Computational Methodology for Knocking Combustion Analysis in Compression-Ignited Advanced Concepts

: In the present work, a numerical methodology based on three-dimensional (3D) computational ﬂuid dynamics (CFD) was developed to predict knock in a 2-Stroke engine operating with gasoline Partially Premixed Combustion (PPC) concept. Single-cycle Unsteady Reynolds-Averaged Navier Stokes (URANS) simulations using the renormalization group (RNG) k − ε model were performed in parallel while the initial conditions are accordingly perturbed in order to imitate the variability in the in-cylinder conditions due to engine operation. Results showed a good agreement between experiment and CFD simulation with respect to cycle-averaged and deviation of the ignition timing, combustion phasing, peak pressure magnitude and location. Moreover, the numerical method was also demonstrated to be capable of predicting knock features, such as maximum pressure rise rate and knock intensity, with good accuracy. Finally, the CFD solution allowed to give more insight about in-cylinder processes that lead to the knocking combustion and its subsequent effects.


Introduction
The automotive industry is currently confronted with the hard challenge of achieving a compromise between performance and sustainability [1]. Most research efforts are focused on further developing spark-ignited (SI) engines and the exploration of new advanced combustion modes due to their advantages in terms of pollutant emissions [2]. In both concepts, knocking combustion is a major drawback to achieving higher thermal efficiency.
The overall tendency to knock is highly dependent on engine operating conditions as well as other aspects such as fuel anti-knock properties or combustion chamber design. It is, therefore, critical to gain a better understanding of knock generation mechanisms in order to develop robust knock mitigation strategies.
Owing to the clear propensity to generate extremely high burning rates, Low Temperature Combustion (LTC) concepts such HCCI (Homogeneous Charge Compression Ignition) [3,4], PCCI (Premixed Charge Compression Ignition) [5,6] or PPC (Partially Premixed Combustion) [7,8] could mean a significant improvement [9]. However, the extreme thermodynamic conditions achieved inside the combustion chamber due to the higher compression ratios and boosting pressures increase the knock propensity, thereby being an important constraint for their application to commercial vehicles.
A research version of a 2-stroke HSDI CI engine was used as baseline engine. The main specifications of the engine and the injector configuration are summarized in Table 1. The control of the poppet valves relies on a hydraulic cam-driven Variable Valve Timing (VVT) system that allows to modify the opening/closing valve timings. Thanks to its flexibility to adjust the overlap among intake and exhaust periods, and the effective compression-expansion ratios, this system ensures an adequate in-cylinder flow pattern and optimizes the scavenging of burnt gases by reducing the short-circuit losses.
The equipped fuel injection system grants a maximum rail pressure of 110 MPa when operates with RON95 gasoline fuel. This is a prototype Delphi injection system which comes from a common-rail DFI 1.5 system.
The engine was installed in a completely instrumented test cell which supplies all required fluids for the engine operation through multiple auxiliary devices. The installation have independent water and oil cooling circuits and a low EGR system to supply arbitrary levels of cooled exhaust gas in any operating condition.
The in-cylinder pressure was measured with a Kistler 6061B pressure transducer flush-mounted between the intake and exhaust valves. A different piezo-resistive pressure sensor located at the cylinder liner close to Bottom Dead Center (BDC) was used to reference this pressure signal. Instantaneous signals, such as in-cylinder pressure, were sampled using a state-of-the-art acquisition system and recorded during 100 engine cycles for each operation condition.

Numerical Methodology
The main limiting aspect of traditional methodologies for the validation of CI engines operation, which are based on reproducing the in-cylinder pressure profile averaged from a given number of recorded cycles using simple turbulence schemes (URANS), is the incapacity to assess the cyclical deviation and its subsequent effects on combustion.
The use of more complex turbulence approaches (LES) and the simulation of several consecutive cycles is currently the standard approach to reproduce the CCV in spark-ignited (SI) engines [31,32] in which the combustion variability due to the larger turbulent scales is traditionally considered as the main cause of the cycle-to-cycle variation [33]. However, the huge increase of computational burden hardly compromises the application of LES modelling in most of the industry cases. Furthermore, it is not clear that pure stochastic fluctuations could explain the whole variation of flow conditions among consecutive cycles in gasoline PPC mode.
Available literature on CCV [34] claims that CCV observed in CI engines is mostly originated from the casuistic variability in fuel mass or trapped-gas conditions, rather than from arising in random variations in the turbulent flow and combustion process.
Therefore, other authors [35,36] employed URANS schemes to analyse CCV sources in several LTC strategies, where CCV is larger than in conventional Diesel engines but still far from SI engines. They investigated the cyclical dispersion from the point of view of the operation uncertainties. The basis of their approach is to perform many parallel URANS simulations in which one or more key operating conditions are perturbed about the reference conditions.
Here, a methodology based on this latter approach was used in an attempt of reproducing the experimental CCV and its effects on the combustion. Therefore, conditions at the intake valves closing (IVC) of a baseline cycle simulated were considered as the reference. These conditions, after being validated to ensure realistic in-cylinder conditions, were artificially modified in order to imitate the variation of the injected fuel, trapped mass, injection timing, etc.
The selection of those parameters that significantly affect the combustion was made by taking into account the conclusions obtained by Klos and Kokjohn [35] to reduce the number of parallel simulations as much as possible. Klos and Kokjohn found clear relationships among the dispersion of three operating parameters (EGR, mean gas temperature at IVC and fuel mass) and the combustion behaviour. Thus, these parameters and their recommended variations were utilized for modifying IVC baseline conditions. Nonetheless, an additional parameter must be considered in this study since the 2-stroke engine has a particular in-cylinder flow motion. While in traditional CI engines the swirl flow motion is clearly dominant, the tumble motion-characteristic of SI engines-prevails in this particular engine design. As reported by Vermorel et al. [31], the tumble intensity significantly changes among consecutive cycles. They observed from LES simulations data that the magnitude of this rotational velocity could vary up to 25% at IVC. Therefore, this parameter was also included together with the other three determined by Klos. The parameters and their maximum variations used to perturb baseline conditions are displayed in Table 2. Note that EGR value was replaced by the percentage of combustion products within the cylinder at IVC, this is an equivalent parameter that define the amount of inert gases available during the closed-cycle. In addition to the baseline simulated case, ten parallel closed-cycle simulations were performed whereas the initial conditions at IVC were accordingly perturbed by randomly distributed variations of these four parameters to sample the four-dimensional domain.
This procedure was applied to the operation condition detailed in Table 3. This is defined by a medium speed (1500 rpm) and medium-high engine load (1.04 MPa of indicated mean effective pressure) that shows moderate levels of knock.

Numerical Model Set-Up
The numerical model of the engine was developed using the commercial CFD code CONVERGE [37]. The numerical domain, as shown in Figure 1, included the complete single cylinder geometry and the intake/exhaust ports, allowing to perform complete cycle simulations. The mesh discretization was done using the cut-cell Cartesian method available in the code. The base mesh size was 3 mm throughout the domain in the reference grid configuration. Three levels of fixed embedding (0.375 mm of cell size) were added to the walls of the combustion chamber, ports and region near the fuel injector, to improve boundary layer prediction and the accuracy of spray atomization, droplet breakup/coalescence, etc. Mesh size in the chamber was reduced by two levels of embedding (0.75 mm of cell size) after the start of combustion, for an improved recreation of the interaction and reflection of the pressure waves while avoiding undesired spatial aliasing effects. The code also employed adaptive mesh refinement (AMR) to increase grid resolution by three levels of additional refinement (up to 0.375 mm minimum cell size) based on the velocity and temperature sub-grid scales of 1 ms −1 and 2.5 K, respectively. As a result, the total number of cells varied between 1.5 million at BDC and 0.5 million at Top Dead Centre (TDC). This mesh configuration was achieved after a grid sensitivity analysis [27], offering a grid-independent solution when simulating combustion and its produced unsteady pressure field in internal combustion engines.
The Mach Courant-Friedrich-Lewy was set to 1.0 during the combustion in order to properly capture the local pressure oscillations caused by combustion. Thereby, the calculation time-step was gathered between 0.05 and 0.5 µs. This value was also obtained from the previously referred work performed by Torregrosa et al. [27], whose demonstrated that the energy of the unsteady pressure field is highly sensitive to CFL Mach number, but also that the energy does not change when this parameter is close to or below one.
The renormalization group (RNG) k − ε URANS model [18] coupled with the heat transfer approach proposed by Angelberger et al. [38] was chosen for simulating the turbulent properties of the flow.
For combustion modelling, the SAGE detailed chemistry solver [39] was employed along with a multi-zone (MZ) approach, with bins of 5 K in temperature and 0.05 in equivalence ratio [40]. This combustion model, despite not using an explicit turbulent combustion closure [17], has demonstrated to perform well for simulating spray combustion under URANS schemes in previous works [41]. A reduced chemical kinetic mechanism for primary reference fuels (PRF) based on Brakora et al. [42] was used in this work to account for fuel chemistry. A blend of 5% n-heptane and 95% iso-octane was utilized for predicting the physical properties of the gasoline fuel, being a suitable surrogate for predicting the ignition features of the RON95 gasoline used in experiments. Activating iso-octane reactions, the chemical mechanism resulted in a 45 species and 152 reactions.
Coupled with appropriate turbulence models, Kodavasal et al. [43] demonstrated that a similar combustion approach allows an accurate reproduction of gasoline autoignition, while other researchers [29,44] established realistic rates of heat release under gasoline compression-ignited conditions. The fuel injection was described by the standard Discrete Droplet Model (DDM) [45] and Kelvin Helmholtz (KH)-Rayleigh Taylor (RT) breakup model was employed to model spray atomization [46]. The injection rate was determined from the experimental injector characterization. This process measures the mass flow rate and spray momentum flux in a specific test rig [47,48] for the injection configurations defined a priori in similar real test conditions, in order to provide the most realistic injection features.
Cylinder wall temperatures were assumed to be constant and estimated using a lumped heat transfer model [49]. The instantaneous pressure signals registered at intake/exhaust manifolds were used to fix the inflow/outflow boundaries located at the end of the intake/exhaust ports. The temperature at these boundaries was considered constant and equal to the time-averaged value registered at the same manifolds.
This configuration has proven to accurately reproduce the in-cylinder pressure field oscillations over a wide range of operation conditions and combustion regimes [26,50,51].

Results and Discussion
In this section, results from the application of the proposed methodology are presented an discussed. First, the validity of the numerical solution is verified. Then, the knocking combustion is visualized and further analysed using several visualization techniques.

Validation
Following the guidelines depicted during the methodology description in Section 3, a unique engine cycle was calculated and validated prior to run the multiple parallel executions with the modified initial conditions. The target of this preliminary step is to obtain a numerical solution that reproduces the mean behaviour of the experiments.
In this way, experimental and simulated cylinder pressure profiles of the baseline simulation are compared in Figure 2. As it can be seen, the CFD model correctly predicts the in-cylinder pressure. Indeed, the predicted pressure shows a similar deviation as measurements dispersion. Although RoHR traces show that the combustion phasing is slightly delayed and its peak value is minimally overestimated, they do not affect the maximum peak pressure in a significant way. Given that the calculation of this parameter depends on material deformations and blow-by losses that the model does not take into account, this effect may be attributed to a minor underestimation of the effective compression ratio. Once that the baseline simulation can be considered representative of the real operating conditions, ten parallel executions were performed with randomly distributed variations of the IVC conditions. In Figure 3, the same comparison previously done in Figure 2 can be seen but including now the CCV spread of this latter simulations. As can be seen from the graph, the standard deviation of simulations is similar to that observed in the measurements proving the validity of the methodology in this particular case of study. However, the interest of the analysis is not only to check the performance of the methodology to reproduce a realistic CCV but also to examine the effects of this variability on the traditional combustion/knock parameters. In order to accomplish this target, the maximum pressure rise rate and the Maximum Amplitude Pressure Oscillation (MAPO) are plotted at each measured and simulated engine cycle in Figure 4. The standard deviation is also included to evaluate the capability of the methodology to reproduce CCV effects. Again, comparable results were obtained in terms of mean and dispersion levels for both parameters.

Knocking Combustion Visualization
After the validation of the methodology, an analysis of the knock onset is performed in this section. The study is conducted for two extreme knocking cases. On the one hand, the simulated cycle number 8, highlighted in Figure 4, is selected as the upper limit since it exhibit the higher MAPO value. And, on the other hand, cycle number 9 is chosen as the lower limit, being the cycle with the slightest knock.
A series of snapshots were conscientiously chosen and plotted together in Figure 5 for studding the combustion process. They were specifically selected considering different stages of combustion to allow a proper visualization of the endgas auto-ignition.
In this figure, the combustion tracking is done by clipping the temperature field at 2000 K and colouring it by the fuel energy release, thus showing the location of the reaction zones. Besides, pressure profiles registered at the transducer position are included to distinguish at which cycle step is located each snapshot while allowing to relate the combustion with its corresponding pressure effects [51,52].
As can be seen in both sequences of snapshots, combustion starts spontaneously as a result of a first auto-ignition event located inside the piston bowl where local temperature and mixing conditions are more favourable. Then, the combustion rapidly progresses by consuming the charge located within the bowl. At this point, the pressure rise due to combustion compresses the unburned gases at the squish region, causing the appearance of additional hot spots as a result of a second auto-ignition event. Looking at the colour scale, the rate of energy released by these hot spots is very localized and noticeably greater than that released during the previous combustion phase.
Examination of the pressure profiles also reveals that the onset of these hot spots coincides with the instant at which pressure oscillations become apparent, showing again that this abnormal combustion event has many similarities with the traditional knocking combustion in SI engines. Furthermore, it is possible to see that the knock intensity decreases as combustion is shifted towards the expansion stroke.
Besides the visualization of the combustion progress, Figure 5 shows a comparison between two cycles with heavy and slight knocking conditions. It is clear from this figure that, while the ignition is produced 2 cad after TDC in the cycle with heavy knock, combustion is delayed almost 2 cad in the slight knock cycle. Moreover, the burning rate is significantly higher in the former case since temperature iso-volumes grow faster. Thereby, the endgas auto-ignition is produced closer to the TDC, contributing to increase the pressure rise and its associated local oscillations to a greater extent. However, despite these differences, it is important to note that spatial patterns are quite similar at the knock onset. Figure 5. Visualization of the combustion process. A sequence of snapshots is depicted in order to identify the differences between two extreme cases with a remarkable knock level variation. The combustion process is visualized by clipping the temperature field at 2000 K and colouring it by the fuel energy release.

Conclusions
In view of the challenges to manage the gasoline partially premixed combustion in compression-ignited engines, this paper proposes a numerical approach based on multi-dimensional CFD in order to improve the knowledge and understanding of this particular combustion concept. In particular, the presented methodology was specifically developed to capture knocking combustion, allowing an comprehensive analysis of all involved phenomena and their undesired effects.
The proposed methodology allows a realistic estimation of both the cycle-averaged and dispersion values of the main combustion/knock metrics while keeping the computational burden under reasonable values. Thereby it offers the chance to include these parameters in the design process, optimizing them altogether with the rest of relevant emissions and performance metrics.
Combining distinct visualization methods, such as iso-surfaces of temperature and energy release contours, allowed to identify the differences in the combustion process among two extreme cycles, thereby enhancing the understanding the knock phenomenon.
Results revealed that the propensity of the knock onset is reduced as the combustion is delayed towards the expansion stroke. In this sense, cycles with lower burning rates lead to a slight knocking combustion whereas high burning speed cycles tends to significantly increase the knock.
Nonetheless, further efforts must be taken to confirm, through LES simulations, that URANS is capturing all relevant phenomena in the knocking combustion. Moreover, further analysis should be done for providing more insight about the combustion process itself and its related knocking generation mechanisms. Funding: The work has been partially supported by the Spanish Ministerio de Economía y Competitividad through grant number TRA2016-79185-R. The equipment used in this work has been partially supported by FEDER project funds "Dotación de infraestructuras científico técnicas para el Centro Integral de Mejora Energética y Medioambiental de Sistemas de Transporte (CiMeT), (FEDER-ICTS-2012-06)" from the operational program of unique scientific and technical infrastructure of the Spanish Ministerio de Economía y Competitividad. In addition, J. Gomez-Soriano is partially supported by an FPI contract (FPI-S2-2016-1353) of the "Programa de Apoyo para la Investigación y Desarrollo (PAID-01-16)" of the Universitat Politècnica de València.

Acknowledgments:
The authors want to express their gratitude to CONVERGENT SCIENCE Inc. and Convergent Science GmbH for their kind support for the CFD calculations with the CONVERGE software.

Conflicts of Interest:
The authors declare no conflict of interest. The founding sponsors had no role in the design of the study; in the collection, analyses or interpretation of data; in the writing of the manuscript; nor in the decision to publish the results.

Abbreviations
The following abbreviations are used in this manuscript: