Large-eddy simulation study of combustion cyclic variation in a lean-burn spark ignition engine

Applied Energy 255 (2019) 113812

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Large-eddy simulation study of combustion cyclic variation in a lean-burn spark ignition engine

T

S. Wadekara, , P. Janasb, M. Oevermanna,c ⁎

a

Division of Combustion and Propulsion Systems, Chalmers University of Technology, Göteborg, Sweden Chair of Fluid Dynamics, Institute of Combustion and Gas-Dynamics, Universität Duisburg-Essen, Duisburg, Germany c Brandenburgische Technische Universität Cottbus-Senftenberg, Cottbus, Germany b

HIGHLIGHTS

cyclic variability in a homogenous lean-burn SI engine. • Combustion flame transition time develops the initial variations. • Laminar-to-turbulent flow field around the spark-plug controls cyclic discrepancies. • Local • Flow velocity vector have significant involvement in flame advancement and confinement. ARTICLE INFO

ABSTRACT

Keywords: Large-eddy simulation Combustion cyclic variation Flame surface density Ignition modelling Lean combustion

Multi-cycle large-eddy simulation (LES) was performed to investigate combustion cyclic variability (CCV) in a single cylinder spark ignition engine with a homogeneous lean ( = 1.25) isooctane-air mixture. The aim was to obtain physical insights into the early stage of combustion and its influence on CCV. Propagation of the flame was modeled by a transport equation for the filtered flame surface density within the LES framework. The ignition process was represented by the imposed stretch spark ignition model (ISSIM-LES). Ten consecutive cold flow LES cycles followed by two initialization cycles (12 cycles in total) were used to perform the reactive simulations concurrently. The simulation results were compared with experimental data. Although the number of computed cycles was fairly low, the LES was able to reproduce the cyclic variability observed in experiments both quantitatively and qualitatively. Firstly, validation of the simulation was done by comparing measured pressure traces. Secondly, correlations between the timing of the 10% fuel burnt mass fraction with early flame kernel growth and initial-to-turbulent transition period (in which there was an asymmetric flame kernel that persisted through the early development periods) were determined. Thirdly, calculated results of the flame propagation were analyzed at two cross-sections (in swirl and tumble planes) of the combustion chamber, which highlighted differences in instantaneous flame structures and propagation characteristics between the fastest and slowest cycles. Good overall agreement was obtained between the measurements and simulation data. The results revealed that the instantaneous velocity and fluctuation of flows around the spark vicinity affect growth of the early flame kernel and cause combustion cyclic variability.

⁎

Corresponding author. E-mail address: [email protected] (S. Wadekar).

https://doi.org/10.1016/j.apenergy.2019.113812 Received 23 April 2019; Received in revised form 9 August 2019; Accepted 29 August 2019 0306-2619/ © 2019 Elsevier Ltd. All rights reserved.

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Nomenclature

discharge characteristics, spark gap, electrode shape and cylinder charge. One of the main causes is variation in flow among individual cycles, which leads to variation in flame kernel growth. The initial flame kernel growth is a crucial phase of the whole combustion cycle and had been proposed to be responsible for up to 50% CCV [23,24]. Moreover, during the initial flame kernel evolution, different combustion regimes are expected depending on engine load and speed [25]. Hence, it is extremely important to investigate initial flame development, which is largely affected by the local flow, turbulence, mixture fraction and ignition system properties. Due to the negative impact of cyclic variability, there is a clear need for detailed understanding of the origin of deviations in the combustion processes and development of strategies to reduce CCV, especially in lean combustion. Conventionally, deviations in the evolution of in-cylinder pressure during combustion cycles have been used to detect and characterize cyclic variations, but they are not sufficient to identify causes of the variability. For this, detailed cyclic-resolved information is needed to analyze the local and global in-cylinder flows, together with thermal stratification and flame propagation features, including their complex interactions. In recent years, significant improvements have been made in experimental techniques, making it possible to identify the origin of CCV [26–28]. For instance, Alegiferis [29,30] showed that the flame kernel is strongly influenced by in-cylinder turbulence, causing the flame kernel to travel away from the electrode, which is considered a major source of CCV. Zeng [31] analyzed particle image velocimetry images along with heat-release data and showed that the large-scale flow plays a primary role in flame development variations, and led to conclusions that 50% of the flame variation in the studied system was caused by the flow and the rest was due to flame speed variation. Jung [32] investigated the effect of spark discharge energy and in-cylinder turbulence on CCV. They suggested that the combination of high spark discharge energy and high in-cylinder turbulence favors combustion stability. However, despite these advances, efforts to identify sources of CCV and quantify their contribution through measurement techniques are generally restricted by limitations of optical accessibility and ability to determine 3D flow characteristics. Due to the limitations of current diagnostic methods, 3D computational fluid dynamics (CFD) simulations are considered to be a reliable tool for analyzing in-cylinder processes. 3D-CFD simulations can also provide detailed insights into sources of cycle-to-cycle variations. Three well-known CFD techniques are available, with their own strengths and weaknesses. First, the Reynolds average Navier-Stokes (RANS) technique is extensively used for engine simulations [33,34]. This technique provides access to mean phase-averaged quantities with low a computational cost, but their ensemble-averaging nature restricts their use to global predictions only. Thus, RANS cannot be used to investigate unsteady features and formation of CCV [35]. Second, direct numerical simulation (DNS) can be used to resolve all the scales involved in the flow. However, this approach is computationally expensive, which limits its use to academic test cases. The third approach, large-eddy simulation (LES), can potentially address various phenomena by directly resolving large-scale structures and modeling small-scale structures of instantaneous flows. Thus, LES can be reliably used to model turbulent and reactive flows in SI engines. Some of the reacting LES studies in the context of CCV in SI engines can be found in [36–38]. Vermorel [39] investigated nine consecutive LES cycles in a single cylinder SI engine fueled with the premixed gaseous propane-air mixture and showed that the variation in coherent tumble motion, generated during the intake stroke, and high turbulence intensity during ignition, were the major sources of cyclic discrepancies. They also concluded that overall or local mixture variations did not have a significant influence. Truffin [21] explored the origin of CCV for a stable and unstable operating point in a propane-fueled SI engine. Qualitative comparison between fast and slow cycles at a specific operating point suggested that the local velocity fields around the spark plug induced variation in early flame kernel growth, and

All quantities are expressed in SI units. Greek characters p

density pressure air-fuel equivalence ratio flame surface density wrinkling factor efficiency function grid size

Subscripts res sgs b u eff ign d spk lam turb

resolved sub-grid scale burnt unburnt effective ignition displacement spark location laminar turbulent

Superscripts ~ – ∧ ° lam

Favre average Reynolds average combustion filter degree laminar

1. Introduction To meet stringent demands for lower emissions and higher fuel efficiency, various advanced technological solutions have been suggested. Promising solutions for clean and efficient combustion processes in spark ignition (SI) engines include geometrical improvement (downsizing) [1], advanced combustion modes (direct-injection, charge stratification and lean combustion) [2,3], turbo-charging [4], controlled auto-ignition [5], and exhaust gas recirculation [6]. These advanced technologies can improve fuel efficiency by 10–30% [7,8] and reduce pollutant emissions in comparison with conventional engines [9,10]. However, the operational range of such technologies is often limited by cyclic combustion variability (CCV) [11], defined as scatter of individual cycle characteristics around phase-averaged mean cycle characteristics, which result in different work outputs compared to targeted output of an engine. Cyclic variability of up to around 5% is considered acceptable [12]. Cycles with higher amplitude of pressure variation behaves very differently compared to mean cycle, potentially resulting in either a misfiring event (at the low-end of the range of variations induced by CCV) or abnormal combustion/knock (at the high-end of the same range) [13,14]. Moreover, large cyclic discrepancies can lead to increases in emissions [15] and fuel consumption by up to 10% for the same power output [16]. Causes of CCV have been studied using experimental techniques [17–19] and numerical models [20–22] for many years. Previous studies have demonstrated links between CCV and variations in spark 2

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consequently overall flame propagation. The results also indicated that CCV depends on the engine type and operational mode. Similar observations regarding the importance of aerodynamic variations around the spark plug were reported by Enaux [40], Granet [20] and Goryntsev [41]. Fontanesi [42] investigated CCV for different spark electrode orientations and positions, and the effects of flow fields around the spark plug in a high speed, fully loaded turbo-charged GDI engine. The results suggested that the orientation of the spark electrode plays an insignificant role in CCV, whereas, the velocity and fuel distribution around the spark plug were important influencing factors. Recently, Masouleh [43] investigated the effects of flow and thermal fields on CCV. They reported that variations in local thermodynamics and fluid dynamic conditions around the spark location induce discrepancies between the cycles, which are then magnified by the progress of early flame area. However, only a simplified engine-like geometry was investigated. As a summary of the literature review, some research gaps have been identified concerning CCV, particularly for lean-burn combustion in SI engine. First, investigation of effects of thermal and turbulence fields on CCV at local and global levels in lean burn conditions is required. Second, deeper understanding of the effects of initial flame kernel growth and transition from a laminar-to-turbulent flame is needed. Third, the role of the flow structure on flame spreading is currently not fully understood and needs further analysis. The numerical investigation presented here focused on effects of flow and thermal fields on CCV in a typical passenger car-sized SI-engine configuration with the following objectives: (1) validation of a numerical model for emulating cyclic variations observed in measurement, (2) numerically explore the origin of CCV during the initial flame growth period, (3) characterization of the origin of CCV through analysis of effects of the flow field and thermal stratification at the ignition timing, (4) comparison of the fastest and slowest cycles to identify effects of local variables on CCV, (5) assessment of the asymmetric nature of the flame in the combustion system. The paper is structured in five sections. This introductory section is followed by Section 2, which briefly describes the experimental configuration. The numerical model, geometry and numerical set-up are outlined in Section 3. In Section 4, numerical and experimental results are compared to validate the numerical model. Correlations between the burnt mass fraction (BMF), early burnt characteristics and laminarto-turbulent flame transition, and effects of global and local fields on CCV are presented. Differences between fastest and slowest cycles, and the asymmetric nature of the flame, are also discussed. The major conclusions are summarized in Section 5.

Fig. 1. Experimental setup used to measure flame positions in the tumble and swirl planes. Green color shows the setup used for the horizontal (swirl) plane, red color shows the vertical (tumble) plane. Reprinted from Chao He [26] with permission from Taylor & Francis.

in Table 1. Detailed description of the test facility and experimental boundary conditions can be found in [45,46]. For the fired measurement configuration, isooctane fuel was injected through a port-fuel injector located approximately 1 m upstream of the combustion chamber to ensure a homogeneous fuel-air mixture (air-fuel equivalence ratio = 1.25). The pressure and temperature were measured using piezoelectric pressure sensors and a PT-100 thermocouple, respectively. Fig. 1 shows the experimental setup used to determine the enflamed region. Measurements were made in the symmetric tumble plane (y = 0) and a horizontal (swirl) plane located 1.4 mm below the spark plug. Visibility was limited by the optical window of 38 × 12 mm and 43 × 70 mm frames in the tumble and swirl planes, respectively. Measurements were acquired separately in the tumble and swirl planes. For each plane, three runs with 200 fired cycles per run were recorded. Statistics of the flame measurements were calculated from data recorded in the last hundred cycles of each run. Therefore, the flame statistics corresponded to 300 cycles for each plane. Image recording was started from the ignition timing −16 °CA until 2 °CA for every second crank angle degree. The negative values of °CA correspond to the piston position before compression top dead center.

2. Experimental configuration The Darmstadt optical research engine [44] was chosen for this investigation because of the extensive databases available for validation. This SI engine featured a centrally-mounted spark plug, a pentroof wall-guided cylinder head and four valves. Optical access was provided through a flat piston window and quartz glass liner. Specifications of the optical engine and fired operating conditions are shown

3. Modeling approach 3.1. Large-eddy simulation

Table 1 Specifications and operating conditions of the optical research engine [26]. Bore/stroke (mm )

Displacement volume (cm3 ) Compression ratio Fuel Air-fuel equivalence ratio ( ) Engine speed (rpm ) Spark time Intake Valve Open/Close (° CA) Exhaust Valve Open/Close (° CA)

For the large-eddy simulation of flow and flame propagation, open source library OpenFoam-2.3.x was used to solve the Favre-filtered equations for mass (1), momentum (2), and energy (3) on a moving unstructured grid:

86/86 499

8.5:1 Isooctane 1.25 800 16° bTDC

¯ + t

325/−125

( ¯ uj )

( ¯ ui ) + t

105/−345

3

xj

= 0,

( ¯ u i uj ) xj

(1)

=

¯ij xj

+

sgs ij

xj

p¯ , xi

(2)

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( ¯ huj )

( ¯h ) + t

xj

( ¯K ) + t

+

( ¯ Kuj ) xj

=

xj

eff

h + xj

(pu ¯ j) xj

.

¯ lam ¯ Csgs = SL ((c c¯)/c¯ (1 c¯))( ¯ c = 4/3, model conc ) c , where c = 0.5, stant and laminar flame surface density ¯ lam = c + (¯c c ) ·N . Note that, the flame curvature was in conc cave shape towards the fresh gases for the positive value of curvature term, and vice versa. The flame strain rate corresponded to the resolved part was Sres = ( ·u NN : u ) ¯ c , and to the influence of unresolved eddies was Ssgs = (u / SL, / l ) u / ¯ c . The strain rate was mainly induced by the mean flow and turbulent fluctuations. The efficiency function was described by the intermittent turbulent net flame stretch (ITNES) function [52] as = 0.7exp [ 1.2/(u / SL) 0.3]( x / L) 2/3 . The term 2rb 1 (1 + ) SL ¯ c accounted for sub-grid scale stretch, come from the curvature during ignition phase generated by the turbulent wrinkling factor , laminar flame speed SL , and flame radius rb . Here, the wrinkling factor was set to unity due to low turbulent intensity at the ignition timing [51]. Finally, the ignition FSD source term for the creation of FSD at spark timing was furnished as ¯ c ) t 1, 0) . w¯ ign = max (( ¯ ign The transition between the resolved and sub-grid scale contributions to the flame was controlled by the global coefficient . This reformation complied to the continuous changeover from ignition to a fully developed turbulent flame. Its value approached unity when the radius of the flame reached the size of the combustion filter. Therefore, acted as a permuting factor, which remained close to zero during the ignition phase (c < 1), then progressively approached unity as ignition neared completion and the ¯ c equation switched to the fully developed transport equation. The global coefficient (x , t ) was defined in Eq. (9) as:

(3)

Here, the overbars denote filtered Reynolds averages and tildes denote Favre-filter quantities, with the relation q = q/ ¯ . In the governing equations, is density, uj is a flow velocity vector, p is pressure, K is kinetic energy, and ij denotes the filtered viscous shear stress. The effective diffusivity eff was calculated as the sum of laminar and turbulent thermal diffusivity. The unresolved sub-grid stress sgs was modeled with the standard Smagorinsky model [47], expressed by Eqs. (4)–(6): sgs ij

=

2 ¯ t (Sij

= CS2

t

Sij =

1 2

2 x

(4)

1/3 ij Skk ),

2Sij Sij ,

(5)

uj ui + . xj xi

(6)

In Eq. (4), t is the turbulent viscosity, ij is the Kronecker delta, and the Smagorinsky constant Cs was set equal to 0.2. The grid size x was calculated using the cubic root of the cell volume. 3.2. Combustion modeling A turbulent premixed combustion process was modeled with the assumption of a single step reaction mechanism. During the combustion process, a reacting wave front propagates from the burnt gas to the fresh gas region. The propagation can be described by a progress variable c, which equals zero in the fresh gas area and unity in the burnt gas region. Assuming equal thermal and molecular diffusivity (the unity Lewis number assumption) and no heat losses (adiabatic combustion), the transport equation (Eq. (7)) of the combustion progress variable was modeled:

¯c + t

· ¯u c

·

t

c

= w¯ c ,

= 0.5(1 + (tanh(rb+

t

= Tres + Tsgs +

)2rb 1 (1 + ) SL ¯ c + w¯ ign.

(9)

Here, is the flame radius resolved at the combustion filter, and the actual flame radius was calculated, assuming a spherical flame kernel, c d V)1/3 . as: rb = (3/4 0 ), the ignition source term was active and acAt ignition ( counted for flame surface production because of sub-grid scale stretch. As the flame kernel volume expanded and the value of rose from 0 to 1, the ignition source term was gradually suppressed, while the Cres, Csgs, ·(Sd N c ), Sres terms were triggered. These terms contributed to the sub-grid and resolved curvature, production and the resolved strain in the FSD equation, forming the standard FSD equation for the turbulent flame propagation and thereby enabling use of the transport equation from the earliest stage of ignition and its interaction with the local environment.

(7)

3.3. Ignition modeling Spark ignition and early flame kernel growth were modeled by the imposed stretch spark ignition model (ISSIM) [51], which was coupled with the ECFM-LES turbulent combustion model in the OpenFoam-2.3.x framework. The ISSIM model can deal with a flame kernel during both under-developed and fully-developed stages of the combustion processes, because it can solve the FSD transport equation immediately after a spark discharge and a flame front during the transition to propagation phase. It depicts the ignition process in two successive steps. The first step is imposition of the initial gaussian profile (Eq. (10)) of the flame kernel at the spark plug location on the ignition time tign .

(Cres + Csgs ) + Sres + Ssgs

·( Sd N ¯ c ) + (1

rb+ = rb/ .

rb+

Here t is a turbulent diffusion coefficient, and w c is a reaction source term. The filtered source term was modeled as w¯ c = u SL ¯ c , where the unclosed filtered flame surface density ( ¯ c or FSD) could be modeled using a simple algebraic expression, assuming equilibrium between flame surface production and destruction [48–50]. However, in this study, a modified FSD transport equation was solved, as previously suggested by Colin and Truffin [51]. This FSD transport equation can handle both the ignition phase (where the burnt gas volume is too small to resolved on a common engine mesh) and resolved flame front during propagation. The FSD can be expressed by Eq. (8): ¯c

0.75)/0.15)),

(8)

Here Tres, Cres and Sres are the resolved transport, curvature and strain rate terms, respectively, while Tsgs, Csgs and Ssgs are the unresolved transport, curvature and strain rate terms, respectively. The FSD equation was solved on a combustion filter width rather than the grid filter x , because the typical stoichiometric premixed flame thickness in a SI engine is around 0.1 mm [15], which is smaller than the grid resolution (in this work x 0.5 mm). The combustion filter reads x = nres , where the resolution number (nres ) varies between 5 and 10. The contribution of c transport due to convection of the resolved ·(u ¯ c ) , while, the sub-grid scale convecfield was defined as Tres = tion was modeled, under a gradient assumption, as Tsgs = ·( t ¯ c ). The resolved curvature of the flame structure was expressed as Cres = Sd ( · N) ¯ c , where Sd is the displacement speed (Sd = (1 + c ) SL ), N is the flame normal, and the thermal expansion rate = u / b 1. The sub-grid part of the flame curvature was represented as

c¯ign x , tign = c0exp

x

xspk 0.62

2 2

.

(10)

Here, xspk is the spark plug location, and c0 is an arbitrary model constant. After imposing the initial kernel, it permits the kernel to develop in turbulent atmosphere and the transport equation of the filtered progress variable (Eq. (7)) is solved using the reaction source term described in Eq. (11), as: 4

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Fig. 2. (a) Complete computational domain, (b) top view of cylinder head grid, (c) grids on tumble plane.

w¯ c = max ( u SL ¯ c ,

cign b (¯

c¯) t 1).

considered. The total number of cells at spark timing (16° bTDC) was around 1.4 million. Numerical setup: A time-dependent measured absolute pressure profile was imposed 530 mm upstream of the intake valves and 360 mm downstream of the exhaust valves. The in-cylinder pressure traces of the motored operation were validated with the averaged pressure traces from crank-resolved experiment data, shown in the previous work of Janas [55]. The flow fields of 12 consecutive cold flow LES cycles were used to perform the reactive simulation concurrently. The initial two cycles were excluded, because of dilution from the initial boundary condition, and results are presented for the last 10 cycles. The fired calculations started from the spark ignition timing (16° bTDC). The conservation of energy was accounted for by solving the filtered enthalpy equation. The temperature of the burnt and unburnt gases was calculated by the JANAF polynomial. The Sutherland law [56] was used to compute the molecular viscosity. A lean mixture of isooctane and air was considered with the air-fuel equivalence ratio = 1.25. The laminar flame speed was computed by a previously proposed empirical relation [57]. A fixed-temperature boundary condition with a wall temperature of 333 K was applied at all walls. A zero-gradient boundary condition was applied for all scalar quantities at walls, and a no-slip boundary condition was applied (except for the piston and valves) for the velocity. No additional wall modeling was considered for heat fluxes since the focus was away from walls. A pressure-based solver was used with strong pressure-density-velocity coupling, as it allowed to take advantage of bigger time steps. The time-step width was calculated by the CurrantFriedrichs-Lewy (CFL) criterion with a maximum CFL number of 0.5. The time integration was executed via an implicit second-order backward differencing scheme. Convective fluxes of the momentum were handled with a pure second-order accurate central differencing scheme. The FSD transport equation was solved over the combustion filter with the number of resolution nres = 5. The ignition model constant was fixed at c0 = 0.2 for all the combustion simulations presented here.

(11)

Here, t represents the computational time-step. The second step is to calculate the ¯ c for the mean reaction rate by solving the Eq. (8). 3.4. Simulation set-up Mesh handling: A good quality mesh (with low stretch, low skewness, and orthogonality) is essential for higher-order numerical schemes for a LES. Furthermore, to obtain correct solutions, mesh-induced errors, numerical instabilities, and artificial dissipation must be minimized. In this study, the entire meshing work was performed using a fully automated tool based on OpenFOAMs mesh generation utilities. The valves were closed by internal walls namely curtains around the valve seat regions. The complete computational domain, cylinder head with the grids, and the grids on the cutting plane (tumble plane) through the geometric center of cylinder are shown in Fig. 2. The grids consist of mostly equidistant hexahedral cells with a local mesh refinement around the spark plug and valve seat regions. The average grid cell sizes inside the combustion chamber, near the spark plug and around the valve seat region were 0.5, 0.2 and 0.1–0.4 mm, respectively. The mesh resolution at the intake and exhaust port was reduced to 1.5 mm. A mesh motion combined with a mapping strategy was applied without any topological changes, where each mesh was only valid for a certain crank angle interval. The calculated result at the end of each interval was mapped onto a new previously generated mesh for every 5 °CA. The simulation was then continued for the new interval. This procedure maintained high mesh quality during the whole numerical calculation. The maximum displacement in each 5 °CA interval was not more than 2.4 mm. For the mesh motion, a Laplacian equation (Eq. (12)) describing the cell node velocity uc was solved, in accordance with the boundary condition prescribed for piston and valve motion [53,54]:

xk

uc , k xk

=0

(12)

4. Results and Discussion

A smooth mesh deformation was controlled using the mesh diffusivity by introducing an artificial stiffness. The new position of the grid points was calculated by multiplying the deformation velocity by the time-step width [53]. Therefore, 144 grids were used for a full-cycle cold flow simulation. Here, the 12 grids relevant to the fired intervals were

4.1. Reproduction of experimental CCV This part focuses on validation of the numerical model by evaluating its reproduction of the experimental trends. Conventionally, in5

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Fig. 4. Comparison of correlations between peak pressures and crank angle positions of peak pressure in LES and experimentally monitored combustion cycles.

Fig. 3. Evolution of in-cylinder pressure and apparent heat release rate for 10 concurrent LES cycles plotted together with the experimental envelope (light gray traces).

satisfactorily reproduced the experimental findings, although it predicted slightly earlier and higher peak pressure in some LES cycles than the measured values. Both the measured and computed data were scattered around a straight line (R2 = −0.88), indicating stable combustion cycles as suggested by Matekunas. In summary, the numerical model accurately reproduced the experimental trends, the results suggest a high level of cyclic discrepancies, which needs a thorough investigation to identify and characterize sources of CCV. The crank angle resolved LES cycles help to identify the source of cyclic variation.

cylinder pressures and heat release rates are used to validate the accuracy of numerical models. Fig. 3 compares the evolution of the incylinder pressure and apparent heat release rate (AHRR) calculated for 10 concurrent LES cycles with experimental data obtained from observations of 300 fired engine cycles. Despite the limited number of simulated cycles, LES showed large dispersion of the in-cylinder pressures, suggesting high variability. Note that the simulated pressure curves showed no trends related to cycle number (sequences of relatively fast and slow cycles appeared to be random with respect to the cycle number) and did not precisely match any empirically determined curves, but had a similar range of variation. These findings indicate that the calculated pressure variability was not due to initialization but represented real cycle-to-cycle variation captured by the LES method (Objective 1). The simulation results accurately reproduced the high cyclic variability observed in the experiments. However, the results in Fig. 3 suggest that the cycle predicted by LES were generally faster than the experimentally observed cycles. The maximum pressure in most of the LES cycles were also higher than the statistical mean experimental cycle (not shown) and no LES cycles corresponded to the slowest experimental cycles. Cycle-3 was considered the slower LES cycle as it showed the highest deviation from the other cycles, while cycle-10 was the fastest, with slightly over-predicted pressure. The insert in Fig. 3 shows evolution of the in-cylinder pressure just after the spark discharge (at 16 °CA bTDC). The results suggest that the pressure rise was slightly affected by the initial flame kernel. However, flame kernel growth appeared to be more significant at later CA degrees after spark discharge. Moreover, the measured pressure curves indicate that combustion was almost completed by 30 °CA after TDC in all cycles. Ayala and Heywood [58] suggested that this condition is necessary for stable engine operation. The LES cycles also showed a similar combustion duration and CCV to those observed in the experimentally observed cycles. The LES cycles also exhibited negligible variation during the expansion stroke (after 15 °CA), suggesting trapped mass was nearly identical in all the cycles. Fig. 4 presents a Matekunas [59] diagram comparing peak cylinder pressures, and their timing of occurrence (in crank angle degrees), in the LES cycles and experimental data. It shows that the LES model

4.2. Early-burn variability of the flame development This sub-section reports examination of the early development of the flame kernel to study the occurrence of CCV during the laminar-toturbulent flame transition (Objective 2). The evolution of BMF (traditionally used to characterize early flame development) in the 10 LES cycles is shown in Fig. 5(a). These data enable statistical characterization of combustion variability by distinguishing the progress of each cycle, particularly highlighting fast and slow LES cycles. Note that, consistent with Fig. 3, combustion was fastest in cycle-10 and slowest in cycle-3. The insert in Fig. 5(a) displays the combustion progress just after the spark discharge event (16 °CA bTDC), and reveals that it varied substantially from the beginning of spark discharge. Similar observations of burnt mass variance before 10 °CA after spark time have been reported by Truffin [21] and Enaux [40]. To demonstrate the distribution of the combustion progress, distribution of CA at which three selected BMF values were reached in the simulated cycles are also shown in Fig. 5(a). Fig. 5(b) presents crank angle Probability Density Functions (PDFs) for each of these four BMF values, i.e. possibilities of reaching them at each crank angle position. The results demonstrate that the early flame kernel (at BMF = 0.02) was already dispersed (−10 ± 5 °CA) with a narrow quasi-Gaussian like distribution. As the flame propagated, the spread retained with a Gaussian-like distribution, but at BMF 0.9, the dispersion was more irregular and the distribution was no longer Gaussian. Before examining the flow characteristics, expected to have an influence on CCV, we investigated variations in the flame volume. Fig. 6(a) shows the progress of burnt gas volume after the spark discharge time for 10 LES cycles. Based on the variation in flame volume 6

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Fig. 5. (a) Right: Evolution of fuel burnt mass fraction in the LES cycles, (b) Left: Crank angle PDFs to reach four predefined BMF (0.02, 0.1, 0.5 and 0.9).

growth rate, flame development could be divided into three periods (marked by points A and B in Fig. 6(a)): laminar (initial) flame, transitional, and fully developed turbulent flame. The evolution of the flame volume indicates that the flame kernel deviated from the start consistent with the results presented in Fig. 5. Moreover, the flame development period between the ignition and transition from laminar to a turbulent could be critical for CCV. Thus, investigation of this transition was important. The period of this transition ( lam turb ), estimated from the 3D flame volume as proposed by Arpaci [60], is illustrated in Fig. 6(b). For initial estimation of the transition time, the positive peak curvature of the flame volume (Vf ) is calculated. Then, a linear fit between the flame volume and time is made for the laminarto-turbulent flame period. The intersection of the lines is defined as the laminar-to-turbulent flame transition. Our results show that lam turb occurred when BMF was still less than 10%. Crank angles corresponding to 1–10% BMF (CA1-CA10) were the most important for establishing the subsequent combustion event in each cycle. As the laminar-to-turbulent flame transition appeared to occur earlier than the crank angle corresponding to 10% BMF, we investigated the relation between early burning stages to CA10. Fig. 7 shows the correlation of CA10 with CA05, CA1, CA2 and CA5, as well as its relation with lam turb , in each of the LES cycles. Where, CAX is the period when the burnt mass fraction reaches X%. Equivalent

Fig. 7. Correlation of the CA10 combustion phase and initial combustion phases (CA05, CA1, CA2 and CA5) and laminar-to-turbulent transition time lam turb .

Fig. 6. (a) Right: Progress of burnt gas volume in 10 concurrent LES cycles. (b) Left: Estimation of the transition from laminar-to-turbulent flame propagation period in Cycle-5.

7

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Fig. 8. Iso-surface of the combustion progress variable colored by the flow velocity at 3 different instances for 3 consecutive LES cycles.

measurement values were not available owing to the complexity of measuring the early flame kernel. The results suggest that the combustion phase at CA10 was largely established by very early combustion phases, such as CA05, CA1 and CA5, as evident from the high correlation (R2 > 95). In contrast, there was poor correlation (R2 = 0.356 ) between CA10 and lam turb , possibly due to aerodynamic and thermodynamic features. However, lam turb still marked the transition between different growth rates. Fig. 8 shows the effect of large-scale velocities on the flame surface at different instants (TDC, 10 °CA aTDC and 20 °CA aTDC) in three consecutive, arbitrarily chosen, cycles. The flame is represented by an iso-surface of the filtered combustion progress variable colored by the flow velocity. The results show that the flame was progressively stretched (or compressed) and wrinkled by the turbulent flow. It also show that the flame spread more rapidly toward the intake side due to the tumble motion, whereas in the y-direction the flame propagation was more or less symmetrical in all three cycles. At TDC, the flame remained at the center and was well distributed in all directions. From 10 °CA aTDC onward, the flame propagation was faster in the y-directions than x-directions. The flame structure remained similar globally after 10 °CA. Based on these results alone, it is difficult to establish any correlation between the velocities, BMFs and lam turb . However, the results imply that the velocity is a major participant in the combustion variability. In summary, the combustion phase at CA10 correlated weakly with lam turb . However, analysis of the flow structure on the flame surface development suggested that the flow velocity substantially influences CCV and needs further investigations at the spark timing.

spark timing in all LES cycles. These data were collected in whole combustion chamber. The normalized PDF plots reveal negligible global statistical variation among the cycles. The normalized PDFs for the instantaneous velocity and velocity fluctuations indicate minor deviations, in the range 2–4 m/s and 0.5–1.5 m/s, respectively. These small differences can be considered negligible compared to the scale of combustion cyclic variations. However, as the data in Figs. 3 and 5 suggest, the local conditions around the spark plug might have some influence on the observed CCV. Hence, we extended the global analysis to a more local statistical analysis. Notably, the combustion rates of the cycles began to deviate from one another rather quickly after the spark time. Therefore, the local temperature and instantaneous flow fields around the spark plug at the spark timing were investigated. Fig. 10 shows the local flow statistics through cell-volume weighted normalized PDFs of the instantaneous velocity, velocity fluctuations and temperature at the spark time in all LES cycles. Local data were collected from with-in a radius of 3.5 mm of the spark plug location. The local flow PDFs reveal significant differences between the cycles. The instantaneous velocity distribution in the spark vicinity showed higher variations than the global variation, and seemed to be a potential source of CCV. Note that, the fastest cycle (cycle-10) corresponded to the highest instantaneous velocity PDF and vice versa. Moreover, the velocity fluctuations indicated similar behavior as the instantaneous mean velocity. Interestingly, the local temperature PDF exhibited very small variation compared to the instantaneous velocity and velocity fluctuations. These results indicate that the local instantaneous velocity and local velocity fluctuations were potential sources of CCV, whereas the local temperature field had negligible effect on CCV. To summarize, the global statistical analysis detected no clear correlation of global flow parameters as a source of CCV. However, the local statistical analysis suggested that the local flow conditions near the spark plug have a substantial influence on CCV, whereas the temperature field does not (or negligible) participate as a source of CCV.

4.3. Global and local analysis of the flow structure at spark timing The work reported in this sub-section focused on identifying the major contributors to early variations in the combustion cycles (Objective 3). Initially, global statistical information of the 3D turbulent flow fields at the spark timing was analyzed to explore these variations. Since the mixture was premixed, variation of the mixture fractions was minute, so the only factors probed were the thermal and turbulence fields. Fig. 9 shows cell-volume weighted normalized PDFs of the global flow instantaneous velocity, velocity fluctuation and temperature at the

4.4. Comparison of slowest and fastest cycle The fastest and slowest LES cycles were compared with corresponding measurements to examine effects of local variables on CCV 8

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Fig. 9. Statistics of global flow fields in all LES cycles: probability density functions for instantaneous velocity (top left), velocity fluctuation (top right) and temperature (bottom).

with the cylinder head (not shown) on the intake side, it subsequently propagated faster toward the intake than exhaust side, resulting in an elliptical shape overall. Unburnt fuel in the positive x-direction was consumed later by the flame propagation (not shown). Moreover, flame wrinkling increased throughout the propagation, enhancing its strong asymmetry. Fig. 12 shows a comparison of the flame propagation from measurements and individual LES cycles (cycle-3 and cycle-10) at three instants after spark ignition on the swirl plane (defined in Fig. 1). The flame propagation at the 2D swirl plane again reflected the strong cyclic variations. In particular, the flame shapes in the LES cycles strongly varied in terms of local wrinkling and covered different regions. Cycle-3 showed only small burnt pockets, whereas cycle-10 showed a more widely distributed burnt gas area. Moreover, the flame in cycle-10 exceeded the radial extent at almost all locations, in contrast to cycle-3 and the measurements. Overall, the burnt gases in the swirl plane were well distributed in all directions, unlike in the tumble plane. The flame expansion was relatively symmetrical since the in-cylinder flow had no swirl motion. At 10 °CA bTDC, the simulation of the flame kernel in cycle-3 corresponded well with the measurements, but its growth was over predicted in cycle-10. However, at later instants, the flame kernel growth remained small in cycle-3, while in cycle-10 it grew extensively and covered a nearly identical region to the measured region. There were significant differences between the calculated fastest and slowest cycles, possibly due to the varying instantaneous and fluctuating velocity gradients in the spark plug vicinity. Thus, it was

(Objective 4) and then the flow structure was investigated. Fig. 11 shows a comparison of the measured and simulated flame propagation, based on two LES cycles at three instants after spark ignition on the tumble plane (see Fig. 1). The selected LES cycles were the fastest (cycle-10) and slowest (cycle-3), identified based on BMF. The measured results were averages of measurements acquired during 300 fired cycles. In Fig. 11, the measured results are shown in a limited field of view (access through optical window), whereas the simulation results cover the whole domain including the highlighted interrogation window. The simulation results showed good overall prediction compared to the measurements, especially, regarding the position of the flame. However, cycle-3 showed slight under-prediction of the flame kernel size. Development of the flame was also different between the cycles: cycle-10 showed faster progression and larger flame area compared to cycle-3. However, the flame propagation was in the same direction in both cycles as well as in the measurements. The differences in flame dispersion were due to differences in the local velocity distribution near the spark plug, as shown in Fig. 10. These results suggest that the velocity of the local flow field plays a vital role in conveying the initial flame kernel out of the spark plug. According to the measurements, the flame kernel was circular due to averaging of instantaneous cycles. In contrast, the calculated results exhibited a relatively elliptical flame shape. The flame also showed preferential propagation toward the negative x-axis (intake side) due to the mean flow velocity at the spark plug resulting from the tumble flow created during the intake stroke. Although the flame interacted earlier 9

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Fig. 10. Statistics of local flow fields in all LES cycles: probability density functions for instantaneous velocity (top left), velocity fluctuation (top right) and temperature (bottom).

interesting to examine how the averaged fields advanced within the combustion chamber. This can be characterized by the spatial averaging of the fields along the flame front surface. The spatial averaging of any field ( ) over the surface (s) can be defined as:

s

=

s

ds

ds s

.

(13)

To further explore the variability between the fastest and slowest cycles, the local thermodynamic and fluid dynamic conditions at the

Fig. 11. Qualitative comparison of calculated and measured flame propagation on the tumble plane in the fastest and slowest cycles at three positions: 10°, 8° and 6° CA bTDC. 10

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Fig. 12. Qualitative comparison of calculated and measured flame propagation on the swirl plane in the fastest and slowest cycles at three positions: 10°, 8° and 6° CA bTDC.

flame surface were compared, in terms of crank angle resolved surfaceweighted average values of temperature, velocity, laminar flame speed and velocity fluctuation, after the spark discharge. The analysis focused on the period after spark discharge, when the first discrepancies appeared in the combustion cycles. The results, presented in Fig. 13, show that the average temperature on the flame surface at the spark timing was higher in cycle-10 (fastest cycle) than in the cycle-3 (slowest cycle). The average temperature in cycle-10 decreased after some crank angle degrees until it coincided with the average temperature of cycle-3 near TDC. The average temperature in cycle-3 then dominated during the rest of the combustion phase. Similarly, the average velocity near the spark timing was higher in cycle-10 compared to cycle-3. The low initial velocity in cycle-3 at least partially explains the initially slow flame propagation during the cycle. However, further justification is needed to analyze the slow combustion behavior of cycle-3. Moreover, velocity fluctuations at the flame surface near the spark timing were also higher in cycle-10 compared to cycle-3, consistent with the instantaneous velocity and temperature plot. This indicates that turbulence had weaker effects on the laminar flame speed (SL ) in cycle-3. Furthermore, the higher average temperature led to higher (SL ) values in cycle-10 at spark timing, compared to cycle-3. The (SL ) plot in Fig. 13 shows similar behavior to the average temperature values. However, the differences in (SL ) were not potentially larger, suggesting that the velocity fluctuation contributed more strongly than the laminar flame speed to the cyclic discrepancies. To summarize, qualitative comparison showed different flame structure in the fastest and slowest cycles, but the flame propagated in the same direction (toward the intake side). This demonstrates the substantial effect of mean flow near the spark plug. Moreover, spatial averaging of the parameters along the flame front surface showed that the instantaneous velocity and fluctuation had a dominant effect on the

laminar flame speed in inducing cyclic discrepancies. A similar study by Fontanesi [42] concluded that the velocity magnitude around the spark plug plays a significant role in flame development, but the velocity vector has no influence on cyclic variations. In contrast, Truffin [21] reported that the velocity vector plays a crucial role in flame development, and consequently influences cyclic variations. Therefore, despite some clear indications on the possible origin of combustion variance revealed by the local statistical analysis and calculation of spatial averaged fields experienced by the flame front, the present investigation of LES cycles was extended to evaluate the role of the flow vector. Fig. 14 shows the interactions between the flow vectors and flame contour (c = 0.5 ± 0.1) on the tumble plane in the fastest and slowest cycles at three instances. It can be seen that the flow directions strongly influenced the flame front propagation. The flame front was transported by the flow field vectors either stretching or compression. The vectors also helped to convey the flame kernel away from the spark electrodes. However, the flow structure in the two cycles looked identical globally. It should be noted that the flow vectors were oriented toward the negative x-direction. This flow was generated by the residual tumble vortex. The flame development was enhanced by the early propagation toward the intake side when it interacted with the low-scale tumble residuals. In cycle-10, the flow vectors induced spreading of the flame toward their flow direction at all considered instances. However, in cycle-3 a local recirculation zone that inhibited the flame was observed at 10 °CA bTDC. This hindrance prevented uniform flame growth. At later instances, the recirculation became weaker and promoted distribution of the flame. To further understand the link between the velocity vector and flame geometry, their interactions on the swirl plane were examined in the fastest and slowest cycles (Fig. 15). Globally, the flow pattern was 11

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Fig. 13. Crank angle resolved surface-weighted average temperature (top left), instantaneous velocity (top right), laminar flame speed (bottom left) and velocity fluctuation (bottom right) in the fastest (cycle-10) and slowest (cycle-3) cycles.

similar in both cycles, as manifested by the flame propagation (toward the negative x-direction). However, there were variations at the local level. In cycle-10, the flow vectors stretched the flame along their flow direction (highlighted by arrows in Fig. 15). This comparison clearly highlights the importance of the flow vectors (or residual tumble motion) at early ignition timing as they affect the initial kernel development in the spark plug vicinity. Obstruction of a strong local flow vortex affects flame kernel development. If the

kernel is completely confined, then partial quenching or ignition delay may also occur. 4.5. Quadrant analysis of asymmetric combustion The combustion variance analysis was further extended to more localized quadrant analysis to gain deeper understanding of the asymmetric flame behavior (Objective 5). This analysis focused on an

Fig. 14. Filtered flow field and iso-lines of the combustion progress variable (c = 0.5 ± 0.1 values) on the tumble plane in the fastest (above) and slowest (below) cycles at three instances: 10°, 8° and 6° CA bTDC.

12

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Fig. 15. Filtered flow field and iso-lines of the combustion progress variable (c = 0.5 ± 0.1 values) on the swirl-plane in the fastest (above) and slowest (below) cycle at three instances: 10°, 8° and 6 °CA bTDC.

arbitrarily chosen LES cycle (cycle-8). Fig. 16 shows the burnt flame field (left) on the swirl plane at 5 °CA aTDC and progression of the burnt gas volume in corresponding quadrants after the spark discharge (right). The results show that the flame approached the cylinder liner more quickly in quadrant-3 than in the other quadrants. Fig. 17 shows the normalized PDFs of temperature, laminar flame speed, instantaneous velocity and velocity fluctuation for the unburnt region in each of the quadrants at 16 °CA after the spark (TDC). The laminar flame speed and temperature PDFs are similar in all quadrant, and hence do not provide any clear inclination of variation in flame behavior. The velocity was highest in quadrant-3, which (interestingly) also had the highest burnt volume (Fig. 16). The instantaneous velocity and fluctuation PDFs are consistent with those of the burnt gas volume, indicating that the instantaneous velocity and fluctuation were largely responsible for the variation in flame behavior. In summary, results of the quadrant analysis suggest that the temperature and laminar flame speed make minimal contributions, while the instantaneous velocity and velocity fluctuation make significant contributions, to variations in flame propagation.

5. Conclusion Reactive simulations of 10 concurrent LES cycles in a real engine configuration were numerically investigated using the ISSIM ignition model to provide insights into CCV formation. The main conclusions were as follows: 1. The numerical model accurately reproduced experimentally observed combustion cyclic variations using ten concurrent LES cycles. 2. The early flame kernel highly deviated from a very early stage (spark discharge time). The laminar-to-turbulent flame transition preserved initial discrepancies, which persisted until the flame became fully turbulent. 3. Local flow fields around the spark plug at the spark time were the main factors controlling the cyclic variations, while the global flow statistics had little or no influence on the cyclic variations. Thermal stratification had negligible impact on cyclic variability at both global and local levels. 4. Comparison of the fastest and slowest cycles revealed a correlation

Fig. 16. Left: Combustion progress field in four quadrants at 5 °CA aTDC. Right: Growth of burnt gas volume in each of the quadrants. 13

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Fig. 17. Cell volume-weighted PDFs of temperature, laminar flame speed (SL ), instantaneous velocity and velocity fluctuation at 16 °CA after spark timing (TDC) in the unburnt regions of the four quadrants.

between the local variable and CCV. Initial differences in instantaneous velocity and velocity fluctuations between the cycles contributed to not only to early flame kernel deviation but also differences in burning rates of the cycles. 5. The results show that the flow vectors together with the velocity magnitude and fluctuations significantly affected flame propagation. The flow vectors were largely responsible for flame advancement and confinement. 6. The results clearly showed the unsymmetrical nature of flame behavior and development. Flame quadrant analysis revealed that the flow instantaneous velocity and fluctuations were the major factors affecting the flame asymmetry.

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