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System overview: a 3D surface view for showing droplet surfaces, consisting of filter panel (i), coloring tool (ii), bar chart (iii), main 3D view (iv) (here color mapped to anomaly measure e), time view (v) for selected droplet (crosshair in (iv)) with temporal scrolling. The similarity search (vi) provides cases similar to the selection, based on feature vector distance. In addition, we depict droplet instance information (vii), droplet trace similarities (viii) for (vi), and spider chart as a complement for (iii). b Quantity relation view: Input parallel coordinates plot for data filtering (x), scatterplot matrix (xi), and second parallel coordinates plot (xii) allows analysis of data. Moreover, any quantity can be mapped to color. c A ParaView instance is integrated within the system for analysis of the raw flow field for a single selected droplet and advanced flow feature extraction. A droplet selected in the 3D surface view can be automatically loaded into ParaView, including a useful default filter pipeline as shown within the figure
Source publication
We present a data-driven visual analysis approach for the in-depth exploration of large numbers of droplets. Understanding droplet dynamics in sprays is of interest across many scientific fields for both simulation scientists and engineers. In this paper, we analyze large-scale direct numerical simulation datasets of the two-phase flow of non-Newto...
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... provides an overview of extracted droplet characteristics and supports analyzing the interdependencies between them. Finally, the flow view can be used for the detailed investigation of a single selected droplet using complete raw input data. Different views are linked to supplement each other efficiently. An overview of the system can be seen in Fig. 4, and the different views are described in detail ...
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... surface view. The 3D droplet surface view allows a user to explore the droplet dataset spatially (Fig. 4a (iv)). Droplets of interest can be selected directly via picking (indicated with a crosshair). As showing all droplets would lead to significant occlusion and visual clutter, filtering the data is crucial ( Fig. 4a (i)). We support filtering w.r.t. arbitrary physical or geometrical quantities, clusters, and prediction errors (and ...
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... surface view. The 3D droplet surface view allows a user to explore the droplet dataset spatially (Fig. 4a (iv)). Droplets of interest can be selected directly via picking (indicated with a crosshair). As showing all droplets would lead to significant occlusion and visual clutter, filtering the data is crucial ( Fig. 4a (i)). We support filtering w.r.t. arbitrary physical or geometrical quantities, clusters, and prediction errors (and combinations thereof). Color mapping can flexibly depict chosen quantities, with the color-coded anomaly measure e being the default choice ( Fig. 4a (ii)). A user can navigate within the full trace of a selected droplet and ...
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... lead to significant occlusion and visual clutter, filtering the data is crucial ( Fig. 4a (i)). We support filtering w.r.t. arbitrary physical or geometrical quantities, clusters, and prediction errors (and combinations thereof). Color mapping can flexibly depict chosen quantities, with the color-coded anomaly measure e being the default choice ( Fig. 4a (ii)). A user can navigate within the full trace of a selected droplet and explore its temporal evolution (Fig. 4a (v)). Below, similar traces are shown that were identified via feature vector distance, i.e., by Euclidean distance between droplet instances in the 11-dimensional quantity space. This helps, on the one hand, to assess the ...
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... w.r.t. arbitrary physical or geometrical quantities, clusters, and prediction errors (and combinations thereof). Color mapping can flexibly depict chosen quantities, with the color-coded anomaly measure e being the default choice ( Fig. 4a (ii)). A user can navigate within the full trace of a selected droplet and explore its temporal evolution (Fig. 4a (v)). Below, similar traces are shown that were identified via feature vector distance, i.e., by Euclidean distance between droplet instances in the 11-dimensional quantity space. This helps, on the one hand, to assess the uniqueness of a droplet evolution, and on the other hand, the comparison to similar droplets can help to gain further ...
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... i.e., by Euclidean distance between droplet instances in the 11-dimensional quantity space. This helps, on the one hand, to assess the uniqueness of a droplet evolution, and on the other hand, the comparison to similar droplets can help to gain further insights into which commonalities or differences have led to certain behavior patterns (Fig. 4a (vi)). Additionally, we also provide the values for the selected droplet in our time view with a bar chart (Fig. 4a (iii)) and a spider chart (Fig. 4a (ix)), which can present its prediction error for different physical quantities. Detailed droplet instance information (Fig. 4a (vii)) and droplet trace similarities (Fig. 4a (viii)) are ...
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... the one hand, to assess the uniqueness of a droplet evolution, and on the other hand, the comparison to similar droplets can help to gain further insights into which commonalities or differences have led to certain behavior patterns (Fig. 4a (vi)). Additionally, we also provide the values for the selected droplet in our time view with a bar chart (Fig. 4a (iii)) and a spider chart (Fig. 4a (ix)), which can present its prediction error for different physical quantities. Detailed droplet instance information (Fig. 4a (vii)) and droplet trace similarities (Fig. 4a (viii)) are provided as ...
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... of a droplet evolution, and on the other hand, the comparison to similar droplets can help to gain further insights into which commonalities or differences have led to certain behavior patterns (Fig. 4a (vi)). Additionally, we also provide the values for the selected droplet in our time view with a bar chart (Fig. 4a (iii)) and a spider chart (Fig. 4a (ix)), which can present its prediction error for different physical quantities. Detailed droplet instance information (Fig. 4a (vii)) and droplet trace similarities (Fig. 4a (viii)) are provided as ...
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... commonalities or differences have led to certain behavior patterns (Fig. 4a (vi)). Additionally, we also provide the values for the selected droplet in our time view with a bar chart (Fig. 4a (iii)) and a spider chart (Fig. 4a (ix)), which can present its prediction error for different physical quantities. Detailed droplet instance information (Fig. 4a (vii)) and droplet trace similarities (Fig. 4a (viii)) are provided as ...
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... behavior patterns (Fig. 4a (vi)). Additionally, we also provide the values for the selected droplet in our time view with a bar chart (Fig. 4a (iii)) and a spider chart (Fig. 4a (ix)), which can present its prediction error for different physical quantities. Detailed droplet instance information (Fig. 4a (vii)) and droplet trace similarities (Fig. 4a (viii)) are provided as ...
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... other. Here, we use classical information visualization methods, namely parallel coordinates plots (PCP) and a scatterplot matrix (SPLOM), to present an overview of the physical quantities in the dataset as well as all derived quantities (e.g., clusters and prediction errors). In detail, this view consists of three separate components as shown in Fig. 4b. On top, we see the quantities of all droplets, shown within an interactive PCP (Fig. 4b (x)), where sliders on each axis can be used to filter the data. Positioned below are a scatterplot matrix (Fig. 4b (xi)) and a second PCP (Fig. 4b (xii)), in which we can analyze the filtered data. We provide both SPLOM and PCP to make use of the ...
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... plots (PCP) and a scatterplot matrix (SPLOM), to present an overview of the physical quantities in the dataset as well as all derived quantities (e.g., clusters and prediction errors). In detail, this view consists of three separate components as shown in Fig. 4b. On top, we see the quantities of all droplets, shown within an interactive PCP (Fig. 4b (x)), where sliders on each axis can be used to filter the data. Positioned below are a scatterplot matrix (Fig. 4b (xi)) and a second PCP (Fig. 4b (xii)), in which we can analyze the filtered data. We provide both SPLOM and PCP to make use of the strengths of both visualization techniques. The PCP is ideal for getting an overview of the ...
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... as well as all derived quantities (e.g., clusters and prediction errors). In detail, this view consists of three separate components as shown in Fig. 4b. On top, we see the quantities of all droplets, shown within an interactive PCP (Fig. 4b (x)), where sliders on each axis can be used to filter the data. Positioned below are a scatterplot matrix (Fig. 4b (xi)) and a second PCP (Fig. 4b (xii)), in which we can analyze the filtered data. We provide both SPLOM and PCP to make use of the strengths of both visualization techniques. The PCP is ideal for getting an overview of the data and locating single data points with the overall value range context, while the SPLOM can show pairwise relations ...
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... (e.g., clusters and prediction errors). In detail, this view consists of three separate components as shown in Fig. 4b. On top, we see the quantities of all droplets, shown within an interactive PCP (Fig. 4b (x)), where sliders on each axis can be used to filter the data. Positioned below are a scatterplot matrix (Fig. 4b (xi)) and a second PCP (Fig. 4b (xii)), in which we can analyze the filtered data. We provide both SPLOM and PCP to make use of the strengths of both visualization techniques. The PCP is ideal for getting an overview of the data and locating single data points with the overall value range context, while the SPLOM can show pairwise relations and is well-suited to identify ...
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... an overview of the data and locating single data points with the overall value range context, while the SPLOM can show pairwise relations and is well-suited to identify patterns and relations within the data. Naturally, highlighting data in one view also will highlight the data in the other view. They are also linked to the droplet surface view (Fig. 4a), i.e., brushing within the SPLOM or PCP can be used to filter in the 3D surface view. This can help to obtain spatial context regarding location and surface shape to the abstract quantity data points. This component is implemented on top of MegaMol ( Gralka et al. 2019), employing OpenGL to render millions of points and lines at highly ...
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... view. For an in-depth exploration of the underlying flow field, e.g., to analyze the reason for a high anomaly, we further incorporate various classic flow visualization techniques by directly integrating ParaView (Ayachit 2015) into our system (Fig. 4c). ParaView is controlled from our application by loading the droplet data of the currently selected droplet within our 3D droplet surface view and automatically setting up the ParaView visualization pipeline. Not only the droplet itself is exported, but its full trace (in a dropletlocal coordinate system for convenience), allowing ...
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... first consider a single time step with the quantity relationship view (Fig. 4b). As the jet we are looking at is fully converged, all time steps are quite similar regarding general structure. First, we investigate the filter PCP at the top to get an overview of the different value ranges. We notice the wide value range of the droplet quantities due to single outliers, which leads to the majority of droplets being ...
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... such problematic cases is important for studying edge cases in the simulation and discarding them from further consideration. Figure 4a shows the 3D surface view depicting time step 410. Color depicts our anomaly estimation e, with higher anomaly indicated by reddish colors and lower anomaly by yellowish ones. ...
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... the chosen filtering criteria, leading to Fig. 12b. This way, we observe many long traces in the 3D surface view, which provides the point of origin for our further investigations. We now pick a trace with exceptionally high anomaly estimation (selection indicated by a black cross in Fig. 12a). A closer inspection of that trace in the time-view (Fig. 4a (v)) reveals that the droplet becomes rounder over time and that the anomaly indicator e stays almost constant over time. This observation turned out to be quite rare, since typically, the anomaly measure reduces quite quickly, particularly if the respective droplet becomes roundish. A thorough investigation of the respective plots of the ...
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... of the respective plots of the original traces and the individual deviations of the predicted quantities from the original ones did not provide insights on the causes of this behavior. We started to hypothesize that the internal flow within the droplet might provide insights. We thus initiated flow visualization of the liquid phase of the droplet (Fig. 14) (left). Note that we use a linear mapping of velocity magnitude to glyph color, but a logarithmic mapping of velocity magnitude to glyph size within Fig. 14 and following. Interestingly, we observed a distinguished and strong saddle-type flow pattern in the internal flow, in the frame of reference moving with the velocity of the center ...
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... causes of this behavior. We started to hypothesize that the internal flow within the droplet might provide insights. We thus initiated flow visualization of the liquid phase of the droplet (Fig. 14) (left). Note that we use a linear mapping of velocity magnitude to glyph color, but a logarithmic mapping of velocity magnitude to glyph size within Fig. 14 and following. Interestingly, we observed a distinguished and strong saddle-type flow pattern in the internal flow, in the frame of reference moving with the velocity of the center of mass of the droplet. We investigated other cases with high anomaly measure e, either by direct selection in the 3D Fig. 12 Exploration of the dataset ...
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... investigated other cases with high anomaly measure e, either by direct selection in the 3D Fig. 12 Exploration of the dataset within the 3D surface view (cf. Figure 4a (iv)). After loading the dataset, the time filter is set to show only a single time step and a second filter omits all droplet instances that lack total error (our anomaly indicator) e, leading to the view in a. ...
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... user now selects a droplet of interest for further analysis (black cross). Here, the droplet shown in Figure 14 (left) is selected. b Further example. ...
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... of e, supporting the hypothesis of insufficient resolution of the simulation grid view or using our similarity search, as provided in the lower half of our tool. Interestingly, most cases of non-ligament (more or less roundish) droplets with high e turned out to exhibit such saddle-type flow patterns in their interior, including the case shown in Fig. 14 (right), found as most similar to that droplet by similarity ...
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... Anomaly Droplet II case. Fig. 12a. We found that droplets with low temporal decay of e exhibit distinguished saddle-type flow patterns in their interior flow, in the frame of reference moving with the center of mass of the droplet. Right: This is the droplet found most similar by similarity search in Fig. 4a (vi) Fig. 15 An increasing anomaly droplet case. The scarce case of temporally increasing e brought our attention to this case, which, in the frame of reference moving with the center of mass of the droplet, exhibits a strong vortex in its interior flow. This droplet has been the only one we could identify to contain a vortex ...
Citations
... Then it should design an implementation that, for example, allows to robustly ignore interactions that are irrelevant or not yet implemented and take part in the rest of the communication. This effectively describes a generalization of the implementation in Heinemann et al. [14]. A first internal draft of this is outlined by G. Reina. ...
... Furthermore, we applied the density-based spatial clustering of applications with noise (DBSCAN) algorithm [25,26] on the iso surface of the phase fraction field to isolate and analyse the droplets of a Taylor cone jet, as we see on Figure 5. By employing DBSCAN on the iso-surface of the field, we could accurately segment the droplets from the continuous phase of the flow, even when they were in close proximity or overlapping. ...
Taylor cone liquid jets occurs when a conductive liquid is placed on a capillary nozzle and a strong electric field is applied. The electric field causes the surface of the droplet to deform into a conical shape, and a liquid jet is ejected from the tip of the cone. This phenomenon has a wide range of applications, such as in inkjet printing, drug delivery, and electrohydrodynamic propulsion. An understanding of the underlying physics of the Taylor cone jet is essential for optimizing the performance of devices that utilize this phenomenon. Computational fluid dynamics (CFD) has become a powerful tool for studying the Taylor cone jet, and in this paper, we propose the utilization of a full three-dimensional model to study the complete dynamics of the Taylor cone jet. These electrohydrodynamic jets are a method to accomplish the controlled emission of microdroplets, with applications from constructing nanofibers to micro-propulsion. For the numerical computations, we use the interIsoFoam solver on OpenFOAM, which resolves an immiscible two-phase flow, and coupled it with a transport equation for the electric charges as well the simplified version of the Maxwell equations for an electrostatic field. The advection equation of the phase fraction is solved by a geometric Volume-Of-Fluid (VOF). Moreover, the hydrody-namic momentum equation incorporates electrically generated body forces using the Maxwell Stress Tensor (MST). While axisymmetric simulations are computationally less expensive, they fail to capture an important behavior of this type of jet, such as the whipping effect and the tiny droplets emitted during the receding of the jet emission cycle. In contrast, the three-dimensional simulations used in this study offer a more accurate representation of the physics involved in the jet formation process, including the formation of instabilities and the resulting complex jet shapes. As we show in our results the droplets are radially scattered on the target collector due to the formation of the ionic wind, which we also show the three-dimensional structures. The current study begins with the numerical validation of the Taylor cone formation, by comparing the cone shape with the experimental results of the literature. Then simulations were performed for different electric potentials and inlet flow rates, which showed that the stable window is narrowed by the applied electric potential. The results revealed that the instability of the jet is due to the concentration of the electric charges, which led to a breakup of the jet into droplets, in the direction of the electric field. Overall, this study emphasizes the value of using three-dimensional numerical simulations to study Taylor cone jet instabilities because they provide a more accurate depiction of the physics at play and can offer useful information for optimizing Taylor cones jet-using equipment like inkjet printers and electrospray systems.
... We exemplify the utility of our technique using multiphase flow simulation data. The investigation of droplets is an active area of research (Focke and Bothe 2012;Heinemann et al. 2021;Jadidi et al. 2019;Tryggvason et al. 2011;Yokoi 2008), as is the analysis of liquid jets (Ertl and Weigand 2015;Li et al. 2010). We refer the reader to for a detailed introduction to multiphase flow simulations and Lefebvre (1989) for a thorough description of liquid atomization and sprays. ...
In multiphase flows, the evolution of fluid-fluid interfaces is of interest in many applications. In addition to fluid dynamic forces governing the flow in the entire volume, surface tension determines droplet interfaces. Here, the analysis of interface kinematics can help in the investigation of interface deformation and the identification of potential breakups. To this end, we developed a visualization technique using metric and shape tensors to analyze interface stretching and bending. For interface stretching, we employ the eigenpairs of the metric tensor defined for the deformation rate of the fluid surface. For interface bending, we present a technique that locally captures the interface curvature change in terms of a shape tensor, extracting its principal directions and curvatures. We then visualize interface deformation by combining both representations into a novel glyph design. We apply our method to study multiphase flow simulations with particular emphasis on interface effects. These include the interplay between fluid dynamics and surface tension forces leading to breakup processes following droplet collisions, as well as droplet-droplet interactions of different fluids where Marangoni convection along the surface is explicitly taken into account.
Graphical abstract
... Generally, a rendering module within MegaMol is provided with a render target and a camera, both of which can be modified by other modules before the renderer is executed, and the render target provides access to the rendering result for further processing afterward. Our technique was implemented as a module that we can simply insert in front of any 2D renderer into existing projects (see also Fig. 1 Iris is taken from the UCI Machine Learning Repository (Dua and Graff 2017), Concrete Beam is from an FEM structural mechanics simulation of a beam (containing nodes and stress tensors) (Kelleter et al. 2020), and Droplets are extracted physical quantities per droplet of a multiphase jet simulation as used by Heinemann et al. (2021). We picked Parallel Coordinates Plot and Scatterplot Matrix renders as typical representatives of 2D visualizations. ...
Data visualization relies on efficient rendering to allow users to interactively explore and understand their data. However, achieving interactive frame rates is often challenging, especially for high-resolution displays or large datasets. In computer graphics, several methods temporally reconstruct full-resolution images from multiple consecutive lower-resolution frames. Besides providing temporal image stability, they amortize the rendering costs over multiple frames and thus improve the minimum frame rate. We present a method that adopts this idea to accelerate 2D information visualization, without requiring any changes to the rendering itself. By exploiting properties of orthographic projection, our method significantly improves rendering performance while minimizing the loss of image quality during camera manipulation. For static scenes, it quickly converges to the full-resolution image. We discuss the characteristics and different modes of our method concerning rendering performance and image quality and the corresponding trade-offs. To improve ease of use, we provide automatic resolution scaling in our method to adapt to user-defined target frame rate. Finally, we present extensive rendering benchmarks to examine real-world performance for examples of parallel coordinates and scatterplot matrix visualizations, and discuss appropriate application scenarios and contraindications for usage.
Graphical Abstract
In a cylindrical chamber, the ionic liquid 1-ethyl-3-methylimidazolium tetrafluoroborate was used to compress gaseous hydrogen from 220 to 752.3 bar, concurrently raising its temperature from 298.15 to 394.2 K over approximately six seconds. A three-dimensional liquid-piston compressor model was established and validated against the experimental data. Two-phase flow was simulated using the finite volume method and the volume of fluid model in ANSYS Fluent software. A novel heat transfer enhancement technique using cooling pipes was investigated inside a liquid-piston compressor to achieve near-isothermal compression. Multiple cooling scenarios were explored to enhance the compression and thermal performance, considering the number of pipes, cross-sectional shape, diameter, and pipe temperature. This approach provided a more comprehensive understanding of the flow regimes and heat transfer behaviors of working fluids throughout the compression process. To achieve the desired pressure ratio, using four circular pipes reduced the hydrogen temperature from 394.2 to 355 K, marking 40.8% improvement in thermal efficiency. Furthermore, compression performance reached 95.8% with a power density of 3221.4 kW·m−3, compared to 90.9% and 4550.6 kW·m−3 without cooling.
Physics of supercritical fluids is extremely complex and not yet fully understood. The importance of the presented investigations into the physics of supercritical fluids is twofold. First, the presented approach links the microscopic dynamics and macroscopic thermodynamics of supercritical fluids. Second, free falling droplets in a near to supercritical environment are investigated using spontaneous Raman scattering and a laser induced fluorescence/phosphorescence thermometry approach. The resulting spectroscopic data are employed to validate theoretical predictions of an improved evaporation model. Finally, laser induced thermal acoustics is used to investigate acoustic damping rates in the supercritical region of pure fluids.
High-voltage composite insulators are specially designed to withstand different environmental conditions to ensure a reliable and efficient electric power distribution and transmission. Especially, outdoor insulators are exposed to rain, snow or ice, which might significantly affect the performance of the insulators. The interaction of sessile water droplets and electric fields is investigated under various boundary conditions. Besides the general behavior of sessile droplets, namely the deformation and oscillation, the inception field strength for partial discharges is examined depending on the droplet volume, strength and frequency of the electric field and the electric charge. Particularly, the electric charge is identified to significantly affect the droplet behavior as well as the partial discharge inception field strength. In addition to ambient conditions, the impact of electric fields on ice nucleation is investigated under well-defined conditions with respect to the temperature and electric field strength. High electric field strengths are identified to significantly promote ice nucleation, especially in case of alternating and transient electric fields. Different influencing factors like the strengths, frequencies and time constants of the electric fields are investigated. Consequently, the performed experiments enhance the knowledge of the behavior of water droplets under the impact of electric fields under various conditions.
The present paper aims at developing a generally valid, consistent numerical description of a turbulent multi-component two-phase flow that experiences processes that may occur under both subcritical and trans-critical or supercritical operating conditions. Within an appropriate LES methodology, focus is put on an Euler-Eulerian method that includes multi-component mixture properties along with phase change process. Thereby, the two-phase flow fluid is considered as multi-component mixtures in which the real fluid properties are accounted for by a composite Peng-Robinson (PR) equation of state (EoS), so that each phase is governed by its own PR EoS. The suggested numerical modelling approach is validated while simulating the disintegration of an elliptic jet of supercritical fluoroketone injected into a helium environment. Qualitative and quantitative analyses are carried out. The results show significant coupled effect of the turbulence and the thermodynamic on the jet disintegration along with the mixing processes. Especially, comparisons between the numerical predictions and available experimental data provided in terms of penetration length, fluoroketone density, and jet spreading angle outline good agreements that attest the performance of the proposed model at elevated pressures and temperatures. Further aspects of transcritical jet flow case as well as comparison with an Eulerian-Lagrangian approach which is extended to integrate the arising effects of vanishing surface tension in evolving sprays are left for future work.
A fundamental understanding of droplet dynamics is important for the prediction and optimization of technical systems involving drops and sprays. The Collaborative Research Center (CRC) SFB-TRR 75 was established in January 2010 to focus on the dynamics of basic drop processes, and in particular on processes involving extreme ambient conditions, for example near thermodynamic critical conditions, at very low temperatures, under the influence of strong electric fields, or in situations involving extreme gradients of the boundary conditions. The goal of the CRC was to gain a profound physical understanding of the essential processes, which is the basis for new analytical and numerical descriptions as well as for improved predictive capabilities. This joint initiative involved scientists at the University of Stuttgart, the TU Darmstadt, the TU Berlin, and the German Aerospace Center (DLR) in Lampoldshausen. This first chapter provides a brief overview of the overall structure of this CRC as well as a summary of some selected scientific achievements of the subprojects involved. For further details the reader is referred to the subsequent chapters of this book related to the individual subprojects.
