TWI745994B - Cleaning system, heat exchanging system and method for cleaning heat exchanger - Google Patents

Abstract

A cleaning system includes a ball tank, a first pipe, a first sensor, a second pipe and a second sensor. The ball tank is used for accommodating a plurality of washing balls. The first pipe is communicated with the ball tank, and is used for the washing balls to leave the ball tank. The first sensor is disposed on the first pipe, and is used for counting the number of the washing balls passing by. The second pipe is communicated with the ball tank, and is used for the washing balls to come back the ball tank. The second sensor is disposed on the second pipe, and is used for counting the number of the washing balls passing by.

Description

Cleaning system, heat exchanger assembly and heat exchanger cleaning method

The present invention relates to cleaning systems, and more specifically, to cleaning systems and methods for heat exchangers.

The purpose of the water-cooled heat exchanger suitable for the air-conditioning system of the production line is to discharge the heat of the cooling water to lower the temperature of the cooling water and allow the air-conditioning system to continue to operate. However, the cooling water in the tube body of the heat exchanger will be concentrated when it evaporates, and it is easy to accumulate impurities on the inner wall of the tube body, which may cause blockage or corrosion of the tube body. When the tube body is blocked, the heat exchanger must increase more power to promote the heat exchange of the cooling water through the tube body. This not only increases energy consumption, but the shutdown and cleaning will also reduce the productivity of the production line and shorten the main engine of the heat exchanger. And the life of the tube body.

In one embodiment, a cleaning system includes a ball groove, a first tube, a first sensor, a second tube, and a second sensor. The ball slot is used to store a plurality of cleaning balls. The first tube is connected to the ball groove for the cleaning balls to leave the ball groove. The first sensor is located in the first tube body and is used to count the number of cleaning balls passing through. The second tube is connected to the ball groove for the cleaning balls to return to the ball groove. The second sensor is located in the second tube body, and is used to count the number of cleaning balls passing through.

In one embodiment, a heat exchanger assembly includes at least one heat exchanger and a cleaning system. The at least one heat exchanger has a plurality of tube bodies. The cleaning system includes a ball groove, a ball groove screen, a cleaning ball supply path and a cleaning ball recovery path. The ball slot is used to store a plurality of cleaning balls. The ball groove screen is located in the ball groove and has a plurality of through holes, wherein the inner diameter of the through hole of the ball groove screen is smaller than the preset ball diameter of the cleaning balls. The cleaning ball providing path communicates with the ball groove and a first end of the heat exchanger for providing the cleaning balls to the tube body of the heat exchanger. The cleaning ball recovery path communicates with the ball groove and a second end of the heat exchanger for the cleaning balls to return to the ball groove.

In one embodiment, a method for cleaning a heat exchanger includes: (a) providing a ball groove for storing a plurality of cleaning balls; (b) injecting clean water into the ball groove so that all the cleaning balls leave the ball groove ; (C) Count the number of the cleaning balls leaving the ball groove; (d) Inject the cleaning balls into the tube body of a heat exchanger under pressure to clean the inner wall of the tube body of the heat exchanger ; (E) Return a part of the waste water after cleaning and all the cleaning balls to the ball groove; and (f) Count the number of the cleaning balls returned to the ball groove.

Common reference numbers are used throughout the drawings and embodiments to indicate the same or similar components. It will be easier to understand the embodiments of the present invention from the following detailed description in conjunction with the accompanying drawings.

The following disclosure provides many different embodiments or examples for implementing different features of the provided subject matter. Specific examples of components and configurations are described below to clarify specific aspects of the invention. Of course, these components, values, operations, materials, and configurations are only examples and are not intended to be limiting. For example, in the description provided herein, the formation of the first feature on or on the second feature may include an embodiment in which the first feature and the second feature are formed or arranged in direct contact, and may also include additional features An embodiment may be formed or disposed between the first feature and the second feature so that the first feature and the second feature may not directly contact. In addition, the present invention may repeat reference numbers and/or letters in various examples provided herein. This repetition is for the purpose of simplification and clarity, and does not in itself indicate the relationship between the various embodiments and/or configurations discussed.

In a comparative embodiment, an automatic cleaning system is used to clean the tube body of the heat exchanger. The automatic cleaning system uses an air compressor to prepare a plurality of cleaning balls with a diameter larger than the inner diameter of the tube. The ball groove is pushed into the tube body of the heat exchanger, and the friction between the sphere and the tube wall is used to achieve the purpose of cleaning the fouling on the inner wall of the tube. However, in this comparative embodiment, an automatic cleaning system is used with a heat exchanger, and a large number of three-way valves are used as the choice of cooling water direction, which not only consumes too much hardware cost, but also Moreover, the damage rate of the three-way valve is extremely high; in addition, when the heat exchanger is cleaned frequently every day, it is necessary to spend extra manpower to repair and maintain the three-way valve. Moreover, the cleaning ball may remain in the tube and cause damage to the heat exchanger.

Fig. 1 shows a schematic diagram of a heat exchanger assembly 7 according to an embodiment of the present invention. The heat exchanger assembly 7 of the present invention includes at least one heat exchanger (including, for example, a first heat exchanger 74, a second heat exchanger 75, a third heat exchanger 76, a fourth heat exchanger 77, and a fifth heat exchanger器78), a cleaning system 1, a clean water supply path 5, at least one heat exchanger water inlet pump (including for example: the first heat exchanger water inlet pump 84, the second heat exchanger water inlet pump 85, and the third heat exchange Water inlet pump 86, fourth heat exchanger inlet pump 87 and fifth heat exchanger inlet pump 88), a ball groove pump system 9, a waste water recovery path 6, a front solenoid valve (including, for example, the first A front solenoid valve 34a, a second front solenoid valve 35a, a third front solenoid valve 36a, a fourth front solenoid valve 37a, and a fifth front solenoid valve 38a), a rear solenoid valve (including, for example, the first rear solenoid valve 44a, The second rear solenoid valve 45a, the third rear solenoid valve 46a, the fourth rear solenoid valve 47a, and the fifth rear solenoid valve 48a), at least one concentration tank (including, for example, the first concentration tank 24, the second concentration tank 25, and the Three concentrated troughs 26, fourth concentrated troughs 27 and fifth concentrated troughs 28) and a control module 17.

In this embodiment, the at least one heat exchanger includes a plurality of heat exchangers, for example: the first heat exchanger 74, the second heat exchanger 75, the third heat exchanger 76, and the fourth heat exchange器77 and the fifth heat exchanger 78. The heat exchangers are connected to the cleaning system 1 in parallel. However, in other embodiments, the number of heat exchangers may be more than five or less than five. The first heat exchanger 74 has a plurality of tubes 741, a first end 743, and a second end 744 opposite to the first end. The pipe bodies 741 can allow cooling water to flow. The second heat exchanger 75 has a plurality of tube bodies 751. The third heat exchanger 76 has a plurality of tube bodies 761. The fourth heat exchanger 77 has a plurality of tube bodies 771. The fifth heat exchanger 78 has a plurality of tube bodies 781.

The cleaning system 1 includes a ball groove 12, a ball groove screen 13, a water injection port 121, a water outlet 122, a supplementary inlet 123, a first pipe body 32, a first sensor 16, and a second pipe body 42 and a second sensor 18. The ball groove 12 is used to store a plurality of cleaning balls 14. The cleaning balls 14 have a predetermined ball diameter, for example, about 2 cm. In the present invention, the "ball diameter" is defined as the maximum outer diameter of the sphere. The cleaning balls 14 are elastic spheres, and the preset ball diameter of the cleaning balls 14 is greater than or equal to the inner diameter of the tube 741 of the heat exchanger 74. Therefore, the cleaning balls 14 pass through the The tube body (for example: tube body 741) of the heat exchanger (for example: the first heat exchanger 74) can be squeezed and slightly deformed. Furthermore, the ball groove 12 has a transparent upper cover 126 through which the operator can observe the condition of the cleaning balls 14 in the ball groove 12 through the transparent upper cover 126. For example, when the cleaning balls 14 are obviously damaged, the operator can The transparent upper cover 126 is opened and replaced immediately. In addition, the bottom of the ball groove 12 has a cone-shaped accommodating space 124, which is a large space at the top and a small space at the bottom. The cone-shaped accommodating space 124 has a discharge opening 125 at the bottom.

The ball groove screen 13 is located in the ball groove 12, and is substantially one piece with a plurality of through holes 131. The inner diameter of the through hole 131 of the ball groove screen 13 is smaller than the preset ball diameter of the cleaning balls 14. For example, the inner diameter of the through hole 131 of the ball groove screen 13 may be 1.5 cm. Therefore, when the cleaning balls 14 are worn out after the cleaning process and the ball diameter is reduced, they are defined as bad cleaning balls 19 (For example: the diameter of the bad cleaning ball 19 is less than or equal to 1.5 cm), and the bad cleaning balls 19 will pass through the ball because the ball diameter is less than or equal to the inner diameter of the through hole 131 of the ball groove screen 13 The through hole 131 of the ball groove screen 13 falls down and is accommodated in the bottom of the ball groove 12 (ie, the cone-shaped accommodation space 124). In addition, the outer circumference of the ball groove screen 13 is completely connected to the inner side wall of the ball groove 12 to prevent the cleaning balls 14 from moving from the outer circumference of the ball groove screen 13 to the inner side wall of the ball groove 12 The gap therebetween falls to the cone-shaped accommodating space 124.

The water injection port 121 is connected to the ball groove 12 for injecting clean water into the ball groove 12. The water outlet 122 is connected to the ball tank 12 for draining the waste water after cleaning to the outside of the ball tank 12. The supplementary inlet 123 is connected to the ball groove 12 to provide a plurality of supplementary cleaning balls 15 into the ball groove 12. These supplementary cleaning balls 15 are good cleaning balls.

The first tube 32 communicates with the ball groove 12 for the cleaning balls 14 to leave the ball groove 12. The first sensor 16 is located on the first tube body 32 for counting the number of cleaning balls 14 passing through. The second tube body 42 is connected to the ball groove 12 for the cleaning balls 14 to return to the ball groove 12. The second sensor 18 is located on the second tube 42 and is used to count the number of cleaning balls 14 passing through. In one embodiment, the first sensor 16 and the second sensor 18 are both a grating or a photointerrupter, and the grating or the photointerrupter provides only one cleaning ball 14 to pass at the same time. The number of cleaning balls 14 passing through can be accurately calculated. The control module 17 (including, for example, a Programmable Logic Controller (PLC), a computing unit, and a memory unit) is electrically connected to the first sensor 16 and the second sensor 18 for recording and/ Or compare the calculation results of the first sensor 16 and the second sensor 18. That is, the calculation results of the first sensor 16 and the second sensor 18 are transmitted to the control module 17.

The cleaning ball providing path 3 communicates with the ball groove 12 and the first end (eg, the first end 743) of the heat exchanger (eg, the first heat exchanger 74) to provide the cleaning balls 14 To the tube body (for example: the tube body 741) of the heat exchanger (for example: the first heat exchanger 74). In one embodiment, the cleaning ball supply path 3 includes the first tube body 32, a ball distribution pipe 33, and at least one heat exchanger inlet tube (including, for example, the first heat exchanger inlet tube 34, the second The heat exchanger inlet tube 35, the third heat exchanger inlet tube 36, the fourth heat exchanger inlet tube 37, and the fifth heat exchanger inlet tube 38). The first tube body 32 is adjacent to and connected to the ball groove 12 for the cleaning balls 14 to leave the ball groove 12. The first pipe body 32 is connected to the ball distribution pipe 33. As shown in FIG. 1, the first heat exchanger inlet tube 34 is adjacent to the first heat exchanger 74 and communicates with the first tube body 32, the sphere distribution tube 33, and the first heat exchanger 74. One end 743 is used to provide the cleaning balls 14 to the tube body 741 of the first heat exchanger 74. The second heat exchanger inlet tube 35 is adjacent to the second heat exchanger 75 and communicates with the first tube body 32, the sphere distribution tube 33, and a first end of the second heat exchanger 74 to provide The cleaning balls 14 reach the tube body 751 of the second heat exchanger 75. The third heat exchanger inlet tube 36 is adjacent to the third heat exchanger 76 and communicates with the first tube body 32, the sphere distribution tube 33, and a first end of the third heat exchanger 76 for providing The cleaning balls 14 to the tube 761 of the third heat exchanger 76. The fourth heat exchanger inlet tube 37 is adjacent to the fourth heat exchanger 77 and communicates with the first tube body 32, the sphere distribution tube 33, and a first end of the fourth heat exchanger 77 to provide The cleaning balls 14 to the tube body 771 of the fourth heat exchanger 77. The fifth heat exchanger inlet tube 38 is adjacent to the fifth heat exchanger 78 and communicates with the first tube body 32, the sphere distribution tube 33, and a first end of the fifth heat exchanger 78 to provide The cleaning balls 14 to the tube 781 of the fifth heat exchanger 78.

The front solenoid valves (including, for example, the first front solenoid valve 34a, the second front solenoid valve 35a, the third front solenoid valve 36a, the fourth front solenoid valve 37a, and the fifth front solenoid valve 38a) are respectively located in the heat Exchanger ball inlet tube (including for example: the first heat exchanger ball inlet tube 34, the second heat exchanger ball inlet tube 35, the third heat exchanger ball inlet tube 36, the fourth heat exchanger ball inlet tube 37 and the second heat exchanger ball inlet tube Five heat exchanger inlet tube 38), which is electrically connected to the control module 17, to control the flow of the liquid in the heat exchanger inlet tube 34, 35, 36, 37, 38, and then Control the movement of the cleaning balls 14 in the ball inlet tubes 34, 35, 36, 37, and 38 of the heat exchangers.

The cleaning ball recovery path 4 communicates with the ball groove 12 and the second end (eg, the second end 744) of the heat exchanger (eg, the first heat exchanger 74) for the cleaning balls 14 Return to the ball groove 12. In one embodiment, the cleaning ball recovery path 4 includes the second tube 42, a spherical concentrating tube 43, and at least one heat exchanger outlet tube (including, for example, the first heat exchanger outlet tube 44, the second The heat exchanger outlet tube 45, the third heat exchanger outlet tube 46, the fourth heat exchanger outlet tube 47, and the fifth heat exchanger outlet tube 48).

As shown in FIG. 1, the first heat exchanger outlet tube 44 is adjacent to and communicates with the second end 744 of the first heat exchanger 74 and the spherical collecting tube 43 for the cleaning balls 14 to leave the first heat exchanger. A heat exchanger 74 to the spherical concentrating pipe 43. The second heat exchanger outlet ball tube 45 is adjacent to and communicates with a second end of the second heat exchanger 75 and the ball collecting tube 43 for the cleaning balls 14 to leave the second heat exchanger 75 to the Sphere centralized tube 43. The third heat exchanger outlet ball pipe 46 is adjacent to and communicates with a second end of the third heat exchanger 76 and the ball collecting pipe 43 for the cleaning balls 14 to leave the third heat exchanger 76 to the Sphere centralized tube 43. The fourth heat exchanger outlet ball tube 47 is adjacent to and communicates with a second end of the fourth heat exchanger 77 and the ball collecting tube 43 for the cleaning balls 14 to leave the fourth heat exchanger 77 to the Sphere centralized tube 43. The fifth heat exchanger outlet tube 38 is adjacent to and communicates with a second end of the fifth heat exchanger 78 and the spherical tube 43 for the cleaning balls 14 to leave the fifth heat exchanger 78 to the Sphere centralized tube 43. The second tube body 42 is adjacent to the ball groove 12, and the second tube body 42 communicates with the ball groove 12, the ball collecting tube 43 and the heat exchangers 74, 75, 76, 77, 78 for the The cleaning ball 14 returns to the ball groove 12.

The rear solenoid valves (including, for example, the first rear solenoid valve 44a, the second rear solenoid valve 45a, the third rear solenoid valve 46a, the fourth rear solenoid valve 47a, and the fifth rear solenoid valve 48a) are respectively located in the heat The heat exchanger outlet tube (including, for example, the first heat exchanger outlet tube 44, the second heat exchanger outlet tube 45, the third heat exchanger outlet tube 46, the fourth heat exchanger outlet tube 47, and the second Five heat exchanger outlet tubes 48), which are electrically connected to the control module 17, to control the flow of liquid in the heat exchanger outlet tubes 44, 45, 46, 47, 48, and then Control the movement of the cleaning balls 14 in the outlet tubes 44, 45, 46, 47, and 48 of the heat exchangers.

The concentrated troughs (including, for example, the first concentrated trough 24, the second concentrated trough 25, the third concentrated trough 26, the fourth concentrated trough 27 and the fifth concentrated trough 28) are respectively located in the heat exchanger outlet tubes 44 One end of ,45,46,47,48 is used to temporarily concentrate the cleaning balls 14.

The clear water supply path 5 is connected to the ball groove 12 to provide clear water into the ball groove 12. As shown in FIG. 1, the clear water supply path 5 is connected to the first end (for example: the first end 743) of the heat exchanger (for example: the first heat exchanger 74). In one embodiment, the clean water supply path 5 includes an outlet pipe 52, at least one heat exchanger inlet pipe (including, for example, a first heat exchanger inlet pipe 54, a second heat exchanger inlet pipe 55, and a second heat exchanger inlet pipe. Three heat exchanger water inlet pipe 56, a fourth heat exchanger water inlet pipe 57 and a fifth heat exchanger water inlet pipe 58) and a ball groove water inlet path (including for example: the first water inlet pipe body 53 and the second water inlet pipe body 51). The outlet pipe 52 is used to provide clean water (or clean water). In one embodiment, the first heat exchanger inlet pipe 54 communicates with the outlet pipe 52 and the first end 743 of the first heat exchanger 74 for injecting clean water into the first heat exchanger 74, and One end of the first heat exchanger inlet tube 34 is connected to the first heat exchanger inlet tube 54. The second heat exchanger inlet pipe 55 communicates with the outlet pipe 52 and the first end of the second heat exchanger 75 for injecting clean water into the second heat exchanger 75, and the second heat exchanger enters One end of the ball tube 35 is connected to the water inlet tube 55 of the second heat exchanger. The third heat exchanger inlet pipe 56 communicates with the outlet pipe 52 and the first end of the third heat exchanger 76 for injecting clean water into the third heat exchanger 76, and the third heat exchanger enters One end of the ball tube 36 is connected to the water inlet pipe 56 of the third heat exchanger. The fourth heat exchanger inlet pipe 57 communicates with the outlet pipe 52 and the first end of the fourth heat exchanger 77 for injecting clean water into the fourth heat exchanger 77, and the fourth heat exchanger enters One end of the ball tube 37 is connected to the fourth heat exchanger inlet pipe 57. The fifth heat exchanger inlet pipe 58 communicates with the outlet pipe 52 and the first end of the fifth heat exchanger 78 for injecting clean water into the fifth heat exchanger 78, and the fifth heat exchanger enters One end of the ball tube 38 is connected to the water inlet tube 58 of the fifth heat exchanger.

The first heat exchanger water inlet pump 84 is located in the first heat exchanger water inlet pipe 54 for pressurizing the liquid in the first heat exchanger water inlet pipe 54. The second heat exchanger water inlet pump 85 is located in the second heat exchanger water inlet pipe 55 for pressurizing the liquid in the second heat exchanger water inlet pipe 55. The third heat exchanger water inlet pump 86 is located in the third heat exchanger water inlet pipe 56 for pressurizing the liquid in the third heat exchanger water inlet pipe 56. The fourth heat exchanger water inlet pump 87 is located in the fourth heat exchanger water inlet pipe 57 for pressurizing the liquid in the fourth heat exchanger water inlet pipe 57. The fifth heat exchanger water inlet pump 88 is located in the fifth heat exchanger water inlet pipe 58 for pressurizing the liquid in the fifth heat exchanger water inlet pipe 58.

The ball groove pump system 9 includes a first pump 80, a second pump 81, a first pump tube 82, a second pump tube 83, a first connecting tube 90, and a second connecting tube. Tube body 91. The first connecting tube body 90 communicates with the first pump tube body 82 and the second pump tube body 83. The second connecting tube 91 also communicates with the first pump tube 82 and the second pump tube 83. The first pump 80 is located on the first connecting pipe body 90, and the second pump 81 is located on the second connecting pipe body 91. In one embodiment, one of the first pump 80 and the second pump 81 is a use pump, and the other is a standby pump. In one embodiment, the ball groove pump system 9 communicates with the ball groove water inlet path (including, for example, the first water inlet pipe body 53 and the second water inlet pipe body 51) for the ball groove water inlet path (including, for example: The liquid in the first water inlet pipe body 53 and the second water inlet pipe body 51) is pressurized.

The ball groove water inlet path (including, for example, the first water inlet pipe body 53 and the second water inlet pipe body 51) connects the water outlet pipe 52 and the water injection port 121 of the ball groove 12 for injecting clean water into the ball groove 12. As shown in FIG. 1, the first water inlet pipe body 53 communicates with the water outlet pipe 52 and the first pump pipe body 82, and the second water inlet pipe body 51 communicates with the second pump pipe body 83 and the water injection port 121. . In addition, a first water inlet solenoid valve 53a is located on the first water inlet pipe body 53, which is electrically connected to the control module 17 and used to control the flow of liquid in the first water inlet pipe body 53. Furthermore, a second water inlet solenoid valve 51a is located on the second water inlet pipe body 51, which is electrically connected to the control module 17 and used to control the flow of liquid in the second water inlet pipe body 51.

The waste water recovery path 6 is connected to the second end (e.g., the second end 744) of the heat exchanger (e.g., the first heat exchanger 74) for draining the waste water after cleaning to an external water tank 70. In an embodiment, the waste water recovery path 6 is connected to the ball groove 12. In one embodiment, the waste water recovery path 6 includes a waste water recovery pipe 62, at least one heat exchanger outlet pipe (including, for example, a first heat exchanger outlet pipe 64, a second heat exchanger outlet pipe 65, and The third heat exchanger outlet pipe 66, a fourth heat exchanger outlet pipe 67 and a fifth heat exchanger outlet pipe 68) and a spherical groove water outlet path (including for example: the first outlet pipe body 63 and the second outlet pipe Body 61). The waste water recovery pipe 62 is used to drain the waste water after cleaning to the external water tank 70. In one embodiment, the first heat exchanger outlet pipe 64 communicates with the waste water recovery pipe 62 and the second end 744 of the first heat exchanger 74 for draining the waste water leaving the first heat exchanger 74 To the waste water recovery pipe 62, and one end of the first heat exchanger outlet tube 44 is connected to the first heat exchanger outlet pipe 64. The second heat exchanger outlet pipe 65 communicates with the waste water recovery pipe 62 and the second end of the second heat exchanger 75 for draining the waste water leaving the second heat exchanger 75 to the waste water recovery pipe 62, In addition, one end of the outlet tube 45 of the second heat exchanger is connected to the outlet tube 65 of the second heat exchanger. The third heat exchanger outlet pipe 66 communicates with the waste water recovery pipe 62 and the second end of the third heat exchanger 76 for draining the waste water leaving the third heat exchanger 76 to the waste water recovery pipe 62, Moreover, one end of the third heat exchanger outlet tube 46 is connected to the third heat exchanger outlet tube 66. The fourth heat exchanger outlet pipe 67 communicates with the waste water recovery pipe 62 and the second end of the fourth heat exchanger 77 for draining the waste water leaving the fourth heat exchanger 77 to the waste water recovery pipe 62 , And one end of the outlet tube 47 of the fourth heat exchanger is connected to the outlet tube 67 of the fourth heat exchanger. The fifth heat exchanger outlet pipe 68 communicates with the waste water recovery pipe 62 and the second end of the fifth heat exchanger 78 for draining the waste water leaving the fifth heat exchanger 78 to the waste water recovery pipe 62, Moreover, one end of the outlet tube 48 of the fifth heat exchanger is connected to the outlet tube 68 of the fifth heat exchanger.

In one embodiment, the ball groove pump system 9 also communicates with the ball groove water outlet path (including, for example, the first water outlet pipe body 63 and the second water outlet pipe body 61) for the ball groove water outlet path (including, for example, : The liquid in the first outlet pipe body 63 and the second outlet pipe body 61) is pressurized. The water outlet path of the ball groove (including, for example, the first water outlet pipe body 63 and the second water outlet pipe body 61) connects the waste water recovery pipe 62 and the water outlet 122 of the ball groove 12 for the waste water in the ball groove 12 Discharge to the waste water recovery pipe 62. As shown in FIG. 1, the first water outlet pipe body 63 communicates with the waste water recovery pipe 62 and the second pump pipe body 83, and the second water outlet pipe body 61 communicates with the first pump pipe body 82 and the water outlet. 122. In addition, a first water outlet solenoid valve 63a is located in the first water outlet pipe body 63, which is electrically connected to the control module 17 and used to control the flow of liquid in the first water outlet pipe body 63. Furthermore, a second water outlet solenoid valve 61a is located in the second water outlet pipe body 61, which is electrically connected to the control module 17 and used to control the flow of liquid in the second water outlet pipe body 61.

FIG. 2 shows a schematic cross-sectional view of the ball groove 12 of FIG. 1. In Fig. 2, the ball groove screen 13 has not been cut, so it still maintains a complete disc shape. As shown in FIG. 2, the ball groove screen 13 is not perpendicular to the inner wall of the ball groove 12. That is, there is an acute angle between the bottom of the ball groove screen 13 and the inner wall of the ball groove 12. In addition, the water outlet 122 is located below the ball groove screen 13, and the water injection port 121 is located above the ball groove screen 13.

3 shows a schematic cross-sectional view of the first concentration tank 24, the first heat exchanger outlet tube 44, and the first heat exchanger outlet tube 64 of FIG. 1. FIG. 4 shows a three-dimensional schematic diagram of the first screen 241 according to an embodiment of the present invention. As shown in Figures 3 and 4, the inner ring of the first concentration tank 24 is provided with a screen (for example: the first screen 241), and the screen (for example: the first screen 241) has a plurality of screen holes ( For example: mesh 242). The inner diameter of the screen hole 242 is smaller than the predetermined ball diameter of the cleaning balls 14, for example, 1.2 cm. A first end 2411 of the first screen 241 is located at the first heat exchanger outlet pipe 64, and the inner diameter of the first end 2411 of the first screen 241 is slightly smaller than that of the first heat exchanger outlet pipe 64 the inside diameter of. The second end 2412 of the first screen 241 penetrates the first concentration groove 24, and the inner diameter of the second end 2412 of the first screen 241 is slightly smaller than the inner diameter of the first concentration groove 24. The second end 2412 of the first screen 241 is connected to the first heat exchanger outlet tube 44. Since the inner diameter of the screen hole 242 is smaller than the preset ball diameter of the cleaning balls 14, when the cleaning balls 14 together with the waste water move from the left to the right of the first heat exchanger outlet pipe 64, the cleaning The ball 14 and part of the waste water will move upward along the first screen 241 to the first heat exchanger outlet tube 44. That is, only part of the waste water will pass through the screen holes 242 of the first screen 241 and flow to the right side of the first heat exchanger outlet pipe 64, and no cleaning ball 14 will move to the first heat exchanger outlet. The right side of the water pipe 64.

5 to 7 show schematic diagrams of a method for cleaning a heat exchanger according to an embodiment of the present invention. Referring to FIG. 5, a ball groove 12 is provided, which stores a plurality of cleaning balls 14. The ball groove 12 in FIG. 5 is similar to the ball groove 12 in FIGS. 1 and 2, and it has a ball groove screen 13. The ball groove screen 13 has a plurality of through holes 131, and the inner diameter of the through holes 131 of the ball groove screen 13 is smaller than the predetermined ball diameter of the cleaning balls 14.

Then, clean water is poured into the ball groove 12 to make all the cleaning balls 14 leave the ball groove 12. In this embodiment, the method of injecting clear water into the ball groove 12 is as follows. First, the control module 17 turns on the first water inlet solenoid valve 53a, the second water inlet solenoid valve 51a, and the first front solenoid valve 34a, and activates the first pump 80 or the second pump 81. Subsequently, water from the outside into the water tank 53 into the first (e.g. flow path P shown in FIG. _1), followed by the first electromagnetic valve 53a, the first pump tube 82 via a tube member delivery tube 52, the second pump Pu tubular body 83 and the second solenoid valve 51a into the water enters into the second tube 51 (such as shown in the flow path P _2). Next, the water 51 within the second tube member into the groove 12 of the ball (as shown in the flow path P ₃₎ via the injection port 121.

Referring to FIG. 6, then, clean water brings all the cleaning balls 14 in the ball groove 12 out of the ball groove 12 through the first pipe body 32 (as shown by the water flow path P ₄ ). At this time, the first sensor 16 counts the number of the cleaning balls 14 leaving the ball groove 12, and transmits the calculation result to the control module 17 (FIG. 1). Subsequently, the cleaning water will enter the spherical ball 14 dispensing tube 33 (as shown in the flow path P _5), after entering the first heat exchanger tube 34 goal (as indicated by the flow path P _6).

Then, start the first heat exchanger inlet pump 84 to repressurize part of the clean water located in the outlet pipe 52 and introduce it into the first heat exchanger inlet pipe 54 together with the inlet pipe from the first heat exchanger. 34 with the water within the cleaning ball 14 with the first heat exchanger 74 is injected from a first end of the tubular body 743 to 741 within the first heat exchanger 74 (such as shown in the flow path P _7). It should be noted that, in one embodiment, the pressure (water pressure) from the first heat exchanger inlet tube 34 is greater than the pressure (water pressure) generated by the first heat exchanger inlet pump 84, so that The cleaning balls 14 enter the first heat exchanger inlet tube 54 from the first heat exchanger inlet tube 34, and then enter the tube body 741 in the first heat exchanger 74. Otherwise, if the pressure (water pressure) from the first heat exchanger inlet tube 34 is less than the pressure (water pressure) generated by the first heat exchanger inlet pump 84, then the first heat exchanger enters the ball The cleaning ball 14 in the tube 34 may not easily enter the water inlet tube 54 of the first heat exchanger. Although the preset ball diameters of the cleaning balls 14 are greater than or equal to the inner diameter of the tube body 741 of the first heat exchanger 74, the cleaning balls When the ball 14 passes through the tube body 741 of the first heat exchanger 74, it can completely contact the inner side wall of the tube body 741, and can take away the impurities on the inner side wall of the tube body 741, so as to surely clean the inner side wall of the tube body 741. At this time, the cleaning ball 14 is squeezed in the tube body 741 and slightly deformed into a substantially ellipsoidal shape.

Then, after cleaning the first heat exchanger 74, the clean water will become waste water. At this time, the first pump 80 or the second pump 81 is turned off, but the first heat exchanger inlet pump 84 is maintained. Therefore, the waste water and the cleaning balls 14 pass from the second end of the first heat exchanger 74 744 leaves the first heat exchanger 74 via the first heat exchanger outlet pipe 64. Due to the guiding and blocking of the first screen 241, part of the waste water together with the cleaning balls 14 will all enter the first concentration tank 24. In addition, part of the waste water is discharged through the first heat exchanger outlet pipe 64 to the waste water recovery pipe 62 (as _{shown in the water flow path P 8} ), and then discharged into the external water tank 70 through the waste water recovery pipe 62 (as shown in the water flow path P 8). ₉ ).

Referring to Figure 7, the control module 17 (Figure 1) closes the first water inlet solenoid valve 53a, the second water inlet solenoid valve 51a and the first front solenoid valve 34a, and opens the first water outlet solenoid valve 63a, the second water outlet solenoid valve 61a and The first rear solenoid valve 44a. Then, the first pump 80 or the second pump 81 is started again. At this time, the waste water located in the first concentrated tank 24 together with the cleaning balls 14 will enter the first heat exchanger outlet tube 44 (as shown by the water flow path P ₁₀ ), and then enter the spherical concentrated tube 43 (as shown in the water flow path). P ₁₁ ), and then enter the second pipe body 42 (as shown by the water flow path P ₁₂ ). After that, the waste water is returned to the ball tank 12 together with the cleaning balls 14. In this case, the second sensor 18 calculates the return groove 12 such that the ball 14 of the cleaning ball number (e.g., flow path as shown in P _13), and the calculation result is transmitted to the control module 17. At this time, the control module 17 compares the calculation result of the first sensor 16 and the calculation result of the second sensor 18. If the calculation result of the second sensor 18 (for example: the calculated quantity) does not match the calculation result of the first sensor 16 (for example: the calculated quantity), it means that some cleaning balls 14 remain in the first heat exchange The tube body 741 of the device 74 or other tube bodies. Therefore, the control module 17 will issue an alarm.

Since the inner wall of the cleaning ball 14 and the tube body (for example: the tube body 741 of the first heat exchanger 74 or other tubes) will wear the ball diameter after repeated friction cleaning, it is defined as a bad cleaning ball 19 (for example: The diameter of the bad cleaning balls 19 is less than or equal to 1.5 cm), and the bad cleaning balls 19 will pass through the ball groove screen because the ball diameter is less than or equal to the inner diameter of the through hole 131 of the ball groove screen 13 The through hole 131 of 13 falls down and is accommodated in the bottom of the ball groove 12 (that is, the cone-shaped accommodation space 124).

Next, the waste water within the tank 12 will via the ball outlet 122 to the second exhaust outlet pipe 61 (as shown in the flow path P _14), after the solenoid valve via the second outlet 61a, the first pump pipe 82, the the second tube pump 83 and the first solenoid valve 63a and the water outlet pipe 63 into the first (e.g. flow path P ₁₅ shown). Then, the waste water in the first water outlet pipe body 63 is discharged to the waste water recovery pipe 62 and then discharged into the external water tank 70.

In one embodiment, the discharge port 125 located at the bottom of the cone-shaped accommodating space 124 can be opened to discharge the bad cleaning ball 19, part of the waste water and impurities brought from the tube body 741 of the first heat exchanger 74.

This completes the cleaning of the first heat exchanger 74. To clean other heat exchangers, such as the second heat exchanger 75, the third heat exchanger 76, the fourth heat exchanger 77, or the fifth heat exchanger 78, the above-mentioned method can be used to complete the cleaning. It should be noted that at the beginning of the next cleaning process, the calculation result of the first sensor 16 can know how many cleaning balls 14 are accommodated in the bottom of the ball groove 12 due to wear (that is, the cone-shaped accommodation Space 124). At this time, a supplementary cleaning ball 15 can be provided from the supplementary inlet 123 to the ball groove 12. In addition, all the above-mentioned cleaning processes can be automatically controlled by the program of the control module 17 (FIG. 1), or manually controlled by humans.

In the present invention, a plurality of heat exchangers can be sequentially cleaned. Furthermore, the arrangement of the solenoid valves, the first sensor 16 and the second sensor 18 can ensure a proper amount of cleaning balls 14 to clean the heat exchanger, and can effectively carry the cleaning balls 14 into and out of the ball groove 12 The number control prevents the cleaning ball 14 from remaining in the heat exchanger or other tubes and damaging the heat exchanger, so as to achieve the purpose of saving hardware costs and prolonging the service life. In addition, the number of 19 bad balls that have been worn can also be known for timely replenishment.

The above-mentioned embodiments only illustrate the principles and effects of the present invention, and do not limit the present invention. Therefore, those skilled in the art can modify and change the above-mentioned embodiments without departing from the spirit of the present invention. The scope of rights of the present invention should be listed in the scope of patent application described later.

1: Cleaning system 5: Clean water supply path 6: Waste water recovery path 7: Heat exchanger component 9: Ball tank pump system 12: Ball tank 13: Ball tank screen 14: Cleaning ball 15: Supplementary cleaning ball 16: First Sensor 17: control module 18: second sensor 19: bad cleaning ball 24: first concentration tank 25: second concentration tank 26: third concentration tank 27: fourth concentration tank 28: fifth concentration tank 32: The first tube 33: the ball distribution tube 34: the first heat exchanger into the ball tube 34a: the first front solenoid valve 35: the second heat exchanger into the ball tube 35a: the second front solenoid valve 36: the third heat exchanger Ball inlet tube 36a: third front solenoid valve 37: fourth heat exchanger inlet tube 37a: fourth front solenoid valve 38: fifth heat exchanger inlet tube 38a: fifth front solenoid valve 42: second tube body 43: Spherical Concentrating Tube 44: First Heat Exchanger Outlet Tube 44a: First Rear Solenoid Valve 45: Second Heat Exchanger Outlet Tube 45a: Second Rear Solenoid Valve 46: Third Heat Exchanger Outlet Tube 46a : The third rear solenoid valve 47: the fourth heat exchanger outlet tube 47a: the fourth rear solenoid valve 48: the fifth heat exchanger outlet tube 48a: the fifth rear solenoid valve 51: the second water inlet pipe body 51a: the first Two water inlet solenoid valve 52: water outlet pipe 53: first water inlet pipe body 53a: first water inlet solenoid valve 54: first heat exchanger water inlet pipe 55: second heat exchanger water inlet pipe 56: third heat exchanger water inlet pipe 57 : The fourth heat exchanger inlet pipe 58: the fifth heat exchanger inlet pipe 61: the second outlet pipe body 61a: the second outlet solenoid valve 62: the waste water recovery pipe 63: the first outlet pipe body 63a: the first outlet solenoid valve 64: Outlet pipe of the first heat exchanger 65: Outlet pipe of the second heat exchanger 66: Outlet pipe of the third heat exchanger 67: Outlet pipe of the fourth heat exchanger 68: Outlet pipe of the fifth heat exchanger 70: External water tank 74 : First heat exchanger 75: Second heat exchanger 76: Third heat exchanger 77: Fourth heat exchanger 78: Fifth heat exchanger 80: First pump 81: Second pump 82: First Pump tube 83: second pump tube 84: first heat exchanger inlet pump 85: second heat exchanger inlet pump 86: third heat exchanger inlet pump 87: fourth heat exchanger inlet pump Pump 88: the fifth heat exchanger inlet pump 90: the first connecting pipe body 91: the second connecting pipe body 121: the water injection port 122: the water outlet 123: the supplementary inlet 124: the cone-shaped accommodation space 125: the discharge port 126 : Transparent upper cover 131: Through hole 241: First screen 242: Screen hole 741: Tube body 743: First end 744: Second end 751: Tube body 761: Tube body 771: Tube body 781: Tube body 2411: No. The first end of a screen 2412: The second end of the first screen P ₁ : Water flow path P ₂ : Water flow path P ₃ : Water flow path P ₄ : Water flow path P ₅ : Water flow path P ₆ : Water flow path P ₇ : Water flow path P ₈ : Water flow path P ₉ : Water flow path P ₁₀ : Water flow path P ₁₁ : Water flow path P ₁₂ : Water flow path P ₁₃ : Water flow path P ₁₄ : Water flow path P ₁₅ : Water flow path

When read in conjunction with the accompanying drawings, it is easy to understand the aspects of some embodiments of the present invention from the following detailed description. It should be noted that the various structures may not be drawn to scale, and the size of the various structures may be increased or decreased arbitrarily for clarity of discussion.

Fig. 1 shows a schematic diagram of a heat exchanger assembly according to an embodiment of the present invention.

Fig. 2 shows a schematic cross-sectional view of the ball groove of Fig. 1.

3 shows a schematic cross-sectional view of the first concentration tank, the first heat exchanger outlet tube, and the first heat exchanger outlet tube of FIG. 1.

Fig. 4 shows a three-dimensional schematic diagram of a first screen according to an embodiment of the present invention.

5 to 7 show schematic diagrams of a method for cleaning a heat exchanger according to an embodiment of the present invention.

1: Cleaning system

5: Clear water provides a path

6: Wastewater recycling path

7: Heat exchanger components

9: Ball groove pumping system

12: Ball groove

13: Ball slot screen

14: Cleaning the ball

15: Replenish cleaning ball

16: first sensor

17: Control module

18: second sensor

19: Poor cleaning ball

24: The first concentration slot

25: The second concentration slot

26: Third Concentration Slot

27: The fourth concentration slot

28: Fifth Concentration Slot

32: The first tube body

33: Ball distribution pipe

34a: The first front solenoid valve

34: The first heat exchanger into the ball tube

35a: The second front solenoid valve

35: The second heat exchanger enters the ball tube

36a: The third front solenoid valve

36: The third heat exchanger enters the ball tube

37a: Fourth front solenoid valve

37: The fourth heat exchanger enters the ball tube

38a: Fifth front solenoid valve

38: The fifth heat exchanger enters the ball tube

42: second tube body

43: Sphere Concentrating Tube

44a: First rear solenoid valve

44: Outlet tube of the first heat exchanger

45a: second rear solenoid valve

45: Outlet tube of the second heat exchanger

46a: Third rear solenoid valve

46: The third heat exchanger outlet tube

47a: Fourth rear solenoid valve

47: The fourth heat exchanger tube

48a: Fifth rear solenoid valve

48: Fifth heat exchanger outlet tube

51: The second inlet pipe body

51a: The second water inlet solenoid valve

52: Outlet pipe

53: The first inlet pipe body

53a: The first water inlet solenoid valve

54: The first heat exchanger inlet pipe

55: The second heat exchanger inlet pipe

56: The third heat exchanger inlet pipe

57: The fourth heat exchanger inlet pipe

58: Fifth heat exchanger inlet pipe

61: The second outlet pipe body

61a: The second water outlet solenoid valve

62: Wastewater recovery pipe

63: The first outlet pipe body

63a: The first water outlet solenoid valve

64: Outlet pipe of the first heat exchanger

65: The second heat exchanger outlet pipe

66: The third heat exchanger outlet pipe

67: The fourth heat exchanger outlet pipe

68: Fifth heat exchanger outlet pipe

70: External sink

74: The first heat exchanger

75: second heat exchanger

76: third heat exchanger

77: The fourth heat exchanger

78: Fifth heat exchanger

80: The first pump

81: second pump

82: The first pump tube

83: The second pump tube

84: The first heat exchanger enters the water pump

85 second heat exchanger inlet pump

86: The third heat exchanger enters the water pump

87: The fourth heat exchanger enters the water pump

88: Fifth heat exchanger inlet pump

90: The first connecting pipe body

91: The second connecting pipe body

121: water injection port

122: water outlet

123: Supplemental Entrance

124: Cone-shaped accommodating space

125: Drain

126: transparent upper cover

131: Through Hole

241: First Screen

741: tube body

743: first end

744: second end

751: tube body

761: tube body

771: tube body

781: tube body

Claims (30)

A cleaning system includes: a ball groove for storing a plurality of cleaning balls; a first pipe body connected to the ball groove for allowing the cleaning balls to leave the ball groove; and a first sensor located on the first pipe. A tube body for counting the number of cleaning balls passing through; a second tube body connected to the ball groove for the cleaning balls to return to the ball groove; and a second sensor located in the second tube The body is used to count the number of cleaning balls passed; wherein the bottom of the ball groove has a cone-shaped accommodating space for accommodating bad cleaning balls. Such as the cleaning system of claim 1, wherein the first sensor and the second sensor are both a photo-interrupter, and the photo-interrupter provides only one cleaning ball to pass through at the same time. For example, the cleaning system of claim 1, further comprising: a ball groove screen, located in the ball groove, and having a plurality of through holes, wherein the inner diameter of the through holes of the ball groove screen is smaller than that of the cleaning balls Set the ball diameter. Such as the cleaning system of claim 3, wherein the outer periphery of the ball groove screen is connected to the inner side wall of the ball groove. For example, the cleaning system of claim 1, including: A water injection port is connected to the ball groove for injecting clean water into the ball groove. For example, the cleaning system of claim 1 further includes: a water outlet connected to the ball tank for draining the waste water after cleaning to the outside of the ball tank. For example, the cleaning system of claim 1 further includes: a supplementary inlet connected to the ball groove to provide supplementary cleaning balls into the ball groove. For example, the cleaning system of claim 1, further comprising: a control module electrically connected to the first sensor and the second sensor for comparing the calculation results of the first sensor and the second sensor. Such as the cleaning system of claim 1, wherein the ball groove further includes a transparent upper cover. A heat exchanger assembly includes: at least one heat exchanger with a plurality of tube bodies; and a cleaning system, including: a ball groove for storing a plurality of cleaning balls, and the preset ball diameters of the cleaning balls are larger than The inner diameter of the tube body of the heat exchanger; a ball groove screen is located in the ball groove and has a plurality of through holes, wherein the inner diameter of the through holes of the ball groove screen is smaller than that of the cleaning balls A ball diameter is provided; a cleaning ball provides a path connecting the ball groove and a first end of the heat exchanger to provide the cleaning balls to the tube body of the heat exchanger; and A cleaning ball recovery path communicates with the ball groove and a second end of the heat exchanger for the cleaning balls to return to the ball groove. Such as the heat exchanger assembly of claim 10, wherein the at least one heat exchanger includes a plurality of heat exchangers, which are connected in parallel to the cleaning system. Such as the heat exchanger assembly of claim 10, wherein the ball groove screen is accommodated in the bottom of the ball groove for the passage of defective cleaning balls. For example, the heat exchanger assembly of claim 10 further includes: a clean water supply path connected to the spherical groove for supplying clean water into the spherical groove. The heat exchanger assembly of claim 13, wherein the clean water supply path is connected to the first end of the heat exchanger. For example, the heat exchanger assembly of claim 13, wherein the clean water supply path includes: a water outlet pipe for providing clean water: at least one heat exchanger water inlet pipe connected to the water outlet pipe and the first end of the heat exchanger, To inject clear water into the heat exchanger; and a ball groove water inlet path, which connects the water outlet pipe and a water injection port of the ball groove, for injecting clear water into the ball groove. For example, the heat exchanger assembly of claim 15, including: At least one heat exchanger water inlet pump located in the heat exchanger water inlet pipe for pressurizing the liquid in the heat exchanger water inlet pipe; and a ball groove pump system connected to the ball groove water inlet path for The ball groove enters the liquid in the water path to pressurize. For example, the heat exchanger assembly of claim 10 further includes: a waste water recovery path connected to the second end of the heat exchanger for draining waste water after cleaning to an external water tank. Such as the heat exchanger assembly of claim 17, wherein the waste water recovery path is connected to the ball tank. For example, the heat exchanger assembly of claim 17, wherein the waste water recovery path includes: a waste water recovery pipe for discharging waste water: at least one heat exchanger outlet pipe connecting the outlet pipe and the second end of the heat exchanger, It is used to discharge waste water to the waste water recovery pipe; and a ball tank water outlet path is connected to the waste water recovery pipe and one of the water outlets of the ball tank to discharge the waste water in the ball tank to the waste water recovery pipe. For example, the heat exchanger assembly of claim 19 further includes: a ball groove pumping system connected to the water outlet path of the ball groove for pressurizing the liquid in the water outlet path of the ball groove. For example, the heat exchanger assembly of claim 10, wherein the path provided by the cleaning ball includes: A first tube adjacent to and connected to the ball groove for the cleaning balls to leave the ball groove; and at least one heat exchanger inlet tube adjacent to the heat exchanger and connected to the first tube body and the ball groove The first end of the heat exchanger is used to provide the cleaning balls to the tube body of the heat exchanger. For example, the heat exchanger assembly of claim 21 further includes: a first sensor located in the first tube body for calculating the number of cleaning balls passed; and at least one front solenoid valve located in the heat exchanger inlet The ball tube is used to control the flow of liquid in the heat exchanger into the ball tube. For example, the heat exchanger assembly of claim 10, wherein the cleaning ball recovery path includes: at least one heat exchanger outlet pipe, adjacent to and communicating with the second end of the heat exchanger, for the cleaning balls to leave the heat Exchanger; and a second tube body adjacent to the ball groove and connected to the heat exchanger out of the ball pipe and the ball groove for the cleaning balls to return to the ball groove. For example, the heat exchanger assembly of claim 23 further includes: a second sensor located in the second tube body for calculating the number of cleaning balls passed; and at least one rear solenoid valve located at the outlet of the heat exchanger The ball tube is used to control the flow of liquid in the tube out of the heat exchanger. For example, the heat exchanger assembly of claim 23 further includes: at least one concentration tank located at one end of the heat exchanger outlet tube for temporarily collecting the cleaning balls, wherein the concentration tank ring is provided with a screen, the screen The net has a plurality of sieve holes, and the inner diameter of the sieve holes is smaller than the preset ball diameters of the cleaning balls. A method for cleaning a heat exchanger includes: (a) providing a ball tank, which stores a plurality of cleaning balls; (b) injecting clean water into the ball tank, so that all cleaning balls leave the ball tank; (c) calculating The number of the cleaning balls leaving the ball groove; (d) pressurizing the cleaning balls into the tube body of a heat exchanger to clean the inner wall of the tube body of the heat exchanger, wherein the cleaning balls The default ball diameter of the ball is larger than the inner diameter of the tube body of the heat exchanger; (e) return a part of the waste water after cleaning and all the cleaning balls to the ball groove; and (f) calculate the return to the ball groove The number of cleaning balls. Such as the cleaning method of claim 26, wherein in the step (a), the ball groove has a ball groove screen with a plurality of through holes, and the inner diameter of the through hole of the ball groove screen is smaller than the Wait for the preset ball diameter of the cleaning ball; in this step (e), if the cleaning ball after cleaning is smaller than the inner diameter of the through hole of the ball groove screen, it will pass through the ball groove screen and be contained The bottom of the ball groove. For example, the cleaning method of claim 26, after the step (d), the cleaning method further includes: (d1) discharging a part of the waste water after cleaning to a waste water recovery pipe. Such as the cleaning method of claim 26, after the step (e), the cleaning method further includes: (e1) draining the wastewater in the ball tank to a wastewater recovery pipe. For example, the cleaning method of claim 26, after the step (f), the cleaning method further includes: (g) comparing the calculation result of step (c) with the calculation result of step (f).

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