Method for designing startup critical tube diameter of pulsating heat pipe in vertical state

Abstract

A method for designing startup critical tube diameter of pulsating heat pipe in vertical state, including the following steps: step 1. establishing a first model of working medium mass in pulsating heat pipe; step 2. establishing a second model of working medium mass in pulsating heat pipe, the second model including the vapor working medium mass model and the liquid working medium mass model in the pulsating heat pipe; step 3. according to the law of conservation of mass, combining the first model and the second model, and determining the volume percentage of the liquid working medium in the total length of the pulsating heat pipe under the condition of heat addition; step 4. determining the startup critical tube diameter of the pulsating heat pipe according to the volume percentage of the liquid working medium in the total length of the pulsating heat pipe under the condition of heat addition obtained in step 3, the physical properties of the working medium in the pulsating heat pipe, the temperatures at the heat-absorbing end and heat-releasing end, the heating power, and the filling factor.

Claims

1. A method for determining a startup critical diameter of a pulsating heat pipe in vertical state, wherein the pulsating heat pipe comprises a plurality of single pipes connected together to form a closed loop, and wherein the pulsating heat pipe comprises a channel that contains a working medium configured to absorb heat at a heat-absorbing end and to release heat at a heat-releasing end of the pulsating heat pipe, comprising: step 0: selecting the working medium for the pulsating heat pipe; step 1: establishing a first equation defining a relationship between a mass of the working medium in the pulsating heat pipe and a first set of parameters prior to being heated, wherein the first set of parameters comprises an effective length of the pulsating heat pipe, a cross-sectional area of the channel, a density of the working medium at an operating temperature, and a filling ratio of the working medium in the pulsating heat pipe; step 2: establishing a second equation defining the mass of working medium in the pulsating heat pipe when being heated to form a mixture of liquid and gaseous working medium, wherein the mass of the working medium is a sum of a mass of the gaseous working medium and a mass of the liquid working medium, wherein the mass of the gaseous working medium is a function of a second set of parameters of gaseous working medium when being heated, which comprises an average density of the gaseous working medium, a volume percentage of the gaseous working medium in the pulsating heat pipe, the effective length of the pulsating heat pipe, and the cross-sectional area of the channel, wherein the mass of the liquid working medium is a function of a third set of parameters of the liquid working medium when being heated, which comprises an average density of liquid working medium, a volume percentage of the liquid working medium in the pulsating heat pipe, the effective length of the pulsating heat pipe, and the cross-sectional area of the channel; step 3: assuming the mass of working medium prior to being heated and the mass of working medium when being heated are the same, calculating, based on the first equation and the second equation, the volume percentage of the liquid working medium in the pulsating heat pipe when being heated; and step 4: determining a startup critical diameter of the pulsating heat pipe using parameters comprising the volume percentage of the liquid working medium in the pulsating heat pipe when being heated, a plurality of physical properties of the working medium, a temperature at the heat-absorbing end, and a temperature at the heat-releasing end, a heating power that heats the pulsating heat pipe, and the filling ratio of the working medium in the pulsating heat pipe.

2. The method according to claim 1, wherein the first equation is
M=ΦLAρ.sub.L,0; wherein, M represents the mass of the working medium in the pulsating heat pipe prior to being heated, having a unit of kg; L represents the effective length of the pulsating heat pipe, having a unit of m; A represents the cross-sectional area of the channel, having a unit of m.sup.2; ρ.sub.L,0 represents the density of the working medium at an operating temperature prior to being heated, having a unit of kg/m.sup.3; and Φ represents the filling ratio of the working medium in the pulsating heat pipe, having a unit of %.

3. The method for according to claim 1, wherein the second equation is
M=M.sub.G,1+M.sub.L,1,
wherein:
M.sub.L,1=φALρ.sub.L,av, M.sub.G,1=(1−φ)ALρ.sub.G,av, M.sub.L,1 represents the mass of liquid working medium in one of the plurality of single pipes when being heated, having a unit of kg, M.sub.G,1 represents the mass of gaseous working medium in the one of the plurality of single pipe when being heated, having a unit of kg, ρ.sub.L,av represents the average density of the liquid working medium when being heated, having a unit of kg/m.sup.3, ρ.sub.G,av represents the average density of the gaseous working medium when being heated, having a unit of kg/m.sup.3, and φ represents the volume percentage of the liquid working medium in the pulsating heat pipe when being heated, having a unit of %.

4. The method according to claim 1, wherein $\phi =\frac{\Phi {\rho }_{L,0}-{\rho }_{G,\mathrm{av}}}{{\rho }_{L,\mathrm{av}}-{\rho }_{G,\mathrm{av}}};$ wherein φ represents the volume percentage of the liquid working medium in the pulsating heat pipe when being heated, having a unit of %.

5. The method according to claim 1, wherein the startup critical diameter of the pulsating heat pipe is D, and $$\begin{gathered} D={\left\{\frac{4p_{g}q}{u\pi h_c\left[\frac{\Phi }{\phi }{\rho }_{L,0}-{\rho }_{L,\mathrm{av}}\right]}\right\}}^{\frac{1}{2}}, \\ A=\frac{1}{4}\pi D^2,u={1.53\left[\frac{g\left(p_{L,\mathrm{av}}-p_{G,\mathrm{av}}\right){\sigma }_{\mathrm{av}}}{{\rho }_{L,\mathrm{av}}^2}\right]}^{\frac{1}{4}},q=\frac{Q}{t},t=\frac{\phi L}{u},p_g=\frac{{\stackrel{.}{m}}_G{h}_{c}t}{Q},{\stackrel{.}{m}}_{G}t=M_{G,1}=M-M_{L,1}=M-\mathrm{LA}{\mathrm{\phi \rho }}_{L,\mathrm{av}}, \end{gathered}$$ wherein: u represents a terminal velocity of a rising bubble relative to the liquid, having a unit of m/s, φ.sub.av represents a surface tension of the working medium, having a unit of N/m, g is the acceleration of gravity, having the unit of N/kg, t represents a time for a bubble moving from the heat-absorbing end to the heat-releasing end without taking into account an impact of a single bubble on a height of liquid level, Q represents a heat input during time t, having a unit of J, q represents an input of heating power, having a unit of J/s, {dot over (m)}.sub.G represents a mass flow of gaseous working medium, having a unit of kg/s, h.sub.c represents a latent heat of vaporization of the working medium at a temperature of the heat-absorbing end, having a unit of J/kg, and p.sub.g represents a proportion of the latent heat, having a unit of %.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) In order to illustrate more clearly the embodiments of the present disclosure or the technical solutions in the prior art, the drawings required in the description of the embodiments will be briefly introduced blow. Obviously, the drawings in the following descriptions are some embodiments of the present disclosure. For those of ordinary person skilled in the art, other drawings can be obtained based on these drawings without inventive effort.

(2) FIG. 1 is a schematic diagram of the forming process of the vapor plug in a pulsating heat pipe in the visualization experiment of the present disclosure.

(3) FIG. 2 is a schematic diagram of part A in FIG. 1, wherein (a) and (b) are the generating process of small bubbles, and (c), (d), (e) and (f) are the process of small bubbles coalesce and grow into large bubbles, (g) and (h) are the process of large bubbles continuously coalesce and grow into long columnar bubbles.

(4) FIG. 3 is a schematic diagram of the pulsating heat pipe at different states of the present disclosure, wherein (a) shows a distribution of working fluid before heating, (b) shows a bubble formed in the liquid after heating, and (c) shows the working condition that reaches the working state.

(5) FIG. 4 is a schematic diagram of the theoretical calculation results of startup critical tube diameter of the pulsating heat pipe when the working medium is anhydrous ethanol, wherein (a) and (b) are the calculation results respectively at 20° C. and 60° C. when the filling ratio is 30%, (c) and (d) are the calculation results respectively at 20° C. and 60° C. when the filling ratio is 50%, and (e) and (f) are the calculation results respectively at 20° C. and 60° C. when the filling ratio is 70%.

(6) FIG. 5 is a schematic diagram of the theoretical calculation results of startup critical tube diameter of the pulsating heat pipe when the working medium is deionized water, wherein (a) and (b) are the calculation results respectively at 20° C. and 60° C. when the filling ratio is 30%, (c) and (d) are the calculation results respectively at 20° C. and 60° C. when the filling ratio is 50%, and (e) and (f) are the calculation results respectively at 20° C. and 60° C. when the filling ratio is 70%.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

(7) In order to make those of ordinary person skilled in the art better understand the technical solutions of the present disclosure, a clear and complete description in the embodiments of the present disclosure may be given herein after in combination with the accompany drawings in the embodiments of the present disclosure. Obviously, the described embodiments are parts of the present disclosure, but not all of them. Based on the embodiments in the present disclosure, all other embodiments obtained by those of ordinary person skilled in the art without inventive effort are within the protection scope of the present disclosure.

(8) The technical terms used in following embodiments are described below:

(9) The equation of startup critical tube diameter: refers to the calculation equation of startup critical tube diameter of pulsating heat pipe obtained according to the method for designing startup critical tube diameter of pulsating heat pipe in vertical state in the present disclosure;

(10) $D={\left\{\frac{4p_{g}q}{u\pi h_c\left[\frac{\Phi }{\phi }{\rho }_{L,0}-{\rho }_{L,\mathrm{av}}\right]}\right\}}^{\frac{1}{2}};$

(11) For the induction process of the equation and the definition of each parameter in the equation, please refer to the summary of the invention, which will not be repeated here.

(12) The calculation equation of maximum hydraulic diameter: refers to the maximum diameter of the liquid slug formed automatically by the working medium in the pipe depending on its own surface tension without external input power in the pulsating heat pipe. Its definition equation is as follows:

(13) $D_{\mathrm{cl}}=2\sqrt{\frac{{\sigma }_{0}Bo}{g\left({\rho }_{l,0}-{\rho }_{v,0}\right)}}$

(14) wherein, D.sub.cl represents the maximum hydraulic diameter, Bo is the Bond number, generally set at 0.85, g is the acceleration of gravity, ρ.sub.l,0 and ρ.sub.v,0 respectively represent the densities of liquid and vapor phases at operating temperature, and σ.sub.0 represents the surface tension at operating temperature.

(15) In the following embodiments, those of person skilled in the art can directly calculate the startup critical tube diameter and the maximum hydraulic diameter under the corresponding conditions according to the given operating temperature, working medium, and the above calculation equations of startup critical tube diameter and maximum hydraulics diameter.

Embodiment 1

(16) FIG. 1 and FIG. 2 are schematic diagrams of the forming process of the vapor plug in the visualization experiment of the supercritical tube diameter pulsating heat pipe. The reason for the operation of the supercritical tube diameter pulsating heat pipe is the formation of the vapor plug. According to the experimental results, when the pipe diameter of the pulsating heat pipe exceeds the maximum hydraulic diameter, the vapor plug is formed in the working process, which includes the following processes: (1) generation of small bubbles, as shown in pictures (a) and (b) in FIG. 2; (2) small bubbles coalesce and grow into large bubbles (the diameter of the bubble is smaller than the pipe diameter), as shown pictures (c), (d), (e) and (f) in FIG. 2; (3) large bubbles continuously coalesce and growth into long columnar bubbles (forming vapor plug), as shown in pictures (g) and (h) in FIG. 2.

(17) FIG. 3 is a schematic diagram of the pulsating heat pipe at different states. Before heat addition, ignoring the vapor mass produced by vaporization after the working medium is charged, and the charged working medium in each pipe of the pulsating heat pipe is evenly distributed with a same liquid level height ΦL, ignoring the influence of the turn on the liquid level height, as shown in picture (a) in FIG. 3; after heat addition, the working medium in the pulsating heat pipe is in a vapor-liquid mixed state, the liquid level height of the working medium is φL in this condition and increases gradually, as shown in picture (b) in FIG. 3; when the liquid level of the vapor-liquid mixed working medium after heat addition reaches the effective length L, the pulsating heat pipe is in a normal working state, as shown in picture (c) in FIG. 3.

Embodiment 2

(18) The working condition of this embodiment was that the input power of a single pipe was 30 W, the operating temperature was 20° C., the working medium was anhydrous ethanol, the filling ratio was 30%, and the temperature at the heat-absorbing end was respectively 30° C., 50° C., 70° C. and 90° C.

(19) In MATLAB software, under the working condition, the parameters of working medium property, operating temperature, heating power, and filling ratio were substituted into the equation of startup critical tube diameter to obtain the theoretical calculation results of startup critical tube diameter of the pulsating heat pipe and the schematic diagram thereof, as shown in picture (a) in FIG. 4, wherein ET represents the temperature at the heat-absorbing end, and CT represents the operating temperature; and the transverse line represents the calculation results of the maximum hydraulic diameter obtained by the calculation equation of the maximum hydraulic diameter, which is only related to the operating temperature. The corresponding critical tube diameter and startup critical tube diameter under the working condition are shown in Table 1.

(20) TABLE-US-00001 TABLE 1 The corresponding maximum hydraulic diameter and startup critical tube diameter under the working condition Heat- Startup absorbing Maximum critical Filling Input Operating end hydraulic tube Working ratio power temperature temperature diameter diameter medium (%) (W) (° C.) (° C.) (mm) (mm) Anhydrous 30 30 20 30 3.13 8.18473846 ethanol 50 3.13 5.79946108 70 3.13 4.06703996 90 3.13 2.91531718

Embodiment 3

(21) The working condition of this embodiment was that the input power of a single pipe was 30 W, the operating temperature was 20° C., the working medium was anhydrous ethanol, the filling ratio was 50%, and the temperature at the heat-absorbing end was respectively 30° C., 50° C., 70° C. and 90° C.

(22) In MATLAB software, under the working condition, the parameters of working medium property, operating temperature, heating power, and filling ratio were substituted into the equation of startup critical tube diameter to obtain the theoretical calculation results of startup critical tube diameter of the pulsating heat pipe and the schematic diagram thereof, as shown in picture (c) in FIG. 4, wherein ET represents the temperature at the heat-absorbing end, and CT represents the operating temperature; and the transverse line represents the calculation results of the maximum hydraulic diameter obtained by the calculation equation of the maximum hydraulic diameter, which is only related to the operating temperature. The corresponding maximum hydraulic diameter and startup critical tube diameter under the working condition are shown in Table 2.

(23) TABLE-US-00002 TABLE 2 The corresponding maximum hydraulic diameter and startup critical tube diameter under this condition Heat- Startup absorbing Maximum critical Filling Input Operating end hydraulic tube Working ratio power temperature temperature diameter diameter medium (%) (W) (° C.) (° C.) (mm) (mm) Anhydrous 50 30 20 30 3.13 12.5233213 ethanol 50 3.13 8.90425616 70 3.13 6.26929407 90 3.13 4.51537807

Embodiment 4

(24) The working condition of this embodiment was that the input power of a single pipe was 30 W, the operating temperature was 20° C., the working medium was anhydrous ethanol, the filling ratio was 70%, and the temperature at the heat-absorbing end was respectively 30° C., 50° C., 70° C. and 90° C.

(25) In MATLAB software, under the working condition, the parameters of working medium property, operating temperature, heating power, and filling ratio were substituted into the equation of startup critical tube diameter to obtain the theoretical calculation results of startup critical tube diameter of the pulsating heat pipe and the schematic diagram thereof, as shown in picture (e) in FIG. 4, wherein ET represents the temperature at the heat-absorbing end, and CT represents the operating temperature; and the transverse line represents the calculation results of the maximum hydraulic diameter obtained by the calculation equation of the maximum hydraulic diameter, which is only related to the operating temperature. The corresponding maximum hydraulic diameter and startup critical tube diameter under the working condition are shown in Table 3.

(26) TABLE-US-00003 TABLE 3 The corresponding maximum hydraulic diameter and startup critical tube diameter under the working condition Heat- Startup absorbing Maximum critical Filling Input Operating end hydraulic tube Working ratio power temperature temperature diameter diameter medium (%) (W) (° C.) (° C.) (mm) (mm) Anhydrous 70 30 20 30 3.13 19.2001081 ethanol 50 3.13 13.760411 70 3.13 9.77739743 90 3.13 7.11840283

Embodiment 5

(27) The working condition of this embodiment was that the input power of a single pipe was 30 W, the operating temperature was 60° C., the working medium was anhydrous ethanol, the filling ratio was 30%, and the temperatures at the heat-absorbing end was respectively 70° C., 90° C., 110° C. and 130° C.

(28) In MATLAB software, under the working condition, the parameters of working medium property, operating temperature, heating power, and filling ratio were substituted into the equation of startup critical tube diameter to obtain the theoretical calculation results of startup critical tube diameter of the pulsating heat pipe and the schematic diagram thereof, as shown in picture (b) in FIG. 4, wherein ET represents the temperature at the heat-absorbing end, and CT represents the operating temperature; and the transverse line represents the calculation results of the maximum hydraulic diameter obtained by the calculation equation of the maximum hydraulic diameter, which is only related to the operating temperature. The corresponding maximum hydraulic diameter and startup critical tube diameter under this condition are shown in Table 4.

(29) TABLE-US-00004 TABLE 4 The corresponding maximum hydraulic diameter and startup critical tube diameter under the working condition Heat- Startup absorbing Maximum critical Filling Input Operating end hydraulic tube Working ratio power temperature temperature diameter diameter medium (%) (W) (° C.) (° C.) (mm) (mm) Anhydrous 30 30 60 70 2.83 3.376928 ethanol 90 2.83 2.663269 110 2.83 2.073034 130 2.83 1.620994

Embodiment 6

(30) The working condition of this embodiment was that the input power of a single pipe was 30 W, the operating temperature was 60° C., the working medium was anhydrous ethanol, the filling ratio was 50%, and the temperature at the heat-absorbing end was respectively 70° C., 90° C., 110° C. and 130° C.

(31) In MATLAB software, under the working condition, the parameters of working medium property, operating temperature, heating power, and filling ratio were substituted into the equation of startup critical tube diameter to obtain the theoretical calculation results of startup critical tube diameter of the pulsating heat pipe and the schematic diagram thereof, as shown in picture (d) in FIG. 4, wherein ET represents the temperature at the heat-absorbing end, and CT represents the operating temperature; and the transverse line represents the calculation results of the maximum hydraulic diameter obtained by the calculation equation of the maximum hydraulic diameter, which is only related to the operating temperature. The corresponding maximum hydraulic diameter and startup critical tube diameter under the working condition are shown in Table 5.

(32) TABLE-US-00005 TABLE 5 The corresponding maximum hydraulic diameter and startup critical tube diameter under the working condition Heat- Startup absorbing Maximum critical Filling Input Operating end hydraulic tube Working ratio power temperature temperature diameter diameter medium (%) (W) (° C.) (° C.) (mm) (mm) Anhydrous 50 30 60 70 2.83 5.172435 ethanol 90 2.83 4.098364 110 2.83 3.208506 130 2.83 2.527283

Embodiment 7

(33) The working condition of this embodiment was that the input power of a single pipe was 30 W, the operating temperature was 60° C., the working medium was anhydrous ethanol, the filling ratio was 70%, and the temperature at the heat-absorbing end was respectively 70° C., 90° C., 110° C. and 130° C.

(34) In MATLAB software, under the working condition, the parameters of working medium property, operating temperature, heating power, and filling ratio were substituted into the equation of startup critical tube diameter to obtain the theoretical calculation results of startup critical tube diameter of pulsating heat pipe and the schematic diagram thereof, as shown in picture (f) in FIG. 4, wherein ET represents the temperature at the heat-absorbing end, and CT represents the operating temperature; and the transverse line represents the calculation results of the maximum hydraulic diameter obtained by the calculation equation of the maximum hydraulic diameter, which is only related to the operating temperature. The corresponding maximum hydraulic diameter and startup critical tube diameter under the working condition are shown in Table 6.

(35) TABLE-US-00006 TABLE 6 The corresponding maximum hydraulic diameter and startup critical tube diameter under the working condition Heat- Startup absorbing Maximum critical Filling Input Operating end hydraulic tube Working ratio power temperature temperature diameter diameter medium (%) (W) (° C.) (° C.) (mm) (mm) Anhydrous 70 30 60 70 2.83 7.93828 ethanol 90 2.83 6.353064 110 2.83 5.034048 130 2.83 4.024905

Embodiment 8

(36) The working condition of this embodiment was that the input power of a single pipe was 30 W, the operating temperature was 20° C., the working medium was deionized water, the filling ratio was 30%, and the temperature at the heat-absorbing end was respectively 30° C., 50° C., 70° C. and 90° C.

(37) In MATLAB software, under the working condition, the parameters of working medium property, operating temperature, heating power, and filling ratio were substituted into the equation of startup critical tube diameter to obtain the theoretical calculation results of startup critical tube diameter of pulsating heat pipe and the schematic diagram thereof, as shown in picture (a) in FIG. 5, wherein ET represents the temperature at the heat-absorbing end, and CT represents the operating temperature; and the transverse line represents the calculation results of the maximum hydraulic diameter obtained by the calculation equation of the maximum hydraulic diameter, which is only related to the operating temperature. The corresponding maximum hydraulic diameter and startup critical tube diameter under the working condition are shown in Table 7.

(38) TABLE-US-00007 TABLE 7 The corresponding maximum hydraulic diameter and startup critical tube diameter under the working condition Heat- Startup absorbing Maximum critical Filling Input Operating end hydraulic tube Working ratio power temperature temperature diameter diameter medium (%) (W) (° C.) (° C.) (mm) (mm) Deionized 30 30 20 30 3.13 11.2786993 water 50 3.13 7.81365013 70 3.13 5.36450771 90 3.13 3.77741972

Embodiment 9

(39) The working condition of this embodiment was that the input power of a single pipe was 30 W, the operating temperature was 20° C., the working medium was deionized water, the filling ratio was 50%, and the temperature at the heat-absorbing end was respectively 30° C., 50° C., 70° C. and 90° C.

(40) In MATLAB software, under the working condition, the parameters of working medium property, operating temperature, heating power, and filling ratio were substituted into the equation of startup critical tube diameter to obtain the theoretical calculation results of startup critical tube diameter of the pulsating heat pipe and the schematic diagram thereof, as shown in picture (c) in FIG. 5, wherein ET represents the temperature at the absorption end, and CT represents the operating temperature; and the transverse line represents the calculation results of the maximum hydraulic diameter obtained by the calculation equation of the maximum hydraulic diameter, which is only related to the operating temperature. The corresponding maximum hydraulic diameter and startup critical tube diameter under the working condition are shown in Table 8.

(41) TABLE-US-00008 TABLE 8 The corresponding maximum hydraulic diameter and startup critical tube diameter under the working condition Heat- Startup absorbing Maximum critical Filling Input Operating end hydraulic tube Working ratio power temperature temperature diameter diameter medium (%) (W) (° C.) (° C.) (mm) (mm) Deionized 50 30 20 30 3.13 17.2350751 water 50 3.13 11.9534699 70 3.13 8.21943756 90 3.13 5.79895111

Embodiment 10

(42) The working condition of this embodiment was that the input power of a single pipe was 30 W, the operating temperature was 20° C., the working medium was deionized water, the filling ratio was 70%, and the temperature at the heat-absorbing end was respectively 30° C., 50° C., 70° C. and 90° C.

(43) In MATLAB software, under the working condition, the parameters of working medium property, operating temperature, heating power, and filling ratio were substituted into the equation of startup critical tube diameter to obtain the theoretical calculation results of startup critical tube diameter of the pulsating heat pipe and the schematic diagram thereof, as shown in picture (e) in FIG. 5, wherein ET represents the temperature at the absorption end, and CT represents the operating temperature; and the transverse line represents the calculation results of the maximum hydraulic diameter obtained by the calculation equation of the maximum hydraulic diameter, which is only related to the operating temperature. The corresponding maximum hydraulic diameter and startup critical tube diameter under the working condition are shown in Table 9.

(44) TABLE-US-00009 TABLE 9 The corresponding maximum hydraulic diameter and startup critical tube diameter under the working condition Heat- Startup absorbing Maximum critical Filling Input Operating end hydraulic tube Working ratio power temperature temperature diameter diameter medium (%) (W) (° C.) (° C.) (mm) (mm) Deionized 70 30 20 30 3.13 26.3496976 water 50 3.13 18.322403 70 3.13 12.6441629 90 3.13 8.96086689

Embodiment 11

(45) The working condition of this embodiment was that the input power of a single pipe was 30 W, the operating temperature was 60° C., the working medium was deionized water, the filling ratio was 30%, and the temperature at the heat-absorbing end was respectively 70° C., 90° C., 110° C. and 130° C.

(46) In MATLAB software, under the working condition, the parameters of working medium property, operating temperature, heating power, and filling ratio were substituted into the equation of startup critical tube diameter to obtain the theoretical calculation results of startup critical tube diameter of the pulsating heat pipe and the schematic diagram thereof, as shown in picture (b) in FIG. 5, wherein ET represents the temperature at the absorption end, and CT represents the operating temperature; and the transverse line represents the calculation results of the maximum hydraulic diameter obtained by the calculation equation of the maximum hydraulic diameter, which is only related to the operating temperature. The corresponding maximum hydraulic diameter and startup critical tube diameter under the working condition are shown in Table 10.

(47) TABLE-US-00010 TABLE 10 The corresponding maximum hydraulic diameter and startup critical tube diameter under the working condition Heat- Startup absorbing Maximum critical Filling Input Operating end hydraulic tube Working ratio power temperature temperature diameter diameter medium (%) (W) (° C.) (° C.) (mm) (mm) Deionized 30 30 60 70 2.83 4.430809 water 90 2.83 3.437193 110 2.83 2.636271 130 2.83 2.03948

Embodiment 12

(48) The working condition of this embodiment was that the input power of a single pipe was 30 W, the operating temperature was 60° C., the working medium was deionized water, the filling ratio was 50%, and the temperature at the heat-absorbing end was respectively 70° C., 90° C., 110° C. and 130° C.

(49) In MATLAB software, under the working condition, the parameters of working medium property, operating temperature, heating power, and filling ratio were substituted into the equation of startup critical tube diameter to obtain the theoretical calculation results of startup critical tube diameter of the pulsating heat pipe and the schematic diagram thereof, as shown in picture (d) in FIG. 5, wherein ET represents the temperature at the absorption end, and CT represents the operating temperature; and the transverse line represents the calculation results of the maximum hydraulic diameter obtained by the calculation equation of the maximum hydraulic diameter, which is only related to the operating temperature. The corresponding maximum hydraulic diameter and startup critical tube diameter under the working condition are shown in Table 11.

(50) TABLE-US-00011 TABLE 11 The corresponding maximum hydraulic diameter and startup critical tube diameter under the working condition Heat- Startup absorbing Maximum critical Filling Input Operating end hydraulic tube Working ratio power temperature temperature diameter diameter medium (%) (W) (° C.) (° C.) (mm) (mm) Deionized 50 30 60 70 2.83 6.774296 water 90 2.83 5.265249 110 2.83 4.047725 130 2.83 3.140018

Embodiment 13

(51) The working condition of this embodiment was that the input power of a single pipe was 30 W, the operating temperature was 60° C., the working medium was deionized water, the filling ratio was 70%, and the temperature at the heat-absorbing end was respectively 70° C. 90° C., 110° C. and 130° C.

(52) In MATLAB software, under the working condition, the parameters of working medium property, operating temperature, heating power, and filling ratio were substituted into the equation of startup critical tube diameter to obtain the theoretical calculation results of startup critical tube diameter of the pulsating heat pipe and the schematic diagram thereof, as shown in picture (f) in FIG. 5, wherein ET represents the temperature at the absorption end, and CT represents the operating temperature; and the transverse line represents the calculation results of the maximum hydraulic diameter obtained by the calculation equation of the maximum hydraulic diameter, which is only related to the operating temperature. The corresponding maximum hydraulic diameter and startup critical tube diameter under the working condition are shown in Table 12.

(53) TABLE-US-00012 TABLE 12 The corresponding maximum hydraulic diameter and startup critical tube diameter under the working condition Heat- Startup absorbing Maximum critical Filling Input Operating end hydraulic tube Working ratio power temperature temperature diameter diameter medium (%) (W) (° C.) (° C.) (mm) (mm) Deionized 70 30 60 70 2.83 10.36761 water 90 2.83 8.093519 110 2.83 6.254887 130 2.83 4.882471

Embodiment 14

(54) As shown in FIG. 4, according to the calculation results of pictures (a) to (f) in FIG. 4 (i.e., Embodiment 2 to 7), it can be seen that, under the same condition, the calculated value of the pipe diameter obtained by the equation of the startup critical tube diameter in the present disclosure is higher than that of the pipe diameter obtained by the equation of the maximum hydraulic diameter of the pulsating heat pipe. By comparing the calculation results of picture (a) and (b) in FIG. 4 (i.e., Embodiments 2 and 5), or pictures (c) and (d) in FIG. 4 (i.e., Embodiments 3 and 6), or pictures (e) and (f) in FIG. 4 (i.e., Embodiments 4 and 7), it can be seen that, under the same working condition of working medium, filling ratio, and heat-absorbing end temperature, the lower the operating temperature, the larger the pipe diameter of the pulsating heat pipe. According to the calculation results of any one of pictures (a) to (f) in FIG. 4 (i.e., Embodiments 2 to 7), it can be seen that, under the same working condition of heating power, working medium, filling ratio, and operating temperature, the lower the temperature at the hot end and the lower the temperature difference between the cold and hot end, the larger the pipe diameter of the pulsating heat pipe. By comparing the calculation results of pictures (a), (c) and (e) in FIG. 4 (i.e., Embodiments 2, 3 and 4), or pictures (b), (d) and (f) in FIG. 4 (i.e., Embodiments 5, 6 and 7), it can be seen that under the same working condition of heating power, working medium, hot end temperature, and operating temperature, the higher the filling ratio, the larger the pipe diameter of the pulsating heat pipe.

(55) As shown in FIG. 5, according to the calculation results of pictures (a) to (f) in FIG. 5 (i.e., Embodiment 8 to 13), it can be seen that, when the working medium of the pulsating heat pipe was deionized water, the change rules of the hot and cold end temperatures, filling ratio, operating temperature, and heating power was the same as that of FIG. 4 which the working medium was anhydrous ethanol. By comparing the calculation results in FIG. 5 and FIG. 4, it can be seen that under the same working conditions of cold end temperature, filling ratio, operating temperature, and heating power, the startup critical tube diameter calculated with the working medium of deionized water is larger than the startup critical tube diameter calculated with the working medium of anhydrous ethanol. Therefore, the property of the working medium is one of the important factors affecting the startup critical tube diameter of the pulsating heat pipe.

(56) In conclusion, the pulsating heat pipe can still work when the pipe diameter exceeds the maximum hydraulic diameter, and the heat transfer performance is excellent.

(57) Finally, it should be stated that the above embodiments are only used to illustrate the technical solutions of the present disclosure without limitation; and despite reference to the aforementioned embodiments to make a detailed description of the present disclosure, those of ordinary skilled in the art should understand that the described technical solutions in above various embodiments may be modified or the part of or all technical features may be equivalently substituted; while these modifications or substitutions do not make the essence of their corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present disclosure.