considered to be accomplished when the variation of during a minute

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inlet/outlet temperatures of the water and refrigerant streams are within

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4 Data reduction

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period before each measurement is taken.

The measured temperatures and pressures during the experiments are used to calculate the

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specific enthalpy of the refrigerant in the different locations of the VCRS. It should be noted that each experiment is repeated three times, and the average readings of the measured

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variables are recorded despite the tinny difference between these repeated readings. Microsoft Excel sheets are prepared to process the experimental data for the COP and the other characteristic parameters of the VCRS. The specific enthalpy of the refrigerant is estimated using its measured pressure and temperature at the evaporator and condensers inlet end exit. Schematic representation of the VCRS on the P-h chart is revealed in Fig. 4. The estimated specific enthalpies are used for calculating the following parameters: - 12 -

ACCEPTED MANUSCRIPT ( ) ( ) ( ) ( ) ) is

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It should be noted that the specific enthalpy of the refrigerant entering the evaporator (

assumed to be equal to the specific enthalpy of the refrigerant entering the capillary tube (

).

In addition, the refrigerant mass flow rate in the VCRS is estimated in the present work based on the consumed electrical power by the compressor (neglecting any mechanical or thermal

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energy losses in the compressor); this is by measuring the voltage drop and the current passing across it. ̇

( ) , for the

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According to the Ministry of Electricity and Energy in Egypt, the power factor,

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public network is ranged from 0.93 to 0.97. In the present study, the AC power factor is assumed to be 0.95 [26, 27]. Additionally, to ensure the veracity of the measured data and

data as follows:

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calculations, the evaporator heat transfer rate is calculated from refrigerant and heating water

̇

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(

̇

CE

̇

)

( ) (

)

)

(

)

)

(

)

(

)

With the same method, the condenser load is calculated;

̇

̇

̇ (

(

Assuming that the measurements are sufficiently accurate without heat gain or loss, there is an energy balance between the two streams

and

. While in the

real experiments, there would always be some discrepancy between the two rates. Therefore, - 13 -

ACCEPTED MANUSCRIPT the arithmetical mean of the two,

and

is used as the heat load of each

exchanger.

|

|

|

|

|

|

)

(

)

(

)

(

)

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|

(

|

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For all experimental tests, the water and refrigerant loads in the evaporator and the condenser did not differ by more than 2.2% and 3%, respectively. The heat loads of the evaporator and the condenser are used for calculating their effectiveness’s,

(

̇

(

)

ED

̇

, respectively, as

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follows;

and

)

) and the condenser (

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For the water Dean Number in the evaporator (

(

)

(

)

) annuli are

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calculated as follows;

(

(

̇

)

)

̇

(

(

)

)

(

)

(

)

5 Uncertainty analyses Commonly, the accuracy of different measuring instruments affects the uncertainty in the experimental determinations. Consistent with the manufacturer, the uncertainty ( ) in the - 14 -

ACCEPTED MANUSCRIPT tubes diameters is 0.05 mm. The uncertainties in the lengths, in addition to the coils spacing (S), height and diameter are 0.5 mm. Here, the uncertainty in the parameters is estimated using Kline and McClintock [28] method. For all runs, the maximum determined uncertainties in the parameters are revealed in Table 4. For the assessed uncertainties in the

Appendix A.

6 Results and discussions

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6.1 Effect of CCTIT evaporator geometry

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other variables and parameters used in this research, additional information is introduced in

In this analysis, the twelve coils no. 1 to 12 shown in Table 1 are considered as evaporators, while coil no. 13 is used as a condenser. The evaporators are of a tube torsion from 0.0777 to 0.01311, and of a taper angle from 0 to 135. The operating conditions are varied according

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to Table 2. Figs. 5 and 6 present the obtained results due to varying the CCTIT evaporator

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taper angle and torsion in addition to its heating water Dean Number.

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6.1.1 VCRS operating conditions

Effect of CCTIT evaporator taper angle: It is revealed from Fig. 5 that increasing the taper

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angle of the CCTIT evaporator leads to a significant increase in the average pressure of both the evaporator and the condenser, and in the refrigerant subcooling inside the condenser, in

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addition to a noticeable decrease in the superheating of the refrigerant inside the evaporator. With increasing the taper angle of the CCTIT evaporator from 0 to 135, the evaporator and condenser average pressures increase from 1.44 bar to 1.97 bar, and from 8.47 bar to 10.55 bar, respectively. In addition, the refrigerant is superheated inside the evaporator and subcooled inside the condenser by average values of 13.1C and 6C, respectively, at ev = 0 and by 5C and 7.9C, respectively, at ev = 135. Furthermore, with increasing ev from 0 to - 15 -

ACCEPTED MANUSCRIPT 135, the refrigerant average pressure loss in the evaporator decreases from 56.3 kPa to 23.4 kPa, while the variation in the refrigerant pressure loss in the condenser is exceedingly small and can be negligible. This can be attributed to decreasing the centrifugal forces in both sides of the CCTIT evaporator with increasing its taper angle (the evaporator coil mean diameter increases), which weakens the secondary flow formation. This reduces the pressure drop in

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the evaporator and rises the compressor suction pressure, and consequently increases the VCRS pressures. This leads to increasing their corresponding saturation temperatures and consequently reduces the refrigerant superheating in the evaporator. Besides, increasing the refrigerant saturation temperature in the condenser is accompanied with increasing its

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corresponding saturation pressure. This leads to two phenomena’s; the first is decreasing the refrigerant latent heat, and the second is increasing the driving force for delivering more heat energy from the refrigerant in the condenser to the cooling water. This induces a relatively

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slight increase in the refrigerant subcooling inside the condenser coil and leads also to an insignificant effect of the evaporator taper angle on the quality of the refrigerant at the

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evaporator inlet.

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Effect of CCTIT evaporator torsion: It is observed from Fig. 5 that the effect of coil torsion is lower than that of the coil taper angle in the investigated range of these parameters. It is

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clear that increasing the CCTIT evaporator torsion slightly increases the average pressures of both the evaporator and condenser, in addition to the refrigerant subcooling inside the

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condenser, and slightly reduces the superheating of the refrigerant in the evaporator. With increasing the torsion of the CCTIT evaporator from 0.0777 to 0.1311, the evaporator and condenser average pressures increase from 1.58 bar to 1.79 bar, and from 9.4 bar to 9.6 bar, respectively. In addition, the refrigerant is superheated inside the evaporator and subcooled inside the condenser by average values of 10.6C and 6.9C, respectively, at ev = 0.0777 and by 8.2C and 7.2C, respectively, at ev = 0.1311. Furthermore, with increasing ev from - 16 -

ACCEPTED MANUSCRIPT 0.0777 to 0.1311, the refrigerant average pressure loss in the evaporator slightly decreases from 44.2 kPa to 35.7 kPa, while the variation in the refrigerant pressure loss in the condenser is very small and can be negligible. This can be returned to increasing the rotational forces in both sides of the evaporator as a result of increasing the coil torsion, which weakens the secondary flow that established by the centrifugal effect. This also

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reduces the pressure drop in the evaporator and rises the compressor suction pressure, and consequently increases the VCRS pressures. This raises their corresponding saturation

temperatures, which slightly reduces the amount of the refrigerant superheating inside the evaporator.

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Effect of heating water Dean Number: It is indicated from Fig. 5 that the heating water

Dean Number slightly affects the VCRS operating conditions. It is clear that with increasing Deev, w, the average pressures of the evaporator and condenser, in addition to the refrigerant

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superheating inside the evaporator slightly increase, while the refrigerant subcooling in the condenser slightly decreases. With increasing Deev, w from 119.8 to 756.4, the evaporator and

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condenser average pressures increase from 1.59 bar to 1.77 bar, and from 9.34 bar to 9.62

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bar, respectively. In addition, the refrigerant is superheated inside the evaporator and subcooled inside the condenser by average values of 8.7C and 7.4C, respectively, at Deev, w

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= 119.8 and by 10.1C and 6.6C, respectively, Deev, w = 756.4. Furthermore, with increasing Deev, w from 119.8 to 756.4, the refrigerant average pressure loss in the evaporator slightly

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decreases from 42.6 kPa to 37 kPa, while the variation in the refrigerant pressure loss in the condenser is very small and can be negligible. This can be returned to increasing the corresponding evaporator saturation temperature and pressure as a result of increasing the heating water flow rate in addition to increasing the annulus side centrifugal force. This slightly raises the compressor suction pressure, which consequently raises the condenser pressure. Furthermore, increasing the heating water Dean number enhances the rate of heat - 17 -

ACCEPTED MANUSCRIPT exchange in the evaporator, which increases the amount of the refrigerant superheating inside the evaporator. Additionally, increasing the heating water Dean number slightly reduces the refrigerant subcooling inside the condenser as a result of increasing the refrigerant temperature at the condenser inlet. Besides, the refrigerant pressure loss slightly decreases with increasing the heating water Dean number. This can be backed to increasing the rate of

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phase change from liquid to vapor, which increases the superheated vapor refrigerant region in the internal tube. Because the superheated vapor has a lower viscosity, it provides a lower overall pressure drop.

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6.1.2 VCRS specifications

Effect of CCTIT evaporator taper angle: It is evident that the CCTIT evaporator taper angle significantly affects the VCRS performance parameters as illustrated in Fig. 6. Increasing the

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evaporator taper angle from 0 to 135 reduces both the evaporator refrigeration effect and the compressor specific work by an average percentage decrease of 12.3% and 25.4%,

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respectively. This augments the COP of the VCRS by an average percentage increase of

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17.4%. The decrease in the evaporator refrigeration effect is due to decreasing the centrifugal forces in both sides of the CCTIT evaporator with increasing the coil taper angle (the coil

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mean diameter increases), which weakens the secondary flow formation. Therefore, the refrigerant superheating inside the evaporator decreases, and consequently reduces the

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evaporator refrigeration effect. Simultaneously, the specific volume of the refrigerant at the compressor inlet decreases with decreasing the refrigerant temperature at the compressor inlet, and consequently the specific work required to compress the refrigerant molecules decreases. This is also the reason for increasing the refrigerant mass flow rate (by 31.3%) as a result of increasing the taper angle of the CCTIT evaporator. It is clear that increasing the refrigerant flow rate (31.3%) is larger than the reduction in the RE (12.3%), which resulted in

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ACCEPTED MANUSCRIPT increasing the cooling capacity at the same conditions by 15%. Additionally, increasing the evaporator taper angle decreases the temperature of the refrigerant at the condenser inlet, which leads to decreasing the condenser load. It is also seen that the variation of the evaporator taper angle significantly affects the evaporator effectiveness. Increasing the CCTIT evaporator taper angle from 0 to 135 enhances its effectiveness by 62%. This may

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be due to decreasing the evaporator taper angle leads to reducing the single-phase region of the refrigerant in the internal tube, which has less heat transfer coefficient than that in the case of the two-phase.

Effect of CCTIT evaporator torsion: It is demonstrated in Fig. 6 that the effect of coil torsion

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is lower than that of the coil taper angle in the investigated range of these parameters. It is clear that increasing the CCTIT evaporator torsion from 0.0777 to 0.1311 reduces both the evaporator refrigeration effect and the compressor specific work by an average percentage

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decrease of 7.5% and 10.8%, respectively. This slightly enhances the COP of the VCRS by an average percentage of 3.5%, while the condenser load is decreased by 8.3%. As mentioned

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before, increasing the evaporator torsion slightly reduces the refrigerant superheating inside

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the evaporator, which slightly minimizes the evaporator refrigeration effect. Simultaneously, the specific volume of the refrigerant at the compressor inlet decreases, and consequently the

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specific work required to compress the refrigerant molecules decreases. This is also the reason for increasing the refrigerant mass flow rate by increasing the torsion of the CCTIT

AC

evaporator. Increasing the CCTIT evaporator torsion from 0.0777 to 0.1311 augments the refrigerant mass flow rate by 12.1%. Additionally, increasing the evaporator torsion reduces the temperature of the refrigerant at the condenser inlet, which leads to minimizing the condenser load. In addition, it is observed that increasing the evaporator torsion enhances evaporator effectiveness. Increasing the CCTIT evaporator torsion from 0.0777 to 0.1311 augments the evaporator effectiveness by 22.5%. This also may be due to increasing the

- 19 -

ACCEPTED MANUSCRIPT evaporator torsion leads to reducing the single-phase region of the refrigerant in the internal tube, which has less heat transfer coefficient than that in case of the two-phase. Effect of heating water Dean Number: It is indicated from Fig. 7 that the heating water Dean Number slightly affects the VCRS specifications. It is clear that with increasing the heating water Dean Number from 119.8 to 756.4, both the evaporator refrigeration effect and

CR IP T

the compressor specific work slightly increase by an average percentage of 2.7% and 6.8%, respectively. This slightly reduces the COP of the VCRS by an average percentage of 3.7%. The slight increase in the evaporator refrigeration effect is due to increasing the superheating of the refrigerant inside the evaporator with increasing the heating water Dean Number in the

AN US

CCTIT evaporator annulus, which induces more effective secondary flow. Therefore, the refrigerant superheating inside the evaporator increases, which augments the evaporator refrigeration effect. Additionally, the specific volume of the refrigerant at the compressor

M

inlet increases with increasing heating water Dean Number, which raises the refrigerant temperature at the compressor inlet, and consequently the specific work required to compress

ED

the refrigerant molecules increases. This is also the reason for decreasing the refrigerant mass

PT

flow rate (by 6.2%) as a result of increasing the heating water Dean Number from 119.8 to 756.4. Moreover, the condenser load is slightly augmented (by 3.6%). This may be due to

CE

increasing the condenser saturation temperature, which increases the driving forces for enhancing the heat exchange. Furthermore, the evaporator effectiveness significantly

AC

decreases with increasing its heating water Dean Number. Increasing the heating water Dean Number from 119.8 to 756.4 reduces the evaporator effectiveness by 39.8%. This is compatible with and assures Kang et al. [19] findings. The author experimentally investigated the condensation heat transfer in an HCTIT condenser, and the results indicated that increasing annulus-side Dean Number increased the single-phase region in the internal tube, which has less heat transfer coefficient than that in case of the two-phase.

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ACCEPTED MANUSCRIPT

6.2 Effect of CCTIT condenser geometry In this analysis, the twelve coils no. 1 to 12 shown in Table 1 are considered as condensers, while coil no. 13 is used as an evaporator. The condensers are of a tube torsion from 0.0777 to 0.01311, and of a taper angle from 0 to 135. The operating conditions are varied

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according to Table 3. Figs. 7 and 8 illustrate the obtained results due to varying the CCTIT condenser taper angle and torsion in addition to its cooling water Dean Number.

6.2.1 VCRS operating conditions

AN US

Effect of CCTIT condenser taper angle: It is indicated from Fig. 7 that increasing the

CCTIT condenser taper angle leads to a significant increase in the average pressures of both the evaporator and the condenser, and to a noticeable decrease in the refrigerant superheating

M

and subcooling inside the evaporator and condenser, respectively. With increasing the taper angle of the CCTIT condenser from 0 to 135, the evaporator and condenser average

ED

pressures increase from 1.40 bar to 1.92 bar, and from 8.65 bar to 10.55 bar, respectively. In

PT

addition, the refrigerant is superheated inside the evaporator and subcooled inside the condenser by average values of 11.8C and 9.6C, respectively, at c = 0 and by 9.5C and

CE

5.2C, respectively, at c = 135. Furthermore, with increasing c from 0 to 135, the

AC

refrigerant average pressure loss in the condenser decreases from 75.8 kPa to 53 kPa, while the refrigerant pressure loss variation inside the evaporator can be neglected. This can be attributed to decreasing the centrifugal forces in both sides of the condenser with increasing its taper angle (the condenser coil mean diameter increases), which weakens the secondary flow formation. Therefore, the refrigerant pressure loss and subcooling inside the condenser decrease. This leads to increasing the average pressures of the VCRS as a result of increasing

- 21 -

ACCEPTED MANUSCRIPT their corresponding saturation temperatures, and consequently, the refrigerant superheating in the evaporator decreases for the same heating water load. Effect of CCTIT condenser torsion: It is detected from Fig. 7 that the effect of CCTIT condenser torsion is lower than that of its taper angle in the investigated range of these parameters. It is shown that increasing the CCTIT condenser torsion slightly increases the

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average pressures of both the evaporator and condenser and slightly reduces the refrigerant superheating and subcooling inside the evaporator and condenser, respectively. With

increasing the CCTIT condenser torsion from 0.0777 to 0.1311, the evaporator and condenser average pressures increase from 1.59 bar to 1.77 bar, and from 9.37 bar to 9.77 bar,

AN US

respectively. In addition, the refrigerant is superheated inside the evaporator and subcooled inside the condenser by average values of 11.3C and 8C, respectively, at c = 0.0777 and by 10.3C and 7.1C, respectively, at c = 0.1311. Furthermore, with increasing c from

M

0.0777 to 0.1311, the refrigerant average pressure loss in the condenser slightly decreases from 67.7 kPa to 62.7 kPa, while the refrigerant pressure loss variation inside the evaporator

ED

can be neglected. This can be returned to increasing the rotational forces in both sides of the

PT

condenser as a result of increasing the coil torsion, which weakens the secondary flow that established by the centrifugal effect. This reduces the refrigerant subcooling inside the

CE

condenser in addition to its the pressure drop, which raises the condenser average pressure, and consequently increases the VCRS pressures. This raises the evaporator corresponding

AC

saturation temperature, which slightly reduces the amount of the refrigerant superheating inside the evaporator. Effect of cooling water Dean Number: It is indicated from Fig. 7 that the condenser cooling water Dean Number slightly affects the VCRS operating conditions. It is evident that with increasing Dec, w, the average pressures of both the evaporator and condenser slightly decrease, while the refrigerant superheating inside the evaporator and subcooling in the - 22 -

ACCEPTED MANUSCRIPT condenser slightly increase. With increasing Dec, w from 166.3 to 1050.6, the evaporator and condenser average pressures decrease from 1.76 bar to 1.58 bar, and from 9.73 bar to 9.35 bar, respectively. In addition, the refrigerant is superheated inside the evaporator and subcooled inside the condenser by average values of 10.4C and 7.1C, respectively, at Dec, w = 166.3 and by 11.2C and 7.9C, respectively, Dec, w = 1050.6. Furthermore, with increasing

CR IP T

Dec, w from 166.3 to 1050.6, the refrigerant average pressure loss in the condenser slightly increases from 61.4 kPa to 68.9 kPa, while the variation in the refrigerant pressure loss in the evaporator is very small and can be negligible. The decrease in the cycle pressures can be

AN US

returned to decreasing the corresponding condenser saturation temperature as a result of

increasing the rate of heat exchange in the condenser with increasing its cooling water flow rate in addition to increasing the annulus side centrifugal force. This slightly enhances the refrigerant subcooling in the condenser and reduces the condenser pressure, which

M

consequently reduces the evaporator pressure. This reduction in the evaporator pressure reduces its refrigerant saturation temperature, which enhances the refrigerant superheating.

ED

Furthermore, with increasing Dec, w from 166.3 to 1050.6, the refrigerant average pressure

PT

loss in the condenser slightly increases from 61.4 kPa to 68.9 kPa, while the variation in the refrigerant pressure loss in the evaporator is very small and can be negligible. This may be

CE

due to increasing the liquid region in the condenser, which has a higher viscosity and

AC

consequently provides a higher pressure drop.

6.2.2 VCRS specifications Effect of CCTIT condenser taper angle: It is clear that the CCTIT condenser taper angle significantly affects the VCRS performance parameters as illustrated in Fig. 8. Increasing the condenser taper angle from 0 to 135 reduces both the evaporator refrigeration effect, the compressor specific work and the condenser load by an average percentage decrease of - 23 -

ACCEPTED MANUSCRIPT 14.4%, 28.9% and 18.1, respectively. This augments the COP of the VCRS by an average percentage increase of 20.4%. The decrease in the condenser load is due to decreasing the centrifugal forces in both sides of the CCTIT condenser with increasing its taper angle (the coil mean diameter increases), which weakens the secondary flow formation. Therefore, the refrigerant subcooling inside the condenser decreases, which reduces the condenser cooling

CR IP T

load. Simultaneously, the average pressure of the evaporator increases, and the superheating of the refrigerant slightly decreases. Therefore, the specific volume of the refrigerant at the compressor inlet decreases, and consequently the specific work required to compress the refrigerant molecules decreases. This is also the reason for increasing the refrigerant mass

AN US

flow rate as a result of increasing the CCTIT condenser taper angle. It is also evident that the variation of the condenser taper angle significantly affects the condenser effectiveness. Increasing the CCTIT condenser taper angle from 0 to 135 enhances its effectiveness by

M

36.2%. This may be due to decreasing the condenser taper angle leads to reducing the singlephase region of the refrigerant in the internal tube, which has less heat transfer coefficient

ED

than that in the case of the two-phase.

PT

Effect of CCTIT condenser torsion: It is demonstrated from Fig. 8 that the effect of condenser torsion is also lower than that of the condenser taper angle in the investigated

CE

range of these parameters. It is clear that increasing the CCTIT condenser torsion from 0.0777 to 0.1311 reduces both the evaporator refrigeration effect, the compressor specific

AC

work and the condenser cooling load by an average percentage decrease of 6.1%, 9.2%, and 6.8%, respectively. This slightly enhances the COP of the VCRS by an average percentage of 3.4%. As mentioned before, this is due to increasing the rotational force as a result of increasing the coil torsion, which weakens the secondary flow that established by the centrifugal effect. Consequently, the refrigerant subcooling inside the condenser decreases, which slightly minimizes the condenser cooling and the evaporator refrigeration effect. In

- 24 -

ACCEPTED MANUSCRIPT addition, the decrease in the superheating of the refrigerant in the evaporator reduces the specific volume of the refrigerant at the compressor inlet decreases, and so the specific work needed to compress the refrigerant molecules decreases. This is also the reason for the slight increase in the refrigerant mass flow rate by increasing the torsion of the CCTIT condenser. Increasing the CCTIT condenser torsion from 0.0777 to 0.1311 augments the refrigerant mass

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flow rate by 10.1%. It is also seen that increasing the condenser torsion from 0.0777 to

0.1311 improves its effectiveness with an average increase of 16.9%. This also may be due to increasing the condenser torsion leads to reducing the single-phase region of the refrigerant in the internal tube, which has less heat transfer coefficient than that in case of the two-phase.

AN US

Effect of cooling water Dean Number: It is indicated from Fig. 8 that the condenser cooling water Dean Number slightly affects the VCRS specifications. With increasing the cooling water Dean Number from 166.3 to 1050.6, both the evaporator refrigeration effect, the

M

compressor specific work and the condenser cooling load increase by an average percentage of 1.5%, 7.8%, and 3%, respectively. This reduces the COP of the VCRS by an average

ED

percentage of 5.7%. The slight increase in the condenser cooling load and the evaporator

PT

refrigeration effect is due to increasing the subcooling and superheating of the refrigerant inside the condenser and the evaporator, respectively, with increasing the cooling water Dean

CE

Number in the CCTIT condenser annulus. While the compressor specific work increases because of increasing the specific volume of the refrigerant at the compressor inlet due

AC

increasing the vapor refrigerant temperature by decreasing the evaporator pressure. Therefore, the refrigerant mass flow rate decreases; increasing the cooling water Dean Number from 166.3 to 1050.6 reduces the refrigerant mass flow rate by 7.2%. Furthermore, the condenser effectiveness significantly decreases with increasing its cooling water Dean Number. Increasing the cooling water Dean Number from 166.3 to 1050.6 reduces the condenser effectiveness by 57.7%. This is compatible with and assures Kang et al. [19]

- 25 -

ACCEPTED MANUSCRIPT findings. The author experimentally investigated the condensation heat transfer in an HCTIT condenser, and it was shown that increasing annulus-side Dean Number increased the singlephase region in the internal tube, which has less heat transfer coefficient than that in case of

7 Experimental correlations

CR IP T

the two-phase.

Using the present experimental data, empirical correlations are developed to predict the COP of the VCRS, and the effectiveness of the CCTIT evaporator and condenser in their taper

(

AN US

angles, torsions and annulus-side Dean Number as follows; )

(

(

)

)

M

(

)

(

)

(

)

(

)





,

PT

,

ED

Eqs. (21) to (23) are applicable for a VCRS with CCTIT evaporator and condenser of

( ⁄

,

)



, ,

. Comparisons of the COP of the VCRS and the

CE

, and

, 

,

effectiveness of both the CCTIT evaporator and condenser with those calculated by the

AC

proposed correlations are shown in Fig. 9. In addition, the results of condenser effectiveness; Eq. (23) are compared with the results obtained by Kang et al [19] for HCTIT condenser. The result of this comparison is shown in Fig. 10. From Fig. 9, the proposed correlations are in good agreement with the present experimental data. It is clearly seen that the data falls of the proposed equations within maximum deviations of

,

and

for the COP of the VCRS, and the effectiveness of

- 26 -

ACCEPTED MANUSCRIPT the CCTIT evaporator and condenser, respectively. Furthermore, a fair agreement is noticed between the present results with the published data [19] with an average deviation of 9.1%. This good agreement in the comparison reveals the accuracy of the proposed correlation.

8 Conclusions

CR IP T

The present study investigates the effect of the geometrical parameters of a vertical conically coiled tube-in-tube evaporator/condenser and their operating conditions on their effectiveness and the coefficient of performance (COP) of a vapor compression refrigeration system

(VCRS). Twelve CCTIT evaporator/condenser of different taper angles and torsions are

AN US

tested for different water Dean numbers in their annuli, while R134a flows in their internal tube. The investigated operating parameters are  , 

, ,

,

,

,

, and

( ⁄

)

M

,





. According to the obtained results, the following conclusions can be expressed: Increasing the CCTIT evaporator and condenser taper angles augment both the COP of

ED



PT

the VCRS and the evaporator and condenser effectiveness.  Increasing the evaporator taper angle from 0 to 135 augments the COP of the VCRS

CE

and the evaporator effectiveness by 17.4% and 62%, respectively.

AC

 Increasing the condenser taper angle from 0 to 135 augments the COP of the VCRS and the condenser effectiveness by 20.4% and 36.2%, respectively.



Increasing the CCTIT evaporator and condenser torsions augment both the COP of the VCRS and the evaporator and condenser effectiveness.  Increasing the CCTIT evaporator torsion from 0.0777 to 0.1311 enhances the COP of the VCRS and the evaporator effectiveness by 3.5% and 22.5%, respectively.

- 27 -

ACCEPTED MANUSCRIPT  Increasing the CCTIT condenser torsion from 0.0777 to 0.1311 enhances the COP of the VCRS and the condenser effectiveness by 3.4% and 16.9%, respectively. 

Decreasing the CCTIT evaporator heating water and condenser cooling water Dean Numbers augments both the COP of the VCRS and the evaporator and condenser effectiveness.

CR IP T

 Increasing the heating water Dean Number from 119.8 to 456.4 reduces the COP of the VCRS and the evaporator effectiveness by 3.7% and 39.8%, respectively.

 Increasing the cooling water Dean Number from 116.3 to 1050.6 reduces the COP of the VCRS and the condenser effectiveness by 5.7% and 57.7%, respectively.

Experimental correlations are developed to predict the COP of the VCRS in addition to

AN US



the effectiveness of both CCTIT evaporator and condenser.

M

9 Appendix A

In the present study the root sum square combination of the effects of each of individual

ED

inputs as introduced by Kline and McClintock [28] are applied to determine the uncertainty

PT

in all parameters as;

)

CE

√(

AC

√(

√(

√(

√(

)

(

)

)

(24)

(

(

)

)

)

(

)

(

(25)

(26)

)

(27)

)

(28)

- 28 -

ACCEPTED MANUSCRIPT

)

(

)

(

√(

̇

√(

)

̇

̇

(

)

(

)

√(

)

(

)

√(

)

(

)

)

(32)

(33)

CE

)

)

(

)

̇

)

̇

(

)

(

(

̇

̇

(35)

(37)

)

(38)

)

̇

)

̇

(

(34)

(36)

ED (

PT

)

√(

√(

(

)

(

√(

(31)

)

)

√(

AC

)

̇

√(

√(

̇

(30) ̇

(

)

√(

̇

)

M

̇

(29)

CR IP T

√(

)

AN US

√(

(39)

)

(

)

)

(40)

(41)

- 29 -

ACCEPTED MANUSCRIPT

̇

)

(

√(

)

√(

√(

√(

)

)

(

)

(

)

(

(

(42)

(43)

(44)

)

̇

)

̇

̇

̇

)

)

)

References

(

(

)

)

(

(

)

)

(45)

(46)

N.Q. Minh, N.J. Hewitt, P.C. Eames. Improved vapour compression refrigeration

M

[1]

(

CR IP T

̇

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√(

ED

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PT

[2]

CE

in membrane helical-coil heat exchanger and membrane serpentine-tube heat exchanger. International Communications in Heat and Mass Transfer. 38(9), 1189–1194. T.A. Pimenta, J.B.L.M. Campos, 2012. Friction losses of Newtonian and non-

AC

[3]

newtonian fluids flowing in laminar regime in a helical coil. Experimental Thermal and Fluid Science. 36, 194–204. [4]

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helical circular tube. Fluid Dynamics Research. 16(4), 237–249.

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ACCEPTED MANUSCRIPT [5]

S.A. Klein, D.T. Reindl, K. Brownell, 2000. Refrigeration system performance using

liquid-suction heat exchangers. International Journal of Refrigeration. 23(8), 588–596. [6]

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heat exchanger influence on a vapour compression plant energy efficiency working with R22,

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CR IP T

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in an adiabatic spiral capillary tube. Journal of Thermal Science and Engineering

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R600a nano-refrigerant as working fluid. Energy Conversion and Management. 52, 733737.

AC

characteristics of Al2O3-R141b nanorefrigerant in horizontal smooth circular tube. Procedia Engineering. 56, 323–329. [12]

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X. Ma, W. Zhang, S.A. Omer, S.B. Riffat, 2010. Experimental investigation of a novel

steam ejector refrigerator suitable for solar energy applications. Applied Thermal Engineering. 30, 1320–1325. [14]

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a controllable ejector. International Journal of Refrigeration. 35(6), 1604–1616. S. Varga, P.M.S. Lebre, A.C. Oliveira, 2013. CFD study of a variable area ratio ejector

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refrigeration systems. Exergy, An International Journal. 2(4), 266–272. S. Garimella, D.E. Richards, R.N. Christensen, 1988. Experimental investigation of

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heat transfer in coiled annular duct. Journal of Heat Transfer, ASME. 110, 329–336.

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helicoidal pipe. International Journal of Heat and Mass Transfer. 43, 2553–2564. Y. Murai, H. Oiwa, T. Sasaki, K. Kondou, S. Yoshikawa, F. Yamamoto, 2005.

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Backlight imaging tomography for gas–liquid two-phase flow in a helically coiled tube. Measuring Science and Technology. 16, 1459–1468. [21]

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coil curvature effect on heat transfer and pressure drop characteristics of shell and coil heat exchanger. Journal of Thermal Science and Engineering Applications. 7(1), 011005. [23]

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transfer and pressure drop characteristics of shell and coil heat exchanger. Journal of Thermal Science and Engineering Applications. 8(1), 011015. [25]

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nanofluid on the thermal performance of shell and coil heat exchanger with different coil

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ED

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guide fence: an experimental study. Experimental Thermal and Fluid Science. 33, 728–734.

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AC

vanes: an experimental study. International Journal of Thermal Sciences. 122, 172-185. [28]

S.J. Kline, F.A. McClintock, 1953. Describing uncertainties in single-sample

experiments. Mechanical Engineering. 75(1), 3–8.

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List of Figures Fig. 1 Basic geometry of a HCT. Fig. 2 Schematic diagram of the experimental setup.

CR IP T

Fig. 3 A schematic representation of the CCTIT evaporator/condenser. Fig. 4 Schematic representation of the VCRS on the P-h chart.

Fig. 5 Effect of CCTIT evaporator geometry on VCRS operating conditions; (a) Pev, (b) Pc,

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(c) Tsup, ev, (d) Tsub, c, (e) Pev, (f) Pc.

Fig. 6 Effect of CCTIT evaporator geometry on VCRS specifications; (a) RE, (b) wc, (c) COP, (d) qc, (e) ̇

,

(f)

rev.

Fig. 7 Effect of CCTIT condenser geometry on VCRS operating conditions; (a) Pev, (b) Pc,

M

(c) Tsup, ev, (d) Tsub, c, (e) Pev, (f) Pc.

,

(f) c.

PT

COP, (d) qc, (e) ̇

ED

Fig. 8 Effect of CCTIT condenser geometry on VCRS specifications; (a) RE, (b) wc, (c)

Fig. 9 Comparison of the present experimental values with that correlated by Eqs. (21) to cev,

CE

(23); (a) COP, (b)

(c) c.

AC

Fig. 10 Comparison of the results of Eq. (23) with that by Kang et al. [19].

- 34 -

ACCEPTED MANUSCRIPT

S dt, o dc

dc, o

p Lc

AC

CE

PT

ED

M

AN US

CR IP T

Fig. 1 Basic geometry of a HCT.

- 35 -

ACCEPTED MANUSCRIPT

To drain Differential Pressure Transducer 2

Water Flow Meter 2 Domestic Water Supply

T

T

T

Temperature sensor

T

Sight glass

Capillary Tube

Filter drier

Water Heating Tank

Water heated evaporator

Ball Valve

T

T

M

Pump

T

AN US

By-Pass Line

Water Flow Meter 1

CR IP T

T

AC

CE

PT

ED

Fig. 2 Schematic diagram of the experimental setup.

- 36 -

Water cooled condenser

Compressor

T

Differential Pressure Transducer 1

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ACCEPTED MANUSCRIPT

AC

CE

PT

ED

M

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Fig. 3 A schematic representation of the CCTIT evaporator/condenser.

- 37 -

ACCEPTED MANUSCRIPT

P 2

4 1 h

CR IP T

3

AC

CE

PT

ED

M

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Fig. 4 Schematic representation of the VCRS on the P-h chart.

- 38 -

2.2 2.1 2.0 1.9 1.8 1.7 1.6

11.0

(a)

(b)

10.5 10.0

Pc (bar)

Pev (bar)

ACCEPTED MANUSCRIPT

1.5 1.4 1.3 1.2

9.5 9.0 8.5 8.0

100

200

300

400

500

600

700

800

100

Evaporator annulus Dean number, Deev, w      

400

500

600

700

800

8.7

14

8.2

12

7.7

Tsub (C)

10 8 6

     

CR IP T

     

16

(d)

7.2 6.7 6.2

4

5.7

(c)

2

5.2

100

200

300

400

500

600

700

800

Evaporator annulus Dean number, Deev, w

37 31 25

AC

19

200

300

600

700

800

M

     

62.0 61.5 61.0 60.5 60.0

(e)

(f)

59.5

13

100

500

62.5

CE

43

400

     

Pc (kPa)

49

300

63.0

PT

55

200

Evaporator annulus Dean number, Deev, w

     

67 61

100

ED

     

Pev (kPa)

300

Evaporator annulus Dean number, Deev, w

AN US

Tsup (C)

     

200

400

500

600

700

100

800

200

300

400

500

600

700

800

Evaporator annulus Dean number, Deev, w

Evaporator annulus Dean number, Deev,w            

     

     

Fig. 5 Effect of CCTIT evaporator geometry on VCRS operating conditions; (a) Pev, (b) Pc, (c) Tsup, ev, (d) Tsub, c, (e) Pev, (f) Pc.

- 39 -

ACCEPTED MANUSCRIPT

187

62

182 57

wc (kJ/kg)

RE (kJ/kg)

177 172 167 162 157

52 47 42

152

(b)

(a)

147

37 100

200

300

400

500

600

700

800

100

Evaporator annulus Dean number, Deev, w      

500

      250

(c)

240 230

600

700

800

qc (kJ/kg)

     

220 210 200 190

(d)

180

100

200

300

400

500

600

700

21

AC

19

200

300

600

700

800

M

     

(f)

ev

0.7 0.6 0.5 0.4 0.3 0.2

17

100

500

0.8

CE

23

400

0.9

(e)

PT

25

300

     

     

29

200

Evaporator annulus Dean number, Deev, w

ED

     

27

100

800

Evaporator annulus Dean number, Deev, w

mref (g/s)

400

CR IP T

4.0 3.9 3.8 3.7 3.6 3.5 3.4 3.3 3.2 3.1 3.0

300

Evaporator annulus Dean number, Deev, w

AN US

COP

     

200

400

500

600

700

100

800

     

200

300

400

500

600

700

     

     

     

Fig. 6 Effect of CCTIT evaporator geometry on VCRS specifications; (a) RE, (b) wc, (c) COP, (d) qc, (e) ̇

,

(f)

800

Evaporator annulus Dean number, Deev, w

Evaporator annulus Dean number, Deev, w

rev.

- 40 -

2.2 2.1 2.0 1.9 1.8 1.7 1.6 1.5 1.4 1.3 1.2

11.0

(a)

(b)

10.5

Pc (kPa)

Pev (kPa)

ACCEPTED MANUSCRIPT

10.0 9.5 9.0 8.5 8.0

100

300

500

700

900

100

1100

11

12.5

10

12.0 9

Tsub (C)

11.5

AN US

Tsup (C)

700

     

     

13.0

11.0 10.5 10.0

900

1100

     

8 7 6

9.5 9.0

(c)

8.5 100

300

500

700

900

63.5

62.0 61.0 60.5 60.0

AC

59.5

300

500

900

1100

     

75 70 65 60 55 50

(e) 700

900

(f)

45 100

1100

300

500

700

900

1100

Condenser annulus Dean number, Dec

Condenser annulus Dean number, Dec

     

700

85

59.0

100

500

80

CE

61.5

300

     

M

     

Pc (kPa)

62.5

100

Condenser annulus Dean number, Dec

PT

63.0

(d)

4

ED

     

5

1100

Condenser annulus Dean number, Dec

Pev (kPa)

500

CR IP T

     

300

Condenser annulus Dean number, Dec

Condenser annulus Dean number, Dec

     

     

     

Fig. 7 Effect of CCTIT condenser geometry on VCRS operating conditions; (a) Pev, (b) Pc, (c) Tsup, ev, (d) Tsub, c, (e) Pev, (f) Pc.

- 41 -

ACCEPTED MANUSCRIPT

190

68

185 63

175

wc (kJ/kg)

RE (kJ/kg)

180 170 165 160

58 53 48

155 43

150

(a)

(b)

145

38 100

300

500

700

900

1100

100

Condenser annulus Dean number, Dec, w      

      255

(c)

900

1100

245

qc (kJ/kg)

     

235 225 215 205 195

(d)

185

100

300

500

700

900

1100

Condenser annulus Dean number, Dec, w

20

AC

18

300

M

500

900

(f)

0.75

c

0.65 0.55 0.45 0.35 0.25 0.15

700

900

100

1100

     

300

500

700

900

     

     

     

Fig. 8 Effect of CCTIT condenser geometry on VCRS specifications; (a) RE, (b) wc, (c) ,

1100

Condenser annulus Dean number, Dec, w

Condenser annulus Dean number, Dec, w

COP, (d) qc, (e) ̇

1100

     

0.85

16

100

700

0.95

CE

22

500

     

(e)

PT

24

300

Condenser annulus Dean number, Dec, w

     

28 26

100

ED

     

mref (g/s)

700

CR IP T

3.7 3.6 3.5 3.4 3.3 3.2 3.1 3.0 2.9 2.8 2.7

500

AN US

COP

     

300

Condenser annulus Dean number, Dec, w

(f) c.

- 42 -

ACCEPTED MANUSCRIPT

4.0

0.9

(a) (Correlated)

3.4 3.2

6.8%

0.7

+5.9%

0.6

5.3%

0.5

ev

3.0

0.4

2.8

0.3 0.2

2.6 2.6

2.8

3.0

3.2

3.4

3.6

3.8

0.2

4.0

COP (Experimental)

(c)

0.75

6.1% 5.9%

c

0.45 0.35 0.25 0.15 0.15

0.25

0.35

0.45

0.55

0.65

0.5

0.75

0.85

0.95

M

c (Experimental)

0.6

0.7

0.8

(Experimental)

AN US

0.65 0.55

0.4

ev

0.95 0.85

0.3

CR IP T

COP (Correlated)

6.8%

3.6

(Correlated)

(b)

0.8

3.8

Fig. 9 Comparison of the present experimental values with that correlated by Eqs. (21) to cev,

(c) c.

AC

CE

PT

ED

(23); (a) COP, (b)

- 43 -

0.9

ACCEPTED MANUSCRIPT

0.50

Present 0.45

Condenser Effectiveness,

c

Kang et al. [19]

0.40

0.35

0.30

0.20 300

400

500

600

700

800

Condenser annulus Dean number, Dec, w

900

CR IP T

0.25

AC

CE

PT

ED

M

AN US

Fig. 10 Comparison of the results of Eq. (23) with that by Kang et al. [19].

- 44 -

ACCEPTED MANUSCRIPT

List of Tables Table 1 Characteristic dimensions of the tested coils. Table 2 Range of operating conditions (Evaporator Experiments).

Table 4 Maximum uncertainties in the estimated parameters.

Coil No.

Taper Angle ()

S1 (mm)

Pc, 1 (mm)



10.00

29.05

0.0777

39.05

0.1044

Outer Tube (Annulus Side) 1 2

20.00

0°

30.00

4 5 6 7 8

90°

10 11

135°

CE

12

PT

9

13

0°

15.92

Lc (mm)

462.35 780.66

49.05

0.1311

29.05

0.0777

6.47

392.70

20.00

39.05

0.1044

5.57

471.70

30.00

49.05

0.1311

4.96

549.90

10.00

29.05

0.0777

4.19

318.40

20.00

39.05

0.1044

3.60

370.30

30.00

49.05

0.1311

3.31

428.50

10.00

29.05

0.0777

2.74

231.20

20.00

39.05

0.1044

2.19

277.70

30.00

49.05

0.1311

2.15

343.80

20.00

39.05

0.1044

15.92

780.66

19.53

29.05

0.0777

ED

45°

N

10.00

M

3

AN US

Table 1 Characteristic dimensions of the tested coils.

CR IP T

Table 3 Range of operating conditions (Condenser Experiments).

1098.97

Inner Tube

AC

1

0°

452.82 15.92

29.53

39.05

0.1044

3

39.53

49.05

0.1311

4

19.53

29.05

0.0777

6.47

383.17

29.53

39.05

0.1044

5.57

462.17

39.53

49.05

0.1311

4.96

540.37

19.53

29.05

0.0777

4.19

308.87

29.53

39.05

0.1044

3.60

360.77

39.53

49.05

0.1311

3.31

418.97

19.53

29.05

0.0777

2.74

221.67

29.53

39.05

0.1044

2.19

268.17

2

5

45°

6 7 8

90°

9 10 11

135°

- 45 -

771.13 1089.44

ACCEPTED MANUSCRIPT

12 0°

49.05

0.1311

2.15

334.27

29.53

39.05

0.1044

15.92

771.13

AC

CE

PT

ED

M

AN US

CR IP T

13

39.53

- 46 -

ACCEPTED MANUSCRIPT Table 2 Range of operating conditions (Evaporator Experiments).

Evaporator

Shape

CCTIT

Parameters

Range or value

Coiled tube torsion

0.07770.1311

Taper angle, 

0, 45, 90, 135

Heating water flow rate, l/min

1.814

Heating water inlet temperature, C

20

Heating water Dean Number

119.8756.4

Coiled tube torsion

0.1044

Taper angle,  Condenser

HCTIT

CR IP T

Component

0

Cooling water flow rate, l/min Cooling water inlet temperature, C

28

AC

CE

PT

ED

M

AN US

Cooling water Dean Number

6

- 47 -

ACCEPTED MANUSCRIPT Table 3 Range of operating conditions (Condenser Experiments). Component

Evaporator

Shape

HCTIT

Parameters

Range or value

Coiled tube torsion

0.1044

Taper angle, 

0

Heating water flow rate, l/min

6

Heating water inlet temperature, C

20

Heating water Dean Number Taper angle,  Condenser

CCTIT

0.07770.1311

CR IP T

Coiled tube torsion

0, 45, 90, 135

Cooling water flow rate, l/min Cooling water inlet temperature, C

28

166.31050.6

AC

CE

PT

ED

M

AN US

Cooling water Dean Number

1.814

- 48 -

ACCEPTED MANUSCRIPT Table 4 Maximum uncertainties in the estimated parameters. Uncertainty (%)

AC

CE

PT

ED

M

AN US

Coil cone angle Coil curvature ratio Coil torsion Annulus-side Dean number Refrigeration effect Compressor specific work Condenser specific heat Evaporator cooling capacity COP Evaporator effectiveness Condenser effectiveness

CR IP T

Parameter

- 49 -