scholarly journals Graupel and Hail Terminal Velocities: Does a “Supercritical” Reynolds Number Apply?

2014 ◽  
Vol 71 (9) ◽  
pp. 3392-3403 ◽  
Author(s):  
Andrew Heymsfield ◽  
Robert Wright
Keyword(s):  
Reynolds Number ◽  
Drag Coefficient ◽  
Critical Reynolds Number ◽  
Terminal Velocity ◽  
Ice Crystals ◽  
Particle Sizes ◽  
Model Simulations ◽  
Ice Particles ◽  
Wide Range ◽  
Large Spherical

Abstract This study characterizes the terminal velocities of heavily rimed ice crystals and aggregates, graupel, and hail using a combination of recent drag coefficient and particle bulk density observations. Based on a nondimensional Reynolds number (Re)–Best number (X) approach that applies to atmospheric temperatures and pressures where these particles develop and fall, the authors develop a relationship that spans a wide range of particle sizes. The Re–X relationship can be used to derive the terminal velocities of rimed particles for many applications. Earlier observations suggest that a “supercritical” Reynolds number is reached where the drag coefficient for large spherical ice—hail—drops precipitously and the terminal velocities increase rapidly. The authors draw on observations and model simulations for slightly roughened large ice particles that suggest that the critical Reynolds number is dampened and that the rapid increase in the terminal velocity of smooth spherical ice particles rarely occurs for natural hailstones.

Golf Ball Aerodynamics

1976 ◽  
Vol 27 (2) ◽  
pp. 112-122 ◽  
Author(s):  
P W Bearman ◽  
J K Harvey
Keyword(s):  
Reynolds Number ◽  
Wind Tunnel ◽  
Drag Coefficient ◽  
Critical Reynolds Number ◽  
Lift Coefficient ◽  
Golf Course ◽  
Aerodynamic Forces ◽  
Wide Range ◽  
Tunnel Technique ◽  
Smooth Sphere

SummaryA wind tunnel technique has been developed to measure the aerodynamic forces acting on golf balls over a wide range of Reynolds number and spin rate. Balls with round dimples and hexagonal dimples have been investigated. The dimples are found to induce a critical Reynolds number behaviour at a lower value of Reynolds number than that experienced by a smooth sphere and beyond this point, unlike the behaviour of a sand-roughened sphere, there is little dependence of the forces on further increases in Reynolds number. A hexagonally-dimpled ball has a higher lift coefficient and a slightly lower drag coefficient than a conventional round-dimpled ball. Trajectories are calculated using the aerodynamic data and the ranges are compared with data obtained from a driving machine on a golf course.

An Experimental Investigation for Bubble Rising in Non-Newtonian Fluids and Empirical Correlation of Drag Coefficient

2010 ◽  
Vol 132 (2) ◽  
Author(s):  
Fan Wenyuan ◽  
Ma Youguang ◽  
Jiang Shaokun ◽  
Yang Ke ◽  
Li Huaizhi
Keyword(s):  
Reynolds Number ◽  
Aqueous Solutions ◽  
Drag Coefficient ◽  
Bubble Diameter ◽  
Video Camera ◽  
Solution Concentration ◽  
Terminal Velocity ◽  
Newtonian Fluids ◽  
Rising Bubble ◽  
Moderate Reynolds Number

The velocity, shape, and trajectory of the rising bubble in polyacrylamide (PAM) and carboxymethylcellulose (CMC) aqueous solutions were experimentally investigated using a set of homemade velocimeters and a video camera. The effects of gas the flowrate and solution concentration on the bubble terminal velocity were examined respectively. Results show that the terminal velocity of the bubble increases with the increase in the gas flowrate and the decrease in the solution concentration. The shape of the bubble is gradually flattened horizontally to an ellipsoid with the increase in the Reynolds number (Re), Eötvös number (Eo), and Morton number (Mo). With the increase in the Re and Eo, the rising bubble in PAM aqueous solutions begin to oscillate, but there is no oscillation phenomena for CMC aqueous solutions. By dimensional analysis, the drag coefficient of a single bubble in non-Newtonian fluids in a moderate Reynolds number was correlated as a function of Re, Eo, and Archimedes number (Ar) based on the equivalent bubble diameter. The predicted results by the present correlation agree well with the experimental data.

Explicit relationships for the terminal velocity of spherical particles

1990 ◽  
Vol 55 (2) ◽  
pp. 403-408 ◽  
Author(s):  
Miloslav Hartman ◽  
Václav Veselý ◽  
Karel Svoboda ◽  
Vladimír Havlín
Keyword(s):  
Drag Coefficient ◽  
Free Fall ◽  
Terminal Velocity ◽  
Spherical Particles ◽  
Wide Range ◽  
Archimedes Number

The Turton-Levenspiel correlation for the drag coefficient of a sphere is employed to compare recently proposed explicit equations to predict the free-fall conditions. Predictions of four different expressions are explored over a wide range of Archimedes number.

scholarly journals Ice formation and development in aged, wintertime cumulus over the UK: observations and modelling

2012 ◽  
Vol 12 (11) ◽  
pp. 4963-4985 ◽  
Author(s):  
I. Crawford ◽  
K. N. Bower ◽  
T. W. Choularton ◽  
C. Dearden ◽  
J. Crosier ◽  
...  
Keyword(s):  
Particle Production ◽  
Ice Crystals ◽  
Dust Particles ◽  
Ice Formation ◽  
Crystal Formation ◽  
Surface Acting ◽  
Model Simulations ◽  
Ice Nuclei ◽  
Ice Particles ◽  
High Concentrations

Abstract. In situ high resolution aircraft measurements of cloud microphysical properties were made in coordination with ground based remote sensing observations of a line of small cumulus clouds, using Radar and Lidar, as part of the Aerosol Properties, PRocesses And InfluenceS on the Earth's climate (APPRAISE) project. A narrow but extensive line (~100 km long) of shallow convective clouds over the southern UK was studied. Cloud top temperatures were observed to be higher than −8 °C, but the clouds were seen to consist of supercooled droplets and varying concentrations of ice particles. No ice particles were observed to be falling into the cloud tops from above. Current parameterisations of ice nuclei (IN) numbers predict too few particles will be active as ice nuclei to account for ice particle concentrations at the observed, near cloud top, temperatures (−7.5 °C). The role of mineral dust particles, consistent with concentrations observed near the surface, acting as high temperature IN is considered important in this case. It was found that very high concentrations of ice particles (up to 100 L−1) could be produced by secondary ice particle production providing the observed small amount of primary ice (about 0.01 L−1) was present to initiate it. This emphasises the need to understand primary ice formation in slightly supercooled clouds. It is shown using simple calculations that the Hallett-Mossop process (HM) is the likely source of the secondary ice. Model simulations of the case study were performed with the Aerosol Cloud and Precipitation Interactions Model (ACPIM). These parcel model investigations confirmed the HM process to be a very important mechanism for producing the observed high ice concentrations. A key step in generating the high concentrations was the process of collision and coalescence of rain drops, which once formed fell rapidly through the cloud, collecting ice particles which caused them to freeze and form instant large riming particles. The broadening of the droplet size-distribution by collision-coalescence was, therefore, a vital step in this process as this was required to generate the large number of ice crystals observed in the time available. Simulations were also performed with the WRF (Weather, Research and Forecasting) model. The results showed that while HM does act to increase the mass and number concentration of ice particles in these model simulations it was not found to be critical for the formation of precipitation. However, the WRF simulations produced a cloud top that was too cold and this, combined with the assumption of continual replenishing of ice nuclei removed by ice crystal formation, resulted in too many ice crystals forming by primary nucleation compared to the observations and parcel modelling.

scholarly journals A Comprehensive Observational Study of Graupel and Hail Terminal Velocity, Mass Flux, and Kinetic Energy

2018 ◽  
Vol 75 (11) ◽  
pp. 3861-3885 ◽  
Author(s):  
Andrew Heymsfield ◽  
Miklós Szakáll ◽  
Alexander Jost ◽  
Ian Giammanco ◽  
Robert Wright
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
Mass Flux ◽  
Three Dimensional ◽  
Acrylonitrile Butadiene Styrene ◽  
Terminal Velocity ◽  
Three Dimensions ◽  
Cross Sectional ◽  
Wide Range ◽  
3D Volume

Abstract This study uses novel approaches to estimate the fall characteristics of hail, covering a size range from about 0.5 to 7 cm, and the drag coefficients of lump and conical graupel. Three-dimensional (3D) volume scans of 60 hailstones of sizes from 2.5 to 6.7 cm were printed in three dimensions using acrylonitrile butadiene styrene (ABS) plastic, and their terminal velocities were measured in the Mainz, Germany, vertical wind tunnel. To simulate lump graupel, 40 of the hailstones were printed with maximum dimensions of about 0.2, 0.3, and 0.5 cm, and their terminal velocities were measured. Conical graupel, whose three dimensions (maximum dimension 0.1–1 cm) were estimated from an analytical representation and printed, and the terminal velocities of seven groups of particles were measured in the tunnel. From these experiments, with printed particle densities from 0.2 to 0.9 g cm−3, together with earlier observations, relationships between the drag coefficient and the Reynolds number and between the Reynolds number and the Best number were derived for a wide range of particle sizes and heights (pressures) in the atmosphere. This information, together with the combined total of more than 2800 hailstones for which the mass and the cross-sectional area were measured, has been used to develop size-dependent relationships for the terminal velocity, the mass flux, and the kinetic energy of realistic hailstones.

scholarly journals Aerodynamic properties of lentil seeds

2015 ◽  
Vol 29 (3) ◽  
pp. 391-396 ◽  
Author(s):  
Feizollah Shahbazi ◽  
Saman Valizadeh ◽  
Ali Dowlatshah ◽  
Ezatollah Hassanzadeh
Keyword(s):  
Reynolds Number ◽  
Moisture Content ◽  
Drag Coefficient ◽  
Terminal Velocity ◽  
Mean Value ◽  
Probability Level ◽  
Solid Materials ◽  
Aerodynamic Properties ◽  
Red Variety ◽  
Mathematical Relationships

Abstract Aerodynamic properties of solid materials have long been used to convey and separate seeds and grains during post-harvest operations. The objective of this study was evaluation of the aerodynamic properties of green and red lentil seeds as a function of moisture content from 10 to 25% (w.b.). The results showed that as the moisture content increased from 10 to 25%, the terminal velocity of seeds increased, following a linear relationship, from 6.90 to 9.14 and from 6.37 to 7.67 m s−1 for green and red lentil seeds, respectively. Seeds of the green variety had terminal velocities with a mean value of 7.89 m s−1, while the red variety had a mean value of 7.02 m s−1, for moisture content from 10 to 25%. The Reynolds number increased linearly from 2 310.90 to 3 269.23 and from 1 215.02 to 1 535.09 for green and red lentil seeds, respectively, with the increase of seeds moisture content from 10 to 25%. While, drag coefficient decreased from 0.69 to 0.40 and from 0.84 to 0.69 for green and red lentil seeds, respectively, with the increase of moisture content. Mathematical relationships were developed to relate the change in seeds moisture content with the values of aerodynamic properties obtained. The analysis of variance showed that the effect of moisture content on all aerodynamic properties of lentil beans was significant at the 1% probability level.

The effects of surface roughness and tunnel blockage on the flow past spheres

1974 ◽  
Vol 65 (1) ◽  
pp. 113-125 ◽  
Author(s):  
Elmar Achenbach
Keyword(s):  
Surface Roughness ◽  
Reynolds Number ◽  
Drag Coefficient ◽  
Critical Reynolds Number ◽  
Measurement Techniques ◽  
Flow Conditions ◽  
Number Range ◽  
Flow Past ◽  
Reynolds Number Range ◽  
Shedding Frequency

The effect of surface roughness on the flow past spheres has been investigated over the Reynolds number range 5 × 104 < Re < 6 × 106. The drag coefficient has been determined as a function of the Reynolds number for five surface roughnesses. With increasing roughness parameter the critical Reynolds number decreases. At the same time the transcritical drag coefficient rises, having a maximum value of 0·4.The vortex shedding frequency has been measured under subcritical flow conditions. It was found that the Strouhal number for each of the various roughness conditions was equal to its value for a smooth sphere. Beyond the critical Reynolds number no prevailing shedding frequency could be detected by the measurement techniques employed.The drag coefficient of a sphere under the blockage conditions 0·5 < ds/dt < 0·92 has been determined over the Reynolds number range 3 × 104 < Re < 2 × 106. Increasing blockage causes an increase in both the drag coefficient and the critical Reynolds number. The characteristic quantities were referred to the flow conditions in the smallest cross-section between sphere and tube. In addition the effect of the turbulence level on the flow past a sphere under various blockage conditions was studied.

scholarly journals Evaluation and modeling of aerodynamic properties of mung bean seeds

2015 ◽  
Vol 29 (1) ◽  
pp. 121-126 ◽  
Author(s):  
Feizollah Shahbazi
Keyword(s):  
Reynolds Number ◽  
Moisture Content ◽  
Drag Coefficient ◽  
Mung Bean ◽  
Terminal Velocity ◽  
Mean Value ◽  
Probability Level ◽  
Solid Materials ◽  
Aerodynamic Properties ◽  
Mathematical Relationships

Abstract Aerodynamic properties of solid materials have long been used to convey and separate seeds and grains during post harvest operations. The objective of this study was the evaluation of the aerodynamic properties of mung bean seeds as a function of moisture content and two grades referred to above and below a cut point of 4.8 mm in length. The results showed that as the moisture content increased from 7.8 to 25% (w.b.), the terminal velocity of seeds increased following a polynomial relationship, from 7.28 to 8.79 and 6.02 to 7.12 m s-1, for grades A and B, respectively. Seeds at grade A had terminal velocities with a mean value of 8.05 m s-1, while at grade B had a mean value of 6.46 m s-1. The Reynolds number of both grades increased linearly with the increase of seeds moisture content, while the drag coefficient decreased with the increase of moisture content. Mathematical relationships were developed to relate the change in seeds moisture content with the obtained values of aerodynamic properties. The analysis of variance showed that moisture content had a significant effect, at 1% probability level, on all the aerodynamics properties of mung beans.

Transition to turbulence in oscillating pipe flow

1975 ◽  
Vol 68 (3) ◽  
pp. 567-576 ◽  
Author(s):  
P. Merkli ◽  
H. Thomann
Keyword(s):  
Reynolds Number ◽  
Thermal Effects ◽  
Critical Reynolds Number ◽  
Reynolds Numbers ◽  
Transition To Turbulence ◽  
Unexpected Result ◽  
Stokes Layer ◽  
Wide Range ◽  
Hot Wires ◽  
Vortex Patterns

Published results on transition in a Stokes layer indicate a wide range of transition Reynolds numbers. As thermal effects in a resonance tube (Merkli & Thomann 1975) depend on the state of the boundary layer, the transition Reynolds number was determined, and a critical Reynolds numberAc≈ 400 was found. The observations were made with hot wires and with flow visualization by means of smoke, and provide new details on turbulence in a Stokes layer. With this knowledge an explanation of the large discrepancies between some stability theories and the experiments is suggested. The main point is that turbulence occurs in the form of periodic bursts which are followed byrelaminarimtionin the same cycle and donotlead to turbulent flow during the whole cycle.A further, unexpected result of the present investigation is the discovery of vortex patterns superimposed on the normal laminar acoustic motion.

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