Numerical simulation and validation of flame acceleration and DDT in hydrogen air mixtures

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Numerical simulation and validation of flame acceleration and DDT in hydrogen air mixtures Aditya Karanam*, Pavan K. Sharma, Sunil Ganju Reactor Safety Division, BARC, Mumbai, India

article info

abstract

Article history:

Combustion of hydrogen can take place in different modes such as laminar flames, slow

Received 2 April 2018

and fast deflagrations and detonations. As these modes have widely varying propagation

Received in revised form

mechanisms, modeling the transition from one to the other presents a challenging task.

13 July 2018

This involves implementation of different sub-models and methods for turbulence-

Accepted 17 July 2018

chemistry interaction, flame acceleration and shock propagation. In the present work, a

Available online xxx

unified numerical framework based on OpenFOAM has been evolved to simulate such phenomena with a specific emphasis on the Deflagration to Detonation Transition (DDT) in

Keywords:

hydrogen-air mixtures. The approach is primarily based on the transport equation for the

Flame acceleration

reaction progress variable. Different sub-models have been implemented to capture tur-

Deflagration to detonation

bulence chemistry interaction and heat release due to autoignition. The choice of sub-

transition

models has been decided based on its applicability to lean hydrogen mixtures at high

Numerical simulation

pressures and is relevant in the context of the present study. Simulations have been car-

OpenFOAM

ried out in a two dimensional rectangular channel based on the GraVent experimental

Hydrogen safety

facility. Numerical results obtained from the simulations have been validated with the experimental data. Specific focus has been placed on identifying the flame propagation mechanisms in smooth and obstructed channels with stratified initial distribution. In a smooth channel with stratified distribution, it is observed that the flame surface area increases along the propagation direction, thereby enhancing the energy release rate and is identified to be the key parameter leading to strong flame acceleration. When obstacles are introduced, the increase in burning rate due to turbulence induced by the obstacles is partly negated by the hindrance to the unburned gases feeding the flame. The net effect of these competing factors leads to higher flame acceleration and propagation mechanism is identified to be in the fast deflagration regime. Further analysis shows that several pressure pulses and shock complexes are formed in the obstacle section. The ensuing decoupled shock-flame interaction augments the flame speed until the flame coalesces with a strong shock ahead of it and propagates as a single unit. At this point, a sharp increase in propagation speed is observed thus completing the DDT process. Subsequent propagation takes place at a uniform speed into the unburned mixture. © 2018 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.

* Corresponding author. Reactor Safety Division (RSD), Bhabha Atomic Research Centre (BARC), Room-422, Hall-7, Bhabha Atomic Research Centre (BARC), Trombay, Mumbai, 400 085, India. E-mail addresses: [email protected] (A. Karanam), [email protected] (P.K. Sharma), [email protected] (S. Ganju). https://doi.org/10.1016/j.ijhydene.2018.07.108 0360-3199/© 2018 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article in press as: Karanam A, et al., Numerical simulation and validation of flame acceleration and DDT in hydrogen air mixtures, International Journal of Hydrogen Energy (2018), https://doi.org/10.1016/j.ijhydene.2018.07.108

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ru > 3:75 rb

Introduction

s¼

Management of hydrogen in nuclear reactors during severe accidents is very important and research in this area has attracted renewed interest. During severe accidents, hydrogen can be produced in the nuclear reactor core, primarily due to the reaction between heated zirconium present in the fuel rods and steam [1]. Hydrogen generated in the core will be released into the surrounding containment structure. Hydrogen is a highly combustible gas and has minimum ignition energies of the order of 0.02 mJ [2]. As a result, any small electrostatic discharge, hot surface, mechanical friction or a minute increase in local temperature may lead to ignition. The ignition and subsequent combustion of this mixture is a possible scenario which can lead to significant overpressurization of the containment. In the worst case, the combustion loads may exceed the strength of the containment thereby compromising its structural integrity as demonstrated in the severe nuclear accident at Fukushima, Japan [3]. As the containment is the last barrier separating the highly radioactive fission products inside and the surrounding atmosphere, maintaining the integrity of the reactor containment is of critical importance during severe accidents. Combustion of hydrogen can occur in different modes such as laminar flames, deflagrations and detonations with progressively increasing severity. Deflagrations are typically subsonic expansion waves that propagate through the diffusion of heat and mass from the reaction zone to effect ignition in the unburned gases. Due to expansion across the flame front, various flame instabilities set in and create a turbulent flow in the reactant mixture thus significantly enhancing the burning rate in the reaction zone. Since an increase in the burning rate results in an increase of turbulence in the unburned gases, a positive feedback loop is established between the turbulence and the reaction zone. The flame front can also interact with various geometrical features such as obstacles, which provides additional increase in the flame surface area. The net result is a continuously increasing propagation speed and is termed as weak flame acceleration. At very high turbulence levels, the reaction zone may get quenched due to high flame stretch and the rapid mixing of cold reactants with hot products. Thus, there is an upper limit on the maximum flame speeds that can be reached due to weak flame acceleration. Typically turbulent flame speeds are known to be ten times higher than the laminar burning velocity [4]. Hydrogen air flames are however known to be more resistant to turbulent quenching [5]. Flames continuously generate acoustic waves which propagate into the unburned mixture at the local speed of sound. These waves may coalesce and form precursor shocks thus pre-compressing the reactant mixture and increasing its temperature. Shock-flame interaction increases the energy-release rate and promotes further strong flame acceleration. In this regime, the propagation speed may be supersonic with respect to the unburned gases but is still subsonic with respect to the pre-compressed reactants. For the transition between weak and strong flame acceleration, the expansion factor (s) expressed as the ratio of the densities of the unburned (ru) and burned (rb) gas mixtures shown in Eq. (1) has to be satisfied [6].

Flow in a reactive mixture is invariably associated with gradients in mixture composition, temperature and pressure. This can lead to a spatially varying field of induction delay time. At certain critical conditions, a local explosion may take place in the vicinity of a shock front. According to the induction time gradient theory proposed by Zeldovich et al. [7] in 1970, it is postulated that a local explosion (due to autoignition) takes place in the region with the least induction time delay. The explosion process will thereafter continue at locations with longer induction times. This theory suggests that spontaneous wave formation and propagation happens in a spatial region with a gradient in induction time. Closely related but physically more insightful theory is the ‘Shock Wave Amplification through Coherent Energy Release’ (SWACER) concept published in the seminal paper by Lee and Moen [8]. According to the SWACER theory, DDT starts with the formation of a local explosion due to autoignition. As the speed of this explosion wave reaches the local speed of sound in the unburned gas, a local shock wave is formed. If the amount of energy released from the explosion is sufficient to sustain the local shock propagation and the rate of energy release corresponds to the local shock time scale, then a spontaneous coupling can take place between the exothermic reactions and the shock, eventually leading to a transition from deflagration to detonation. Some of the more recent reviews on the DDT phenomenon are highlighted by Shepherd and Lee [9] and Cicarelli and Dorofeev [10]. Due to highly transient behavior and dependence on geometric features, a universal criterion for DDT has not yet been established. However, a necessary condition [6] required for the transition from fast deflagration to detonation is expressed in terms of the detonation cell width (l) as described in Eqn. (2). For complex geometries, it is difficult to define the characteristic length scale L. Also, there is no universal rule that such a length scale exists. L > 7l

(1)

(2)

After DDT, a detonation wave propagates into the unburned mixture. Detonations are unsteady three dimensional structures with intersecting transverse shock fronts and reacting zones whose propagation is assisted by coherent and synchronized release of chemical energy from the local explosions. The aforementioned physical and chemical mechanisms are illustrated in Fig. 1. Oran [11] has succinctly summarized the complexity of numerically modeling the DDT phenomenon: “The quantitative prediction of DDT in energetic gases is an extremely difficult scientific problem because of the complex nonlinear interactions among all of the contributing physical processes, such as turbulence, shock interactions and energy release and the wide range of space and time scales on which they are important.” Khokhlov et al. [12] have extensively used numerical modeling to study the effects of shock flame interaction in turbulent flames and its role in deflagration to detonation transition. In their work, the numerical modeling is based on fully resolved two dimensional reactive Navier-Stokes equations to study shock flame interactions under both incident

Please cite this article in press as: Karanam A, et al., Numerical simulation and validation of flame acceleration and DDT in hydrogen air mixtures, International Journal of Hydrogen Energy (2018), https://doi.org/10.1016/j.ijhydene.2018.07.108

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Fig. 1 e Different mechanisms leading to DDT.

and reflected shock conditions for acetylene-air mixtures. The effects of viscosity, thermal conduction, molecular diffusion and chemical reactions are included. The modeling uses a highly refined grid with adaptive mesh refinement [13] to adequately resolve the internal structure of the turbulent flame brush, its propagation and interaction with shocks. They concluded that the Richtmyer-Meshkov (RM) instability caused due to the repeated interaction of shock and flame is the main reason for maintaining the highly turbulent flame brush. Pressure fluctuations generated in the region of the turbulent flame brush creates local hot spots in the unburned region which may finally lead to DDT through the gradient mechanisms. These highly resolved simulations highlight that shock flame interactions create conditions which are amenable for DDT to take place. The review paper by Oran and Gamezo [14] provides a comprehensive summary of the numerical effort to understand the mechanisms involved in the transition from deflagration to detonation. These simulations highlight the importance of conditions created by shock flame interactions under which DDT can take place. In each DDT simulation they performed, the origin of detonation was a localized hot spot in a sensitized mixture region, forming a local explosion which eventually evolved into a detonation wave through the induction time gradient mechanism. In a real accident scenario, flame propagation can take place in a confined geometric enclosure with obstacles or blockages. Interaction of flame with such geometric features can increase the turbulence levels leading to higher flame acceleration. In addition, these features can also geometrically stretch the flame leading to a higher flame surface area and therefore a higher burning rate. In the strong flame acceleration regime, precursor shock waves may reflect not only from the end wall but also from the obstacles and increase the turbulence in the flame brush through the RM instability as explained in Ref. [12] [13], and [14]. Therefore geometric features can have significant effect on flame propagation as opposed to flame propagation in a smooth channel. Gamezo et al. [15] have carried out numerical simulations of flame propagation and DDT in a rectangular channel with evenly spaced obstacles and filled with stoichiometric hydrogen air mixture. The combustion modeling is based on one step

Arrhenius kinetics. Their numerical simulations have indicated that the obstacle wakes induce different types of instabilities including the RM instability which are responsible for increasing the flame surface area, energy release rate and amplifying the shock strength. These simulations identify that the collision between Mach stem created by the reflection of lead shock from the bottom wall with the obstacle is the main reason for transition from quasi fast flame propagation to DDT and eventually to detonation. In another paper by Gamezo et al. [16], the effect of obstacle spacing on flame acceleration and DDT had been studied with symmetric and staggered obstacle spacing. An important conclusion from this study is that a higher number of obstacles per unit length leads to a higher increase in flame surface area and therefore a faster growth in the flame speed. When the spacing is large, the detonation is ignited when a Mach stem formed by the shock reflecting from the bottom wall collides with an obstacle. As the spacing is reduced, Mach stems do not form, but the leading shock becomes strong enough to ignite a detonation by a direct collision with the top part of an obstacle. Gamezo et al. [17] have also studied the effect of blockage ratio on DDT in hydrogen air mixtures. The effect of blockage ratio has been identified with the effect of two competing factors. A higher blockage ratio promotes flame acceleration but weakens the diffracting shocks required for DDT. Hence the propensity for DDT is relatively constant for a geometry specific range of blockage ratios but can increase sharply beyond this range. Many researchers have also worked on flame acceleration and DDT in a multidimensional array of obstacles. Ogawa et al. [18] have studied flame acceleration in an inclined array of cylinders. They suggest that highest propensity for flame acceleration and DDT is when the row of cylinders is parallel to the flame propagation direction. As the inclination increases the entrainment of flame around the cylinders weakens and the growth rate of flame speed is lowered. Ogawa et al. have also studied flame acceleration and DDT in an array of square obstacles [19]. Gaathaug et al. [20] have carried out experimental and numerical investigation of DDT in hydrogen air mixture in a square channel with a single obstacle. The numerical simulations were two dimensional and based on flux limited

Please cite this article in press as: Karanam A, et al., Numerical simulation and validation of flame acceleration and DDT in hydrogen air mixtures, International Journal of Hydrogen Energy (2018), https://doi.org/10.1016/j.ijhydene.2018.07.108

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centered Total Variation Diminishing (TVD) convective scheme with the FLIC code developed by Vaagsaether [21]. The experiments and numerical simulation showed that the mode of propagation upstream of the obstacle was mainly a deflagration and DDT occurred in the region downstream of the obstacle. Several local explosions were observed out of which only some transition to detonations. The authors concluded that the local explosions should have sufficient strength and should explode in a layer of sufficient height to result in a detonation. Homogeneous mixtures of hydrogen and air have been thoroughly investigated in the past. In an accident scenario, hydrogen stratifies in air due to its lower density. This leads to a non-uniform spatial distribution with higher concentration in the upper portions of the facility. Boeck et al. [22] have carried out experimental investigation on detonation propagation in hydrogen air mixture with transverse concentration gradient. According to this work, DDT can be significantly promoted by transverse concentration gradient. Thus for the same overall concentration, an inhomogeneous distribution poses a larger explosion hazard than a uniform concentration. From the vast literature available in the field of flame acceleration and DDT for hydrogen air mixtures, it can be concluded that the phenomena and the underlying mechanisms are well understood. The modeling methodologies involving fully resolved simulations of the governing reactive Navier-Stokes equations are also well established. Such numerical modeling and the associated experimental work has improved our understanding on the microscopic interplay between instabilities, turbulence and shock-flame interactions involved in DDT. While such models can capture the physics in full detail, they are limited to relatively simple and smaller domains. In the context of hydrogen safety for Indian Pressurized Heavy Water Reactors (PHWRs) with an installed capacity of 700MWe, the geometric volume of the containment is of the order of 70000 m3. Thus, scaling up the fully resolved simulations to real-world containment applications will increase the grid requirement exponentially, to a limit beyond the present availability of computational and time resources. Therefore, modeling methods are required which can work on relatively coarse grids and compute the pressure buildup in the domain and the flame propagation characteristics in a consistent manner. The models should also be able to predict flow transitions between parabolic (subsonic) to hyperbolic (supersonic) governing equations within a single framework. Substantial progress has been made on this front as well as explained in the works of Middha and Hansen [23], Ettner et al. [24], Gaathaug et al. [20] and Hasselberger et al. [25]. The present work is aimed at contributing further to the development of models suitable for large scale computations. A numerical framework has been evolved based on the opensource finite volume code OpenFOAM [26] for the modeling of flame acceleration and DDT in hydrogen air mixtures. This framework is based on the solver originally developed by Ettner et al. [24] but incorporates different sub-models specifically tuned for hydrogen flame propagation in enclosed geometries. Several simulations with concentration gradients in the presence of obstacles have been carried out. A detailed analysis of the interaction between pressure waves, precursor

shocks and flame fronts has been presented to explain the DDT process in a channel with obstacles and homogeneous mixture distribution. The shock-flame interaction which has been observed in fully resolved simulations carried out by earlier researchers [12e14] has also been observed in the present work. The modeling details, validation and some key results and conclusions are presented in this paper.

Numerical method In the present work the open-source numerical library OpenFOAM [26] has been adopted for CFD modeling. OpenFOAM is short form of Open Field Operation and Manipulation. OpenFOAM core technology consists of Cþþ implementations of various numerical methods, linear system solvers, Ordinary Differential Equation (ODE) solvers and also parallel computing. It also provides various library functionalities for turbulence models, transport models and thermo-physical models. These libraries can be combined along with the OpenFOAM core technology to represent various systems of partial differential equations that are relevant to different types of fluid flow problems. Recently Ettner et al. [24] have developed an OpenFOAM based framework for modelling flame acceleration and DDT. This framework uses a Favre-averaged transport equation for the progress variable (c) with closure terms evaluated using the Turbulent Flame Closure (TFC) model by Zimont [27] as described in Eq. (3). Since the chemical time scale of hydrogen reactions are much smaller than the turbulent time scales, the region with gradients in chemical species is thin compared to the overall domain. Thus the approximation of replacing the transport equation of every species with a single transport equation for the progress variable is justified. Moreover, it takes significantly lower computational time which is crucial for obtaining scalability for large scale geometries.    v v
v v~c ej ~c ¼ ðr~cÞ þ ru rDt þ ru St jV~cj vt vxj vxj vxj

(3)

The first term on the RHS of Eq. (3) represents the turbulent flux of the progress variable and is modelled using a turbulent diffusivity Dt as described in Eq. (4). Dt ¼

1 mt r Sct

(4)

Here mt is the eddy viscosity which can be obtained from the turbulence model and Sct is the turbulent Schmidt number for which a constant value of 0.7 has been used. The second term represents the mean reaction rate and accounts for heat release. The turbulent flame speed St is modelled as a product of the laminar flame speed Sl and the sub grid flame wrinkling factor c as shown in Eq. (5). The laminar flame speed is calculated from Eq. (6) and the standard state laminar flame speed Sl,o is obtained based on correlations developed by Konnov [28]. St ¼ cSl

Sl ¼ Sl;o

 1:75  0:2 T P To Po

(5)

(6)

Please cite this article in press as: Karanam A, et al., Numerical simulation and validation of flame acceleration and DDT in hydrogen air mixtures, International Journal of Hydrogen Energy (2018), https://doi.org/10.1016/j.ijhydene.2018.07.108

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The original formulation by Ettner et al. [24] uses the model of Weller [29] to account for c. Weller provides both algebraic and transport equation based closure for c. A more recent model due to Dinkelacker et al. [30] also account for c in the form of a transport equation as shown in Eq. (7). OpenFOAM provides libraries for implementing the c transport equation. The terms Gc and Rc represent the generation and reduction of flame surface area respectively and are modelled according to Eq. (8). The equilibrium flame wrinkling factor term ceq is calculated based on Eq. (9). The terms th, Le and u' are the Kolmogorov time scale, Lewis number and fluctuating component of velocity respectively. Ret is the turbulent Reynolds number.    v v
v vc ej c ¼ ðrcÞ þ ru rD þ rGc c  rRc ðc  1Þ vt vxj vxj vxj Gc ¼

ceq 0:28 ; Rc ¼ Gc th ceq  1

ceq ¼ 1 þ

 0:3  0:2 0:46 0:25 u' P Ret Le P0 Sl

(7)

(8)

(9)

The Dinkelacker model accounts for the effect of thermodiffusive instabilities through its dependence on Lewis number. In addition, this model captures the effects of increasing pressure on the turbulent flame speed. For the present problem where the sub-unity Lewis number of lean hydrogen flames and the associated pressure rise plays a significant role, the Dinkelacker model is highly appropriate. It is to be noted that the transport equation based approaches for c takes more time due to the additional numerical calculations. The algebraic closure model is an alternative approach to get solutions relatively faster. The comparison between different models is presented in the next section. To model quenching of flame at high turbulent intensities, a factor Q is multiplied with the resulting turbulent flame speed [31]. Since detonations also have to be modelled, the transport equation of the progress variable is further modified by adding another source term on RHS of Eqn. (3). The Heaviside function H activates the second source term when t is 1. The t term can be considered as a normalized induction delay time and is modelled through a separate transport equation as described in Gaathaug et al. [20]. The final assembled transport equation for progress variable is described in Eq. (10).    v v
v v~c 1  ~c ej ~c ¼ ðr~cÞ þ Hð~t  1Þ ru rDt þ ru QcSl jV~cj þ r vt vxj vxj vxj Dt (10)

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Numerical setup The experimental setup used in this study is based on shocktube experiments conducted at the ‘GraVent’ facility [32]. This facility is an entirely closed explosion channel with a rectangular cross-section. The length of the channel is 5.1 m. The width of the channel is 0.3 m and the height is 0.06 m. The mixture is ignited at one end of the channel and the flame propagation characteristics are studied along the channel length. Experiments can be conducted in a ‘smooth channel’ i.e. without any obstacles. The explosion channel also has a provision to include obstacles (Obs.1eObs.7) at regular intervals to induce turbulence in the flow which can assist flame acceleration. Up to 7 obstacles (0.25 me2.05 m) can be introduced. The blockage ratio can be varied to 30% or 60%. A schematic of the experimental setup (not to scale) is depicted in Fig. 2. The facility is equipped with optical measurement and photodiodes to measure flame arrival and pressure transducers to record the pressures at various stations along the direction of flame propagation. Further details on the exact location of the measuring instruments can be found in Ref. [32]. The numerical modelling on this facility has been carried out initially by Ettner et al. [24] although for a longer pipe section of 5.4 m and also more recently by Wang and Wen [33]. The setup also has a provision to create a transverse (normal to flow direction) gradient of hydrogen distribution to capture the effects of stratification of hydrogen during an accident scenario. In the experimental studies, the gradients have been created by controlling the diffusion time between hydrogen injection and ignition. A low value of the diffusion time of 3 s leads to the steepest gradient and a diffusion time of 60 s leads to an almost homogeneous mixing. In accordance with its relevance to flame propagation in reactor containments, two factors have been identified for constructing the parametric study: initial distribution of the hydrogen air mixture and the blockage ratio. Overall hydrogen concentrations corresponding to 22.5% of mol fraction has been considered in all the simulations. Only the steepest gradient (corresponding to diffusion time of 3 s) case has been chosen as this may represent the worst case scenario of highest stratification. This is referred to as the ‘stratified’ configuration in the further discussions. The case with 60 s of diffusion time which leads to a nearly homogenized mixture is referred to as ‘uniform’ configuration. For a given bulk quantity of hydrogen, the gradient will lead to the upper regions having higher mol fraction as compared to the lower regions. The initial conditions for uniform and stratified configurations are depicted in Fig. 3 for a bulk hydrogen mol fraction of 22.5%.

Fig. 2 e Schematic diagram of the GraVent experimental facility (not to scale). Please cite this article in press as: Karanam A, et al., Numerical simulation and validation of flame acceleration and DDT in hydrogen air mixtures, International Journal of Hydrogen Energy (2018), https://doi.org/10.1016/j.ijhydene.2018.07.108

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Fig. 3 e Initial stratified hydrogen distribution.

The stratified distribution can be seen from the contour with 41.2% at the upper region and 5.9% at the lower region thus establishing a vertical gradient. The left most part of the contour plot which shows zero hydrogen is the ignition patch. The initial conditions in the channel are 293 K and 1 atm. The mixture has been assumed to be in quiescent state and hence the initial velocity in the domain is set to 0 m/s. After a systematic grid independence study, a uniform hexahedral grid with grid size of 4 mm has been used in all the simulations. The gridding has been carried out in a 2D domain using preprocessing capabilities available in OpenFOAM itself. It is to be noted that this is a relatively coarse grid size as compared to the grid size requirements for flame and shock resolving models. Since the main objective is to get the pressure transients and overall flame propagation, even this coarse grid is suitable. The boundary conditions are described as adiabatic no-slip walls and the side walls as modelled with the symmetry boundary condition. Turbulence is modelled using the Shear Stress Transport (SST) k-u model. This ensures that turbulence in both the near wall region and the free stream are adequately resolved. The problem has been solved in a transient mode with the explicit Euler scheme for time discretization and second order schemes for spatial discretization for the diffusion terms to ensure higher accuracy. For low speed flow (Mach number < 0.1), the convective terms are discretized using the second order upwind schemes and PISO algorithm is adopted for pressure-velocity coupling. For flows with higher Mach number, a density based solver with the flux limited TVD scheme is used for better shock capturing. An adaptive time stepping has been employed with a maximum acoustic Courant number of 0.5 to ensure stability.

Numerical results The tools used for quantitative analysis of flame propagation in various configurations are the graphs of pressures at different locations vs. time (p-t), flame position vs. time (x-t) and the flame speed vs. flame position (v-x). The flame position is obtained as the distance travelled by the flame from the point of ignition. This is dynamically calculated by tracking the flame surface at each time step and extracting the average location of the leading edge of the flame. Using this information, the flame speeds have been calculated by a linear interpolation between successive records. The raw data obtained from the simulations have been filtered using 20 point based

moving averages and it has been verified that the filtering process does not add any error to the results. In addition, a qualitative but more visual understanding has been presented through contour plots of different relevant variables. Results have been presented in different parts. In the first part, the performances of the different TFC models have been compared by validating with experimental data. Then, the effects of distribution and presence of obstacles on flame propagation behaviour have been analyzed. The isolated effect of each parameter has been identified. A critical analysis on the detailed mechanism of DDT is presented through various quantitative estimates. Numerical simulation of flame propagation in the smooth channel with 22.5% of bulk hydrogen in both stratified and uniform distribution has been used for validation. The v-x plot obtained for different TFC models along with the flame speeds measured experimentally are presented in Fig. 4. The different black lines represent the experimental data obtained from Boeck et al. [32] and the numerical results from different submodels obtained from the present study. The plot is also overlaid with experimental data and numerical results from the case with uniform distribution (red lines). Focusing on the results for the stratified case (black lines), it can be observed that the in the initial section of the channel where the flame speed is highly subsonic with respect to unburned reactant (<0.5 m), the agreement between the models and experimental data is quite good. In the latter part of the channel (>0.5 m), the Mach number increases to higher than 0.1 and compressibility effects become dominant. All the models predict the location of the jump in flame speed at an earlier axial location compared to experiments. This may be attributed to the fact that the simulations were carried out in a two dimensional domain with symmetry boundary conditions and perfectly adiabatic walls. In reality, the flame propagation is three dimensional and therefore has more room to expand. This can considerably reduced the rate of energy release thereby also reducing the growth of flame speed. Additionally, some heat loss from the enclosing walls is expected in the experiments and this can also lower the energy release rate. From safety point of view, the magnitude of peak flame speed is important. The peak predicted by the model due to Dinkelacker et al. [30] matches within 3% while the Weller transport model [29] over-predicts the peak by ~15% compared to the experimental value. Also, the location of the peak predicted by Dinkelacker et al. [30] model is closer to the experimental data. The algebraic version of the Weller model also predicts the

Please cite this article in press as: Karanam A, et al., Numerical simulation and validation of flame acceleration and DDT in hydrogen air mixtures, International Journal of Hydrogen Energy (2018), https://doi.org/10.1016/j.ijhydene.2018.07.108

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Fig. 4 e Comparison of different TFC models with experimental data for stratified and uniform distribution in a smooth channel.

peak velocity correctly but the location is further offset compared to the Dinkelacker model. While the simulations definitely show that the sub-model by Dinkelacker et al. [30] matches the experimental data more closely, the difference is not much. This can again be attributed to the two dimensional simulations where the energy release rate from all the models may be artificially increased thus masking the actual performance to some extent. Better performance of the Dinkelacker model has been established by other researchers in three dimensional simulations such as in Ref. [25]. For the case of uniform distribution (red lines), the different sub-model predictions were very similar and hence only the results from the Dinkelacker model is presented. It can be observed that both the experimental and numerical prediction are entirely subsonic with respect to the unburned gases and hence in the deflagration regime. The numerical models implemented are able to capture the overall trend of increasing flame speed (i.e. flame acceleration) and then reaching a stable speed through a peak. The models are also able to distinguish between the energy release rates in stratified and uniform distribution (with the same overall concentration) and the resulting differences in the propagation regime of the flame. This has also been validated with the experimental data as depicted in Fig. 4. Although the transient propagation prediction may need to be improved further, the peak velocity predictions are quite agreeable. Owing to the additional transport equation incorporated into the Dinkelacker model, these simulations takes approximately 30% higher computational time compared to the relatively simpler algebraic models of Weller for the same grid size. From various simulations the consistency in terms of results and timing between the different sub-models has been verified.

The marked difference between the flame propagation behaviour between the stratified and uniform configurations can be explained based on flame shape and flame surface area. Flames in stratified configuration are observed to elongate over the propagation distance whereas more symmetric flame shape can be observed in uniformly mixed initial distribution. This can be observed on the contour plots of the progress variable at time ¼ 8 ms as shown in Fig. 5. It can be observed that for the stratified configuration, the flame preferentially propagates towards the upper regions of the domain where the hydrogen concentration is higher. The upper edge of the flame front reaches ~0.24 m while the lower edge is at ~0.1 m thus inclining the flame. The uniform configuration displays an almost symmetric flame front located at a constant axial location of 0.2 m. The elongation directly affects flame speed due to increase in flame surface area and the associated increase in burning rate. Thus flame acceleration in stratified mixtures is expected to be higher than the uniform mixtures. As the flames propagate in the axial direction, the flame surface becomes more elongated. Thus flame acceleration is expected to increase in the propagation direction. Referring to Fig. 4 again, flame speeds for both stratified and uniform cases are or the order of 50 m/s close to the ignition end (x < 0.5 m). As flame propagation occurs, the flame speed increases. This is attributed to the turbulence-flame interaction and growth in flame surface area which increases the effective burning rate. However, it may be noted that the rate of increase for the stratified case is significantly higher than for the uniform case. This phase represents the weak flame acceleration and the mode of combustion is slow deflagration. As the flame speed increases, the Mach number with respect to unburned side also increases and compressibility effects become important. For the uniform case, the flame

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Fig. 5 e Flame propagation with stratified distribution (top) and uniform distribution (bottom).

propagation occurs entirely in the subsonic regime and precursor shocks cannot form. Thus, the uniform case is entirely in the mode of slow deflagration. However, for the stratified case, strong turbulence chemistry interaction leads to the unburned Mach number reaching the sonic value at ~1.6 m. This marks the transition from slow to fast deflagration. Further flame acceleration takes place mainly because of interaction with shocks and is in the regime of strong flame acceleration. At ~3 m, the burned Mach number reaches the sonic value. At this condition, a sudden jump in propagation velocity can be observed and interpreted as the transition from deflagration to detonation. The mechanism for DDT has to be inferred from the p-t plots and is presented in a further section. From this analysis, it may be inferred that DDT has occurred mainly due to the presence of gradients in the initial hydrogen concentration. The uniform distribution displays only weak flame acceleration and remains entirely deflagrative. The interaction of flame with the obstacles with different blockage ratios and the resulting trends on flame acceleration and DDT are explicated. A first impression of the flameobstacle interaction is depicted in Fig. 6 which shows the flame shapes at time ¼ 10 ms. The three simulations represent smooth channel and channel with obstacles (30% and 60% blockage ratio). The overall hydrogen mol fraction is 22.5% with stratified initial distribution. It can be observed that there is a distinct difference in the flame shapes between the smooth and obstructed channels. While for the smooth channel, the flame shape is highly inclined (as observed earlier also), the leading edge of the flame front corresponding to the obstructed channels are more rounded. Since the flow in the early parts of the channel is subsonic, the flame front is forewarned about the presence of the obstacle and therefore, the flow streamlines turn to avoid the obstacles and correspondingly, the flame front also turns. The turning of the flame front is clearly illustrated in the geometry with 60% blockage. Also, after crossing the blockage, the flame suddenly expands into a larger area. These two factors contribute to the different flame shape as compared to flames in smooth channels.

The effect of obstacles on flame speed is quantified through the v-x plot depicted in Fig. 7 for smooth channel and channels with 30% and 60% blockage. The axial locations of the seven obstacles are also shown. It can be observed from the above graph that there is a significant difference in the flame speed trends between the smooth and obstructed geometries. The flame acceleration for the obstructed geometry is significantly higher than the smooth geometry leading to advancement in transition from slow to fast deflagration. This observation is consistent with the findings of Gamezo et al. [17]. The interaction of flames with obstacles can be understood in terms of two competing factors. In a smooth channel, the unburned gases are available to the flame in an unhindered manner. When obstacles are introduced, the constriction hinders the flow to unburned gases towards the flame front. Thus the flames have a tendency to grow faster in the transverse direction compared to longitudinal direction. This makes the flame more rounded as also explained in Fig. 6. On the other hand, as the blockage ratio increases, the unburned gases are fed with a higher turbulence which increases the local transport near the flame. A higher blockage ratio is also associated with a higher geometric increase in flame surface area. As per the simulations at 30% and 60% blockage ratios, the location at which DDT occurs is seen to be nearly constant. Thus it may be interpreted that the relatively unhindered flow of unburned gases at 30% blockage is equally compensated by the higher intensity turbulence in the case with 60% blockage albeit at a lower flow rate. The insensitivity of the location of DDT on the blockage ratio has also been observed in the studies by Gamezo et al. [17]. Moreover, the flame speeds in both the cases reach the sonic value at nearly the same location thus chocking the upstream flow. The case with 30% blockage has the same peak flame speed as the smooth channel but the location at which DDT occurs is comparable to the case with 60% blockage. It may also be noted that the final propagation velocity after the obstacle section is the same for all the cases independent of the blockage ratio. While the flame acceleration is monotonic for the smooth channel, the obstructed channel demonstrates an oscillatory

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Fig. 6 e Flame propagation in a smooth channel (top), 30% blockage (middle) and 60% blockage (bottom).

Fig. 7 e v-x plot for smooth and obstructed channels with stratified distribution.

behaviour. Six representative points (a-f) have been marked on the case with 60% blockage for explanation. When the flame passes from a to b, it crosses the second obstacle and hence a significant jump in speed can be observed due to increased turbulence levels. The flame speed at b is

supersonic with respect to the unburned state and hence represents the transition from slow to fast deflagrations. The drop in speed from b to c is a result of sudden expansion which is possible only for subsonic flows. Thus it can be inferred that the flame may be passing into a region which is

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preheated by a shock that may have reflected from one of the obstacles. Therefore the flame at b is subsonic with respect to shock heated reactants and hence in the deflagrative regime. The flame acceleration from c to d can be attributed to shockflame interaction and strong acceleration. When the flame crosses the fifth obstacles after f, the burned Mach number reaches unity and DDT can take place. This results in a sudden jump in speed when the flame reaches the end of the obstacle section. Since a detonation wave is supersonic with respect to the un-shocked state, a drop in speed from obs.5 to obs.6 does not occur. Clearly, the onset of detonation takes place at a much earlier axial location due to the presence of obstacles. The flame speed becomes constant after the seventh obstacle and reaches the same value as the flame speed in the smooth channel at the end of the channel. A similar oscillatory behaviour is also seen in the case with 30% blockage but the peaks and valleys are smaller compared to 60% blockage as expected.

Discussion Fig. 8 depicts the flame propagation in an obstructed channel with 30% blockage and a smooth channel both with uniform hydrogen distribution at 22.5% concentration. It can be clearly observed that strong flame acceleration and DDT takes place in the presence of obstacles. The mechanism of DDT has been explained in the configuration with obstacles using v-x plot and x-t/p-t plots depicted in Figs. 8 and 9 respectively. In Fig. 9, the pressure traces correspond to over-pressures. These have been scaled appropriately and shifted along the vertical axis to indicate the position at which the pressure is obtained. The plot is overlayed with the flame trace (x-t) as well to identify

the location of the flame front relative to the pressure traces. Some of the phenomena leading to DDT are elucidated below. From the x-t and v-x plots, it is observed that the flame speed achieves sonic conditions w.r.t unburned gases for the first instant at 13 ms at a flame position of 0.8e0.9 m. Therefore, compressibility effects are expected to become prominent after 13 ms. Motion of the flame induces pressure waves to travel upstream as can be observed from the regions of high pressure from the contour plot in the vicinity of 1 m (Fig. 10-a). From the p-t plots, it can be observed that weak overpressures are recorded at the 1.4 m location while at the 2.3 m location; the pressure signal is virtually non-existent. At 14.85 ms, the flame crosses the 1.4 m mark as seen in the x-t plot. Also, the pressure contours show mild discontinuity just before 1.7 m (Fig. 10-b). This discontinuity shows a moderate but not abrupt gradient in pressure. At this point, the flame is trailing the pressure discontinuity by a distance of 0.3 m. After a further transient of 0.05 ms, a reasonably strong (but not abrupt) discontinuity can be observed at the 1.4 m pressure probe. This may be attributed to pressure waves working their way upstream as a result of the discontinuity at 1.7 m. Weak pressure signals can be observed at the 2.3 m location. At 15 ms, a fast moving (~750 m/s) flame front can be observed between 1.5 and 1.6 m. This corresponds to a fast deflagration as the flame speed is subsonic w.r.t the burned gases. The fast moving flame front acts as a piston which displaces the gases ahead of it at very high speeds and promotes the formation of precursor shocks. Thus at 15 ms the amenable conditions for DDT to occur have been attained. At 15.15 ms the flame front is just before the 1.7 m mark and a relatively strong pressure discontinuity is created just after 1.7 m (Fig. 10-c) before the sixth obstacle. This discontinuity may be attributed to coalescence of pressure waves which are

Fig. 8 e v-x plot for obstructed channel with 30% blockage and smooth channel and uniform distribution. Please cite this article in press as: Karanam A, et al., Numerical simulation and validation of flame acceleration and DDT in hydrogen air mixtures, International Journal of Hydrogen Energy (2018), https://doi.org/10.1016/j.ijhydene.2018.07.108

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Fig. 9 e Flame and pressure traces along with incident shock for flame propagation in an obstructed channel with 30% blockage and uniform distribution.

rapidly emanated from the moving flame front. The discontinuity is not self sustained as it moves through the channel and is not observed to record a signal at the 2.3 m pressure probes. The reason behind the attenuation of this discontinuity is the reduction in flame speed as it passes through the sixth obstacle (from x-t and v-x plots). Another instance of a strong discontinuity can be observed at 15.55 ms (Fig. 10-d). At this instant the flame front and discontinuity are located in

much closer proximity than what was observed at 15.15 ms. The pressure jump across the discontinuity is ~12. This discontinuity becomes steeper and forms a shock because the flame speeds have become sonic w.r.t burned gases (from x-t and v-x plots) and hence are capable of continuously providing the driving force required to steepen. The signature of this incident shock can be clearly observed at the 2.3 m location. Thus it may be postulated that the DDT process has

Fig. 10 e (a) Pressure contour in bar at 13 ms, (b) Pressure contour in bar at 14.85 ms, (c) Progress variable contour (top) and pressure contour in bar (bottom) at 15.15 ms, (d) Progress variable contour (top) and pressure contour in bar (bottom) at 15.55 ms, (e) Temperatures contours at 16 ms(top), 16.05 ms (middle) and 16.1 ms (bottom), (f) Pressure contour in bar (top) and temperature contour (bottom) at 17 ms. Please cite this article in press as: Karanam A, et al., Numerical simulation and validation of flame acceleration and DDT in hydrogen air mixtures, International Journal of Hydrogen Energy (2018), https://doi.org/10.1016/j.ijhydene.2018.07.108

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been initiated. Whether DDT leads to a fully formed detonation will depend on whether the flame and shock move together or separate out. During the time interval between 15.55 ms and 16 ms, it can be been observed from the pressure trace and flame trace that the flame front and shock remain in close proximity at different instants. At 16 ms, both the flame front and the leading shock wave have crossed the final obstacle and are located at ~2.5 m. From the p-t plots (at 16 ms), no pressure signals are observed at probes located at 2.9 m and further. At 16 ms, the shock-flame complex is moving at ~1500 m/s (from x-t and v-x plots) and directly into the unburnt mixture. As this speed is supersonic, pressure waves cannot travel ahead of the shock-flame complex and cause signals at downstream locations. Thus the absence of pressure signal at 2.9 m and further is physically justified. The shock flame interaction shown here is similar to the studies presented in Ref. [12] but with fully resolved simulation on a much finer grid. In the interval between 16.0 and 16.1 ms, it can be observed from the temperature contours (Fig. 10-e) that flame and shock completely merges thus completing the DDT process. During this time, a significant jump in flame propagation speed can be observed (1500 m/s to 2600 m/s). The pressure jump across the shock-flame complex is significantly higher than 12. After 16.1 ms, a fully formed detonation front moves into the unburnt mixture (Fig. 10-f). The pressure spikes which can be observed from the 2.9 m location and further is a direct signature of the detonation front moving across these probes. The discontinuity front tracked from the p-t plots exactly overlaps with the flame front. From this, it can be concluded that the combustion wave is indeed in the detonation mode.

Conclusions Flame propagation in hydrogen air mixtures can take place in different modes such as laminar flames, slow and fast deflagrations and detonations. As these modes have widely varying propagation mechanisms, modeling the transition from one to the other presents a challenging task. This involves accurately capturing phenomena such as turbulence-chemistry interaction, autoignition and shock propagation. The present work investigates the numerical modeling of flame acceleration and DDT in hydrogen air mixtures in the shock tube geometry of the GraVent experimental facility. The numerical modeling is carried out based on the open-source library OpenFOAM. A transport equation for the reaction progress variable has been implemented with Turbulent Flame Closure (TFC) to include heat release due to chemical reactions. A separate sub-model is added to consider autoignition. Several recent TFC models have been implemented and compared against the experimental data available from the GraVent facility. The numerical results indicate higher flame acceleration compared to experiments and an earlier location at which DDT is triggered. This may be attributed to the two dimensional nature of the simulations in which the artificially imposed symmetry boundary conditions on the side walls can lead to preferential flame propagation in the axial direction. Among the models considered, the model due to Dinkelacker et al. gives better comparison with the

experimental data in terms of the peak flame propagation speed and its location compared to the relatively simpler algebraic flame closure model by Weller. Several simulations have been carried out in smooth and obstructed channels with stratified and uniform hydrogen distribution. In a smooth channel with stratified distribution, it is observed that the flame surface area increases along the propagation direction thereby enhancing the energy release rate and is identified to be the key parameter leading to strong flame acceleration. On the other hand, with a uniform distribution, the flame shape is rather flat and the energy release rate is significantly lower and the propagation regime is entirely deflagrative. Thus it may be concluded that a stratified mixture has a higher propensity to undergo DDT compared to a uniform mixture with the same overall concentration. When obstacles are introduced, the increase in burning rate due to turbulence induced by the obstacles and the geometric increase in flame surface area can significantly increase the likelihood of DDT as demonstrated in the present work. Obstacles also have the effect of hindering the flow of unburned gases towards the flame front and can attenuate flame growth to some extent. In general, the competing effects of higher turbulence and higher hindrance caused by obstacles have to be assessed specific to the geometric configuration being considered. Studies on pressure traces in a simulation with obstacles revealed that compressibility effects induced due to the fast moving flame front creates shock complexes in the obstacle section of the channel. The mechanism of DDT in this case is a self sustaining shock flame interaction that ultimately leads to coalescence. Further propagation happens as a fully formed detonation wave. In this study, an attempt has been made to capture mechanism involved in flame acceleration and DDT in a hydrogen air mixture using open source based numerical simulations. Due to the coarse grids considered in this study, some of the sub-grid scale processes such as the induction distance, shock-boundary layer interaction and the instabilities arising from the interaction between shock and the expanding flame front have not been resolved. The long term objective will be to scale up such simulations to three dimensions and apply them on larger domains such as the full scale reactor containment. In addition, an important future activity is to implement higher resolution models such as LES with detailed chemistry for small scale geometric configurations to get a better understanding of the instabilities leading to DDT.

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