arXiv subjects

Matthias Kramer

Publications and source records attributed to Matthias Kramer.

11 recordsLinked to original sources

arXiv2026

Clustering and surface distributions of buoyant particles in open-channel flows

This study investigates the clustering behaviour and surface distributions of buoyant particles at the air-water interface in open-channel turbulent flow, focusing on the interplay between capillary attraction, hydrodynamic drag, and flow-driven lateral transport. Using controlled laboratory flume experiments, we systematically examine clustering dynamics for two particle types differing in size and density. To interpret the observed behaviour, we extend capillary-based clustering frameworks to open-channel flows by introducing a dimensionless clustering Weber number (We_cl) that captures the balance between the flow-induced disruptive force and capillary attraction, providing a compact description of the observed clustering behaviour. In addition, we demonstrate that secondary currents play a central role in surface particle transport, producing systematic lateral accumulation that depends on channel aspect ratio. Together, these findings extend capillary-driven clustering theory to open-channel turbulence and reveal secondary currents as a key mechanism controlling particle surface distributions.

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arXiv2026

A Favre-Averaging Shallow Water Framework for Aerated Flows with Friction Factor Decomposition

Accurate prediction of flow resistance in high-Froude-number aerated flows remains challenging due to air entrainment, which causes strong spatial variability in mixture density. Here, we introduce for the first time a density-weighted (Favre) averaging approach within a Shallow Water Equation framework specifically tailored to account for this strong mixture density variability. Within this framework, we present a novel Darcy-Weisbach friction factor formulation that decomposes contributions associated with uniform flow, spatially varying flow, and temporally evolving flow, and incorporates momentum and pressure correction factors reflecting the vertical structure of the mixture. Application to experimental data demonstrates that spatial flow development systematically reduces the effective friction factor relative to the uniform-flow estimate, and that momentum-based and energy-based formulations yield nearly identical results. The framework recovers classical uniform-flow predictions in the quasi-uniform downstream region and reduces to standard single-phase formulations in the absence of aeration. Overall, it provides a physically consistent tool for resistance prediction in high-Froude-number spillways, chutes, and open-channel systems, with a structure compatible with depth-averaged numerical solvers.

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arXiv2025

Discussion on "Resurrecting a Neglected Measurement Technique for Air-Water Flows"

Over the last years, there has been a renewed interest in differentiating various contributions to the air concentration in high Froude-number self-aerated flows, see for example Kramer (2024), comprising entrained and entrapped air. The former is characterized by entrained air packets and bubbles, while entrapped air corresponds to air transported along wave peaks and troughs. Entrapped air was first measured by Killen (1968) using a so-called dipping probe, while a physical interpretation of the dipping probe signals was provided only later by Wilhelms and Gulliver (2005). Since then, it has been commonly accepted that two different measurement instruments, for example a dipping probe and a common phase-detection probe, are required to fully quantify entrained and entrapped air. Recently, an article entitled "Resurrecting a Neglected Measurement Technique for Air-Water Flows" was published by Wilhelms and Gulliver (2024), who re-iterated the importance of applying these concepts for cavitation prevention and air-water gas transfer, as well as the need for two separate measurement instruments. The authors are congratulated for their seminal works on entrained and entrapped air (Wilhelms and Gulliver 2005; Wilhelms and Gulliver 2024), and it is stipulated that these concepts have been overlooked in the last two decades. In this discussion, a simple discrimination technique for phase-detection probe signals is proposed, which allows to differentiate entrained and entrapped air from existing datasets, recorded with a state-of-the-art dual-tip phase-detection probe. It is believed that this novel signal processing method will make Killen's (1968) dipping probe redundant, and that it will be useful for the validation of non-intrusive measurements of entrapped air, as well as for the development of physics-based models for air-water mass transfer in self-aerated flows.

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arXiv2025

On the estimation of specific interfacial areas in aerated flows

This work provides a short clarification on the definition of specific interfacial areas in aerated flows, thereby distinguishing between the specific interfacial area related to the volume of an air-water mixture, and the specific interfacial area related to the water volume. This distinction is important when it comes to solving the air-water mass transfer equation, as there has been some misconception on the past. It is hoped that this contribution will help to clarify on these basic fundamentals, which is anticipated to be important for the future development and application of advanced air-water mass transfer models to aerated flows.

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arXiv2024

Improving the measurement of air-water flow properties using remote distance sensing technology

In recent years, there has been an increasing research interest in the application of remote sensing technology to highly aerated flows, which is because this technology holds the ultimate promise to enable safe and accurate measurements of real-word air-water flows in natural and human made environments. Despite the increasing number of publications, some fundamental questions, such as ``what do we measure'' or ``what can we measure'', have not been answered conclusively. In this study, we hypothesize that laser distance sensors are able to measure the concentration of entrapped air, which we demonstrate using two seminal air-water flow types, namely a submerged hydraulic jump and flows down a stepped spillway. By converting our free-surface signals into time series of instantaneous air concentrations, we also show that a dual laser triangulation setup enables the extraction of basic air-water flow parameters of the upper flow region, comprising interface count rates, interfacial velocities, and turbulence levels, while we acknowledge that some sensor characteristics, such as beam diameters, can lead to measurement biases. Overall, this study represents a major advancement in the remote measurement of air-water flow properties. Future collective research effort is required to overcome remaining challenges.

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arXiv2024

Developing the next generation of dual-tip phase-detection probes for air-water flow experiments

Self-aeration is a fascinating phenomenon that commonly occurs in high Froude-number flows in natural or human made environments. The most common air-water flow measurement instrument to characterize such flows is the intrusive dual-tip phase-detection needle probe, which identifies phase changes around the needle tips due to a change of resistivity (phase-detection conductivity probe) or light refraction (phase-detection fiber optical probe). Phase-detection conductivity probes are typically custom made for research purposes, with current design dating back to the 1980ies. In the present study, the next generation of dual-tip conductivity probes is developed and validated against a state-of-the-art system. The novel probe design comprises two main features, including (1) a printed circuit board of the sensor's electrodes and (2) a detachable sensor head. These features offer many advantages over the classical needle-type design. For example, the circuit boards can be manufactured with high precision and the sensor head can be easily replaced in case of damage or deterioration. As such, it is anticipated that this relatively cheap and robust design will enable a better repeatability of air-water flow experiments, combined with an enhanced accessibility for the air-water flow research community.

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arXiv2024

Surface detachment and bed entrainment of fluvial plastics

Over the last decade, fluvial plastics have been identified as major threat to aquatic environments and human health. In order to develop adequate mitigation strategies for plastic pollution, a fundamental process understanding of riverine plastic transport is of significant importance. In this context, the implementation of research findings into numerical simulation environments is anticipated to enhance modelling capabilities and to support a rigorous decision making. Recent experimental research has focused on the incipient motion of plastic particles, as well as on the effects of surface tension on plastic concentration profiles. While these investigations have advanced the state-of-the-art knowledge, current literature still displays a lack of basic insights into layer-specific plastic transport physics. In this study, first principles are applied to advance knowledge on free-surface detachment and bed entrainment of fluvial plastics. A novel relationship for the critical surface detachment velocity is derived, followed by the development of a framework that allows to relate plastic Shields parameters to those of natural sediments. Overall, it is anticipated that these developments will trigger new research within the plastics community, and it is hoped that present findings will be implemented into Lagrangian particle tracking software.

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arXiv2023

Turbulent free-surface in self-aerated flows: Superposition of entrapped and entrained air

The characterisation and the modelling of air concentration distributions in self-aerated free-surface flows has been subject to sustained research interest since the 1970s. Recently, a novel two-state formulation of the structure of a self-aerated flow was proposed by Kramer & Valero [2023 J. Fluid Mech. 966, A37], which physically explains the air concentration through the weak interaction of two canonical flow momentum layers, comprising a Turbulent Boundary Layer (TBL) and a Turbulent Wavy Layer (TWL). The TWL was modelled using a Gaussian error function, assuming that the most dominant contribution are wave troughs. Here, it is shown that air bubbles form an integral part of the TWL, and its formulation is expanded by adopting a superposition principle of entrapped air (waves) and entrained air (bubbles). Combining the superposition principle with the two-state formulation, an expression for the depth-averaged (mean) air concentration is derived, which allows to quantify the contribution of different physical mechanisms to the mean air concentration. Overall, the presented concepts help to uncover new flow physics, thereby contributing fundamentally to our understanding of self-aerated flows.

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arXiv2023

Linking turbulent waves and bubble diffusion in self-aerated open-channel flows: Two-state air concentration

High Froude-number flows become self-aerated when the destabilizing effect of turbulence overcomes gravity and surface tension forces. Traditionally, the resulting air concentration profile has been explained using single-layer approaches that invoke solutions of the advection-diffusion equation for air in water, i.e., bubbles' dispersion. Based on a wide range of experimental evidences, we argue that the complete air concentration profile shall be explained through the weak interaction of different canonical turbulent flows, namely a Turbulent Boundary Layer (TBL) and a Turbulent Wavy Layer (TWL). Motivated by a decomposition of the streamwise velocity into a pure wall flow and a free-stream flow [Krug et al., J. Fluid Mech. (2017), vol. 811, pp. 421--435], we present a physically consistent two-state formulation of the structure of a self-aerated flow. The air concentration is mathematically built upon a modified Rouse profile and a Gaussian error function, resembling vertical mass transport in the TBL and the TWL. We apply our air concentration theory to over 500 profiles from different data sets, featuring excellent agreement. Finally, we show that the turbulent Schmidt number, characterizing the momentum-mass transfer, ranges between 0.2 to 1, which is consistent with previous mass-transfer experiments in TBLs. Altogether, the proposed flow conceptualization sets the scene for more physically-based numerical modelling of turbulent mass diffusion in self-aerated flows.

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arXiv2019

Best practices for velocity estimations in highly aerated flows with dual-tip phase-detection probes

Dual-tip phase-detection probes can be used to measure flow properties in gas-liquid flows. Traditionally, time-averaged interfacial velocities have been obtained through cross-correlation analysis of long time-series of phase fraction signals. Using small groups of detected particles, a recently developed adaptive window cross-correlation (AWCC) technique enables the computation of pseudo-instantaneous interfacial velocities and turbulence quantities in highly aerated flows, albeit subject to some smoothing which is due to the use of a finite window duration. This manuscript provides guidance on the selection of optimum processing parameters for the AWCC technique, additionally addressing shortcomings such as velocity bias correction in turbulent flows and extrapolation of turbulence levels to single particles. The presented technique was tested for three highly turbulent air-water flows: smooth and rough-wall boundary layers (tunnel chute and stepped spillway), as well as breaking shear layer flows of a hydraulic jump. Robust estimations of mean velocities and velocity fluctuations were obtained for all flow situations, either using dual-tip conductivity or fiber optical probe data. The computation of integral time scales and velocity spectra is currently limited by the data rate and must be treated with caution.

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arXiv2019

Turbulence and self-similarity in highly-aerated shear flows: the stable hydraulic jump

Hydraulic jumps are oftentimes encountered in natural and human-made environments. The transition from supercritical to subcritical flow involves large energy dissipation rates and substantial air entrainment, preventing the use of monophasic flow measurement instrumentation. This paper presents an experimental study of a stable hydraulic jump with a Froude number of 4.25, utilizing novel intrusive phase-detection probe techniques and image-based velocimetry from a side perspective. Turbulence estimations were obtained for the impinging region and the roller region of the jump including Reynolds stresses, turbulent integral scales and velocity fluctuations spectra. The velocity spectra had a -5/3 slope in the inertial subrange and flattened at larger frequencies. This is thought to be linked to an energy transfer from the inertial range to the frequencies associated with bubble scales. Overall, the collected data is of particular interest for high-fidelity numerical model validation and the study represents an advancement in air-water flow research.

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