High-temperature pulsating heat pipe liquid bomb pulsation and heat transfer calculation method

Abstract

The invention relates to a high-temperature pulsating heat pipe liquid bomb pulsation and heat transfer calculation method which comprises the following steps: S1, establishing a pulsating heat pipe model, and determining the temperatures of a working medium, an evaporation section and a condensation section in a heat pipe; s2, the initial liquid film thickness and the initial vapor bomb temperature of the pulsating heat pipe model are determined; s3, calculating the temperature of the liquid bomb according to the temperatures of the evaporation section and the condensation section; s4, calculating initial bomb pressure according to the initial bomb temperature, calculating liquid bomb displacement according to the initial bomb pressure, and calculating bomb pressure; s5, calculating the temperature of the steam bomb according to the pressure of the steam bomb, comparing the temperature of the steam bomb with the initial temperature of the steam bomb, and if not, returning to S2; s2, liquid bomb temperature distribution is updated according to the steam bomb temperature, the theoretical thickness of the liquid film is calculated, the theoretical thickness of the liquid film is compared with the initial thickness of the liquid film, if the difference value meets a second relative error, the step S7 is executed, and if the difference value does not meet the second relative error, the step S2 is executed; and S7, calculating sensible heat and flow heat resistance transmitted in and out of the liquid bomb according to the displacement of the liquid bomb.

Description

Technical Field

[0001] The invention relates to the technical field of phase change heat transfer equipment, and in particular to a high-temperature pulsating heat pipe liquid-elastic pulsation and heat transfer calculation method. Background Art

[0002] With the development of science and technology, the local heat flux density of components is gradually increasing, which brings with it many problems such as reduced service life, performance degradation, and low energy conversion rate. Therefore, the demand for efficient heat dissipation materials is increasing. As an efficient heat dissipation device, the pulsating heat pipe couples two heat transfer methods: phase change heat transfer and oscillating motion sensible heat transfer in micro channels. It utilizes the phase change process of the internal working medium and the vapor pressure difference generated by the latent heat transfer between the evaporation end and the condensation end to drive the liquid bullet to oscillate in the channel. It is a heat pipe with high thermal conductivity.

[0003] When the pulsating heat pipe works normally, it is accompanied by strong reciprocating oscillations of gas and liquid. In this phase change model, the flow and heat transfer phenomena are extremely complex. The determination of the evaporation and condensation coefficients lacks a clear theoretical basis, which increases the uncertainty of the calculated heat transfer coefficient and makes it difficult for theoretical research to fully explain its mechanism. In particular, the phenomena observed in the experiment cannot be fully explained by theory, which hinders further understanding of the heat transfer performance of the pulsating heat pipe. Summary of the invention

[0004] The purpose of the present invention is to provide a high-temperature pulsating heat pipe liquid-elastic pulsation and heat transfer calculation method, which can be applied to different evaporation section and condensation section temperatures, different pulsating heat pipe scales and different working fluid working conditions, and has wide applicability.

[0005] To achieve the above object, the present invention provides the following solutions:

[0006] A high-temperature pulsating heat pipe liquid-elastic pulsation and heat transfer calculation method, comprising:

[0007] S1. Establish a pulsating heat pipe model and determine the working fluid, evaporation section and condensation section temperatures in the heat pipe;

[0008] S2. Determine the initial liquid film thickness and initial steam bomb temperature of the pulsating heat pipe model;

[0009] S3. Calculate the liquid bomb temperature according to the evaporation section and condensation section temperature;

[0010] S4. Calculate the initial steam bomb pressure according to the initial steam bomb temperature, calculate the liquid bomb displacement according to the initial steam bomb pressure, obtain the steam mass change based on the liquid bomb displacement, and calculate the steam bomb pressure according to the steam mass change;

[0011] S5. Calculate the steam bomb temperature according to the steam bomb pressure, compare the steam bomb temperature with the initial steam bomb temperature, and if the difference satisfies the first relative error, proceed to step S5; if not, return to S2 to determine the initial steam bomb temperature;

[0012] S6. Update the liquid bomb temperature distribution according to the steam bomb temperature and calculate the theoretical thickness of the liquid film, compare the theoretical thickness of the liquid film with the initial liquid film thickness, and if the difference satisfies the second relative error, proceed to step S7; if not, return to S2 to determine the initial liquid film thickness;

[0013] S7. Calculate the sensible heat transferred into and out of the liquid bomb according to the displacement of the liquid bomb and the temperatures of the evaporation section and the condensation section, and calculate the flow thermal resistance of the pulsating heat pipe.

[0014] Optionally, calculating the liquid bomb temperature according to the temperatures of the evaporation section and the condensation section in S3 includes:

[0015] A liquid-bomb energy equation is constructed, and the liquid-bomb temperature in the liquid-bomb energy equation is solved according to a finite difference format of initial conditions and gas-liquid interface boundary conditions to obtain the liquid-bomb temperature, wherein the liquid-bomb energy equation is related to the wall temperature, and the wall temperature is obtained according to the temperatures of the evaporation section and the condensation section.

[0016] Optionally, calculating the liquid elastic displacement according to the initial steam elastic pressure in S4 includes:

[0017] A momentum equation of the liquid bomb is constructed based on the current gas bomb pressure, and the liquid bomb displacement is calculated based on the momentum equation of the liquid bomb, wherein the momentum equation of the liquid bomb is the relationship between momentum change and pressure, gravity and shear stress.

[0018] Optionally, in S4, obtaining a steam mass change based on the liquid bomb displacement, and calculating the steam bomb pressure according to the steam mass change includes:

[0019] According to the thickness of the thin liquid film deposited in the tube, the heat transfer coefficient of the liquid film on the wall is calculated;

[0020] Calculate the phase change heat transfer coefficient of condensation or evaporation at the gas-liquid interface based on the specific volume difference between steam and liquid;

[0021] Obtaining a total heat transfer coefficient according to the heat transfer coefficient of the wall liquid film and the phase change heat transfer coefficient;

[0022] According to the liquid-elastic displacement, the liquid film length of the condensation section and the liquid film length of the evaporation section are obtained; according to the total heat transfer coefficient, the liquid film length, the steam-elastic temperature, and the temperatures of the evaporation section and the condensation section, the latent heat of evaporation and the latent heat of condensation are calculated, and the rate of change of the steam mass caused by evaporation and condensation is calculated through the latent heat of evaporation, the latent heat of condensation, and the liquid-elastic displacement;

[0023] According to the steam mass change rate and the first law of thermodynamics, an energy equation of the steam bomb is constructed to calculate the steam bomb pressure.

[0024] Optionally, the energy equation of the gas bomb is:

[0025]

[0026] Among them, m v1 、m v2 is the mass of the steam bombs on the left and right sides, c p is the constant-pressure molar heat capacity of the working fluid, T v1 and T v2 is the steam bomb temperature, P v1 and P v2 are the steam pressure on the left and the steam bomb pressure on the right, d is the diameter of the heat pipe, x p is the liquid-elastic displacement, c v is the constant volume molar heat capacity of the working fluid.

[0027] Optionally, updating the liquid bomb temperature distribution and calculating the liquid film theoretical thickness according to the steam bomb temperature in S6 includes:

[0028] updating the heat transfer coefficient of the wall liquid film according to the changes in density, viscosity and specific heat capacity caused by the temperature of the steam bomb;

[0029] updating the phase change heat transfer coefficient according to changes in the liquid bomb temperature and the specific volume difference between the steam and the liquid;

[0030] According to the heat transfer coefficient of the wall liquid film and the phase change heat transfer coefficient, the gas-liquid interface condition is updated and the liquid bomb temperature distribution is calculated. According to the liquid bomb temperature distribution, the average temperature and average velocity of the liquid bomb are obtained, and the theoretical thickness of the liquid film is calculated.

[0031] Optionally, the calculation method of the sensible heat transmitted by the liquid bomb in S7 is:

[0032]

[0033] The calculation method of the sensible heat transmitted by the liquid bomb is:

[0034]

[0035] Among them, Q h is the sensible heat transferred by the liquid bomb, L p is the length of the liquid bullet, x p is the displacement of the liquid bomb, h sen is the convective heat transfer coefficient, T l,i is the liquid bomb temperature, T c is the condensation temperature, x1 is the liquid bomb position, x p is the liquid-elastic displacement, Qc is the sensible heat transferred by the liquid bullet.

[0036] Optionally, the method for calculating the flow thermal resistance of the pulsating heat pipe in S7 is:

[0037]

[0038] Where R is the thermal resistance, T e is the evaporation temperature, is the average sensible heat, is the average latent heat, Q c is the average sensible heat transferred by the liquid bomb, Q h is the average sensible heat transferred by the liquid bomb, Q cond is the average condensation heat, Q evp is the average heat of evaporation.

[0039] The beneficial effects of the present invention are as follows: 1) Through heat transfer analysis, the internal flow heat transfer model of the heat pipe is reasonably simplified while ensuring the model calculation speed and accuracy. The iteration process is simple and has good convergence. By iterating the temperature of the steam bomb on the left and right sides of the pulsating heat pipe, the wall liquid film heat transfer coefficient and the phase change heat transfer coefficient can be calculated more accurately, and then the heat transfer rate can be predicted;

[0040] (2) The present invention can calculate the motion state of the working fluid in the pulsating heat pipe, including the temperature distribution and velocity distribution of the working fluid;

[0041] (3) The output can obtain simpler and clearer result diagrams and actual motion diagrams, which can provide design ideas and data references for the design of high-temperature pulsating heat pipes that can select new high-temperature working fluids and other conventional working fluids.

[0042] (4) It can be applied to pulsating heat pipes under different evaporation and condensation section temperatures, different pulsating heat pipe scales, and different working fluid conditions, and has wide applicability.

[0043] (5) The liquid film thickness is calculated by the average temperature and average velocity of the liquid bomb, and compared with the initial liquid film thickness and continuously corrected to obtain the accurate liquid film thickness, thereby more accurately calculating the wall liquid film heat transfer coefficient. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0045] Figure 1The present invention is a flowchart of a high-temperature pulsating heat pipe liquid-elastic pulsation and heat transfer calculation method according to an embodiment of the present invention. DETAILED DESCRIPTION

[0046] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0047] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0048] When the working fluid is liquid metal, the thermal resistance is mainly concentrated in the wall liquid film, and the temperature of the gas-liquid interface is approximately equal to the temperature of the steam. At this time, by calculating the heat transfer coefficient of the wall liquid film and the phase change heat transfer coefficient of condensation or evaporation of the gas-liquid interface, it is more convenient to calculate the evaporation and condensation heat transfer. In addition, the study of liquid elastic pulsation phenomenon includes the analysis of the start-up performance, heat transfer performance and heat transfer limit of the pulsating heat pipe. These performance indicators are crucial for the practical application of pulsating heat pipes.

[0049] This embodiment provides a high-temperature pulsating heat pipe liquid-elastic pulsation and heat transfer calculation method, including:

[0050] S1. Establish a pulsating heat pipe model and determine the working fluid, evaporation section and condensation section temperatures in the heat pipe;

[0051] S2. Determine the initial liquid film thickness and initial steam bomb temperature of the pulsating heat pipe model;

[0052] S3. Calculate the liquid bomb temperature according to the evaporation section and condensation section temperature;

[0053] S4. Calculate the initial steam bomb pressure according to the initial steam bomb temperature, calculate the liquid bomb displacement according to the initial steam bomb pressure, obtain the steam mass change based on the liquid bomb displacement, and calculate the steam bomb pressure according to the steam mass change;

[0054] S5. Calculate the steam bomb temperature according to the steam bomb pressure, compare the steam bomb temperature with the initial steam bomb temperature, and if the difference satisfies the first relative error, proceed to step S5; if not, return to S2 to determine the initial steam bomb temperature;

[0055] S6. Update the liquid bomb temperature distribution according to the steam bomb temperature and calculate the theoretical thickness of the liquid film, compare the theoretical thickness of the liquid film with the initial liquid film thickness, and if the difference satisfies the second relative error, proceed to step S7; if not, return to S2 to determine the initial liquid film thickness;

[0056] S7. Calculate the sensible heat transferred into and out of the liquid bomb according to the displacement of the liquid bomb and the temperatures of the evaporation section and the condensation section, and calculate the flow thermal resistance of the pulsating heat pipe.

[0057] Furthermore, in S3, the temperature of the liquid bomb is calculated according to the temperature of the evaporation section and the condensation section, including:

[0058] A liquid bomb energy equation is constructed, and the liquid bomb temperature in the liquid bomb energy equation is solved according to the finite difference format of the initial conditions and the gas-liquid interface boundary conditions to obtain the liquid bomb temperature, wherein the liquid bomb energy equation is related to the wall temperature, and the wall temperature is obtained according to the temperatures of the evaporation section and the condensation section; the liquid bomb energy equation is shown in formula (1).

[0059] Specifically, this embodiment uses the liquid-bomb energy equation shown in formula (1) to derive the temperature distribution in the liquid bomb, and solves the liquid-bomb temperature T in (1) using the finite difference format of the corresponding initial condition (2) and the gas-liquid interface boundary condition formulas (3) and (4). l :.

[0060] Further, calculating the liquid elastic displacement according to the initial steam elastic pressure in S4 includes:

[0061] The momentum equation of the liquid bomb is constructed based on the current steam bomb pressure, and the displacement of the liquid bomb is calculated based on the momentum equation of the liquid bomb, wherein the momentum equation of the liquid bomb is the relationship between the momentum change and the pressure, gravity and shear stress.

[0062] Specifically, the momentum equation of the liquid bomb is constructed to calculate the displacement of the liquid bomb; the term on the left of the momentum equation of the liquid bomb represents the change in momentum, and the terms on the right represent the pressure term, gravity term, and shear stress term, respectively. The momentum equation of the liquid bomb is shown in formula (11).

[0063] Further, in S4, obtaining the steam mass change based on the liquid bomb displacement, and calculating the steam bomb pressure according to the steam mass change includes:

[0064] According to the thickness of the thin liquid film deposited in the tube, the heat transfer coefficient of the liquid film on the wall is calculated;

[0065] Calculate the phase change heat transfer coefficient of condensation or evaporation at the gas-liquid interface based on the specific volume difference between steam and liquid;

[0066] Obtaining a total heat transfer coefficient according to the heat transfer coefficient of the wall liquid film and the phase change heat transfer coefficient;

[0067] According to the liquid-elastic displacement, the liquid film length of the condensation section and the liquid film length of the evaporation section are obtained; according to the total heat transfer coefficient, the liquid film length, the steam-elastic temperature, and the temperatures of the evaporation section and the condensation section, the latent heat of evaporation and the latent heat of condensation are calculated, and the rate of change of the steam mass caused by evaporation and condensation is calculated through the latent heat of evaporation, the latent heat of condensation, and the liquid-elastic displacement;

[0068] According to the steam mass change rate and the first law of thermodynamics, an energy equation of the steam bomb is constructed to calculate the steam bomb pressure.

[0069] Specifically, according to the first law of thermodynamics, the energy equations (23) and (24) of the steam bomb are constructed, and combined with the ideal gas state equation, the pressure of the steam bomb is calculated.

[0070] Furthermore, the energy equation of the gas bomb is:

[0071]

[0072] Among them, m v1 、m v2 is the mass of the steam bombs on the left and right sides, c p is the constant-pressure molar heat capacity of the working fluid, T v1 and T v2 is the steam bomb temperature, P v1 and P v2 are the steam pressure on the left and the steam bomb pressure on the right, d is the diameter of the heat pipe, x p is the liquid-elastic displacement, c v is the constant volume molar heat capacity of the working fluid.

[0073] Further, in S6, updating the temperature distribution of the liquid bomb according to the temperature of the steam bomb and calculating the theoretical thickness of the liquid film includes:

[0074] updating the heat transfer coefficient of the wall liquid film according to the changes in density, viscosity and specific heat capacity caused by the temperature of the steam bomb;

[0075] updating the phase change heat transfer coefficient according to changes in the liquid bomb temperature and the specific volume difference between the steam and the liquid;

[0076] According to the heat transfer coefficient of the wall liquid film and the phase change heat transfer coefficient, the gas-liquid interface condition is updated and the liquid bomb temperature distribution is calculated. According to the liquid bomb temperature distribution, the average temperature and average velocity of the liquid bomb are obtained, and the theoretical thickness of the liquid film is calculated.

[0077] Specifically, the steam bomb temperature T υ1 、T υ2 The changes in density, viscosity and specific heat capacity caused by the change and the momentum equation of the liquid bomb (11) are used to update the heat transfer coefficient h of the wall liquid film by equation (7): sen ; Through the steam bomb temperature T in step 6 υ1 、Tυ2 The phase change heat transfer coefficient h of condensation or evaporation at the gas-liquid interface is updated by equation (16) due to the change in the specific volume difference between vapor and liquid caused by the evaporation and condensation process. i The temperature of the gas-liquid interface changes, and the liquid bomb moves, causing the gas-liquid boundary conditions (3) and (4) to change. The updated liquid bomb temperature distribution is calculated by the energy equation of the liquid bomb shown in equation (1), the initial condition (2) and the changed boundary conditions (3) and (4). According to equation (29), the theoretical liquid film thickness is calculated by the average temperature and average velocity of the liquid bomb.

[0078] Furthermore, the method for calculating the sensible heat transferred by the liquid bomb in S7 is as shown in formulas (30) and (31), and the method for calculating the flow thermal resistance of the pulsating heat pipe in S7 is as shown in formulas (32), (33), and (34).

[0079] The method of this embodiment will be described in detail below with reference to the accompanying drawings:

[0080] A method for calculating the pulsation and heat transfer of a high-temperature pulsating heat pipe liquid bomb includes: an open-loop pulsating heat pipe composed of an evaporation section and a condensation section, selecting the working fluid properties in the pulsating heat pipe, and calculating the target parameters of the working fluid properties, and using a numerical method to study the performance of the high-temperature pulsating heat pipe working with different working fluids. The heat transfer process is calculated by solving the mass, momentum, and energy equations of each vapor bomb and liquid bomb, thereby predicting the oscillation phenomenon in the high-temperature pulsating heat pipe. The convective heat transfer rate of the high-temperature pulsating heat pipe and the influence of the evaporation section temperature on the pulse amplitude and frequency, and the convection rate are studied, and the convective heat transfer coefficient is calculated based on the liquid film thickness, thereby calculating a new algorithm for calculating the heat transfer of the pulsating heat pipe.

[0081] like Figure 1 As shown, the specific steps include:

[0082] A high-temperature pulsating heat pipe liquid-elastic pulsation and heat transfer calculation method, comprising:

[0083] Step 1: Establish a pulsating heat pipe model, determine the size and structural parameters of the pulsating heat pipe, and divide the pulsating heat pipe into the evaporation section and the condensation section. Select the working fluid in the heat pipe. In this embodiment, the liquid metal working fluid is selected, and the relevant parameters of the selected working fluid properties are determined. Assume the initial liquid film thickness; given the evaporation section and condensation section temperatures, T e 、T c Assume that the temperatures of the steam bombs on the left and right sides are T v1 、T v2 , construct the energy equation of the liquid bomb and calculate the temperature of the liquid bomb;

[0084] The temperature distribution in the liquid bomb is derived by the liquid bomb energy equation shown in equation (1). The liquid bomb temperature T in (1) is solved by the finite difference format according to the corresponding initial conditions (2) and the gas-liquid interface boundary conditions (3) and (4). l :

[0085]

[0086] T=T0,t=0,0<x1<L p (2)

[0087] T=T i,1 ,x1=0 (3)

[0088] T=T i,2 ,x1=L p (4)

[0089] In formula (1)-(4):

[0090] t——time / s

[0091] k l ——Thermal conductivity / W·m -1 ·K -1

[0092] T1——Liquid bomb temperature / K

[0093] α1——thermal diffusion coefficient / m 2 ·s -1

[0094] A——Cross-sectional area / m 2

[0095] d——heat pipe diameter / m

[0096] L p ——Liquid bullet length / m

[0097] x1——liquid bullet position / m

[0098] h sen ——Convection heat transfer coefficient / W·m -2 ·K -1

[0099] T w ——Wall temperature / K

[0100] T i,1 ——Initial temperature of the gas-liquid interface on the left / K

[0101] T i,2 ——Initial temperature of the gas-liquid interface on the right / K

[0102] Evaporation section and condensation section temperature T e 、Tc It is related to the position of the liquid bomb and can be determined by equations (5) and (6) to determine the wall temperature T w :

[0103]

[0104] In formula (5) and (6):

[0105] x p ——Displacement of liquid bullet / m

[0106] The convective heat transfer coefficient h of the working fluid in the pulsating heat pipe is calculated by equations (7) and (8): sen :

[0107]

[0108] Pe=Re×Pr (8)

[0109] In formula (7) and (8):

[0110] k l ——Thermal conductivity / W·m -1 ·K -1

[0111] Pe——Peclet number

[0112] Re——Reynolds number

[0113] Pr——Prandtl number

[0114] Nu——Nussell number

[0115] Step 2: Calculate the initial steam bomb pressure P according to equations (9) and (10): υ1 '、P υ2 ', the initial steam bomb pressure is solved as the initial value of the pressure, and the update iteration is based on this:

[0116]

[0117] In formula (9) and (10):

[0118] T υ0 ——Initial steam temperature / K

[0119] P υ0 ——Initial steam pressure / Pa

[0120] γ——Heat capacity ratio

[0121] Step 3: Construct the momentum equation of the liquid bomb and calculate the displacement x of the liquid bomb p ; The momentum equation of the liquid bomb, the term on the left represents the change in momentum, and the terms on the right represent the pressure term, gravity term, and shear stress term respectively:

[0122]

[0123] In formula (11):

[0124] A——Cross-sectional area of ​​high temperature pulsating heat pipe / m 2

[0125] L p ——Liquid bullet length / m

[0126] ρ l ——Liquid bomb density / kg·m -3

[0127] x p ——Displacement of liquid bullet / m

[0128] P υ1 ——Steam pressure on the left side / Pa

[0129] P υ2 ——Steam pressure on the right side / Pa

[0130] D——diameter of high temperature pulsating heat pipe / m

[0131] τ——shear stress / N·m -2

[0132] ΔP b ——Pressure loss at the elbow / Pa

[0133]

[0134] In formula (12):

[0135] ξ——Pressure loss coefficient

[0136] υ p ——Steam speed / m·s -1

[0137] τ=f l ρ l v 2 / 2 (13)

[0138] Liquid flow friction coefficient f l The friction coefficient f in the capillary wick region is different from that in the smooth region. l for:

[0139]

[0140] In formula (13) and (14):

[0141] f1——friction coefficient

[0142] According to the above equation, the liquid elastic displacement x p .

[0143] Step 4: Calculate the latent heat of evaporation and condensation, and then solve the change in steam quality caused by evaporation and condensation through latent heat calculation:

[0144] The thermal resistance of steam condensation and liquid film evaporation mainly includes the thermal conductivity resistance of the wall liquid film and the phase change resistance of condensation or evaporation. The heat transfer coefficient of the wall liquid film is:

[0145]

[0146] Where γ≤1; in the Nikolayev model, this coefficient is 0.47.

[0147] In formula (15):

[0148] δ film ——Thickness of thin liquid film deposited in the tube / m

[0149] h film ——Wall liquid film heat transfer coefficient / W·m -2 ·K -1

[0150] Phase change heat transfer coefficient h for condensation or evaporation at the gas-liquid interface i for:

[0151]

[0152] In formula (16):

[0153] h i ——Phase change heat transfer coefficient / W·m -2 ·K -1

[0154] V lυ ——Specific volume difference between vapor and liquid

[0155] ——Use 0.01

[0156] The thermal resistance between the steam and the heat pipe condensation wall is mainly the thermal conductivity resistance of the wall liquid film and the thermal conductivity resistance of the gas-liquid interface condensation. The total heat transfer coefficient h sum for:

[0157]

[0158] In formula (17):

[0159] h sum ——Total heat transfer coefficient / W·m -2 ·K -1

[0160] When the liquid bomb flows through the smooth channel, a layer of liquid film remains on the wall. When the gas-liquid interface of the liquid bomb is in the evaporation section, the length of the liquid film gradually increases as the liquid bomb moves toward the condensation section. When the liquid bomb moves toward the evaporation section, the length of the liquid film gradually decreases. At the same time, as the thin liquid film evaporates, the length of the liquid film gradually decreases. When the gas-liquid interface of the liquid bomb is in the condensation section, only evaporation reduces the length of the liquid film. The length of the thin liquid film in the smooth tube is calculated by formula (18):

[0161]

[0162] In formula (18):

[0163] L c,i ——Liquid film length in condensation section / m

[0164] L e,i ——Liquid film length in evaporation section / m

[0165] m v ——Steam quality / kg

[0166] The thermal resistance of working fluid condensation and evaporation is mainly concentrated in the condensation and evaporation parts. The gas-liquid interface temperature is very different from the steam temperature. The gas-liquid interface temperature is:

[0167]

[0168] In formula (19):

[0169] T i ——Gas-liquid interface temperature / K

[0170] T υ,i ——Steam bomb temperature / K

[0171] When the steam enters the condensation section, heat transfer occurs between the steam and the condenser wall, the steam condenses, and the mass decreases; when the liquid bomb enters the evaporation section, the heat transfer between the liquid bomb and the evaporator wall causes the liquid bomb to boil, and the steam mass increases. Under certain conditions, due to the increase in steam mass and the work done by the liquid bomb on the steam when it moves, the temperature of the steam may rise above the evaporation section temperature. At this time, condensation occurs due to the heat transfer between the steam and the evaporator wall, and the steam mass decreases.

[0172]

[0173] In formula (20):

[0174] Q cond,i ——Latent heat of liquid film condensation / W

[0175] Q evp,i ——Latent heat of liquid film evaporation / W

[0176] The steam quality change rate caused by evaporation and condensation is calculated by equations (21) and (22):

[0177]

[0178] In formula (21) and (22):

[0179] h fg ——Latent heat of working fluid phase change / J·kg -1

[0180] Step 5: According to the first law of thermodynamics, construct the energy equations (23) and (24) of the steam bomb, and combine them with the ideal gas state equation to calculate the pressure of the steam bomb:

[0181]

[0182] In formula (23) and (24):

[0183] c p ——Molar heat capacity at constant pressure of working fluid / J·mol -1 ·K -1

[0184] c v ——Molar heat capacity at constant volume of working fluid / J·mol -1 ·K -1

[0185]

[0186] In formula (25) and (26):

[0187] R g ——Gas constant / J·kg -1 ·K -1

[0188] The relationship between the mass and pressure of the two steam bombs is shown in equations (27) and (28):

[0189]

[0190] Substitute the steam mass change obtained in step 5 into equations (27) and (28) to calculate the steam bomb pressure P υ1 , P υ2 .

[0191] Step 6: Calculate the temperature T of the steam bomb by using equations (9) and (10) υ1 、T υ2 , and compare the obtained results with the assumed T υ1 、T υ2 The iterative convergence criterion is set to an error less than 10 -4If it is satisfied, the iteration is stopped; if it is not satisfied, it is repeated from step 2 until the iteration requirements are met and the steam bomb temperature T is calculated. υ1 、T υ2 .

[0192] Step 7: Use the steam bomb temperature T in step 6 υ1 、T υ2 The changes in density, viscosity and specific heat capacity caused by the change and the momentum equation of the liquid bomb (11) are used to update the convective heat transfer coefficient h by equation (7): sen ; Through the steam bomb temperature T in step 6 υ1 、T υ2 The phase change heat transfer coefficient h of condensation or evaporation at the gas-liquid interface is updated by equation (16) due to the change in the specific volume difference between vapor and liquid caused by the evaporation and condensation process. i The convective heat transfer coefficient and the phase change heat transfer coefficient of the gas-liquid interface in the pulsating heat pipe jointly determine the temperature distribution of the liquid bomb by affecting the flow and phase change process of the working fluid, thereby affecting the heat transfer performance of the pulsating heat pipe. By optimizing the convective heat transfer coefficient and the phase change heat transfer coefficient of the gas-liquid interface, the heat transfer efficiency and stability of the pulsating heat pipe can be improved.

[0193] Step 8: The temperature of the gas-liquid interface changes, and the liquid bomb is displaced, causing the gas-liquid boundary conditions (3) and (4) to change. The updated liquid bomb temperature distribution is calculated by the energy equation of the liquid bomb shown in equation (1), the initial condition (2) and the changed boundary conditions (3) and (4). According to equation (29), the theoretical liquid film thickness is calculated by the average temperature and average velocity of the liquid bomb, and compared with the liquid film thickness assumed in step 1 until the error condition is met.

[0194]

[0195] In formula (29):

[0196] μ——dynamic viscosity / Pa·s

[0197] ρ——density / kg·m-3

[0198] υ——average speed / m·s -1

[0199] ΔP——pressure drop along the length of the liquid film / Pa

[0200] L——Liquid film length / m

[0201] Step 9: Calculate the sensible heat transferred into and out of the liquid bomb, and calculate the flow thermal resistance of the working fluid in the pulsating heat pipe.

[0202] The sensible heat generated by the liquid bomb due to unidirectional convection is calculated by equations (30) and (31);

[0203]

[0204] In formula (30) and (31):

[0205] Q h ——Sensible heat input by liquid bomb / W

[0206] Q c ——Sensible heat transferred by liquid bullet / W

[0207] T 1,i ——Liquid bomb temperature / K

[0208] When the pulsating heat pipe is in steady state, the thermal resistance can be calculated by (32), (33), and (34):

[0209]

[0210] In formula (32), (33), (34):

[0211] R——Thermal resistance / K·W -1

[0212] ——Average sensible heat input by liquid bomb / W

[0213] ——Average sensible heat transferred by the liquid bomb / W

[0214] ——Average condensation heat / W

[0215] ——Average evaporation heat / W

[0216] ——Average sensible heat / W

[0217] ——Average latent heat / W

[0218] Step 10: Output the calculation results. During the periodic oscillation of the liquid bomb pulsation, the junction of the evaporation section and the condensation section is taken as the zero point. The calculation results can be used to obtain the displacement of the liquid bomb. The temperature distribution of the liquid bomb can be solved by the energy equation, and the velocity distribution of the liquid bomb can be solved by the momentum equation. The output results are the temperature and pressure of the steam bomb and the temperature distribution and velocity distribution of the liquid bomb, as well as the displacement of the liquid bomb, and the steam mass change, sensible heat, latent heat and thermal resistance of the pulsating heat pipe calculated based on the above results. The steam mass change in the pulsating heat pipe is caused by the evaporation section and the condensation section. The pressure difference caused by the temperature gradient of the evaporation section drives the liquid-elastic pulsation. This pulsation can promote the circulation of the working fluid between the evaporation section and the condensation section, thereby realizing the heat transfer; latent heat is the heat absorbed or released by the working fluid during the phase change process, and sensible heat is the heat absorbed or released by the working fluid when the temperature changes during the heating or cooling process. The sensible heat transfer of the liquid-elastic pulsation in the pulsating heat pipe is the main way of heat transfer; thermal resistance is the ratio of the temperature difference between the evaporation section and the condensation section to the input heat flow. The smaller the thermal resistance, the less heat is retained in the tube, and the better the heat transfer performance of the pulsating heat pipe. The above results can be used to perform simple calculations and analysis on the heat transfer performance of high-temperature pulsating heat pipes with different working fluids, such as oscillation height, oscillation speed, and thermal resistance, and draw a motion real-time diagram based on the calculation results.

[0219] The embodiments described above are only descriptions of the preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should all fall within the protection scope determined by the claims of the present invention.

Claims

1. A high-temperature pulsating heat pipe liquid-elastic pulsation and heat transfer calculation method, characterized in that: include: S1. Establish a pulsating heat pipe model and determine the working fluid, evaporation section and condensation section temperatures in the heat pipe; S2. Determine the initial liquid film thickness and initial steam bomb temperature of the pulsating heat pipe model; S3. Calculate the liquid bomb temperature according to the evaporation section and condensation section temperature; S4. Calculate the initial steam bomb pressure according to the initial steam bomb temperature, calculate the liquid bomb displacement according to the initial steam bomb pressure, obtain the steam mass change based on the liquid bomb displacement, and calculate the steam bomb pressure according to the steam mass change; S5. Calculate the steam bomb temperature according to the steam bomb pressure, compare the steam bomb temperature with the initial steam bomb temperature, and if the difference satisfies the first relative error, proceed to step S5; if not, return to S2 to determine the initial steam bomb temperature; S6. Update the liquid bomb temperature distribution according to the steam bomb temperature and calculate the theoretical thickness of the liquid film, compare the theoretical thickness of the liquid film with the initial liquid film thickness, and if the difference satisfies the second relative error, proceed to step S7; if not, return to S2 to determine the initial liquid film thickness; S7. Calculate the sensible heat transferred into and out of the liquid bomb according to the displacement of the liquid bomb and the temperatures of the evaporation section and the condensation section, and calculate the flow thermal resistance of the pulsating heat pipe.

2. The high temperature pulsating heat pipe liquid elastic pulsation and heat transfer calculation method according to claim 1, characterized in that: In S3, the temperature of the liquid bomb is calculated according to the temperatures of the evaporation section and the condensation section, including: A liquid-bomb energy equation is constructed, and the liquid-bomb temperature in the liquid-bomb energy equation is solved according to a finite difference format of initial conditions and gas-liquid interface boundary conditions to obtain the liquid-bomb temperature, wherein the liquid-bomb energy equation is related to the wall temperature, and the wall temperature is obtained according to the temperatures of the evaporation section and the condensation section.

3. The high temperature pulsating heat pipe liquid elastic pulsation and heat transfer calculation method according to claim 1, characterized in that: Calculating the liquid elastic displacement according to the initial steam elastic pressure in S4 includes: A momentum equation of the liquid bomb is constructed based on the current gas bomb pressure, and the displacement of the liquid bomb is calculated based on the momentum equation of the liquid bomb, wherein the momentum equation of the liquid bomb is the relationship between momentum change and pressure, gravity and shear stress.

4. The high temperature pulsating heat pipe liquid elastic pulsation and heat transfer calculation method according to claim 1, characterized in that: In S4, the steam mass change is obtained based on the liquid-bomb displacement, and the steam-bomb pressure is calculated according to the steam mass change, including: According to the thickness of the thin liquid film deposited in the tube, the heat transfer coefficient of the liquid film on the wall is calculated; Calculate the phase change heat transfer coefficient of condensation or evaporation at the gas-liquid interface based on the specific volume difference between steam and liquid; Obtaining a total heat transfer coefficient according to the heat transfer coefficient of the wall liquid film and the phase change heat transfer coefficient; According to the liquid-elastic displacement, the liquid film length of the condensation section and the liquid film length of the evaporation section are obtained; according to the total heat transfer coefficient, the liquid film length, the steam-elastic temperature, and the temperatures of the evaporation section and the condensation section, the latent heat of evaporation and the latent heat of condensation are calculated, and the rate of change of the steam mass caused by evaporation and condensation is calculated through the latent heat of evaporation, the latent heat of condensation, and the liquid-elastic displacement; According to the steam mass change rate and the first law of thermodynamics, an energy equation of the steam bomb is constructed to calculate the steam bomb pressure.

5. The high temperature pulsating heat pipe liquid elastic pulsation and heat transfer calculation method according to claim 4, characterized in that: The energy equation of the steam bomb is: Among them, m v1 、m v2 is the mass of the steam bombs on the left and right sides, c p is the constant-pressure molar heat capacity of the working fluid, T v1 and T v2 is the steam bomb temperature, P v1 and P v2 are the steam pressure on the left and the steam bomb pressure on the right, d is the diameter of the heat pipe, x p is the liquid-elastic displacement, c v is the constant volume molar heat capacity of the working fluid.

6. The high temperature pulsating heat pipe liquid elastic pulsation and heat transfer calculation method according to claim 4, characterized in that: In S6, updating the temperature distribution of the liquid bomb according to the temperature of the steam bomb and calculating the theoretical thickness of the liquid film include: updating the heat transfer coefficient of the wall liquid film according to the changes in density, viscosity and specific heat capacity caused by the temperature of the steam bomb; updating the phase change heat transfer coefficient according to changes in the liquid bomb temperature and the specific volume difference between the steam and the liquid; According to the heat transfer coefficient of the wall liquid film and the phase change heat transfer coefficient, the gas-liquid interface condition is updated and the liquid bomb temperature distribution is calculated. According to the liquid bomb temperature distribution, the average temperature and average velocity of the liquid bomb are obtained, and the theoretical thickness of the liquid film is calculated.

7. The high temperature pulsating heat pipe liquid elastic pulsation and heat transfer calculation method according to claim 1, characterized in that: The calculation method of the sensible heat transferred into and out of the liquid bomb in S7 is: The calculation method of the sensible heat transmitted by the liquid bomb is: Among them, Q h is the sensible heat transferred by the liquid bomb, L p is the length of the liquid bullet, x p is the displacement of the liquid bomb, h sen is the convective heat transfer coefficient, T l,i is the liquid bomb temperature, T c is the condensation temperature, x1 is the liquid bomb position, x p is the liquid-elastic displacement, Q c is the sensible heat transferred by the liquid bomb, T e is the evaporation temperature.

8. The high temperature pulsating heat pipe liquid elastic pulsation and heat transfer calculation method according to claim 7, characterized in that: The method for calculating the flow thermal resistance of the pulsating heat pipe in S7 is: Where R is the thermal resistance, T e is the evaporation temperature, is the average sensible heat, is the average latent heat, is the average sensible heat transferred by the liquid bomb, is the average sensible heat transferred by the liquid bomb, is the average condensation heat, is the average heat of evaporation.

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