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Back to Table of Contents THIRD EUROPEAN COMBUSTION MEETING ECM 2007 Study on Suppression of a Reacting Plume by Evaporating Droplets Using Large-Eddy Simulation J. Xia∗, 1, 2, K.H. Luo1, S. Kumar2 1 Energy Technology Research Group, School of Engineering Sciences, University of Southampton, Southampton SO17 1BJ, UK 2 BRE, Garston, Watford WD25 9XX, UK Abstract Suppression of a reacting plume by water spray is investigated using dynamic large-eddy simulations. A hybrid Eulerian-Lagrangian approach is employed for the gas-liquid flow, with finite-rate chemistry for reaction. The dynamics of large droplets are studied in two configurations. With a spray angle of 30 degrees, the thinly spread droplets are not able to extinguish the reacting plume, but can significantly reduce the peak reaction rates and temperatures. When concentrated droplets are directed towards the fuel source, combustion is effectively suppressed. Both the thermal and mechanical interactions between the two phases are found to be important. The budget analysis of a modified gas internal energy shows that the relative importance of various terms contributing to the cooling effects of droplets. Introduction around 1 mm or more, are widely deployed for water To suppress or extinguish fire is of scientific and spray systems. The evaporation effect due to latent heat practical interest. One application is the water-based fire of vaporization is thus restricted due to a small total extinguisher, which is promoted as an environmentally surface area exposed and short residence time as friendly alternative to a halogen-based system. The droplets cross over the flame region. suppression mechanisms include direct cooling of flame The objective of this paper is to pursue a better zones, cooling of the fuel surface, dilution of the understanding of the mechanisms of suppression of a reactants through the production of water vapour and reacting plume by water sprays, using dynamic large- attenuation of radiation. Strong interactions between eddy simulations. A simplified practical configuration flow turbulence and finite-rate chemistry may also lead of fire suppression systems is employed to explore the to flame extinction [1,2]. An important parameter is the complex physiochemical phenomena, which is local Damköhler number [3], a measure of competition formidable for a theoretical framework, such as laminar between a characteristic flow diffusion time scale and a counterflow diffusion flames. The paper is organized as characteristic chemical time scale. A laminar follows: the mathematical formulations, numerical counterflow diffusion flame diluted with water droplets procedure and computational setup are briefly reviewed on the oxidizer is a widely used configuration for first. The main section is on the problem set-up and fundamental theoretical investigation of flame analysis of the results, which is followed by concluding extinction due to intensified strain rate in the presence remarks. of water droplets [4,5]. If the chemistry cannot catch up with the pace at which reactants diffuse into reaction Methodology zones due to promoted strain rate, then the local In the present study, the flow field is described with Damköhler number becomes too small to sustain unsteady Navier-Stokes equations, and reaction with reaction and local flame quenching takes place. A one-step irreversible finite rate chemistry. The non- theoretical analysis of counterflow flame extinction with dimensional heat release rate due to combustion, ωT, is polydisperse water spray by Dvorjetski and Greenberg expressed by υ υ [5] was based on a reduced Damköhler number and ρ Y ρ Y f o Ze large activation-energy asymptotics for the analysis of ωT = Da g f g o exp − (1) Wf Wo Tg flame structure [6]. The main suppression mechanism for water-based where Da is the Damköhler number, Ze the Zel’dovich fire suppression systems varies in different scenarios. number, ρ density, T temperature, Y mass fraction, υ the The water mist systems, in which the initial mean molar stoichiometric coefficient, W molecular weight. droplet diameter is smaller than 200 µm, have been The subscripts “g” and “d” are used for gas and droplet receiving renewed attention, since they can make full phase quantities, and “f” and “o” for fuel and oxidizer use of the potential of complete evaporation due to large variables, respectively. The species reaction rate is surface area per unit volume. However, the penetration correlated with ωT by ωi = - υiWiωT. The filtered heat capacity [7,8] is important, if the droplets have to release rate ωT is directly closed by a scale similarity penetrate deep into the fire or even reach the fuel source model developed for a turbulent planar reacting jet with in an urgent situation. To this end, much bigger droplets, similar configurations as in this study. Radiation is not ∗ Corresponding author: J.Xia@soton.ac.uk Proceedings of the European Combustion Meeting 2007 Back to Table of Contents THIRD EUROPEAN COMBUSTION MEETING ECM 2007 explicitly calculated, but the combustion parameters are Grid Scale (SGS) flow information is not seen by carefully chosen so that the peak temperature of the fire droplets in the present study, partly due to the is similar to a realistic fire with radiation heat loss. complexity of evaluating these SGS thermodynamic The droplet phase is traced in the Lagrangian frame. quantities and partly due to their secondary importance The normalized droplet mass, momentum and energy to the behaviour of heavy droplets with big inertia (in terms of the droplet temperature) equations can be investigated here for fire suppression systems. written as High-order compact finite difference schemes are dmd 1 Sh md (2) employed for spatial discretization, and a 3rd-order md ≡ =− HM dt 3 Sc St Runge-Kutta method for time advancement of the gas dvd,i f g Fdrag,i gi phase. A semi-analytical approach is used for the dt = St ( ug,i − vd,i + i = Fr )md + Fr (3) droplet phase, taking into consideration the accuracy, cost and stability. The time step t for the gas phase is 1 Nu dTd = dt 3St Pr (Tg − Td ) − (γ − 1) Ma 2 Sh H M hfg Sc used for the droplet phase as well, with a careful supervision on the ratio of t*/τd* (= t/St) to ensure (4) meaningful numerical results for two-phase reacting Standard nomenclature is used in all the equations flow simulations. Non-reflecting type of boundary throughout this paper. The Stokes number St is the ratio conditions are used at all the boundaries, except that the of the characteristic droplet responsive time to the spanwise direction is periodic. To further attenuate the characteristic large-scale flow time, numerical wave reflection at the outflow boundary, a τ* ρ D2 (5) sponge layer is attached at the end of the physical St = d = Re d d * domain, but inside the outflow boundary, in the τg 18µ streamwise direction. In this paper, x, y and z designate The superscript “*” is used for dimensional quantities. the spanwise, lateral and streamwise directions, As seen from Eq. (5), the initial Stokes number is respectively. proportional to the squared initial droplet diameter. The Dynamic large-eddy simulation of an upwardly vector Fdrag is the drag force exerted by the flow field on three-dimensional (3D) turbulent planar reacting plume, a droplet, which interacts with downward water droplets as in a f Fdrag = md ( u g − v d ) (6) practical fire suppression system, has been performed to St investigate the mutual interactions between the two where f is an empirical correction coefficient to the phases in the plume region. Spray break-up is not Stokes drag due to droplet Reynolds numbers Red of modelled in this study. The simulation parameters are order unity or larger, presented in Table 1, where S is the temperature ratio f = 1 + 0.15 Red0.687 (7) between the ambient oxidizer and the hot fuel ejecting Equation (7) is valid for Red ≤ 1000. Finally, HM is the from the jet slit nozzle; Qh is the heat of combustion; driving potential for mass transfer, described with the MLR0 is the initial ratio of the mass flow rate of the classical equilibrium evaporation model. hfg is the latent water spray at the sprinkler nozzle to that of the fuel gas heat of vaporization. at the jet nozzle, illustrating the amount of water used to The integrated coupling on mass, momentum and suppress the reacting plume; θ0 is the initial discharge energy between the Eulerian gas and Lagrangian angle of the fire sprinkler. Intensive “counterflow” type droplets has been taken into account to properly reflect of interactions between the reacting plume and the unsteady and nonlinear interactions between the evaporating droplets take place around the centreline reacting flow and evaporating droplets. The droplet region due to the deployment of all the droplets going source terms, which appear at the right-hand-side of the directly toward the plume source for Case C, i.e., θ0=0. gas phase governing equations, can be written as An identical velocity magnitude, |vd0|, is set for all the 1 droplets when they are initially disseminated from the S ms = − ∑ md,k (8) sprinkler nozzle according to a two-dimensional (2D) V k 1 random uniform distribution. The flow and combustion S mo,i = − V ∑ (F k drag , k ,i + md,k vd,k ,i ) (9) parameters are similar to those in [9], except that a smaller Froude number, Fr=10, is used in the present 1 1 Nuk md,k study to introduce strong buoyancy effect as usually Sen = − ∑ V k 3 ( γ − 1) Ma 2 Pr Stk (Tg,k − Td,k ) found for domestic fires. The initial droplet diameter for St0=128 is Dd0*≈800 µm, and the dimensional initial 1 + md,k Td,k + md,k hfg droplet velocity magnitude for |vd0|=2 is |vd0*|≈4 m/s, ( γ − 1) Ma 2 both of which are typical values for standard spray fire 1 sprinklers [10]. + Fdrag,k ,i vd,k ,i + md,k vd,k ,i vd,k ,i A slit sprinkler nozzle with the same size as the fuel 2 (10) nozzle is deployed at z=38. The sponge layer starts at In Eqs. (2)-(10), the gas properties at droplet locations z=40, after which no physical results are found. The are obtained by a 4th-order Lagrangian interpolation sprinkler nozzle is activated at t=100, when the reacting scheme with filtered quantities. In this sense, the Sub- 2 Back to Table of Contents THIRD EUROPEAN COMBUSTION MEETING ECM 2007 plume has been established in the computational domain, in the presence of strong buoyancy. Details on mathematical equations, numerical procedure and subgrid models can be found in [11] and are not repeated here due to page limits. Table 1 – Simulation parameters Re Fr S Da Ze Qh 4000 10 0.76 120 12 250 hfg Lx×Ly×Lz nx×ny×nz 250 8×31.8×42.785 41×160×200 Cases St0 MLR0 θ0 |vd0| A - 0 - - ◦ B 128 3 30 2 C 128 3 0 2 Results and Discussion Figure 1 presents the filtered reaction rate contours on the central spanwise plane for Cases A and B at t=120. The droplet distribution is shown in Fig. 1(b) as well to clearly indicate how the instantaneous interactions between droplets and reaction takes place. Due to finite rate chemistry, the main reaction zones appear at downstream locations where z>15 for the buoyancy-driven reacting plume. The regions with peak reaction rates in Fig. 1(a) disappear in Fig. 1(b) in regions covered by the droplet trajectories. The magnitude of the peak reaction rate over the whole domain for Case B decreases about 10% as compared to Case A, while in the droplet-covered regions the decrease is far dramatic. Shown in Fig. 2 are the gas temperature records for both cases at one monitored point, [x,y,z] = [4,16,32]. The peak temperature has been decreased due to the presence of droplet at various time instants. As droplets discharging continues, an Figure 1 – Filtered reaction rate contours on the central increasing phase delay of the temperature records for spanwise plane at t=120 for (a) Case A and (b) Case B. Case B compared to those for Case A is seen, since The instantaneous droplet distribution is also shown in downward marching of droplets results in strong (b). accumulative effects of drag force on the flow field, hindering the upward movement of the reacting plume. Although considerable droplet effects are found for Case B, the main features of the reacting plume in Case A and its reaction structures have not changed significantly. To introduce stronger droplet effects, the initial sprinkler discharge angle is set to 0 for Case C to deploy intensive counterflow interactions between the two phases around the centreline region, while keeping the droplet mass loading ratio the same. Figure 2 – Gas temperature records at point [x,y,z] = [4,16,32]. Black line – Case A; Red line – Case B. 3 Back to Table of Contents THIRD EUROPEAN COMBUSTION MEETING ECM 2007 Figure 3 shows the Favre-filtered mixture fraction contour plots for Cases A and C. The mixture fraction is defined as: sY − Yo − Yv + 1 (19) Ymf = f 1+ s where s is the stoichiometric ratio, 1 in this study under the assumption of equal molar stoichiometric coefficients υ and molecular weights W for fuel and oxidizer. Yv = 0 for Case A. Although Ymf is not a conserved scalar for Case C due to the presence of Yv , it is found that Yv < 5% in the whole domain due to a weak level of evaporation and it thus affects Ymf negligibly. To compare with Cases A and C, the locations where Ymf = 0.5 are delineated to show the approximate stoichiometric mixture fraction positions. (a) Stoichiometric mixture is found at downstream areas for Case A. The stoichiometric mixture fraction positions approximately represent the high heat release rate regions, except for the upstream areas where the reaction has not been activated. For the droplet case, the rise of the fuel stream is partially blocked due to the presence of droplets and especially their drag effects on the gas upward velocity, so that the stoichiometric mixture is only found in a region close to the inflow boundary below z=10. Consequently, the reactant mixture beyond z ≈ 20 is so diluted that combustion cannot sustain. Even in the region where the stoichiometric mixture fraction is found, i.e., z<10, for Case C, the correlation between ωT and Ymf (not shown here) would reveal a high level of local flame extinction. Apart from the droplet thermal cooling effect of inhibiting ignition, the dynamic effect induced by droplets is considered to be a significant factor. Around the centreline regions where (b) the droplet number density is high, the drag force exerted by droplets on the reacting plume causes intense counterflow interactions in the region close to the plume source. The local scalar dissipation rate is expected to Figure 3 – The Favre-filtered mixture fraction at t=120 increase, which would cause local flame extinction. The for: (a) Case A; (b) Case C. The black lines illustrate the penetration of droplets would also trigger the leakage of stoichiometric mixture fraction locations. reactants from the vicinity of the stoichiometric mixture fraction surfaces, which represents another mechanism For fire suppression systems, one key role played by for local flame extinction. Scrutiny of the subgrid-scale droplets is to extract thermal energy from the hot plume phenomena, where interactions between droplets, via cooling and evaporating, and thus reduce the peak turbulence and chemical reactions take place, would be reaction rate and temperature of the gas phase. As necessary to further prove the above statements. In the shown by Eq. (4), the convective heat transfer due to the present LES, the scalar dissipation rate cannot be temperature difference between the two phases provides directly obtained. Models such as those proposed by the driving potential to raise the droplet temperature and Domingo et al. [12] may be used to evaluate the subgrid drive evaporation. scalar dissipation rate, but validation must be carried out The gas phase cooling effect induced by droplets can against DNS or experimental data. be analyzed in detail via a transport equation on the Filtered Reduced Internal Energy (FRIE) of the two- ' phase reacting flow, ρg eg , defined as ' ρ gTg (11) ρ g eg = γ ( γ − 1) Ma 2 The filtered internal energy of the gas phase 4 Back to Table of Contents THIRD EUROPEAN COMBUSTION MEETING ECM 2007 Tg 1 1 ρ g eg = ρ g γ ( γ − 1) Ma 2 + Yv hv = ρ g eg + ρ gYv hv 0 ' 0 Sevt = − ∑ V k ( γ − 1) Ma 2 md,k Td,k (17) (12) 1 ug,i ug,i v v under the assumption of identical heat capacities for all Sevm = − V ∑ m 2 d, k − ug,i vd,k ,i + d,k ,i d,k ,i 2 the species. In Eq. (12), Yv is the Favre-filtered mass k 0 (18) fraction of water vapour and hv is the reference As indicated, Sth is the thermal cooling effect due to the enthalpy for vapour. While Eq. (12) provides convective heat transfer between the two phases; Sme is comprehensive information on the filtered internal the mechanical work done by the drag force; Sevt is the energy, the FRIE defined in Eq. (11) is only and directly droplet internal energy which is transferred into the gas temperature-dependent and thus of more practical after evaporation; Sevm is a contribution arising from the interest. interaction of kinetic energy between the two phases. The transport equation on FRIE can be written as The latent heat of vaporization, hfg, plays its role via Sth, D ∂R ∂u as shown in Eq. (4), and impact the evaporation rate md Dt ( ) ρg eg = k − p g,k + Qh ωT + σ ik Sik − ρgτ ik Sik ' ∂xk ∂xk indirectly, but it does not appear explicitly in all the III IV V I II droplet source/sink terms, which are expressed by Eqs. 0 ug,i ug,i (15)-(18). This is a direct consequence of the fact that − hv − S ms − ug,i S mo,i + Sen the budget analysis is upon the temperature-dependent 2 VII VIII internal energy ρg eg , but not the total internal energy ' VI (13) ρg eg . where σ ik and ρgτ ik are the grid scale and subgrid scale Statistics on the budget terms in Eq. (14) have been stress tensors, the latter of which is determined by the obtained. From the time when flow data are recorded for the averaging purpose, droplets have covered the whole dynamic Smagorinsky model. Sik is the strain rate plume region from the sprinkler nozzle down to the tensor. The cap symbol “ f ” designates function f is plume source at the inflow boundary. The reacting evaluated with filtered quantities. plume then experiences another “droplet through time” Terms II-VIII in Eq. (13) designate the pressure period to finish the data recording. The spatial ensemble dilatation, combustion released heat, grid scale averaging over the spanwise direction is performed dissipation, subgrid scale dissipation, and effects due to finally. droplet mass, momentum and energy source terms, Shown in Fig. 4 are the centreline budgets of Eq. respectively. To simplify the analysis and, more (14) for Cases A and C. The combustion released heat importantly, reveal the pertinent factors responsible for dominates over other terms in Case A, as anticipated. It the rate of change of FRIE, all the redistributive terms also directly causes the pressure-dilatation term, which have been categorized into term I. These terms are not shows as a sink, to be the second contribution due to traced, since their integral effect is to transport internal volume expansion following reaction. The close energy from one place to another through various correlation between these two terms can be clarified by physical mechanisms, such as convection, diffusion, the fact that the peak for term III and the valley for term grid and subgrid scale transportation, etc., instead of II appear at the same location, z ≈ 22, where strong producing or dissipating internal energy as source or reaction takes place. Contributions from the dissipation sink terms [13]. To further distinguish among the terms, IV and V, can be neglected. A further scrutiny of thermal, dynamic and evaporating contributions from these two terms reveals that the magnitude of the SGS droplets, substituting Eqs. (8)-(10) into Eq. (13) and dissipation is much bigger than that of the GS rearranging the droplet-related terms yield dissipation. D ∂R ∂u In Case C, the gas phase cooling effect due to term Dt ( ) ρ g eg = k − p g,k + Qh ωT + σ ik Sik − ρ gτ ik Sik ' ∂xk ∂xk VI shows as a strong sink for FRIE. The sudden drop of III IV V term VI at the sprinkler nozzle location is partly due to I II the high droplet number density found there and partly + S th + S me + Sevt + S evm due to the huge temperature difference between the two VI VII VIII IX phases. A peak of heat release rate at z ≈ 12 induces a (14) valley of term VI, since the gas temperature is promoted where and the temperature of most droplets stabilizes at a level 1 1 Nuk md,k close to the normal boiling temperature. It is noteworthy S th = − V ∑ 3 (γ − 1) Ma Pr 2 Stk (T g, k − Td,k ) that the mechanical work term VII serves as a k (15) considerable source to FRIE. This can be explained by 1 the simple fact that “Friction produces heat”. This effect S me = − V ∑ −F k drag, k , i (u g, i ) − vd,k ,i (16) due to the inter-phase drag has been seldom discussed, as it is difficult to be investigated with a convection-free configuration such as counterflow diffusion flame laden 5 Back to Table of Contents THIRD EUROPEAN COMBUSTION MEETING ECM 2007 with water droplets, which is widely adopted in droplets are able to penetrate deep into the reacting previous studies on this topic. It is found in this study plume and suppress the upward convection of the fuel that for turbulent forced reacting plumes, for which the stream. The mixture along the trajectories of droplets momentum and buoyancy effects are equally important becomes too diluted to sustain combustion. Near the [14], Sme could be an important contribution to the gas fuel source region, where stoichiometric mixture is phase internal energy, and thus the temperature. As found, the thermal cooling effect and the mechanical shown in Fig. 4(b), its magnitude is comparative to that drag effect of droplets extinguish any surviving reaction of term II throughout the whole centreline. The peak of and suppress any combustion ignition. A transport term VII at the droplet discharging position is also due equation for the modified internal energy of the gas to the high droplet number density there. Terms VIII phase, which is directly temperature-dependent, has and IX have weak effect on FRIE due to the overall been derived and budget analysis on the equation have small evaporation rate, md , of large droplets used in the been performed. The convective heat transfer between present study. Both of them show as source terms, and the two phases is a main mechanism for thermal the magnitude of term VIII is bigger than that of term cooling. On the other hand, the mechanical work due to IX. the inter-phase drag produces heat. Acknowledgements Supercomputing resources on the HPCx were provided by the UK Consortium on Computational Combustion for Engineering Applications under EPSRC grant No. EP/D080223/1. Financial support for the first author from the BRE Trust and the EPSRC grant No. EP/E011640/1 are gratefully acknowledged. References [1] J. Xu, S.B. Pope, Combust. Flame 123 (2000) 281- 307. [2] K. Xiao, D. Schmidt, U. Maas, Proc. Combust. Inst. 28 (2000) 157-165. [3] F.A. Williams, Prog. Energy Combust. Sci. 26 (2000) 657-682. [4] A.M. Lentati, H.K. Chelliah, Combust. Flame 115 (1998) 158-179. [5] A. Dvorjetski, J.B. Greenberg, Fire Safety J. 39 (2004) 309-326. [6] F.A. Williams, Combustion Theory (2nd Edition), The Benjamin/Cummings Publishing Company, Inc., California, 1985. [7] G. Grant, J. Brenton, D. Drysdale, Prog. Energy Combust. Sci. 26 (2000) 79-130. [8] S. Nam, Fire Safety J. 32 (1999) 307-329. [9] K. Mehravaran, F.A. Jaberi, Phys. Fluids 16 (2004) 4443-4461. [10] J.A. Schwille, R.M. Lueptow, Fire Safety J. 41 (2006) 390-398. [11] J. Xia, K.H. Luo, S. Kumar, FEDSM2006-98443, 2006 ASME Joint U.S. – European Fluids Engineering Summer Meeting, Miami, FL, 2006. Figure 4 – The centreline budget analysis on the filtered [12] P. Domingo, L. Vervisch, K. Bray, Combust. reduced internal energy for: (a) Case A; (b) Case C. Theory Modelling 6 (2002) 529-551. [13] K.H. Luo, Combust. Flame 119 (1999) 417-435. Conclusions [14] X. Zhou, K.H. Luo, J.J.R. Williams, Eur. J. Mech. Dynamic large-eddy simulations of a reacting plume B – Fluids 20 (2001) 233-254. interacting with water spray droplets have been performed to investigate the mechanisms of combustion suppression due to unsteady interactions between the two phases. Droplets from a spray angle of 30 degrees are found to reduce the peak reaction rates and peak temperatures. By concentrating droplets in the centraline regions and directing them to the fuel source, 6