5 results
Averaging theory for heat transfer in circular hydraulic jumps with a separation bubble
- R. Solana Gómez, T. Bohr, S. Nielsen, W. Rohlfs, R. Kneer, H. Askarizadeh
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- Journal:
- Journal of Fluid Mechanics / Volume 979 / 25 January 2024
- Published online by Cambridge University Press:
- 18 January 2024, A41
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Analytical investigations of heat transfer during the vertical impingement of an unsubmerged axisymmetric liquid jet on a horizontal plate have been limited to the regions ahead of the jump. This limitation is due to the complex flow physics in the jump region arising from sudden changes in the flow field. This is addressed in here by extending the averaging theory (AT) introduced by Bohr et al. (Phys. Rev. Lett., vol. 79, issue 6, 1997, pp. 1038–1041) which was further developed by Watanabe et al. (J. Fluid Mech., vol. 480, 2003, pp. 233–265), to describe the heat transfer problem in circular hydraulic jumps including separation. The applicability of the resulting theory to determine the temperature field in the jump region is evaluated using the data available in the literature and also by means of fully resolved numerical solutions. Good agreement is observed for moderate Prandtl numbers. However, for sufficiently high Prandtl numbers, deviations become notable. The reasons for the deviations according to their relevance are (i) monotonically decreasing temperature profile inherent to the AT, whereas the fully resolved numerical solutions exhibit a local maximum in the temperature profile away from the plate; and (ii) inapplicability of the concept of dividing the flow field into a region affected and a region unaffected by heat transfer according to the thermal boundary layer thickness. This concept leads to the overestimation of the temperature close to the wall and to the existence of a threshold Prandtl number, for which the thermal boundary layer thickness does not meet the free surface anymore. Around this threshold Prandtl number, the temperature field shows a discontinuous behaviour.
Three-dimensional flow structures in laminar falling liquid films
- Georg F. Dietze, W. Rohlfs, K. Nährich, R. Kneer, B. Scheid
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- Journal:
- Journal of Fluid Mechanics / Volume 743 / 25 March 2014
- Published online by Cambridge University Press:
- 04 March 2014, pp. 75-123
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Full numerical simulations of the Navier–Stokes equations for four cases of vertically falling liquid films with three-dimensional surface waves have been performed. Flow conditions are based on several previous experimental studies where the streamwise and spanwise wavelengths were imposed, which we exploit by simulating periodic wave segments. The considered flows are laminar but approach conditions at which intermittent wave-induced turbulence has been observed elsewhere. Working liquids range from water to silicone oil and cover a large interval of the Kapitza number ($\textit {Ka}=18\mbox{--}3923$), which relates capillary to viscous forces. Simulations were performed on a supercomputer, using a finite-volume code and the volume of fluid and continuum surface force methods to account for the multiphase nature of the flow. Our results show that surface waves, consisting of large horseshoe-shaped wave humps concentrating most of the liquid and preceded by capillary ripples on a thin residual film, segregate the flow field into two regions: an inertia-dominated one in the large humps, where the local Reynolds number is up to five times larger than its mean value, and a visco-capillary region, where capillary and/or viscous forces dominate. In the inertial region, an intricate structure of different-scale vortices arises, which is more complicated than film thickness variations there suggest. Conversely, the flow in the visco-capillary region of large-$\textit {Ka} $ fluids is entirely governed by the local free-surface curvature through the action of capillary forces, which impose the pressure distribution in the liquid film. This results in flow separation zones underneath the capillary troughs and a spanwise cellular flow pattern in the region of capillary wave interference. In some cases, capillary waves bridge the large horseshoe humps in the spanwise direction, coupling the two aforementioned regions and leading the flow to oscillate between three- and two-dimensional wave patterns. This persists over long times, as we show by simulations with the low-dimensional model of Scheid et al. (J. Fluid Mech., vol. 562, 2006, pp. 183–222) after satisfactory comparison with our direct simulations at short times. The governing mechanism is connected to the bridging capillary waves, which drain liquid from the horseshoe humps, decreasing their amplitude and wave speed and causing them to retract in the streamwise direction. Overall, it is observed that spanwise flow structures (not accounted for in two-dimensional investigations) are particularly complex due to the absence of gravity in this direction.
Experimental study of flow separation in laminar falling liquid films
- GEORG F. DIETZE, F. AL-SIBAI, R. KNEER
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- Journal:
- Journal of Fluid Mechanics / Volume 637 / 25 October 2009
- Published online by Cambridge University Press:
- 18 September 2009, pp. 73-104
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In a previous publication, Dietze, Leefken & Kneer (J. Fluid Mech., vol. 595, 2008, p. 435) showed that flow separation takes place in the capillary wave region of falling liquid films. That investigation focused on the mechanistic explanation of the phenomenon mainly on the basis of numerical data. The present publication for the first time provides clear experimental evidence of the phenomenon obtained by way of highly resolving velocity measurements in a specifically designed optical test set-up. Characteristically, the refractive index of the working fluid was matched to that of the glass test section to provide optimal access to the cross-section of the film for the employed optical velocimetry techniques, namely, laser doppler velocimetry (LDV) and particle image velocimetry (PIV). Using LDV, time traces of the streamwise velocity component were recorded in high spatial (0.025 mm) and temporal resolutions (0.4 ms) showing negative velocity values in the capillary wave region. In addition, simultaneous film thickness measurements were performed using a Confocal Chromatic Imaging (CCI) technique enabling the correlation of velocity data and wave dynamics. Further, using PIV the spatio-temporal evolution of the velocity field in the cross-section of the film was measured with high spatial (0.02 mm) and temporal (0.5 ms) resolutions yielding insight into the topology of the flow. Most importantly these results clearly show the existence of a separation eddy in the capillary wave region. Due to the high temporal resolution of the PIV measurements, enabled by the use of a high-speed camera with a repetition rate of up to 4500 Hz, the effect of wave dynamics on the velocity field in all regions of the wavy film was elucidated. All experiments were performed using a dimethylsulfoxide (DMSO)–water solution and focused on laminar vertically falling liquid films with externally excited monochromatic surface waves. Systematic variations of both the Reynolds number (Re = 8.6–15.0) and the excitation frequency (f = 16–24 Hz) were performed. Results show that an increase in the wavelength of large wave humps, produced either by an increase in the Reynolds number or a decrease in the excitation frequency, leads to an increase in the size of the capillary separation eddy (CSE). Thereby, the CSE is shown to grow larger than the local film thickness, assuming an open shape with streamlines ending at the free surface.
Investigation of the backflow phenomenon in falling liquid films
- GEORG F. DIETZE, A. LEEFKEN, R. KNEER
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- Journal:
- Journal of Fluid Mechanics / Volume 595 / 25 January 2008
- Published online by Cambridge University Press:
- 08 January 2008, pp. 435-459
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The phenomenon of backflow in the capillary wave region of laminar falling liquid films is studied in detail. For the first time, the mechanism leading to the origination of the phenomenon is identified and explained. It is shown that backflow forms as the result of a separation eddy developing at the bounding wall similar to the case of classical flow separation. Results show that the adverse pressure distribution causing the separation of the flow in the capillary wave region is induced by the strong third-order deformation (i.e. change in curvature) of the liquid–gas free surface there. This deformation acts on the interfacial pressure jump, and thereby the wall pressure distribution, as a result of surface tension forces. It is shown that only the capillary waves, owing to their short wavelength and large curvature, impose a pressure distribution satisfying the conditions for flow separation. The effect of this capillary separation eddy on momentum and heat transfer is investigated from the perspective of modelling approaches for falling liquid films. The study is centred on a single case of inclined liquid film flow in the visco-capillary regime with surface waves externally excited at a single forcing frequency. Investigations are based on temporally and spatially highly resolved numerical data obtained by solving the Navier–Stokes equations for both phases. Computation of phase distribution is performed with the volume of fluid method and the effect of surface tension is modelled using the continuum surface force approach. Numerical data are compared with experimental data measured in the developed region of the flow. Laser-Doppler velocimetry is used to measure the temporal distribution of the local streamwise velocity component, and confocal chromatic imaging is employed to measure the temporal distribution of film thickness. Excellent agreement is obtained with respect to film thickness and reasonable agreement with respect to velocity.
Identification of a Complete Sample of Northern Rosat All-Sky Survey X-Ray Sources
- J. Krautter, I. Thiering, F.-J Zickgraf, I. Appenzeller, R. Kneer, W. Voges, A. Serrano, R. Mujica
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- Journal:
- Symposium - International Astronomical Union / Volume 179 / 1998
- Published online by Cambridge University Press:
- 25 May 2016, p. 449
- Print publication:
- 1998
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We present results of the optical identification of a spatially complete, flux limited sample of about 700 ROSAT All-Sky X-ray sources contained in 6 study areas north of δ = −9° with |bII|> 20° (including one region near the North Galactic pole (NGP), another one near the North Ecliptic pole (NEP)). Countrate limits are 0.01 cts s–1 near the NEP and 0.03 cts s–1 for the other areas. The optical observations were performed at the 2.15-m telescope of the Guillermo Haro Observatory, Mexico, using the Landessterwarte Faint Object Spectrograph Camera which allows to carry out direct CCD imaging and multi-object spectroscopy. The limiting magnitude is about 19m for spectroscopy and about 23m for B and R direct imaging. Our analysis shows a dependency of the ratio of ‘extragalactic’ (e.g., AGN, cluster of galaxies) to ‘stellar’ (e.g., coronal emitters, active binaries) counterparts on NH. In the area near the NGP (low NH) ‘extragalactic’ counterparts dominate, while in the area with the highest NH ‘stellar’ counterparts dominate.