Numerical study of a chemical method applied to instantaneous heat removal under high heat flux

Transcription

1 Heat Mass Transfer (2013) 49: DOI /s ORIGINAL Numerical study f a chemical methd applied t instantaneus heat remval under high heat flux Jing Li Ga-Ming He Cheng Zeng Ye-Ming Liu Received: 1 Nvember 2012 / Accepted: 15 May 2013 / Published nline: 28 May 2013 Ó The Authr(s) This article is published with pen access at Springerlink.cm Abstract In this study, a methd f chemical cling is put frward, that is, C CO 2 endthermic reactin is applied t instantaneus heat remval under high heat flux. A methd in which theretical research is in cmbinatin with numerical simulatin is used t study C CO 2 endthermic reactin. In cmparisn with the theretically cmputatinal results, numerical cde is validated. A high heat flux f 500 W/cm 2 is applied t the research f the heat dissipatin characteristics f C CO 2 endthermic reactin. The theretical calculatin results shw that, under a certain temperature and pressure cnditin, the C CO 2 chemical endthermic reactin culd remve heat frm the system prmptly; the prduct CO culd be used as a supplementary medium f pwer surce fr cycling. Cmpared with water phase change, the C CO 2 endthermic reactin appears t have strnger heat remval ability. Species Transprt mdule in FLUENT was adpted t simulate the reactin. Under the same temperature and pressure cnditin, the numerical simulatin results are fund t be well cngruus with theretical results. The C CO 2 endthermic reactin culd make a high temperature in the reactin system due t a high heat J. Li (&) G.-M. He C. Zeng Y.-M. Liu Key Labratry f Enhanced Heat Transfer and Energy Cnservatin, Ministry f Educatin, Suth China University f Technlgy, Guangzhu, Peple s Republic f China ljing@scut.edu.cn G.-M. He hegaming1501@163.cm flux reduce t a lw temperature (belw zer) prmptly. The heat remval and reactin time are in cnsistence with theretical calculatin. List f symbls A Pre-expnential factr (1/s) c Reactant cncentratin (ml/m 3 ) C p Heat capacity (J/kg K) D I,m Mass diffusivity f gas I in gas mixture (m 2 /s) Ea Activatin energy (kj/ml) m Mass (kg) n Reactin rder ( ) P Pressure (Pa) q Vlumetric heat surce (W/m 3 ) Q Heat (KJ) R Gas cnstant (J/ml K) S m Mass surce term t Time T Temperature (K) u, v Velcities in axial and radial directins, respectively (m/s) U Velcity vectr in the x-directin and y-directin, u and v x Crdinate in axial directin (m) y Radial crdinate (m) Y Mass fractin (%) Greek letters j Reactin rate cnstant h Surface fractin b Absrptin capacity c Reactin rate q Density (kg/m 3 ) l Dynamic viscsity (kg/m*s) k Thermal cnductivity (W/m* C)

2 1300 Heat Mass Transfer (2013) 49: Intrductin With the develpment f new high-techs, ccasins due t high and even ultra high heat flux appear. High heat flux results in high temperatures, which need higher requirements fr the prperty f material and perating cnditins and prduce a negative effect n the service life-span f material. S heat remval prblem caused by dense situatin f high heat flux becmes increasingly serius. Fr example, ablatin n the electrde surface caused by high heat flux, nt nly results in degradatin f the verall perfrmance f equipment, but als prduces a negative effect n the service lifespan f equipment [1, 2]; in rder t imprve the thermal efficiency and pwer utput, advanced gas turbine engines usually wrk under high temperatures f 1,300 1,500 C,which cause the perating temperature f turbine blade t be much higher than that f metal materials allwable temperature, s reasnable cling fr blade becmes a prblem which we have t be faced with [3]; heat flux density n the thermal depsit surface f high pwer semicnductr laser can reach as high as 400 W/cm 2, which is limited t a certain level f perfrmance and further imprvement by heat remval prblem [4]; temperature f hypersnic aircraft (Mach number is 8 r abve) head can reach 2,300 C, and cmbustin indr temperature can reach abve 3,000 C [5]. Sme mature frced cling methds at present are based n physical heat sink, including frced air cling, water phase change, pl biling, spray cling, micrchannel cling and micr-jet array cling et al. Frced air cling [6] is a physical cling methd which uses the fan t blast r ventilate t imprve air flw rate t achieve the purpse f cling. It is widely used in high-pwer electrnic device field, because its heat transfer capacity is several times mre than that f natural air cling, it is, hwever, rarely applied t LED thermal design but nly applied t electrnic devices whse uter surface heat flux density des nt exceed 10 W/cm 2 due t its cmplex system, heavy nise, lw reliability, expensive maintenance csts and extra pwer dissipatin. Pl biling, als knwn as large cntainer biling, which is ne f liquid biling methds in industry, is t immerse the heating surface int liquid, and the liquid heats n the wall surface. Pl biling is greatly valuable in the field f industrial applicatin. In the past few decades, the schlars in different cuntries have dne a lt f research by cnducting many biling heat transfer experiments and put frward varius heat transfer mechanism mdels, but due t the limitatins f experiments and assumptins, these mdels have their wn defects [7]. Water phase change cling, which is based n physical phase change, can nly prvide 67 kj/ml f heat transfer capacity; the mst cmmnly used gravity heat pipe can nly prvide \30 W/cm 2 f heat transfer capacity. In sme extreme physical situatins, such as super high temperature reactin kettle, super high temperature gas turbine engine, super mach number prpeller, high pwer laser pump and s n, physical heat sink cling methds [8] based n physical phase change f wrking medium are limited by the latent heat f vaprizatin ability and unable t meet the requirement f heat remval due t high heat flux density. Therefre, since the 1960s, the United States has int practice the study f chemical heat sink applicatin as cling methd [9]. Many studies fcused n hw t make the chemical endthermic reactin applied t heatdissipatin prblem [10 12]. The reactin f ethanl dehydratin t ethylene is an endthermic reactin with gd thermal effect. In the preparatin f ethylene, by using the adiabatic tube reactr, heat culd be remved frm the reactr with the endthermic reactin, while cke frmatin is avided. Thrugh endthermic reactin, heat culd be remved frm a lw temperature heat surce, and thrugh exthermic reactin, heat culd be upgraded t heat sink at a high temperature. Karaca et al. [13] studied the chemical heat pump system made up with methanl frmaldehyde hydrgen, ethanl acetaldehyde hydrgen, prpanl acetne hydrgen, butanl butyraldehyde hydrgen and s n at a lw temperature. In the system, dehydrgenatin is endthermic while hydrgenatin is exthermic. On the basis f ecnmic analysis, a large amunt f waste heat is greatly needed t achieve the thermal efficiency. A new chemical apprach, which use C CO 2 endthermic reactin applied t instantaneus heat remval in a high heat flux density situatin, is put frward in this paper, which is rarely reprted currently at hme and abrad. Li et al. [14] explred the effect f CO 2 n hard cke degradatin reactin, but they did nt study the methd f applicatin f C CO 2 endthermic reactin t instantaneus heat remval. In this paper, bth theretical calculatin and numerical simulatin methds are applied t the study f C CO 2 endthermic chemical reactin. Bth f the results shwed that C CO 2 endthermic chemical reactin culd help realize instantaneus heat remval under high heat flux. 2 Theretical calculatin The aim f this study is ging t verify that instantaneus heat remval can be realized by C CO 2 endthermic reactin. In the study, activated carbn particles and carbn dixide gas are used as reactants. As the reactin prceeds, high energy renewable material-co wuld be prduced. CO culd be used as supplementary medium f pwer

3 Heat Mass Transfer (2013) 49: surce, prviding energy thrugh cmbustin exthermic reactin, the prduct-co 2 culd be used again as a reactant f endthermic reactin. Thus a material cycle will frm thrugh abve prcess. Because f the strng heat absrptin capacity and the special relatinship between reactants and prducts, this thinking will help realize instantaneus heat remval and material cycle. Wd activated carbn is t be used in a subsequent experiment, whse specific surface area is mre than 1,000 m 2 /g. Thus CO 2 can diffuse t internal f activated carbn particle fully fr its prsity, which means activated carbn particles will react with CO 2 directly. Therefre, the influence f diffusin n reactin rate can be neglected. C CO 2 reactin can be simplified as fllws [15]: CO 2 +C! j 1 ½CO]! j 2 CO CO + [CO] ðaþ ðbþ Accrding t slid surface reactin mdel, tw rate equatins can be cncluded: dp CO ¼ j 1 P CO2 ð1 hþþj 2 h ð1þ dt dh dt ¼ 1 b ½j 1P CO2 ð1 hþ j 2 hš ð2þ In the equatins, P CO and P CO2 refers t partial pressures f CO and CO 2, j 1 and j 2 are the reactin rate cnstant f reactin (A) and (B), h is t refer t surface fractin ccupied by surface xide [CO]. b means absrptin capacity. At a high temperature, C CO 2 reactin can be cnsidered as first-rder reactin, and starting frm 800 C, rder f reactin will be clse t 1. The higher the temperature is, the clser t the first-rder reactin. A cnclusin can be drawn frm the abve tw equatins. The higher the temperature is, the h is clser t 0. Then reactin rate is: dp CO dt P CO2 ¼ j 2 P CO2, which means reactin rate is prprtinal t (n = 1); the lwer the temperature is, the h is clser t 1. Then the reactin rate is: dp CO dt ¼ j 2 h, which means the reactin rate is independent f P CO2 (n = 0). C CO 2 reactin is a strng endthermic ne, its temperature prduces a slight effect n activatin energy. Table 1 shws the pre-expnential factr A and reactin activatin energy Ea [16]. Accrding t Arrhenius frmula and chemical reactin rate equatin, j ¼ Ae Ea RT c ¼ j c ð3þ ð4þ Time fr remving 500 W/cm 2 heat at different temperatures can be calculated. In the reactin, CO 2 cncentratin is used. Table 2 and Fig. 1 shw time fr remving 500 W/cm 2 heat at different temperatures with C CO 2 endthermic reactin. Frm Table 2, it can be seen that, the higher a reactin temperature is, the less time it needs. Time fr cmpleting the endthermic reactin can reach the level f ne percent secnd at a certain temperature (abut 1,573 K). T illustrate the strng endthermic capacity f C CO 2 reactin, a cmparisn can be made between heat remval capacity f C CO 2 endthermic reactin and water phase change under the same cnditins (the same temperature, pressure and mlar amunt). Air density is kg/m 3, heat capacity is kj/ kg C under cnstant pressure (frm FLUENT database). Length f cylindrical reactr used in numerical simulatin is 2 m, and its bttm radius is m. If ht air is cled frm 1,500 t 300 K, heat t be remved is kj. Reactin equatins f C CO 2 reactin and water phase change are as fllws: Table 2 Relatinship between reactin temperature and time Temperature/ K 973 1,073 1,173 1,273 1,373 1,473 1,573 Time/s time/s Table 1 Reactin parameters Reactin Pre-expnential factr A/1/s CO 2? C = 2CO Activatin energy Ea/ (kj/ml) temperature/k Fig. 1 The graph f time variatin with reactin temperatures

4 1302 Heat Mass Transfer (2013) 49: C+CO 2! 2CO; Q = 172:5 kj/ml ðcþ H 2 O(l)! H 2 O(g); Q = 67 kj/ml ðdþ If Q is f psitive value, the reactin is endthermic. T remve kj heat, CO 2 needed is 2.73 ml, while nly kj heat can be remved thrugh water phase change if the amunt f mlar water is the same, which means the temperature f ht air can nly be cled t 1,034 K. In cmparisn f heat absrptin capacity f C CO 2 reactin with water phase change, the frmer is much strnger than the latter. At the same time, the calrific value f CO, the prduct, is abut 6 % higher, which is equivalent t transfer energy frm ne medium t the ther. CO can be used as a high calrific value fuel fr cycle, which prvides necessary cnditins fr energy cycle. ðquuþ ðyquvþ ¼ P x y y x þ l v yl u x x y y y þ l u yl v x x y y x ð7þ ðquvþ ðyqvvþ ¼ P x y y y þ l v yl u x x y y y þ l u yl v 2lv x y y y y y 2 ð8þ Energy equatin [18]: qc p ut ypc p vt ¼ k T yk T x y y x x y y y þ q ð9þ 3 Numerical simulatin 3.1 Gverning equatins An axial-symmetrical tw-dimensinal (x y) cmputatinal dmain is prfiled as shwn in Fig. 2, which includes tw flw streams. The mdel has the fllwing dimensins: Diameter f inlet-1 and inlet-2 are 0.01 and 0.45 m, respectively; thickness f the sheet is m. The fllwing gverning equatins, Eqs. (5) (10), fr mass, mmentum, energy and species transfer are universally applicable t the entire cmputatinal dmain. Hwever, zer velcities need t be assigned t the slid area in the numerical treatment. Mass equatin [17]: q þ div qu t ð Þ ¼ 0 ð5þ Mmentum equatin [18]: ðquþ ðyqvþ ¼ 0 x y y ð6þ Species transprt equatin [18]: ðquy I Þ ðyqvy I Þ ¼ Y I qd I;m x y y x x y y yqd I;m Y I y þ S m ð10þ The energy equatin applied t the slid cmpnents f the cmputatinal dmain reduces t a heat cnductin equatin since zer velcity is assigned there. Heat generatin rates are intrduced int the surce terms f Eq. (9). 3.2 Bundary cnditins Simulatins are perfrmed using the FLUENT [19] cde. The bundary cnditins fr the mmentum, heat and mass cnservatin equatins are as fllws. On the surface f wall, unifrm heat flux is utilized t indicate heat surce. The mdel is set t symmetric t accunt fr the symmetrical cmputatinal dmain. The wall is specified as heat flux with 500 W/cm 2. Interir side f the wall is set as cupled wall. The velcity f inlet-1 and inlet-2 is set t 2 and 10 m/s, Fig. 2 The symmetrical gemetric plane structure f the reactr

5 Heat Mass Transfer (2013) 49: respectively. A pressure utlet bundary cnditin is set at the utlet. The reactants adpted are activated carbn particles and mixture f CO 2 H 2 O (g), respectively. In the mixture, water vapr is used as inert gas, and mass fractin f carbn dixide is 0.4. Activated carbn particles enter the reactr frm inlet-1, while the mixture enters frm inlet-2. Three thin pieces f sheets are set fr the reactants t mix each ther better and at the same time, the mdel is divided int fur parts. And then pressure-based slver is selected. Thrugh calculatin, flws f activated carbn particles and CO 2 gas belng t turbulent flw. Therefre, k-epsiln (2 eqn) standard turbulent mdel is adpted and then standard wall surface functin is used t simulate gas flw. All the abve gverning equatins are discretised by using the finite vlume apprach and the SIMPLE algrithm is adpted t treat the cupling f the velcity and pressure fields. The first rder upwind scheme is selected fr the slutin t the mmentum and energy equatins. 3.3 Results and discussin Heat and mass transfer under high heat flux The minimum temperature is K when C CO 2 reactin begins [14]. Temperature in the reactr is abut 1,500 K befre reactin begins, which means the reactin can ccur. Figure 3a refers t the temperature field after C CO 2 endthermic reactin is cmpleted and Fig. 3b is an average temperature distributin graph crrespnding t Fig. 3a. Figure 4a is cncerned with CO mass fractin field and Fig. 4b is relevant t CO average mass fractin distributin graph crrespnding t Fig. 4a. These figures and graphs are extracted under these cnditins: velcity f CO 2 is 10 m/s, velcity f activated carbn particles is 2 m/s, and perating pressure is kpa. It can be seen frm Fig. 3a, b that temperature in the reactr drps bviusly after C CO 2 endthermic reactin is cmpleted. The maximum temperature is just abut 330 K and average temperature is 222 K. Temperature is much lwer, which is belw average temperature at the first part f mdel, and this means that the purpse f lwering temperature has cme true. Heat that has been remved and CO 2 that has been used in the prcess can be calculated. Mixture f CO 2 and water vapr is cled frm 1,500 t 222 K, accrding t the endthermic equatin belw: Q ¼ C p mdt ð11þ Q means endthermic r exthermic. In the case, C p is a equivalent value f C pco2 and C ph2 OðlÞ, 1, J/(kg K); m refers t the mass f mixture: kg; DT stands fr temperature change: 1,278 K. Therefre, heat that has been remved is kj; mlar number f CO 2 is If the same amunt f water is used t remve the heat by water phase change, nly kj heat will be remved, which means mixture f CO 2 and water vapr will drp t 1,003.6 K. It can be fund frm Figs. 3 and 4 that temperature field and CO mass fractin field have the same distributin trend: Fig. 3 a Cnturs f temperature and b the distributin graph f average temperature with psitin n the symmetry plane f the reactr

6 1304 Heat Mass Transfer (2013) 49: Fig. 4 a Cnturs f CO mass fractin and b the distributin graph f average CO mass fractin with psitin n the symmetry plane f the reactr In the first part f mdel, CO mass fractin is highest and temperature is lwest; in ther parts, CO mass fractin is lwer and temperature is higher than that f the first part. Because the inlets f reactants are in the first part, then the amunt f CO 2 gas and activated carbn particles is larger, which makes them mix mre fully and react mre cmpletely. CO 2 gas and activated carbn particles need t be filled int the area cnstantly t keep the reactin mving, s that the amunt f CO 2 gas and activated carbn particles flwing int the rest parts is less and less. Later, the less the amunt is, the mre slightly the reactin is, s the temperature des nt drp s lw as that f the first part des. It can be seen frm Fig. 4 that CO mass fractin is almst 0 in the furth part f mdel, crrespnding t Fig. 3, there is a small high temperature area in the furth part. In spite f the fact that except the first part f the mdel, the reactin prceeds mre and mre slwly and slightly in ther parts. Because f the drastic endthermic reactin in the first part, heat frm the rest parts transfers t this part, which results in the drp f temperature in ther parts Instantaneus heat remval Thrugh the calculatin abve, kj heat need t be remved fr cling mixture f CO 2 and water vapr frm 1,500 t 222 K by emplying C CO 2 endthermic reactin, 3.52 ml CO 2 will be cnsumed in the prcess. The results f numerical simulatin shw that average mass fractin f CO 2 reaches at the end f reactin. In cmparisn with the mass fractin 0.4 prir t reactin, it is insignificant. S it can be cnsidered that CO 2 reacts cmpletely. Frm Figs. 3 and 4, it is knwn that after CO 2 gas and activated carbn particles enter the reactr, they react at a high temperature cnditin. Accrding t the data f numerical simulatin, time fr remving 500 W/cm 2 heat at temperature f 1,500 K needs s. The result prves that the destinatin f instantaneus heat remval can be realised if C CO 2 endthermic reactin is used, because the temperature in the reactr drps t such a lw level during such a shrt time Validatin f numerical study In the part f theretical calculatin, heat t be remved was calculated when temperature drpped frm 1,500 t 300 K by cling by means f C CO 2 endthermic reactin, which was kj. And in the numerical simulatin, temperature was cled frm 1,500 t 222 K, heat t be remved was kj. Cmpared with the theretical results, it is reasnable and receivable. Table 2 shws time fr remving 500 W/cm 2 heat at different temperatures. When temperatures are 1,473 and 1,573 K, it takes 0.17 and 0.09 s, respectively. In the numerical simulatin, the highest temperature in the mdel was 1,500 K, and the reactin time culd be calculated, s, which agreed with the law f temperature and time. 4 Cnclusin In this study, C CO 2 chemical endthermic reactin prcess is studied by means f theretical calculatin and

7 Heat Mass Transfer (2013) 49: numerical simulatin. Theretical calculatin results shw that C CO 2 chemical endthermic reactin can pssibly remve heat enrmusly and instantaneusly under a high heat flux density situatin. The results f numerical simulatin agree with theretical calculatin. Bth f the results shw that C CO 2 chemical endthermic reactin has strnger heat absrptin capacity than water phase change (abut 2.57 times) des, which is a typical physical heat sink. It takes less time t remve the same heat. In ther wrds, using a small amunt f C and CO 2 can have the effect f instantaneus and large heat remval, instead f using a large amunt f water. At the same time, the prduct CO can be used as supplementary medium f pwer surce, prviding energy by cmbustin exthermic reactin. CO 2, caused by the exthermic reactin, can als be used as a reactant f endthermic reactin. Thus the abve prcess can frm a material cycle. In this way, instantaneus heat remval and a material cycle are realized simultaneusly. Open Access This article is distributed under the terms f the Creative Cmmns Attributin License which permits any use, distributin, and reprductin in any medium, prvided the riginal authr(s) and the surce are credited. References 1. Chen X (1998) Ersin n slid electrde surface caused by high density electric arc effect. High Vlt Apparatus 4: Lu M, Jiang J, Chang A, Zha D (2004) Study n mechanism f electrde ersin f high-pwer gas spark gap switch. High Pwer Laser Part Beams 16(6): Han Y, Wang X, Qiu L, Yu M, Zha S, Jia W, Ai S (2010) Numerical study n heat transfer characteristics f jet array impingement. Turbine Technl 52(3): Tian C, Xu H, Ca H, Si C (2009) Cling technlgy fr highpwer slid-state laser. Chin J Lasers 36(7): He F, Mi Z, Sun H (2006) Imprvement f heat sink f endthermic hydrcarbn fuels. Prg Chem 18(7/8): Huang M (2006) Thermal degine f the frced air-cling radar cabinet. Electr-Mech Eng 22(2): Xia B-Q et al (2009) Mathematical analysis f pl biling heat transfer. Acta Phys Sin 58(4): Yang J, Chu LC, Pais MR (1996) Nucleate biling heat transfer in spray cling. J Heat Transf 118: Bland RB et al. (1962) US , Cling with endthermic chemical reactins 10. Wessberg S, Rasmussen JN (2007) (Carlsberg Brewery C., Ltd.). CN , Chemical cling 11. Gu H-b (J&R Fire Fighting Grup). (2010) CN , Chemical clant fr ht aersl catalyst and preparatin methd 12. Liu J, Sha J, Liu C, Ra H, Li Z, Li X (2010) Pyrlysis mechanism f hydrcarbn fuels and kinetic mdeling. Acta Chim Sin 68(3): Karaca F et al (2002) Ecnmic analysis and cmparisn f chemical heat pump systems. Appl Therm Eng 22: Li J, Lu K, Wang J, Wang P (2008) Influence f H 2 O CO 2 gas mixture n cke degradatin. J Anhui Univ Technl 25(3): Chen Z (1984) Study n kinetic and mechanism f CO 2 C reactin. Tech Equip Envirn Pllut Cntrl 5(1): Cen K, Ya Q, Ca X et al (1997) Thery and applicatin f cmbustin, flw, heat transfer, gasificatin f cal slurry. Zhe Jiang University Press, Hangzhu 17. Patankar SV (1980) Numerical heat transfer and fluid flw. McGraw-Hill, New Yrk 18. Li P-W, Chyu MK (2003) Simulatin f the chemical/electrchemical reactins and heat/mass transfer fr a tubular SOFC in a stack. J Pwer Surces 124: FLUENT 6 User s Guide, Fluent Inc, Lebann, NH, 2000