Canopy Wick For Extreme Heat Transfer And Small Resistance

Abstract

A flow-boiling canopy wick (FBCW) employing film (meniscus) evaporation and perforated distribution layer separating the liquid stream from the underlying vapor space is provided. The vapor vents continuously through periodic perforations, in contrast to plain surface which becomes completely covered by vapor at high heat flux. The FBCW allows streamwise liquid tracks on the distribution layer between perforations providing capillary liquid flow toward heated surface and evaporation on high-effective-conductivity monolayer wick. Under extreme heat flux, various hydrodynamic limits prevent liquid supply and vapor removal, i.e., the capillary-viscous, wick superheat, perforation pressure drop and chocking and liquid-vapor stability limits. The liquid and vapor inertia control the streamwise continuous liquid track (with isolated and/or merged vapor track) and, for saturated water at 1 atm CFD and wick pressure drop, predict heat flux up to 0.1qmax=20 MW/m2, an order-of-magnitude larger than the nucleate flow-boiling limit.

Description

FIELD

The present disclosure relates to a flow-boiling canopy wick for extreme heat transfer and small resistance.

BACKGROUND AND SUMMARY

This section provides background information related to the present disclosure which is not necessarily prior art. This section provides a general summary of the disclosure, and is not a comprehensive disclosure of its full scope or all of its features.

The maximum theoretical boiling heat transfer q_max is set by interface unidirectional thermal vapor flux, and quest continues for achieving a high fraction of it under saturated liquid flow. According to the principles of the present teachings, a flow-boiling canopy wick (FBCW) employing film (meniscus) evaporation and perforated distribution layer separating the liquid stream from the underlying vapor space is provided. In some embodiments, the vapor vents continuously through periodic perforations, in contrast to plain surface which becomes completely covered by vapor at high heat flux. The FBCW of the present teachings allows streamwise liquid tracks on the distribution layer between perforations providing capillary liquid flow toward heated surface and evaporation on a high-effective-conductivity monolayer wick. Under extreme heat flux, various hydrodynamic limits prevent liquid supply and vapor removal, i.e., the capillary-viscous, wick superheat, perforation pressure drop and chocking and liquid-vapor stability limits. The liquid and vapor inertia control the streamwise continuous liquid track (with isolated and/or merged vapor track) and, for saturated water at 1 atm computational fluid dynamics (CFD) and wick pressure drop, predict heat flux up to 0.1qmax=20 MW/m², an order-of-magnitude larger than the nucleate flow-boiling limit. In addition, its thermal resistance is of the lowest (5 microK/(W/m²). The concept of replacing the chaotic nucleated bubbles with the structured, continuous vapor venting in the periodic FBCW transforms boiling heat transfer and its upper limit to achieve unexpected benefits.

Generally, boiling heat flux limit is governed by the supply of heat and liquid for evaporation, and removal of vapor (allowing for liquid irrigation) with the upper limit set by the maximum vapor flow rate predicted by the kinetic theory of gases. The surface-convection thermal-hydraulic limitations by boundary layers and liquid-vapor phase competition can be controlled using 3-D multiscale, unit-cell based boiling metamedium. The metamedium combines (a) high-effective-thermal-conductivity capillary monolayer for evaporation, (b) high-permeability liquid supply posts separating the liquid and vapor phases, and flows, and (c) uniquely designed liquid—and vapor-tracks—leading to record high heat flux and thermal conductance. Metamaterials are engineered (synthesized from multiple elements in repeating patterns) to provide properties not naturally available employing heterogeneities for effective macroscopic transport (e.g., multiscale function-designed porous media).

While low thermal resistance has been observed for subcooled boiling, the saturated flow boiling, even at very large liquid speed (up to 10 m/s), has not yet been able to reach the low thermal resistance achieved with multidimensional wicks under saturation. Based on a review of boiling in coated surface, according to some embodiments of the present disclosure a multiscale 3-D flow-boiling canopy wick (FBCW) is disclosed to achieve low thermal resistance and high critical heat flux (CHF) in boundary-layer flow boiling. The selection of flow conditions is to initially avoid the effect of the channel hydraulic diameter, although it should be mentioned that this wick has dimensions on the order of millimeter, so it is suitable for multi-millimeter and larger channels (for thermal management and vapor production). The structure allows for film evaporation over a thin porous-layer coating called the monolayer, as shown in FIG. 1. The structure is periodic in two directions, and its simplest unit cell will contain four posts, a distribution layer (two or three layers) acting as roof with a centered perforation, and a thin porous layer making the floor of the canopy wick. While thin, this layer has an optimal combination of permeability and maximum capillary pressure to spread the liquid supplied through the high permeability posts. The aim is to create and maintain a vapor space for steady and uniform film evaporation, while allowing for liquid supply and vapor escape.

It should be understood that bubbles formed in boiling have random behavior and inhibit liquid supply to the heated surface. To remedy this and increase the dryout limit and the thermal conductance, the flow-boiling canopy wick (FBCW) according to some embodiments of the present teachings uses porous and perforated bodies enabling capillary suction to separate and direct the liquid and vapor paths at the heated surface. However, in some embodiments, especially for long heaters, the liquid path can be guided by levees (ducts) on a porous perforated layer connected to posts and a monolayer-evaporator to form the canopy. In such embodiments, the vapor escapes through the perforations in between the levees with an upstream wall to prevent the vapor moving upstream and blocking the liquid track. The dryout limits (liquid-vapor hydrodynamic instability, capillary-viscous, and superheat) of this leveed FBCW are examined using analytical and numerical simulation (CFD, including the VOF technique). As the heater length along the liquid flow direction increases (local vapor quality increases), due to the two-phase hydrodynamic instabilities the liquid track dries out. For a 4 cm long heated area in saturated water channel flow, the role of the perforation/levee design and the liquid velocity on this hydrodynamic critical heat flux (q_CHF,Ig) are examined and the predictions are compared with the experimental results and good agreements are found, which shows the location-independent FBCW high thermal conductance of 0.15 MW/m²-K as well as multiple-fold q_CHF,Ig CHF enhancement over the plain surface. The upper limit heat flux for the wick is the capillary-viscous limit and is reached when the liquid ducts are covered forming milli-channels, in some embodiments.

Further areas of applicability will become apparent from the description provided herein. The description and specific examples in this summary are intended for purposes of illustration only and are not intended to limit the scope of the present disclosure.

DRAWINGS

The drawings described herein are for illustrative purposes only of selected embodiments and not all possible implementations, and are not intended to limit the scope of the present disclosure.

FIG. 1 is a schematic of FBCW showing the multiscale (monolayer, posts, and distribution layer), 3-D wick structures and vapor venting from distribution layer perforations into crossing liquid flow. The geometric parameters are also shown. The upstream isolated vapor tracks and downstream, merged vapor tracks are shown.

FIG. 2 is a range and regimes of flow-boiling heat flux and heat transfer coefficient (G/A) for saturated water at 1 atm. The record modulated porous coated pool boiling (PB), flow boiling (FB), and multi-artery heat-pipe spreader (MAHPS) experimental results, as well as predicted performance of FBCW, are shown. The highest possible q (limited by unidirectional thermal vapor flux) and G/A (solid-liquid atomic-vibration boundary conductance) are marked. The capillary-viscous, perforation chocking and pressure drop, wick superheat, and Zuber pool boiling and plain-surface flow boiling limits are also shown.

FIG. 3 is a pressure distribution of the liquid and vapor phases in the wicks and in the liquid stream. q is reached to the CHF when the total pressure drop is equal to the maximum capillary pressure in the monolayer. The monolayer and perforation pressure drop dominates at high heat flux.

FIG. 4 is an instantaneous void-fraction distribution and velocity fields at (a) t=0.65, (b) 5, (c) 27.5 ms, for two axial perforations, 20 MW/m² and 2 m/s. Cross-sectional flow fields (xz and yz planes) at different x and y positions are also shown.

FIG. 5 shows variations of the time-average liquid track width and cross-section area, at three x locations, with respect to the perforation separation distance and for conditions listed in Table 1. The other perforation parameters are also shown. To the left no stable liquid track is formed, and to the right the compressibility or the capillary-viscous limits are reached.

FIG. 6 shows that for q=20 MW/m², time variations of the predicted (a and c) A_l, and (b and d) w_l at three streamwise locations at u_l,o=2 (a and b) and 1 (c and d) m/s. The instantaneous CFD results and shaded guiding bands are shown, as well as the snapshots of the liquid track profile. Very thin extensions are not included in w_l.

FIG. 7 shows variations of the surface coverage with isolated and/or merged-vapor tracks with respect to the liquid velocity and Re_l/Re_g. The transition criterion (x-coordinate) between isolated-vapor track and oscillation regimes (L_l), and between oscillation and merged vapor track regimes (L_M) are also marked. Ma_g,max(x)>0.3 limit is indicated, and correlated L_l/L_c and L_M/L_c are plotted.

FIG. 8 is a variation of key quantities, namely the time-averaged liquid track width and area, and cross-section and time-averaged void fraction, as a function of number of computational cells, for q=20 MW/m² and u₁₀=2 m/s. The results show using 10⁵ cells would lead to no mesh-size dependence.

FIG. 9 shows variations of dimensionless monolayer unit-cell pressure drop with respect to Re_Km, for different liquid thickness δ_l. Re_Km range of q=20 MW/m² is also marked.

FIG. 10A is a perspective view of a canopy wick according to some embodiments of the present teachings.

FIG. 10B is a perspective view of a canopy wick according to some embodiments of the present teachings having a pair of levees.

FIG. 10C is a perspective view of a canopy wick according to some embodiments of the present teachings having a milli-channel or otherwise enclosed channel.

The top row of Table 1 is the q=MW/m², u₁₀=2 m/s case with geometric conditions. The middle row shows flow dimensionless umbers. The bottom row shows pressure drops, thermal conductance and superheat. Channel height H_c, perforation distance in x and y directions W_l and L_per, monolayer particle diameter and porosity d_m and ∈_m, gas velocity at perforation v_g,o, and permeation liquid velocity at distribution layer v_l,o.

Table 2 shows the geometric parameters: monolayer d_m, ∈_m, L_p and θ_c (particle diameter, porosity, post pitch and contact angle); post d_p, ∈_p, D_p, H_p, and K_p (particle diameter, porosity, height, and permeability); distribution layer d_s,sh, d_s,wa, D_s,po and n_sh×n_wa (diameters, pore size, and number density of shute and warp wires).

Corresponding reference numerals indicate corresponding parts throughout the several views of the drawings.

DETAILED DESCRIPTION

Example embodiments will now be described more fully with reference to the accompanying drawings.

Example embodiments are provided so that this disclosure will be thorough, and will fully convey the scope to those who are skilled in the art. Numerous specific details are set forth such as examples of specific components, devices, and methods, to provide a thorough understanding of embodiments of the present disclosure. It will be apparent to those skilled in the art that specific details need not be employed, that example embodiments may be embodied in many different forms and that neither should be construed to limit the scope of the disclosure. In some example embodiments, well-known processes, well-known device structures, and well-known technologies are not described in detail.

The terminology used herein is for the purpose of describing particular example embodiments only and is not intended to be limiting. As used herein, the singular forms “a,” “an,” and “the” may be intended to include the plural forms as well, unless the context clearly indicates otherwise. The terms “comprises,” “comprising,” “including,” and “having,” are inclusive and therefore specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. The method steps, processes, and operations described herein are not to be construed as necessarily requiring their performance in the particular order discussed or illustrated, unless specifically identified as an order of performance. It is also to be understood that additional or alternative steps may be employed.

When an element or layer is referred to as being “on,” “engaged to,” “connected to,” or “coupled to” another element or layer, it may be directly on, engaged, connected or coupled to the other element or layer, or intervening elements or layers may be present. In contrast, when an element is referred to as being “directly on,” “directly engaged to,” “directly connected to,” or “directly coupled to” another element or layer, there may be no intervening elements or layers present. Other words used to describe the relationship between elements should be interpreted in a like fashion (e.g., “between” versus “directly between,” “adjacent” versus “directly adjacent,” etc.). As used herein, the term “and/or” includes any and all combinations of one or more of the associated listed items.

Although the terms first, second, third, etc. may be used herein to describe various elements, components, regions, layers and/or sections, these elements, components, regions, layers and/or sections should not be limited by these terms. These terms may be only used to distinguish one element, component, region, layer or section from another region, layer or section. Terms such as “first,” “second,” and other numerical terms when used herein do not imply a sequence or order unless clearly indicated by the context. Thus, a first element, component, region, layer or section discussed below could be termed a second element, component, region, layer or section without departing from the teachings of the example embodiments.

Spatially relative terms, such as “inner,” “outer,” “beneath,” “below,” “lower,” “above,” “upper,” and the like, may be used herein for ease of description to describe one element or feature's relationship to another element(s) or feature(s) as illustrated in the figures. Spatially relative terms may be intended to encompass different orientations of the device in use or operation in addition to the orientation depicted in the figures. For example, if the device in the figures is turned over, elements described as “below” or “beneath” other elements or features would then be oriented “above” the other elements or features. Thus, the example term “below” can encompass both an orientation of above and below. The device may be otherwise oriented (rotated 90 degrees or at other orientations) and the spatially relative descriptors used herein interpreted accordingly.

Boiling heat transfer can achieve very high heat fluxes that are often associated with corresponding high heat transfer coefficients. Due to the random nature of vapor bubbles generation, however, a point is reached where the supply of liquid to the heated surface is interrupted, leading to dryout. The heat flux at this point is the critical heat flux (CHF), it is succeeded by a rapid increase in the wall superheating that can lead to catastrophic failure.

The flow-boiling canopy wick (FBCW) 10 of the present teachings replaces this chaotic bubble formation with a well-behaved and controllable evaporation of the liquid film (meniscus in a thin wick) resulting in separated preferential paths for the liquid and vapor phases. By eliminating the competition between the phases close to the heated surface and allowing for a continuous supply of liquid through its capillary net while the vapor can rise freely in the vapor space, the present teachings overcome the traditional critical heat flux associated with the hydrodynamic induced dryout, thus enabling it to reach other limiting phenomena.

In some embodiments, as illustrated in FIGS. 1 and 10A, the FBCW structure 10 is periodic in two directions, and its simplest unit cell can contain four posts 12, a perforated distribution layer 14 acting as roof, and a thin, single-particle porous layer 16 making the floor of the canopy wick 18. The particle porous layer 16 can rest or be coupled to a cooper substrate 15. While thin, this layer 16 has an optimal combination of permeability and maximum capillary pressure to spread the liquid supplied through the high permeability posts 12. The aim is to create and maintain a vapor space for steady and uniform film evaporation, while allowing for uninterrupted liquid supply and vapor escape.

In some embodiments, the FBCW structure 10 can be divided into two main components, a channel 20 and the wick 18. In the wick 18, liquid is evaporated, and the flow of liquid and vapor is separated by establishing preferred paths, thereby removing the competition between the phases, thus preventing the traditional vapor-induced dryout. In the channel, as illustrated in FIG. 10B-10C, there is fluid flow of liquid that should both drag the wick generated vapor, as well as keep the supply of liquid to the heated surface 15.

Generally, it should be understood that channel flow refers to flow directed by ducts and tubes. In the present disclosure, the flow enters as liquid and then become a combined (two-phase) liquid and vapor stream. This is referred to as channel because the flow is restricted laterally and moves in a single direction. The channel flow is forced through use of pumps and thus is a laterally confined forced flow. Using the canopy wick, the channel refers to the space over the canopy (perforated layer).

The two parts, namely the wick 18 and the channel 20, are kept apart by a porous layer 14 with rectangular perforations 24, the distribution layer 14. This layer 14 is supported by vertical porous posts 12 that also direct the liquid to the heated surface upon which we have the monolayer 16—a single layer of sintered copper particles that enables phase change through convective evaporation.

Posts 12 can be positioned along the perforation and their lateral spacing must be at least the perforation width, as to not hinder the flow of vapor. This way, the FBCW geometry can be parameterized by the post diameter D_p, post spacing Δ_p, the number of posts along the perforation N_p,x, and the perforation width W_per.

Even though aspects of the channel 20 and the wick 18 are intertwined, they are evaluated separately as to discretize the sources of instabilities that may impair the liquid supply, leading to dryout.

The addition of porous levees 22, in some embodiments as illustrated in FIG. 10B, to the side of the perforations 24 reduces the effect of vapor lateral spreading, establishing a duct for the liquid to flow. A series of milli-channels or enclosed channels 26, in some embodiments as illustrated in FIG. 10C, can be created by replacing the levees 22 by solid sidewalls 28 with a closed top wall 30, nullifying the effects of vapor spreading, establishing two distinct single-phase flows.

Traditionally, the concept of critical heat flux is associated with the boiling crisis—vapor generation prevents wetting of the heated surface. In flow boiling, on the other hand, this concept is extended as the heat transfer can now be limited by different events, some of the most relevant are shown in FIG. 2. Since the surface-convection resistance is in series with the substrate conduction resistance, the conduction conductance is also shown (under copper or synthetic diamond as material). The predicted superior performance [q up to 20 MW/m² and (G/A) over 0.2 MW/m²−K] of the FBCW of the present teachings is also shown. In general, coatings and nano/microstructures reduce the surface superheat T_s−T_lg (T_lg is saturation temperature) by either increasing the nucleation sites or creating film evaporation over thin, high effective conductivity wicks. They also tend to enhance the CHF governed by the liquid-vapor hydrodynamic instability or the capillary-viscous limit of liquid flow through porous bodies. The vapor escaping paths are more readily accommodated, but vapor chocking limit can occur.

The maximum theoretical heat flux is based on the interfacial, unidirectional thermal flux of vapor q_max

q _max=ρ_gΔh_lg(k_BT_lg/2πm)^1/2  (1)

With ρ_g vapor density, Δh_lg heat of evaporation, kB Boltzmann constant, and m average molecular mass. This Schrage formulation-relation has been critically reviewed, but the perturbative non-equilibrium corrections are not easily incorporated and also not very significant.

The modulated wick in pool boiling allows control of the instability wavelength with the pitch of permeable periodic stacks λ_m shown in FIG. 2 with the CHF as

$\begin{array}{cc}\frac{q_{\mathrm{CHF},\mathrm{PB}}}{\pi /24{\rho }_g^{1/2}\Delta {h_{\lg }\left[\sigma g\left({\rho }_i-{\rho }_g\right)\right]}^{1/4}}=\frac{{3\left[\sigma /g\left({\rho }_l-{\rho }_g\right)\right]}^{1/4}}{{\lambda }_m^{1/2}}& \left(2\right)\end{array}$

With ρ₁ liquid density, σ surface tension, and g gravitational acceleration. For plain surface this wavelength is governed by fluid properties (in the Zuber hydrodynamic limit q_CHF,Z), i.e.,

λ_m=9[σ/g(ρ_l−ρ_g)]^1/2.  (3)

The flow-boiling limit q_CHF,FB,1 is given by empirical relation

$\begin{array}{cc}\frac{q_{\mathrm{CHF}.\mathrm{FB},1}}{{\rho }_lu_{l,o}\Delta h_{\lg }}=C_1{{\mathrm{We}}_{D,c}^{C_2}\left({\rho }_l/{\rho }_g\right)}^{C_3}\times \frac{\left[1-{C_4\left({\rho }_l/{\rho }_g\right)}^{C_5}X_i\right]}{1+C_1C_4{{\mathrm{We}}_{D,c}^{C_2}\left({\rho }_l/{\rho }_g\right)}^{\left(C_3+C_5\right)}\left(L_c/D_c\right)}& \left(4\right)\end{array}$

With C_1-5 (0.0722, −0.312, −0.644, 0.900, 0.724), D_c hydraulic diameter of channel, L_c channel length, We_D,c Weber number ρ_lu_l²D_c/σ, and x_i is the pseudo-inlet quality (which represent the inlet liquid subcooling). The experimental result is presented as which is higher than predicted by Eq. 4 and is shown as q_CHF,FB,2 in FIG. 2.

The FBCW hydrodynamic limits include the perforation choking limit q_CHF,ch (sonic flow through contraction)

$\begin{array}{cc}{q}_{\mathrm{CHF},\mathrm{ch}}=c_d{\frac{N_{\mathrm{per}}{\lambda }_{\mathrm{per}}W_{\mathrm{per}}}{A_m}\left[{\mathrm{\gamma \rho }}_g{p_g\left(\frac{2}{\gamma +1}\right)}^{\left(\gamma +1\right)/\left(\gamma -1\right)}\right]}^{1/2},& \left(5\right)\end{array}$

With c_d discharge coefficient, N_per ratio of monolayer unit cell per perforation, λ_per and W_per perforation length and width, A_m monolayer unit cell area, y heat capacity ration, and ρ₉ is vapor pressure in monolayer. This relation uses the perforation unit-cell geometry to determine the vapor speed.

The FBCW capillary-viscous limit q_CHF,c−v is governed by capillary liquid flow through the 3-D wick (distribution layer 14, posts, and monolayer), and in approximate closed form is

$\begin{array}{cc}{q}_{\mathrm{CHF},c-v}=\left(p_{c,\max }-\Delta p_{s,\updownarrow }-\Delta p_{s,\leftrightarrow }\right){\frac{{\rho }_l}{{\mu }_l}\left[\frac{H_p}{K_pA_p}+\frac{\left(L_p-D_p\right)/2}{K_mA_{m,\mathrm{ac}}}\right]}^{-1}\frac{\Delta h_{\lg }}{A_e}& \left(6\right)\end{array}$

With p_c,max maximum capillary pressure in monolayer, Δp_spressure drop across and Δp_s,↔ along distribution layer 14, μ_i liquid viscosity, H_p post height, K_p post permeability, A_p post cross-sectional area, L_p unit cell size, D_p post diameter, K_m monolayer in the unit cell [defined as π(L_p−D_p)(δ_l)_m, and A_e evaporator area.

The monolayer wick boiling limit q_CHF,b occurring when bubbles form inside the wick due to large liquid superheat, as modeled as

$\begin{array}{cc}{q}_{\mathrm{CHF},\mathrm{sh}}=\frac{{〈k〉}_m}{{〈{\delta }_l〉}_m}\Delta T_{\mathrm{sh},\max }& \left(7\right)\\ \Delta T_{\mathrm{sh},\max }=\frac{T_{\lg }}{\Delta h_{\lg }{\rho }_g}\left(\frac{2\sigma }{r_{\mathrm{cr}}}-p_{c,\max }\right)& \left(8\right)\end{array}$

Where maximum critical superheat T_sh,max is determined by the critical nucleation site radius r_cr and maximum capillary pressure p_c,max driven by meniscus curvature in the monolayer. For conventional metallic material, r_cr is from 0.2 μm to 25 μm. In the monolayer vapor chamber where the copper particles are oxidized for improved wetting, r_cr is observed in order of 100 nm typical of other experiments. The above wick superheat limit for the wick consider in this study is shown in FIG. 2.

Over the distribution layer 14 saturated water flows at pressure p_l,o (1 atm), and the vapor is injected into this stream through the distribution layer 14 perforation undergoing pressure drop Δp_per. The FBCW perforation vapor pressure drop limit q_CHF,per occurs when Δp_per is equal to the maximum capillary pressure ρ_c,max (vapor flows through the perforations only), and the liquid-gas stability limit q_CHF,l−g,st occurs when the liquid track becomes unstable and ruptures downstream.

The maximum conductance is when the heat transfer is limited only by the Kapitza interfacial limit due to mismatch of atomic-vibrational modes of the meniscus, substrate and liquid water. In analysis of extreme heat transfer, it is suggested that the synthetic diamond substrate is suitable and would provide the highest solid thermal conductivity and the largest structurally-stable temperature change across it and would set conductance limit indicated in FIG. 2 and is 34 MW/m² for conditions given in Table 1. The FBCW of the present teachings is predicted to reach record 0.1q_max, under record conductance.

In FBCW, the maximum capillary pressure p_c,max in the monolayer should be large enough to overcome the pressure drops along and across the distribution layer 14 Δ and Δp_s,↔, and along the post Δp_p and monolayer Δp_m, as well as Δp_per. FIG. 3 shows the liquid monolayer pressure p_l,m at its lowest liquid thickness should give capillary pressure enabling vapor flow through the perforation at pressure p_l,o+Δp_per. q_CHF,l−g,st can be reached under this condition, and details of pressure drop calculations are reported in Appendix C.

The fluid dynamics of the vapor venting into the liquid stream, is governed by the inertia, viscous, buoyancy, and surface tension forces. In addition, at high heat flux the vapor flux can lead to vapor compressibility effects (not included in current analysis). Since our CFD assumes phasic incompressibility, we limit the Ma_g,o to 0.3. In FBCW, typical values of dimensionless numbers are the Reynolds (liquid/and vapor g), Weber, Froude and Mach numbers, i.e.,

$\begin{array}{cc}{\mathrm{Re}}_l=\frac{{\rho }_lu_{l,o}W_l}{{\mu }_l},{\mathrm{Re}}_g=\frac{{\rho }_gv_{g,o}D_{\mathrm{per}}}{{\mu }_g},{\mathrm{We}}_{D,c}=\frac{{\rho }_lu_{l,o}^2D_c}{\sigma },{\mathrm{Fr}}_{D,\mathrm{per}}={\left[\frac{{\rho }_lu_{l,o}^2}{g\left({\rho }_l-{\rho }_g\right)D_{\mathrm{per}}}\right]}^{1/2},{\mathrm{Ma}}_{g,o}=\frac{v_{g,o}}{u_a}& \left(9\right)\end{array}$

Which are listed in Table 1 for q=20 MW/m², liquid inlet velocity u_l,o=2 m/s, and geometric parameters of FIG. 1. Here D_per is a hydraulic diameter of perforation, and u_a is speed of sound at vapor. Characteristic lengths in the dimensionless numbers are critical length scales of liquid and vapor motions. The large We_D,C and Fr_D,per ensure dominance of liquid inertia over surface tension and buoyancy, and optimal selection of the perforation geometry ensures that vapor compressibility is not significant (Ma_g,o<0.3). IN FBCW, the base channel size [L_c(W_l+W_per)] is the total monolayer area, and a perforation size (λ_per W_per) in Table 1 is determined to satisfy the pressure drop condition in FIG. 2 and to keep vapor flows incompressible. Two screen layers are used, and their specifications are introduced in detail in Table 1. Once evaporation begins, the vapor pressure exceeds the channel liquid pressure, and meniscus at the perforation is not ruptured. The volume-averaged conductance and superheat T_s−T_lg at the monolayer (q=20 MW/m²) are calculated by using q=(G/A)(T_s−T_lg) and Equation 7, and the latter is 93 K (Table 1).

The stable liquid track heat flux limit q_CHF,l−g,st, along with the capillary-viscous limit, determine the optimal FBCW performance (FIG. 2), and the corresponding instantaneous liquid and vapor flow fields are shown in FIG. 4 (Table 1 parameters and two axial perforations). As vapor is injected through the perforation, it spreads in x, y, and z directions and in the first few ms the vapor continues to spread in the z direction with small velocity at the exit (FIG. 4A). After this initial period, the vapor track in the z direction becomes established (with time variations), and steady exit vapor flow occurs. This wavy interface is similar to that observed in plain-surface flow boiling and gas-sheared liquid film, where some vapor track breakdown happen intermittently (induced by the liquid shear) (FIG. 4B). As shown in FIG. 4C, at the exit the liquid track area A_l and width w_l in yz plane are clearly observable. The w_l and A_l are the width and cross-section area of the liquid track over the distribution layer 14 unit cell, and w_l is along the y-direction at z=0 and A_l is in the yz-plane and varies with x. For u_l,o=2 m/s, the droplets entrained at the vapor interface can be seen in FIG. 4C. Droplet ligaments are also formed between two neighboring fast vapor tracks similar to gas-sheared liquid film. These entrained droplets join the liquid track and assist in liquid supply to the wick. In plain-surface flow-boiling, the liquid supply is obstructed by vapor blanket grown from bubbles and cause dryout, and FBCW defer this by marinating the narrow, periodic liquid track reaching much higher dryout limit (q=MW/m²). In the channel, there are two vapor track regimes; one is an isolated-vapor track, and the other is an oscillation track which has both isolated- and merged-vapor tracks. The isolated-vapor track is a state where vapor tracks have streamwise continuity while not being merged with adjacent vapor tracks. In the merged-vapor tracks, vapor tracks are combined laterally. These two types of vapor track regimes are marked in FIG. 4.

In selecting the perforation geometry, we first note that the optimal unit cell for perforation needs to match the wick unit cell formed by the posts. The periodic liquid tracks are formed along the x direction and within the perforation separation distance w_l shown in inset of FIG. 5. The variation of the time-averaged liquid track width w_l and cross-section area A_l as a function of W_l for the conditions in Table 1 are shown in this figure. For W_l<2.55 mm no stable liquid track is formed, while for W_l<5.5 mm the perforation flow area is reduced such that the vapor compressibility and capillary viscous limits are reached. Within these limits, w_l and A_l increase with W_l. This optimal perforation geometry would result in the large liquid track width and area to ensure stable liquid supply, and this is the geometry used in the simulation.

FIGS. 6A-6B show the predicted temporal variations of A_l and w_l, at three streamwise locations, for q=20 MW/m² and u_l,o=2 m/s with the snapshots of the liquid profile. For guiding convenience, shaded bands are marked to show the trends and continuous liquid track (along x and z directions). At the upstream of the exit, the vapor tracks emerging from the perforations remain isolated and separated by the liquid track extending to the top of the channel. With increase in x, the vapor track oscillates between the isolated and merged states, while the liquid track remains continuous liquid supply to the distribution layer 14. For formation of streamwise continuous liquid track between perforations, the liquid inertia should overcome the lateral vapor spreading, which in turn depends on the vapor inertia through the perforation. In addition to streamwise (x), the liquid track continuity in vertical (z) direction (larger A_l) improves the liquid supply. So, as the coverage of isolated vapor track increases, the FBCW has improved irrigation for higher heat flux of q_CHF,l−g,st(=20 MW/m²). For comparison with FIGS. 6A-6B, the results for q=20 MW/m² and u_l,o=1 m/s are shown in FIGS. 6C-6D. For loweru_l,o, the isolated-vapor track regime is less sustainable, and at x=7.55 mm, the z-direction continuity breaks down. At x=15 mm, during the most of the time (greater than 90% of time) there is merged-vapor track state (with smaller z-direction extension), which is in the oscillation regime.

The optimal condition for continuous liquid track in x and z directions is determined from the Re_l and Re_g, giving a threshold liquid velocity u_l,o, for while satisfying the compressibility requirement. Also considering the role of viscosities, and large We_D,c, and Fr_D,per (Table 1), Re_l/Re_g controls the fate of the liquid track continuity and stability. FIG. 7 shows the extent of isolated-vapor track regime L_l/L_c over the surface, as a function of liquid velocity. Larger liquid coverage occurs with larger liquid velocity, however the increase of liquid coverage diminishes as liquid velocity increases. Where the isolated-vapor track regime ends, a region where the vapor track oscillated between isolated and merged [also shown in FIG. 6A] begins. For lower liquid velocities, this oscillating region is followed by the merged-vapor track regime (starts at L_M/L_C), where liquid track is enclosed by the surrounding vapor flows [in FIG. 6C]. For liquid velocity larger than 2 m/s, the local streamwise vapor velocity become large enough so the compressibility (not included in the CFD analysis) may be significant, and this is also marked in FIG. 7. At u_l,o=2 m/s, the FBCW has the largest extent of isolated-vapor track regimes (L_l,max) under the vapor compressibility limit. From the saturated, plain-surface forced correlation, q_CHF,FB is

$\begin{array}{cc}\frac{q_{\mathrm{CHF},\mathrm{FB}}}{{\rho }_Lu_l\Delta h_{\lg }}~{\left(\frac{{\rho }_g}{{\rho }_l}\right)}^{1/2}{\mathrm{We}}_{L,c}^{-1/4}& \left(10\right)\end{array}$

Where L_c is the characteristic length of the Weber number. Using L_i/L_c (i=I,M), we start with

$\begin{array}{cc}\frac{q_{\mathrm{FBCW}}}{{\rho }_lu_l\Delta h_{\lg }}~{\left(\frac{L_i}{L_c}\right)}^{-a},& \left(11\right)\end{array}$

And CHF occurs when bubble crowding completely covers the surface corresponding to the merged-vapor track in FBCW. However, in FBCW, liquid track can be sustained beneath the vapor blanket by distribution layer 14 perforation separation and capillarity, with liquid-gas stability limit of FBCW q_CHF,l−g,st>q_CHF,FB. In the FBCW, F_BCW=ρ_gu_gΔh_lgN_perλ_perW_per/L_c(W_per+w_l). With a=1 and using Equations 10 and 11, we suggest (i=L, M)

$\begin{array}{cc}\frac{L_i}{L_c}=c_i\frac{{\mathrm{Re}}_l}{{\mathrm{Re}}_g}{\left(\frac{{\rho }_g}{{\rho }_l}\right)}^{1/2}{\mathrm{We}}_{L,c}^{-1/4}\times \frac{A_m}{N_{\mathrm{per}}{\lambda }_{\mathrm{per}}W_{\mathrm{per}}}\frac{{\mu }_l}{{\mu }_g}\frac{D_{\mathrm{per}}}{W_l},& \left(12\right)\end{array}$

With coefficient c_i fitted with the least squares method to the numerical results in FIG. 7, which are 0.37 (c_l) and 0.54 (C_M).

We have shown that FBCW a boiling metamedium enables extreme heat transfer by controlling heat transfer/vapor generation and hydrodynamics of the vapor and liquid tracks. FBCW separates and directs these tracks to ensure the highest liquid supply rate and smallest thermal resistance. Heat flux up to 0.1q_max is predicted, and the increase of the liquid velocity extends the isolated-vapor track coverage, and gradually leads to the streamwise local vapor compressibility limit. The FBCW transforms boiling heat transfer using unit-cell, 3-D capillary structure under saturated liquid flow and is capable of achieving record fraction of the theoretical maximum heat flux limit.

CFD Methods

The liquid supply and monolayer evaporation use numerical solutions to (i) the point-wise Navier-Stokes and energy equations and the principles of meniscus minimum-surface energy, and (ii) local volume-average momentum and energy equations in the porous media. Here the two-phase channel flow is solved using ANSYS FLUENT with the volume of fluid (VOF) method under incompressibility, i.e. solving

$\begin{array}{cc}\frac{\partial \rho }{\partial t}+\nabla *u=0& \left(A1\right)\\ \frac{\partial }{\partial t}\left(\rho u\right)+\nabla *\left(\rho \mathrm{uu}\right)=-\nabla p+\nabla *\left[\mu \left(\nabla u+\nabla u^T\right)\right]+\rho g+f_s& \left(A2\right)\end{array}$

With velocity u, pressure p, surface tension force f_s, and mixture density ρ and dynamic viscosity μ. The liquid-gas mixture is treated as compressible while each phase is assumed as incompressible. The vapor volume fraction α equation and mixture properties are

$\begin{array}{cc}\frac{\partial }{\partial t}\left({\mathrm{\alpha \rho }}_g\right)+\nabla *\left({\mathrm{\alpha \rho }}_gu_g\right)=0& \left(\mathrm{A3}\right)\\ \rho ={\mathrm{\alpha \rho }}_g+\left(1-\alpha \right){\rho }_l,\mu ={\mathrm{\alpha \mu }}_g+\left(1-\alpha \right){\mu }_l& \left(\mathrm{A4}\right)\end{array}$

The continuum surface force f_s model is

$\begin{array}{cc}{f}_s=\sigma \frac{\rho k_g\nabla \alpha }{\frac{1}{2}\left({\rho }_g+{\rho }_l\right)},& \left(\mathrm{A5}\right)\end{array}$

Where k_g=∇*(∇α/α), which is the interface curvature (interface normal defined as gradient of vapor volume fraction).

The vapor interface reconstruction used the geometric reconstruction scheme, and the SIMPLE scheme is applied for the pressure-velocity coupling. The quadrilateral mesh is used with uniform grid size of 0.25 mm, and the mesh-size independence is tested using progressively smaller mesh size (FIG. 8). A typical perforation size (two perforations, 5.5×1.5 mm²) in a computational domain (15×15×7 mm³) with two prism layers (growth ratio of 1.2 is applied to the top and bottom boundaries. The channel height H_C is selected for a boundary-layer liquid flow behavior (i.e., independent of channel height, while avoiding very long computing time). When H_C is extended by 40%, Ai in oscillating regime changes by 3.6% (merged-vapor track) and 5.6% (isolated-vapor track with consideration of cross-section area extension). w_l also changes within 2%. Liquid velocity u_l,o toward inside the domain (x direction) is given to liquid inlet. Liquid velocity v_l,o flowing into distribution layer 14 (negative z direction) is

$\begin{array}{cc}{v}_{l,o}=\frac{m_e}{{\rho }_lA_m\left(1-1/N_{\mathrm{per}}\right)},& \left(\mathrm{A6}\right)\end{array}$

Where m_e=aA_m/Δh_lg, Δh_lg is heat of evaporation, A_m is monolayer unit cell area, and m_e is mass flow rate of evaporation. Perforation vapor velocity v_g,o is

$\begin{array}{cc}{v}_{g,o}=\frac{m_e}{{\rho }_g\left(2{\lambda }_{\mathrm{per}}W_{\mathrm{per}}\right)}& \left(\mathrm{A7}\right)\end{array}$

As shown in Table 1, there is vapor pressure drop across the perforation and the vapor density change accordingly, but this is neglected in the current calculations. Periodic boundary conditions are imposed to the side surfaces, top wall has no-slip condition, and outflow condition is defined at the outlet.

To ensure the numerical results are independent of grid size, progressively larger number of computational cells were used, and FIG. 8 shows that with 10⁵ cells the results will become independent of the mesh size. The results are for q=20 MW/m² and u_l,o=2 m/s, and show the variations in the time-averaged liquid track width and area, and cross-section and time-averaged void fraction, at three different streamwise locations.

Wick Geometric Parameters

The optimized geometric parameters (marked in FIG. 1) of the FBCW are listed in Table 2 and are based on the MAHPS design.

Pressure Drop Relations

Since the vapor passes only through the perforations, the distribution layer 14 is a perforated finite thickness plate. For 0.006<β<0.75 and H_s/D_per<0.8, the pressure drop through the perforated plate is

$\begin{array}{cc}\Delta p_{\mathrm{per}}=\frac{1}{2}{\rho }_gu_{g,m}^2\times {\left[\frac{1.642}{\beta \left(1-{\beta }^{2.6}\right)\left(1+{\stackrel{\_}{l_1}}^{3.5}+{\beta }^{3.6}\right)}-1\right]}^2-{\rho }_g{\mathrm{gH}}_s,& \left(\mathrm{C1}\right)\end{array}$

With l₁=H_s/D_per,H_s distribution layer 14 thickness, D_per hydraulic diameter of perforation, u_g,m vapor velocity before perforation, and β ratio of perforation area to area before it. Idelchik suggested another empirical correlation

$\begin{array}{cc}\Delta p_{\mathrm{per}}=\frac{{\rho }_gu_{g,m}^2}{2{\beta }^2}\left[\frac{{\left(1-\beta \right)}^{0.75}}{2}+{\left(2.4-\stackrel{\_}{l_1}\right)}^{\stackrel{\_}{l_2}}{\left(1-\beta \right)}^{1.375}+{\left(1-\beta \right)}^2+f\stackrel{\_}{l_1}\right]-{\rho }_g{\mathrm{gH}}_s,& \left(\mathrm{C2}\right)\end{array}$

With l₂ and friction coefficient f as

$\begin{array}{cc}\stackrel{\_}{l_2}=0.25+\left(\frac{0.535{\stackrel{\_}{l_1}}^8}{0.05+{\stackrel{\_}{l_1}}^7}\right),f=\frac{0.316}{{\mathrm{Re}}_g^{0.25}}.& \left(\mathrm{C3}\right)\end{array}$

In Equations C1-C3, the hydrostatic pressure drop by gravitational force is also included, and both correlations give very close results.

The monolayer with closely hexagonal-packed particles d_m=50 μm and ∈_m=0.40 gives optimal performance over a range of heat flux, and this geometry is also adopted in this study. Using the minimum-surface energy principle, the meniscus topology is obtained using the Surface Evolver. Since the monolayer Weber number We_m=ρ_lu_lm²δ_lm/σ and capillary number Ca_m=u_lu_lm/σ are small, so the static meniscus is used. In the monolayer, for low heat flux, the liquid Reynolds number Re_l,m<<1, and pressure drop Δp_l,m varies linearly with velocity u_lm (Darcean flow). For Re_l,m of O(1) at high heat flux used here, the so-called Forchheimer (non-Darcean) range, the quadratic u_lm term for Δp_l,m is presented with the permeability-based Reynolds number Re_Km=ρ_lu_lmK_m^1/2/μ_l

$-\frac{K_m}{{\mu }_l{〈u_l〉}_m}\frac{{\mathrm{dp}}_{l,m}}{\mathrm{dx}}=c_{F,1}+c_{F,2}{\mathrm{Re}}_{\mathrm{Km}},$

With dp_l,m/dx liquid pressure gradient, and K_m permeability. The dimensionless pressure gradient across the unit cell shown in FIG. 9 is calculated by ANSYS FLUENT, and covers the Darcy regimes. Here C_F,1=1, and for given range of Re_lm, C_F,2 is comparable to empirical results from experiments. The results show that the meniscus liquid film thickness δ_lm, influences C_F,2 under laminar flow condition (monolayer Reynolds number Re_l,m<200.

The wick side is capable of increasing the critical heat flux up to 18.4 MW/m², the capillary-viscous limit. In this case, the bottleneck becomes the channel side, where the hydrodynamics of the two-phase flow are of great importance, and the vapor spreading prevents the liquid from reaching the distribution layer, responsible for wicking it all the way to the heated surface. In order to avoid this problem and reduce hydrodynamic effects, different solutions are provided as illustrated in FIGS. 10A-10C. A plain surface embodiment is shown in FIG. 10A, whereby the lateral vapor spreading occupies the region between the perforations, restricting the liquid track width and leading to an early dry-out. However, in some embodiments as illustrated in FIG. 10B, the addition of vertical levees 22 to the side of each perforation 24 helps create a liquid duct within which the vapor influence is less pronounced but not yet nullified. Therefore dry-out is delayed in this configuration, but the CHF is still smaller than the capillary-viscous limit. In some embodiments, as illustrated in FIG. 10C, channel 20 can comprise a milli-channel configuration, whereby the porous levees 22 are replaced by solid walls 28 and the upper surface 30 is closed, establishing an enclosed liquid space undisturbed by the vapor. The entirety of liquid is wicked and evaporated. This comes at the cost of increased pressure drop in the liquid phase.

The FBCW structure 10 can be manufactured as illustrated in FIGS. 11A-11D, whereby a plain copper surface is provided upon which monolayer particles are deposited and sintered. The posts are then sintered thereupon and a separation layer or distribution layer having perforations is added. The sintering of the monolayer is preferred to provide a good packing of the particles, which leads to a higher capillary pressure. In some embodiments, this is done using the Langmuir-Blodgett film method, which ensures a very accurate film thickness. In some embodiments, the particles are first poured into degassed water and then sonically excited, which leads to the formation of a homogenous floating layer. After spurious particles are removed, water is evaporated and only the particles are left to be sintered on the plain surface.

In summary, according to some embodiments of the teachings herein, the canopy wick routes liquid by capillary action through a porous canopy that separates the vapor space below it from the liquid supply above. The canopy is connected below to porous posts and finally to a porous, thin evaporator layer that covers the heated surface. This ensures the smallest thermal resistance through an optimized three-dimensional, porous (capillary) structure.

On top of the canopy wick, the liquid supply to the canopy is by direct condensation (as in the vapor chambers), or through a pumped liquid channel. The pumped liquid channel can mix with the vapor stream (created by evaporation) leaving a perforated canopy (this is called the flow boiling arrangement), or the pumped liquid can flow through liquid milli-channels which are isolated from the vapor flow (this keeps the liquid and vapor completely separate and direct the vapor to the distant condenser). In some embodiments, the flow-boiling canopy wick uses designed levees around the perforations to prevent the exiting vapor flow from destabilizing the liquid supply. This allows for high heat flux limit. The canopy wick will provide the smallest thermal resistance and with the management or separation of the liquid and vapor flows (using levees, milli-channels, etc.) will provide the highest heat flux (or dryout) limit.

The foregoing description of the embodiments has been provided for purposes of illustration and description. It is not intended to be exhaustive or to limit the disclosure. Individual elements or features of a particular embodiment are generally not limited to that particular embodiment, but, where applicable, are interchangeable and can be used in a selected embodiment, even if not specifically shown or described. The same may also be varied in many ways. Such variations are not to be regarded as a departure from the disclosure, and all such modifications are intended to be included within the scope of the disclosure.

Claims

1. A flow-boiling canopy wick comprising: a monolayer configured to be disposed on a copper layer;a distribution layer being parallel to the monolayer, the distribution layer being spaced apart from the monolayer to define a vapor space, the distribution layer having a plurality of perforations fluidly open to the vapor space and configured to permit vapor within the vapor space to continuously vent, the distribution layer being configured to separate a liquid stream from the vapor space;a plurality of permeable posts extending between the monolayer and the distribution layer; andstreamwise liquid tracks on the distribution layer between the plurality of perforations, the streamwise liquid tracks configured to provide capillary liquid flow toward a heated surface and evaporation, the liquid and vapor inertia control the streamwise liquid track.

2. The flow-boiling canopy wick according to claim 1, further comprising: a channel formed on the distribution layer between the plurality of perforations, the channel configured to separate the vapor from the streamwise liquid tracks.

3. The flow-boiling canopy wick according to claim 2 wherein the channel comprises at least a pair of upward levees extending between the liquid tracks and the plurality of perforations.

4. The flow-boiling canopy wick according to claim 2 wherein the channel comprises at least a pair of sidewalls and a top wall extending between the pair of sidewalls to define an enclosed channel.

5. The flow-boiling canopy wick according to claim 4 wherein the vapor is substantially outside the enclosed channel.

6. The flow-boiling canopy wick according to claim 1 wherein the plurality of perforations are disposed in a periodic arrangement.

7. The flow-boiling canopy wick according to claim 1 wherein the plurality of permeable posts are each configured to permit the liquid stream to travel from the distribution layer down to the monolayer there through.

8. A flow-boiling canopy wick comprising: a first layer configured to be disposed on a heated layer;a second layer being parallel to the first layer, the second layer being spaced apart from the first layer to define a vapor space, the second layer having a plurality of perforations fluidly open to the vapor space and configured to permit vapor within the vapor space to continuously vent, the second layer being configured to separate a liquid stream from the vapor space;a plurality of permeable posts extending between the first layer and the second layer; andwherein the second layer is configured to permit streamwise liquid tracks to flow along the second layer between the plurality of perforations, the streamwise liquid tracks configured to provide at least capillary liquid flow toward the heated layer within the first layer and result in evaporation,

9. The flow-boiling canopy wick according to claim 8, further comprising: a channel formed on a side of the second layer opposite the vapor space between the plurality of perforations, the channel configured to separate the vapor from the streamwise liquid tracks.

10. The flow-boiling canopy wick according to claim 9 wherein the channel comprises at least a pair of upward levees extending between the liquid tracks and the plurality of perforations.

11. The flow-boiling canopy wick according to claim 9 wherein the channel comprises at least a pair of sidewalls and a top wall extending between the pair of sidewalls to define an enclosed channel.

12. The flow-boiling canopy wick according to claim 11 wherein the vapor is substantially outside the enclosed channel.

13. The flow-boiling canopy wick according to claim 8 wherein the plurality of perforations are disposed in a periodic arrangement.

14. The flow-boiling canopy wick according to claim 8 wherein the plurality of permeable posts are each configured to permit the liquid stream to travel from the second layer down to the first layer there through.