CN114239435B - Numerical calculation method for three-dimensional flat plate water heat pipe - Google Patents

Abstract

The invention discloses a numerical calculation method of a three-dimensional flat plate water heat pipe, which comprises the following steps: establishing a three-dimensional geometric model of the flat water heat pipe according to the real design parameters; grid division is carried out on the flat plate water heat pipe geometric model by using grid division software; the grid is led into computational fluid dynamics software, and the boundary condition of the heat pipe is set according to the real situation; setting initial conditions required by transient calculation; programming the UDF to calculate evaporation/condensation mass flow rate, temperature and pressure at the wick-vapor interface, and liquid and vapor densities per time step; and calculating the flowing heat transfer in the three-dimensional flat plate hydrothermal pipe by using computational fluid dynamics software. The method can calculate the operation of the heat pipe with unsteady high heat flux density by using a computational fluid mechanics means, has better stability and convergence in calculation, and provides reference for the design of the newly-appearing heat pipe.

Description

A numerical calculation method for three-dimensional flat plate water heat pipe

Technical Field

The invention belongs to the technical field of thermal hydraulic numerical calculation, and in particular relates to a numerical calculation method for a three-dimensional flat water heat pipe.

Background Art

Heat pipes are passive heat transfer devices that have found widespread use in thermal systems due to their ability to provide efficient heat transfer with minimal losses. With chip-level heat fluxes reaching 200-300W/ ^cm2 , one of the driving forces behind heat pipe development has been the need to reliably manage heat dissipation in electronic systems while maintaining device temperatures within specification. The passive nature of their operation and their ability to transfer heat over reasonable distances with only minor changes in surface temperature make them particularly attractive in electronic cooling and packaging design. Heat pipes are also widely used as heat sinks. They utilize latent heat exchange to achieve high heat transfer rates. The ever-increasing power density of electronic chips requires that the performance of these devices be optimized to be able to effectively remove heat from the electronic chip while limiting the temperature difference between the chip and the environment. The capillary porous media (wick) used in the device is the primary factor affecting the heat transfer efficiency of the heat pipe and vapor chamber. The wick also determines the maximum heat transfer capacity. The study of the phase change heat and mass transfer characteristics in the wick can help optimize the wick design and improve the performance of phase change cooling devices.

In transient operation, the system pressure in the heat pipe changes as vaporization and condensation occur at the liquid/vapor interface in the wick. Due to the large density of liquid and vapor, small changes in the phase change rate can cause large changes in the system pressure. The system pressure in turn changes the interface pressure and thus the saturation temperature via the Clausius-Clapeyron equation. The evaporation and condensation rates depend on the interface evaporation resistance, which depends on both the interface pressure and the volume pressure. In addition, the system pressure also directly changes the vapor density via the ideal gas law. These nonlinear relationships can cause difficulties in the convergence of numerical schemes, especially at high heat additions.

Summary of the invention

The purpose of the present invention is to provide a numerical calculation method for a flat water heat pipe, which can use computational fluid dynamics to calculate the operation of an unsteady high heat flux heat pipe, has good stability and convergence, and provides a reference for the design of newly emerging heat pipes.

In order to achieve the above object, the present invention adopts the following technical solution:

A three-dimensional flat plate water heat pipe numerical calculation method, characterized in that it includes the following steps:

Step 1: Use the geometric model building software SolidWorks to create a three-dimensional geometric model of the flat water heat pipe based on the actual design. The three-dimensional geometric model includes the pipe wall, the liquid absorption core, the vapor cavity, the evaporation section and the condensation section;

Step 2: Use meshing software to mesh the flat plate water heat pipe geometric model obtained in step 1;

Step 3: Import the mesh divided in step 2 into the computational fluid dynamics software, set the evaporation section and condensation section of the heat pipe as heat flow boundary conditions and convection boundary conditions respectively, set other walls as adiabatic walls, and set the heat flux density of the evaporation section heating, the heat transfer coefficient and coolant temperature of the condensation section according to the actual situation, and set the porosity of the wick;

Step 4: Set the initial conditions required for transient calculation: set the initial steam mass to 0, initialize the temperature field, and set the initial steam region working pressure to the saturated pressure at the current temperature;

Step 5: Use the user defined procedure UDF to calculate the gas-liquid interface mass flow rate, the temperature and pressure at the wick-vapor interface, and the liquid and vapor densities at each time step:

Step 5-1: Assuming that the phase change between the liquid working medium and the vapor working medium occurs at the interface between the wick and the vapor chamber, calculate the temperature _Ti at the interface according to the energy conservation equation at the interface:

The energy conservation equation at the interface is expressed as:

in:

λ _wick and λ _v represent the thermal conductivity of the wick and vapor chamber, respectively, in W·m ^-1 ·K ^-1 ;

A _i —interface area, m ² ;

T——temperature, where _Ti is the interface temperature, K;

y——distance perpendicular to the interface, m;

_mi ——interface mass transfer, _mi < 0 means evaporation, _mi > 0 means condensation, kg;

h _fg ——latent heat of vaporization, J/kg;

C _l ——liquid phase specific heat at constant pressure, J/(kg·K);

C _v ——gas phase constant pressure specific heat, J/(kg·K);

Assuming that the two control bodies on both sides of the gas-liquid interface are PW and PV, where PW represents the side of the wick and PV represents the side of the vapor chamber, the energy conservation equation is discretized to obtain the temperature _Ti at the interface:

in:

_TPW — the first layer grid temperature of the wick near the interface, K;

T _PV ——the first grid temperature of the steam chamber near the interface, K;

Δx——interface area, m ² ;

The interface temperature _Ti is calculated according to formula (2):

Step 5-2: Based on the interface temperature obtained in step 5-1, use the Clausius-Clapeyron equation to calculate the interface pressure P _i :

in:

P _o ——reference pressure, Pa;

P _i ——interface pressure, Pa;

T _o ——reference temperature, K;

R——gas constant, J/kg;

进行计算：Step 5-3: Mass flow rate at the gas-liquid interface

Perform the calculation:

in:

——交界面质量流率，kg/s；

——interface mass flow rate, kg/s;

σ——adjustment coefficient; surface tension, N/m;

P _v ——vapor chamber pressure, Pa;

T _v ——vapor chamber temperature, K;

Step 5-4: Calculate the vapor zone working pressure based on the ideal gas equation and the overall mass balance of the vapor zone, and calculate the vapor density:

in:

_Pop - working pressure of steam area, Pa;

——上一时间步长计算得到的蒸气腔内蒸气质量，kg；

——The steam mass in the steam chamber calculated at the previous time step, kg;

——交界面质量流率，kg/s；

——interface mass flow rate, kg/s;

Δt——time step, s;

R——gas constant;

V _cell ——vapor chamber pressure, Pa;

Based on the incompressible assumption of the fluid, the vapor density in the control volume is calculated from the system pressure:

Step 5-5: Calculate the average density ρ _l of the liquid:

In the transient process, the wick is unsaturated, and the unsaturated problem is not considered. Instead, the average liquid density is used for calculation to maintain the liquid mass balance;

Calculate the mass of liquid in the wick at the current moment:

in:

M _l ——mass of liquid in the absorbent core, kg;

——上一时间步长计算得到的吸液芯内液体质量，kg；

——The mass of liquid in the wick calculated at the previous time step, kg;

——交界面质量流率，kg/s；

——interface mass flow rate, kg/s;

Δt——time step, s;

Based on the mass of liquid in the wick, calculate the average density of the liquid:

in:

ε——Porosity of wick;

V _l ——volume of liquid wick/m ³ ;

Step 6: Use computational fluid dynamics software to calculate the flow and heat transfer in the three-dimensional flat plate water heat pipe:

Step 6-1: Solve the momentum equations of the wick and the vapor chamber respectively according to the interface mass flow rate, pressure, and temperature parameters obtained in step 5 to obtain velocity distribution, and use the pressure correction equation to correct the pressure;

Step 6-2: Solve the energy conservation equation of the calculation area to obtain the temperature field of the calculation area;

Step 6-3: Check whether the calculation has converged: When the residual value is less than 0.000001, the calculation is considered to have converged. If it has converged, the calculation of the next time step is performed, otherwise return to step 5 to continue the calculation.

Preferably, in step 2, considering the high requirements on mesh quality for fine simulation of heat pipes, pure hexahedral meshes are used to mesh the computational domain.

Compared with the prior art, the present invention has the following beneficial effects:

1) The present invention adopts a method of calculating the wick and the vapor chamber separately and calculating the heat pipe by adding the interaction between the two, which can simulate the internal flow of the wick more precisely;

2) A numerical format for calculating the incompressible limit pressure of the system using the overall mass balance is adopted. The stability of the standard sequential program is improved by considering the coupling between the mass flow rate of the evaporation section/condensation section and the concentration and pressure of the interface and the system pressure.

3) The model is independent and the method is highly versatile and can be used to calculate heat pipes of other shapes.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a schematic diagram of the structure of a three-dimensional flat heat pipe;

FIG2 is a schematic diagram of the energy transfer process in a heat pipe;

FIG3 is a schematic diagram of a control body at the interface between the wick and the steam chamber;

FIG4 is a flow chart of the method of the present invention.

DETAILED DESCRIPTION

The present invention is further described in detail below with reference to the flow chart shown in FIG4 , taking a typical three-dimensional flat water heat pipe as an example:

The present invention provides a numerical calculation method for a three-dimensional flat water heat pipe, comprising the following steps:

Step 1: FIG1 is a schematic diagram of the structure of a three-dimensional flat plate heat pipe. A three-dimensional geometric model of the flat plate water heat pipe is created based on a real design using the geometric model building software solidworks. The three-dimensional geometric model includes a pipe wall, a liquid wick, a vapor cavity, and an evaporation section and a condensation section.

Step 2: Use meshing software to mesh the flat water heat pipe geometric model obtained in step 1. In this embodiment, considering the high requirements for mesh quality for fine simulation of heat pipes, pure hexahedral meshes are used to mesh the calculation domain;

Step 3: Import the mesh divided in step 2 into the computational fluid dynamics software, set the evaporation section and condensation section of the heat pipe as heat flow boundary conditions and convection boundary conditions respectively, set other walls as adiabatic walls, and set the heat flux density of the evaporation section heating, the heat transfer coefficient and coolant temperature of the condensation section according to the actual situation, and set the porosity of the wick;

Step 4: Set the initial conditions required for transient calculation: set the initial steam mass to 0, initialize the temperature field, and set the initial steam region working pressure to the saturated pressure at the current temperature;

Step 5: Use the user defined procedure UDF to calculate the gas-liquid interface mass flow rate, the temperature and pressure at the wick-vapor interface, and the liquid and vapor densities at each time step:

Step 5-1: Assuming that the phase change between the liquid working medium and the vapor working medium occurs at the interface between the wick and the vapor chamber, calculate the temperature _Ti at the interface according to the energy conservation equation at the interface:

The energy transfer process in the heat pipe is shown in Figure 2. In the evaporation section, the liquid turns into steam under the action of heating, and the heat is transferred from the evaporation section to the steam chamber; in the condensation section, the steam condenses under the action of cooling, and the heat is transferred from the steam chamber to the condensation section. The energy conservation equation at the interface is expressed as:

in:

λ _wick and λ _v represent the thermal conductivity of the wick and vapor chamber, respectively, in W·m ^-1 ·K ^-1 ;

A _i —interface area, m ² ;

T——temperature, where _Ti is the interface temperature, K;

y——distance perpendicular to the interface, m;

_mi ——interface mass transfer, _mi < 0 means evaporation, _mi > 0 means condensation, kg;

h _fg ——latent heat of vaporization, J/kg;

C _l ——liquid phase specific heat at constant pressure, J/(kg·K);

C _v ——gas phase constant pressure specific heat, J/(kg·K);

FIG3 is a schematic diagram of the control volume at the interface between the wick and the vapor chamber. Assuming that the two control volumes on both sides of the gas-liquid interface are PW and PV, PW represents the wick side and PV represents the vapor chamber side, the energy conservation equation is discretized to obtain the temperature _Ti at the interface:

in:

_TPW — the first layer grid temperature of the wick near the interface, K;

T _PV ——the first grid temperature of the steam chamber near the interface, K;

Δx——interface area, m ² ;

The interface temperature _Ti is calculated according to formula (2):

Step 5-2: Based on the interface temperature obtained in step 5-1, use the Clausius-Clapeyron equation to calculate the interface pressure P _i :

in:

P _o ——reference pressure, Pa;

P _i ——interface pressure, Pa;

T _o ——reference temperature, K;

_Ti —interface temperature, K;

h _fg ——latent heat of vaporization, J/kg;

R——gas constant, J/kg;

进行计算：Step 5-3: Mass flow rate at the gas-liquid interface

Perform the calculation:

in:

——交界面质量流率，kg/s；

——interface mass flow rate, kg/s;

σ——adjustment coefficient; surface tension, N/m;

P _v ——vapor chamber pressure, Pa;

T _v ——vapor chamber temperature, K;

Step 5-4: Calculate the vapor zone working pressure based on the ideal gas equation and the overall mass balance of the vapor zone, and calculate the vapor density:

in:

_Pop - working pressure of steam area, Pa;

——上一时间步长计算得到的蒸气腔内蒸气质量，kg；

——The steam mass in the steam chamber calculated at the previous time step, kg;

——交界面质量流率，kg/s；

——interface mass flow rate, kg/s;

Δt——time step, s;

R——gas constant;

V _cell ——vapor chamber pressure, Pa;

Based on the incompressible assumption of the fluid, the vapor density in the control volume is calculated from the system pressure:

Step 5-5: Calculate the average density ρ _l of the liquid:

In the transient process, the wick is generally unsaturated. The unsaturated problem is not considered, and the average liquid density is used for calculation to maintain the liquid mass balance.

Calculate the mass of liquid in the wick at the current moment:

in:

M _l ——mass of liquid in the absorbent core, kg;

——上一时间步长计算得到的吸液芯内液体质量，kg；

——The mass of liquid in the wick calculated at the previous time step, kg;

——交界面质量流率，kg/s；

——interface mass flow rate, kg/s;

Δt——time step, s;

Based on the mass of liquid in the wick, calculate the average density of the liquid:

in:

ε——Porosity of wick;

V _l ——volume of liquid wick/m ³ ;

Step 6: Use computational fluid dynamics software to calculate the flow and heat transfer in the three-dimensional flat plate water heat pipe:

Step 6-1: Solve the momentum equations of the wick and the steam chamber respectively according to the interface mass flow rate, pressure, temperature and other parameters obtained in step 5 to obtain the velocity distribution, and use the pressure correction equation to correct the pressure;

Step 6-2: Solve the energy conservation equation of the calculation area to obtain the temperature field of the calculation area;

Step 6-3: Check whether the calculation has converged: When the residual value is less than 0.000001, the calculation is considered to have converged. If it has converged, the calculation of the next time step is performed, otherwise return to step 5 to continue the calculation.

Claims (2)

1. A three-dimensional flat plate water heat pipe numerical calculation method, characterized in that it includes the following steps: Step 1: Use the geometric model building software SolidWorks to create a three-dimensional geometric model of the flat water heat pipe based on the actual design. The three-dimensional geometric model includes the pipe wall, the liquid absorption core, the vapor cavity, the evaporation section and the condensation section; Step 2: Use meshing software to mesh the flat plate water heat pipe geometric model obtained in step 1; Step 3: Import the mesh divided in step 2 into the computational fluid dynamics software, set the evaporation section and condensation section of the heat pipe as heat flow boundary conditions and convection boundary conditions respectively, set other walls as adiabatic walls, and set the heat flux density of the evaporation section heating, the heat transfer coefficient and coolant temperature of the condensation section according to the actual situation, and set the porosity of the wick; Step 4: Set the initial conditions required for transient calculation: set the initial steam mass to 0, initialize the temperature field, and set the initial steam region working pressure to the saturated pressure at the current temperature; Step 5: Use the user defined procedure UDF to calculate the gas-liquid interface mass flow rate, the temperature and pressure at the wick-vapor interface, and the liquid and vapor densities at each time step: Step 5-1: Assuming that the phase change between the liquid working medium and the vapor working medium occurs at the interface between the wick and the vapor chamber, calculate the temperature _Ti at the interface according to the energy conservation equation at the interface: The energy conservation equation at the interface is expressed as:

in: λ _wick and λ _v represent the thermal conductivity of the wick and vapor chamber, respectively, in W·m ^-1 ·K ^-1 ; A _i —interface area, m ² ; T——temperature, where _Ti is the interface temperature, K; y——distance perpendicular to the interface, m; _mi ——interface mass transfer, _mi < 0 means evaporation, _mi > 0 means condensation, kg; h _fg ——latent heat of vaporization, J/kg; C _l ——liquid phase specific heat at constant pressure, J/(kg·K); C _v ——gas phase constant pressure specific heat, J/(kg·K); Assuming that the two control bodies on both sides of the gas-liquid interface are PW and PV, where PW represents the side of the wick and PV represents the side of the vapor chamber, the energy conservation equation is discretized to obtain the temperature _Ti at the interface:

in: _TPW — the first layer grid temperature of the wick near the interface, K; T _PV ——the first grid temperature of the steam chamber near the interface, K; Δx——interface area, m ² ; The interface temperature _Ti is calculated according to formula (2):

Step 5-2: Based on the interface temperature obtained in step 5-1, use the Clausius-Clapeyron equation to calculate the interface pressure P _i :

in: P _o ——reference pressure, Pa; P _i ——interface pressure, Pa; T _o ——reference temperature, K; R——gas constant, J/kg; Step 5-3: Mass flow rate at the gas-liquid interface

Perform the calculation:

in:

——interface mass flow rate, kg/s; σ——adjustment coefficient; surface tension, N/m; P _v ——vapor chamber pressure, Pa; T _v ——vapor chamber temperature, K; Step 5-4: Calculate the vapor zone working pressure based on the ideal gas equation and the overall mass balance of the vapor zone, and calculate the vapor density:

in: _Pop - working pressure of steam area, Pa;

——The steam mass in the steam chamber calculated at the previous time step, kg;

——interface mass flow rate, kg/s; Δt——time step, s; R——gas constant; V _cell ——vapor chamber pressure, Pa; Based on the incompressible assumption of the fluid, the vapor density in the control volume is calculated from the system pressure:

Step 5-5: Calculate the average density ρ _l of the liquid: In the transient process, the wick is unsaturated, and the unsaturated problem is not considered. Instead, the average liquid density is used for calculation to maintain the liquid mass balance; Calculate the mass of liquid in the wick at the current moment:

in: M _l ——mass of liquid in the absorbent core, kg;

——The mass of liquid in the wick calculated at the previous time step, kg;

——interface mass flow rate, kg/s; Δt——time step, s; Based on the mass of liquid in the wick, calculate the average density of the liquid:

in: ε——Porosity of wick; V _l ——volume of liquid wick/m ³ ; Step 6: Use computational fluid dynamics software to calculate the flow and heat transfer in the three-dimensional flat plate water heat pipe: Step 6-1: Solve the momentum equations of the wick and the vapor chamber respectively according to the interface mass flow rate, pressure, and temperature parameters obtained in step 5 to obtain velocity distribution, and use the pressure correction equation to correct the pressure; Step 6-2: Solve the energy conservation equation of the calculation area to obtain the temperature field of the calculation area; Step 6-3: Check whether the calculation has converged: When the residual value is less than 0.000001, the calculation is considered to have converged. If it has converged, the calculation of the next time step is performed, otherwise return to step 5 to continue the calculation. 2. A three-dimensional flat water heat pipe numerical calculation method according to claim 1, characterized in that: in step 2, considering the high requirements for mesh quality for fine simulation of heat pipes, a pure hexahedral mesh is used to mesh the calculation domain.

Images