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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.

Understanding the complex, transient spray phenomena associated with Gasoline Direct Injection (GDI) technologies continues to be key when designing injection systems to meet the stringent performance and emissions standards of modern internal combustion engines. Internal flow phenomena, such as string cavitation and hole-to-hole flow variations, are often highly transient and affected by turbulence. To better understand the current degree to which turbulence modeling influences simulations of GDI sprays, RANS and LES simulations have been performed on the multi-hole Spray G injector through the start of injection phase, with results compared to previously available X-Ray radiography data. Specifically, the k-ω SST RANS model and the k-equation LES model with a WALE sub-grid scale stress model have been tested on grids generated with the Generation 3 Spray G geometry, which includes as-produced injector dimensions based on X-Ray radiography measurements.

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.

The dense spray region in the near-field of diesel fuel injection remains an enigma. This region is difficult to interrogate with light in the visible range and difficult to model due to the rapid interaction between liquid and gas. In particular, modeling strategies that rely on Lagrangian particle tracking of droplets have struggled in this area. To better represent the strong interaction between phases, Eulerian modeling has proven particularly useful. Models built on the concept of surface area density are advantageous where primary and secondary atomization have not yet produced droplets, but rather form more complicated liquid structures. Surface area density, a more general concept than Lagrangian droplets, naturally represents liquid structures, no matter how complex. These surface area density models, however, have not been directly experimentally validated in the past due to the inability of optical methods to elucidate such a quantity.

The salient features of modern gasoline direct injection include cavitation, flash boiling, and plume/plume interaction, depending on the operating conditions. These complex phenomena make the prediction of the spray behavior particularly difficult. The present investigation combines mass-based experimental diagnostics with an advanced, in-house modeling capability in order to provide a multi-faceted study of the Engine Combustion Network’s Spray G injector. First, x-ray tomography is used to distinguish the actual injector geometry from the nominal geometry used in past works. The actual geometry is used as the basis of multidimensional CFD simulations which are compared to x-ray radiography measurements for validation under cold conditions. The influence of nozzle diameter and corner radius are of particular interest. Next, the model is used to simulate flash-boiling conditions, in order to understand how the cold flow behavior corresponds to flashing performance.

A computational and experimental study was performed to characterize the flow within a gasoline injector and the ensuing sprays. The computations included the effects of turbulence, cavitation, flash-boiling, compressibility, and the presence of non-condensible gases. The flow domain corresponded to the Engine Combustion Network's Spray G, an eight-hole counterbore injector operating in a variety of conditions. First, a rate tube method was used to measure the rate of injection, which was then used to define inlet boundary conditions for simulation. Correspondingly, injection under submerged conditions was simulated for direct comparison with experimental measurements of discharge coefficient. Next, the internal flow and external spray into pressurized nitrogen were simulated under the base spray G conditions. Finally, injection under flashing conditions was simulated, where the ambient pressure was below the vapor pressure of the fuel.

Cavitation plays a significant role in high pressure diesel injectors. However, cavitation is difficult to measure under realistic conditions. X-ray phase contrast imaging has been used in the past to study the internal geometry of fuel injectors and the structure of diesel sprays. In this paper we extend the technique to make in-situ measurements of cavitation inside unmodified diesel injectors at pressures of up to 1200 bar through the steel nozzle wall. A cerium contrast agent was added to a diesel surrogate, and the changes in x-ray intensity caused by changes in the fluid density due to cavitation were measured. Without the need to modify the injector for optical access, realistic injection and ambient pressures can be obtained and the effects of realistic nozzle geometries can be investigated. A range of single and multi-hole injectors were studied, both sharp-edged and hydro-ground. Cavitation was observed to increase with higher rail pressures.

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.

The internal flow in an injector is greatly affected by cavitation formation, and this in turn impacts the spray characteristics of diesel injectors. In the current work, the performance of the Homogeneous Relaxation Model (HRM) in simulating cavitation inside a diesel injector is evaluated. This model is based on the assumption of homogeneous flow, and was originally developed for flash boiling simulations. However, the model can potentially simulate the spectrum of vaporization mechanisms ranging from cavitation to flash boiling through the use of an empirical time scale which depends on the thermodynamic conditions of the injector fuel. A lower value of this time scale represents a lower deviation from thermal equilibrium conditions, which is an acceptable assumption for small-scale cavitating flows. Another important advantage is the ability of this model to be easily coupled with real fuel models.

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.

Flash boiling conditions, where the fuel is superheated with respect to cylinder pressure, are often found in gasoline direct injection engines. This phenomenon affects the flowrate of the fuel and can cause choking of the nozzle. In this work we present multi-dimensional simulations of flashing internal injector flow. The modeled fluid quality (mass fraction of vapor) tends towards the equilibrium quality based on the Homogenous Relaxation Model. The relaxation time is dependent on the local pressure, the vapor pressure, and the void fraction. Simulations of the internal flow are presented and, where possible, validated with experimental data. Both two- and three- dimensional computational results show geometrically-induced phase change, similar to cavitation, near the nozzle entrance. Near the nozzle exit plane the phase change occurs at all radial locations and can be quite sensitive to temperature.

Past experiments have shown that numerous micro-hole sprays in close proximity produce drop sizes that are sensitive to the nozzle arrangement. Numerical studies have been performed to identify the interaction mechanisms between closely spaced sprays. It is shown that nozzle configurations can lower the drop-gas relative velocity and droplet Weber number, leading to reduced atomization intensity. However, the collisions involving droplets from neighboring sprays have a much greater effect on droplet size. Thus, neighboring sprays primarily interfere with each other through droplet collision.

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.

Computational fluid dynamic (CFD) analysis of in-cylinder events in the automotive industry is heavily dependent on spray simulations for almost all advanced engine concepts. As the upper bound of efficiency in these engines is pursued, the accurate prediction of sprays is critical, since the mixture preparation and ignition, whether by spark or auto-ignition, needs to be precisely controlled. While most of the spray literature closely examines various drop processes, especially breakup, comparatively less attention has been focused on the momentum coupling between the liquid and the gas phases, in particular the numerical aspects. In fact, adjusting models for the evolution of drop size has been one of the dominant means of controlling predictions of spray shape and liquid penetration.

Improved numerical methods and physical models have been applied to droplet collision modeling. Contrary to the common practice of using the fixed gas phase mesh to calculate droplet collision incidence, a new algorithm generates a collision mesh independent of the gas phase mesh at each time step. By partitioning collision cells according to the number density of parcels, the algorithm is capable of achieving higher spatial resolution than that of the gas phase mesh. At the same time this method maintains an adequate statistical sample of parcels in the collision cells to ensure statistically accurate results. The continual random rotation of the mesh ensures that parcels that are near each other will, on average, be in the same collision cell. This produces the physically reasonable result that parcels in close proximity should have the opportunity to collide. Another important advantage of the algorithm is that it can be applied to any orifice configuration.