The present disclosure relates to the efficient configuration of bundles of helical tubes, particularly in heat transfer applications.
Helical tubing is a long-established technology for effective heat exchange between two fluids. In one application, as illustrated by U.S. Pat. No. 2,693,346, heat is transferred from fluid inside the helical tube to the fluid flowing around the tube, for example, high pressure steam from a remote steam generator is forced through the helical tubes to heat water flowing around them. In another, as illustrated by U.S. Pat. No. 9,605,912, hot vehicle exhaust gases inside the helical tubes are cooled by transfer of heat to engine coolant flowing around the coils.
A significant advantage of a helical tube or coil over a straight tube is that for a given enclosure length and tube diameter, a coil affords substantially more surface area over which to exchange heat with the surrounding fluid. Multiple coils may be interleaved around a common central axis to form a coil bundle. Coil bundles may be precisely positioned next to each other to optimize the number of tubes in an enclosure.
U.S. Pat. No. 9605912 discloses configuration of helical coil tube bundles in a heat exchanger for transferring heat between two fluids, for example between a hot exhaust gas and a liquid coolant. In one embodiment, the heat exchanger comprises a shell surrounding at least two tube bundles attached at both ends to a tube header. Each of the tube bundles is constructed from a plurality of individual tubes that are twisted into identical helixes formed about a common helical axis.
In the preferred configuration, two 3-tube bundles are formed with opposite helical twists, i.e., the first tube bundle has tubes wound in a helix having a right-hand helix and the second tube bundle has tubes wound in a left-hand helix. The tubes have identical diameter, pitch and helical diameter, and the helical axes of the bundles are parallel. Because the tubes in the bundles having opposite-twist can nest together without the helixes crossing over, the tube bundles can be positioned with their helical axes closer to each other than would be possible if all of the tube bundles had the same direction of twist. The heat exchanger may then be formed of several tube bundles arranged in a rectangular array with each tube bundle having the opposite twist from each of the adjacent tube bundles. This configuration increases the number of helical tube bundles that fit within the heat exchanger shell.
US Pat. No. 9964077 discloses efficient configurations of 2-tube bundles formed with opposite helical twists in patterns of two or four bundles.
The foregoing patents disclose arrangements of bundles where the bundles have opposite helical twists. It may be desirable in some circumstances to configure a heat exchanger with helical tube bundles that all have the same twist. For example, if tubes are all the same twist it is not necessary to maintain the tooling and programs to produce tubes of different twist direction. Moreover, assembly is simpler because it is not necessary to correctly position the different bundles, and bundle inventory management is simplified because there is only one type of bundle.
An improved packing efficiency of helical tube bundles of the same twist in a heat exchanger is achieved by selecting the angular orientation of the tube bundles so as to allow them to nest together in phase so that peaks of adjacent tube bundles are located between each other, forming a bundle overlap.
A helix can be mathematically defined by a system of parametric equations. A mathematical helix (defined as a curve for which the tangent makes a constant angle with a fixed line) with a diameter D and pitch P, can be parameterized by Θ is:
The centerline 100 of a cylindrical tube 101 or wire formed into a helix is shown in
additional tubes are spaced at an angle of ϕ. This makes the centerline equations of additional tubes of the bundle:
As used herein, d will refer to the outside diameter of the tube, so the helical bundle outside diameter is D+d, as seen in
Obviously, as seen in
However, the waves of the helical tube bundle create peaks 120 and valleys 130. When adjacent bundles have the same pitch, they can be rotationally positioned or phased such that the peaks of one bundle align with the valleys of the adjacent bundle.
When the number of tubes per bundle increases, the clearance, and thus the possible amount of bundle overlap, is reduced, as illustrated with 4-tube bundles in
To center the peaks 120 of one tube bundle in the valleys 130 of an adjacent bundle, permitting the minimum bundle spacing, the phase shift between bundles is:
which is depicted graphically in
This derivation shifts the corresponding tube of an adjacent bundle such that the valley of the corresponding adjacent tube wave is phased with the peak of the initial tube wave. The peak and valley of a sine wave are 180° apart. However, when there are more than two (2) tubes per bundle, N>2, this phase shift is greater than necessary as the corresponding tube of the adjacent bundle could be shifted to be in phase with a different tube of the initial bundle. In actuality, bundles of an odd number of tubes do not require a phase shift to be in phase with an adjacent bundle, whereas bundles of an even number of tubes require a minimum phase shift of (ϕ/2).
The minimum bundle spacing is where the helical tubes or wires touch tangent to each other.
As discussed above, pairs of same-twist helical tube bundles can be positioned adjacent to each other to yield closer spacing than the standard D+d boundary. In a multi-tube heat exchanger, many tube bundles must be packed together. The fact that pairs of bundles can be phased with each other does not necessarily generate close spacing throughout the enclosure.
It has been discovered that when the number of bundles in a pattern is an integer times the number of tubes in bundle, then a special situation occurs where the last bundle of the pattern falls in phase with the first bundle of the pattern. This allows the maximum bundle overlap between the last bundle of the pattern and the first bundle of the pattern. This holds true for pattern units of two or four 2-tube bundles, three 3-tube bundles, four 4-tube bundles and five 5-tube bundles. See
A tube and shell heat exchanger, comprising an encasement carrying one fluid and a plurality of tubes carrying another fluid is an example of an apparatus that benefits from inserting the maximum practical number of tubes inside the casing. A particular embodiment of such a heat exchanger is an EGR cooler that cools the exhaust gas of a diesel engine. EGR cooler designs are discussed in U.S. Pat Nos. 9,605,912 and 9,964,077, both of which are incorporated by reference hereby. These patents explain the advantages of helical coil tube components and an arrangement of opposite-twist coils that increases the number of tubes in a defined cooler enclosure.
The improved configuration of tubes disclosed in U.S. Pat. No. 9,605,912 works only with an even number of bundles per pattern unit. Where a configuration using an odd number (such as 3) bundles per pattern unit is desired, at least 2 of the helical tubes must have the same hand twist. Although adjacent tube bundles of the same hand twist cannot be positioned as close together as adjacent bundles of opposite hand twist, the current discovery that adjacent bundles of the same hand twist can be spaced closer than S=D+d when positioned in phase does yield a packing efficiency improvement.
The advantage achieved by positioning tube bundles as described herein may be seen by calculating two parameters: bundle spacing and packing efficiency. If the centerline of a helical, constant diameter tube is modeled by
{right arrow over (r)}=(y(t), z(t))
Then its outside surface is a parallel curve can be described by the equation
{right arrow over (r)}
k
={right arrow over (r)}(t)+k{right arrow over (n)}(t)
Where |k| is the normal distance from the centerline to the parallel curve and {right arrow over (n)}(t) is the unit normal vector. (Note that the parameter θ has been replaced with t to reduce confusion). The distance |k| would be the tube radius, or
Two adjacent bundles with tubes having the centerline equations
{right arrow over (r)}
1=(y1(t), z(t))
{right arrow over (r)}
1=(y1(t), z(t))
Would have outside surfaces
Where d1 is the tube diameter of bundle 1 and d2 is the tube diameter of bundle 2. The unit normal vector {right arrow over (n)}(t) of {right arrow over (r)}k
The tubes would have a minimum bundle spacing and touch tangent where
{right arrow over (r)}
k
(t1)={right arrow over (r)}k
{right arrow over (r)}′
k
(t1)={right arrow over (r)}′k
If y2(t) is of the form
y
2(t)=y(t)+Smin
Then this system of equations can be solved to find the minimum bundle spacing Smin.
A simplified example utilizing identical adjacent tube bundles, each tube having a constant helix diameter, pitch, and tube diameter, positioned perfectly in phase may be analyzed with reference in
The centerline 121 of a tube of bundle 1 is
The centerline 122 of a tube of bundle 2 which is perfectly phased with bundle 1 making its centerline
z
1(θ)=z2(θ)
The tubes of the adjacent bundles have outside surfaces 123 and 124 offset by a tube radius 126. The two adjacent tube centerlines when are spaced at a normal distance of a tube diameter d 127 (2 tube radii). If the outside surface 123 of the tube, parameterized by t, is
{right arrow over (r)}k=(yk(t),zk(t))
Where k=d/2, then the point of contact 125 occurs at
Therefore, the minimum possible bundle spacing Smin or maximum possible bundle overlap qmax is dependent on the number of tubes per bundle N, the pitch P, the helix diameter D, and the tube diameter d.
The performance of a heat exchanger is directly related to the amount of surface area available to transfer heat. The amount of heat transfer capacity that can be fit into a given sized heat exchanger describes the volumetric efficiency of the heat exchanger. In the case of a tube and shell heat exchanger, more tubes inside of a given sized shell allows for more heat transferring surface area thus improving the volumetric efficiency. The packing efficiency of a tube and shell heat exchanger can be expressed as a fraction of the total volume that is occupied by tubes. Since each tube usually has one inlet, one outlet, and is of constant diameter along its length, this can be simplified from a volumetric efficiency to a two-dimensional area efficiency:
To compare the packing efficiency of different helical tube bundle pattern units, the packing area can be defined as the area of the polygon having its corners at the helical axis of the bundles in the pattern unit. The tube area is the cross-sectional area of tubing within this polygon.
For comparison purposes, bundle overlap and packing efficiency were calculated in the context of tubing for an EGR cooler. In general, one of the design and manufacturing limitations of an EGR heat exchanger is the tube-to-tube spacing. The tubes may require sufficient flow and surface area available for heat exchange to avoid certain adverse effects such as localized boiling. Production of the end bulkhead or tube sheet may require a minimum web distance between holes. Reducing the spacing between tubes would increase the packing efficiency. So, for comparison purposes, it is advantageous to hold the tube-to-tube spacing “t” constant across all bundle configurations. This spacing applies not only to the spacing between tubes of the same bundle, but to the spacing between tubes of adjacent bundles as well.
With reference to
Using this model, one can calculate bundle overlap, bundle spacing and packing efficiency. In an EGR cooler manufactured for use as disclosed in U.S. Pat. No. 9,605,912, the preferred standard helical tube dimensions are d=.250″, t=.0531″ (due to manufacturing tooling) and p=2.500″. The results are shown in Table 1.
It is also possible to achieve bundle to bundle spacing less than the outside diameter (D+d) by positioning in phase certain dissimilar adjacent bundles. Table 2 shows bundle overlap, bundle spacing and packing efficiency for square patterns of 4 bundles per pattern where adjacent bundles with standard dimension t=.0531″ have dissimilar pitch P, number of tubes N, and/or tube diameter d.
A preferred embodiment of the invention is an EGR cooler implementing a 3×3 pattern unit (3 bundle patterns of 3-tube bundles). See
A shell 28 extends between bulkhead 16 and bulkhead 26 and is mechanically coupled to bulkhead 16 and to bulkhead 26 (e.g., by welding, brazing, or similar rigid attachment) to form a fluid-tight seal between the bulkheads and the shell. Shell 28 is provided with a coolant inlet passage 30 and a coolant outlet passage 32 to enable a flow of coolant to flow into shell 28 past the tubes contained within shell 28 and then out of shell 28 to an external radiator or other means of discharging the heat rejected from tubes 20-24. Although in the illustrative embodiment of
With additional reference to
With additional reference to
Tube bundles 34, 50 and 60 are positioned in phase with one another. The outer surface of tube 24, constituting the peak of tube bundle 34, is aligned with the valley between tubes 64 and 66 (of tube bundle 60). The outer surface of tube 66 is aligned with the valley formed by tubes 52 and 56 (of tube bundle 50). The outer surface of tube 52 is aligned with the valley formed by tubes 22 and 24 (of tube bundle 34). As discussed in connection with
The 3×3 pattern unit, comprising three adjacent 3-tube bundles, can be repeated to form a matrix of tube bundles, as seen in
With additional reference to
With reference to the figures and in particular the example embodiment, incorporating features of the present invention may be used as a heat exchanger for a variety of purposes in which it is desired to transfer heat from one fluid medium to another fluid. In one example, the heat exchanger may be used as an exhaust gas recirculation (EGR) cooler. A heat exchanger incorporating features of the present invention may, however, used in connection with any appropriate application to transfer heat from a fluid on one side of a barrier to a fluid on the other side of the barrier without bringing the fluids into contact. A heat exchanger incorporating the teachings of the present invention may be used with all types of fluids, for example air-to-air, air-to-liquid, liquid-to-liquid as appropriate to meet the particular needs of the application.
Although certain illustrative embodiments and methods have been disclosed herein, it will be apparent from the foregoing disclosure to those skilled in the art that variations and modifications of such embodiments and methods may be made without departing from the invention. Additionally, although the tubes forming the tube bundles in the illustrative embodiment are circular in cross section, tubes having non-circular cross sections may be advantageously used in a heat exchanger incorporating features of the present invention and therefore are considered within the scope of the invention. Also, it should be observed that although the helical axis of the tube bundles extends from bulkhead-to-bulkhead, it is not necessary that the tube bundles be continuously helical from bulkhead-to-bulkhead as long as they are helical about a common helical axis over some portion of their length. Accordingly, it is intended that the invention should be limited only to the extent required by the appended claims and the rules and principles of applicable law. Additionally, as used herein, references to direction such as “up” or “down” are intended to be exemplary and are not considered as limiting the invention and, unless otherwise specifically defined, the terms “generally” “substantially,” or “approximately” when used with mathematical concepts or measurements mean within +10 degrees of angle or within 10 percent of the measurement, whichever is greater.
Number | Date | Country | |
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63430484 | Dec 2022 | US |