CN115031282A

CN115031282A - Pipe shell type heat storage and supply device and design method

Info

Publication number: CN115031282A
Application number: CN202210774683.0A
Authority: CN
Inventors: 谯耕; 金露; 徐桂芝; 张娜
Original assignee: State Grid Electric Power Research Institute Of Sepc; State Grid Smart Grid Research Institute Co ltd; State Grid Corp of China SGCC; Global Energy Interconnection Research Institute Europe GmbH
Current assignee: State Grid Electric Power Research Institute Of Sepc; State Grid Smart Grid Research Institute Co ltd; State Grid Corp of China SGCC; Global Energy Interconnection Research Institute Europe GmbH
Priority date: 2022-07-01
Filing date: 2022-07-01
Publication date: 2022-09-09

Abstract

The invention relates to the technical field of heat storage, in particular to a shell-and-tube heat storage and supply device and a design method. The shell-and-tube heat storage and supply device comprises: the shell is of a cylindrical closed structure, an outlet and an inlet are arranged on the shell, and the outlet and the inlet are communicated with an inner cavity of the shell; the heat storage device is arranged in the shell and comprises a plurality of PCM pipes which are uniformly distributed on the cross section of the shell, each PCM pipe is parallel to the axial direction of the shell and is distributed at intervals, the distance between every two adjacent PCM pipes is equal to the distance between the PCM pipe and the inner wall of the shell, and the PCM pipes are filled with phase change materials; and the heating structures correspond to the PCM tubes one by one and are arranged on the outer sides of the PCM tubes, and the heating device is suitable for heating the PCM tubes and storing heat of the phase-change materials in the PCM tubes. The shell-and-tube heat storage and supply device with the structure improves the contact area of fluid and the PCM tube, improves the heat conductivity of the PCM tube and reduces the heat loss.

Description

Pipe shell type heat storage and supply device and design method

Technical Field

The invention relates to the technical field of heat storage, in particular to a shell-and-tube heat storage and supply device and a design method.

Background

The heat storage technology is an important technology for reasonably and effectively utilizing the existing energy, optimizing and using renewable energy and improving energy efficiency. In the prior art, most of the existing heat storage technologies adopt phase-change materials for heat storage, the phase-change materials can change phase near the phase-change temperature of the phase-change materials and release or absorb a large amount of heat, and the characteristics of the phase-change materials can be used for storing energy or controlling the environmental temperature. The existing device for heat storage and heat supply by using phase-change materials generally comprises a shell and a heat storage pipe inside the shell, wherein the phase-change materials are filled in the heat storage pipe, and fluid is filled between the heat storage pipe and the shell. However, the heat in the heat storage pipe with the existing structure cannot be efficiently dissipated in fluid, so that the heat exchange efficiency is low, and the structural compactness of the whole device is also low.

Disclosure of Invention

Therefore, the technical problem to be solved by the present invention is to overcome the defects of low heat exchange efficiency and low compactness of the device for storing and supplying heat by using a phase change material in the prior art, so as to provide a tube-shell type heat storage and supply device and a design method thereof.

In order to solve the above problems, the present invention provides a shell-and-tube heat storage and supply apparatus, comprising:

the shell is of a cylindrical closed structure, an outlet and an inlet are arranged on the shell, and the outlet and the inlet are communicated with an inner cavity of the shell;

the heat storage device is arranged in the shell and comprises a plurality of PCM pipes which are uniformly distributed on the cross section of the shell, each PCM pipe is parallel to the axial direction of the shell and is distributed at intervals, the distance between every two adjacent PCM pipes is equal to the distance between each PCM pipe and the inner wall of the shell, and the PCM pipes are filled with phase-change materials;

and the heating structures correspond to the PCM tubes one by one and are arranged on the outer sides of the PCM tubes, and the heating device is suitable for heating the PCM tubes and storing heat of the phase-change materials in the PCM tubes.

Furthermore, still be provided with two end plates in the shell, two the end plate sets up respectively both ends in the shell, the both ends of PCM pipe are connected with two end plates respectively.

Further, the method also comprises the following steps:

and one end of the separator is connected with the end plate, a gap is reserved between the other end of the separator and the end plate on the other side, and the separator is suitable for separating a plurality of PCM tubes arranged in the shell.

Furthermore, the outlet is arranged at one end of the uppermost layer of the partition board connected with the end board, and the inlet is arranged at one end of the lowermost layer of the partition board connected with the end board.

Further, the heating structure is an electric heating tape wound on the surface of the PCM tube.

Further, the method also comprises the following steps:

a first control valve disposed at the inlet, the first control valve adapted to control a flow of fluid into the inlet;

a second control valve disposed between the inlet and the outlet, the second control valve adapted to control a temperature of an outlet fluid.

Further, the distance between the adjacent PCM pipes is 2-4 mm.

The invention also provides a design method of the shell-and-tube heat storage and supply device, which comprises the following steps:

s1: determining the required heat storage capacity E, determining the required phase-change material dosage a according to the phase-change material heat storage density Qm, and calculating the formula as follows:

s2: the method comprises the following steps of determining the length of a stainless steel pipe according to the actual situation of a site, selecting the stainless steel pipe with the inner diameter of d to load a phase change material to obtain a PCM pipe, and calculating the mass m of the phase change material contained in each stainless steel pipe according to the inner diameter d, the length l and the density rho of the phase change material, wherein the calculation formula is as follows:

s3: calculating the required number qty of PCM tubes according to the phase-change material usage a and the phase-change material mass m, wherein the calculation formula is as follows:

s4: presetting the space between adjacent PCM pipes and the space between the PCM pipes and the inner wall of the shell to be k, and calculating the radius R of a fitting circle according to k _tube The calculation formula is as follows: r _tube ＝(d+k/2)mm；

S5: bound to R _tube And qty, calculating the coordinates of each fitting circle by the circle packing problem, thereby calculating the diameter d' of the packing circle;

s6: calculating the inner diameter d of the housing from d' and k _shell The calculation formula is as follows: d _shell ＝d’+k。

Furthermore, the aspect ratio AR is determined by the ratio of the length of the PCM tube to the outer diameter of the shell, and the dimensions of the PCM tube and the shell are adjusted according to the influence of the aspect ratio on the energy density.

Further, the area of the PCM tube surface 1/3 was covered with an electrical heating tape.

The invention has the following advantages:

1. the invention provides a shell-and-tube heat storage and supply device, which comprises: shell, heat accumulation device and heating structure. The shell is of a cylindrical closed structure, an outlet and an inlet are arranged on the shell, and the outlet and the inlet are communicated with an inner cavity of the shell; the heat storage device is arranged in the shell and comprises a plurality of PCM pipes which are uniformly distributed on the cross section of the shell, each PCM pipe is parallel to the axial direction of the shell and is distributed at intervals, the distance between every two adjacent PCM pipes is equal to the distance between each PCM pipe and the inner wall of the shell, and the PCM pipes are filled with phase-change materials; a plurality of heating structures correspond to the PCM pipe one by one and are arranged on the outer side of the PCM pipe, and the heating device is suitable for heating the PCM pipe and enabling the phase-change material in the PCM pipe to store heat.

The shell and tube heat storage and supply device of the structure uniformly arranges a plurality of PCM tubes in the shell, and enables the space between the PCM tubes and the PCM tubes to be the same, meanwhile, the space between the PCM tubes and the inner wall of the shell is equal, and the space between the PCM tubes is equal to 2 times of the space between the PCM tubes and the inner wall of the shell, so that the thickness of fluid enclosed outside the PCM tubes is the same, the heat dissipation rate of each PCM tube basically keeps the same, the path of heat transfer is reduced, and the heat exchange efficiency is improved. In addition, compare in traditional shell and tube type heat accumulation heating device, this device structural arrangement is also compacter.

2. The shell-and-tube heat storage and supply device with the structure has the advantages that the partition plate is arranged in the shell, the outlet and the inlet are arranged at one end of the partition plate connected with the end plate, so that the fluid can be fully contacted with the PCM tube in the shell, the heat transfer performance of the PCM tube is further improved, and the heat loss is reduced.

3. The shell-and-tube heat storage and supply device with the structure has the advantages that the second control valve is arranged between the inlet and the outlet, so that when the temperature of outlet fluid exceeds required temperature, cold fluid at the inlet is combined with hot fluid at the outlet, the temperature of the outlet fluid is reduced, the outlet fluid reaches required temperature, and the heat release effect is further improved.

4. The shell-and-tube heat storage and supply device with the structure can avoid the loss caused by corrosion of the phase-change material by isolating the heating equipment from the phase-change material.

Drawings

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the embodiments or the prior art descriptions will be briefly introduced below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and other drawings can be obtained by those skilled in the art without creative efforts.

Fig. 1 is a schematic view of a shell-and-tube heat storage and supply apparatus according to embodiment 1 of the present invention;

fig. 2 is a structural view of a shell-and-tube heat storage and supply apparatus in embodiment 1 of the present invention;

fig. 3 is a sectional view of the shell-and-tube heat storage and supply apparatus according to embodiment 1 of the present invention;

FIG. 4 is a graph comparing the void fractions of different gaps in example 2 of the present invention;

FIG. 5 is a graph comparing aspect ratio and energy density in example 2 of the present invention;

description of reference numerals:

1. a housing; 2. an outlet; 3. an inlet; 4. a PCM tube; 5. an end plate; 6. a partition plate; 7. an electrical heating belt; 8. a first control valve; 9. a second control valve.

Detailed Description

The technical solutions of the present invention will be described clearly and completely with reference to the accompanying drawings, and it should be understood that the described embodiments are some, but not all embodiments of the present invention. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, are within the scope of the present invention.

In the description of the present invention, it should be noted that the terms "inside", "outside", etc. indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings only for the convenience of describing the present invention and simplifying the description, but do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus, should not be construed as limiting the present invention. Furthermore, the terms "first," "second," and the like are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.

In addition, the technical features involved in the different embodiments of the present invention described below may be combined with each other as long as there is no conflict between them.

Example 1

As shown in fig. 1 to 3, the present embodiment discloses a shell-and-tube heat storage and supply apparatus including: a housing 1, a thermal storage device and a plurality of heating structures. The shell 1 is a cylindrical closed structure, an outlet 2 and an inlet 3 are arranged on the shell 1, and the outlet 2 and the inlet 3 are both communicated with an inner cavity of the shell 1. It will be readily appreciated that a cylindrical enclosure structure, i.e., a structure formed by enclosing both ends of a tubular cylindrical structure. The heat storage device is arranged in the shell 1 and comprises a plurality of PCM tubes 4 uniformly distributed on the cross section of the shell, each PCM tube 4 is axially parallel to the shell 1 and distributed at intervals, the distance between every two adjacent PCM tubes 4 is equal to the distance between each PCM tube 4 and the inner wall of the shell, and the PCM tubes 4 are filled with phase-change materials. The plurality of heating structures correspond to the PCM tubes 4 one by one and are arranged outside the PCM tubes 4, and the heating device is used for heating the PCM tubes 4 and storing heat in the phase-change materials in the PCM tubes 4. It should be noted that the number of heating structures corresponds to the number of PCM tubes 4, and preferably, twenty-six PCM tubes 4 are provided in the housing 1 in this embodiment. In other possible embodiments, twenty-five or twenty-seven PCM tubes 4 may be disposed within the housing 1.

Preferably, the spacing between adjacent PCM tubes 4 is 2mm in this embodiment. In other possible embodiments, the pitch of adjacent PCM tubes 4 is 3mm or 4mm or other distances. Similarly, the space between the PCM pipe 4 and the inner wall of the shell is 2 mm.

Preferably, the heating structure is an electric heating tape 7, the electric heating tape 7 is wound around the surface of the PCM tube 4, and an area of the surface 1/3 of the PCM tube 4 is covered with the electric heating tape 7. The electric heating tape 7 heats the PCM tube 4 and allows the PCM tube 4 to store heat. It is common knowledge that the electric heating tape 7 is connected to a power source, and the electric heating tape 7 is supplied with power by the power source, and it is not described here much. Alternatively, the heating belt may also adopt other common heating structures such as a heating film.

Further, still be provided with two end plates 5 in the shell 1, two end plate 5 sets up the both ends in shell 1 respectively, and the both ends of PCM pipe 4 are connected with two end plates 5 respectively, and end plate 5 is used for the PCM pipe 4 in the fixed casing. Compared with the scheme of directly fixing the two ends of the PCM pipe 4 on the inner wall of the shell, the PCM pipe can be integrally installed in the shell 1 after being preassembled on the end plate 5, and the installation is more convenient.

Further, a partition plate 6 is arranged in the shell 1, one end of the partition plate 6 is connected with the end plate 5, a gap is reserved between the other end of the partition plate 6 and the end plate 5 on the other side, and the partition plate 6 is suitable for partitioning the PCM tubes 4 arranged in the shell 1. In fig. 2, the left end of a partition plate 6 is connected to the end plate 5 at the left end in the case 1, a gap is provided between the right end of the partition plate 6 and the end plate 5 at the right end in the case 1, the partition plate 6 divides the inside of the case 1 into two chambers and equally divides the PCM tubes 4 into the two chambers, and thirteen PCM tubes 4 are provided in each chamber. It should be noted that when the partition plate 6 is provided, the partition plate 6 should be regarded as the case 1, that is, it is required to ensure that the PCM tubes 4 in each chamber are equally spaced, and the spacing between the PCM tubes 4 and the partition plate 6 should be half the spacing between the PCM tubes 4.

Further, the outlet 2 is provided at an end of the uppermost partition plate 6 connected to the end plate 5, and the inlet 3 is provided at an end of the lowermost partition plate 6 connected to the end plate 5. Preferably, in this embodiment, a partition is provided in the housing 1, and in fig. 2, the outlet 2 and the inlet 3 are provided at the left end of the housing 1. Fluid enters the first chamber in the housing through inlet 3, then enters the second chamber through the gap between the partition 6 and the end plate 5, and then exits through outlet 2, where it can exchange heat with the PCM tubes 4, sufficient in both chambers of the housing 1. In other embodiments, two partition plates 6 may be disposed in the housing 1, the two partition plates 6 divide the housing into three chambers, the left end of the upper partition plate 6 is fixedly connected to the left end plate 5, the right end of the lower partition plate 6 is fixedly connected to the right end plate 5, the outlet 2 is disposed at the left end of the housing 1, and the inlet 3 is disposed at the right end of the housing 1.

Further, a first control valve 8 and a second control valve 9 are included. A first control valve 8 is provided at the inlet 3, the first control valve 8 being used to control the flow of fluid into the inlet 3. A second control valve 9 is arranged between the inlet 3 and the outlet 2, the second control valve 9 being capable of regulating the temperature of the outlet fluid. By opening the second control valve 9, the cold fluid at the inlet can be mixed with the hot fluid at the outlet, and the temperature of the superheated fluid at the outlet can be reduced to the required temperature.

In particular, the fluid may be a liquid or a gas, preferably, in the present embodiment, the fluid is a gas.

Example 2

The embodiment discloses a design method of a tube-shell type heat storage and supply device, which comprises the following steps:

it should be noted that, according to the actual application requirements, phase change materials with a melting point range of 300-700 ℃ are selected, including but not limited to nitrates, carbonates, chlorides, hydroxides; selecting materials such as magnesium oxide, aluminum oxide, silicon oxide, foamed ceramics, honeycomb ceramics and the like as framework materials; graphite, silicon carbide, metal simple substance and other materials are selected as heat conduction reinforcing materials. Wherein the mass fraction of the phase-change material is less than or equal to 60 percent, the mass fraction of the heat-conducting reinforcing material is less than or equal to 5 percent, and the balance is framework material.

S2: and determining the length of the stainless steel pipe according to the actual situation of the site, and selecting the stainless steel pipe with the inner diameter of d to load the phase change material to obtain the PCM pipe 4. Calculating the mass m of the phase change material which can be contained in each stainless steel pipe according to the inner diameter d, the length l and the density rho of the phase change material, wherein the calculation formula is as follows:

preferably, in the embodiment of the present embodiment, a DN20 stainless steel tube is used.

S3: the number qty of the needed PCM tubes 4 is calculated according to the phase-change material usage a and the phase-change material mass m, and the calculation formula is as follows:

s4: presetting the distance between adjacent PCM tubes 4 as k, and calculating the radius R of a fitting circle according to k _tube The calculation formula is as follows: r _tube ＝(d+k/2)mm。

It should be noted that the fitting circle is a circle preset by adding k/2 to the radius of the PCM tube 4. The pitch k can be found experimentally by those skilled in the art, and is found experimentally to be an optimal pitch of 2-4 mm. Preferably, k is 2mm in this embodiment.

S5: radius R of the combined fitting circle _tube And the number qty of PCM tubes 4, the diameter d' of the packing circle is calculated by calculating the coordinates of each fitting circle through the circle packing problem.

It should be noted that the problem of circle packaging is prior art and is not specifically described herein to determine the radius R of a fitted circle _tube And the number qty of PCM tubes 4, the coordinates of each fitting circle can be determined by the circle packing problem, and thus the coordinates of each PCM tube 4 can be confirmed. A packing circle, i.e. a large circle that encloses all fitting circles and is inscribed in the peripheral fitting circle.

S6: calculating the inner diameter d of the housing 1 from d' and k _shell The calculation formula is as follows: d _shell ＝d’+k。

The diameter D of the packing circle is obtained by fitting the coordinates of the circle, and the fitting circle is fitted to the packing circle, and the inner diameter D of the housing 1 can be obtained by adding the pitch k to the diameter D of the packing circle because the pitch between the PCM tubes 4 and the inner wall of the housing 1 is the same as the pitch between the adjacent PCM tubes 4 _shell . In the present embodiment, the distance k is 2mm, so that the inner diameter D of the housing 1 can be obtained by adding 2mm to the diameter D of the packing circle _shell 。

Further, as shown in FIG. 4, by obtaining the inner diameter d of the housing 1 _shell And the outer diameter R of the PCM tube 4 _tubes The porosity is calculated experimentally, and the smaller the porosity, the larger the contact area of the fluid and the PCM tube 4, and therefore the better the heat transfer effect. The formula for calculating the void fraction is:

A _shell is the cross-sectional area of the housing 1, A _tubes The cross-sectional area of the PCM tube 4.

The cross-sectional area of the housing 1 is calculated as:

the calculation formula of the cross-sectional area of the PCM tube 4 is: a. the _tubes ＝N _tubes ·π·R _tubes ² 。

The void fraction of different gap sizes between different numbers of PCM tubes 4 when the shell diameter is fixed at 212mm is shown in fig. 4. The experimental result shows that when the clearance of the PCM pipe 4 is 2-4mm, the void ratio is small, and a better heat transfer effect can be obtained. Preferably, in this embodiment, the clearance of the PCM tube 4 is 2 mm.

It is to be understood that in fig. 4, in the case where there is no gap, the porosity is minimal, but there is a risk that the phase change material expands upon heating, causing the PCM tubes 4 to be pressed against each other, thereby causing explosion, and therefore, a certain distance between the PCM tubes 4 will occur to those skilled in the art.

Further, as shown in fig. 5, the aspect ratio AR is determined by the ratio of the length of the PCM tube to the diameter of the outer shell 1, and the dimensions of the PCM tube 4 and the shell are adjusted according to the influence of the aspect ratio on the energy density.

In particular, the aspect ratio will affect the heat loss profile within the device. Heat loss is a function of exposed surface area, heat exchange length and diameter. Fig. 5 shows the effect of aspect ratio AR on system energy density, which is the ratio of the length of PCM tube 4 to the diameter of housing 1 in a 5 kwh system capacity (700 PCM). The figure shows that the maximum energy density can be achieved when the aspect ratio is 1. However, for an optimal shell-and-tube regenerative heating device design, heat transfer, pressure drop, etc. considerations may be taken into account, and may be achieved at an aspect ratio of 3 to 5. Based on these aspects, an optimal design may take an aspect ratio of 2-4, where the system energy density varies by less than 10%. Based on the calculations here, an iterative adjustment of the PCM tube 4 and thus the housing 1 design is possible. The outer diameter of the housing 1 can be adjusted to adjust the aspect ratio; the PCM tube length, and thus the number of PCM tubes 4 and the inner diameter of the outer shell 1, may also be adjusted.

Further, the area of the surface 1/3 of the PCM tube 4 is covered with the electric heating tape 7. Since the heat release is achieved by convection between the PCM tube and the fluid, the use of heating elements will reduce the contact surface between the PCM tube and the fluid. After the experiment, the best balance between heat storage and release was achieved when approximately 1/3 area of the PCM tube surface was covered by the electrical heating tape 7. It is specifically stated that the values are fully accessible to the skilled person after experimentation and are not described in detail herein.

It should be understood that the above-described embodiments are merely examples for clarity of description and are not intended to limit the scope of the embodiments. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. This list is neither intended to be exhaustive nor exhaustive. And obvious variations or modifications therefrom are within the scope of the invention.

Claims

1. A shell-and-tube heat storage and supply apparatus, comprising:

the device comprises a shell (1) which is of a cylindrical closed structure, wherein an outlet (2) and an inlet (3) are arranged on the shell (1), and the outlet (2) and the inlet (3) are both communicated with an inner cavity of the shell (1);

the heat storage device is arranged in the shell (1) and comprises a plurality of PCM tubes (4) which are uniformly distributed on the cross section of the shell (1), each PCM tube (4) is parallel to the axial direction of the shell (1) and is distributed at intervals, the intervals between the adjacent PCM tubes (4) are equal, the intervals between each PCM tube (4) and the inner wall of the shell (1) are also equal, and the PCM tubes (4) are filled with phase-change materials;

the heating structures correspond to the PCM tubes (4) one by one and are arranged on the outer sides of the PCM tubes (4), and the heating device is suitable for heating the PCM tubes (4) and enabling the phase change materials in the PCM tubes (4) to store heat.

2. A shell-and-tube heat storage and supply apparatus according to claim 1, characterized in that:

still be provided with two end plates (5) in shell (1), two end plate (5) set up respectively both ends in shell (1), the both ends of PCM pipe (4) are connected with two end plates (5) respectively.

3. A shell and tube heat storage and supply apparatus according to claim 2, further comprising:

a separator plate (6), one end of the separator plate (6) is connected with the end plate (5), a gap is arranged between the other end of the separator plate (6) and the end plate (5) on the other side, and the separator plate (6) is suitable for separating a plurality of PCM tubes (4) arranged in the shell (1).

4. A shell-and-tube heat storage and supply apparatus according to claim 3, characterized in that:

the outlet (2) is arranged at one end where the uppermost layer partition plate (6) is connected with the end plate (5), and the inlet (3) is arranged at one end where the lowermost layer partition plate (6) is connected with the end plate (5).

5. A shell-and-tube heat storage and supply apparatus according to claim 4, characterised in that:

the heating structure is an electric heating tape (7), and the electric heating tape (7) is wound on the surface of the PCM pipe (4).

6. A shell and tube heat accumulating and supplying apparatus according to any one of claims 1 to 5, further comprising:

a first control valve (8) arranged at the inlet (3), the first control valve (8) being adapted to control the fluid flow into the inlet (3);

a second control valve (9) arranged between the inlet (3) and the outlet (2), the second control valve (9) being adapted to control the temperature of the outlet (2) fluid.

7. A shell and tube heat storage and supply apparatus according to any one of claims 1 to 5, characterised in that:

the distance between the adjacent PCM pipes (4) is 2-4 mm.

8. A design method of a shell-and-tube heat storage and supply device is characterized by comprising the following steps:

s1: determining the required heat storage capacity E, and determining the required phase change material dosage a according to the phase change material heat storage density Qm, wherein the calculation formula is as follows:

s2: the method comprises the following steps of determining the length of a stainless steel pipe according to the actual situation of a site, selecting a stainless steel pipe with the inner diameter of d to load a phase change material to obtain a PCM pipe (4), and calculating the mass m of the phase change material which can be contained in each stainless steel pipe according to the inner diameter d of the stainless steel pipe, the length l and the density rho of the phase change material, wherein the calculation formula is as follows:

s4: presetting the space between the adjacent PCM pipes (4) and the space between the PCM pipes (4) and the inner wall of the shell (1) to be k, and calculating the radius R of a fitting circle according to k _tube The calculation formula is as follows: r _tube ＝(d+k/2)mm；

S5: bound to R _tube And qty calculating the diameter d 'of the packing circle by calculating the coordinates of each fitting circle through the circle packing problem'；

S6: calculating the inner diameter d of the housing (1) from d' and k _shell The calculation formula is as follows: d _shell ＝d’+k。

9. A method of designing a shell and tube thermal storage and heating apparatus according to claim 8, further comprising:

the aspect ratio AR is determined by the ratio of the length of the PCM tube to the outer diameter of the shell, and the size of the PCM tube and the size of the shell are adjusted according to the influence of the aspect ratio on the energy density.

10. A method of designing a shell and tube thermal storage and heating apparatus according to claim 9, further comprising:

the area of the PCM tube surface 1/3 was covered with an electrical heating tape.