Heat transfer calculation method for interval capillary core pulsating heat pipe

Abstract

The invention discloses a heat transfer calculation method for an interval capillary core pulsating heat pipe, which comprises the following steps of: constructing a relational expression of steam bomb temperature and pressure, and calculating the steam bomb pressure; constructing a liquid bomb energy equation, and calculating a liquid bomb temperature initial value; constructing an interval capillary core pulsating heat pipe liquid elastic momentum equation, and calculating liquid elastic displacement; constructing different pipe section liquid film length calculation formulas, and calculating different pipe section liquid film lengths; the heat transfer amount of liquid film evaporation and condensation is obtained, and the corresponding mass variation of the steam bomb is calculated; obtaining a relational expression of mass flow and pressure of the steam bomb, and calculating to obtain a new pressure value of the steam bomb; constructing a relational expression between the temperature and the pressure of the steam bomb, and obtaining a new value of the temperature of the steam bomb; constructing a liquid bomb energy equation, obtaining a new liquid bomb temperature value, and carrying out comparison iteration; obtaining sensible heat transferred in and out of the liquid bomb, and calculating the thermal resistance of the pulsating heat pipe; and outputting the calculation result to complete the calculation of the heat transfer model. The method provides guidance for design and development of the pulsating heat pipe covering the capillary cores at intervals.

Description

Technical Field

[0001] The invention belongs to the technical field of phase change heat exchange equipment, and in particular relates to a heat transfer calculation method for an interval capillary wick pulsating heat pipe. Background Art

[0002] With the trend of miniaturization and compactness of electronic devices, the heat flux density of microelectronic devices continues to increase, seriously affecting the performance and service life of the equipment. Therefore, the demand for efficient heat dissipation materials continues to increase. As an efficient heat dissipation device, the pulsating heat pipe couples two heat transfer modes: phase change heat transfer and oscillating motion sensible heat transfer in micro channels. The vapor pressure difference generated by the latent heat transfer between the evaporation end and the condensation end drives the liquid bullet to oscillate in the channel. It is a heat pipe with high thermal conductivity and is considered to be one of the most effective ways to cope with the challenge of high heat flux density. Limited by the working principle, the pulsating heat pipe is difficult to start when placed horizontally and against gravity. By adding a capillary wick to the pulsating heat pipe, the problems of the evaporation section of the low-tube pulsating heat pipe being difficult to reflux and replenish due to gravity, the evaporation section being easy to burn dry under high-flux heat flux conditions, and the difficulty in starting can be solved. In addition, compared with the fully covered capillary wick, the spaced capillary wick can bring a larger unbalanced pressure difference to the adjacent pipelines, improve the effective driving force, and at the same time reduce the resistance of the capillary wick to the liquid elastic oscillation, significantly improve the effective thermal conductivity of the liquid working fluid, and enhance the heat transfer performance of the pulsating heat pipe.

[0003] The liquid wick, condensed liquid film and liquid bomb inside the spaced capillary wick pulsating heat pipe have heat and mass transfer coupling characteristics, and the heat transfer and working fluid movement state in the pulsating heat pipe are complex. In view of this, how to provide a numerical simulation calculation for the spaced capillary wick pulsating heat pipe while ensuring the speed and accuracy of the numerical calculation is an urgent problem to be solved by people in this field. Summary of the invention

[0004] In order to solve the above technical problems, the present invention proposes a heat transfer calculation method for an interval capillary wick pulsating heat pipe, which can obtain the transient heat transfer flow characteristics of the working fluid inside the interval capillary wick pulsating heat pipe and the full coverage capillary wick pulsating heat pipe, perform numerical simulation on the capillary wick pulsating heat pipe under different working conditions, calculate the temperature and pressure of the steam bomb in the pulsating heat pipe, calculate the oscillation height, liquid film length, temperature distribution and thermal resistance of the liquid bomb and other heat transfer properties, provide suggestions and guidance for the design and engineering application of the capillary wick pulsating heat pipe, and solve the problems existing in the above-mentioned prior art.

[0005] To achieve the above object, the present invention provides a heat transfer calculation method for a spaced capillary wick pulsating heat pipe, comprising the following steps:

[0006] Obtain the heat pipe size and structure parameters and the capillary wick structure parameters, and build a pulsating heat pipe model;

[0007] In the pulsating heat pipe model, the initial temperature values ​​of the two steam bombs are preset, a functional relationship between the steam bomb temperature and pressure is constructed, and the initial pressure value of the steam bomb is calculated based on the functional relationship between the steam bomb temperature and pressure;

[0008] Constructing a liquid-elastic energy equation, and calculating the liquid-elastic temperature distribution based on the liquid-elastic energy equation and corresponding initial conditions and boundary conditions;

[0009] The hydraulic dynamic equation of the spaced capillary wick pulsating heat pipe is constructed to obtain the shear stress of the smooth pipe section and the capillary wick covered pipe section respectively, and the hydraulic displacement is calculated based on the hydraulic dynamic equation of the spaced capillary wick pulsating heat pipe, the shear stress of different pipe sections and the initial value of the steam elastic pressure;

[0010] The liquid film length calculation formulas of the smooth tube segment and the capillary wick covered tube segment are respectively constructed, and the corresponding liquid film lengths are obtained based on the liquid film length calculation formulas of different tube segments;

[0011] Acquire the heat transfer of liquid film evaporation and condensation, and calculate the corresponding steam bomb mass changes based on the heat transfer of liquid film evaporation and condensation;

[0012] Obtaining a relationship between the mass flow rate and pressure of the steam bomb, and calculating a new value of the steam bomb pressure based on the relationship between the mass flow rate and pressure of the steam bomb and the obtained change in the mass of the steam bomb;

[0013] Based on the functional relationship between the steam bomb temperature and pressure and the new value of the steam bomb pressure, a new value of the steam bomb temperature is obtained;

[0014] Based on the liquid bomb energy equation and the new value of the steam bomb temperature, obtaining a new value of the liquid bomb temperature;

[0015] The obtained new value of the steam bomb temperature is compared with the given initial value of the steam bomb temperature to iteratively obtain the final new values ​​of the steam bomb and liquid bomb temperature;

[0016] Acquire the sensible heat amount transferred into and out of the liquid bomb, and calculate the thermal resistance of the pulsating heat pipe based on the sensible heat amount;

[0017] Output the liquid bomb temperature, liquid bomb displacement, liquid film length, steam bomb mass change, new steam bomb pressure value, new steam bomb temperature value and thermal resistance of the pulsating heat pipe to complete the heat transfer calculation.

[0018] Optionally, the functional relationship between the steam bomb temperature and pressure is as follows:

[0019]

[0020] Among them, T v0 is the initial temperature of the steam bomb; P v0 is the initial pressure of the steam bomb; γ is the heat capacity ratio; P v1 , P v2 is the steam bomb pressure; T V1, T V2 are the steam bomb temperatures respectively.

[0021] Optionally, the liquid-elastic energy equation and the corresponding initial conditions and boundary conditions are expressed as follows:

[0022]

[0023] T=T0,t=0,0<x l <L p

[0024] T=T v1 ,x l =0

[0025] T=T v2 ,x l =L p

[0026] Where T1 is the liquid bomb temperature; α l is the thermal diffusion coefficient; A is the cross-sectional area; d is the heat pipe diameter; L p is the length of the liquid bullet; x l is the liquid bomb position; h sen is the convective heat transfer coefficient; T W is the wall temperature; T V1 , T V2 are the steam bomb temperatures; t is the time; π is a constant.

[0027] Optionally, the expression of the fluid elastic momentum equation of the spaced capillary wick pulsating heat pipe is as follows:

[0028]

[0029] Among them, ρ l is the liquid density; ΔP b is the pressure loss at the elbow; L p,wick is the length of the liquid bomb in the capillary core area; τ p,wick is the shear stress in the capillary core area; L p,smooth is the length of the liquid bullet in the smooth area; τ p,smooth is the shear stress in the smooth area; P v1 , P v2 is the pressure of the two gas bombs; g is the acceleration due to gravity.

[0030] Optionally, the calculation formula for the liquid film length of the smooth tube section and the capillary wick covered tube section is as follows:

[0031] The calculation formula of the thin liquid film length in the smooth pipe section is:

[0032]

[0033] The calculation formula for the length of the thin liquid film covering the tube section of the capillary core is:

[0034]

[0035] Among them, L c,i is the length of the liquid film in the condensation section; L e,i is the liquid film length in the evaporation section; δ smooth is the thickness of the liquid film in the smooth pipe section; δ wick is the thickness of the liquid film in the wick; m v is the mass of the steam bomb; u is the velocity of the condensate in the capillary wick in the x direction; v p is the liquid bullet velocity; ε is the porosity of the wire mesh capillary core; ρ is the liquid density.

[0036] Alternatively, the heat transfer formula for liquid film evaporation and condensation is as follows:

[0037]

[0038] Among them, Q cond,i Q is the heat transfer of liquid film condensation; evp,i h is the heat transfer of liquid film evaporation; sum is the total heat transfer coefficient; L c,i is the length of the liquid film in the condensation section; L e,i is the liquid film length in the evaporation section; T e 、T c are the wall temperatures of the evaporation section and the condensation section, respectively.

[0039] Optionally, the calculation formula of the steam bomb mass change rate is as follows:

[0040]

[0041] Among them, m v1 、m v2 is the mass of the gas bomb; h fg is the latent heat of phase change of the working fluid.

[0042] Optionally, the process of obtaining the relationship between the mass flow rate and pressure of the steam bomb includes: constructing an energy equation and an ideal gas state equation of the steam bomb, and obtaining a relationship between the mass flow rate and pressure of the steam bomb based on the functional relationship between the energy equation and the ideal gas state equation of the steam bomb, wherein the relationship between the mass flow rate and pressure of the steam bomb is as follows:

[0043]

[0044] Among them, R g is the gas constant; P v1 , P v2 are respectively the steam bomb pressure; d is the heat pipe diameter; P v0 is the initial pressure of the steam bomb; γ is the heat capacity ratio; Le is the liquid film length in the evaporation section.

[0045] Optionally, the calculation formula for the sensible heat transferred into and out of the liquid bomb is as follows:

[0046]

[0047] Among them, Q h is the sensible heat transferred by the liquid bomb; Q c is the sensible heat transferred by the liquid bomb; T l,i is the liquid bomb temperature; h sen is the convective heat transfer coefficient; T e 、T c are the wall temperatures of the evaporation section and the condensation section respectively; L p is the length of the liquid bullet.

[0048] Optionally, the calculation formula of the thermal resistance of the pulsating heat pipe is as follows:

[0049]

[0050] Where R is thermal resistance; is the average sensible heat transferred by the liquid bomb; is the average sensible heat transferred by the liquid bomb; is the average condensation heat; is the average heat of evaporation; is the average sensible heat; is the average latent heat.

[0051] Compared with the prior art, the present invention has the following advantages and technical effects:

[0052] (1) The present invention provides a novel heat transfer calculation method for a pulsating heat pipe with a spaced-covered capillary wick, which can calculate and analyze the flow characteristics such as the liquid-elastic oscillation displacement, liquid-elastic temperature distribution, and liquid film length of a pulsating heat pipe with a spaced-covered capillary wick or a fully covered capillary wick, as well as the heat transfer performance such as the heat transfer amount and thermal resistance of the heat pipe.

[0053] (2) It can be applied to uniform pore capillary wicks, non-uniform pore combination capillary wicks, and interval coverage and full coverage capillary wick pulsating heat pipes with multiple working fluids. Among them, the applicable capillary wick structures include metal powder sintered capillary wicks, braided wire mesh sintered capillary wicks, grooved capillary wicks, fiber sintered capillary wicks and other single structure capillary wicks and composite structure capillary wicks, which have wide applicability.

[0054] (3) A new algorithm is provided to calculate the length and thickness of the liquid film based on the presence or absence of capillary wick coverage, and then to calculate the liquid-elastic flow conditions and heat transfer of the pulsating heat pipe.

[0055] (4) The constructed iterative equation is simple in form and has good convergence.

[0056] (5) The output can obtain a simpler and clearer result diagram, which is convenient for providing design ideas and data references for the design of pulsating heat pipes with interval-covered capillary cores. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] The drawings constituting a part of the present application are used to provide a further understanding of the present application. The illustrative embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0058] Figure 1 It is a schematic flow chart of a heat transfer calculation method of a spaced capillary wick pulsating heat pipe according to an embodiment of the present invention;

[0059] Figure 2 Schematic diagram of a theoretical model of a spaced capillary wick pulsating heat pipe according to an embodiment of the present invention. DETAILED DESCRIPTION

[0060] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0061] In order to make the technical personnel in the field of the present invention better understand the solution of the present invention, the following will be combined with the accompanying drawings of the present invention to clearly and completely describe the technical solution in the embodiment of the present invention. Figure 1 The steps shown in the flowchart may 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 performed in an order different from that shown here.

[0062] Embodiment 1

[0063] like Figure 1-Figure 2 As shown, this embodiment provides a method for calculating heat transfer of a pulsating heat pipe with spaced capillary wicks, including:

[0064] Step 1: Determine the size and structural parameters of the capillary pulsating heat pipe and establish a pulsating heat pipe model: divide the evaporation section, adiabatic section and condensation section. Select the working fluid properties in the heat pipe and calculate the target parameters of the working fluid properties; set the wall temperatures of the evaporation section and condensation section as T e 、T c ; Given the initial value of the steam bomb temperature is T V1 、T V2 .

[0065] The structural parameters include: the diameter and length of the pulsating heat pipe; the thickness, mesh number, material, permeability and porosity of the capillary core.

[0066] Step 2: According to the initial temperature value T of the steam bombV1 、T V2 And formula (1) and (2) to calculate the initial value of steam bomb pressure P v1 , P v2 ;

[0067]

[0068] Among them, T v0 ——Initial temperature of steam bomb / K; P v0 ——initial pressure of steam bomb / Pa; γ——heat capacity ratio;

[0069] Step 3: Construct the liquid bomb energy equation to calculate the liquid bomb temperature;

[0070] The initial temperature value T of the liquid bomb is calculated by the energy equation of the liquid bomb shown in formula (3) and the corresponding initial conditions and boundary conditions (4)-(6): l :

[0071]

[0072] In formulas (3)-(6): T1——liquid bomb temperature / K; α l ——Thermal diffusivity / m 2 ·s -1 ; A——cross-sectional area / m 2 ; d——heat pipe diameter / m; L p ——Liquid bullet length / m; x l ——Liquid bullet position / m;

[0073] h sen ——Convection heat transfer coefficient / W·m -2 ·K -1 ; T W ——wall temperature / K;

[0074] The wall temperature is related to the position of the liquid bomb. The wall temperature T is determined by equations (7) and (8): W :

[0075]

[0076] In formula (7) and (8): x p ——Liquid-elastic displacement / m;

[0077] The convective heat transfer coefficient h is calculated by formula (9): sen :

[0078]

[0079] In formula (9): k l ——Thermal conductivity of condensate / W·m -1 ·K -1 ;

[0080] Step 4: Construct the corresponding momentum equation of the liquid bomb according to the arrangement of the capillary core and calculate the displacement x of the liquid bomb p ;

[0081] The fluid dynamic equation for the fully covered capillary wick pulsating heat pipe is shown in equation (10):

[0082]

[0083] In formula (10): l ——Liquid density / kg·m -3 ; ΔP b ——Pressure loss at the elbow / Pa; L p,wick ——The length of the liquid bullet in the capillary core area / m; τ p,wick ——Shear stress in the capillary core area / Pa;

[0084] The equation for the fluid elasticity of the spaced capillary wick pulsating heat pipe is shown in equation (11):

[0085]

[0086] In formula (11): L p,smooth ——The length of the liquid bullet in the smooth area / m; τ p,smooth ——shear stress in smooth area / Pa;

[0087] Pressure loss at elbow ΔP b for:

[0088]

[0089] In formula (12): ΔP b ——pressure loss / Pa; ζ——pressure loss coefficient; ν p ——Steam bullet speed / m·s -1 ; Shear stress τ p for:

[0090] τ p =f l ρ l v 2 / 2 (13)

[0091] In formula (13): p ——shear stress; f l ——friction coefficient; v——condensate flow rate / m·s -1 ;

[0092] Liquid flow friction coefficient f l The friction coefficient f in the capillary wick region is different from that in the smooth tube. l for:

[0093]

[0094] Assuming that the capillary wick area is a rough tube, the friction coefficient f of the pulsating heat pipe covered with the capillary wick can be calculated by the Colebrook-White rough tube equation: l :

[0095]

[0096] In formula (15): e——absolute height of roughness peak, i.e. thickness of capillary core / m;

[0097] According to the above equation, the liquid elastic displacement x p .

[0098] Step 5: Calculate the liquid film length of the smooth tube section and the capillary wick covered tube section according to equations (16) and (17) respectively;

[0099] When the liquid bullet flows through the smooth pipe section, a layer of liquid film remains on the wall. The length of the thin liquid film on the smooth pipe section can be calculated by formula (16):

[0100]

[0101] In formula (16): L c,i ——Liquid film length in condensation section / m; L e,i ——Liquid film length in evaporation section / m; δ smooth ——Liquid film thickness in smooth section / m; m v ——mass of gas bomb / kg;

[0102] For the tube section covered by the capillary wick, the speed of the liquid film spreading driven by the capillary force needs to be considered. The length of the liquid film spreading on the capillary wick surface can be calculated by formula (17):

[0103]

[0104] In formula (17): wick ——Liquid film thickness in the capillary core / m; u——Speed ​​of the condensed liquid in the capillary core in the x direction / m·s -1 ;v p ——Liquid-elastic oscillation speed / m·s -1 ;ε——Porosity of the wire mesh capillary core;

[0105] Through the Brinkman equation, the velocity distribution equation of the condensate in the capillary wick is obtained:

[0106]

[0107] In formula (18): μ——Condensate viscosity / N·s·m -2; P——partial pressure of condensate / Pa; g——gravitational acceleration / m·s -2 ;

[0108] Assuming that there is no-slip boundary condition at the bottom of the capillary wick, i.e., the position where the capillary wick contacts the steam, and there is no shear force at the top of the capillary wick, i.e., the position where the capillary wick contacts the steam, the local velocity distribution of the condensate is calculated by the boundary condition shown in equation (19):

[0109]

[0110] The structural parameters of the capillary core are calculated by equations (20)-(21):

[0111] The porosity ε of the wire mesh capillary core is:

[0112]

[0113] In formula (20): N is the mesh number of the screen; d wick ——Wire diameter of wire mesh capillary core / mm;

[0114] The permeability κ of the wire mesh capillary wick is:

[0115]

[0116] In formula (21): κ——permeability / m 2 ;

[0117] The pressure gradient of the condensate is the Laplace pressure at the inlet of the liquid condensation section and the outlet of the evaporation section, so the capillary pressure P cap for:

[0118]

[0119] In formula (22): γ——Surface tension of condensate / N·m -1 ;θ——Contact angle between condensate and capillary core / °; r e ——Effective capillary radius of the capillary core in the evaporation section / m;

[0120] For wire mesh wicks, the effective radius r of the wick is e for:

[0121]

[0122] In formula (23): w is the pore size of the wire mesh capillary core / m;

[0123] The pressure gradient in the capillary wick drives the movement of the liquid for:

[0124]

[0125] In formula (24): L wick ——length of capillary core / m;

[0126] Liquid film thickness δ in smooth pipe section smooth Calculated by Aussillous model formula:

[0127]

[0128] In formula (25): r is the radius of the heat pipe / m; Ca is the capillary criterion number;

[0129] Capillary wick covering tube section liquid film thickness δ wick is the capillary wick thickness;

[0130] Step 6: Calculate the latent heat of evaporation and condensation according to equation (26), and calculate the change in mass of the steam bomb caused by evaporation and condensation through the latent heat;

[0131] Heat transfer of liquid film evaporation and condensation:

[0132]

[0133] In formula (26): Q cond,i ——Liquid film condensation heat transfer / W; Q evp,i ——Liquid film evaporation heat transfer / W; h sum ——Total heat transfer coefficient / W·m -2 ·K -1 ;

[0134] For the capillary wick covered pipe section, the thermal resistance between the steam and the heat pipe condensation wall is mainly the thermal conductivity resistance of the capillary wick and the thermal conductivity resistance of the gas-liquid interface condensation, so the total heat transfer coefficient h sum for:

[0135]

[0136] Condensation heat transfer coefficient h of the interface i for:

[0137]

[0138] In formula (28): V lv - the difference in specific volumes between vapor and liquid; ——The range is 0.02-0.04, here we take 0.03; M——molecular molar mass / kg·kmol -1 ;

[0139] Capillary wick effective thermal conductivity k eff for:

[0140]

[0141] In formula (29): k eff ——Effective thermal conductivity of capillary wick / W·m -1 ·K -1 ;k l ——Thermal conductivity of liquid / W·m -1 ·K -1 ;k s ——Thermal conductivity of the capillary wick material / W·m -1 ·K -1 ; The rate of change of the mass of the steam bomb caused by evaporation and condensation is calculated by equations (30) and (31):

[0142]

[0143] In formula (30) and (31), m v1、 m v2 ——mass of gas bomb / kg; h fg ——Latent heat of working fluid phase change

[0144] / J·kg -1 ;

[0145] Step 7: According to the first law of thermodynamics, construct the energy equation and ideal gas state equation of the steam bomb and calculate the new value of the steam bomb pressure.

[0146] The energy equations of the steam bomb are shown in equations (32) and (33):

[0147]

[0148]

[0149] In formula (32) and (33): c P ——Molar heat capacity at constant pressure of working fluid / J·mol -1 ·K -1 ;c V ——Molar heat capacity at constant volume of working fluid / J·mol -1 ·K -1 ;

[0150] Steam is assumed to be an ideal gas, and the corresponding ideal gas state equation is shown in equations (34) and (35):

[0151]

[0152] In formula (34) and (35), R g ——Gas constant / J·kg -1 ·K -1 ;

[0153] Then the relationship between the steam bomb mass flow rate and pressure is shown in equations (36) and (37):

[0154]

[0155] Substitute the change in the mass of the steam bomb obtained in step 6 into equations (36) and (37) to calculate the new value of the steam bomb pressure P v1 * , P v2 * .

[0156] Step 8: Substitute the new value of the steam bomb pressure obtained in step 7 into equations (1)-(2) to calculate the new value of the steam bomb temperature T V1 * 、T V2 * .

[0157] Step 9: Calculate and update the convection heat transfer coefficient h using equation (9) sen ; Substitute the new value of the vapor bomb temperature obtained in step 8 into equations (5) and (6), update the vapor-liquid boundary conditions, and calculate the new value of the liquid bomb temperature T through the energy equation of the liquid bomb shown in equation (3) and the initial and boundary conditions equations (4)-(6) l * .

[0158] Step 10: Set the new value of the steam bomb temperature T obtained in step 8 V1 * 、T V2 * With a given steam bomb temperature T V1 、T V2 The iterative convergence criterion is set to an error less than 10 -4 If it is satisfied, the iteration stops. If it is not satisfied, repeat steps 4-10 until the iteration requirements are met and the new value of the steam bomb temperature T is calculated. V1 * 、T V2 * and the new value of liquid bomb temperature T l * .

[0159] Step 11: Calculate the sensible heat transferred into and out of the liquid bomb, and calculate the thermal resistance of the pulsating heat pipe.

[0160] The sensible heat generated by the liquid bomb due to unidirectional convection can be calculated by equations (38) and (39):

[0161]

[0162] In formula (38) and (39): Q h ——Sensible heat amount transmitted by liquid bomb / W; Q c ——Sensible heat transferred by the liquid bomb / W; Tl,i ——Liquid bomb temperature / K;

[0163] In steady state, the thermal resistance of the pulsating heat pipe can be calculated by (40)-(42):

[0164]

[0165] In formula (40)-(42): R——thermal resistance / K·W -1 ; ——Average sensible heat input by liquid bomb / W; ——Average sensible heat transferred by the liquid bomb / W; ——Average condensation heat / W; ——Average evaporation heat / W;

[0166] Step 12: Output the calculation results. The outputs are the temperature and pressure of the steam bomb and the temperature distribution and position of the liquid bomb, as well as the mass of the steam bomb, the length of the liquid film, the latent heat, the sensible heat and the thermal resistance of the pulsating heat pipe calculated based on the above results. It can be used to perform simple calculations and analyses on the flow characteristics such as the oscillation height and oscillation speed of the liquid bomb of the pulsating heat pipe with a spaced capillary wick, as well as the heat transfer performance such as the heat transfer and thermal resistance, and draw graphs based on the calculation results.

[0167] The above are preferred specific implementations of the present application, which are only used to illustrate the technical solution of the present invention, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by any technician familiar with the technical field within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims

1. A heat transfer calculation method for a spaced capillary wick pulsating heat pipe, characterized in that: The following steps are involved: Obtain the heat pipe size and structure parameters and the capillary wick structure parameters, and build a pulsating heat pipe model; In the pulsating heat pipe model, the initial temperature values ​​of the two steam bombs are preset, a functional relationship between the steam bomb temperature and pressure is constructed, and the initial pressure value of the steam bomb is calculated based on the functional relationship between the steam bomb temperature and pressure; Constructing a liquid-elastic energy equation, and calculating the liquid-elastic temperature distribution based on the liquid-elastic energy equation and corresponding initial conditions and boundary conditions; The hydraulic dynamic equation of the spaced capillary wick pulsating heat pipe is constructed to obtain the shear stress of the smooth pipe section and the capillary wick covered pipe section respectively, and the hydraulic displacement is calculated based on the hydraulic dynamic equation of the spaced capillary wick pulsating heat pipe, the shear stress of different pipe sections and the initial value of the steam elastic pressure; The liquid film length calculation formulas of the smooth tube segment and the capillary wick covered tube segment are respectively constructed, and the corresponding liquid film lengths are obtained based on the liquid film length calculation formulas of different tube segments; Acquire the heat transfer of liquid film evaporation and condensation, and calculate the corresponding steam bomb mass changes based on the heat transfer of liquid film evaporation and condensation; Obtaining a relationship between the mass flow rate and pressure of the steam bomb, and calculating a new value of the steam bomb pressure based on the relationship between the mass flow rate and pressure of the steam bomb and the obtained change in the mass of the steam bomb; Based on the functional relationship between the steam bomb temperature and pressure and the new value of the steam bomb pressure, a new value of the steam bomb temperature is obtained; Based on the liquid bomb energy equation and the new value of the steam bomb temperature, obtaining a new value of the liquid bomb temperature; The obtained new value of the steam bomb temperature is compared with the given initial value of the steam bomb temperature for iteration to obtain the final new values ​​of the steam bomb and liquid bomb temperature; the sensible heat amount transmitted into and out of the liquid bomb is obtained, and the thermal resistance of the pulsating heat pipe is calculated based on the sensible heat amount; Output the liquid bomb temperature, liquid bomb displacement, liquid film length, steam bomb mass change, steam bomb pressure, steam bomb temperature and thermal resistance of the pulsating heat pipe to complete the heat transfer calculation.

2. The heat transfer calculation method of the spaced capillary wick pulsating heat pipe according to claim 1 is characterized in that: The functional relationship between the temperature and pressure of the steam bomb is as follows: Among them, T v0 is the initial temperature of the steam bomb; P v0 is the initial pressure of the steam bomb; γ is the heat capacity ratio; P v1 , P v2 is the steam bomb pressure; T V1 , T V2 are the steam bomb temperatures respectively.

3. The heat transfer calculation method of the spaced capillary wick pulsating heat pipe according to claim 1, characterized in that: The expressions of the liquid-elastic energy equation and the corresponding initial conditions and boundary conditions are as follows: T=T0,t=0,0<x l <L p T=T v1 ,x l =0 T=T v2 ,x l =L p Where T1 is the liquid bomb temperature; α l is the thermal diffusion coefficient; A is the cross-sectional area; d is the heat pipe diameter; L p is the length of the liquid bullet; x l is the liquid bomb position; h sen is the convective heat transfer coefficient; T W is the wall temperature; T V1 、T V2 are the steam bomb temperatures; t is the time; π is a constant.

4. The heat transfer calculation method of the spaced capillary wick pulsating heat pipe according to claim 3 is characterized in that: The expression of the fluid dynamic equation of the spaced capillary wick pulsating heat pipe is as follows: Among them, ρ l is the liquid density; ΔP b is the pressure loss at the elbow; L p,wick is the length of the liquid bomb in the capillary core area; τ p,wick is the shear stress in the capillary core area; L p,smooth is the length of the liquid bullet in the smooth area; τ p,smooth is the shear stress in the smooth area; P v1 , P v2 is the pressure of the two gas bombs; g is the acceleration due to gravity.

5. The heat transfer calculation method of the spaced capillary wick pulsating heat pipe according to claim 1, characterized in that: The calculation formula for the liquid film length of the smooth pipe section and the capillary core covered pipe section is as follows: The calculation formula of the thin liquid film length in the smooth pipe section is: The calculation formula for the length of the thin liquid film covering the tube section of the capillary core is: Among them, L c,i is the length of the liquid film in the condensation section; L e,i is the liquid film length in the evaporation section; δ smooth is the thickness of the liquid film in the smooth pipe section; δ wick is the thickness of the liquid film in the wick; m v is the mass of the steam bomb; u is the velocity of the condensate in the capillary wick in the x direction; v p is the liquid bullet velocity; ε is the porosity of the wire mesh capillary core; ρ is the liquid density.

6. The heat transfer calculation method of the spaced capillary wick pulsating heat pipe according to claim 1, characterized in that: The calculation formula for the heat transfer of liquid film evaporation and condensation is as follows: Among them, Q cond,i Q is the heat transfer of liquid film condensation; evp,i h is the heat transfer of liquid film evaporation; sum is the total heat transfer coefficient; L c,i is the length of the liquid film in the condensation section; L e,i is the liquid film length in the evaporation section; T e , T c are the wall temperatures of the evaporation section and the condensation section, respectively.

7. The heat transfer calculation method of the spaced capillary wick pulsating heat pipe according to claim 6, characterized in that: The calculation formula of the steam bomb mass change rate is as follows: Among them, m v1 、m v2 is the mass of the gas bomb; h fg is the latent heat of phase change of the working fluid.

8. The heat transfer calculation method of the spaced capillary wick pulsating heat pipe according to claim 7, characterized in that: The process of obtaining the relationship between the mass flow rate and pressure of the steam bomb includes: constructing the energy equation and the ideal gas state equation of the steam bomb, and obtaining the relationship between the mass flow rate and pressure of the steam bomb based on the functional relationship between the energy equation and the ideal gas state equation of the steam bomb. The relationship between the mass flow rate and pressure of the steam bomb is as follows: Among them, R g is the gas constant; P v1 , P v2 are respectively the steam bomb pressure; d is the heat pipe diameter; P v0 is the initial pressure of the steam bomb; γ is the heat capacity ratio; L e is the liquid film length in the evaporation section.

9. The heat transfer calculation method of the spaced capillary wick pulsating heat pipe according to claim 1, characterized in that: The calculation formula for the sensible heat transferred into and out of the liquid bomb is as follows: Among them, Q h is the sensible heat transferred by the liquid bomb; Q c is the sensible heat transferred by the liquid bomb; T l,i is the liquid bomb temperature; h sen is the convective heat transfer coefficient; T e , T c are the wall temperatures of the evaporation section and the condensation section respectively; L p is the liquid bullet length.

10. The heat transfer calculation method of the spaced capillary wick pulsating heat pipe according to claim 9, characterized in that: The calculation formula of the thermal resistance of the pulsating heat pipe is as follows: Where R is thermal resistance; is the average sensible heat transferred by the liquid bomb; is the average sensible heat transferred by the liquid bomb; is the average condensation heat; is the average heat of evaporation; is the average sensible heat; is the average latent heat.

Images