The influence of fuel surface roughness and surface structures on ignition an exploratory analysis

Transcription

1 The fluece of fuel urface roughe ad urface tructure o gto a exploratory aaly Rckard Hae Nchola Dembey Reearch report

2 Table of Cotet Abtract... 3 Notato Itroducto Defg urface roughe parameter Igto proce Goverg equato of the old/ga terface Network aaly Vew factor Expermet ad two-dmeoal aaly Coe calormeter expermet Fte Dfferece Method Set up of two-dmeoal aaly Procedure of the model calculato Reult ad dcuo Igto tme of expermet Surface temperature at gto from expermet Surface temperature at t=5 from two-dmeoal aaly Surface temperature at gto from two-dmeoal aaly Comparo of expermet ad reult from two-dmeoal aaly Surface temperature dtrbuto at gto Decompoto zoe ad ourface plot Other Cocluo Ackowledgemet Referece... 36

3 Abtract The evromet heavy dutre dtguhed by heavy tear ad rough fuel urface. The urface roughe magtude of the gauge, det etc. could be ubtatal, where the roughe depth would rage from le tha a mllmeter up to everal mllmeter. Foret fuel urface wll geerally have rough urface charactertc, roof ad facade o redetal home the wldlad urba terface wll mot cae be o-flat. Performg fre expermet ad tetg the gto charactertc of the fuel urface, the fluece of urface roughe ad urface tructure hould be vetgated ad accouted for. Igto would occur frt at ay part expoed by heat trafer from everal drecto ad we are facg a two/three-dmeoal gto cearo. I th paper the gauge depth, agle ad dtace wa vared to depct roughe. I fve out of thrtee expermetal cae the average gto tme howed gfcat dfferece whe compared to the flat urface cae, but o clear patter wa detected. No clear patter were foud whe tudyg the two-dmeoal aaly reult at the tme of gto. I both expermet ad the two-dmeoal aaly a majorty of the temperature were wth the oe tadard devato varato ad dd ot how ay gfcat dfferece compared wth the flat cae, except whe comparg the gauge bottom temperature ad upper urface temperature of the two-dmeoal aaly where gfcat dfferece wa foud all cae. 3

4 Notato A m = area of urface m (m ) c p = pecfc heat (kj kg - K - ) c, = pecfc heat of old (kj kg - K - ) p D = dffuo coeffcet (m - ) E b = emve power of urface (kw m - ) E coe = emve power of coe calormeter (kw m - ) F = vew factor betwee urface m ad m h = heght of coe (m) h c = covectve heat trafer coeffcet (kw m - K - ) k = thermal coductvty (kw m - K - ) k = thermal coductvty of old (kw m - K - ) k g = thermal coductvty of flud (kw m - K - ) '' q e = exteral cdet heat flux (kw m - ) q m = et heat flow from urface m to urface (kw) '' q = et radato term for the upper urface ( = 0 et, rad, ecloure '' q = heat flux at fuel urface (kw m - ) r = radu of coe (m) R a = average heght (m) R da = average abolute lope (degree) x ) (kw m - ) R = radatve heat flow retace betwee urface m ad (m - ) m R = radatve heat flow retace of urface (m - ) S = mea dtace betwee adjacet peak (m) t = tme () t g = tme to gto () t py = heatg tme for the old to atta a temperature where fuel vapor emtted cocetrato whch make gto poble () t mx = traport tme eeded for fuel vapor ad oxyge to reach gto ource () t chem = tme for the fuel vapor ad oxyge mxture to combut after reachg the gto ource () t = tme cremet () 4

5 T = temperature (K) T 0 = ambet ar temperature (K) T g = flud temperature (K) T, = ode temperature at tme tep (K) m T = urface temperature of urface (K) T = urface temperature (K) u = ga velocty the x-drecto (m - ) v = ga velocty the y-drecto (m - ) x = dtace to pot of teret (m) x = dtace cremet (m) y = dtace to pot of teret (m) Y F = the ma fracto of fuel Y FS = the ma fracto of fuel the volatle Y O = the ma fracto of oxyge Y = the ma fracto of oxyge the ambet ar O z = dtace betwee coe calormeter ad upper fuel urface (m) α = thermal dffuvty (m - ) α = aborptvty of the fuel urface δ = boudary layer thcke (m) = lope of the roughe tructure (degree) ε = emvty of urface ε = emvty of the fuel urface η = agle betwee two oppog urface wth a commo edge (degree) ρ = dety of fuel vapor (kg m -3 ) ρ = dety of old (kg m -3 ) σ = Stefa-Boltzma cotat, kw m - K -4 τ = tramvty of ar τ ytem = tme cotat of the ytem () φ = agle betwee two oppog urface wthout a commo edge (degree) 5

6 . Itroducto Whe degg the overall heat releae rate of a object, calculatg the approprate gto tme of the varou fuel package wll be decve. Durg a umber of earler tude o the heat releae rate of mg vehcle (Hae (05a), Hae (05b)) the queto o how the urface roughe wll affect the gto wa raed. The evromet mg dutre dtguhed by heavy tear ad rough fuel urface. The urface roughe magtude of the gauge, det etc. could be ubtatal, where the roughe depth would rage from le tha a mllmeter up to everal mllmeter. A mportat compoet whe quatfyg the pread ad behavor of a wldfre the gtablty of a fuel tem, for example a fuel bed or a buldg facade. Typcally fuel tem gto charactertc are meaured baed o flat urface. May fuel tem have o-flat urface that ca be characterzed baed o urface geometry ug the cocept of a urface roughe. The roughe depth for dfferet tree truk ca vary from le tha a mllmeter to everal mllmeter (Eberhardt (05), Yaovak et al. (06)), for buldg urface - uch a woode pael - ma-made depth of 0-0 mm ca be foud. How the urface roughe effect fuel tem gto ot well defed at th tme. Ay urface protuberace o a ueve urface would gte frt; a thee wll be expoed by heat trafer from everal drecto a we are facg a two/three-dmeoal gto cearo. Heketad (979) performed gto tet o ample wth varable urface roughe ad foud that the gto tme wa largely affected by the urface tructure for dffuo flame a well a premxed flame. Akta (959) performed gto tet o wood wth varable urface roughe ad foud o dfferece gto tme. Thee two tude pot dfferet drecto but the umber of expermet the paper wa lmted ad the ubject ha ot bee vetgated to ay larger extet. The work preeted cot of a aaly where reult from coe calormeter expermet ad a two-dmeoal aaly were ued for explorg potetal relatohp wth repect to the gto of rough fuel elemet. The am ad purpoe of th paper to perform a exploratory aaly o the fluece of urface roughe wth repect to gto that may act a a ba for future tude. Bede urface characterzed by roughe, the reult may alo be applcable to o-flat urface where the urface tructure are part of the deg of the equpmet uch a tyre thread or a buldg facade. 6

7 . Defg urface roughe parameter Surface roughe ca be dtguhed by the radom ature ad foud two dmeo. Perpedcular to the urface the heght of the protuberace ca be dtguhed. Parallel to the urface the texture of the protuberace ca be dtguhed (Thoma (999)). Iteretg parameter order to characterze the roughe of a urface would thu be the ampltude ad the dtrbuto of the protuberace. The feature of urface roughe ca be decrbed umerou way. Due to the radom ature of the protuberace a average value of the pecfc parameter ofte bet uted whe characterzg the urface roughe. The followg parameter are example of average value: - Ampltude of roughe tructure to get a pcture of the vertcal charactertc of the urface tructure. Th could be defed a the average abolute devato of the roughe tructure from the mea le: R = a x = () - Dtace betwee roughe tructure to get a pcture of the horzotal charactertc. Th could be decrbed by the average dtace betwee local peak: S = S = () - The lope or agle of the roughe tructure wll provde a pcture of the combato of the vertcal ad horzotal charactertc. Th could be decrbed by average abolute lope of the roughe tructure: R da = = (3) The three parameter above repreet the three group that urface roughe tructure are ormally dvded to: ampltude parameter, horzotal dtace parameter ad parameter repreetg a combato of ampltude ad horzotal dtace parameter. I the eug twodmeoal aaly ad coe calormeter expermet gauge wth certa agle, depth ad dtace were appled order to depct roughe feature. I fgure the parameter are decrbed for a two-dmeoal cro-ecto of a pecme. The mplfed urface roughe feature ad the mllg of the tructure were performed to obta cotrolled ad homogeeou tructure utable for a exploratory aaly. 7

8 Fgure. Surface roughe parameter appled the expermet ad aaly. 8

9 3. Igto proce Igto of a fuel tem wll deped o t flat urface reachg a crtcal codto uch a a temperature. The gto temperature repreet the pot tme whe a flat urface ca upport flamg gto (Atreya (998), Babrauka (003)). For th crtcal codto to be reached, the cdet heat flux ha to exceed the urface loe at the gto temperature. Surface roughe wll the be expected to affect the local cdet heat flux ad the local urface loe. I tur the local temperature would be expected to vary baed o the charactertc of the roughe. Fgure depct the gto proce at a rough urface where the fuel ample ha a horzotal oretato ad the ma flow the drecto of the heat ource. I the cae of a vertcal fuel ample oretato the phyc wll dfferet, alo a forced flow wll preet a dfferet tuato a oppoed to the buoyatly geerated flow ee fgure. Fgure. Igto procee at a rough urface. I the followg the two-dmeoal goverg equato for the old/ga terface for a rough horzotal urface expoed to radat heatg are preeted ad dcued. The preeted model are prmarly baed upo the oe-dmeoal model of Atreya (998). I the aaly ad expermet oly the ploted gto accouted for, a the ploted gto wa ued at the coe calormeter tet. The goverg equato of the ga phae ad the old phae ca be foud for example a paper by Atreya (998). 9

10 3. Goverg equato of the old/ga terface Qutere (006) preeted a expreo cotag the dvdual gto tme compoet: t = t + t + t (4) g py mx chem The t py -compoet decrbe the tme to atta the temperature where adequate fuel vapor cocetrato are emtted. The tmx -compoet accout for the tme eeded for fuel vapor ad oxyge to reach the gto ource. The t chem -compoet accout for the tme from whe the flammable mxture reache the gto ource utl combuto. The focu wll be o the t py - ad the tmx -compoet a thee wll domate over the tchem -compoet (eglgble where trog gto codto preval whch ca be aumed for the expermet). Ital boudary codto ( t = 0 ) wth the boudary layer ( < x < δ 0 ): Y F ( x,0) = 0 (5) Y x,0) O ( (6) = Y O T ( x,0) = T (7) 0 Fuel coervato at the urface ( x = 0 ), > 0 t : YF ρ D = ρ u ( YF YFS ) + ρ v ( YF YFS ) (8) y Oxyge coervato at the urface, t > 0 : YO ρ D = ρ u YO + ρ v YO (9) y Fuel temperature at the urface, t > 0 : T 0, t) = ( (0) T S Boudary codto at the boudary layer ( x = δ ), > 0 t : 0

11 Y F ( δ, t) = 0 () Y, t) O (δ () = Y O T (, t) = T δ (3) 0 '' '' q ( δ, t) q = E F τ (4) = e coe CoeBoudaryLayer Aumg optcally th codto, the ga phae aborpto of radato ca be eglected ad the heat flux from the coe calormeter ca be expreed a: q '' = F q (5) BoudarLayer FuelSurface '' e The heat flux from the coe meaured at the urface whch tregthe the eglectg of the ga phae aborpto. The old boudary codto at a urface plae: T k dy = ρ c x + q et, rad, ecloure p T v y v dy + T dy dx + ρ c y p ( u T ) dy (6) The temperature chage the y-drecto aumed to be mall ad the coducto the flow drecto eglgble. The et radato to the old urface the fal term o the RHS of the equato ad olved through a etwork aaly decrbed below. The temperature cotuty at the terface: T (7) g = T x=0 x=0 The heat flux cotuty (o-lp codto):

12 k T x x= 0 = k g T g x x= 0 + q '' et, rad, ecloure (8) Fgure 3 dplay the atural covecto cae ad the covectve eergy flow of a cotrol volume at the terface. The reultg ecod-order dfferetal of the covectve eergy were eglected equato (6). Fgure 3. Natural covecto cae for a rough urface. Gve that the mxg tme mall compared wth the heatg tme - ee below for aaly - the ga phae detal ca be mplfed wth repect to the mxg tme, where a heat trafer coeffcet ued equato (6): T k = hc ( T0 T ) + q et, rad, ecloure (9) x To vetgate the ga phae flow feld over the old urface, the boudary layer thcke wa calculated for two cae: forced flow ad atural covecto over a horzotal pecme facg upward. For the forced flow cae, the boudary layer thcke wa calculated baed upo the Reyold umber reultg a lamar flow cae (Holma (00)). Fgure 4 dplay the boudary layer thcke a a fucto of the dtace from the edge of the pecme.

13 Fgure 4. The boudary layer thcke; forced flow cae. For the atural covecto cae, the boudary layer thcke wa calculated applyg a paper by Lewadowk et al. (000). The model aume that the thermal ad hydraulc boudary layer have comparable thckee. The equato for the two cae are vald for flat urface ad the boudary layer thcke for a urface wth mlled gauge wll ot be detcal. Neverthele, the equato are appled order to obta approxmate value. Gve the boudary layer thcke, the mxg tme wa calculated applyg a bary dffuo coeffcet for carbo mooxde. The mxg tme above the cetre of the pecme for both cae wa foud to be mall comparo wth the gto tme of the expermet ad therefore the ga phae detal ca be mplfed wth relato to the mxg tme. The park gter the expermet located 3 mm above the cetre of the pecme, whch wth the boudary layer for both cae. Th wll mply that o addtoal traport tme bede the mxg tme hould be codered ad ploted gto preval. I the two-dmeoal aaly the followg aumpto were made: - Heat loe due to moture cotet of the fuel ample are eglected, aumg low moture cotet. - The fuel decompoto wll occur depth of the fuel ample ad charrg aumed. - The ma flux low pror to gto ad the heat of pyroly eglected. - A opaque materal aumed a well a gray ad dffue fuel urface. - The ga of the boudary layer a o-partcpatg ga a the optcal pathlegth wll be mall due to the hort dtace betwee the coe elemet ad the pecme. - The radato aborbed at the urface. - The ftely th urface of the ample wth vrtual de repreetg the boudary layer ad the ambet above the boudary layer regarded a a ecloure whe accoutg for the radatve heat trafer from the coe to the terface. 3

14 - The cotrbuto of the ga-phae exothermc reacto eglgble the eergy balace at the terface. 4

15 4. Network aaly The followg aumpto were made related to the etwork aaly: - The temperature alog a gauge urface ad for a upper urface egmet wll vary ad therefore the urface were dvded to fte part. - For the gauge a three ded ecloure aumed, cotg of the two gauge lope ad the upper vrtual de - level wth the upper urface of the pecme. - Uform emvty for the fte part. - The cdet radato upo the upper urface et to 35 kw m - at the cetre of the pecme, equvalet to the meaured heat flux at the pecme urface durg the calbrato procedure. Th requre that the boudary layer ga a o-partcpatg ga. The emve power of the dvdual urface: E = σ (0) 4 b T The radatve heat flow retace: R m = A F m () R ε = A ε () The dvdual et terchage betwee two urface: E E b bm q m = (3) R + Rm + Rm The et terchage betwee the coe ad a urface: q F E '' radal bm q coem = (4) Rcoem + Rm F radal decrbe the vew factor alog the urface. 5

16 6 The dvdual et terchage term for a urface are ummed up to a total et heat flow: = = m m bm b m m coe bm radal m R R R E E R R E F q q '' (5) The et radato term of equato (9): m m ecloure rad et A q q = α '',, (6) 4. Vew factor The varato of the cdet radato wth the radal dtace from the cetre for a upper urface: The cdet radato vare wth the radal dtace from the cetre ad ca be decrbed applyg (Wlo et al. (003)): A da R Z R H R Z R H F d + + = (7) a z H = (8) a r R = (9) R H Z + + = (30) ( ) a z h H + = 4 (3) a r R 4 4 = (3)

17 Z H 4 R4 = (33) The parameter of equato (8-33) are ee fgure 5. Fgure 5. Vew factor parameter for the coe calormeter urface (3) ad a urface elemet ( da ). Fgure 6 dplay the vew factor acro the upper urface a a fucto of the radal dtace from the cetre. I the calculato the vew factor at the cetre wa et to ad the vew factor of adjacet egmet wa adjuted accordgly. 7

18 Fgure 6. Vew factor of the upper urface a a fucto of the radal dtace from the cetre. The vew factor term equato () ca be dfferetated to three cae: a) Two ftely log urface havg a commo edge wth a cluded agle (Schröder ad Haraha (993)). b) Two ftely log urface of equal wdth havg a commo edge wth a cluded agle (Segel ad Howell (00)). c) Two ftely log urface wthout a commo edge wth a cluded agle (Segel ad Howell (00)). a) Two ftely log urface havg a commo edge wth a cluded agle (Schröder ad Haraha (993)): a A = (34) b = A + ( A + A coη) F (35) The parameter of equato (34) ad (35) are foud fgure 7. 8

19 9 Fgure 7. Vew factor parameter for two oppog urface wth a commo edge. b) Two ftely log urface of equal wdth havg a commo edge wth a cluded agle (Segel ad Howell (00)): = η F (36) c) Two ftely log urface wthout a commo edge wth a cluded agle (Segel ad Howell (00)): ( ) ( ) ( ) ( ) ( ) / / / / co co co co x x y y x x y y x x y y x x y y x x F = φ φ φ φ (37) The parameter of equato (37) are foud fgure 8. Fgure 8. Vew factor parameter for two oppog urface wth o commo edge.

20 5. Expermet ad two-dmeoal aaly 5. Coe calormeter expermet Coe calormeter expermet were coducted the Fre Scece Laboratory at WPI. The pecme were whte pe board (0.x0.x0.05 m (LxWxH)) a the urface would ot chage hape durg the pre-gto phae, exceedg the legth cale of the roughe tructure. Meauremet were performed to verfy thermally-thck behavor. V-haped gauge were mlled the ame drecto a the gra - depctg roughe feature - varyg the depth, agle ad dtace; ee Table ad Fgure. Table alo clude the ormalzed charactertc legth of the cae, wth repect to the wdth/legth of the coe pecme (.e. 00 mm). The lmted data et wa due to the copg tudy ature of the project. Cae # had o roughe feature for referece. Throughout the expermet the cdet heat flux wa et to 35 kw m -. A umber of expermet were alo coducted wth a heat flux of 50 kw m -, but the creae heat flux reulted vrtually o dfferece gto tme betwee the expermet. The gto tme, temperature o upper urface ad a gauge (ug gla brad ulated thermocouple wth 0.5 mm dameter ad a. C tolerace) were recorded. The thermocouple the gauge were potoed the upper thrd part of the gauge a t wa dffcult to poto the thermocouple at the bottom. The average pecme moture cotet wa meaured at 5.8%, ug a P-000 electrcal retacetype moture meter from Delmhort Itrumet. Outler elmato of gto tme ad urface temperature were coducted a gle value tood out. Whe outler elmato wa appled the chage the average value wa mmal. Whe lookg to the temperature data of the coe expermet t wa otced that whe the hutter opeed a udde temperature creae occurred followed by a perod where the temperature levelled out ad fally a rapd temperature creae. A gto crtero wa defed th paper a the pot of tme whe the temperature tated th fal ad udde creae. 5. Fte Dfferece Method A two-dmeoal aaly applyg a fte dfferece methodology of the heat coducto to the pecme wa coducted, varyg: gauge depth, agle ad dtace. Table lt the dfferet cae, detcal wth the expermet. Uteady-tate coducto ad o eergy geerato were aumed. Neglectg heat of pyroly ad aumg a opaque materal, the eergy equato of the old phae: T T T ρ c p, = k + k (38) t x x y y wa appled. The expoed face old boudary codto of equato (9) wa appled a well. 0

21 The roughe parameter ca be lked to equato (9). The covectve heat trafer, frt term o rght had de of equato (9), aumed cotat relatve to the urface roughe due to the hallow ormalzed depth (up to 5%). The radato heat trafer, ecod term o the rght had de of equato (9), accout for the chagg apect of the urface roughe. It aumed that the cdet radato to each ode vare wth the radal dtace from the cetre of the pecme. It alo aumed that the cdet radato de a gauge ecloure wll vary wth the gauge agle ad depth. Fgure 9 dplay the ode et-up two cae; the upper cae ha a mm gauge depth, 45 gauge agle ad 0 mm gauge dtace, the lower cae a 5 mm gauge depth, 60 gauge agle ad mm gauge dtace. The blue quare repreet teror ode, the red repreet urface ode, the orage exteror corer ode ad the gree teror corer ode. Fgure 9. Node et-up two cae. Each upper urface ode how Fgure 9 exchage radato wth the ambet evromet oly. Each urface ode that part of a gauge, ee Fgure 9, exchage radato wth the ambet ad the other part of the gauge that ca be ee from the gve ode. A vrtual ecloure etablhed for each gauge baed o t charactertc ad the approprate vew factor are calculated to etablh the radatve exchage wth the vrtual ecloure. 5.3 Set up of two-dmeoal aaly Uteady-tate coducto ad o eergy geerato were aumed the aaly. Neglectg the heat of pyroly ad aumg a opaque materal, the eergy equato of the old phae (equato (38)) appled where the ecod partal dervatve ad the tme dervatve are approxmated by: x T + T T m+, m, ( x) T m, (39) T Tm, + Tm, y + ( y) T m, (40) T t T + m, T t m, (4)

22 Iertg the approxmato to equato (38) reult the followg approxmato for a teror ode: ( T + T + T + T ) + ( τ ) T + T m, = ytem m, m, + m+, m, 4 ytem m, τ (4) t τ = α (43) ytem ( x) k = ρ c α (44) p, Fgure 0 dplay a teror ode ytem. Fgure 0. Node ytem for a teror ode. The old boudary codto at a urface plae (equato (9)) ca be approxmated by the followg approxmato for a urface ode (ettg the eergy coducted, covected ad radated to the ode equal to the teral eergy creae of the ode): '' ( h ( T T ) + q ) c ρ c 0 p, ( x) et, rad, ecloure T + m,0 T t m,0 x = k T m,0 T m, T + m,0 T m+,0 T + m,0 T m,0 + (45) For a upper urface ode, the heat flux term o the LHS of equato (45) oly cota the et terchage betwee the coe heater ad the urface ode. See fgure for the ode ytem.

23 Fgure. Set up of ode for a urface ode. The approxmato of equato (9) for a exteror corer ode: x Tm Tm Tm T '' '',,, m, ( ) ( x) q + q = k + + ρ c et, rad, ecloure et, rad, ecloure T T + m, m, p, 4 (46) t The frt term o the LHS of equato (46) oly volve the et heat flux term from coe calormeter to the upper urface of the corer ode. The ecod term volve both the et heat flux term from coe calormeter to the lope egmet ad the et terchage term of the lope egmet. See fgure for the ode ytem. Fgure. Node ytem for a exteror corer ode. Approxmato of equato (9) for a teror corer ode: x ρ c '' m, m, + m, m, ( q ) = k + + ( T T ) + ( T T ) et, rad, ecloure p, ( x) 3 4 T + m, T T m, T T T m, m+, t (47) m, m, + See fgure 3 for the ode ytem. 3

24 Fgure 3. Set up of ode for a teror corer ode. Approxmato of equato (9) for a exteror corer ode wth oe de ulated: x Tm Tm Tm T '',,, m, ( ( ) ) ( x) h T T + q = k + + ρ c c 0 et, rad, ecloure T T + m, m, p, 4 (48) t For a corer ode alog the upper urface, the heat flux term o the LHS of equato (45) wll oly cota the et terchage betwee the coe heater ad the urface ode. See fgure 4 for the ode ytem. Fgure 4. Node ytem for a exteror corer ode wth oe de ulated (bold le). Approxmato for a teral ode - applyg equato (9) - wth oe de ulated: ( T + T + T ) + ( τ ) T τ (49) + T m, = ytem m, + m+, m, 4 ytem m, See fgure 5 for the ode ytem. 4

25 Fgure 5. Set up of ode for a teral ode wth oe de ulated (bold le). Tabulated value for pe (moture cotet of 0%) (Babrauka (003)) were appled the aaly: - Heat capacty:.8 kj kg - K - - Thermal coductvty: 0.85 W m - K - - Dety: 50 kg m -3 A etvty aaly wa carred out to fd the optmal dtace cremet, applyg (Holma (00)): ( x) α t 4 (50) Baed upo the reult, the tme cremet wa et to 0.5 ad the dtace: x = y = m. The aborptvty ad the emvty of the whte pe urface wa aumed to be 0.88, a there were o expermetal data avalable (Babrauka (003)). The covectve heat trafer coeffcet wa et to 0.04 kw m - K -, vald for a heat flux of 35 kw m - a coe calormeter (Babrauka (003)). 5.4 Procedure of the model calculato I order to further clarfy the model detal, the tep-by-tep procedure preeted here: The frt tep volved ettg up the geometry of the pecfc cae ad dvdg the ample to the dfferet type of ode wth the optmal dtace cremet. Itally the temperature of the gauge ad upper urface ode were et to the ame temperature a the thermocouple recorded whe the hutter wa opeed. Durg the ecod tep the vew factor for the dfferet urface ode were calculated ug expreo decrbed above, both wth repect to the coe heater a well a for ode facg each other the gauge. The thrd tep volved ug equato (9) ad applyg the exteral heat flux from the coe heater ad the urface temperature of the prevou tme tep, the cdet heat flux at the varou urface ode were calculated. The et terchage term for a gauge urface ode wa calculated ug equato (5) ad for a upper urface ode equato (4) wa ued. I both cae the emve 5

26 power of the dvdual urface ode were calculated applyg the urface temperature from the prevou tme tep. I the fourth tep the temperature of the urface ode a well a the teral ode were calculated applyg the dfferet approxmate equato decrbed above a well a the ode temperature from the prevou tme tep. The calculato are repeated for the thrd ad fourth tep for each tme tep. 6

27 Table. The cofgurato of each expermetal cae; reultg gto tme ad temperature of the expermet. Cae # Normalzed depth Normalzed dtace Depth of gauge (mm) Agle of gauge (degree) Dtace betwee gauge (mm) Number of Gauge Average gto tme () Stadard devato gto tme Average upper urface temperature ( C) Stadard devato upper urface temperature Average gauge temperature ( C) Stadard devato gauge temperature A 4 B 6 37 C A CD A 33 B 300 D A A C 6 Avg = Avg = 0 Avg = 8 A Show gfcat dfferece baed o SD varato (4 ec) compared to Cae # for gto tme. B Show gfcat dfferece baed o SD varato (40 C) compared to Cae # for upper urface temperature. C Idcate gfcat dfferece baed o SD varato (38 C) betwee upper urface ad gauge temperature. D Show gfcat dfferece baed o SD varato (36 C) compared to Cae # for gauge temperature.

28 6. Reult ad dcuo Etablhg a gfcat dfferece betwee the mea expermetal value, a crtero where the rage of oe tadard devato of the mea dd ot overlap each other wa appled, ee Table. 6. Igto tme of expermet Table dplay the average tme of gto for all expermetal cae. Fve of the thrtee cae howed gfcat dfferece whe compared to the flat urface cae. Thee fve cae dd ot how ay clear patter related to the gauge charactertc. 6. Surface temperature at gto from expermet Table dplay the average upper urface ad gauge temperature for all expermetal cae. Two out of thrtee cae for the upper urface temperature ad two out of thrtee cae for the gauge temperature howed gfcat dfferece whe compared to the flat cae. Thee cae how o clear patter related to the gauge charactertc. Comparg the upper urface ad gauge temperature for each cae howed gfcat temperature dfferece three out of thrtee cae. Thee cae how o clear patter related to the gauge charactertc. 6.3 Surface temperature at t=5 from two-dmeoal aaly Table dplay the average ode temperature at t=5 from the two-dmeoal aaly. Th fxed tme wll be ued to verfy the two-dmeoal aaly. The pot of tme at t=5 wa elected a t wa jut pror to the gto of a majorty of the expermet ad dtct temperature dfferece had bee etablhed at that tme. The average upper urface temperature wa the average urface ode temperature betwee two gauge the cetre of the ample. The upper mm gauge lope temperature wa the average urface ode temperature for a corer ode ad the correpodg ode below t to the gauge for a dtace of mm. The average gauge bottom temperature wa the ode temperature of the bottom ode. The locato of both thee temperature wa the gauge cloet to the pecme cetre. The upper urface ad upper mm gauge temperature creae a gauge depth creae for all agle ad pacg. Th cotet wth the fact that the et dfferece betwee heatg (cdet heat flux from coe ad re-radato wth gauge) ad coolg (covectve coolg ad re-radato out of the gauge) creae wth creag depth. The gauge bottom temperature decreae a the gauge depth creae for all agle ad pacg. Th cotet wth the fact that the vew factor from the coe heater to the bottom ode alway decreae wth creag depth ad the vew factor from oppote gauge lope to bottom ode alo decreae wth creag depth. The upper urface ad upper mm gauge temperature decreae a gauge pacg creae for all agle ad depth - except the 30 degree cae wth a mm gauge depth. Th cotet wth the fact that the temperature of the edge ode are geerally hgher tha the upper urface temperature a the edge ode expoed to heat flux from two drecto. Wth creag gauge dtace betwee edge ode, the upper urface temperature wll decreae a edge ode heatg effect decreae. Wth a loger dtace betwee two edge ode, the coolg effect of the upper urface wll creae ad reult lower upper mm gauge temperature. The edge ode temperature the 30 degree ad mm depth cae are lower tha the upper urface temperature a the et dfferece betwee heatg ad coolg lowet for the 30 degree cae.

29 The gauge bottom temperature decreae or doe ot chage a gauge pacg creaed for all agle ad depth - except for the 30 degree cae. Th cotet wth the fact that varato of the gauge dtace wll fluece the upper ode ad upper urface but ot the gauge bottom to the ame degree. I the 30 degree cae - a the edge ode ha a lower temperature - a creag pacg wll reult hgher upper urface temperature whch wll effect to ome extet the gauge bottom temperature. The upper urface, the upper mm gauge ad gauge bottom temperature all creae wth creag gauge agle for all depth ad pacg. The upper rego temperature creae ha a peak at a gauge agle of 60 for the mm depth ad at a 45 agle for the 5 mm depth. Th cotet wth a creae the urface area ad that the et dfferece betwee heatg ad coolg creae a the gauge agle creae. A the depth creae a larger porto of the radatve eergy reradated from ode the upper lope rego to the lower ode the 60 degree cae tha for the 45 or 30 degree cae. Gve the reult of the model at t=5, the output of the model were foud to be cotet wth the defto of the boudary codto ad the vrtual ecloure for the gauge. 6.4 Surface temperature at gto from two-dmeoal aaly Table dplay the average temperature at the tme of gto from the two-dmeoal aaly. The upper thrd gauge lope temperature wa calculated for comparo wth the expermetal reult a the thermocouple the gauge were potoed th part of the lope. The upper thrd gauge lope temperature wa the average urface ode temperature for a corer ode ad the correpodg ode below t to the gauge for a dtace of oe thrd of the total lope legth. The locato of the temperature wa the gauge cloet to the pecme cetre. The upper urface ad gauge bottom average temperature are defed the ame a prevouly oted for the t=5 dcuo. The gfcat dfferece of the model wa defed a the level of gfcace of the expermetal data - oe tadard devato - whch ca be ee Table. Ue of the expermetal tadard devato reaoable a a model caot be verfed or valdated to a level of ucertaty better tha the avalable expermetal data. Whe tudyg the gto tme Table, x out of thrtee cae for the upper urface temperature howed gfcat dfferece whe compared to the flat cae. I all but oe of thee cae the gauge dtace were mm. Fve out of thrtee cae for the upper thrd gauge lope temperature howed gfcat dfferece whe compared to the flat cae. Thee cae how o clear patter related to the gauge charactertc. Comparg the upper urface ad upper thrd gauge lope temperature for each cae howed gfcat temperature dfferece two out of thrtee cae. Both of thee two cae repreet the 30 degree agle ad 5 mm depth cae. Thee reult of the two-dmeoal aaly are mlar to the expermet where for a morty of cae gfcat dfferece are oberved due to chage gauge charactertc. Gauge bottom temperature behavor mlar to that oted for t=5. Whe comparg the gauge bottom temperature wth the correpodg upper urface temperature gfcat dfferece wa foud all cae. 9

30 Table. The average upper urface ad gauge temperature at gto from the two-dmeoal aaly. Cae # Average upper urface temp. at gto ( C) Average upper thrd gauge lope temp. at gto ( C) Average gauge bottom temp. at gto ( C) Average dfferece temp.: upper urface ad upper thrd gauge lope at gto ( C) Average dfferece temp.: upper urface ad gauge bottom at gto ( C) Average upper urface temp. at t=5 ( C) Average gauge bottom temp. at t=5 ( C) Average upper mm gauge lope temp. at t=5 ( C) E F 363 G 86 E F E F 38 G 88 E G 35 E H 93 E E E G 40 E F 37 H 04 E F E F E G 35 E Comparo of expermet ad reult from two-dmeoal aaly Whe comparg the temperature at tme to gto foud Table ad Table, oly two cae dd the temperature how gfcat dfferece cocdg both expermet ad the twodmeoal aaly. Thee cae how o clear patter related to the gauge charactertc. I both expermet ad two-dmeoal aaly a majorty of the temperature were wth the oe tadard devato varato ad dd ot how ay gfcat dfferece compared wth the flat cae. 6.6 Surface temperature dtrbuto at gto A flat urface wll be dtguhed by the relatve uform urface temperature, a oppoed to a urface wth roughe tructure where the urface temperature could vary coderably. A average temperature for the etre urface would be approprate for a flat urface but ot for a urface wth ubtatal roughe tructure. The queto what kd of gto crtero could be appled for a rough urface? Studyg the temperature dtrbuto of the two-dmeoal aaly at gto - E Idcate gfcat dfferece baed o SD varato (38 C) betwee upper urface ad gauge bottom temperature. F Show gfcat dfferece baed o SD varato (40 C) compared to Cae # for upper urface temperature. G Show gfcat dfferece baed o SD varato (36 C) compared to Cae # for upper thrd gauge lope temperature. H Idcate gfcat dfferece baed o SD varato (38 C) betwee upper urface ad upper thrd gauge lope temperature. 30

31 earchg for cotet temperature pecfc porto of the urface - t wa foud that the average temperature of the gauge ad adjacet upper urface the mddle of the ample played a key role ad foud to reult cotet temperature at gto. I the 45 degree cae: a temperature of 64 K reulted a mea percetage error of 0.06% whe comparg the calculated gto tme wth the actual tme. I the 60 degree cae a temperature of 579 K reulted a mea percetage error of.7%. I the 30 degree cae t wa foud that a average temperature of 55 K led to cotet temperature wth a mea percetage error of 0.0%. For the flat urface cae a urface temperature of 589 K for the etre urface wa calculated, reultg a mea percetage error of.0%. It wa foud that - both for the expermetal value ad the calculated value - that tally the upper urface temperature creaed more tha the gauge temperature but pror to gto the gauge temperature tarted to creae more tha the upper urface temperature. Thee fdg ugget that the effectvee of the gauge a a heat k wll largely determe the gto of the ample. A the gauge bottom temperature creae, the thermal retace of the gauge wll creae ad the effectvee a a heat k wll decreae, reultg gto. The depth of the gauge wll alo determe the effectvee of the gauge a a heat k, creag depth lead to creaed effectvee. 6.7 Decompoto zoe ad ourface plot Photo were take to documet the dfferece decompoto for cae #3, 5, 7 ad. Comparg the decompoto zoe wth the ourface plot of the two-dmeoal aaly, the appearace wa foud to ft very well. For cae #3 a wave wa oberved - ee fgure 6 - ad for cae #5 a traght le (ee fgure 7). For cae #7 fgure 8 - the appearace wa le wavy tha for cae #3. For cae # fgure 9 - the decompoto zoe ad the temperature dtrbuto wa evely to the ample. Fgure 6. Cro ectoal area ad ourface plot of cae #3. Fgure 7. Cro ectoal area ad ourface plot of ere #5. Fgure 8. Cro ectoal area ad ourface plot of ere #7. 3

32 Fgure 9. Cro ectoal area ad ourface plot of ere #. Photo were take of the upper urface ad compared wth the ourface plot of cae #6, #7 ad #0. The greatet colour chage were for cae #6 ad the leat for cae #7 where uaffected part could be foud. The colour chage of cae #6 correpod to the exteve temperature peetrato of the three cae. The largely uaffected gauge of cae #7 ca be lked to the lower gauge temperature. See fgure 0 ad. Fgure 0. The colour chage - ee from above - for cae #7, cae #0 ad cae #6. Fgure. Iourface plot of cae #7, 0 ad 6. The mlarte of the exteo of the decompoto zoe veru the temperature zoe of the ourface plot further tregthe the uefule of the model. 6.8 Other Uform emvty wa aumed for the fte part. Th may be vald for pecme wth maller depth, but wth larger depth charrg may have tarted the upper part of the gauge whle the lower part may tll be uaffected ad emvty wll vary. The two-dmeoal aaly could be refed accordgly. Ivarat covecto wa aumed. Roughe wll affect flow patter ad alo the covectve heat trafer. Eve though feature were mlled to the pecme ad o tructure were terferg wth the flow, the varat covecto aumpto wll have to be vetgated further. Expermet hould be performed wth other heat fluxe ad depth. Preferably lower heat fluxe ad larger depth. 3

33 33

34 7. Cocluo It wa foud that fve out of thrtee expermetal cae the average gto tme howed gfcat dfferece whe compared to the flat urface cae, but o clear patter related to the gauge charactertc wa detected. Two out of thrtee expermetal cae for the upper urface ad the gauge temperature howed gfcat dfferece whe compared to the flat urface cae. Thee cae howed o clear patter related to the gauge charactertc. Comparg the upper urface ad gauge temperature for each cae howed gfcat temperature dfferece three out of thrtee cae, aga o clear patter wa detected. Verfyg the two-dmeoal aaly, the reultg output were foud to be cotet wth the defto of the boudary codto ad the vrtual ecloure for the gauge. Whe tudyg the aaly reult at the tme of gto, x out of thrtee cae for the upper urface temperature howed gfcat dfferece. Fve out of thrtee cae for the upper thrd gauge lope temperature howed gfcat dfferece, but o clear patter wa detected. Comparg the upper urface ad upper thrd gauge lope temperature howed gfcat temperature dfferece two out of thrtee cae. Whe comparg the expermetal reult wth the aaly reult, oly two cae howed gfcat temperature dfferece ad cocded both expermet ad aaly. I both expermet ad the two-dmeoal aaly wth ormalzed roughe feature the rage % to 0% a majorty of the temperature were wth the oe tadard devato varato ad dd ot how ay gfcat dfferece compared wth the flat cae, except whe comparg the gauge bottom temperature ad upper urface temperature of the two-dmeoal aaly where gfcat dfferece wa foud all cae. A umber of expermet were alo coducted wth a heat flux of 50 kw m -, but reulted vrtually o dfferece gto tme. Th ugget that the mportace of urface roughe wll creae wth decreag heat flux, for example whe the dtace betwee the fre ad the fuel tem creae or whe the heat releae rate decreae. 34

35 Ackowledgemet Rckard Hae coducted the work at Worceter Polytechc Ittute a part of h doctoral tude at Mälardale Uverty. Radall Harr, Fre Laboratory Maager at Worceter Polytechc Ittute, ackowledged for valuable atace durg the fre expermet. 35

36 Referece Akta K (959) Stude o the Mecham of Igto of Wood. Report of Fre Reearch Ittute of Japa 9, -44, 5-54, 77-83, Atreya A (998) Igto of fre. Phloophcal Traacto: Mathematcal, Phycal ad Egeerg Scece 356, Babrauka V (003) Igto Hadbook (Fre Scece Publher, Iaquah) Eberhardt TL (05) Thcke ad roughe meauremet for ar-dred logleaf pe bark. Proceedg of the 7 th Beal Souther Slvcultural Reearch Coferece. Ahevlle, USA Hae R. (05a) Aaly of Methodologe for Calculatg the Heat Releae Rate of Mg Vehcle Fre Udergroud Me. Fre Safety Joural 7, 94 6 Hae R. (05b) Study of Heat Releae Rate of Mg Vehcle Udergroud Hard Rock Me. Doctoral The, Mälardale Uverty, Väterå Heketad G (979) Eae of gto of fabrc expoed to flamg heat ource. Joural of Coumer Product Flammablty 6, 8-88 Holma JP (00) Heat Trafer 9 th edto (McGraw-Hll, New York) Lewadowk WM, Radzemka E, Buzuk M ad Bezk H (000) Free covecto heat trafer ad flud flow above horzotal rectagular plate. Appled Eergy 66, Qutere JG (006) Fudametal of fre pheomea (Joh Wley & So Ic, Hoboke) Schröder P ad Haraha P (993) O the form factor betwee two polygo. Computer Graphc, Proc., A. Cof. Sere, SIGGRAPH 93, Segel R ad Howell JR (00) Thermal Radato Heat Trafer 4 th edto (Taylor ad Frac- Hemphere, Wahgto) Thoma TR (999) Rough Surface (Imperal College Pre, Lodo) Wlo MT, Dugogork BZ ad Keedy EM (003) Uformty of Radat Heat Fluxe Coe Calormeter. Fre Safety Scece 7, Yaovak SP, Slver C, Stark AY, Va Sta II J ad Leva Jr. DF (06) Surface roughe affect the rug peed of tropcal caopy at. Botropca 36