Heat transfer calculation method for pulsating heat pipe with gradient wetted surface

Abstract

The invention discloses a heat transfer calculation method for a pulsating heat pipe with a gradient wetted surface. The heat transfer calculation method comprises the following steps: S1, establishing a pulsating heat pipe model; 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 and liquid bomb change length 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 the temperature of the steam bomb does not meet the initial temperature, returning to S2 and re-assuming; 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 again, and assumption is executed again; 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] This invention belongs to the technical field of phase change heat exchange equipment, and particularly relates to a method for calculating heat transfer in a pulsating heat pipe with a gradient wetting surface. Background Technology

[0002] Pulsating heat pipes rely on the vapor pressure difference between the evaporation and condensation sections, driven by the latent heat transfer, to propel the liquid bobble into oscillating motion. Due to their characteristics of requiring no wick, diverse pipe fabrication methods, and excellent heat transfer performance, they have become highly promising heat dissipation devices in the field of electronic cooling. With the increasing portability and integration of electronic components, pulsating heat pipes are also trending towards miniaturization in design and fabrication. As a highly efficient heat dissipation device, the pulsating heat pipe couples two heat transfer mechanisms: phase change heat transfer and sensible heat transfer through oscillating motion within microchannels.

[0003] In studies on the influence of surface wettability on pulsating heat pipes, introducing gradient wettable surfaces into the pulsating heat pipe significantly improves its heat transfer performance by enhancing wall wettability. Current research on improving surface wettability in pulsating heat pipes is relatively limited, mainly focusing on studies of single wettable surfaces such as hydrophilic, superhydrophilic, and hydrophobic surfaces. It is difficult to control the surface wettability of pulsating heat pipes, thus significantly affecting the motion of the liquid-elastic fluid, increasing the uncertainty in calculating the heat transfer coefficient, and making it difficult for theoretical studies to fully explain the mechanism. In particular, phenomena observed in experiments cannot be fully explained by theory, hindering further understanding of the heat transfer performance of pulsating heat pipes. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention proposes a heat transfer calculation method for pulsating heat pipes with gradient wetting surfaces. This invention analyzes and calculates the heat transfer performance and working fluid motion state of pulsating heat pipes with gradient wetting surfaces, providing guidance for the parameter-related development and engineering applications of pulsating heat pipes.

[0005] To achieve the above objectives, the present invention provides a method for calculating heat transfer in a pulsating heat pipe with a gradient wetting surface, comprising:

[0006] S1. Establish a pulsating heat pipe model and determine the working fluid, evaporation section, and condensation section temperatures within the heat pipe;

[0007] S2. Determine the initial liquid film thickness and initial vapor bomb temperature of the pulsating heat pipe model;

[0008] S3. Calculate the liquid bullet temperature based on the temperatures of the evaporation section and the condensation section;

[0009] S4. Calculate the initial gas bomb pressure based on the initial gas bomb temperature, and calculate the liquid bomb displacement based on the initial gas bomb pressure. Obtain the steam mass change based on the liquid bomb displacement, liquid bomb length, and transformed liquid bomb length. Calculate the gas bomb pressure for subsequent iterations based on the steam mass change.

[0010] S5. Calculate the gas bomb temperature based on the gas bomb pressure, compare the gas bomb temperature with the initial gas bomb temperature, and if the difference satisfies the first relative error, proceed to step S6; otherwise, return to S2 to re-assume the initial gas bomb temperature and assume a new initial gas bomb temperature.

[0011] S6. Update the liquid bullet temperature distribution according to the gas bullet temperature and calculate the theoretical thickness of the liquid film. Compare the theoretical thickness of the liquid film 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 and assume a new initial liquid film thickness.

[0012] S7. Calculate the sensible heat transferred into and out of the liquid bomb based on the liquid bomb displacement and the temperatures of the evaporation and condensation sections, and calculate the flow thermal resistance of the pulsating heat pipe.

[0013] Optionally, in S3, the calculation of the liquid bomb temperature based on the temperatures of the evaporation section and the condensation section includes:

[0014] 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 scheme of the initial conditions and the gas-liquid interface boundary conditions to obtain the liquid-bomb temperature. The liquid-bomb energy equation is related to the wall temperature, which is obtained based on the temperatures of the evaporation section and the condensation section.

[0015] Optionally, S4 includes calculating the liquid-propellant displacement based on the initial vapor-propellant pressure, which includes:

[0016] The 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. The momentum equation of the liquid bomb is the relationship between momentum change and pressure, gravity and shear stress.

[0017] Optionally, in S4, the change in steam mass is obtained based on the displacement of the liquid explosive, and the steam explosive pressure is calculated based on the change in steam mass, including:

[0018] The heat transfer coefficient of the liquid film on the wall is calculated based on the thickness of the thin liquid film deposited inside the pipe.

[0019] 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.

[0020] The overall heat transfer coefficient is obtained based on the heat transfer coefficient of the liquid film on the wall and the phase change heat transfer coefficient.

[0021] Based on the liquid bomb displacement, the liquid film lengths of the condensation section and the evaporation section are obtained; the latent heat of vaporization and latent heat of condensation are calculated based on the overall heat transfer coefficient, liquid film length, vapor bomb temperature, and the temperatures of the evaporation and condensation sections; and the steam mass change rate caused by evaporation and condensation is calculated using the latent heat of vaporization, the latent heat of condensation, the liquid bomb displacement, the liquid film length, and the liquid film transformation length.

[0022] Based on the steam mass change rate and the first law of thermodynamics, the energy equation of the steam bomb is constructed to calculate the steam bomb pressure.

[0023] Optionally, the energy equation for the gas bomb is:

[0024] ;

[0025] ;

[0026] in, , The mass of the gas bombs on the left and right sides, The isobaric molar heat capacity of the working fluid. and For the temperature of the gas bomb, and These are the steam pressure on the left and the vapor pressure on the right, respectively. The diameter of the heat pipe. For the displacement of the liquid spring, The molar heat capacity at constant volume of the working fluid. For time.

[0027] Optionally, in S6, updating the liquid bullet temperature distribution based on the vapor bullet temperature and calculating the theoretical thickness of the liquid film includes:

[0028] The heat transfer coefficient of the liquid film on the wall is updated based on the changes in density, viscosity, and specific heat capacity caused by the temperature of the vapor bomb.

[0029] The phase change heat transfer coefficient is updated based on the changes in the liquid bomb temperature, the specific volume difference between the vapor and the liquid;

[0030] Based on the heat transfer coefficient of the liquid film on the wall and the phase change heat transfer coefficient, the gas-liquid interface conditions are updated and the liquid-elastic temperature distribution is calculated. Based on the liquid-elastic temperature distribution, the average temperature and average velocity of the liquid-elastic related to the capillary number are obtained, thereby calculating the theoretical thickness of the liquid film.

[0031] Optionally, the sensible heat calculation method for the liquid bomb's input and output in S7 is as follows:

[0032] ;

[0033] The calculation method for the sensible heat transferred from the liquid bomb is as follows:

[0034] ;

[0035] in, The sensible heat transferred by the liquid bomb. For the length of the liquid bullet, The displacement caused by the liquid bullet The convective heat transfer coefficient, For the temperature of the liquid bomb, This refers to the temperature of the condensation section. Position of the liquid bullet. The sensible heat transferred from the liquid bomb This is the diameter of the heat pipe.

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

[0037] ;

[0038] ;

[0039] ;

[0040] in, For thermal resistance, The temperature of the evaporation section. For average sensible heat, The average latent heat, The average sensible heat transferred from the liquid bomb. The average sensible heat transferred by the liquid bomb. For average condensation heat, This represents the average heat of evaporation.

[0041] Compared with the prior art, the present invention has the following advantages and technical effects:

[0042] (1) Under the premise of ensuring the calculation speed and accuracy of the model, the present invention makes reasonable simplification to the heat transfer model inside the heat pipe, and the iteration process is simple and has good convergence. By iterating the temperature of the vapor bomb and the liquid film thickness on the left and right sides of the pulsating heat pipe, the phase change heat transfer coefficient can be calculated more accurately, and the heat transfer rate can be predicted.

[0043] (2) The present invention can calculate the motion state of the working fluid in the pulsating heat pipe, including velocity distribution, temperature distribution, amplitude, etc.;

[0044] (3) The output can provide simpler and clearer result diagrams and motion diagrams, which can provide ideas and data references for the design of pulsating heat pipes with different contact angles of inner surfaces;

[0045] (4) The present invention is applicable to conditions where the pulsating heat pipe is at different temperatures in the evaporation and condensation sections, different sizes of the pulsating heat pipe, and different contact angles of the inner surface, and has wide applicability;

[0046] (5) The present invention calculates the length of the liquid film and liquid bullet based on the inner surface of different contact angles, and then compares and continuously corrects the liquid film thickness, thereby more accurately calculating the heat transfer performance of the pulsating heat pipe. Attached Figure Description

[0047] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings:

[0048] Fig. 1 This is a flowchart of a heat transfer calculation method for a pulsating heat pipe with a gradient wetting surface according to an embodiment of the present invention.

[0049] Fig. 2 This is a schematic diagram of the gradient wetting surface of the pulsating heat pipe in an embodiment of the present invention. Detailed Implementation

[0050] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0051] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0052] This embodiment proposes a method for calculating heat transfer in a pulsating heat pipe with a gradient wetting surface, such as... Figs. 1-2 As shown, the specific steps include:

[0053] Step 1: Establish a pulsating heat pipe model, determine the dimensional and structural parameters of the pulsating heat pipe, and divide the pulsating heat pipe into evaporation and condensation sections. Select the working medium inside the pulsating heat pipe, determine the relevant parameters of the selected working fluid properties, and assume the initial liquid film thickness; give the wall temperatures of the evaporation and condensation sections as follows: , Assume the initial temperatures of the left and right gas bombs are respectively... , Construct the energy equation of the liquid bomb to calculate its temperature;

[0054] Step 2: Calculate the initial vapor bomb pressure from the initial vapor bomb temperature assumed in Step 1. , The initial pressure of the vapor chamber is calculated and used as the initial value of the pressure. Updates and iterations are then performed based on this initial value.

[0055] Step 3: Construct the momentum equation of the liquid bullet and calculate its displacement. ;

[0056] Step 4: Gradiently wet the surface, calculate the liquid film length and liquid blast length; calculate the latent heat of vaporization and latent heat of condensation, and then use the latent heat calculation to solve for the change in steam mass caused by evaporation and condensation;

[0057] Step 5: Based on the first law of thermodynamics, construct the energy equation for the gas bomb, and combine it with the ideal gas law to calculate the pressure of the gas bomb. , ;

[0058] Step 6: Calculate the temperature of the gas bomb , Compare the results with the hypothesis. , The comparison is iterated, and the convergence criterion is set to an error of less than 10. -4 If the condition is met, the iteration stops; otherwise, the iteration is repeated from step 2 until the iteration requirement is met, and the vapor bomb temperature is calculated. , ;

[0059] Step 7: Measure the temperature of the gas bomb in Step 6. , The changes in density, viscosity, and specific heat capacity caused by the variations, along with the updated momentum equation of the liquid elasticity, lead to the calculation of the convective heat transfer coefficient. ; through the temperature of the gas bomb in step 6 , The changes in the specific volume difference between vapor and liquid during evaporation and condensation are used to update the calculated phase change heat transfer coefficient at the gas-liquid interface during condensation or evaporation. ;

[0060] Step 8: The gas-liquid interface temperature changes, causing the liquid bullet to shift and altering the gas-liquid boundary condition equation. The calculated liquid bullet temperature distribution is then updated. The theoretical liquid film thickness is calculated using the average temperature and average velocity of the liquid bullet. This thickness is then compared with the assumed liquid film thickness from Step 1 until the error condition is met.

[0061] 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.

[0062] Step 10: Output Calculation. During the periodic oscillation motion of the liquid bomb, with the boundary between the evaporation and condensation sections as the zero point, the displacement of the liquid bomb can be calculated. The temperature distribution of the liquid bomb can be solved using the energy equation, and the velocity distribution of the liquid bomb can be solved using the momentum equation. The output results are the temperature and pressure of the vapor bomb, 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.

[0063] Time step size is used in all numerical simulations. .

[0064] Specifically, step 1: Establish a pulsating heat pipe model, determine the dimensional and structural parameters of the pulsating heat pipe, and divide the pulsating heat pipe into evaporation and condensation sections. Select the working medium inside the pulsating heat pipe, determine the relevant parameters of the selected working medium's properties, and assume the initial liquid film thickness; give the wall temperatures of the evaporation and condensation sections as follows: , Assume the first iteration temperatures of the gas bombs on the left and right sides are respectively... , Construct the energy equation of the liquid bomb to calculate its temperature;

[0065] The temperature distribution in the liquid bomb is derived from the liquid bomb energy equation shown in equation (1). The liquid bomb temperature in equation (1) is solved using the finite difference scheme of the corresponding initial conditions (2) and gas-liquid interface boundary conditions (3) and (4). :

[0066] ;

[0067] ;

[0068] ;

[0069] ;

[0070] In equations (1)-(4): Thermal diffusivity / m 2 ·s -1 , The temperature of the liquid explosive is in K. For time / s, The coordinates are in meters along the direction from the condensation section to the evaporation section. The convective heat transfer coefficient is given by W·m. -2 ·K -1 , The value is the heat pipe diameter in meters (m). Thermal conductivity of the working fluid / W·m -1 ·K -1 , Cross-sectional area / m 2 , The wall temperature is in K. The initial temperature of the liquid bomb is K. The length of the liquid bullet is in meters. The temperature of the gas bomb on the left is in K. The temperature of the gas bomb on the right is given in K.

[0071] The wall temperature is related to the position of the liquid bomb, and can be determined by equations (5) and (6). :

[0072] ;

[0073] ;

[0074] In equations (5) and (6): The evaporator section wall temperature is in K. The condensation section wall temperature is given in K. The displacement of the liquid spring is expressed in meters.

[0075] The convective heat transfer coefficient of the working fluid inside the pulsating heat pipe is calculated using equation (7). :

[0076] ;

[0077] In equation (7): For Nusselt numbers, Let Reynolds number be 1. It is a Prandtl number.

[0078] Step 2: Calculate the pressure of the first iteration of the gas spring according to equations (8) and (9). , The solution is used as the initial value of the pressure, and the update iteration is based on this:

[0079] ;

[0080] ;

[0081] In equations (8) and (9): The initial temperature of the steam is in K. The initial steam pressure is given in Pa. The pressure on the left side is the vapor spring pressure in Pa. The pressure on the right is the air spring pressure in Pa. This is the heat capacity ratio.

[0082] Step 3: Construct the momentum equation of the liquid bullet and calculate its displacement. In the momentum equation of a liquid bullet, the terms on the left represent the change in momentum, and the terms on the right are represented as pressure, gravity, and shear stress terms respectively:

[0083] ;

[0084] In formula (10): working fluid density / kg·m -3 , The pressure loss at the bend (in Pa) Shear stress / Pa;

[0085] The initial conditions for a pulsating heat pipe include:

[0086] ;

[0087] ;

[0088] In equations (11) and (12): Initial liquid propellant position / m;

[0089] Pressure loss at bend for:

[0090] ;

[0091] In equation (13): This is the pressure loss coefficient. Steam velocity / m·s -1 ;

[0092] Shear stress is solved using equations (14) and (15). The coefficient of friction of fluid flow in the pipe is :

[0093] ;

[0094] ;

[0095] In equations (14) and (15): The coefficient of friction;

[0096] The displacement of the hydraulic elastic element can be calculated based on the above equations. .

[0097] Step 4: Gradiently wet the surface, calculate the liquid film length and liquid blast length; calculate the latent heat of vaporization and latent heat of condensation, and then use the latent heat calculation to solve for the change in steam mass caused by evaporation and condensation:

[0098] The latent heat of phase change for liquid film evaporation and condensation is calculated using the evaporation and condensation of the thin liquid film at the droplet tail; the thickness of the thin liquid film is calculated using the Aussillous model.

[0099] ;

[0100] In equation (16): The thickness of the thin liquid film inside the pulsating heat pipe is given in meters (m). It is the gross number.

[0101] The thermal resistance of steam condensation and evaporation mainly includes the thermal resistance of the liquid film on the wall and the phase change thermal resistance of evaporation and condensation.

[0102] The heat transfer coefficient of the liquid film on the wall is:

[0103] ;

[0104] In equation (17): The wall liquid film heat transfer coefficient / W·m -2 ·K -1 ;

[0105] Phase change heat transfer coefficient of gas-liquid interface condensation or evaporation Determined using the Schlager model:

[0106] ;

[0107] In formula (18): Phase change heat transfer coefficient / W·m -2 ·K -1 , The fitness coefficient is set to 0.03. The specific volume difference between steam and liquid. The relative mass of the working fluid is expressed in g·mol⁻¹. -1 ;

[0108] Overall heat transfer coefficient for:

[0109] ;

[0110] In equation (19): The overall heat transfer coefficient is given by W·m.-2 ·K -1 ;

[0111] For gradient wetting channels, the driving force includes the Laplace-Young capillary force and the driving force generated by the wetting gradient, as shown in equation (20):

[0112] ;

[0113] The local contact angle of the gradient wetting channel satisfies equation (21):

[0114] ;

[0115] Substituting equation (21) into equation (20), we obtain equation (22) for the driving force of the working fluid motion on the gradient-wetting surface:

[0116] ;

[0117] In equations (20)-(22): The surface tension of the working fluid is expressed as a degree. for The static contact angle at that location for Static contact angle size / degree at the location for Static contact angle size / degree at the location;

[0118] ;

[0119] In equation (23): The average velocity of the liquid film / m·s -1 , The dynamic viscosity of the working fluid is expressed in Pa·s. The total length of the pulsating heat pipe channel is given in meters (m).

[0120] When the liquid bomb flows through the channel, a 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 towards the condensation section; when the liquid bomb moves towards the evaporation section, the length of the liquid film gradually decreases, and simultaneously, the thin liquid film evaporates, causing the liquid film length to gradually decrease. When the gas-liquid interface of the liquid bomb is in the condensation section, only evaporation causes the length of the liquid film to decrease. The length of the thin liquid film inside the tube can be calculated using equation (26):

[0121] ;

[0122] In equation (24): The length of the liquid film in the condensation section is in meters. The length of the liquid film in the evaporation section is in meters. Steam mass / kg.

[0123] The changed length of the liquid bomb is calculated using equations (25) and (26), and the obtained changed length of the liquid bomb is then used in equation (10) for the next stage of iteration.

[0124] ;

[0125] ;

[0126] In equations (25) and (26): The length of the changed liquid explosive is given in meters. The initial liquid bullet length is given in meters. The length of the liquid-gel section on the left (in meters) is [length of liquid-gel section on the left]. The length of the liquid bomb in the left evaporation section is given in meters. The length of the liquid-gel section on the right is given in meters. The length of the liquid bomb in the evaporation section on the right is given in meters. The cross-sectional area of ​​the thin liquid film / m 2 , The cross-sectional area of ​​the thin liquid film on the left is / m 2 , The cross-sectional area of ​​the thin liquid film on the right is / m 2 .

[0127] When steam enters the condensing section, heat transfer occurs between the steam and the condensing section wall, causing the steam to condense and its mass to decrease. When the liquid bomb enters the evaporating section, heat transfer between the liquid bomb and the evaporating section wall causes the liquid bomb to boil, increasing the steam's mass. Under certain conditions, due to the increase in steam mass and the work done on the steam by the moving liquid bomb, the steam temperature may rise above the evaporating section temperature. At this point, condensation occurs due to heat transfer between the steam and the evaporating section wall, further reducing the steam's mass.

[0128] ;

[0129] In equation (27): The latent heat (W) for liquid film condensation and vapor condensation at the gas-liquid interface. The latent heat of liquid film evaporation and liquid-liquid interface evaporation (in W);

[0130] The rate of change in steam mass due to evaporation and condensation is calculated using equations (26) and (27):

[0131] ;

[0132] ;

[0133] In equations (28) and (29): Latent heat of phase transition of working fluid / J·kg -1 ;

[0134] Step 5: Based on the first law of thermodynamics, construct the energy equations (28) and (29) for the gas bomb, and calculate the pressure of the gas bomb by combining them with the ideal gas law:

[0135] ;

[0136] ;

[0137] In equations (30) and (31): The constant-pressure heat capacity of the working fluid / J·kg -1 ·K -1 ; The constant volume heat capacity of the working fluid / J·kg -1 ·K -1 ;

[0138] ;

[0139] ;

[0140] In equations (32) and (33): Gas constant / J·mol -1 ·K -1 .

[0141] The relationship between the mass and pressure of the two gas bombs is shown in equations (34) and (35):

[0142] ;

[0143] ;

[0144] Substitute the steam mass change obtained in step 5 into equations (34) and (35) to calculate the pressure of the steam bomb. , .

[0145] Step 6: Calculate the temperature of the gas bomb using equations (8) and (9). , Compare the results with the hypothesis. , The comparison is iterated, and the convergence criterion is set to an error of less than 10. -4 If the condition is met, the iteration stops; otherwise, the iteration is repeated from step 2 until the iteration requirement is met, and the vapor bomb temperature is calculated. , .

[0146] Step 7: Measure the temperature of the gas bomb in Step 6. , The changes in density, viscosity, and specific heat capacity caused by the change, as well as the momentum equation (10) of the liquid elasticity, are used to update the convective heat transfer coefficient by equation (7). ; through the temperature of the gas bomb in step 6 , The changes in vapor and liquid specific volume difference due to evaporation and condensation are updated by equation (18) for the phase change heat transfer coefficient at the gas-liquid interface during condensation or evaporation. In a pulsating heat pipe, the convective heat transfer coefficient and the gas-liquid interface phase change heat transfer coefficient jointly determine the temperature distribution of the liquid blast by influencing the flow and phase change process of the working fluid, thus affecting the heat transfer performance of the pulsating heat pipe. Optimizing the convective heat transfer coefficient and the gas-liquid interface phase change heat transfer coefficient can improve the heat transfer efficiency and stability of the pulsating heat pipe.

[0147] Step 8: The gas-liquid interface temperature changes, causing the liquid bomb to shift and altering the gas-liquid boundary conditions (3) and (4). The updated liquid bomb temperature distribution is calculated using the liquid bomb energy equation shown in equation (1), the initial condition (2), and the altered boundary conditions (3) and (4). Based on equation (16), the theoretical liquid film thickness is calculated using the average temperature and average velocity of the liquid bomb. This is then compared with the liquid film thickness assumed in step 1 until the error condition is met.

[0148] 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.

[0149] The heat generated by the liquid bomb due to unidirectional convection is calculated using equations (36) and (37);

[0150] ;

[0151] ;

[0152] In equations (36) and (37):

[0153] Sensible heat transferred by the liquid bomb / W;

[0154] The sensible heat transferred from the liquid bomb / W;

[0155] When the pulsating heat pipe is in steady state, the thermal resistance can be calculated using equation (38); the total heat transfer can be calculated using equations (38), (39), and (40). Sensible heat transfer Latent heat transfer :

[0156] ;

[0157] ;

[0158] ;

[0159] ;

[0160] In equations (38)-(41): Thermal resistance / K·W -1 , Latent heat transfer rate / W Sensible heat transfer rate (W), Total heat transfer / W.

[0161] Step 10: Output Calculation. During the periodic oscillating motion of the liquid bomb, taking the boundary between the evaporation and condensation sections as the zero point, the displacement of the liquid bomb can be calculated. The temperature distribution of the liquid bomb can be solved using the energy equation, and the velocity distribution of the liquid bomb can be solved using the momentum equation. The output results are the temperature and pressure of the vapor bomb, 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 and condensation sections... The pressure difference caused by the temperature gradient drives the liquid-elastic pulsation, which promotes the circulation of the working fluid between the evaporation and condensation sections, 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 liquid-elastic pulsation is the main heat transfer pathway in pulsating heat pipes. Thermal resistance is the ratio of the temperature difference between the evaporation and condensation sections to the input heat flow. The smaller the thermal resistance, the less heat is retained inside the pipe, and the better the heat transfer performance of the pulsating heat pipe. The above results can be used to perform simple calculations and analyses of the oscillation height, oscillation speed, and thermal resistance of pulsating heat pipes operating with different working fluids, and to draw motion diagrams based on the calculation results.

[0162] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for calculating heat transfer in a pulsating heat pipe with a gradient wetting surface, 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. Determine the initial liquid film thickness and initial vapor bomb temperature of the pulsating heat pipe model; S3. Calculate the liquid bullet temperature based on the temperatures of the evaporation section and the condensation section; S4. Calculate the initial gas bomb pressure based on the initial gas bomb temperature, and calculate the liquid bomb displacement based on the initial gas bomb pressure. Obtain the steam mass change based on the liquid bomb displacement, liquid bomb length, and transformed liquid bomb length. Calculate the gas bomb pressure for subsequent iterations based on the steam mass change. S5. Calculate the gas bomb temperature based on the gas bomb pressure, compare the gas bomb temperature with the initial gas bomb temperature, and if the difference satisfies the first relative error, proceed to step S6; otherwise, return to S2 to re-assume the initial gas bomb temperature and assume a new initial gas bomb temperature. S6. Update the liquid bullet temperature distribution according to the gas bullet temperature and calculate the theoretical thickness of the liquid film. Compare the theoretical thickness of the liquid film 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 and assume a new initial liquid film thickness. S7. Calculate the sensible heat transferred into and out of the liquid bomb based on the liquid bomb displacement and the temperatures of the evaporation and condensation sections, and calculate the flow thermal resistance of the pulsating heat pipe.

2. The method for calculating heat transfer in a pulsating heat pipe with a gradient wetting surface according to claim 1, characterized in that, In S3, the calculation of the liquid bomb temperature based on the temperatures of the evaporation and condensation sections includes: 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 scheme of the initial conditions and the gas-liquid interface boundary conditions to obtain the liquid-bomb temperature. The liquid-bomb energy equation is related to the wall temperature, which is obtained based on the temperatures of the evaporation section and the condensation section.

3. The method for calculating heat transfer in a pulsating heat pipe with a gradient wetting surface according to claim 1, characterized in that, S4 includes calculating the liquid-bulk displacement based on the initial vapor pressure, including: The 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. The momentum equation of the liquid bomb is the relationship between momentum change and pressure, gravity and shear stress.

4. The method for calculating heat transfer in a pulsating heat pipe with a gradient wetting surface according to claim 1, characterized in that, In S4, the change in steam mass is obtained based on the displacement of the liquid explosive, and the steam explosive pressure is calculated based on the change in steam mass, including: The heat transfer coefficient of the liquid film on the wall is calculated based on the thickness of the thin liquid film deposited inside the pipe. 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. The overall heat transfer coefficient is obtained based on the heat transfer coefficient of the liquid film on the wall and the phase change heat transfer coefficient. Based on the liquid bullet displacement, the lengths of the liquid film in the condensation section and the liquid film in the evaporation section are obtained; The latent heat of vaporization and latent heat of condensation are calculated based on the overall heat transfer coefficient, liquid film length, vapor bomb temperature, and evaporation and condensation section temperatures. The rate of change of steam mass due to evaporation and condensation is calculated using the latent heat of vaporization, the latent heat of condensation, the liquid bomb displacement, the liquid film length, and the liquid film transformation length. Based on the steam mass change rate and the first law of thermodynamics, the energy equation of the steam bomb is constructed to calculate the steam bomb pressure.

5. The method for calculating heat transfer in a pulsating heat pipe with a gradient wetting surface according to claim 4, characterized in that, The energy equation for the gas bomb is: ； ； in, , The mass of the gas bombs on the left and right sides, The isobaric molar heat capacity of the working fluid. and For the temperature of the gas bomb, and These are the steam pressure on the left and the vapor pressure on the right, respectively. The diameter of the heat pipe. For the displacement of the liquid spring, The molar heat capacity at constant volume of the working fluid. For time.

6. The method for calculating heat transfer in a pulsating heat pipe with a gradient wetting surface according to claim 4, characterized in that, S6 includes updating the liquid bomb temperature distribution based on the vapor bomb temperature and calculating the theoretical thickness of the liquid film, including: The heat transfer coefficient of the liquid film on the wall is updated based on the changes in density, viscosity, and specific heat capacity caused by the temperature of the vapor bomb. The phase change heat transfer coefficient is updated based on the changes in the liquid bomb temperature, the specific volume difference between the vapor and the liquid; Based on the heat transfer coefficient of the liquid film on the wall and the phase change heat transfer coefficient, the gas-liquid interface conditions are updated and the liquid-elastic temperature distribution is calculated. Based on the liquid-elastic temperature distribution, the average temperature and average velocity of the liquid-elastic related to the capillary number are obtained, thereby calculating the theoretical thickness of the liquid film.

7. The method for calculating heat transfer in a pulsating heat pipe with a gradient wetting surface according to claim 1, characterized in that, The sensible heat calculation method for the liquid bomb's input and output as described in S7 is as follows: ； The calculation method for the sensible heat transferred from the liquid bomb is as follows: ； in, The sensible heat transferred by the liquid bomb. For the length of the liquid bullet, For the displacement caused by the liquid bullet, The convective heat transfer coefficient, For the temperature of the liquid bomb, This refers to the temperature of the condensation section. Position of the liquid bullet. The sensible heat transferred from the liquid bomb. This is the diameter of the heat pipe.

8. The method for calculating heat transfer in a pulsating heat pipe with a gradient wetting surface according to claim 7, characterized in that, The method for calculating the flow thermal resistance of a pulsating heat pipe in S7 is as follows: ； ； ； in, For thermal resistance, The temperature of the evaporation section. For average sensible heat, The average latent heat, The average sensible heat transferred from the liquid bomb. The average sensible heat transferred by the liquid bomb. For average condensation heat, This represents the average heat of evaporation.

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