A method for calculating liquid slug pulsation and heat transfer of high-temperature pulsating heat pipe

Abstract

The application relates to a high-temperature pulsating heat pipe liquid bullet pulsation and heat transfer calculation method, which comprises the following steps: S1. establishing a pulsating heat pipe model, and determining working medium in the heat pipe, evaporation section and condensation section temperature; S2. determining initial liquid film thickness and initial bullet temperature of the pulsating heat pipe model; S3. calculating the bullet temperature according to the evaporation section and condensation section temperature; S4. calculating the initial bullet pressure according to the initial bullet temperature, calculating the bullet displacement according to the initial bullet pressure, and calculating the bullet pressure; S5. calculating the bullet temperature according to the bullet pressure, comparing the bullet temperature with the initial bullet temperature, if not satisfied, returning to S2; updating the bullet temperature distribution according to the bullet temperature and calculating the liquid film theoretical thickness, comparing the liquid film theoretical thickness with the initial liquid film thickness, if the difference satisfies the second relative error, entering step S7, if not satisfied, returning to S2; and S7. calculating the sensible heat and flow thermal resistance of the bullet according to the bullet displacement.

Description

Technical Field

[0001] The present 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 advancement of technology, the local heat flux density of components is gradually increasing, bringing with it numerous problems such as reduced service life, performance degradation, and low energy conversion efficiency. Consequently, the demand for high-efficiency heat dissipation materials continues to grow. As a highly efficient heat dissipation device, pulsating heat pipes couple two heat transfer methods: phase change heat transfer and sensible heat transfer via oscillating motion within microchannels. By utilizing the phase change of the internal working medium and the vapor pressure differential generated by latent heat transfer between the evaporation and condensation ends, the liquid bullet oscillates within the channel, resulting in a heat pipe with high thermal conductivity.

[0003] When the pulsating heat pipe is working 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 has hindered 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 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 within the heat pipe.

[0008] S2 determines the initial liquid film thickness of the pulsating heat pipe model, the initial steam bomb temperature;

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

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

[0011] S5. Calculate the steam bomb temperature according to the steam bomb pressure and compare the steam bomb temperature with the initial steam bomb temperature. 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 liquid film thickness. Compare the theoretical liquid film thickness with the initial liquid film thickness. 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 based on 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 vapor 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 a 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] Calculate the heat transfer coefficient of the wall liquid film based on the thickness of the thin liquid film deposited in the tube;

[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-bomb 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-bomb 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 using the latent heat of evaporation, the latent heat of condensation, and the liquid-bomb 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 left and right bombs, 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 conditions are 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 transferred 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 section 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 present invention has the following beneficial effects: 1) Through heat transfer analysis, the internal flow heat transfer model of the heat pipe is rationally simplified while ensuring model calculation speed and accuracy. The iterative process is simple and has good convergence. By iterating the temperatures of the steam bombs 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 more accurately calculated, thereby predicting the heat transfer rate;

[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 at different evaporation and condensation section temperatures, different pulsating heat pipe scales, and different working fluids, 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 following briefly introduces the drawings required for use in the embodiments. 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 any creative work.

[0045] Figure 1A flow chart of a liquid spring pulsation and heat transfer calculation method of a high-temperature pulsating heat pipe according to an embodiment of the present application. DETAILED DESCRIPTION

[0046] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative effort fall within the protection scope of the present application.

[0047] In order to make the above objectives, characteristics and advantages of the present application more apparent, further specific description will be given to the present application with reference to the drawings and embodiments.

[0048] When the working medium is a liquid metal, the thermal resistance is mainly concentrated in the wall film, and the temperature at the gas-liquid interface is approximately equal to the temperature of the vapor. At this time, by calculating the heat transfer coefficient of the wall film and the phase change heat transfer coefficient of the condensation or evaporation at the gas-liquid interface, the evaporation and condensation heat transfer amount can be more conveniently calculated. In addition, the research on the liquid spring 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 the pulsating heat pipe.

[0049] The embodiment provides a liquid spring pulsation and heat transfer calculation method of a high-temperature pulsating heat pipe, which comprises the following steps:

[0050] S1. establishing a pulsating heat pipe model, and determining the working medium in the heat pipe, the evaporation section and the condensation section temperature;

[0051] S2. determining the initial liquid film thickness and the initial vapor spring temperature of the pulsating heat pipe model;

[0052] S3. calculating the liquid spring temperature according to the evaporation section and the condensation section temperature;

[0053] S4. calculating the initial vapor spring pressure according to the initial vapor spring temperature, and calculating the liquid spring displacement according to the initial vapor spring pressure, obtaining the vapor mass change amount based on the liquid spring displacement, and calculating the vapor spring pressure according to the vapor mass change amount;

[0054] S5. calculating the vapor spring temperature according to the vapor spring pressure, comparing the vapor spring temperature with the initial vapor spring temperature, if the difference satisfies a first relative error, then entering step S5, and if the difference does not satisfy the first relative error, then returning to S2 to determine the initial vapor spring temperature;

[0055] S6. Update the liquid bomb temperature distribution according to the steam bomb temperature and calculate the theoretical liquid film thickness. Compare the theoretical liquid film thickness with the initial liquid film thickness. 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 based on 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 liquid bomb temperature is calculated based on the temperatures 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 derives the temperature distribution in the liquid bomb by the liquid bomb energy equation shown in formula (1), 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 conditions (3) and (4). l :.

[0060] Furthermore, 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, where the momentum equation of the liquid bomb is the relationship between the momentum change and pressure, gravity and shear stress.

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

[0063] Furthermore, 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 include:

[0064] Calculate the heat transfer coefficient of the wall liquid film based on the thickness of the thin liquid film deposited in the tube;

[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-bomb 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-bomb 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 using the latent heat of evaporation, the latent heat of condensation, and the liquid-bomb 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 the pressure of the steam bomb is calculated by combining the ideal gas state equation.

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

[0071]

[0072] Among them, m v1 、m v2 is the mass of the left and right bombs, 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] Furthermore, in S6, updating the liquid bomb temperature distribution according to the steam bomb temperature and calculating the liquid film theoretical thickness 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 conditions are 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 step 6 steam bomb temperature T 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 (Equations (3) and (4) to change. The updated liquid bomb temperature distribution is calculated using the energy equation of the liquid bomb shown in Equation (1), the initial condition (2), and the changed boundary conditions (Equations (3) and (4). According to Equation (29), the theoretical liquid film thickness is calculated using the average temperature and average velocity of the liquid bomb.

[0078] Furthermore, the calculation method of the sensible heat transferred by the liquid bomb in S7 is as shown in formulas (30) and (31), and the calculation method of 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 consisting 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 numerical methods to study the performance of high-temperature pulsating heat pipes working with different working fluids. By solving the mass, momentum, and energy equations of each vapor bomb and liquid bomb, the calculation of the heat transfer process is completed, 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, the convective heat transfer coefficient is calculated based on the liquid film thickness, and then a new algorithm for calculating the heat transfer of the pulsating heat pipe is developed.

[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, liquid metal is selected as the working fluid, and determine the relevant parameters of the selected working fluid. Assume the initial liquid film thickness; given the evaporation section and condensation section temperatures, T e 、T c Assume that the temperatures of the left and right bombs 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 from the liquid bomb energy equation shown in formula (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 formulas (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 diffusivity / 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 the wall temperature T is determined by equations (5) and (6). w :

[0103]

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

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

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

[0107]

[0108] Pe=Re×Pr (8)

[0109] In formulas (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——Nussel 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 formulas (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 - length of liquid bullet / m

[0126] p l - density of liquid bullet / kg-m -3

[0127] x p - displacement of liquid bullet / m

[0128] P υ1 - left-side vapor pressure / Pa

[0129] P υ2 - right-side vapor pressure / Pa

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

[0131] τ - shear stress / N-m -2

[0132] ΔP b - pressure loss at bend / Pa

[0133]

[0134] In formula (12):

[0135] ξ - pressure loss coefficient

[0136] υ p - vapor velocity / m-s -1

[0137] τ = f l p l v 2 / 2 (13)

[0138] Liquid flow friction coefficient f l is different in the capillary core region and the smooth region, where the friction coefficient f l is:

[0139]

[0140] In formulas (13), (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 use the latent heat calculation to solve the steam quality change caused by evaporation and condensation:

[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 thermal 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 liquid bomb's gas-liquid interface is in the evaporation section, the liquid film length gradually increases as the liquid bomb moves toward the condensation section. As the liquid bomb moves toward the evaporation section, the liquid film length gradually decreases. At the same time, as the thin liquid film evaporates, the liquid film length gradually decreases. When the liquid bomb's gas-liquid interface 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 using 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 the 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 steam enters the condensing section, heat transfer occurs between the steam and the condenser walls, causing the steam to condense and its mass to decrease. When the liquid bomb enters the evaporating section, the heat transfer between the liquid bomb and the evaporator walls causes the liquid bomb to boil, increasing the steam mass. Under certain conditions, due to the increase in steam mass and the work done on the steam by the liquid bomb during its movement, the steam temperature may rise above the evaporating section temperature. At this point, condensation occurs due to the heat transfer between the steam and the evaporator walls, reducing the steam mass.

[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 due to evaporation and condensation is calculated by equations (21) and (22):

[0177]

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

[0179] h fg ——Latent heat of phase change of working fluid / 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 formulas (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 formulas (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 using equations (9) and (10) υ1 、T υ2 , and compare the 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 stops; 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 density, viscosity and specific heat capacity changes 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 step 6 steam bomb temperature T 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 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 at the gas-liquid interface in a pulsating heat pipe jointly determine the temperature distribution of the liquid bomb by influencing 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 at the gas-liquid interface, the heat transfer efficiency and stability of the pulsating heat pipe can be improved.

[0193] Step 8: The gas-liquid interface temperature changes, and the liquid bomb displaces, causing the gas-liquid boundary conditions (Equations (3) and (4) to change. The updated liquid bomb temperature distribution is calculated using the liquid bomb energy equation shown in Equation (1), the initial condition (2), and the changed boundary conditions (Equations (3) and (4). According to Equation (29), the theoretical liquid film thickness is calculated using the average temperature and average velocity of the liquid bomb. This is compared with the assumed liquid film thickness 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 formulas (30) and (31):

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

[0206] Q c ——Sensible heat transferred by the 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 formulas (32), (33), and (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 bullet / 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, velocity distribution and displacement of the liquid bomb, as well as 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 in the evaporation section drives the liquid-elastic pulsation. This pulsation promotes the circulation of the working fluid between the evaporation section and the condensation section, thereby achieving heat transfer. Latent heat is the heat absorbed or released by the working fluid during phase change, while sensible heat is the heat absorbed or released by the working fluid during temperature changes during heating or cooling. Sensible heat transfer through the liquid-elastic pulsation in the pulsating heat pipe is the primary heat transfer mechanism. Thermal resistance is the ratio of the temperature difference between the evaporation section and the condensation section to the input heat flow rate. The smaller the thermal resistance, the less heat is retained in the pipe, and the better the heat transfer performance of the pulsating heat pipe. These results can be used to perform a simple calculation and analysis of the heat transfer performance of high-temperature pulsating heat pipes operating with different working fluids, such as oscillation height, oscillation speed, and thermal resistance, and to draw a motion diagram based on the calculation results.

[0219] The embodiments described above are merely descriptions of preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by persons skilled in the art should fall within the scope of protection defined 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 within the heat pipe. S2 determines the initial liquid film thickness and initial steam bomb temperature of the pulsating heat pipe model; S3. Calculate the liquid bomb temperature based on the evaporation and condensation section temperatures; S4. Calculate the initial steam bomb pressure based on the initial steam bomb temperature, calculate the liquid bomb displacement based on the initial steam bomb pressure, obtain the steam mass change based on the liquid bomb displacement, and calculate the steam bomb pressure based on the steam mass change; S5. Calculate the steam bomb temperature according to the steam bomb pressure and compare the steam bomb temperature with the initial steam bomb temperature. If the difference satisfies the first relative error, proceed to step S6. 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 liquid film thickness. Compare the theoretical liquid film thickness with the initial liquid film thickness. 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 based on 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 vapor 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: Calculate the heat transfer coefficient of the wall liquid film based on the thickness of the thin liquid film deposited in the tube; 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-bomb 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-bomb 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 using the latent heat of evaporation, the latent heat of condensation, and the liquid-bomb 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: ; ； in, 、 is the mass of the left and right side gas bombs, is the constant-pressure molar heat capacity of the working fluid, and is the steam bomb temperature, and They are the steam pressure on the left and the bomb pressure on the right, is the heat pipe diameter, is the liquid-elastic displacement, is the constant volume molar heat capacity of the working fluid, For time.

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 liquid bomb temperature distribution according to the steam bomb temperature and calculating the liquid film theoretical thickness 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 conditions are 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 for the sensible heat transferred into and out of the liquid bomb in S7 is: ； The calculation method of the sensible heat transferred by the liquid bomb is: ； in, is the sensible heat transferred by the liquid bomb, is the length of the liquid bullet, is the displacement of the liquid bullet, is the convective heat transfer coefficient, is the liquid bomb temperature, is the condensation temperature, is the liquid bullet position, is the sensible heat transferred by the liquid bullet, is the evaporation temperature, is the heat pipe diameter.

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: ； ； ； in, is the thermal resistance, 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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