arXiv subjects

Alexandra von Kameke

Publications and source records attributed to Alexandra von Kameke.

10 recordsLinked to original sources

arXiv2026

Can we live Danckwerts' dream? Mixing Analysis in a Baffled Stirred Tank Reactor Based on 4D-Particle Tracking Experiments

We present an experimental investigation of mixing dynamics within a laboratory-scale 3-liter stirred tank reactor (STR) equipped with two Rushton turbines and three baffles. Using time-resolved, four-dimensional particle tracking velocimetry, we successfully capture trajectories of up to 40,000 tracer particles in the full reactor volume despite obstructions by stirrer and baffles, providing unprecedented time-resolved flow and mixing information. From these Lagrangian data, we analyze velocities, accelerations, and spatial dispersion, revealing anisotropic mixing. By utilizing novel network-based analysis methods on the experimental particle trajectories, we identify coherent fluid compartments that exhibit strong internal mixing but weak exchange with neighboring compartments. We uncover five distinct compartments acting as transport barriers, which have a high impact on substrate distribution in chemical and biochemical processes. Our approach thus realizes and extends early thought experiments from Danckwerts and Levenspiel by providing detailed insight into the behavior of single fluid parcels and Lagrangian mixing withing chemical and biochemical reactors, offering a valuable approach for evaluation and optimization of chemical and biochemical processes. The trajectory data are made freely available to serve as an experimental reference for further research.

physics.flu-dyn↗

arXiv2026

Tracking in-silico Lagrangian sensors in a lab-scale stirred tank reactor

Lagrangian sensors have shown promise to improve operator awareness of conditions inside a chemical reactor but three-dimensional tracking remains a mostly unsolved challenge. We explore a setup where in-silico sensors, based on a recently proposed real-world design, are tracked using data from an accelerometer and magnetometer available from a built-in inertial measurement unit. Filtering algorithms, using a bespoke dynamical model, are used to process these readings into position estimates. We compare tracking performance of an extended Kalman filter, a particle filter and the unscented Kalman filter implemented in the pykalman library. Our numerical experiments track in-silico particles moving in an analytically given three dimensional vortex as well as in the experimentally measured flow-field of a lab-scale stirred tank reactor. Using the Maxey-Riley-Gatignol equations for the movement of inertial particles as ground-truth, we demonstrate that trajectories can be reconstructed from noisy synthetic data with errors below 10%.

math.NA↗

arXiv2026

Lagrangian description and quantification of scalar mixing in fluid flows from particle tracks

Understanding, quantifying and controlling transport and mixing processes are central in the study of fluid flows. Many different Lagrangian approaches have been proposed for detecting organizing flow structures that determine material transport, including recent data-based methods that aim to identify such coherent objects directly from tracer trajectories. These methods have helped to gain a better understanding of the underlying dynamics. However, the quantification of scalar mixing has not been the focus. Here, we develop a data-driven description and quantification of transport and mixing of scalar quantities by combining a diffusion map approach for the extraction of coherent flow structures with aspects of deterministic particle methods.

physics.flu-dyn↗

arXiv2026

Dynamical compartments in stirred tank reactors and Markov state modeling for mixing quantification: a transfer operator approach

Identifying coherent flow structures in chemical reactors is crucial for understanding the mixing dynamics, which is essential for optimizing reactor performance. We demonstrate the use of a transfer operator method to find coherent flow structures such as almost-invariant sets and coherent sets, which are characterized by minimal mixing with the surrounding fluid, in a lab-scaled stirred tank reactor using both simulated and experimental Lagrangian trajectory data. The proposed method further enables a detailed analysis of the mixing behavior by computing expected residence times and mixing times. Additionally, a Markov-state-model describes the macroscopic transport dynamics between compartments in the reactor.

physics.flu-dyn↗

arXiv2025

Effect of filter kernel on scale-energetics of near-wall turbulent structures

Inter-scale energy fluxes, $Π^λ$, are widely used as a diagnostic tool to analyse energy transfer across length scales, $λ$, in turbulence data. Here, we investigate how the choice of filter kernel (sharp spectral, Gaussian, box) affects the computed energy fluxes at constant filter width. We apply spatial filtering to a turbulent pipe flow simulation dataset and assess the effect on the local structure of $Π$. While the mean energy flux profile at each wall-normal distance is qualitatively robust across kernels, we observe significant differences in the intensity and spatial distribution of localised $Π$ events. Correlations between typical flow structures in the buffer layer (streaks, vortices, and Q-events) and regions of forward/backward transfer in the instantaneous $Π$ field differ markedly between kernel types. Cross-correlations appear strongly upstream--downstream symmetric when using the sharp spectral kernel, but asymmetric for the Gaussian and box kernels. For the Gaussian and box kernels $Π$ events tend to localise along the inclined meander of streaks, while they are centred on top of the streaks for the sharp spectral kernel. Moreover, using the sharp spectral kernel, we observe a coincidence of backward scatter and fluid transport away from the wall ($Q_1$), which does not appear with the Gaussian and box kernels. All kernels, however, predict backward scatter directly downstream of $Q_1$ events. The results suggest that interpretations of inter-scale energy flux based on sharp spectral scale separation should be treated with caution, since such kernels act non-local in physical space, whereas $Π$ events are inherently localised. Our python post-processing tool eFlux for scale separation and energy flux analysis in pipe flows is freely available and readily adaptable to other flow configurations and filter widths.

physics.flu-dyn↗

arXiv2025

Relevance of the Basset history term for Lagrangian particle dynamics

The movement of small but finite spherical particles in a fluid can be described by the Maxey-Riley equation (MRE) if they are too large to be considered passive tracers. The MRE contains an integral "history term" modeling wake effects, which causes the force acting on a particle at some given time to depend on its full past trajectory. The history term causes complications in the numerical solution of the MRE and is therefore often neglected, despite both numerical and experimental evidence that its effects are generally not negligible. By numerically computing trajectories with and without the history term of a large number of particles in different flow fields, we investigate its impact on the large-scale Lagrangian dynamics of simulated particles. We show that for moderate to large Stokes numbers, ignoring the history term leads to significant differences in clustering patterns. Furthermore, we compute finite-time Lyapunov exponents and show that, even for small particles, the differences in the resulting scalar field from ignoring the BHT can be significant, in particular if the underlying flow is turbulent.

physics.flu-dyn↗

arXiv2023

lcs4Foam -- An OpenFOAM Function Object to Compute Lagrangian Coherent Structures

To facilitate the understanding and to quantitatively assess the material transport in fluids, a modern characterisation method has emerged in fluid dynamics in the last decades footed in dynamical systems theory. It allows to examine the most influential material lines which are called Lagrangian Coherent Structures (LCS) and order the material transport into dynamically distinct regions at large scales which resist diffusion or mixing. LCS reveal the robust skeleton of material surfaces and are essential to assess material transport in time-dependent flows quantitatively. Candidates of LCS can be estimated and visualised from finite-time stretching and folding fields by calculating the Finite-Time Lyapunov Exponents (FTLE). In this contribution, we provide an OpenFOAM function object to compute FTLE during CFD simulation. This enables the OpenFOAM community to assess the geometry of the material transport in any flow quantitatively on-the-fly using principally any OpenFOAM flow solver.

physics.flu-dyn↗

arXiv2021

Simultaneous 2D and 3D turbulent flows in Faraday Waves

In nature turbulent flows exist that are neither simply 2D nor 3D but boundary conditions, such as varying stratification, force them towards the one or the other. Here, we report the first evidence of the co-existence of 2D and 3D turbulence in an experimental flow driven by Faraday waves in water. We find that an inverse energy cascade at the fluid surface and a direct energy cascade in the 3D bulk flow underneath exist simultaneously. We base our analysis on temporally and spatially well-resolved velocity fields measured at horizontal and vertical planes. The findings suggest that the strongly turbulent 2D surface flow drives the 3D bulk flow through sporadic vertical jets as a source of momentum.

physics.flu-dyn↗

arXiv2020

Measurements of Sub-Surface Velocity Fields in Quasi-2D Faraday Flow

Faraday waves are capillary ripples that form on the surface of a fluid being subject to vertical shaking. Although it is well known that the form and shape of the waves pattern depend on driving amplitude and frequency, only recent studies discovered the existence of a horizontal velocity field at the surface, called Faraday flow, which exhibits attributes of two-dimensional turbulence. However, despite the increasing attention towards the inverse energy flux in the Faraday flow and other not strictly two-dimensional systems, very little is known about the velocity fields developing beneath the fluid surface. In this study planar velocity fields are measured by means of particle image velocimetry (PIV) with high spatial and temporal resolution on the water surface and below it. A sudden drop in velocity is observed immediately below the water surface, such that at 5 mm below the water surface the mean absolute velocities are already about 6.5 times smaller than the surface velocity. Additionally, the flow structures below the surface are found to comprise much larger spatial scales than those on the surface. These large structures are also found to be slow and temporarily persistent, as proven by analysing the autocorrelation of the velocity fields in time.

physics.flu-dyn↗

arXiv2019

How coherent structures dominate the residence time in a bubble wake: an experimental example

Mixing timescales and residence times in reactive multiphase flows can be essential for product selectivity. For instance when a gas species is consumed e.g. by a competitive consecutive reaction with moderate reaction kinetics where reaction timescales are comparable to relevant mixing timescales. To point out the importance of the details of the fluid flow, we analyze experimental velocity data from a Taylor bubble wake by means of Lagrangian methods. By adjusting the channel diameter in which the Taylor bubble rises, and thus the rise velocity, we obtain three different wake regimes. Remarkably the normalized residence times of passive particles advected in the wake velocity field show a peak for intermediate rise velocities. This fact seems unintuitive at first glance because one expects a faster removal of passive tracers for a faster overall flow rate. However, the details of the flow topology analyzed using Finite Time Lyapunov Exponent (FTLE) fields and Lagrangian Coherent Structures (LCS) reveal the existence of a very coherent vortical pattern in the bubble wake which explains the long residence times. The increased residence times within the vortical structure and the close bubble interface acting as a constant gas species source could enhance side product generation of a hypothetical competitive consecutive reaction, where the first reaction with the gas species forms the desired product and the second the side product.

physics.flu-dyn↗