Progress Towards a Miromained Heat Exanger for a Cryosurgial Probe D. W. Ho W. Zu G. F. Nellis S. D. Suetter S. A. Klein Y. B. Gianandani University of Wisonsin Madison Wisonsin USA University of Miigan Ann Arbor Miigan USA ABSTACT Tis aer desribes develoments towards a litogray-based miro-fabriated reuerative eat exanger tat is intended to be a omonent witin a ryosurgial robe. A ryosurgial robe must aieve a temerature below -50 C in order to be linially useful for te treatment of aner. Cryosurgial robes based on te mixed gas Joule-Tomson (JT yle require only a reuerative eat exanger and an exansion valve in te old-ead. Terefore tis yle as te otential for ig reliability and miniaturization. Te objetive of tis rojet is to exlore te otential for alying miromaining teniques to te design and fabriation of te reuerative eat exanger. Te eat exanger must maintain ig stream-to-stream termal ondutane wile restriting axial ondution losses. Te st generation eat exanger onsists of rows of fins omosed of ig ondutivity silion tat are bonded onto a single 00 µm tik base late omosed of low ondutivity Pyrex glass. Tis design minimizes te number of wafers tat must be bonded omared to more favorable designs based on interleaving many ig ondutivity silion lates wit low ondutivity Pyrex saers. However tere are several disadvantages assoiated wit te design most notably te fragility of te tin Pyrex base late searating te ig and low ressure streams; tis limits te ability of te eat exanger to witstand te relatively large ressure differene tat is required to energize te Joule-Tomson ooling yle. Te st generation eat exanger was fabriated and tested and te results of tese tests will be rovided in te aer. In arallel a bonding tenique as been develoed tat allows multile lates to be ermetially joined using a metallization layer. Terefore a nd generation eat exanger design is resented wi overomes many of te limitations of te st generation devie. Seifially it will be more robust and will rovide enaned termal erformane. Te design of tis nd generation eat exanger is disussed. INTODUCTION Over te ast tree deades ryosurgery as beome a standard treatment for several tyes of aners loated in easily aessible areas of te body inluding rostate and liver aner. Canerous tumors are loally destroyed using ryosurgery by exosing te malignant tissue to
reeated freeze/taw yles []. Te resulting dead tissue is absorbed by te body wi minimizes blood loss and te ost-oerative disomfort tat is usually assoiated wit exision. Te ultimate goal of tis resear effort is to develo a fully integrated miromained ryosurgial robe based on te Joule-Tomson (JT ooling yle. Su a robe may ave signifiant advantages over onventional ryosurgial robes in terms of termal erformane size flexibility and ost. Te seifi subjet of tis aer is te develoment of a mirofabriated reuerative eat exanger te key omonent witin te JT yle. An overview of te st generation miromained reuerative eat exanger and exerimental results are resented. Te st generation devie was designed to minimize te number of bonding stes and as a result is not otimally designed bot in terms of meanial reliability and termal erformane. A nd generation eat exanger design as been enabled by te develoment of advaned bonding teniques based on a metallization roess. Te nd generation devie uses a erforated late tye design and will terefore be more robust and ave iger termal erformane. Te design of tis eat exanger is disussed. ST GENEATION DESIGN AND FABICATION One of te allenges in te develoment of a miromained J-T ooler is te reuerative eat exanger wi must simultaneously maintain good stream-to-stream eat ondutane wile restriting arasiti stream-wise ondution losses and suorting a large stream-to-stream ressure differene. Tese requirements are neessary in order to maintain a large entaly differene between te two fluid streams and tus aieve ig ooling erformane for te robe. Te st generation eat exanger is a lanar miromained devie in wi silion wafers are anodially bonded to eiter side of a very tin low ondutivity Pyrex base late. Te silion wafers are miromained [] so tat rows of silion fins are left beind. Tese rows are aligned on te ig and low ressure sides and inlude miro-sale fluid annels (larger on te low ressure tan te ig ressure tat fore te fluid into intimate ontat wit te fins. Tis design is in ontrast to onventional reuerative eat exangers for ryosurgery tat use eiter erforated late designs in wi ig ondutivity oer lates are interleaved wit stainless steel saers [3] or finned tube designs tat use one or more finned tubes wound on a mandrel. Silion as termal ondutivity tat is similar to oer and Pyrex as termal ondutivity tat is an order of magnitude less tan stainless steel; tis ombination of very ig and low termal ondutivity suggests tat a silion and Pyrex omosite eat exanger will be attrative. In order to allow adequate termal ommuniation between te streams reliminary simulation of an otimized design [4] suggest tat wen using a mixture of ydroarbons at a working ressure of 0 bar te Pyrex base late between te ig ressure annel and low ressure annel an be no tiker tan about 00 µm in order to rovide adequate refrigeration ower. Figure sows a fabriated miro reuerative eat exanger. Te size of tis devie is 6 m.5 m wit.5 mm total tikness. Figure. st generation eat exanger illustrating te Pyrex a silion fins and green anodi glass-frit bond. Figure. Measured effetiveness based on ot side energy balane and te redited effetiveness using te miro eat exanger model as a funtion of te mass flow rate.
MEASUED ESULTS Te glass frit bonding roess used to join te Pyrex outer as to te Pyrex base late in te st generation design does not rovide a ermeti seal and tis as revented its installation into a termal vauum faility. Instead te eat exanger was laed into a avity witin a iee of Styrofoam and surrounded by fiberglass insulation in an effort to minimize te arasiti eat load. N-butane was used as te working fluid in an oen loo Joule-Tomson yle and exanded troug an orifie. Te self-ooling data are limited to relatively small temerature differenes due to te redued JT effet assoiated wit te small ressure differene tat ould be suorted aross te base late. Te ressure differene antiiated for a ryosurgial robe may be as ig as 400 kpa (00 si wereas te testing was limited to less tan 70 kpa (0 si in order to avoid fraturing te base late. A tiker base late would rovide greater strutural integrity but te inreased termal resistane between fluid streams would furter redue ooling ower. Te redited and measured effetiveness as a funtion of mass flow rate (based on te ot side energy balane are illustrated in Figure. Te effetiveness of te eat exanger ( is defined as te ratio of te eat transfer rate witin te eat exanger to te maximum ossible eat transfer rate for te given inut fluid onditions. Te effetiveness an be omuted based on an energy balane for eiter te ot or old side of te eat exanger ( or resetively: qhx qhx or ( q q HX max HX max 3 were q is te atual eat transfer (evaluated from an energy balane on te ot or old side HX and q is te ideal eat transfer in erfet onditions. Te error bars in Fig. sow roagated HX max unertainty in te effetiveness based on unertainty in te termooule temerature measurements. Note tat te unertainty inreases as te mass flow rate is redued due to te smaller temerature differenes tat are required to omute te effetiveness. Te measured results agree wit te teoretial model for te flow rates tat are onsistent wit aurate measurements. Te results of te st generation tests indiate te limitations of te design but also validate te ability of te omuter model to redit te termal erformane of te eat exanger. Terefore tese modeling teniques ave been used to develo a more robust design enabled by te develoment of more advaned multi-wafer joining teniques tat will rovide ooling erformane omarable to ommerially available ryosurgial robes. ND GENEATION HEAT EXCHANGE MODEL A new bonding tenique tat sows te otential to ermetially join many multile lates as been develoed in arallel wit te st generation eat exanger testing. Te joining tenique uses a metallization layer tat is alied to te wafers and aommodates te bond. Tis nd generation eat exanger design is similar to most erforated late eat exangers: ig ondutivity silion lates are alternated wit low ondutivity Pyrex saers. Figure 3 illustrates te nd generation design sowing te erforated late eat exanger onet. Many narrow slots are mained into te silion late in order to rovide te two streams wit a large amount of surfae area for eat exange. Te lates are divided into two regions by te Pyrex saer (indiated by te gray area in Fig. 3. Te ig ressure region allows flow of te ig ressure working fluid in one diretion (into te aer in Figure 3 wile te low ressure region allows flow of te low ressure working fluid in te oosite diretion. Te ig and low ressure regions are searated and sealed from ea oter via bonds formed between te late and te saer. Te eat transferred from te ig ressure fluid into te silion late material is onduted troug te silion late into te low ressure region were it is transferred
4 saer ig ressure region of late low ressure region of late slots eted troug late for ig ressure fluid flow slots eted troug late for low ressure fluid flow Figure 3. Conet for miromained erforated late eat exanger. finally to te low ressure fluid. Many of tese late/saer sets are staked u to aieve ig effetiveness. A numerial model as been develoed to otimize te geometry of te eat exanger; te basi struture of te model is te termal-fluid simulation of a single late oerating at te average ondition witin te eat exanger. Te eynolds numbers for te flow troug te slots on te ig and low ressure sides (e and e are given by: e e ρ d u m ( μ ρd um (3 μ were ρ is te fluid density u m is te mean veloity and μ is te fluid visosity; te subsrits and refer to te ig and low ressure fluids resetively. Te variables d is te ydrauli diameter of te assage. For laminar flow (e < 300 te Nusselt numbers under fully develoed onditions for a retangular dut subjet to a onstant wall temerature (Nu lam are given by osenow et al. [5]: ( 3 3 4 ( 3 3 4 Nu 7.54.6α + 4.97α 5.9α +.70α + 0.548α (4 lam Nu 7.54.6α + 4.97α 5.9α +.70α + 0.548α (5 lam were α and α are te aset ratios of te slot: min ( ws Lf α (6 max ( ws Lf min ( ws Lf α (7 max w L ( s f and w s and L f are te widt and lengt of te slot resetively. Te Nusselt number under fully develoed onditions for a turbulent flow (Nu turb and Nu turb is redited by te Gnielinski [6]: Nu Nu ( /8( 000 f e Pr (8 + turb turb /3.7 fturb /8 ( Pr ( /8( 000 f e Pr (9 + turb turb /3.7 fturb /8 Figure 4. Fin effetiveness as a funtion of fin number of transfer units for several values of te fin onstant. ( Pr
were f turb is te frition fator for fully develoed turbulent flow and Pr is te Prandtl number omuted aording to: μ Pr (0 k μ Pr ( k were is te onstant ressure seifi eat aaity and k is te termal ondutivity of te fluid. Te frition fator for fully develoed turbulent flow an be alulated aording to Petukov et al. [7]: f ( ( turb 0.79ln e.64 ( f ( ( turb 0.79ln e.64 (3 Tese orrelations are seleted beause tey are valid down to a eynolds number of 3000; lower eynolds numbers are assumed to orresond to laminar flow (wi is onservative relative to te redited Nusselt number. Tese Nusselt number orrelations are onservative bot beause te enanement in te eat transfer related to te develoing region of te annel is not aounted for and also beause te two-ase eat transfer tat ours over te majority of te eat exanger for fluid mixture working fluids will be araterized by larger eat transfer oeffiients [8]. Te eat transfer oeffiients (t are: 5 t t Nu k (4 d Nuk (5 d It is assumed tat te fluid will omletely mix in te sae between adjaent lates so tat te temerature of te ot fluid is uniform as it enters all of te slots on te ig ressure side (T in and te temerature of te old fluid is uniform as it enters all of te slots on te low ressure side (T in. Te fluid assing troug ea fin row does not maintain a onstant temerature; rater its temerature will ange due to its finite aaity rate. As a result of tis as well as axial (i.e. in te flow diretion temerature variations in te fin material it is inorret and non-onservative to use onventional fin equations tat assume onstant fluid temerature. A numerial model tat solves te ouled differential equations governing te two-dimensional temerature distribution in te fluid and te fin material as been develoed validated and non-dimensionalized. Te result of te numerial model is te redition of te fin effetiveness ( f as a funtion of te fin onstant (β f and te fin number of transfer units (NTU f sown in Figure 4. Te fin effetiveness ( f is defined as te ratio of te atual eat transfer troug te base of te fin ( q f to te maximum ossible eat transfer; i.e. te eat transfer tat would our if te fluid temerature was redued to te base temerature of te fin (T b. On te ig-ressure side tis leads to: q f f (6 m ( Tin Tb were T b is te base temerature of te fins (te material between adjaent slots on te igressure side of te eat exanger. On te low-ressure side te fin effetiveness is: q f f (7 m T T ( b in Te fin onstants (β f and fin number of transfer units (NTU f are defined as:
Lf t β f (8 k w f Lf t β f (9 k w f 6 NTU NTU f f L f t t N f m L f t t N f m (0 ( were k is te late termal ondutivity t is te late tikness N f is te number of fins w f is te widt of te material between slots and m is te mass flow rate. Ea of te urves for f as a funtion of NTU f in Fig. 4 an be aroximately reresented by Eqs. ( and (3: ( β f ( β f b ( f ( f ln( NTU f f ex a NTU β + β f ( b ( f ( f ln( NTU f f ex a NTU β + β f (3 Equations for a b and as funtions of te fin onstant are listed below and te required onstants are ontained in Table ; tese onstants are obtained troug best fits to te numerial results. a( β f ex ao β 5 f bi i 0 6 f i i 0 ( a + aβf + a3βf f i [ log0 ( β f ] (4 b( β (5 i [ log0 ( β f ] ( β (6 Equations ( troug (6 allow te effetiveness of te fins on bot sides of te late to be alulated from te fin onstant and number of transfer units. Te maximum error assoiated wit te use of tese urve fits in te range 0.0 < NTU < 000 and 0.0 < β < 5 is 3.% and te rms error over tis range is 0.04%. Equations (6 and (7 may be re-written in te form of termal resistane ( f between te fluid inlet temerature and te temerature at te base of te fins: ( Tin Tb q f were f ( Tb T in f f q f were f m f m f (7 (8 Te termal resistane from te enter-line of te material tat searates te ig and low ressure streams to te fluid inlet temerature ( late is larger tan te termal resistane f due to te additional ondution resistane reresented by te late material: ws w + + N k t w w late. f ( + f s f (9
Table. Constants required for fin effetiveness solution. 7 Index i a i b i i 0 0.97959 0.97496-0.049798866.4954-0.07330646-0.06555996-0.08006078 0.06074063 0.0046859 3 0.0036993 0.063076 0.444469 4 - -0.067908807 0.03966 5 - -0.0303648-0.04859957 6 - - -0.08543303 ws w + + N k t w w late. f ( + f s f (30 Te total rate of eat transfer for ea late is terefore: ( Tin Tl q f late (3 ( Tl T in q f (3 late were T l is te temerature at te enter-line of te late. Combining Eqs. (3 and (3 leads to: ( Tin Tin q f (33 + late late and te effetiveness of an individual late ( is terefore given by te ratio of te atual eat transfer to te maximum ossible eat transfer for te late: q f MIN m m T T MIN m m ( ( in ( in ( late + late (34 Te axial resistane of a single saer is ( saer is: t s saer ksaer A (35 saer and so te total effetiveness of te eat exanger inluding a enalty for axial ondution ( an be estimated aording to: N + N MIN m m ( saer Te equivalent number of transfer units (NTU eq assoiated wit a ontinuous eat exanger wit no axial ondution is: ln if Cr < Cr Cr NTUeq (37 if Cr (36
were C r is te aaity ratio: C r MIN m MAX m ( m ( m (38 8 Te equivalent ondutane assoiated wit te eat exanger erformane (UA eq is terefore: ( UA MIN m m NTU (39 eq eq Te design of te eat exanger requires bot te equivalent ondutane and te ressure loss. It is non-onservative to neglet te effet of te develoing region wen evaluating te ressure loss. Te aarent frition fator for develoing laminar flow (f alam deends on te eynolds number te aset ratio of te slot and te dimensionless tikness of te late. For an aset ratio of zero (i.e. arallel lates te aarent frition fator is given by osenow et al. [5]. Te aarent frition fator for turbulent flow may be iger altoug te develoing region is less imortant wen te flow is turbulent. Te aarent laminar or fully develoed turbulent frition fator is seleted based on te eynolds number; a eynolds number of 3000 is used to indiate transition. Te visous ressure loss (Δ v is atured by te frition fator: t Δ v ρ um fa (40 d t Δ v ρum fa (4 d In addition to te visous ressure loss tere are ontration and exansion effets tat must be onsidered. Te flow ontration and exansion ressure loss oeffiients (K and K e for bot sides are onservatively assumed to be unity. Te inertial ressure losses (Δ i are terefore: Δ i ρum ( Ke+ Ki (4 Δ i ρum ( Ke+ Ki (43 Te total ressure loss (Δ is te sum of te inertial and visous ressure losses over all of te lates. Δ N Δ +Δ (44 ( ( i v Δ N Δ +Δ (45 i v ND GENEATION HEAT EXCHANGE OPTIMIZATION A manufaturing onstraint assoiated wit te miromaining roess tat ontrols te design is related to te lengt of te slots in te silion late. As te slot lengt inreases te ability to ontrol te slot widt is lost; eventually te over-eting during te KOH roess may beome severe enoug tat all of te fin material is removed. Terefore te slot lengt must be less tan 0 times te slot widt and webs tat san te widt of te slot are added to reate a series of smaller more robust oenings witin te original slot. Additionally te tikness of ea web sould be twie te widt of te slot. Tese onstraints are integrated wit te numerial model desribed above; te model is imlemented in te matematial software EES - Engineering Equation Solver [9]. Te lengt and widt of ea late and saer was set to 0 mm to maximize te yield of ea silion-pyrex mask wile still roviding erformane omarable to ommerially available
ryosurgial robes. A Joule-Tomson yle model was develoed tat takes te redited equivalent eat exanger ondutane UA eq and ressure dro on ea side Δ and Δ as inuts and alulates a orresonding ooling aaity and robe ti temerature for a given mass flow rate. Te onentration of te working fluid is otimized as disussed in [0]. Figure 5 illustrates a maximum ooling ower at a flow rate of 0.55 g/s. Figure 6 sows te redited ooling ower assoiated wit several web onfigurations as a funtion of te robe ti temerature for a 0mm x 0mm eat exanger wit 50 silion lates at te otimal mass flow rate of 0.55 g/s. Figure 6 indiates a late wit webs er slot rovides te best erformane above 3 K. Te erformane of a ommerially available ryosurgial robe is also inluded in Figure 6. Te ressure dro as a funtion of te mass flow rate troug te old side of te eat exanger is illustrated in Figure 7 for several web onfigurations. Te ressure dro troug te ot side of te eat exanger is aroximately an order of magnitude smaller tan te old side due to te relatively large differene in densities of te two streams. Te oerating onditions used during te otimization and te orresonding geometry are listed in Table. 9 SUMMAY Tis aer desribes develoments towards a mirofabriated reuerative eat exanger tat is intended to be a omonent witin a ryosurgial robe based on te mixed gas Joule- Tomson (JT yle. A first generation eat exanger as been designed and tested tat utilizes anodi bonding to join rows of fins omosed of ig ondutivity silion onto a single 00µm base late omosed of low ondutivity Pyrex glass. Tis design minimizes te number of wafers tat must be bonded but te tin Pyrex late required to minimize axial ondution along te lengt of te eat exanger limits te ability of te eat exanger to witstand te relatively large ressure differene tat is required by a Joule-Tomson ooling yle. However numerous manufaturing onstraints ave been overome during te develoment of tis design and te data olleted ave allowed te eat exanger model to be verified over a limited temerature range. In arallel a bonding tenique as been develoed tat sows te otential to allow multile lates to be ermetially joined using a metallization layer. Tis new joining tenique and te verified numerial model ave been used to design a nd generation eat exanger tat uses ig ondutivity silion lates tat are alternated wit low ondutivity Pyrex saers. Te nd generation eat exanger as been otimized so tat it is robust to te stream-to-stream ressure differene and rovides enaned termal erformane as omared to te st generation design. Our intention is to build several roof-of-onet nd generation eat 40 70 webs 35 Webs 60 Cooling ower [W] 30 5 0 5 0 Cooling ower [W] 50 40 30 0 0 9 webs 5 webs Commerially available ryosurgial robe 5 0.000 0.000 0.0003 0.0004 0.0005 0.0006 0.0007 0.0008 Mass flow rate [kg/s] Figure 5. Cooling ower as a funtion of te mass flow rate for te web onfiguration. 0 0 30 40 50 60 70 80 90 00 Probe temerature [K] Figure 6. Cooling ower as a funtion of te robe ti temerature for several web onfigurations. Te ooling ower of a ommerially available robe is also inluded.
Cold side ressure dro [sia].8.6.4. 0.8 0.6 0.4 0. webs 0 0.000 0.000 0.0003 0.0004 0.0005 0.0006 0.0007 0.0008 Mass flow rate [kg/s] 9 webs 5 webs Figure 7. Pressure dro troug old side of eat exanger as a funtion of mass flow rate for several web onfigurations. 50 µm Table. Parameters used during otimization of eat exanger. Parameters Heat exanger lengt 0mm Heat exanger widt 0mm Mass flow rate 0.55 g/s Hot side inlet ressure 500 kpa No. of fin rows N f 70 No. of slots in a row N s 3 No. of web N web Lengt of ea slot L s 500 µm Lengt of ea fin L f 7700 µm Lengt of ea web L web 00 µm Widt of ea slot w s 50 µm Distane between ea slot row w f Tikness of Si late t 500 µm Tikness of glass saer t s 50 µm Minimum distane from edge of 00 µm slot to Pyrex saer W 0 exangers based on te otimized design tat an be installed into a termal vauum amber and erformane tested. Te exerimental results will allow furter verifiation and imrovement of te omuter model. ACKNOWLEDGEMENT Tis work was funded by a grant from te US National Institutes of Healt ( EB003349-0. EFEENCES. Dobak J. A eview of Cryobiology and Cryosurgery Advanes in Cryogeni Engineering Vol. 43 (998. 889-896.. Zu W. Ho D.W. Nellis G.F. Klein S.A. and Gianandani Y.B. "A Planar Glass/Si Miromaining Proess for te Heat Exanger in a J-T Cryosurgial Probe" resented at te 006 Solid-State Sensors Atuator and Mirosystem Workso Hilton Head Island SC (006. 3. Dobak J. Marguardt E.D. and adebaug. A Cryogeni Cateter for Treating Heart Arrytmia Advanes in Cryogeni Engineering Vol. 43. 903-90 (998. 4. Frank M. euerative Heat Exanger for a MEMS Cryorobe M.S. Tesis University of Wisonsin Det. of Meanial Engineering 004. 5. osenow W.M. Hartnett J.P. and Co Y.I Handbook of Heat Transfer MGraw-Hill New York (998. 6. Gnielinski V. Int. Cem. Eng. Vol. 6 (976. 359. 7. Petukov B.S. in Irvine T.F. and Hartnett J.P. eds. Advanes in Heat Transfer Vol. 6 Aademi Press NY (970. 8. Nellis G.F. Huges C.B. and Pfotenauer J.M. "Heat Transfer Coeffiient Measurements for Mixed Gas Working Fluids at Cryogeni Temeratures" Cryogenis Vol. 45 No. 8. 546-556 August (005. 9. Klein S. A. 006 EES-Engineering Equation Software F-Cart Software tt://www.fart.om. 0. F. Keler G. Nellis and S. Klein Otimization of te Comosition of a Gas Mixture in a Joule- Tomson Cyle" International Journal of Heating Ventilation Air Conditioning and efrigeration esear Vol. 0 No.. 3-30 (004.