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Item type:Publication, Access status: with files , Data-driven transport modeling for tracer injection and mixing time screening in stirred tank reactors(Elsevier, 2026-10-30); ; ; ; Transient CFD of liquid mixing in stirred tanks is too expensive for systematic design studies, and mixing time predictions deviate from experiment even at scale-resolving resolution. Transport-based recurrence CFD (rCFD) decouples scalar transport from the flow solve, replaying a short pre-computed flow database through cell-to-cell displacement maps, so that transport level corrections can be applied without repeating the momentum solution. This is exploited here for the 95% mixing time in a 30 L dual-impeller stirred tank reactor, using a 4.5 s LB-LES flow database from M-Star as the sole input. The rCFD first results inherit the over-prediction of its input flow field (33.1 ± 1.4 s, against 30.1 ± 3.0 s for M-Star and 28.1 ± 2.7 s for Ansys Fluent at comparable spatial resolution, and 25.0 ± 3.0 s measured by conductivity probes in experiment part). Calibrating a single face-swap diffusion parameter in rCFD transport model against one probe measurement brings the prediction to 24.5 ± 1.0 s, recovering experimental agreement without re-running the flow simulation. The rCFD simulation requires approximately 3 s of wall-clock time per second of process time (423 × M-Star, 1200 × Ansys Fluent) and is almost insensitive to a fivefold increase in extrapolation time step. Ninety injection locations spanning radius, height, and azimuth are therefore screened from the single database in 2.25 h, against estimates of 40 and 113 days for the reference solvers, resolving a 3.6-fold spread in mixing time (13.6–48.8 s) in which injection height and baffle-relative azimuth dominate. The main objective of this work is a fast, spatially and temporally resolved description of scalar transport; the 95% mixing time is used as the quantitative metric for validating it against sparse experimental data.Publicationtype: Journal Article4 3 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Lagrangian μ-particle tracking velocimetry analysis of microscale flow over structured surfaces(American Chemical Society (ACS), 2026-10-08); ; ; ; This work aims to provide an experimental basis for the improvement of (bio)reactors by studying flow over micro- and nanostructured surfaces, with a focus on microscale mass transport toward and away from the surface. μ-Particle tracking velocimetry is employed in a microreactor to experimentally obtain Lagrangian trajectories of flow-following tracer particles. The method also resolves three-dimensional, time-dependent velocity fields. The derived mean velocity profiles agree well with the theory of flow over porous walls. Beyond averaged Eulerian velocities, the Lagrangian framework captures near-surface interactions. The Lagrangian analysis of different surfaces indicates that rectangular structured microgrooves increase the wall contact of the tracer particles, especially when the flow is oriented perpendicular to the microgrooves. Particularly, this approach enables resolution of trapping phenomena and localized recirculation dynamics. Nanostructuring by growing a carbon nanotube forest increases surface area and modifies local fluid dynamics, thereby enhancing contact with (bio)catalysts that are potentially functionalized on the nanotubes in future applications.Publicationtype: Journal Article43 18 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Tracking in-silico Lagrangian sensors in a lab-scale stirred tank reactor.(Elsevier, 2026-09-28); ; ; ; 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 threedimensional 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 the extended Kalman filter and the particle filter reconstruct trajectories from noisy synthetic data with mean relative errors below 3%.Publicationtype: Journal Article52 34 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Dynamical compartments in stirred tank reactors and Markov state modeling for mixing quantification: A transfer operator approach(American Chemical Society (ACS), 2026-08-31); ; ; ; 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.Publicationtype: Journal Article58 24 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Model-based computational study of reactive fluid systems using transfer operator methods(2026-08-14); ; In many industrial applications one aims for the design of efficient chemical reactions. This is often done using experimental analysis of the reactors in combination with numerical twins. However, the simultaneous modeling of flow, mixing and chemical reaction remains a complicated task because the computational costs are still significant and oftentimes prohibitive. Here, we model and analyze mixing processes of chemical substances by a transfer operator method using the Lagrangian trajectories of passive particles. In practice, we represent the spatial distributions of the chemical species concentrations by density vectors. These are evolved by means of a stochastic transition matrix, which is obtained as a numerical approximation of a transfer operator. In a further step, we model the reaction of the fluids by specific update rules of the density vectors. The method is applicable for closed and open example systems and different chemical processes such as competitive consecutive reactions. We demonstrate that the dynamic processes are reflected well by this method. Furthermore, we evaluate the interdependence of the reaction fronts with Lagrangian coherent structures which we define using set-oriented methods that also work well on three dimensional data.Publicationtype: Preprint44 32 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Can we live Danckwerts' dream? Mixing analysis in a baffled stirred tank reactor based on 4D-particle tracking experiments(2026-07-29); ; ; ; 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.Publicationtype: Preprint32 26 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Fast risk certification of candidate trajectories under uncertain time-varying constraints(2026-06-30); ; ; This paper studies the certification of a fixed candidate trajectory on a finite certification grid under parametric uncertainty. For each constraint-time pair, we define a scalar measure of constraint violation and aggregate the resulting pointwise chance constraints into a worst-case Value-at-Risk (VaR) margin. The goal is not to generate a new trajectory, but to assess online whether a trajectory produced by a planner or predictive controller is sufficiently safe on the certification grid. Direct evaluation requires repeated uncertainty propagation and is often too expensive for computationally demanding models. We therefore adopt an offline-online scheme: offline, a surrogate of the constraint violation map along the candidate trajectory is constructed using polynomial chaos expansion (PCE) when the uncertainty law is known, or kernel regression when only sampled input-output data are available; online, the surrogate is sampled to evaluate conservative VaR bounds at low computational cost. On the theoretical side, we derive a finite-sample upper bound for the grid-based VaR margin using empirical quantiles, the Dvoretzky-Kiefer-Wolfowitz (DKW) inequality, and a union bound over all constraint-time pairs, without assuming a parametric family for the underlying violation distribution. We also show how a uniform surrogate error bound transfers to the certified VaR margin. The approach is illustrated on a crystallization population balance model, where the surrogate-based risk estimates track direct Monte Carlo results while substantially reducing online evaluation time.Publicationtype: Preprint53 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Tracking in-silico Lagrangian sensors in a lab-scale stirred tank reactor(2026-06-11); ; ; 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%.Publicationtype: Preprint71 66 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Experimental analysis of time resolved three-dimensional velocity and vorticity fields behind single rising bubbles using Lagrangian particle tracking velocimetry(Elsevier, 2026-01-29); ; ; ; The present study utilizes highly resolved Lagrange particle tracking measurements to analyze the time-dependent three-dimensional fluid dynamics in the wake of air bubbles rising in quiescent bidistilled water. Two bubble sizes are studied with regard to the velocity fields and the temporal evolution of the generated vorticity in their wakes. The range of bubble sizes is of particular interest, as it corresponds to other recent studies. The bubbles are reconstructed in three dimensions to determine the bubble rise trajectory and the bubble shape. The analysis of the aforementioned measurements, particularly the calculation of the Q-criterion, supports prior numerical findings of a wake mode exhibiting secondary vortex loops. Additionally, the energy spectra of the velocity fields and their temporal evolution are analyzed, providing a unique experimental dataset for the validation of numerical simulations and the further study of bubbly flows.Publicationtype: Journal Article149 63 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Lagrangian description and quantification of scalar mixing in fluid flows from particle tracks(2025-09-29); ; 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.Publicationtype: Preprint42 67