CN116541640B - Normalized steam heat transfer calculation method of alkali metal heat pipe - Google Patents
Normalized steam heat transfer calculation method of alkali metal heat pipe Download PDFInfo
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- 229910052783 alkali metal Inorganic materials 0.000 title claims abstract description 36
- 150000001340 alkali metals Chemical class 0.000 title claims abstract description 36
- 238000004364 calculation method Methods 0.000 title claims abstract description 34
- 239000007788 liquid Substances 0.000 claims abstract description 91
- 239000000463 material Substances 0.000 claims abstract description 22
- 238000010521 absorption reaction Methods 0.000 claims abstract description 8
- 238000004422 calculation algorithm Methods 0.000 claims abstract description 4
- 238000001704 evaporation Methods 0.000 claims description 29
- 230000008020 evaporation Effects 0.000 claims description 24
- 238000009833 condensation Methods 0.000 claims description 17
- 230000005494 condensation Effects 0.000 claims description 17
- 238000000034 method Methods 0.000 claims description 11
- 238000009413 insulation Methods 0.000 claims description 7
- NAWXUBYGYWOOIX-SFHVURJKSA-N (2s)-2-[[4-[2-(2,4-diaminoquinazolin-6-yl)ethyl]benzoyl]amino]-4-methylidenepentanedioic acid Chemical compound C1=CC2=NC(N)=NC(N)=C2C=C1CCC1=CC=C(C(=O)N[C@@H](CC(=C)C(O)=O)C(O)=O)C=C1 NAWXUBYGYWOOIX-SFHVURJKSA-N 0.000 claims description 6
- 238000004134 energy conservation Methods 0.000 claims description 6
- 238000009834 vaporization Methods 0.000 claims description 6
- 230000008016 vaporization Effects 0.000 claims description 6
- 230000003416 augmentation Effects 0.000 claims description 5
- 238000001816 cooling Methods 0.000 claims description 3
- 238000010438 heat treatment Methods 0.000 claims description 3
- 238000000329 molecular dynamics simulation Methods 0.000 claims description 3
- 238000000638 solvent extraction Methods 0.000 claims description 3
- DGAQECJNVWCQMB-PUAWFVPOSA-M Ilexoside XXIX Chemical group C[C@@H]1CC[C@@]2(CC[C@@]3(C(=CC[C@H]4[C@]3(CC[C@@H]5[C@@]4(CC[C@@H](C5(C)C)OS(=O)(=O)[O-])C)C)[C@@H]2[C@]1(C)O)C)C(=O)O[C@H]6[C@@H]([C@H]([C@@H]([C@H](O6)CO)O)O)O.[Na+] DGAQECJNVWCQMB-PUAWFVPOSA-M 0.000 claims description 2
- ZLMJMSJWJFRBEC-UHFFFAOYSA-N Potassium Chemical group [K] ZLMJMSJWJFRBEC-UHFFFAOYSA-N 0.000 claims description 2
- 239000012530 fluid Substances 0.000 claims description 2
- 229910052700 potassium Inorganic materials 0.000 claims description 2
- 239000011591 potassium Substances 0.000 claims description 2
- 229910052708 sodium Inorganic materials 0.000 claims description 2
- 239000011734 sodium Substances 0.000 claims description 2
- 238000004088 simulation Methods 0.000 abstract description 3
- 230000001052 transient effect Effects 0.000 abstract description 2
- 230000005540 biological transmission Effects 0.000 description 3
- 238000005555 metalworking Methods 0.000 description 2
- 230000008878 coupling Effects 0.000 description 1
- 238000010168 coupling process Methods 0.000 description 1
- 238000005859 coupling reaction Methods 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- BTCSSZJGUNDROE-UHFFFAOYSA-N gamma-aminobutyric acid Chemical compound NCCCC(O)=O BTCSSZJGUNDROE-UHFFFAOYSA-N 0.000 description 1
- 230000000704 physical effect Effects 0.000 description 1
- 239000000126 substance Substances 0.000 description 1
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Abstract
The calculation method of normalized vapor heat transfer of alkali metal heat pipe includes 1, determining calculation parameters of alkali metal heat pipe including geometry, material, boundary condition, mesh division and initial condition; 2. calculating the saturation pressure of a gas-liquid interface of the heat pipe; 3. constructing an analytical function taking the vapor temperature as an independent variable; 4. iteratively solving the normalized steam temperature; 5. calculating the temperature change rate of the pipe wall and the liquid absorption core area of the heat pipe; 6. solving a discrete control equation set by using a Gear algorithm to obtain the temperature distribution of the pipe wall and the liquid suction core of the heat pipe; 7. and (5) after the calculation is completed, outputting a calculation result. According to the invention, the isothermal characteristics of the heat pipes are considered, numerical simulation is carried out on the alkali metal heat pipes with different geometric dimensions and boundary conditions, the normalized vapor temperature of the vapor region of the heat pipe is calculated, the transient heat transfer characteristics of the alkali metal heat pipes are further obtained, and advice and guidance are provided for engineering application and analysis and calculation of the alkali metal high-temperature heat pipes.
Description
Technical Field
The invention relates to the technical field of heat transfer calculation of phase change heat exchange equipment, in particular to a normalized steam heat transfer calculation method of an alkali metal heat pipe.
Background
A heat pipe is a highly efficient heat transfer device whose operating characteristics are passive, and failure of a single heat pipe does not affect the heat transfer function and inherent safety of the overall system. The heat energy transmission system can transmit a large amount of heat, has strong heat transmission capacity and high efficiency, and can obviously improve the working performance of the heat energy transmission system. The heat pipe is widely applied to the fields of aerospace, chemical industry, nuclear energy and the like. The heat pipe mainly relies on phase change heat transfer, the working medium absorbs heat in the evaporation section and evaporates into vapor, the vapor flows to the condensation section through the vapor cavity, the heat is released in the condensation section to condense into liquid, and the liquid returns to the evaporation section through capillary action, so that circulation is completed. High temperature heat pipes typically operate at temperatures in excess of 600 c, which typically use alkali metals as the working medium. Complex heat and mass transfer coupling characteristics exist in the pipe wall, the liquid absorption core and the steam area inside the alkali metal heat pipe, and the nonlinearity of the whole alkali metal heat pipe system is high, so that the numerical simulation calculation for the heat pipe is difficult to ensure the calculation speed and the calculation precision at the same time.
Disclosure of Invention
In order to overcome the problems in the prior art, the invention aims to provide a normalized vapor heat transfer calculation method of an alkali metal heat pipe, which considers the isothermal characteristics of the heat pipe, performs numerical simulation on the alkali metal heat pipes with different geometric dimensions and boundary conditions, calculates the normalized vapor temperature of a vapor region of the heat pipe, further obtains the transient heat transfer characteristics of the alkali metal heat pipe, and provides suggestions and guidance for engineering application and analysis calculation of the alkali metal high-temperature heat pipe.
In order to achieve the above purpose, the invention adopts the following technical scheme:
the normalized vapor heat transfer calculation method of the alkali metal heat pipe comprises the following steps:
step 1: determining the calculation parameters of the alkali metal heat pipe: determining the geometry of the alkali metal heat pipe and the materials of the pipe wall, the liquid suction core and the working medium; the evaporation section gives heat flow density, and the condensation section gives convective heat transfer coefficient; constructing grids, dividing an evaporation section, a heat insulation section and a condensation section of the heat pipe into a layer of grids of a, b and c respectively, dividing the pipe wall and a liquid suction core of the heat pipe into m layers of grids and n layers of grids respectively, and dividing a vapor area into 1 layer of grids; setting the initial temperature of each grid node and calculating the time step;
step 2: calculating the saturation pressure of the gas-liquid interface of the heat pipe: according to the temperature on the gas-liquid interface of the heat pipe, calculating the saturation pressure on the gas-liquid interface by adopting a fitting function relation shown in the formula (1):
in the formula (1):
P f -saturation pressure/Pa;
t-interfacial temperature/K;
p (T) -the fitted functional relationship of saturation pressure and temperature;
n-an augmentation factor;
i-index coefficient;
m, fitting coefficients;
step 3: constructing an analytical function taking the vapor temperature as an independent variable: assuming that the alkali metal vapor temperature is the same and the total evaporative condensing amount is conserved throughout the vapor zone, the energy conservation equation for vapor heat transfer is shown in equation (2):
in the formula (2):
i-gas-liquid interface node number;
-mass evaporation rate of gas-liquid interface node/(kg.s) -1 )；
h fg Latent heat of vaporization/(kJ.kg) -1 )；
Δl i -gas-liquid interface node boundary length/m;
calculating mass evaporation rate of gas-liquid interface node by adopting molecular dynamics equationAs shown in formula (3):
in the formula (3):
-evaporating the condensation regulation factor;
epsilon-wick porosity;
M atom molar mass of vapor in vapor zone/(kg. Mol) -1 )；
R u General gas constant/(R) u ＝8.314J·mol -1 ·K -1 )；
T li -node liquid working medium temperature/K on gas-liquid interface;
P li -node liquid working medium saturation pressure/Pa on gas-liquid interface;
T v -temperature of vapor in vapor zone/K;
P v -saturation pressure of vapor in vapor zone/Pa;
the calculation adopts equipartition grid, and the boundary length delta l of each gas-liquid interface node i Equal and consider the vaporization latent heat h of the same working medium fg The simplified energy conservation equation of the formula (3) of the combined formula (2) is shown as the formula (4):
due to the vapour saturation vapour pressure P v Only the vapor temperature T v Is a function of the node temperature T at the gas-liquid interface li The saturation pressure is known to have been found in step 2, so equation (4) can be written as relating to the vapor temperature T v As shown in the formula (5) -formula (7):
C 2 ＝a+c (7)
in the formulae (5) to (7):
C 1 -interface coefficients determined by boundary conditions;
C 2 -geometric coefficients determined by geometric partitioning;
substituting the fitting function relation P (T) in the step 2In (5), the vapor temperature T is obtained v The complete analytical function for the argument is shown in equation (8):
step 4: iteratively solving the normalized steam temperature: solving for the vapor temperature T v I.e. into a function f (T v ) Adopts an iteration method to solve, and constructs an iteration relation as shown in the formula (9):
in the formula (9):
-the vapor temperature obtained by the n-th iteration;
-the vapor temperature obtained by iteration in step n+1;
substituting the vapor temperature obtained in the n-th iteration into a value obtained by a vapor temperature analytical function;
substituting the vapor temperature obtained in the n-th iteration into a value obtained by a derivative function of the vapor temperature analytic function;
the average temperature of the node liquid working medium temperature on the gas-liquid interface is taken as the initial value needed by the iteration of the formula (9), and is shown as the formula (10):
in the formula (10):
T v 0 -an iterative initial value of vapor temperature;
T li -the temperature of the liquid working medium of the ith node on the gas-liquid interface;
the derivative f' required for the iteration of equation (9) is derived from equation (8), as shown in equation (11):
in the formula (11):
P(T v ) -steam temperature T v Substituting the vapor saturation pressure obtained by the fitting function relation P (T) of the saturation pressure and the temperature;
when iterating, presetting the iteration precision epsilon, and firstly, setting the initial value T required by the iteration v 0 Substituting (9) to calculate to obtain the vapor temperature T calculated in the 1 st step v 1 Judging whether or not |f (T) v 1 )|<Epsilon, if yes, stopping iteration to obtain normalized vapor temperature T v Is approximated by T v 1 The method comprises the steps of carrying out a first treatment on the surface of the If not, repeating the step, and iteratively calculating the vapor temperature in the nth stepSubstituting (9) to calculate the vapor temperature of n+1 step iterative calculation +.>Until meeting->Stopping the iteration to obtain the normalized steam temperature T v Is approximated as +.>
Step 5: calculating temperature change of heat pipe wall and liquid absorption core areaRate ofEstablishing a two-dimensional heat conduction equation in the pipe wall area of the heat pipe, as shown in a formula (12):
in the formula (12):
ρ w density of tube wall material/(kg.m) -3 )；
c w Heat capacity/(J.kg) of pipe wall material -1 ·K -1 )；
T w -temperature of the tube wall/K;
t-time/s;
r-radial coordinate/m;
k w -thermal conductivity of the tube wall material/(w·m) -1 ·K -1 )
z-axial coordinate/m;
the boundary condition of the two-dimensional heat conduction equation (12) is shown as the following formula (13) -formula (15):
and (3) an evaporation section:
and (3) an insulation section:
condensing section:
hA c (T w -T sur )＝Q c (15)
in the formulas (13) - (15):
A e -heat pipe evaporation zone area/m 2 ；
A c Area/m of condensation section of heat pipe 2 ；
Q e ——Heating power/W of the evaporation section;
Q c -condensing section cooling power/W;
h-convection heat transfer coefficient of outer surface of condensing section/(W.m) -2 ·K -1 )；
T sur -ambient temperature/K;
neglecting the flow of the working fluid in the wick, a two-dimensional heat conduction equation is also established in the wick region of the heat pipe, and the control equation is shown in the formula (16) -formula (18):
(ρc) eff ＝ερ l c l +(1-ε)ρ ws c ws (17)
in the formula (16) -formula (18):
(ρc) eff equivalent volumetric heat capacity/(J.m) of the wick -3 ·K -1 )；
T ws -temperature of the wick/K;
k eff equivalent thermal conductivity of the wick/(W.m) -1 ·K -1 )
ρ l -density/(kg.m) of liquid working medium in wick -3 )；
c l -heat capacity/(J.kg) of liquid working medium in wick -1 ·K -1 )；
ρ ws Density of the wick material/(kg.m) -3 )；
c ws -heat capacity of the wick material/(j·kg) -1 ·K -1 )；
k l -thermal conductivity/(w·m) of the liquid working medium in the wick -1 ·K -1 )；
k ws -thermal conductivity of the wick material/(W.m -1 ·K -1 )；
The boundary condition of the control equation (16) is shown in equation (20):
A i ＝2πrΔl i (20)
in the formula (19) -formula (20):
T i -temperature/K of gas-liquid interface node;
A i -heat exchange area/m of gas-liquid interface node and vapor zone 2 ；
Step 6: dispersing the two-dimensional heat conduction equation and the boundary condition in the step 5 to generate an unsteady heat conduction control equation set, solving the equation set by adopting a Gear algorithm, and calculating to obtain the temperature distribution of the heat pipe wall and the liquid absorption core at the current time t;
step 7: and (5) after the calculation is completed, outputting a calculation result.
Compared with the prior art, the invention has the following advantages:
(1) The temperature of the vapor zone of the alkali metal heat pipe can be rapidly and accurately calculated by considering the isothermicity of the heat pipe;
(2) The constructed iterative equation has higher precision and better convergence;
(3) The heat and mass transfer of the heat pipe gas-liquid interface is calculated by a theoretical formula and is coupled with the heat and mass transfer of the steam area;
(4) The heat pipe is applicable to alkali metal heat pipes with various geometric structures and working media, and has wide applicability.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Fig. 2 is a schematic diagram of system node division according to the present invention.
Detailed Description
The invention is described in further detail below with reference to the drawings and the detailed description.
As shown in fig. 1, the method for calculating normalized vapor heat transfer of the alkali metal heat pipe comprises the following steps:
step 1: determining the calculation parameters of the alkali metal heat pipe: determining the geometry of the alkali metal heat pipe and the materials of the pipe wall, the liquid suction core and the working medium; the evaporation section gives heat flow density, and the condensation section gives convective heat transfer coefficient; constructing grids, dividing an evaporation section, a heat insulation section and a condensation section of the heat pipe into a layer of grids of a, b and c respectively, dividing the pipe wall and a liquid suction core of the heat pipe into m layers of grids and n layers of grids respectively, and dividing a vapor area into 1 layer of grids as shown in fig. 2; setting the initial temperature of each grid node and calculating the time step;
step 2: calculating the saturation pressure of the gas-liquid interface of the heat pipe: according to the temperature on the gas-liquid interface of the heat pipe, based on An Tuo factor equation form of physical properties of alkali metal working media, calculating saturation pressure on the gas-liquid interface by adopting a fitting function relation shown as formula (1):
in the formula (1):
P f -saturation pressure/Pa;
t-interfacial temperature/K;
p (T) -the fitted functional relationship of saturation pressure and temperature;
n-an augmentation factor;
i-index coefficient;
m, fitting coefficients;
step 3: constructing an analytical function taking the vapor temperature as an independent variable: since the isothermal nature of the alkali metal heat pipe is good, assuming that the alkali metal vapor temperature is the same in the whole vapor region and the total evaporation and condensation amount is conserved, the energy conservation equation of vapor heat transfer is shown as formula (2):
in the formula (2):
i-gas-liquid interface node number;
-mass evaporation rate of gas-liquid interface node/(kg.s) -1 )；
h fg Latent heat of vaporization/(kJ.kg) -1 )；
Δl i -gas-liquid interface node boundary length/m;
calculating mass evaporation rate of gas-liquid interface node by adopting molecular dynamics equationAs shown in formula (3):
in the formula (3):
-evaporating the condensation regulation factor;
epsilon-wick porosity;
M atom molar mass of vapor in vapor zone/(kg. Mol) -1 )；
R u General gas constant/(R) u ＝8.314J·mol -1 ·K -1 )；
T li -node liquid working medium temperature/K on gas-liquid interface;
P li -node liquid working medium saturation pressure/Pa on gas-liquid interface;
T v -temperature of vapor in vapor zone/K;
P v -saturation pressure of vapor in vapor zone/Pa;
the calculation adopts equipartition grid, and the boundary length delta l of each gas-liquid interface node i Equal and consider the vaporization latent heat h of the same working medium fg The simplified energy conservation equation of the formula (3) of the combined formula (2) is shown as the formula (4):
due to the vapour saturation vapour pressure P v Only the vapor temperature T v Is a function of the node temperature T at the gas-liquid interface li The saturation pressure is known to have been found in step 2, so equation (4) can be written as relating to the vapor temperature T v As shown in the formula (5) -formula (7):
C 2 ＝a+c (7)
in the formulae (5) to (7):
C 1 -interface coefficients determined by boundary conditions;
C 2 -geometric coefficients determined by geometric partitioning.
Substituting the fitting function relation P (T) in step 2 into equation (5) to obtain the vapor temperature T v The complete analytical function f, which is an argument, is shown in equation (8):
step 4: iteratively solving the normalized steam temperature: solving for the vapor temperature T v I.e. into a function f (T v ) Can be solved by adopting an iteration method, and an iteration relation is constructed as shown in formula (9):
in the formula (9):
-the vapor temperature obtained by the n-th iteration;
-the vapor temperature obtained by iteration in step n+1;
substituting the vapor temperature obtained in the n-th iteration into a value obtained by a vapor temperature analytical function;
substituting the vapor temperature obtained in the n-th iteration into a value obtained by a derivative function of the vapor temperature analytic function;
when the alkali metal heat pipe works, the temperature of the gas-liquid interface of the evaporation section is generally higher than the vapor temperature, and the temperature of the gas-liquid interface of the condensation section is generally lower than the vapor temperature, so that heat transfer can be realized, and the average temperature of the node liquid working medium temperature on the initial gas-liquid interface required by the iteration of the formula (9) is shown as the formula (10):
in the formula (10):
T v 0 -an iterative initial value of vapor temperature;
T li -the temperature of the liquid working medium at the i-th node on the gas-liquid interface.
The derivative f' required for the iteration of equation (9) is derived from equation (8), as shown in equation (11):
in the formula (11):
P(T v ) -steam temperature T v Substituting the vapor saturation pressure obtained by the fitting function relation P (T) of the saturation pressure and the temperature;
when iterating, presetting the iteration precision epsilon, and firstly, setting the initial value T required by the iteration v 0 is substituted into (9) to calculate and obtain the steam temperature T of the iterative calculation in the 1 st step v 1 Judging whether or not |f (T) v 1 )|<Epsilon, if yes, stopping iteration to obtain normalized vapor temperature T v Is approximated by T v 1 The method comprises the steps of carrying out a first treatment on the surface of the If not, repeating the step, and iteratively calculating the vapor temperature in the nth stepSubstituting (9) to calculate the vapor temperature of n+1 step iterative calculation +.>Until meeting->Stopping the iteration to obtain the normalized steam temperature T v Is approximated as +.>
Step 5: calculating the temperature change rate of the heat pipe wall and the liquid absorption core areaEstablishing a two-dimensional heat conduction equation in the pipe wall area of the heat pipe, wherein the control equation is shown in a formula (12):
in the formula (12):
ρ w density of tube wall material/(kg.m) -3 )；
c w -pipe wall materialHeat capacity/(J.kg) of material -1 ·K -1 )；
T w -temperature of the tube wall/K;
t-time/s;
r-radial coordinate/m;
k w -thermal conductivity of the tube wall material/(w·m) -1 ·K -1 )
z-axial coordinate/m;
for alkali metal heat pipes, the evaporation section generally adopts a second type boundary condition, the condensation section generally adopts a third type boundary condition, and the heat insulation section only plays a mass transfer role, so that the boundary condition of the two-dimensional heat conduction equation (12) is shown as the following formula (13) -formula (15):
and (3) an evaporation section:
and (3) an insulation section:
condensing section:
hA c (T w -T sur )＝Q c (15)
in the formulas (13) - (15):
A e -heat pipe evaporation zone area/m 2 ；
A c Area/m of condensation section of heat pipe 2 ；
Q e -evaporation section heating power/W;
Q c -condensing section cooling power/W;
h-convection heat transfer coefficient of outer surface of condensing section/(W.m) -2 ·K -1 )；
T sur -ambient temperature/K;
because the flow speed of the alkali metal working medium in the liquid suction core of the alkali metal heat pipe is very slow and the heat conduction capacity is very high, the flow of the working medium in the liquid suction core can be ignored, a two-dimensional heat conduction equation is also established in the liquid suction core area of the heat pipe, and the control equation is shown as the following formula (16) -formula (18):
(ρc) eff ＝ερ l c l +(1-ε)ρ ws c ws (17)
in the formula (16) -formula (18):
(ρc) eff equivalent volumetric heat capacity/(J.m) of the wick -3 ·K -1 )；
T ws -temperature of the wick/K;
k eff equivalent thermal conductivity of the wick/(W.m) -1 ·K -1 )
ρ l -density/(kg.m) of liquid working medium in wick -3 )；
c l -heat capacity/(J.kg) of liquid working medium in wick -1 ·K -1 )；
ρ ws Density of the wick material/(kg.m) -3 )；
c ws -heat capacity of the wick material/(j·kg) -1 ·K -1 )；
k l -thermal conductivity/(w·m) of the liquid working medium in the wick -1 ·K -1 )；
k ws -thermal conductivity of the wick material/(w·m) -1 ·K -1 )；
The boundary conditions of control equation (16) are as shown in equation (20), regardless of the heat transfer at the vapor-to-heat pipe vapor-liquid interface:
A i ＝2πrΔl i (20)
in the formula (19) -formula (20):
T i -temperature/K of gas-liquid interface node;
A i -heat exchange area/m of gas-liquid interface node and vapor zone 2 ；
Step 6: dispersing the two-dimensional heat conduction equation and the boundary condition in the step 5 to generate an unsteady heat conduction control equation set, solving the equation set by adopting a Gear algorithm, and calculating to obtain the temperature distribution of the heat pipe wall and the liquid absorption core at the current time t;
step 7: and (5) after the calculation is completed, outputting a calculation result.
In this embodiment, the augmentation factor N, the index factor I, and the fitting factor M described in step 2 are 5567.0 for N, 0.5 for I, and 2.29×10 for M when the working medium is sodium 11 The method comprises the steps of carrying out a first treatment on the surface of the When the working medium is potassium, N is 4625.3, I is 0.7, M is 4.0168 multiplied by 10 11 。
In this embodiment, in step 4, the iteration accuracy ε is 10 -7 。
Claims (2)
1. A normalized vapor heat transfer calculation method of an alkali metal heat pipe is characterized in that: the method comprises the following steps:
step 1: determining the calculation parameters of the alkali metal heat pipe: determining the geometry of the alkali metal heat pipe and the materials of the pipe wall, the liquid suction core and the working medium; the evaporation section gives heat flow density, and the condensation section gives convective heat transfer coefficient; constructing grids, dividing an evaporation section, a heat insulation section and a condensation section of the heat pipe into a layer of grids of a, b and c respectively, dividing the pipe wall and a liquid suction core of the heat pipe into m layers of grids and n layers of grids respectively, and dividing a vapor area into 1 layer of grids; setting the initial temperature of each grid node and calculating the time step;
step 2: calculating the saturation pressure of the gas-liquid interface of the heat pipe: according to the temperature on the gas-liquid interface of the heat pipe, calculating the saturation pressure on the gas-liquid interface by adopting a fitting function relation shown in the formula (1):
in the formula (1):
P f -saturation pressure/Pa;
t-interfacial temperature/K;
p (T) -the fitted functional relationship of saturation pressure and temperature;
n-an augmentation factor;
i-index coefficient;
m, fitting coefficients;
step 3: constructing an analytical function taking the vapor temperature as an independent variable: assuming that the alkali metal vapor temperature is the same and the total evaporative condensing amount is conserved throughout the vapor zone, the energy conservation equation for vapor heat transfer is shown in equation (2):
in the formula (2):
i-gas-liquid interface node number;
-mass evaporation rate of gas-liquid interface node/(kg.s) -1 )；
h fg Latent heat of vaporization/(kJ.kg) -1 )；
Δl i -gas-liquid interface node boundary length/m;
calculating mass evaporation rate of gas-liquid interface node by adopting molecular dynamics equationAs shown in formula (3):
in the formula (3):
-evaporating the condensation regulation factor;
epsilon-wick porosity;
M atom molar mass of vapor in vapor zone/(kg. Mol) -1 )；
R u General gas constant/(R) u ＝8.314J·mol -1 ·K -1 )；
T li -node liquid working medium temperature/K on gas-liquid interface;
P li -node liquid working medium saturation pressure/Pa on gas-liquid interface; t (T) v -temperature of vapor in vapor zone/K;
P v -saturation pressure of vapor in vapor zone/Pa;
the calculation adopts equipartition grid, and the boundary length delta l of each gas-liquid interface node i Equal and consider the vaporization latent heat h of the same working medium fg The energy conservation equation after the simplified of the formula (3) of the combined formula (2) is shown as the formula (4):
due to the vapour saturation vapour pressure P v Only the vapor temperature T v Is a function of the node temperature T at the gas-liquid interface li It is known that the saturation pressure has been found in step 2, so equation (4) is written as relating to the vapor temperature T v As shown in the formula (5) -formula (7):
C 2 ＝a+c (7)
in the formulae (5) to (7):
C 1 -interface coefficients determined by boundary conditions;
C 2 -geometric coefficients determined by geometric partitioning;
substituting the fitting function relation P (T) in step 2 into equation (5) to obtain the vapor temperature T v The complete analytical function for the argument is shown in equation (8):
step 4: iteratively solving the normalized steam temperature: solving for the vapor temperature T v I.e. into a function f (T v ) Adopts an iteration method to solve, and constructs an iteration relation as shown in the formula (9):
in the formula (9):
T v n -the vapor temperature obtained by the n-th iteration;
T v n+1 -the vapor temperature obtained by iteration in step n+1;
f(T v n ) Substituting the vapor temperature obtained in the n-th iteration into a value obtained by a vapor temperature analytical function;
f'(T v n ) Substituting the vapor temperature obtained in the n-th iteration into a value obtained by a derivative function of the vapor temperature analytic function;
the average temperature of the node liquid working medium temperature on the gas-liquid interface is taken as the initial value needed by the iteration of the formula (9), and is shown as the formula (10):
in the formula (10):
T v 0 -an iterative initial value of vapor temperature;
T li -the temperature of the liquid working medium of the ith node on the gas-liquid interface;
the derivative f' required for the iteration of equation (9) is derived from equation (8), as shown in equation (11):
in the formula (11):
P(T v ) -steam temperature T v Substituting the vapor saturation pressure obtained by the fitting function relation P (T) of the saturation pressure and the temperature;
when iterating, presetting the iteration precision epsilon, and firstly, setting the initial value T required by the iteration v 0 Substituting (9) to calculate to obtain the vapor temperature T calculated in the 1 st step v 1 Judging whether or not |f (T) v 1 )|<Epsilon, if yes, stopping iteration to obtain normalized vapor temperature T v Is approximated by T v 1 The method comprises the steps of carrying out a first treatment on the surface of the If not, repeating the step, and calculating the vapor temperature T of the n-th iterative calculation v n Substituting (9) to calculate and obtain the vapor temperature T of the n+1 step iterative calculation v n+1 Until |f (T) v n+1 )|<Epsilon, stopping iteration to obtain normalized steam temperature T v Is approximated by T v n+1 ；
Step 5: calculating the temperature change rate of the heat pipe wall and the liquid absorption core areaEstablishing a two-dimensional heat conduction equation in the pipe wall area of the heat pipe, as shown in a formula (12):
in the formula (12):
ρ w density of tube wall material/(kg.m) -3 )；
c w Heat capacity/(J.kg) of pipe wall material -1 ·K -1 )；
T w -temperature of the tube wall/K;
t-time/s;
r-radial coordinate/m;
k w -thermal conductivity of the tube wall material/(w·m) -1 ·K -1 )
z-axial coordinate/m;
the boundary condition of the two-dimensional heat conduction equation (12) is shown as the following formula (13) -formula (15):
and (3) an evaporation section:
and (3) an insulation section:
condensing section:
hA c (T w -T sur )＝Q c (15)
in the formulas (13) - (15):
A e -heat pipe evaporation zone area/m 2 ；
A c Area/m of condensation section of heat pipe 2 ；
Q e -evaporation section heating power/W;
Q c -condensing section cooling power/W;
h-convection heat transfer coefficient of outer surface of condensing section/(W.m) -2 ·K -1 )；
T sur -ambient temperature/K;
neglecting the flow of the working fluid in the wick, a two-dimensional heat conduction equation is also established in the wick region of the heat pipe, as shown in equations (16) - (18):
(ρc) eff ＝ερ l c l +(1-ε)ρ ws c ws (17)
in the formula (16) -formula (18):
(ρc) eff equivalent volumetric heat capacity/(J.m) of the wick -3 ·K -1 )；
T ws -temperature of the wick/K;
k eff equivalent thermal conductivity of the wick/(W.m) -1 ·K -1 )
ρ l -density/(kg.m) of liquid working medium in wick -3 )；
c l -heat capacity/(J.kg) of liquid working medium in wick -1 ·K -1 )；
ρ ws Density of the wick material/(kg.m) -3 )；
c ws -heat capacity of the wick material/(j·kg) -1 ·K -1 )；
k l -thermal conductivity/(w·m) of the liquid working medium in the wick -1 ·K -1 )；
k ws -thermal conductivity of the wick material/(w·m) -1 ·K -1 )；
The boundary condition of equation (16) is shown in equation (20):
A i ＝2πrΔl i (20)
in the formula (19) -formula (20):
T i -temperature/K of gas-liquid interface node;
A i -heat exchange area/m of gas-liquid interface node and vapor zone 2 ；
Step 6: dispersing the two-dimensional heat conduction equation and the boundary condition in the step 5 to generate an unsteady heat conduction control equation set, solving the equation set by adopting a Gear algorithm, and calculating to obtain the temperature distribution of the heat pipe wall and the liquid absorption core at the current time t;
step 7: and (5) after the calculation is completed, outputting a calculation result.
2. The normalized vapor heat transfer calculation method of an alkali metal heat pipe of claim 1, wherein: the augmentation coefficient N, the index coefficient I and the fitting coefficient M in the step 2 are 5567.0 when the working medium is sodium, 0.5 is taken by I, and 2.29 multiplied by 10 is taken by M 11 The method comprises the steps of carrying out a first treatment on the surface of the When the working medium is potassium, N is 4625.3, I is 0.7, M is 4.0168 multiplied by 10 11 。
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Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2009080567A (en) * | 2007-09-25 | 2009-04-16 | Toshiba Corp | Electronic equipment, cooler, and heat pipe |
| CN110345787A (en) * | 2019-07-24 | 2019-10-18 | 西安交通大学 | A kind of design method for integrated high temp alkali metal heat pipe |
| CN112528435A (en) * | 2020-12-07 | 2021-03-19 | 西安交通大学 | High-temperature heat pipe design optimization method |
| CN112597640A (en) * | 2020-12-08 | 2021-04-02 | 清华大学 | Heat pipe simulation method and device and electronic equipment |
| CN114154438A (en) * | 2021-12-07 | 2022-03-08 | 西安交通大学 | Three-stage calculation method for cold start of alkali metal heat pipe |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2009080567A (en) * | 2007-09-25 | 2009-04-16 | Toshiba Corp | Electronic equipment, cooler, and heat pipe |
| CN110345787A (en) * | 2019-07-24 | 2019-10-18 | 西安交通大学 | A kind of design method for integrated high temp alkali metal heat pipe |
| CN112528435A (en) * | 2020-12-07 | 2021-03-19 | 西安交通大学 | High-temperature heat pipe design optimization method |
| CN112597640A (en) * | 2020-12-08 | 2021-04-02 | 清华大学 | Heat pipe simulation method and device and electronic equipment |
| CN114154438A (en) * | 2021-12-07 | 2022-03-08 | 西安交通大学 | Three-stage calculation method for cold start of alkali metal heat pipe |
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| 钾热管稳态数值模拟分析;柴宝华 等;原子能科学技术(05);全文 * |
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