ESTIMATION OF HEAT TRANSFER COEFFICIENT DURING QUENCHING STEEL IN WATER

Transcription

1 Šefik Behem Bahudin Hnjica hps://doi.og/ /tof.42si106 ISSN eissn ESTIMATION OF HEAT TRANSFER COEFFICIENT DURING QUENCHING STEEL IN WATER Summay The pape pesens he pocess of wo-dimensional axisymmeic quenching of cylindical samples in wae a 40 C. Expeimenal wok consiss of quenching hee dimensionally diffeen cylindical pobes. The dimensions of he pobes ae: 25x50 50x150 and 75x225 mm. Thee measuing poins ae 1.5 mm below he cylinde suface posiioned a he cylinde heigh wheeas he fouh measuing poin is in he cene of gaviy of he cylinde. The quenching was conduced in sic conolled ae of wae flow a he cylinde head. The poblem of he ask belongs o invese poblems of hea conducion o ill posed poblems so ha he soluion o he poblem leads o a sufficienly accuae esimae of he unknown hea ansfe coefficien imposed on he oue suface of he cylinde. Compue model soluions use expeimenal esuls of empeaue measuemens o minimie eos beween compue calculaions and measued empeaue values in he same place. The seleced soluion algoihm is a hybid algoihm ha consiss of a combinaion of hee diffeen algoihms of soluion conneced ino a single uni. Key wods: Cylindical pobe seel quenching opimiaion invese hea ansfe hea ansfe coefficien 1. Poblem descipion In egad o he quenching of cylindical samples many published sudies ae mosly based on 1D axisymmeic poblems of olde [1] [2] [3]... and moe ecen [9] [10] dae while 2D axisymmeic and 3D poblems ae vey ae o none [11] [12] [13]. Fig. 1 depics veical immesion of he cylinde wih diamee D heigh H iniial empeaue 850 C and ae w a = m/s in he cooling fluid ha flows upwads wih speed w 1 = m/s. Duing he immesion of he pobe ino he cooling fluid empeaue values ae coninuously measued in fou poins of he pobe using embedded hemoelemens. Fig. 1 shows qualiaive values of esed physical model. Based on he obained values of empeaue in he pobe hea ansfe coefficien is esimaed fom he suface of submeged pobe o he cooling fluid. The idea fo he pape was ceaed accoding o [1] [2] and [5]. TRANSACTIONS OF FAMENA XLII- Special issue

2 Esimae of Hea Tansfe Coefficien Fig. 1 Poblem descipion 2. Expeimenal seing Expeimenal seing consiss of quenching of hee dimensionally diffeen cylindical pobes. The maeial of he pobes is seel AISI 304 wihou cysal convesion. Quenching was conduced in sic conolled wae flow ae of m/s aound he cylinde as well as mainenance of wae empeaue wihin a maximum of C duing cylinde quenching. The expeimen consiss of he following: chaging he sysem wih quenchan heaing and mainenance of he quenchan a 40 C wih ciculaion veical dopping of cylindical pobe in he cene of he heaing funace using mechanical dive closing and waming he pobe in niogen amosphee up o 850 C fo a maximum of fou hous opening funace lowe doo and veical descen wih a simulaneous sa of daa acquisiion dopping pobes a a consan ae in he cooling bah quenching he pobe o he seady sae wih he ineupion fo daa acquisiion and aising he pobe o he saing posiion which maks he end of he expeimen. Realisic and schemaic display of he measuemen line is shown in Fig. 2 and 3 [12]. Fig. 2 Laboaoy layou measuing lines 62 TRANSACTIONS OF FAMENA XLII- Special issue

3 Esimae of Hea Tansfe Coefficien Fig. 3 Schemaic dawing of measuemen lines The ae of daa acquisiion is wo samples/seconds on high-pecision mode simulaneously fom fou poins inside he cylinde. Daa colleco is NI USB-9213 module wih 16-channel hemocouple inpus. Thee measuing poins ae 1.5 mm below he cylinde suface aanged a he heigh of he cylinde while he fouh measuing poin is in he cene of gaviy of he cylinde. Technical dawing of he es cylinde 50x150 is shown in Fig. 4 while he acual display of he pobe 75x225 is shown in Fig. 5. The ohe wo pobes have he same aangemen of hemocouples. TRANSACTIONS OF FAMENA XLII- Special issue

4 Fig. 4 Technical dawing of he es cylinde 50x150 Esimae of Hea Tansfe Coefficien Fig. 5 Laboaoy view of he es cylinde 75x225 above he space fo quenching The measuemen esuls o cooling cuves fo he pobe 75x225 ae shown in Fig. 6 wheeas cooling cuves fo he ohe wo pobes ae shown in he compaison of he measued and simulaed esuls [12]. Fig. 6 Cooling cuves fo he pobe 75x225 in maked poins and 12 Fig. 7 Video image of he vapo film on he suface of he pobe 75x225 in = 1.75 s afe immesion [12] Mak TCm in Fig. 6 epesens hemocouple measuemen in seleced poins of individual pobes. Poins and 4 ae maked in he pobe 25x100 poins and 8 ae maked in he pobe 50x150 and poins and 12 ae maked in he pobe 75x225. Fig. 7 shows he video image of he vapo film posiion in 1.75 seconds afe he immesion of he pobe 75x225 ino he wae. Fig. 7 clealy shows ha he movemen of vapo film does no saisfy he assumpion of axisymmeic quenching of he pobe which will lae be inoduced. This assumpion will affec he accuacy of he final soluion. Duing he ieaive esimaion of he hea ansfe coefficien he compue soluion model used expeimenal esuls of empeaue measuemen o minimie eos beween compued calculaions and measued empeaue values in he same place. 64 TRANSACTIONS OF FAMENA XLII- Special issue

5 Esimae of Hea Tansfe Coefficien 3. Compue seing of he poblem Accoding o he adoped assumpions he es maeial is homogeneous and isoopic hea ansfe hough he cylinde is wo-dimensional axisymmeic and unseady wheeas he empeaue ae of cooling fluid duing quenching is consan. Since physical popeies of he pobe depend on he empeaue he poblem is nonlinea. Diffeenial equaion of hea conducion in cylindical coodinaes which descibes hese poblems has he following fom: 1 c. 1 I saes ha: is unseady empeaue field wheeas c ae physical popeies of he pobe [12]. The iniial condiion epesens he empeaue disibuion =0 850 C a each poin of each pobe. A simplified compuaional domain is shown in Fig. 8. The bounday condiions fo his poblem ae as follows [12]: Fig. 8 Compuaional domain 0 0 axial symmey =0 and 0 R 3 2 R =R and 0 H 4 3 H H =H and 0 R. 5 TRANSACTIONS OF FAMENA XLII- Special issue

6 Esimae of Hea Tansfe Coefficien Equaions 3 4 and and 3 H ae he unknown hea ansfe coefficiens on he paicula sufaces which ae descibed by he funcion 0 H ha pesens he objec of he eseach. The sudy poblem belongs o invese poblems of hea conducion o ill posed poblems so ha he poblem soluion adds up o a sufficienly accuae esimae of he unknown hea ansfe coefficien imposed on he oue suface of he cylinde. Compue algoihm soluion Compue soluion model [9] and [11] was ceaed in coopeaion wih D. Ime Felde of he Faculy of Infomaics Technical Univesiy of Obuda in Budapes. A compue model of he ask is based on hybid opimiaion algoihms. The algoihm used in he pape is a combinaion of diec numeical analysis FEM non-dominan soing geneic algoihm NSGA II [8] and Levenbeg Maquad mehod LMM [3]. The algoihm fis uses NSGA II which in elaion o clien/seve o FEM and on he condiion of eo minimiaion gives half-soluion of he hea ansfe coefficien. Subsequenly he second LMM algoihm akes ove he las NSGAII soluion which in elaion o clien/seve o FEM finishes up he final soluion also on he condiion of eo minimiaion. Fig. 9 shows flow diagam of he soluion algoihm. 3.1 Fig. 9 Applied hybid algoihm soluion Cuen hea ansfe coefficien is deemined in a way ha hee poins ae seleced on he oue suface of he pobe in he 2D compuaional domain. Esimaed poins of ime funcions ae seleced hoionally opposie o measuing poin o nea he measuing poin as shown in Fig. 10. In his way hee ime funcions of he hea ansfe coefficien ae fomed f1 f2 and f3 i.e. hee paallel 1D seach poins. The hee funcions ae found using wo fo loops. The oue loop is a ime loop 1... k whee k is he numbe of caefully seleced ime seps whee hea ansfe coefficien is equesed. The inne loop is he heigh of he pobe. Subsequenly hese hee funcions ae linea 3D inepolaed/exapolaed and in he fom of funcion applied o he oue suface of he cylinde as he bounday condiions of FEM. 66 TRANSACTIONS OF FAMENA XLII- Special issue

7 Esimae of Hea Tansfe Coefficien Fig. 10 The posiion of seach poins =fi i=123 Example of seach esuls is a ex gid file in Fig. 11. The fis ow epesens he ime momens of he seach while ohe ows epesen hee heighs of he pobe. The las hee ows epesen ime funcions f1 f2 and f3. Fig. 11 Tex gid file of he seach esuls of hea ansfe coefficien duing quenching of he pobe 75x225 in 40 0C wae Malab/Comsol sofwae was used o esimae he hea ansfe coefficien beween seve/clien. Fig. 12 shows he Paeo fons duing he seach which is divided ino an appopiae numbe of subses while bowsing hea ansfe coefficien fo all hee dimensions of he pobe in he same cha. The numbe of Paeo opimal fons is deemined by he seach algoihm iself accoding o he numbe of local opima. Fig. 12 Paeo fons of seach flow of he hea ansfe coefficien fo all hee pobe dimensions TRANSACTIONS OF FAMENA XLII- Special issue Fig. 13 Soluion conou lines of he hea ansfe coefficien fo he pobe 75x225 67

8 Esimae of Hea Tansfe Coefficien The fis cuve o he lef in Fig. 12 coesponds o he Paeo opimal soluion in Fig 13. This picue shows he conou lines of he fou expessed local maxima and hee local minima seven cicles coesponding o he numbe of Paeo opimal subses. The populaion sie is beween 250 and 475 depending on he pobe dimension. The smalle diamee pobes need a lage populaion because he smalle diamees have bigge local opima and cooling ae. The esuls of hea ansfe coefficien fo hee dimensionally diffeen pobes ae given in he nex secion. 4. Analysis and compaison of he obained esuls 4.1 The quenching of he pobe 25x100 The esuls of 1D seach of hea ansfe coefficien duing quenching of he pobe 25x100 in 40 C empeaue wae in maked poins ae shown in Fig. 14. Fig. 15 shows linea inepolaed/exapolaed hea ansfe coefficien. Fig. 14 Time funcions f1 f2 and f3 fo he pobe 25x100 Fig. 15 Hea ansfe coefficien fo he pobe 25x100 Fig. 16 shows he esuls of compaison of measued TCm and calculaed TCc empeaues in all fou maked compuaional domain. The lages local deviaion in Fig. 16 max 40 0C 4.7 % is shown in he cenal measuing poin poin 3 coesponds o TC 3. Ohe cooling cuves have local deviaion less han 10 C 1.1 %. The explanaion of cenal deviaion is given in he conclusion of he pape. 68 TRANSACTIONS OF FAMENA XLII- Special issue

9 Esimae of Hea Tansfe Coefficien Fig. 16 Compaison of simulaed and measued empeaues duing quenching of he pobe 25x100 Fig. 17 and 18 depic hea ansfe coefficien as a funcion of suface empeaue and heigh of he pobe esablished wih is own epaameiaion algoihm [12] and [7]. I was calculaed in five values of he coodinae. Wih he smalle numbe of coodinaes hee was a dange of losing some of he local exemes. Fig. 17 Paameic display of hea ansfe coefficien fo he pobe 25x100 Fig. 18 Linea inepolaed hea ansfe coefficien fo he pobe 25x The quenching of he pobe 50x150 The esuls of 1D seach of hea ansfe coefficien duing quenching of he pobe 50x150 in 40 C empeaue wae in maked poins of he axis ae shown in Fig. 19. The spaial linea inepolaion of hea ansfe coefficien and is no given due o limied space of he pape. Fig. 20 depics he hea ansfe coefficien as a funcion of suface empeaue fo he pobe 50x150 calculaed in he six values of he coodinae. TRANSACTIONS OF FAMENA XLII- Special issue

10 Esimae of Hea Tansfe Coefficien Fig. 19 Time funcions f1 f2 and f3 fo he pobe 50x150 in maked poins of axis Fig. 20 Hea ansfe coefficien fo he pobe 50x150 in maked poin of axis Fig. 21 shows he esuls of compaison of measued TCm and calculaed TCc empeaues in all fou obseved poins of compuaional domain. The lages local deviaion in Figue 21 max 38 C 4.5 % is shown in he cenal measuing poin. Ohe cooling cuves have local deviaion less han 1.2 %. Fig. 21 Compaison of simulaed and measued empeaues duing quenching of he pobe 50x The quenching of he pobe 75x225 The esuls of 1D seach of hea ansfe coefficien duing quenching of he pobe 75x225 in 40 C empeaue wae in maked poins of he axis ae shown in Fig. 22. Fig. 23 depics he hea ansfe coefficien as a funcion of suface empeaue fo he pobe 75x225 calculaed in he six values of he coodinae. 70 TRANSACTIONS OF FAMENA XLII- Special issue

11 Esimae of Hea Tansfe Coefficien Fig. 22 Time funcions f1 f2 and f3 fo he pobe 75x225 in maked poins of axis Fig. 23 Hea ansfe coefficien fo he pobe 75x225 in maked poins Fig. 24 shows he esuls of compaison of measued TCm and calculaed TCc empeaues in all fou obseved poins of compuaional domain. The lages local deviaion in Fig. 24 max 40 C 4.7 % is shown in he cenal measuing poin. Ohe cooling cuves have local deviaion less han 1.2 %. Fig. 24 Compaison of simulaed and measued empeaues duing quenching of he pobe 75x225 Figues and 22 local hea ansfe coefficiens a heigh =H/2 of each pobe have expessed exemes due o lowe influence of hea ansfe of pobes o wae wheeas hea ansfe base o wae has ponounced effec on hea ansfe coefficiens a heighs =0 and =H. Figues and 23 local hea ansfe coefficiens ae no expessed a heigh =H/2. The eason is insufficien numbe of linea inepolaions of he hea ansfe coefficien a specific heighs of axis which cus ceain peaks. TRANSACTIONS OF FAMENA XLII- Special issue

12 Esimae of Hea Tansfe Coefficien The common eview of dependence of hea ansfe coefficien on diamee and suface empeaue a heigh =H/2 of each pobe is shown in Fig. 25. Fig. 25 Hea ansfe D a a heigh H/2 The maximum values of local hea ansfe coefficiens fom lowe o highe pobe diamee ae W/m2K. 5. Conclusion In ode fo esuls of hea ansfe coefficien o be in accepable boundaies i was necessay o povide qualiy guidance of expeimenal wok as well as compue simulaions of conduced expeimens. The common obsevaion fo all he obained hea ansfe coefficien soluions is efleced in he deviaion of he measued and simulaed cooling cuves. Significan deviaions ae shown in he cenal measuemen poin fo each simulaion. The maximum value of he deviaion is 4.7%. Ohe measuing poins wee below accepable 3%. Thee cooling cuves wee obained wih measuemens nea o he cooling suface of he pobe while he cenal cooling cuve is he fuhes one and is heefoe he leas sensiive o changes ha come wihin he cylinde suface. The deviaion in he measued and calculaed cooling cuves can be aibued o he inoduced assumpions in he 2D axisymmeic compued model. In addiion hee ae also he accuacy and ae of colleced daa as well as expeience in manual selecion of ime seps which equie he value of hea ansfe coefficien. Fase quenchans have song dynamics of he vapo film which caused he incease in numbe of seach imes so as o descibe he cooling cuves moe accuaely o acquie local exemes of hea ansfe coefficien. Novelies used in he pape ae efleced hough he expeimenal and simulaion pa of he pape. In he expeimenal pa of he pape he novely is consucion of measuing equipmen ha povides he consan flow ae of he cooling fluid aound he es cylinde and also he es cylindical pobes ae impoved fom wo [1] o fou [12] hemocouples aanged wihin he pobe. The simulaion pa of he pape is efleced hough he applicaion of hybid algoihm fo deemining he hea ansfe coefficien in 2D axisymmeic invese hea conducion poblem [11]. Finally we expanded he knowledge on numeous ealisic values of hea ansfe coefficien fo hee dimensionally diffeen es cylindes. 72 TRANSACTIONS OF FAMENA XLII- Special issue

13 Esimae of Hea Tansfe Coefficien REFERENCES [1] Galović A. The conibuion o he heoy of hea exchange beween fluidied bah and immesed fixed wall PhD Thesis Faculy of Mechanical Engineeing and Naval Achiecue Zageb [2] Liščić B. and Tensi H.M Luy W. Theoy and Technology of Quenching Spinge Velag hps://doi.og/ / [3] Öisik M. N. and Olande H. R. B. Invese hea ansfe fundamenals and applicaions Depamen of Mechanical Engineeing Noh Caolina Sae Univesiy [4] Kim H. K. Oh S. I.: Evaluaion of hea ansfe coefficien duing hea eamen by invese analysis Jounal of Maeial Pocessing Technology Vol pp hps://doi.og/ /s [5] Liščić B.: Ciical Hea Flux Densiies Quenching Inensiy and Hea Exacion Dynamics Duing Quenching in Vapoiable Liquids Hea Teamen of Meals p.p [6] K. Aimoo C. Jin S. Tamua K. Funaani M. Tajima Veificaion of Invese Quench-Hadening Phenomena in Beaing Seel Specimens by Expeimen and Compue Simulaion 14h Congess of Inenaional Fedeaion fo Hea Teamen and suface Engineeing Ocobe Shanghai China p.p [7] Hnjica B. and Juković M. Modelling and opimiaion of he ool sess in dilling pocess by evoluion algoihms Academic Jounal of Manufacuing Engineeing Vol. Issue 2/2007 Buchaes [8] Deb K. Muli-Objecive Opimiaion using Evoluionay Algoihms Wiley Wes Sussex Unied Kingdom [9] Felde I. Réi T. Samieno G. Smoljan B. and A. Deus Analysis of a numeical mehod developed fo esimaion of he hea ansfe coefficien obained duing quenching NETSU SHORI Jounal of he Japan Sociey fo Hea Teamen Vol p [10] Henánde-Moales B. Vegaa-Henánde H.J. Soloio-Día G. Toen G.E.: Expeimenal and Compuaional Sudy of Hea Tansfe Duing Quenching of Meallic Pobes Evapoaion Condensaion and Hea ansfe Amimul Ahsan ISBN p.p Sepembe [11] Felde I. Esimaion of Themal Bounday Condiions by using Hybid Invese Appoach Maeials Science Foum ISSN: Vol pp [12] Behem Š. The influence of he weing kinemaics and cylindical pobe diamees on he hea ansfe coefficien duing seel quenching PhD Thesis Univesiy of Bihac Faculy of Technical Engineeing [13] Melhem Oma A. Sahin Ahme Z Yilbas Beki S. Enopy geneaion due o exenal fluid flow and hea ansfe fom a cylinde beween paallel planes Themal science Volume 21 Issue hps://doi.og/ /tsci m Submied: Acceped: Assis. Pof. Šefik Behem Assis. Pof. Bahudin Hnjica Univesiy of Bihac Faculy of Technical Engineeing D. Ifana Ljubijankića bb Bihać Bosnia and Heegovina TRANSACTIONS OF FAMENA XLII- Special issue