Flash Methods to Examine Diffusivity and Thermal Conductivity of Metal Foams A Comparison with Data of a Comparative Set-Up

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1 Fs Metods to Exmine Diffsivity nd erm Condctivity of Met Foms: W. Hoener, D. Lger Fs Metods to Exmine Diffsivity nd erm Condctivity of Met Foms A Comprison wit Dt of Comprtive et-up W. Hoener, D. Lger Accepted for pbiction - Proc. 30 ICC 17 IE Pittsbrg, PA 009 ABAC e nysis of te stndrd ncertinty of term condctivity rests obtined by comprtive set-p motivted te se of ser fs device to determine te term condctivity of metic fom mteris. In prticr Mgnesim oy is investigted. o meet te reqirements of fs tecniqes copnr smpes re prepred. erefore te srfce ner open porosity is fied wit cermic pste e.g. ic. A finite eement mode is generted to stdy te infences of te preprtion metod to te mesrement rests. is enbes to seprte te condctivity bevior of te fom strctre from te inomogeneity effects of te prepred smpe. ests from fs bsed diffsivity mesrements re sed to exmine term condctivity sing = ρ x c p x. Dt re compred wit tose obtined from comprtive set-p. For bot metods detied nysis of te ncertinty of te mesrement rests is done. ests from bot metods re witin te overpping ncertinty eves of bot metods. A significnt improvement of te ncertinty eve of condctivity dt obtined from ser fs dt cod be confirmed. INODUCION Metic foms represent specific css of mteris in engineering nd design. erefore one s to know teir bsic termo-pysic properties: term expnsion, et cpcity nd term condctivity. In former mesrement cmpigns comprtive set-p ws sed. It mnges te retivey ig term condctivity of ~10 W/m.K in sfficienty wide tempertre rnge of [, ~400 C]. Bt te metod sffers from its dependency of igy ccrte tempertre mesrement of set of 6 termocopes minimm. erefore n terntive tec- AI Astrin Institte of ecnoogy 110 Wien 1

2 Fs Metods to Exmine Diffsivity nd erm Condctivity of Met Foms: W. Hoener, D. Lger niqe to perform condctivity dt ws serced. Here metod to mesre term diffsivity of fomy mteris wit ser fs [13-456] is described. e reqirement of copnr specimen is met by fiing te srfce ner porosity wit cermic pste. e term condctivity is ccted from diffsivity dt sing = ρ x c p x. Condctivity rests re compred wit tose obtined from te comprtive set-p. e stndrd ncertinty of rests from bot metods is estimted in ccordnce to te recommendtions of te GUM gide to express ncertinty in mesrement rests [7]. o regrd to te infences of te fier mteri in te open srfce porosity finite eement FE - bsed simtion of te trnsient nd spti et propgtion ws done. e sperposition of te trnsient spti eting of te cermic fier nd te metic fom nd its conseqences to te I detection of te LF were nysed. As rest te trnsient tempertre response of te metic body itsef cn be sed to evte its term diffsivity nd condctivity s we. EXPEIMENAL AND FE-CONCEP Preprtion Metod: ecniqe nd Conseqences Of copnr prepred cyindric specimen s sown in Figre 1 ny open porosity ner te top nd bottom srfce of te specimen is fied wit cermic pste e.g. ic. Its term condctivity is significnty ower tn tose of te metic body. In comprison to te fiing wit ig condctivity pste or te cosing of te top nd te bottom side of te smpe wit ig-condctivity foi tis sowed te best rests. Before fsing bt fter te drying of te pste te smpe is grinded. e I detector sees copnr specimen wic is nontrnsprent for te ser bem. Bt te cermic fier mteri in te srfce ner porosity infences te et trnsfer in te metic strctre. And from princip it is in confict to te ssmption of omogeneos mteri. A sperposition of te trnsient tempertre responses of bot te metic strctre nd te cermic fier occrs. Figre 1: LFA smpe of Mg fom mteri AI Astrin Institte of ecnoogy 110 Wien

3 Fs Metods to Exmine Diffsivity nd erm Condctivity of Met Foms: W. Hoener, D. Lger e I device detects n integr of te spti term rdition. is cses n verge trnsient tempertre response nd sift in te f time. o evte te term diffsivity of te fom mteri its specific f time mst be known. s te different rntimes of te et pses t te rer side of te specimen in te met nd in te cermic pste mst be seprted. Comprtive et-up verss Lser Fs Metods nd te bsic eqtions to determine term condctivity Comprtive et-up [8] nd term diffsivity Lser Fs [9] re formted in eqtions 1 nd respectivey. In ccordnce to te GUM Gide to Express Uncertinty in Mesrement ests: ENV [7] te corresponding mtemtic modes to estimte te Eqipment pecific Uncertinties EU re given tere too. e sed symbos re expined in ABLE 1. As sown in Figre in cse of comprtive condctivity mesrement te dependency of term condctivity dt strongy corretes to te ncertinty of te inpt estimte of te tempertres ². is significnty rests from te dependency of te EU from ². Under optimm conditions it is minimm 10% of te mesred condctivity. By contrst fs rests sow rter ow EU mosty ess tn 1% of te mesred diffsivity dt Figre 3. o consider effects from te mesred smpes te stndrd devition of te individ mesred rests DV² is dded to te EU² Gssin teory to estimte te stndrd ncertinty ² c. o derive te EU² Prkers w is ppied. In gener specific teories re sed to exmine term diffsivity from te detected t crve. e ccrcy of te ve strongy depends on te fitqity from tis teoretic pproc [ ]. In te teoretic mode to estimte te stndrd ncertinty ² c te stndrd devition DV² is sed to cptre effects from te fit-qity. Figre. Comprtive device: Eqipment pecific Uncertinty EU of term condctivity dt. LEF: Uncertinty of te tempertre inpt = 1K. = 3% = 0,1mm. IGH: Uncertinty of te tempertre inpt = 3K. = 3% = 0,1mm. AI Astrin Institte of ecnoogy 110 Wien 3

4 Fs Metods to Exmine Diffsivity nd erm Condctivity of Met Foms: W. Hoener, D. Lger Figre 3. Expected ncertinties from Lser Fs dt: LEF: Diffsivity dt in dependence from smpe tickness nd f time IGH: Eqipment pecific Uncertinty EU of term diffsivity dt. e Mg fom mteris sow diffsivity ~0 x 10-6 m²/s. o exmine te trnsient t-response bot 5000 tempertre ves re detected witin te reqired observtion time: ~10000 ms. Wit respect to verstie smpe dimensions of ~ 10 mm nd φ ~ 0 mm tis rests to n EU < 1% of te mesred ve. ABLE 1. Mtemtic ymbos Comprtive set-p term condctivity of te reference / smpe distnce between termocopes in te smpe sperscript indictes pper / ower reference body distnce between termocopes in reference body sperscript indictes pper / ower reference body tempertre difference between termocopes in te smpe sperscript indictes pper / ower reference body tempertre difference between termocopes in reference body sperscript indictes pper / ower reference body Fs device term diffsivity eigt of ser fs specimen f time of te trnsient tempertre response in fs experiment t 1/ Oters term diffsivity ncertinty of n individ inpt estimte stndrd ncertinty of n otpt estimte x - defined s fnction C x of server inpt estimtes: x = fx 1,,x i x n EU Eqipment pecific Uncertinty DV stndrd devition of set of dt AI Astrin Institte of ecnoogy 110 Wien 4

5 Fs Metods to Exmine Diffsivity nd erm Condctivity of Met Foms: W. Hoener, D. Lger AI Astrin Institte of ecnoogy 110 Wien 5 1 i c DV EU = = 1 ².. ² ².. ². ². EU = 4 n 1 1 i c DV EU t = π = 4 n1/ 4 1 / t EU π FE Mode nd imtion o qntify te distortion of te specimen properties by te cermic pste simpe finite eement mode ws deveoped. A cbic, mono-sized porosity is ssmed. Modes re designed from nit ce 8 nodes 3-D term soid eements. ey differ from teir rtio of crcteristic size of pore to te tickness of te remining metic ws of te smpe. In dependence of te porosity of smpe or density respectivey sitbe smpe geometry cn be identified. As et trnsfer mecnisms condctivity nd rdition bt no convection re considered. DICUION FE imtion of Fomy mpes e imges in Figre 4 sow te trnsient tempertre response of te Mgnesim fom strctre ines wit mximm ves nd te ic fier ines wit minimm ves for tree crcteristic types of smpes wit pproximtey te sme eigt ~10 mm. Additiony te rdition dependent detector sign ines between is sown. Imge I sows smpe wit pore size of 1 mm. Compred to te smpe size tis represents qsi-omogeneos metic body. No significnt differences in te tempertre responses of te met, te ic fier nd te detector occr. Imge II sows typic smpe wit pore size of -3 mm. e I-detected tempertre cod be verified by mesrement. It is significnty different from te re tempertre response of te metic strctre. s te f time t 1/ s to be corrected by fctor ~5. Imge III sows smpe wit ony one open pore competey fied wit ic. e detector identifies te tempertre response of te ic!

6 Fs Metods to Exmine Diffsivity nd erm Condctivity of Met Foms: W. Hoener, D. Lger I II III Figre 4. FE simtion of te trnsient tempertre response of Mg-fom mteris. mpes differ in teir porosity. Porosity is fied wit ic. - LFA - LFA-corr. - Comp / W/m.K 10 c LFA < % 10 x 10 6 /m²/s 5 c Comp ~ 0.. 0% / C 0 Figre 5. erm diffsivity nd condctivity of Mg-fom mteri. comprison between condctivity dt from comprtive set-p nd dt ccted from fs bsed diffsivity dt. AI Astrin Institte of ecnoogy 110 Wien 6

7 Fs Metods to Exmine Diffsivity nd erm Condctivity of Met Foms: W. Hoener, D. Lger FE Bsed Correction of Fs ests in Comprison wit Comprtive Dt: A fom from Mgnesim-oy s sown in te figre bove ws mesred. e term condctivity of te Mg bk is 156 W/mK, te ttribted ncertinty is estimted wit ± 5%. e bk density is g/cm³. e density of te fom t 0 C is ρ f = ± g/cm³ ~ 5% ρ MgA. e rdis of te smpe mesres 0 mm nd is pproximtey twice it s eigt. s te nmber of pores mono-sized pores re ssmed in te vome cn be ccted wit n V = ½.n 3/ identifying n s te nmber of pores visibe t te top srfce of te smpe. Eqtion [².π. n V. 4 / 3.π.r³]. ρ f = ².p..ρ MgA gives te crcteristic rdis of te pores r foowing to: r = [/n 1/ ].[ 3 /.ρ MgA ρ f ]. Wit n ~ 100 one estimtes r ~ mm. is conseqences FE-mode wit 5 yers s istrted in imge I. From first view no correction seems to be necessry. Bt te FE-nysis sows tt f time correction of bot 10% sod be done. e corrected diffsivity dt nd bot te corrected nd te n-corrected condctivity dt s we re sown in te figre bove. Corrected condctivity dt re sigty iger. In comprison to condctivity rests from comprtive set-p LFA bsed dt re bot 10% to 15% iger. LFA bsed dt nd Comprtive dt give rests witin te ncertinty eves of bot metods. Comprtive dt were ttribted wit constnt ncertinty of 15% from teir sppier. erefore ere is ssmed tt eiter rog description of te EU wit n ncertinty of te tempertre of ~ C ws sed for te set-p or no sttistics from set of mesred smpes ws done. o correct tis c = x EU² 1/ 0% of is ssmed. LFA bsed condctivity dt sow n ncertinty eve 95% Conf. Int. k = from ~10%. EUL e sef consistency of te nmeric rests nd te greement of te fs bsed condctivity rests wit tose obtined from comprtive device ve been proved. As rest for ftre crcteristion of met fom mteris fs devices cn be sed. For te mesred mgnesim oy n verge ncertinty of diffsivity rests is estimted to ~7%. In ddition DC nd ditometry re sed to determine et cpcity nd term density. Dt from tese metods re sed to ccte term condctivity. For ncertinty of condctivity dt ess tn 10% bsed on confidenti interv of 95% coverge fctor k = cod be cieved. e density of te mesred fom mteri is bot 4% of te bk density. s te exmined term condctivity dt of te fom mteri of bot 4% compred to tose of te bk mteri cn be nderstood comprison done t room tempertre. o formte te retion between te fom density nd te term condctivity of te fomy strctre ws not scope of tis work. Bt it cod be sown tt te nmber of visibe pores t te top srfce of smpe provides sfficient informtion to perform exceent mesrement rests. AI Astrin Institte of ecnoogy 110 Wien 7

8 Fs Metods to Exmine Diffsivity nd erm Condctivity of Met Foms: W. Hoener, D. Lger LIEAUE 1 L. Vozr Fs Metods for erm Diffsivity Mesrement Constntine te Piosoper University in Nitr K, Fcty of Ntr ciences 001 Y.. ookin,.w. Powe, C.Y. Ho, C.M. Nicoo ermopysic Properties of Mtter, Vo.10 erm Diffsivity of Eements nd Aoys New York, Wsington, IFI/Penm D.K. Mgic, A. Ceziriyn, V.E. Peetsky Compendim of ermopysic Property Mesrement Metods, Vo.1 rvey of Mesrement ecniqes London, Penm Pbising Corp D.K. Mgic, A. Ceziriyn, V.E. Peetsky Compendim of ermopysic Property Mesrement Metods, Vo. ecommended Mesring ecniqes nd Prcticies London, Penm Pbising Corp L. Kbicr, V. Boc eview of ever Dynmic Metods of Mesring ermopysic Prmeters, pp.135 in erm Condctivity 14, Pittsbrg, ecnomic Pbiction Compgny, Inc W.J. Prker,.J. Jenkins, C.P. Bter, G.L. Abbott Fs Metod of Determining erm Diffsivity, Het Cpcity, nd erm Condctivity J. App. Pysics, Vo.3, No.9 ept ENV Gide to te expression of ncertinty in mesrement DIN Bestimmng der Wärmeeitfäigkeit nc einem Vergeicsverfren Feststoffe Apri E tndrd est Metod for erm Diffsivity by te Fs Metod Feb F. igini, A. Ceziriyn Pse Metod of te erm Diffsivity Mesrement A eview, Hig emp. Hig Press. Vo E. yor, D.K. Mgic Pse Metod for erm Diffsivity Mesrement in D.K. Mgic, A. Ceziriyn, V.E. Peetsky Compendim of ermopysic Property Mesrement Metods, Vo.1 rvey of Mesrement ecniqes London, Penm Pbising Corp L.M. Crk,.E. yordition Loss in te Fs Metod for erm Diffsivity J.App.Pys. Vo.46, A. Digiovnni, M. Lrent Une novee tecniqe d intifiction de diffsivité termiqe por metode fs eve Pys. App. Vo.1, J.A. Cpe, G.W. Lemnn J. App. Pys., Vo.34, J. Bmm, J. Opfermnn Improvement of te mtemtic modeing of fs mesrements Hig emp. Hig Press. Vo.34, AI Astrin Institte of ecnoogy 110 Wien 8