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Item type:Publication, Access status: with files , Data assimilation and parameter identification for water waves using the nonlinear Schrödinger equation and physics-informed neural networks(Multidisciplinary Digital Publishing Institute (MDPI), 2024-10-01); ; ; The measurement of deep water gravity wave elevations using in situ devices, such as wave gauges, typically yields spatially sparse data due to the deployment of a limited number of costly devices. This sparsity complicates the reconstruction of the spatio-temporal extent of surface elevation and presents an ill-posed data assimilation problem, which is challenging to solve with conventional numerical techniques. To address this issue, we propose the application of a physics-informed neural network (PINN) to reconstruct physically consistent wave fields between two elevation time series measured at distinct locations within a numerical wave tank. Our method ensures this physical consistency by integrating residuals of the hydrodynamic nonlinear Schrödinger equation (NLSE) into the PINN’s loss function. We first showcase a data assimilation task by employing constant NLSE coefficients predetermined from spectral wave properties. However, due to the relatively short duration of these measurements and their possible deviation from the narrow-band assumptions inherent in the NLSE, using constant coefficients occasionally leads to poor reconstructions. To enhance this reconstruction quality, we introduce the base variables of frequency and wavenumber, from which the NLSE coefficients are determined, as additional neural network parameters that are fine tuned during PINN training. Overall, the results demonstrate the potential for real-world applications of the PINN method and represent a step toward improving the initialization of deterministic wave prediction methods.Publicationtype: Journal Article33 38 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Characterization data for the establishment of scale-up and process transfer strategies between stainless steel and single-use bioreactors(Multidisciplinary Digital Publishing Institute (MDPI), 2024-05-16); ; ; 38 99 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , The influence of characteristic sea state parameters on the accuracy of irregular wave field simulations of different complexity(Multidisciplinary Digital Publishing Institute (MDPI), 2022-07-15); ; ; ; The accurate description of the complex genesis and evolution of ocean waves, as well as the associated kinematics and dynamics is indispensable for the design of offshore structures and the assessment of marine operations. In the majority of cases, the water-wave problem is reduced to potential flow theory on a somehow simplified level. However, the nonlinear terms in the surface boundary conditions and the fact that they must be fulfilled on the unknown water surface make the boundary value problem considerably complex. Hereby, the contrary objectives with respect to a very accurate representation of reality and numerical efficiency must be balanced wisely. This paper investigates the influence of characteristic sea state parameters on the accuracy of irregular wave field simulations of different complexity. For this purpose, the high-order spectral method was applied and the underlying Taylor series expansion was truncated at different orders so that numerical simulations of different complexity can be investigated. It is shown that, for specific characteristic sea state parameters, the boundary value problem can be significantly reduced while providing sufficient accuracy.Publicationtype: Journal ArticleScopus© Citations 4 105 141 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Coexistence of inverse and direct energy cascades in faraday waves(Multidisciplinary Digital Publishing Institute (MDPI), 2022-04-24); ; ; ; In nature, turbulent flows exist that are neither simply 2D nor 3D but are forced towards one state or the other by boundary conditions such as varying stratification. Here, we report the first evidence of the co-existence of an inverse and a direct energy cascade 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 co-exist. We base our analysis on temporally and spatially well-resolved velocity fields obtained by particle image velocimetry measurements at planes parallel and perpendicular to the water surface. The findings also provide strong evidence that the intense turbulent 2D surface flow drives the 3D bulk flow through sporadic vertical jets as a source of momentum to the bulk liquid.Publicationtype: Journal ArticleScopus© Citations 4 78 205 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Electrical Capacitance Volume Tomography (ECVT) for Characterization of Additively Manufactured Lattice Structures (AMLS) in Gas-Liquid Systems(Multidisciplinary Digital Publishing Institute (MDPI), 2021-09-08); ; ; ; Against the background of current and future global challenges, such as climate change, process engineering requires increasingly specific solutions adapted to the respective problem or application, especially in gas–liquid contact apparatuses. One possibility to adjust the conditions in this kind of apparatuses is an intelligent and customized structuring, which leads to consistent fluid properties and flow characteristics within the reactor. In the course of this, the interfacial area for mass transfer, as well as residence times, have to be adjusted and optimized specifically for the respective application. In order to better understand and advance the research on intelligent customized additively manufactured lattice structures (AMLS), the phase distributions and local gas holdups that are essential for mass transfer are investigated for different structures and flow conditions. For the first time a tomographic measurement technique is used, the Electrical Capacitance Volume Tomography (ECVT), and validated with the volume expansion method and a fiber optical needle probe (A2PS-B-POP) for an air-water system for different modes of operation (with or without co-current liquid flow in empty or packed state). The ECVT proved to be particularly useful for both in the empty tube and the packed state and provided new insights into the phase distributions occurring within structured packings, which would have led to significantly underestimated results based on the visual reference measurements, especially for a densely packed additively manufactured lattice structure (5 mm cubic on the tip). Particularly for the modified structures, which were supposed to show local targeted differences, the ECVT was able to resolve the changes locally. The additional use of a pump for co-current flow operation resulted in slightly higher fluctuations within the ECVT data, although local events could still be resolved sufficiently. The final comparison of the empty tube at rest data with a fiber optical needle probe showed that the results were in good agreement and that the local deviations were due to general differences in the respective measurement techniques.Publicationtype: Journal ArticleScopus© Citations 5 159 313 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , On the deterministic prediction of water waves(Multidisciplinary Digital Publishing Institute (MDPI), 2020-01-07); ; ; ; This paper discusses the potential of deterministic wave prediction as one basic module for decision support of offshore operations. Therefore, methods of different complexity - the linear wave solution, the non-linear Schrödinger equation (NLSE) of two different orders and the high-order spectral method (HOSM) - are presented in terms of applicability and limitations of use. For this purpose, irregular sea states with varying parameters are addressed by numerical simulations as well as model tests in the controlled environment of a seakeeping basin. The irregular sea state investigations focuses on JONSWAP spectra with varying wave steepness and enhancement factor. In addition, the influence of the propagation distance as well as the forecast horizon is discussed. For the evaluation of the accuracy of the prediction, the surface similarity parameter is used, allowing an exact, quantitative validation of the results. Based on the results, the pros and cons of the different deterministic wave prediction methods are discussed. In conclusion, this paper shows that the classical NLSE is not applicable for deterministic wave prediction of arbitrary irregular sea states compared to the linear solution. However, the application of the exact linear dispersion operator within the linear dispersive part of the NLSE increased the accuracy of the prediction for small wave steepness significantly. In addition, it is shown that non-linear deterministic wave prediction based on second-order NLSE as well as HOSM leads to a substantial improvement of the prediction quality for moderate and steep irregular wave trains in terms of individual waves and prediction distance, with the HOSM providing a high accuracy over a wider range of applications.Publicationtype: Journal ArticleScopus© Citations 42 573 270 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , The effect of random wind forcing in the nonlinear Schrödinger equationThe influence of a strong and gusty wind field on ocean waves is investigated. How the random wind affects solitary waves is analyzed in order to obtain insights about wave generation by randomly time varying wind forcing. Using the Euler equations of fluid dynamics and the method of multiple scales, a random nonlinear Schrödinger equation and a random modified nonlinear Schrödinger equation are obtained for randomly wind forced nonlinear deep water waves. Miles theory is used for modeling the pressure variation at the wave surface resulting from the wind velocity field. The nonlinear Schrödinger equation and the modified nonlinear Schrödinger equation are computed using a relaxation pseudo spectral scheme. The results show that the influence of gusty wind on solitary waves leads to a randomly increasing ocean wave envelope. However, in a laboratory setup with much smaller wave amplitudes and higher wave frequencies, the influence of water viscosity is much higher. This leads to fluctuating solutions, which are sensitive to wind forcing.Publicationtype: Journal ArticleScopus© Citations 3 1102 307 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Experimental analysis of a bubble wake influenced by a vortex street(Multidisciplinary Digital Publishing Institute (MDPI), 2018-01-20); ; Bubble column reactors are ubiquitous in engineering processes. They are used in waste water treatment, as well as in the chemical, pharmaceutical, biological and food industry. Mass transfer and mixing, as well as biochemical or chemical reactions in such reactors are determined by the hydrodynamics of the bubbly flow. The hydrodynamics of bubbly flows is dominated by bubble wake interactions. Despite the fact that bubble wakes have been investigated intensively in the past, there is still a lack of knowledge about how mass transfer from bubbles is influenced by bubble wake interactions in detail. The scientific scope of this work is to answer the question how bubble wakes are influenced by external flow structures like a vortex street behind a cylinder. For this purpose, the flow field in the vicinity of a single bubble is investigated systematically with high spatial and temporal resolution. High-speed Particle Image Velocimetry (PIV) measurements are conducted monitoring the flow structure in the equatorial plane of the single bubble. It is shown that the root mean square (RMS) velocity profiles downstream the bubble are influenced significantly by the interaction of vortices. In the presence of a vortex street, the deceleration of the fluid behind the bubble is compensated earlier than in the absence of a vortex street. This happens due to momentum transfer by cross-mixing. Both effects indicate that the interaction of vortices enhances the cross-mixing close to the bubble. Time series of instantaneous velocity fields show the formation of an inner shear layer and coupled vortices. In conclusion, this study shows in detail how the bubble wake is influenced by a vortex street and gives deep insights into possible effects on mixing and mass transfer in bubbly flows.Publicationtype: Journal ArticleScopus© Citations 5 397 486