1 Introduction. Keywords: explosion protection; PDF method; transient jet ignition; turbulent premixed combustion; REDIM.

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1 Z. Phys. Chem. 2017; 231(10): Simon Fischer*, Detlev Markus, Asghar Ghorbani and Ulrich Maas PDF Simulations of the Ignition of Hydrogen/Air, Ethylene/Air and Propane/Air Mixtures by Hot Transient Jets DOI /zpch Received September 30, 2016; accepted March 7, 2017 Abstract: A numerical investigation is carried out to study ignition events of different premixed stoichiometric fuel/air mixtures by hot exhaust gas jets. The simulations are performed for premixed, stoichiometric hydrogen/air, ethylene/ air and propane/air mixtures in configurations relevant to safety applications. The ignition events of the different fuel/air mixtures by their corresponding exhaust gas jet are examined qualitatively analyzing processes and conditions leading to ignition. A stand-alone probability density function (PDF) method in connection with a projection method (PM) to calculate the mean pressure is used to model the turbulent flow. The transport equation for the joint velocity turbulent frequency scalar PDF is solved by a Monto Carlo/particle method. In order to reduce the computational costs concerning the chemical kinetics the reaction diffusion manifolds (REDIM) technique is used to get an appropriate reduced kinetic scheme. Keywords: explosion protection; PDF method; transient jet ignition; turbulent premixed combustion; REDIM. 1 Introduction In many industrial plants the existence of combustible gases in the ambient atmosphere is inevitable in certain hazardous areas. These may occur as a result of an unplanned event, occasionally in normal operation or from constant activities [1]. Hazardous areas are defined as zones in which a combustible or *Corresponding author: Simon Fischer, Karlsruhe Institute of Technology (KIT), Kaiserstr. 12, Karlsruhe, Germany, simon.fischer@kit.edu Detlev Markus and Asghar Ghorbani: Physikalisch-Technische Bundesanstalt (PTB), Bundesallee 100, Braunschweig, Germany Ulrich Maas: Karlsruhe Institute of Technology (KIT), Kaiserstr. 12, Karlsruhe, Germany

2 1774 S. Fischer et al. explosive atmosphere may be present in quantities such that special precautions and safety procedures need to be taken [1, 2]. They are assessed based on a combination of the probability of a failure event, depending on i.a. frequency and duration of the occurrence of an explosive gas atmosphere, and its severity [1, 2]. Depending on the classification of such areas and the flammable gases several types of protections have been developed. Concerning electrical equipment the basic requirements are described in the IEC [3]. A well-known concept is the flameproof enclosure [4], which encapsulates a potential ignition source. An internal explosion is allowed to take place, although the flameproof enclosure has to withstand the explosion pressure and flame transmission has to be avoided. However, due to unavoidable gaps hot exhaust gas is able to impinge into the outer, eventually combustible atmosphere in form of a hot free jet. Test cases such as the test for non-transmission of an internal ignition, which covers the case of a hot turbulent free jet, are described in [4]. The ignition of a combustible ambient by a hot jet is dominated by the complex interaction of the turbulent flow and chemical reactions. Considering the turbulence intensity of a specific combustible/air mixture a strong dependence on the exit velocity of the jet, which itself is dependent on the pressure ratio of inner pressure and ambient pressure at the gap [5], can be observed. The spatial and temporal evolution of the ignition process is examined experimentally in several studies using optical diagnostics [5 8]. Phillips developed a semi-analytical approach for a thermal ignition model. The model describes the heat transfer within the joint of the entrainment rate into the jet head vortex and the combustion in the jet by a single set of equations [9, 10]. Numerical investigations concerning the minimum jet radius required for ignition by hot jets are discussed in [11, 12]. The influence of the hot jet temperature and the mixing processes between hot and ambient gases is studied experimentally and numerically in [5, 8]. Using a probability density function (PDF) model detailed investigations of the interaction of turbulence and chemical reactions during the ignition are discussed in [13 15]. According to the standard IEC [16], various mixtures of gases and vapors with air are classified into groups regarding to their explosion safety properties. The test gases are classified according to the maximum experimental safe gap (MESG) values. In this work exemplary test gases relevant for ignition by hot turbulent jets resulting from inevitable gaps are examined. The corresponding gases are presented in Table 1. The study is performed numerically using a standalone probability density function model extended by a projection method (PDF- PM) [13, 15] and is based on former studies such as [17 19]. The aim of the current analysis is to investigate qualitatively the conditions and processes leading to ignition. Furthermore, the study assesses the

3 PDF Simulations of the Ignition by Hot Free Jets 1775 Tab. 1: Classification of the test gases according to their MESG. Gas group Combustible MESG in mm [16] IIA Propane 0.92 IIB Ethylene 0.65 IIC Hydrogen 0.29 applicability of the PDF-PM method to capture the qualitative behavior of the different test gases according to their safety group. The results of this study can be used to strengthen the understanding of ignition processes by hot turbulent jets and improve the knowledge of preventing accidental explosions. The article is structured as follows. First the state of the art of numerical approaches to investigate turbulent flows is presented. Subsequently, the PDF-PM method and the applied REDIM model reduction method is discussed. In the further course of the article the framework of the numerical experiments conducted is explained specifying the simulation domain and boundary conditions. Finally, numerical results from free jet flow calculations are presented, using the described PDF-PM/REDIM approach. 2 Methods of turbulent flow modelling state of the art In order to treat turbulent flows numerically different approaches are available [20, 21]. The most direct and simple approach is the direct numerical simulation (DNS) of a turbulent flow [20 22]. Applying DNS, a solution is obtained for a single realization of the flow. The Navier Stokes equations are solved for a timedependent velocity field, while all length and time scales are resolved. Hence, no models regarding closure of turbulence flow modeling are required in DNS, but the computational costs are increasing strongly with the Reynolds number and the size of the domain [20]. That results in a limited applicability of DNS to low-moderate Reynolds number flows and small domains. Other approaches pursue the statistical evolution of the turbulent flow and, hence, are computational less expensive, as e.g. large eddy simulation (LES) or Reynolds-averaged Navier Stokes (RANS). The RANS equations are solved for the mean velocity field, whereas all scales of turbulence are modeled [20]. Hence, all quantities are divided up into mean and fluctuating quantities, which introduces the closure problem of this method [23]. That means not all terms in the equations describing

4 1776 S. Fischer et al. the statistical evolution of the flow can be obtained from the Navier Stokes equations and, hence, need to be modeled. Turbulence models, especially two-equations models (e.g. k-ε model [20]) and Reynolds-stress models [20], are solved together with the RANS equations to provide closure [20, 23 25]. LES is intermediate in terms of required modeling and computational costs between DNS and RANS. In LES the large scale turbulent motions are computed explicitly, smaller scale motions need to be modeled [20]. The velocity is decomposed by a filtering operation into a resolved (filtered) component, representing large scale motions, and a sub-grid scale (residual) component, representing small scale motions [20]. Closure of the standard Navier Stokes equations is achieved by modelling the sub-grid scale (residual) stress tensor occurring in the momentum equation [20]. Most of the turbulent energy is in the large eddies [21], whereas in high Reynolds number turbulent flows the small scales are assumed to be flow-independent ( Kolmogorov hypothesis) and, hence, can be represented by simple models [20, 21], e.g. the Smagorinsky model [26]. Considering reacting flows chemical reactions occur on small scales in statistically transient premixed reactive turbulent flows and, hence, are not resolved directly in the above mentioned RANS and LES method and need to be modeled [21]. According to [21], due to the highly non-linear behavior of chemical reactions the modeling of the chemical source term introduces great difficulties. Probability density function (PDF) methods are related to the RANS equations, as the mean velocity and the Reynolds stresses are the first and second moments of the Eulerian pdf of the velocity. However, PDF methods do not apply time averaging of the flow field. PDF methods are in principle based on solving a modeled transport equation for the velocity-composition joint pdf [20]. They achieve closure at the level of one-point, one-time joint pdfs and the effects of convection and reactions are treated without the need for modeling, as they appear exactly in the transport equation [27, 28]. The method can be particularly well adapted to flows with complex thermochemistry and has been used in the study and simulation of turbulent combustion and turbulent reactive flows for a long time [27, 29, 30]. However, the transport equation for the joint pdf contains unclosed terms. The effects of pressure gradients and mixing processes due to molecular diffusion need to be modeled [15]. 3 Methodology In order to investigate the ignition process numerically a stand-alone probability density function projection method (PDF-PM) technique is used. In turbulent reacting flow modeling, PDF methods have been used for a long time to simulate

5 PDF Simulations of the Ignition by Hot Free Jets 1777 combustion and reactive flows [29]. In turbulent reacting flow modeling, PDF methods achieve closure at the level of one-point, one-time joint PDFs. To simplify chemical kinetics a REaction DIfusion Manifold (REDIM) method is used [31]. Both methods are described in the following. 3.1 PDF-PM approach The PDF-PM method used throughout this study has been developed based on the joint pdf of velocity, turbulent frequency and composition in physical space and time [27, 32]. The modeled pdf transport equation is solved by using a Lagrangian particle method. The flow is represented by an ensemble of notional particles. The evolution of these notional particles is governed by a set of stochastic differential equations. The simplified Langevin model (SLM) [33, 34] is used for the evolution of the particle velocity. For closure of the SLM, the turbulent frequency is modeled by a stochastic differential equation as a particle property [28]. The scalars are evolved by molecular mixing and chemical reactions [21]. Stöllinger and Heinz discussed the strong dependence of the accuracy of PDF methods on the model for micromixing [35]. Molecular mixing is modeled by the Modified Curl mixing model (MC) [36], which is applied as a particle interaction model. The MC model shows good agreement compared to experimental results regarding the jet penetration rate and the spreading rate of transient jets [15]. The same model equations and constants as described in [13] are used. The mean pressure gradient appears exactly in the velocity equation, but a Poisson equation has to be solved in order to obtain the mean pressure gradient. A robust formulation of a projection method (PM) is used to calculate mean pressure. A detailed description and application to low-mach number transient reacting flows of the pressure algorithm is given in [15]. 3.2 Chemical kinetics Numerical methods regarding detailed and accurate models of chemical kinetics in simple configurations as homogeneous reactors or 1D laminar flows are well developed [37]. Even the use of reaction mechanisms consisting of hundreds of species and elementary reactions is possible regarding the numerical costs. Due to the closed chemical source term in the pdf transport equation, in principle a detailed description of the chemical kinetics is possible in PDF methods. However, due to the high dimensionality, the presence of a wide range of time scales and the coupling of molecular diffusion and reaction, detailed simulations

6 1778 S. Fischer et al. are prohibitively expensive for more complex and turbulent flows. Hence, in a more complex, i.e. realistic, configuration and simulation of practical combustion devices, simplified models are necessary, while preserving a desired accuracy [37, 38]. One typical approach to overcome the complexity of the chemical mechanism is the use of reduced chemical models. In order to reduce the number of dependent variables in the simulation, a reduced description of the thermochemical state is applied. Due to the need for taking into account the coupling of chemical reactions and molecular diffusion the REDIM technique is used [31]. A two-dimensional manifold is identified to describe the thermochemical state. The parametrization variables of the manifold are a chemical progress variable and a variable to represent the mixing state of the system consisting of two flows. For the hydrogen/air case the progress variable is represented by the specific mole number of H 2 O, φ, which is defined as w /M, where M H2 is the O H 2 O H 2 O H 2 O molar mass and w is the mass fraction of H H2 O. For the hydrocarbon-fuel/air O 2 cases the progress variable is represented by the specific mole number of CO 2, φ CO2. The state of mixing is represented by the enthalpy, which also accounts for the heat losses due to nozzle walls. Thus the chemical progress variable, φ and H2 O φ CO2 respectively, and the enthalpy are the only additional variables that have to be solved in the simulations of reactive turbulent flows. All thermochemical information is stored in a two-dimensional look-up table, where all chemical compositions, the temperature and other variables are a function of the chemical progress variable and enthalpy. This look-up table, i.e. the REDIM, is generated in a pre-processing step, which is explained in the further course of this chapter. During the PDF calculation the thermochemical state is updated by retrieving the required data from the REDIM look-up table correspondingly to the given dependent variables (φ or φ H2 and the enthalpy) [39]. In the current study differential O CO 2 diffusion and non-unity Lewis number effects are neglected, however, it is possible to extend the REDIM concept to systems with non-equal diffusivities [39]. The following section discusses the determination of the REDIM in detail. The REDIM is obtained by the integration of the REDIM evolution equation, which is an evolution equation of the thermochemical state [31]. For solving the evolution equation initial conditions, namely an initial guess of the manifold (initial manifold) and estimated gradients of the solution variable, are needed. The initial conditions can be derived from local structures of the problem [40]. These local structures can be modeled in simplified terms using detailed kinetics and one-dimensional scenarios. To determine a preferable realistic scenario to deduce flamelets, from which the initial guess and estimation of gradients can be derived from, the entry of hot exhaust gas jet into the combustible ambient is considered. In Figure 1 the exiting of hot, burnt exhaust gas into a combustible ambient and the resulting mixing process is illustrated.

7 PDF Simulations of the Ignition by Hot Free Jets 1779 Fuel+O 2 Φ = 1 Products (H 2 O, CO 2, OH, H,...) reactive mixture, fuel-air T u, p u, Φ u T b, w i H 2 O+CO 2 +OH+O+... T J, w i,j, p u Fig. 1: Stoichiometric (Φ = 1) combustion in a chamber (1) leading to hot, burnt exhaust gas (with temperature T b and mass fractions w i ), which exits the chamber through a nozzle (2) into combustible ambient as a hot free jet (with jet temperature T J and mass fractions w i,j at atmospheric pressure p u ) and mixing with ambient combustible fuel-air mixture (3). Based on the experiments described in [5, 8] a combustion takes place in a chamber (marked by the number 1 in Figure 1), where the same stoichiometric fuel-air mixture is present as is in the combustible ambient outside the chamber. Due to an increase in pressure, exhaust gas is forced to exit the chamber through the nozzle (number 2 in Figure 1). On its way through the nozzle the exhaust gas cools down before entering the combustible fuel-air ambient as a turbulent free jet (number 3 in Figure 1) [5]. Due to shear generated turbulence combustible ambient mixes with the hot exhaust gas jet, which, depending on flow conditions, may lead to ignition. In this study conditions and processes leading to ignition due to hot, turbulent free jets is investigated. Hence, a turbulent reactive jet is under consideration. The numerical model needs to capture both, the turbulent flow and the chemical reactions, due to the ignition processes under consideration, of the jet. The domain of the jet simulation will only cover the jet itself, i.e. number 3 in Figure 1. At that, the treatment of the flow is covered by the above described PDF-PM model. Regarding the chemical kinetics, the REDIM technique is used. The REDIM is obtained by taking a closer look into the interaction of the burnt exhaust gas of the jet with the fresh, unburnt gas of the ambient. The local flow conditions, i.e. the turbulent mixing processes, can be captured by a counterflow flame setup using the states of pure exhaust gas and pure combustible ambient as boundary conditions [41]. Note, the counterflow setup is used to derive the initial guess of the manifold and the gradient estimates needed to solve the REDIM evolution equation only. While in principle any initial guess could be used to initialize the evolution equation, for non-premixed turbulent flames non-premixed scenarios are more suitable regarding the gradient estimation.

8 1780 S. Fischer et al. The sensitivity of the REDIM itself on the estimated gradients is small since a two-dimensional REDIM is used to generate the look-up table for the PDF calculations [31]. In order to solve the evolution equation of a REDIM concerning the turbulent jet, the following steps are performed to get the initial conditions, i.e. initial manifold and estimated gradients: laminar flat flame calculation in order to get the state of the exhaust gas in the chamber simulation of the cooling of the exhaust gas in the nozzle via a homogeneous reactor calculation in order to get the state of the exhaust gas at the exit of the nozzle or rather at the entry of the jet into the ambient counterflow flamelets to approximate the mixing processes of the free jet with the ambient in order to construct the initial manifold and derive the needed gradients from. In the following the single steps are described in more detail. Starting from the counterflow setup, due to the lack of information about the state of the exhaust gas at the nozzle exit, then the other two scenarios are embedded in the context of getting the state of the exhaust gas at the nozzle exit. R microscopic view: approximation by 1-D counterflow configuration burnt gas - fuel-air fuel-air burnt gas fuel-air T v u v=0 v u Fig. 2: The flow conditions leading to mixing of burnt, hot exhaust gas and combustible ambient gas can locally be approached by counterflow setups. Only the rectangle is considered and the boundary conditions are set to the states of exhaust gas and combustible ambient, respectively. R

9 PDF Simulations of the Ignition by Hot Free Jets 1781 The counterflow setup is shown in Figure 2. Only the illustrated rectangle is considered in the detailed calculations of the counterflow setup (upper left und lower right picture). At the left boundary, which represents the centerline of the free jet, burnt, hot exhaust gas is present, forming a local ignition kernel, and symmetry conditions (v = 0 m/s, Neumann boundary condition for temperature and mass fractions) are applied. From the right boundary fresh, combustible gas at ambient temperature is flowing into the domain. The ignition kernel of hot exhaust gas mixes with the combustible ambient and may lead to an ignition. The counterflow scenario is perturbed by applied strain. The higher the strain rate a is chosen the more the flame is perturbed by transport processes and its structure changes. Reaching a critical strain rate, the cold combustible ambient dominates and the hot exhaust gas ignition kernel is extinguished without leading to ignition. For the counterflow calculations the strain rate is chosen so that ignition can take place. Depending on the fuel considered, a is in the range of 90 1/s. At the right boundary in the counterflow setup, the state of the combustible ambient is set to the stoichiometric fuel-air mixture at ambient temperature of the respective fuel. The left boundary in the counterflow setup represents the hot exhaust gas of the free jet. The state of the burnt hot exhaust gas is not recorded exactly in [5], therefore it is approximated by calculating the states after the combustion in the chamber and after the cooling down in the nozzle according to the experiments [8]. The combustion of fuel-oxidizer in the chamber, which is illustrated by the number 1 in Figure 1, is captured by a laminar flat flame scenario. Note that the enthalpy of the gases remains constant in a laminar flat flame setup. The obtained exhaust gas (adiabatic flame temperature and equilibrium composition) is able to exit the chamber via a nozzle (number 2 in Figure 1), which causes the exhaust gas to cool down. The cooling is captured in a homogeneous reactor calculation, in which the exhaust gas is forced to cool down from adiabatic flame temperature to a specific temperature. The cool-down time and the target temperature are estimated corresponding to the experiments [5] and are set to t = 1 ms and T = 1400 K. The composition of the burnt hot exhaust gas in the counterflow setup is set to the cooled exhaust gas of the respective homogeneous reactor calculation with nearly equilibrium composition according to the set cool-down temperature. Due to the cooling the exhaust gas enthalpy is lower than the enthalpy of the fresh, unburnt combustible ambient. Thus, regarding the counterflow calculations the enthalpy can be interpreted as mixing variable. In Figure 3 the time-dependent development of counterflow flamelets is shown for an ignition event, with the mixing line representing the initial solution. Here the specific mole number of CO 2 represents the reaction progress variable. The state of the exhaust gas is represented by the upper left end of the mixing line, whereas the lower right end of the mixing line

10 1782 S. Fischer et al. φ Fig. 3: Exemplary counterflow flamelets of an ignition event of cooled, burnt hot exhaust gas and combustible ambient in a two-dimensional projection of h-φ CO2 -state space. The state of the exhaust gas is represented by the upper left end of the mixing line, the state of the combustible ambient by the lower right end of the mixing line. represents the fresh combustible ambient. The flamelets are shown in the h-φ CO2 - projection of the state space and the ignition event is highlighted via dotted lines. The thermochemical state space, accessible for the counterflow flame, is limited by the mixing line, on which no chemical reactions take place, and the stationary solution of the specific counterflow setup. The accessible thermochemical states in-between are defined by the flamelets developing in time. The flame profiles can be combined to a discretized initial manifold and the needed gradients can be estimated by means of the flamelets. For the REDIM the initial conditions are derived from such counterflow setups and the REDIM evolution equation now can be solved. Compressibility can be neglected for the ignition of hot exhaust gas free jet. Hence, a constant thermodynamic pressure of 1 bar is applied according to the experiment [8, 42]. Besides the assumption of ideal gases, heat flux due to heat radiation is neglected. Equal diffusivity of all species and Lewis number Le = 1 assumption is applied. It depends on the considered case, if this assumption is satisfied well or if the detailed description of molecular transport is needed [43]. According to [44], the assumption of simplified molecular transport at high Reynolds number flows may be reasonable.

11 PDF Simulations of the Ignition by Hot Free Jets 1783 Three detailed mechanisms have been used for the REDIM calculations. The mechanism for hydrogen consists of nine species and 38 elementary reactions [37], the skeletal mechanism for ethylene consists of 32 species and 206 elementary reactions [45] and the mechanism for propane consists of 63 species and 487 elementary reactions [46]. The REDIM calculation, including all detailed calculations, are performed using the programs HOMREA and INSFLA [47]. 4 Computational setup For the simulations a round jet of hot exhaust gas is considered, which enters the combustible ambient with a statistically stationary flow rate at the nozzle exit. For nozzle diameter D J values in a range of 0.6 mm to 3.0 mm are considered. The simulations are performed using a 2D axisymmetric cylindrical coordinate system. The computational domain is rectangular and extends to 23 D J along the radial direction and up to 233 D J along the axial direction. It is discretized by a non-uniform grid with cells and a nominal number of 320 particles per cell. Neither a higher resolution of the domain nor a higher number of particles per cell has shown a considerable improvement regarding the results [13]. A schematic sketch of the computational domain is illustrated in Figure 4. At the inlet the PDF of the joint velocity is assumed to have a normal distribution. The mean values and fluctuations are defined based on the assumption of a fully developed turbulent pipe flow condition of the jet at the nozzle exit. The radial profile of the mean stream wise velocity is obtained using a power law formulation, r fresh premixed fuel/air U e 23D J hot exhaust gas Nozzle fresh premixed fuel/air U e UJ x D J up to 233 D J Fig. 4: Schematic sketch of the computational domain.

12 1784 S. Fischer et al. 2r α U = U 1 J D J 1 (1) where U J is the mean jet velocity at the centerline of the nozzle exit and α is a constant. According to [48] α is set to 7. The mean jet velocity is in the range of U J = 50 to 300 m/s throughout this study. Note that this is well below the speed of sound for the respective mixtures. The flow in the domain consists of a fresh stoichiometric premixed fuel/air mixture with a velocity in the range of U e = 0.03 to 0.1 U J. The rms fluctuation of velocity components and the Reynolds stresses are adapted using profiles of fully developed pipe flow conditions. At the inlet the turbulent frequency is described by a gamma distribution as explained in [28]. Further details concerning the calculation of the fluctuations can be found in [13]. In the experimental measurements a strong cooling down of the exhaust gas due to the nozzle wall is observed [5]. Hence, the emitted exhaust gas has a lower temperature than the adiabatic temperature of the considered fuel. The jet temperature therefore is varied in the range of T J = 1400 to 1550 K. The composition of the jet inlet is set to the exhaust gas of the respective stoichiometric mixture with nearly equilibrium composition according to T J. The co-flow temperature of the fresh gas is set to a temperature of 300 K. The composition and the density at the inlet are set to be uniform. The thermodynamic pressure is assumed to be 1 bar. Symmetry conditions are applied at the centerline and a slip boundary condition is assumed at the side wall. The pressure at the outlet is assumed to be uniform. 5 Results and discussion In this section numerical results from free jet flow calculations are presented, using the PDF-PM/REDIM approach described above. The purpose of this study is to investigate the qualitative behavior of the different fuels in order to get an overall perception of the processes leading to ignition. A qualitative comparison of the fuel/air mixtures of hydrogen, ethylene and propane according to the gas groups IIA, IIB and IIC is shown in this section. First, results from detailed numerical simulations are shown to give a brief overview of the different behavior of the fuels hydrogen, ethylene and propane and, furthermore validate the numerical tools used for the chemical kinetics in this study. The mechanisms used throughout this study have been validated in many studies before [45 47, 49]. Nevertheless, to exemplarily test and validate the software used for the calculations of chemical kinetics, ignition delay times of ethylene are compared to experimental [50 52] and numerical data in the temperature

13 PDF Simulations of the Ignition by Hot Free Jets 1785 range of T = 1000 K to T = 2000 K at atmospheric pressure. Moreover, the skeletal mechanism for ethylene [45], which is used in this study, is tested against a detailed ethylene mechanism by Wang and Laskin [53]. The calculation is performed using the program HOMREA [47], which is also used for obtaining the description of the reduced chemical state. Both other fuels used in this study, hydrogen and propane, have been applied using HOMREA and the PDF-PM/ REDIM approach in many studies before, e.g. [18, 47, 49], which is why they are not shown here. Figure 5 shows ignition delay times normalized by oxygen concentration for stoichiometric ethylene/air mixtures as dashed line. The result shows excellent agreement to the numerical results obtained from a group led by Prof. Thévenin using the DINOSOARS software [54] as solid line and from the detailed mechanism using HOMREA as dash-dotted line at atmospheric pressure. The ignition delay times measured experimentally (symbols) show very good agreement as well. The slight differences seen in the data are attributed to the pressure effect, since the experimental data are obtained at different pressure levels. A comparison of all three fuels used throughout this study regarding the adiabatic laminar flat flame speed is illustrated in Figure 6. The numerical data is obtained from the software 10-2 τ ign x [O 2 ] 0 in ms*mol/cm K/T Fig. 5: Ignition delay times for stoichiometric ethylene/air mixtures normalized by initial oxygen concentration. Numerical results at atmospheric pressure: HOMREA [47] with detailed mechanism [53] as dash-dotted line; HOMREA with skeletal mechanism [45] as dashed line; DINOSOARS [54] with the skeletal mechanism as solid line. Experimental results by Baker and Skinner [50] at p = 3 atm as crosses; Jachimowski [51] at p = atm as triangles; Kumar [52] at p = bar as squares.

14 1786 S. Fischer et al ν L in m/s Φ Fig. 6: Sensitivity of the adiabatic laminar flat flame velocities on the equivalence ratio Φ for hydrogen: numerically as dash-dotted line and experimentally as triangles [55, 56]; ethylene: numerically as dashed line and experimentally as diamonds [57]; propane: numerically as solid line and experimentally as circles [58]. INSFLA [47], which is also used to derive the initial conditions for the REDIM integration. The results are analyzed against experimental data [55 58] shown as symbols. The numerical data for laminar flat flame velocities is determined by the flow speed of the unburnt gas in a laminar flat flame configuration in steady state. These show very good agreement to the data measured experimentally in all three cases. Figure 6 allows a comparison of adiabatic burning velocities of hydrogen as dash-dotted line, ethylene as dashed line and propane as solid line. The adiabatic flame velocity of hydrogen is clearly faster than the flame velocity of the other fuels. The maximum flame speed of propane is like that of the most hydrocarbons at around v L = 50 cm/s [37], whereas the flame speed of ethylene is in between that of propane and hydrogen. Regarding the curve characteristics in terms of the position of the maximum burning velocity, ethylene and propane behave very similar, as the maximum is reached at a slightly rich fuel/air mixture at an equivalence ratio of about Φ = 1.1. Hydrogen behaves differently, as the maximum flame speed is reached at a rich mixture at Φ = 1.8. Even at stoichiometric equivalence ratio the adiabatic flame velocity of hydrogen is clearly faster than the other fuels. In the following section simulation results using the PDF-PM/REDIM approach are presented with the aim of having an overall perception concerning the qualitative behavior of the fuels. As with any comparison, an optimal approach would be to use exact same parameters and initial conditions in all calculations. However, for simulations with a meaningful result it is difficult to implement exact same conditions regarding burnt exhaust gas temperature,

15 PDF Simulations of the Ignition by Hot Free Jets 1787 mean velocity and nozzle diameter. If a typical configuration results in an ignition for one combustible, it might not lead to an ignition for the other combustibles. Due to different chemical time scales and scalar mixing time scales during the penetration of the jet into the ambient [17], the combustibles behave differently regarding re-ignition, ignition delay times and location of the ignition. Hence, the conditions and initial conditions slightly differ in each case. Yet, it is very useful to see qualitatively the different behavior of the fuels. Figure 7 shows contour plots for mean temperature shortly after initiating ignition of each fuel. To approximate and illustrate the boundaries of the hot exhaust gas jet contour levels of mean mixture fraction are shown. For mixture fractions values between ξ = 0 (pure stoichiometric combustible/air ambient) to ξ = 1 (pure hot exhaust gas) are possible. Figure 7a shows the numerical results of hydrogen, Figure 7b for ethylene and Figure 7c for propane case. Concerning the initial conditions and parameters the three cases are listed below: hydrogen: T J = 1500 K; U J = 300 m/s; D J = 1.0 mm ethylene: T J = 1550 K; U J = 100 m/s; D J = 1.5 mm propane: T J = 1550 K; U J = 50 m/s; D J = 1.5 mm Despite different initial conditions the qualitative behavior of the different fuels can be observed very well. The conditions of the hydrogen case regarding jet temperature, nozzle diameter and outlet velocity, which influences shear stresses and, subsequently, turbulent mixing [13], are the most difficult considering ignition. Nevertheless, the time needed to initiate ignition (ignition delay time) observed in this very case is of order of magnitude lower than in ethylene case and of two orders of magnitude lower than in propane case, respectively. The ignition delay time in the ethylene case is of order of magnitude lower compared to the propane case, despite the slightly favorable conditions, i.e. lower jet exiting velocity, in propane case. The dependence of the ignition delay time on the nozzle diameter results from the influence of shear generated turbulence, i.e. turbulent mixing, on the hot core region of the jet [13]. Figure 8 illustrates ignition delay times over nozzle diameters for hydrogen, ethylene and propane case, respectively. As stated above it is difficult to implement exact same conditions for the three considered fuels. Regarding the hydrogen case, nozzle diameters from D J = 0.6 up to D J = 1.0 mm are applied to a jet with a temperature of T J = 1400 K and a jet exiting velocity of U J = 300 m/s in Figure 8a. Figure 8b shows ignition delay times for ethylene case with boundary conditions of T J = 1450 K, U J = 100 m/s and nozzle diameters from D J = 0.6 up to D J = 2.0 mm. In propane case ignition delay times are shown in Figure 8c for T J = 1450 K, U J = 50 m/s and nozzle diameters from D J = 1.0 up to D J = 3.0 mm. Considering propane no ignition is observed neither for

16 1788 S. Fischer et al. Fig. 7: Contour plot of mean temperature shortly after initiating ignition. (a) Simulation result for hydrogen case: T J = 1500 K, U J = 300 m/s, D J = 1.0 mm. (b) Simulation results for ethylene case: T J = 1550 K, U J = 100 m/s, D J = 1.5 mm. (c) Simulation result for propane case: T J = 1550 K, U J = 50 m/s, D J = 1.5 mm. jet temperatures of T J = 1400 K, nor for jet exit velocities of U J = 100 m/s and jet temperatures of T J = 1450 K. In ethylene case no ignition is observed for jet exit velocities of U J = 300 m/s, whereas in hydrogen case ignition cannot be detected

17 PDF Simulations of the Ignition by Hot Free Jets a) hydrogen case T J = 1400K; U J = 300m/s τ ign in ms 1 no ignition D J in mm τ ign in ms no ignition b) ethylene case T J = 1450K; U J = 100m/s D J in mm τ ign in ms no ignition c) propane case T J = 1450K; U J = 50m/s D J in mm Fig. 8: Sensitivity of ignition delay times on nozzle diameter. (a) Numerical result for hydrogen case: T J = 1400 K, U J = 300 m/s. (b) Numerical results for ethylene case: T J = 1450 K; U J = 100 m/s. (c) Numerical result for propane case: T J = 1450 K; U J = 50 m/s.

18 1790 S. Fischer et al. for jet temperatures of T J = 1450 K, since ignition happens directly at the exit of the nozzle. Hence, exemplary initial conditions are chosen for the considered fuels, which clearly pre-classify the fuels, as for propane the most favorable conditions are applied (highest jet exit temperature and lowest exit velocity, i.e. lowest impact of turbulence), whereas for hydrogen the most unfavorable conditions are used. Nevertheless, the ignition delay times still show a significant difference in values for the fuels among themselves. In all cases the ignition delay times increase due to a decrease of the nozzle diameter. The impact of the shear generated turbulence on the hot core region is higher in jets exiting from smaller nozzles. In the considered cases with the given boundary conditions no ignition is observed at the smallest nozzle diameter specified above, which is illustrated by the dashed line in Figure 8a c. As shown in Figure 7 before the ignition delay times of each fuel likewise differ significantly from each other despite the slightly favorable conditions in hydrogen and ethylene cases compared to ethylene/ propane and propane cases, respectively. Since the ignition delay times of hydrogen, ethylene and propane are observed to differ significantly the question arises if the processes leading to ignition are the same for all combustibles. The ignition process of turbulent jets is governed by an interaction of turbulent mixing and chemical reaction. Hence, to investigate such processes the competing rates of reaction and mixing are compared [17]. Turbulence frequency is chosen as an indicator for mixing time scales, as turbulence enhances diffusion processes by turbulent mixing. High values of turbulence frequency indicate fast micromixing. In this study the micromixing time scale is represented by the mean scalar mixing frequency. According to the mixing model the turbulence frequency converts into scalar mixing frequency by a ratio defined as C φ. Throughout this study C φ is chosen to be 2.0 [13]. Chemical time scales are defined as the inverse of the time that it takes for a fluid element with a certain mixture fraction to ignite and reach a certain state that is considered burnt. This time scale is of great interest, as fluid elements with small mixture fractions are not able to reach burnt states due to chemical reactions only within the relevant time scales of explosion, e.g. ignition delay times. Hence, compositions with smaller mixture fractions in the state space will only be available at the relevant time scales due to burnt fluid elements mixing with unburnt fluid elements leading to a combustible mixture, which burns due to chemical reactions [59]. Ignition is possible only, if fluid elements with higher temperatures from burnt states mix with fresh unburnt gas. Therefore, the time that it takes for such burnt fluid elements to be present is crucial. Due to a strong dependence on initial states, the chemical time scales are represented by their maximum values only [59]. By comparing the two time scales, the competition of turbulent mixing and chemical reactions can be illustrated. The progress of

19 PDF Simulations of the Ignition by Hot Free Jets 1791 mean temperature indicates the competition of heat release due to chemical reaction and heat dissipation due to scalar dissipation. From mean temperature can be deduced at which regions global ignition is suppressed and where global ignition takes place due to chemical reactions are superior compared to mixing processes. Figure 9 compares mean scalar mixing frequency (solid line) and mean temperature (dashed line) along the centerline axis after initiating ignition. The initial conditions are as follows: hydrogen: T J = 1400 K; U J = 300 m/s; D J = 1.0 mm ethylene: T J = 1550 K; U J = 100 m/s; D J = 1.5 mm propane: T J = 1550 K; U J = 50 m/s; D J = 1.5 mm In the hydrogen case the graphs are displayed after t = 3 ms in Figure 9a. Ethylene is shown in Figure 9b after t = 6 ms and propane is illustrated after t = 17 ms in Figure 9c. The dotted line indicates the maximum chemical rate regarding the considered fuel. In all cases a strong turbulence frequency can be observed close to the nozzle. The mean temperature at the centerline holds its initial temperature until the mixing process impacts the core region of the exhaust gas jet. Consequently, the mean temperature decreases due to mixing of the hot jet with cold ambient gas. Close to the nozzle the mixing, i.e. scalar dissipation rate, is so high that heat release due to chemical reaction is not able to compensate for heat dissipation and ignition is suppressed. Mixing prevents ignition in this region. In the location at which ignition occurs, a much reduced turbulence frequency is observed. As in Figure 9a c only mean values are shown, there are still volume elements at high temperature available. Hence, these volume elements are able to start ignition as the jet is elongated less. The increase in mean temperature coincides where the time scales of mixing frequency and chemical reaction happen to be in the same range. The reaction rate (heat release) is then able to overcome the heat dissipation leading to ignition and, hence, to a rise in global temperature. In order to observe global ignition one requirement for all three combustibles is that time scales of mixing and chemical reactions need to be in the same range [18, 19]. This can be seen in Figure 9a c independently of the combustible used. Hence, all combustibles under study show a strong dependence on the interaction of turbulence and reaction. Due to the fact that the mixing frequency needs to decrease to the scale of the chemical reaction rate of the considered fuel, the value of the reaction rate influences ignition. The time at which ignition is able to take place is dependent on the fuel specific chemical reaction rate. For hydrogen, the combustible with the highest reaction rate, the fastest ignition delay time is observed, despite applying the highest turbulence. Propane, the fuel with the lowest chemical reaction rate,

20 1792 S. Fischer et al. mixing frequency and max. chemical rate in 1/s mixing frequency and max. chemical rate in 1/s a) x/d J b) x/d J T in K T in K mixing frequency and max. chemical rate in 1/s x/d J c) T in K Fig. 9: Scalar mixing frequency (solid line), mean temperature (dashed line) and maximum chemical rate (dotted line) along the centerline axis shortly after global ignition for (a) hydrogen at t = 3 ms: T J = 1400 K, U J = 300 m/s, D J = 1.0 mm, (b) ethylene at t = 6 ms: T J = 1550 K, U J = 100 m/s, D J = 1.5 mm and (c) propane at t = 17 ms: T J = 1550 K, U J = 50 m/s, D J = 1.5 mm.

21 PDF Simulations of the Ignition by Hot Free Jets 1793 yields the slowest ignition delay time while applying the most favorable conditions for ignition of all fuels under study. Cleary the chemical reaction rate and its interaction with turbulence frequency is an indicator regarding the ignition processes and delay times. 6 Conclusions In this work the initiation of ignition events in a premixed fuel/air mixture caused by a hot exhaust gas jet resulting from a combustion of the very same fuel/air mixture is investigated numerically by means of a PDF-PM/REDIM method. The qualitative behavior of different fuels is studied in order to get an overall perception of the processes leading to ignition. The simulations are performed for exemplary test gases according to safety engineering relevant explosion safety gas groups IIA (propane), IIB (ethylene) and IIC (hydrogen). The PDF-PM/REDIM model is able to qualitatively assess the different ignition properties of the combustibles. In all cases the ignition appears first at the jet head [17] and at locations where turbulence frequency and chemical reaction rate are in the same range. A qualitative classification of the fuels is possible by means of the method. To get meaningful results the calculations are performed using slightly different initial conditions. If a typical configuration results in an ignition for one fuels, it might not lead to ignition for the other combustibles. Using propane/air mixtures no ignition was observed neither at a jet temperature of T J = 1400 K nor at exiting velocities of U J = 100 m/s and higher jet temperatures. In ethylene case no ignition was observed using jet exiting velocities of U J = 300 m/s at any jet temperatures. Because of that the combustibles are already classifiable. The model further is able to distinguish the combustible by different ignition delay times. Typical ignition delay times are shown to differ significantly from each other. However, it is not possible to quantitatively compare the results regarding e.g. the maximum experimental safe gaps (MESG) of the fuels without undergoing a great number of parameter studies. For that more information about the fuel/air mixture prior to a combustion leading to jetting of exhaust gases, and detailed parameters of the jet, like e.g. the mean exit velocity, mean exit temperature, turbulent kinetic energy and turbulent fluctuation, are necessary. The influence of walls on the jet, the validity of the symmetry condition etc., need to be verified by the means of experimental data as well. Hence, more accurate information on the setup, boundary conditions and inlet data from experimental measurement is required. Moreover, more experimental data on transient reacting jet flows is needed to validate the model.

22 1794 S. Fischer et al. Acknowledgements: This work was supported by the Deutsche Forschungsgemeinschaft within the Research Group FOR The authors gratefully acknowledge the support of DLR-Institute of Combustion Technology (Stuttgart) for providing access to the detailed description of the propane mechanism. References 1. A. W. Cox, F. P. Lees, M. L. Ang, Classification of Hazardeous Locations, 6th ed., Institution of Chemical Engineers, Warwickshire, UK (2000). 2. G. Bottrill, D. Cheyne, C. Vijayaraghavan, Practical Electrical Equipment and Installations in Hazardous Areas, Newnes, London (2005). 3. IEC , Explosive Atmospheres Part 0: Equipment General Requirements (2011). 4. IEC , Explosive Atmospheres Part 1: Equipment Protection by Flameproof Enclosures d (2014). 5. R. Sadanandan, Ignition by hot Gas Jets A detailed Investigation using 2D time resolved Laser Techniques and numerical Simulations, Phd. thesis, University of Karlsruhe, Karlsruhe (2007). 6. M. Beyer, Über den Zünddurchschlag explodierender Gasgemische an Gehäusen der Zündschutzart Druckfeste Kapselung, Phd. thesis, University of Braunschweig, Braunschweig (1996). 7. Ø. Larson, R. Eckhoff, J. Loss Prev. Proc. Industr. 13 (2000) R. Sadanandan, D. Markus, R. Schiessl, U. Maas, J. Olofsson, H. Seyfried, M. Richter, M. Aldén, Proc. Combust. Inst. 31 (2007) H. Phillips, Combust. Flame 7, (1963) H. Phillips, Combust. Flame 20, (1973) J. Carpio, I. Iglesias, M. Vera, A. Sánchez, A. Liñán, Int. J. Hydrog. Energ. 38, (2013) J. Carpio, I. Iglesias, M. Vera, A. Sánchez, Int. J. Hydrog. Energ. 42 (2017) A. Ghorbani, G. Steinhilber, D. Markus, U. Maas, Combust. Sci. Technol. 186 (2014) A. Ghorbani, D. Markus, G. Steinhilber, U. Maas, J. Loss Prevent. Proc. Ind. 36 (2015) A. Ghorbani, G. Steinhilber, D. Markus, U. Maas, Combust. Theor. Model. 19 (2015) IEC , Explosive Atmospheres Part 20-1: Test Methods and Data Classification of Mixtures of Gases or Vapours with Air (2010). 17. A. Ghorbani, G. Steinhilber, D. Markus, U. Maas, Proc. Combust. Inst. 35 (2015) A. Ghorbani, S. Fischer, G. Steinhilber, D. Markus, U. Maas, Numerical Investigation and Comparison of Hydrogen/Air and Propane/Air Explosion by Hot Jets, in Proceedings of the 25th International Colloquium on the Dynamics of Explosions and Reactive Systems, paper 306 (2015). 19. S. Fischer, D. Markus, U. Maas, Numerical Investigation of the Ignition of Diethyl Ether/Air and Propane/Air Mixtures by Hot Jets, Proceedings of the 11th International Symposium on Hazards, Prevention and Mitigation of Industrial Explosions, ISH140 (2016). 20. S. B. Pope, Turbulent Flows, Cambridge University Press, New York (2000). 21. R. Fox, Computational Models for Turbulent Reacting Flows, Cambridge University Press, New York (2003). 22. S. A. Orszag, G. S. Patterson Jr., Phys. Rev. Lett. 28 (1972) 76.