An Eulerian–Lagrangian hybrid model for the coarse-grid simulation of turbulent liquid jet breakup

In this paper we present a numerical model for the coarse-grid simulation of turbulent liquid jet breakup using an Eulerian–Lagrangian coupling. To picture the unresolved droplet formation near the liquid jet interface in the case of coarse grids we considered a theoretical model to describe the unresolved flow instabilities leading to turbulent breakup. These entrained droplets are then represented by an Eulerian–Lagrangian hybrid concept. On the one hand, we used a volume of fluid method (VOF) to characterize the global spreading and the initiation of droplet formation; one the other hand, Lagrangian droplets are released at the liquid–gas interface according to the theoretical model balancing consolidating and disruptive energies. Here, a numerical coupling was required between Eulerian liquid core and Lagrangian droplets using mass and momentum source terms. The presented methodology was tested for different liquid jets in Rayleigh, wind-induced and atomization regimes and validated against literature data. This comparison reveals fairly good qualitative agreement in the cases of jet spreading, jet instability and jet breakup as well as relatively accurate size distribution and Sauter mean diameter (SMD) of the droplets. Furthermore, the model was able to capture the regime transitions from Rayleigh instability to atomization appropriately. Finally, the presented sub-grid model predicts the effect of the gas-phase pressure on the droplet sizes very well.     

Shock wave interactions with particles and liquid fuel droplets

Shock waves traveling through a multiphase flow environment are studied numerically using the Flux Corrected Transport (FCT) algorithm. Both solid particles and liquid droplets are used as the dispersed phase with their trajectories being computed using a Lagrangian tracking scheme. The phases are coupled by including source terms which account for mass transfer, momentum, and energy exchange from the dispersed phase in the governing equations of motion for the gas phase. For solid particles, droplet size effects are examined at constant mass loading. Deceleration of the shock wave is observed with effects increasing with decreasing particle size. The equilibrium velocity attained is found to agree with analytical results for an equivalent dense gas with a modified specific heat ratio. For liquid droplets, a droplet breakup model is introduced and the results show a faster attenuation rate than with the solid particle model. The inclusion of vaporization to the breakup model is seen to increase the attenuation rate but does not alter the final equilibrium velocity. When an energy release model is used in the simulations, behavior resembling a detonation is observed under certain conditions, with energy release coupling with and accelerating the shock front. Received 17 July 2000 / Accepted 20 August 2002 / Published online 4 December 2002 Correspondence to: Dr. K. Kailasanath (e-mail: kailas@lcp.nrl.navy.mil)     

Transport modeling of sedimenting particles in a turbulent pipe flow using Euler–Lagrange large eddy simulation

A volume-filtered Euler–Lagrange large eddy simulation methodology is used to predict the physics of turbulent liquid–solid slurry flow through a horizontal periodic pipe. A dynamic Smagorinsky model based on Lagrangian averaging is employed to account for the sub-filter scale effects in the liquid phase. A fully conservative immersed boundary method is used to account for the pipe geometry on a uniform cartesian grid. The liquid and solid phases are coupled through volume fraction and momentum exchange terms. Particle–particle and particle–wall collisions are modeled using a soft-sphere approach. Three simulations are performed by varying the superficial liquid velocity to be consistent with the experimental data by Dahl et al. (2003). Depending on the liquid flow rate, a particle bed can form and develop different patterns, which are discussed in light of regime diagrams proposed in the literature. The fluctuation in the height of the liquid-bed interface is characterized to understand the space and time evolution of these patterns. Statistics of engineering interest such as mean velocity, mean concentration, and mean streamwise pressure gradient driving the flow are extracted from the numerical simulations and presented. Sand hold-up calculated from the simulation results suggest that this computational strategy is capable of predicting critical deposition velocity.     

Multiscale simulations and experiments on water jet atomization

Numerical simulation of primary atomization at high Reynolds number is still a challenging problem. In this work a multiscale approach for the numerical simulation of liquid jet primary atomization is applied, using an Eulerian-Lagrangian coupling. In this approach, an Eulerian volume of fluid (VOF) method, where the Reynolds stresses are closed by a Reynolds stress model is applied to model the global spreading of the liquid jet. The formation of the micro-scale droplets, which are usually smaller than the grid spacing in the computational domain, is modelled by an energy-based sub-grid model. Where the disruptive forces (turbulence and surface pressure) of turbulent eddies near the surface of the jet overcome the capillary forces, droplets are released with the local properties of the corresponding eddies. The dynamics of the generated droplets are modelled using Lagrangian particle tracking (LPT). A numerical coupling between the Eulerian and Lagrangian frames is then established via source terms in conservation equations. As a follow-up study to our investigation in Saeedipour et al. (2016a), the present paper aims at modelling drop formation from liquid jets at high Reynolds numbers in the atomization regime and validating the simulation results against in-house experiments. For this purpose, phase-Doppler anemometry (PDA) was used to measure the droplet size and velocity distributions in sprays produced by water jet breakup at different Reynolds numbers in the atomization regime. The spray properties, such as droplet size spectra, local and global Sauter-mean drop sizes and velocity distributions obtained from the simulations are compared with experiment at various locations with very good agreement.     

Development of an efficient statistical volumes of fluid–Lagrangian particle tracking coupling method

The breakup of a liquid jet into irregular liquid structures and droplets leading to the formation of a dilute spray has been simulated numerically. To overcome the shortcomings of certain numerical methods in specific flow regimes, a combined approach has been chosen. The intact liquid core, its primary breakup and the dense spray regime are simulated using the volumes of fluid (VOF) method in combination with LES, whereas the Lagrangian particle tracking (LPT) approach in the LES context is applied to the dilute spray regime and the secondary breakup of droplets. A method has been developed to couple both simulation types on a statistical basis. This statistical coupling approach (SCA) reflects the dominating physical mechanisms of the two‐phase flow in each regime to a high degree. The main benefit of the SCA is computational efficiency as compared with the more straightforward approach where one follows each structure, denoted here as the direct coupling approach. The computational benefits stem from the reduction of computational time since the VOF simulation is run only until statistical convergence and not during the whole spray development. A second benefit using the SCA is the possibility to use the stochastic parcel method in the LPT simulation whereby a large number of droplets may be handled. The coupling approach is applied to the atomization of a fuel jet in a high pressure chamber, demonstrating the gain of efficiency of the SCA as compared with direct coupling approach. Copyright © 2014 The Authors. International Journal for Numerical Methods in Fluids published by John Wiley & Sons Ltd.     

Simultaneous velocity field measurements in two-phase flows for turbulent mixing of sprays by means of two-phase PIV

This paper describes a novel derivative of the PIV method for measuring the velocity fields of droplets and gas phases simultaneously using fluorescence images rather than Mie scattering images. Two-phase PIV allows the simultaneous and independent velocity field measurement of the liquid phase droplets and ambient gas in the case of two-phase flow mixing. For phase discrimination, each phase is labelled by a different fluorescent dye: the gas phase is seeded with small liquid droplets, tagged by an efficient fluorescent dye while the droplets of the liquid phases are tagged by a different fluorescent dye. For each phase, the wavelength shift of fluorescence is used to separate fluorescence from Mie scattering and to distinguish between the fluorescence of each phase. With the use of two cross-correlation PIV cameras and adequate optical filters, we obtain two double frame images, one for each phase. Thus standard PIV or PTV algorithms are used to obtain the simultaneous and independent velocity fields of the two phases. Because the two-phase PIV technique relies on the ability to produce two simultaneous and independent images of the two phases, the choice of the labelling dyes and of the associated optical filter sets is relevant for the image acquisition. Thus a spectroscopic study has been carried out to choose the optimal fluorescent dyes and the associated optical filters. The method has been evaluated in a simple two-phase flow: droplets of 30–40 μm diameter, produced by an ultrasonic nozzle are injected into a gas coflow seeded with small particles. Some initial results have been obtained which demonstrate the potential of the method.     

Consistency issues of Lagrangian particle tracking applied to a spray jet in crossflow

Numerical simulations are performed for multiphase jets in crossflow. The flow solver uses an Eulerian/Lagrangian approach. Turbulence in the gas phase is modeled in the framework of large eddy simulation. The dispersed phase is handled using Lagrangian particle tracking. The model assumptions of solvers for Lagrangian particle tracking are critically assessed for typical flow conditions of spray jets in crossflow. The droplets are assumed to be spherical and isolated. It is shown that several model assumptions are apparently inconsistent in larger portions of the flow field. Firstly, average Weber numbers can be so large that the model assumption to regard droplets as spherical is questionable, not only near the nozzle, but also in the far-field. Secondly, the average droplet spacing can be so low that droplets directly interact with each other, again also in the far-field. Thirdly, the average Stokes numbers in the jet region can be so large that the phase coupling between the dispersed and continuous phase is weak. Some remedies to these deficiencies are proposed.     

离心泵叶轮内密相液固两相湍流的数值模拟

利用作者建立的描述密相液固两相湍流的 KET模型和推导的基本控制方程组 ,在处理壁面边界条件时考虑了颗粒和叶片的相互碰撞作用 ,对离心泵叶轮内密相液固两相流动进行了数值模拟 ,得到了泵叶轮内两相流动的一些规律 ,为液固两相流泵的设计提供了一定的理论依据。