A Vaporization Rate Model for Flammable Liquid Pool under Vertical Air Jet Impingement

Transcription

1 A Vaprizatin Rate Mdel fr Flammable Liquid Pl under Vertical Air Jet Impingement HONG-ZENG YU 1, SAN-PING HO 2 and ROBERT G. ZALOSH 3 1 FM Glbal 1151 Bstn-Prvidence Turnpike Nrwd, MA 02062, USA 2 Chang Jung Christian University 396 Chang Jung Rad Sec. 1 Kway Jen, Tainan, Taiwan 3 Wrcester Plytechnic Institute 100 Institute Rad Wrcester, MA 01609, USA ABSTRACT A theretical mdel was develped t predict the flammable liquid vaprizatin rate frm a heated pl subjected t impingement f a vertical air jet. The mdel divides the air flw field int tw regins: ne is the bulk air jet turning regin and the ther is the thin bundary layer frmed n the liquid surface. The mdel is based n the premise that the thickness f the bundary layer in which vapr diffusin takes place abve a liquid pl is mainly cntrlled by the impinging air jet. The mdel predicts that the liquid vaprizatin rate increases with the pl temperature and increases linearly with the impinging velcity, as ppsed t the square-rt dependence in the case f air flw parallel t the pl surface. The mdel was validated with vaprizatin rate data f high flash-pint liquids. It is shwn in this paper that the vapr blwing effect n bundary layer thickness greatly diminishes as the impinging air velcity increases frm quiescence t 3.3 m/s fr the high flash-pint liquid pls analyzed in this study. The analysis als indicated that the bundary layer thickness n a small curbed pl culd be greater than that predicted fr an infinite pl. The resulting thicker fuel vapr diffusin layer tends t lead t lwer vaprizatin rates than thse expected frm an infinite liquid pl under the same air impingement cnditin. KEYWORDS: vaprizatin rate, flammable liquid pl, air jet impingement NOMENCLATURE D Mass diffusivity (m 2 /s) δ Bundary layer thickness (m) D pl Liquid pl diameter (m) µ Dynamic viscsity (kg/ms) g Gravitatinal acceleratin (m/s 2 ) ν Kinematic viscsity (m 2 /s) m& evp Vaprizatin rate (kg/s) ρ Density (kg/m 3 ) p Pressure (N/m 2 ) Subscripts r r crdinate (m) c Centerline z z crdinate (m) ο Pl surface u Velcity in the r directin (m/s) z An elevatin abve the pl v Velcity in the z directin (m/s) δ The edge f bundary layer Greek β Cnstant (1/s) FIRE SAFETY SCIENCE PROCEEDINGS OF THE EIGHTH INTERNATIONAL SYMPOSIUM, pp COPYRIGHT 2005 INTERNATIONAL ASSOCIATION FOR FIRE SAFETY SCIENCE 659

2 INTRODUCTION Heated il pl fires such as thse riginating frm metal treatment and fd prcessing peratins are highly challenging t water spray and water mist spray systems [1,2]. When a water mist spray verpwers the fire plume f a curbed flammable liquid pl, it is typical that the flames in the pl s central regin are pushed tward the pl edge [3,4]. When the central regin f the liquid pl is free f flames under such cnditins, fuel vapr is still being generated prfusely n the nn-flaming pl surface due t high il temperature. Fr a water mist system designed fr fire extinguishment, it is essential that the persisting flames alng the pl edge d nt flashback t the pl s central area and are gradually weakened and eventually extinguished befre the system depletes its water supply. Water mist sprays tend t induce strnger air currents than water sprays which prduce larger drplets fr the same water discharge rate [5,6]. Fr dual-fluid mist nzzles, air r ther inert gases are discharged frm the nzzle t prmte water atmizatin, resulting in even higher air velcity in the water mist spray than the single-fluid nzzles. The air current in the water mist spray helps cling the pl and diluting fuel vapr but at the same time als enhances the fuel vaprizatin rate. The fuel vaprizatin enhancement wrks against the first tw afrementined beneficial air current actins fr reducing fuel vapr cncentratin abve the pl surface. T ensure that the fuel vapr cncentratin in the pl s central regin stays belw the flammability limit during the extinguishing prcess, the fuel vapr generatin rate as a functin f pl surface temperature under air flw envirnment is therefre ne f the key cnsideratins in the prcess f water mist spray selectin. Crrelatins fr evapratin rate frm a liquid surface in envirnment f air flw parallel t the pl surface have been available [7]. Hwever, such crrelatins are currently unavailable in the literature fr a flammable liquid surface subjected t air jet impingement. Althugh the cling f slid surfaces by impinging air jets has been investigated extensively, such as the studies listed in References 8-11, uncertainty arises when these heat transfer results are used t estimate liquid vaprizatin rates because bth heat and mass transfer are invlved in the prcess. On the ther hand, studies were perfrmed t investigate the burning behavir f slid cmbustibles in stagnatin flw fields [12-15]. Again, the uncertainty is high in deducing liquid vaprizatin rates in cmbustin-free stagnatin flw fields frm these burning rate results. This paper presents a theretical mdel by which an explicit expressin can be btained fr the vaprizatin rate frm the stagnatin area f a heated flammable liquid pl expsed t vertical impinging air current. THEORETICAL MODEL It has been shwn that the heat transfer rate peaks at the stagnatin pint n a slid flat surface when impinged by an air jet with the jet axis perpendicular t the surface [9,16]. S it is expected that the vaprizatin rate n a liquid surface under a vertical impinging air jet wuld als reach a maximum at the stagnatin pint. Frm the fire prtectin pint f view, the use f liquid vaprizatin rate determined in the stagnatin area prvides a cnservative assessment n whether the fuel vapr mixture n the pl surface culd be ignited. 660

3 As illustrated in Fig. 1, the flw field in the stagnatin area may be divided int tw distinct regins: ne is the bulk air jet turning regin and the ther is the thin bundary layer that frms n the liquid surface. The vaprizatin rate frm the liquid surface is gverned by the liquid s attempt t maintain the equilibrium vapr pressure at the liquid surface in a given air flw envirnment. The released fuel vapr then diffuses acrss the thin bundary layer and is swept away by the turning air jet. S the fuel vapr pressure (r cncentratin) tends t vary frm its equilibrium value at the liquid surface t an ambient value (zer is assumed in the mdeling belw) at the edge f the bundary layer. z g V z 0 δ(exaggerated thickness) U D pl Fig. 1. An illustratin f the physical mdel. Fr typical fully develped water mist sprays used in fire prtectin, the velcity f the induced air current is arund 3 m/s r higher, which is at least tw rders f magnitude greater than the blwing velcity f the fuel vapr released frm the pl surface under free-burn cnditins fr typical hydrcarbn liquids [17]. Therefre, it is reasnable t assume that the diffusin depth f the fuel vapr is mainly cntrlled by the air jet impingement. T determine the bundary layer thickness, the main cncern is that the liquid surface tends t be indented by the impinging air jet, thus deviating frm the flat surface cnditin. Fr an air jet with a centerline velcity f 5 m/s, the deepest liquid surface indentatin is estimated t be abut 3 mm. Therefre, fr typical air current induced by water mist sprays, the liquid surface in the stagnatin area can be reasnably apprximated as a flat surface due t the small surface curvature, assuming that the mist flw cnfrms t the air current perfectly s that n sputtering ccurs n the liquid surface. Anther imprtant cnsideratin in the mdeling is the effect f the turbulence in the air jet utside the bundary layer n the evapratin rate. Fr the case f nrmally impinging laminar air jet n a flat slid surface, the Nusselt number is prprtinal t the square rt f the Reynlds number if the bundary layer is laminar, but is prprtinal t 0.8 pwer f the Reynlds number if the bundary layer is turbulent [18]. Fr impinging turbulent jets, studies have shwn that the Nusselt number is prprtinal t the square rt f Reynlds number, but with values higher than thse expected fr the case where r 661

4 the bundary layer is laminar [5,9,10]. The reasning [9] is that, due t the strngly favrable radial pressure gradient in the stagnatin area, the bundary layer behaves as a laminar layer but is disturbed by the turbulence carried in frm the free jet. It has been reprted that 15% free stream turbulence intensity culd enhance heat transfer by 25% frm the nn-disturbed laminar layer [5]. Fr the case f vaprizatin n a heated pl, it is expected that the bundary layer in the stagnatin area als behaves like a laminar layer and the free stream turbulence wuld induce similar vaprizatin enhancement. Based n the abve discussins, the fllwing three primary assumptins are made fr mdeling the vaprizatin rate f a liquid pl subjected t impingement f a vertical air jet: 1) the liquid surface is flat; 2) the air jet is axisymmetrical, pinted vertically dwnward, and centered with the pl; and 3) the bundary layer is laminar. Frm Schlichting [19], the thickness f the bundary layer in the stagnatin area n an infinite flat surface induced by a nrmally impinging jet is ν δ = 2.0( ) 1/ 2 (1) β In Eq. (1), ν is the gas kinematic viscsity in the bundary layer; β is a cnstant which relates the hrizntal and vertical cmpnents f air velcity t the radial distance frm the stagnatin pint and vertical distance frm the flat surface, i.e., u = β r and v = -2β z (2) The next step is t relate the appraching air jet velcity t the thickness δ. Again, frm Schlichting [19], the vertical cmpnent f the velcity at the edge f the bundary layer is v δ = 2.8(νβ) 1/2 (3) Using Eqs. 1 and 3, we have v δ = 1.4(δβ) (4) Equatins 1 and 4 lead t the fllwing expressin f the bundary layer thickness in the stagnatin area n an infinite flat surface: ν δ = 5.6( ) (5) v δ which can be used t estimate the bundary layer thickness n a pl with n freebard under a vertical air jet impingement. 662

5 Frm the mmentum equatin in the radial directin (u-cmpnent) and Eq. 2, we can relate the cnstant β and the radial pressure gradient near the stagnatin pint with the expressin belw, 1 p β = ( ) 1/ 2 (6) ρr r Dnaldsn et al. shwed that the radial pressure gradient n a flat surface is greater than that n the surface inside a cylindrical cup, similar t a pl with freebard, in the impingement regin [20]. As a result, the β value in Eq. 6 is expected t be smaller fr a pl with freebard than fr an infinite pl r a pl withut freebard. Frm Eq. 4, the bundary layer n a liquid pl with freebard is therefre expected t be thicker than that n an infinite pl fr a cnstant impinging air velcity. Fr a liquid pl with freebard, the general expressin fr the bundary layer thickness is therefre expected t be ν δ = k( ) (7) v δ where k is a psitive value and is a functin f air jet characteristics n the pl surface, pl diameter and freebard depth, prvided that the blwing effect f evapratin at the pl surface n δ is negligible cmpared t the effect f the impinging air current. Outside the bundary layer, the air temperature is the appraching air jet temperature and the fuel vapr cncentratin is assumed t be zer. S the prblem is nw reduced t film diffusin frm the pl surface t the upper edge f the bundary layer. If the liquid vapr pressure at the pl surface is at equilibrium, the classical film diffusin slutin gives the pl vaprizatin rate as fllws [21]: π Y Y 2 ρd ) ln[1 m& evp = ( D pl )( + ] (8) 4 δ 1 Y where ρ and D are the density and mass diffusivity f the gas mixture in the diffusin layer, and Y and Y are the saturated fuel vapr mass fractin at the pl surface and the fuel vapr mass fractin in the ambient, respectively. Using Eq. 7, the liquid vaprizatin rate frm a liquid pl is related t the air jet velcity as fllws: π ρdv δ Y Y m& 2 evp = ( D pl )( ) ln[1 + ] (9) 4k ν 1 Y Under the cnditin that (Y Y )/(1 Y ) << 1 663

6 Equatin 9 can be apprximated with π Y Y 2 ρd m& evp = ( D pl )( )( )v 4k ν 1 Y δ (10) Equatin 10 indicates that the fuel vaprizatin rate frm a liquid pl is prprtinal t the impinging air velcity, as ppsed t the case f air flw parallel t a semi-infinite surface where the vaprizatin rate is prprtinal t the square rt f free stream air velcity [21]. Since the calculated values f δ is less than 1.3 mm fr the experiments discussed belw, it is reasnable t apprximate v δ in Eq. 10 with the jet velcity at the elevatin f pl surface when the pl is nt present. EXPERIMENTAL VALIDATION AND DISCUSSIONS Few experimental data can be fund in the literature fr the fuel vaprizatin rate frm a heated pl impinged nrmally by an air jet. In the fllwing, fuel vaprizatin rates calculated frm Eq. 10 will be cmpared with the data fund in the literature fr high flash-pint liquids. Limited data are available frm H s thesis wrk n water spray suppressin and intensificatin f high flash-pint pl fires [22]. In studying the effect f fuel splattering by water sprays n fire intensificatin, H quantified in separate experiments the fuel vapr riginating frm the splashed fuel drplets and the fuel vapr frm a heated pl subjected t an impinging air jet. He bserved that the frmer fuel vapr surce dminated the latter fr the tw high flash-pint liquids used in his experiments. H s measurements f fuel vaprizatin rates frm a heated pl are briefly described belw. A sybean il f unknwn cmpsitin and a mineral seal il (CAS number ) were used in H s evapratin experiments. Bth ils are in the Class IIIB categry accrding t the NFPA 30 standard [23]. The flash pints f the mineral seal il and sybean il are reprted t be 137 C and 291 C, respectively [22]. The il vaprizatin rates were measured at selected il temperature and impinging air velcities. In the experiments, a 0.3-m diameter steel pan 76 mm high was psitined n a ht plate (Sybrn Thermdyne Type 2200) which in turn was placed n an electrnic scale (GSE series 4440). In these experiments, the pan was filled with the tested il t result in a freebard f abut 13 mm deep. The il was then heated t a designated temperature. In the heating prcess, a stirrer was used t btain unifrm il temperature inside the pan. A temperature cntrller (Omega CN7000) was used t maintain the liquid pl at the designated temperature during the experiment. After the pl temperature reached the designated temperature, an air jet was discharged vertically frm a nzzle (Spraying System 1/8 HH 1.5) lcated 0.91 m directly abve the pl. The spray angle f the air jet was abut 60 degrees. As a result, the jet diameter at the tp f the pan was slightly greater than the pan diameter. An anemmeter (Taylr Biram Mdel 3132) was used t measure the air velcity at an elevatin f 0.15 m abve the pan. Figures 2 and 3 shw the vaprizatin rate data f mineral seal il and sybean il btained frm Ref. 22. Fr mineral seal il, at il temperatures f 90 C and 110 C, the experiments were cnducted with n air jet impingement and with centerline air jet 664

7 0.030 Oil Vaprizatin Rate (g/s) C 110 C Air Jet Centerline Velcity (m/s) Fig. 2. Mineral il vaprizatin rates frm a 0.3-m diameter pl impinged by an air jet riginated 0.91 m abve the pl surface. The il temperature was at 90 r 110 C Oil Vaprizatin Rate (g/s) C Air Jet Centerline Velcity (m/s) Fig. 3. Sybean il vaprizatin rates frm a 0.3-m, 270 C pl impinged by an air jet riginated 0.91 m abve the pl surface. 665

8 velcities f 1.5 m/s and 3.3 m/s. Fr sybean il, the experiments were cnducted with an il temperature f 270 C and with the same air impingement cnditins fr the mineral il except that an additinal air jet centerline velcity f 4.1 m/s was emplyed. Bth Figs. 2 and 3 shw that, at a given il temperature, the il vaprizatin rate increases linearly with the impinging air velcity, as indicated by Eq. 10. By perfrming least square regressin f the data, the vaprizatin rate f the mineral seal il can be expressed by: m & evp = u C fr 90 C and u C 3.3 m/s (11) and m & evp = u C fr 110 C and u C 3.3 m/s (12) The vaprizatin rate f sybean il is m & evp = u C fr 270 C and u C 4.1 m/s (13) The unit f the vaprizatin rate in the abve three equatins is in g/s. Since the value f k in Eq. 7 is unknwn fr each afrementined impinging air velcity used in the experiments described in Ref. 22, Eq. 10 cannt be used directly t make predictins. Hwever, by assuming that the il vapr diffusin depth δ was little affected by the pl temperature under the air impingement cnditins described abve, the vaprizatin rates at a given il temperature can then be predicted using Eq. 10 after the diffusin depth at the same air impinging velcity is determined fr a different pl temperature. The abve assumptin is reasnable since the il vapr blwing velcity in H s experiments is much lwer than the air jet velcity. As a result, the diffusin depth is expected t be mainly cntrlled by the air jet impingement. When the air jet is absent, the diffusin depth is expected t be affected by the pl temperature, freebard depth and rm draft. T calculate the vaprizatin rate using Eq. 10, the density, mass diffusivity and kinematic viscsity f the gas mixture in the diffusin layer has t be first estimated, as well as the il vapr mass fractin at the pl surface. Since mst f the prperties f sybean il required in the analysis are nt available (particularly the vapr pressure infrmatin), the discussin belw is fcused n the mineral seal il. The Material Safety Data Sheet (MSDS) des nt prvide the mlecular frmula f the mineral seal il [24]. Hwever, the MSDS des state that it is a hydr-treated middle distillate with biling pint ranging frm 277 t 321 C and flash pint ranging frm 120 t 135 C. The material prperty data base f Reference 25 shws that, in the grup f paraffin cmpunds, hexadecane (C 16 H 34 ) gives the best match t bth the flash pint and biling pint f the mineral seal il. The flash pint and biling pint f the hexadecane are reprted t be 135 C and 289 C, respectively [25]. As a result, it is assumed that the vapr pressure f hexadecane can reasnably represent that f the mineral seal il. The il vapr pressures f hexadecane at 90 C and 110 C are 63 and 178 Pascal [25], respectively. The Schmidt number (rati f kinematic viscsity and mass diffusivity) f dilute hexadecane-air mixture is estimated t be abut 2.8 [18]. Since the lw 666

9 cncentratin f il vapr, the density and kinematic viscsity f the vapr-air mixture in the diffusin layer can be reasnably apprximated by thse f air at the temperature equal t the average f the pl surface temperature and the ambient temperature (arund 20 C). Therefre, in the fllwing analysis, the air density and kinematic viscsity f kg/m 3 and 1.868x10-5 m 2 /s (at 55 C) will be used fr the 90 C pl, and kg/m 3 and 1.978x10-5 m 2 /s (at 65 C) will be used fr the 110 C pl. The mass diffusivity f the vapr-air mixture is then apprximated by the rati f air kinematic viscsity and Schmidt number. Based n the abve values f the air-vapr mixture prperties and the vaprizatin rates measured with the 90 C pl, the diffusin depths and the crrespnding k values were calculated using Eq. 8 and Eq. 7, respectively, which are presented in Table 1. As expected, the diffusin depth decreases as the air jet velcity n the pl surface increases. The calculated diffusin depths are greater than thse predicted fr an infinite flat surface, i.e., mm fr an impinging air velcity f 1.5 m/s and mm fr 3.3 m/s. The diffusin depth under n impingement case is 1.02 mm, much smaller than the freebard depth f 13 mm. It is speculated that the reasn why the vapr layer des nt reach the pan rim fr n air jet impingement is due t the small vaprizatin rate, rm draft and relatively large rati f pan diameter versus freebard. Table 1. Calculated il vapr diffusin depths and k values based n the vaprizatin data btained with a 90 C pl. Centerline Air Jet Velcity Measured Vaprizatin Rate Calculated Diffusin Depth Using Eq. (8) (mm) k Value in Eq. (7) (m/s) (g/s) After the k values are determined, the vaprizatin rates fr the 110 C pl can be predicted with Eq. 10. As shwn in Table 2, the predicted vaprizatin rates at air velcities f 1.5 and 3.3 m/s agree well with the crrespnding measured rates. The predicted rate fr n air impingement was btained with Eq. (8) and the diffusin depth f 1.02 mm determined fr the 90 C pl, which als has a gd agreement with the measured value, but with a slightly higher rate. Under the absence f air jet, the diffusin depth tends t be thicker as pl temperature increases. Therefre, it is expected that using the thinner diffusin depth determined fr the 90 C pl verestimates the vaprizatin rate fr the 110 C pl. The calculated diffusin depth f 1.21 mm (using the measured vaprizatin rate and Eq. 8) cnfirms the abve expectatin. The calculated diffusin depths fr u=1.5 and 3.3 m/s als agree well with the crrespnding depths fr the 90 C pl as shwn in Table 1. The variatins f diffusin depth with impinging air velcity exhibited in bth Tables 1 and 2 indicate that the effect f vapr blwing frm the pl surface n the diffusin depth diminishes quickly as the impinging velcity increases fr the data analyzed in this study. 667

10 Table 2. Predicted il vaprizatin rates fr the 110 C pl based n the diffusin depths and k values presented in Table 1. Centerline Air Jet Velcity Measured Vaprizatin Rate Predicted Vaprizatin Rate Using Eq. (10) (g/s) Calculated Diffusin Depth Using Eq. (8) (mm) (m/s) (g/s) a 1.21 b b b a The rate fr n air impingement was calculated with Eq. 8 and with the diffusin depth f 1.02 mm (presented in Table 1) determined fr the 90 C pl. b Calculated with the measured vaprizatin rates fr the 110 C pl. CONCLUSIONS A theretical mdel was develped fr the predictin f liquid vaprizatin rates frm a heated flammable liquid pl impinged by a vertical air jet. The mdel is based n the assumptin that the thickness f the bundary layer in which vapr diffusin takes place abve the liquid pl is mainly cntrlled by the impinging air jet, and little affected by the blwing effect f the vaprizatin prcess. The mdel crrectly predicts that the liquid vaprizatin rate increases with pl temperature and increases linearly with impinging air velcity. The mdel predictins agree well with the vaprizatin rate data btained fr high flash-pint liquids. The analysis f available high flash-pint vaprizatin data shwed that the blwing effect n the bundary layer thickness diminishes quickly as the impinging velcity increases. The analysis als shwed that the bundary layer thickness n a curbed pl tends t be thicker than that predicted fr an infinite pl. The thicker layer leads t lwer vaprizatin rates as cmpared t thse expected frm an infinite pl at the same liquid temperature and under the same air impingement cnditin. The vaprizatin rate mdel presented in this paper is useful in determining the reignitin prpensity in the flame-absent area f a burning pl under the impingement f water mist sprays. The mdel is als useful fr the risk assessment f fuel vapr explsin riginating frm a flammable liquid pl r spill in an envirnment f frced dwnward ventilatin. It is recmmended that the mdel be further validated with ther lw vlatility, single cmpnent liquids. The general applicability f the mdel shuld als be evaluated with vaprizatin rate measurements made with high vlatility liquids, where strnger vapr blwing actin frm a heated pl is expected t have greater impact n the thickness f the bundary layer induced by an impinging air jet. REFERENCES [1] Liu, Z. and Kim, A.K., Fire Prtectin f a Restaurant Cking Area with Water Mist System, Prceedings f the Third Internatinal Cnference n Fire Research and Engineering, Sciety f Fire Prtectin Engineers, 1999, pp

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12 [17] Tewarsn, A., Generatin f Heat and Chemical Cmpunds in Fires, The SFPE Handbk f Fire Prtectin Engineering (3 rd ed), DiNenn P.J. (ed.), Natin Fire Prtectin Assciatin, Quincy, MA 02269, 2002, Sectin 3, Chapter 4. [18] Kays, W.M., Cnvective Heat and Mass Transfer, McGraw-Hill Bk Cmpany, New Yrk, [19] Schlichting, H., Bundary Layer Thery, McGraw-Hill Bk Cmpany, New Yrk, [20] Dnaldsn, C.D., Snedeker, R.S. and Marglis, D.P., A Study f Free Jet Impingement. Part 1: Mean Prperties f Free and Impinging Jets, Jurnal f Fluid Mechanics, 45, 2: , [21] Glassman, I., Cmbustin, Academic Press, New Yrk, [22] H, S-P, Water Spray Suppressin and Intensificatin f High Flash Pint Hydrcarbn Pl Fires, Wrcester Plytechnic Institute, Ph.D. Thesis, Wrcester, Massachusetts, USA, [23] NFPA 30: Flammable and Cmbustible Liquids Cde, Natinal Fire Prtectin Assciatin, 2003 Editin, Quincy, Massachusetts, USA. [24] Mineral Seal Oil Material Safety Data Sheet, MSDS N , Revisin Date 12/04/2000, CITGO Petrleum Crpratin, Rlling Meadws, Illinis, USA. [25] The Prperties f Gases and Liquids, Design Institute fr Physical Prperties, American Institute f Chemical Engineers, New Yrk, New Yrk, USA. 670