Mass of different snow crystal shapes derived from fall speed measurements

Abstract. Meteorological forecast and climate models require good knowledge of the microphysical properties of hydrometeors and the atmospheric snow and ice crystals in clouds, for instance, their size, cross-sectional area, shape, mass, and fall speed. Especially shape is an important parameter in that it strongly affects the scattering properties of ice particles and consequently their response to remote sensing techniques. The fall speed and mass of ice particles are other important parameters for both numerical forecast models and the representation of snow and ice clouds in climate models. In the case of fall speed, it is responsible for the rate of removal of ice from these models. The particle mass is a key quantity that connects the cloud microphysical properties to radiative properties. Using an empirical relationship between the dimensionless Reynolds and Best numbers, fall speed and mass can be derived from each other if particle size and cross-sectional area are also known. In this study, ground-based in situ measurements of snow particle microphysical properties are used to analyse mass as a function of shape and the other properties particle size, cross-sectional area, and fall speed. The measurements for this study were done in Kiruna, Sweden, during snowfall seasons of 2014 to 2019 and using the ground-based in situ Dual Ice Crystal Imager (D-ICI) instrument, which takes high-resolution side- and top-view images of natural hydrometeors. From these images, particle size (maximum dimension), cross-sectional area, and fall speed of individual particles are determined. The particles are shape-classified according to the scheme presented in our previous study, in which particles sort into 15 different shape groups depending on their shape and morphology. Particle masses of individual ice particles are estimated from measured particle size, cross-sectional area, and fall speed. The selected dataset covers sizes from about 0.1 to 3.2 mm, fall speeds from 0.1 to 1.6 m s−1, and masses from 0.2 to 450 µg. In our previous study, the fall speed relationships between particle size and cross-sectional area were studied. In this study, the same dataset is used to determine the particle mass, and consequently, the mass relationships between particle size, cross-sectional area, and fall speed are studied for these 15 shape groups. Furthermore, the mass relationships presented in this study are compared with the previous studies. For certain crystal habits, in particular columnar shapes, the maximum dimension is unsuitable for determining Reynolds number. Using a selection of columns, for which the simple geometry allows the verification of an empirical Best-number-to-Reynolds-number relationship, we show that Reynolds number and fall speed are more closely related to the diameter of the basal facet than the maximum dimension. The agreement with the empirical relationship is further improved using a modified Best number, a function of an area ratio based on the falling particle seen in the vertical direction.

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Mass of different snow crystal shapes derived from fall speed measurements

10.5194/acp-2021-203 ◽

2021 ◽

Author(s):

Sandra Vázquez-Martín ◽

Thomas Kuhn ◽

Salomon Eliasson

Keyword(s):

Particle Size ◽

Climate Models ◽

Cross Sectional Area ◽

Particle Mass ◽

Sectional Area ◽

Cross Sectional ◽

Microphysical Properties ◽

Ice Particles ◽

Fall Speed

Abstract. Meteorological forecast and climate models require good knowledge of the microphysical properties of hydrometeors and the atmospheric snow and ice crystals in clouds. For instance, their size, cross-sectional area, shape, mass, and fall speed. Especially shape is an important parameter in that it strongly affects the scattering properties of ice particles, and consequently their response to remote sensing techniques. The fall speed and mass of ice particles are other important parameters both for numerical forecast models and for the representation of snow and ice clouds in climate models. In the case of fall speed, it is responsible for the rate of removal of ice from these models. The particle mass is a key quantity that connects the cloud microphysical properties to radiative properties. Using an empirical relationship between the dimensionless Reynolds and Best numbers, fall speed and mass can be derived from each other if particle size and cross-sectional area are also known. In this work, ground-based in-situ measurements of snow particle microphysical properties are used to analyse mass as a function of shape and the other properties particle size, cross-sectional area, and fall speed. The measurements for this study were done in Kiruna, Sweden during snowfall seasons of 2014 to 2019 and using the ground-based in-situ instrument Dual Ice Crystal Imager (D-ICI), which takes high-resolution side- and top-view images of natural hydrometeors. From these images, particle size (maximum dimension), cross-sectional area, and fall speed of individual particles are determined. The particles are shape classified according to the scheme presented in our previous work, in which particles sort into 15 different shape groups depending on their shape and morphology. Particle masses of individual ice particles are estimated from measured particle size, cross-sectional area, and fall speed. The selected dataset covers sizes from about 0.1 mm to 3.2 mm, fall speeds from 0.1 m s−1 to 1.6 m s−1, and masses from close to 0.2 μg to 320 μg. In our previous work, the fall speed relationships between particle size and cross-sectional area were studied. In this work, the same dataset is used to determine the particle mass, and consequently, the mass relationships between particle size, cross-sectional area, and fall speed are studied for these 15 shape groups. Furthermore, the mass relationships presented in this study are compared with the previous studies.

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Shape dependence of snow crystal fall speed

Atmospheric Chemistry and Physics ◽

10.5194/acp-21-7545-2021 ◽

2021 ◽

Vol 21 (10) ◽

pp. 7545-7565

Author(s):

Sandra Vázquez-Martín ◽

Thomas Kuhn ◽

Salomon Eliasson

Keyword(s):

Particle Size ◽

Numerical Models ◽

Area Ratio ◽

Cross Sectional Area ◽

Sectional Area ◽

Maximum Dimension ◽

Cross Sectional ◽

Ice Particles ◽

Fall Speed

Abstract. Improved snowfall predictions require accurate knowledge of the properties of ice crystals and snow particles, such as their size, cross-sectional area, shape, and fall speed. The fall speed of ice particles is a critical parameter for the representation of ice clouds and snow in atmospheric numerical models, as it determines the rate of removal of ice from the modelled clouds. Fall speed is also required for snowfall predictions alongside other properties such as ice particle size, cross-sectional area, and shape. For example, shape is important as it strongly influences the scattering properties of these ice particles and thus their response to remote sensing techniques. This work analyzes fall speed as a function of particle size (maximum dimension), cross-sectional area, and shape using ground-based in situ measurements. The measurements for this study were done in Kiruna, Sweden, during the snowfall seasons of 2014 to 2019, using the ground-based in situ instrument Dual Ice Crystal Imager (D-ICI). The resulting data consist of high-resolution images of falling hydrometeors from two viewing geometries that are used to determine particle size (maximum dimension), cross-sectional area, area ratio, orientation, and the fall speed of individual particles. The selected dataset covers sizes from about 0.06 to 3.2 mm and fall speeds from 0.06 to 1.6 m s−1. Relationships between particle size, cross-sectional area, and fall speed are studied for different shapes. The data show in general low correlations to fitted fall speed relationships due to large spread observed in fall speed. After binning the data according to size or cross-sectional area, correlations improve, and we can report reliable parameterizations of fall speed vs. particle size or cross-sectional area for part of the shapes. For most of these shapes, the fall speed is better correlated with cross-sectional area than with particle size. The effects of orientation and area ratio on the fall speed are also studied, and measurements show that vertically oriented particles fall faster on average. However, most particles for which orientation can be defined fall horizontally.

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Shape dependence of snow crystal fall speed

10.5194/acp-2020-1056 ◽

2020 ◽

Author(s):

Sandra Vázquez-Martín ◽

Thomas Kuhn ◽

Salomon Eliasson

Keyword(s):

Remote Sensing ◽

Numerical Models ◽

Area Ratio ◽

Cross Sectional Area ◽

Sectional Area ◽

Cross Sectional ◽

Ice Particles ◽

Fall Speed ◽

Remote Sensing Techniques

Abstract. Improved snowfall predictions require accurate knowledge of the properties of ice crystals and snow particles, such as their size, cross-sectional area, shape, and fall speed. In particular, the shape is an important parameter as it strongly influences the scattering properties of these ice particles, and thus their response to remote sensing techniques such as radar measurements. The fall speed of ice particles is a critical parameter for the representation of ice clouds and snow in atmospheric numerical models, as it determines the rate of removal of ice from the modelled clouds. They are also required for snowfall predictions alongside other properties such as ice particle size, cross-sectional area, and shape. For example, shape is important as it strongly influences the scattering properties of these ice particles, and thus their response to remote sensing techniques. This work analyses fall speed as a function of shape and other properties using ground-based in-situ measurements. The measurements for this study were done in Kiruna, Sweden during the snowfall seasons of 2014 to 2019, using the ground-based in-situ instrument Dual Ice Crystal Imager (D-ICI). The resulting data consist of high-resolution images of falling hydrometeors from two viewing geometries that are used to determine size (maximum dimension), cross-sectional area, area ratio, orientation, and the fall speed of individual particles. The selected dataset covers sizes from about 0.06 to 3.2 mm and fall speeds from 0.06 to 1.6 m s−1. The particles are shape-classified into 15 different shape groups depending on their shape and morphology. For these 15 shape groups relationships are studied, firstly, between size and cross-sectional area, then between fall speed and size or cross-sectional area. The data show in general low correlations to fitted fall-speed relationships due to large spread observed in fall speed. After binning the data according to size or cross-sectional area, correlations improve and we can report reliable parameterizations of fall speed vs. size or cross-sectional area for part of the shapes. The effects of orientation and area ratio on the fall speed are also studied, and measurements show that vertically orientated particles fall faster on average. However, most particles for which orientation can be defined fall horizontally.

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Effective Radius of Ice Particles in Cirrus and Contrails

Journal of the Atmospheric Sciences ◽

10.1175/2010jas3562.1 ◽

2011 ◽

Vol 68 (2) ◽

pp. 300-321 ◽

Cited By ~ 46

Author(s):

U. Schumann ◽

B. Mayer ◽

K. Gierens ◽

S. Unterstrasser ◽

P. Jessberger ◽

...

Keyword(s):

Water Content ◽

Effective Radius ◽

Cross Sectional Area ◽

Sectional Area ◽

Small Particles ◽

Particle Volume ◽

Cross Sectional ◽

Ice Particles ◽

Ice Water Content ◽

Ice Water

Abstract This paper discusses the ratio C between the volume mean radius and the effective radius of ice particles in cirrus and contrails. The volume mean radius is proportional to the third root of the ratio between ice water content and number of ice particles, and the effective radius measures the ratio between ice particle volume and projected cross-sectional area. For given ice water content and number concentration of ice particles, the optical depth scales linearly with C. Hence, C is an important input parameter for radiative forcing estimates. The ratio C in general depends strongly on the particle size distribution (PSD) and on the particle habits. For constant habits, C can be factored into a PSD and a habit factor. The PSD factor is generally less than one, while the habit factor is larger than one for convex or concave ice particles with random orientation. The value of C may get very small for power-law PSDs with exponent n between −4 and 0, which is often observed. For such PSDs, most of the particle volume is controlled by a few large particles, while most of the cross-sectional area is controlled by the many small particles. A new particle habit mix for contrail cirrus including small droxtal-shape particles is suggested. For measured cirrus and contrails, the dependence of C on volume mean particle radius, ambient humidity, and contrail age is determined. For cirrus, C varies typically between 0.4 and 1.1. In contrails, C = 0.7 ± 0.3, with uncertainty ranges increasing with the volume radius and contrail age. For the small particles in young contrails, the extinction efficiency in the solar range deviates considerably from the geometric optics limit.

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Numerical Study on the Flow Past a Twisted Elliptic Cylinder With Subcritical Reynolds Number

ASME-JSME-KSME 2011 Joint Fluids Engineering Conference: Volume 1, Symposia – Parts A, B, C, and D ◽

10.1115/ajk2011-25006 ◽

2011 ◽

Author(s):

Min Ho Kim ◽

Jin Woog Lee ◽

Hyun Sik Yoon ◽

Man Yeong Ha

Keyword(s):

Reynolds Number ◽

Numerical Study ◽

Elliptic Cylinder ◽

Cross Sectional Area ◽

Stream Velocity ◽

Spanwise Direction ◽

Sectional Area ◽

Cross Sectional ◽

Flow Past ◽

Smooth Cylinder

Large eddy simulation of flow past a torsional cylinder has been carried out at a Reynolds number of 3900 based on the cylinder diameter and the free stream velocity using finite volume method. The torsional cylinder has been formed by rotating the elliptic cross sectional area along the spanwise direction. For an ellipse, different eccentricities are considered to observe the effect of eccentricity on the flow fields. The excellent comparisons with previous studies for the cases of a smooth cylinder and a wavy cylinder having sinusoidal variation in cross sectional area along the spanwise direction guarantee the accuracy of present numerical methods. The effect of eccentricity on the drag and lift coefficients representing the fluid flow characteristics has been investigated by comparing with those of the smooth cylinder, resulting in enhancement of drag reduction and suppression of vortex-induced vibration. The isosurface of swirling strength has been adopted to identify the vortical structures in the turbulent wake.

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EMPIRICAL RELATIONSHIP BETWEEN INLET CROSS-SECTIONAL AREA AND TIDAL PRISM: A RE-EVALUATION

Coastal Engineering Proceedings ◽

10.9753/icce.v32.sediment.86 ◽

2011 ◽

Vol 1 (32) ◽

pp. 86 ◽

Cited By ~ 2

Author(s):

Marcel Stive ◽

Liang Ji ◽

Ronald L Brouwer ◽

Co Van de Kreeke ◽

Roahanka Ranasinghe

Keyword(s):

Empirical Relationship ◽

Cross Sectional Area ◽

Similarity Criteria ◽

Tidal Range ◽

Published Data ◽

Sectional Area ◽

Tidal Prism ◽

Q Value ◽

Cross Sectional ◽

Theoretical Finding

The well-known empirical relationship between the equilibrium cross-sectional area of tidal inlet entrances (A) and the tidal prism (P), first developed by O’Brien (1931), has been extensively reviewed. Our theoretical investigations indicate that a unique A-P relationship should only be expected for clusters of inlets that are phenomenological similar (i.e. fairly similar hydrodynamic and morphological conditions), and that the exponent q in the A-P relation should be larger than 1. However, relevant published data available to date do not clearly support this theoretical finding. A re-analysis of the available data sets by Stive et al. (2009) indicated that they may not be sufficiently reliable to verify our theoretical finding with regard to q>1 due to the violation of the condition of phenomenological similarity, and possibly also due to violating the initial definitions given by O’Brien (1931) in estimating the tidal prism. The resolution of this issue is important because slightly different values of q result in significantly variable values for the equilibrium cross-sectional area of the tidal entrance. This may have significant implications in determining the true stable equilibrium entrance cross-sectional area. Here we present a re-analysis of the available data with a focus on determining the phenomenological dependencies of the A-P relationship. The available A-P data from the US Pacific, Atlantic and Gulf coasts (Jarrett, 1976 and Powell, 2003) have been re-scrutinized and categorized following the above mentioned phenomenological similarity criteria, viz. similar tidal range, similar sediment size, similar littoral transport and similar hydraulic radius. All together, some 20 different categories were considered and A-P relationships were obtained for each category. Generally, high correlations were found between the stable inlet predicted by each A-P relationship and the corresponding data. However, only in a limited number of categories were they significantly better than the correlations for the complete datasets. Finally, we point out that only in a number of categories the q value associated with the A-P relationship exceeded unity as suggested by the theoretical derivations. In the majority of categories the q value associated with the A-P relationship does not exceed unity. This is truly disappointing, and we have no physical explanation for this and consider this issue unresolved.

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Manufacturing Influences on Pressure Losses of Channel Fed Holes

Volume 3C: Heat Transfer ◽

10.1115/gt2013-95236 ◽

2013 ◽

Author(s):

Michael Barringer ◽

Karen A. Thole ◽

Vaidyanathan Krishnan ◽

Evan Landrum

Keyword(s):

Reynolds Number ◽

Pressure Loss ◽

Cross Sectional Area ◽

Channel Inlet ◽

Sectional Area ◽

Exit Hole ◽

Cross Sectional ◽

Flow Rates ◽

Channel Exit ◽

Loss Coefficients

Variations from manufacturing can influence the overall pressure drop and subsequent flow rates through supply holes in such applications as film-cooling, transpiration cooling, and impingement cooling that are supplied by micro-channels, pipe-flow systems, or secondary air systems. The inability to accurately predict flow rates has profound effects on engine operations. The objective of this study was to investigate the influence of several relevant manufacturing features that might occur for a cooling supply hole being fed by a range of channel configurations. The manufacturing variances included the ratio of hole diameter to channel width, the number of channel feeds (segments), the effect of hole overlap with respect to the channel sidewalls, and channel Reynolds number. Results showed that the friction factors for the typically long channels in this study, were independent of the inlet and exit hole configurations tested. Results also showed that the non-dimensional pressure loss coefficients for the flow passing through the channel inlet holes and through the channel exit holes were found to be independent of the channel flow Reynolds number over the range tested. The geometric scaling ratio of the hole cross-sectional area to the channel cross-sectional area collapsed the pressure loss coefficients the best for both one and two flow segments for both the channel inlet and channel exit hole.

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Mass transfer in 3D printed electrolyzers: The importance of inlet effects

10.22541/au.160929686.65765835/v1 ◽

2020 ◽

Author(s):

Stéphane Weusten ◽

Luc Murrer ◽

Matheus de Groot ◽

John van der Schaaf

Keyword(s):

Mass Transfer ◽

Reynolds Number ◽

Turbulent Flow ◽

Cross Sectional Area ◽

Transfer Performance ◽

Sectional Area ◽

Entrance Length ◽

Cross Sectional ◽

3D Printed ◽

The Cross

This paper investigates the effect of inlet shape, entrance length and turbulence promoters on mass transfer by using 3D printed electrolyzers. Our results show that the inlet design can promote turbulence and lead to an earlier transition to turbulent flow. The Reynolds number at which the transition occurs can be predicted by the ratio of the cross-sectional area of the inlet to the cross-sectional area of the electrolyzer channel. A longer entrance length results in more laminar behavior and a later transition to turbulent flow. With an entrance length of 550mm, the inlet design did no longer affect the mass transfer performance significantly. The addition of gyroid type turbulence promoters resulted in a factor 2 to 4 increase in mass transfer depending on inlet design, entrance length and the type of promoter. From one configuration to another, there was a minimal variation in pressure drop (<16 mbar).

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Manufacturing Influences on Pressure Losses of Channel Fed Holes

Journal of Turbomachinery ◽

10.1115/1.4025226 ◽

2013 ◽

Vol 136 (5) ◽

Author(s):

Michael Barringer ◽

Karen A. Thole ◽

Vaidyanathan Krishnan ◽

Evan Landrum

Keyword(s):

Reynolds Number ◽

Pressure Loss ◽

Cross Sectional Area ◽

Channel Inlet ◽

Sectional Area ◽

Exit Hole ◽

Cross Sectional ◽

Flow Rates ◽

Channel Exit ◽

Loss Coefficients

Variations from manufacturing can influence the overall pressure drop and subsequent flow rates through supply holes in such applications as film-cooling, transpiration cooling, and impingement cooling that are supplied by microchannels, pipe-flow systems, or secondary air systems. The inability to accurately predict flow rates has profound effects on engine operations. The objective of this study was to investigate the influence of several relevant manufacturing features that might occur for a cooling supply hole being fed by a range of channel configurations. The manufacturing variances included the ratio of the hole diameter to the channel width, the number of channel feeds (segments), the effect of hole overlap with respect to the channel sidewalls, and the channel Reynolds number. The results showed that the friction factors for the typically long channels in this study were independent of the tested inlet and exit hole configurations. The results also showed that the nondimensional pressure loss coefficients for the flow passing through the channel inlet holes and through the channel exit holes were found to be independent of the channel flow Reynolds number over the tested range. The geometric scaling ratio of the hole cross-sectional area to the channel cross-sectional area collapsed the pressure loss coefficients the best for both one and two flow segments for both the channel inlet and channel exit hole.

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Effects of Masts on the Aerodynamics of Sail Sections

Marine Technology and SNAME News ◽

10.5957/mt1.1978.15.1.35 ◽

1978 ◽

Vol 15 (01) ◽

pp. 35-42

Author(s):

Jerome H. Milgram

Keyword(s):

Reynolds Number ◽

Drag Coefficient ◽

Lift Coefficient ◽

Limited Range ◽

Cross Sectional Area ◽

Water Tunnel ◽

Two Dimensional ◽

Sectional Area ◽

Cross Sectional ◽

Coefficient Versus

The effects of the addition of masts of varying geometries to two different sail-like two-dimensional airfoil sections were determined by water tunnel tests. Thirteen different mast-sail combinations were tested with four of the sections retested at a different time to confirm repeatability of the data. The results were found to be best presented and best understood by means of graphs of drag coefficient versus lift coefficient for fixed values of d/c(mast diameter/sail chord). The additional drag caused by the addition of a mast was found to be substantial, especially as the ratio d/cbecame relatively large. Results were found to be insensitive to changes in Reynolds number of a factor of two for d/cless than 0.3 for round masts, and 0.2 for elliptical masts (d for an elliptical mast is taken as the diameter of a circle having the same cross-sectional area). Elliptical masts with d/c greater than 0.3 gave results which exhibited a sensitivity to Reynolds number and which, over a limited range of lift coefficients, gave an unexpectedly high value of the ratio of lift coefficient/drag coefficient.

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