EFFECT OF CELL SIZE OF A HONEYCOMB POROUS PLATE ATTACHED TO A HEATED SURFACE ON CHF IN SATURATED POOL BOILING

Proceedings of te International Heat Transfer Conference IHTC14 August 8-13, 1, Wasington, DC, USA Draft IHTC14-349 EFFECT OF CELL SIZE OF A HONEYCOMB POROUS PLATE ATTACHED TO A HEATED SURFACE ON CHF IN SATURATED POOL BOILING Soji Mori Yokoama National University Yokoama, Kanagawa, Jaan Lujie Sen Yokoama National University Yokoama, Kanagawa, Jaan Kunito Okuyama Yokoama National University Yokoama, Kanagawa, Jaan ABSTRACT Te critical eat flux (CHF) in saturated ool boiling of water was investigated exerimentally under te condition in wic a oneycomb orous late is attaced to te eated surface. In a revious study, te CHF was sown exerimentally to be enanced to more tan twice tat of a lain surface in te case of a oneycomb orous late wit a vaor escae cannel widt of 1.4 mm and a cannel eigt (late tickness) of 1. mm (Mori and Okuyama (9)). Te enancement is considered to result from te caillary suly of liuid onto te eated surface and te release of generated vaor troug te cannels. In te resent aer, te vaor escae cannel widt was varied in te range of 1.4 mm to 7.9 mm, wic was smaller tan te Taylor instability wavelengt (aroximately 15.6 mm), and te effect of te cannel widt on te saturated ool boiling CHF of water as been investigated. Te CHF values redicted by caillary limit models were comared wit measured values. As a result, it is clear tat te main mecanisms for CHF enancement using a oneycomb orous late are due to liuid suly to te eated surface as a result of not only caillary suction but also te inflow of liuid troug vaor escae cannels from te to surface due to gravity. Te ratio of te contribution in te mecanisms of te CHF enancement deends on te vaor escae cannel widts. In articular, in te case of a larger cell widt, te CHF is enanced rimarily due to te inflow of liuid troug vaor escae cannels from te to surface. INTRODUCTION Various surface modifications of te boiling surface, e.g., integrated surface structures, suc as cannels and microin fins, and te coating of a orous layer onto te eat transfer surface, ave been roven to effectively enance te eat transfer coefficient and te critical eat flux (CHF) in saturated ool boiling (Bar-Coen 1993; Honda and Wei, 4; Lienard et al., 1973; Coursey et al., 5). Honda and Wei (4) ointed out tat microin-fins can increase te CHF in FC-7 (u to aroximately.33 MW/m ) more effectively tan oter surface modifications, e.g., microorous coating, dendritic eat sinks, and microstuds, for te exerimental conditions of less tan 85ºC of wall surface temerature, wic is te uer limit for a reliable oeration of LSI cis. Lienard et al. (1973) alied an egg-crate solid structure to enance te CHF and ave sown CHF augmentation u to aroximately.36 times (u to aroximately.49 MW/m ) as comared to te lain surface using acetone. In addition, te following ydrodynamic limit model for CHF rediction as also been suggested: CHF CHF, z N j = 1.14 AH λ d ( ρ ρ ) f g 3σ λd = π () g ( ρ ρ ) π.5 4 CHF, z ρg fg gσ f g (3) 4 were CHF is te CHF, CHF, z is Zuber s rediction for te CHF of te lain surface, AH is te area of te eater, N j is te number of escaing vaor jets on a eater of area A H, λd is te most suscetible Taylor unstable wavelengt in a orizontal liuid-vaor interface, fg is te latent eat of vaorization,σ is te surface tension between a liuid and its 1 Coyrigt xx by ASME

vaor, ρ f is te density of te saturated liuid, and ρ g is te density of te saturated vaor. Te coating of a tin orous layer of uniform tickness onto boiling surfaces can increase te CHF and reduce te surface suereat for a given surface eat flux in comarison wit a lain surface (Webb 1983; Muga and Plumb 1996; Cang and You 1997; Hwang and Kaviany 6; Arik, Bar-Coen, You 7; Hwang and Kaviany 6). In general, te CHF on te surface wit a tin and uniform coating of a orous layer is enanced to aroximately twice tat of a lain surface (Hwang and Kaviany 6; Liter and Kaviany 1). Boiling eat transfer on orous layer coated surfaces may be augmented due to nucleation from numerous sites, evaoration inside te ore structure, vaor ejection, and liuid suction from te to surface of te orous layer. Wit te increase in te surface eat flux, te flow rates of liuid and vaor troug te orous layer increase. Te increased flow resistance inside te orous layer may cause te formation and extension of a vaor layer near te eated surface, wic may result in te transition from nucleate boiling to film boiling. Several researcers ave resented novel structures of orous media in wic te liuid and vaor flow ats are searate. Suc searation of te flow ats may reduce flow resistance and, as a result, increase te CHF. Malysenko (1991) was te first to exerimentally investigate te boiling curves for a surface on wic a orous layer wit vaor escae cannels is coated. Stubos and Buclin (1999) examined analytically te effect of vaor cannels traversing te orous layer on te CHF. Semenic et al. (8) dissiated aroximately 4.9 MW/m in ool boiling at a suereat of 18 K using a bi-orous wick consisting of clusters of fine owder. Micro-ores inside te clusters continuously suly te working liuid to te surface of te clusters, were te evaoration takes lace, wile macro-ores between te clusters allow for easy escae of vaor. Note tat te geometric surface area of te bi-orous wick (diameter: 57 mm) was muc larger tan te eated surface area (diameter: 9.7 mm) (Semenic et al. 8). Te effect of te orous layer on CHF enancement may deend on te diameter of te orous layer relative to tat of te eated surface because liuid may be umed along te surface toward te center of te eated surface by caillary suction. Wu et al. () sowed exerimentally te effects of te size and density of vaor cannels on ool boiling eat transfer. Te CHF, owever, as not been enanced to a degree greater tan tat acieved by extending te surface area. Liter and Kaviany sowed tat modulated (eriodically non-uniform tickness) orous layer coating enances te ool boiling critical eat flux of entane by nearly tree times (.76 MW/m ) comared to a lain surface (.5 MW/m ). Two ossible liuid coking limits, i.e., te ydrodynamic limit and te viscous drag limit, were roosed as mecanisms by wic to determine te CHF. For te tested surface coating and fluid system, te measured CHFs were in good agreement wit te redicted CHFs based on te ydrodynamic limit, were Zuber s ydrodynamic teory is modified to account for te effect of te coating modulation wavelengt on te develoment of te stable vaor layer above te coated surface. In addition, te ydrodynamic limit model for te CHF rediction as also been suggested to be as follows:.5 π σρg, 8 CHF =, (4) fg λm were λ m is te modulation wavelengt. Based on te studies mentioned above, te mecanism of CHF enancement will be exlained by te caillary suction effect, te extended surface area effect, or liuid suly caused by te ydrodynamic effect. Comared wit te lain surface, te rate of CHF enancement caused by te ydrodynamic unstable effect or te extended surface area effect as been sown to be large (u to aroximately tree times), as described above (Honda and Wei (4), Lienard et al. (1973), and Liter and Kaviany ). However, te absolute value itself was not so large (maximum of aroximately.76 MW/m ) because an organic liuid or a refrigerant was often used as te test liuid. On te oter and, Semenic et al. (8) sowed tat te CHF was extremely augmented (u to 4.9 MW/m ) due to te caillary effect using water. Note tat, at resent, a large eated surface wit a ig eat flux aears to be difficult to cool. Terefore, in order to remove te ig eat flux of large eated surface, we focused on te use of caillary suction for enancement of te CHF. A oneycomb-structured ceramic orous late, wic is commercially available as a filter for urifying exaust gases from combustion engines, was selected as te test material. Tis oneycomb orous late as considerably smaller micro-ores, on te order of.1 µm, as comared to tose of sintered metal owders and is simly attaced to te test surface witout any treatment, suc as sraying or sintering. Te CHF as been enanced exerimentally u to more tan aroximately twice tat of a lain surface (aroximately. to.5 MW/m ) wit 3 mm in eated surface diameter for te case of a vaor escae cannel widt of 1.4 mm and a cannel eigt (late tickness) of 1. mm in te oneycomb orous late (Mori and Okuyama,(9)). Moreover, taking a simle one-dimensional caillary limit model into consideration, te enancement was considered to be caused by te caillary suly of liuid onto te eated surface. In te resent aer, te vaor escae cannel widt was varied in te range of 1.4 mm to 7.9 mm, wic was smaller tan te Taylor instability wavelengt (aroximately 15.6 mm), and te effect of te cannel widt in te saturated ool boiling CHF of water as been investigated exerimentally. Te CHF as redicted by caillary limit models was comared wit te measured CHF. As a result, te main mecanisms for te CHF enancement using a oneycomb Coyrigt xx by ASME

orous late were found to be due to liuid suly to te eated surface caused by not only caillary suction but also te inflow of liuid troug vaor escae cannels from te to surface by gravity. Te ratio of contribution in te mecanisms of te CHF enancement deends on te cell widts. EXPERIMENTAL APPARATUS AND PROCEDURE Exerimental Aaratus A scematic diagram of te ool boiling test facility is sown in Fig. 1. Te main vessel, wic is made of Pyrex glass, as an inner diameter of 87 mm and a eigt of mm. Te ool container was filled wit distilled water to a eigt above te eated surface of aroximately 6 mm. Te eater comonent was a coer cylinder aving a diameter of 3 mm and a eigt of 1 mm. Te eat flux was sulied to te boiling surface troug a coer cylinder using a cartridge electric eater, wic was inserted into te coer cylinder and was controlled by an AC voltage regulator. Te eat loss from te sides and bottom of te coer cylinder was reduced using a ceramic fiber insulation material. Te to orizontal surface of te coer cylinder wit a diameter of 3 mm is smoot and is used as te eat transfer surface in te exeriments. Two seated termocoules wit outer diameters of.5 mm were inserted orizontally along te center line of te coer cylinder. Te termocoules (TC1 and TC in Fig. 1) in te coer cylinder were searated axially by 6. mm. Te closest termocoule to te surface was located 5.4 mm below te boiling surface. Tese termocoules were calibrated using a latinum resistance termometer. Te wall temerature and te wall eat flux were calculated by alying Fourier s Law, were te termal conductivity of te coer was evaluated at te aritmetic averaged temerature between TC1 and TC. Exerimental Procedure Exeriments were carried out using distilled water as a working fluid under saturated conditions at atmoseric ressure. A seated eater was installed above te eated surface in te liuid bat in order to maintain te liuid temerature at te saturation temerature. For eac run, te eat flux was increased in increments of aroximately.1 MW/m until burnout occurred. All of te measurements were erformed in te steady state, wic was regarded as being reaced wen te temeratures did not cange more tan.5 K for at least 1 minutes. Wen burnout occurred, te eating was immediately stoed in order to revent damage to te eater or termocoules. Te final uasi-steady state eat flux was ten measured before te transition to film boiling and was taken as te CHF. All of te measurements were taken only for increasing eat flux, and te effects of ysteresis were not considered. Honeycomb Porous Plates Figure sows te oneycomb orous late used in te resent study, and a microgra of its structure is sown on te rigt-and side of te figure. Te oneycomb orous late, wic is commercially available, was used as a filter for urifying exaust gases from combustion engines. Te constituting ingredients consist of CaOAl O 3 (3-5 wt%), fused SiO (4-6 wt%), and TiO (5- wt%). Te vaor escae cannel widt (cell widt) d V, te wall tickness δ S of te grid, te aerture rate, te eigt of te oneycomb orous late δ, and te diameter of te oneycomb orous late are sown in Fig.. Tese wicks were attaced to te to of te All dimensions are in mm δ φ 3 δ S d v d v δ s Aerture ratio [ - ] δ 1.4.45.57 1.,., 5., and 1. 5. 1..66 3.3, 5. 7.9 1..75 5. Fig.1 Scematic diagram of te exerimental aaratus Fig. Dimensions of te oneycomb orous late 3 Coyrigt xx by ASME

boiling surface by using te oneycomb orous late against te boiling surface using a stainless steel wire net (mes size: 1) witout a termally conductive grease. Te ore radius distribution of te oneycomb orous lates was measured by mercury enetration orosimetry, and was found to eak at aroximately.17 µm, as sown in Fig. 3. Te average ore radius, te median ore radius, and te orosity of te oneycomb orous lates decided by orosimetry are.37 µm,.13 µm, and 4.8%, resectively. Uncertainty Analysis Te individual standard uncertainties are combined to obtain te estimated standard deviation of te results, wic is calculated using te law of roagation of uncertainty (Taylor and Kuyatt (1993)). Te uncertainties of eat flux, suereat Tsat, and eat transfer coefficient are evaluated using te following euations: (5) = λ + δ1 + T1 + T λ δ T1 T ( T ) sat = = Log differntial ore volume dv ore /d(logv ore ) cc/g ( T ) ( ) ( ) sat Tsat Tsat ( Tsat ) + T1 + δ + λ T δ λ ( T ) sat..1 1 ( T ) sat + Median ore radius:.19 μm Porosity: 4.8 %.1.1 1 1 1 Pore Radius r ore μm (6) (7) were T 1 and T are te temeratures at TC1 and TC, resectively, λ is te termal conductivity of te coer evaluated at te aritmetic mean value of T 1 and T, δ 1 is te distance between TC1 and TC, and δ is te distance between TC1 and te boiling surface. Table 1 sows an examle of te results for te relative uncertainties calculated from Es. (5) troug (7). As sown in te table, relative uncertainties deend on te exerimental conditions, and te relative uncertainties tend to become smaller wit increasing eat flux. CAPILLARY LIMIT MODEL CONSIDERING THE FORMATION OF A DRYOUT REGION IN THE POROUS STRUCTURE In order to redict te CHFs and effective eat transfer coefficients in te inverted meniscus tye evaorator, Krustalev and Fagri (1995) develoed a one-dimensional matematical model of te eat transfer during evaoration of te liuid from te liuid-vaor interface formed inside te orous structure along te eated surface. In tis model, te vaor flow troug te dry region of te orous structure is rovided by te caillary ressure gradient caused by te difference in te curvature of te menisci along te liuid-vaor interface. Te model can redict, for examle, te tickness of te dryout region inside orous material close to te eated surface, te eat transfer coefficient, te eat flux, and te ressure decrease due to te vaor flow troug te narrow dry orous region along te eated surface. Tese values are used in te caillary limit model to calculate te CHF for te case of te attacment of a oneycomb-structured orous late on te eated surface, as described below. Figure 4 sows a scematic diagram of te steam and water flows in a oneycomb orous late. As sown in te figure, liuid is transorted toward te eated surface witin te orous medium by caillary force. Vaor generated inside Wetted region of te orous structure Fig. 3 Pore radius distribution of te test orous material Table 1 Relative uncertainties of te exerimental measurements. Steam v,c l Steam v, [MW/m ] T [K] [kw/(m K)] / [%] T sat /T sat [%] / [%].5 17 8 13. 6. 14.5 1. 8 41 5.6 3.7 6.7 1.7 36 46 4.1 3.1 5.1.3 47 49 3.1.4 3.9 Dry region of te orous structure Fig. 4 Scematic diagram of steam and water flow in a oneycomb orous late attaced to a eated surface 4 Coyrigt xx by ASME

te orous structure in te vicinity of te eated surface flows troug te narrow dry orous zone along te eated surface toward te vaor cannel, and te vaor escaes uward troug te vaor cannels. It is assumed tat liuid suly to te eated surface troug te vaor escae cannel from te to surface by gravity does not occur because te cell widts (d v =1.4, 5., or 7.9 mm) are smaller tan te Taylor unstable wavelengt (15.6 mm). Te CHF is considered to be acieved under conditions suc tat te maximum caillary ressure is eual to te sum of te ressure losses along te vaor-liuid at in te following: = l + v, + v, c (8) were l and v, are te frictional ressure dros caused by te liuid and vaor flows in te orous medium,, resectively, and v c is te frictional ressure dro caused by te vaor flow troug te vaor escae cannels. Note tat te accelerational ressure dro, wic is caused by te ase cange from liuid to vaor at te liuid-vaor interface, is considered wen te osition of te liuid-vaor interface is determined in te eat transfer model of Krustalev and Fagri (1995). Te effect of v, c in E. (8) aears in te region of less tan.3 mm in vaor escae cannel widts d v (Mori and Okuyama (9)), wile is negligible for te tested v, c oneycomb orous lates of te resent study because te vaor escae cannel widt d v is more tan 1. mm, i.e., d v =1.4, 5., and 7.9 mm. Te maximum caillary ressure can be calculated by δ s y 1 3 δ s = 9 μm Wetted region of orous structure Dry region of orous structure loc [MW/m ] 1 1 1 1-1 δ s = 3 μm δ s = 3 μm P =.1 MPa δ = 1. mm T w = 15 δ v(x) δ s = 9 μm K =.4 1-14 m r eff = 1.8 μm λ eff = 4 W/(m K) x ΔP [kpa] δ v [μm] 1 1 1 δ s = 3 μm δ s = 3 μm P =.1 MPa δ = 1. mm T w = 15 K =.4 1-14 m r eff = 1.8 μm λ eff = 4 W/(m K) 1 1-1 1 1 1 1 1 3 x [μm] 1 1 1 1 3 1-1 1 1 1 1 1 3 δ s [μm] x [μm] Fig. 5 Examles of calculated results (δ v (x), loc (x),, l v,, and ave, ) as 5 4 3 1 ΔP l P =.1 MPa δ = 1. mm T w = 15 ΔP v, K =.4 1-14 m r eff = 1.8 μm λ eff = 4 W/(m K) ave, a function of δ s for a oneycomb orous late eigt δ of 1. mm (Krustalev and Fagri (1995)) 6 5 4 3 1 ave, [MW/m ] 5 Coyrigt xx by ASME

σ (9) c,max = r eff cosθ men,min were r eff is te effective ore radius, σ is te surface tension, and is te minimum wetting contact angle. θ men, min Te ressure decrease l using Darcy s law is exressed as µ lave, ( δ δv, ave ) = l Kρlfg were µ l is te viscosity of te liuid, ave, is te average eat flux at te contact area between te oneycomb orous late and te eated surface, δ is te eigt of te oneycomb orous late, δ v,ave is te average tickness in te dry region of te orous structure, K is te ermeability, ρ l is te density of te liuid, and fg is te latent eat of vaorization. Substituting Es. (9) and into E. (8), and omitting v, c as exlained above, te following euation can be obtained: σ µ ( δ δ ) (11) r eff cosθ men,min = l ave, l Kρ fg v, ave + Calculation of te redicted CHFs in te resent study as been erformed in te following stes: Te average temeratures of te eated surface were given as constant values based on te exerimental results, and te initial values of te vaor blanket tickness δ v at x = were assumed (see Fig. 5(a)). () Te values of ave,, v,, and δ v,ave, were calculated from te eat transfer model of Krustalev and Fagri (1995) and were substituted into E. (11). (3) If E. (11) is satisfied, ten ave, is converted into CHF, wic corresonds to te eated surface area A (diameter: 3. mm), as follows: AW = CHF ave, A were A w is te contacted area of te oneycomb orous late wit te eated surface and A is te eated surface area (aroximately 7.7 cm ). Conversely, if E. (11) was not satisfied, ten a smaller value of δ v at x = was set, and stes troug (3) were reeated several times wit different δ v at x = until E. (11) as been satisfied. Te results were obtained wit constant termoysical roerties corresonding to te saturation temerature under te atmoseric ressure condition. In te following, te calculated results are comared wit te observed results. Figure 5 sows examles of te calculated results (δ v (x), loc (x),, l v,, and ave, ) as a function of δ s for a oneycomb orous lates eigt δ of 1. mm. Te values of ermeability K and te effective ore radius r eff were measured v, for te orous material used in te resent study ( K =.4 1 14 m, r eff = 1.6 µm), and te effective termal conductivity λ eff was sulied by Nagamine Co. (te manufacturer of te oneycomb orous late). Te data available in te literature for θ was used (33 degrees, men, min Steanov et al. (1977)). Figure 5 sows tat loc at x = is te maximum value because te vaor blanket tickness δ v at x = is minimum, and ave, is significantly sensitive to te cange in δ s. EXPERIMENTAL RESULTS AND DISCUSSION Effects of eigt of te oneycomb orous late δ on CHF, suereat Tsat, and eat-transfer coefficient Figure 6 sows CHF, Tsat, and for te cases of (d v, δ s ) = (1.4 mm,.45 mm) and (d v, δ s ) = (5. mm, 1. mm), resectively. Te symbols and error bars reresent te average values and te standard deviations of te resent data obtained from more tan tree searate exeriments, resectively. Te symbols and error bars in te following figures are te same meaning as described above, resectively. Te solid and dased lines are te calculated CHFs from te caillary limit model, as stated in te revious section. Figure 6 indicates te following: Te saturated ool-boiling CHF of a oneycomb orous late for te case of (d v, δ s, δ ) = (1.4 mm,.45 mm, 1. mm) is imroved u to more tan twice (aroximately.1 to.5 MW/m ) as comared wit te saturated oolboiling CHF for a lain surface (aroximately 1.1 MW/m ). Te observed CHF is increased wit te decrease of δ for te case of (d v, δ s ) = (1.4 mm,.45 mm), wereas te CHF for te case of (d v, δ s ) = (5. mm, 1. mm) does not cange significantly, irresective of te value of δ. Te measured values are muc larger tan te values calculated using te caillary limit model. Te tendencies of te calculated and measured values differ for te cases of (d v, δ s ) = (1.4 mm,.45 mm) and (d v, δ s ) = (5. mm, 1. mm). In oter words, te measured values for te case of (d v, δ s ) = (5. mm, 1. mm) are larger tan te measured values for te case of (d v, δ s ) = (1.4 mm,.45 mm). On te oter and, te calculated values ave te oosite tendency comared to te measured values. Te reason for tis is exlained in te following section. Tere are ig eat removal conditions of greater tan MW/m. However, Tsat s (aroximately 5 K) of a oneycomb orous late in te CHF conditions is not so large comared to te Tsat s of a lain surface (aroximately 34 K). 6 Coyrigt xx by ASME

of te oneycomb orous late is enanced u to aroximately 1 to 135% comared to tat of te lain surface. ΔT sat [ K ] CHF [MW/m ] [ kw/(m K) ] 3 P =.1 MPa ΔT SUB = K 1 (d v,δ s ) = (1.4 mm,.45 mm) (d v,δ s ) = (5. mm, 1. mm) 5 1 15 6 5 4 3 1 (d v,δ s ) = (1.4 mm,.45 mm) δ Plain surface P =.1 MPa ΔT SUB = K (d v,δ s ) = (5. mm, 1. mm) Δ = Δ l + Δ v, (Krustalev and Fagri(1995)) 5 1 15 6 5 4 3 1 (d v,δ s ) = (5. mm, 1. mm) δ Plain surface P =.1 MPa ΔT SUB = K 5 1 15 δ (d v,δ s ) = (1.4 mm,.45 mm) Plain surface Mecanism of liuid suly to te eated surface caused by te oneycomb orous lates Note tat te measured values are muc larger tan te calculated values in te revious section, as sown in Fig. 6(a). Tis suggests tat te liuid suly to te eated surface is caused by oter effects as well as te caillary suction effect. Figure 7 sows a scematic diagram of te liuid suly mecanism in a oneycomb orous late. As sown in te figure,, (), and (3) deict te liuid flow caused by te caillary force, te inflow of liuid troug te vaor escae cannels from te to surface by gravity, and te vaor bubble generation from te clearance between te oneycomb orous late and te eated surface (see te boiling configuration sown in Fig. 7), resectively. In order to evaluate te effect of (3) in Fig. 7, CHF exeriments in wic vaor bubble generation is revented using an O-ring ave been erformed for te case of (d v, δ s, δ ) = (1.4 mm,.45 mm, 5 mm). As a result, for te case wit an O-ring, te CHF decreases, and te difference in CHF between te cases wit and witout an O-ring is aroximately.3 MW/m. Te eat fluxes, wic are subtracted.3 MW/m from te CHF of oneycomb orous late witout an O-ring in Fig. 6, can still be larger tan te CHF of te lain surface in some exerimental conditions. Tis indicates tat te cooling tecnology using oneycomb orous lates may be alied to te large eated surface wit ig eat flux. Te CHF exeriments using a oneycomb solid late witout micro-ores, wic was fabricated by imregnating a oneycomb orous late wit adesive, were conducted in order to consider te effect of () in Fig. 7. Figure 8 sows te eat flux *(= CHF -.3 MW/m ) of te oneycomb orous late and te solid oneycomb late, resectively, as functions of d v for te case of δ = 5 mm. Vaor bubble (3) Honeycomb orous late Steam () Fig. 6 CHF, Tsat, and as a function of δ Fig. 7 Scematic diagram of te liuid suly mecanisms to te eated surface caused by a oneycomb orous late 7 Coyrigt xx by ASME

Te solid and dased lines in tis figure reresent te ydrodynamic limit as calculated by Es. and (4), resectively. It can be seen from te figure as follows: All of te *s of te oneycomb orous late are larger tan tose of te solid oneycomb late, and tese differences are caused by te caillary effect. Te CHF of oneycomb solid late is not so small even for te case of a cell widt d v of 1.4 mm (.6 MW/m ), wic is muc smaller tan te Taylor unstable wavelengt (15.6 mm). Tis indicates tat te liuid can be sulied to te eated surface due to te inflow of liuid troug te vaor escae cannels from te to surface by gravity, even in tis case. Note tat te fin effect can be neglected due to te low termal conductivity of te ceramic Rate of contribution of liuid suly mecanisms in te CHF [%] Rate of te effect of liuid suly mecanisms on CHF [%] * (= CHF -.3 ) [MW/m ] 1 1 8 6 4 3 1 Hydrodynamic limit by e.(4) (Liter and Kaviany,1) P =.1 MPa ΔT SUB = K δ = 5. mm Hydrodynamic limit by e. (Lienard et al. 1973) * +() Honeycomb orous late (CHF is enanced by te effect of and () in Fig.7) * () Honeycomb solid late (CHF is enanced by te effect of () in Fig.7) 1 5 1 5 d v () (3) Fig. 8 * as a function of d v () (3) δ = 5. mm () (3) d v = 1.4 mm d v = 5. mm d v = 7.9 mm Liuid suly caused by caillary suction. () Liuid suly caused by te inflow of liuid troug vaor escae cannels. (3) Liuid suly caused by vaor bubble generation from te clearance between te oneycomb orous late and te eated surface. Fig. 9 Rate of contribution of liuid suly mecanisms in te CHF material. Moreover, te *s of te oneycomb solid late increase wit te increase in cell widts d v. Tis tendency is different from tat described by E. (4), as roosed by Liter and Kaviany. Lienard et al. (1973) roosed te CHF model given by E.. According to E., te CHF sould increase wit te decrease of A H. Actually, te measured CHF becomes smaller tan te CHF redicted using E. in te region of smaller A H because te effect of viscosity in te liuid is not negligible (Lienard et al. (1973)). Since all of te cell widts d v considered in te resent study are smaller tan te Taylor unstable wavelengt, and considering te above discussions, te tendency of te oneycomb solid late in Fig. 8, in wic te CHFs decrease wit te decrease of d v, may be caused by te viscosity of te liuid. Figure 9 sows te ratio of te effects of, (), and (3) in Fig. 7 as a function of d v for te case of δ = 5 mm. Tis ratio is calculated as follows: First, * wic corresonds to te caillary effect, was calculated by subtracting * () from * +(). Ten, * +() consists of te eat fluxes tat corresond to te caillary effect and te effect of te inflow of liuid troug te vaor escae cannels from te to surface. Here, * () indicates only te effect of te liuid inflow troug te vaor escae cannels, wic is evaluated based on te results for te oneycomb solid late. Next, * (3) (=.3 MW/m ), wic is assumed to ave te same value for all of te tested oneycomb orous lates, corresonds to te effect of te vaor bubble generation from te sace between te oneycomb orous late and te eated surface. Using te values described above, te ratios of contribution for te CHFs of, (), and (3) in Fig. 7 were estimated. Note tat eat flux * for te caillary effect may be underestimated because te values of * +() and * () at te same cell widt d v are different, as sown in Fig. 8, i.e., te vaor velocities from te vaor escae cannel are different. As sown in Fig. 9, te effect of () becomes dominant wit te increase of d v. In articular, for te case in wic d v = 7.9 mm, te contribution ratio for te CHF is more tan 6%. Figure 1 sows *, wic corresonds to te caillary effects, as functions of δ for te cases of (d v, δ s ) = (1.4 mm,.45 mm) and (d v, δ s ) = (5. mm, 1. mm). In addition te redicted CHFs are also given for te following two cases, i.e., = l + v, and c, max = l. Te former is te case in wic te frictional ressure dros caused by te liuid and vaor flows inside te orous medium are considered, and te latter is te case in wic te dryout region in te orous structure is assumed not to form, i.e., v, is omitted. Te difference between te CHFs calculated from = l + v, and c, max = l decreases wit te increase in δ, as sown in te figure. Tis is because l becomes dominant in te region of larger δ. As sown in Fig. 1, te measured CHF tends to be lotted between te 8 Coyrigt xx by ASME

CHFs calculated from = l + v, and c, max = l. Te reason for tis is exlained in detail in te following. Figure 11 deicts te surface rougness of a oneycomb orous late tat is measured using a Laser Focus Dislacement Meter (LT-811, Keyence Co.). Te surface rougness of te oneycomb orous late is on te order of ten microns, as sown in Fig. 11. Te oneycomb orous late contacts locally wit te eated surface because te oneycomb orous lates were attaced to te to of te boiling surface by just using against te surface using te stainless steel wire net witout a termally conductive grease. Based on te above discussion, te steam and water flows inside a oneycomb orous late are exected to be as sown in Fig. 1. Te situation inside te orous material attaced locally to te eated surface is considered to be similar to te case in wic te value of δ s is very small in Fig. 5. For te case of smaller δ s, te average eat flux just beneat te orous material is very large because te tickness of te vaor blanket is very small. Provided tat several arts of te oneycomb orous late are in contact wit te eated surface, it is reasonable for te average eat flux * over te entire eated surface to be larger tan te CHF calculated from = +. * ( = CHF(orous) - CHF(solid) ) [MW/m ] l v, 3 Δ = Δ l Mori and Okuyama(9) P =.1 MPa ΔT SUB = K 1 5 1 δ Fig. 1 * (d v,δ s ) = (1.4 mm,.45 mm) (d v,δ s ) = (5. mm, 1. mm) Δ = Δ l + Δ v, Krustalev and Fagri(1995) as a function of δ Steam v,c In contrast, te maximum eat flux due to te caillary effect is considered to be te eat flux calculated from c, max = l. Te CHF from = l sould be overestimated because v, is neglected and te bottom of te oneycomb orous late is assumed to be in erfect contact wit te eated surface. Considering te above discussion, it is reasonable to suose tat te measured * is lotted between te CHFs redicted from = l + v, and c, max = l. Tese results lead to te conclusion tat local contact wit te orous material may enance te caillary effect and contribute to te increase in CHF, as comared wit te case in wic te oneycomb orous late is in erfect contact wit te eated surface in te resent exerimental range. CONCLUSIONS Te effect of te cell widt on te CHF and te mecanisms for CHF enancement by te attacment of a oneycomb-structured orous late on te eated surface were investigated exerimentally using water under te saturated ool boiling conditions. Te following conclusions were obtained: 1. Te main mecanisms for CHF enancement using a oneycomb orous late are due to liuid suly to te eated surface caused by caillary suction and te inflow of liuid troug vaor escae cannels from te to surface. Te ratio of te contribution of tese mecanisms of te CHF enancement deends on te cell widts. Wetted region of te orous structure y[μm] 1-1 - 1 3 4 x[μm] Fig. 11 Surface rougness of a oneycomb orous late Wetted region of te orous structure Fig. 1 Scematic diagram of exected steam and water flow in a oneycomb orous late in te vicinity of a eated surface 9 Coyrigt xx by ASME

. Te CHF is more tan MW/m in te resent exerimental range, and te suereat Tsat is aroximately 5 K, wic is not so large comared wit te case of a lain surface (aroximately 3 K). 3. Te liuid at te to surface of te oneycomb orous late can be transorted to te eated surface troug vaor escae cannels by gravity, even in te case of a cell widt d v of 1.4 mm, wic is muc smaller tan te Taylor unstable wavelengt (15.6 mm). For te case of larger cell widt, te CHF is enanced rimarily due to te inflow of liuid troug te vaor escae cannels from te to surface. 4. Calculated CHFs were comared wit measured CHFs. As a result, it is ossible tat local contact between te orous material and te eated surface contributes to te CHF enancement. NOMENCLATURE A : eated surface area A H : area of eater A W : contact area between te oneycomb orous late and te eated surface d v : vaor escae cannel widt (cell widt) of te oneycomb orous late : eat transfer coefficient fg : latent eat of vaorization K : ermeability N j : number of escaing vaor jets on a eater of area A H : eat flux ave, : average eat flux at te contact area between te oneycomb orous late wit a eated surface : critical eat flux CHF, : Zuber s rediction for te CHF of a lain surface CHF z loc (x) : local eat flux just beneat te orous material * : eat flux (= CHF -.3 MW/m ) r eff : effective ore radius T 1 : temeratures at TC1 T : temeratures at TC δ 1 : distance between TC1 and TC δ : distance between TC1 and te boiling surface δ : eigt of te oneycomb orous late δ S : wall tickness between te vaor escae cannels δ v,ave : average tickness in te dry region of te orous structure δ v (x): local vaor blanket tickness just beneat te orous material l : frictional ressure dro caused by te filtration of liuid troug te orous structure v, : frictional ressure dro caused by te filtration of te vaor troug te dry region of te orous structure v, c : frictional ressure dro caused by te vaor flow troug te vaor escae cannel : maximum caillary ressure c,max T sat : suereat λ : termal conductivity of te coer λ d : most suscetible Taylor unstable wavelengt in a orizontal liuid-vaor interface λ eff : effective termal conductivity λ m : modulation wavelengt. µ l : viscosity of te liuid θ : minimum wetting contact angle men,min ρ f : density of te saturated liuid ρ g : density of te saturated vaor σ : surface tension between a liuid and its vaor ACKNOWLEDGMENTS Tis study was suorted in art by te Kurata Memorial Hitaci Science and Tecnology Foundation. REFERENCES Arik M., Bar-Coen A., You S.M., 7. Enancement of Pool Boiling Critical Heat Flux in Dielectric Liuids by Microorous Coatings, International Journal of Heat and Mass Transfer 5, 997-19. Bar-Coen A., 1993. Termal Management of Electronic Comonents wit Dielectric Liuids, JSME International Journal 36, 1-5. Cang J.Y. and You S.M., 1997. Enanced Boiling Heat Transfer from Micro-orous Surfaces: Effects of a Coating Comosition and Metod, International Journal of Heat and Mass Transfer 4, 4449-446. Coursey, J. S., Kim, J., and Boudreaux, P.J.,5, Performance of graite foam evaorator for use in termal management, Journal of Electronic Packaging, Vol. 17, No., 17-134. Honda H. and Wei J, 4. Enanced Boiling Heat Transfer from Electronic Comonents by Use of Surface Microstructures, Exerimental Termal and Fluid Science 8, 159-169. 1 Coyrigt xx by ASME

Hwang G. S. and Kaviany M., 6. Critical Heat Flux in Tin, Uniform Particle Coatings, International Journal of Heat and Mass Transfer 49, 844-849. Lienard J.H., Dir V.K., Rierd D.M., 1973, Peak Pool Boiling Heat-Flux Measurements on Finite Horizontal Flat Plates, Journal of Heat Transfer, 95(4), 477-8. Liter S.G. and Kaviany M., 1. Pool Boiling CHF Enancement by Modulated Porous layer Coating: Teory and Exeriment, International Journal of Heat and Mass Transfer 44, 487-4311. Malysenko S.P., 1991, Features of Heat Transfer wit Boiling on Surfaces wit Porous Coatings, Termal Engineering 38 (), 38-45. Mori S. and Okuyama K., 9, Enancement of te critical eat flux in saturated ool boiling using oneycomb orous media, International Journal of Multiase Flow, 35, 946-951. Muga M.P. and Plumb O.A., 1996. An exerimental study of boiling on a wicked surface, International Journal of Heat and Mass Transfer 39, 771-777. Stubos A.K. and Buclin J.M., 1999. Enanced Cooling via Boiling in Porous layers: Te Effect of Vaor Cannels, Journal of Heat Transfer 11, 5-1. Semenic T., Lin Y.Y., Catton I., Sarraf D.B., 8. Use of Biorous Wicks to Remove Hig Heat Fluxes, Alied Termal engineering 8, 78-83. Taylor B.N. and Kuyatt C.E., 1993. Guidelines for evaluation and exressing te uncertainty of NIST measurement results, NIST Tec. Note 197, 1-. Webb R.L., 1983. Nucleate Boiling on Porous Coated Surfaces, Heat Transfer Engineering 4, 71-8. Wu W., Du JH, Hu XJ, Wang BX,. Pool Boiling Heat Transfer and Simlified One-dimensional Model for Prediction on Coated Porous Surfaces wit Vaor Cannels, International Journal of Heat and Mass Transfer 45, 1117-115. 11 Coyrigt xx by ASME