CN112528435B - High-temperature heat pipe design optimization method - Google Patents
High-temperature heat pipe design optimization method Download PDFInfo
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Abstract
The invention discloses a design optimization method of a high-temperature heat pipe, which mainly comprises the following steps: 1. determining the working environment of the high-temperature heat pipe, including the working temperature range, the geometric size requirement and the mechanical property requirement; 2. selecting independent design variables of the high-temperature heat pipe; 3. determining an optimized target variable of the high-temperature heat pipe; 4. determining the design constraint conditions of the high-temperature heat pipe; 5. setting and calculating a multi-target optimization algorithm of the high-temperature heat pipe; 6. the steady-state and transient characteristics of the high-temperature heat pipe are calculated for the first generation design; 7. and after the calculation is finished, outputting a calculation result. The invention considers the steady-state heat and mass transfer characteristics of the high-temperature heat pipe and the transient response characteristics of freezing start, guides the performance improvement of the multi-target parameters of the heat pipe based on the design analysis result of the high-temperature heat pipe and the multi-target optimization algorithm, and provides guidance for the design and analysis of the high-temperature heat pipe.
Description
Technical Field
The invention relates to the technical field of phase change heat exchange equipment, in particular to a design optimization method for a high-temperature heat pipe.
Background
As a high-efficiency reliable passive heat transfer device, the high-temperature heat pipe is widely applied to the fields of aerospace, chemical engineering, nuclear reactors and the like due to the high-efficiency heat transfer capacity, excellent safety and simple structure. The structure of a typical heat pipe comprises a pipe shell, a liquid absorption core and a working medium. The inner wall of the heat pipe shell is attached with a liquid absorption core, and working medium is filled in the liquid absorption core. The working temperature of the heat pipe depends on the kind of working medium. Heat pipes are usually artificially divided into three sections: an evaporation section, an adiabatic section and a condensation section. The evaporation section absorbs heat from the heat source to evaporate the working medium, and steam in the condensation section is condensed to release heat. The main function of the heat insulation section is to connect the evaporation section and the condensation section. The starting and operating processes of the high-temperature heat pipe comprise various complex physical phenomena, including steam flow in a steam area, liquid flow in a liquid suction core, interaction of gas-liquid two-phase flow, heat conduction of a pipe wall and phase change of a working medium. Due to the mutual coupling of the heat transfer and mass transfer and flow characteristics of the vapor, the liquid absorption core and the pipe wall area in the heat pipe, the analysis and research of the heat pipe are difficult.
Disclosure of Invention
The invention discloses a high-temperature heat pipe design optimization method, which realizes multi-target design optimization of a high-temperature heat pipe, considers the steady-state heat and mass transfer characteristics of the high-temperature heat pipe and the transient response characteristics of freezing start, guides the performance improvement of multi-target parameters of the heat pipe based on the combination of the design analysis result of the high-temperature heat pipe and a multi-target optimization algorithm, and provides guidance for the development of the high-performance high-temperature heat pipe.
In order to realize the purpose, the invention adopts the following technical scheme to implement:
a design optimization method for a high-temperature heat pipe comprises the following steps:
step 1: determining the working environment of the high-temperature heat pipe, including the diameter D of the pipe wall wall Length L of heat pipe HP In the evaporation stage L e Heat insulation section L a A condensation section L c Required range of length of (1), mechanical strength σ operation Required, working temperature T operation Interval, maximum heat transfer power Q max Starting time τ start Requesting;
and 2, step: determining independent design variable X of the high-temperature heat pipe, including working medium WM of the heat pipe and pipe wall thickness delta wall WICK type WICK, WICK porosity ε, WICK thickness δ wick Diameter of vapor zone D v Length L of evaporation section e And length L of the condensation zone c ；
X＝(WM,WICK,δ wall ,δ wick ,D v ,ε,L e ,L c ,…) T (1)
And step 3: determining the optimized target variable F of the high-temperature heat pipe, including the mass M of the heat pipe HP Heat transfer power Q HP Angle of inclination theta of operation HP Equivalent thermal resistance R HP And a start-up time τ start ；
F＝(M HP ,Q HP ,θ HP ,R HP ,τ start …) T (2)
And 4, step 4: determining a high-temperature heat pipe constraint condition G, including material compatibility constraint, heat transfer limit, geometric limitation and design requirement; the material compatibility constraints are: the pipe wall material WALLM and the liquid absorption core material WICKM are compatible with the heat pipe working medium WM; the heat transfer limit constraints are: boiling limit Q boi Entrainment limit Q ent Viscosity limit Q vis Harmonic speed limit Q son Require more power than the heat pipe delivers; the geometric constraint is: the length L and the diameter D are not negative, and the void ratio is in a preset range; the design requirements are as follows: the design parameters meet the working environment in the step 1;
WALLM∈g(WM) (3)
WICKM∈g(WM) (4)
Q boi -Q HP ＞0 (5)
Q ent -Q HP ＞0 (6)
Q vis -Q HP ＞0 (7)
Q son -Q HP ＞0 (8)
L＞0 (9)
D＞0 (10)
0＜ε＜1 (11)
and 5: selecting a multi-objective optimization algorithm, inputting a high-temperature heat pipe independent design variable X, a high-temperature heat pipe optimization target variable F and a high-temperature heat pipe constraint condition G into the multi-objective optimization algorithm, and setting iteration times and population number; initializing the population into the number of individuals for generating the initial population by dividing each variable of the high-temperature heat pipe independent design variable X into a plurality of groups within a preset range and performing cross combination; the high-temperature heat pipe optimization target variable F is obtained through calculation of the steady-state and transient characteristics of the high-temperature heat pipe in the step 6; continuously evaluating the adaptability of the population individuals through a multi-objective optimization algorithm, and calculating the result of the set iteration times;
step 6: calculating steady-state and transient characteristics of the high-temperature heat pipe: the high-temperature heat pipe independent design variable X generated by the multi-objective optimization algorithm is used as a high-temperature heat pipe design parameter to calculate the heat pipe from a freezing state to a steady state, and the method specifically comprises the following steps:
establishing an unsteady heat conduction model of the pipe wall, an unsteady heat transfer model of the liquid absorption core and a working medium melting model of the liquid absorption core;
the unsteady heat conduction model of the tube wall is shown as formula (12), which adopts a two-dimensional unsteady heat conduction equation to solve the temperature of the tube wall, and considers the change of the heat conductivity of the tube wall caused by the temperature:
in the formula:
ρ wall the density of the tube wall material/(kg. M) -3 )；
Cp wall Thermal capacity/(J.kg) of pipe wall material -1 ·K -1 )；
T wall -temperature of the tube wall/K;
τ -time/s;
r-radial coordinate/m;
k wall -thermal conductivity of the material of the tube wall/(W.m) -1 ·K -1 )
z-axial coordinate/m;
unsteady state heat transfer model of wick: the heat transfer process of the liquid absorbing core ignores the flowing of the liquid working medium in the liquid absorbing core, the heat transfer process of the liquid absorbing core area is simplified into a pure heat conduction model with an assumed heat transfer coefficient, the temperature of the liquid absorbing core is solved by adopting a two-dimensional unsteady heat conduction equation, and the temperature-induced changes of the physical properties of the liquid absorbing core material and the working medium are considered as formulas (13) - (15):
(ρCp) eff ＝ερ l Cp l +(1-ε)ρ wick,s Cp wick,s (14)
in formulae (13) to (15):
(ρCp) eff -equivalent heat capacity of wick/(J.K) -1 )；
T wick -temperature of wick/K;
τ -time/s;
r-radial coordinate/m;
k eff -equivalent thermal conductivity of the wick/(W.m) -1 ·K -1 )
z-axial coordinate/m;
ε -porosity of the wick;
ρ l density/(kg. M) of liquid working medium in wick -3 )；
Cp l -heat capacity/(J.kg) of liquid working medium in wick -1 ·K -1 )；
ρ wick,s Density of solid material in wick/(kg. M) -3 )；
Cp wick,s Thermal capacity/(J.kg) of solid material in wick -1 ·K -1 )；
k l -thermal conductivity/(W.m) of liquid working medium in wick -1 ·K -1 )；
k wick,s -thermal conductivity of the solid material of the wick/(W.m) -1 ·K -1 )；
Working medium melting model of liquid absorption core: assuming that the working medium is melted independently of the wick structure, an equivalent apparent heat capacity method based on temperature is adopted for description, and the formula is as follows (16) to (20):
in formulae (16) to (20):
(ρCp) eff -equivalent heat capacity of wick/(J.K) -1 )；
ε -porosity of the wick;
ρ s density of solid working medium in wick/(kg m) -3 )；
Cp s -heat capacity/(J.kg) of solid working medium in wick -1 ·K -1 )；
ρ wick,s Density of solid material in wick/(kg. M) -3 )；
Cp wick,s Thermal capacity/(J.kg) of solid material in wick -1 ·K -1 )；
T mel -melting point/K of working medium in wick;
delta T is one half/K of the phase change temperature range of the working medium in the liquid suction core;
ρ l density/(kg. M) of liquid working medium in wick -3 )；
Cp l -heat capacity/(J.kg) of liquid working medium in wick -1 ·K -1 )；
h fg -latent heat of fusion/(J.kg) of liquid working medium in wick -1 )；
Cp m -mixing ratio heat capacity/(J.kg) of liquid working medium in wick -1 ·K -1 )；
k eff -equivalent thermal conductivity of the wick/(W.m) -1 ·K -1 )
k le -equivalent thermal conductivity/(W.m) of pure liquid working medium of liquid absorption core -1 ·K -1 )
k se -equivalent thermal conductivity/(W.m) of pure solid working medium of wick -1 ·K -1 )
T wick -temperature of wick/K;
k l -thermal conductivity/(W.m) of liquid working medium in wick -1 ·K -1 )；
k s -thermal conductivity/(W.m) of solid working substance in wick -1 ·K -1 )；
k wick,s -thermal conductivity/(W.m) of the solid material of the wick -1 ·K -1 )；
Judging the steam state of a steam area of the high-temperature heat pipe by adopting a Knudsen number as shown in formulas (21) and (22), and if the Knudsen number is more than 0.01, and the steam temperature is lower than the transition temperature, considering that the steam is thin; if the Knudsen number is less than 0.01, the vapor temperature is above the transition temperature, and the vapor is continuous; respectively constructing a lean steam heat transfer model and a continuous steam flow heat transfer model, wherein the specific models are as follows:
in formulae (21) to (22):
Kn-Knudsen number;
λ — mean free path of vapor molecules in the vapor zone/(m);
d-diameter of the vapor zone/(m);
k B boltzmann (Boltzmann) constant/(k) B ＝1.380649×10 -23 J·K -1 )；
T vapor Temperature of vapor in vapor zone/(K);
P vapor -the saturation pressure of the vapour in the vapour zone/(Pa);
d-the molecular diameter of the vapor in the vapor zone/(m);
the lean vapor heat transfer model is: the mean molecular free path of the rarefied vapor molecules is much greater than the characteristic length of the vapor zone; the heat transfer of the thin steam is mainly carried out through the collision of steam molecules and pipe walls, the heat transfer efficiency is extremely low at the moment, and the temperature of the thin steam is considered to be the same as the temperature of a gas-liquid phase interface, as shown in a formula (23);
T vapor ＝T l-v (23)
in formula (23):
T vapor temperature of vapor in vapor zone/(K);
T l-v temperature of the gas-liquid interface/(K);
flow heat transfer model of continuous vapor: assuming that steam is saturated steam laminar flow, adopting a one-dimensional steady-state compressible flow model, simplifying the radial velocity into an average velocity, considering momentum and energy correction, and considering the friction of the steam; in order to consider the evaporation and condensation of the working medium, the simulation is carried out by adopting the theory of molecular dynamics, and the molecular dynamics are shown as formulas (24) to (30):
in formulae (24) to (30):
ρ vapor saturated density of vapor in vapor zone/(kg. M) -3 )；
V vapor The velocity of the vapor in the vapor zone/(m.s) -1 )；
A vapor The cross-sectional area of the vapor zone/(m) 2 )；
Alpha is the momentum correction factor of the vapor in the vapor zone;
P vapor -the saturation pressure of the vapour in the vapour zone/(Pa);
f-friction factor of vapor in vapor zone;
S vapor -side area of vapor zone/(m) 2 )；
h vapor Specific enthalpy of vapor saturation in vapor zone/(J.kg) -1 )；
Beta-energy correction factor for vapor in the vapor zone;
V l-v -gas and liquidRadial velocity/(m.s) of phase boundary vapor -1 )；
Re-axial Reynolds number of the vapor in the vapor zone;
phi is the evaporation condensation regulation coefficient;
M atom the molar mass of the vapors in the vapor zone/(kg. Mol) -1 )；
R u -universal gas constant/(R) u ＝8.314J·mol -1 ·K -1 )；
T l The temperature/(K) of the liquid working medium in the liquid suction core;
P l -saturation pressure/(Pa) of liquid working medium in wick;
dispersing the control equation, respectively solving the unsteady heat transfer equations of the pipe wall and the liquid absorption core by adopting a Gear algorithm, if the temperature of the liquid absorption core is lower than the melting point of the working medium, simulating the melting process of the working medium by adopting an equivalent apparent heat capacity method, and calculating to obtain the temperature distribution of the pipe wall and the liquid absorption core of the heat pipe at the current time t; for the flowing heat transfer model of the continuous steam, solving by adopting a fourth-order Runge-Kutta algorithm to obtain a speed field, a temperature field and a pressure field of the steam in the high-temperature heat pipe;
and 7: and after the calculation is finished, outputting a calculation result.
Compared with the prior art, the invention has the following advantages:
the invention utilizes the multi-objective optimization algorithm to carry out design optimization on the high-temperature heat pipe, and can comprehensively consider the performance parameters of the heat pipe, such as the quality, the heat transfer efficiency, the starting time and the like. The invention takes the heat pipe performance indexes of the conditions of the steady state, the freezing start transient state and the like of the heat pipe as optimization targets, and can directly guide the design optimization of the actual heat pipe. The invention is suitable for various working mediums and has wide applicability.
Detailed Description
The invention will now be further described with reference to the examples:
a design optimization method for a high-temperature heat pipe comprises the following steps:
step 1: determining the working environment of the high-temperature heat pipe, including the diameter D of the pipe wall wall Long heat pipeDegree L HP In the evaporation stage L e Heat insulation section L a A condensation section L c Required range of length of (1), mechanical strength σ operation Required, working temperature T operation Interval, maximum heat transfer power Q max Starting time τ start Requesting;
and 2, step: determining independent design variable X of the high-temperature heat pipe, including working medium WM of the heat pipe and pipe wall thickness delta wall WICK type WICK, WICK porosity ε, WICK thickness δ wick Diameter of vapor zone D v Length L of evaporation section e And length L of the condensation section c ；
X＝(WM,WICK,δ wall ,δ wick ,D v ,ε,L e ,L c ,...) T (1)
And 3, step 3: determining the optimized target variable F of the high-temperature heat pipe, including the mass M of the heat pipe HP Heat transfer power Q HP Angle of inclination of operation theta HP Equivalent thermal resistance R HP And a start-up time τ start ；
F＝(M HP ,Q HP ,θ HP ,R HP ,τ start ...) T (2)
And 4, step 4: determining a high-temperature heat pipe constraint condition G, including material compatibility constraint, heat transfer limit, geometric limitation and design requirement; the material compatibility constraints are: the pipe wall material WALLM and the liquid absorption core material WICKM are compatible with the heat pipe working medium WM; the heat transfer limit constraints are: boiling limit Q boi Entrainment limit Q ent Viscosity limit Q vis Harmonic speed limit Q son Require more power than the heat pipe delivers; the geometric constraint is: the length L and the diameter D are not negative, and the void ratio is in a preset range; the design requirements are as follows: the design parameters meet the working environment in the step 1;
WALLM∈g(WM) (3)
WICKM∈g(WM) (4)
Q boi -Q HP ＞0 (5)
Q ent -Q HP ＞0 (6)
Q vis -Q HP ＞0 (7)
Q son -Q HP ＞0 (8)
L＞0 (9)
D＞0 (10)
0＜ε＜1 (11)
and 5: selecting a multi-objective optimization algorithm comprising NSGAII, CMOEA-MS, GEO, MOGS and other algorithms, inputting a high-temperature heat pipe independent design variable X, a high-temperature heat pipe optimization target variable F and a high-temperature heat pipe constraint condition G into the multi-objective optimization algorithm, and setting iteration times and population number; initializing the population into the number of individuals of an initial population, wherein each variable of the high-temperature heat pipe independent design variable X is divided into a plurality of groups within a preset range and is subjected to cross combination; the high-temperature heat pipe optimization target variable F is obtained through calculation of the steady-state and transient characteristics of the high-temperature heat pipe in the step 6; continuously evaluating the adaptability of the population individuals through a multi-objective optimization algorithm, and calculating the result of the set iteration times;
step 6: calculating steady-state and transient characteristics of the high-temperature heat pipe: the high-temperature heat pipe independent design variable X generated by the multi-objective optimization algorithm is used as a high-temperature heat pipe design parameter to calculate the heat pipe from a freezing state to a steady state, and the method specifically comprises the following steps:
establishing an unsteady heat conduction model of the pipe wall, an unsteady heat transfer model of the liquid absorption core and a working medium melting model of the liquid absorption core;
the unsteady heat conduction model of the pipe wall is shown as formula (12), which adopts a two-dimensional unsteady heat conduction equation to solve the temperature of the pipe wall, and considers the change of the heat conductivity of the pipe wall caused by the temperature:
in the formula:
ρ wall density of the pipe wall material/(kg. M) -3 )；
Cp wall Thermal capacity/(J.kg) of pipe wall material -1 ·K -1 )；
T wall -temperature of the tube wall/K;
τ -time/s;
r-radial coordinate/m;
k wall -thermal conductivity of the material of the tube wall/(W.m) -1 ·K -1 )
z-axial coordinate/m;
unsteady state heat transfer model of wick: the heat transfer process of the liquid absorbing core ignores the flowing of the liquid working medium in the liquid absorbing core, the heat transfer process of the liquid absorbing core area is simplified into a pure heat conduction model with an assumed heat transfer coefficient, the temperature of the liquid absorbing core is solved by adopting a two-dimensional unsteady heat conduction equation, and the temperature-induced changes of the physical properties of the liquid absorbing core material and the working medium are considered as formulas (13) - (15):
(ρCp) eff ＝ερ l Cp l +(1-ε)ρ wick,s Cp wick,s (14)
in formulae (13) to (15):
(ρCp) eff -equivalent heat capacity of wick/(J. K) -1 )；
T wick -temperature of wick/K;
τ -time/s;
r-radial coordinate/m;
k eff -equivalent thermal conductivity of the wick/(W.m) -1 ·K -1 )
z-axial coordinate/m;
ε -porosity of the wick;
ρ l liquid in wickDensity of working medium/(kg. M) -3 )；
Cp l -heat capacity/(J.kg) of liquid working medium in wick -1 ·K -1 )；
ρ wick,s Density of solid material in wick/(kg m) -3 )；
Cp wick,s Thermal capacity/(J.kg) of solid material in wick -1 ·K -1 )；
k l -thermal conductivity/(W.m) of liquid working medium in wick -1 ·K -1 )；
k wick,s -thermal conductivity/(W.m) of the solid material of the wick -1 ·K -1 )；
Working medium melting model of liquid absorption core: assuming that the working medium is melted independently of the wick structure, an equivalent apparent heat capacity method based on temperature is adopted for description, and the formula is as follows (16) to (20):
in formulae (16) to (20):
(ρCp) eff -equivalent heat capacity of wick/(J. K) -1 )；
ε -porosity of the wick;
ρ s density of solid working medium in wick/(kg m) -3 )；
Cp s -heat capacity/(J.kg) of solid working medium in wick -1 ·K -1 )；
ρ wick,s Density of solid material in wick/(kg m) -3 )；
Cp wick,s Thermal capacity/(J.kg) of solid material in wick -1 ·K -1 )；
T mel -melting point/K of working medium in wick;
delta T is one half/K of the phase change temperature range of the working medium in the liquid suction core;
ρ l density of liquid working medium in wick/(kg. M) -3 )；
Cp l -heat capacity/(J.kg) of liquid working medium in wick -1 ·K -1 )；
h fg -latent heat of fusion/(J.kg) of liquid working medium in wick -1 )；
Cp m -mixing ratio heat capacity/(J.kg) of liquid working medium in liquid suction core -1 ·K -1 )；
k eff -equivalent thermal conductivity of the wick/(W.m) -1 ·K -1 )
k le -equivalent thermal conductivity/(W.m) of pure liquid working medium of liquid absorption core -1 ·K -1 )
k se -equivalent thermal conductivity/(W.m) of pure solid working medium of wick -1 ·K -1 )
T wick -temperature of wick/K;
k l -thermal conductivity/(W.m) of liquid working medium in wick -1 ·K -1 )；
k s -thermal conductivity/(W.m) of solid working medium in wick -1 ·K -1 )；
k wick,s -thermal conductivity/(W.m) of the solid material of the wick -1 ·K -1 )；
Judging the steam state of a steam area of the high-temperature heat pipe by adopting a Knudsen number as shown in formulas (21) and (22), and if the Knudsen number is more than 0.01 and the steam temperature is lower than the transition temperature, considering that the steam is thin; if the Knudsen number is less than 0.01, the vapor temperature is above the transition temperature, and the vapor is continuous; respectively constructing a lean steam heat transfer model and a continuous steam flow heat transfer model, wherein the specific models are as follows:
in formulae (21) to (22):
Kn-Knudsen number;
λ — the mean free path of vapor molecules in the vapor zone/(m);
d-diameter of the vapor zone/(m);
k B boltzmann (Boltzmann) constant/(k) B ＝1.380649×10 -23 J·K -1 )；
T vapor Temperature of vapor in vapor zone/(K);
P vapor -the saturation pressure of the vapour in the vapour zone/(Pa);
d-the molecular diameter of the vapor in the vapor zone/(m);
the lean vapor heat transfer model is: the mean molecular free path of the rarefied vapor molecules is much greater than the characteristic length of the vapor zone; the heat transfer of the thin steam is mainly carried out through the collision of steam molecules and pipe walls, the heat transfer efficiency is extremely low at the moment, and the temperature of the thin steam is considered to be the same as the temperature of a gas-liquid phase interface, as shown in a formula (23);
T vapor ＝T l-v (23)
in formula (23):
T vapor temperature of vapor in vapor zone/(K);
T l-v temperature of the gas-liquid interface/(K);
flow heat transfer model of continuous vapor: assuming that steam is saturated steam laminar flow, adopting a one-dimensional steady-state compressible flow model, simplifying the radial velocity into an average velocity, considering momentum and energy correction, and considering the friction of the steam; in order to consider the evaporation and condensation of the working medium, the simulation is carried out by adopting the theory of molecular dynamics, and the molecular dynamics are expressed as formulas (24) to (30):
in formulae (24) to (30):
ρ vapor the saturation density/(kg. M) of the vapor in the vapor zone -3 )；
V vapor The velocity/(m.s) of the vapor in the vapor zone -1 )；
A vapor The cross-sectional area of the vapor zone/(m) 2 )；
Alpha is the momentum correction factor of the vapor in the vapor zone;
P vapor -the saturation pressure of the vapour in the vapour zone/(Pa);
f-friction factor of vapor in vapor zone;
S vapor -side area of vapor zone/(m) 2 )；
h vapor -specific enthalpy of vapor saturation in the vapor zone/(J kg) -1 )；
Beta-energy correction factor for vapor in the vapor zone;
V l-v radial velocity/(m.s) of vapor at gas-liquid interface -1 )；
Re-axial Reynolds number of vapor in the vapor zone;
phi is the evaporation condensation regulation coefficient;
M atom -molar mass of vapor in vapor zone/(kg. Mol) -1 )；
R u -universal gas constant/(R) u ＝8.314J·mol -1 ·K -1 )；
T l The temperature/(K) of the liquid working medium in the liquid suction core;
P l -saturation pressure/(Pa) of liquid working medium in wick;
dispersing the control equation, respectively solving the unsteady heat transfer equations of the pipe wall and the liquid absorption core by adopting a Gear algorithm, if the temperature of the liquid absorption core is lower than the melting point of the working medium, simulating the melting process of the working medium by adopting an equivalent apparent heat capacity method, and calculating to obtain the temperature distribution of the pipe wall and the liquid absorption core of the heat pipe at the current time t; for the flowing heat transfer model of the continuous steam, solving by adopting a fourth-order Runge-Kutta algorithm to obtain a speed field, a temperature field and a pressure field of the steam in the high-temperature heat pipe;
and 7: and after the calculation is finished, outputting a calculation result.
The invention is not described in detail in the content of the common general knowledge in the field.
Claims (1)
1. A high-temperature heat pipe design optimization method is characterized by comprising the following steps: the method comprises the following steps:
step 1: determining the working environment of the high-temperature heat pipe, including the diameter D of the pipe wall wall Length L of heat pipe HP In the evaporation stage L e Heat insulating section L a A condensation section L c Length required range of (2), mechanical strength σ operation Required, working temperature T operation Interval, maximum heat transfer power Q max Starting time τ start Requiring;
step 2: determining independent design variables X of the high-temperature heat pipe, including working medium WM of the heat pipe and pipe wall thickness delta wall WICK type WICK, WICK porosity ε, WICK thickness δ wick Diameter of vapor zone D v Length L of evaporation zone e And length L of the condensation section c ；
X＝(WM,WICK,δ wall ,δ wick ,D v ,ε,L e ,L c ,...) T (1)
And 3, step 3: determining the optimized target variable F of the high-temperature heat pipe, including the mass M of the heat pipe HP Heat transfer power Q HP Angle of inclination theta of operation HP Equivalent thermal resistance R HP And a start-up time tau start ；
F＝(M HP ,Q HP ,θ HP ,R HP ,τ start ...) T (2)
And 4, step 4: determining a high-temperature heat pipe constraint condition G, including material compatibility constraint, heat transfer limit, geometric limitation and design requirement; the material compatibility constraints are: the pipe wall material WALLM and the liquid absorption core material WICKM are compatible with the heat pipe working medium WM; the heat transfer limit constraints are: boiling limit Q boi Entrainment limit Q ent Viscosity limit Q vis Harmonic speed limit Q son Require more heat transfer than a heat pipe(ii) the power delivered; the geometric constraints are: the length L and the diameter D are not negative, and the void ratio is in a preset range; the design requirements are as follows: the design parameters meet the working environment in the step 1;
WALLM∈g(WM) (3)
WICKM∈g(WM) (4)
Q boi -Q HP ＞0 (5)
Q ent -Q HP ＞0 (6)
Q vis -Q HP ＞0 (7)
Q son -Q HP ＞0 (8)
L＞0 (9)
D＞0 (10)
0＜ε＜1 (11)
and 5: selecting a multi-objective optimization algorithm, inputting a high-temperature heat pipe independent design variable X, a high-temperature heat pipe optimization target variable F and a high-temperature heat pipe constraint condition G into the multi-objective optimization algorithm, and setting iteration times and population number; initializing the population into the number of individuals of an initial population, wherein each variable of the high-temperature heat pipe independent design variable X is divided into a plurality of groups within a preset range and is subjected to cross combination; the high-temperature heat pipe optimization target variable F is obtained through calculation of the steady-state and transient characteristics of the high-temperature heat pipe in the step 6; continuously evaluating the adaptability of the population individuals through a multi-objective optimization algorithm, and calculating the result of the set iteration times;
and 6: calculating steady-state and transient characteristics of the high-temperature heat pipe: the high-temperature heat pipe independent design variable X generated by the multi-objective optimization algorithm is used as a high-temperature heat pipe design parameter to calculate the heat pipe from a freezing state to a steady state, and the method specifically comprises the following steps:
establishing an unsteady heat conduction model of the pipe wall, an unsteady heat transfer model of the liquid absorption core and a working medium melting model of the liquid absorption core;
the unsteady heat conduction model of the tube wall is shown as formula (12), which adopts a two-dimensional unsteady heat conduction equation to solve the temperature of the tube wall, and considers the change of the heat conductivity of the tube wall caused by the temperature:
in the formula:
ρ wall the density of the tube wall material/(kg. M) -3 )；
Cp wall Thermal capacity/(J.kg) of pipe wall material -1 ·K -1 )；
T wall -temperature of the tube wall/K;
τ -time/s;
r-radial coordinate/m;
k wall -thermal conductivity of the material of the tube wall/(W.m) -1 ·K -1 )
z-axial coordinate/m;
unsteady state heat transfer model of wick: the flowing of a liquid working medium in the liquid absorption core is neglected in the heat transfer process of the liquid absorption core, the heat transfer process of the liquid absorption core area is simplified into a pure heat conduction model assuming a heat transfer coefficient, the temperature of the liquid absorption core is solved by adopting a two-dimensional unsteady heat conduction equation, and the changes of the physical properties of the liquid absorption core material and the working medium caused by the temperature are considered as formulas (13) - (15):
(ρCp) eff ＝ερ l Cp l +(1-ε)ρ wick,s Cp wick,s (14)
in formulae (13) to (15):
(ρCp) eff -equivalent heat capacity of wick/(J.K) -1 )；
T wick -temperature of wick/K;
τ -time/s;
r-radial coordinate/m;
k eff of wicks or the likeEffective thermal conductivity/(W.m) -1 ·K -1 )
z-axial coordinate/m;
ε -porosity of the wick;
ρ l density/(kg. M) of liquid working medium in wick -3 )；
Cp l -heat capacity/(J.kg) of liquid working medium in wick -1 ·K -1 )；
ρ wick,s Density of solid material in wick/(kg m) -3 )；
Cp wick,s Thermal capacity/(J.kg) of solid material in wick -1 ·K -1 )；
k l -thermal conductivity/(W.m) of liquid working medium in wick -1 ·K -1 )；
k wick,s -thermal conductivity/(W.m) of the solid material of the wick -1 ·K -1 )；
Working medium melting model of liquid absorption core: assuming that the working medium is melted independently of the wick structure, an equivalent apparent heat capacity method based on temperature is adopted for description, and the formula is as follows (16) to (20):
in formulae (16) to (20):
(ρCp) eff -equivalent heat capacity of wick/(J. K) -1 )；
ε -porosity of the wick;
ρ s density of solid working medium in wick/(kg m) -3 )；
Cp s -heat capacity/(J.kg) of solid working medium in wick -1 ·K -1 )；
ρ wick,s Density of solid material in wick/(kg m) -3 )；
Cp wick,s Thermal capacity/(J.kg) of solid material in wick -1 ·K -1 )；
T mel -melting point/K of working medium in wick;
delta T is one half/K of the phase change temperature range of the working medium in the liquid suction core;
ρ l density of liquid working medium in wick/(kg. M) -3 )；
Cp l -heat capacity/(J.kg) of liquid working medium in wick -1 ·K -1 )；
h fg -latent heat of fusion/(J.kg) of liquid working medium in wick -1 )；
Cp m -mixing ratio heat capacity/(J.kg) of liquid working medium in wick -1 ·K -1 )；
k eff -equivalent thermal conductivity of the wick/(W.m) -1 ·K -1 )
k le -equivalent thermal conductivity/(W.m) of pure liquid working medium of liquid absorption core -1 ·K -1 )
k se -equivalent thermal conductivity/(W.m) of pure solid working medium of wick -1 ·K -1 )
T wick -temperature of wick/K;
k l -thermal conductivity/(W.m) of liquid working medium in wick -1 ·K -1 )；
k s -thermal conductivity/(W.m) of solid working medium in wick -1 ·K -1 )；
k wick,s -thermal conductivity/(W.m) of the solid material of the wick -1 ·K -1 )；
Judging the steam state of a steam area of the high-temperature heat pipe by adopting a Knudsen number as shown in formulas (21) and (22), and if the Knudsen number is more than 0.01, and the steam temperature is lower than the transition temperature, considering that the steam is thin; if the Knudsen number is less than 0.01, the vapor temperature is above the transition temperature, and the vapor is continuous; respectively constructing a lean steam heat transfer model and a continuous steam flow heat transfer model, wherein the specific models are as follows:
in formulae (21) to (22):
Kn-Knudsen number;
λ — the mean free path of vapor molecules in the vapor zone/(m);
d-diameter of the vapor zone/(m);
k B boltzmann constant/(k) B ＝1.380649×10 -23 J·K -1 )；
T vapor Temperature of vapor in vapor zone/(K);
P vapor -the saturation pressure of the vapour in the vapour zone/(Pa);
d-the molecular diameter of the vapor in the vapor zone/(m);
the lean vapor heat transfer model is: the mean molecular free path of the rarefied vapor molecules is much longer than the characteristic length of the vapor zone; the heat transfer of the thin steam is mainly carried out through the collision of steam molecules and the pipe wall, the heat transfer efficiency is extremely low at the moment, and the temperature of the thin steam is considered to be the same as that of a gas-liquid phase interface, as shown in a formula (23);
T vapor ＝T l-v (23)
in formula (23):
T vapor temperature of vapor in vapor zone/(K);
T l-v temperature of the gas-liquid interface/(K);
flow heat transfer model of continuous vapor: assuming that steam is saturated steam laminar flow, adopting a one-dimensional steady-state compressible flow model, simplifying the radial velocity into an average velocity, considering momentum and energy correction, and considering the friction of the steam; in order to consider the evaporation and condensation of the working medium, the simulation is carried out by adopting the theory of molecular dynamics, and the molecular dynamics are expressed as formulas (24) to (30):
in formulae (24) to (30):
ρ vapor saturated density of vapor in vapor zone/(kg. M) -3 )；
V vapor The velocity of the vapor in the vapor zone/(m.s) -1 )；
A vapor The cross-sectional area of the vapor zone/(m) 2 )；
Alpha is the momentum correction factor of the vapor in the vapor zone;
P vapor -the saturation pressure of the vapour in the vapour zone/(Pa);
f-friction factor of vapor in vapor zone;
S vapor -side area of vapor zone/(m) 2 )；
h vapor -specific enthalpy of vapor saturation in the vapor zone/(J kg) -1 )；
Beta-energy correction factor for vapor in the vapor zone;
V l-v radial velocity/(m.s) of vapor at gas-liquid interface -1 )；
Re-axial Reynolds number of vapor in the vapor zone;
phi is the evaporation condensation regulation coefficient;
M atom -molar mass of vapor in vapor zone/(kg. Mol) -1 )；
R u -universal gas constant/(R) u ＝8.314J·mol -1 ·K -1 )；
T l -temperature/(K) of liquid working substance in wick;
P l the saturation pressure/(Pa) of the liquid working medium in the liquid suction core;
dispersing the control equation, respectively solving the unsteady heat transfer equations of the pipe wall and the liquid absorption core by adopting a Gear algorithm, if the temperature of the liquid absorption core is lower than the melting point of the working medium, simulating the melting process of the working medium by adopting an equivalent apparent heat capacity method, and calculating to obtain the temperature distribution of the pipe wall and the liquid absorption core of the heat pipe at the current time t; for a flowing heat transfer model of continuous steam, solving by adopting a fourth-order Runge-Kutta algorithm to obtain a velocity field, a temperature field and a pressure field of the steam in the high-temperature heat pipe;
and 7: and after the calculation is finished, outputting a calculation result.
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