JP2008008573A - Designing method for loop heat pipe - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a method for designing size of each component of a loop heat pipe from predetermined operation conditions and predetermined design parameters. <P>SOLUTION: In the designing method for the loop heat pipe, on the basis of the predetermined operation conditions and the predetermined design parameters, a steam pipe diameter, a liquid pipe diameter, bayonet pipe diameter, a wick inner diameter, a wick outer diameter, a wick thickness, and a cross-section area ratio between a steam channel and a liquid channel are calculated, an evaporator length is calculated, a loop pressure loss of adding all pressure losses caused by a steam passage, a liquid passage, a condenser, an evaporator, ports, and fittings of the loop heat pipe is calculated, a capillary tube radius and velocity of a wick are calculated, a condenser pipe diameter, a condenser length, reservoir volume, a reservoir diameter, and a reservoir length are calculated, and an area of a radiator, an interval of a feeder, and a thickness of fins are calculated. <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

  The present invention relates to a method for designing components of a loop heat pipe, and more particularly to a method for calculating dimensions of components of a loop heat pipe based on predetermined operating conditions and predetermined design parameters.

  Conventionally, the design of the loop heat pipe has been performed separately for each component. For example, regarding an evaporator, Patent Document 1 proposes an evaporator that is designed to improve heat exchange efficiency when a wick absorbs a refrigerant and transfers it to the outside. However, this does not provide a way to specify the evaporator sizing and wick formation structure. In addition, as a design of the entire loop heat pipe, there has been no sizing of an evaporator, a condenser, a steam pipe / liquid pipe, a reservoir, etc. with a consistent design concept. For this reason, in the current loop heat pipe, the thermal performance mismatch occurs between the elements, so that the original performance is not obtained. Moreover, since the correlation formula of the evaporator, the capillary radius of the wick and the porosity is unknown, the wick production specification that matches the operating conditions cannot be presented. Further, since analytical formulas that can be commonly used for sizing the above-described components are not yet developed, the actual situation is that the inner diameter and thickness of the wick, the capacitor length, and the like are determined from the similar prototype results. Thus, a rational design method for loop heat pipe has not been developed.

JP 2005-106313 A

  The present invention has been made on the basis of the technical background as described above, and an object thereof is to size an evaporator in a loop heat pipe and to specify a formation structure of a wick. In addition, in order to design the loop heat pipe as a system that conforms to the operating conditions for the entire loop heat pipe configuration, a top-down design calculation algorithm that uses the operating conditions as a calculation input and the design analysis that constitutes it Is to provide an expression.

In order to solve the above problems, according to the present invention characterized by theoretical analysis,
An evaporator having a tubular wick disposed therein, a reservoir located inside the wick, a serpentine condenser subcooler that dissipates and condenses refrigerant vapor, a radiator that disposes the condenser subcooler, and steam from the evaporator A steam pipe for sending the refrigerant liquid to the condenser subcooler, a liquid pipe for transferring the refrigerant liquid condensed and radiated by the condenser subcooler to the reservoir, and extending from the liquid pipe into the reservoir In a loop heat pipe composed of a bayonet tube having an opening, a method for calculating the ratio between the outer diameter and inner diameter of the evaporator wick,
The evaporator shows the ratio of the evaporator axial temperature difference, which is the difference between the evaporator liquid tube side temperature and the steam pipe side temperature, to the evaporator radial temperature difference, which is the difference between the bayonet tube temperature and the wick outer diameter temperature. Calculating the number of transmission units as the negative of the natural logarithm of the value obtained by subtracting the temperature efficiency of 1 from
The radial conductance of the evaporator is obtained from the temperature gradient at the wick inner diameter of the radial temperature distribution obtained as a solution of the energy equation for heat conduction and liquid permeation of the wick, and the number of evaporator transmission units and the wick Relational expression of ratio of outer diameter to inner diameter,
Calculating the ratio of the outer diameter and the inner diameter of the wick from the relational expression that the power of the radial distance of the wick appearing in the solution of the energy equation is the reciprocal of the number of transmission units when the evaporator is regarded as a heat exchanger. A method characterized by comprising:

According to another feature of the present invention,
An evaporator having a tubular wick disposed therein, a reservoir located inside the wick, a serpentine condenser subcooler that dissipates and condenses refrigerant vapor, a radiator that places the condenser subcooler therein, and a vapor from the evaporator A steam pipe for sending the refrigerant liquid to the condenser subcooler, a liquid pipe for releasing the refrigerant liquid condensed by the condenser subcooler, and a supercooled refrigerant liquid to the reservoir, and extending from the liquid pipe into the reservoir In a loop heat pipe composed of a bayonet tube having an opening, a method for calculating a porosity indicating the porosity of an evaporator wick,
Capillary radius of wick, wick capillary head, ratio of wick pressure loss to capillary pressure head, liquid constant pressure specific heat, liquid viscosity coefficient indicating the ratio between viscosity coefficient and density of saturated liquid, evaporator liquid side temperature and steam Evaporator temperature efficiency indicating the ratio of the evaporator axial temperature difference, which is the difference from the pipe side temperature, to the evaporator radial temperature difference, which is the difference between the temperature of the bayonet tube and the outer diameter of the wick, is given as a set value. In the state
The method
Calculating the number of transmission units as the negative of the natural logarithm of the value obtained by subtracting the temperature efficiency of the evaporator from 1;
The radial conductance of the evaporator is obtained from the temperature gradient at the wick inner diameter of the radial temperature distribution obtained as a solution of the energy equation for heat conduction and liquid permeation of the wick, and the number of evaporator transmission units and the wick obtained from the radial conductance are obtained. From the relational expression of the ratio of the outer diameter and the inner diameter of the wick, and the relational expression that the power of the radial distance of the wick appearing in the solution of the energy equation is the reciprocal of the number of transmission units when the evaporator is regarded as a heat exchanger. Calculating the ratio of the outer diameter to the inner diameter of the wick;
The ratio of the outer diameter and inner diameter of the wick, the number of the transmission units, the constant fluid pressure specific heat, the fluid dynamic viscosity coefficient, the ratio between the wick pressure loss and the capillary pressure head, and the thermal conductivity and liquid permeability of the wick determined from the capillary pressure head. The step of calculating the porosity of the wick so that the calculated value of the ratio of the thermal conductivity of the wick determined by the physical properties and structure of the wick material and the ratio of the liquid permeability is equal,
The relationship between the capillary radius and porosity of the wick, which is determined based on the wick formation structure, and the liquid permeability specific to the wick material,
The relationship between the thermal conductivity of the wick and the porosity and the effective thermal conductivity of the wick, determined based on the wick formation structure,
The relationship between the ratio between the wick shape correction liquid permeability and the wick effective thermal conductivity, the wick capillary radius, and the ratio between the wick outer diameter and the inner diameter, determined from the correlation between wick heat conduction and liquid permeation. A wick porosity is calculated.

Further, the present invention has the following mathematical formula configuration that does not require iterative calculation. According to yet another feature of the invention,
An evaporator having a tubular wick disposed therein, a reservoir located inside the wick, a serpentine condenser subcooler that dissipates and condenses refrigerant vapor, a radiator that disposes the condenser subcooler, and steam from the evaporator A steam pipe for sending the refrigerant liquid to the condenser subcooler, a liquid pipe for releasing the refrigerant liquid condensed by the condenser subcooler, and a supercooled refrigerant liquid to the reservoir, and extending from the liquid pipe into the reservoir In a loop heat pipe composed of a bayonet tube having an opening, loop heat from a predetermined operating condition specified as a design specification of the loop heat pipe and a predetermined design parameter given as a set value based on the design specification A method for calculating the dimensions of each component of a pipe.
The dimensions of each of the constituent elements are as follows: vapor pipe diameter, liquid pipe diameter, bayonet pipe diameter, wick inner diameter, wick outer diameter, wick thickness, a vapor channel that is a refrigerant vapor passage and a liquid channel that is a refrigerant liquid passage. Cross-sectional area ratio, evaporator length, wick capillary radius, porosity indicating wick porosity, condenser subcooler tube diameter, condenser subcooler length, reservoir volume, reservoir diameter, radiator area, feeder half-spacing The thickness of the fins,
The predetermined operating conditions include the heat load on the evaporator, the steam temperature, the ambient temperature that is the ambient temperature of the evaporator and the reservoir, the heat sink temperature that is the heat dissipation environment temperature of the radiator, the steam path length, the liquid path length, the evaporator and the condenser The height difference between and the values of gravity acceleration are specified,
The predetermined design parameter is the difference between the temperature of the bayonet tube and the outer diameter temperature of the wick of the evaporator axial temperature difference, which is the difference between the liquid pipe side temperature and the vapor pipe side temperature of the evaporator. Evaporator temperature efficiency indicating the ratio to temperature difference, critical bond number indicating the ratio of gravity to stable capillary force to capillary force, cross-sectional area ratio of steam channel and steam tube, and design margin of loop pressure loss in determining the maximum capillary pressure of wick Capillary crush factor, heat load per unit area on the evaporator, the ratio of the evaporator's effective length to the total length, the ratio of the evaporator saddle width to the wick outer diameter, the location of the evaporator Thermal conductance between ambient ambient and wick, per unit length of steam path Vapor path pressure loss gradient indicating the loss, liquid pressure loss gradient indicating the pressure loss per unit length of the liquid path, condenser pressure loss ratio indicating the pressure loss per unit exhaust heat amount of the condenser, ratio of wick pressure loss to capillary pressure head, subcooler Subcooler temperature efficiency, which indicates the ratio of the radial temperature difference that is the difference between the subcooler inlet liquid temperature and the tube wall temperature to the subcooler axial temperature difference that is the difference between the inlet liquid temperature and the outlet liquid temperature, reservoir Used for heat dissipation of both the front and back sides of the radiator panel, the volume ratio of the liquid at the time of cold start in the reservoir indicating the ratio of the refrigerant liquid in the tank, the volume ratio of the steam at the high temperature start-up in the reservoir indicating the ratio of the refrigerant vapor in the reservoir Heat dissipation when considering the effective area ratio of the radiator that shows the possible ratio, and that the temperature of the radiator panel decreases with increasing distance from the fin root And each value given radiator fin efficiency indicating a ratio of the heat radiation amount if,
Vapor specific heat ratio indicating the ratio of the saturated vapor pressure at a given temperature of the refrigerant, the pressure gradient that is the temperature differential coefficient of the saturated vapor pressure curve, the vapor density, and the constant vapor specific heat and the constant vapor specific heat using the refrigerant physical property calculation formula. In a state where the vapor viscosity coefficient, liquid density, liquid constant pressure specific heat, liquid viscosity coefficient, liquid dynamic viscosity coefficient indicating the ratio of saturated liquid viscosity coefficient and density, liquid surface tension, and latent heat of vaporization are calculated.
The method
Steam pipe diameter, liquid pipe diameter, bayonet pipe diameter, wick based on heat load, steam pipe pressure drop slope, liquid pipe pressure drop slope, critical number of bonds, evaporator temperature efficiency, and cross-sectional area ratio between steam channel and steam pipe Evaporator radial sizing step to calculate inner diameter, wick outer diameter, wick thickness, and cross-sectional area ratio of vapor channel and liquid channel;
An axial sizing step of the evaporator that calculates the evaporator length based on the thermal load, the ratio between the effective length and total length of the evaporator, the ratio between the saddle width and the wick outer diameter, and the thermal load per unit area;
A step of calculating a loop pressure loss including the pressure loss due to the steam path, liquid path, condenser, evaporator, port, and fitting of the loop heat pipe, and
A wick characterization step that calculates the capillary radius and porosity based on the elevation difference between the evaporator and the capacitor, gravitational acceleration, capillary crest factor, and the ratio of wick pressure drop to capillary crest;
Based on heat load, ambient temperature, condenser pressure loss rate, subcooler temperature efficiency, cold start liquid volume ratio in the reservoir, and hot start steam volume ratio in the reservoir, condenser tube diameter, condenser subcooler length, reservoir A capacitor and reservoir sizing step to calculate the volume of the reservoir, the reservoir diameter, and the reservoir length;
Radiator sizing step to calculate radiator area, feeder half-space, and fin thickness based on heat load, steam temperature, heat sink temperature, radiator area ratio, and radiator fin efficiency And
In the radial sizing step of the evaporator,
The steam pipe diameter is calculated from the relationship between the steam viscosity coefficient, the steam density, the latent heat of vaporization, the heat load, and the steam path pressure drop gradient when the steam pipe flow is turbulent.
The liquid pipe diameter is calculated from the relationship between the liquid kinematic viscosity coefficient, latent heat of vaporization, heat load, and liquid pressure loss gradient when the flow of the liquid pipe is assumed to be laminar.
The bayonet tube diameter is calculated as being the same as the liquid tube diameter,
The wick inner diameter is calculated by adding the full width of the annular space of the liquid channel determined by the critical bond number, liquid surface tension, liquid density, vapor density, and gravitational acceleration, and the bayonet tube diameter,
The wick outer diameter is calculated by converting the evaporator temperature efficiency into the number of transmission units and multiplying the ratio of the outer diameter and inner diameter of the wick determined by the number of transmission units by the inner diameter of the wick,
The wick thickness is calculated as the value obtained by subtracting 1 from the wick outer diameter to inner diameter ratio multiplied by the wick inner diameter and dividing by two.
The cross-sectional area ratio of the liquid channel to the steam channel is calculated as a value obtained by dividing the square of the value obtained by dividing the steam pipe diameter by the wick inner diameter by the area ratio of the steam channel and the steam pipe,
In the axial sizing step of the evaporator,
The evaporator length is the heat per unit length of the evaporator multiplied by the ratio of the evaporator saddle width to the wick outer diameter, the ratio of the evaporator effective length to the total length, the wick outer diameter and the heat load per unit area. Calculated as the value divided by the load,
In the step of calculating the loop pressure loss,
Steam path pressure loss is calculated by multiplying the steam path pressure loss gradient and the steam path length,
The fluid pressure loss is calculated by multiplying the fluid pressure loss gradient by the fluid path length,
Capacitor pressure loss is the value obtained by subtracting the steam temperature from the ambient temperature and the thermal conductance between the ambient and the wick multiplied by the intrusion heat from the reservoir plus the heat load on the evaporator. Calculated by multiplying,
The evaporator pressure loss is proportional to the evaporator pressure loss coefficient determined from the ratio of the cross-sectional area of the steam channel to the steam tube and the ratio of the bayonet tube to the wick inner diameter, inversely proportional to the fourth power of the bayonet tube diameter, and proportional to the square of the heat load. , Proportional to the value obtained by dividing the liquid kinematic coefficient by the latent heat of vaporization, proportional to the square of the thermal load, and calculated from the relationship inversely proportional to the thermal load per unit length of the evaporator,
The port pressure loss is a value obtained by squaring the steam port pressure loss coefficient determined from the cross-sectional area ratio of the steam channel and the steam pipe, the critical Mach number that is 1/1000 of the cross-sectional area ratio of the liquid channel to the steam channel, and the steam specific heat ratio. And half the value obtained by multiplying the saturated vapor pressure,
Fitting pressure loss is determined from the cross-sectional area ratio of the condenser and the liquid pipe to the value obtained by dividing the steam fitting pressure loss coefficient determined from the cross-sectional area ratio of the steam pipe and the condenser by the value obtained by multiplying the vapor density by the fourth power of the steam pipe diameter. Vaporization of heat load is proportional to the sum of the value obtained by multiplying the liquid fitting pressure loss coefficient by the square of the cross-section change factor at the condenser outlet and the liquid density multiplied by the fourth power of the liquid pipe diameter. Calculated from the relationship that is proportional to the square of the value divided by the latent heat,
The loop pressure loss is calculated by adding the vapor path pressure loss, the liquid path pressure loss, the condenser pressure loss, the evaporator pressure loss, the port pressure loss, and the fitting pressure loss,
In the wick property specifying step,
The wick capillary radius is proportional to the liquid surface tension, is proportional to the ratio of the wick pressure drop to the capillary pressure head minus 1, and is multiplied by the capillary pressure head factor and the loop pressure drop between the evaporator and the capacitor. Calculate from the relationship proportional to the value obtained by adding the gravity loss determined from the height difference,
Wick's porosity is
Analytical values of the number of transmission units, liquid constant pressure specific heat, fluid dynamic viscosity coefficient, ratio of wick pressure loss to capillary pressure head, and ratio of thermal conductivity and liquid permeability of wick determined from capillary pressure head, physical properties of wick material and The calculated value of the ratio of thermal conductivity and liquid permeability of the wick determined from the structure is equal.
The relationship between the capillary radius and porosity of the wick, which is determined based on the wick formation structure, and the liquid permeability specific to the wick material,
The relationship between the thermal conductivity of the wick and the porosity and the effective thermal conductivity of the wick, determined based on the wick formation structure,
The relationship between the ratio between the wick shape correction liquid permeability and the wick effective thermal conductivity, the wick capillary radius, and the ratio between the wick outer diameter and the inner diameter, determined from the correlation between wick heat conduction and liquid permeation. Calculated from
In the sizing step of the capacitor and reservoir,
The value obtained by dividing the value obtained by adding the gravity loss to the value obtained by multiplying the capillary pressure head factor and the loop pressure loss by the pressure gradient at the steam temperature is obtained, and the value obtained by dividing the latent heat of vaporization by the specific heat of the liquid constant pressure is obtained. Add the temperature difference in the wick radial direction and multiply the value by the value obtained by dividing the intrusion heat from the reservoir by the heat load to obtain the degree of supercooling, and multiply the latent heat of vaporization by the liquid constant pressure specific heat by the supercooling degree of the subcooler. The ratio of the latent heat and the sensible heat is obtained by dividing by the obtained value, and the value obtained by multiplying the ratio of the latent heat and the sensible heat by the subcooler temperature efficiency is a two-phase heat transfer coefficient multiplication multiplier determined from the density ratio of the steam and liquid. By dividing the value obtained by adding 1 to the temperature efficiency of the subcooler and the natural logarithm of the value obtained by adding 1 to the temperature efficiency of the subcooler, the area ratio between the two phases of the capacitor and the single phase is obtained. The tube diameter of the subcooler is determined by multiplying the vapor pipe diameter by the two-phase area ratio determined from the two-phase and single-phase area ratio of the capacitor and the single-phase area ratio determined from the two-phase and single-phase area ratio of the capacitor. Is calculated by adding the value obtained by multiplying the liquid pipe diameter by
The steam pipe flow is turbulent and the liquid pipe flow is laminar, and the steam pressure loss and liquid area are determined from the steam viscosity coefficient, steam density, liquid dynamic viscosity coefficient, latent heat of vaporization, heat load, and condenser subcooler pipe diameter. Determine the ratio of pressure loss. The length of the condenser / subcooler is proportional to the condenser pressure loss ratio and inversely proportional to the liquid path pressure drop gradient, and the condenser / subcooler pipe diameter is divided by the steam pipe diameter. Proportional to the fourth power of the measured value, proportional to the value obtained by adding the intrusion heat from the reservoir to the heat load, the average two-phase friction coefficient multiplication multiplier, the ratio of the two-phase region, and the ratio of the vapor region pressure loss to the liquid region pressure loss. Calculated from the relationship that the multiplied value is inversely proportional to the single-phase region ratio and the added value,
The volume of the reservoir is the sum of the condenser volume determined from the length of the condenser / subcooler and the condenser / subcooler pipe diameter and the steam pipe volume determined from the steam pipe diameter, and the liquid volume ratio at low temperature startup and steam volume at high temperature startup. Calculate by adding the rate and multiplying it by the value subtracted from 1.
The reservoir diameter is calculated from the volume of the reservoir to minimize the surface area,
The reservoir length is calculated as the same value as the reservoir diameter,
In the sizing step of the radiator,
The fin root temperature is determined by subtracting the subcooler supercooling degree from the value obtained by adding 1 to the reciprocal of the subcooler's temperature efficiency, and subtracting it from the saturated steam temperature. Calculated from the relationship that is proportional to the value obtained by adding the intrusion heat and inversely proportional to the value obtained by multiplying the effective area ratio of the radiator, the radiator fin efficiency, the radiant heat transfer coefficient, and the value obtained by subtracting the heat sink temperature from the fin root temperature. And
The half-interval of the feeder is calculated as the value obtained by dividing the area of the radiator by twice the length of the capacitor / subcooler,
The thickness of the fin is inversely proportional to the thermal conductivity of the fin, proportional to the effective area ratio of the radiator, proportional to the radiant heat transfer coefficient, and the square of the value obtained by dividing the feeder half-space by the fin conduction parameter determined from the fin efficiency. A method characterized in that it is calculated from a relationship proportional to.

  Thus, according to the present invention, the evaporator in the loop heat pipe can be sized and the wick formation structure can be specified. In addition, when designing the entire loop heat pipe, simply providing operating conditions and design parameter values enables consistent design calculations in terms of fluid heat, so sizing empirically based on past prototype results. There is no need to specify the characteristics of the wick, and the design results of each element are systematically consistent. Therefore, the loop heat pipe designed by this method has the maximum performance because it is optimally sized.

  Embodiments of the present invention will be described below with reference to the drawings. However, the following description is merely an example of the present invention, and the technical scope of the invention is not limited by the following description. The present invention relates to a rational method for sizing the components of a loop heat pipe, and for the understanding thereof, first, a loop heat pipe to be designed will be described.

[Outline of loop heat pipe configuration]
FIG. 1 is a diagram showing a configuration of a loop heat pipe to be designed in the present invention with respect to an axial cross section of an evaporator. FIG. 4 is a view showing the appearance of the loop heat pipe. The loop heat pipe includes an evaporator 100 including a first wick 160, a second wick 170, a reservoir 180 integrated with the first wick 160, a condenser / subcooler 210 to which a radiator 200 is attached, a steam pipe 150, and a liquid pipe 220. Has been. FIG. 2 shows a cross section in the radial direction of the evaporator 100. The evaporator 100 has a double-pipe structure having the radial cross section shown in FIG. 2, and the inner tube side is a liquid channel and the outer tube side is a steam channel. The inner tube is a thick-walled cylindrical wick generating force wick (first wick 160), and the inner wall is provided between the reservoir 180 and the liquid channel as shown in the axial cross section at the top of FIG. A coarse wick (second wick 170) is attached to the liquid link. A bayonet tube 190 is inserted into the liquid channel for supplying liquid as an extension of the liquid pipe. The outer tube is a circular tube with a saddle 110, and a steam groove 120 is carved on the inner wall for a steam channel, and the outlet of the outer tube is a steam port 130. The condenser subcooler 210 has a serpentine shape so as to function as a radiator feeder. When heat is applied to the evaporator 100 via the saddle 110, the refrigerant liquid evaporates from the outer surface of the first wick 160. The generated steam is collected in the steam port 130 through the steam groove 120 and enters the condenser 210 via the steam pipe 150 where it dissipates heat and condenses. The condensed liquid is supercooled by the subcooler 210 and enters the evaporator 100 via the liquid pipe 220 and the bayonet pipe 190. In the liquid channel, the refrigerant liquid is sucked up by the capillary force from the inner surface of the first wick 160, so that a heat circulation refrigerant circulation loop is formed.

  The present invention performs design (sizing) of each component of the loop heat pipe as described above.

1, 2, and 3 show components that are the object of sizing a loop heat pipe. 3A is a view showing a radiator 200 having the same shape and cross section as that shown in FIG. 1, and FIG. 3B is a cross-sectional view taken along line AA in FIG. c) is a cross-sectional view of BB in FIG. The components to be sizing are steam pipe diameter D _VL (symbol k), liquid pipe diameter D _LL (symbol g), _bayonet pipe diameter D _bayo (symbol f), _wick inner diameter D _win (symbol c), wick Outer diameter D _wout (symbol b), _wick thickness δ _w (symbol d), liquid channel cross-sectional area ratio ε _vch (in FIG. 2, A _vch is the total steam channel area of all steam grooves 120 ( A _vch = A _v1 + A _v2 +... + A _vN ), where A _lch is the liquid channel area consisting of an annular space and a _bayonet tube, ε _vch = A _vch / A _lch ), the evaporator length L _evap (symbol e), _wick capillary radius r _c , wick porosity ε _w , condenser subcooler tube diameter D _cond (symbol j), condenser subcooler length L _cond (symbol m), reservoir volume V _res , Lizar The bar diameter D _res (symbol a), the radiator area A _R , the feeder half-interval W _F (symbol h), and the fin thickness δ _R (symbol l).
In order to perform the above sizing, the following operating conditions and design parameters are used as a premise.

The operating conditions are: heat load Q to the evaporator, steam temperature Tυ, ambient temperature Ta which is the ambient temperature of the evaporator and reservoir, heat sink temperature Ts which is the radiator environment temperature of the radiator, steam path length L _VL , liquid path length L _LL The height difference Δh between the evaporator and the capacitor, and the gravitational acceleration g.

The design parameter is the difference between the evaporator axial temperature, which is the difference between the evaporator liquid tube temperature and the steam pipe side temperature, and the evaporator radial temperature difference, which is the difference between the bayonet tube temperature and the wick outer diameter temperature. The evaporator temperature efficiency Φ _evap , the critical bond number Bo ^* , which indicates the ratio of gravity to the stable capillary force, the cross-sectional area ratio of the steam channel to the steam tube (steam tube / steam channel cross-sectional ratio) Φ _{vch / VL} In determining the maximum capillary pressure, the capillary pressure head factor f _H indicating the design margin of the loop pressure loss, the thermal load q per unit area for the evaporator, the effective length that is the length of the evaporator wick mountable portion, and the total length of the evaporator the ratio of (evaporator enable / full-length ^{ratio) (L (a) / L} ) * evap, the ratio of the saddle width and wick outer diameter of the evaporator (evaporator Sad Width / wick outside diameter _{^{ratio) (W / D) * evap}} , thermal conductance (between Ambient / wick conductance between the ambient and the wick is location near the evaporator) K _aw, pressure loss per unit length of the steam path Vapor path pressure loss gradient (△ PVL / LVL) ^* , pressure loss per unit length of liquid path (△ PLL / LLL) ^* , capacitor pressure loss ratio indicating pressure loss per unit heat quantity of condenser (△ Pcond / Q) ^* , ratio of wick pressure drop to capillary pressure head (Wick pressure drop / capillary pressure head ratio) (△ Pwick / △ Pcap) ^* , difference between subcooler inlet liquid temperature and outlet liquid temperature Subcooler temperature efficiency Φ _sub , which indicates the ratio of the axial temperature difference of the subcooler to the radial temperature difference, which is the difference between the liquid temperature at the inlet of the subcooler and the temperature of the tube wall, and the ratio of the liquid in the reservoir Liquid volume ratio α _L at low temperature startup, steam in reservoir The steam volume ratio β _V at the time of high-temperature start-up, which indicates the proportion of the radiator, the effective area ratio η _{S of} the radiator, which indicates the proportion of the front and back surfaces of the radiator panel that can be used for heat dissipation, and the temperature of the radiator panel move away from the fin root The radiator fin efficiency η _F indicates the ratio of the heat dissipation amount when considering the decrease in accordance with the above and the heat dissipation amount when the heat dissipation is uniform without decreasing.

  The operating conditions, design parameters, and other related physical quantities can be easily understood by the designer by referring to the [Terminology] column described later.

[Loop heat pipe design theory (analysis modeling)]
Here, the design theory (analysis modeling) of LHP, which is the basis of the design method of the top-down loop heat pipe (LHP) according to the present invention, will be described.

（１） Since the LHP first wick is typically a relatively long thick-walled cylinder, the fluid and heat flow therethrough is one-dimensional in the radial direction. Therefore, the energy equation is as follows.

(1)

（２） Where r is the radial distance from the cylinder center line, T is the local temperature of the wick, v _r is the radial velocity of the liquid, C _pl is the specific heat of the liquid constant pressure, ρ _l is the liquid density, and k _eff is the effective wick Thermal conductivity. Considering the flow rate passing through the cylindrical surface at the position of the radius r, the mass flow rate is expressed as in equation (2).

(2)

は、エバポレータ活動領域長であり、式（１）は以下のように書き換えられる。

（３） here,

Is the evaporator active region length, and equation (1) can be rewritten as follows.

(3)

は定数であり、式（４）のように表すことができる。

（４） here,

Is a constant and can be expressed as in equation (4).

(4)

（５） The analytical solution of Equation (3) that satisfies the boundary conditions of T (r _win ) = T _win and T (r _wout ) = T _wout is expressed as follows.

(5)

（６） The amount of heat transfer across the wick from r _out to r _in is determined from equation (6).

(6)

（７） Here, K _evap is the evaporator radial conductance, and T ′ (r _winn ) is the temperature gradient of the _wick inner surface. Expression (7) is derived from Expression (5) and Expression (6).

(7)

（８） Here, R _W is the ratio of the outer diameter and the inner diameter of the wick, it is expressed as follows.

(8)

（９） Since the LHP evaporator can be regarded as a heat exchanger, the concept of the number of transfer units can be used for the performance of the evaporator. The number of transmission units is generally defined as follows:

(9)

（１０） Substituting equation (7) into equation (9) yields:

(10)

（１１） Further, the conductance is derived from the equation (6) as follows.

(11)

（１２） When Expression (4) is applied to Expressions (9) and (11), the following Expression (12) is obtained.

(12)

（１３） According to this relationship, Expression (10) is expressed as follows.

(13)

（１４） Therefore, the ratio between the outer diameter and the inner diameter of the wick is determined from the following equation (14).

(14)

（１５） _A more convenient figure of _merit than NTU _evap is the evaporator temperature efficiency Φ _evap . The equation representing these two relationships is known as equation (15).

(15)

（１６） Further, from the equation (15), NTU _evap can be expressed as follows.

(16)

（１７） Since the LHP evaporator has a double pipe structure, the wick inner diameter _Dwin is expressed as follows.

(17)

（１８ａ） At this time, the bayonet tube diameter can be expressed as follows.

(18a)

（１８ｂ） Here, D _LL is the diameter of the liquid pipe. The size of the number of bonds depends on annular space W _ann formed between the cylindrical wick and bayonet tube. From the definition of the critical bond number, the following equation is obtained.

(18b)

（１９ａ）

（１９ｂ） Here, Bo ^* is the critical number of bonds for stable condensation, σ _l is the liquid surface tension, ρ _l is the vapor density, and g is the gravitational acceleration. The _wick outer diameter D _wout and the _wick thickness δ _w are determined from the following equations.

(19a)

(19b)

（２０） The evaporator length L _evap is proportional to the heat load Q and has the following size.

(20)

は、以下の式によって与えられる。

（２１） Sizing parameters for evaporator with saddle

Is given by:

(21)

は全長に対する活動領域長の割合であり、

はエバポレータのサドル幅とウイックの外径との比であり、qは単位面積当りの熱負荷である。したがって、ＬＨＰエバポレータの寸法は、別途決定されるD_LL値に対して１つの値が特定され得る。 here,

Is the ratio of the active area length to the total length,

Is the ratio between the evaporator saddle width and the wick outer diameter, and q is the heat load per unit area. Accordingly, one value can be specified for the dimension of the LHP evaporator with respect to the _DLL value determined separately.

（２２） Here, the estimation of the loop pressure loss is made in order to find the necessary capillary pressure head. The loop pressure loss ΔP _loop that occurs in the layout shown in FIG. 1 is expressed as follows.

(22)

はエバポレータ液チャネル圧損、

はエバポレータ蒸気グルーブ圧損、ΔP_portはエバポレータポート圧損、ΔP_fittはエバポレータ／コンデンサのフィッティング圧損である。このとき、蒸気路圧損、液路圧損、およびコンデンサ圧損は、以下のようにそれぞれ見積られる。

（２３ａ）

（２３ｂ）

（２３ｃ） Where ΔP _VL is vapor path pressure loss, ΔP _LL is liquid path pressure loss, ΔP _cond is capacitor pressure loss,

Is the evaporator liquid channel pressure drop,

Is the evaporator steam groove pressure loss, ΔP _port is the evaporator port pressure loss, and ΔP _fitt is the evaporator / condenser fitting pressure loss. At this time, the vapor path pressure loss, the liquid path pressure loss, and the condenser pressure loss are estimated as follows.

(23a)

(23b)

(23c)

（２４ａ）

（２４ｂ）

（２４ｃ） Here, L _VL is the vapor path length, L _LL is the liquid path length, and Q ′ is the heat input from the reservoir.
In calculating the equation (23a-23c), the vapor pressure loss gradient (ΔP _VL / L _VL ) ^* , the liquid pressure loss gradient (ΔP _LL / L _LL ) ^* , and the condenser pressure loss rate (ΔPcond / Q) ^* Specified based on system requirements. The last four terms of equation (22) can be expressed as:

(24a)

(24b)

(24c)

（２５） Here, ν _l is the fluid dynamic viscosity coefficient, λ is the latent heat of vaporization, γυ is the steam specific heat ratio, and ρυ is the vapor density. The respective pressure loss coefficients ζ _evap , ζ _port , ζ _fitt ^(v) , and ζ _fitt ^(l) are respectively given by the equations (A1a), (A2a), (A3a), and (A4a) in the appendix. The last three terms are also commonly expressed as formula (A5a). In deriving the respective coefficients, the related cross-sectional area ratios are defined using equations (A1b), (A2b), (A3b), and (A4b). The factor φ _{cond / LL in} the equation (24c) is defined by the equation (A4b), and indicates a cross-sectional change at the capacitor outlet. Expression (24b) including the square of the Mach number is derived from the relationship that the pressure loss is proportional to the square of the vapor velocity. Since the vapor velocity is usually very low, Ma ^* is 1 / 1000ε _vch . At this time, the cross-sectional area ratio ε _vch is defined by the equation (A2c). Considering the _wick pressure drop Δp _wick and the gravity pressure drop Δp _grav , the required capillary pressure head Δp _cap is given by:

(25)

（２６） Here, f _H is a capillary crest factor indicating a pressure loss calculation margin. When the meniscus formed on the outer surface of the wick is completely degenerated in the capillary hole under the pressure balance represented by the equation (25), the capillary pressure head is as follows.

(26)

（２７） Here, r _c is the capillary radius (1/2 of the average capillary pore size). Given the ratio of the _wick pressure loss to the capillary head (Δp _wick / Δp _cap ) ^* , the following equation is obtained:

(27)

（２８） Substituting equations (26) and (27) into equation (25) yields the following equation:

(28)

  In this way, the required capillary radius is determined.

（２９） Applying Darcy's law to the wick permeate flow and considering equation (2), a radial pressure gradient dp / dr can be obtained. Integrating it from r _win to r _wout gives:

(29)

はウイック材固有の液透過率K_pとは異なり、以下のように定義される。

（３０） here,

Is defined as follows, unlike the liquid permeability K _p inherent to the wick material.

(30)

（３１） From the equations (27) and (29), the following equation is obtained.

(31)

（３２） There are various empirical formulas for K _p , many of which are of the Break-Kozni type shown below. Note that the empirical formula to be applied differs depending on whether the wick formation structure corresponds to a fiber, powder, bead, foam, or the like.

(32)

（３３） Here, ε _w is the wick porosity, n is a power, and c _w is a constant. The relationship between K _p and k _eff is obtained as follows. That is, substituting equation (11) into equation (9) results in the following.

(33)

（３４） When Expression (33) is divided by Expression (31), the result is as follows.

(34)

（３５） Equation (30) can then be rewritten as follows:

(35)

The right side of Expression (35) depends on Φ _evap , (Δp _wick / Δp _cap ) ^* , and f _H and is calculated from Expressions (14), (28), and (34). The empirical formula for k _eff is shown in Appendix B. Formula (B1a) for mesh / screen, Formula (B1b) for sintered fiber, Formula (B2a) for powder, Formula (B2b) for sintered powder, The formula (B3) is used for beads and the formula (B4) is used for foum. The required wick porosity is calculated from equation (35) using equation (32) and the appropriate equation in Appendix B.

（３６） From the pressure versus temperature relationship, there are three saturation states in the LHP. Although they are found in capacitors, evaporators, and reservoirs, it should be noted that they relate to the latter two states. _{Focusing on the} hydraulic pressure p _l , there is a relationship of p _evap = p _l + Δp _cap and p _res = p _l + Δp _wick under the design conditions. Therefore, the pressure difference between the evaporator and the reservoir is Δp _cap −Δp _wick . This causes the slight temperature difference shown below in the second wick.

(36)

（３７） Here, T _v ^′ (p _v ) is the slope of the pT curve with respect to the pressure axis. When Expression (25) is used in Expression (36), the temperature difference in the radial direction of the wick can be expressed as follows.

(37)

（３８） Here, p _v ^′ (T _v ) is inversely related to T _v ^′ (p _v ), is the slope of the pT curve at the steam temperature T _v , and is calculated from the Clausius-Clapeyron equation Can do. In the steady state, the magnitude of the applied heat quantity Q can be removed from the evaporator by the refrigerant phase change, but part of it leaks into the reservoir. Therefore, the following equation is obtained.

(38)

（３９） Also, the heat inflow and outflow through the reservoir is generally given by:

(39)

（４０） Here, K _aw is the thermal conductance between the ambient (ambient environment) and the wick, and T _a is the ambient temperature. Equation (39) takes a negative value when T _a <T _v , but in such a case, Q ^{′ is set} to zero. This stems from the design philosophy that capacitors and radiators should be somewhat larger. The subcooler is necessary to absorb the heat inflow Q ^′ by the supercooled reflux liquid. The relationship is expressed as follows.

(40)

（４１） Here, ΔT _sub is the degree of supercooling. Dividing equation (40) by equation (38) gives the following equation:

(41)

（４２） At this time, the ratio of latent heat to sensible heat is expressed as follows.

(42)

が費される。ポンプ効率は、そのため以下のように定義される。

（４３） If LHP is regarded as a heat pump, the heat input is Q + Q '.

Is spent. Pump efficiency is therefore defined as:

(43)

（４４） Substituting equations (38) and (40) into equation (43) yields the following equation:

(44)

（４５ａ）

（４５ｂ） Assuming that the steam pipe flow is turbulent and the liquid pipe flow is laminar, and is characterized by Colburn's coefficient of friction, the following equation is obtained.

(45a)

(45b)

は式（３８）から以下のように導かれる。

（４６） Here, mu _v is the vapor viscosity coefficient, D _VL is steam pipe diameter. Refrigerant mass flow rate

Is derived from equation (38) as follows.

(46)

（４７ａ）

（４７ｂ） Applying equation (46) to equations (45a) and (45b) yields:

(47a)

(47b)

の割合で、η_1Φの領域から

の割合で取り除かれる。軸方向の熱の除去は、作動流体からコンデンサ管への径方向の熱伝達に等しいため、それぞれの割合は、以下のように表される。

（４８ａ）

（４８ｂ） Therefore, the bayonet tube diameter shown in the equation (18a) can be determined from the equation (47b). Equations (47a) and (47b) are used for sizing the capacitor tube diameter and the capacitor length. In order to develop a practical method of sizing, a two-zone model consisting of a condensed vapor zone and a supercooling zone is used. At this time, the two-phase region and the single-phase region are defined using the standardized lengths η _2Φ and η _1Φ . Heat from the area of η _2Φ

From the region of η _1Φ

Removed at a rate of Since the removal of heat in the axial direction is equal to the radial heat transfer from the working fluid to the condenser tube, the respective proportions are expressed as follows:

(48a)

(48b)

は二相域出口の液とラジエータとの間の温度差、ΔT_lmは対数平均温度差であり、それらは、ΔT_subに依存し、以下のように表される。

（４９ａ）

（４９ｂ） Where A _h is the heat transfer surface area, U _2Φ is the overall heat transfer coefficient in the active condenser area (two phase area), U _1Φ is the overall heat transfer coefficient in the subcooler area (single phase area),

Is the temperature difference between the liquid at the two-phase zone outlet and the radiator, ΔT _lm is the logarithmically averaged temperature difference, which depends on ΔT _sub and is expressed as:

(49a)

(49b)

（５０） Here, Φ _sub is the temperature efficiency of the subcooler. Since U _2Φ and U _1Φ are regarded as two-phase and single-phase heat transfer coefficients h _2Φ and h _1Φ , respectively, U _2Φ / U _1Φ is generally expressed as:

(50)

は、式（Ａ６ｂ）のもとで式（Ａ７ｂ）から算出される。式（４８ａ）を式（４８ｂ）で除すれば、二相・単相領域比が得られる。式（４９ａ）、（４９ｂ）、および（５０）から、その比は、以下のようになる。

（５１） Average two-phase heat transfer coefficient multiplier

Is calculated from equation (A7b) under equation (A6b). By dividing equation (48a) by equation (48b), a two-phase / single-phase region ratio can be obtained. From equations (49a), (49b), and (50), the ratio is as follows:

(51)

（５２ａ）

（５２ｂ）
である。 At this time, the two-phase region ratio and the single-phase region ratio are respectively

(52a)

(52b)
It is.

（５３） Since D _VL should be greater than D _LL, a relationship of _{D VL> D cond> D LL} . Therefore, the capacitor tube diameter is determined as follows.

(53)

（５４ａ）
ここで、Ψは平均二相摩擦係数増倍乗数であり、式（Ａ８ｂ）から算出される。

および

は、それぞれ、表現が式（４５ａ）および（４５ｂ）と同様であり、式（４６）が成り立つので、蒸気域圧損と液域圧損の比（コンデンサの二相域/単相域圧損比）は、以下のようになる。

（５４ｂ） The two-region model is also used to determine the active capacitor pressure loss and the subcooler pressure loss. The sum of the two gives the total pressure loss of the capacitor.

(54a)
Here, Ψ is an average two-phase friction coefficient multiplication multiplier, and is calculated from the equation (A8b).

and

Respectively, the expressions are the same as the expressions (45a) and (45b), and the expression (46) is established, so the ratio of the vapor pressure loss to the liquid pressure loss (the two-phase / single-phase pressure loss ratio of the capacitor) is It becomes as follows.

(54b)

および

の設計仕様値が決まると、必要とされる除去熱量はQ+Q’であるので、以下の式を得る。

（５５ａ）

and

When the design specification value of is determined, the amount of heat to be removed is Q + Q ′, so the following equation is obtained.

(55a)

と

との類似性を考慮すると、その比は、以下のように与えられる。

（５５ｂ） Formula (45b) and

When

The ratio is given as follows, considering the similarity to:

(55b)

に関しては、式（５４ａ）、式（５５ａ）および式（５５ｂ）から導かれ、それら２つを等置すると、以下のように必要とされる全コンデンサ長が求められる。

（５６）

Is derived from Equation (54a), Equation (55a) and Equation (55b), and when they are placed equally, the total required capacitor length is determined as follows.

(56)

（５７ａ）

（５７ｂ） The condenser volume V _cond can be calculated from the equations (53) and (56), the vapor pipe volume V _VL can be calculated from the equation (47a), and the liquid pipe volume V _LL can be calculated from the equation (47b). The required reservoir volume V _res depends on the amount of liquid movement in the loop heat pipe, and the condenser and steam pipe are flooded at low temperatures but not flooded at high temperatures. It is decided from that. At this time, some liquid must remain in the reservoir during cold start and some steam must remain there during hot start. This request is as follows because the liquid filling amount is preserved.

(57a)

(57b)

はエバポレータ液チャンネルの体積であり、α_Lはリザーバ体積に対する液体積の割合（リザーバ内の低温起動時液体積率）であり、β_Vは蒸気体積の割合（高温起動時蒸気体積率）である。式（５７ａ）および（５７ｂ）をまとめると、以下のように表すことができる。

（５８） here,

Is the volume of the evaporator liquid channel, α _L is the ratio of the liquid volume to the reservoir volume (low volume startup liquid volume ratio in the reservoir), and β _V is the ratio of the vapor volume (high temperature startup steam volume ratio) . The formulas (57a) and (57b) can be summarized as follows.

(58)

（５９ａ）

（５９ｂ） When α _L = β _V = 0.1, equations (57b) and (58) are as follows:

(59a)

(59b)

（６０ａ）

（６０ｂ） Regarding the sizing of the tube diameter and length of the reservoir, the method has not yet been established, but in the present invention, it can be determined as follows.

(60a)

(60b)

（６１） Equations (60a) and (60b) minimize the total surface area of the constant volume cylindrical reservoir. Since the reservoir is exposed to the surrounding environment and connected to the second wick, the thermal conductance K _aw introduced in equation (39) to define Q ′ is expressed as:

(61)

（６２ａ）

（６２ｂ） K _{a / res} and K _{res / w} are practically given as follows.

(62a)

(62b)

である。式（４９ａ）を

に代入して、T_vを飽和液温度とすると、以下の式が導かれる。

（６３） Here, the superscript macron means a reference value. Radiator temperature T _R is not uniform exactly, but substituting the fin root temperature at condenser outlet, can be performed sizing of the radiator. Here, the temperature difference in the radial direction of the radiator is

It is. Equation (49a)

And substituting _Tv for the saturated liquid temperature, the following equation is derived.

(63)

（６４） By specifying the heat sink temperature T _s area A _R of the radiator is determined from the following equation.

(64)

If eta _S is the effective area ratio of the radiator showing the percentage which may be used for heat dissipation of the double-sided front and rear radiator panels, eta _F is obtained by considering that decreases as the temperature of the radiator panel is moved away from the feeder i.e. fin root Is the fin efficiency of the radiator showing the ratio of the amount of heat released and the amount of heat released when it is uniform without decreasing, and h _S is the radiant heat transfer coefficient.

（６５） At this time, the fourth power law of radiation gives the following equation.

(65)

はステファン・ボルツマン定数である。矩形状フィンのη_Fは以下のように表される。

（６６） Where ε _t is the surface infrared emissivity,

Is the Stefan-Boltzmann constant. The η _{F of the} rectangular fin is expressed as follows.

(66)

（６７） Here, ω _F is a fin conduction parameter. The numerical inverse transform of equation (66) is given by equation (A9), and η _F can be converted to ω _F. In the formula (56) and (64), the feeder half width W _F is calculated from the following equation.

(67)

（６８） ω _F is obtained from the solution of the fin linearized heat conduction equation and is given by

(68)

Here, k _R is the thermal conductivity of the fin, is [delta] _R is the thickness of the fins. k _R δ _R represents the required fin thermal conductance. The LHP mass model is shown in Appendix C for reference because the designers consider weight as well as size.

[Method of designing a loop heat pipe according to an embodiment of the present invention]
Next, a method for designing various dimensions of a loop heat pipe according to an embodiment of the present invention based on the above-described LHP design theory will be described.

First, a method for designing an LHP evaporator wick according to an embodiment of the present invention will be described. In the design of the wick, the porosity indicating the ratio of the outer diameter and the inner diameter of the wick and the porosity of the wick is calculated.

  The ratio of the outer diameter to the inner diameter of the wick can be calculated as follows. That is, first, the evaporator axial temperature difference, which is the difference between the evaporator liquid pipe side temperature and the steam pipe side temperature, with respect to the evaporator radial temperature difference, which is the difference between the bayonet tube temperature and the wick outer diameter temperature. The number of transmission units is calculated as the negative value of the natural logarithm of the value obtained by subtracting the temperature efficiency of the evaporator indicating the ratio from 1 (the above equation (16)). Next, the radial conductance of the evaporator is calculated from the temperature gradient (formula (6)) at the wick inner diameter of the radial temperature distribution obtained as a solution of the energy equation for wick heat conduction and liquid permeation (formula (5) above). The wick appearing in the solution of the energy equation (the above formula (7)), the relational expression (the above formula (10)) of the ratio between the number of transmission units of the evaporator and the outer diameter and the inner diameter of the wick, which is determined from the radial conductance The relational expression (the above formula (12)) is derived that the power of the radial distance is the reciprocal of the number of transmission units when the evaporator is regarded as a heat exchanger. Finally, using these relational expressions, the ratio of the outer diameter and the inner diameter of the wick can be calculated (the above formula (14)).

In addition, the porosity indicating the porosity of the wick is based on the assumption that the wick capillary radius, the wick capillary head, the ratio between the wick pressure drop and the capillary pressure head, the constant pressure specific heat, the ratio between the viscosity coefficient and the density of the saturated liquid. Assuming that the dynamic viscosity coefficient and the evaporator temperature efficiency are given as set values, it can be calculated as follows. That is, first, as in the case of calculating the ratio between the outer diameter and the inner diameter of the wick, the number of transmission units is calculated (the above formula (16)), and the ratio between the outer diameter and the inner diameter of the wick is calculated (the above formula ( 14)). And the ratio of the outer diameter and inner diameter of the wick, the number of transmission units, the specific heat of liquid constant pressure, the fluid viscosity coefficient, the ratio of the wick pressure loss to the capillary pressure head, and the thermal conductivity and liquid permeability of the wick determined from the capillary pressure head The porosity of the wick is calculated so that the analytical value of the ratio of the ratio and the calculated value of the ratio of thermal conductivity and liquid permeability of the wick determined from the physical properties and structure of the wick material are equal. More specifically, based on the wick's capillary radius and porosity determined based on the wick formation structure and the relationship between the liquid permeability K _p specific to the wick material (formula (32) above) and the wick formation structure. It is determined from the correlation between the wick's porosity, the thermal conductivity of the wick material and the refrigerant liquid, and the effective thermal conductivity k _eff of the _wick (the formula in Appendix B), and the correlation between the wick's thermal conductivity and liquid permeation. Equations showing the relationship between the wick shape correction liquid permeability, the effective thermal conductivity of the wick, the square of the wick capillary radius, and the natural logarithm of the ratio of the outer diameter and the inner diameter of the wick (the above formulas (34) and (35 )) Can be used to calculate the wick porosity.

  Next, a method for designing the entire LHP according to an embodiment of the present invention will be described. FIG. 5 shows a schematic flow of an entire LHP design method according to an embodiment of the present invention. This is based on the above-described LHP design theory, extracting physical quantities that are essential for calculating the dimensions of each component of the LHP, and specifying the order in which the dimensions of each component are determined from the relationship between the physical quantities. In this way, the LHP can be designed top-down. In the design flow, first, the physical property value of the fluid is calculated (S1), then the sizing in the radial direction and the axial direction of the evaporator is performed (S2), then the pressure loss is calculated (S3), The wick characteristic is calculated (S4), then the capacitor and the reservoir are sized (S5), and finally the radiator is sized (S6). Hereinafter, the design method according to the present invention will be described in detail in correspondence with the equations used in the above LHP design theory.

  First, the step (S1) of calculating the physical property value of fluid will be described.

In order to design each component of the LHP described above, it is necessary to calculate the physical property value of the fluid. Here, the physical property values of the fluid are the saturated vapor pressure Pυ at a predetermined temperature Tυ of the refrigerant, the pressure gradient P′υ which is the temperature derivative of the saturated vapor pressure curve, the vapor density ρυ, the steam (constant pressure / constant product) specific heat ratio γυ. , steam viscosity Myuupushiron, liquid density [rho _l, liquid specific heat at constant pressure Cp _l, Ekinetsu conductivity k _l, liquid viscosity coefficient mu _l, Ekido viscosity coefficient showing a ratio between the viscous modulus and the density of the saturated liquid [nu _l, liquid The surface tension σ _l and the latent heat of vaporization λ. These physical property values can be obtained based on the converted temperature obtained from the critical temperature and the converted pressure obtained from the critical pressure, using the refrigerant physical property calculation formula. There are various methods for calculating the physical property value of the fluid for each fluid, but the method may be obtained based on any of these methods.

  Next, the step (S2) of performing sizing in the radial direction and the axial direction of the evaporator will be described. First, the radial sizing of the evaporator will be described.

The steam pipe diameter D _VL is the above equation (representing the relationship among the steam viscosity coefficient, the steam density, the latent heat of vaporization, the steam pipe diameter, the heat load, and the steam path pressure drop gradient when the steam pipe flow is turbulent. 47a).

Further, Ekikan径D _LL is the expression that indicates when a flow of the liquid pipe and to be laminar flow, the relationship between the latent heat of vaporization and the liquid pipe diameter and the thermal load and the fluid passages pressure loss gradient Ekido viscosity ( 47b).

_Further , the bayonet _tube diameter D _bayo is equal to the liquid _tube diameter D _LL, and can be obtained from the equation (18a).

At this time, the wick inner diameter D _win is _obtained by adding the total width W _{ann of the} liquid channel determined by the critical bond number Bo ^* , the liquid surface tension, the liquid density, the vapor density and the gravitational acceleration, and the _{bayonet tube} diameter D _bayo. From the above equation (17).

The _wick outer diameter D _wout is obtained from the above equation (19a) by converting the evaporator temperature efficiency into the number of transmission units and _{multiplying the wick} outer diameter / inner diameter ratio determined by the number of transmission units by the inner diameter of the _wick. It is done.

Next, the wick thickness δ _w is obtained from the above equation (19b) as a value obtained by dividing a value obtained by subtracting 1 from the wick outer diameter / inner diameter ratio by the wick inner diameter D _win by 2.

Further, the cross-sectional area ratio ε _vch of the steam channel to the liquid channel is _expressed by the formula (A2c) in the appendix as a value obtained by dividing the square of the value obtained by dividing the steam pipe diameter by the _wick inner diameter by the cross-sectional area ratio of the steam channel and the steam pipe. Can be determined from

  Next, the step (S2) of performing axial sizing of the evaporator will be described.

Evaporator length L _evap is the heat load _divided by the heat load per unit area of the evaporator multiplied by the heat load per unit area, _wick outer diameter, evaporator saddle width / wick outer diameter ratio, and evaporator effective / full length ratio. The obtained value can be obtained as in the above equation (20).

Thus, in the step of sizing the evaporator in the radial direction and the axial direction (S2), the steam pipe diameter D _VL , the liquid pipe diameter D _LL , the _bayonet pipe diameter D _bayo , the _wick inner diameter D _win , and the _wick outer diameter D _{The wout} , the _wick thickness δ _w , the cross-sectional area ratio ε _{vch of the} vapor channel to the liquid channel, and the evaporator length L _evap can be determined.

  Next, the step (S3) for calculating the pressure loss will be described.

First, the steam path pressure loss can be obtained from the above equation (23a) by multiplying the steam path pressure loss gradient (ΔPVL / LVL) ^* and the steam path length L _VL .

Further, the liquid passage pressure loss can be obtained from the above equation (23b) by multiplying the liquid passage pressure loss gradient (ΔPLL / LLL) ^* by the liquid passage length L _LL .

Further, the condenser pressure loss is obtained by multiplying the intrusion heat Q ^′ (formula (39)) from the reservoir, which is a value obtained by multiplying the ambient temperature by subtracting the steam temperature from the ambient temperature and the conductance K _aw between the ambient and wick, into the heat load Q on the evaporator. Is multiplied by the capacitor pressure loss rate (ΔPcond / Q) ^* to obtain the above equation (23c).

  The evaporator pressure loss is proportional to the evaporator pressure loss coefficient determined from the steam channel / steam pipe cross-sectional area ratio and the bayonet pipe / wick inner diameter ratio, and is inversely proportional to the fourth power of the bayonet pipe diameter. From the relationship that it is proportional to the divided value, proportional to the square of the thermal load, and inversely proportional to the thermal load per unit length of the evaporator, it can be obtained as the above equation (24a).

  The port pressure loss is a value obtained by squaring a steam port pressure loss coefficient determined from the steam channel / steam pipe cross-sectional area ratio, a critical Mach number that is 1/1000 of the cross-sectional area ratio of the liquid channel to the steam channel, The constant pressure / constant product) specific heat ratio and the saturated vapor pressure are obtained as one half of the value obtained by multiplying the saturated vapor pressure by the above equation (24b).

  The fitting pressure loss is determined from the value obtained by dividing the steam fitting pressure loss coefficient determined from the steam pipe / capacitor cross-sectional area ratio by the value obtained by multiplying the vapor density by the fourth power of the steam pipe diameter, and the capacitor / liquid pipe cross-sectional area ratio. A value obtained by multiplying the value obtained by multiplying the liquid fitting pressure loss coefficient by the square of the cross-section change factor (formula (A4b)) at the outlet of the capacitor and the value obtained by dividing the liquid density by the value obtained by multiplying the liquid pipe diameter by the fourth power. From the relationship that it is proportional and proportional to the square of the value obtained by dividing the thermal load by the latent heat of vaporization, it can be obtained as the above equation (24c).

  Therefore, the loop pressure loss can be obtained as the above equation (22) by adding the respective pressure losses. The loop pressure loss is used in the following step (S4) for specifying a wick.

  Next, the step (S4) for specifying the characteristics of the wick will be described.

First, the wick capillary radius r _c, proportional to the liquid surface tension, wick pressure loss / capillary圧頭ratio proportional to the value obtained by subtracting from 1, between the capillary pressure loss factor value to the evaporator and condenser and a loop pressure loss obtained by multiplying From the relationship that it is inversely proportional to the value obtained by adding the gravity loss determined as ΔPgrav = ρ _l gΔh from the height difference Δh, the above equation (28) can be calculated.

The wick's porosity is the analytical value of the number of transmission units, liquid constant pressure specific heat, fluid dynamic viscosity coefficient, the ratio of wick pressure loss to capillary pressure head, and the ratio of thermal conductivity and liquid permeability of wick determined from the capillary pressure head, The calculated value of the ratio between the thermal conductivity of the wick and the liquid permeability determined from the physical properties and structure of the wick material is determined to be equal. That is, the relational expression (the above formula (32)) between the capillary radius and porosity of the wick determined based on the wick formation structure and the liquid permeability K _p specific to the wick material, and the wick determined based on the wick formation structure Of the wick determined by the correlation between the porosity of the wick, the thermal conductivity of the wick material and the refrigerant liquid, and the effective thermal conductivity k _eff of the _wick (the formula in Appendix B), and the correlation between the thermal conductivity of the wick and liquid permeation The correction liquid permeability, the effective thermal conductivity of the wick, the square of the wick capillary radius, and the natural logarithm of the ratio of the outer diameter and the inner diameter of the wick (the above formula (35)) can be obtained. .

Thus, in step (S4) of performing characteristics specified wick, it can be determined wick capillary radius r _c and a wick porosity epsilon _w.

  Next, the step of sizing the capacitor and the reservoir (S5) will be described.

と、サブクーラの温度効率に１を加算した値と、サブクーラの温度効率に１を加算した値に対する自然対数とを乗算した値で除算すること（上記式（５１））から求める。最終的に、コンデンサ管径は、前記コンデンサの二相/単相領域比から定まる二相域割合（上記式（５２ａ））を蒸気管径と乗算した値と、前記コンデンサの二相/単相領域比から定まる単相域割合（上記（５２ｂ））を液管径と乗算した値とを加算することにより、上記式（５３）として求めることができる。 In obtaining the condenser tube diameter, first, the temperature difference in the wick radial direction is divided by a value obtained by multiplying the capillary pressure head factor and the loop pressure loss by the gravity loss by the pressure derivative at the steam temperature (the above formula (37)). ) Next, the value obtained by dividing the latent heat of vaporization by the specific heat of the liquid constant pressure is added to the temperature difference in the wick radial direction, and the value is multiplied by the value obtained by dividing the intrusion heat from the reservoir by the heat load (the above formula (41)). Obtain the degree of supercooling. Next, the latent heat / sensible heat ratio is obtained by dividing the latent heat of vaporization by the value obtained by multiplying the specific heat of the liquid constant pressure and the degree of subcooling of the subcooler (the above formula (42)). Then, the two-phase / single-phase region ratio of the capacitor is multiplied by the latent heat / sensible heat ratio and the temperature efficiency of the subcooler to obtain a two-phase heat transfer coefficient multiplication multiplier determined from the steam / liquid density ratio.

And the value obtained by multiplying the value obtained by adding 1 to the temperature efficiency of the subcooler and the natural logarithm of the value obtained by adding 1 to the temperature efficiency of the subcooler (the above formula (51)). Finally, the condenser tube diameter is obtained by multiplying the vapor pipe diameter by the two-phase region ratio (the above formula (52a)) determined from the two-phase / single-phase region ratio of the capacitor, and the two-phase / single-phase capacitor. By adding the value obtained by multiplying the liquid pipe diameter by the single-phase region ratio (above (52b)) determined from the region ratio, the above equation (53) can be obtained.

The steam pipe flow is turbulent, and the liquid pipe flow is laminar, and the vapor pressure loss and liquid pressure loss are calculated from the vapor viscosity coefficient, vapor density, liquid dynamic viscosity coefficient, latent heat of vaporization, heat load, and condenser tube diameter. The capacitor length L _cond is a value obtained by dividing the capacitor tube diameter by the steam tube diameter, the capacitor length being proportional to the capacitor pressure loss rate and inversely proportional to the liquid path pressure loss gradient. Proportional to the value raised to the fourth power, proportional to the value obtained by adding the intrusion heat from the reservoir to the heat load, the average two-phase friction coefficient multiplication multiplier ψ, the ratio of the two-phase region, and the ratio of the vapor region pressure loss to the liquid region pressure loss From the relationship that the value obtained by multiplying is inversely proportional to the value obtained by adding the single-phase region ratio, the above equation (56) can be obtained.

The reservoir volume V _res is obtained by adding the condenser volume determined from the condenser length and condenser pipe diameter (the above formulas (53) and (56)) and the vapor pipe volume determined from the steam pipe diameter (the above formula (47a)). By dividing the value by the value obtained by adding the ratio of the liquid volume to the reservoir volume and the ratio of the vapor volume to the reservoir volume and subtracting it from 1, it can be obtained as the above equation (58).

The reservoir diameter D _res can be obtained as being proportional to the 1/3 power of the volume of the reservoir (the above formula (60) a).

  The reservoir length can be determined as the same value as the reservoir diameter (the above formula (60) b).

Thus, in the step of sizing the condenser and the reservoir (S5), the condenser subcooler tube diameter D _cond , the condenser subcooler length L _cond , the reservoir volume V _res , and the reservoir diameter D _res are determined. it can.

  Finally, the step of sizing the radiator (S6) will be described.

  The fin root temperature is obtained by subtracting the value obtained by adding 1 to the reciprocal of the subcooler temperature efficiency and the subcooler subcooling degree from the saturated steam temperature (formula (63) above), and the area of the radiator is The value obtained by multiplying the value obtained by subtracting the heat sink temperature from the effective area ratio of the radiator, the fin efficiency of the radiator, the radiant heat transfer coefficient, and the fin root temperature It can obtain | require as said Formula (64) from the inversely proportional relationship.

Further, semi-interval W _F of the feeder can be obtained radiator area as a value obtained by dividing by two times the value of the capacitor length (the formula (67)).

The fin thickness δ _R is inversely proportional to the thermal conductivity of the fin, proportional to the effective area ratio of the radiator, proportional to the radiant heat transfer coefficient, and the feeder half-distance divided by the fin conduction parameter determined from the fin efficiency. From the relationship proportional to the square of the value, it can be obtained as the above equation (68).

Thus, in the step of sizing the radiator (S6), the area A _{R of} the radiator, the feeder interval W _F , and the fin thickness δ _R can be determined.

  The mathematical formulas used in the design of each component of the LHP described so far do not necessarily have to be the same mathematical formula. Although an ideal design value can be obtained according to the above calculation formula, a predetermined error range may be specified in each of the above calculation formulas assuming an actual scene to which the present invention is applied. Also, considering that coefficients based on empirical formulas may involve experimental errors, design values for each component may be obtained by introducing parameters for allowing errors within a predetermined range. Good.

  As described above, the design method of the loop heat pipe according to the present invention is obtained by modeling the evaporator as a heat exchanger, that is, based on the temperature efficiency, thereby obtaining the ratio between the outer diameter and the inner diameter of the wick. By introducing the critical bond number, the entire annular space of the evaporator / liquid channel can be determined, and the capillary pressure radius of the wick can be determined by calculating the loop pressure loss by calculating the pressure loss of each part from the design conditions, the shape of the wick The wick porosity is defined from the empirical formulas for correction liquid permeability, material intrinsic liquid permeability and thermal conductivity, and the refrigerant subcooling degree is determined from the inflow heat from the reservoir and the wick radial temperature difference. It has been found that the ratio of capacitor two-phase region and single-phase region is determined, and the tube diameter and length of the capacitor are determined. Those that have been realized by.

  That is, the present invention relates the relationship between the number of transmission units of an evaporator and the outer diameter / inner diameter ratio of the wick from the solution of the wick's heat / mass transfer equation, and the number of transmission units on the contrary from the temperature efficiency of the evaporator. The pressure loss of each part from the rate, the shape-corrected liquid permeability from the solution of the wick's liquid permeation equation, the temperature difference in the wick radial direction from the loop pressure loss and saturated vapor pressure curve gradient, and the condenser two-phase from the average two-phase heat transfer coefficient multiplier / Introduces analytical formulas that give single-phase region ratios, and creates analytical models for loop heat pipes with theoretical support.

[Glossary of terms (physical quantities)]
Here, various physical quantities will be described as follows.
Heat load: The amount of heat applied to the evaporator. In the case of an actual machine, the heat generation amount of the electronic device on the saddle, and in the experiment, generally indicates the heat amount of the heater.
Liquid permeability: degree of difficulty of liquid permeation of wick, unit m ² , the smaller this value, the harder the liquid penetrates.
Temperature efficiency: The ratio of the temperature difference in the axial (flow) direction of the evaporator or sub-cooler to the temperature difference in the diameter (tube thickness) direction, unitless dimension, corresponding to the energy exchange rate when regarded as a heat exchanger.
Degree of supercooling: the difference between the temperature in a refrigerant saturated state and the temperature in a further cooled state (supercooled state).
Effective thermal conductivity: It is the thermal conductivity of the wick in a state where all the pores are impregnated with the liquid.
Gravity loss: Pressure difference due to the height difference between the evaporator and the condenser and gravitational acceleration, unit Pa, zero under zero gravity.
Single-phase region ratio: The ratio of the length of the region of the condenser where the refrigerant is in a supercooled state (liquid single-phase state) to the total length.
Conduction parameter: a factor that determines fin efficiency, in the case of constant thickness plate fins, it is the square root of the ratio of radiation conductance to conduction conductance.
Number of transfer units: ratio of thermal conductance to flow capacitance, unit is dimensionless.
Two-phase region ratio: The ratio of the length of the region of the condenser where the refrigerant is saturated (gas / liquid two-phase state) to the total length.
Two-phase pressure loss coefficient multiplier: The ratio of the pressure loss when flowing in the two-phase state under the same flow rate to the pressure loss when flowing in the single-phase state.
Two-phase heat transfer coefficient multiplication multiplier: The ratio between the heat transfer coefficient when flowing while condensing under the same flow rate and the heat transfer coefficient when flowing without phase change.
Fin efficiency: The ratio of the heat dissipation when considering that the temperature of the radiator panel decreases as it moves away from the feeder (fin route) and the heat dissipation when it is uniform without decreasing.
Porosity: The wick porosity (ratio of the total volume occupied by the holes).
Bond number: Ratio of gravity to capillary force. Under microgravity, condensation becomes unstable when it exceeds a critical value.
Mach number: Ratio of flow velocity to sound velocity.
Capillary pressure head: Maximum capillary pressure (capillary pressure when the contact angle with respect to the pore wall of the liquid meniscus in the wick hole is 0 deg).
Capillary radius: Radius when the wick hole is regarded as a fine cylinder, the generated capillary force is proportional to its reciprocal.

[Glossary of terms (components)]
Here, each component of the loop heat pipe will be described as follows.
Annular space: An annular portion in the evaporator / liquid channel formed between the cylindrical wick and the bayonet tube.
Ambient: The surrounding environment where the evaporator and reservoir are installed.
Wick: Porous material for generating capillary force (first wick) and supplying liquid (second wick). The first wick unless otherwise stated.
Evaporator: An evaporator composed of a liquid channel and a vapor channel.
Condenser: Snake tubular condenser.
Saddle: A heating device mounting plate directly connected to the evaporator.
Subcooler: A part for condenser supercooling.
Steam groove: A groove that forms a steam channel.
Steam channel: Combines all steam grooves.
Liquid channel: Combined annular space and bayonet tube.
Steam port: An accumulation part of generated steam.
Heat sink: Radiation environment of the radiator.
Bionette tube: A circular tube inserted as an extension of the liquid return pipe into the liquid channel, equalizing the liquid temperature in the channel.
Feeder: One meandering segment of a tubular condenser meandered at equal intervals parallel to the width direction of the radiator.
Radiator: A flat radiator that consists of a feeder, fins, and panels.
Reservoir: The liquid supply wick compensates for changes in the liquid distribution in the loop due to the difference between the liquid reservoir connected to the evaporator and liquid channel, and the starting conditions.

[Numeric result]
Next, an embodiment in which the dimensions of each component are determined by applying the LHP design method according to the present invention will be described. That is, hereinafter, the design code created for the LHP having the basic configuration based on the above analysis model will be described. LHP _{is, Q, T v, T S} , T a, when L _VL and L _LL is given as operating conditions, it is possible to sizing. The following were used as design parameter values for the model.
Φ _evap = 0.90
Bo ^* = 10.0
Φ _{vch / VL} = 0.833
q = 10.0kW / m ²
(L ^(a) / L) ^* _evap = 1.0
(W / D) ^* _evap = 4.0
f _H = 10.0
(△ Pwick / △ Pcap) ^* = 0.60
Φ _sub = 0.90
η _F = 0.90
ε _t = 0.85
(△ Pcond / Q) ^* = 1.0Pa / W
(△ PVL / LVL) ^* = 40.0Pa / m
(△ PLL / LLL) ^* = 10.0Pa / m
Δh = Δp _grav / ρ _l g = 0.10m
At this time, the operating conditions are as follows unless otherwise specified.
Ts = 43K
Ta = 313K
L _VL = L _LL = 3.0m
Since it is a general type, the LHP of ammonia refrigerant / titanium powder wick having a double-sided radiator is used for sizing calculation. The numerical results of the calculation are shown in the figure as a graph. Each figure contains two groups of curves to show the results in a compact manner. The thick curve is drawn with respect to the left vertical axis coordinate, while the thin curve is drawn with respect to the right vertical axis coordinate. Since LHP is usually designed for a specific combination of Q and T _v , in FIGS. 6 to 11, Q is taken from 0 W to 800 W with the horizontal axis coordinate, and T _v is taken as a curve identification parameter every 273K to 10K. Up to 333K. FIG. 6 displays the required capillary radius r _c and the desired wick porosity ε _w . As expected, FIG. 6, as Q increases and T _v is increased, highly porous wick indicates that it is required a fine pore diameter. It can be seen from the curves B4 / 5 and F4 / 5 in FIG. 6 that r _C = 2.85 μm and ε _w = 0.354 for a typical design point Q = 300 W and T _v = 308 K. The developed wick has r _c = 1.6 μm to 3.2 μm and ε _w = 0.33. 7 and 8 show the radial / axial dimensions of the LHP. The _{bayonet tube} diameter D _bayo and the _wick inner diameter D _win are displayed in FIG. On the other hand, FIG. 8 shows the thickness δ _{W of the wick} and the length L _{evap of the} evaporator. 7 and 8, it can be seen that the required radial size increases as Q increases and _Tv decreases. At this time, FIG. 8 shows that L _evap changes almost linearly with Q and T _v . This is what results from equations (19a), (20) and (21). Curves B4 / 5 and F4 / 5 in FIGS. 7 and 8 are obtained when Q = 300 W and T _v = 308K.
This _{shows that} D _bayo = 4.0 mm, D _win = _9.7 mm, δ _W = 6.3 mm, and L _evap = 0.34 m.

の場合には
Q’＝0としてモデル化されるので、曲線Ｂ５−７およびＦ５−７は図には現われていない。このように、Q’およびΔT_subはT_vに依存する。図１１の曲線Ｂ１／４およびＦ１／４から推論されるのは、Q＝300KのときにQ’＝6.2WおよびΔT_sub＝5.6Kであり、Q＝300KおよびT_v＝303KのときにQ’＝1.1WおよびΔT_sub＝0.88Kであるということである。 Also required in the LHP evaporator design are the cross-sectional area ratio ε _vch of the vapor channel to the liquid channel and the reservoir volume V _res . FIG. 9 is used to find a suitable combination of these, for example, when Q = 300 W and T _v = 308K, ε _vch = 0.38 and V _res = 0.22l. According to equations (47a) and (47b), the curves in FIG. 9 show that ε _vch and V _res tend to increase as Q increases and T _v decreases. FIG. 10 is for LHP capacitor design and provides the appropriate tube diameter D _cond and the required tube total length L _cond . The values D _cond = 5.4 mm and L _cond = 4.6 m are obtained from the curves B4 / 5 and F4 / 5 in FIG. 10 when Q = 300 W and T _v = 308K. The upward trend of the curve in the figure results from equations (53) and (56). FIG. 11 shows the estimated heat penetration Q ′ and the required degree of subcooling ΔT _sub . Can be found Q 'from the curve B1-4, when T _v> T _a, can be found [Delta] T _sub from the curve F1-4. LHP is

In Case of
Since it is modeled as Q ′ = 0, curves B5-7 and F5-7 do not appear in the figure. Thus, Q ′ and ΔT _sub depend on T _v . Inferred from the curves B1 / 4 and F1 / 4 in FIG. 11 are Q ′ = 6.2 W and ΔT _sub = 5.6 K when Q = 300K, and Q when Q = 300 K and T _v = 303K. '= 1.1 W and ΔT _sub = 0.88K.

In order to specify the characteristics of the wick, FIGS. 12 and 13 show r _c and ε _w in a different way from FIG. The horizontal axis is the length of the steam / liquid pipe when L _FL / 2, not Q, is 0.0 m to 8.0 m and is half the total flow path length. The curve in FIG. 12 shows 50 W, 100 W,. . . , Takes a value of 600W or 800W. Here, the evaporation temperature T _v is fixed as 303 K. Curve B1 / 8 and F1 / 8 in FIG. 12, when the possible range of r _c and epsilon _w is Q = 50 W, 0.35 from 3.0μm and 0.26 from 11.3μm respectively, when Q = 800 W, respectively 1.7 It is shown to be from μm to 1.2 μm and from 0.39 to 0.42. FIG. 13 shows the values of r _c and desirable ε _w required for the eight types of wicks at this time. In the forming structure, fibers, powders, beads or foams are considered, and nickel or titanium are considered as materials. All curves in FIG. 13 are applicable to LHP specified as Q = 300 W and T _v = 313K. Of course, r _c does not depend on the type of wick, but ε _w is very dependent on it. The conclusions drawn from the curves NIPW / TIPW (Nickel Powder / Titanium Powder) and NIFI / TIFI (Nickel Fiber / Titanium Fiber) in FIG. It is necessary.

In actual design, it may be more convenient to take T _v as the primary variable instead of Q. In this case, FIGS. 7-9, is replaced in FIG. 16 from FIG. 14, T _v is taken from 273 in the horizontal axis to 333 K, Q is taken as the curve identification parameter. Use parameter values are the same as in FIG. When roughly estimating the size of LHP, D _bayo and D _wim are _determined from FIG. 14, δ _w and L _evap are determined from FIG. 15, and ε _vch and V _res are determined from FIG. In the first wick design, the important sizing parameters are Φ _evap because δ _w and L _evap depend on R _w in the manner defined by equations (19a), (19b), (20) and (21). It is. Thus, FIG. 17 _displays δ _w and L _evap as a function of Φ _evap with a possible range from 0.78 to 0.98. At this time, the curve is drawn under the condition of Q = 50 W, 100 W or 500 W and T _v = 313K. The two groups of curves in FIG. 17 show that thicker and slightly shorter _wicks are needed to increase the Φ _evap value, and δ _w and L _evap naturally increase as Q is increased. Show. Considering the case of Q = 300 W in FIG. 17, this is, [delta] _w from it curves B4 is 6.8mm from 5.5 mm, L _evap is understood that it is 0.32m from the curve F4 from 0.37 m.

ならばQ’＝0であるという計算モデルによるものである。このとき、図１９は、必要とされるコンデンサ管径D_condおよび必要とされる全コンデンサ長L_condを示す。この図からわかることは、T_aおよびT_vの上昇と共にD_condおよびL_condの両方が減少することである。この下降傾向は、式（４２）、（５１）、（５２ａ）、（５２ｂ）および（５３）はΔT_subが大きくなるときにD_cond/D_LLを小さくするように半径をサイジングした結果として生じるものである。しかしながら、式（５６）のQ＋Q’のために、L_condの上昇傾向が、熱侵入が我々の推定よりかなり大きい場合に現れることもある。 Since LHP obtains heat at a rate calculated from equation (39), it is very important to understand the effect of ambient temperature on LHP design. Q = 300W and T _v = 283K, 293K,. . . 18 or 19 conceptually shows the degree of the influence obtained under the condition of 333K. Here, the curve is drawn with respect to T _a in the range of 323K from 283 K. FIG. 18 shows the required degree of subcooling ΔT _sub and the resulting pump efficiency η _P. From FIG. 18, it can be seen that as T _a increases and T _v decreases, η _P decreases while ΔT _sub increases. It can also be seen from the figure that ΔT _sub = 0.0K when T _v = 323K or 333K. this is,

Then, it is based on the calculation model that Q ′ = 0. At this time, FIG. 19 shows the required capacitor tube diameter D _cond and the required total capacitor length L _cond . It can be seen from this figure that both the D _cond and L _cond decreases with increasing T _a and T _v. This downward trend occurs as a result of sizing the radius so that D _cond / D _LL is reduced when ΔT _sub is increased in equations (42), (51), (52a), (52b) and (53). Is. However, because of Q + Q ′ in equation (56), the upward trend in L _cond may appear when the heat penetration is significantly greater than our estimate.

(A1b)

(A2a)

(A2b)

(A2_C)

(A3a)

(A3b)

(A4a)

(A4b)

(A5a)

(A5b)

(A6a)

(A6b)

(A7a)

(A7b)

(A8a)

(A8b)

(A9)

[付録Ｂ]実効熱伝導率
(B1a)

(B1b)

(B2a)

(B2b)

(B3)

(B4)

(B5)

[付録Ｃ]質量モデル
(C1a)

(C1b)

(C1c)

(C1d)

(C2a)

(C2b)

(C2c)

(C2d)

(C2e)

(C3a)

(C3b)

[Appendix A] Coefficient representation
(A1a)

(A1b)

(A2a)

(A2b)

(A2 _C )

(A3a)

(A3b)

(A4a)

(A4b)

(A5a)

(A5b)

(A6a)

(A6b)

(A7a)

(A7b)

(A8a)

(A8b)

(A9)

[Appendix B] Effective thermal conductivity
(B1a)

(B1b)

(B2a)

(B2b)

(B3)

(B4)

(B5)

[Appendix C] Mass Model
(C1a)

(C1b)

(C1c)

(C1d)

(C2a)

(C2b)

(C2c)

(C2d)

(C2e)

(C3a)

(C3b)

It is the figure which showed the structure of the general loop heat pipe as a cross section of the axial direction of an evaporator. It is the figure which showed the cross section of the radial direction of an evaporator. It is the figure which showed each cross section of the radiator. It is the figure which showed the external appearance of the structure of a general loop heat pipe. It is the figure which showed the flow of the design of the loop heat pipe which concerns on one Embodiment of this invention. Is a graph showing the capillary radius and porosity of the wick relative to the thermal load _{(# B / F1: T v} = 273K, # B / F2: T v = 283K, ···, # B / F7: T v = 333K ( 10K step)). Is a graph showing the bayonet tube diameter and wick inside diameter to thermal loads _{(# B / F1: T v} = 273K, # B / F2: T v = 283K, ···, # B / F7: T v = 333K (10K step)). Is a graph showing the thickness and length of the evaporator wick to thermal loads _{(# B / F1: T v} = 273K, # B / F2: T v = 283K, ···, # B / F7: T v = 333K (10K steps)). Vapor / liquid channel cross-sectional area ratio against thermal load and is a graph showing the reservoir volume _{(# B / F1: T v} = 273K, # B / F2: T v = 283K, ···, # B / F7: T _v = 333K (10K steps)). Is a graph showing the capacitor tube diameter and condenser length to thermal load _{(# B / F1: T v} = 273K, # B / F2: T v = 283K, ···, # B / F7: T v = 333K ( 10K step)). Is a graph showing the heat intrusion and supercooling degree from the reservoir to heat the load _{(# B / F1: T v} = 273K, # B / F2: T v = 283K, ···, # B / F7: T v = 333K (10K steps)). It is the graph which showed the capillary radius and porosity of the wick with respect to the length of a vapor tube / liquid tube (# B / F1: Q = 50W: # B / F2: Q = 100W, ..., # B / F7: Q = 600 W (100 W step), # B / F8: Q = 800 W). FIG. 4 is a graph showing the capillary radius and porosity of a wick against the length of a vapor tube / liquid tube (NI / TIFI: Ni / Ti fiber, NI / TIPW: Ni / Ti powder, NI / TIBD: Ni / Ti beads, NI / TIFO: Ni / Ti Foum). It is the graph which showed the bayonet tube diameter with respect to steam temperature, and a wick internal diameter (# B / F1: Q = 50W, # B / F2: Q = 100W, ..., # B / F7: Q = 600W (100W step) ), # B / F8: Q = 800 W). It is the graph which showed the wick thickness with respect to steam temperature, and the evaporator length (# B / F1: Q = 50W, # B / F2: Q = 100W, ..., # B / F7: Q = 600W (100W step) # B / F8: Q = 800 W). It is the graph which showed the vapor / liquid channel cross-sectional area ratio with respect to vapor | steam temperature, and a reservoir volume (# B / F1: Q = 50W, # B / F2: Q = 100W, ..., # B / F7: Q = 600W) (100 W step), # B / F8: Q = 800 W). It is the graph which showed the wick thickness with respect to evaporator temperature efficiency, and the evaporator length (# B / F1: Q = 50W, # B / F2: Q = 100W, ..., # B / F6: Q = 500W (100W step) )). A supercooling degree and graph showing pump efficiency for ambient temperature _{(# B / F1: T v} = 283K, # B / F2: T v = 293K, ···, # B / F6: T v = 333K ( 10K step)). It is a graph showing the condenser tube diameter and condenser length with respect to ambient temperature (# B / F1: T _v = 283K, # B / F2: T _v = 293K,..., # B / F6: T _v = 333K ( 10K step)).

Explanation of symbols

100 evaporator 110 saddle 120 steam groove 130 steam port 140 annular space 150 steam pipe 160 first wick 170 second wick 180 reservoir 190 bayonet pipe 200 radiator 210 subcooler / condenser 220 liquid pipe 230 feeder 240 fin

Claims (3)

An evaporator having a tubular wick disposed therein, a reservoir located inside the wick, a serpentine condenser subcooler that dissipates and condenses refrigerant vapor, a radiator that disposes the condenser subcooler, and steam from the evaporator A steam pipe for sending the refrigerant liquid to the condenser subcooler, a liquid pipe for transferring the refrigerant liquid condensed and radiated by the condenser subcooler to the reservoir, and extending from the liquid pipe into the reservoir In a loop heat pipe composed of a bayonet tube having an opening, a method for calculating the ratio between the outer diameter and inner diameter of the evaporator wick,
The evaporator shows the ratio of the evaporator axial temperature difference, which is the difference between the evaporator liquid tube side temperature and the steam pipe side temperature, to the evaporator radial temperature difference, which is the difference between the bayonet tube temperature and the wick outer diameter temperature. Calculating the number of transmission units as the negative of the natural logarithm of the value obtained by subtracting the temperature efficiency of 1 from
The radial conductance of the evaporator is obtained from the temperature gradient at the wick inner diameter of the radial temperature distribution obtained as a solution to the energy equation for heat conduction and liquid permeation of the wick, and the number of evaporator transmission units and the wick of the wick determined from the radial conductance are obtained. From the relational expression of the ratio of the outer diameter to the inner diameter and the relational expression that the power of the radial distance of the wick appearing in the solution of the energy equation is the reciprocal of the number of transmission units when the evaporator is regarded as a heat exchanger. And a step of calculating a ratio of the outer diameter and the inner diameter. An evaporator having a tubular wick disposed therein, a reservoir located inside the wick, a serpentine condenser subcooler that dissipates and condenses refrigerant vapor, a radiator that places the condenser subcooler therein, and a vapor from the evaporator A steam pipe for sending the refrigerant liquid to the condenser subcooler, a liquid pipe for releasing the refrigerant liquid condensed by the condenser subcooler, and a supercooled refrigerant liquid to the reservoir, and extending from the liquid pipe into the reservoir In a loop heat pipe composed of a bayonet tube having an opening, a method for calculating a porosity indicating the porosity of an evaporator wick,
Capillary radius of wick, wick capillary head, ratio of wick pressure loss to capillary pressure head, liquid constant pressure specific heat, liquid viscosity coefficient indicating the ratio between viscosity coefficient and density of saturated liquid, evaporator liquid side temperature and steam Evaporator temperature efficiency indicating the ratio of the evaporator axial temperature difference, which is the difference from the pipe side temperature, to the evaporator radial temperature difference, which is the difference between the temperature of the bayonet tube and the outer diameter of the wick, is given as a set value. In the state
The method
Calculating the number of transmission units as the negative of the natural logarithm of the value obtained by subtracting the temperature efficiency of the evaporator from 1;
The radial conductance of the evaporator is obtained from the temperature gradient at the wick inner diameter of the radial temperature distribution obtained as a solution of the energy equation for heat conduction and liquid permeation of the wick, and the number of evaporator transmission units and the wick obtained from the radial conductance are obtained. From the relational expression of the ratio of the outer diameter and the inner diameter of the wick, and the relational expression that the power of the radial distance of the wick appearing in the solution of the energy equation is the reciprocal of the number of transmission units when the evaporator is regarded as a heat exchanger. Calculating the ratio of the outer diameter to the inner diameter of the wick;
The ratio of the outer diameter and inner diameter of the wick, the number of the transmission units, the constant fluid pressure specific heat, the fluid dynamic viscosity coefficient, the ratio between the wick pressure loss and the capillary pressure head, and the thermal conductivity and liquid permeability of the wick determined from the capillary pressure head. The step of calculating the porosity of the wick so that the calculated value of the ratio of the thermal conductivity of the wick determined by the physical properties and structure of the wick material and the ratio of the liquid permeability is equal,
The relationship between the capillary radius and porosity of the wick, which is determined based on the wick formation structure, and the liquid permeability specific to the wick material,
The relationship between the thermal conductivity of the wick and the porosity and the effective thermal conductivity of the wick, determined based on the wick formation structure,
The relationship between the ratio between the wick shape correction liquid permeability and the effective thermal conductivity of the wick and the ratio between the wick capillary radius and the wick outer diameter and inner diameter, determined from the correlation between the wick thermal conductivity and the liquid permeation. Calculating a wick porosity from the method. An evaporator having a tubular wick disposed therein, a reservoir located inside the wick, a serpentine condenser subcooler that dissipates and condenses refrigerant vapor, a radiator that disposes the condenser subcooler, and steam from the evaporator A steam pipe for sending the refrigerant liquid to the condenser subcooler, a liquid pipe for releasing the refrigerant liquid condensed by the condenser subcooler, and a supercooled refrigerant liquid to the reservoir, and extending from the liquid pipe into the reservoir In a loop heat pipe composed of a bayonet tube having an opening, loop heat from a predetermined operating condition specified as a design specification of the loop heat pipe and a predetermined design parameter given as a set value based on the design specification A method for calculating the dimensions of each component of a pipe.
The dimensions of each of the constituent elements are as follows: vapor pipe diameter, liquid pipe diameter, bayonet pipe diameter, wick inner diameter, wick outer diameter, wick thickness, a vapor channel that is a refrigerant vapor passage and a liquid channel that is a refrigerant liquid passage. Cross-sectional area ratio, evaporator length, wick capillary radius, porosity indicating wick porosity, condenser subcooler tube diameter, condenser subcooler length, reservoir volume, reservoir diameter, radiator area, feeder half-spacing The thickness of the fins,
The predetermined operating conditions include the heat load on the evaporator, the steam temperature, the ambient temperature that is the ambient temperature of the evaporator and the reservoir, the heat sink temperature that is the heat dissipation environment temperature of the radiator, the steam path length, the liquid path length, the evaporator and the condenser The height difference between and the values of gravity acceleration are specified,
The predetermined design parameter is the difference between the temperature of the bayonet tube and the outer diameter temperature of the wick of the evaporator axial temperature difference, which is the difference between the liquid pipe side temperature and the vapor pipe side temperature of the evaporator. Evaporator temperature efficiency indicating the ratio to temperature difference, critical bond number indicating the ratio of gravity to stable capillary force to capillary force, cross-sectional area ratio of steam channel and steam tube, and design margin of loop pressure loss in determining the maximum capillary pressure of wick Capillary crush factor, heat load per unit area on the evaporator, the ratio of the evaporator's effective length to the total length, the ratio of the evaporator saddle width to the wick outer diameter, the location of the evaporator Thermal conductance between ambient ambient and wick, per unit length of steam path Vapor path pressure loss gradient indicating the loss, liquid pressure loss gradient indicating the pressure loss per unit length of the liquid path, condenser pressure loss ratio indicating the pressure loss per unit exhaust heat amount of the condenser, ratio of wick pressure loss to capillary pressure head, subcooler Subcooler temperature efficiency, which indicates the ratio of the radial temperature difference that is the difference between the subcooler inlet liquid temperature and the tube wall temperature to the subcooler axial temperature difference that is the difference between the inlet liquid temperature and the outlet liquid temperature, reservoir Used for heat dissipation of both the front and back sides of the radiator panel, the volume ratio of the liquid at the time of cold start in the reservoir indicating the ratio of the refrigerant liquid in the tank, the volume ratio of the steam at the high temperature start-up in the reservoir indicating the ratio of the refrigerant vapor in the reservoir Heat dissipation when considering the effective area ratio of the radiator that shows the possible ratio, and that the temperature of the radiator panel decreases with increasing distance from the fin root And each value given radiator fin efficiency indicating a ratio of the heat radiation amount if,
Vapor specific heat ratio indicating the ratio of the saturated vapor pressure at a given temperature of the refrigerant, the pressure gradient that is the temperature differential coefficient of the saturated vapor pressure curve, the vapor density, and the constant vapor specific heat and the constant vapor specific heat using the refrigerant physical property calculation formula. In a state where the vapor viscosity coefficient, liquid density, liquid constant pressure specific heat, liquid viscosity coefficient, liquid dynamic viscosity coefficient indicating the ratio of saturated liquid viscosity coefficient and density, liquid surface tension, and latent heat of vaporization are calculated.
The method
Steam pipe diameter, liquid pipe diameter, bayonet pipe diameter, wick based on heat load, steam pipe pressure drop slope, liquid pipe pressure drop slope, critical number of bonds, evaporator temperature efficiency, and cross-sectional area ratio between steam channel and steam pipe Evaporator radial sizing step to calculate inner diameter, wick outer diameter, wick thickness, and cross-sectional area ratio of vapor channel and liquid channel;
An axial sizing step of the evaporator that calculates the evaporator length based on the thermal load, the ratio between the effective length and total length of the evaporator, the ratio between the saddle width and the wick outer diameter, and the thermal load per unit area;
A step of calculating a loop pressure loss including the pressure loss due to the steam path, liquid path, condenser, evaporator, port, and fitting of the loop heat pipe, and
A wick characterization step that calculates the capillary radius and porosity based on the elevation difference between the evaporator and the capacitor, gravitational acceleration, capillary crest factor, and the ratio of wick pressure drop to capillary crest;
Based on heat load, ambient temperature, condenser pressure loss rate, subcooler temperature efficiency, cold start liquid volume ratio in the reservoir, and hot start steam volume ratio in the reservoir, condenser tube diameter, condenser subcooler length, reservoir A capacitor and reservoir sizing step to calculate the volume of the reservoir, the reservoir diameter, and the reservoir length;
Radiator sizing step to calculate radiator area, feeder half-space, and fin thickness based on heat load, steam temperature, heat sink temperature, radiator area ratio, and radiator fin efficiency And
In the radial sizing step of the evaporator,
The steam pipe diameter is calculated from the relationship between the steam viscosity coefficient, the steam density, the latent heat of vaporization, the heat load, and the steam path pressure drop gradient when the steam pipe flow is turbulent.
The liquid pipe diameter is calculated from the relationship between the liquid kinematic viscosity coefficient, latent heat of vaporization, heat load, and liquid pressure loss gradient when the flow of the liquid pipe is assumed to be laminar.
The bayonet tube diameter is calculated as being the same as the liquid tube diameter,
The wick inner diameter is calculated by adding the full width of the annular space of the liquid channel determined by the critical bond number, liquid surface tension, liquid density, vapor density, and gravitational acceleration, and the bayonet tube diameter,
The wick outer diameter is calculated by converting the evaporator temperature efficiency into the number of transmission units and multiplying the ratio of the outer diameter and inner diameter of the wick determined by the number of transmission units by the inner diameter of the wick,
The wick thickness is calculated as the value obtained by subtracting 1 from the wick outer diameter to inner diameter ratio multiplied by the wick inner diameter and dividing by two.
The cross-sectional area ratio of the liquid channel to the steam channel is calculated as a value obtained by dividing the square of the value obtained by dividing the steam pipe diameter by the wick inner diameter by the area ratio of the steam channel and the steam pipe,
In the axial sizing step of the evaporator,
The evaporator length is the heat per unit length of the evaporator multiplied by the ratio of the evaporator saddle width to the wick outer diameter, the ratio of the evaporator effective length to the total length, the wick outer diameter and the heat load per unit area. Calculated as the value divided by the load,
In the step of calculating the loop pressure loss,
Steam path pressure loss is calculated by multiplying the steam path pressure loss gradient and the steam path length,
The fluid pressure loss is calculated by multiplying the fluid pressure loss gradient by the fluid path length,
Capacitor pressure loss is the value obtained by subtracting the steam temperature from the ambient temperature and the thermal conductance between the ambient and the wick multiplied by the intrusion heat from the reservoir plus the heat load on the evaporator. Calculated by multiplying,
The evaporator pressure loss is proportional to the evaporator pressure loss coefficient determined from the ratio of the cross-sectional area of the steam channel to the steam tube and the ratio of the bayonet tube to the wick inner diameter, inversely proportional to the fourth power of the bayonet tube diameter, and proportional to the square of the heat load. , Proportional to the value obtained by dividing the liquid kinematic coefficient by the latent heat of vaporization, proportional to the square of the thermal load, and calculated from the relationship inversely proportional to the thermal load per unit length of the evaporator,
The port pressure loss is a value obtained by squaring the steam port pressure loss coefficient determined from the cross-sectional area ratio of the steam channel and the steam pipe, the critical Mach number that is 1/1000 of the cross-sectional area ratio of the liquid channel to the steam channel, and the steam specific heat ratio. And half the value obtained by multiplying the saturated vapor pressure,
Fitting pressure loss is determined from the cross-sectional area ratio of the condenser and the liquid pipe to the value obtained by dividing the steam fitting pressure loss coefficient determined from the cross-sectional area ratio of the steam pipe and the condenser by the value obtained by multiplying the vapor density by the fourth power of the steam pipe diameter. Vaporization of heat load is proportional to the sum of the value obtained by multiplying the liquid fitting pressure loss coefficient by the square of the cross-section change factor at the condenser outlet and the liquid density multiplied by the fourth power of the liquid pipe diameter. Calculated from the relationship that is proportional to the square of the value divided by the latent heat,
The loop pressure loss is calculated by adding the vapor path pressure loss, the liquid path pressure loss, the condenser pressure loss, the evaporator pressure loss, the port pressure loss, and the fitting pressure loss,
In the wick property specifying step,
The wick capillary radius is proportional to the liquid surface tension, is proportional to the ratio of the wick pressure drop to the capillary pressure head minus 1, and is multiplied by the capillary pressure head factor and the loop pressure drop between the evaporator and the capacitor. Calculate from the relationship proportional to the value obtained by adding the gravity loss determined from the height difference,
Wick's porosity is
Analytical values of the number of transmission units, liquid constant pressure specific heat, fluid dynamic viscosity coefficient, ratio of wick pressure loss to capillary pressure head, and ratio of thermal conductivity and liquid permeability of wick determined from capillary pressure head, physical properties of wick material and The calculated value of the ratio of thermal conductivity and liquid permeability of the wick determined from the structure is equal.
The relationship between the capillary radius and porosity of the wick, which is determined based on the wick formation structure, and the liquid permeability specific to the wick material,
The relationship between the thermal conductivity of the wick and the porosity and the effective thermal conductivity of the wick, determined based on the wick formation structure,
The relationship between the ratio between the wick shape correction liquid permeability and the wick effective thermal conductivity, the wick capillary radius, and the ratio between the wick outer diameter and the inner diameter, determined from the correlation between wick heat conduction and liquid permeation. Calculated from
In the sizing step of the capacitor and reservoir,
The value obtained by dividing the value obtained by adding the gravity loss to the value obtained by multiplying the capillary pressure head factor and the loop pressure loss by the pressure gradient at the steam temperature is obtained, and the value obtained by dividing the latent heat of vaporization by the specific heat of the liquid constant pressure is obtained. Add the temperature difference in the wick radial direction and multiply the value by the value obtained by dividing the intrusion heat from the reservoir by the heat load to obtain the degree of supercooling, and multiply the latent heat of vaporization by the liquid constant pressure specific heat by the supercooling degree of the subcooler. The ratio of the latent heat and the sensible heat is obtained by dividing by the obtained value, and the value obtained by multiplying the ratio of the latent heat and the sensible heat by the subcooler temperature efficiency is a two-phase heat transfer coefficient multiplication multiplier determined from the density ratio of the steam and liquid. By dividing the value obtained by adding 1 to the temperature efficiency of the subcooler and the natural logarithm of the value obtained by adding 1 to the temperature efficiency of the subcooler, the area ratio between the two phases of the capacitor and the single phase is obtained. The tube diameter of the subcooler is determined by multiplying the vapor pipe diameter by the two-phase area ratio determined from the two-phase and single-phase area ratio of the capacitor and the single-phase area ratio determined from the two-phase and single-phase area ratio of the capacitor. Is calculated by adding the value obtained by multiplying the liquid pipe diameter by
The steam pipe flow is turbulent and the liquid pipe flow is laminar, and the steam pressure loss and liquid area are determined from the steam viscosity coefficient, steam density, liquid dynamic viscosity coefficient, latent heat of vaporization, heat load, and condenser subcooler pipe diameter. Determine the ratio of pressure loss. The length of the condenser / subcooler is proportional to the condenser pressure loss ratio and inversely proportional to the liquid path pressure drop gradient, and the condenser / subcooler pipe diameter is divided by the steam pipe diameter. Proportional to the fourth power of the measured value, proportional to the value obtained by adding the intrusion heat from the reservoir to the heat load, the average two-phase friction coefficient multiplication multiplier, the ratio of the two-phase region, and the ratio of the vapor region pressure loss to the liquid region pressure loss. Calculated from the relationship that the multiplied value is inversely proportional to the single-phase region ratio and the added value,
The volume of the reservoir is the sum of the condenser volume determined from the length of the condenser / subcooler and the condenser / subcooler pipe diameter and the steam pipe volume determined from the steam pipe diameter, and the liquid volume ratio at low temperature startup and steam volume at high temperature startup. Calculate by adding the rate and multiplying it by the value subtracted from 1.
The reservoir diameter is calculated from the volume of the reservoir to minimize the surface area,
The reservoir length is calculated as the same value as the reservoir diameter,
In the sizing step of the radiator,
The fin root temperature is determined by subtracting the subcooler supercooling degree from the value obtained by adding 1 to the reciprocal of the subcooler's temperature efficiency, and subtracting it from the saturated steam temperature. Calculated from the relationship that is proportional to the value obtained by adding the intrusion heat and inversely proportional to the value obtained by multiplying the effective area ratio of the radiator, the radiator fin efficiency, the radiant heat transfer coefficient, and the value obtained by subtracting the heat sink temperature from the fin root temperature. And
The half-interval of the feeder is calculated as the value obtained by dividing the area of the radiator by twice the length of the capacitor / subcooler,
The thickness of the fin is inversely proportional to the thermal conductivity of the fin, proportional to the effective area ratio of the radiator, proportional to the radiant heat transfer coefficient, and the square of the value obtained by dividing the feeder half-space by the fin conduction parameter determined from the fin efficiency. A method characterized by being calculated from a relationship proportional to

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