A Combined Numerical and Experimental Investigation of Cycle-to-Cycle Variations in an Optically Accessible Spark-Ignition Engine

Environmental pollution and global warming have prompted the need for the use of high-efficiency and low-emission propulsion technologies. Besides electric powertrains in vehicles, internal combustion engines (ICE) will still be used in the near future due to the advanced state of ICE technologies including their reliability, durability, and the existing mature supply chain, manufacturing infrastructure, and recycling facilities (Leach et al. 2020). Indeed, ICE operated with non-fossil fuels (e.g. e-fuels, biofuels, or hydrogen) will play an important role in the future transport sector, especially in combination with electrification for heavy-duty vehicles (Onorati et al. 2022). To reduce greenhouse gas emissions, thermal efficiencies are essential for ICE. Concepts such as exhaust gas recirculation (EGR) (Fontana and Galloni 2010; Kargul et al. 2019) and ultra lean-burn (Luszcz et al. 2018; Ye et al. 2021) are promising to improve the efficiency of spark-ignition (SI) engines. However, cycle-to-cycle variations (CCV), which are characterized by the non-repeatability of combustion events for consecutive engine cycles under the same nominal operating conditions (Heywood 2018), represent a limit to the achievable dilution level of stable operations, and thus limit the improvements of engine efficiency and emissions. The predictive description of CCV and fundamental understanding of its causes are still limited but are essential for the development of high-efficiency ICE.

The significant enhancement of engine diagnostics enables detailed experimental investigations of the in-cylinder process and CCV (Buschbeck et al. 2012; Zeng et al. 2015; Bode et al. 2017; Zeng et al. 2019). Important sources for CCV were identified, which include the kinetic energy of the flow field at stoichiometric operating conditions (Buschbeck et al. 2012), the flow-spray interaction for direct-injection spark-ignition (DISI) engines (Zeng et al. 2015), and flow features in specific regions (Bode et al. 2017; Zeng et al. 2019). Experimental studies typically focus on the global quantities, such as the in-cylinder pressure or heat release rate, and two-dimensional quantities, such as the mixture composition, velocity, and flame location in selected planes, due to the limited access to the three-dimensional fields. However, the availability of in-cylinder optical measurements allows a detailed comparison with numerical studies, where the three-dimensional fields are available. Such combined numerical and experimental investigations are promising to gain further understanding of CCV.

The advance of large-eddy simulations (LES) as an inherently unsteady simulation technique reflecting the stochastic nature of turbulent flows, enables numerical studies on CCV, such as qualitative analysis considering selected fast and slow cycles and systematic quantitative correlation analysis. Granet et al. (2012) carried out LES of stable and unstable engine operation conditions and demonstrated that LES can be used to distinguish a stable operation condition from an unstable one. Zembi et al. (2019) performed LES of three engine operation conditions with different values of relative air-fuel ratio. It was shown that LES has the capability to predict the transition from stable to unstable lean operation conditions. Enaux et al. (2011) reproduced the range of the variations of the in-cylinder pressure observed in experiments using LES. By comparing the selected typical fast and slow cycles, it was found that the velocity fluctuations at the spark plug play a significant role for early flame kernel development and the overall combustion. Using LES of a stable engine operation condition, Zembi et al. (2022) also showed that valuable indicators of the combustion rate can be derived based on the local flow fields around the spark plug. Under the investigated conditions, greater velocities lead to faster combustion processes. Zhao et al. (2018) conducted correlation studies using LES and showed that the velocity field close to the spark plug determines differences in flame propagation from cycle to cycle. Truffin et al. (2015) performed correlation studies to systematically investigate the influence of the global (referring to the whole cylinder) and local (referring to only the region close to the spark plug) variables at spark timing, such as the averaged local and global temperature, pressure, and flow features, on the indicated mean effective pressure (IMEP). Significant correlations were identified and it was found that the most relevant influencing variables are notably different for varying operating conditions. Using LES of two relevantly different engines, d’Adamo et al. (2019) demonstrated significant correlations between the global as well as the local variables and the duration of the first 1% of mass fraction burned (MFB1). They also found that the most influencing factors for determining CCV are case specific. In the literature, reactive LES results for CCV investigations are commonly validated with experiments using global variables, such as the in-cylinder pressure, or mean velocity fields as well as flame images. However, detailed comparisons between LES and experiments, especially including both the velocity fields and flame images conditioned to the fast and slow cycles, are rare. The correlation analyses of CCV usually focus on a single combustion parameter, such as IMEP, MFB1, or the maximal in-cylinder pressure. In addition, the large-scale flow features are typically represented by global quantities, such as the tumble and swirl ratio based on the center of in-cylinder mass considering gas motion inside the whole cylinder, which are not suitable for some engine geometries or operating conditions. A systematic analysis of multiple aspects is expected to further increase the understanding of CCV, such as the separate evaluation of combustion phases in combination with their main different governing effects and proper description of the coherent vortex structure.

The present study aims to systematically assess the influence of variables extracted from different length scales on the CCV of different combustion phases. For this purpose, a combined numerical and experimental investigation of an optically accessible SI engine with a detailed comparison between LES and experiments has been carried out. The comparison includes the flow fields, the spatial flame distribution, and especially the fields conditioned on the fast and slow cycles. The method presented by Buhl et al. (2017) has been employed to detect the three-dimensional vortex structure in the complex in-cylinder flows. Stable and unstable operating conditions have been considered.

The remainder of the paper is organized in the following manner. First, the experimental methods and operating conditions are given in Sect. 2, followed by the numerical methods in Sect. 3. Then, a detailed comparison between LES and experiments, including the in-cylinder pressure, the velocity fields, and the flame propagation, is presented in Sect. 4. Afterwards, CCV of the early flame kernel development and the flame propagation are analyzed along with their sources in Sect. 5. Finally, the paper finishes with a summary and conclusions.

The engine considered in this study is the well-characterized single-cylinder four-valve optically accessible engine at TU Darmstadt (Baum et al. 2014). The research engine employs a Bowditch piston extension, a flat quartz glass piston surface, and quartz glass cylinder liner to allow optical access from the bottom and the sides of the cylinder. The engine’s spray-guided cylinder head configuration with a pent-roof and a bore and stroke each of 86 mm results in a compression ratio of 8.7:1. Using two large plenums upstream of the intake pipe, vibrations and acoustic oscillations are controlled to provide precise boundary conditions. Two part-load operating conditions with an intake pressure of 0.4 bar and an engine speed of 1500 rpm were selected to represent a stable (stab) and an unstable (unst) condition for fired engine experiments of stoichiometric iso-octane fuel introduced via port fuel injection. The stab case is characterized by the continuous firing of a stoichiometric fuel-air mixture. For the unst case, nitrogen and carbon-dioxide are mixed with the intake air to simulate 12.9% external EGR. To ensure a constant amount of total EGR, the unst case employed skip-firing in which only every 7th cycle was ignited in order to flush out residual exhaust gases due to internal EGR before the next ignition cycle. Furthermore, the unst case has an earlier ignition timing. The ignition timing of both conditions was optimized such that the average cycle’s 50% mass fraction burned (MFB50) occurred at 8 crank-angle-degrees (CAD). In this study, 0 CAD stands for compression top dead center. The resulting coefficient of variation (COV) of the maximum in-cylinder pressure for the unst case is 12.8% compared to 3.51% for the stab case. Although the stab case has a higher amount of residual gases due to the internally induced EGR by the valve overlap, the condition is nevertheless more stable than the carefully controlled external EGR case due to the different spark timings. The later spark timing of the stab case results in a stable operation and an average exhaust temperature of more than \(250\,^{\circ }\)C greater than the unst case. Engine specifications and operating conditions are summarized in Table 1.

High-speed planar Mie scattering of oil droplets was used to measure the velocity field via particle image velocimetry (PIV). The burned gas areas where oil droplets were evaporated represent the position of the flame. The velocity and burned gas measurements of the stab case were conducted using the setup (and same vector processing) as described in detail by Hanuschkin et al. (2021) and Dreher et al. (2021), who measured image pairs from \(-\,360\) to 0 CAD in increments of 5 CAD (1.8 kHz). For the unst case, oil droplets were illuminated by two laser sheets from pulsed \(\hbox {Nd:}{\hbox {YVO}_{4}}\) cavities and were captured by a Phantom v2640 ultra high-speed camera equipped with a Sigma lens (APO Macro 180 mm F2.8 EX DG OS HSM, set to f/5.6), 532 nm bandpass filter, and a correction lens of focal length \(\textit{f} = +\,2000\) (to counteract the astigmatism caused by the curved cylinder glass) at a sampling rate of 4.5 kHz (\(-\,180\) to \(-\,4\) CAD , increments of 2 CAD). Burned gas regions were captured using the second frame of each image pair and indicate the position of the flame; therefore, the rest of this work will refer to extracted burned gas regions as the flame. The different laser and optical systems used coupled with the improved painting of the back of the cylinder glass resulted in fewer reflections in the PIV images of the unst case. Therefore, the resulting flame images of the unst case require less masking before analysis.

Vector processing of the unst case was conducted using the software DaVis 10.1.2 and employed a multi-pass cross-correlation technique (first 2 passes: \(64 \times 64\), 50% overlap; last 2 passes: \(32 \times 32\), 75% overlap; after each pass: peak ratio criterion of 1.3, universal outlier detection of \(7 \times 7\), and a vector group removal criterion of size 5). Further processing of velocity fields such as obtaining instantaneous line profiles or the mean vector field was conducted using MATLAB. Likewise, extraction of the flame for both cases from burned gas regions was conducted using an in-house MATLAB script whose procedure is as follows: After masking and dewarping (3rd order polynomial), raw images were grouped by their respective cycle then the intensity counts of each image were normalized by the maximum intensity achieved in the respective cycle. Afterwards, a sliding entropy filter (5 px \(\times\) 5 px) was applied, followed by the division of each image by the first image without a flame. Next, the pixels whose intensities were less than 1 were set to 0, an erosion (disk radius of 4) removed small structures around all edges, a minimum area criterion of 200 px was applied, all holes were filled within each flame, and finally a dilation of the same size of the erosion was applied to restore the flame size.

In this study, LES of the optical engine was performed using a commercial 3D-CFD code, CONVERGE (version 3.0) (2009), which is based on a finite-volume approach. The computational domain is discretized with a Cartesian mesh with local mesh refinement as shown in Fig. 1. The largest cell size in the cylinder is 0.5 mm. Local refinement is applied in the region close to the cylinder walls, near the spark plug, and in the crevice, with a cell size of 0.25 mm. Similar resolutions were employed in previous engine LES studies (d’Adamo et al. 2019; Truffin et al. 2015; Zembi et al. 2019) and proposed by Zembi et al. (2019) as the best compromise to resolve more than \(80\%\) of turbulent kinetic energy with a computational cost not overly expensive. A coarser mesh is used in the intake and exhaust ports with the largest cell size of 4 mm. The computational domain is composed of about 2.5 million cells at top dead center (TDC) and about 7.5 million cells at bottom dead center (BDC). Simulation of a full engine cycle of 720 CAD took about 60 h on 480 cores.

The intake and exhaust boundaries of the computational domain are specified at the positions where experimental boundary conditions are available. In particular, measured instantaneous static pressures and average temperatures are imposed at the boundaries. Since the variations of those boundary conditions over different cycles are negligible (\(<0.1\)  bar for pressure and \(<\,1\) K for the intake temperature), they are kept constant for multiple LES cycles. Blow-by is expected to be small in the investigated engine (Baum et al. 2014) and is not considered in the LES. The temperature on the walls of the combustion chamber and on the walls of the manifolds are specified as \(60\,^\circ\)C and \(36\,^\circ\)C in the LES, respectively. Dirichlet boundary conditions are applied for the crevice and cylinder walls, while the velocity wall model by Werner and Wengle (1993) and the heat transfer model by Amsden et al. (1989) are used for the walls of the manifolds where mesh resolution is coarser.

The compressible Favre-filtered governing equations of mass, momentum, energy, and species are solved using the finite-volume method and discretized by a blending second-order scheme in space. The Pressure Implicit with Splitting of Operator (PISO) method (Issa 1986) is used for the pressure-velocity coupling. A second-order Crank-Nicolson (Crank and Nicolson 1947) time integration is employed. Details about the discretization schemes and the iterative algorithms can be found in the CONVERGE manual (2020). The one-equation eddy viscosity model (Yoshizawa and Horiuti 1985; Menon and Calhoon Jr 1996) is used for the LES sub-grid scale (SGS) closure, where a transport equation for the SGS kinetic energy, \(k^\mathrm {sgs}\), is solved. The G-equation model (Pitsch 2002) is applied to describe the turbulent flame propagation, where the flame front is tracked using a levelset approach by solving a transport equation of the variable \({\widetilde{G}}\) (Peters 2009). The flame front is defined at \({\widetilde{G}}=0\). \({\widetilde{G}}<0\) and \({\widetilde{G}}>0\) indicate the regions of unburned and burned mixtures, respectively. Chemical equilibrium (Pope 2003, 2004) is assumed for the burned mixtures. The transport equation for \({\widetilde{G}}\) readswhere \(s_\mathrm {t}\) is the turbulent flame speed. \(\left( -{\overline{\rho }} D_t {\widetilde{\kappa }} + \rho _u s_t \right)\) can be understood as the propagation speed of the filtered flame front. The filtered flame front curvature \({\widetilde{\kappa }}\) and turbulent diffusivity \(D_\mathrm {t}\) are given byandwhere \(\varepsilon ^\mathrm {sgs}\) is the SGS turbulent dissipation modeled by \(C_\varepsilon \left( k^\mathrm {sgs} \right) ^{3/2}/\Delta\). \(\Delta\) is the filter width. The SGS Schmidt number Sc and the modeling constants \(C_\mu\) and \(C_\varepsilon\) are set as 0.78, 0.0845, and 0.05, respectively. The turbulent flame speed \(s_\mathrm {t}\) is given by Pitsch (2002)where \(s_\mathrm {l}\) is the laminar flame speed, \(\mu\) is the dynamic viscosity, \(\mu _\mathrm {t}\) is the turbulent viscosity, \(u^\prime\) is the SGS velocity, and \(b_1\) and \(b_3\) are modeling constants. Eq. (1) is solved using the levelset approach. Outside the flame surface, the scalar is required to satisfy \(\mid \nabla {\widetilde{G}}\mid =1\). The \({\widetilde{G}}\)-field is reinitialized as unburned in every cycle before ignition. A look-up table for the laminar flame speed \(s_\mathrm {l}\) has been generated with FlameMaster (Pitsch 1998) using a detailed iso-octane mechanism (Cai et al. 2019). The modeling constants \(b_1\) and \(b_3\) in the turbulent flame speed model are calibrated to match the mean in-cylinder pressure in the experiments. The necessity of such calibration might be attributed to the poor prediction of the SGS velocity and the underresolved flame wrinkling in the performed LES. Due to the different thermodynamic conditions of the stab and unst cases, \(b_1\) and \(b_3\) have different values for both cases. The ignition is realized by adding an energy source of 100 mJ within a sphere with a radius of 0.5 mm. Positive \({\widetilde{G}}\) is initialized in the region with a temperature higher than a threshold of 4000 K. The same ignition is used for both cases. Because of this simplified ignition model, which resulted in faster early kernel development, the ignition timing is calibrated to match the experimental mean pressure trace, especially for the first 10–20 CAD after ignition, as proposed by Esposito et al. (2020). An increase of \(b_1\) or \(b_3\) or earlier ignition timing leads to higher in-cylinder pressure. The calibrated model parameters are summarized in Table 2 for both cases.

For the stab case, consecutive cycles are simulated. For the unst case, the skip-firing mode is realized in the LES by first simulating consecutive non-reactive cycles without ignition and then using these results as initial conditions for the reactive simulations to reduce the computational cost.

This section presents a detailed comparison of the LES and the experiments. More than thirty cycles were simulated for both cases. The first two simulation cycles are not considered in the analysis, since they are influenced by the assumed initial condition (Truffin et al. 2015). In the experiments, about 200 and 1000 cycles are measured for cases stab and unst, respectively.

After the detailed comparison of LES and experiments shown in the previous section, the sources of the CCV in the simulations are analyzed here. Despite the differences between the LES and experiments, the analysis of the CCV in the LES may shed new light on the causal chain of engine CCV with the available three-dimensional data.

This paper presents a combined numerical and experimental investigation of an optically accessible SI engine with port fuel injection. Two operating conditions are considered: a stable operating condition with continuous firing of a stoichiometric fuel-air mixture and an unstable operating condition in a skip-firing mode with homogeneous external EGR.

The LES is carried out with well-established turbulence, combustion, and ignition models. A detailed comparison between LES and experiments is performed. Even with some difference in the expansion stroke of the unst case, a good agreement of the in-cylinder pressure, especially the maximal in-cylinder pressure and its cycle-to-cycle variation, is obtained. It is also confirmed that LES is able to distinguish the stable and unstable operating conditions in terms of the flow field and flame propagation. Good agreements for the general flow structure, the phase averaged velocities, and their fluctuations during the intake and compression strokes are achieved. However, small discrepancies are observed for the location of the vortex center in the compression stroke. The spatial flame distribution is also well reproduced in the LES when considering all cycles of each case. For the stab case, the same trends as the experiments are also found in the LES for the flow fields and the spatial flame distribution conditioned on the high and low pressure cycles. Conversely, discrepancies are observed for the conditionally averaged quantities of the unst case, an observation that is likely attributed to the lack of a spark plasma and subsequent flame kernel growth in the ignition model.

A systematic quantitative correlation analysis between the influencing variables extracted from different scales of the 3D LES and the CCV of the early flame kernel development and the consequential flame propagation is conducted. The influencing variables include the spatially averaged mean temperature and pressure and the flow features in the spherical region (\(r=3\) mm) centered between the spark plug electrodes, parameters for the three-dimensional coherent vortex structure (\(r=12\) mm), and the large-scale parameters that consider the whole cylinder (\(r=43\) mm). The most relevant influencing variables are different for different operating conditions and combustion phases. However, for both cases, the location of the coherent vortex center plays a significant role in the combustion process, which is also confirmed by the conditionally averaged flow fields in the measurement of the unst case. For the unst case, the flow direction in the region close to the spark plug is found to influence the early flame kernel development. A slower growth of the early flame kernel is observed if it is pushed towards the spark plug. For the stab case, the internal EGR is found to significantly correlate to the flame propagation. The large-scale flow features are also found to influence the flame propagation for both cases. Such main findings in terms of sensitivities regarding CCV are in close agreement with the experimental study by Welch et al. (2022). Finally, the flame kernel interactions with the flow close to the spark plug and the coherent vortex structure are found to be the cause for the misfire cycle in LES of the unst case, which indicates that proper control of the vortex location might be promising to avoid misfire.