Flamelet-based Combustion Model Research Articles

Ultra-Lean Premixed Turbulent Combustion: Challenges of RANS Modelling

The main challenge of improving spark ignition (SI) engines to achieve ever increasing thermal efficiencies and near-zero pollutant emissions today concerns developing turbulent combustion under homogeneous ultra-lean premixed mixtures (HULP). This continuous shift of the lean operation limit entails questions on the applicability limits of the combustion models used to date for SI engine design and optimization. In this work, an assessment of flamelet-based models, widely used in RANS SI engines simulations of premixed turbulent combustion, is carried out using an open-source 3D-CFD platform to clarify the applicability limits on HULP mixtures. Two different consolidated approaches are selected: the Coherent Flame Model (CFM) and the Flame Area Model (FAM). Both methodologies are embedded by the authors into the same numerical structure and compared against measurements over a simplified and controlled flame configuration, which is representative of engine-like conditions. The experimental steady-state flame of type “A” of the Darmstadt Turbulent Stratified Flame (TSF) burner is selected for the assessment. This configuration is characterized by flame measurements over a strong shear and mixing layer between the central high-speed CH4-air jet and the surrounding slow air co-flow, hence, it represents an interesting controlled condition to study turbulent HULP mixtures. A comparison between computed results and experimental data on trends of mean flow velocity, turbulence, temperature and mixture stratification was carried out. This enabled us to assess that the investigated flamelet-based combustion models failed in providing accurate and reliable results when the flame approaches turbulent HULP mixture conditions, demonstrating the urgency to develop models able to fill this gap.

MILD combustion of hydrogen and air – An efficient modelling approach in CFD validated by experimental data

The present work deals with the development of an efficient modelling approach for the flameless combustion of pure hydrogen with highly preheated air. It contains an application of different flamelet-based combustion models to achieve convergence in a computationally cheap way in contrast to time consuming methods such as the Eddy Dissipation Concept (EDC) model. Moreover, an evaluation of three detailed reaction mechanisms for the application of flameless hydrogen combustion is also included. The selection and implementation of a “Weighted Sum of Gray Gas” (WSGG) model to predict the radiative heat transfer as accurate as possible constitutes another important goal in the present work. The results of all modelling approaches were compared with extensive temperature measurements in the reaction zone. Additional temperatures of the test rig's control thermocouples were also compared with the results of the simulation to strengthen the validation. Maximum temperature deviation in the burner's axis of about 50 K can be achieved. Furthermore, the experimental and numerical results in this paper were compared with the results of flameless combustion of natural gas at equal furnace conditions and the same burner test rig. Higher temperatures in the burner axis up to a distance of 1855 mm were observed at hydrogen operation with a maximum difference of about 150 K to the natural gas case. A concluding evaluation of the furnace efficiency showed an increase by about 7% by changing the fuel from natural gas to hydrogen. This is achieved by reduced flue gas loss and an improved heat transfer.

Canonical Validation of a Modeling Strategy for Carbon Monoxide Emissions in Staged Operation of Gas Turbine Combustors

Canonical validation of a holistic modeling strategy for the prediction of CO emissions in staged operation of gas turbine combustors is subject of this study. Results from various validation cases are presented. Focus is on operating conditions that can be considered typical for modern, flexible gas turbines that meet the requirements of the upcoming new energy age. Reducing load in gas turbines is usually achieved by redistributing fuel referred to as fuel staging. Fuel-staged operation may lead to various mechanism like strong interaction of the flame with secondary air leading to quenching and elevated CO emissions and is - due to technical relevance - stressed in this work. In the recent past, our group published a new modeling strategy for the precise prediction of heat release distributions as well as CO emissions. An extension to the CO modeling strategy that is of high relevance for the introduced validation cases is addressed by this work. The first part of this study presents relevant aspects of the overall modelling strategy. Furthermore, a validation of the models is shown to demonstrate the ability of precisely predicting CO in two different multi-burner cases. Both validation cases feature a silo combustion chamber with 37 burners. The burner groups are switched off at partial load leading to intense interactions between hot and cold burners. Major improvement in comparison to CO predictions from the flamelet-based combustion model can be achieved as the modeling strategy is demonstrated to be capable of predicting global CO emissions accurately. Furthermore, the model’s precision in fuel staging scenarios are demonstrated and discussed.

Evaluation of flamelet-based combustion models for the use in a flameless burner under different operating conditions

The thermal input of a flameless burner is commonly realized by its switch on-time at a unique, optimized design point. This typical on–off regulation approach may provide temporal-inhomogeneous temperature distributions in continuous operating furnaces. An alternative way of regulation is a modulated controlled flameless burner, which deals with off-design points and reaches so a more temporal-homogeneous temperature distribution. Influences on the temperature field of the flameless reaction zone, caused by the off-design operation are investigated in this paper. This is done by experimental investigations with an aspirated thermocouple and with numerical simulations, using several flamelet-based combustion models. Additionally, Nitrogen oxide emissions were measured for each design point, which starts from 165 kW at nominal power to lower limit of 60 kW. The results suggest, that the non-premixed flamelet model is suitable for the application of flameless combustion in design and off-design. Furthermore, local temperature peaks in the flameless reactions zone increase (from about 1450 to 1530 °C) and the NOx emissions increase (from about 32 to 88 ppm) by decreasing the thermal input of the flameless burner at constant furnace temperatures.

Numerical Investigation of Combustion Instabilities in a Single-Element Lean Direct Inject Combustor Using Flamelet Based Approaches

Abstract In this paper, high-fidelity large eddy simulations (LES) along with flamelet-based combustion models are assessed to predict combustion dynamics in low-emission gas turbine combustor. A model configuration of a single-element lean direct injection (LDI) combustor from Purdue University (Huang et al., 2014, “Combustion Dynamics Behavior in a Single-Element Lean Direct Injection (LDI) Gas Turbine Combustor,” 50th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, Cleveland, OH, July 28–30.) is used for the validation of simulation results. Two combustion models based on the flamelet concept, i.e., steady diffusion flamelet (SDF) model and flamelet generated manifold (FGM) model are employed to predict combustion instabilities. Simulations are carried out for two equivalence ratios of φ = 0.6, and 0.4. The results in the form of mode shapes, peak to peak pressure amplitude and power spectrum density (PSD) are compared with the experimental data of Huang et al. (2014, “Combustion Dynamics Behavior in a Single-Element Lean Direct Injection (LDI) Gas Turbine Combustor,” 50th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, Cleveland, OH, July 28–30.). The effect of variation in the time-step size hence acoustic courant number is studied. Further, two numerical solver options, i.e., pressure-based segregated solver and pressure-based coupled solver, are used to understand their effect on the solution convergence regarding the number of time-steps required to reach the limit cycle of the pressure oscillations. A truncated (half) domain simulation is performed by applying an appropriate acoustic impedance boundary condition at the truncated location. Overall, the simulation results compare well with the experimental data and trends are captured accurately in all simulations. It builds confidence in flamelet-based combustion models for the use in combustion instability modeling which is traditionally done using finite rate chemistry models based on reduced kinetics.

DNS-driven analysis of the Flamelet/Progress Variable model assumptions on soot inception, growth, and oxidation in turbulent flames

Modeling suites for Large-Eddy Simulations of soot evolution in turbulent flames include a number of submodels describing the chemistry of soot precursors, particle dynamics, heterogeneous soot chemistry, turbulent mixing, and combustion. To understand the reasons for model failure and to enhance the overall model performance, it is necessary to identify and subsequently improve model components with a leading order effect on the overall error. In this work, errors in soot predictions associated with flamelet-based combustion models are isolated and quantified in a combined a-priori and partial a-posteriori analysis using large-scale Direct Numerical Simulation (DNS) data of a sooting turbulent jet diffusion flame. Gas-phase quantities entering the calculation of the soot source terms and hence coupling the combustion model to the soot model are analyzed in the DNS first. The performance of a Flamelet/Progress Variable model with respect to these quantities is then analyzed a-priori for two DNS cases employing a mixture-averaged transport model and unity Lewis numbers. Then, the soot evolution along Lagrangian trajectories extracted from the DNS is re-computed using rate coefficients directly taken from the DNS and from the flamelet table. In the context of this partial a-posteriori analysis, flamelet-induced errors are also compared to errors induced by the chemical soot model. The soot surface growth and oxidation rate coefficients are reasonably well predicted by the flamelet library. Considerably larger errors in the model-predicted soot mass originate from the tabulated quantities entering the calculation of PAH-based soot growth rates. However, these errors can be reduced to a few percent if the rate is appropriately scaled with the mass fraction of polycyclic aromatic hydrocarbons (PAH). However, this requires the solution of a transport equation for the PAH mass fraction, and modeling the source term in this equation is shown to be challenging. Overall, the largest uncertainties can be attributed to the chemical mechanism for PAH formation and the model for the PAH source term.

Effects of Soret diffusion on turbulent non-premixed H2 jet flames

Recent studies have shown that Soret diffusion (SD), driven by temperature gradients, could play an important role in both laminar and turbulent premixed H2 flames. However, comparatively little effort has been made to investigate SD effects on turbulent non-premixed H2 flames, in spite of the relevance of these flames in safety and their potential application in clean power and propulsion systems. To this end, the impact of SD on turbulent non-premixed H2 combustion is investigated numerically in this work by comparing two three-dimensional direct numerical simulations of temporally evolving turbulent jet flames. In one simulation, a mixture-averaged diffusion (MD) model is used to approximate multicomponent transport, while in the other the MD model is supplemented with a Soret term to consider SD effects. The emphasis is placed on examining and interpreting the impact of SD on flame structure, differential diffusion, and flame-tangential diffusion. It is found that H and OH mass fractions are significantly affected by SD, while SD has a negligible impact on temperature, heat release rate and H2 mass fraction. This is due to the fact that larger SD flux of H radical is strongly coupled with the main chemical reactions. However, for H2 its larger SD flux is located in the fuel-rich zone and decoupled from the main reactions. The difference between a conserved scalar (mixture fraction Z) and a non-conserved scalar (Bilger mixture fraction ZBilger) is employed as a diagnostic parameter to characterize differential diffusion, and the results show that the effects of SD on differential diffusion are reflected in two aspects: (i) increasing the absolute value of Z−ZBilger and (ii) increasing the degree of misalignment between the gradients of Z and ZBilger. Furthermore, the analysis of the contribution of SD to flame-tangential diffusion occurring in mixture fraction isosurfaces indicates that for H radical SD can augment the relative contribution of flame-tangential diffusion, especially in the region of high scalar dissipation rate. On the other hand, for H2, SD has a negligible impact on both flame-normal and flame-tangential diffusion. The present study contributes to providing insights into how SD affects turbulent non-premixed H2 flames and into modeling SD effects with flamelet-based combustion models.

Understanding the diesel-like spray characteristics applying a flamelet-based combustion model and detailed large eddy simulations

This investigation analyses the structure of spray A from engine combustion network (ECN), which is representative of diesel-like sprays, by means of large eddy simulations and an unsteady flamelet progress variable combustion model. A very good agreement between modelled and experimental measurements is obtained for the inert spray that supports further analysis. A parametric variation in oxygen concentration is carried out in order to describe the structure of the flame and how it is modified when mixture reactivity is changed. The most relevant trends for the flame metrics, ignition delay and lift-off length are well-captured by the simulations corroborating the suitability of the model for this type of configuration. Results show that the morphology of the flame is strongly affected by the boundary conditions in terms of the reactive scalar spatial fields and Z–T maps. The filtered instantaneous fields provided by the simulations allow investigation of the structure of the flame at the lift-off length, whose positioning shows low fluctuations, and how it is affected by turbulence. It is evidenced that small ignition kernels appear upstream and detached from the flame that eventually merge with its base in agreement with experimental observations, leading to state that auto-ignition plays a key role as one of the flame stabilization mechanisms of the flame.

A numerical study of the effect of nozzle diameter on diesel combustion ignition and flame stabilization

The role of nozzle diameter on diesel combustion is studied by performing computational fluid dynamics calculations of Spray A and Spray D from the Engine Combustion Network. These are well-characterized single-hole sprays in a quiescent environment chamber with thermodynamic conditions representative of modern diesel engines. First, the inert spray evolution is described with the inclusion of the concept of mixing trajectories and local residence time into the analysis. Such concepts enable the quantification of the mixing rate, showing that it decreases with the increase in nozzle diameter. In a second step, the reacting spray evolution is studied focusing on the local heat release rate distribution during the auto-ignition sequence and the quasi-steady state. The capability of a well-mixed-based and a flamelet-based combustion model to predict diesel combustion is also assessed. On one hand, results show that turbulence–chemistry interaction has a profound effect on the description of the reacting spray evolution. On the other hand, the mixing rate, characterized in terms of the local residence time, drives the main changes introduced by the increase of the nozzle diameter when comparing Spray A and Spray D.

Influence of flow topology and scalar structure on flame-tangential diffusion in turbulent non-premixed combustion

Flamelet-based combustion models have been extensively used in the modeling of turbulent non-premixed combustion due to their notable advantages in reducing computational cost. The classical one-dimensional flamelet equations are derived based on an assumption: flame-normal transport of thermochemical state variables in mixture fraction gradient direction dominates over flame-tangential transport along iso-surfaces of mixture fraction. The motivation of this work is to quantify the contribution of tangential diffusion (TD) and seek the source of TD, since several recent studies have shown that TD effects may play an important role in the regions with large curvature and finite-rate chemistry. In this work, the most probable cause and effect chain that elucidates the source of TD in a turbulent non-premixed jet flame is proposed for the first time from a flow topology perspective. To this end, local flow topology and its effects on scalar structure are first investigated. It is found that the local flow structures with unstable focus compressing (UFC) topology have the highest probability of large compressive strain and that the negative correlation between curvature and strain strongly depends on local flow topology, scalar structure and reaction. Then, the influence of flow topology and scalar structure on the relevance of TD is assessed with the angle between reactive scalars and mixture fraction. The results show that TD effects mainly exist in the regions with high curvatures and low strain rates or scalar dissipation rates. These findings suggest that the local flow structures with low probability of UFC topology tend to cause significant flame-tangential diffusion in the turbulent non-premixed flame.

A systematic approach to high-fidelity modeling and efficient simulation of supercritical fluid mixing and combustion

Advances in fluid-flow modeling and simulation techniques over the past two decades have improved understanding of the intricate flow physics and combustion dynamics in the supercritical regime. However, there remain many numerical issues to be addressed, including turbulence closure modeling, combustion modeling, and the evaluation of real-fluid thermodynamic and transport properties. The challenges can be broadly categorized into two areas: (1) achieving highly accurate simulation through inclusion of all the necessary physics and (2) developing a computationally efficient framework to achieve simulation results in a reasonable turnaround time. This paper investigates these challenges and presents a systematic approach to achieve high-fidelity and efficient simulation of supercritical fluid mixing and combustion using large-eddy simulation (LES) techniques. The unresolved subgrid-scale (SGS) term in the filtered equation of state (EOS), which is generally neglected for ideal gases, becomes significant for real fluids, especially in regions of strong property gradients at supercritical conditions. The relative error for the filtered density can reach up to 40%, and this uncertainty can propagate and contaminate calculations of the conservation equations. Two closure models for the SGS term in the EOS are proposed: a gradient-based and a mixing-based approach. Both approaches reduce the modeling error considerably. Flamelet-based combustion models are also examined at supercritical conditions. The probability density functions (PDFs) for mixture fraction and scalar dissipation rate are evaluated using a data-driven approach. The presumed beta-function distribution accurately describes the PDF of the mixture fraction at low mixture fraction variance, but deviates at high variance (> 0.01). The lognormal distribution can capture the shape of the extracted PDF of the scalar dissipation rate but underestimates the peak value. An alternative combustion model using finite-rate chemistry integrated with dynamic adaptive chemistry and correlated transport is developed, rendering a computationally efficient and affordable framework. The efficiency of evaluating real-fluid thermodynamic and transport properties, a computationally expensive procedure, is dramatically enhanced using tabulation and correlated dynamic evaluation techniques. Finally, suggestions are provided regarding opportunities for future research.

Nonadiabatic Flamelet Formulation for Predicting Wall Heat Transfer in Rocket Engines

A flamelet-based combustion model is proposed for the prediction of wall heat transfer in rocket engines and confined combustion systems. To account for convective heat loss due to the interaction of the flame with the wall, a permeable thermal boundary condition is introduced in the counterflow diffusion flame configuration. The solution of the resulting nonadiabatic flame structure forms a three-dimensional manifold, which is parameterized in terms of mixture fraction, progress variable, and temperature. The performance of the model is first evaluated through a direct numerical simulation analysis of an diffusion flame that is stabilized at an inert isothermal wall. The developed nonadiabatic flamelet model is shown to accurately predict the temperature, chemical composition, and wall heat transfer. Combined with a presumed probability density function closure, the model is then applied to large-eddy simulation of a single-injector rocket combustor to examine effects of heat transfer on the turbulent flame structure in rocket engines.

Computation of Forced Premixed Flames Dynamics

ABSTRACTBluff body stabilized turbulent premixed flames subject to inlet velocity oscillation over a wide range of forcing frequency and amplitude are simulated using a flamelet-based combustion model. Two sets of detailed chemical kinetic schemes are used to model combustion chemistry. It is observed that the computed dynamics of forced flames agree reasonably well with experimental measurements. The flame elongation and shortening at a frequency of 40 Hz and strong flame-vortex interaction at a higher frequency of 160 Hz are captured well in the computations. The global flame describing function extracted from the computational results shows a linear response at 40 Hz and a nonlinear behavior at 160 Hz as observed in the experiments. The nonlinear response is due to vortex roll-up and its subsequent shedding. The quantitative agreement of the computed flame describing function (FDF) with experimental measurement is uniformly good over a wide range of forcing frequency and amplitude. Some influence of chemical kinetics on the FDFs is observed, which mainly stems from the difference in laminar burning velocity and spatial heat release rate distribution.

Incipient thermal choking and stable shock-train formation in the heat-release region of a scramjet combustor. Part II: Large eddy simulations

The flow in the HyShot II scramjet combustor is studied using large eddy simulations (LES). The computations are made feasible by two important modeling ingredients: an equilibrium wall-model and a flamelet-based combustion model. The first objective of the study is to assess the accuracy of this modeling approach through a validation study. Comparisons are made between simulation results and those from shock-tunnel experiments at nominal flow conditions, with favorable agreement. The second objective is to study the flow for increased fuel/air equivalence ratios (ERs). A qualitative change in the flow occurs for ER ≳ 0.39, with the appearance of a seemingly stable combustor shock-train, similar to standard isolator shock-trains, but occurring spatially co-located with the combustion and heat release. This behavior accurately reproduces that seen in an accompanying experimental study. A detailed flow analysis identifies the factors contributing to the stabilization of the shock-train, and estimates are made of its effect on the overall combustor performance.

An efficient flamelet-based combustion model for compressible flows

A combustion model based on a flamelet/progress variable approach for high-speed flows is introduced. In the proposed formulation, the temperature is computed from the transported total energy and tabulated species mass fractions. Only three additional scalar equations need to be solved for the combustion model. Additionally, a flamelet library is used that is computed in a pre-processing step. This approach is very efficient and allows for the use of complex chemical mechanisms. An approximation is also introduced to eliminate costly iterative steps during the temperature calculation. To better account for compressibility effects, the chemical source term of the progress variable is rescaled with the density and temperature. The compressibility corrections are analyzed in an a priori study. The model is also tested in both Reynolds-averaged Navier–Stokes (RANS) and large-eddy simulation (LES) computations of a hydrogen jet in a supersonic transverse flow. Comparison with experimental measurements shows good agreement, particularly for the LES case. It is found that the disagreement between RANS results and experimental data is mostly due to the mixing model deficiencies and the presumed probability density functions used in the RANS formulation. A sensitivity study of the proposed model shows the importance of the compressibility corrections especially for the source term of the progress variable.

Regularization of reaction progress variable for application to flamelet-based combustion models

Many combustion models that are based on the flamelet paradigm employ a reaction progress variable. While such a progress variable is well defined for one-step reaction kinetics, this is typically not the case for complex chemical mechanisms. Consequently, several expressions for a progress variable have been utilized. In this paper a formal method for the generation of a reaction progress variable is proposed that is optimal with respect to a set of constraints. The potential of the method is demonstrated in applications to partially premixed and diffusion flames, and the extension to premixed combustion is discussed. It is shown that the proposed method can lead to significant improvements in the definition of an optimal progress variable over conventional formulations, essentially eliminating the expert knowledge previously required in identifying such quantities.

On the Generation of Direct Combustion Noise in Turbulent Non-Premixed Flames

Generation of combustion noise in an unconfined turbulent non-premixed flame is investigated. For this, a model is developed, combining Lighthill's acoustic analogy with a flamelet-based combustion model to consistently express all thermochemical quantities by a set of reduced scalars. The model is applied in a large-eddy simulation, and the acoustic pressure in the far field is obtained from an integral solution. Three relevant acoustic source terms with different source characteristics and Mach number scaling are identified. The spatial distribution and spectral characteristics of the acoustic sources are analyzed, and it is shown that the acoustic source due to chemical reaction is the main noise contributor, and is located in the upper part of the flame. Contributions from the acoustic sources due to Reynolds stresses and fluctuating mass flux are found to be virtually insignificant at low frequencies. Discrepancies in the prediction of high-frequency sound pressure level in the jet forward direction were analyzed and are attributed to high-frequency acoustic refraction effects due to variations in sound speed. The directivity exhibits a weak directionality in the 30° forward direction, and some phase cancellation between individual acoustic sources is evident.

Assessing the Predictive Capabilities of Combustion LES as Applied to the Sydney Flame Series

Large Eddy Simulation (LES) and flamelet-based combustion models were applied to four bluff-body stabilized nonpremixed and partially premixed flames selected from the Sydney flame series, based on Masri’s bluff-body test rig (University of Sydney). Three related non-reacting flow cases were also investigated to assess the performance of the LES solver. Both un-swirled and swirled cases were studied exhibiting different flow features, such as recirculation, jet precessing and vortex breakdown. Due to various fuel compositions, flow rates and swirl numbers, the combustion characteristics of the flames varied greatly. On six meshes with different blocking structure and mesh sizes, good prediction of flow and scalar fields using LES/flamelet approaches and known fuel and oxidizer mass fluxes was achieved. The accuracy of predictions was strongly influenced by the combustion model used. All flames were calculated using at least two modeling strategies. Starting with calculations of isothermal flow cases, simple single flamelet based calculations were carried out for the corresponding reacting cases. The combustion models were then adjusted to fit the requirements of each flame. For all flame calculations good agreement of the main flow features with the measured data was achieved. For purely nonpremixed flames burning attached to the bluff-body’s outer edge, flamelet modeling including strain rate effects provided good results for the flow field and for most scalars. The prediction of a partially premixed swirl flame could only be achieved by applying a flamelet-based progress variable approach.

Modeling of radiation and nitric oxide formation in turbulent nonpremixed flames using a flamelet/progress variable formulation

A model for the prediction of the nitric oxide (NO) formation in turbulent nonpremixed flames is proposed. Since the NO formation has a strong temperature sensitivity, the accurate prediction of the flame temperature under the consideration of radiative heat losses is required. The first part of the paper addresses the extension of a flamelet-based combustion model to account for radiative heat loss effects by introducing enthalpy as an additional parameter. A transport equation for enthalpy is solved, and the radiative sink term in this equation is obtained from unsteady flamelet solutions. The model is applied to a large-eddy simulation (LES) of Sandia flame D, and the importance of the interaction between turbulence and radiation on temperature and mixture fraction is investigated. Based on the radiative flamelet formulation, a consistent model for the prediction of NO formation is developed in the second part of the paper. In this model, an additional transport equation for the NO mass fraction is solved, and the chemical source term is obtained from a flamelet library. Since the consumption rate is dependent on the NO mass fraction, this term requires modeling, which is discussed in this paper. By employing a scale similarity argument, a closure model for application in LES is presented. After the analysis of the proposed model for the thermal, nitrous oxide, and prompt pathways for NO formation, the NO model is integrated into the extended flamelet/progress variable model and applied in LES of Sandia flame D and a Pratt & Whitney aircraft engine combustor configuration.

COMBUSTION AND HEAT TRANSFER IN COMPARTMENT FIRES

Field modeling that incorporates increasingly complex representations of the physical and chemical processes for compartment fires warrants a detailed evaluation. Detailed quantitative comparisons of our predicted velocity and temperature fields against established the computed results of Lewis, Moss, and Rubini and the experimental data of Steckler, Quintiere, and Rinkinen of a single compartment fire are in good agreement. The prospect of using a flamelet-based combustion model is encouraging. Here, more detailed chemistry can be incorporated, especially that used to predict toxic CO concentrations. This, together with the discrete ordinates radiation method, offers potential in building fire prediction.