3. Loop heat pipe

Loop heat pipe was developed to overcome the inherent problem of incorporating a long wick with small pore radius in conventional heat pipe by Gerasimov and Maydanik in 1972. LHP is a two-phase heat transfer device that utilizes the evaporation and condensation of a working fluid to remove heat and the capillary forces developed in fine porous wicks to circulate the fluid. Figure 2 shows schema of LHP. It consists of an evaporator with wick structure, a compensation chamber, a condenser, and a liquid and vapor line. Wick structure is only in the evaporator and the compensation chamber. The rest parts of the LHP are made of smooth wall pipe. The wick structure of the evaporator has fine pores to create a capillary pressure and ensure working fluid circulation in the loop. The wick structure of the compensation chamber has larger pores for the purpose to transport working fluid to the evaporator. Heat applied to the evaporator causes that working fluid to start to evaporate and the vapor is pushed through the vapor line to the condenser due the capillary forces in the evaporator wick. Vapor condenses in the condenser and the liquid flows through the liquid line to the compensation chamber. The function of the compensation chamber is to store excess liquid and to control the operating temperature of the loop heat pipe. Thus, working fluid circulates without external pump in the loop [8, 9].

LHP can operate only if the capillary pressure developed in the evaporator wick is greater than the total pressure drop in the loop. The total pressure drop in the loop heat pipe is the sum of frictional pressure drops in the evaporator grooves, the vapor line, the condenser, the liquid line, the evaporator wick, and static pressure drop due to gravity:

$$
\Delta P\_{\text{total}} = \Delta P\_{\text{grove}} + \Delta P\_{\text{vap}} + \Delta P\_{\text{con}} + \Delta P\_{\text{liq}} + \Delta P\_w + \Delta P\_g \tag{4}
$$

The capillary pressure of the evaporator wick is given by expression

$$
\Delta P\_{cap} = \frac{2\sigma.\cos\theta}{R} \tag{5}
$$

Williams and Harris [11] investigated the in-plane and cross-plane properties of step-graded metal felt wicks for heat pipe applications. Porosity, effective pore radius, and liquid permeability were determined using imbibition, capillary flow porometry, and pressure-flow rate data, respectively. The authors determined that many of the correlations in the literature for pore size and permeability are too general in nature, echoing the conclusions of Bonnefoy and

Holley and Faghri [13] outlined methods for permeability and effective pore radius measure-

Typically, the rate-of-rise test requires observing the liquid front as it rises in a dry wick partially immersed in a liquid pool. As the precise location of this front can be difficult to detect, the authors devised a method using mass uptake rather than the meniscus front to determine the rate-of-rise of liquid in the wick. By analyzing the climbing meniscus, the authors developed a series of equations which could be used to numerically reduce the mass

Several relationships for permeability can be found, the most common is the Blake-Kozeny

vε3 37:5 1ð Þ � ε

<sup>2</sup> (8)

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147

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<sup>K</sup> <sup>¼</sup> <sup>r</sup><sup>2</sup>

equation [14, 15], which gives the permeability of a bed of packed spheres as

Ochterbeck [12] in regard to effective thermal conductivity.

uptake data to yield permeability and pore size results.

where, K is permeability, rp is pore radius, and ε is porosity.

ments based on the rate-of-rise test.

Figure 2. Schema of loop heat pipe.

where, σ is the surface tension of the working fluid, θ is the contact angle between the liquid and the wick, and R is the radius of curvature of the meniscus in the wick. Increasing the heat load to the evaporator increases the mass flow rate and the total pressure drop in the system. The reaction to it, is the decrease of radius of curvature of the meniscus so that a capillary pressure will be higher than the pressure drop of total system. Increasing the heat load will decrease radius of curvature of the meniscus until the pore radius of the wick. The maximum capillary pumping capability of the wick is given by expression.

$$
\Delta P\_{cap,\max} = \frac{2\sigma.\cos\theta}{R\_v} \tag{6}
$$

Further increase of the heat load will lead to vapor penetration through the wick and system deprime. Thus, under normal operation, the following condition must be satisfied at all times [10]:

$$
\Delta P\_{\text{total}} \le \Delta P\_{\text{cap}} \tag{7}
$$

Figure 2. Schema of loop heat pipe.

3. Loop heat pipe

146 Porosity - Process, Technologies and Applications

external pump in the loop [8, 9].

Loop heat pipe was developed to overcome the inherent problem of incorporating a long wick with small pore radius in conventional heat pipe by Gerasimov and Maydanik in 1972. LHP is a two-phase heat transfer device that utilizes the evaporation and condensation of a working fluid to remove heat and the capillary forces developed in fine porous wicks to circulate the fluid. Figure 2 shows schema of LHP. It consists of an evaporator with wick structure, a compensation chamber, a condenser, and a liquid and vapor line. Wick structure is only in the evaporator and the compensation chamber. The rest parts of the LHP are made of smooth wall pipe. The wick structure of the evaporator has fine pores to create a capillary pressure and ensure working fluid circulation in the loop. The wick structure of the compensation chamber has larger pores for the purpose to transport working fluid to the evaporator. Heat applied to the evaporator causes that working fluid to start to evaporate and the vapor is pushed through the vapor line to the condenser due the capillary forces in the evaporator wick. Vapor condenses in the condenser and the liquid flows through the liquid line to the compensation chamber. The function of the compensation chamber is to store excess liquid and to control the operating temperature of the loop heat pipe. Thus, working fluid circulates without

LHP can operate only if the capillary pressure developed in the evaporator wick is greater than the total pressure drop in the loop. The total pressure drop in the loop heat pipe is the sum of frictional pressure drops in the evaporator grooves, the vapor line, the condenser, the liquid

<sup>Δ</sup>Pcap <sup>¼</sup> <sup>2</sup>σ: cos <sup>θ</sup>

where, σ is the surface tension of the working fluid, θ is the contact angle between the liquid and the wick, and R is the radius of curvature of the meniscus in the wick. Increasing the heat load to the evaporator increases the mass flow rate and the total pressure drop in the system. The reaction to it, is the decrease of radius of curvature of the meniscus so that a capillary pressure will be higher than the pressure drop of total system. Increasing the heat load will decrease radius of curvature of the meniscus until the pore radius of the wick. The maximum

<sup>Δ</sup>Pcap,max <sup>¼</sup> <sup>2</sup>σ: cos <sup>θ</sup>

Further increase of the heat load will lead to vapor penetration through the wick and system deprime. Thus, under normal operation, the following condition must be satisfied at all times [10]:

Rv

ΔPtotal ¼ ΔPgrove þ ΔPvap þ ΔPcon þ ΔPliq þ ΔPw þ ΔPg (4)

<sup>R</sup> (5)

ΔPtotal ≤ ΔPcap (7)

(6)

line, the evaporator wick, and static pressure drop due to gravity:

The capillary pressure of the evaporator wick is given by expression

capillary pumping capability of the wick is given by expression.

Williams and Harris [11] investigated the in-plane and cross-plane properties of step-graded metal felt wicks for heat pipe applications. Porosity, effective pore radius, and liquid permeability were determined using imbibition, capillary flow porometry, and pressure-flow rate data, respectively. The authors determined that many of the correlations in the literature for pore size and permeability are too general in nature, echoing the conclusions of Bonnefoy and Ochterbeck [12] in regard to effective thermal conductivity.

Holley and Faghri [13] outlined methods for permeability and effective pore radius measurements based on the rate-of-rise test.

Typically, the rate-of-rise test requires observing the liquid front as it rises in a dry wick partially immersed in a liquid pool. As the precise location of this front can be difficult to detect, the authors devised a method using mass uptake rather than the meniscus front to determine the rate-of-rise of liquid in the wick. By analyzing the climbing meniscus, the authors developed a series of equations which could be used to numerically reduce the mass uptake data to yield permeability and pore size results.

Several relationships for permeability can be found, the most common is the Blake-Kozeny equation [14, 15], which gives the permeability of a bed of packed spheres as

$$K = \frac{r\_v^2 \varepsilon^3}{37.5(1 - \varepsilon)^2} \tag{8}$$

where, K is permeability, rp is pore radius, and ε is porosity.

Ren and Wu [16] modeled the effect of wick effective thermal conductivity in LHP evaporators; a two-dimensional axisymmetric model was developed yielding results in agreement with the literature in some respects, namely the position of the liquid front in relation to a heated fin [17, 18].

Zhao and Liao [18] presented temperature profiles indicating decreasing heat leak for increasing heat flux in a bed of packed spheres.

Iverson et al. [19] studied heat and mass transport in sintered copper wick structures. Wick samples were mounted vertically with the lower section immersed in a pool of water. A heater mounted to the back face of the wick applied power to the sample and the resulting temperature gradients were measured along with the mass flow rate of working fluid.

The majority of heat load is used in vaporization on the outer surface of wick [20]. The rest of heat input (called "heat leak") is conducted across the wick and is proportional to the effective thermal conductivity (ETC) of the capillary wicks [21]. Lower thermal conductivity of the porous wick ensures lesser heat conduction to the liquid inside the wick inner surface and maintains the operating temperature and thus the thermal resistance of the whole LHP.

Ku [10] and Furukawa [22] developed simplest LHP heat leak model that utilizes conductance parameter which varies with geometry and operating conditions.

$$Q\_{\mathfrak{e},cc} = G\_{\mathfrak{e},cc}(T\_{\mathfrak{e}} - T\_{cc}) \tag{9}$$

where Qleak is heat leak power, keff is effective thermal conductivity, A is area, L is characteristic length, Nu is Nusselt number, kf is fluid thermal conductivity, and ς represents a non-

> <sup>ς</sup> <sup>¼</sup> <sup>m</sup> : cp

In his analysis and experiment, Chuang assumed this parameter to be zero, i.e., pure conduction. For the low power cases studied, this assumption was valid and resulted in low error; however, for high power levels or low wick conductivity, this assumption loses validity.

Wick structure is one of the main parts of loop heat pipe. To achieve good heat transfer ability of the LHP, wick structure with high porosity and permeability and fine pore radius is expected. The most frequently used wick structures in loop heat pipe are made of sintered metals, such as cooper, nickel, stainless steel, titanium or polymers (polypropylene, polyethyl-

Reimbrechta et al. used a tap powder sintering technique by using a graphite matrix, to manufacture Ni wicks for capillary pump applications [27]. It shows that the graphite has low interaction with nickel by sintering the nickel powders at common sintering temperatures. Combination of two different methods, the cold-pressing sintering and the direct loose sintering, was used by Gongming et al. [28], for development of Ni and Ni-Cu (90% nickel and 10% copper) wicks for loop heat pipes. They found that using direct loose sintering technique with mean pore radii of 0.54 μm, an optimal Ni-Cu wick structure is prepared. Huang and Franchi [29] used copper screen mesh and two powder materials (nickel filamentary powder and spherical copper powder) to manufacture of bimodal wick structure. But it showed that these wicks may be produced with failures. Samanta et al. [30] developed metal injection molding Ni wick structures and performed study on its physical characteristic depending on sintering time (30, 60, and 90 min) and temperature (900, 930, and 950�C). Gernert et al. [31] developed fine pore wick structure for LPH. Wu et al. [32] discussed about the effect of sintering temperature curve in wick structure manufactured for LHP. Launay et al. referred a porosity, pore diameter, and permeability as the main parameters of wick structure in the work [20]. There is the optimal porosity of sintered wick referred between 30 and 75%,

wick structure decreases when the sintering temperature or the forming pressure increases. Majority of the sintered porous materials has pore diameters between 1 and 20 μm, except

In Ref. [33], the optimal capillary wick was found to be sintered at 650�C for 30 min, using direct loose sintering technique, with 90% nickel and 10% copper. The wick reaches the porosity of 70% and a mean pore diameter of 1.8 μm. In Ref. [10], biporous nickel wicks were fabricated. A porosity of 77.4% was achieved using cold pressure sintering method, at a

and the optimal permeability referred between 10�<sup>14</sup> and 3 � <sup>10</sup>�<sup>13</sup> m2

copper, which has pore diameters between 20 and 1000 μm.

temperature of 700�C, with a pore former content of 30% in volume.

<sup>2</sup>πkeff <sup>L</sup> (13)

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. The porosity of the

dimensional ratio of advection and conduction given by

3.1. LHP wick structure

ene, PTFE) [24–26].

where Q is power, G is conductance parameter, and T is temperature of the evaporator and compensation chamber.

In steady state operation, the heat leak to the compensation chamber must be offset by the liquid returning from the condenser; Eq. (7) results, where ΔT represents the subcooling of the returning fluid

$$Q\_{e,cc} = \dot{m}c\_p \Delta T \tag{10}$$

where m is mass flow and cp is specific heat.

Chuang [23] developed a steady state LHP model which breaks the overall heat leak into two separate components: axially from the evaporator to the compensation chamber and radially from the heat source to the evaporator core. These two effects are related in that the formation of vapor bubbles in the evaporator core due to radial leak reduces the overall heat flow path back to the compensation chamber, increasing axial leak [10].

Chuang derived the following expressions for the axial and radial heat leak, respectively:

$$Q\_{\rm leak, \, a} = k\_{\rm eff} A \left( \frac{T\_{\rm \epsilon} - T\_{\rm cc}}{L} \right) + \left( \text{N} \mu k\_{\uparrow} \pi L \right) \left( \frac{T\_{\rm \epsilon} - T\_{\rm cc}}{2} \right) \tag{11}$$

$$Q\_{leak,r} = \frac{2\pi k\_{\text{eff}}L\zeta}{\left(\frac{r\_o}{r\_i}\right)^{(\zeta - 1)}}\Delta T\_W \tag{12}$$

where Qleak is heat leak power, keff is effective thermal conductivity, A is area, L is characteristic length, Nu is Nusselt number, kf is fluid thermal conductivity, and ς represents a nondimensional ratio of advection and conduction given by

$$\zeta = \frac{\dot{m}c\_p}{2\pi k\_{\text{eff}}L} \tag{13}$$

In his analysis and experiment, Chuang assumed this parameter to be zero, i.e., pure conduction. For the low power cases studied, this assumption was valid and resulted in low error; however, for high power levels or low wick conductivity, this assumption loses validity.

### 3.1. LHP wick structure

Ren and Wu [16] modeled the effect of wick effective thermal conductivity in LHP evaporators; a two-dimensional axisymmetric model was developed yielding results in agreement with the literature in some respects, namely the position of the liquid front in relation to a heated fin [17, 18]. Zhao and Liao [18] presented temperature profiles indicating decreasing heat leak for increas-

Iverson et al. [19] studied heat and mass transport in sintered copper wick structures. Wick samples were mounted vertically with the lower section immersed in a pool of water. A heater mounted to the back face of the wick applied power to the sample and the resulting tempera-

The majority of heat load is used in vaporization on the outer surface of wick [20]. The rest of heat input (called "heat leak") is conducted across the wick and is proportional to the effective thermal conductivity (ETC) of the capillary wicks [21]. Lower thermal conductivity of the porous wick ensures lesser heat conduction to the liquid inside the wick inner surface and maintains the operating temperature and thus the thermal resistance of the whole LHP.

Ku [10] and Furukawa [22] developed simplest LHP heat leak model that utilizes conductance

where Q is power, G is conductance parameter, and T is temperature of the evaporator and

In steady state operation, the heat leak to the compensation chamber must be offset by the liquid returning from the condenser; Eq. (7) results, where ΔT represents the subcooling of the

Chuang [23] developed a steady state LHP model which breaks the overall heat leak into two separate components: axially from the evaporator to the compensation chamber and radially from the heat source to the evaporator core. These two effects are related in that the formation of vapor bubbles in the evaporator core due to radial leak reduces the overall heat flow path

Qe, cc ¼ m :

Chuang derived the following expressions for the axial and radial heat leak, respectively:

Qleak,r <sup>¼</sup> <sup>2</sup>πkeff <sup>L</sup><sup>ς</sup> ro ri

<sup>þ</sup> Nukf <sup>π</sup><sup>L</sup> Te � Tcc

2 

ð Þ <sup>ς</sup>�<sup>1</sup> <sup>Δ</sup>TW (12)

(11)

L 

Qe, cc ¼ Ge, ccð Þ Te � Tcc (9)

cpΔT (10)

ture gradients were measured along with the mass flow rate of working fluid.

parameter which varies with geometry and operating conditions.

ing heat flux in a bed of packed spheres.

148 Porosity - Process, Technologies and Applications

compensation chamber.

where m is mass flow and cp is specific heat.

back to the compensation chamber, increasing axial leak [10].

Qleak, <sup>a</sup> <sup>¼</sup> keff <sup>A</sup> Te � Tcc

returning fluid

Wick structure is one of the main parts of loop heat pipe. To achieve good heat transfer ability of the LHP, wick structure with high porosity and permeability and fine pore radius is expected. The most frequently used wick structures in loop heat pipe are made of sintered metals, such as cooper, nickel, stainless steel, titanium or polymers (polypropylene, polyethylene, PTFE) [24–26].

Reimbrechta et al. used a tap powder sintering technique by using a graphite matrix, to manufacture Ni wicks for capillary pump applications [27]. It shows that the graphite has low interaction with nickel by sintering the nickel powders at common sintering temperatures. Combination of two different methods, the cold-pressing sintering and the direct loose sintering, was used by Gongming et al. [28], for development of Ni and Ni-Cu (90% nickel and 10% copper) wicks for loop heat pipes. They found that using direct loose sintering technique with mean pore radii of 0.54 μm, an optimal Ni-Cu wick structure is prepared. Huang and Franchi [29] used copper screen mesh and two powder materials (nickel filamentary powder and spherical copper powder) to manufacture of bimodal wick structure. But it showed that these wicks may be produced with failures. Samanta et al. [30] developed metal injection molding Ni wick structures and performed study on its physical characteristic depending on sintering time (30, 60, and 90 min) and temperature (900, 930, and 950�C). Gernert et al. [31] developed fine pore wick structure for LPH. Wu et al. [32] discussed about the effect of sintering temperature curve in wick structure manufactured for LHP. Launay et al. referred a porosity, pore diameter, and permeability as the main parameters of wick structure in the work [20]. There is the optimal porosity of sintered wick referred between 30 and 75%, and the optimal permeability referred between 10�<sup>14</sup> and 3 � <sup>10</sup>�<sup>13</sup> m2 . The porosity of the wick structure decreases when the sintering temperature or the forming pressure increases. Majority of the sintered porous materials has pore diameters between 1 and 20 μm, except copper, which has pore diameters between 20 and 1000 μm.

In Ref. [33], the optimal capillary wick was found to be sintered at 650�C for 30 min, using direct loose sintering technique, with 90% nickel and 10% copper. The wick reaches the porosity of 70% and a mean pore diameter of 1.8 μm. In Ref. [10], biporous nickel wicks were fabricated. A porosity of 77.4% was achieved using cold pressure sintering method, at a temperature of 700�C, with a pore former content of 30% in volume.
