EP0114640B1

EP0114640B1 - Finned heat exchanger tube having optimized heat transfer characteristics

Info

Publication number: EP0114640B1
Application number: EP19840100427
Authority: EP
Inventors: David L. Kienast
Original assignee: Wickes Products Inc
Current assignee: Wickes Products Inc
Priority date: 1983-01-25
Filing date: 1984-01-17
Publication date: 1988-03-02
Also published as: EP0114640A2; DE3469591D1; EP0114640A3

Description

Background of the invention

1. Field of the invention

The present invention relates to a direct expansion shell and tube evaporator in mechanical systems having metal heat exchanger tubes, each comprising an integral external fin structure and an integral internal helical fin structure having a predetermined helix lead angle measured relative to the longitudinal central axis of the tube.
Heat exchanger elements, such as metal tubes which are employed for heat transfer purposes and which may constitute components of direct expansion shell and tube evaporators for mechanical refrigeration systems, are well known in the art; particularly in configurations wherein the tubes are plain, in essence, they are unfinned and have essentially smooth bores. Heretofore, in order to improve upon the heat transfer properties of such metal heat exchanger tubes, the tubes have, in general, been provided with a plurality of integral internal fins transverse of the length of the tubes in a parallel spaced or helical pattern, thereby increasing the internal heat transfer surface area of the tubes and improving the heat transfer capabilities thereof. Although such internally finned heat exchanger tubes evidence improved heat transfer characteristics in comparison with plain or unfinned tubes, in essence, tubes which do not possess any internal fins, have a degree of improvement in heat transfer capability over unfinned tubes which is still insufficient to achieve the potential optimum heat transfer capacity of such heat exchanger tubes. Consequently, more recently, finned metal heat exchanger tubes have been developed for this type of refrigeration technology wherein the addition of external integral fins and has been incorporated into the physical geometries of the heat exchanger tubes for the purpose of still further enhancing the heat transfer capacities of the tubes. Numerous analytical investigations and actual physical experiments have been undertaken in the industry with regard to correlating the dimensions and configurations of the heat exchanger tubes and those of the integral external and internal tube fins in order to attempt to optimize, br at least improve upon, the heat transfer characteristics of such finned heat exchanger tubes. For this purpose, extensive mathematical formulae have been developed in the heat exchanger technology, through the application of which there are derived metal heat transfer tube configurations, particularly for metal heat exchanger tubes which are adapted to be employed in the direct expansion shell and tube evaporators of mechanical refrigeration systems, and wherein the formulae are predicated upon relatively predictable parameters, such as the operating conditions of the system, type of heat exchange fluids being conducted within and externally of the heat exchanger tubes, and upon the actual external and internal dimensions and configurations of the heat exchanger tube.
Although considerable efforts have been expended in the technology in attempting to obtain an optimization of externally and internally finned heat exchanger tubes in order to achieve improved heat transfer properties, at best, the results have only been partially successful in achieving the desired goals.

2. Discussion of the prior art

Basically, in calculating the geometrical dimensions and/or physical criteria in the design of externally and internally finned metal heat exchanger tubes having potentially optimized heat transfer characteristics, particularly tubes which are to be employed in the direct expansion shell and tube evaporators of mechanical refrigeration systems, various operating and physical parameters are taken into consideration. These parameters may be summarized as follows:
An extensive discussion of finned metal heat exchanger tubes of the type disclosed in US-A-3,826,304 is set forth by James G. Withers and Edward P. Habdas in Paper No. 87d presented at the 47th National Meeting of the American Institute of Chemical Engineers, New Orleans, LA, March 11-15, 1973, entitled "Heat Transfer Characteristics of Helical-Corrugated Tubes for Intube Boiling of Refrigerant R-12". Although the article describes the intended optimization of internally ridged (finned) heat exchanger tubes, notwithstanding the complex theoretical calculations involved, no criteria can be ascertained which would readily lead to or support the attainment of tube dimensions or geometries providing optimized performance characteristics in the employment of the tubes in the direct expansion shell and tube evaporators of mechanical refrigeration systems within the normal operating ranges of such systems. Consequently, although various design methods have been developed with respect to the provision of externally and internally finned heat exchanger tubes, which may present performance improvements over plain or unfinned tubing for use in-direct expansion evaporators, the prior art heat exchanger tubes and design methods are not in the optimum range for maximum heat transfer. Thus, externally and internally finned tubes have been designed for use in direct expansion evaporators in which the heat transfer capacity of these tubes is limited by the geometrical relationships of the external and internal fin surface areas and the internal flow cross-section of the tube, without taking into consideration the lead angle of the internal helical fins and any correlation of these tube dimensions. Consequently, these tubes are not designed for operation within the optimum range for maximum heat transfer.
Other design methods for heat exchanger tubes employed for intube boiling of refrigeration systems are not suitable for optimization of the tube configurations with respect to maximum heat transfer. Specifically, in these methods, the so-called severity factor of the tubing is not dependent upon the lead angle of the internal helical fins of the tubes, whereas extensive investigation pursuant to the present invention indicate that the heat transfer capacity is an important function of the lead angle of the internal helical fins of the tubes. Moreover, prior art finned tubes have severity factors which are outside of the "optimum range" for the particular inventive application, and previously described heat exchanger tube design methods are not applicable to optimization of direct expansion evaporator applications. Moreover, the geometrical relationships of presently known and commercially available externally and internally finned tubes, particularly with respect to the correlation among the surface areas of the external and internal fins and the flow cross-sectional areas of the tubes, fall outside the optimum range for maximum heat transfer capacity of the tubes.
Other design data currently employed in the technology is adapted for tubes having either plain (unfinned) or slightly knurled outer surfaces, and wherein it can be ascertained that the addition of external fins to the tubes significantly improves their heat transfer capacities. Such design methods, in general, do not take into consideration the geometrical or physical interrelationships of the heat exchanger tube dimensions and, in many instances, the methods are not adapted for superheating applications, which is most likely encountered in the operation of direct expansion evaporators.
Among various currently known finned heat exchanger tubes, a number of these come into consideration with respect to the invention concept, although none of the prior art tubes are designed for or adapted to optimization of the extent of the heat transfer of the tubes.
Thus, Lord et al. US-A-4,118;944 disclose an internally finned heat exchanger tube wherein the fin configuration is selected so as to restrict the temperature drop of the refrigerant in the tube to within a preselected range as the refrigerant flows therethrough. The dimensions of the finned tubing disclosed in Lord et al. clearly indicates, both as to the configuration of the helical internal fins, and the lack of any external fins which may be integrally formed with the tube that the heat exchanger tubes disclosed therein would not be suitable for optimization of the maximum heat transfer range, particularly when the tube is to be employed in the direct expansion evaporator of a mechanical refrigeration system.
Withers Jr., et al. US-A-3,847,212 disclose an extenally finned metal heat transfer tube which includes helical ridging (finning) on the inner diameter of the tube so as to provide for improved heat transfer capabilities. However, review of the calculations and physical dimensions and geometry of this heat exchanger tube construction clearly evidences that there is no correlation in evidence between the surface or heat transfer areas of the external and internal tube fins, the flow cross-sectional area of the heat exchanger tube and the lead angle of the internal helical fins which would provide for optimization of the maximum heat transfer capacity of the tube in a manner analogous to that contemplated by the present invention. In essence, the heat exchanger tubing disclosed in Withers Jr., et al., does not provide for optimum maximum heat transfer capability, particularly when the tubes are to be employed in direct expansion shell and tube evaporators for mechanical refrigeration systems.
Similarly, Thorne US-A-3,881,342, Rieger US-A-3,768,291 and Goodyer US-A-2,432,308 each disclose externally and internally finned metal heat exchanger tubes. However, as in the above-discussed instances, none of these tubes evidence nor suggest geometric and dimensional interrelationships among the external and internal fins, the flow cross-sectional area of the tube and the lead angle of the helical interior fins which would provide for optimization of the heat transfer capacity of such tubes to thereby render these highly efficient when employed in direct expansion evaporators, particularly evaporators utilized for mechanical refrigeration systems.
US-A-4 305 460 and FR-A-1 275 867 are directed to tube configurations which are designed for steam condensing service, wherein water is directed through the interior of the tube and steam onto its external surface. The patents teach little or nothing which would be useful to one working with direct expansion evaporators. In a steam condenser, steam condenses on the exterior surface of a tube at essentially constant pressure. As recognized by the reference, the principal concern in the design of such tubes is to provide an exterior surface which promotes drop-wise condensation and an interior surface which induces the highest degree of turbulence possible without incurring excessive pressure drop. As the interior heat transfer fluid is at all times liquid, its flow characteristics are well understood and easily calculated.
Direct expansion evaporators utilize forced convection boiling which is characterized by three complex flow regimes which are not subject to easy analysis. The designer of direct expansion evaporator tube must deal with a number of counterbalancing considerations to produce a tube with superior heat transfer characteristics.

Summary of the invention

Accordingly, in order to obviate the limitations and drawbacks encountered in direct expansion shell and tube evaporators according to the preamble of claim 1 designed and constructed pursuant to the prior art, and particularly heat exchanger tubes which are designed for utilization in the direct expansion shell and tube evaporators of mechanical refrigeration systems, pursuant to the present invention the metal heat exchanger tubes incorporate integral external and internal fins wherein

(a) the ratio of the internal heat transfer area of said tube per unit of tube length relative to the square-root of the internal cross-sectional flow area of said tube is within the range of about 4.60 to 6.20;
(b) the ratio of the external heat transfer area of said tube per unit of tube length relative to the internal heat transfer area of said tube per unit of tube length is within the range of about 1.5 to 5.0, and
(c) said helix lead angle of the internal fins is within the range of about 30° to 60°, in order to optimize the heat transfer capacities of the tubes, particularly when the tubes are to be employed in direct expansion evaporator of mechanical refrigeration systems.

The inventive heat exchanger tube design and construction is based on actual experimental test data gathered from direct expansion coolers in refrigeration systems incorporating various correlated combinations of the external and internal finned heat exchanger surface areas, cross-sectional flow areas of the tube, and the lead angle of the internal fins, which will lead to optimized heat transfer characteristics.
Specifically, the Bo Pierre boiling and AP equations which were published during the 1950's and which are referred to in the article by James G. Withers and Edward P. Habdas, Paper No. 87d, entitled "Heat Transfer Characteristics of Helical-Corrugated Tubes for Intube Boiling of Refrigerant R-12", presented at the 47th National Meeting of the American Institute of Chemical Engineers, New Orleans , LA, March 11-15, 1973, have been inventively modified to account for the lead angle of the internal helical tube fins and the hydraulic diameter of an internally finned tube. In calculating the optimum physical parameters for the heat exchanger tube pursuant to the invention, these modifications have been added to the known general heat transfer equation Q=UxAxMTD. A relationship has been found which allows for the coupling of the modified heat transfer and AP equations within the general equation, as expressed in terms of the physical dimensions of the heat exchanger tube as set forth hereinabove. This relationship remains valid for values of the internal cross-sectional flow area of the heat exchanger tube, or the hydraulic diameter which are optimal over the normal operating range of direct expansion evaporators of mechanical refrigeration systems as currently employed in the industry.
More specifically, optimal interrelationships have been found between the external and internal heat transfer surface areas of the tube fins, the internal cross-sectional flow area of the heat exchanger tube, and the lead angle of the internal helical tube fins. Thus, specific optimal operating ranges have been found, pursuant to the invention, at lead angles of between about 30 to 60° for the internal helical tube fins measured relative to the longitudinal axis of the tube, with such geometrical relationships not at all having been heretofore contemplated or employed in prior art heat exchanger tube structures.
Accordingly, it is a primary object of the present invention to provide for a finned metal heat exchanger tube of the type described which optimizes the heat transfer characteristics due to its physical parameters.
A more specific object of the present invention resides in the provision of a metal heat exchanger tube having integral external and internal helical fins wherein the physical dimensions of the external and internal tube fins, the lead angle of the internal fins, and the cross-sectional flow area of the tube are correlated with each other to provide for optimum heat transfer capacities, particularly when the tube is to be employed in the direct expansion shell and tube evaporator of a mechanical refrigeration system.

Brief description of the drawings

Reference may now be had to the following detailed description of a finned metal heat exchanger tube, in which the tube is particularly adapted to provide for optimized heat transfer characteristics when employed as a component in direct expansion evaporators for mechanical refrigeration systems; taken in conjunction with the accompanying drawings; in which:

Figure 1 illustrates a longitudinal view, partly in section, of an externally and internally finned heat exchanger tube pursuant to the invention; and
Figure 2 is a cross-sectional view taken along line 2-2 in Figure 1.

Detailed description

Referring now in detail to the drawings, a metal heat exchanger tube having a cylindrical wall construction 12 incorporates, integrally formed therewith, external fins 14 and internal fins 16.
As illustrated, the external fins 14, which are integrally formed with the cylindrical tube wall 12, may be of a generally helical configuration. Similarly, the internal fins which protrude into the flow passage way 18 of the heat exchanger tube 10 are also of a helical configuration.
In order to optimize the heat transfer capacity of the heat exchanger tube, particularly when the tube is to be employed in a direct expansion evaporator of a mechanical refrigeration system, extensive experimentation and actual testing pursuant to the invention has been undertaken in order to derive an optimum heat exchanger tube design based on the physical and dimensional interrelationship of the external area Ao of the tube for each meter of length of heat exchanger tubing (m²/m), the internal area Ai of the tube for each meter of tube length (m²), the internal cross-sectional flow area Aix of the heat exchanger tube (m²), and the lead angle 8 of the internal helical fins measured relative to the longitudinal axis of the heat exchanger tube (degrees). Through suitable correlation of the dimensional interrelationships of these heat exchanger tube design parameters, extensive experimental test data has indicated thatthe thermal performance of shell-and-tube type direct expansion evaporators for mechanical refrigeration systems can be predicted within predetermined bounds so as to allow for a heat exchanger tube design which considers the operating conditions of the cooler and provides an optimized heat transfer performance over the most likely employed range of operating conditions for such evaporators.
Basically, the physical design criteria for the heat exchanger tube 10 takes into consideration the operating conditions of the cooler; in effect, wherein

-m=refrigerant mass flowrate per tube kg/hr
Δx=refrigerant quality change
- Refrigerant
-SST=refrigerant saturated exit temperature from the tube.

The design for the heat exchanger tube is adapted for use when the heat exchanger tubes are utilized to boil and superheat the refrigerant flowing within the tubes (approximately 4° to 6°C superheat).
In essence, the heat exchanger tube 10, based on the foregoing operating conditions of a cooler which is employed in the direct expansion evaporators of mechanical refrigeration systems, employs dimensional parameters in the design of the heat exchanger tubes, based on each unit of tube length (L) as measured in meters. These dimensional parameters are as follows:
The outside heat transfer area Ao (m²/m) for the heat exchanger tube 10, which is measured as the total external tube surface for each meter of tube length L.
The internal heat transfer area Ai (m²/m) of the tube 10 which, in effect, is the total internal tube surface area for each meter of tube length L, the lead angle 0 of the internal fins, in degrees, measured relative to the longitudinal axis of the heat exchanger tube 10;
and the cross-sectional flow area Aix (m²) of the heat exchanger tube 10.
Thus, inventively, the following geometrical relationships have imparted optimized heat transfer characteristics to the heat exchanger tube 10, when maintained within the following parameters:
Moreover, the following tube geometries, utilizing the above dimensional parameters, have been found to be an optimization over prior art heat exchanger tube designs:
The present invention distinguishes with respect to prior art heat exchanger tube designs in that the dimensional proportions of Ao, Ai, Aix, and 0 are uniquely employed in a manner which will optimize the heat transfer capacity of the heat exchanger tube 10, which is of particular significance when employed in the direct expansion shell and tube evaporator of a mechanical refrigeration system.
In effect, an optimal interrelationship has been found between Ao, Ai, and Aix which will vary with 8. Moreover, the optimal operating range for each heat exchanger tube has also been shown to vary with 8. Consequently, set forth herein is the physical and dimensional correlation between Ao, Ai, Aix and 8 which is applicable over the optimum operating range for each heat exchanger tube; for example, the optimum operating range for a heat exchanger tube having θ=45° is somewhat different from the optimum operating range for a heat exchanger tube having 0=60°. The same relationship between Ao, Ai and Aix which is applicable for the heat exchanger tube having 8=4₅° has been found to be applicable for a tube having 8=60°.
In summation, the invention sets forth a novel geometrical interrelationship for the various dimensional parameters of a heat exchanger tube which differs from those commercially available, inventively utilizing a simplified mathematical computation and design method which is not contemplated in the prior art.

Claims

1. Direct expansion shell and tube evaporator in mechanical systems having metal heat exchanger tubes, each comprising an integral external fin structure and an integral internal helical fin structure having a predetermined helix lead angle measured relative to the longitudinal central axis of the tube, characterized by the following features:

(a) the ratio of the internal heat transfer area of said tube per unit of tube length relative to the square-root of the internal cross-sectional flow area of said tube is within the range of about 4.60 to 6.20;

(b) the ratio of the external heat transfer area of said tube per unit of tube length relative to the internal heat transfer area of said tube per unit of tube length is within the range of about 1.5 to 5.0;

(c) said helix lead angle of the internal fins is within the range of about 30° to 60°.

2. Direct expansion shell and tube evaporator according to claim 1, characterized in that the ratio of the heat transfer area of said internal fin relative to the square-root of the internal cross-sectional flow area of said tube is within the range of about 4.25 to 6.20, and wherein the helix lead angle of the internal fins of said tube is within the range of about 40° to 50°.