A pulsating heat pipe heat transfer model and calculation method and system of a mutual-solvent mixed working medium

Abstract

The application belongs to the technical field of phase change heat transfer equipment, and discloses a pulsating heat pipe heat transfer model of mutually soluble mixed working medium, and a calculation method and system thereof, which comprises the following steps: establishing a pulsating heat pipe model, assuming pulsating amplitude, frequency, liquid film thickness and gas bomb temperature; according to the temperatures of the evaporation section and the condensation section, sequentially calculating liquid bomb temperature, gas bomb pressure, liquid bomb displacement, liquid film flow rate, liquid film and liquid bomb length; obtaining the bubble point and dew point temperature difference through the activity coefficient method, comparing the gas bomb temperature after updating with the initial value, and reassuming the gas bomb temperature if the first relative error is not satisfied; further calculating the liquid film theoretical thickness, and reassuming the liquid film thickness if the second relative error is not satisfied; then calculating the pulsating frequency and amplitude, and reassuming the pulsating frequency if the third relative error is not satisfied; and finally calculating the sensible heat and thermal resistance after convergence.

Description

Technical Field

[0001] This invention belongs to the technical field of phase change heat exchange equipment, specifically relating to a heat transfer model, calculation method and system for a pulsating heat pipe with a miscible mixed working fluid. Background Technology

[0002] Pulsating heat pipes achieve high heat flux density transfer through the dynamic phase change cycle of a gas-liquid two-phase fluid; they are also known as oscillating heat pipes. Pulsating heat pipes have gained attention and widespread development due to their high heat transfer efficiency, low design and manufacturing costs, and the elimination of the need for a wick. Pulsating heat pipes can transfer latent heat not only through phase change but also sensible heat through gas-liquid elastic oscillation. In the evaporation section, the liquid working fluid absorbs a large amount of heat, generating numerous bubbles that rapidly expand and increase pressure, propelling the working fluid towards the condensation section. In the condensation section, the gaseous working fluid condenses into a liquid state, causing a pressure drop, and the liquid returns to the evaporation section for the next cycle. The working fluid oscillates and undergoes a phase change process in these two regions, giving the pulsating heat pipe its highly efficient heat transfer performance.

[0003] The physical properties of the working fluid affect the heat transfer performance of a pulsating heat pipe. Different substances have significantly different physical properties; some improve the heat transfer performance of a pulsating heat pipe, while others weaken it. By mixing different working fluids in varying volume proportions, it is possible to expect the heat pipe to have better heat transfer performance. Existing heat transfer calculations for pulsating heat pipes mostly focus on a single working fluid, neglecting the changes in heat transfer characteristics caused by the interactions between components in a mixed working fluid. Directly applying these calculations results in significant errors. Summary of the Invention

[0004] To address the problems existing in the prior art, this invention provides a heat transfer model, calculation method, and system for a pulsating heat pipe with a miscible mixed working fluid. This invention analyzes and calculates the heat transfer performance of the pulsating heat pipe with the mixed working fluid and the motion state of the mixed working fluid, providing guidance for the calculation of mixed working fluid parameters and engineering applications of pulsating heat pipes.

[0005] To achieve the above objectives, the present invention provides the following solution: A heat transfer model and calculation method for a pulsating heat pipe with a miscible mixed working fluid, the method comprising: S1. Establish a pulsating heat pipe model, select the heat pipe working medium, give the temperatures of the evaporation section and the condensation section, and determine the pulsation amplitude, pulsation frequency, initial liquid film thickness and initial gaseous temperature of the pulsating heat pipe model. S2. Calculate the liquid bomb temperature based on the temperatures of the evaporation and condensation sections; S3. Calculate the initial gaseous pressure based on the initial gaseous temperature, calculate the liquid bullet displacement based on the initial gaseous pressure, and calculate the liquid film flow velocity, liquid film length, and liquid bullet length based on the initial liquid film thickness. S4. Preset the bubble point temperature and dew point temperature of the mixed working fluid, and calculate and update the bubble point temperature and vapor dew point temperature of the liquid working fluid using the activity coefficient method to obtain the difference between the dew point temperature and the bubble point temperature. S5. Calculate the latent heat and obtain the change in steam mass, and calculate the gas spring pressure based on the change in steam mass; S6. Calculate the gas cylinder temperature based on the gas cylinder pressure, compare the gas cylinder temperature with the initial gas cylinder temperature. If the difference meets the first relative error, proceed to S7. If not, return to S1 to redetermine the initial gas cylinder temperature and preset a new initial gas cylinder temperature. S7. Update the liquid-bomb displacement and the calculated convective heat transfer coefficient based on the calculated liquid-bomb displacement; S8. Update the gas cylinder temperature based on the calculated gas cylinder temperature and calculate the theoretical thickness of the liquid film. Compare the theoretical thickness of the liquid film with the initial preset liquid film thickness. If the difference meets the second relative error, proceed to S9. If not, return to S1 to redetermine the initial liquid film thickness and preset a new initial liquid film thickness. S9. Calculate the pulsation frequency and pulsation amplitude of the pulsating heat pipe, compare the pulsation frequency and amplitude with the initial pulsation frequency and amplitude, if the difference meets the third relative error, proceed to S10, if not, return to S1 to redetermine the pulsation frequency and preset a new pulsation frequency. S10. Calculate sensible heat and thermal resistance based on the liquid explosive displacement, temperature, and temperatures of the evaporation and condensation sections.

[0006] Preferably, S2. The method for calculating the liquid bomb temperature based on the temperatures of the evaporation section and the condensation section includes: The energy equation of the liquid bomb is constructed, and the liquid bomb temperature is solved using a finite difference scheme based on the initial conditions and the gas-liquid interface boundary conditions to obtain the liquid bomb temperature; the calculation formula is as follows: ; ; ; ; In the formula: Thermal diffusivity / m 2 ·s -1 ; The temperature of the liquid explosive is given in K. Heat pipe diameter / m; Position of the liquid bullet in meters; The convective heat transfer coefficient is given by W·m. -2 ·K -1 ; Thermal conductivity of the working fluid / W·m -1 ·K -1 ; Cross-sectional area / m 2 ; Wall temperature / K; Time / s; The temperature of the gas bomb on the left is in K. The temperature of the gas bomb on the right is in K. For temperature variables; The initial temperature of the liquid bomb is given in K. The length of the liquid bullet is in meters. This represents the mole fraction of the working fluid in the liquid phase.

[0007] Preferably, S3. The method for calculating the liquid-elastic displacement based on the initial gaseous pressure includes: ; In the formula: Cross-sectional area / m 2 ; The length of the liquid bullet is in meters. working fluid density / kg·m -3 ; Pressure loss at the bend / Pa; Shear stress / Pa; The pressure of the air spring on the left is in Pa. The pressure of the air spring on the left is in Pa. The displacement of the liquid spring is expressed in meters. The value is the heat pipe diameter in meters (m).

[0008] Preferably, S4. The method for presetting the bubble point temperature and dew point temperature of the mixed working fluid, and calculating and updating the bubble point temperature and vapor dew point temperature of the liquid working fluid using the activity coefficient method to obtain the difference between the dew point temperature and the bubble point temperature includes: Assuming the bubble point temperature, calculate the saturated vapor pressure of the components using the Antoine equation: ; In the formula, The saturated vapor pressure of water is given in Pa. The saturated vapor pressure of acetone is given in Pa. , , The Antoine constant for water; , , The antoine constant for acetone; For temperature variables; The liquid phase activity coefficient is calculated based on the Wilson equation, and the phase equilibrium constant is calculated as follows: ; ; ; In the formula, and The liquid phase activity coefficient, , This represents the liquid mole fraction of water. This represents the liquid phase mole fraction of acetone. and For Wilson parameters; It refers to air pressure; according to The calculation results are used to determine whether the assumed bubble point temperature meets the preset requirements. Assuming the dew point temperature, calculate the saturated vapor pressure of the components using the Antoine equation. and Then, calculate the liquid phase activity coefficient according to the Wilson equation. and Then calculate the phase equilibrium constant. ;according to The calculation results, among which, This represents the vapor mole fraction of water. Given the vapor mole fraction of acetone, determine whether the assumed dew point temperature meets the preset requirements. Based on the bubble point temperature and dew point temperature that meet the preset requirements, the difference between the dew point temperature and the bubble point temperature is calculated. .

[0009] Preferably, S5. Calculating the latent heat and obtaining the change in steam mass, and the method for calculating the gas spring pressure based on the change in steam mass includes: The average heat transfer coefficient of the condensate film is calculated based on the average length of the liquid film, the steam temperature, and the condensation section temperature. The falling film boiling heat transfer coefficient of the evaporation section is calculated based on the falling film Reynolds number. The convective heat transfer coefficient on the gas side is calculated based on the pulsation frequency and the liquid elastic displacement. Based on the equilibrium model, the total heat transfer coefficient on the condenser side and the total heat transfer coefficient on the evaporator side are calculated according to the average heat transfer coefficient of the condensate film, the boiling heat transfer coefficient of the falling film in the evaporation section and the convective heat transfer coefficient on the gas phase side. The latent heat of vaporization and latent heat of condensation are calculated based on the total heat transfer coefficient on the condensing side, the total heat transfer coefficient on the evaporating side, the liquid film length, the gaseous temperature, and the temperatures of the evaporating and condensing sections. The steam mass change rate is calculated using the latent heat of vaporization, latent heat of condensation, liquid bullet displacement, liquid film length, and liquid film transition length. Based on the rate of change of steam mass and the first law of thermodynamics, an energy equation for the gas bomb is constructed to calculate the gas bomb pressure.

[0010] The preferred method for calculating the gas-phase side convective heat transfer coefficient is as follows: ; In the formula, The gas-phase side convective heat transfer coefficient is... The working fluid's gas phase thermal conductivity is... Let Reynolds number be the number of motion. The amplitude of the pulsation; The value is the heat pipe diameter in meters (m).

[0011] Preferably, based on an equilibrium model, the method for calculating the total heat transfer coefficient on the condensing side and the total heat transfer coefficient on the evaporating side according to the average heat transfer coefficient of the condensate film, the boiling heat transfer coefficient of the falling film in the evaporating section, and the convective heat transfer coefficient on the gas phase side includes: ; ; In the formula, To measure the overall heat transfer coefficient during condensation, The overall heat transfer coefficient on the evaporator side is... The heat transfer coefficient of the condensation film, The falling film boiling heat transfer coefficient in the evaporation section. The gas-phase side convective heat transfer coefficient is... The heat transferred in the sensible heat phase of the gas phase. This refers to the heat transferred to the liquid phase side.

[0012] Preferably, S7. The method for updating the liquid-bone displacement based on the calculated liquid-bone displacement, and updating the calculated convective heat transfer coefficient, includes: ; In the formula, For Nusel number, The diameter of the heat pipe. For the thermal conductivity of the working fluid, Let Reynolds number be the number of motion. The amplitude of the pulsation. The convective heat transfer coefficient is given.

[0013] This invention also provides a heat transfer model and calculation system for a pulsating heat pipe with a miscible mixed working fluid. The system is used to implement the aforementioned method and includes: a model initialization module, a liquid bullet temperature calculation module, a gas bullet pressure-liquid bullet displacement calculation module, a phase change temperature update module, a vapor mass-gas bullet pressure calculation module, a gas bullet temperature iterative verification module, a liquid bullet displacement update module, a liquid film thickness iterative verification module, a pulsation characteristic iterative verification module, and a sensible thermal resistance calculation module. The model initialization module is used to establish a pulsating heat pipe model, select the heat pipe working medium, give the temperatures of the evaporation section and the condensation section, and determine the pulsation amplitude, pulsation frequency, initial liquid film thickness and initial gaseous temperature of the pulsating heat pipe model. The liquid bomb temperature calculation module is used to calculate the liquid bomb temperature based on the temperatures of the evaporation section and the condensation section. The gas-bulb pressure-liquid-bulb displacement calculation module is used to calculate the initial gas-bulb pressure based on the initial gas-bulb temperature, calculate the liquid-bulb displacement based on the initial gas-bulb pressure, and calculate the liquid film flow velocity, liquid film length, and liquid-bulb length based on the initial liquid film thickness. The phase change temperature update module is used to preset the bubble point temperature and dew point temperature of the mixed working fluid, and calculate and update the bubble point temperature and vapor dew point temperature of the liquid working fluid by using the activity coefficient method to obtain the difference between the dew point temperature and the bubble point temperature. The steam mass-gas spring pressure calculation module is used to calculate the latent heat and obtain the change in steam mass, and calculate the gas spring pressure based on the change in steam mass. The gas cylinder temperature iteration verification module is used to calculate the gas cylinder temperature based on the gas cylinder pressure, compare the gas cylinder temperature with the initial gas cylinder temperature, and if the difference meets the first relative error, then enter the liquid cylinder displacement update module; if not, return to the model initialization module to redetermine the initial gas cylinder temperature and preset a new initial gas cylinder temperature. The liquid bullet displacement update module is used to update the liquid bullet displacement and update the calculated convective heat transfer coefficient based on the calculated liquid bullet displacement. The liquid film thickness iteration verification module is used to update the gas bullet temperature according to the calculated gas bullet temperature and calculate the theoretical liquid film thickness. The theoretical liquid film thickness is compared with the initial preset liquid film thickness. If the difference meets the second relative error, it enters the pulsation characteristic iteration verification module. If it does not meet the second relative error, it returns to the model initialization module to redetermine the initial liquid film thickness and preset a new initial liquid film thickness. The pulsation characteristic iterative verification module is used to calculate the pulsation frequency and pulsation amplitude of the pulsation heat pipe, compare the pulsation frequency and amplitude with the initial pulsation frequency and amplitude, and if the difference meets the third relative error, then enter the sensible thermal resistance calculation module; if not, return to the model initialization module to redetermine the pulsation frequency and preset a new pulsation frequency. The sensible heat and thermal resistance calculation module is used to calculate sensible heat and thermal resistance based on the liquid ball displacement, temperature, and the temperatures of the evaporation and condensation sections.

[0014] Compared with the prior art, the beneficial effects of the present invention are as follows: (1) The present invention uses the activity coefficient method to iteratively calculate the bubble dew point temperature of the mixed working fluid, describes the phase equilibrium relationship of the multi-component working fluid, solves the problem of the difficulty in quantifying the phase change temperature of the mixed working fluid, and can be adapted to the calculation of different binary mixed working fluids, and has wide applicability.

[0015] (2) This invention proposes the assumption of the proportional relationship between mass transfer resistance and gas phase sensible heat resistance, transforming the component diffusion resistance into a quantifiable mathematical model, so that the heat transfer coefficient is more in line with the actual heat transfer process of the mixed working fluid.

[0016] (3) The present invention can calculate the motion state of the working fluid inside the pulsating heat pipe, including heat transfer performance parameters such as velocity distribution, temperature distribution and amplitude.

[0017] (4) The iterative process constructed by the present invention is simple and has good convergence.

[0018] (5) The output can provide more concise and clear result diagrams and motion diagrams, which can provide ideas and data references for the design of mixed working fluid pulsating heat pipes. Attached Figure Description

[0019] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 This is a flowchart of a heat transfer model and calculation method for a pulsating heat pipe with a miscible mixed working fluid according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the inside of the pulsating heat pipe with a miscible mixed working fluid in an embodiment of the present invention. Detailed Implementation

[0021] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0022] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0023] Example 1 This invention provides a heat transfer model and calculation method for a pulsating heat pipe with a miscible mixed working fluid, the method comprising: S1. Establish a heat pipe model, select the heat pipe working medium, and specify the temperatures of the evaporation and condensation sections; S2. Determine the pulsation amplitude, pulsation frequency, initial liquid film thickness, and initial aeroelastic temperature of the pulsating heat pipe model; S3. Calculate the liquid bomb temperature based on the temperatures of the evaporation and condensation sections; S4. Calculate the initial gaseous pressure based on the initial gaseous temperature, calculate the displacement of the liquid bullet based on the initial gaseous pressure, and calculate the liquid film flow velocity, liquid film length and liquid bullet length based on the assumed liquid film thickness. S5. Assuming the bubble point temperature and dew point temperature of the mixed working fluid, calculate and update the bubble point temperature and vapor dew point temperature of the liquid working fluid using the activity coefficient method to obtain the difference between the dew point temperature and the bubble point temperature. S6. Calculate the latent heat and obtain the change in steam mass, and calculate the aeroelastic pressure for subsequent iterations based on the change in steam mass; S7. Calculate the gas cartridge temperature based on the gas cartridge pressure, compare the gas cartridge temperature with the initial gas cartridge temperature, if the difference satisfies the first relative error, proceed to step S8, if not, return to S2 to redetermine the initial gas cartridge temperature and assume a new initial gas cartridge temperature. S8. Update the liquid bullet displacement and the calculated convective heat transfer coefficient based on the calculated liquid bullet displacement; S9. Update the gas cylinder temperature based on the calculated gas cylinder temperature and calculate the theoretical thickness of the liquid film. Compare the theoretical thickness of the liquid film with the initial assumed liquid film thickness. If the difference satisfies the second relative error, proceed to step S10. If not, return to S2 to redetermine the initial liquid film thickness and assume a new initial liquid film thickness. S10. Calculate the pulsation frequency and pulsation amplitude of the pulsating heat pipe, compare the pulsation frequency and amplitude with the initial pulsation frequency and amplitude, if the difference satisfies the third relative error, proceed to step S11, if not, return to S2 to redetermine the pulsation frequency and assume a new pulsation frequency. S11. Calculate sensible heat and thermal resistance based on the liquid bullet displacement, temperature, and the temperatures of the evaporation section and condensation section.

[0024] In this embodiment, S3. The method for calculating the liquid bomb temperature based on the temperatures of the evaporation section and the condensation section includes: An energy equation for a liquid bomb is constructed, and the liquid bomb temperature is solved using a finite difference scheme based on the initial conditions and the gas-liquid interface boundary conditions. The liquid bomb temperature is obtained by solving this equation, where the energy equation is related to the wall temperature, which is obtained based on the temperatures of the evaporation and condensation sections. The calculation formula is as follows: ; ; ; ; In the formula: Thermal diffusivity / m 2 ·s -1 ; The temperature of the liquid explosive is given in K. Heat pipe diameter / m; Position of the liquid bullet in meters; The convective heat transfer coefficient is given by W·m. -2 ·K -1 ; Thermal conductivity of the working fluid / W·m -1 ·K -1 ; Cross-sectional area / m 2 ; The value is the wall temperature in K.

[0025] In this embodiment, S4. The method for calculating the liquid-elastic displacement based on the initial gaseous pressure includes: A liquid-elastic momentum equation is constructed, and the liquid-elastic displacement is calculated based on the gas-elastic pressure. The liquid-elastic momentum equation represents the relationship between the change in liquid-elastic momentum and the driving force of the vapor pressure difference, gravity, and shear force. The calculation formula is as follows: ; In the formula: Cross-sectional area / m 2 ; The length of the liquid bullet is in meters. working fluid density / kg·m -3 ; Pressure loss at the bend / Pa; The shear stress is expressed in Pa.

[0026] In this embodiment, S5. The method for calculating and updating the bubble point temperature and dew point temperature of the mixed working fluid using the activity coefficient method to obtain the difference between the dew point temperature and the bubble point temperature includes: Assuming the bubble point temperature, calculate the saturated vapor pressure of the components using the Antoine equation: ; In the formula, The saturated vapor pressure of water is given in Pa. The saturated vapor pressure of acetone is given in Pa. , , The Antoine constant for water; , , The antoine constant for acetone; The liquid phase activity coefficient is calculated based on the Wilson equation, and the phase equilibrium constant is calculated as follows: ; ; ; In the formula, and The liquid phase activity coefficient, and The mole fraction of the working fluid in the liquid phase. and For Wilson parameters, It is the heat capacity ratio; according to The calculation results are used to determine whether the assumed bubble point temperature meets the preset requirements. Assuming the dew point temperature, calculate the saturated vapor pressure of the components using the Antoine equation. and Then, calculate the liquid phase activity coefficient according to the Wilson equation. and Then calculate the phase equilibrium constant. ;according to The calculation results are used to determine whether the assumed dew point temperature meets the preset requirements. Based on the bubble point temperature and dew point temperature that meet the preset requirements, the difference between the dew point temperature and the bubble point temperature is calculated. .

[0027] In this embodiment, S6. Calculating the latent heat and obtaining the change in steam mass, and calculating the gas spring pressure based on the change in steam mass includes: The average heat transfer coefficient of the condensate film is calculated based on the average length of the liquid film, the steam temperature, and the condensation section temperature. The falling film boiling heat transfer coefficient of the evaporation section is calculated based on the falling film Reynolds number. The convective heat transfer coefficient on the gas side is calculated based on the pulsation frequency and the liquid elastic displacement. Based on the equilibrium model, the total heat transfer coefficient on the condenser side and the total heat transfer coefficient on the evaporator side are calculated according to the average heat transfer coefficient of the condensate film, the boiling heat transfer coefficient of the falling film in the evaporation section and the convective heat transfer coefficient on the gas phase side. The latent heat of vaporization and latent heat of condensation are calculated based on the total heat transfer coefficient on the condensing side, the total heat transfer coefficient on the evaporating side, the liquid film length, the gaseous temperature, and the temperatures of the evaporating and condensing sections. The steam mass change rate is calculated using the latent heat of vaporization, latent heat of condensation, liquid bullet displacement, liquid film length, and liquid film transition length. Based on the rate of change of steam mass and the first law of thermodynamics, an energy equation for the gas bomb is constructed to calculate the gas bomb pressure.

[0028] In this embodiment, the method for calculating the gas-phase side convective heat transfer coefficient is as follows: ; In the formula, The gas-phase side convective heat transfer coefficient is... The working fluid's gas phase thermal conductivity is... Let Reynolds number be the number of motion. This represents the amplitude of the pulsation.

[0029] In this embodiment, based on the equilibrium model, the method for calculating the total heat transfer coefficient on the condensing side and the total heat transfer coefficient on the evaporating side according to the average heat transfer coefficient of the condensate film, the boiling heat transfer coefficient of the falling film in the evaporation section, and the convective heat transfer coefficient on the gas phase side includes: ; ; In the formula, To measure the overall heat transfer coefficient during condensation, The overall heat transfer coefficient on the evaporator side is... The heat transfer coefficient of the condensation film, The falling film boiling heat transfer coefficient in the evaporation section. The heat transfer coefficient on the gas phase side is... The heat transferred in the sensible heat phase of the gas phase. This refers to the heat transferred to the liquid phase side.

[0030] In this embodiment, S7. The method for updating the liquid-bone displacement based on the calculated liquid-bone displacement and updating the calculated convective heat transfer coefficient includes: ; In the formula, For Nusel number, The diameter of the heat pipe. For the thermal conductivity of the working fluid, Let Reynolds number be 1. The amplitude of the pulsation. The convective heat transfer coefficient is given.

[0031] Example 2 The preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0032] like Figures 1-2 As shown, the specific method steps include: 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 within the pulsating heat pipe and determine its physical properties. Assume the pulsation frequency of the pulsating heat pipe. and pulsation amplitude Assuming the initial thickness of the liquid film... Given the wall temperature of the evaporation section and condensation section wall temperature Assume the temperatures of the gas bombs on the left and right sides are respectively... and Constructing the liquid bomb energy equation to calculate the liquid bomb temperature ; The temperature of the liquid bomb is solved using the liquid bomb energy equation shown in equation (1) and the corresponding initial and boundary conditions in equations (2)-(4). : (1) (2) (3) (4) In equations (1)-(4): Thermal diffusivity / m 2 ·s -1 ; The temperature of the liquid explosive is given in K. Heat pipe diameter / m; Position of the liquid bullet in meters; The convective heat transfer coefficient is given by W·m. -2 ·K -1 ; Thermal conductivity of the working fluid / W·m -1 ·K -1 ; Cross-sectional area / m 2 ; Wall temperature / K; Time / s; The initial temperature of the liquid bomb is given in K. The temperature of the gas bomb on the left is in K. The temperature of the gas bomb on the right is in K. For temperature variables; Wall temperature and The wall temperature can be obtained from equations (5) and (6) depending on the position of the liquid bomb. : (5) (6) In equations (5) and (6): The displacement of the liquid spring is expressed in meters. The convective heat transfer coefficient can be determined using equation (7). : (7) In equation (7): For Nusselt number; The motion Reynolds number; The motion Reynolds number is defined as: (8) (9) In the formula: Angular frequency / rad·s -1 ; kinematic viscosity of fluid / m 2 ·s -1 ; amplitude The relationship with the displacement of the hydraulic elastic element is as follows: (10) Step 2: Calculate the steam pressure of the first iteration according to equations (11) and (12). and , as the initial value of the pressure: (11) (12) In the formula: Initial steam temperature in K; Initial steam pressure (Pa); It is the heat capacity ratio; The pressure of the air spring on the left is in Pa. The pressure of the air spring on the left is in Pa. Step 3: Construct the momentum equation of the liquid bullet and calculate its displacement. : (13) In equation (13): Cross-sectional area / m 2 ; The length of the liquid bullet is in meters. working fluid density / kg·m -3 ; Pressure loss at the bend / Pa; Shear stress / Pa; The initial conditions for a pulsating heat pipe are: (14) (15) (16) In equation (14): Initial liquid propellant position / m; Pressure loss at bend for: (17) In equation (17): This is the pressure loss coefficient; Steam velocity / m·s -1 ; Calculate the shear stress according to equation (18): (18) in The coefficient of friction for fluid flow and the coefficient of friction in a smooth pipe are: (19) In equation (19): The Reynolds number is the flow number. Step 4: Calculate the liquid film flow velocity; calculate the liquid film length and the length of the liquid boulders: The thickness of the condensate film was calculated based on Nusselt's film condensation theory. (20) In equation (20): The dynamic viscosity of the working fluid is expressed in kg·m³. -1 ·s -1 ; The average length of the condensate film is given in meters. Density of the gaseous working fluid / kg·m -3 ; Latent heat of vaporization of the working fluid / J·kg -1 ; The temperature of the gas bomb is in K. Calculate the velocity of the liquid film flowing downwards, due to gravity: (twenty one) In equation (21): The velocity of the liquid film flowing downwards / m·s -1 ; The distance from the liquid film to the pipe wall is in meters (m). average speed The result is calculated using equation (21): (twenty two) The length of the liquid film on the wall is calculated using equation (23): (twenty three) In equation (23): 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; The changed length of the liquid bomb is calculated using equation (24), and the obtained changed length of the liquid bomb is then used in equation (13) for the next stage of iteration. (twenty four) In equation (24): The length of the changed liquid explosive is given in meters. The initial liquid bullet length is given in meters. The cross-sectional area of ​​the liquid film on the left is given in m². 2 ; The cross-sectional area of ​​the liquid film on the right is given in m². 2 ; The length of the liquid bobbin in the left condensation section is given in meters. 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 liquid film is calculated according to equation (25): (25) Step 5: Calculate the bubble point temperature of the liquid using the activity coefficient method. and vapor dew point temperature Iterative calculations are required; then the difference between the dew point temperature and the bubble point temperature needs to be calculated: (26) The latent heat of vaporization of the mixed working fluid is calculated by equation (27): (27) In equation (27): and These are the enthalpy of the gas phase and the enthalpy of the liquid phase, respectively, and the enthalpy difference. Approximate latent heat of vaporization of the working fluid ; Assuming the bubble point temperature, calculate the saturated vapor pressure of the components using the Antoine equation. and : (28) In equation (28): The saturated vapor pressure of water is given in Pa. The saturated vapor pressure of acetone is given in Pa. , , The Antoine constant for water; , , The antoine constant for acetone; Calculate the liquid phase activity coefficient according to the Wilson equation. and : (29) (30) In the formula This represents the liquid mole fraction of water. This represents the liquid phase mole fraction of acetone. and For Wilson parameters; Calculate the phase equilibrium constant for: (31) in, It refers to air pressure; calculate ,if This indicates that the assumed bubble point temperature is too high and needs to be lowered; if If the bubble point temperature is assumed to be too low, it needs to be increased until it meets the requirements. .

[0033] In equation (31): , This represents the liquid mole fraction of water. This represents the liquid phase mole fraction of acetone. Let be the phase equilibrium constant of water. is the phase equilibrium constant of acetone; The calculation of dew point temperature is similar. Assuming a dew point temperature, the saturated vapor pressure of the component is calculated using the Antoine equation. and Then, calculate the liquid phase activity coefficient according to the Wilson equation. and Then calculate the phase equilibrium constant. ;calculate ,if This indicates that the assumed dew point temperature is too low and needs to be increased; if If the assumed dew point temperature is too high, the dew point temperature needs to be lowered until it meets the requirements. ,in This represents the vapor mole fraction of water. denoted as the gaseous mole fraction of acetone.

[0034] The difference between the dew point temperature and the bubble point temperature can be calculated from this. .

[0035] Step 6: Calculate the latent heat of vaporization and latent heat of condensation, and use the latent heat to calculate the change in steam mass caused by evaporation and condensation; The average heat transfer coefficient of the Nusselt condenser film is: (32) The heat transfer coefficient of the falling film boiling in the evaporation section was calculated using the Chun and Seban model: (33) The descending film Reynolds number is calculated using equation (34): (34) (35) (36) In the formula: Liquid film mass flow rate per unit length / kg·m -1 ·s -1 ; Liquid film mass flow rate / kg·s -1 ; For mixed working fluids, based on the equilibrium model, two key assumptions are proposed: the mass transfer resistance is approximately proportional to the sensible heat transfer resistance in the gas phase, and the mass transfer resistance generated by component diffusion during the phase change of the mixed working fluid can be characterized by the proportional relationship of the sensible heat resistance in the gas phase; there is diffusion resistance on the gas phase side of the gas-liquid interface, and the multi-component characteristics of the mixed working fluid cause the phase change process to be accompanied by component diffusion, generating additional resistance.

[0036] Overall heat transfer coefficient on the condenser side With the overall heat transfer coefficient on the evaporator side Calculate using equations (37) and (38): (37) (38) In the formula: The heat transferred in the sensible gas phase is expressed in J. Heat transferred on the liquid side / J; Gas phase side convective heat transfer coefficient Calculated using equation (39): (39) In equation (39): Thermal conductivity of the working fluid in the gas phase / W·m -1 ·K -1 .

[0037] Mass transfer resistance Equation (40) represents: (40) In equation (40): Specific heat capacity of working fluid at constant pressure / J·mol -1 ·K -1 ; In the condensation section, steam exchanges heat with the cooler wall surface, releasing heat and undergoing a condensation phase change, resulting in a decrease in the steam mass within the system. In the evaporation section, the liquid buoy absorbs heat upon contact with the hotter wall surface, undergoing a boiling phase change and generating new steam, thus increasing the steam mass within the system. Under specific operating conditions, the continuous generation of steam in the evaporation section and the work done by the liquid buoy's motion on the steam compression will together cause the steam temperature to rise above the evaporation section wall temperature. At this point, the steam will release heat to the wall surface and condense, further reducing the steam mass within the system.

[0038] (41) In equation (41): 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); The rate of change of steam mass due to evaporation and condensation is calculated using equations (42) and (43): (42) (43) In the formula: The latent heat of vaporization of the mixed working fluid / J·kg -1 ; The steam mass on the left is in kg. The steam mass on the right is in kg. Step 7: According to the first law of thermodynamics, the energy equation of the gas bomb can be obtained; combining this with the ideal gas law, the pressure of the gas bomb can be calculated: (44) (45) In the formula: Specific heat capacity of working fluid at constant volume / J·kg -1 ·K -1 ; The pressure of the air spring on the left is in Pa. The pressure of the air spring on the left is in Pa. The temperature of the gas bomb on the left is in K. The temperature of the gas bomb on the right is in K. Since the gaseous bomb satisfies the ideal gas law, equations (46) and (47) can be derived. (46) (47) In the formula: Gas constant / J·mol -1 ·K -1 ; The length of the aerogel is in meters. The relationship between the mass and pressure of the two gas cylinders is given by the following equations (48) and (49): (48) (49) Substituting the steam mass change obtained in step 7 into equations (48) and (49), the gas spring pressure is calculated. and ; Step 8: Calculate the gas bullet temperature using equations (11) and (12) and The results are compared with the initially assumed aeroelastic temperature, and the iteration convergence criterion is set as an error 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 aeroelastic temperature is calculated. and .

[0039] Step 9: Calculate the updated convective heat transfer coefficient using equation (7). .

[0040] Step 10: The gas-liquid interface temperature changes, causing the liquid bomb to shift, which alters 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 equation (2), and the changed boundary conditions (3) and (4). The theoretical liquid film thickness is calculated according to equation (20) and compared with the assumed liquid film thickness in step 1 until the error condition is met.

[0041] Step 11: Calculate the pulsation frequency and pulsation amplitude Compare the value assumed in the first step with the value assumed in the second step. If the relative error is less than the tolerance of 10... -3 If the convergence condition is met, proceed to the next step; otherwise, repeat step 1 until the convergence condition is met.

[0042] Step 12: 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. The heat generated by the liquid bomb due to unidirectional convection is calculated by equations (50) and (51). (50) (51) In the formula: Sensible heat transferred by the liquid bomb / W; The sensible heat transferred from the liquid bomb / W; Sensible heat transfer of pulsating heat pipe and latent heat transfer Expressed by equations (52) and (53) respectively: (52) (53) The thermal resistance of a pulsating heat pipe is calculated using equation (54): (54) Total heat transfer It consists of two parts: the latent heat generated by liquid film evaporation and condensation, and the sensible heat carried by liquid elastic oscillation. (55) Step 13: Output Calculation. The calculation results can be obtained as follows: displacement, temperature distribution, and velocity distribution of the liquid bomb, temperature and pressure of the gas bomb, and latent heat, sensible heat, and thermal resistance of the pulsating heat pipe. The frequency of the pulsating heat pipe oscillation can be obtained by using the relationship between the Nusselt number and the convective heat transfer coefficient.

[0043] Example 3 This invention provides a heat transfer model and calculation system for a pulsating heat pipe with a miscible mixed working fluid. The system is used to implement the method described in Embodiment 1. The system includes: a model initialization module, a liquid bullet temperature calculation module, a gas bullet pressure-liquid bullet displacement calculation module, a phase change temperature update module, a vapor mass-gas bullet pressure calculation module, a gas bullet temperature iterative verification module, a liquid bullet displacement update module, a liquid film thickness iterative verification module, a pulsation characteristic iterative verification module, and a sensible thermal resistance calculation module. The model initialization module is used to establish a pulsating heat pipe model, select the heat pipe working medium, give the temperatures of the evaporation section and the condensation section, and determine the pulsation amplitude, pulsation frequency, initial liquid film thickness and initial aeroelastic temperature of the pulsating heat pipe model. The liquid bomb temperature calculation module is used to calculate the liquid bomb temperature based on the temperatures of the evaporation and condensation sections. The gas-bulk pressure-liquid-bulk displacement calculation module is used to calculate the initial gas-bulk pressure based on the initial gas-bulk temperature, calculate the liquid-bulk displacement based on the initial gas-bulk pressure, and calculate the liquid film flow velocity, liquid film length, and liquid-bulk length based on the initial liquid film thickness. The phase change temperature update module is used to preset the bubble point temperature and dew point temperature of the mixed working fluid, and calculates and updates the bubble point temperature and vapor dew point temperature of the liquid working fluid by using the activity coefficient method, so as to obtain the difference between the dew point temperature and the bubble point temperature. The steam mass-gas spring pressure calculation module is used to calculate latent heat and obtain the change in steam mass, and then calculate the gas spring pressure based on the change in steam mass. The gas cylinder temperature iteration verification module is used to calculate the gas cylinder temperature based on the gas cylinder pressure, compare the gas cylinder temperature with the initial gas cylinder temperature, and if the difference meets the first relative error, it enters the liquid cylinder displacement update module; if it does not meet the first relative error, it returns to the model initialization module to redetermine the initial gas cylinder temperature and preset a new initial gas cylinder temperature. The liquid-bomb displacement update module is used to update the liquid-bomb displacement based on the calculated liquid-bomb displacement and update the calculated convective heat transfer coefficient. The liquid film thickness iteration verification module is used to update the gas shell temperature based on the calculated gas shell temperature and calculate the theoretical liquid film thickness. The theoretical liquid film thickness is compared with the initial preset liquid film thickness. If the difference meets the second relative error, it enters the pulsation characteristic iteration verification module. If it does not meet the requirement, it returns to the model initialization module to redetermine the initial liquid film thickness and preset a new initial liquid film thickness. The pulsation characteristic iterative verification module is used to calculate the pulsation frequency and pulsation amplitude of the pulsation heat pipe. It compares the pulsation frequency and amplitude with the initial pulsation frequency and amplitude. If the difference meets the third relative error, it enters the sensible thermal resistance calculation module. If it does not meet the requirement, it returns to the model initialization module to redetermine the pulsation frequency and preset a new pulsation frequency. The sensible heat and thermal resistance calculation module is used to calculate sensible heat and thermal resistance based on the liquid explosive displacement, temperature, and the temperatures of the evaporation and condensation sections.

[0044] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A heat transfer model and calculation method for a pulsating heat pipe with a miscible mixed working fluid, characterized in that, The method includes: S1. Establish a pulsating heat pipe model, select the heat pipe working medium, give the temperatures of the evaporation section and the condensation section, and determine the pulsation amplitude, pulsation frequency, initial liquid film thickness and initial gaseous temperature of the pulsating heat pipe model. S2. Calculate the liquid bomb temperature based on the temperatures of the evaporation and condensation sections; S3. Calculate the initial gaseous pressure based on the initial gaseous temperature, calculate the liquid bullet displacement based on the initial gaseous pressure, and calculate the liquid film flow velocity, liquid film length, and liquid bullet length based on the initial liquid film thickness. S4. Preset the bubble point temperature and dew point temperature of the mixed working fluid, and calculate and update the bubble point temperature and vapor dew point temperature of the liquid working fluid using the activity coefficient method to obtain the difference between the dew point temperature and the bubble point temperature. S5. Calculate the latent heat and obtain the change in steam mass, and calculate the gas spring pressure based on the change in steam mass; S6. Calculate the gas cylinder temperature based on the gas cylinder pressure, compare the gas cylinder temperature with the initial gas cylinder temperature. If the difference meets the first relative error, proceed to S7. If not, return to S1 to redetermine the initial gas cylinder temperature and preset a new initial gas cylinder temperature. S7. Update the liquid-bomb displacement and the calculated convective heat transfer coefficient based on the calculated liquid-bomb displacement; S8. Update the gas cylinder temperature based on the calculated gas cylinder temperature and calculate the theoretical thickness of the liquid film. Compare the theoretical thickness of the liquid film with the initial preset liquid film thickness. If the difference meets the second relative error, proceed to S9. If not, return to S1 to redetermine the initial liquid film thickness and preset a new initial liquid film thickness. S9. Calculate the pulsation frequency and pulsation amplitude of the pulsating heat pipe, compare the pulsation frequency and amplitude with the initial pulsation frequency and amplitude, if the difference meets the third relative error, proceed to S10, if not, return to S1 to redetermine the pulsation frequency and preset a new pulsation frequency. S10. Calculate sensible heat and thermal resistance based on the liquid explosive displacement, temperature, and temperatures of the evaporation and condensation sections.

2. The method according to claim 1, characterized in that, S2. Methods for calculating the liquid bomb temperature based on the temperatures of the evaporation and condensation sections include: The energy equation of the liquid bomb is constructed, and the liquid bomb temperature is solved using a finite difference scheme based on the initial conditions and the gas-liquid interface boundary conditions to obtain the liquid bomb temperature; the calculation formula is as follows: ； ； ； ； In the formula: Thermal diffusivity / m 2 ·s -1 ; The temperature of the liquid explosive is given in K. Heat pipe diameter / m; Position of the liquid bullet in meters; The convective heat transfer coefficient is given by W·m. -2 ·K -1 ; Thermal conductivity of the working fluid / W·m -1 ·K -1 ; Cross-sectional area / m 2 ; Wall temperature / K; Time / s; The temperature of the gas bomb on the left is in K. The temperature of the gas bomb on the right is in K. For temperature variables; The initial temperature of the liquid bomb is given in K. The length of the liquid bullet is in meters. This represents the mole fraction of the working fluid in the liquid phase.

3. The method according to claim 1, characterized in that, S3. Methods for calculating hydroelastic displacement based on initial aeroelastic pressure include: ； In the formula: Cross-sectional area / m 2 ; The length of the liquid bullet is in meters. working fluid density / kg·m -3 ; Pressure loss at the bend / Pa; Shear stress / Pa; The pressure of the air spring on the left is in Pa. The pressure of the air spring on the left is in Pa. The displacement of the liquid spring is expressed in meters. The value is the heat pipe diameter in meters (m).

4. The method according to claim 1, characterized in that, S4. The bubble point and dew point temperatures of the pre-set mixed working fluid are used to calculate and update the bubble point and dew point temperatures of the liquid working fluid using the activity coefficient method. Methods for obtaining the difference between the dew point temperature and the bubble point temperature include: Assuming the bubble point temperature, calculate the saturated vapor pressure of the components using the Antoine equation: ； In the formula, The saturated vapor pressure of water is given in Pa. The saturated vapor pressure of acetone is given in Pa. , , The Antoine constant for water; , , The antoine constant for acetone; For temperature variables; The liquid phase activity coefficient is calculated based on the Wilson equation, and the phase equilibrium constant is calculated as follows: ； ； ； In the formula, and The liquid phase activity coefficient, , This represents the liquid mole fraction of water. This represents the liquid phase mole fraction of acetone. and For Wilson parameters; It refers to air pressure; according to The calculation results are used to determine whether the assumed bubble point temperature meets the preset requirements. Assuming the dew point temperature, calculate the saturated vapor pressure of the components using the Antoine equation. and Then, calculate the liquid phase activity coefficient according to the Wilson equation. and Then calculate the phase equilibrium constant. ;according to The calculation results, among which, This represents the vapor mole fraction of water. Given the vapor mole fraction of acetone, determine whether the assumed dew point temperature meets the preset requirements. Based on the bubble point temperature and dew point temperature that meet the preset requirements, the difference between the dew point temperature and the bubble point temperature is calculated. .

5. The method according to claim 1, characterized in that, S5. Calculate the latent heat and obtain the change in steam mass. Methods for calculating the gaseous pressure based on the change in steam mass include: The average heat transfer coefficient of the condensate film is calculated based on the average length of the liquid film, the steam temperature, and the condensation section temperature. The falling film boiling heat transfer coefficient of the evaporation section is calculated based on the falling film Reynolds number. The convective heat transfer coefficient on the gas side is calculated based on the pulsation frequency and the liquid elastic displacement. Based on the equilibrium model, the total heat transfer coefficient on the condenser side and the total heat transfer coefficient on the evaporator side are calculated according to the average heat transfer coefficient of the condensate film, the boiling heat transfer coefficient of the falling film in the evaporation section and the convective heat transfer coefficient on the gas phase side. The latent heat of vaporization and latent heat of condensation are calculated based on the total heat transfer coefficient on the condensing side, the total heat transfer coefficient on the evaporating side, the liquid film length, the gaseous temperature, and the temperatures of the evaporating and condensing sections. The steam mass change rate is calculated using the latent heat of vaporization, latent heat of condensation, liquid bullet displacement, liquid film length, and liquid film transition length. Based on the rate of change of steam mass and the first law of thermodynamics, an energy equation for the gas bomb is constructed to calculate the gas bomb pressure.

6. The method according to claim 5, characterized in that, The method for calculating the gas-phase side convective heat transfer coefficient is as follows: ； In the formula, The gas-phase side convective heat transfer coefficient is... The working fluid's gas phase thermal conductivity is... Let Reynolds number be the number of motion. The amplitude of the pulsation; The value is the heat pipe diameter in meters (m).

7. The method according to claim 5, characterized in that, Based on the equilibrium model, methods for calculating the total heat transfer coefficient on the condensing side and the total heat transfer coefficient on the evaporating side include: (The methods are not provided in the original text.) ； ； In the formula, To measure the overall heat transfer coefficient during condensation, The overall heat transfer coefficient on the evaporator side is... The heat transfer coefficient of the condensation film, The falling film boiling heat transfer coefficient in the evaporation section. The gas-phase side convective heat transfer coefficient is... The heat transferred in the sensible heat phase of the gas phase. This refers to the heat transferred to the liquid phase side.

8. The method according to claim 1, characterized in that, S7. The methods for updating the calculated liquid-elastic displacement and the convective heat transfer coefficient include: ； In the formula, For Nusel number, The diameter of the heat pipe. For the thermal conductivity of the working fluid, Let Reynolds number be the number of motion. The amplitude of the pulsation. The convective heat transfer coefficient is given.

9. A heat transfer model and calculation system for a pulsating heat pipe with a miscible mixed working fluid, the system being used to implement the method described in any one of claims 1-8, characterized in that, The system includes: a model initialization module, a liquid bullet temperature calculation module, a gas bullet pressure-liquid bullet displacement calculation module, a phase change temperature update module, a steam mass-gas bullet pressure calculation module, a gas bullet temperature iterative verification module, a liquid bullet displacement update module, a liquid film thickness iterative verification module, a pulsation characteristic iterative verification module, and a sensible thermal resistance calculation module. The model initialization module is used to establish a pulsating heat pipe model, select the heat pipe working medium, give the temperatures of the evaporation section and the condensation section, and determine the pulsation amplitude, pulsation frequency, initial liquid film thickness and initial gaseous temperature of the pulsating heat pipe model. The liquid bomb temperature calculation module is used to calculate the liquid bomb temperature based on the temperatures of the evaporation section and the condensation section. The gas-bulb pressure-liquid-bulb displacement calculation module is used to calculate the initial gas-bulb pressure based on the initial gas-bulb temperature, calculate the liquid-bulb displacement based on the initial gas-bulb pressure, and calculate the liquid film flow velocity, liquid film length, and liquid-bulb length based on the initial liquid film thickness. The phase change temperature update module is used to preset the bubble point temperature and dew point temperature of the mixed working fluid, and calculate and update the bubble point temperature and vapor dew point temperature of the liquid working fluid by using the activity coefficient method to obtain the difference between the dew point temperature and the bubble point temperature. The steam mass-gas spring pressure calculation module is used to calculate the latent heat and obtain the change in steam mass, and calculate the gas spring pressure based on the change in steam mass. The gas cylinder temperature iteration verification module is used to calculate the gas cylinder temperature based on the gas cylinder pressure, compare the gas cylinder temperature with the initial gas cylinder temperature, and if the difference meets the first relative error, then enter the liquid cylinder displacement update module; if not, return to the model initialization module to redetermine the initial gas cylinder temperature and preset a new initial gas cylinder temperature. The liquid bullet displacement update module is used to update the liquid bullet displacement and update the calculated convective heat transfer coefficient based on the calculated liquid bullet displacement. The liquid film thickness iteration verification module is used to update the gas bullet temperature according to the calculated gas bullet temperature and calculate the theoretical liquid film thickness. The theoretical liquid film thickness is compared with the initial preset liquid film thickness. If the difference meets the second relative error, it enters the pulsation characteristic iteration verification module. If it does not meet the second relative error, it returns to the model initialization module to redetermine the initial liquid film thickness and preset a new initial liquid film thickness. The pulsation characteristic iterative verification module is used to calculate the pulsation frequency and pulsation amplitude of the pulsation heat pipe, compare the pulsation frequency and amplitude with the initial pulsation frequency and amplitude, and if the difference meets the third relative error, then enter the sensible thermal resistance calculation module; if not, return to the model initialization module to redetermine the pulsation frequency and preset a new pulsation frequency. The sensible heat and thermal resistance calculation module is used to calculate sensible heat and thermal resistance based on the liquid ball displacement, temperature, and the temperatures of the evaporation and condensation sections.

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