Dual-plane ultrasound flow measurements in liquid metals

Büttner, Lars; Nauber, Richard; Bürger, Markus; Räbiger, D.; Franke, Sven; Eckert, Sven; Czarske, Jürgen

doi:10.1088/0957-0233/24/5/055302

Cited by 26 publications

(7 citation statements)

References 26 publications

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“…Rayleigh-Bénard convection (RBC), a fluid flow in a layer that is cooled from above and heated from below, is a paradigm for all of these examples. One reason for significantly fewer low-Pr RBC studies is that laboratory measurements have to be conducted in opaque liquid metals such as mercury or gallium at Pr = 0.021 (10)(11)(12). The lowest value for a Prandtl number that can be obtained in optically transparent fluids is Pr = 0.2 for binary gas mixtures (13), i.e., an order of magnitude larger than in liquid metals.…”

mentioning

confidence: 99%

Enhanced enstrophy generation for turbulent convection in low-Prandtl-number fluids

Schumacher

Götzfried

Scheel

2015

Proc. Natl. Acad. Sci. U.S.A.

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Turbulent convection is often present in liquids with a kinematic viscosity much smaller than the diffusivity of the temperature. Here we reveal why these convection flows obey a much stronger level of fluid turbulence than those in which kinematic viscosity and thermal diffusivity are the same; i.e., the Prandtl number Pr is unity. We compare turbulent convection in air at Pr = 0.7 and in liquid mercury at Pr = 0.021. In this comparison the Prandtl number at constant Grashof number Gr is varied, rather than at constant Rayleigh number Ra as usually done. Our simulations demonstrate that the turbulent Kolmogorov-like cascade is extended both at the large-and small-scale ends with decreasing Pr. The kinetic energy injection into the flow takes place over the whole cascade range. In contrast to convection in air, the kinetic energy injection rate is particularly enhanced for liquid mercury for all scales larger than the characteristic width of thermal plumes. As a consequence, mean values and fluctuations of the local strain rates are increased, which in turn results in significantly enhanced enstrophy production by vortex stretching. The normalized distributions of enstrophy production in the bulk and the ratio of the principal strain rates are found to agree for both Prs. Despite the different energy injection mechanisms, the principal strain rates also agree with those in homogeneous isotropic turbulence conducted at the same Reynolds numbers as for the convection flows. Our results have thus interesting implications for small-scale turbulence modeling of liquid metal convection in astrophysical and technological applications. T urbulent convection depends strongly on the material properties of the working fluid that are quantified by the Prandtl number, the ratio of kinematic viscosity of the fluid to thermal diffusivity of the temperature, Pr = ν=κ. Compared with the vast number of investigations at Pr ≥ 1 (1, 2), the very-low-Pr regime appears almost as a "terra incognita" despite many applications. Turbulent convection in the Sun is present at Prandtl numbers Pr < 10 −3 (3-5). The Prandtl number in the liquid metal core of the Earth is Pr ∼ 10 −2 (6). Convection in material processing (7), nuclear engineering (8), or liquid metal batteries (9) has Prandtl numbers between 3 × 10 −2 and 10 −3 . Rayleigh-Bénard convection (RBC), a fluid flow in a layer that is cooled from above and heated from below, is a paradigm for all of these examples. One reason for significantly fewer low-Pr RBC studies is that laboratory measurements have to be conducted in opaque liquid metals such as mercury or gallium at Pr = 0.021 (10-12). The lowest value for a Prandtl number that can be obtained in optically transparent fluids is Pr = 0.2 for binary gas mixtures (13), i.e., an order of magnitude larger than in liquid metals. Direct numerical simulations (DNS) are currently the only way to gain access to the full 3D convective turbulent fields in low-Pr convection (14-18). These simulations turn out to become very demanding if the...

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mentioning

confidence: 99%

Enhanced enstrophy generation for turbulent convection in low-Prandtl-number fluids

Schumacher

Götzfried

Scheel

2015

Proc. Natl. Acad. Sci. U.S.A.

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“…The lateral resolution x is given by the width of the ultrasound beam, which is a result of the transducer geometry, the frequency f 0 , and the speed of sound c in the fluid. The temporal resolution t of the velocity measurement is determined through the following: (Nauber et al, 2016;Büttner et al, 2013).…”

Section: Measurement Principlementioning

confidence: 99%

Measurement uncertainty analysis of field-programmable gate-array-based, real-time signal processing for ultrasound flow imaging

Nauber

Büttner

Czarske

2020

J. Sens. Sens. Syst.

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Abstract. Research in magnetohydrodynamics (MHD) aims to understand the complex interactions of electrically conductive fluids and magnetic fields. A promising approach for investigating complex instationary flow phenomena are lab-scale experiments with low-melting alloys. They require a noninvasive flow instrumentation for opaque liquids with a high spatiotemporal resolution, a low velocity uncertainty and a long measurement duration. Ultrasound Doppler velocimetry can achieve multiplane, multicomponential flow imaging with multiple linear ultrasound arrays. However the average raw data output amounts to 1.2 GBs−1 at a frame rate of 33 Hz in a typical configuration for 200 transducers. This usually prevents long-duration measurements when offline signal processing is used. In this paper, we propose an online signal-processing chain for pulsed-wave Doppler velocimetry that is tailored to the specific requirements of flow imaging for lab-scale experiments. The trade-off between measurement uncertainty and computational complexity is evaluated for different algorithmic variants in relation to the Cramér–Rao bound. By utilizing selected approximations and parameter choices, a prepossessing could be efficiently implemented on a field-programmable gate array (FPGA), enabling a typical reduction of the data bandwidth of 6.5:1 and online flow visualization. We validated the performance of the signal processing on a test rig, yielding a velocity standard deviation that is a factor of 3 above the theoretical limit despite a low computational complexity. Potential applications for this signal processing include multihour flow measurements during a crystal-growth process and closed-loop velocity feedback for model experiments.

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“…A promising approach is to affect the flow of electrically conductive fluids by using spatiotemporally varying magnetic fields, thus applying magnetohydrodynamics (MHD). The influence of the flow on material and heat transfer is investigated by means of numerical simulation and laboratory-scale model-experiments [1][2][3]. In low temperature models the phased array ultrasound Doppler velocimeter (PAUDV) is capable of providing planar velocity measurements with a spatial resolution of under 1 mm [4].…”

Section: Introductionmentioning

confidence: 99%

C2.1 - Ultrasound imaging through multimode waveguides using time reversal virtual array method

Kalibatas¹,

Nauber²,

Dawidowski³

et al. 2017

Proceedings Sensor 2017

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Dual-plane ultrasound flow measurements in liquid metals

Cited by 26 publications

References 26 publications

Enhanced enstrophy generation for turbulent convection in low-Prandtl-number fluids

Enhanced enstrophy generation for turbulent convection in low-Prandtl-number fluids

Measurement uncertainty analysis of field-programmable gate-array-based, real-time signal processing for ultrasound flow imaging

C2.1 - Ultrasound imaging through multimode waveguides using time reversal virtual array method

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