Similarity of Turbulent Wall Fires

Transcription

1 Similarity o Turbulent Wall Fires J. L. de RIS, G. H. MARKSTEIN, L. ORLOFF and P. A. BEAULIEU FM Global Research Norwood, MA 6, USA ABSTRACT The study establishes a similarity relationship controlling the buoyant turbulent boundary layer combustion o wall ires. Measurements o soot deposition onto glass rods allow one to iner the characteristic thickness, δ S, o propylene lames at dierent heights, z, and mass transer rates, m &. The normalized lame thickness, δ S z, is successully correlated by the overall uel to air mass ratio o the lames, Ψ. Similarly, Ψ, correlates the measured boundary layer temperature proiles o the lames normal to the wall. It correlates measurements o the outward directed radiance, N r rom the same propylene wall ires with a uniorm eective lame radiation temperature, T, and uniorm soot absorption/emission coeicient being independent o both height, z, and uel mass transer rate, m &. Finally the same uel to air ratio, Ψ, correlates, here or the irst time, the LDV velocity measurements o Most et al or turbulent ethane wall lames perormed at Factory Mutual Research in 198. The data presented here are suitable or development o analytical and CFD models o turbulent wall ires. KEY WORDS: Turbulent Diusion Flames, Wall Fires, Flame Radiation, Flame Heat Transer INTRODUCTION The overall objective is the development o models predicting the total heat transer rom the lames to the wall in both the pyrolysis and orward heat transer zones o a spreading ire. The present study ocuses on the pyrolysis zone supplying uel to the ire. Figure 1, shows the burner used to study twodimensional burning o a single wall. This is the simplest wall geometry or studying buoyant boundary layer mixing and combustion. A goal is to identiy a undamental similarity parameter that controls the buoyant luid mechanics and turbulent combustion, but is insensitive to uel chemistry. Having ound such a parameter, one can then ocus on the uel without being distracted by the luid HEAT TRANSFER PLATE SINTERED-BRONZE BURNERS WATER-COOLED SIDE-WALLS Figure 1. Gas Burner Apparatus FIRE SAFETY SCIENCE--PROCEEDINGS OF THE SEVENTH INTERNATIONAL SYMPOSIUM, pp Copyright International Association or Fire Saety Science

2 mechanics. The uel mass transer, m&, emerges uniormly rom all active water-cooled sintered-metal burners. Each burner measures 13 mm high and 38 mm wide resulting in an overall height o 13 mm or the ten burners. The apparatus is certainly large enough to achieve ully turbulent lames. The 15 mm deep water-cooled sidewalls maintain the low as two-dimensional. Further details o the apparatus are available[1,,3]. SOOT DEPTH Our irst task is to characterize the thickness o the luminous turbulent lames. The soot depth, δ S, was measured very simply by inserting arrays o 5 mm diameter glass rods into the lame perpendicular to the wall surace and rapidly withdrawing them ater a two second exposure. Megaridis and Dobbins [] showed that the amount o soot deposited is proportional to the local soot volume raction in the gas phase. Soot is deposited by action o thermophoresis. The rate o soot deposition: is driven by the temperature dierence between the lame and glass rod, is proportional to the soot volume raction and is independent o the soot particle size. The glass rods heat up only K during the two second measurement time. Two arrays, each containing ive rods, were inserted sequentially or each measurement at heights o 365, 57, 771, 1 and 1317 mm. See FLAME 1 GLASS ROD ARRAY 8 SOOT DENSITY GLASS ROD (mm) δ s Figure. Sketch and detail o soot depth measurements δ 6 8 m& (g/m s) Figure 3. Measured soot depth, δ s, vs. uel mass transer, m&, at several heights, z Fig.. The lowest height o 365 mm insures readings well within the turbulent region. The rods are laterally spaced 1 mm apart and the array was centered on the midpoint o the 38 mm wide burner surace. The uniormity o the thickness o the soot deposition was judged visually by holding the rod in ront o a light source. As shown in Fig., the soot deposition was uniorm to the let o the irst dotted line and then decreased gradually to zero over a distance about equal to the uniorm deposition distance on the let. The soot depth, δ S, is deined as the distance where the soot deposit is visually judged to have decreased to 5 % o the maximum (e.g. uniorm) deposit on that rod. The two-second exposure was chosen on the ollowing basis. A shorter exposure o one second results in intermittent deposition making it diicult to judge any distance. Conversely, longer exposures o our to six 6

3 seconds give a uniorm heavy deposition that is biased to extra large values o δ S. The average value o δ S is insensitive to exposure times that are near two seconds. Each indicated data point was the average o the 1 readings ( arrays o 5 rods each). Typically, the standard deviation o the ten individual soot lengths was 1 % o their averaged value so that the estimate o the averages has a 3. % standard deviation. Figure 3 shows the variation o soot depth, δ S, with mass transer rate, m&, at various heights. The data o Fig. 3 apply only to luminous turbulent lames. The luminosity comes rom the soot in the lames. For mass transer rates less than g/ms the lames became non-luminous and blue[3]. At these very low mass transer rates the thickness o the blue lames as well as the total heat transer become independent o height. The data and correlations presented in this paper are or mass transer rates greater than g/m and do not apply to the blue lame regime. Figure shows the correlation o normalized soot depth, δ S z, by the uel to air mass ratio, Ψ, o the luminous turbulent lames. The uel to air mass ratio, Ψ, is proportional to the total uel supplied up to a given height divided by the accumulated entrainment o air up to the same height. As shown later in Fig. 1, the maximum mean upward velocity is insensitive to the uel mass transer and correlates according to umax =.95 gz. According to Taylor s entrainment concept [5], the local air entrainment, m& air, into the lames is proportional to this upward velocity, m& air ρ A gz, where ρ A is the density o ambient air. [Strictly speaking, the entrainment is slightly dependent on the boundary layer width, which in turn depends on Ψ.] The integral o the entrainment into the lame boundary layer up to height z is proportional to ρ A z gz. This is to be compared to the stoichiometric air requirement equal to the sum o all the uel supplied up to height z multiplied by the stoichiometric oxidant to uel mass ratio, s. So that the relative richness is proportional to z s m& dz Ψ = (1) ρ A z g z The correlation gives the empirical ormula (solid line) or the lame thickness, δ S 1/ =.3( Ψ Ψ ) with Ψ =. 6 () z This ormula says that the soot depth disappears as Ψ Ψ or all heights, z, in the pyrolysis zone. Indeed, the lames turn blue near this limit. The above ormula applies to the turbulent region. Theoretical arguments say that the lame thickness, δ S, increases with the ¼ power o z in the laminar zone near the leading edge [6]. One can thus extend the soot depth ormula to the laminar region by 1/1 9 δ S zt = 1 + [.3( Ψ Ψ ) ] 1/ (3) z z 61

4 where z = 11 mm is a nominal laminar to turbulent transition height. This correction t has negligible eect on δ S or z zt in the turbulent zone..15 The correlation, Eq. 3, is based entirely on data rom the pyrolysis zone. Never the less, it is curious to note that setting Ψ = Ψ in Eq. (1) also gives the overall turbulent lame height,, in meters, or a line ire against a wall z /3 s M& s Q& / 3 z = = =.7[ Q& ] () Ψ ρ A g Ψ H c ρ A g or typical uels releasing H / =13. kj/g o O consumed with theoretical heat c sy O release rates per unit width, Q &, in kw/m, and the constant.7 in units o m z δ s / 3 ( kw / m) / 3 [7],.5[ ] z.1.5. z (mm) Correlation Figure Correlation (solid line) o measured (symbols) normalized soot depth, δ z, vs. relative uel richness, Ψ, at dierent heights, z. s. This expression compares avorably with Ahmed s empirical correlation = Q&, o visible lame heights against a wall. Thus in both cases when Ψ = Ψ, the abundance o air is suicient to cause the disappearance o luminous lames TEMPERATURE A thermocouple rake measured the temperature proile across the lame boundary layer. The rake consisted o 15 ungrounded Chromel-Alumel thermocouples inside 1.6-mm Inconel sheaths protruding 1.5 cm downward into the rising low. The rake was oriented in a horizontal plane such that the thermocouple spacing was 7.1 mm normal to the wall. Ater an initial transient, the mean temperature showed no sign o drit, suggesting that soot deposits did not inluence them over the measurement period. The temperatures were time-averaged over 95 seconds. Ψ /3 6

5 Thermocouples are oten used to measure local gas temperatures both inside and near a lame. However, radiation heat loss rom thermocouples signiicantly depresses measured temperatures inside the lame, while radiation rom the lame signiicantly increases the measured temperatures outside the lame. Correction o these eects was perormed rom our detailed knowledge o the radiation ield together with a simple heat transer model, summarized below. T (K) m& (g / m s) (a) uncorrected y (mm) T (K) m& (g / m s) (b) corrected y (mm) Figure 5. Temperature, T, vs. stando, y, or various propylene mass transer rates, m&, at z = 771 mm rom the leading edge: (a) uncorrected, and (b) corrected. Figure 5(a) shows the uncorrected measured temperature at a height z = 771 mm or various mass transer rates, while Figure 5(b) shows the corresponding corrected temperature proiles. In steady state, the convective heat transer to the thermocouple rom the gas lowing over the thermocouple must equal the radiative heat loss rom its surace minus the rate o heat gain by radiation rom nearby lames, or 63

6 h ( T T ) = ( T T ) ε ε σ ( T T ) per unit thermocouple surace area. Here g σ (5) t g T, T, T and T, respectively, are the thermocouple, gas, ambient and eective lame radiation temperatures, h is the ε y is convective heat transer coeicient, σ is the Stean-Boltzmann constant and ( ) the average lame emissivity as viewed by the thermocouple at location y. It was implicitly assumed that the thermocouple was coated with a thin layer o black soot causing it to have unit surace absorptivity and emissivity, ε t = 1. Solving or T g, one has σ ε ( y) Tg = T + ( T T ) σ ( T T ) (6) h h The convective heat transer coeicient is obtained rom the Nusselt number [8] / 5 / 5 u κ N κ T T h = = 1 W / m K d d T T (7) that takes into account the temperature dependence o the gas thermal conductivity, κ. T (K) m& (g / m s), Ψ.9,.13.37, , , , , Figure 6 Corrected temperature, T, vs. normalized distance, y / δ S, or various propylene mass transer rates, m&, at z = 771mm rom the leading edge. The lame emissivity ( y) ε was calculated rom the sum o the inward and outward directed radiant luxes coming rom a uniorm slab o lame having measured: eective lame temperature, T = 1375 K, thickness, δ S, and optical thickness o the various propylene lames [1]. The detailed knowledge o the radiation ield produced by these propylene lames makes it possible to accurately calculate these radiation corrections. Figure 6, above, shows the corrected temperatures plotted instead against 6 y/δ s y / δ S. The

7 temperatures are well correlated inside the lame envelope. That is, the temperature proile inside the lame is largely independent o the uel to air ratio, Ψ. In particular, the temperature at the lame boundary y = δ S remains around 1 K or all values o relative richness, Ψ. The similarity correlation is excellent within.5 y / δ S 1. 5, but not as good outside these limits. For leaner lames, i.e. lames having lower values o Ψ, the temperatures are slightly higher at larger values o y / δ S but lower or smaller values o y / δ S. The similarity applies to the buoyant turbulent combustion controlling the basic combustion process, in the neighborhood o y δ z( Ψ Ψ ) 1/ S. Away rom the central zone, near the wall the laminar sub-layer tends to be independent o height, whereas ar rom the wall the turbulent low scales more nearly according y z. As shown later, this same lack o perect similarity occurs or the velocity proiles. RADIANCE Measurements [1,3] o the local outward radiance also support the similarity concept. Here the outward radiance is deined as the radiant lux per unit solid angle in the outward normal direction. Scanning radiometer measurements were averaged at the midheight o each 13-mm high burner segment. Figure 7 shows the outward radiance rom the lames vs. mass transer at our dierent heights. Radiation comes only rom the lames (i.e. the water-cooled sintered-metal burner emits negligible radiation.) In the case o propylene radiation comes almost entirely rom soot. More speciically, the radiance depends on the eective lame radiation temperature, T, the soot depth, δ S and the absorption coeicient. The eective lame radiation temperature was measured by comparing the radiant emission rom the lames to the absorption o externally imposed radiation. The comparisons were made or radiation at the same wavelength. Measurements at both.9 and 1. µ m wavelengths yielded the same eective lame radiation temperature, T = 1375 K [1]. In addition to being independent o wavelength, λ, the eective temperature o these propylene lames was independent height, z and mass transer rate, m&. This invariance is, indeed, welcome. It simpliies the interpretation o data and development o models. Making the usual assumption that the soot absorption coeicient α λ = k v / λ, varies inversely with wavelength, λ, it is shown [9] that the radiance, N r, rom a homogeneous cloud o soot having volume raction, v, and depth, δ S, is given by σ T ( ) = 15 k (3) vδ S T N r T, v, δ S 1 ψ 1 + (8) π π C where σ is the Stean-Boltzmann constant, C is Plank s second constant, k = 8. 6, is (3) the soot extinction constant [1] and ( 1+ x) 15 ) ψ is the Pentagamma unction [9]. The (3 expression, ( 1+ x), can be conveniently approximated [11] by exp( 3.6x), to yield π ψ 65

8 N r ( T,, ) v σ T 3.6 kv δ S T δ = S 1 exp. (9) π C Nr (kw/m sr) m& (g / m s) z (mm) Eq Eq Eq Eq Figure 7. Measured and modeled lame radiance, N r, vs. mass transer, m&, at our heights, z, or propylene. Finally, upon rearranging Eq. (9), δ S rom Eq. (3), one has 3.6k 1/1 v zc δ T S 1 π N ln 1 z σ T = r [.3( Ψ Ψ ) ] 1/ and substituting or 9 N z 3.6 k T Y ln π r t v 1 z 1 + = Y 1 T z C σ The radiance measurements are plotted against Ψ in Fig. 8 using the ormula or Y together with an eective lame temperature T = 1375 K and laminar to turbulent transition height, 1/1 z t =. 11m. The correction or the laminar lame at the leading edge 9 z 1 + t becomes important only at the lowest height o 66 mm height. As z expected the radiance increases approximately with the ¼ power o height, z, rom the leading edge. The model curve in Fig. 8 is obtained rom Eq. (1) using 6 k v = or the present propylene lames [1]. The correlation and model it are excellent yielding urther substantiation or the proposed similarity. The outward radiance also correlates simiarly or methane, ethane and ethylene lames [13]. (1) 66

9 Y Data πn ln 1 Y σ = z t z 1 + z r T k Y = 1 v Model 1/ [.3( Ψ Ψ ) ] Ψ C T z (mm) Model Figure 8. Correlation o measured radiance data, Y, vs. uel to air ratio, Ψ, or propylene lames at various heights, z, and mass transer rates. Solid line is Eq. (1). VELOCITY Most, Sztal and Delichatsios [1] measured the velocity and temperature proiles o vertical turbulent ethane wall ires. The measurements were perormed at FM Global U (m/s) z (mm) y Figure 9. LDV measurements o vertical velocity, U, vs. normal distance, y, or dierent heights, z, rom the leading edge at a mass transer rate, &. = 5. g / m during the summer o 198. The measurements were not correlated at the time. The 67 m s

10 temperature measurements are very similar to those o Fig. 5(b). Now, with the present approach, both the velocity and temperature proiles can be successully correlated. The temperature correlation is equally as good as shown in Fig. 6. Figure 9 shows the measured upward LDV velocities, U vs. distance, y, at dierent heights, z, or ethane lames supplied by a mass transer rate m& = 5. g / m s. Figure 1 shows the same data 1/ correlated as U ( gz) vs. y / δ S. The good correlation o both temperature and velocity lends support to the similarity hypothesis o this paper. Careul examination o the temperature and velocity correlations shows the curves or y / δ S >. decreasing slightly with increasing relative uel richness, Ψ. Similarly, there is a consistent lack o similarity among the curves or y / δ S <. 5. The similarity identiied here applies to the main combustion process. U/(gz) z (mm), Ψ 6,. 8,.17 1,.15 15, y/δ s Figure 1. Correlated velocity, U/(gz).5 vs. normalized distance, y/δ s, or dierent heights, z, at mass transer rate, m & = 5. g/m s CONCLUSIONS The relative uel to air mass ratio, Ψ, successully correlates the: lame thickness, outward directed radiance, and both temperature and velocity proiles across the turbulent boundary layer adjacent to the pyrolysis zone o wall ires. These similarity relationships should simpliy the development o both CFD and analytic models o upward burning wall ires. 68

11 1 de Ris, J. L., Markstein, G. H., Orlo, L. and Beaulieu, P. A., Flame Heat Transer Part I: Pyrolysis Zone, Factory Mutual Research Tech. Report J. I. DJ9.MT, September Markstein, G. H. and de Ris, J., Wall Fire Radiant Emission - Part 1: Slot Burner Flames Comparison with Jet Flames, Proc. Combust. Inst. 3, , (199). 3 Markstein, G. H. and de Ris, J., Wall-Fire Radiant Emission Part : Radiation and Heat Transer rom Porous-Metal Wall Burner Flames, Proc. Combust. Inst., 177-5, (199). Megaridis, C. M. and Dobbins, R. A., Soot Aerosol Dynamics in a Laminar Ethylene Diusion Flame Proc. Combust. Inst., 353-6, (1989). 5 Morton, B. R., Taylor, G. I. and Turner, J. S., Turbulent Gravitational Convection rom Maintained and Instantaneous Sources, Proc. Roy. Soc. A 3, 1 (1956). 6 Kim, J. S., de Ris, J. L. and Kroesser, F. Wm., Laminar Free-Convective Burning o Fuel Suraces, Proc. Combust. Inst. 13, , (1971). 7 Ahmed, T., Investigation o the Combustion Region o Fire-Induced Plumes Along Upright Suraces, Ph.D. Thesis, Pennsylvania State University, (1978). 8 Eckert, E. R. G. and Drake, R. M., Analysis o Heat and Mass Transer, McGraw-Hill, Siegel, R. and Howell, J. R., Thermal Radiation Heat Transer, 3 rd Ed., Hemisphere Publishing Co. (199). 1 Choi, M. Y., Mulholland, G. W., Hamins, A. and Kashiwagi, T., Comparisons o the Soot Volume Fraction Using Gravimetric and Light Extinction Techniques, Combustion and Flame, 1, (1995). 11 Yuen, W. W. and Tien, C. L., A Simple Calculation Scheme or the Luminous Flame Emissivity, Proc. Combust. Inst. 16, , Most, J. M., Sztal, B. and Delichatsios, M. A., Turbulent Wall Fires LVD and Temperature Measurements and Implications, Presented at the Second International Symposium on Applications o Laser Anemometry to Fluid Mechanics, Lisbon, Portugal, July -, 198, (Also Factory Mutual Report Number, RC8-PT-11.) 69