numerical investigation of stationary shrub ﬁre in crosswind · 8th us combustion meeting –...

Paper # 070FR-0073 Topic: Fire

8th US National Combustion MeetingOrganized by the Western States Section of the Combustion Institute

and hosted by the University of UtahMay 19-22, 2013.

Numerical investigation of stationary shrub fire in crosswind

Satyajeet Padhi Ambarish Dahale Babak Shotorban∗

Shankar Mahalingam

Department of Mechanical and Aerospace Engineering,The University of Alabama in Huntsville, Huntsville, AL 35899, USA

A variant of a three-dimensional multiphase, physics-based model (Dahale et al., Int. J. WildlandFire, in press) is used to analyze the effects of crosswind on flames generated from the burning of anisolated shrub. The shrub considered in this investigation is Chamise, found in abundance in chaparralvegetation and highly susceptible to bush fires. The shrub is represented as a porous medium comprisingof branches and foliage. It is assumed that the thermal decomposition of the shrub results only inpyrolysis gases. The effects of moisture and char oxidation for the conditions investigated are assumednegligibly small, and hence neglected. Drag force arising due to the interaction between the solidand gaseous phases is modeled through the inclusion of source terms in the gas phase momentumequation. The mass and temperature of the solid phase are kept constant so that a statistically stationarystate is reached. This approach makes a detailed statistical analysis of the flame and plume possiblethrough time averaging. The source terms due to pyrolysis are included in the gas phase conservationequations. Radiative heat transfer is modeled by the discrete ordinates method. Turbulence is dealt withby large-eddy simulation with dynamic Smagorinsky subgrid-scale modeling. Subgrid-scale turbulentcombustion is modeled based on a flame surface density concept proposed by Zhou and Mahalingam(Phys. Fluids, 2002). In this work, the shrub fires are modeled for cases with different wind speeds.In each case, the flow field generated due to the interaction of fire-induced flow field with the ambientflow field is studied. The second invariant of the velocity-gradient tensor is used to locate the variouscoherent structures formed due to the turbulent flow. A qualitative conclusion was made on the co-existence of the higher temperatures and turbulent kinetic energy in the flow. The regions of highertemperatures have lower turbulent kinetic energy and vice-versa.

1 Introduction

Wildland fires are complex phenomena. This complexity is mainly due to the presence of multiplelength and time scales, the presence of highly coupled physics from fluid dynamics, combustionand radiation effects, and due to the transient nature of the process. Physics-based modeling isoften used to improve our understanding of mechanisms that are responsible for fire behavior [1–5]. Flame characteristics have been studied in laboratory tests [6–8] and experimental field fires[9, 10], to name a few. Flame geometry of a 2D fire from a fuel bed was calculated with appreciableaccuracy by [2] using a physics-based model. Flame characteristics for stationary area and line firesfor different wind speeds were calculated by [11] by a physics-based model and showed reasonableagreement with available experimental data and empirical correlations. While most of the work on

∗To whom correspondence should be addressed. Email: [email protected]

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8th US Combustion Meeting – Paper # 070FR-0073 Topic: Fire

the study of flame characteristics and associated statistics are studied for line fires or surface fires,very little work, has been carried out on fuels representative of a shrub.

The focus of this paper is to study the flow field of a flow generated from the burning of a shrub.Two different cases are considered viz., with and without crosswind. The shrub considered in thisstudy is chamise (Adenostoma fascilatum), found in abundance in chaparral vegetation. One ofthe difficulties in studying the burning behavior of an isolated shub is the transient nature of theproblem, leading to a non-stationary situation. In order to circumvent this difficulty, a method bywhich the solid phase temperature and mass are maintained constant, is developed in this paper.The resulting stationary fire facilitates a detailed statistical analysis through time averaging.

2 Modeling Approach and Setup

The solid phase in this study consists of a chamise shrub, which is assumed to be a porous mediumconsisting of two components — branches and foliage. The shrub is assumed to be homeogeneousin nature, i.e., local solid phase properties are independent of position. Thus, bulk density —defined as the amount of fuel that may be consumed by a crown fire per unit volume of shrub —is fixed in this study. The solid phase can exchange energy with the gas phase via convection andradiation. The rate of pyrolysis of the gases produced from the thermal decomposition of the solidphase is deduced from an Arrhenius-type law.

Since this paper focuses on flames from statistically stationary shrub fires, the following assump-tions are made: (i) the flame is generated by the combustion of pyrolysis products generated froma fixed mass of shrub, (ii) the temperature of the shrub is kept at a constant value of 500 K, (iii)the effect of moisture and char oxidation is neglected. Combustion is started by an auto-ignitionprocess facilitated by the hot fuel. With these assumptions, no equations are solved for the solidphase and the gas phase conservation equations, which include source terms from solid phase, aresolved. The solid phase influences the gas phase through the source terms that include the dragforces arising from solid-gas interaction.

Transport equations are solved for mass, momentum, energy and species. Various source termsappearing in the conservation equations can be summarized as: mass exchange between solid andgas phase in the continuity equation, drag forces arising due to the presence of solid fuel particlesin the flow field in the momentum equation, convective and radiative heat exchange between thetwo phases in the energy equation, and mass exchange due to combustion and the chemical sourceterm in the species equation. Turbulence is modeled by large eddy simulation (LES) in this work.A spatial filtering is applied on the governing transport equations and the resulting unresolvedsubgrid scale (SGS) terms are modeled by an eddy viscosity model in which the eddy viscositycoefficient is given by the dynamic Smagorinsky formula.

The filtered chemical reaction term ωK , appearing as a source term in the gas phase species trans-port equation is modeled using a flame surface density based approach. The filtered reaction rateis modeled as, ωK = mKΣ(x, t) , where mK is the flamelet consumption rate and Σ is the flamesurface density. Further details can be found in [13]. A radiation transport equation (RTE) is solvedfor obtaining the source term appearing in the energy equation, which determines the rate of heattransfer between the solid phase and the gas phase. The methodology used to solve the RTE isbased on the discrete ordinates method. For further details, refer [5, 14].

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Figure 1: Schematic of computational domain for (a) no crosswind; (b) with crosswind.

The governing equations are discretized in a three dimensional Cartesian coordinate system on auniform rectangular mesh, using finite-volume formulation and collocated variable arrangement.For the gas phase equations, the quadratic upwind interpolation for convective kinematics withestimated streaming terms (QUICKEST) finite volume scheme [16] has been used. To solve thepressure-velocity coupling, a fractional step method similar to that proposed by [17] is used witha difference that our time integration procedure is fully explicit. Open boundary conditions, wheregradients of variables normal to the boundary are set to zero, are imposed on all boundaries exceptfor the bottom boundary where a closed boundary condition (no inflow/outflow) has been imposed.The computations are parallelized through the Message Passing Interface (MPI) protocol. Detailsof the modeling approach in this work are given in [5].

A schematic of the problem setup is shown in Figure 1. The dimensions of the domain for a casewith no crosswind are 2.4 m × 3.5 m × 2.4 m with a resolution of 120 × 175 × 120. For the casewith a crosswind of 1 m/s, the dimensions are 3.0 m × 2.8 m × 2.4 m with a resolution of 150 ×140 × 120. The dimensions of the shrub are chosen based on the height and width of the shrubas indicated in the figure. The height of the shrub is chosen to be 0.7 m and maximum width ofthe shrub is taken as 0.6 m, as suggested in [5]. The choice of grid resolution was dictated by theextensive grid resolution studies carried out by closely related works [4, 5, 15]. The crosswind isimposed on the y − z plane at x = 0 for the case with a crosswind. The bulk density of the shrubis set at 7.6 kg/m3, with no moisture present in the shrub. Time-averaged values are calculated forsimulation times of 150 s.

3 Results and Discussion

The cases studied in this paper correspond to statistically stationary fires. The two cases studiedin this paper are statistically stationary fires without crosswind and with crosswind. To achieve astatistically stationary state, the simulations are run with assumptions described in Section 2.

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Figure 2: Gas phase temperature profile along the symmetry axis of the shrub for the case with nocrosswind at five different times — instantaneous temperature (—); time-averaged temperature (-.-).

For the case with no crosswind, Figure 2 shows the profiles of instantaneous values of the gas phasetemperature and the time-averaged gas phase temperature along the symmetry axis of the shrub atdifferent times. It can be observed that the temperatures in the plume region are the highest nearits source, i.e., the shrub. The isosurfaces of instantaneous resolved gas phase temperature at 500K are shown in Figure 3-a. The time-averaged resolved field of gas phase temperature on a x − yplane position at z = 1.2 m is shown in Figure 7-a. The time-averaged flame is fairly symmetricabout the axis of symmetry of the shrub.

Examination of vorticity can provide a more complete picture of the turbulent flow field in thedomain. The isosurfaces of instantaneous field of vorticity magnitude |Ω| are shown in Figure3-b. After a short region above the shrub, the large-scale vortices spiral along the plume axis andbreakdown into small scale vortices, as seen in the top portion of the figure. The second invariantof velocity gradient tensor , Q can be used to locate the coherent structures formed due to theturbulent flow. The second invariant of velocity gradient can be defined as Q = (|Ω|2 − |S|2)/2,where Ω is the rate-of-rotation tensor and S is the strain-rate tensor. It identifies vortices as flowregions where Q > 0 [18]. The isosurfaces of instantaneous resolved field of the second invariantof the velocity gradient tensor are shown in Figure 3-c. Coherent structures formed due to roll-up of vortices can be seen in the figure. The presence of these vortices increases as one movesupwards in the plume direction.

It has been observed that in the regions of high temperatures the vorticity magnitude is lower, and asone moves away from the source of heat, the temperatures drop and large coherent structures startforming in the flow. The instantaneous resolved fields of turbulent kinetic energy on the x−y planepositioned at z = 1.2 m is shown in Figure 6-a. Most of the turbulent kinetic energy is concentratedin the upper section of the plume. This observation is consistent with Figures 3-b and 3-c wherethe coherent structures are formed downstream in the plume. Hence, a qualitative conclusion canbe drawn on the co-existence of the higher temperatures and turbulent kinetic energy in the flow.The regions of higher temperatures have lower turbulent kinetic energy and vice-versa.

For the case with a crosswind of 1 m/s, the isosurfaces of instantaneous resolved field for the

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Figure 3: Isosurfaces of instantaneous resolved fields for the case with no crosswind - (a) gas phasetemperature at 500 K; (b) vorticity magnitude at 20 s−1; (c) second invariant of the velocity gradienttensor at 20 s−2.

gas phase temperature are shown in Figure 4-a. The time-averaged resolved field of gas phasetemperature on a x − y plane positioned at z = 1.2 m is shown in Figure 7-b. As observed in thecase with no crosswind, higher temperatures are seen in the regions closer to the source of heati.e., the shrub.

The isosurfaces of instantaneous resolved field of vorticity magnitude are shown in Figure 4-b.The flow field of vorticity magnitude is tilted in the direction of the crossflow and it can observedthat most of vortices are concentrated along the direction of the plume and downstream in theplume. Also, the generation of the vortical structures is due to the turbulence generated from theinteraction of the thermal plume – generated from the burning of the shrub – with the crosswind.

The isosurfaces of the instantaneous resolved field of second invariant of the velocity gradienttensor are shown in Figure (5). In the aforementioned figures, it can be seen that the vorticesand the coherent structures grow in size further downstream in the thermal plume. Moreover, thecoherent structures seem to start forming from the edges of the shrub, separating into two distinctflanks of vortices, thus creating a vortex pair. Figure 6-b shows the instantaneous resolved fieldsof turbulent kinetic energy on the y − z plane at three different positions along the x-direction. Asseen in Figure 6-b most of the turbulent kinetic energy is concentrated downstream in the plume.This observation is consistent with the vorticity and Q field where their respective concentrationsincreases downstream in the plume. Hence, the qualitative conclusion made in the no crosswindcase about the co-existence of the temperature and turbulent kinetic energy field holds true for thecase with crosswind where the plume interacts with a crossflow.

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Figure 4: Isosurfaces of instantaneous resolved fields for the case with crosswind - (a) gas phasetemperature at 500 K; (b) vorticity magnitude at 20 s−1.

Figure 5: Isosurface of instantaneous resolved field of the second invariant of velocity-gradienttensor at 35 s−2 for the case with crosswind.

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Figure 6: Instantaneous turbulent kinetic energy in m2/s2 (color contours) (a) no crosswind — withsolid fuel bulk density (line contours) ; (b) with crosswind — xy-slices located at x = 1.0 m, 2.0 mand 3.0 m .

Figure 7: Time-averaged gas phase temperature in Kelvin (color contours) and solid fuel bulk den-sity (line contours) : (a) no crosswind ; (b) with crosswind. Snapshots are from a xy-slice passingthrough z = 1.2 m.

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4 Conclusion and Future Work

A qualitative description of the flow field generated due to the steady burning of a shrub was de-scribed using a physics-based model. Two cases were considered i.e., statistically stationary fireswith and without crosswind. The gas phase temperature field, vorticity magnitude and secondinvariant of velocity-gradient tensor fields were used to study the flow field generated from the in-teraction of fire-induced flow with crosswind. The second invariant of velocity-gradient tensor wasused to locate the various coherent flow structures formed in the domain. A qualitative conclusionwas made regarding the co-existence of the vortical structures in the flow and temperature field.Future work includes obtaining a quantitative description of the flow field, identifying the variousvortex structures quantitatively along with correlations for the flame structure from shrub fires.

Acknowledgments

The authors are grateful to the National Science Foundation for providing financial support throughgrant number CBET 1049560 for the work presented in this paper. The computing resources areprovided by the Alabama Supercomputer Authority (ASA) and Extreme Science and Engineer-ing Discovery Environment (XSEDE), which is supported by National Science Foundation grantnumber OCI-1053575.

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numerical investigation of stationary shrub ﬁre in crosswind · 8th us combustion meeting –...

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