12 results
Filters
Settings
Now showing1 - 10 of 12
- Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Approximation of the Basset force in the Maxey-Riley-Gatignol equations via universal differential equations(Institute of Physics (IOP), 2026-10-27); ; ; The Maxey-Riley-Gatignol equations (MaRGE) model the motion of spherical inertial particles in a fluid. They contain the Basset force, an integral term which models history effects due to the formation of wakes and boundary layer effects. This causes the force that acts on a particle to depend on its past trajectory and complicates the numerical solution of MaRGE. Therefore, the Basset force is often neglected, despite substantial evidence that it has both quantitative and qualitative impact on the movement patterns of modelled particles. Using the concept of universal differential equations, we propose an approximation of the history term via neural networks which approximates MaRGE by a system of ordinary differential equations that can be solved with standard numerical solvers like Runge-Kutta methods. In particular, for long-term and high-resolution simulations of trajectories, where the number of required time-steps is large, the UDE approach can reduce time-to-solution.Publicationtype: Journal Article56 2 - 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 36 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Millimeter-scale Lagrangian sensor spheres for local state monitoring in SMART reactors: towards energy-autonomous operation(American Chemical Society (ACS), 2026-09-18); ; ; ; Flow-following sensor particles are a promising route to obtaining spatially resolved measurements in (bio)chemical reactors. However, their practical deployment is limited by miniaturization, power supply, and packaging. This work presents a millimeter-scale Lagrangian sensor-node platform that integrates an inertial measurement unit (IMU) and a low-power microcontroller unit (MCU) on a high-density interconnect (HDI) printed circuit board (PCB), illustrating the evolution from a first demonstrator (V1) toward a reduced-footprint design (V2) intended for spherical encapsulation. The main contribution is a quantitative system-level feasibility boundary that links miniaturized sensor-node design, duty-cycled energy demand, candidate energy-input routes, and spherical packaging constraints at the targeted millimeter scale. We analyze the baseline power demand of the current duty-cycled implementation, including a cycle-based charge and energy budget, and relate this demand to two experimentally investigated energy-input routes: photovoltaic harvesting under controlled optical illumination and resonant inductive power transfer at 13.56 MHz. The harvesting experiments are performed on dedicated evaluation platforms and are used to quantify candidate energy-input routes. A closed energy-autonomous sensor-in-flow demonstration is not yet claimed. The results show that the platform concept, compact HDI integration, low-power duty cycling, optical data transmission, and a glass-based encapsulation route are technically feasible at the targeted size. At the same time, neither harvesting route yet closes the gap to robust energy-autonomous operation under realistic reactor conditions. Photovoltaic powering appears strongly constrained by alignment, optical access, and geometric coupling. Inductive transfer is more promising but remains highly sensitive to orientation, field distribution, and RF-to-DC conversion efficiency. The presented measurements therefore define both the current feasibility range and the remaining engineering requirements for future energy-autonomous sensor spheres.Publicationtype: Journal Article43 24 - 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 , Numerical modeling of inertial particles in three‐dimensional fluid flowThe motion of inertial particles in a fluid is modeled by the Maxey–Riley–Gatignol equation (MaRGE). The MaRGE contains an integral term that arises due to the viscous diffusion of vorticity in the fluid around the particle. Because it makes MaRGE difficult to solve numerically, the integral term is often neglected or approximated, despite its demonstrated importance for obtaining realistic trajectories. There are some studies that propose algorithms to solve the full MaRGE numerically for two dimensional flows fields. For simple flows like a vortex, analytical solutions exist that can serve as test cases to verify implementations. However, in most practical applications, fluids will be three dimensional. This article extends a multi‐step algorithm proposed by Daitche to the three‐dimensional case. Based on an approach by Candelier et al., it derives an analytical solution for a particle moving in a three‐dimensional vortex while being subject to gravity. Numerical examples compare empirical and theoretical convergence orders and demonstrate order reduction in particular for particles with non‐zero relative initial velocity.Publicationtype: Journal Article62 54 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Enforcing boundary conditions for physics-informed neural operators(2025-10-28); ; Machine-learning based methods like physics-informed neural networks and physics-informed neural operators are becoming increasingly adept at solving even complex systems of partial differential equations. Boundary conditions can be enforced either weakly by penalizing deviations in the loss function or strongly by training a solution structure that inherently matches the prescribed values and derivatives. The former approach is easy to implement but the latter can provide benefits with respect to accuracy and training times. However, previous approaches to strongly enforcing Neumann or Robin boundary conditions require a domain with a fully $C^1$ boundary and, as we demonstrate, can lead to instability if those boundary conditions are posed on a segment of the boundary that is piecewise $C^1$ but only $C^0$ globally. We introduce a generalization of the approach by Sukumar \& Srivastava (doi: 10.1016/j.cma.2021.114333), and a new approach based on orthogonal projections that overcome this limitation. The performance of these new techniques is compared against weakly and semi-weakly enforced boundary conditions for the scalar Darcy flow equation and the stationary Navier-Stokes equations.Publicationtype: Preprint29 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , On Sinkhorn's DAD theorem and the self-consistency equation in COSMO-based activity coefficient modelsIn a 1966 paper, Sinkhorn proved that for any real square matrix A which has only positive entries there exists a uniquely determined real diagonal matrix D with positive diagonal entries such that 𝐵:=DAD is stochastic, i.e. all row sums of B are equal to 1. Moreover, Sinkhorn stated an iterative method for computing D. Nowadays, Sinkhorn's result and its variants are often referred to as DAD theorems. The purpose of this article is twofold. On the one hand, we give the link between Sinkhorn's DAD theorem and the self-consistency equation in COSMO-based activity coefficient models in chemical engineering. On the other hand, we give a new constructive proof of Sinkhorn's DAD theorem by using classical fixed-point theory. Hereby, the larger class of nonnegative matrices with positive diagonal is considered. Our proof uniformly provides convergence for a number of iterative methods for computing D. Some of them are used in practice although, to the best of our knowledge, a formal proof of convergence is missing.Publicationtype: Journal Article46 58 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Relevance of the Basset history term for Lagrangian particle dynamicsThe 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.Publicationtype: Journal Article108 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Efficient numerical methods for the Maxey-Riley-Gatignol equations with Basset history termThe Maxey-Riley-Gatignol equations (MRGE) describe the motion of a finite-sized, spherical particle in a fluid. Because of wake effects, the force acting on a particle depends on its past trajectory. This is modeled by an integral term in the MRGE, also called Basset force, that makes its numerical solution challenging and memory intensive. A recent approach proposed by Prasath et al. (2019) [9] exploits connections between the integral term and fractional derivatives to reformulate the MRGE as a time-dependent partial differential equation on a semi-infinite pseudo-space. They also propose a numerical algorithm based on polynomial expansions. This paper develops a numerical approach based on finite difference instead, by adopting techniques by Koleva (2005) [35] and Fazio and Jannelli (2014) [37] to cope with the issues of having an unbounded spatial domain. We compare convergence order and computational efficiency for particles of varying size and density of the polynomial expansion by Prasath et al., our finite difference schemes and a direct integrator for the MRGE based on multi-step methods proposed by Daitche (2013) [29]. While all methods achieve their theoretical convergence order for neutrally buoyant particles with zero initial relative velocity, they suffer from various degrees of order reduction if the initial relative velocity is non-zero or the particle has a different density than the fluid.Publicationtype: Journal Article75 63 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Miniaturized Lagrangian sensor-systems for position detection in (bio-)chemical reactorsReal-time monitoring of process parameters in (bio-)chemical reactors offers significant potential for process optimiza-tion, energy savings, and waste reduction. This paper presents the development of miniaturized, flow-following sensor nodes designed to overcome the limitations of conventional fixed sensor systems and imaging approaches. The proposed system integrates an inertial measurement unit (ICM-20948) and microcontroller (MAX32660) on a high-density interconnect PCB measuring 7.5 × 7.4 × 2.6 mm. Wireless data transmission is achieved through optical communication using on-off keying modulated LEDs. Experimental results demonstrate future possible motion tracking capabilities with 60 Hz data transmission rate, while revealing accuracy limitations requiring advanced filtering techniques.Publicationtype: Conference Paper46