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We present an automatic data-driven machine learning (ML) approach for the development, evaluation and interpretation of deep neural networks (DNNs) for turbulence closures and demonstrate their usage in the context of cold-flow large-eddy simulation (LES) of the four-stroke Darmstadt engine using an open-source compressible multi-dimensional CFD solver OFICE, in a hybrid PDE-ML framework. Rather than explicitly using canonical formulations of closure terms, these DNNs robustly discover the functional relationships between the large-scale features of the resolved flow (cell Re, strain and rotation rate tensors etc.) obtained by solving the Navier Stokes to the small-scale unresolved terms. Experimentally validated high-fidelity LES solutions of the engine at different crank angles are utilized as the ground truth to train the DNN based closure models.

Reduced-order models typically assume that the flow through the injector orifice is quasi-steady. The current study investigates to what extent this assumption is true and what factors may induce large-scale variations. Experimental data were collected from a single-hole metal injector with a smoothly converging hole and from a transparent facsimile. Gas, likely indicating cavitation, was observed in the nozzles. Surface roughness was a potential cause for the cavitation. Computations were employed using two engineering-level Computational Fluid Dynamics (CFD) codes that considered the possibility of cavitation. Neither computational model included these small surface features, and so did not predict internal cavitation. At steady state, it was found that initial conditions were of little consequence, even if they included bubbles within the sac. They however did modify the initial rate of injection by a few microseconds.

Sac-type nozzles, which are often used in gasoline direct injection (DI), induce asymmetry to the spray. The drill angle, that is, the angle between the axis of the nozzle and the axis of the injector, is one of the key causes of the asymmetric flow. Despite its significance, the influence of the drill angle on spray is poorly understood. In the current work, a parametric study has been carried out using single-hole sac-type nozzles by varying the drill angle. The drill angle was varied from a value of 0° to 45° in steps of 15°. Apart from the geometric variation, the ambient pressure and the fuel temperature were varied to achieve flash-boiling and non-flash-boiling spray conditions. Simulations were carried out using an in-house computational fluid dynamics (CFD) solver that accounts for thermodynamic non-equilibrium coupled with a liquid-gas interface-area-density transport model to account for primary atomization of the fuel.

Given the importance of the fuel-injection process on the combustion and emissions performance of gasoline direct injected engines, there has been significant recent interest in understanding the fluid dynamics within the injector, particularly around the needle and through the nozzles. The pressure losses and transients that occur in the flow passages above the needle are also of interest. Simulations of these injectors typically use the nominal design geometry, which does not always match the production geometry. Computed tomography (CT) using x-ray and neutron sources can be used to obtain the real geometry from production injectors, but there are trade-offs in using these techniques. X-ray CT provides high resolution, but cannot penetrate through the thicker parts of the injector. Neutron CT has excellent penetrating power but lower resolution.

This paper implements a coupled approach to integrate the internal nozzle flow and the ensuing fuel spray using a Volume-of-Fluid (VOF) method in the CONVERGE CFD software. A VOF method was used to model the internal nozzle two-phase flow with a cavitation description closed by the homogeneous relaxation model of Bilicki and Kestin [1]. An Eulerian single velocity field approach by Vallet et al. [2] was implemented for near-nozzle spray modeling. This Eulerian approach considers the liquid and gas phases as a complex mixture with a highly variable density to describe near nozzle dense sprays. The mean density is obtained from the Favreaveraged liquid mass fraction. The liquid mass fraction is transported with a model for the turbulent liquid diffusion flux into the gas.

Mesh generation is frequently one of the most labor-intensive aspects of in-cylinder engine simulation with computational fluid dynamics (CFD). This expense makes parameter studies, such like engine geometry, valve timing or injection timing, a particularly challenging endeavor. The present paper introduces a CFD approach for the simulation of the in-cylinder processes of an internal combustion engine that minimizes user-required meshing effort and can handle almost unlimited boundary motion. The adaptation is fully automated and avoids the use of target meshes and global solution remapping. The intention of the approach is to use CFD for numerous parameter variations involving combustion system variabilities. Therefore, an open source base is chosen to avoid limitations of individual simulations due to a finite number of commercial licenses. The approach is used here for the simulation of a modern direct injection spark igniton (DISI) engine.

Two cavitation models are evaluated based on their ability to reproduce the development of cavitation experimentally observed by Winklhofer et al. inside injector hole geometries. The first is Singhal's model, derived from a reduced form of the Rayleigh-Plesset equation, implemented in the commercial CFD package Fluent. The second is the homogeneous relaxation model, a continuum model that uses an empirical timescale to reproduce a range of vaporization mechanisms, implemented in the OpenFOAM framework. Previous work by Neroorkar et al. validated the homogeneous relaxation model for one of the nozzle geometries tested by Winklhofer et al. The present work extends that validation to all the three geometries considered by Winklhofer et al in order to compare the models' ability to capture the effects of nozzle convergence.

Given the complexities of simulating fuel injection, most models contain empirical parameters. This work presents a method of automatically adjusting empirical model parameters in a computational fluid dynamics (CFD) sub-model in order to best agree with an ensemble of experimental measurements. The method is demonstrated by a multiphase flow simulation of flash-boiling fuel injector nozzles. This paper describes a framework to automatically set inputs, launch individual runs, read the output of these runs, and intelligently choose new input values based on the difference between calculated mass flow rates and experimental values, in order to minimize error. The Hooke-Jeeves search algorithm was chosen for the optimization process, since it is reasonably efficient, does not require calculating derivatives, and is robust. The scheme scales well when employed on computer clusters, where numerous calculations can be run simultaneously using a batch queuing system.

Gasoline-direct injection using multi-hole nozzles is prone to flash-boiling due to the transfer of thermal energy to the fuel combined with the sub-atmospheric pressures present in the cylinder during injection. Flash boiling is governed by a finite rate interphase heat-transfer mechanism and hence a thermal non-equilibrium model was used for simulations. Additionally, the fuel composition plays an important role in flash boiling and hence, any modeling of this phenomena must account for the type of fuel being used. In the current work, in addition to single component fuels, a non-ideal mixing model is used to calculate the properties of gasoline-ethanol blends. The flash boiling of the different single and multi-component fuels is compared and a parametric study is conducted to observe the importance of flash boiling. The purpose of this study is to use CFD calculations to propose dimensionless parameters that can help to understand how multiple time scales interact.

The burden of creating meshes increases the cost of Computational Fluid Dynamics (CFD) and slows the rate at which new engine geometries can be investigated. Internal Combustion Engines (ICEs) with moving valves and piston present a special challenge, often requiring numerous different target meshes or case-specific codes for adapting the mesh. The goal of the present paper is to facilitate remeshing by calculating vertex motion, in parallel, for hybrid tetrahedral and hexahedral meshes. The calculated vertex motion is intended to maintain good mesh quality and reduce the need for interpolation to a new mesh. The demonstrated approach uses Laplacian-based smoothing for hexahedral cells and optimization-based smoothing for tetrahedral cells. Further, planar and cylindrical surfaces in the engine geometry are automatically recognized. As the engine volume changes shape, vertices may slide along the planar and cylindrical surfaces.