Apparatus, System and Method for Heat Exchanger End Plate Erosion Resistance

Abstract

A shell-and-tube heat exchanged is described herein which includes abrasion-resistant plates disposed on the inner walls of the end plates and the outer walls of the terminal tubesheets. The abrasion-resistant plates reduce erosion of the end plates and tubesheets, extending the useful life of the heat exchanger. The plates can comprise carbon fiber reinforced polymer. Corresponding systems and methods also are disclosed.

Description

BACKGROUND

[0001] Refrigerant condensers are typically of two design types, air or water cooled. Air cooled condensers occupy a larger installation footprint but have an infinite supply of air to move across the fin coils to induce refrigerant condensation. Water cooled condensers offer a compact installation footprint, which allows for smaller refrigeration or air conditioning systems to be utilized. Water cooled condensers require a supply of water to be pumped through the condenser tubes, where this supply could be a closed circuit that requires cooling or the supply could also be deemed infinite in the case of ocean water. Ocean water is utilized on small to larger vessels to cool the condenser tubes for refrigerant condensation.

[0002] To induce refrigerant condensation energy must be removed from the hot refrigerant gas. The condenser is downstream from the compressor. The compressor increases the gas pressure and temperature of the refrigerant. The condenser must dispense this added energy or latent heat, resulting in refrigerant condensing to a liquid. A shell and tube condenser allows refrigerant gas to travel with the shell side, whereas water passes through the tube side. With the water at a lower temperature than the refrigerant gas heat transfer can occur. This results in refrigerant gas condensing on the outside diameter of the tube, within which water is flowing.

[0003] It would be useful to develop shell and tube condensers having improved wear resistance.SUMMARY OF THE INVENTION

[0004] One embodiment described herein is a heat exchanger comprising a shell portion having a tubular side wall with a first end portion including a first end wall formed from a first end plate, an opposite second end portion including a second end wall formed from a second end plate, and a central portion. A plurality of tubes are disposed in the central portion of the shell. The heat exchanger has a first tube support disposed in the central portion near the first end portion, and a second tube support disposed in the central portion near the second end portion, the tube supports having a plurality of apertures dimensioned to receive the tubes in a fluid-tight arrangement. The heat exchanger also includes first and second abrasion-resistant plates disposed at the first end portion of the shell portion between the first end wall and the first tube support (tubesheet), the first abrasion-resistant plate being mounted adjacent the inner wall of the first end plate and the second abrasion-resistant plate being mounted to the outer wall of the first tube support, the first and second abrasion-resistant plates being configured to reduce or prevent erosion of at least one of the first end plate and the first tube support.

[0005] In some cases the heat exchanger further includes third and fourth abrasion-resistant plates disposed at the second end portion of the shell portion between the second end wall and the second tube support, the third abrasion-resistant plate being mounted on the outer wall of the second tube support and the fourth abrasion-resistant plate being mounted adjacent the inner wall of the second end plate, the third and fourth abrasion-resistant plates being configured to reduce or prevent erosion of at least one of the second end plate and the second tube support.

[0006] Another embodiment is an air conditioning system including a condenser. The condenser comprises a shell portion having a tubular side wall with a first end portion including a first end wall formed from a first end plate, an opposite second end portion including a second end wall formed from a second end plate, and a central portion. A plurality of tubes are disposed in the central portion of the shell portion. The heat exchanger has a first tube support disposed in the central portion near the first end portion, and a second tube support disposed in the central portion near the second end portion, the tube supports having a plurality of apertures dimensioned to receive the tubes in a fluid-tight arrangement. The heat exchange also has first and second abrasion-resistant plates disposed at the first end portion of the shell portion between the first end wall and the first tube support, the first abrasion-resistant plate being mounted adjacent the inner wall of the first end plate and the second abrasion-resistant plate being mounted to the outer wall of the first tube support, the first and second abrasion-resistant plates being configured to reduce or prevent erosion of at least one of the first end plate and the first tube support. In some cases, the abrasion resistant plates comprise carbon fiber or a titanium alloy.

[0007] In some cases, the system includes third and fourth abrasion-resistant plates formed from a reinforced polymer and being disposed at the second end portion of the shell portion between the second end wall and the second tube support, the third abrasion-resistant plate being mounted on the outer wall of the second tube support and the fourth abrasion-resistant plate being mounted adjacent the inner wall of the second end plate, the third and fourth abrasion-resistant plates being configured to reduce or prevent erosion of at least one of the second end plate and the second tube support.

[0008] A further embodiment described herein is a pair of abrasion-resistant plates for a shell and tube hear exchanger configured for receiving water on the tube side and refrigerant on the shell side, each of the abrasion-resistant plates being formed from a carbon fiber reinforced polymer or a titanium alloy and being configured to be disposed on opposite sides of a gasket positioned between a tubesheet and an end plate.BRIEF DESCRIPTION OF THE DRAWINGS

[0009] FIG. 1 shows a side sectional view of a shell and tube heat exchanger according to a first embodiment.

[0010] FIG. 2 shows an enlarged side sectional view of the left end of the heat exchanger shown in FIG. 1 having the connection end plate.

[0011] FIG. 3 illustrates an end view of the end of the heat exchanger shown in FIG. 2 with the connection end plate removed.

[0012] FIG. 4 shows a cross sectional view of one end of the heat exchanger of FIG. 1.

[0013] FIG. 5 shows a perspective sectional view of the left end of the heat exchanger that includes the connection end plate.

[0014] FIG. 6 shows a perspective sectional view of the right end of the heat exchange that includes the blank end plate.

[0015] FIG. 7 is a left end view of the heat exchanger showing a connection end plate and the water inlet and outlet openings.

[0016] FIG. 8 shows the connection end (left end) with the end plate removed.

[0017] FIG. 9 shows the blank end (right end) with the blank end plate removed.

[0018] FIG. 10 shows a refrigeration system in which the heat exchanger of FIG. 1 is used as the condenser.

[0019] FIG. 11 shows the results of experimental wear testing of the carbon fiber plates in accordance with a first embodiment described herein.

[0020] FIG. 12 shows the results of experimental wear testing of the carbon fiber plates and end plates in accordance with the first embodiment.

[0021] FIG. 13 shows the results of experimental wear testing of the carbon fiber plates and end plates.

[0022] FIG. 14 shows the results of experimental wear testing of the carbon fiber plates and end plates.

[0023] FIG. 15 shows the results of experimental wear testing of the carbon fiber plates and end plates.DETAILED DESCRIPTION

[0024] Increasing a fluid flow rate through a shell and tube condenser would allow for increased heat exchange. However, condensers of this design type are susceptible to end plate and tubesheet erosion if the water velocities within the inner tubes are greater than design limits. Typical materials of construction for these devices limit the water velocity, as higher water velocities may induce the material erosion. An example of a solution to this erosion and wear problem, thereby allowing for higher fluid flow rates, is to provide a water-cooled refrigerant condenser of shell and tube construction utilizing abrasion-resistant plates attached to the inner surface of the end plates and tubesheets.

[0025] In embodiments disclosed herein, abrasion-resistant plates are disposed between the tubesheet and end wall in the shell in order to absorb some of the impact of high velocity water that otherwise would jet against the end walls and tubesheets at the tube outlet proximate the water inlet and outlet of the heat exchanger. In some embodiments, the abrasion-resistant plates are formed from a reinforced polymer such as a carbon fiber reinforced polymer, as a favorable characteristic of carbon fiber is its abrasion resistance. Applying an abrasion-resistant plate to the surface with constant interaction to high velocity water will prevent pre-mature failure of the end plates due to erosion. In certain embodiments, the abrasion-resistant plates comprise carbon fiber and / or a titanium alloy.

[0026] Air conditioning condensers configured as shell and tube heat exchangers typically are made with metallic shells formed from carbon steel. The tubes typically are formed from copper and copper alloys and stainless steel. The shell and tube materials are selected based on the requirements for corrosion resistance as well as strength and thermal conductivity.

[0027] A shell and tube heat exchanger configuration is described herein in which a single carbon fiber-reinforced polymeric plate, or a pair of carbon fiber reinforced polymeric plates, are inserted at one or both ends of the tube, inside relative to the end plates. When the carbon fiber plates are used in a shell and tube heat exchanger having a shell outer diameter in the range of about 6 inches to about 13 inches, the carbon fiber plates have a circular cross section comparable to that of the tubesheets and end plates, and a thickness of about 0.25 inches to about 0.50 inches. The carbon fiber plates adjacent to the tubesheets have a plurality of apertures corresponding to, and aligned with, the apertures in the adjacent tubesheets. The carbon fiber plate adjacent to the connection end plate has apertures aligned with the water inlet and outlet lines.

[0028] The carbon fiber plates are fixed in a stationary position in the heat exchanger. In embodiments, the carbon fiber plates are connected to end plates or tubesheets with an adhesive. In the embodiment shown in FIGS. 1-9, the first (leftmost) carbon fiber plate is adhered to the inner wall of the connecting end plate and has apertures corresponding to the water inlet and outlet lines. The second (second to the left) carbon fiber plate is adhered to the left wall of the left tubesheet and has apertures corresponding to the apertures in the left tubesheet. The left terminal end of the tubes is flush with the left side of the second carbon fiber plate. The third (second-to-the-right) carbon fiber plate is adhered to the right wall of the right tubesheet and has apertures corresponding to the apertures in the right tubesheet. The right terminal end of the tubes is flush with the right side of the third carbon fiber plate. The fourth (rightmost) carbon fiber plate is adhered to the left wall of the blank end plate.

[0029] The carbon fibers are combined with a polymeric resin to form a composite. Non-limiting examples of precursors to form the carbon fibers include polyacrylonitrile and rayon. Non-limiting examples of binding polymers to be used to form the composites include thermoset resins, such as an epoxy, or a thermoplastic material, such as a polyester or a vinylester. The epoxy resins are preferred in maintaining the binding of the carbon fibers, where providing a stable matrix to maintain the final shape preferred by the application.

[0030] As mentioned above, as a non-limiting alternative to carbon fiber plate material, the abrasion-resistant plates can be formed from titanium alloys (for example Ti-6Al-4V). Additionally a coating of titanium nitride (TiN) may be applied to the surface to increase abrasion resistance.

[0031] Referring to FIGS. 1-9 in more detail, the first embodiment illustrated herein includes a heat exchanger 10 having a shell 12, a (first) connection end plate 14 shown on the left side of FIG. 1, and a (second) blank end plate 16 shown on the right side of FIG. 1. The connection end plate 14 includes a tube side fluid inlet 22 and a tube side fluid outlet 24 for the tube side fluid. A shell side fluid inlet 18 is disposed on the upper side of the shell on the right side of the shell 12, and a shell side fluid outlet 20 is disposed on the left side of the shell at the lower end of the shell 12. A first tubesheet 26 is disposed insider the heat exchanger near the blank end plate 16, and a second tubesheet 28 is disposed inside the heat exchanger near the connection end plate 14. The heat exchanger is supported by a pair of mounting brackets 27, and has an overpressure valve port 29 on the upper side of the shell 12.

[0032] FIGS. 2-9 illustrate details of the right and left ends of the heat exchanger shown in FIG. 1. In FIG. 3 the blank end plate has been removed. The first tubesheet 26 has an inner surface 30 and an outer surface 32. The second tubesheet 28 has an inner surface 34 and an outer surface 36. The first tubesheet 26 and the second tubesheet 28 have a plurality of tubes 40 connected thereto, extending from the first tubesheet 26 on the left side of the heat exchanger 10 to the second tubesheet 28 on the right side of the heat exchanger 10. The first tubesheet 26 and the second tubesheet 28 support and seal the tubes 40.

[0033] The connection end plate 14 has an internal surface 50 and an external surface 52. The blank end plate 16 has an internal surface 54 and an external surface 56. A first abrasion-resistant plate 60 is disposed on the internal surface 50 of the connection end plate 14, and a second abrasion-resistant plate 62 is disposed on the outer surface 32 of the first tubesheet 26. The first abrasion-resistant plate 60 and the second abrasion-resistant plate 62 are typically maintained in position using an adhesive, such as an epoxy, but other fastening techniques can also be used, including mechanical fastening, vibration welding, etc.

[0034] A first gasket 64 is positioned between the first abrasion-resistant plate 60 and the second abrasion-resistant plate 62. As is shown in FIG. 5, the first gasket 64 contacts an inner surface 65 of the first abrasion-resistant plate 60 and an outer surface 67 of the second abrasion-resistant plate 62. In the illustrated embodiments, the first abrasion-resistant plate 60 and the second abrasion-resistant plate 62 are formed from carbon fiber. The first gasket 64 is held in place by a gasket retaining ring 69.

[0035] A third abrasion-resistant plate 70 is disposed on the outer surface 36 of the second tubesheet 28, and a fourth abrasion-resistant plate 72 is disposed on an internal surface 54 of the blank end plate 16. The third abrasion-resistant plate 70 and the fourth abrasion-resistant plate 72 are typically mounting using an adhesive, such as an epoxy, but other fastening techniques can also be used, including mechanical fastening, vibration welding, etc.

[0036] A second gasket 74 is positioned between the third abrasion-resistant plate 70 and the fourth abrasion-resistant plate 72. As is shown in FIG. 6, the second gasket 74 contacts an outer surface 75 on the third abrasion-resistant plate 70 and contacts an inner surface 77 on the fourth abrasion-resistant plate 72. The tubes 40 are joined to the tubesheets 26, 28 and the abrasion-resistant plates 62, 70 with an internal expansion tool. In the illustrated embodiments, the third abrasion-resistant plate 70 and the fourth abrasion-resistant plate 72 are formed from carbon fiber. The second gasket 74 is held in place by a gasket retaining ring 71.

[0037] In some cases, the thickness of the abrasion-resistant plates is from 20%-40% of the thickness of the tubesheet. Tubesheet thickness is directly dependent on the internal pressure within the vessel and vessel diameter. Tubesheet thickness may need to indirectly consider temperature variations of the fluids on each side of the tubes to account for expansion and contraction of the tubesheets. In some non-limiting cases, the tubesheets have a thickness in the range of about ½ in. to about 1 in., and the abrasion-resistant plates have a thickness in the range of about ¼ in. to about ⅝ in., or about ⅜ in. to about ½ in. In the illustrated embodiment, all four abrasion-resistant plates have the same thickness.

[0038] A multi-component epoxy resin, or another suitable adhesive, can be used to bind the abrasion-resistant plates to the tubesheets and end plates during heat exchanger manufacturing. Typical heat exchanger manufacturing requires the tubes to be internally expanded into the tubesheet holes to form a pressure tight seal. Application of the carbon fiber plates to the tubesheet with the epoxy resin will result in the tubes being expanded into the carbon fiber plates also.Heat Transfer Calculations Using Water As the Circulating Fluid

[0039] The quantity of heat transfer (q) to the water is as follows:q=mf*Cp*(To-Ti)[Eq. 1]where:

[0041] q=heat rate transferred to water (BTU / hr)

[0042] mf=water mass flow rate (lb / hr)

[0043] Cp=water specific heat (BTU / lb*F)

[0044] To=water temperature leaving condenser

[0045] Ti=water temperature entering condenser

[0046] Water inlet temperature could be reduced to increase heat transfer, however this isn't always practical. Increasing the water mass flow (mf) rate will result in To approaching Ti. This will increase the logarithmic mean temperature difference (LMTD). Increasing the LMTD will increase heat transfer per Eq.3.LMTD=(GTD-LTD) / (ln⁡(GTD / LTD))[Eq. 2]where:

[0048] CST=refrigerant condensing temperatureGTD=CST-Ti,greatest⁢ temperature⁢ difference[Eq. 2.1]LTD=CST—To, least temperature difference

[0050] [Eq.2.2]

[0051] Increasing the LMTD results from decreasing the ‘To’ component of Eq.2.2, which results from increasing the mass flow rate of Eq.1.

[0052] Overall heat transfer (Q):Q=LMTD*As*Uo[Eq. 3]where:

[0054] As=heat transfer surface area

[0055] Uo=overall heat transfer coefficient

[0056] Overall heat transfer coefficient (Uo):Uo=1 / ((1 / hi+ffi)+Wr+1 / ho+ffo)[Eq. 4]where:

[0058] hi=tube internal heat transfer coefficient

[0059] ffi=tube internal fouling factor

[0060] Wr=tube wall resistance (wall thickness / material conductivity)

[0061] ho=tube external heat transfer coefficient

[0062] ffo=tube external fouling factor

[0063] Increasing the mass flow ‘mf’ increases the ‘hi’ component as shown in equation 5 and sub-components.

[0064] Inside heat transfer coefficient with turbulent flow (hi):hi=0.027*Re^0.8*Pr^0.333*k / di[Eq. 5]where:

[0066] Re=Reynolds numberRe=((mf / Ai)*di) / (u*Nt / Np)[Eq. 5.1]where:

[0068] mf=water mass flow (same component Eq.1)

[0069] Ai=tube inside surface area

[0070] di=tube inside diameter

[0071] u=wáter viscosity

[0072] Nt=number of tubes

[0073] Np=number of tube passes

[0074] Pr=Prandtl number

[0075] k=thermal conductivity of tube

[0076] Di=Internal Diameter of Tube

[0077] Proper tube material selection and protection of surfaces impacted by the high water flow, from the addition of carbon fiber plates, can allow for a heat exchanger to exchange heat more efficiently assuming no change in surface area.

[0078] FIG. 10 shows an example of an air conditioning system in which the disclosed embodiments can be used, for example, as a condenser heat exchanger. The system is generally designated as 108. The system 108 includes a compressor 122 that includes a refrigerant inlet 114, and a refrigerant outlet 116. The condenser 120 is responsible for condensing high pressure, hot discharge gas from the compressor 122. The refrigerant is then expanded to a lower pressure, lower temperature liquid in the expansion device 124. The refrigerant is then evaporated in the evaporator 126 producing a net cooling effect for the heat transfer medium passing through the evaporator coils. Air is distributed by an air handling system.Example

[0079] FIGS. 11-15 and the accompanying text describe the results of experimental testing for a heat exchanger with the abrasion-resistant plates as shown in FIGS. 1-9.

[0080] A two-pass heat exchanger having a length of 24 in. and a diameter of 6 in. was formed using the shell, end plates, abrasion-resistant plates, tubesheets, and tubes shown in FIGS. 1-9. The heat exchanger shell was made from carbon steel and had a diameter of about 6 in. and a thickness of about 3 / 16 in. The end plates were made from cupronickel alloy. The connection end plate had a thickness of about ¾ in. The blank end plate had a thickness of about ½ in. The abrasion-resistant plates each had a thickness of about ¼ in. The abrasion-resistant plates were formed from carbon fiber. The tubesheets had a thickness of ¾ in. and were made from cupronickel alloy. The tubes had an outer diameter of ¾ in. and were made from titanium. In an open loop test system the water flow rate was 29-30 GPM (12-13 ft / s tube velocity) using a water pump. One tablespoon of sand was added every 7 days to simulate abrasive materials that could be suspended within seawater if near a shallow port, given these condensers are installed on marine boats., The amount of abrasive material added is expected to be exaggerated to accelerate the test timeline. The heat exchanger was operated for 81 days (1944 hours).

[0081] FIG. 11 shows the first pass at 0 hours, at which time there was no notable wear. FIG. 12 shows the first pass at 1944 hours (81 days), at which point there was evidence of wear. FIG. 13 shows the blank end plate at 0 hours, which can be compared with FIG. 14, showing the blank end plate at 1944 hours (81 days). The wear on the carbon fiber plate in FIGS. 14 and 220 and 224 is evident more on the exit of the bottom tube, where the depth of the worn portion is about 30% of the thickness of the plate. FIG. 15 shows the most wear of all impingement points at 226 and 228. This Figure shows the carbon fiber plate at the water inlet at 1944 hours (81 days). The greatest amount of wear occurred at the water inlet (see FIG. 15). It is estimated the wear on the cupronickel alloy would be greater than twice the depth as shown on the carbon fiber plates in FIG. 14 if no carbon fiber plates had been used. The ultimate tensile strength (UTS) of carbon fiber is 2500-3500 MPa, compared to cupronickel alloy C70600 is 275 MPa. UTS is a common physical property of materials for comparing toughness and strength.

[0082] A number of alternatives, modifications, variations, or improvements therein may be subsequently made by those skilled in the art, which are also intended to be encompassed by the following claims.

Claims

1. A heat exchanger comprising:a shell portion having a tubular side wall with a first end portion including a first end wall formed from a first end plate, an opposite second end portion including a second end wall formed from a second end plate, and a central portion,a plurality of tubes disposed in the central portion of the shell portion,a first tube support disposed in the central portion near the first end portion,a second tube support disposed in the central portion near the second end portion, the tube supports having a plurality of apertures dimensioned to receive the tubes in a fluid-tight arrangement, andfirst and second abrasion-resistant plates disposed at the first end portion of the shell portion between the first end wall and the first tube support, the first abrasion-resistant plate being mounted adjacent the inner wall of the first end plate and the second abrasion-resistant plate being mounted to the outer wall of the first tube support, the first and second abrasion-resistant plates being configured to reduce or prevent erosion of at least one of the first end plate and the first tube support.

2. The heat exchanger of claim 1, further including third and fourth abrasion-resistant plates disposed at the second end portion of the shell portion between the second end wall and the second tube support, the third abrasion-resistant plate being mounted on the outer wall of the second tube support and the fourth abrasion-resistant plate being mounted adjacent the inner wall of the second end plate, the third and fourth abrasion-resistant plates being configured to reduce or prevent erosion of at least one of the second end plate and the second tube support.

3. The heat exchanger of claim 1, wherein the abrasion-resistant plates are formed from at least one of a reinforced polymer and a titanium alloy.

4. The heat exchanger of claim 3, wherein the reinforced polymer is a carbon fiber reinforced polymer.

5. The heat exchanger of claim 3, wherein the reinforced polymer comprises a thermoset material.

6. The heat exchanger of claim 1, wherein the reinforced polymer comprises a thermoplastic material.

7. The heat exchanger of claim 1, wherein the first abrasion-resistant plate is adhered to the inner surface of the first end wall and the second abrasion-resistant plate is adhered to the first tube support proximate a gasket.

8. The heat exchanger of claim 2, wherein the first abrasion-resistant plate is adhered to the inner surface of the first end wall and the second abrasion-resistant plate is adhered to the first tube support proximate a gasket.

9. The heat exchanger of claim 8, wherein the third carbon fiber plate is adhered to the second tube support proximate a gasket, and the fourth carbon fiber plate is adhered to the inner surface of the second end wall.

10. The heat exchanger of claim 2, wherein the heat exchanger is a 4-pass heat exchanger.

11. The heat exchanger of claim 1, wherein the heat exchanger is a 2-pass heat exchanger.

12. The heat exchanger of claim 1, wherein the heat exchanger is a single pass heat exchanger.

13. The heat exchanger of claim 1, wherein the heat exchanger is a condenser.

14. The heat exchanger of claim 1, wherein the heat exchanger is a condenser for an air conditioning system.

15. An air conditioning system including a condenser, the condenser comprising:a shell portion having a tubular side wall with a first end portion including a first end wall formed from a first end plate, an opposite second end portion including a second end wall formed from a second end plate, and a central portion,a plurality of tubes disposed in the central portion of the shell portion,a first tube support disposed in the central portion near the first end portion,a second tube support disposed in the central portion near the second end portion, the tube supports having a plurality of apertures dimensioned to receive the tubes in a fluid-tight arrangement, andfirst and second abrasion-resistant plates formed from a reinforced polymer and being disposed at the first end portion of the shell portion between the first end wall and the first tube support, the first abrasion-resistant plate being mounted adjacent the inner wall of the first end plate and the second abrasion-resistant plate being mounted to the outer wall of the first tube support, the first and second abrasion-resistant plates being configured to reduce or prevent erosion of at least one of the first end plate and the first tube support.

16. The system of claim 15, further including third and fourth abrasion-resistant plates formed from a reinforced polymer and being disposed at the second end portion of the shell portion between the second end wall and the second tube support, the third abrasion-resistant plate being mounted on the outer wall of the second tube support and the fourth abrasion-resistant plate being mounted adjacent the inner wall of the second end plate, the third and fourth abrasion-resistant plates being configured to reduce or prevent erosion of at least one of the second end plate and the second tube support.

17. The heat exchanger of claim 15, wherein the first carbon fiber plate is adhered to the inner surface of the first end wall and the second carbon fiber plate is adhered to the first tube support proximate a gasket.

18. The heat exchanger of claim 16, wherein the first carbon fiber plate is adhered to the inner surface of the first end wall and the second carbon fiber plate is adhered to the first tube support proximate a gasket.

19. The heat exchanger of claim 16, wherein the third carbon fiber plate is adhered to the second tube support proximate a gasket, and the fourth carbon fiber plate is adhered to the inner surface of the second end wall.

20. A method of transferring heat in an air conditioning system comprising using the heat exchanger of claim 1 as a condenser.

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