A calculation method for capillary heat pipe capillary wick liquid film condensation and flow model

Abstract

This invention discloses a method for calculating the liquid film condensation and flow model of a capillary heat pipe wick, comprising: selecting the physical properties of the working fluid inside the heat pipe and calculating the target parameters of the working fluid properties; obtaining the average volumetric flux of the condensate based on the target parameters; obtaining a first vapor temperature based on the average volumetric flux of the condensate; calculating a second vapor temperature at the maximum condensation rate based on the first vapor temperature; calculating the vapor flow velocity and gas-liquid shear force based on the second vapor temperature; and calculating the wall temperature of the evaporation section based on the gas-liquid shear force, thus completing the calculation of the flow model. This invention analyzes the influence of uniform pore size capillary wicks and non-uniform pore size combination capillary wicks on the capillary limit of the heat pipe, providing suggestions and guidance for the design and engineering application of capillary heat pipes.

Description

Technical Field

[0001] The invention relates to the technical field of phase change heat transfer equipment, and more particularly to a method for calculating a capillary heat pipe capillary core liquid film condensation and flow model. Background Art

[0002] With the development of high performance and high integration of microelectronics, the power of electronic chips has reached 100W / cm 2 As mentioned above, the miniaturization of equipment is also a development trend of electronic equipment. In order to maintain the stable operation of electronic chips, ultra-thin and efficient heat pipes are a research hotspot for efficient heat dissipation of electronic equipment. Capillary heat pipes are a highly efficient passive heat transport device. Heat is input into the evaporation section, and the working fluid in the heat pipe evaporates from the liquid phase to the gas phase. The gas phase working fluid condenses in the condensation section of the heat pipe to output heat. The capillary suction force of the capillary wick on the wall drives the condensed liquid in the condensation section to move toward the evaporation section. There is a heat and mass transfer coupling characteristic between the liquid wick and the steam zone inside the capillary heat pipe, and the liquid flow in the liquid wick is complicated, which makes it difficult to simultaneously ensure the calculation speed and accuracy for the numerical simulation calculation of the heat pipe. Summary of the invention

[0003] In order to solve the above technical problems, the present invention proposes a calculation method for capillary heat pipe capillary wick liquid film condensation and flow model, which can obtain the transient heat transfer flow characteristics of the working fluid inside the capillary heat pipe and provide suggestions and guidance for capillary heat pipe design and engineering applications.

[0004] To achieve the above object, the present invention provides a method for calculating a capillary heat pipe capillary wick liquid film condensation and flow model, comprising:

[0005] Selecting the working fluid properties in the heat pipe and calculating target parameters of the working fluid properties;

[0006] According to the target parameters, an average volume flux of condensate is obtained;

[0007] Obtaining a first steam temperature according to an average volume flux of the condensate, and calculating a second steam temperature at a maximum condensation amount according to the first steam temperature;

[0008] Calculating the steam flow velocity and the gas-liquid shear force according to the second steam temperature;

[0009] According to the gas-liquid shear force, the wall temperature of the evaporation section is calculated to complete the calculation of the flow model.

[0010] Optionally, before selecting the physical properties of the working fluid in the heat pipe, the method further includes: obtaining structural parameters of the capillary heat pipe and the capillary wick;

[0011] The structural parameters include: the length, radius, capillary core thickness, capillary core mesh number, capillary core material, capillary core permeability, and capillary core porosity of the capillary heat pipe.

[0012] Optionally, the physical properties of the working fluid in the heat pipe include: an evaporation section, an insulation section and a condensation section.

[0013] Optionally, the target parameters for calculating the working fluid properties include:

[0014] Acquiring a first volume flux of the condensation section, and calculating a local capillary pressure gradient according to the first volume flux;

[0015] Obtaining the wall temperature of the first evaporation section, and calculating the physical properties of the condensate in combination with the first volume flux;

[0016] The first gas-liquid shear force is obtained, and the average velocity of the condensed liquid is calculated in combination with the local capillary pressure gradient.

[0017] Optionally, obtaining the average volume flux of the condensate includes:

[0018] Calculating a second volume flux of the condensate according to the average velocity of the condensate;

[0019] According to the second volume flux, obtaining an average volume flux of condensate;

[0020] determining whether the average volume flux converges according to the first volume flux;

[0021] If converged, obtaining the first steam temperature;

[0022] If it does not converge, the first volume flux is acquired again until the average volume flux converges.

[0023] Optionally, calculating the second steam temperature at the maximum condensation amount according to the first steam temperature includes:

[0024] determining whether the second steam temperature converges according to the first steam temperature;

[0025] If convergence, the steam flow velocity and gas-liquid shear force are calculated based on;

[0026] If it does not converge, the first steam temperature is rebuilt and acquired until the second steam temperature converges.

[0027] Optionally, calculating the steam flow velocity and the gas-liquid shear force according to the second steam temperature includes:

[0028] Calculating the gas-liquid shear force according to the steam flow velocity;

[0029] judging whether the gas-liquid shear force converges according to the first gas-liquid shear force;

[0030] If converged, calculate the evaporation section wall temperature;

[0031] If it does not converge, the first gas-liquid shear force is acquired again until the gas-liquid shear force converges.

[0032] Optionally, the calculation of the evaporator wall temperature includes:

[0033] Calculating the wall temperature of the evaporation section according to the heat conservation of the evaporation section and the condensation section;

[0034] According to the first evaporation section wall temperature, judging whether the evaporation section wall temperature converges:

[0035] If converged, the wall temperature of the evaporation section is output;

[0036] If it does not converge, the first evaporation section wall temperature is acquired again until the evaporation section wall temperature converges.

[0037] Compared with the prior art, the present invention has the following advantages and technical effects:

[0038] The present invention can calculate the pressure distribution and velocity distribution of the liquid working medium in the capillary wick; the constructed algorithm is concise and has good convergence; it can be applied to capillary heat pipes with uniform pore size, capillary wicks with non-uniform pore size combination and various working mediums, and has wide applicability; the output can obtain a simpler and clearer result graph, which is convenient for providing design ideas and data references for the capillary heat pipe design; the calculation of the flow model in the capillary wick is appropriately simplified under the actual situation, and the calculation speed and accuracy of the algorithm are guaranteed; and a new algorithm for calculating the flow velocity and pressure according to the volume flux of the condensate is provided. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] 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:

[0040] Figure 1 It is a flow chart of a method for calculating a capillary heat pipe capillary wick liquid film condensation and flow model according to an embodiment of the present invention. DETAILED DESCRIPTION

[0041] 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.

[0042] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0043] This embodiment proposes a method for calculating the condensation and flow model of a capillary heat pipe capillary wick liquid film, including: Figure 1 As shown:

[0044] Step 1: Determine the size and structural parameters of the capillary heat pipe and the capillary wick structure parameters, and establish a heat pipe model; divide the heat pipe into evaporation section, adiabatic section, and condensation section, and divide the heat pipe into two parts: the wick and the steam zone according to the internal state of the heat pipe; select the working fluid properties in the heat pipe, where water is selected as the working fluid, and set the condensation section to a given wall temperature T c .

[0045] Step 2: Assume that the volume flux of the working fluid in the condensation section is V cond , and the velocity of the working fluid in the y direction is defined as the volume flux V of the working fluid condensation cond , then the pressure gradient and pressure distribution of the porous structure condensed liquid can be obtained by the following formula:

[0046]

[0047]

[0048]

[0049] in, is the pressure gradient inside the porous structure, P cap is the capillary pressure of the porous medium / Pa, P is the working fluid pressure / Pa, x is the x-direction position / m, A is an artificially defined coefficient (for the convenience of equation writing), V cond is the volume flux of the working fluid in the condensation section, L is the length of the capillary heat pipe / m, γ is the surface tension of the liquid working fluid / N·m -1 , θ is the contact angle between the liquid phase and the capillary core / °, r c is the effective capillary radius of the capillary core / m, μ is the viscosity of the condensate / Pa·s, and u is the velocity of the condensate in the capillary core in the x direction / m·s -1 , δ is the thickness of the capillary core / m, ε is the porosity of the capillary core, and κ is the permeability of the capillary core / m 2 .

[0050] Step 3: Calculate the maximum temperature of the steam at the maximum condensation amount in the condensation section based on the heat flux of the steam condensation in the condensation section and the structural parameters of the capillary core. Assume that the wall temperature of the evaporation section is T e , and calculate the working fluid properties based on the average temperature of the condensation section and the evaporation section:

[0051] The structural parameters of the capillary core include: the length, radius, thickness of the capillary core, mesh number of the capillary core, material of the capillary core, permeability of the capillary core, porosity of the capillary core, etc.

[0052] The heat flux of steam condensation in the condensation section is calculated by formula (6):

[0053] q c =ρ1·V cond ·h lv (4)

[0054] Among them, q c is the heat flux of steam condensation in the condensation section, ρ l is the density of the condensate / kg·m -3 ,h lv is the latent heat of vapor-liquid phase change of condensate / W·m -2 .

[0055] The total heat transfer of the condensation section is:

[0056] Q c =q c ·A c (5)

[0057] Among them, Q c is the total heat transfer of the condensation section, A c is the total heat transfer area of ​​the condensation section / m 2 .

[0058] The structural parameters of the capillary core are calculated by equations (6)-(8):

[0059] The porosity of the wire mesh capillary wick is:

[0060]

[0061] Where ε is the porosity of the capillary core, N is the mesh number of the screen, and d wick is the wire diameter of the wire mesh capillary core / m;

[0062] The permeability of the wire mesh capillary wick is:

[0063]

[0064] Where κ is the permeability of the capillary core / m 2 ;

[0065] The effective thermal conductivity of the capillary wick is:

[0066]

[0067] Among them, k eff is the effective thermal conductivity of the capillary wick, k l is the thermal conductivity of the condensate / W·m -1 ·K -1 , k s is the thermal conductivity of the capillary wick material / W·m -1 ·K -1 .

[0068] Step 4: Assume the shear force τ at the gas-liquid interface s , calculate the local velocity distribution inside the capillary core according to formula (9):

[0069] Through the Brinkman equation, the velocity distribution equation of the condensate in the capillary wick is obtained:

[0070]

[0071] Where ρ is the density of the condensate / kg·m -3 , g is the acceleration due to gravity / m·s -2 , μ is the viscosity of the condensate / Pa·s, u is the velocity of the condensate in the capillary core in the x direction / m·s -1 , P is the local pressure of the condensate / Pa;

[0072] The condensate in the capillary wick and the heat pipe wall are in a no-slip boundary condition, and the boundary condition of the gas-liquid interface is the shear force of the gas on the condensate. The boundary condition of equation (9) is:

[0073]

[0074] The continuity equation for the capillary condensate is:

[0075]

[0076] Among them, τ s is the shear force, u x 、u y ——Velocity components of the condensate in the x and y directions within the porous structure / m·s -1 ;

[0077] The local velocity distribution of the condensate is obtained according to the above equation, and the average velocity of the condensate in each discrete unit is calculated.

[0078] Step 5: Calculate the local average velocity of the condensation section and calculate the local condensate volume flux V according to formula (15): cond , and calculate the average condensate volume flux

[0079]

[0080] Among them, L c is the length of the condensation section / m, n c is the number of discrete units in the condensation section, δ c is the thickness of the capillary core / m, is the average speed of the previous discrete unit / m·s -1 , is the average speed of the current discrete unit / m·s -1 .

[0081] The result is compared with the V set in step 2. cond The iterative convergence criterion is set to an error less than 10 -3 If it is satisfied, the iteration stops. If it is not satisfied, it is repeated from step 2 until the iteration requirements are met and the approximate value of the average condensation volume flux is calculated.

[0082] Step 6: Assume the steam temperature T v , calculate the steam properties according to the steam temperature, and calculate the total condensation heat transfer coefficient according to formula (16),

[0083] Assuming that steam is an ideal gas, its state equation is

[0084]

[0085] Among them, ρ v is the density of steam / kg·m -3 , P v is the vapor pressure / Pa, R is the ideal gas constant, 8.314 kJ / mol·K, M is the molar mass of water molecules / g·mol -1 ;

[0086] The condensation heat transfer coefficient of the interface is:

[0087]

[0088] Among them, h c，i is the condensation heat transfer coefficient, v lv is the specific volume difference between vapor and liquid, The range is 0.02~0.04, and 0.03 is selected here.

[0089] The thermal resistance between the steam and the condensation wall of the heat pipe is mainly the thermal conductivity resistance of the capillary wick and the heat transfer resistance of the gas-liquid interface condensation. The total heat transfer coefficient h c,sum for:

[0090]

[0091] Among them, k eff,c is the effective thermal conductivity of the condensation section wire mesh / W·m -1 ·K -1 ;

[0092] The maximum temperature of the steam at the maximum condensation amount in the condensation section is:

[0093]

[0094] Among them, T c is the wall temperature of the condensation section / K;

[0095] The results are compared with the assumed T v The iterative convergence criterion is set to an error less than 10 -3 If it is satisfied, the iteration stops. If it is not satisfied, repeat from step 6 until the iteration requirements are met and the steam temperature T is calculated. v .

[0096] Step 7: Calculate the steam flow velocity and calculate the shear force according to formula (18)

[0097] According to the law of conservation of mass, the velocity of the vapor in the wick area is

[0098]

[0099] Among them, u v is the velocity of the steam in the wick area, ρ1 is the density of the liquid phase / kg·m -3 .

[0100] The shear force at the gas-liquid interface is mainly the momentum change shear force caused by the viscous loss of steam flow. The viscous loss of steam flow is:

[0101]

[0102] Among them, τ v is the viscous loss of steam flow, f v is the friction coefficient between steam and liquid film, which is a function of the Reynolds number of steam flow. The friction coefficient of steam movement in a circular heat pipe is:

[0103]

[0104]

[0105]

[0106] Re v ——Reynolds number of steam;

[0107] The obtained results are compared with the assumed τ v The iterative convergence criterion is set to an error less than 10 -3 If it is satisfied, the iteration stops. If it is not satisfied, repeat from step 6 until the iteration requirements are met and the shear force τ at the gas-liquid interface is calculated. v Since the shear force between water and water vapor is small and can be ignored, this step can be ignored.

[0108] Step 8: Calculate the wall temperature of the evaporation section based on the heat conservation of the evaporation section and the condensation section:

[0109] The heat transfer coefficient of the capillary wick liquid film evaporation in the evaporation section is:

[0110]

[0111] Among them, k eff,e is the effective thermal conductivity of the evaporation section screen / W·m -1 ·K -1 ;

[0112] The evaporation heat transfer coefficient at the gas-liquid interface is:

[0113]

[0114] According to the energy conservation of the condensation section and the evaporation section, Qc = Qe, the wall temperature T of the evaporation section is calculated. e

[0115]

[0116] Compare the result with the T assumed in step 3 e The iterative convergence criterion is set to an error less than 10 -3 If it is satisfied, the iteration stops. If it is not satisfied, repeat from step 6 until the iteration requirements are met and the evaporation section wall temperature T is calculated. e Approximate value of .

[0117] Step 9: The calculation of the current time step is completed, and the calculation results are output. The outputs are the approximate value of the average condensation volume flux, the shear force of the gas-liquid interface and the approximate value of the wall temperature Te of the evaporation section, and the velocity gradient distribution and pressure distribution of the condensate in the capillary core calculated based on the above three results. They are used to describe the flow, complete the calculation of the flow model, and draw the graph based on the calculation results.

[0118] The above are only preferred specific implementations of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art 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 method for calculating a capillary heat pipe capillary wick liquid film condensation and flow model, characterized in that: include: Selecting the working fluid properties in the heat pipe and calculating target parameters of the working fluid properties; According to the target parameters, an average volume flux of condensate is obtained; The target parameters for calculating the working fluid properties include: Acquiring a first volume flux of the condensation section, and calculating a local capillary pressure gradient according to the first volume flux; Obtaining the wall temperature of the first evaporation section, and calculating the physical properties of the condensate in combination with the first volume flux; Obtaining a first gas-liquid shear force, and calculating an average velocity of the condensate in combination with the local capillary pressure gradient; Obtaining the average volume flux of condensate includes: Calculating a second volume flux of the condensate according to the average velocity of the condensate; According to the second volume flux, obtaining an average volume flux of condensate; determining whether the average volume flux converges according to the first volume flux; If convergence, obtain the first steam temperature; If it does not converge, reacquire the first volume flux until the average volume flux converges; Obtaining a first steam temperature according to an average volume flux of the condensate, and calculating a second steam temperature at a maximum condensation amount according to the first steam temperature; Calculating the steam flow velocity and the gas-liquid shear force according to the second steam temperature; According to the gas-liquid shear force, the wall temperature of the evaporation section is calculated to complete the calculation of the flow model.

2. The method for calculating the capillary heat pipe capillary wick liquid film condensation and flow model according to claim 1, characterized in that: Before selecting the physical properties of the working fluid in the heat pipe, the following steps are also included: obtaining the structural parameters of the capillary heat pipe and the capillary wick; The structural parameters include: the length, radius, capillary core thickness, capillary core mesh number, capillary core material, capillary core permeability, and capillary core porosity of the capillary heat pipe.

3. The method for calculating the capillary heat pipe capillary wick liquid film condensation and flow model according to claim 1, characterized in that: The working medium in the heat pipe has physical properties including: an evaporation section, an insulation section and a condensation section.

4. The method for calculating the capillary heat pipe capillary wick liquid film condensation and flow model according to claim 1, characterized in that: The second steam temperature when calculating the maximum condensation amount according to the first steam temperature includes: determining whether the second steam temperature converges according to the first steam temperature; If converged, the steam flow velocity and gas-liquid shear force are calculated based on the second steam temperature; If it does not converge, the first steam temperature is rebuilt and acquired until the second steam temperature converges.

5. The method for calculating the capillary heat pipe capillary wick liquid film condensation and flow model according to claim 1, characterized in that: Calculating the steam flow velocity and the gas-liquid shear force according to the second steam temperature includes: Calculating the gas-liquid shear force according to the steam flow velocity; judging whether the gas-liquid shear force converges according to the first gas-liquid shear force; If converged, calculate the evaporation section wall temperature; If it does not converge, the first gas-liquid shear force is acquired again until the gas-liquid shear force converges.

6. The method for calculating the capillary heat pipe capillary wick liquid film condensation and flow model according to claim 1, characterized in that: Calculation of the evaporation section wall temperature includes: Calculating the wall temperature of the evaporation section according to the heat conservation of the evaporation section and the condensation section; According to the first evaporation section wall temperature, judging whether the evaporation section wall temperature converges: If converged, the wall temperature of the evaporation section is output; If it does not converge, the first evaporation section wall temperature is acquired again until the evaporation section wall temperature converges.

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