MCS 10 Naples, Italy, September 17-21, 2017

NUMERICAL INVESTIGATION OF EARLY FLAME PROPAGATION IN VENTED EXPLOSION

R. Li*, W. Malalasekera* and S.S. Ibrahim**

r.li3@lboro.ac.uk *Wolfson School of Mechanical, Electrical and Manufacturing Engineering, Loughborough University,

Loughborough, LE11 3TU, UK ** Department of Aerospace and Automotive Engineering, Loughborough University, Loughborough, LE11

3TU, UK

Abstract Gas explosions in semi-confined spaces with obstacles are closely related to industrial and building safety and simulation of such situations are still challenging for modelers. This paper presents the modelling of the influence of ignition and early flame propagation on vented explosion simulations. Numerical simulations using the Large Eddy Simulation (LES) technique have been carried out for a stagnant, stoichiometric propane-air mixture. The test case chosen for the present study is the experiments of small-scale Sydney explosion chamber [1]. In LES, the filtered reaction rate is modelled using a dynamic flame surface density (DFSD) model [2]. Two approaches of computing ignition were studied: 1). use of the main combustion model in an appropriate predefined ignition region, 2). use of a flame kernel model to calculate ignition and initial flame propagation. The aim of this study is to investigate the importance and impact of ignition modelling on the critical parameters for safety assessment, including the maximum generated overpressure, time and location of the peak pressure. Validation against the experimental data shows the appropriateness of the flame kernel model in predicting the initial phase of combustion and the timing of the overpressure history. Results and analysis reveal that a realistic description of the early flame kernel growth is important for FSD related approaches used in modelling a highly unsteady explosion phenomenon. Introduction Combustion safety is an important issue in power plants and industrial processes. Partially confined accidental gas explosions occur in leaking fuel tanks, buildings and offshore modules [3]. Compared to stabilized flames, large scale gas explosions cause more hazards and major damage due to forces originated from the generated overpressure. The enormous explosion pressure results from the interactions between the propagating flames and solid obstructions. Such interactions are dependent on various conditions such as initial settings, operating environment, and shape, size and position of the solid obstacles. Therefore, it is a difficult task to estimate the behaviours and consequences of a gas explosion.

Numerical simulations provide an alternative to experiments that help the study and understanding of explosions. Large Eddy Simulation (LES) technique has emerged as a promising computational tool to simulate turbulent premixed combustion particularly for explosion studies [4]–[7]. LES has been proved to be more reliable and advantageous than the classical URANS (Unsteady Reynolds Averaged Navier Stokes) technique in modelling large scale, highly unsteady explosions [8]. A major challenge in LES for premixed flames is to evaluate the filtered chemical source term. As the reaction zone is generally thinner than a typical LES filter width, the flame cannot be resolved and must be accounted for by appropriate sub-grid scale (SGS) models. Earlier studies using a dynamic flame surface density (DFSD) model have shown the capabilities in predicting the key features of propagating premixed flames of propane and hydrogen-air mixtures with built-in solid obstructions [2], [9].

A gas explosion is a highly transient phenomenon. Ignition and the very early stage of flame propagation are relatively short in time and often neglected in the simulation [10] or calculated using the existing combustion model [4]. However, prediction of the very early stage of an explosion may affect the subsequent phases of flame propagation and the overall parameters of interest such as the peak pressure timing. Due to the physical complexity of ignition processes and flame kernel formation, it is often not practical to account for all aspects of an ignition event, such as laser/spark energy transfer to gas, plasma formation, heat conduction to surroundings and shock waves. Compared to a common combustion model for LES, a different treatment is required during the initial period as the kernel size is not large enough to be resolved in LES and a fully established flame is not present.

The main objective of this work is to investigate the modelling of ignition and early flame propagation and to assess different descriptions of ignition specifically in the context of FSD related simulations and their effects on the predictions of critical safety related parameters in vented explosions. Test Case The experimental configuration studied in this work was developed at the University of Sydney [1], [11]. The schematic diagram of the laboratory scale explosion rig is illustrated in Figure 1 (left). The 50×50×250 mm combustion chamber can accommodate a maximum number of 3 baffle plates positioned at equidistance and a solid square obstacle of 12-mm cross section. The schematic of the removable baffles is displayed in Figure 1 (right). Each baffle plate is 3 mm thick, consisting of five 4 mm wide bars each with a 5-mm wide space spreading them throughout the chamber, creating a blockage ratio of 0.4. This chamber is of specific interest due to its smaller volume and its capability to hold a deflagrating flame, because of the strong turbulence environment generated by solid obstacles at different downstream locations from the closed bottom end. In the case considered here a LPG-air mixture is ignited by focusing an infrared output from a Nd:YAG laser 2 mm above the base. Venting at atmospheric pressure is

 

Figure 1. Left: Schematic diagram of the Sydney explosion rig [1], [11]. Right: Removable baffles. Units are in millimetre.

250

S2

3

3

10

12

S1

S3

Obstacle (small)

Inlet Pressure

Transducer 1

Pressure Transducer 2

50

64

20

580

20

50

4 5

5 50

maintained throughout the explosion process. For the present investigation, the configuration with all three baffles and solid obstacle is considered, as shown in Figure 1 (left). The influence of the number and position of the obstructions are presented elsewhere [4], [5], [12]. Experimental measurements recently published by Alharbi et al. [1], [13] are used for validation of LES simulations. Numerical Modelling The present simulations focus on stoichiometric propane-air propagating flames in the chamber configuration of three baffles and one small square obstacle as shown in Figure 1 (left). Favre-filtered conservation equations are solved using the in-house LES code, PUFFIN [14]. Simulations are performed using meshes of 2.7 million cells. The filtered reaction rate in the transport equation is modelled by following the laminar flamelet approach as

Σ, (1) where is the unburned gas density, is the laminar burning velocity and Σ is the flame surface density. Σ is evaluated dynamically using a recently developed DFSD model [2], [5].

A special interest presented in this paper is the ignition modelling. Ignition of the stagnant propane-air mixture is accounted for in two ways: 1). using the main combustion model by setting to 0.5 within a 4-mm wide hemispherical ignition zone at the bottom center of chamber. 2). using a kernel growth model to compute the initial combustion phase until the flame is fully developed and resolvable in LES. A Flame Kernel Model The flame characteristics during the kernel formation and early evolution differ fundamentally from the fully established phase [15], [16]. Both laser-induced and conventional spark ignition are physically complex and typically incorporate laser or electrical energy breakdown, kernel heat losses, curvature-induced stretch and flame front wrinkling at small scales [15], [17].

Since the flame has not achieved equilibrium at the early stage, common combustion models based on equilibrium assumptions are not applicable to the early flame kernel development without specific modifications [18]. On the other hand, the LES filter Δ cannot resolve a too small kernel, typically with a radius no larger than the order of the filter size Δ [19]. Thus, the kernel formation and very early stages of propagation cannot be appropriately included in LES using conventional FSD related models that involve filtering infinitely thin flame fronts [19]. A good attribute of an ignition model should be formulated and coupled to be consistent with the main combustion model used in the simulation [20], [21]. Experimentally based comprehensive models [22], [23] and models using Lagrangian particles [24] have been recently proposed in SI engines. In the present work, a model aiming at calculation of ignition FSD is proposed. It is relatively simple but capable of producing global results of ignition and early stage of flame propagation effectively.

Laser ignition has been used in the experiments considered in this study. Modelling the complete process of kernel formation in a laser ignition event is a formidable task. In the present study, the very short breakdown period is simply neglected and the initiation of the flame kernel is completed by depositing a small amount of burned gases at the laser focus point at 0. As the information of the laser ignition system is not sufficient, the initial burned gases mass is defined with a cylinder of radius 2 in consistent with the critical energy definition [21], [25]:

4 , (2)

where is the laminar flame thickness and is the estimated size of the initial laser-induced spark. Then, this burned gas volume is filtered at scale Δ using a Gaussian function [21] which is imposed relative to the ignition location :

0.6Δ

. (3)

The constant is evaluated to satisfy the integral over the computational domain Ω using the relation [26]. Assuming that the initial kernel is spherical [27], the volume of the flame kernel can be approximated as the total volume occupied by the burned gases :

. (4)

Consequently, the corresponding kernel radius and the mean flame area are estimated as

34

/and 4 . (5)

Taking into account the possible flame front wrinkling by small-scale turbulence, the total flame area is then linked with the mean kernel area by a single wrinkling factor Ξ as

Ξ . (6) Finally, the local ignition flame surface density Σ is computed following Boger’s parabolic profile of [28]:

Σ 1 , (7) where the coefficient is evaluated so that the total flame surface is distributed spatially over the computational grid:

1 . (8)

The resulting filtered reaction rate during ignition is modified to

Σ . (9) The reaction rate defined by Eq. (9) is used until the maximum value of reaches unity somewhere inside the computational domain, representing a complete and fully resolvable flame. Thereafter, is evaluated by the main combustion model.

The wrinkling factor during the kernel growth is estimated such that it evolves from Ξ1 to the value of the equilibrium phase Ξ

Ξ

ΓΔ

Ξ ΞΞ Ξ

Ξ, (10)

where

Σ

Σ (11)

represents the averaging of a scalar variable over the flame surface. Before the flame kernel goes from SGS to resolved scale, the largest possible turbulence scale which can wrinkle the front is of the size of kernel. Thus, the scale Δ is taken as the kernel diameter when the characteristic length of the flame kernel is smaller than the LES filter size Δ. Equilibrium wrinkling factor is evaluated here using the power-law wrinkling model of Charllote et al. [18], [29]:

Ξ 1Δ, Γ

.

, (12)

where is the turbulent fluctuation velocity at scale Δ . The efficiency function Γ is estimated using the general fitting function [29] at scale Δ . It should be noted that as the early flame kernel is essentially laminar, the computed wrinkling factor Ξ remains close to one due to the initial low turbulence intensity within the combustion chamber.

Different from a fully resolved flame front, a rigorous mathematical expression for Ξ would be more complex for the very small flame kernel in the SGS range. An alternative may be to set a unity wrinkling factor during ignition. Used as a first modelling strategy, Colin et al. [21] demonstrated the correctness of this treatment for low turbulence intensities in an SI engine environment.

In the present work, the above flame kernel model has been implemented and coupled with the DFSD combustion model. A comparative simulation is also performed which computes ignition using the main combustion model by initially setting a burning region. A description of the two examined ignition methods is illustrated in Table 1.

Table 1. Comparison of the two investigated strategies for ignition modelling.

Ignition by setting a region Ignition by flame kernel modelInitial profile 0.5 within ignition zone Gaussian profile (Eq.(3)) Ignition region Hemisphere of 4-mm radius Only ignition point is specified Ignition FSD DFSD model Kernel surface evaluation

Results and Discussions Results from the LES simulations of stagnant, stoichiometric propane-air deflagrating flames over repeated obstacles are presented and discussed in this section. A sequence of numerical flame front images (contours of 0.5) are displayed in Figure 2. In general, simulations using both ignition approaches are capable of reproducing the essential flame characteristics at various stages of propagation. It can be seen that at time 0.5 ms, the flame size computed from the combustion model is larger than that from the flame kernel model. Notice that the initial field has very small values (typically the maximum is of the order of10 ) in the flame kernel

model, the kernel size always starts from zero. Then, flame predicted by the kernel model grows up fast and it is just slightly smaller than the one from the main combustion model at 3 ms. However, when the combustion takes over, there is a noticeable lag in the flame propagation with the ignition model after passing the first baffle, e.g. at 10 ms. Note that the flame remains hemispherical and quasi-laminar before reaching the first baffle. The prediction of the initial laminar phase is dependent on the details of ignition modelling. For the case of computing ignition using the combustion model, the predefined ignition zone must be sufficiently large to get enough burning rate to maintain continuous propagation. Nevertheless, it cannot be too large or too close to the first baffle to so that the effects of the early deflagration period are preserved. Initial tuning of the size of the ignition zone is usually needed. Comparatively, the ignition model does not predefine a burning or burned region. It does not encounter the issue of the initial flame size because the kernel starts to form and grow from the ignition point and it is predicted by a separate model.

Figure 2. Iso-lines of 0.5 on the midplane of the chamber at time 0.5, 2, 3, 4.5, 7.5 and 10 ms relative to ignition. Top: ignition by setting a region. Bottom: flame kernel model.

Progressive increase of , on the x-axis of the chamber midplane is shown in Figure 3.

For the flame kernel model, the maximum reaches unity at 0.9 . As the kernel goes from SGS to resolved, evolves gradually from an initial Gaussian profile and transits to a fully resolved shape predicted by the DFSD model. In contrast, when the combustion model is used throughout the early stage, the initial step-function profile ( , 0.5) within the ignition radius diffuses from the edge of the ignition region to the outer unburned gas and generates a relatively more sharp-edged, staircase-like profile. A similar spherical profile can also be observed when the flame is fully established, for instance, at 1.5 .

Figure 4 presents the base overpressure time traces. In order to perform data averaging, experimental pressure signals [13] from different runs have been shifted in time so that the occurrence of maximum overpressure coincides with the mean time to peak. It can be seen from Figure 4 (left) that in both cases the LES is able to reproduce the trend and magnitude of the overpressure is very similar in value in both cases. However, it is clear that the timing of peak pressure is more accurately predicted with the flame kernel model and the results are in better agreement with the experimental data. Early variations in overpressure due to different ignition strategies is shown in Figure 4 (right) between the two simulation. When the flame kernel model is used, there is a sharper initial increase in pressure. Several milliseconds after the main combustion model has taken over, the trends in overpressure become similar. One of the merits for ignition modelling is the timing performance. Evidently, time taken to peak predicted with the flame kernel model is within the range of time of the experiments and is closer to the experimental mean time.

Figure 3. Profiles of after ignition on the x-axis of the bottom of the chamber. Left:

ignition by setting a region. Right: by flame kernel model.

Figure 4. Influence of ignition modelling on overpressure evolution. Left: Overall

overpressure time traces. Right: Variation of overpressure at early stage. Ignition by setting a region (plain with triangle), flame kernel model (plain with circle), experimental mean signal (dashed), statistical envelop (grey background) and experimental range of time to

peak overpressure (closed arrow).

Figure 5 displays the calculated and experimental flame front positions with the two ignition approaches. In experiments, the flame position data extracted from the high speed LIF-OH equipment is only available after the first baffle plate. Numerically, flame front position is referred to as the furthest location of 0.5 from the bottom ignition end. The enhancement in predicting propagation timing and speed by the inclusion of the flame kernel model is noticeable from Figure 5 (left) as the flame propagation speed is generally closer to the experimental measurements at all the stages. The flame position during the early propagation is shown in Figure 5 (right). When the combustion model is replaced by the flame kernel model at the early stage of combustion, the flame propagation speed is lowered before reaching the first baffle. In comparison, the flame is accelerated when the DFSD model is used during ignition. Globally, the duration of the flame kernel model is relatively short and it transits to the DFSD model when the kernel is large enough to be resolved. Consequently, after the flame passes the first baffle, flame position time traces predicted from the two approaches tend to be parallel. This is an indicator of similar propagation speeds evaluated by the combustion model at the turbulent stages when the effects of various initial phases have almost faded away.

Figure 5. Influence of ignition modelling on flame position. Left: Overall flame position

time traces. Right: Flame position at early stage of propagation. Ignition by setting a region (plain with triangle), flame kernel model (plain with circle), experimental mean

measurement (dashed), statistical envelop (grey background) and mean experimental measurement points (cross).

Figure 6. Overpressure and flame position. Left: Overall trend. Right: Early stage. Ignition

by setting a region (plain with triangle), flame kernel model (plain with circle).

Another parameter of interest for safety related studies is the location of the maximum

overpressure. Figure 6 (left) shows the resulting overpressures as a function of flame positions using the two ignition approaches and the results of the early phase is shown in Figure 6 (right). It can be noticed that the two simulations produce similar overpressure magnitudes with the same flame position. Discrepancies can be found in the initial low-pressure region between the chamber base and the first baffle in Figure 6 (right) and the high-pressure region between the peak pressure location and the chamber exit. Evidently, despite of the variance in early flame propagation, the peak pressure inherently takes place at about 185 mm relative to the base ignition source. The overpressure maximises in LES when leading flame front is at a distance downstream the square obstacle and the consumption of the trapped unburned gases takes place. The location of the peak overpressure predicted by LES agrees with the experimental observations for the same configuration [11] and it is almost independent of the variation in initial descriptions of the ignition process. Conclusions The main objective of the numerical study was to predict critical parameters in vented explosion using LES and investigate the effects of ignition and the very early flame propagation. The necessity of different treatment for modelling ignition processes was discussed and a flame kernel model was examined. It is a simple but efficient model for global ignition and kernel parameters and is proposed specifically for the combustion model with the FSD formulation. The flame kernel model is advantageous in the initial simulation set-up because no optimisation of predefined ignition source is needed. Results show that the flame kernel model combined with the DFSD combustion model is able to correctly reproduce the essential flame characteristics and capture overpressure trend and magnitude in the studied configuration. Compared with the use of combustion model throughout the explosion simulation, the separate use of the flame kernel model provides a more appropriate description of progress variable evolution in both time and space. Hence, the resulting initial kernel growth is more realistic. Results of comparative simulations confirm that the ignition modelling influences the flame propagation during the early stage. The overall timing evaluated with the flame kernel model is satisfactory. Specifically, the predicted time to peak pressure is within the experimental range and closer to the experimental mean time. The location of the peak overpressure is found to have limited relevance with the ignition modelling. Variations in overpressure and flame propagation speed are present during the early propagation. The difference between the maximum peak overpressures is observed to be small for the two tested ignition approaches. Therefore, with the same combustion model used, the investigated flame kernel model has a larger influence on the early propagation phase but it has a smaller effect on the later turbulent stage.

References [1] A. Alharbi, A. R. Masri, and S. S. Ibrahim, “Turbulent premixed flames of CNG, LPG,

and H2 propagating past repeated obstacles,” Exp. Therm. Fluid Sci., vol. 56, pp. 2–8, 2014.

[2] M. A. Abdel-Raheem, S. S. Ibrahim, W. Malalasekera, and A. R. Masri, “Large Eddy simulation of hydrogen-air premixed flames in a small scale combustion chamber,” Int. J. Hydrogen Energy, vol. 40, no. 7, pp. 3098–3109, 2015.

[3] B. J. Arntzen, “Modelling of turbulence and combustion for simulation of gas explosions in complex geometries,” Norwegian University of Science and Technology, 1998.

[4] S. S. Ibrahim, S. R. Gubba, A. R. Masri, and W. Malalasekera, “Calculations of explosion deflagrating flames using a dynamic flame surface density model,” J. Loss

Prev. Process Ind., vol. 22, no. 3, pp. 258–264, 2009. [5] S. R. Gubba, S. S. Ibrahim, W. Malalasekera, and A. R. Masri, “Measurements and LES

calculations of turbulent premixed flame propagation past repeated obstacles,” Comb. Flame, vol. 158, no. 12, pp. 2465–2481, 2011.

[6] S. R. Gubba, S. S. Ibrahim, W. Malalasekera, and A. R. Masri, “LES Modeling of Premixed Deflagrating Flames in a Small-Scale Vented Explosion Chamber with a Series of Solid Obstructions,” Comb. Sci. and Tech., vol. 180, no. 10–11, pp. 1936–1955, 2008.

[7] V. Di Sarli, A. Di Benedetto, G. Russo, S. Jarvis, E. J. Long, and G. K. Hargrave, “Large eddy simulation and piv measurements of unsteady premixed flames accelerated by obstacles,” Flow, Turbul. Combust., vol. 83, no. 2, pp. 227–250, 2009.

[8] N. R. Popat et al., “Investigations to improve and assess the accuracy of computational fluid dynamic based explosion models,” J. Hazard. Mater., vol. 45, no. 1, pp. 1–25, 1996.

[9] S. R. Gubba, S. S. Ibrahim, and W. Malalasekera, “Dynamic flame surface density modelling of flame deflagration in vented explosion,” Combust. Explos. Shock Waves, vol. 48, no. 4, pp. 393–405, 2012.

[10] P. Quillatre, O. Vermorel, T. Poinsot, and P. Ricoux, “Large eddy simulation of vented deflagration,” Ind. Eng. Chem. Res., vol. 52, no. 33, pp. 11414–11423, 2013.

[11] A. R. Masri, A. Alharbi, S. Meares, and S. S. Ibrahim, “A comparative study of turbulent premixed flames propagating past repeated obstacles,” Ind. Eng. Chem. Res., vol. 51, no. 22, pp. 7690–7703, 2012.

[12] S. R. Gubba, S. S. Ibrahim, and W. Malalasekera, “LES study of influence of obstacles on turbulent premixed flames in a small scale vented chamber,” in 6th Mediterranean Combustion Symposium, 2009.

[13] A. Alharbi, “Turbulent Premixed Flames Propagating Past Repeated Obstacles,” Ph.D. Thesis University of Sydney, 2013.

[14] M. P. Kirkpatrick, S. W. Armfield, A. R. Masri, and S. S. Ibrahim, “Large Eddy Simulation of a Propagating Turbulent Premixed Flame,” Flow, Turbul. Combust., vol. 70, pp. 1–19, 2003.

[15] J. B. Heywood, “Combustion and its Modeling in Spark-Ignition Engines,” International Symposium COMODIA 94. pp. 1–15, 1994.

[16] R. Herweg and R. Maly, “A fundamental model for flame kernel formation in SI engines,” Int. Fuels Lubr. Meet. Expo., 1992.

[17] P. D. Ronney, “Laser versus conventional iginition of flames,” Opt. Eng., vol. 33, no. 2, pp. 510–521, 1994.

[18] C. Ranasinghe, W. Malalasekera, and A. Clarke, “Large Eddy Simulation of Premixed Combustion in Spark Ignited Engines Using a Dynamic Flame Surface Density Model,” SAE Int. J. Engines, vol. 6, no. 2, pp. 898–910, 2013.

[19] G. Wang, M. Boileau, D. Veynante, and K. Truffin, “Large eddy simulation of a growing turbulent premixed flame kernel using a dynamic flame surface density model,” Comb. Flame, vol. 159, no. 8, pp. 2742–2754, 2012.

[20] S. Richard, O. Colin, O. Vermorel, A. Benkenida, C. Angelberger, and D. Veynante, “Towards large eddy simulation of combustion in spark ignition engines,” Proc. Comb. Inst., vol. 31 II, pp. 3059–3066, 2007.

[21] O. Colin and K. Truffin, “A spark ignition model for large eddy simulation based on an FSD transport equation (ISSIM-LES),” Proc. Comb. Inst., vol. 33, no. 2, pp. 3097–3104, 2011.

[22] R. N. Dahms, M. C. Drake, T. D. Fansler, T. W. Kuo, and N. Peters, “Understanding ignition processes in spray-guided gasoline engines using high-speed imaging and the extended spark-ignition model SparkCIMM. Part A: Spark channel processes and the

turbulent flame front propagation,” Comb. Flame, vol. 158, no. 11, pp. 2229–2244, 2011. [23] R. N. Dahms, M. C. Drake, T. D. Fansler, T. W. Kuo, and N. Peters, “Understanding

ignition processes in spray-guided gasoline engines using high-speed imaging and the extended spark-ignition model SparkCIMM. Part B: Importance of molecular fuel properties in early flame front propagation.,” Comb. Flame, vol. 158, no. 11, pp. 2245–2260, 2011.

[24] T. Lucchini et al., “A Comprehensive Model to Predict the Initial Stage of Combustion in SI Engines,” SAE Pap. 2013-01-1087, pp. 2013-01–1087, 2013.

[25] H. G. Adelman, “A Time Dependent Theory of Spark Ignition,” Symp. Combust., vol. 18, no. 1, pp. 1333–1342, 1981.

[26] T. Poinsot and D. Veynante, Theoretical and Numerical Combustion, 2nd ed. R.T. Edwards, Inc., 2005.

[27] Z. Chen, M. P. Burke, and Y. Ju, “Effects of Lewis number and ignition energy on the determination of laminar flame speed using propagating spherical flames,” Proc. Comb. Inst., vol. 32, no. 1, pp. 1253–1260, 2009.

[28] M. Boger, D. Veynante, H. Boughanem, and A. Trouvé, “Direct numerical simulation analysis of flame surface density concept for large eddy simulation of turbulent premixed combustion,” Symp. Combust., vol. 27, no. 1, pp. 917–925, 1998.

[29] F. Charlette, D. Veynante, and C. Meneveau, “A power-law wrinkling model for LES of premixed turbulent combustion Part I: non-dynamic formulation and initial tests,” Comb. Flame, vol. 131, no. 2, pp. 159–180, 2002.