An extension of a steady-state model for fin-and-tube heat exchangers to include those using capillary tubes for flow control.INTRODUCTION
Multipath fin-and-tube heat exchangers heat exchanger
Any of several devices that transfer heat from a hot to a cold fluid. In many engineering applications, one fluid needs to be heated and another cooled, a requirement economically accomplished by a heat exchanger. (MPHX) are widely used in refrigeration refrigeration, process for drawing heat from substances to lower their temperature, often for purposes of preservation. Refrigeration in its modern, portable form also depends on insulating materials that are thin yet effective. or air-conditioning applications, and the 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 distribution in the paths is very important to the performance of the heat exchangers. Unsuitable refrigerant distribution in evaporators may result in dry-out of circuits and finally result in poor heat transfer and waste of the heat transfer area, while unsuitable refrigerant distribution in condensers may create zones of reduced heat transfer due to high liquid loading. Moreover, unsuitable refrigerant distribution may lead to a high temperature difference between adjacent tubes, which causes the reversed 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 the fins and degrades the performance of the heat exchangers (Romero-Mendez et al. 1997; Wang et al. 1999). In order to get suitable refrigerant distribution, the methods of changing the refrigerant circuit pattern (Romero-Mendez et al. 1997; Wang et al. 1999; Liang et al. 2000, 2001) and changing the refrigerant distributor geometries (Jiao jiao also chiao
n. pl. jiao also chiao
See Table at currency.
[Chinese ji et al. 2003) have been used. Besides these two methods, adding capillary capillary (kăp`əlĕr'ē), microscopic blood vessel, smallest unit of the circulatory system. Capillaries form a network of tiny tubes throughout the body, connecting arterioles (smallest arteries) and venules (smallest veins). tubes to the paths is an effective way to adjust the refrigerant distribution in different paths for MPHX, which is low in cost and especially effective for subtle adjustment. Therefore, research on simulation of MPHX should include those using capillary tubes for flow control.
Many models and algorithms for MPHX were presented, but they either neglected the refrigerant distributions among the paths (Martins and Parise 1993; Jia et al. 1999; Judge and Radermacher 1997; Lee et al. 2003) or only considered the refrigerant distributions among the paths without capillary tubes (Domanski 1991; Lee and Domanski 1997; Bensafi et al. 1997; Liang et al. 2001). We presented a general steady-state model (GSSM GSSM Governor's School for Science and Mathematics (South Carolina)
GSSM Gene Site Saturation Mutagenesis
GSSM Global Sourcing & Supplier Management ) for MPHX with an arbitrary refrigerant circuit (Liu et al. 2004) to simultaneously evaluate the effects of the refrigerant distribution among the paths in any refrigerant circuit, the heat conduction between the adjacent tubes with continuous fins, air-side maldistribution mal·dis·tri·bu·tion
Faulty distribution or apportionment, as of resources, over an area or among a group. , etc., but it still did not consider the refrigerant distribution among the paths of MPHX using capillary tubes for flow control. As to capillary tubes, the mathematical models
v. choked, chok·ing, chokes
1. To interfere with the respiration of by compression or obstruction of the larynx or trachea.
a. characteristics of the capillary tube. Therefore, measures must be taken to extend the GSSM to MPHX using capillary tubes for flow control.
The main difficulty in extending the GSSM for MPHX to those using capillary tubes for flow control is to solve the refrigerant distribution among the paths containing capillary tubes. The GSSM solves the refrigerant distribution among the paths by using iteration One repetition of a sequence of instructions or events. For example, in a program loop, one iteration is once through the instructions in the loop. See iterative development.
(programming) iteration - Repetition of a sequence of instructions. calculations. As capillary tubes have the choked characteristics, an extra constraint Constraint
A restriction on the natural degrees of freedom of a system. If n and m are the numbers of the natural and actual degrees of freedom, the difference n - m is the number of constraints. on the maximum refrigerant mass flow rate is introduced into the refrigerant distribution equations of the MPHX using capillary tubes for flow control. The simulation process may abnormally terminate or output obvious incorrect results if the assumed value of the mass flow rate of refrigerant in one capillary tube is larger than the maximum value during the iteration process. Therefore, the choked characteristics of the capillary tubes should be simultaneously considered during the process of solving equations for the refrigerant distribution among the paths of MPHX using capillary tubes for flow control.
The purpose of this paper is to extend the GSSM to MPHX using capillary tubes for flow control. In this paper, the description of the simulation object and analysis on the problem of directly applying the GSSM to MPHX using capillary tubes for flow control are given at first, then the extended GSSM is presented. Finally, experimental validation See validate.
validation - The stage in the software life-cycle at the end of the development process where software is evaluated to ensure that it complies with the requirements. and conclusions are given.
DESCRIPTION OF THE SIMULATION OBJECT
The simulation object considered in this paper is MPHX using capillary tubes for flow control. The capillary tubes can be added on several or all inlet inlet /in·let/ (-let) a means or route of entrance.
pelvic inlet the upper limit of the pelvic cavity.
thoracic inlet the elliptical opening at the summit of the thorax. paths of the MPHX, and the MPHX can have arbitrary divergent di·ver·gent
1. Drawing apart from a common point; diverging.
2. Departing from convention.
3. Differing from another: a divergent opinion.
4. or confluent con·flu·ent
1. Flowing together; blended into one.
2. Merging or running together so as to form a mass, as sores in a rash. refrigerant paths. All of the geometrical ge·o·met·ric also ge·o·met·ri·cal
a. Of or relating to geometry and its methods and principles.
b. Increasing or decreasing in a geometric progression.
2. parameters of the simulation object as well as the inlet states of both refrigerant and air are known. The target of the simulation is to obtain the general performance of the simulation object and the states of the refrigerant and air on each part of the simulation object.
All of the paths of the simulation object are simply classified into two types--the main path (MP) and the subpath (SP)--in order to conveniently describe the refrigerant distribution. The MP refers to a group of paths that have same inlet tube and same outlet tube, and the SP refers to one of the subpaths in one MP. All of the MPs in the MPHX are coded as [MP.sub.i] (i = 1, 2, ..., [N.sub.m]) in line based on depth-first search (algorithm) depth-first search - A graph search algorithm which extends the current path as far as possible before backtracking to the last choice point and trying the next alternative path. Depth-first search may fail to find a solution if it enters a cycle in the graph. rule (Liu et al. 2004), and all the SPs in the MPHX are coded as [SP.sub.ij] (i = 1, 2, ..., [N.sub.m], and j = 1, 2, ..., m) in line based on breadth-first search In graph theory, breadth-first search (BFS) is a graph search algorithm that begins at the root node and explores all the neighboring nodes. Then for each of those nearest nodes, it explores their unexplored neighbour nodes, and so on, until it finds the goal. rule (Liu et al. 2004) in each [MP.sub.i] (i = 1, 2, ..., [N.sub.m]). In order to identify each tube in the heat exchanger, the tubes are numbered from 1 to N in the order from front row to back row and from bottom to top of the heat exchanger, and the inlet collecting tube and outlet collecting tube are numbered as 0 and N + 1, respectively.
Figure 1a shows the schematic A graphical representation of a system. It often refers to electronic circuits on a printed circuit board or in an integrated circuit (chip). See logic gate and HDL. of an i-column and j-row MPHX using capillary tubes for flow control, and Figure 1b shows the associated MPs and SPs.
[FIGURE 1 OMITTED]
The refrigerant distribution in the No. 1 MP is especially focused on since the capillary tubes are only added on [MP.sub.1] for helping to adjust the refrigerant distribution among the paths. It is better to further simplify the diagram of [MP.sub.1] to Figure 2 for the convenience of the analysis.
[FIGURE 2 OMITTED]
In Figure 2, the refrigerant inlet parameters [M.sub.r,in], [p.sub.r,in], [h.sub.r,in] are given; [M.sub.r,out], [p.sub.r,out], [h.sub.r,out], and [M.sub.r,1j] (j = 1, 2, ..., m) are unknown parameters that need to be calculated.
PROBLEM IN DIRECTLY APPLYING THE GSSM TO MPHX USING CAPILLARY TUBES FOR FLOW CONTROL
In GSSM, the mass flow rates of refrigerant in paths are iteratively adjusted until the pressure drops of refrigerant in all paths from inlet to outlet are equal. The following equation was used to reflect the relationship between the mass flow rate and the pressure drop of refrigerant in [MP.sub.i]:
[DELTA][p.sub.r,ij] = [S.sub.r,ij][M.sub.[r,ij].sup.2](j = 1,2, ..., m) (1)
[DELTA][p.sub.r,ij] = the pressure drop of refrigerant in [SP.sub.ij]
[S.sub.r,ij] = equivalent flow resistance of refrigerant in [SP.sub.ij]
[M.sub.r,ij] = mass flow rate of refrigerant in [SP.sub.ij].
The distribution of refrigerant in each SP of the same MP was adjusted to ensure the same pressure drop of refrigerant in all SPs, and the ratio of the mass flow rate of refrigerant in each SP was expressed as
[M.sub.r,i1]:[M.sub.r,i2]: ...:[M.sub.r,im] = [S.sub.[r,i1].sup.[ - 0.5]]:[S.sub.[r,i2].sup.[ - 0.5]]: ...:[S.sub.[r,im].sup.[ - 0.5]]. (2)
Since the sum of the mass flow rate of refrigerant is equal to the known value of the total mass flow rate of refrigerant in [MP.sub.i], the ratio of the mass flow rate of refrigerant in [SP.sub.ij] was calculated as
[[epsilon].sub.r,ij] = [[S.sub.[r,ij].sup.[ - 0.5]]/[[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 (term)](j = 1) m][S.sub.[r,ij].sup.[ - 0.5]]]] (3)
[[epsilon].sub.r, ij] = the ratio of the mass flow rate of refrigerant in [SP.sub.ij] to the total mass flow rate of refrigerant in [MP.sub.i].
And then, the mass flow rate of refrigerant in each SP of [MP.sub.i] can be determined as:
[M.sub.r,ij] = [[epsilon].sub.r,ij][M.sub.r,i](j = 1,2, ..., m), (4)
[M.sub.r,i] = the total mass flow rate of refrigrant in [MP.sub.i].
The calculation process from Equations 1 to 4 is repeated until the pressure drops of refrigerant in all subpaths are equal.
Incorrect results may occur if we directly apply the above GSSM to the MPHX using capillary tubes for flow control, especially for the cases that the mass flow rate of refrigerant calculated from Equation 4 for one capillary tube is larger than the choked value. For [MP.sub.1] containing capillary tubes, the total mass flow rate of refrigerant may decrease after the xth iteration calculation
[M.sub.r,1.sup.(x)] = [M.sub.r,1.sup.(x - 1)] - [DELTA][M.sub.r,1.sup.(x)] (5a)
[DELTA][M.sub.r,1.sup.(x)] = [summation]([M.sub.r,1k.sup.(0)] - [M.sub.r,1k,c]),([M.sub.r,1k.sup.(0)]>[M.sub.r,1k,c]andk[menber of][SP.sub.c]) (5b)
[M.sub.r, 1.sup.(x-1)] and [M.sub.r, 1.sup.(x)] = the total mass flow rate of refrigerant in [MP.sub.1] after the (x-1)th and the xth iteration calculation
[[DELTA]M.sub.r, 1.sup.(x)] = the discrepant dis·crep·ant
Marked by discrepancy; disagreeing.
[Middle English discrepaunt, from Latin discrep total mass flow rate of refrigerant after the xth iteration calculation
[M.sub.r, 1k.sup.(0)] = the mass flow rate of refrigerant calculated from Equation 4 for [SP.sub.1k]
[M.sub.r, 1k, c] = the choked mass flow rate of refrigerant in capillary tube in [SP.sub.1k]
[SP.sub.c] = the collection of the no. of the subpaths containing choked capillary tubes
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. Equations 5a and 5b, the total mass flow rate of refrigerant may be "lost" during the simulation process. Figure 3 schematically sche·mat·ic
Of, relating to, or in the form of a scheme or diagram.
A structural or procedural diagram, especially of an electrical or mechanical system. shows this refrigerant-lost problem. The simulation result with the GSSM is incorrect due to the unavoidable refrigerant-lost problem in the algorithm. Therefore, new algorithm for solving the refrigerant distributions among the paths of MPHX using capillary tubes for flow control must be developed to overcome this refrigerant-lost problem.
[FIGURE 3 OMITTED]
BASIC IDEA IN EXTENDING THE GSSM TO MPHX USING CAPILLARY TUBES FOR FLOW CONTROL
The refrigerant-lost problem that occurred in GSSM is mainly caused by the extra constraint on the maximum mass flow rate of refrigerant for MPHX using capillary tubes for flow control, and the cause of the refrigerant-lost problem is different for different cases of the choked refrigerant flows. Therefore, auxiliary auxiliary
In grammar, a verb that is subordinate to the main lexical verb in a clause. Auxiliaries can convey distinctions of tense, aspect, mood, person, and number. equations should be introduced in order to calculate the equations for refrigerant distribution among the paths, and different auxiliary equations should be used for different cases.
For the case that not all refrigerant flows in capillary tubes are choked during the iteration process for solving the refrigerant distribution among the paths, auxiliary equations should be introduced to redistribute re·dis·trib·ute
tr.v. re·dis·trib·ut·ed, re·dis·trib·ut·ing, re·dis·trib·utes
To distribute again in a different way; reallocate. the discrepant refrigerant. The reason for the occurring refrigerant-lost problem in GSSM for this case is that the assumed value is larger than the choked value for [m.sub.c] number of refrigerant flows, as shown in Equation 5b. Therefore, the [M.sub.r,1.sup.(x)] discrepant refrigerant should be redistributed re·dis·trib·ute
tr.v. re·dis·trib·ut·ed, re·dis·trib·ut·ing, re·dis·trib·utes
To distribute again in a different way; reallocate.
Adj. 1. to other paths in which the refrigerant flows are not choked, and the value of the total mass flow rate of refrigerant may not change after the redistribution re·dis·tri·bu·tion
1. The act or process of redistributing.
2. An economic theory or policy that advocates reducing inequalities in the distribution of wealth. of the [M.sub.r, 1.sup.(x)] discrepant refrigerant.
For the case that all refrigerant flows in capillary tubes are choked during the iteration process for solving the refrigerant distribution among the paths, auxiliary equations should be introduced to determine the right value of the mass flow rate of refrigerant in each path. The reason for producing discrepant mass flow rate of refrigerant in GSSM for this case is that the given total mass flow rate of refrigerant in the heat exchanger conflicts with the inlet state of refrigerant and the geometry parameters of the capillary tubes. The inlet state of refrigerant and the geometry parameters of the capillary tubes determine the choked mass flow rate of refrigerant in an adiabatic ad·i·a·bat·ic
Of, relating to, or being a reversible thermodynamic process that occurs without gain or loss of heat and without a change in entropy. capillary tube. If the given total mass flow rate of refrigerant in the heat exchanger is larger than the sum of the all-choked mass flow rate of refrigerant, all of the capillary tubes may be choked. Equations 6-9 show the relationship between the given total mass flow rate of refrigerant and the sum of the all-choked mass flow rates of refrigerant, and Equation 9 shows the discrepant total mass flow rate of refrigerant after the xth iteration calculation for this case:
[M.sub.r,in] = [summation][M.sub.r, 1j.sup.(0)](j = 1,2, ...,m) (6)
[M.sub.r,1,max] = [summation][M.sub.r,1j,c](j = 1,2, ...,m) (7)
[M.sub.r,in]>[M.sub.r,1,max]([M.sub.r,1j].sup.(0)]>[M.sub.r,1j,c]andj = 1,2, ...,m) (8)
[DELTA][M.sub.r,1.sup.(x)] = [summation]([M.sub.r,1j.sup.(0)] - [M.sub.r,1j,c])([M.sub.r,1j.sup.(0)]>[M.sub.r,1j,c]andj = 1,2, ...,m) (9)
[M.sub.r,in] = the given total mass flow rate of refrigerant in the heat exchanger
[M.sub.r,1,max] = the sum of the all-choked mass flow rates of refrigerant, respectively
The refrigerant-lost problem may repeat even after redistributing the [DELTA][M.sub.r,1.sup.(x)] refrigerant to other paths because all other capillary tubes are choked and the new discrepant refrigerant may be lost again. Finally, a very small value of the total mass flow rate of refrigerant may be obtained after the simulation with the GSSM. Therefore, auxiliary equations should be introduced to determine the right value of the mass flow rate of refrigerant in each path to avoid such repeat of the refrigerant-lost problem occurring in GSSM.
Governing Equations for the Refrigerant Distribution in the Paths Containing Capillary Tubes
As shown in Figure 2, only the subpaths of [MP.sub.1] contain capillary tubes. The following equations are used to describe the refrigerant flow among the [SP.sub.1j](j = 1,2, ..., m):
[M.sub.r,in] = [summation][M.sub.r,1j](j = 1,2, ...,m) (10)
[M.sub.r,1j][less than or equal to][M.sub.r,1j,c](j = 1,2, ...,m) (11)
[h.sub.r,in] = [h.sub.r,1j](j = 1,2, ...,m) (12)
[p.sub.r,in] = [p.sub.r,1j](j = 1,2, ...,m) (13)
[M.sub.r,in] = the mass flow rate
[h.sub.r,in] = specific 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.
[p.sub.r,in] = pressure of refrigerant at the inlet of the [MP.sub.1]
[M.sub.r,1j] = the mass flow rate
[M.sub.r,1j,c] = the choked mass flow rate
[h.sub.r,1j] = inlet specific enthalpy
[p.sub.r,1j] = inlet pressure of refrigerant in [SP.sub.1j] (j = 1, 2, ..., m)
Equation 14 is used to calculate the pressure drop of refrigerant in [SP.subj.1j] in order to reflect the effect of the capillary tubes on refrigerant side pressure drop:
[[DELTA][p.sub.r,1j]] = [[DELTA][p.sub.r,1j,cap]] + [[DELTA][p.sub.r,1j,tube]] + [[DELTA][p.sub.r,1j,cs]](j = 1,2, ..., m) (14)
[[DELTA]p.sub.r, 1j] = the total pressure drop of refrigerant in [SP.sub.1j]
[[DELTA]p.sub.r, 1j, cap], [[DELTA]p.sub.r, 1j, tube] and [[DELTA]p.sub.r, 1j, cs] = the pressure drop of refrigerant in capillary tubes, in finned finned
Having a fin, fins, or finlike parts. Often used in combination: single-finned; multifinned. tubes and at the connecting section between the capillary and finned tube due to the enlarge TO ENLARGE. To extend; as, to enlarge a rule to plead, is to extend the time during which a defendant may plead. To enlarge, means also to set at liberty; as, the prisoner was enlarged on giving bail. cross-area from capillary to finned tube
If capillary tube is not used, [DELTA][p.sub.r, 1j, cap] and [DELTA][p.sub.r, 1j, dc] in Equation 14 are equal to 0, Equation 14 becomes the same as that in the previously developed GSSM (Liu et al. 2004), and the mass flow rate of refrigerant in [SP.sub.1j] can still be calculated with the previously developed GSSM.
If refrigerant flows in capillary tubes are not choked during the iteration process of solving the refrigerant distribution among the paths, Equation 11 is always satisfied, and the mass flow rate of refrigerant in [SP.sub.1j] can be calculated with Equations 1-4, 10, and 12-14.
Auxiliary Equations for the Case that One or Several Refrigerant Flows in Capillary Tubes Are Choked When Solving the Refrigerant Distribution Among the Paths
If the refrigerant flows in one or several capillary tubes are choked during the iteration process of solving the refrigerant distribution among the paths, the[[DELTA]M.sub.r,1.sup.(x)] refrigerant, which is determined by Equation 5a, should be redistributed among other SPs in order to reflect the real refrigerant distribution characteristics. Since the ratio of the mass flow rate of refrigerant in each path has already been determined by Equation 2, distributing the [[DELTA]M.sub.r,1.sup.(x)] refrigerant equally to the SPs with an unchoked capillary tube may not violently disturb the distribution ratio of the mass flow rate of refrigerant among the SPs. Therefore, a share-distribution strategy, which distributes the [[DELTA]M.sub.r,1.sup.(x)] refrigerant equally to the SPs containing an unchoked capillary tube, is applied to redistribute the above redundant refrigerant. By using the share-distribution strategy,
[M.sub.r,1j] = [M.sub.r,1j.sup.(0)] + ([summation][M.sub.r,1j.sup.(0)] - [summation][M.sub.r,1k])/(m - [m.sub.c])(j = 1,2, ..., m and j[not member of][SP.sub.c],k[member of]S[P.sub.c]) (15)
[M.sub.r,1k] = [M.sub.r,1k,c]/B(k[member of][m.sub.c]) (16)
[M.sub.r,1j.sup.(0)] = the value obtained by Equations 1-4, 10, and 12-14
B = an experiential ex·pe·ri·en·tial
Relating to or derived from experience.
ex·peri·en correction factor and should be in the range of 1.0-2.0
The refrigerant-lost problem can be avoided after redistributing the redundant refrigerant with Equations 15-16. The correction factor B in Equation 16 is necessary and should be larger than 1.0 in order to avoid the abnormal termination of the simulation process. The pressure drop of refrigerant in the choked capillary tube is very large, and sometimes is near the value of the pressure of inlet refrigerant. If B equals 1.0 in Equation 16, the calculated pressure drop of refrigerant on the subpath containing the choked capillary tube may be larger than the pressure of inlet refrigerant, which is wrong and may abnormally terminate the simulation program. If B is very large, the assigned mass flow rate of refrigerant in the subpath containing the choked capillary tube may become very small, which will lead to a smaller pressure drop of refrigerant in the subpath and will prolong pro·long
tr.v. pro·longed, pro·long·ing, pro·longs
1. To lengthen in duration; protract.
2. To lengthen in extent. the iteration process for solving the refrigerant distribution among the paths.
Auxiliary Equations for the Case that All Refrigerant Flows in Capillary Tubes are Choked When Solving the Refrigerant Distribution Among the Paths
If all refrigerant in capillary tubes on all paths are choked during the iteration process of solving the refrigerant distribution among the paths, an incorrect and much smaller value of the mass flow rate of refrigerant may be obtained after simulation with the GSSM because the [M.sub.r,1] refrigerant is always lost during the iteration process for determining the refrigerant distribution among the subpaths. In fact, when refrigerant flows in all capillary tubes are choked, the pressure drop of refrigerant in the MP is dominated by the choked refrigerant flow in the SP with minimum pressure drop of refrigerant. So the refrigerant distribution method should be based on the SP that has minimum pressure drop of refrigerant. Let's denote de·note
tr.v. de·not·ed, de·not·ing, de·notes
1. To mark; indicate: a frown that denoted increasing impatience.
2. the SP that has minimum pressure drop of refrigerant as the standard path and the corresponding minimum pressure drop of refrigerant as [p.sub.r,s]. Then the following equation can be used to determine the mass flow rates of refrigerant in other SPs based on the pressure drop of the standard path:
[M.sub.r, 1j] = [M.sub.r, 1j,c](j = s) (17)
[M.sub.r,1j] = f([[DELTA][p.sub.r,s]]) = f([[DELTA][p.sub.r,1j,cap]] + [[DELTA][p.sub.r,1j,tube]] + [[DELTA][p.sub.r,1j,cs]])(j = 1,2, ..., m and j[not equal to]s) (18)
where function f is derived from Equation 14.
The refrigerant-lost problem can be avoided after redistributing the redundant refrigerant with Equations 17 and 18, but [M.sub.r, 1.sup.(x)]<[M.sub.r, in.sup.(0)] for this case.
Other Governing Equations
The refrigerant flow in the capillary tube is considered as adiabatic one-dimensional homogenous homogenous - homogeneous flow. The details of the governing equations for single capillary tube and fin-and-tube are provided by Liu et al. (2004) and Zhang and Ding (2004), and are summarized in the appendix.
Algorithm Description (language) ALgorithm DEScription - (ALDES) ["The Algorithm Description Language ALDES", R.G.K. Loos, SIGSAM Bull 14(1):15-39 (Jan 1976)].
The whole MPHX using capillary tubes for flow control is divided into many control volumes. The simulation process begins with the first control volume of the inlet tube and ends with the last control volume of the outlet tube with a section-by-section method. A heat transfer and pressure drop alternative iteration algorithm is applied for the simulation of the heat exchanger using capillary tubes for flow control.
Since the refrigerant flow in the capillary tube is considered as adiabatic one-dimensional homogenous flow, the heat transfer via capillary tubes can be neglected. So the heat-transfer calculation algorithm in the previously developed GSSM (Liu et al. 2004) is still applied.
The process of pressure drop calculation starts from the inlet tubes, and then comes to the capillary tube and heat exchanger tube along the SPs of each MP. The pressure drop of refrigerant in each SP is calculated one by one based on the known refrigerant states obtained from the heat-transfer calculation process.
In the pressure drop calculation module, different methods of refrigerant distribution are used to determine the refrigerant distribution among the paths according to the states of the capillary tubes on different paths. Figure 4 shows the flow chart of the pressure drop calculation module developed in this paper. The parts with the gray background are the added parts, as compared to the flow chart of the previously developed GSSM (Liu et al. 2004).
[FIGURE 4 OMITTED]
The right way to validate To prove something to be sound or logical. Also to certify conformance to a standard. Contrast with "verify," which means to prove something to be correct.
For example, data entry validity checking determines whether the data make sense (numbers fall within a range, numeric data the extended GSSM is to validate the submodels of the GSSM for heat exchanger without capillary tubes and the model for single capillary tube at first, and then to validate the effect of the integrated model of the two submodels in the extended GSSM. The validation of the GSSM for heat exchanger without capillary tubes and the model for single capillary tube were already reported in the published papers (Liu et al. 2004; Zhang and Ding 2004), which showed that the cooling capacity calculation deviations and the refrigerant-side pressure drop calculation deviations of GSSM for a MPHX using R-22 were less than [+ or -]10% and [+ or -]20% individually, while the deviation DEVIATION, insurance, contracts. A voluntary departure, without necessity, or any reasonable cause, from the regular and usual course of the voyage insured.
2. of the model for single capillary tube was within [+ or -]15%. Therefore, these two models are not validated val·i·date
tr.v. val·i·dat·ed, val·i·dat·ing, val·i·dates
1. To declare or make legally valid.
2. To mark with an indication of official sanction.
3. in this paper, and only the effect of the integrated model and algorithm in the extended GSSM is verified.
In order to verify the extended GSSM for the MPHX using capillary tubes for flow control, a test rig has been set up and series of experiments have been designed and performed. The schematic of the experimental rig and the refrigerant circuit of the test coil are shown in Figure 5. The experimental conditions are shown in Table 1.
[FIGURE 5 OMITTED]
Table 1. Experimental Conditions (a) Six Capillary Tubes (b) Heat Exchanger Length/width 635/26.6/336 /height, mm 1.5/150, Row number/ 2/16 column 3.0/300, number Inner Diameter/Length, 4.7/300, Path number 2 mm 3.0/150, 1.5/300, Tube diameter, 7.0/enhanced 4.7/300 mm/type Fin type/fin Slit/1.2 pitch, mm (c) Measuring Condition (d)Refrigerant Condition Air Inlet Temperature 300/292 Refrigerant type R410A [T.sub.dry]/[T.sub.wet], K Air Velocity, 1.0, 1.4, Enthalpy 249, 260 m[s.sup.-1] 2.0 of EEV outlet, kJ k[g.sup.-1] Medium Temperature of Condensation, K 308, 317 Mass flow rate, 62-94 kg [h.sup.-1]
The test system consists of four subsystems of wind tunnel wind tunnel, apparatus for studying the interaction between a solid body and an airstream. A wind tunnel simulates the conditions of an aircraft in flight by causing a high-speed stream of air to flow past a model of the aircraft (or part of an aircraft) being tested. , refrigerant circuit, air and refrigerant property control system, and data acquisition system. A variable-speed blower is used to control the airflow rate. The temperature and humidity humidity, moisture content of the atmosphere, a primary element of climate. Humidity measurements include absolute humidity, the mass of water vapor per unit volume of natural air; relative humidity (usually meant when the term humidity of air are controlled in the temperature and humidity control Humidity control
Regulation of the degree of saturation (relative humidity) or quantity (absolute humidity) of water vapor in a mixture of air and water vapor. Humidity is commonly mistaken as a quality of air. room. The mass flow rate of air is measured with a standard nozzle An orifice in an inkjet print head through which ink is sprayed onto the paper. Print heads with six thousand or more nozzles are common in today's printers.
Nozzle . The temperatures of air and refrigerant are measured with Type T thermocouples. The temperature measuring system has been 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): with a standard platinum resistance thermometer resistance thermometer
A device measuring temperature by the change of the electrical resistance of a metal wire. , and the uncertainty is [+ or -]0.05 K for the entire temperature range of 173.15-473.15 K. The mass flow rate of refrigerant is measured by a mass flowmeter See flow meter. with a maximum error less than [+ or -]0.12% in the full range of 0-200 kg.[h.sup.-1]. The refrigerant pressure is measured using absolute pressure transducer Pressure transducer
An instrument component which detects a fluid pressure and produces an electrical, mechanical, or pneumatic signal related to the pressure. with an error less than [+ or -]0.12% in the full range of 0-5 MPa. The mass flow rate of refrigerant is regulated by a pulse-controller for the electric expansion valve (Steam Engine) a cut-off valve, to shut off steam from the cylinder before the end of each stroke.
See also: Expansion (EEV EEV European Embedded Value (EU insurance calculation standardization)
EEV E-Energy Ventures Inc (stock symbol)
EEV English Electric Valve
EEV Equine Encephalitis Virus ). The enthalpy of the coil inlet refrigerant is determined by the measured pressure and temperature at the inlet of the EEV. The air duct and connecting pipes are well insulated in·su·late
tr.v. in·su·lat·ed, in·su·lat·ing, in·su·lates
1. To cause to be in a detached or isolated position. See Synonyms at isolate.
2. to prevent the heat exchange with the surroundings. The cooling capacities are measured with air enthalpy method with a maximum error less than [+ or -]4% in the full range of 0-5 kW. The experimental data are collected after the air-side 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. and wet-bulb temperature Wet-bulb temperature - there are several meanings of this term:
Validation Results of the Extended GSSM
The experimental data are compared with the simulation results of the extended GSSM using the heat transfer and pressure drop correlations listed in Table 2. The simulation results are compared with the experimental results. The comparison results of the cooling capacity and refrigerant-side pressure drop between the simulation and experimental data are shown in Figures 6 and 7, respectively, which show that the difference between the calculated cooling capacity and the experimented one is less than [+ or -]5%, while the difference between the calculated refrigerant-side pressure drop and the experimented one is less than [+ or -]15%.
[FIGURE 6 OMITTED]
[FIGURE 7 OMITTED]
Table 2. List of Applied Heat Transfer and Pressure Drop Correlations Application Region Items Correlations Yun et al. (2002) for two-phase flow, enhanced tube Heat-transfer coefficient Dittus-Boelter equation (Shah 1979) for single-phase flow Goto et al. (2001) for two-phase flow, enhanced tube Refrigerant Chisholm and Sutherland Side (1969) for two-phase flow at the connecting section between the capillary and finned tube Pressure drop Colebrook-White equation (Smith et al. 2001) for single-phase flow Churchill (1977) for the friction factor of capillary Heat-transfer Nakayama and Xu (1983) coefficient for slit fin Air Side Pressure drop Wang et al. (2001) for slit fin
The calculated mass flow rates of refrigerant in each path of four test cases are listed in Table 3 in order to demonstrate the difference between the equal distribution case modeled for heat exchangers only, and the maldistribution case modeled for heat exchangers using capillary tubes for flow control. Among the four test cases, Case 1 does not use capillary tubes, Case 2 and Case 3 use different capillary tubes on different paths and have the same total mass flow rate of refrigerant as that of Case 1, and Case 4 uses the same capillary tubes as those used in Case 3 and has larger total mass flow rate of refrigerant than that of Case 3. In Table 3, the calculation results of Case 1 show that there is an equal refrigerant distribution in the heat exchanger without using capillary tubes. The calculation results of Case 2 and Case 3 show that varying the length or inner diameter of capillary tubes on different paths can control the refrigerant distribution among the paths, and the degree of the refrigerant maldistribution decreases with the increase of the inner diameter of the capillary tubes. The calculation results of Case 3 and Case 4 show that the degree of the refrigerant maldistribution increases with the increase of the total mass flow rate of the refrigerant. Therefore, by considering the effect of the capillary tubes on refrigerant distribution among the paths, the engineering designers can flexibly use the extended GSSM to control the refrigerant distribution in the MPHX by using different kinds of capillary tubes.
Table 3. The Effect of Using Capillary Tube to Control the Refrigerant Distribution in the MPHX Parameters of Capillary Tubes Case Subpath Inner Length, mm Mass Flow Rate Ratio of No. Diameter, mm of Refrigerant Refrigerant, Distribution, kg[h.sup.-1] % 1 SP12 -- -- 31.2 50.0 SP11 -- -- 31.2 50.0 2 SP12 1.5 300 29.3 47.0 SP11 1.5 150 33.1 53.0 3 SP12 3.0 300 31.0 49.7 SP11 3.0 150 31.4 50.3 4 SP12 3.0 300 45.8 49.2 SP11 3.0 150 47.2 50.8
By introducing two auxiliary equations to solve the refrigerant-lost problem in the previously developed GSSM (Liu et al. 2004) for the MPHX without capillary tubes, an improved model and algorithm for MPHX using capillary tubes for flow control is developed. The developed model and algorithm is suitable for not only the MPHX using capillary tubes for flow control, but also the MPHX without capillary tubes. An experimental rig is set up, and series of experiments on heat transfer and pressure drop characteristics of the heat exchanger using capillary tubes for flow control are performed to evaluate the developed model and algorithm. The evaluation results show that the difference between the calculated cooling capacity and the experimented one is less than [+ or -]5%, while the difference between the calculated refrigerant-side pressure drop and the experimented one is less than [+ or -]15%. Using different capillary tubes on different paths can help to control the refrigerant distribution among the paths in MPHX.
This study can theoretically contribute to modeling the MPHX using capillary tubes for flow control and other multicapillary systems, such as the multicapillary domestic refrigeration system, etc. In engineering practice, the associated software can give the users and designers the flexibility of analyzing the performance of the MPHX using capillary tubes for flow control, as well as analyzing the performance of the traditional MPHX without capillary tubes.
NOMENCLATURE nomenclature /no·men·cla·ture/ (no´men-kla?cher) a classified system of names, as of anatomical structures, organisms, etc.
[A.sub.o] = total surface area on air side, [m.sup.2]
[A.sub.i] = inside tube surface area, [m.sup.2]
d = inside diameter Inside diameter is the diameter of the addendum circle of an internal gear.1
1. ANSI/AGMA 1012-G05, "Gear Nomenclature, Definition of Terms with Symbols". , m
f = friction factor Friction factor can refer to:
G = mass flux flux
In metallurgy, any substance introduced in the smelting of ores to promote fluidity and to remove objectionable impurities in the form of slag. Limestone is commonly used for this purpose in smelting iron ores. , kg [m.sup.-2] [s.sup.-1])
h = specific enthalpy, kJ [kg.sup.-1]
L = length, m
M = mass flow rate, kg [s.sup.-1]
m = subpath number
[N.sub.m] = main path number
N = total tube number
p = pressure, kPa
[SP.sub.c] = collection of the no. for the sub paths containing choked capillary tubes
T = temperature, K
x = quality
[alpha] = heat transfer coefficient 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). , kW[m.sup.-2][K.sup.-1]
[DELTA]p = pressure drop, Pa
[[eta].sub.0] = fin surface efficiency
[rho] = density, kg [m.sup.-3]
Subscript (1) In word processing and scientific notation, a digit or symbol that appears below the line; for example, H2O, the symbol for water. Contrast with superscript.
(2) In programming, a method for referencing data in a table.
a = air
acc = acceleration
c = choke (jargon) choke - To fail to process input or, more generally, to fail at any endeavor.
E.g. "NULs make System V's "lpr(1)" choke." See barf, gag.
cap = capillary tube
cs = connecting section between the capillary tube and finned tube
fri = friction
m = mean value
max = maximum
in = inlet
out = outlet
r = refrigerant
s = standard path
tube = tube or fin-and-tube
wall = tube wall
EEV = electric expansion valve
GSSM = general steady-state model
MPHX = multipath fin-and-tube heat exchanger
MP = main path
SP = subpath
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1 River, c.600 mi (970 km) long, issuing as the Ashuanipi River from Ashuanipi Lake, SW Labrador, N.L., Canada, and flowing in an arc north, then southeast through a series of lakes to Churchill Falls and McLean Canyon. .W. 1977. Frictional frictional
pertaining to or emanating from friction.
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1. A long narrow furrow or channel.
2. The spiral track cut into a phonograph record for the stylus to follow.
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Mathematical theory of networks. A graph consists of vertices (also called points or nodes) and edges (lines) connecting certain pairs of vertices. An edge that connects a node to itself is called a loop. . Int. J. Refrig. 27(8):965-73.
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CHP California Highway Patrol
CHP Cumhuriyet Halk Partisi (Turkish: Republican People's Party)
CHP Chemical Hygiene Plan (OSHA)
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The refrigerant flow in the capillary tube is considered as adiabatic one-dimensional homogenous flow. Thermal equilibrium thermal equilibrium
The condition under which two substances in physical contact with each other exchange no heat energy. Two substances in thermal equilibrium are said to be at the same temperature. See also thermodynamics.
Noun 1. in the flashing process is assumed, and the flow resistance for the contraction contraction, in physics
contraction, in physics: see expansion.
contraction, in grammar
contraction, in writing: see abbreviation.
contraction - reduction is neglected. In this paper, the capillary tube is set after the EEV; thus, the refrigerant flow inside capillary tube is assumed to have no subcooling. The choked refrigerant mass flow rate is calculated according to the following criteria:
[dL.sub.cap]/[dp.sub.r,cap] = 0 (A1)
-d[p.sub.r,cap] = [G.sub.r,out,cap.sup.2](1/[[rho].sub.r,out,cap] - 1/[[rho].sub.r,in,cap]) + [[[f.sub.m][G.sub.r,out,cap.sup.2]/[2d.sub.cap][[rho].sub.r,m,cap]]]d[L.sub.cap] (A2)
The refrigerant flow inside the tube is considered a one-dimensional axial axial /ax·i·al/ (ak´se-al) of or pertaining to the axis of a structure or part.
1. Relating to or characterized by an axis; axile.
2. flow, and the axial conduction along the tubes is neglected.
Energy conservation equation for refrigerant flow in tubes is as follows:
[Q.sub.1r] = [Q.sub.2r] (A3)
[Q.sub.1r] = [M.sub.r]([h.sub.r,in] - [h.sub.r,out]) (A4)
[Q.sub.2r] = [[alpha].sub.r][A.sub.i]([[T.sub.r,in] + [T.sub.r,out]]/2 - [T.sub.wall]) (A5)
where [[alpha].sub.r] is calculated from selected empirical correlations.
The continuity equation for refrigerant flow in tubes is as follows:
[G.sub.r,out] = [G.sub.r,in] (A6)
The momentum conservation equation for refrigerant flow in tubes is as follows:
[[DELTA][p.sub.r,tube]] = [[DELTA][p.sub.r,f]] + [[DELTA][p.sub.r,acc]] (A7)
where [p.sub.r,f] and [p.sub.r,acc] are calculated from selected empirical correlations.
The energy conservation equation for air is as follows:
[Q.sub.1a] = [Q.sub.2a] (A8)
[Q.sub.1a] = [M.sub.a].([h.sub.a,in] - [h.sub.a,out]) (A9)
[Q.sub.2a] = [[alpha].sub.a][A.sub.o][[eta].sub.o]([[[T.sub.a,in] + [T.sub.a,out]]/2] - [T.sub.wall]) (A10)
where air mass flow rate [M.sub.a] is calculated based on upstream From the consumer to the provider. See downstream.
(networking) upstream - Fewer network hops away from a backbone or hub. For example, a small ISP that connects to the Internet through a larger ISP that has their own connection to the backbone is downstream from the larger control volumes in front row; [[alpha].sub.a] is calculated from selected empirical correlations.
The continuity equation for air is as follows:
[G.sub.a,out] = [G.sub.a,in] (A11)
The momentum conservation equation for air is as follows:
[[DELTA]p.sub.a]] = [[DELTA]p.sub.a, fin]] + [[DELTA]p.sub.a, tube]] (A12)
where [p.sub.a,fin] is the air-side pressure drop due to the fin surface; [p.sub.a,tube] is the air-side pressure drop due to the tube surface.
The energy conservation equation for fin-and-tube is as follows:
[Q.sub.1r] + [Q.sub.1a] + [Q.sub.cond] = 0 (A13)
[Q.sub.cond] = [Q.sub.front] + [Q.sub.back] + [Q.sub.top] + [Q.sub.bottom] (A14)
where [Q.sub.cond] is the total heat conduction by fins; [Q.sub.front], [Q.sub.back], [Q.sub.top], and [Q.sub.bottom] are heat conductions by fins from nearest front row, back row, upper column, and bottom column, respectively.
For coil with divergence divergence
In mathematics, a differential operator applied to a three-dimensional vector-valued function. The result is a function that describes a rate of change. The divergence of a vector v is given by or confluence confluence /con·flu·ence/ (kon´floo-ins)
1. a running together; a meeting of streams.con´fluent
2. in embryology, the flowing of cells, a component process of gastrulation. , the governing equations at the divergence or confluence points are needed in order to determine the inlet state parameters of refrigerant in downstream branches. Equations 10, 12, 13 are used for No. i divergence flow after replacing "1" with "i," and the following equations are used for No. i confluence flows:
[M.sub.r,i] = [m.[summation over (j = 1)][M.sub.r,ij](j = 1,2, ...,m) (A15)
[h.sub.r,i] = [[m.[summation over (j = 1)]][h.sub.r,ij][M.sub.r,ij]]/[[[m.[summation over (j = 1)]])][M.sub.r,ij]](j = 1,2, ...,m) (A16)
[p.sub.r,i] = [p.sub.r,ij](j = 1,2, ...,m) (A17)
[M.sub.r,i] = the mass flow rate at the point after the of No. i confluence
[h.sub.r,i] = specific enthalpy at the point after the of No. i confluence
[p.sub.r,i] = pressure of refrigerant at the point after the of No. i confluence
[M.sub.r,ij] = the mass flow rate in the No. j sub path of No. i confluence
[h.sub.r,ij] = inlet specific enthalpy in the No. j sub path of No. i confluence
[p.sub.r,ij] = inlet pressure of refrigerant in the No. j sub path of No. i confluence
Guoliang Ding, PhD
Guoliang Ding is a professor in the Institute of Refrigeration and Cryogenics cryogenics: see low-temperature physics.
Study and use of low-temperature phenomena. The cryogenic temperature range is from −238°F (−150°C) to absolute zero. At low temperatures, matter has unusual properties. Engineering and Zhigang Wu is a PhD candidate at Shanghai Jiao Tong University Shanghai Jiao Tong University (Simplified Chinese: 上海交通大学; Traditional Chinese: 上海交通大學 , Shanghai, China. Kaijian Wang is senior engineer and Masaharu Fukaya is an engineer at the Fujitsu General Institute of Air-Conditioning Technology Limited, Kawasaki, Japan.
Received November 16, 2006; accepted August 9, 2007