**1. 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.

In particular, PPC operated with low reacting fuels, such as gasoline, have shown encouraging results to achieve very low pollutant emissions while maintaining, or even improving, the thermal efficiency [10–12]. Indeed, this combustion concept operated in an innovative 2-Stroke high speed direct injection (HSDI) compression-ignited (CI) engine [13] offers a good flexibility to control the combustion timing and to extent the load range [14–16].

This concept operates between completely premixed and fully diffusive conditions, whereby low pollutant emissions may be attained. However, to achieve these conditions while retaining an accurate combustion timing control with the injection event remains as the main drawback of this particular system when operating under transient conditions.

Despite the attractive benefits of this engine system, its complexity due to the large number of parameters to be managed requires the use of optimization techniques which ensure greater flexibility, speed and lower costs than purely experimental procedures.

In this framework, the use of computational fluid dynamics (CFD) simulations is nowadays widely established in both the research community and the automotive industry. Here, aspects such as the simulation of turbulence and how it couples with the chemistry [17] are still the main limiting factors for reproducing the reacting flow field accurately. Since the requirements in both fields tend to differ, specially in terms of time available, the approaches used are also usually different. While in the industry sector, simulations are based on Unsteady Reynolds-averaged Navier–Stokes (URANS) turbulence modelling [18,19] and flamelet-based combustion models [20] owing its lower computational demands, the research community prefer to resort to high-fidelity combustion models and more complex turbulence schemes such as Large Eddy Simulations (LES) [21] or Direct Numerical Simulations (DNS) [22].

Although the industry standard tends to simplify the simulations as much as possible, reproducing only the most pertinent phenomena while dismissing the irrelevant ones, it is not always possible to meet all requirements in complex situations where there is no clearly dominant phenomenon. For instance, knocking combustion in SI engines appears as result of a particular situation in which local thermodynamic conditions are critical. In this context, the recreation of the in-cylinder temperature field (hot-spots, chamber inhomogeneities, etc.), turbulence field (flow velocity and at the spark plug) and species distribution (EGR, fuel injection, etc.) is determinant for the knock [9] and CCV prediction.

Misdariis et al. [23] has proven the suitability of multi-cycle LES and dual heat transfer to reproduce the cycle-to-cycle pressure variations (CCV) under knocking-like conditions [24]. However, requirements in terms of mesh resolution and runtime are prohibitive for practical applications. Furthermore, reproducing pressure effects of knock—local pressure oscillations—is extremely demanding [25–27], further compromising its application to the industry environment.

The main objective of this paper is therefore to develop and validate a robust knock simulation methodology based on 3D CFD modelling that allow to include knock systematically in the design process of future automotive engines. In order to achieve this target, several simplifications should be applied. For example, resorting to single-cycle simulations, using URANS turbulence schemes, perturbing the initial conditions and other strategies based on the experimental observation.

This paper is organised as follows. First, the engine and test cell specifications are briefly described. Then, the methodology is widely explained, along with the details of the CFD model. Subsequently, results from the validation are presented and discussed. A detailed analysis of the knock onset is also included hindsight. Finally, the paper concludes with a summary of the main findings.
