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![Terminal velocities and the corresponding Reynolds numbers for water drops of various diameters in stagnant air; data taken from Gunn and Kinzer [11].](profile/Weibo-Ren-3/publication/344202248/figure/fig1/AS:934511999209474@1599816431908/Terminal-velocities-and-the-corresponding-Reynolds-numbers-for-water-drops-of-various.jpg)
Terminal velocities and the corresponding Reynolds numbers for water drops of various diameters in stagnant air; data taken from Gunn and Kinzer [11].
Source publication
Details on the fall speeds of raindrops are essential in both applications and natural events, such as rain-rate retrieval and soil erosion. Here, we examine the influence of turbulence on the terminal velocity of two water drops of different sizes. For the first time, computations of droplets in turbulent surroundings are conducted with a direct n...
Contexts in source publication
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... the divergence in C d intensifies progressively with increasing Reynolds number (larger drops). Terminal velocities, as well as the corresponding Reynolds numbers, for water drops of various sizes are displayed in Figure 2, according to the measurements of Gunn and Kinzer [11]. Figure 1. ...
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... deformation of the water drop at the instants A, B, and C displays a good match with the photos for the falling rain drops of 2.7 mm and 3.45 mm taken by Pruppacher and Beard [34]. In addition, we compared our results regarding the oscillation frequency, the axis ratio amplitude and the mean axis ratio with the measurements and theoretical models from previous studies (Figures 2-4 from the review of Szakall et al. [30]) and found a quite good agreement for the simulated 3 mm and 2 mm water drops that fall in still air (see Appendix B). Table 4 summarises the time-averaged drop axis ratio, horizontal axis length 2 ¯ a, oscillation frequency and the temporal axis ratio amplitude for all conducted cases. ...
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... validate the velocity field in the near wake region, we compared the stream-wise velocity U x /U on the wake centre-line with previous simulation results (Re = 1000) from Tomboulides and Orszag [46], as well as with the experimental data (Re = 960) by Wu and Faeth [47]. Figure 12 shows a good agreement between the results from FS3D and those from the previous studies. The length of the wake recirculation bubble ¯ L/D of the 2 mm water drop is 2.5D, which is about 47% longer than that of the sphere. ...
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... length of the wake recirculation bubble ¯ L/D of the 2 mm water drop is 2.5D, which is about 47% longer than that of the sphere. This matches well with the displacement of U x /U in the downstream direction, as shown in Figure 12. In the case of a falling water drop, the drop surface deformation and drop oscillation will have some influence on the length and width of the wake recirculation region. ...
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... implies that there is still room for a further reduction of ¯ L/D in the case of a stronger turbulent air flow, where C d continues to increase until the boundary layer and the shear layer become fully turbulent and drag crisis sets in. Figure 20a depicts the time-averaged streamlines for the 3 mm and 2 mm drop falling in stagnant air. The symmetrical wake recirculation area in both cases indicates good statistical convergence. ...
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... the 3 mm water drop, the opposing circulation rarely appears and disappears shortly after as a result of the mixing effect of the near-wake flow. Figure 20b,c displays an example of the streamlines for 3 mm and 2 mm water drops at different time steps, respectively. ...
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... we selected the position of the drop at a stream-wise direction of 6D, with consideration of the decay in the turbulent air flow from the inlet. Figure A2 shows a comparison of the simulated axis ratios, axis ratio amplitudes and drop oscillation frequencies for the 3 mm and 2 mm water drops in still air with results from previous studies. Values from the simulations were averaged over at least 0.5 s after the fall velocity of the water drop stabilised. ...
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... (b) (c) Figure A2. Comparison of the axis ratios, the axis ratio amplitudes and the oscillation frequencies of the simulated 3 mm and 2 mm water drops in stagnant air: (a) Axis ratio. ...
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... the divergence in C d intensifies progressively with increasing Reynolds number (larger drops). Terminal velocities, as well as the corresponding Reynolds numbers, for water drops of various sizes are displayed in Figure 2, according to the measurements of Gunn and Kinzer [11]. Figure 1. ...
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... deformation of the water drop at the instants A, B, and C displays a good match with the photos for the falling rain drops of 2.7 mm and 3.45 mm taken by Pruppacher and Beard [34]. In addition, we compared our results regarding the oscillation frequency, the axis ratio amplitude and the mean axis ratio with the measurements and theoretical models from previous studies (Figures 2-4 from the review of Szakall et al. [30]) and found a quite good agreement for the simulated 3 mm and 2 mm water drops that fall in still air (see Appendix B). Table 4 summarises the time-averaged drop axis ratio, horizontal axis length 2 ¯ a, oscillation frequency and the temporal axis ratio amplitude for all conducted cases. ...
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... validate the velocity field in the near wake region, we compared the stream-wise velocity U x /U on the wake centre-line with previous simulation results (Re = 1000) from Tomboulides and Orszag [46], as well as with the experimental data (Re = 960) by Wu and Faeth [47]. Figure 12 shows a good agreement between the results from FS3D and those from the previous studies. The length of the wake recirculation bubble ¯ L/D of the 2 mm water drop is 2.5D, which is about 47% longer than that of the sphere. ...
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... length of the wake recirculation bubble ¯ L/D of the 2 mm water drop is 2.5D, which is about 47% longer than that of the sphere. This matches well with the displacement of U x /U in the downstream direction, as shown in Figure 12. In the case of a falling water drop, the drop surface deformation and drop oscillation will have some influence on the length and width of the wake recirculation region. ...
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... implies that there is still room for a further reduction of ¯ L/D in the case of a stronger turbulent air flow, where C d continues to increase until the boundary layer and the shear layer become fully turbulent and drag crisis sets in. Figure 20a depicts the time-averaged streamlines for the 3 mm and 2 mm drop falling in stagnant air. The symmetrical wake recirculation area in both cases indicates good statistical convergence. ...
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... the 3 mm water drop, the opposing circulation rarely appears and disappears shortly after as a result of the mixing effect of the near-wake flow. Figure 20b,c displays an example of the streamlines for 3 mm and 2 mm water drops at different time steps, respectively. ...
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... we selected the position of the drop at a stream-wise direction of 6D, with consideration of the decay in the turbulent air flow from the inlet. Figure A2 shows a comparison of the simulated axis ratios, axis ratio amplitudes and drop oscillation frequencies for the 3 mm and 2 mm water drops in still air with results from previous studies. Values from the simulations were averaged over at least 0.5 s after the fall velocity of the water drop stabilised. ...
Citations
... A water droplet reaches its terminal velocity in a fairly short time interval of 2-5 s while moving in the shaft space. The terminal velocity of a water droplet depends on its diameter [12,13]. Let us consider the two most well-known empirical formulas that describe terminal velocity as a function of the droplet diameter: ...
... Thus, droplet moisture can move both down and up the shaft, depending on the ratio of the weight of each droplet and the aerodynamic drag acting on them from the upward air flow. The maximum water drop diameter is ~6 mm, which is consistent with the meteorological studies [11] and numerical experiments [12]. Drops larger than 6 mm will break up under the action of an air flow. ...
... A water droplet reaches its terminal velocity in a fairly short time interval of 2-5 s while moving in the shaft space. The terminal velocity of a water droplet depends on its diameter [12,13]. Let us consider the two most well-known empirical formulas that describe terminal velocity as a function of the droplet diameter: Gunn-Kinzer [14]: ...
A theoretical study of the formation of water build-up, or water blanketing, and its influence on the ventilation of mine upcast shafts was carried out. Two scenarios for droplet moisture accumulation in the shaft were considered: condensation from saturated air rising up the shaft and groundwater inflows through the leaky shaft lining. Analytical dependencies of the pressure drop due to the influence of water build-up versus the outgoing air flow velocity and the height of the groundwater source were obtained, taking into account the fractional composition of the droplet moisture. Practical arrangements are proposed to reduce the influence of the effect of water build-up in upcast shafts in the case of groundwater inflows through the leaky shaft lining.
... Reduced particle fall speeds in turbulent flows have been reported in various studies (Murray 1970;Nielsen 1993;Fung 1993;Stout et al. 1995;Yang and Shy 2003;Kawanisi and Shiozaki 2008;Good et al. 2014;Rosa and Pozorski 2017;Ren et al. 2020). Within the context of rainfall, several studies reported subterminal fall of raindrops (Testik et al. 2006;Montero-Martínez et al. 2009;Thurai et al. 2013;Montero-Martínez and García-García 2016;Bringi et al. 2018;Bolek and Testik 2022). ...
... Therefore, these fall speed deviations, indeed, indicate significant presence of subterminal raindrops and their dominance in the averaging, which is further discussed later in this section. In a recent study by using direct numerical simulations (DNS), Ren et al. (2020) showed that water drops of 2 and 3 mm in diameter experienced turbulence-induced fall speed reductions. Their DNS results indicated that wake Table 4. lengths of the drops were reduced in a turbulent ambient and that wake length reduction is significantly correlated to an increase in the drag coefficient of falling water drops, hence, a reduction in fall speeds. ...
Wind and turbulence effects on raindrop fall speeds were elucidated using field observations over a two-year time-period. Motivations for this study include the recent observations of raindrop fall speed deviations from the terminal fall speed predictions ( V t ) based upon laboratory studies and the utilizations of these predictions in various important meteorological and hydrological applications. Fall speed ( V f ) and other characteristics of raindrops were observed using a High-speed Optical Disdrometer (HOD), and various rainfall and wind characteristics were observed using a 3D ultrasonic anemometer, a laser-type disdrometer, and raingauges. A total of 26951 raindrops were observed during 17 different rainfall events; and of these observed raindrops, 18.5% had a sub-terminal fall speed (i.e. 0.85 V t ≥ V f ) and 9.5% had a super-terminal fall speed (i.e. 1.15 V t ≤ V f ). Our observations showed that distributions of sub- and super-terminal raindrops in the raindrop size spectrum are distinct, and different physical processes are responsible for the occurrence of each. Vertical wind speed, wind shear, and turbulence were identified as the important factors, the latter two being the dominant ones, for the observed fall speed deviations. Turbulence and wind shear had competing effects on raindrop fall. Raindrops of different sizes showed different responses to turbulence, indicating multi-scale interactions between raindrop fall and turbulence. With increasing turbulence levels, while the raindrops in the smaller end of the size spectrum showed fall speed enhancements, those in the larger end of the size spectrum showed fall speed reductions. The effect of wind shear was to enhance the raindrop fall speed towards a super-terminal fall.
... A theoretical study of the flow fields around falling water drops with diameters larger than 1 mm was only recently performed by Ren et al. [34]. They performed calculations to determine the impact of turbulence on the terminal velocity of 2 and 3 mm water drops. ...
... Ren et al. [34] showed that their results correlate well with experimental data on the drop terminal velocities and shape, as described by Pruppacher and Beard [38] and Beard [39], as well as data on drop oscillations, as described by the field observation by Tokay and Beard [40] and Szakall et al. [21]. These comparisons are shown in Figure 5. Ren et al. [34] showed that their results correlate well with experimental data drop terminal velocities and shape, as described by Pruppacher and Beard [38] and [39], as well as data on drop oscillations, as described by the field observation by and Beard [40] and Szakall et al. [21]. ...
... Ren et al. [34] showed that their results correlate well with experimental data on the drop terminal velocities and shape, as described by Pruppacher and Beard [38] and Beard [39], as well as data on drop oscillations, as described by the field observation by Tokay and Beard [40] and Szakall et al. [21]. These comparisons are shown in Figure 5. Ren et al. [34] showed that their results correlate well with experimental data drop terminal velocities and shape, as described by Pruppacher and Beard [38] and [39], as well as data on drop oscillations, as described by the field observation by and Beard [40] and Szakall et al. [21]. These comparisons are shown in Figure 5. Ren et al. [34] showed that their results correlate well with experimental data on drop terminal velocities and shape, as described by Pruppacher and Beard [38] and B [39], as well as data on drop oscillations, as described by the field observation by To and Beard [40] and Szakall et al. [21]. ...
The theoretical studies on the flow fields around falling cloud and precipitation particles are briefly reviewed. The hydrodynamics of these particles, collectively called hydrometeors, are of central importance to cloud development and dissipation, which impact both the short-term weather and long-term climate processes. This review focuses on the solutions of the appropriate Navier–Stokes equations around the falling hydrometeor, particularly those obtained by numerical methods. The hydrometeors reviewed here include cloud drops, raindrops, cloud ice crystals, snow aggregates, conical graupel, and smooth and lobed hailstones. The review is made largely in chronological order so that readers can obtain a sense of how the research in this field has progressed over time. Although this review focuses on theoretical studies, brief summaries of laboratory experiments and field observations on this subject are also provided so as to substantiate the calculation results. An outlook is given at the end to describe future works necessary to improve our knowledge in this area.
... After the positions of each wheel and each spray droplet are determined, the latter have to be rendered as spheres [29]. With a radius of around 200 µm, the droplets are just large enough to influence visible light geometrically, opposed to Mie scattering that occurs when the droplets are smaller, like in fog [30]. ...
... To account for minor disturbances on the surface of a moving water droplet, we approximated the very small waves that would form on the surface [29]. Instead of directly modifying the surface, we apply a pseudo-random three dimensional vector to all vectors that are read from the vector textures. ...
... Especially in terms of fluid dynamics the code is well validated. More recent studies extended the applicability to free falling droplets in turbulent surroundings [9], droplet impact onto a thin film [10] or structured surfaces [11], robust methods for phase change processes [12] as well as droplet interaction with multiple species [13] with the latter two aspects being also interesting to grouping effects in droplet streams. In order to cope with the demanding requirements of DNS FS3D is fully parallelized using MPI and OpenMP. ...
The tendency of convening and coalescing of initially distant droplets, called droplet grouping, can influence the final droplet size distribution, evaporation rates or final settling points. To better understand the factors which govern droplet grouping mechanisms, reliable direct numerical simulations are beneficial. Previous numerical studies have shown that the approaching and collision process of droplets in a stream is extremely sensitive to the applied boundary conditions. Therefore, simulations are performed regarding the influence of domain size and boundary conditions on the grouping behavior. Improved boundary conditions, so called artificial boundary conditions, are derived to allow for suitable velocity approximations in the far field. A comparison to the existing boundary conditions regarding velocity profiles and grouping behavior for different domain widths and Reynolds numbers is investigated. The proposed artificial boundary condition takes into account the decay of velocities near the side boundaries more accurately than the already implemented boundary conditions in combination with periodicity in the direction of droplet motion. Evaluating droplet spacing over time reveals that the domain width using artificial boundaries can be reduced without influencing the grouping behavior.
... The Special Issue "Modelling of Reactive and Non-Reactive Multiphase Flows" collects 11 papers covering a broad range of topics dealing with applications of non-reactive [1][2][3][4][5][6] and reactive [7][8][9][10][11] multiphase flows in natural environment as well as technical applications. The contributions address important numerical and modelling issues, which not only cover fundamental physics but also address the aspect of application. ...
... The characterization of the fall speeds of raindrops is the main topic in Ren et al. [1]. For the first time, computations of droplets in turbulent surroundings are conducted with a DNS code based on a volume of the fluid method, and results for the drop surface deformation and its internal circulation are reported. ...
Multiphase flows are found in several industrial processes encompassing power generation, pharmaceutical and chemical industry and agriculture [...]
div class="section abstract"> Modern automobiles are dependent on complex networks of electronic sensors and controls for efficient and safe operation. These electronic modules are tested for stringent environmental load conditions where product validation consists of one or a combination of loads such as Vibration, Mechanical Shock, Temperature, Water, Humidity, Dust, Chemicals, and Radiation. Exposure of electronics to water leads to many harmful effects resulting in the failure of electronic systems. Previously published technical paper <sup>[</sup> <sup>1</sup> <sup>]</sup> SAE 2023-01-0157 described a methodology to estimate risk in a humid environment, where water is dispersed in air as a gas phase. The present paper extends the scope of virtual validation using Computational Fluid Dynamics (CFD) simulation tools to an environment with water in the liquid phase.
In this paper, a non-sealed automotive electronic module subjected to a water drip test is evaluated using the CFD model. A transient 3D multiphase simulation is performed using the Volume of Fluid method (VOF) to simulate water droplets falling on a module mounted as per the test set-up described in ISO 20653. The study focuses on issues related to the simulation of the IPx2 test set-up at a ‘product level’. Computational challenges of performing such assessment are described with emphasis on rapid evaluation of design concepts along with necessary simplification in model and test set-up. ISO standard does not describe the pass/fail criterion objectively hence practical considerations of evaluation criterion are briefly outlined.
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A 3D numerical model was built to serve as a virtual microphysics laboratory (VML) to investigate rainfall microphysical processes. One key goal for the VML is to elucidate the physical basis of warm precipitation processes toward improving existing parameterizations beyond the constraints of past physical experiments. This manuscript presents results from VML simulations of classical tower experiments of raindrop collisional collection and breakup. The simulations capture large raindrop oscillations in shape and velocity in both horizontal and vertical planes and reveal that drop instability increases with diameter due to the weakening of the surface tension compared with the body force. A detailed evaluation against reference experimental datasets of binary collisions over a wide range of drop sizes shows that the VML reproduces collision outcomes well including coalescence, and disk, sheet, and filament breakups. Furthermore, the VML simulations captured spontaneous breakup, and secondary coalescence and breakup. The breakup type, fragment number, and size distribution are analyzed in the context of collision kinetic energy, diameter ratio, and relative position, with a view to capture the dynamic evolution of the vertical microstructure of rainfall in models and to interpret remote sensing measurements.
Significance Statement
Presently, uncertainty in precipitation estimation and prediction remains one of the grand challenges in water cycle studies. This work presents a detailed 3D simulator to characterize the evolution of drop size distributions (DSDs), without the space and functional constraints of laboratory experiments. The virtual microphysics laboratory (VML) is applied to replicate classical tower experiments from which parameterizations of precipitation processes used presently in weather and climate models and remote sensing algorithms were derived. The results presented demonstrate that the VML is a robust tool to capture DSD dynamics at the scale of individual raindrops (precipitation microphysics). VML will be used to characterize DSD dynamics across scales for environmental conditions and weather regimes for which no measurements are available.
Droplet grouping is important in technical applications and in nature where more than one droplet is seen. Despite its relevance for such problems, the fundamentals of the grouping processes are not yet fully understood. Initial conditions that expedite or impede the formation of droplet groups have been studied, but a thorough investigation of the temporal and spatial evolution of the forces at play has not been conducted. In this work, the grouping process in monodisperse droplet streams is examined in detail by Direct Numerical Simulation (DNS), for the first time, using the multiphase code Free Surface 3D. The code is based on the Volume-of-Fluid (VOF) method and uses the piecewise linear interface calculation (PLIC) method to reconstruct the interface. A method is established to quantify the development and evolving differences of pressure and shear drag forces on each droplet in the stream using the available DNS data. The results show a linear increase in the difference between the forces, where the drag force on the leading droplet is always larger than that on the trailing droplet. A comprehensive parametric study reveals that large initial inter-droplet separation and small group distances increase grouping time due to reduced difference in the drag coefficients. Higher initial Reynolds numbers and larger irregularities in the geometrical arrangement promote droplet grouping. The flow field shows stable wake structures at initial Reynolds numbers of 300 and the onset of vortex shedding at Reynolds numbers of 500 affecting the next pair of droplets, even for larger separation distances.
