Bias in particle tracking acceleration measurement

We investigate sources of error in acceleration statistics from Lagrangian Particle Tracking (LPT) data and demonstrate techniques to eliminate or minimise bias errors introduced during processing. Numerical simulations of particle tracking experiments in isotropic turbulence show that the main sources of bias error arise from noise due to position uncertainty and selection biases introduced during numerical differentiation. We outline the use of independent measurements and filtering schemes to eliminate these biases. Moreover, we test the validity of our approach in estimating the statistical moments and probability densities of the Lagrangian acceleration. Finally, we apply these techniques to experimental particle tracking data and demonstrate their validity in practice with comparisons to available data from literature. The general approach, which is not limited to acceleration statistics, can be applied with as few as two cameras and permits a substantial reduction in the spatial resolution and sampling rate required to adequately measure statistics of Lagrangian acceleration

Lagrangian particle paths and ortho-normal quaternion frames

Experimentalists now measure intense rotations of Lagrangian particles in turbulent flows by tracking their trajectories and Lagrangian-average velocity gradients at high Reynolds numbers. This paper formulates the dynamics of an orthonormal frame attached to each Lagrangian fluid particle undergoing three-axis rotations, by using quaternions in combination with Ertel's theorem for frozen-in vorticity. The method is applicable to a wide range of Lagrangian flows including the three-dimensional Euler equations and its variants such as ideal MHD. The applicability of the quaterionic frame description to Lagrangian averaged velocity gradient dynamics is also demonstrated.Comment: 9 pages, one figure, revise

Computational fluid dynamics applied to gas-liquid contactors.

In this paper a `hierarchy of models¿ is discussed to study the fluid dynamic behaviour of gas-liquid bubble columns. This `hierarchy of models¿ consists of a Eulerian-Eulerian two fluid model, a Eulerian-Lagrangian discrete bubble model and a Volume Tracking or Marker Particle model. These models will be briefly reviewed and their advantages and disadvantages will be highlighted. In addition, a mixed Eulerian-Lagrangian model and a volume tracking model, both developed at Twente University, will be discussed. Some selected results obtained with these models will be presented with emphasis on the results obtained with the volume tracking model. Finally, a brief discussion on advanced experimental techniques, which reflect the recent progress in experimental fluid dynamics, will be presente

Development of a hybrid multi-scale simulation approach for spray processes

This paper presents a multi-scale approach coupling a Eulerian interface-tracking method and a Lagrangian particle-tracking method to simulate liquid atomisation processes. This method aims to represent the complete spray atomisation process including the primary break-up process and the secondary break-up process, paving the way for high-fidelity simulations of spray atomisation in the dense spray zone and spray combustion in the dilute spray zone. The Eulerian method is based on the coupled level-set and volume-of-fluid method for interface tracking, which can accurately simulate the primary break-up process. For the coupling approach, the Eulerian method describes only large droplet and ligament structures, while small-scale droplet structures are removed from the resolved Eulerian description and transformed into Lagrangian point-source spherical droplets. The Lagrangian method is thus used to track smaller droplets. In this study, two-dimensional simulations of liquid jet atomisation are performed. We analysed Lagrangian droplet formation and motion using the multi-scale approach. The results indicate that the coupling method successfully achieves multi-scale simulations and accurately models droplet motion after the Eulerian–Lagrangian transition. Finally, the reverse Lagrangian–Eulerian transition is also considered to cope with interactions between Eulerian droplets and Lagrangian droplets.This work was supported by the Engineering and Physical Sciences Research Council of the UK (grant number EP/L000199/1)

Experimental evidence of chaotic advection in a convective flow

Lagrangian chaos is experimentally investigated in a convective flow by means of Particle Tracking Velocimetry. The Fnite Size Lyapunov Exponent analysis is applied to quantify dispersion properties at different scales. In the range of parameters of the experiment, Lagrangian motion is found to be chaotic. Moreover, the Lyapunov depends on the Rayleigh number as ${\cal R}a^{1/2}$. A simple dimensional argument for explaining the observed power law scaling is proposed.Comment: 7 pages, 3 figur

Lagrangian filtered density function for LES-based stochastic modelling of turbulent dispersed flows

The Eulerian-Lagrangian approach based on Large-Eddy Simulation (LES) is one of the most promising and viable numerical tools to study turbulent dispersed flows when the computational cost of Direct Numerical Simulation (DNS) becomes too expensive. The applicability of this approach is however limited if the effects of the Sub-Grid Scales (SGS) of the flow on particle dynamics are neglected. In this paper, we propose to take these effects into account by means of a Lagrangian stochastic SGS model for the equations of particle motion. The model extends to particle-laden flows the velocity-filtered density function method originally developed for reactive flows. The underlying filtered density function is simulated through a Lagrangian Monte Carlo procedure that solves for a set of Stochastic Differential Equations (SDEs) along individual particle trajectories. The resulting model is tested for the reference case of turbulent channel flow, using a hybrid algorithm in which the fluid velocity field is provided by LES and then used to advance the SDEs in time. The model consistency is assessed in the limit of particles with zero inertia, when "duplicate fields" are available from both the Eulerian LES and the Lagrangian tracking. Tests with inertial particles were performed to examine the capability of the model to capture particle preferential concentration and near-wall segregation. Upon comparison with DNS-based statistics, our results show improved accuracy and considerably reduced errors with respect to the case in which no SGS model is used in the equations of particle motion

Influence of pipe length and flow rate on nano-particle deposition in laminar circular pipe flows

The Lagrangian particle tracking provides an effective method for simulating the deposition of nano-particles as well as micro-particles as it accounts for the particle inertia effect as well as the Brownian excitation. However, using the Lagrangian approach for simulating ultrafine particles has been limited due to computational cost and numerical difficulties. The aim of this paper is to study the deposition of nano-particles in cylindrical tubes under laminar condition using the Lagrangian particle tracking method. The commercial Fluent software is used to simulate the fluid flow in the pipes and to study the deposition and dispersion of nano-particles. Different particle diameters as well as different pipe lengths and flow rates are examined. The results show good agreement between the calculated deposition efficiency and different analytic correlations in the literature. Furthermore, for the nano-particles with higher diameters and when the effect of inertia has a higher importance, the calculated deposition efficiency by the Lagrangian method is less than the analytic correlations based on Eulerian method due to statistical error or the inertia effect