An assessment of heat transfer through fins in a fin-and-tube gas cooler for transcritical carbon dioxide cycles.
In C[O.sub.2] transcritical refrigeration cycles, fin-and-tube coils are still considered possible gas cooling devices due to their lower cost when compared with recent aluminium minichannel heat exchangers. In spite of the very high working pressures, an off-the-shelf coil with four ranks of 3/8 in. (9.52 mm) copper tube and louvered lou·ver also lou·vre
a. A framed opening, as in a wall, door, or window, fitted with fixed or movable horizontal slats for admitting air and light and shedding rain.
b. fins was found suitable to work with high R-744 pressures and has been studied as a gas cooler in a test rig built for testing carbon dioxide carbon dioxide, chemical compound, CO2, a colorless, odorless, tasteless gas that is about one and one-half times as dense as air under ordinary conditions of temperature and pressure. (C[O.sub.2]) equipment operating with air as a secondary fluid. The test rig consists of two closed-loop air circuits acting as heat sink A material that absorbs heat. Typically made of aluminum, heat sinks are widely used in amplifiers and other electronic devices that build up heat. Small heat sinks are the most economical method for cooling microprocessors and other chips. and heat source for the gas cooler and evaporator, respectively. The tested 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. circuit consists of two tube-and-fin heat exchangers as the gas cooler and the evaporator, a back-pressure valve as the throttling device, a double-stage compound compressor equipped with an oil separator, and an intercooler in·ter·cool·er
A device for cooling a fluid between successive heating stages.
inter·cool . A full set of thermocouples, pressure transducers, and flowmeters allows measurement and recording of all the main parameters of the C[O.sub.2] cycle, enabling heat balance to be performed for both air side and refrigerant re·frig·er·ant
1. Cooling or freezing; refrigerating.
2. Reducing fever.
1. A substance, such as air, ammonia, water, or carbon dioxide, used to provide cooling either as the working substance of side.
Tests focused on two different gas coolers, with continuous and cut fins, and on two different circuit arrangements. Tests on each heat exchanger were run at three different inlet conditions, for both C[O.sub.2] and air. A simulation model was developed for this type of heat exchanger and three models (Dang dang
Used to express dissatisfaction or annoyance.
adv. & adj.
tr.v. danged, dang·ing, dangs
n. and Hihara 2004; Gnielinski 1976; Pitla et al. 2002) proposed for the C[O.sub.2] supercritical Adj. 1. supercritical - (especially of fissionable material) able to sustain a chain reaction in such a manner that the rate of reaction increases
critical - at or of a point at which a property or phenomenon suffers an abrupt change especially having enough mass cooling heat transfer coefficients The heat transfer coefficient is used in calculating the convection heat transfer between a moving fluid and a solid in thermodynamics. The heat transfer coefficient is often calculated from the Nusselt number (a dimensionless number). were implemented and compared in the code.
The model results are compared with the experimental data for the finned finned
Having a fin, fins, or finlike parts. Often used in combination: single-finned; multifinned. coil; emphasis is given to the effect of heat conduction Heat conduction or thermal conduction is the spontaneous transfer of thermal energy through matter, from a region of higher temperature to a region of lower temperature, and hence acts to even out temperature differences. through fins between adjacent tube ranks on system efficiency. In the paper, the experimental results for transcritical C[O.sub.2] entering the gas cooler at 87.0[degrees]C (7.911 MPa), 97.6[degrees]C (8.599 MPa), and 107.8[degrees]C (9.102 MPa) with air inlet temperatures of 20.3[degrees]C, 21.5[degrees]C, and 23.0[degrees]C, respectively, are presented. By using a coil with fins modified to reduce the heat conduction, a 3.7% to 5.6% heat flux improvement was gained. This improvement can be clearly translated in terms of coefficient of performance The coefficient of performance, or COP (sometimes CP), of a heat pump is the ratio of the output heat to the supplied work or (COP), since a low value of the C[O.sub.2] temperature at its outlet increases the cooling capacity. Considering a reference cycle with the same operating conditions, a 5.7% to 6.6% increase of COP can be obtained.
Due to the necessity of decreasing the greenhouse effect greenhouse effect: see global warming.
Warming of the Earth's surface and lower atmosphere caused by water vapour, carbon dioxide, and other trace gases in the atmosphere. Visible light from the Sun heats the Earth's surface. , new fluids need to be investigated as 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. . Carbon dioxide (C[O.sub.2]) seems promising because of its environmental friendliness and some excellent thermodynamic ther·mo·dy·nam·ic
1. Characteristic of or resulting from the conversion of heat into other forms of energy.
2. Of or relating to thermodynamics. and transport properties, such as high specific heat, high thermal conductivity, and low viscosity. The "traditional" finned coil heat exchangers still can be considered an opportunity for C[O.sub.2] transcritical cycles. The gas cooling process needs to be investigated, taking into account two points of view: the great variation of thermophysical properties and the large decrease in temperature occurring along the heat exchanger. Very poor evidence is provided in the open literature to the study of finned coil gas coolers (GCs) with "macro" tubes (i.e., the internal diameter of the pipe is larger than 3 mm). Recently, Hwang et al. (2005) proposed an experimental and numerical study of a three-row finned coil GC with 7.9 mm outside diameter Outside diameter is the diameter of the addendum (tip) circle. In a bevel gear it is the diameter of the crown circle. In a throated wormgear it is the maximum diameter of the blank. The term applies to external gears.1
For this research, a set of tests was conducted and experimental results were compared with numerical predictions obtained through a finite volume simulation software Simulation software is based on the process of imitating a real phenomenon with a set of mathematical formulas. It is, essentially, a program that allows the user to observe an operation through simulation without actually running the program. .
Although simulation results gained by our software have been found to be in agreement with experimental results for a large number of refrigerants and test conditions, a systematic deviation was seen using C[O.sub.2]. Therefore, some correlations to predict C[O.sub.2] heat transfer coefficient were tested, but the heat conduction along the heat exchanger, which has not been considered by the software, was deemed to be the most important cause of the disagreement in results. This kind of phenomenon is not considered by the simulation software at the moment, and very poor evidence is given to this problem by papers available in the open literature. Furthermore, it seems to be relevant only to finned coil heat exchangers, since it was shown to be unimportant in microchannel heat exchangers (Asinari et al. 2004).
TEST RIG DESCRIPTION AND UNCERTAINTY ANALYSIS
The C[O.sub.2] circuit (Figure 1) carries out a double compression with gas intercooling between the two compression stages and single throttling, and it is equipped with an internal heat exchanger. The compressor is a two-stage semi-hermetic reciprocating unit running at 1450 rpm (50 Hz). The nominal volumetric flow rate In fluid dynamics and hydrometry, the volumetric flow rate, also volume flow rate and rate of fluid flow, is the volume of fluid which passes through a given surface per unit time (for example cubic meters per second [m3 s-1 of the low-pressure stage (one cylinder) is 3.0 [m.sup.3]/h, while that of the second stage is 1.74 [m.sup.3]/h (volume ratio 1.7). The lubricant Lubricant
A gas, liquid, or solid used to prevent contact of parts in relative motion, and thereby reduce friction and wear. In many machines, cooling by the lubricant is equally important. is a PAG Pag (päg), Ital. Pago, island (101 sq mi/262 sq km), in the Adriatic, off the Dalmatian coast, Croatia. Noted for its fine embroidery and lace, it also has vineyards, a fishing industry, and bauxite deposits. oil 46 ISO (1) See ISO speed.
(2) (International Organization for Standardization, Geneva, Switzerland, www.iso.ch) An organization that sets international standards, founded in 1946. The U.S. member body is ANSI. grade.
The compressor power input is recorded with an electronic transducer transducer, device that accepts an input of energy in one form and produces an output of energy in some other form, with a known, fixed relationship between the input and output. (with an accuracy of [+ or -]0.5% of the reading value).
The intercooler (IC) heat flow is rejected to a water loop. The cooling water inlet temperature and flow rate are controlled through an auxiliary circuit (temperature stability [+ or -]0.05[degrees]C). The IC is a copper tube-in-tube heat exchanger with the C[O.sub.2] flowing inside three pipes (4 mm ID, 6 mm OD) fed in parallel and inserted into a 20 mm ID (22 mm OD) copper tube. The water flows inside the outer tube in countercurrent countercurrent /coun·ter·cur·rent/ (-kur?ent) flowing in an opposite direction.
flowing in an opposite direction. to the C[O.sub.2]. The IC was designed for a 1[degrees]C temperature approach between the two fluids. The water volumetric flow rate is measured with an electromagnetic flow meter flow meter
Device that measures the velocity of a gas or liquid. It has applications in medicine as well as in chemical engineering, aeronautics, and meteorology. Examples include pitot tubes, venturi tubes, and rotameters (tapered graduated tubes with a float inside that is (accuracy [+ or -]0.2% of the reading value).
The internal heat exchanger used was a copper-steel 10 m long tube-in-tube heat exchanger with the high-pressure fluid flowing inside three pipes (6 mm ID, 8 mm OD) fed in parallel and inserted into a 21 mm ID (26.7 mm OD) steel tube. The low-pressure C[O.sub.2] flows inside the outer tube in countercurrent to the high-pressure C[O.sub.2]. The internal heat exchanger was designed for a 2[degrees]C temperature approach between the two fluids. The throttling device used in the tests was a back-pressure valve; this allows the operator to set and keep constant the GC outlet pressure.
The C[O.sub.2] circuit is equipped with an oil separator. A special accumulator A hardware register used to hold the results or partial results of arithmetic and logical operations.
(processor) accumulator - In a central processing unit, a register in which intermediate results are stored. with sight glasses is inserted for visual inspection of the oil returning to the compressor crankcase crank·case
The metal case enclosing the crankshaft and associated parts in a reciprocating engine.
the metal case that encloses the crankshaft in an internal-combustion engine . A metering valve is also installed to control the lubricant level in the compressor and to avoid any hot gas bypass through the oil drainage.
Air is the external fluid for both the GC and the evaporator. For the tests reported here, finned coils with round copper tubes (8.22 mm ID, 9.52 mm OD) are employed. The aluminium fins are louvered with 2.1 mm fin spacing. The face area for both exchangers is 500 x 500 mm. Air temperature at the inlet of each heat exchanger is controlled by way of two separated closed-loop wind tunnels. The air duct layout was designed through computational fluid dynamics Computational fluid dynamics
The numerical approximation to the solution of mathematical models of fluid flow and heat transfer. Computational fluid dynamics is one of the tools (in addition to experimental and theoretical methods) available to solve simulation targeted at getting very uniform velocity velocity in which the same number of units of space are described in each successive unit of time.
See also: Velocity and temperature distribution over the entire heat exchanger face area. The centrifugal fans are equipped with inverters to adjust the volumetric flow rate that is measured with ISA (1) (Instruction Set Architecture) See instruction set.
(2) (Interactive Services Association) See Internet Alliance.
(3) (Internet Security and Acceleration) See .NET. 1932, AISI AISI American Iron and Steel Institute
AISI African Information Society Initiative
AISI Alberta Initiative for School Improvement (Canada)
AISI As I See It
AISI American International Supply, Inc (Oakland, CA) 316L nozzles with pressure taps integrated in the nozzle body. The nozzles were installed according to according to
1. As stated or indicated by; on the authority of: according to historians.
2. In keeping with: according to instructions.
3. EN-ISO Standard 5167 (ISO 2005). Air pressure drop through the nozzles is measured by a strain gauge strain gauge
Device for measuring the changes in distances between points in solid bodies that occur when the body is deformed. Strain gauges are used either to obtain information from which stresses in bodies can be calculated or to act as indicating elements on devices for pressure transducer with an accuracy of [+ or -]1 Pa, while air temperature downstream the nozzles is recorded with a thermocouple. In this way, according to EN-ISO Standard 5167, the estimated accuracy in volumetric flow rate [dot.V] measurement is [+ or -]0.8% of the reading.
[FIGURE 1 OMITTED]
The air in the closed loop serving the GC is reconditioned re·con·di·tion
tr.v. re·con·di·tioned, re·con·di·tion·ing, re·con·di·tions
To restore to good condition, especially by repairing, renovating, or rebuilding. by a cooling finned coil fed with water kept at an inlet constant temperature in an auxiliary circuit equipped with a commercial chiller chill·er
1. One that chills.
2. A frightening story, especially one involving violence, evil, or the supernatural; a thriller.
1. and control system. The air inlet temperature to the GC is then kept at the desired value by electrical heaters, proportional-integral-derivative (PID (1) (Process IDentifier) A temporary number assigned by the operating system to a process or service.
(2) (Proportional-Integral-Derivative) The most common control methodology in process control. ) controlled. Another PID feedback loop is used to control the air dry-bulb temperature The dry-bulb temperature is the temperature of air measured by a thermometer freely exposed to the air but shielded from radiation and moisture. In construction, it is an important consideration when designing a building for a certain climate. at the evaporator inlet by compensating the C[O.sub.2] system cooling power with electrical heating. The air temperature stability thus achieved in steady-state conditions was [+ or -]0.05[degrees]C. Nine thermocouples are placed, evenly distributed, just before the GC inlet. Since the large temperature change of the C[O.sub.2] through the gas cooling process leads to a scattered distribution of the air temperature across the outlet section (depending on the C[O.sub.2] pipe arrangement in the finned coil), an air mixer is placed after the GC and the air temperature is measured again by nine thermocouples placed after the air mixer. The same thermocouple arrangement was used for the evaporator.
C[O.sub.2] temperatures are measured with thermocouples placed inside mixing chambers at the inlet and outlet of each heat exchanger. A thermocouple is also placed at the IC water inlet, whereas the water temperature change across the IC is measured with a four-junction type T thermopile thermopile: see thermoelectricity. .
All the thermocouples for air and C[O.sub.2] are T type; the complete measuring chain, including the multimeter An instrument for measuring electricity (volts, amps, ohms) that is widely used and available in numerous shapes and sizes. An analog multimeter displays results by moving a pointer across a printed scale. and the [+ or -]0.01[degrees]C reference ice point, was calibrated cal·i·brate
tr.v. cal·i·brat·ed, cal·i·brat·ing, cal·i·brates
1. To check, adjust, or determine by comparison with a standard (the graduations of a quantitative measuring instrument): against a Pt100 thermometer thermometer, instrument for measuring temperature. Galileo and Sanctorius devised thermometers consisting essentially of a bulb with a tubular projection, the open end of which was immersed in a liquid. of [+ or -]0.02[degrees]C accuracy. Thus, an accuracy of [+ or -]0.05[degrees]C is estimated for all the temperature measurements.
R-744 pressures are recorded with strain-gauge transducers at the outlet of each heat exchanger and inside the compressor's second-stage (high pressure) suction chamber the chamber of a pump into which the suction pipe delivers.
See also: Suction . The accuracy is [+ or -]1 kPa for evaporator and compressor chamber pressures and [+ or -]2 kPa for GC pressures, according to the calibration report from the manufacturer. Differential pressure transducers were used for pressure drop recording across the GC, the evaporator, and the IC (accuracy [+ or -]400 Pa).
C[O.sub.2] mass flow rate is measured by a Coriolis mass flowmeter See flow meter. placed upstream of the throttling valve. The claimed accuracy is [+ or -]0.1% of the reading. IC water volumetric flow rate was measured by an electromagnetic meter (accuracy [+ or -]0.2% of the reading).
All the measurements are real-time acquired and elaborated. The particular layout of the air tunnels and the accuracy of the instruments led to a heat balance error for each component and for the complete system lower than [+ or -]1%.
According to Moffat's (1988) suggestion, a "single sample uncertainty analysis" was considered for the air velocity w and for the heat flux q.
In general, the uncertainty in a variable y depending on N independent variables ([x.sub.i]) with uncertainties [delta][x.sub.i] is estimated through Equation 1:
[delta]y = [[N.summation summation n. the final argument of an attorney at the close of a trial in which he/she attempts to convince the judge and/or jury of the virtues of the client's case. (See: closing argument) over (i = 1)] ([partial derivative partial derivative
In differential calculus, the derivative of a function of several variables with respect to change in just one of its variables. Partial derivatives are useful in analyzing surfaces for maximum and minimum points and give rise to partial differential ]y/[[partial derivative][x.sub.i]]] [delta][x.sub.i])[.sup.2]][.sup.0.5] (1)
In particular, with
w = [dot.V]/S, (2)
[delta]w = [([1/S][delta][dot.V])[.sup.2] + (-[[dot.V]/[S.sup.2]][delta]S)[.sup.2]][.sup.0.5]. (3)
The heat flux q, air side, is
q = [rho][dot.V][c.sup.p]([t.sub.air, out] - [t.sub.air, in]). (4)
Since a gas-cooling application is considered, air can be treated as dry air (no dehumidification), so the air density [rho] is evaluated through the following ideal gas relationship (ASHRAE ASHRAE American Society of Heating, Refrigerating & Air Conditioning Engineers 2005):
[rho] = p/0.2871(t + 273.15) (5)
Furthermore, a constant value for the specific heat capacity [c.sub.p] = 1006 J x k[g.sup.-1] x [K.sup.-1] was considered.
So it comes out that
[delta]p = [([1/0.2871(t + 273.15)][delta]p)[.sup.2] + (-[0.2871p/(0.2871(t + 273.15))[.sup.2]][delta]t)[.sup.2]][.sup.5], (6)
[delta][rho] = [([dot.V][c.sub.p]([t.sub.air, out] - [t.sub.air, in])[delta]p)[.sup.2] + ([rho][c.sub.p]([t.sub.air, out] - [t.sub.air, in])[delta][dot.V])[.sup.2] + ([square root of (2)][rho] [dot.V][c.sub.p][delta]t)[.sup.2]][.sup.0.5]. (7)
The "single point" estimated uncertainties are listed in Tables 1 and 2.
The heat flux, C[O.sub.2] side, can be expressed as follows:
[q.sub.CO.sub.2] = [dot.m.sub.CO.sub.2]([h.sub.CO.sub.2,out] - [h.sub.CO.sub.2, in]) (8)
Using Equation 1, the related uncertainty is
[delta][q.sub.CO.sub.2] = [(([h.sub.C[O.sub.2], out] - [h.sub.C[O.sub.2], in])[delta][dot.m.sub.CO.sub.2)[.sup.2] + [dot.m.sub.CO.sub.2] [delta]([h.sub.C[O.sub.2], out] - [h.sub.C[O.sub.2], in]))[.sup.2]].sup.0.5]. (9)
As already mentioned, a Coriolis mass flowmeter with 0.1% of the reading accuracy is used for [dot.m.sub.CO.sub.2]. REFPROP v. 7.0 (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. 2002) is used for 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. calculations. It is well known that
[h.sub.CO.sub.2] = f[p, t], (10)
so, in general, enthalpy calculation uncertainty is affected by
* temperature measurement accuracy,
* pressure measurement accuracy, and
* accuracy of the enthalpy calculation approach used for Equation 10.
The evaluation of the last contribution is outside the purpose of this paper; reference should be made to Span and Wagner's (1996) data, since REFPROP v. 7.0 modeling is based on their measurements for the implementation of the Helmholtz approach to Equation 10. In this paper, only the effects of T and p accuracy on [delta]h are taken into consideration. According to Moffat (1998), a "sequential perturbation perturbation (pŭr'tərbā`shən), in astronomy and physics, small force or other influence that modifies the otherwise simple motion of some object. The term is also used for the effect produced by the perturbation, e.g. " method is applied by using the REFPROP code. Considering a temperature measuring accuracy of [+ or -]0.05[degrees]C and a pressure measuring accuracy of [+ or -]2 kPa, the estimated accuracy for the C[O.sub.2] side heat flow rate is reported in Table 2. The reader may appreciate that the difference between air-side and C[O.sub.2]-side heat fluxes is always below 1% of the air-side heat flux.
GAS COOLER DESCRIPTION
Three different heat exchangers were tested, dubbed A, B, and C throughout the paper. The main characteristics of the three finned coils are listed in Table 3. Coils A and B, as depicted in Figure 2a, are identical but for the fins. Referring to Figure 3, in coil B, the fins in adjacent tube rows are separated (cut) along line DE. This expedient contributes to reducing heat conduction between adjacent tube rows. Coil C presents the same fin arrangement as coil B, with different tube layout, as shown in Figure 2b. A simple scheme of the fin type used is given in Figure 3.
SIMULATION MODEL FOR THE FINNED COIL
The heat transfer analysis has been applied to the case of a finned coil GC by developing a dedicated simulation model. Since the flow configuration of a finned coil does not conform to Verb 1. conform to - satisfy a condition or restriction; "Does this paper meet the requirements for the degree?"
coordinate - be co-ordinated; "These activities coordinate well" the elementary and well-known parallel or counterflow patterns, the heat transfer area is subdivided into a three-dimensional array of cells that conforms to the true flow pattern of the air and of the refrigerant streams. Each tube is divided into cells and the total volume, in the form of a parallelepiped, is subdivided into individual nodes, each including a small stretch of tube and the related fins.
The numerical approach to the definition of the circuits is accomplished by means of two arrays, one for the refrigerant [PR(N)] and one for the air [PA(N)]. Each element of the preceding refrigerant (PR) vector indicates the index of the node preceding the N-node, along the refrigerant flow.
[FIGURE 2 OMITTED]
[FIGURE 3 OMITTED]
As described for the refrigerant, the preceding air (PA) value PA(N) represents the air-side node preceding the N-node according to the airflow direction.
This simple approach allows a finned coil to be solved regardless of how complicated the layout of the tube circuits is. For thermal performance determination, the refrigerant temperature and pressure at the GC outlet are calculated by an iterative it·er·a·tive
1. Characterized by or involving repetition, recurrence, reiteration, or repetitiousness.
2. Grammar Frequentative.
Noun 1. procedure, the airflow rate and its inlet temperature being known, as well as the refrigerant pressure, temperature, and flow rate at the GC inlet. The well-known secant method In numerical analysis, the secant method is a root-finding algorithm that uses a succession of roots of secant lines lines to better approximate a root of a function f. is employed.
The refrigerant and air-side heat transfer coefficients are also input parameters in the program. The model can deal with C[O.sub.2] in transcritical conditions; in this case, the heat transfer coefficient is calculated from equations described in the literature, such as Gnielinski's (1976) equation, Pitla et al.'s (2002) equation, and Dang and Hihara's (2004) equation.
The friction factor Friction factor can refer to:
The air-side heat transfer coefficient, including surface efficiency, was evaluated experimentally by feeding the coils with a water flow at a temperature higher than ambient air temperature. An overall heat transfer coefficient U was evaluated from Equation 11, q being the measured heat flux, [A.sub.0] the external heat transfer area, and [DELTA][T.sub.lm] the countercurrent logarithmic mean In mathematics, the logarithmic mean is a function of two numbers which is equal to their difference divided by the logarithm of their quotient. In symbols:
q = U[A.sub.0][DELTA][T.sub.lm] (11)
1/U = [[A.sub.o]/[A.sub.i]][1/[h.sub.i]] + [[A.sub.o]/[A.sub.i]][[r.sub.i]/k]ln([r.sub.o]/[r.sub.i]) + [1/[[eta].sub.o]][1/[h.sub.o] (12)
where r is the radius, h is the heat transfer coefficient, [eta] is the finned surface efficiency, k is the tube thermal conductivity, i means internal, and o means external; [h.sub.i] was evaluated with the Gnielinski equation, so it was possible to obtain [[eta].sub.o][h.sub.o] from Equation 12.
It's worth noting that the investigated finned coils display four tube-side passes, with air in cross-flow. According to Kays and London (1998), the efficiency of this configuration is almost identical to pure counterflow configuration. The consistency of the [[eta].sub.o][h.sub.o] experimental values obtained through Equations 11 and 12 was evaluated by comparison with the ([[eta].sub.o][h.sub.o])[.sub.calc] values calculated according to the Wang et al. (1999) model. All the experimental values were predicted by the Wang et al. model within [+ or -]10% (deviation defined as 100 x [([[eta].sub.o][h.sub.o])[.sub.exp exp
2. exponential ] - ([[eta.sub.o][h.sub.o])[.sub.calc]]/([[eta].sub.o][h.sub.o])[.sub.calc]).
The thermodynamic and thermophysical properties of R-744 in the calculations are obtained from the database REFPROP v. 7.0 by NIST (2002).
A more detailed description of the simulation model is provided by Casson et al. (2002).
COMPARISON BETWEEN NUMERICAL AND EXPERIMENTAL RESULTS
Coil A performance was compared with that of B and C at several operating conditions. In this paper, three different working pressures are analyzed from 7.9 MPa to 9.1 MPa. The pressure range mentioned was considered particularly meaningful because in these working conditions the R-744 Prandtl number The Prandtl number is a dimensionless number approximating the ratio of momentum diffusivity (viscosity) and thermal diffusivity. It is named after Ludwig Prandtl.
It is defined as:
Three sets of tests were conducted at the mentioned conditions, and the experimental results obtained are summarized in Table 2.
In order to analyze the fluid temperature distribution in the heat exchangers, a set of thermocouples was inserted along one circuit of the finned coil, as illustrated in Figure 4. The thermocouples were attached to the outside surface of 15 U-bends using a silicone-based heat transfer compound to improve the thermal contact In thermodynamics, a thermodynamic system is said to be in thermal contact with another system if it can exchange energy with it through the process of heat. Perfect thermal isolation is an idealization as real systems are always in thermal contact with their environment to some to the surface. The thermocouple distribution is shown in Figure 2a for coils A and B and in Figure 2b for coil C. Every thermocouple and its corresponding U-bend were suitably insulated for the environment. Referring to test number 3 for coil A, the temperature profile is shown in Figure 4, where the temperature measurements are numbered according to what is shown in Figure 2a.
The solid line shown in Figure 4 relates to the temperature profile obtained by the numerical simulation. In each test with coil A, a significant difference between the predicted temperatures and measured values was observed. Although the approach and the temperature values are different between tests at different refrigerant and air inlet conditions, in the first row of the heat exchanger (0%-25% of the total surface), the measured temperature values are always lower than the calculated ones, while they are higher in the last three rows (25%-100%).
Several C[O.sub.2] heat transfer coefficient correlations were tested but without any significant change in the prediction (see Table 4). All C[O.sub.2]-specific correlations usually refer to the Gnielinski correlation that was chosen as the reference for the simulation software to evaluate the temperature profile and the heat flux. The other correlations were selected considering the different approaches to the heat transfer coefficient evaluation. Pitlas's correlation makes use of an average between Nusselt numbers referred to bulk and wall temperatures, while Dang and Hihara's correlation uses a film temperature to evaluate C[O.sub.2] properties and therefore the heat transfer coefficient.
Different correlations don't give rise to different results because the heat transfer resistance is chiefly concentrated on the air side in finned coils. Therefore, the C[O.sub.2]-side heat transfer coefficient estimation model doesn't seem to be as important as the air-side coefficient estimation. Starting from the previous considerations, the reason for the difference between predicted and measured values must lie in a phenomenon associated with the gas cooling process and not modeled by the numerical code.
[FIGURE 4 OMITTED]
Unlike condensation or evaporation evaporation, change of a liquid into vapor at any temperature below its boiling point. For example, water, when placed in a shallow open container exposed to air, gradually disappears, evaporating at a rate that depends on the amount of surface exposed, the humidity processes, in which the fluid temperature is almost uniform in a large part of the heat exchanger, the gas cooling process involves a significant temperature glide along the heat exchanger. In particular, the C[O.sub.2] temperature gradient temperature gradient
The rate of change of temperature with displacement in a given direction from a given reference point.
temperature gradient is higher in the first 20% of the heat transfer area (following the R-744 flow direction). Therefore, it seems reasonable to consider the thermal conduction thermal conduction
Transfer of heat energy resulting from differences in temperature between adjacent bodies or adjacent parts of a body. In the absence of a heat pump, the energy will flow from a region of higher temperature to a region of lower temperature. from the first high-temperature tubes to the adjacent low-temperature tubes through the continuous fins as the most important factor responsible for performance penalization and temperature profile disagreement in finned coils. As a consequence of the conductive heat conductive heat
Heat transmitted to the body by direct contact, as by an electric pad. transfer from hotter to colder tubes, the efficiency of the heat exchanger deviates from the ideal counterflow behavior.
To confirm this hypothesis, the continuous fins were cut to eliminate the thermal conduction from any tube row to the adjacent ones. In this way, a separated row finned coil was tested (dubbed B in Table 2). A 3.7% to 5.6% heat flow rate improvement was gained, as can be seen in Table 2, while Figure 5 shows a better agreement of the B temperature profile as compared with the A profile. In the first row of the coil (0%-25%) the temperature values increased, while in the second part of the heat exchanger the temperatures decreased approaching the simulation profile. This is consistent with a decrease in thermal conduction.
This improvement can be clearly transferred in terms of COP, since a low value of the C[O.sub.2] temperature at the GC outlet increases the cooling capacity. Using the "cut-configuration," a 5.7% to 6.6% increase in COP can be obtained, considering a reference cycle with the same operating conditions. The reference cycle considered is the simplest kind of transcritical C[O.sub.2] system using single-stage compression, without the presence of a suction suction /suc·tion/ (suk´shun) aspiration of gas or fluid by mechanical means.
post-tussive suction a sucking sound heard over a lung cavity just after a cough. line heat exchanger. The compressor is simulated with constant isentropic is·en·tro·pic
Without change in entropy; at constant entropy.
[is(o)- + entrop(y) + -ic.]
is efficiency equal to 0.6. Isobaric processes except for compression and throttling were considered, with -10[degrees]C evaporation temperature and 5[degrees]C vapor superheating
In physics, superheating (sometimes referred to as boiling retardation, or boiling delay . Furthermore, a higher COP improvement can be reached by an optimization of the GC pressure.
The C configuration represented in Figure 2b was chosen for a second set of tests to limit the thermal conduction between the two circuits along the vertical direction. Basically, from a geometric point of view, the two circuits were symmetrically fed, to reduce the thermal conduction in the horizontal middle cross section of the heat exchanger.
Referring to the comparison between the C configuration and the B configuration, Figure 6 shows a slightly better approach just in the first tube row (high temperature zone), while in the other three tube rows the measured temperatures are almost the same, and the overall thermal performance is also the same.
[FIGURE 5 OMITTED]
[FIGURE 6 OMITTED]
These experimental results are evidence that the thermal bridge A thermal bridge is created when materials that are poor insulators come in contact, allowing heat to flow through the path created.
Insulation around a bridge is of little help in preventing heat loss or gain due to thermal bridging; the bridging has to be eliminated, through fins contributes to penalize pe·nal·ize
tr.v. pe·nal·ized, pe·nal·iz·ing, pe·nal·iz·es
1. To subject to a penalty, especially for infringement of a law or official regulation. See Synonyms at punish.
2. heat transfer because of the thermal conduction between different tube rows, not between tubes in the same row.
Asinari et al. (2004) pointed out a negligible effect of conduction conduction, transfer of heat or electricity through a substance, resulting from a difference in temperature between different parts of the substance, in the case of heat, or from a difference in electric potential, in the case of electricity. through fins in minichannel air-cooled GCs. It is worth noting that the flow arrangement plays a key role in this respect. Usually minichannel GCs are arranged as a single slab heat exchanger with C[O.sub.2] flowing in multistream with several pipes in parallel (in Asinari et al. , a three pass arrangement in the unique rank with 13, 11, and 10 tubes in parallel, respectively, was analyzed). In this configuration, the heat conduction through fins is only significant in the region of flow inversion caused by the manifolds. In fact, a marked wall temperature difference is only present between the adjacent pipes in the flow inversion portion of the heat exchanger, whereas the other tubes fed in parallel within the same C[O.sub.2] pass are affected by very similar temperature fields, if the air velocity is assumed to be fairly uniform over the whole face area. According to temperature measurements presented in this paper, in the investigated finned coil at least 12 tubes of the first rank are directly set into contact through the fins with tubes having the wall temperature lower by at least 15[degrees]C (and in some cases by up to 35[degrees]C), according to Figures 4-6. From the same figures it is evident that the largest temperature change occurs in the first tube rank: the temperature profile is much more "flat" starting from the second down to the fourth rank. So the "cut-configuration" (coils B and C) interrupts the thermal bridge between the "higher wall temperature" first rank and the "lower wall temperature" part of the finned coil. The "separated" first rank behaves like a single-slab heat exchanger, from the point of view of conduction through fins. In the "cut-configuration" only the first three tubes of each circuit (following the C[O.sub.2] flow from the entrance) in the first rank are in direct contact through the fins with tubes having wall temperature differences higher than 5[degrees]C from the preceding pipe. Thus, the effect of thermal conduction of the first rank arrangement on the overall efficiency of the heat exchanger is expected (and proved experimentally by comparison of the performances of coils B and C) to be negligible.
Experimental tests and numerical analysis numerical analysis
Branch of applied mathematics that studies methods for solving complicated equations using arithmetic operations, often so complex that they require a computer, to approximate the processes of analysis (i.e., calculus). on two identical finned coils, one with continuous fins and the other with separated fins in each tube row, indicates that "internal" heat conduction through the fins is an important factor in finned coil C[O.sub.2] gas coolers. This fact is strictly linked to the high-temperature variation of C[O.sub.2] during the gas cooling process in a transcritical refrigeration cycle. The improvement in temperature approach between C[O.sub.2] outlet temperature and air inlet temperature was found to increase the efficiency of the refrigerating cycle. This point offers a quite promising technological opportunity, since it is easy to build a coil with fins separated among different rows.
Future work will be aimed at developing a more detailed code that also takes into account the heat conduction through the fins; this will be a fundamental tool for the optimized design of finned coil gas coolers.
This research was carried out with the financial support of the Italian Department for Education under the frame of the research programme PRIN-COFIN 2004.
NOMENCLATURE nomenclature /no·men·cla·ture/ (no´men-kla?cher) a classified system of names, as of anatomical structures, organisms, etc.
A = heat transfer area
[c.sub.p] = specific heat
[delta]y = uncertainty in the result, generic
h = heat transfer coefficient
[[eta].sub.0] = finned surface efficiency
k = tube thermal conductivity
q = heat flux
r = tube radius
[rho] = density
N = number of elements in a sample
p = pressure
S = finned coil face area
t = temperature
[DELTA][T.sub.lm] = log mean temperature difference The log mean temperature difference (LMTD) is used to determine the temperature driving force for heat transfer in flow systems (most notably in heat exchangers). The LMTD is a logarithmic average of the temperature difference between the hot and cold streams at each end of the
U = overall heat transfer coefficient
[dot.V] = volumetric volumetric /vol·u·met·ric/ (vol?u-met´rik) pertaining to or accompanied by measurement in volumes.
Of or relating to measurement by volume. airflow rate
w = air velocity
[x.sub.i] = generic ith variable
[delta][x.sub.i] = uncertainty in [x.sub.i]
i = internal
in = inlet
o = external
out = outlet
calc = calculated
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Organization for determining standards in most technical and nontechnical fields. Founded in Geneva in 1947, its membership includes more than 100 countries. .
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Claudio Zilio, PhD
Luca Cecchinato, PhD
Marco Corradi, PhD
Received September 1, 2006; accepted January 12, 2007
Claudio Zilio is an assistant professor, Luca Cecchinato and Marco Corradi are post-doctoral researchers, and Giovanni Schiochet is a PhD student with the Dipartimento di Fisica Tecnica, Universita di Padova, Padova, Italy.
Table 1. Test Conditions C[O.sub.2] Inlet C[O.sub.2] Inlet C[O.sub.2] Mass Test Pressure, MPa Temperature, [degrees]C Flow Rate, kg/h 1 7.911 [+ or -] 0.002 87.0 [+ or -] 0.05 169.0 [+ or -] 0.2 2 8.599 [+ or -] 0.002 97.6 [+ or -] 0.05 167.1 [+ or -] 0.2 3 9.102 [+ or -] 0.002 107.8 [+ or -] 0.05 166.4 [+ or -] 0.2 Test Air Inlet Temperature, [degrees]C Air Inlet Velocity, m/s 1 20.3 [+ or -] 0.05 1.59 [+ or -] 0.01 2 21.5 [+ or -] 0.05 1.59 [+ or -] 0.01 3 23.0 [+ or -] 0.05 1.61 [+ or -] 0.01 Table 2. Experimental Results C[O.sub.2] Outlet Air Outlet Finned Temperature, Temperature, Approach, Coil Test [degrees]C [degrees]C [degrees]C A 1 33.0 [+ or -] 0.05 39.5 [+ or -] 0.05 12.7 [+ or -] 0.05 2 33.1 [+ or -] 0.05 42.7 [+ or -] 0.05 11.6 [+ or -] 0.05 3 33.1 [+ or -] 0.05 45.1 [+ or -] 0.05 10.1 [+ or -] 0.05 B 1 32.1 [+ or -] 0.05 40.6 [+ or -] 0.05 11.8 [+ or -] 0.05 2 31.1 [+ or -] 0.05 43.7 [+ or -] 0.05 9.6 [+ or -] 0.05 3 30.9 [+ or -] 0.05 46.0 [+ or -] 0.05 7.9 [+ or -] 0.05 C 1 32.1 [+ or -] 0.05 40.8 [+ or -] 0.05 11.8 [+ or -] 0.05 2 31.0 [+ or -] 0.05 43.8 [+ or -] 0.05 9.5 [+ or -] 0.05 3 31.0 [+ or -] 0.05 46.2 [+ or -] 0.05 7.9 [+ or -] 0.05 Finned Heat Flow Rate Heat Flow Rate Coil Test (C[O.sub.2] Side), kW (Air Side), kW A 1 9.0 [+ or -] 0.05 9.0 [+ or -] 0.1 2 10.1 [+ or -] 0.06 10.2 [+ or -] 0.1 3 10.9 [+ or -] 0.06 10.8 [+ or -] 0.1 B 1 9.5 [+ or -] 0.05 9.5 [+ or -] 0.1 2 10.6 [+ or -] 0.06 10.6 [+ or -] 0.1 3 11.3 [+ or -] 0.07 11.2 [+ or -] 0.1 C 1 9.5 [+ or -] 0.05 9.5 [+ or -] 0.1 2 10.7 [+ or -] 0.06 10.6 [+ or -] 0.1 3 11.1 [+ or -] 0.07 11.2 [+ or -] 0.1 Table 3. Specifications of the Heat Exchangers Heat exchanger Gas cooler Type Finned coil Dimension (W x H) 500 x 500 mm Number of circuits 2 Number of tubes per row 20 Number of rows 4 Refrigerant path Vertical, countercurrent Tube pitch 25 mm Row pitch 19 mm Geometry Staggered tubes Fin pitch 2.1 mm Fin thickness 0.1 mm Fin type Louver aluminium (Figure 3) Tube outside diameter 9.52 mm Tube thickness 0.65 mm Tube type Smooth Table 4. Simulation Results Using Three Different Correlations Gnielinski (1976) Pitla et al. (2002) Correlation C[O.sub.2] Outlet C[O.sub.2] Outlet Test Temperature, Heat Flow Temperature, Heat Flow [degrees]C Rate, kW [degrees]C Rate, kW 1 32.2 9.5 32.2 9.5 2 31.0 10.6 31.0 10.6 3 30.7 11.3 30.7 11.3 Dang and Hihara (2004) Correlation C[O.sub.2] Outlet Heat Flow Test Temperature, [degrees]C Rate, kW 1 32.3 9.5 2 31.2 10.6 3 30.9 11.2