Jens Kasten

Two-Dimensional Time-Dependent Vortex Regions Based on the Acceleration Magnitude

Acceleration is a fundamental quantity of flow fields that captures Galilean invariant properties of particle motion. Considering the magnitude of this field, minima represent characteristic structures of the flow that can be classified as saddle- or vortex-like. We made the interesting observation that vortex-like minima are enclosed by particularly pronounced ridges. This makes it possible to define boundaries of vortex regions in a parameter-free way. Utilizing scalar field topology, a robust algorithm can be designed to extract such boundaries. They can be arbitrarily shaped. An efficient tracking algorithm allows us to display the temporal evolution of vortices. Various vortex models are used to evaluate the method. We apply our method to two-dimensional model systems from computational fluid dynamics and compare the results to those arising from existing definitions.

On the Extraction of Long-living Features in Unsteady Fluid Flows

This paper proposes aGalilean invariant generalization of critical points ofvector field topology for 2D time-dependent flows. The approach is based upon a Lagrangian consideration of fluid particle motion. It extracts long-living features, likesaddles and centers, and filters out short-living local structures. This is well suited for analysis ofturbulent flow, where standard snapshot topology yields an unmanageable large number of topological structures that are barely related to the few main long-living features employed in conceptual fluid mechanics models. Results are shown for periodic and chaoticvortex motion.

A Scale Space Based Persistence Measure for Critical Points in 2D Scalar Fields

This paper introduces a novel importance measure for critical points in 2D scalar fields. This measure is based on a combination of the deep structure of the scale space with the well-known concept of homological persistence. We enhance the noise robust persistence measure by implicitly taking the hill-, ridge- and outlier-like spatial extent of maxima and minima into account. This allows for the distinction between different types of extrema based on their persistence at multiple scales. Our importance measure can be computed efficiently in an out-of-core setting. To demonstrate the practical relevance of our method we apply it to a synthetic and a real-world data set and evaluate its performance and scalability.

Efficient Computation of Combinatorial Feature Flow Fields

We propose a combinatorial algorithm to track critical points of 2D time-dependent scalar fields. Existing tracking algorithms such as Feature Flow Fields apply numerical schemes utilizing derivatives of the data, which makes them prone to noise and involve a large number of computational parameters. In contrast, our method is robust against noise since it does not require derivatives, interpolation, and numerical integration. Furthermore, we propose an importance measure that combines the spatial persistence of a critical point with its temporal evolution. This leads to a time-aware feature hierarchy, which allows us to discriminate important from spurious features. Our method requires only a single, easy-to-tune computational parameter and is naturally formulated in an out-of-core fashion, which enables the analysis of large data sets. We apply our method to synthetic data and data sets from computational fluid dynamics and compare it to the stabilized continuous Feature Flow Field tracking algorithm.

Hierarchical vortex regions in swirling flow

We propose a new criterion to characterize hierarchical two‐dimensional vortex regions induced by swirling motion. Central to the definition are closed loops that intersect the flow field at a constant angle. The union of loops belonging to the same area of swirling motion defines a vortex region. These regions are disjunct but may be nested, thus introducing a spatial hierarchy of vortex regions. We present a parameter free algorithm for the identification of these regions. Since they are not restricted to star‐ or convex‐shaped geometries, we are able to identify also intricate regions, e.g., of elongated vortices. Computing an integrated value for each loop and mapping these values to a vortex region, introduces new ways for visualizing or filtering the vortex regions. Exemplary, an application based on the Rankine vortex model is presented. We apply our method to several CFD datasets and compare our results to existing approaches.

On the Elusive Concept of Lagrangian Coherent Structures

Many of the recently developed methods for analysis and visualization of time-dependent flows are related to concepts, which can be subsumed under the term Lagrangian coherent structures (LCS). Thereby, no universal definition of LCS exists and different interpretations are used. Mostly, LCS are considered to be features linked to pathlines leading to the ideal conception of features building material lines. Such time-dependent features are extracted by averaging local properties of particles along their trajectories, e.g., separation, acceleration or unsteadiness. A popular realization of LCS is the finite-time Lyapunov exponent (FTLE) with its different implementations. The goal of this paper is to stimulate a discussion on the generality of the underlying assumptions and concepts. Using a few well-known datasets, the interpretation and usability of Lagrangian analysis methods are discussed.

Vortex Merge Graphs in Two-dimensional Unsteady Flow Fields.

Among the various existing vortex definitions, there is one class that relies on extremal structures of derived scalar fields. These are, e.g., vorticity,llsubg2l/subg, or the acceleration magnitude. This paper proposes a method to identify and track extremal-based vortex structures in 2D time-dependent flows. It is based on combinatorial scalar field topology. In contrast to previous methods, merge events are explicitly handled and represented in the resulting graph. An abstract representation of this vortex merge graph serves as basis for the comparison of the different scalar identifiers. The method is applied to numerically simulated flows of a mixing layer and a planar jet.

Extraction of Coherent Structures from Natural and Actuated Flows

We present feature-extraction techniques for numerical and experimental data of complex fluid flows. Focus is placed on efficient analysis and visualization of coherent structures of snapshots, temporal evolution and parameter-dependency of coherent structures. One key enabler are Galilean invariant flow quantities based on pressure, acceleration, vorticity and velocity Jacobians. Other important catalyzers are Lagrangian filters that distill persistent strong particle-fixed features while neglecting weak and short-living ones. The proposed feature extraction framework is exemplified for the time-dependent natural and actuated flow around a high-lift airfoil, as well as other benchmark configurations of the SFB 557.

Modeling the Fuel/Air Mixing to Control the Pressure Pulsations and NO x Emissions in a Lean Premixed Combustor

This paper presents an overviewof the methodology developed to predict, control and optimize the NOx emissions and stability of lean premixed combustors. Investigations are performed firstly in cold flow and are validated with reacting flow measurements. A new cold flow mixing model describes the relevant characteristics of the fuel/airmixing, i.e. themixing quality and convective time delays, for different operating points of the system.Measurements in the combustor are performed to correct the flame position effect or calibrate the cold flowresults.The model is for the first time implemented in an extremum seeking controller to optimize the emissions and pressure pulsations of the combustor by adjusting the fuel mixing profile. A further increase of the fuel/air mixing, necessary for further NOx reductions, with pulsating fuel injection, is demonstrated. At the end, the developed adaptive control strategies demonstrate opportunities for future efficiency increases in industrial combustors.

Analysis of Vortex Merge Graphs

We propose an analysis framework to investigate different flow quantities such as vorticity, λ2 or the acceleration magnitude along vortex merge graphs and within their regions of influence. The explicit extraction of vortex merge graphs enables the application of statistical tools to investigate the vortex core lines themselves. The analysis tool provides common plots as scatter plots and parallel coordinates to explore the correlation of different quantities. An abstract representation of the vortex merge graph highlights birth, death and merges of vortices. Interactive picking of substructures supports a closer insepection of single vortices and their evolution. A further step integrates the regions of influence into the statistical analysis. Minima, maxima, median, mean and other percentiles of the measures along the vortex merge graph and its regions are visualized. The usability of the framework is demonstrated using a simulated flow data set of a mixing layer and a jet.