Study on Suppression of a Reacting Plume by Evaporating Droplets by dfsiopmhy6


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                                                 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
                                               Energy Technology Research Group, School of Engineering Sciences,
                                                    University of Southampton, Southampton SO17 1BJ, UK
                                                             BRE, Garston, Watford WD25 9XX, UK

                    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:
                    Proceedings of the European Combustion Meeting 2007
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                                                                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
                                   ug,i − vd,i + i =
                                                                                           (3)       droplet phase, taking into consideration the accuracy,
                                                                                                     cost and stability. The time step t for the gas phase is
                                  1  Nu
                         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
                        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 = −
                                         ∑ (F
                                                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
                                          +                         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-

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                                                         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.

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                                               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

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                                                                    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
                                                                                                                              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 = −
                                                                                                                                             ∑ 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
                                                                                                                                                                                           
                                                        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
                            ( )
                              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

                                                                  (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
                            ( )
                             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 = −
                                       ∑  3 (γ − 1) Ma Pr
                                                                                              g, k   − Td,k ) 
                                                                                                                         that the mechanical work term VII serves as a
                                       k                                                                     
                                                                                                         (15)             considerable source to FRIE. This can be explained by
                                                                                                                          the simple fact that “Friction produces heat”. This effect
                        S me = −
                                       ∑ −F
                                                    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

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                                               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.

                                                                                        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.

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                        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,


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