CN114239435B - Numerical calculation method for three-dimensional flat plate water heat pipe - Google Patents
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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
Technical Field
The invention belongs to the technical field of thermal hydraulic numerical calculation, and particularly relates to a numerical calculation method of a three-dimensional flat plate water heat pipe.
Background
A heat pipe is a passive heat transfer device that has found wide use in thermal systems because it provides efficient heat transfer with minimal loss. With the chip-level heat flux reaching 200-300W/cm 2 One of the driving forces in heat pipe development is the need to reliably manage the heat dissipation of electronic systems while maintaining the equipment temperature to specification requirements. The passive nature of its operation and the ability to transfer heat over reasonable distances with only small changes in surface temperature make it particularly attractive in electronic cooling and packaging designs. Heat pipes are also widely used as heat sinks. It uses latent heat exchange to realizeThe heat transfer rate is now high. The increasing power density of electronic chips requires that the performance of these devices be optimized in order 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) employed in the device is a major factor affecting the heat transfer efficiency of the heat pipe and vapor chamber. The wick also determines the maximum heat transfer capacity. The research on the phase-change heat and mass transfer characteristics in the liquid suction core is helpful for optimizing the design of the liquid suction core and improving the performance of the phase-change cooling device.
During transient operation, the system pressure in the heat pipe changes as the liquid/vapor interface in the wick evaporates and condenses. Since the liquid-vapor density is relatively large, a small change in the phase change rate causes a large change in the system pressure. The system pressure in turn changes the interface pressure and thus the saturation temperature by the clausius-claperton equation. The evaporation and condensation rates depend on the interfacial evaporation resistance, which depends on both the interfacial pressure and the volumetric pressure. In addition, the system pressure also directly changes the vapor density through the ideal gas law. These non-linear relationships can cause difficulties in convergence of the numerical formats, especially at high heat additions.
Disclosure of Invention
The invention aims to provide a numerical calculation method of a flat plate water heat pipe, which can calculate the operation of an unsteady high heat flux heat pipe by using a computational fluid mechanical means, has good stability and convergence in calculation, and provides reference for newly-appearing heat pipe design.
In order to achieve the above purpose, the invention adopts the following technical scheme:
a numerical calculation method of a three-dimensional flat plate water heat pipe is characterized by comprising the following steps of: the method comprises the following steps:
step 1: establishing a software solidworks through a geometric model to establish a three-dimensional geometric model of the flat water heat pipe according to a real design, wherein the three-dimensional geometric model comprises a pipe wall, a liquid suction core, a vapor chamber, an evaporation section and a condensation section;
step 2: performing grid division on the flat plate water heat pipe geometric model obtained in the step 1 by using grid division software;
step 3: the grids divided in the step 2 are led into computational fluid dynamics software, an evaporation section and a condensation section of the heat pipe are respectively set as a heat flow boundary condition and a convection boundary condition, other wall surfaces are set as heat insulation wall surfaces, the heat flow density heated by the evaporation section, the heat exchange coefficient of the condensation section and the temperature of a coolant are set according to the actual situation, and the porosity of the liquid absorption core is set;
step 4: setting initial conditions required for transient calculation: setting the initial steam mass as 0, initializing a temperature field, and enabling the working pressure of an initial steam area to be the saturation pressure at the current temperature;
step 5: the user-defined program UDF was used to calculate the gas-liquid interface mass flow rate, the temperature and pressure at the wick-vapor interface, and the liquid and vapor densities per time step:
step 5-1: assuming that the phase change of the liquid working medium and the vapor working medium occurs at the interface between the liquid suction core and the vapor cavity, calculating the temperature T at the interface according to the energy conservation equation at the interface i ：
The conservation of energy equation at the interface is expressed as:
wherein:
λ wick and lambda is v Representing the thermal conductivity, W.m, of the wick and vapor chamber, respectively -1 ·K -1 ；
A i Interface area, m 2 ；
T-temperature, where T i Interface temperature, K;
y-distance in the perpendicular direction to the interface, m;
m i interface Mass transfer, m i < 0 is evaporation, m i Condensation > 0 kg;
h fg latent heat of vaporization, J/kg;
C l -liquid phase constant pressure specific heat, J/(kg·k);
C v -gas phase constant pressure specific heat, J/(kg·k);
assuming two control bodies at two sides of a gas-liquid interface are PW and PV respectively, wherein PW represents one side of a liquid suction core, PV represents one side of a vapor cavity, and dispersing an energy conservation equation to obtain the temperature T at the interface i ：
Wherein:
T PW -the first layer mesh temperature, K, of the wick near the interface;
T PV -the first layer mesh temperature, K, of the vapor chamber near the interface;
Δx-interfacial area, m 2 ；
Calculating the temperature T of the interface according to the formula (2) i ：
Step 5-2: calculating the interface pressure P by using Clausius-Clapeyron equation according to the temperature of the interface obtained in the step 5-1 i ：
Wherein:
P o -reference pressure, pa;
P i interface pressure, pa;
T o -reference temperature, K;
r-gas constant, J/kg;
step 5-3: for gas-liquid interface mass flow rate
And (3) performing calculation:
wherein:
sigma-adjustment factor; surface tension, N/m;
P v -vapour chamber pressure, pa;
T v -vapor chamber temperature, K;
step 5-4: calculating the working pressure of the vapor region according to an ideal gas formula and the overall mass balance of the vapor region, and calculating the vapor density:
wherein:
P op -vapour zone working pressure, pa;
Δt-time step, s;
r-gas constant;
V cell -vapour 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: calculating the average density ρ of the liquid l ：
The wick is unsaturated during transients, and the average liquid density is calculated to maintain liquid mass balance, regardless of the problem of unsaturation;
calculating the mass of liquid in the liquid suction core at the current moment:
wherein:
M l -mass of liquid in the wick, kg;
Δt-time step, s;
from the mass of liquid in the wick, the average density of the liquid is calculated:
wherein:
epsilon-wick porosity;
V l wick volume/m 3 ；
Step 6: calculating the flow heat transfer in the three-dimensional flat plate hydrothermal pipe by using computational fluid dynamics software:
step 6-1: respectively solving momentum equations of the liquid suction core and the steam cavity according to the interface mass flow rate, the pressure and the temperature parameters obtained in the step 5 to obtain speed distribution, and correcting the pressure by using a pressure correction equation;
step 6-2: solving an energy conservation equation of the calculation region to obtain a temperature field of the calculation region;
step 6-3: checking whether the calculation converges: and when the residual value is smaller than 0.000001, the calculation is considered to reach convergence, if so, the calculation of the next time step is carried out, otherwise, the step 5 is returned to continue the calculation.
Preferably, in step 2, the calculation domain is gridded by using a pure hexahedral grid in consideration of high requirements on grid quality for fine simulation of the heat pipe.
Compared with the prior art, the invention has the following beneficial effects:
1) According to the invention, the wick and the steam cavity are calculated independently, and the heat pipe is calculated by adding the interaction method of the wick and the steam cavity, so that the internal flow of the wick can be simulated more finely;
2) The numerical format of incompressible limit pressure of the system is calculated by using the whole mass balance, and the stability of a standard sequence program is improved by considering the coupling between the mass flow of an evaporation section/a condensation section, the concentration of an interface substance, the pressure and the system pressure;
3) The model is independent, the method is high in universality, and can be used for calculating heat pipes in other shapes.
Drawings
FIG. 1 is a schematic diagram of a three-dimensional flat heat pipe;
FIG. 2 is a schematic diagram of an energy transfer process within a heat pipe;
fig. 3 is a schematic view of a control body at the interface of a wick and a vapor chamber;
fig. 4 is a flow chart of the method of the present invention.
Detailed Description
The present invention will be described in further detail below with reference to the flow chart of fig. 4, taking a typical three-dimensional flat plate water heat pipe as an example:
the invention discloses a numerical calculation method of a three-dimensional flat plate water heat pipe, which comprises the following steps:
step 1: FIG. 1 is a schematic structural diagram of a three-dimensional flat heat pipe, wherein a software solidworks is established through a geometric model to establish a three-dimensional geometric model of the flat water heat pipe according to a real design, and the three-dimensional geometric model comprises a pipe wall, a liquid suction core, a vapor chamber, an evaporation section and a condensation section;
step 2: grid division is carried out on the flat-plate water heat pipe geometric model obtained in the step 1 by utilizing grid division software, and the embodiment uses a pure hexahedral grid to carry out grid division on a calculation domain in consideration of high requirements on grid quality of fine simulation on the heat pipe;
step 3: the grids divided in the step 2 are led into computational fluid dynamics software, an evaporation section and a condensation section of the heat pipe are respectively set as a heat flow boundary condition and a convection boundary condition, other wall surfaces are set as heat insulation wall surfaces, the heat flow density heated by the evaporation section, the heat exchange coefficient of the condensation section and the temperature of a coolant are set according to the actual situation, and the porosity of the liquid absorption core is set;
step 4: setting initial conditions required for transient calculation: setting the initial steam mass as 0, initializing a temperature field, and enabling the working pressure of an initial steam area to be the saturation pressure at the current temperature;
step 5: the user-defined program UDF was used to calculate the gas-liquid interface mass flow rate, the temperature and pressure at the wick-vapor interface, and the liquid and vapor densities per time step:
step 5-1: assuming that the phase change of the liquid working medium and the vapor working medium occurs at the interface between the liquid suction core and the vapor cavity, calculating the temperature T at the interface according to the energy conservation equation at the interface i ：
The energy transfer process in the heat pipe is shown in fig. 2, in the evaporation section, the liquid is changed into steam under the heating effect, and the heat is transferred from the evaporation section to the steam cavity; in the condensing section, the steam condenses under the cooling action, and heat is transferred from the steam cavity to the condensing section. The conservation of energy equation at the interface is expressed as:
wherein:
λ wick and lambda is v Representing the thermal conductivity, W.m, of the wick and vapor chamber, respectively -1 ·K -1 ；
A i Interface area, m 2 ；
T-temperature, where T i Interface temperature, K;
y-distance in the perpendicular direction to the interface, m;
m i interface Mass transfer, m i < 0 is evaporation, m i Condensation > 0 kg;
h fg latent heat of vaporization, J/kg;
C l -liquid phase constant pressure specific heat, J/(kg·k);
C v -gas phase constant pressure specific heat, J/(kg·k);
FIG. 3 is a schematic diagram of the control body at the interface of the wick and the vapor chamber, assuming two control bodies on both sides of the gas-liquid interface are PW and PV, respectively, where PW represents one side of the wick and PV represents one side of the vapor chamber, and the energy conservation equation is discretized to obtain the temperature T at the interface i ：
Wherein:
T PW -the first layer mesh temperature, K, of the wick near the interface;
T PV -the first layer mesh temperature, K, of the vapor chamber near the interface;
Δx-interfacial area, m 2 ；
Calculating the temperature T of the interface according to the formula (2) i ：
Step 5-2: calculating the interface pressure P by using Clausius-Clapeyron equation according to the temperature of the interface obtained in the step 5-1 i ：
Wherein:
P o -reference pressure, pa;
P i interface pressure, pa;
T o -reference temperature, K;
T i interface temperature, K;
h fg latent heat of vaporization, J/kg;
r-gas constant, J/kg;
step 5-3: for gas-liquid interface mass flow rate
And (3) performing calculation:
wherein:
sigma-adjustment factor; surface tension, N/m;
P v -vapour chamber pressure, pa;
T v -vapor chamber temperature, K;
step 5-4: calculating the working pressure of the vapor region according to an ideal gas formula and the overall mass balance of the vapor region, and calculating the vapor density:
wherein:
P op -vapour zone working pressure, pa;
Δt-time step, s;
r-gas constant;
V cell -vapour 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: calculating the average density ρ of the liquid l ：
The wick is typically unsaturated during transients, and the average liquid density is calculated to maintain liquid mass balance, regardless of the problem of unsaturation.
Calculating the mass of liquid in the liquid suction core at the current moment:
wherein:
M l -mass of liquid in the wick, kg;
Δt-time step, s;
from the mass of liquid in the wick, the average density of the liquid is calculated:
wherein:
epsilon-wick porosity;
V l wick volume/m 3 ；
Step 6: calculating the flow heat transfer in the three-dimensional flat plate hydrothermal pipe by using computational fluid dynamics software:
step 6-1: respectively solving momentum equations of the liquid suction core and the steam cavity according to the parameters of the interface mass flow rate, the pressure, the temperature and the like obtained in the step 5 to obtain speed distribution, and correcting the pressure by using a pressure correction equation;
step 6-2: solving an energy conservation equation of the calculation region to obtain a temperature field of the calculation region;
step 6-3: checking whether the calculation converges: and when the residual value is smaller than 0.000001, the calculation is considered to reach convergence, if so, the calculation of the next time step is carried out, otherwise, the step 5 is returned to continue the calculation.
Claims (2)
1. A numerical calculation method of a three-dimensional flat plate water heat pipe is characterized by comprising the following steps of: the method comprises the following steps:
step 1: establishing a software solidworks through a geometric model to establish a three-dimensional geometric model of the flat water heat pipe according to a real design, wherein the three-dimensional geometric model comprises a pipe wall, a liquid suction core, a vapor chamber, an evaporation section and a condensation section;
step 2: performing grid division on the flat plate water heat pipe geometric model obtained in the step 1 by using grid division software;
step 3: the grids divided in the step 2 are led into computational fluid dynamics software, an evaporation section and a condensation section of the heat pipe are respectively set as a heat flow boundary condition and a convection boundary condition, other wall surfaces are set as heat insulation wall surfaces, the heat flow density heated by the evaporation section, the heat exchange coefficient of the condensation section and the temperature of a coolant are set according to the actual situation, and the porosity of the liquid absorption core is set;
step 4: setting initial conditions required for transient calculation: setting the initial steam mass as 0, initializing a temperature field, and enabling the working pressure of an initial steam area to be the saturation pressure at the current temperature;
step 5: the user-defined program UDF was used to calculate the gas-liquid interface mass flow rate, the temperature and pressure at the wick-vapor interface, and the liquid and vapor densities for each time step:
step 5-1: assuming that the phase change of the liquid working medium and the vapor working medium occurs at the interface between the liquid suction core and the vapor cavity, calculating the temperature T at the interface according to the energy conservation equation at the interface i ：
The conservation of energy equation at the interface is expressed as:
wherein:
λ wick and lambda is v Representing the thermal conductivity, W.m, of the wick and vapor chamber, respectively -1 ·K -1 ；
A i Interface area, m 2 ；
T-temperature, where T i Interface temperature, K;
y-distance in the perpendicular direction to the interface, m;
m i interface Mass transfer, m i < 0 is evaporation, m i Condensation > 0 kg;
h fg latent heat of vaporization, J/kg;
C l liquid phase constant pressure specific heat, J/(kg)K)；
C v -gas phase constant pressure specific heat, J/(kg·k);
assuming two control bodies at two sides of a gas-liquid interface are PW and PV respectively, wherein PW represents one side of a liquid suction core, PV represents one side of a vapor cavity, and dispersing an energy conservation equation to obtain the temperature T at the interface i ：
Wherein:
T PW -the first layer mesh temperature, K, of the wick near the interface;
T PV -the first layer mesh temperature, K, of the vapor chamber near the interface;
Δx-interfacial area, m 2 ；
Calculating the temperature T of the interface according to the formula (2) i ：
Step 5-2: calculating the interface pressure P by using Clausius-Clapeyron equation according to the temperature of the interface obtained in the step 5-1 i ：
Wherein:
P o -reference pressure, pa;
P i interface pressure, pa;
T o -reference temperature, K;
r-gas constant, J/kg;
step 5-3: for gas-liquid interface mass flow rate
And (3) performing calculation:
wherein:
sigma-adjustment factor; surface tension, N/m;
P v -vapour chamber pressure, pa;
T v -vapor chamber temperature, K;
step 5-4: calculating the working pressure of the vapor region according to an ideal gas formula and the overall mass balance of the vapor region, and calculating the vapor density:
wherein:
P op -vapour zone working pressure, pa;
Δt-time step, s;
r-gas constant;
V cell -vapour 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: calculating the average density ρ of the liquid l ：
The wick is unsaturated during transients, and the average liquid density is calculated to maintain liquid mass balance, regardless of the problem of unsaturation;
calculating the mass of liquid in the liquid suction core at the current moment:
wherein:
M l -mass of liquid in the wick, kg;
Δt-time step, s;
from the mass of liquid in the wick, the average density of the liquid is calculated:
wherein:
epsilon-wick porosity;
V l wick volume/m 3 ；
Step 6: calculating the flow heat transfer in the three-dimensional flat plate hydrothermal pipe by using computational fluid dynamics software:
step 6-1: respectively solving momentum equations of the liquid suction core and the steam cavity according to the interface mass flow rate, the pressure and the temperature parameters obtained in the step 5 to obtain speed distribution, and correcting the pressure by using a pressure correction equation;
step 6-2: solving an energy conservation equation of the calculation region to obtain a temperature field of the calculation region;
step 6-3: checking whether the calculation converges: and when the residual value is smaller than 0.000001, the calculation is considered to reach convergence, if so, the calculation of the next time step is carried out, otherwise, the step 5 is returned to continue the calculation.
2. The method for calculating the numerical value of the three-dimensional flat plate water heat pipe according to claim 1, which is characterized in that: in step 2, the calculation domain is grid-divided by using a pure hexahedral grid in consideration of high requirements on grid quality in fine simulation of the heat pipe.
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| CN107704674A (en) * | 2017-09-26 | 2018-02-16 | 吉林省电力科学研究院有限公司 | The method for numerical simulation of air cooling tubes condenser water vapor condensation process |
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