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This article uniquely characterizes the secondary droplets formed during the impingement of a train of ethanol drops, using three-dimensional direct numerical simulations performed under conditions studied experimentally by Yarin and Weiss. Our numerical results have been previously validated against experimental data demonstrating the ability to accurately capture the splashing dynamics. In this work, the predictive ability of the model is leveraged to gain further insight into secondary droplet formation. We present a robust post-processing algorithm, which scrutinizes the liquid volume fraction field in the volume-of-fluid method and quantifies the number, volume and velocity of secondary droplets. The high-resolution computational simulations enable secondary droplet characterization within close proximity of the impingement point at small length and time scales, which is extremely challenging to achieve experimentally. By studying the temporal evolution of secondary droplet formation, direct connections are made between liquid structures seen in the simulation and the instantaneous distribution of secondary droplets, leading to detailed insight into the instability-driven breakup process of lamellae. Time-averaged secondary droplet characteristics are also studied to describe the global distribution of secondary droplets. Such analysis is vital to understanding fuel drop impingement in direct injection engines, facilitating the development of highly accurate spray–wall interaction models for use in Lagrangian solvers. © IMechE 2019.

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Department of Mechanical Engineering

Fulltext

International Journal of Engine Research

Computational characterization of the secondary droplets formed during the impingement of a train of ethanol drops

This work presents experiments and computational simulations of a single diesel droplet impinging on a dry surface to provide a better understanding of the dynamics of the impingement process. The experimental work was carried out at several substrate surface temperatures where a single diesel droplet was dropped from a precision syringe pump to provide a specific droplet diameter and impact velocity. The effect of the surface temperature on the temporal evolution of the droplet spreading factor, dynamic contact angle, and contact line velocity was studied. The experimental study on the temporal evolution of the droplet-wall interaction was used to develop a dynamic contact angle model for computational simulations. Using an in-house multiphase flow solver, simulations of the single diesel droplet impingement were performed. The simulation results of the spreading factor were compared to the experimental results and the effects of liquid temperature and contact angle model parameters were investigated. The development of a dynamic contact angle model for diesel droplets enhances the ability to study diesel droplet impingement, an important factor in diesel fuel injection. With an accurate dynamic contact angle model, future studies can be performed at scales and velocities representative of the conditions present in internal combustion engines. © 2018 Solar Turbines Incorporated.

ICLASS 2018 - 14th International Conference on Liquid Atomization and Spray Systems

An experimental and computational study of a single diesel droplet impinging on a dry surface

We present a novel methodology for accurate treatment of viscous terms in evaporation problems. The proposed scheme is an extension of the sharp viscous treatment of Kang et al. (2000) [7] to 3D phase change problems. To ensure accuracy and grid converging solutions, a new implicit approach to computing viscous fluxes across the phase interfaces is proposed, which was previously unavailable in fixed grid numerical schemes. Analytical relations were derived for the jump in velocity gradients across the 2D and 3D phase interfaces, an important constituent of the proposed scheme. The relations show a non-vanishing jump in the tangential gradients across the phase interface that are associated with evaporative flux and interfacial curvature. The proposed methodology demonstrated first order accuracy in canonical test cases. It is general and applicable to arbitrarily oriented interfaces, and can be readily implemented in existing evaporation flow solvers. © 2020 Elsevier Inc.

Journal of Computational Physics

An implicit, sharp numerical treatment of viscous terms at arbitrarily shaped liquid-gas interfaces in evaporative flows

Numerical modeling of fuel injection in internal combustion engines in a Lagrangian framework requires the use of a spray-wall interaction sub-model to correctly assess the effects associated with spray impingement. The spray impingement dynamics may influence the air-fuel mixing and result in increased hydrocarbon and particulate matter emissions. One component of a spray-wall interaction model is the splashed mass fraction, i.e. the amount of mass that is ejected upon impingement. Many existing models are based on relatively large droplets (mm size), while diesel and gasoline sprays are expected to be of micron size before splashing under high pressure conditions. It is challenging to experimentally distinguish pre- from post-impinged spray droplets, leading to difficulty in model validation. In this study one commonly used splashed mass model, proposed by O'Rourke and Amsden, was studied through Direct Numerical Simulations (DNS) using an in-house 3D multiphase flow solver, which has been validated in previous studies. To test the splashed mass model in scenarios relevant to fuel impingement, input was generated from Lagrangian-Eulerian (LE) diesel injection simulations. A representative combination of droplet diameter and velocity before impact was selected from the LE output. The representative droplet was then used to initialize the DNS calculations, allowing the splashed mass model to be tested for micron-sized droplets. The splashed mass ratio was calculated from the DNS output and was compared to the model of O'Rourke and Amsden. This new LE/DNS framework allows Lagrangian sub-models to be tested in a way that is difficult to examine experimentally and provides unique feedback that will be used to enhance the accuracy of LE spray simulations. © 2018 SAE International; Argonne National Laboratory.

SAE Technical Papers

Using a DNS Framework to Test a Splashed Mass Sub-Model for Lagrangian Spray Simulations

The authors present a computational study of drop-train impingement on a smooth, initially dry surface, with the aim of providing a high-quality dataset to develop reliable spray-wall interaction submodels for engine simulations. Such submodels require information at micron scales, which is unfeasible to obtain experimentally under high-pressure engine conditions. However, supercomputing and high-resolution simulations can resolve thin liquid structures and their breakup, yielding accurate datasets for liquid splashing and film deposition. The current study employs an MPI-parallel multiphase flow solver to simulate surface impingement of a train of ethanol drops. Comparing its results to the experiments, the solvers capability in accurately capturing the sharp splashing threshold and splashed mass ratio was demonstrated. Through a computational technique that tags individual drops, further insight into the splashing dynamics postimpingement was gained, which could be used to formulate more sophisticated spray-wall interaction submodels. © 1999-2011 IEEE.

Computing in Science and Engineering

Advanced computational simulations of surface impingement of a train of ethanol drops: A pathway to developing spray-wall interaction submodels

The d2 law, commonly used to assess the accuracy of computational solvers, corresponds to evaporation under steady-state conditions and in an infinite gaseous domain. In the present work, we propose new alternative benchmarks that relax those constraints. The benchmarks are developed for a spherical as well as a circular drop. First, steady-state analytical relations are derived that are applicable to a finite domain. A radially-symmetric transient model is then proposed that can provide transient benchmark solutions in finite domains. Adaptive mesh-refinement and body-fitted mesh are used for numerical solution and to ensure highly accurate transient results. The proposed steady-state and transient benchmarks are examined in several evaporation problems, and the evolution of drop diameter, temperature and vapor mass fraction fields are analyzed. In one such problem, we report a secondary transient phenomenon that appears towards the end of drop lifetime. The benchmarks proposed in this work are straightforward to be implemented for systematic validation of computational solvers. © 2018 Elsevier Ltd

International Journal of Heat and Mass Transfer

Steady-state and transient solutions to drop evaporation in a finite domain: Alternative benchmarks to the d2 law

Wave energy converter (WEC) devices harness the renewable ocean wave energy and convert it into useful forms of energy, e.g. mechanical or electrical. This paper presents an advanced 3D computational framework to study the interaction between water waves and WEC devices. The computational tool solves the full Navier–Stokes equations and considers all important effects impacting the device performance. To enable large-scale simulations in fast turnaround times, the computational solver was developed in an MPI parallel framework. A fast multigrid preconditioned solver is introduced to solve the computationally expensive pressure Poisson equation. The computational solver was applied to two surface-piercing WEC geometries: bottom-hinged cylinder and flap. Their numerically simulated response was validated against experimental data. Additional simulations were conducted to investigate the applicability of Froude scaling in predicting full-scale WEC response from the model experiments. © 2017 Informa UK Limited, trading as Taylor & Francis Group.

European Journal of Computational Mechanics

Advanced computational simulations of water waves interacting with wave energy converters

We introduce a piecewise-linear, volume-of-fluid method for reconstructing and advecting three-dimensional interfaces and contact lines formed by three materials. The new method employs a set of geometric constructs that can be used in conjunction with any volume-tracking scheme. In this work, we used the mass-conserving scheme of Youngs to handle two-material cells, perform interface reconstruction in three-material cells, and resolve the contact line. The only information required by the method is the available volume fraction field. Although the proposed method is order dependent and requires a priori information on material ordering, it is suitable for typical contact line applications, where the material representing the contact surface is always known. Following the reconstruction of the contact surface, to compute the interface orientation in a three-material cell, the proposed method minimizes an error function that is based on volume fraction distribution around that cell. As an option, the minimization procedure also allows the user to impose a contact angle. Performance of the proposed method is assessed via both static and advection test cases. The tests show that the new method preserves the accuracy and mass-conserving property of the Youngs method in volume-tracking three materials. © 2015 Elsevier Inc.

A three-dimensional volume-of-fluid method for reconstructing and advecting three-material interfaces forming contact lines

We present a three-dimensional (3D) and fully Eulerian approach to capturing the interaction between two fluids and moving rigid structures by using the fictitious domain and volume-of-fluid (VOF) methods. The solid bodies can have arbitrarily complex geometry and can pierce the fluid-fluid interface, forming contact lines. The three-phase interfaces are resolved and reconstructed by using a VOF-based methodology. Then, a consistent scheme is employed for transporting mass and momentum, allowing for simulations of three-phase flows of large density ratios. The Eulerian approach significantly simplifies numerical resolution of the kinematics of rigid bodies of complex geometry and with six degrees of freedom. The fluid-structure interaction (FSI) is computed using the fictitious domain method. The methodology was developed in a message passing interface (MPI) parallel framework accelerated with graphics processing units (GPUs). The computationally intensive solution of the pressure Poisson equation is ported to GPUs, while the remaining calculations are performed on CPUs. The performance and accuracy of the methodology are assessed using an array of test cases, focusing individually on the flow solver and the FSI in surface-piercing configurations. Finally, an application of the proposed methodology in simulations of the ocean wave energy converters is presented. © 2016 Elsevier Inc.

A 3D, fully Eulerian, VOF-based solver to study the interaction between two fluids and moving rigid bodies using the fictitious domain method

The feasibility of running MPI-parallel, GPU-accelerated, multiphase flow simulations on Amazon's Elastic Compute Cloud (EC2) service is evaluated as an alternative computational resource. A cloud cluster on Amazon EC2 is compared to a conventional local high-performance computing cluster in terms of performance and cost. The steps necessary to set up a cloud cluster and acquire the appropriate hardware and software stacks are outlined. The incompressible multiphase flow solver is benchmarked on both cloud and local clusters by performing strong and weak scaling analyses. Amazon's EC2 service is competitive with the local cluster in a certain range of simulations, but there are some performance limitations, particularly in its GPU card performance and cluster network connection, which negatively impact the parallel simulations presented herein. Finally, Amazon's EC2 service is studied from an economic perspective and compared with a conventional local cluster. © 1999-2011 IEEE.

The feasibility of amazon's cloud computing platform for parallel, GPU-accelerated, multiphase-flow simulations

We present a two-dimensional computational flow solver for simulation of two-way interactions between moving rigid bodies and two-fluid flows. The fluids are assumed to be incompressible and immiscible. The two-step projection method along with Graphics Processing Unit (GPU) acceleration is employed to solve the flow equations. The fluid-solid interaction is captured by using the fictitious domain method. A consistent mass and momentum scheme is implemented, which allows for simulation of multiphase flows characterized by large density ratios. The evolution of interfaces in the three-phase system is tracked by using the volume-of-fluid method with two scalar functions, representing the solid domain and one of the fluids. A geometrical approach is employed to reconstruct the interfaces in cells containing three phases and capture the intersection of phase interfaces (triple point). The performance and accuracy of the flow solver are assessed through a set of canonical test cases. Then, it is used to simulate the interactions between a free-floating buoy and waves generated by a bottom-hinged paddle in a wave tank. © 2014 Elsevier Ltd.