Centrifugal Pump Intake Pipe With A Helical Flow Path

REID; KEVIN ;   et al.

Patent Application Summary

U.S. patent application number 14/667352 was filed with the patent office on 2016-09-29 for centrifugal pump intake pipe with a helical flow path. The applicant listed for this patent is SYNCRUDE CANADA LTD. in trust for the owners of the Syncrude Project as such owners exist now and. Invention is credited to STEPHEN HARASYM, KEVIN REID.

Application Number20160281733 14/667352
Document ID /
Family ID56975043
Filed Date2016-09-29

United States Patent Application 20160281733
Kind Code A1
REID; KEVIN ;   et al. September 29, 2016

CENTRIFUGAL PUMP INTAKE PIPE WITH A HELICAL FLOW PATH

Abstract

An intake pipe for directing a slurry towards an impeller of a centrifugal pump defines a helical flow path oriented to swirl the slurry in a rotational direction of the impeller.


Inventors: REID; KEVIN; (Edmonton, CA) ; HARASYM; STEPHEN; (Edmonton, CA)
Applicant:
Name City State Country Type

SYNCRUDE CANADA LTD. in trust for the owners of the Syncrude Project as such owners exist now and

Fort McMurray

CA
Family ID: 56975043
Appl. No.: 14/667352
Filed: March 24, 2015

Current U.S. Class: 1/1
Current CPC Class: F05D 2250/51 20130101; F05D 2250/25 20130101; F04D 29/4293 20130101; F04D 7/04 20130101
International Class: F04D 29/42 20060101 F04D029/42; F04D 29/22 20060101 F04D029/22; F04D 13/12 20060101 F04D013/12; F04D 1/00 20060101 F04D001/00; F04D 7/04 20060101 F04D007/04

Claims



1. An intake pipe for directing a slurry towards an impeller of a centrifugal pump, wherein the intake pipe defines a helical flow path oriented to swirl the slurry in a rotational direction of the impeller.

2. The intake pipe as claimed in claim 1, wherein the intake pipe comprises a helical portion having a diameter and a length, a pitch over diameter of about 2, and an eccentricity radius over diameter of about 0.2.

3. The intake pipe as claimed in claim 1, wherein the intake pipe comprises a helical portion having a length of about 15,000 mm, a pitch of about 1,500 mm, and an eccentricity radius of about 150 mm.

4. The intake pipe as claimed in claim 1, wherein the intake pipe comprises a helical portion having a length of 15,000 mm, a pitch of 1,500 mm, and an eccentricity radius of 150 mm.

5. A pump assembly for a slurry, the assembly comprising: (a) a volute defining an axial pump inlet, a radial pump outlet, and a pump chamber for an impeller rotatable about an axial impeller axis; and (b) an intake pipe in fluid communication with the pump inlet and defining a helical flow path oriented to swirl the slurry in a rotational direction of the impeller.

6. The pump assembly as claimed in claim 5, wherein the intake pipe comprises a helical portion having a diameter and a length, a pitch over diameter of about 2, and an eccentricity radius over diameter of about 0.2.

7. The pump assembly as claimed in claim 5, wherein the intake pipe comprises a helical portion having a length of 15,000 mm, a pitch of 1,500 mm, and an eccentricity radius of 150 mm.

8. A pump system comprising: (a) a first pump; (b) a second pump, wherein the second pump is a centrifugal pump comprising an impeller; and (c) an intake pipe for directing a slurry from the first pump to the impeller of the second pump, wherein the intake pipe defines a helical flow path oriented to swirl the slurry in a rotational direction of the impeller.

9. The pump assembly as claimed in claim 8, wherein the intake pipe comprises a helical portion having a diameter and a length, a pitch over diameter of about 2, and an eccentricity radius over diameter of about 0.2.

10. The pump system as claimed in claim 8, wherein the intake pipe comprises a helical portion having a length of 15,000 mm, a pitch of 1,500 mm, and an eccentricity radius of 150 mm.
Description



FIELD OF THE INVENTION

[0001] The present invention relates to pumping of slurries, and more particularly to intake pipes for centrifugal pumps used to pump slurries.

BACKGROUND OF THE INVENTION

[0002] Oil sands ores mined in Alberta, Canada are crushed and mixed with heated water, steam and caustic (NaOH) to produce slurries to be processed to recover bitumen. Centrifugal pumps are used to hydrotransport these oil sand slurries through pipe lines. Centrifugal pumps are also used to transport oil sands tailings through pipe lines.

[0003] Unlike single phase liquids, these slurries may contain hard, solid lumps that measure up to several inches in diameter. These lumps impact the impeller vanes of the centrifugal pumps with high relative velocity and thereby wear or damage the impeller vanes. The repair or replacement of the impeller vanes and the associated loss of productivity is a significant expense.

[0004] Accordingly, there is a need in the art for devices that may be used to mitigate wear or damage to impeller vanes of centrifugal pumps caused by dense slurries and larger solid particles in slurries.

SUMMARY OF THE INVENTION

[0005] In one aspect, the present invention comprises an intake pipe for directing a slurry towards an impeller of a centrifugal pump, wherein the intake pipe defines a helical flow path oriented to swirl the slurry in a rotational direction of the impeller.

[0006] In another aspect, the present invention comprises a pump assembly for a slurry, the assembly comprising a volute, and an intake pipe. The volute defines an axial pump inlet, a radial pump outlet, and a pump chamber for an impeller rotatable about an axial impeller axis. The intake pipe is in fluid communication with the pump inlet and defines a helical flow path oriented to swirl the slurry in a rotational direction of the impeller. The pump inlet may be positioned to reduce the amount of the volute that solid particles in the slurry flow through before being discharged at the radial pump outlet.

[0007] In another aspect, the present invention comprises a pump system comprising a first pump, a second pump, and an intake pipe that directs a slurry from the first pump to the impeller of the second pump, wherein the intake pipe defines a helical flow path oriented to swirl the slurry in a rotational direction of the impeller.

[0008] In one embodiment, the intake pipe comprises a helical portion having a diameter and length, a pitch over diameter of about 2, and an eccentricity radius over diameter of about 0.2. In one embodiment, the helical portion has a diameter of about 700 mm (28''), a length of about 15,000 mm, a pitch of about 1,500 mm and an eccentricity radius of about 150 mm.

[0009] With the use of a computational fluid dynamics model, it was demonstrated that the intake pipe of the present invention, relative to a straight intake pipe, may result in reduced wear of the impeller and the volute of a centrifugal pump attributable to impacts between these pump components and the larger solid particles (lumps) in the slurry.

[0010] Without restriction to a theory, it is believed that this effect is due to the intake pipe imparting a circumferential velocity to the solid particles in the slurry, which may reduce the impact velocity of the solid particles with these pump components, and the amount of impacts between the solid particles and these pump components, and also to the intake pipe reducing the axial velocity of the solid particles prior to flowing into the centrifugal pump.

[0011] Other features will become apparent from the following detailed description. It should be understood, however, that the detailed description and the specific embodiments, while indicating preferred embodiments of the invention, are given by way of illustration only, since various changes and modifications within the spirit and scope of the invention will become apparent to those skilled in the art from this detailed description.

BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Referring to the drawings wherein like reference numerals indicate similar parts throughout the several views, several aspects of the present invention are illustrated by way of example, and not by way of limitation, in detail in the following figures. It is understood that the drawings provided herein are for illustration purposes only and are not necessarily drawn to scale.

[0013] FIG. 1 is a perspective view of one embodiment of the intake pipe of the present invention.

[0014] FIG. 2 is a schematic depiction of the geometry of one embodiment of the intake pipe of the present invention.

[0015] FIG. 3 is a perspective view of one embodiment of the intake pipe of the present in invention, connected to one embodiment of a centrifugal pump.

[0016] FIG. 4 is a vector diagram illustrating the predicted effect of one embodiment of the intake pipe of the present invention on the impact velocity of a solid particle in the slurry with an impeller vane of a centrifugal pump.

[0017] FIG. 5 shows the flow path of a plurality of solid particles in a slurry flowing through one embodiment of an intake pipe of the present invention, and in the volute of a centrifugal pump, as predicted by a computational fluid dynamics model.

[0018] FIG. 6 is a graph comparing the swirl velocity of a single phase fluid flowing through one embodiment of an intake pipe of the present invention, as predicted by a computational fluid dynamics model to experimental results.

[0019] FIG. 7 is a graph comparing the pressure gradient of a single phase fluid flowing through one embodiment of an intake pipe of the present invention, as predicted by a computational fluid dynamics model, to experimental results.

[0020] FIG. 8 is a graph comparing the average circumferential velocity of solid particles of a slurry flowing through embodiments of the intake pipe of the present invention having different combinations of pitches and eccentric radii, as predicted by a computational fluid dynamics model.

[0021] FIG. 9 is a graph comparing the average circumferential velocity of a single phase fluid of a slurry flowing through embodiments of the intake pipe of the present invention having different combinations of pitches and eccentric radii, as predicted by a computational fluid dynamics model.

[0022] FIG. 10 is a graph comparing the average head loss (above that of an equivalent straight pipe) of a single phase fluid of a slurry flowing through embodiments of the intake pipe of the present invention having different combinations of pitches and eccentric radii, as predicted by a computational fluid dynamics model.

[0023] FIG. 11 is a graph showing the average axial velocity of solid particles in a slurry flowing through one embodiment of an intake pipe of the present invention, as predicted by a computational fluid dynamics model.

[0024] FIG. 12 shows one embodiment of the position of one embodiment of the intake pipe of the present invention relative to the impeller of a centrifugal pump, intended to increase the amount of the volute that the solid particles of the slurry pass through before being discharged from the volute.

[0025] FIG. 13 shows an alternative embodiment of the position of one embodiment of the intake pipe of the present invention relative to the impeller of a centrifugal pump, intended to reduce the amount of the volute that the solid particles of the slurry pass through before being discharged from the volute.

[0026] FIGS. 14A and 14B show the erosion of the volute of a centrifugal pump caused by solid particles of a slurry flowing through a straight pipe and one embodiment of an intake pipe of the present invention, respectively, as predicted by a computational fluid dynamics model.

DESCRIPTION OF THE PREFERRED EMBODIMENT

[0027] The detailed description set forth below in connection with the appended drawings is intended as a description of various embodiments of the present invention and is not intended to represent the only embodiments contemplated by the inventor. The detailed description includes specific details for the purpose of providing a comprehensive understanding of the present invention. However, it will be apparent to those skilled in the art that the present invention may be practiced without these specific details.

[0028] The present invention relates generally to an intake pipe for a centrifugal pump. When describing the present invention, all terms not defined herein have their common art-recognized meanings. To the extent that the following description is of a specific embodiment or a particular use of the invention, it is intended to be illustrative only, and not limiting of the claimed invention. The following description is intended to cover all alternatives, modifications and equivalents that are included in the spirit and scope of the invention, as defined in the appended claims. As used herein, the term "slurry" refers to a fluid mixed with solid particles.

[0029] FIG. 1 shows one embodiment of an intake pipe 10 of the present invention used to supply a slurry to a centrifugal pump. In general, the intake pipe 10 comprises a pipe inlet 12, a pipe outlet 14, and a helical portion 16. The pipe inlet 12 is for fluid communication with a slurry source. The pipe outlet 14 is for fluid communication with the pump inlet of a centrifugal pump. The helical portion 16 of the intake pipe 10 defines a helical flow path to swirl the slurry in the rotational direction of the impeller of a centrifugal pump. The intake pipe 10 may be made of any rigid material suitable for conveying the slurry to a centrifugal pump, and may be formed using any suitable techniques known in the art such as casting, molding, extrusion or a combination of the forgoing.

[0030] FIG. 2 schematically illustrates the geometry of part of the helical portion of one embodiment of the intake pipe 10. As used herein, "longitudinal" refers to the general direction of slurry flow within the helical portion 16 of the intake pipe 10, and "transverse" refers to a direction perpendicular to the longitudinal direction. In this embodiment, the helical portion 16 has a circular transverse cross-section C of constant diameter along the length of the intake pipe 10. The geometric center of the transverse cross-section C is offset from the longitudinal axis L, and revolves around the longitudinal axis L in a substantially circular path P, as the cross-section progresses along the length of the helical portion 16, thus tracing a helical curve H. This geometry of the helical portion 16 may be quantitatively described by its length, pitch and eccentricity radius. The "length" refers to the longitudinal dimension of the helical portion 16, which will be made up of a number of pitches. The "pitch" refers to the longitudinal distance in which the geometric center of the transverse cross-section makes one revolution around the longitudinal axis. The "eccentricity radius" refers to the transverse distance between the geometric center of the transverse cross-section C and the longitudinal axis L.

[0031] FIG. 3 shows one embodiment of the pump assembly 100 of the present invention. In general, the pump assembly 100 comprises a volute 20 of a centrifugal pump and an intake pipe 10.

[0032] The volute 20 provides a chamber in which the pressure and velocity of the slurry is increased by an impeller 30 rotating about an impeller axis. As used herein, the "axial" refers to the direction defined by the impeller axis, and "radial" refers to a direction perpendicular to the axial direction. The volute 20 defines a pump chamber 21 for the rotatable impeller 30 extending between an axial pump inlet 22, and a radial pump outlet 24. In the embodiment shown in FIG. 3, the pump outlet 24 discharges into a short length of discharge pipe 26 with a diffuser 28.

[0033] The intake pipe 10 is as described above in reference to FIG. 1. The pipe outlet 14 connected to the pump inlet 22 to convey the slurry from the intake pipe 10 into the pump chamber 21. The helical flow path of the intake pipe 10 is oriented to swirl the slurry in the same direction as the rotational direction of the impeller 30 as the slurry flows towards the pump inlet 22. In FIG. 3, for example, when viewed from the direction from the pipe inlet 12 towards the pipe outlet 14, the impeller 30 rotates in an anticlockwise direction, and so the helical portion 16 also swirls the slurry in an anticlockwise direction.

[0034] FIG. 4 shows a velocity vector diagram illustrating the theoretical principle of the intake pipe 10 of the present invention. The vector V.sub.it represents the tangential velocity at the leading edge of the rotating impeller 30, at given moment in time. The vector V.sub.pa represents the axial component of the velocity of a solid particle in the slurry flowing towards the impeller 30. The vector V.sub.pt represents the tangential component of the velocity of the solid particle in the slurry, imparted by the swirling effect of the helical portion 16 intake pipe 10 on the slurry. The vector .DELTA.V represents the impact velocity between the impeller and the solid particle of the slurry. The length of the vectors in FIG. 4 represent their respective magnitudes. As such, the impact velocity .DELTA.V of the solid particle with the impeller 30 will approach a minimum value as the tangential velocity of the solid particle approaches the tangential velocity of the impeller 30.

Numerical Modelling of Pump System

[0035] A three-dimensional numerical computational fluid dynamics model implemented with the ANSYS CFX.TM. computational fluid dynamics software package was used to support the above theory and predict parametric effects of different intake pipe 10 geometries. The volute 20 and impeller 30 models were based on an commercially available high-pressure pump, with a 57.5 inch diameter impeller, 28 inch discharge pipe section and a 24 inch.times.28 inch diffuser, without any leakage flow paths. The liquid phase of the slurry was modeled as a single continuous phase having a density of 1500 kg/m.sup.3 and a viscosity of 0.715 cP, which is representative of an oil sands slurry comprising bitumen, sand, clay and air. Turbulence effects in the liquid phase were modeled using the k-.omega. SST turbulence model with scalable wall functions. The solid particles of the slurry were modeled using discrete spherical particles having a diameter of 5 inches, accounting for drag and buoyancy forces, but ignoring blockage effects. The effects of the particles on the flow field, and inter-particle interactions were ignored.

Effect on Particle Flow Path

[0036] The model was used to predict the particle flow path in an intake pipe 10 having a diameter of 28 inches, a helical portion 16 with a length of 9,000 mm, pitch of 1,500 mm and eccentricity radius of 150 mm, with a slurry flow rate of 7,200 m3/hr. Of course, it is understood that other geometries could be used depending upon a number of factors such as pump type, pump size, etc.

[0037] FIG. 5 graphically shows, for one embodiment of the pump system 100, the flow path of a plurality of solid particles of the slurry as the slurry flows through the helical portion of the intake pipe (not shown), impacts the anticlockwise rotating impeller 30 and circulates through part of the volute (not shown).

[0038] As can be seen from FIG. 5, the flow paths of the solid particles have a significant directional component that is tangential to the circular path circumscribed by the vanes of the rotating impeller. The model predicts that the solid particles are mostly concentrated in a ribbon-like stream which follows the helix of the undulating pipe. In reality, the particles may not follow such a concentrated ribbon pattern due to their volume, but it would reasonably be expected that a large number of the solid particles would follow a predictable path governed by the geometry of the helical portion of the intake pipe 10. This is because the particles are expected to follow the outer surface of the inner wall of the intake pipe 10 due to the centrifugal force acting on the particles, and the fact that the density of the particles is greater than the density of the slurry. If the length of straight pipe between the undulating pipe and the pump inlet is kept sufficiently short, it should be possible to control where a large portion of the particles, in particular, the larger lumps within the slurry, e.g., greater than 10 mm, will enter the pump inlet 22 and to control the tangential velocity of the larger lumps.

Effect of Eccentricity Radius and Pitch on Fluid and Solid Particle Swirl Velocity, Fluid Pressure

[0039] The model was validated for an intake pipe 10 having a helical portion with a pitch of 152 mm and an eccentricity radius of 17 mm using experimental data for a single phase fluid in a pipe of laboratory scale. FIG. 6 is a graph comparing the predicted and experimental swirl velocity of single phase liquid at different radial locations across the transverse cross-section of the pipe for slurry flowing at 3 m/s. FIG. 7 is graph comparing the predicted fluid pressure at different axial locations of the intake pipe for fluids flowing at different velocities. These graphs show that the model can adequately predict the swirl velocity and average pressure of a single phase fluid flow through an intake pipe at the laboratory scale, once the flow has fully developed in the helical portion.

[0040] With the model so validated, it was used to predict the single phase fluid pressure drop and swirl velocity generated by commercial scale intake pipes 10 having a helical portion with six turns, and different pitches and eccentric radii. FIG. 8, FIG. 9, and FIG. 10 are graphs showing the predicted effect of these parameters on the average circumferential velocity of the solid particles, the average swirl velocity of the single phase fluid, and the pressure of the fluid, respectively. These graphs show that the model predicts that decreasing the pitch and increasing the eccentricity radius tends to increase the circumferential velocity of the solid particles and fluid phase, and the pressure drop of the fluid phase. Of note, circumferential velocities of the particles are greater than the average circumferential fluid velocity because the majority of the particles travel near the outside wall of the inner surface of the intake pipe 10.

Effect of Length on Solid Particle Axial Velocity

[0041] The model was also used to predict the effect of the helical portion 16 of the intake pipe 10 on the axial velocity of the solid particles for an intake pipe 10 with a helical portion having a length of 15,000 mm, a pitch of 1,500 mm, and an eccentricity radius of 150 mm. FIG. 11 shows that the average axial velocity of the solid particles varies with distance through this geometry and eventually reaches a fairly stable value of 2 m/s within the undulating pipe. Upon exiting the undulating intake pipe, it can be seen that the solid particles are then accelerated back to the expected average velocity of 5 m/s within the straight pipe section. Without restriction to a theory, it is believed that this reduction in axial velocity of the solid particles is due to the solid particles travelling along the periphery of the pipe where the axial velocity is lower than near the center of the pipe, and the solid particles being decelerated by impacts with the inner wall of the intake pipe 10.

[0042] It has been noted in the field that when centrifugal slurry pumps are operated in series, in close proximity to each other, the downstream pump will wear more quickly than the upstream pump. One proposed reason for this is that the particles are accelerated by the upstream pump and carry added velocity to the downstream pump. The predicted effect of the helical portion 16 of the intake pipe 10 in reducing the axial velocity of the solid particles may be used to mitigate the tendency of the downstream pump in a series of pumps to wear more quickly than the upstream pump. Thus, the intake pipe 10 of the present invention may be used as an inter-stage pipe between two centrifugal pumps.

Effect of Helical Portion and Pump Inlet Position on Impeller and Volute Wear

[0043] The model was also used to qualitatively predict the effect of the helical portion 16 of the intake pipe 10 on the wear of the impeller 30 and volute of the centrifugal pump 20. The specific wear model used in this study was that of Tabakoff-Grant. The erosion rate is calculated as per the below equations:

E = [ [ 1 + k 2 k 12 sin ( .theta..pi. 2 .theta. 0 ) ] 2 ( V P V 1 ) 2 cos 2 .theta. ( 1 - R T 2 ) + ( V P V 2 sin ( .theta. ) ) 4 ] N .smallcircle. m p ##EQU00001## where : ##EQU00001.2## R T = 1 - V P V 3 sin ( .theta. ) ##EQU00001.3##

[0044] and:

[0045] k.sub.2=1 if .theta..ltoreq.2.theta..sub.0

[0046] k.sub.2=0 if .theta.>2.theta..sub.0

[0047] E=erosion rate (kg/s)

[0048] k.sub.12, k.sub.2=dimensionless constants

[0049] V.sub.1, V.sub.2, V.sub.3=reference velocities (m/s)

[0050] V.sub.P=relative velocity (m/s)

[0051] .theta.=impact angle (radians)

[0052] .theta..sub.0=impact angle of maximum erosion (radians)

[0053] N=number rate of particle impact on position (s.sup.-1)

[0054] m.sub.P=mass of particle (kg).

The specific coefficient values used in the model are outlined in Table 1.

TABLE-US-00001 TABLE 1 Coefficient Value Units k.sub.12 5.85 .times. 10.sup.-1 Unitless V.sub.1 159.11 m/s V.sub.2 194.75 m/s V.sub.3 190.5 m/s .theta..sub.0 25 degrees

[0055] Three different configurations of pump systems were modeled: a "straight pipe", with a pump inlet axially aligned with the impeller axis; "configuration 1" which was an intake pipe with a helical portion, with a pump; and "configuration 2", which was also an intake pipe with a helical portion. In configuration 1 as shown in FIG. 12, the pipe outlet and pump inlet were positioned to introduce the slurry into the pump such that the solid particles would travel through most of the volute before being discharged through the pump outlet. In contrast, in configuration 2 as shown in FIG. 13, the pipe outlet and pump inlet were positioned to introduce the slurry into the pump such that the solid particles would bypass most of the volute before being discharged through the pump outlet. Each configuration was modelled for both a centrifugal pump with a volute that discharged the slurry at the bottom of the volute, and a volute that discharged the slurry at the top of the volute.

[0056] The predicted erosion of the volute and the impeller are summarized in Table 2, below. FIGS. 14A and 14B illustrate the predicted erosion patterns of the volute 20 of a centrifugal pump caused by solid particles of a slurry flowing through a straight pipe and configuration 2 of the intake pipe 10, respectively, both with a bottom discharge volute.

TABLE-US-00002 TABLE 2 Straight Pipe-Top Discharge Total Impeller Erosion 9.71E-04 kg Total Volute Erosion 1.67E-03 kg Straight Pipe-Bottom Discharge Total Impeller Erosion 1.20E-03 kg Total Volute Erosion 1.66E-03 kg Undulating Pipe-Top Discharge-Config 1 Total impeller Erosion 7.85E-04 kg Total Volute Erosion 2.32E-03 kg Undulating Pipe-Bottom Discharge-Config 1 Total Impeller Erosion 6.29E-04 kg Total Volute Erosion 2.49E-03 kg Undulating Pipe-Top Discharge-Config 2 Total Impeller Erosion 8.38E-04 kg Total Volute Erosion 1.22E-03 kg Undulating Pipe-Bottom Discharge-Config 2 Total Impeller Erosion 5.49E-04 kg Total Volute Erosion 1.14E-03 kg Wear Reduction-Config 1 Total Impeller Erosion 19.2% Total Volute Erosion -39.4% Wear Reduction-Config 1 Total Impeller Erosion 47.6% Total Volute Erosion -50.2% Wear Reduction-Config 2 Total Impeller Erosion 13.7% Total Volute Erosion 27.0% Wear Reduction-Config 2 Total Impeller Erosion 54.2% Total Volute Erosion 31.6%

[0057] These results indicate that the intake pipe of the present invention may reduce the erosion of both the volute and impeller of a centrifugal pump, relative to a straight intake pipe. Further, positioning the pipe outlet and pump inlet to introduce the slurry into the pump such that the solid particles would bypass most of the volute may also be advantageous in this regard.

[0058] Without restriction to a theory, it is believed that the reduction of erosion by using the intake pipe 10 of the present invention is attributable to a decrease in the impact velocity of solid particles in the slurry with the leading edge of the impeller 30, as well as the fact that many of the solid particles avoid impact with the leading edge of the impeller 30 due to the circumferential velocity of the solid particles imparted by the intake pipe 10.

[0059] The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to those embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein, but is to be accorded the full scope consistent with the claims, wherein reference to an element in the singular, such as by use of the article "a" or "an" is not intended to mean "one and only one" unless specifically so stated, but rather "one or more". All structural and functional equivalents to the elements of the various embodiments described throughout the disclosure that are known or later come to be known to those of ordinary skill in the art are intended to be encompassed by the elements of the claims. Moreover, nothing disclosed herein is intended to be dedicated to the public regardless of whether such disclosure is explicitly recited in the claim.

* * * * *


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