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- Author or Editor: R. L. Pitter x
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Abstract
Scavenging of 2 or 4 g cm−3 spherical aerosol particles by thin ice plates, idealized as oblate spheroids of axis ratio 0.05, was numerically modeled for atmospheric conditions of −18°C and 400 mb. Ice crystal semi-major axis lengths of 103 to 366 μm were investigated. The model included hydrodynamic, gravitational and electrostatic (coulombic) forces. The results indicate that theory for electrostatic deposition from an airstream may be applied to thin ice crystal collectors with reasonable accuracy for aerosol particles ≲5 μm radius when considering attractively charged bodies in a thunderstorm environment.
Abstract
Scavenging of 2 or 4 g cm−3 spherical aerosol particles by thin ice plates, idealized as oblate spheroids of axis ratio 0.05, was numerically modeled for atmospheric conditions of −18°C and 400 mb. Ice crystal semi-major axis lengths of 103 to 366 μm were investigated. The model included hydrodynamic, gravitational and electrostatic (coulombic) forces. The results indicate that theory for electrostatic deposition from an airstream may be applied to thin ice crystal collectors with reasonable accuracy for aerosol particles ≲5 μm radius when considering attractively charged bodies in a thunderstorm environment.
Abstract
The investigation of Pitter and Prappacher (1974) was reexamined including the effect of changing drag on the accelerating water drops and the effect of the drop flow field on the ice crystal. The present results indicate that drops greater than 10 µm collide with ice crystals at higher efficiencies than found earlier. The annular collision domain near the small drop cutoff size for any given ice crystal size was not significantly changed.
Abstract
The investigation of Pitter and Prappacher (1974) was reexamined including the effect of changing drag on the accelerating water drops and the effect of the drop flow field on the ice crystal. The present results indicate that drops greater than 10 µm collide with ice crystals at higher efficiencies than found earlier. The annular collision domain near the small drop cutoff size for any given ice crystal size was not significantly changed.
Abstract
Two mechanisms of ice crystal formation, contact freezing and very rapid condensation freezing, were applied to numerical simulations of ground-based seeding with the Guide Model, an orographic cloud model, to study whether different mechanisms of ice crystal formation substantially affect precipitation patterns and intensities. Although the numerical model has limitations, it was expected to indicate how different ice crystal formation rates lead to differences in precipitation patterns and intensities between the two mechanisms.
Numerical simulations of two case studies are presented. One is characterized by moderate wind speeds and colder cloud temperatures, the other by stronger winds and warmer cloud temperatures. The moderate wind field and colder cloud temperatures yielded nearly half an order of magnitude more precipitation than the strong wind field and warmer cloud temperatures. Sensitivity analysis showed that snowfall as a result of forced condensation freezing is strongly dependent on the ambient temperature at the ground-based generator site, while generator site temperature had less effect on the precipitation as a result of contact freezing. Snowfall resulting from contact freezing, however, was found to be strongly dependent on the cloud drop concentration. Liquid water content did not significantly affect the precipitation resulting from ice crystal formation by either mechanism. Precipitation rates induced by forced condensation freezing are about two orders of magnitude greater than those induced by contact freezing in the cases simulated, over the Sierra crest, because of the limited time available for ice particles to grow and precipitate.
Abstract
Two mechanisms of ice crystal formation, contact freezing and very rapid condensation freezing, were applied to numerical simulations of ground-based seeding with the Guide Model, an orographic cloud model, to study whether different mechanisms of ice crystal formation substantially affect precipitation patterns and intensities. Although the numerical model has limitations, it was expected to indicate how different ice crystal formation rates lead to differences in precipitation patterns and intensities between the two mechanisms.
Numerical simulations of two case studies are presented. One is characterized by moderate wind speeds and colder cloud temperatures, the other by stronger winds and warmer cloud temperatures. The moderate wind field and colder cloud temperatures yielded nearly half an order of magnitude more precipitation than the strong wind field and warmer cloud temperatures. Sensitivity analysis showed that snowfall as a result of forced condensation freezing is strongly dependent on the ambient temperature at the ground-based generator site, while generator site temperature had less effect on the precipitation as a result of contact freezing. Snowfall resulting from contact freezing, however, was found to be strongly dependent on the cloud drop concentration. Liquid water content did not significantly affect the precipitation resulting from ice crystal formation by either mechanism. Precipitation rates induced by forced condensation freezing are about two orders of magnitude greater than those induced by contact freezing in the cases simulated, over the Sierra crest, because of the limited time available for ice particles to grow and precipitate.
Abstract
The hydrodynamic interaction between simple ice plates, idealized as oblate spheroids of axis ratio 0.05, and water drops, assumed to be spherical, was numerically investigated for atmospheric conditions of −10C and 700 mb. The ice plates had semi-major axis length between 147 and 404 µm and the water drops had radii up to 53 µm. Since the ratio of the mass of the drop to the mass of the crystal was small, the superposition model was found to be satisfactory. The flow fields around drops were those of LeClair et al., and the flow fields around oblate spheroids were those of Pitter et al. From the trajectories of the water drops relative to the ice crystals, collision efficiencies were determined. The model predicts preferential riming of the drops at the edges of crystals under certain conditions, in agreement with field observations in atmospheric clouds.
Abstract
The hydrodynamic interaction between simple ice plates, idealized as oblate spheroids of axis ratio 0.05, and water drops, assumed to be spherical, was numerically investigated for atmospheric conditions of −10C and 700 mb. The ice plates had semi-major axis length between 147 and 404 µm and the water drops had radii up to 53 µm. Since the ratio of the mass of the drop to the mass of the crystal was small, the superposition model was found to be satisfactory. The flow fields around drops were those of LeClair et al., and the flow fields around oblate spheroids were those of Pitter et al. From the trajectories of the water drops relative to the ice crystals, collision efficiencies were determined. The model predicts preferential riming of the drops at the edges of crystals under certain conditions, in agreement with field observations in atmospheric clouds.
Abstract
A physical model which predicts the shape of water drops falling at terminal velocity in air is presented. The model is based on a balance of the forces which act on a drop falling under gravity in a viscous medium. The model was evaluated by numerical techniques and the shape of water drops of radii between 170 and 4000 μ (equivalent to Reynolds numbers between 30 and 4900) was determined. The results of our investigation show that the drop shapes predicted by the model agree well with those experimentally observed in our wind tunnel. Both theory and experiment demonstrate that: 1) drops with radii ≲170 μ are very slightly deformed and can be considered spherical, 2) the shape of drops between about 170 and 500 μ can be closely approximated by an oblate spheroid, 3) drops between about 500 and 2000 μ are deformed into an asymmetric oblate spheroid with an increasingly pronounced flat base, and 4) drops ≳2000 μ develop a concave depression in the base which is more pronounced for larger drop sizes. The relevance of these findings to the process of drop breakup is discussed.
Abstract
A physical model which predicts the shape of water drops falling at terminal velocity in air is presented. The model is based on a balance of the forces which act on a drop falling under gravity in a viscous medium. The model was evaluated by numerical techniques and the shape of water drops of radii between 170 and 4000 μ (equivalent to Reynolds numbers between 30 and 4900) was determined. The results of our investigation show that the drop shapes predicted by the model agree well with those experimentally observed in our wind tunnel. Both theory and experiment demonstrate that: 1) drops with radii ≲170 μ are very slightly deformed and can be considered spherical, 2) the shape of drops between about 170 and 500 μ can be closely approximated by an oblate spheroid, 3) drops between about 500 and 2000 μ are deformed into an asymmetric oblate spheroid with an increasingly pronounced flat base, and 4) drops ≳2000 μ develop a concave depression in the base which is more pronounced for larger drop sizes. The relevance of these findings to the process of drop breakup is discussed.
Abstract
Numerical solutions have been found for the vapor density field around a simple ice plate, idealized as an oblate spheroid of axis ratio 0.05, having Reynolds numbers between 0.1 and 20, and failing in a fluid of Schmidt number 0.71. The present solutions are compared with experimental data after Thorpe and Mason for evaporating ice plates, the numerical results of Masliyah and Epstein for oblate spheroids of axis ratio 0.2, and the analytical results of Brenner for thin disks. It is shown that the ventilation coefficient varies linearly with N Sc ⅓ N Rc ½ at higher Reynolds numbers, while as the Reynolds number approaches zero it approaches its stationary value via the analytical solution of Brenner. Over the range of Reynolds numbers investigated, ventilation coefficients for thin oblate spheroids were found to be lower than those for spheres.
Abstract
Numerical solutions have been found for the vapor density field around a simple ice plate, idealized as an oblate spheroid of axis ratio 0.05, having Reynolds numbers between 0.1 and 20, and failing in a fluid of Schmidt number 0.71. The present solutions are compared with experimental data after Thorpe and Mason for evaporating ice plates, the numerical results of Masliyah and Epstein for oblate spheroids of axis ratio 0.2, and the analytical results of Brenner for thin disks. It is shown that the ventilation coefficient varies linearly with N Sc ⅓ N Rc ½ at higher Reynolds numbers, while as the Reynolds number approaches zero it approaches its stationary value via the analytical solution of Brenner. Over the range of Reynolds numbers investigated, ventilation coefficients for thin oblate spheroids were found to be lower than those for spheres.
Abstract
The flow past a thin oblate spheroid falling at terminal velocity in an infinite, viscous fluid was investigated using a numerical solution of the steady-state Navier-Stokes equations of motion. The detailed streamfunction and vorticity yielded the drag, pressure distribution, and the extent of the spheroid's downstream wake. Calculations were performed for spheroids of axis ratios 0.05 and 0.2 and Reynolds numbers between 0.1 and 100. The results were compared with other numerical and analytical solutions to the Navier Stokes equations of motion for viscous flow past oblate spheroids and disks and with experimental results in the literature. Our numerical results for oblate spheroids of axis ratio 0.2 agree well with the numerical results of Masliyah and Epstein and with our own experimental results. Our results for oblate spheroids of axis ratio 0.05 agree well with the numerical computations of Michael and available experimental results on disks, but depart significantly from the numerical results of Rimon. In agreement with our earlier studies on spheres, we find that, as the Reynolds number approaches zero, the drag on an oblate spheroid of any axis ratio approaches its value at zero Reynolds number via the Oseen drag rather than via the Stokes drag. The significance of the present study to cloud physics is pointed out.
Abstract
The flow past a thin oblate spheroid falling at terminal velocity in an infinite, viscous fluid was investigated using a numerical solution of the steady-state Navier-Stokes equations of motion. The detailed streamfunction and vorticity yielded the drag, pressure distribution, and the extent of the spheroid's downstream wake. Calculations were performed for spheroids of axis ratios 0.05 and 0.2 and Reynolds numbers between 0.1 and 100. The results were compared with other numerical and analytical solutions to the Navier Stokes equations of motion for viscous flow past oblate spheroids and disks and with experimental results in the literature. Our numerical results for oblate spheroids of axis ratio 0.2 agree well with the numerical results of Masliyah and Epstein and with our own experimental results. Our results for oblate spheroids of axis ratio 0.05 agree well with the numerical computations of Michael and available experimental results on disks, but depart significantly from the numerical results of Rimon. In agreement with our earlier studies on spheres, we find that, as the Reynolds number approaches zero, the drag on an oblate spheroid of any axis ratio approaches its value at zero Reynolds number via the Oseen drag rather than via the Stokes drag. The significance of the present study to cloud physics is pointed out.
Abstract
A theoretical model is presented which allows determination of the efficiency with which electrically charged, simple planar ice crystals collide with electrically charged supercooled cloud drops. The calculations are carried out for ice crystal plates of diameter between 100 and 1300 μm colliding with cloud drops of diameters between 2 and 170 μm. The electric charges Q (esu) residing on the drops and ice crystals were assumed to vary with the radius a (cm) of the drop or crystal according to Q=qa 2, with 0≤q≤2.0. Our results show that the efficiency with which supercooled drops the collected by simple Planar ice crystals is enhanced by electric charges, in particular, if q>0.8, where q=0.8 represents an electric charge still considerably below thunderstorm charge.
Abstract
A theoretical model is presented which allows determination of the efficiency with which electrically charged, simple planar ice crystals collide with electrically charged supercooled cloud drops. The calculations are carried out for ice crystal plates of diameter between 100 and 1300 μm colliding with cloud drops of diameters between 2 and 170 μm. The electric charges Q (esu) residing on the drops and ice crystals were assumed to vary with the radius a (cm) of the drop or crystal according to Q=qa 2, with 0≤q≤2.0. Our results show that the efficiency with which supercooled drops the collected by simple Planar ice crystals is enhanced by electric charges, in particular, if q>0.8, where q=0.8 represents an electric charge still considerably below thunderstorm charge.
Abstract
A system is described for measurement and analysis of precipitation particle charge from an aircraft in the highly variable and harsh environment of a convective cloud. A compromise, practical instrument design enables particle charge and sign to be measured with concentrations up to 5 L−1. The system employs two induction rings in series; it is de-iced both on the electrostatic shield and internally. New techniques are described which enable rapid analysis of sequential charge data over a penetration period of 55 s, with rejection of spurious data pulses resulting from particle impaction.
Abstract
A system is described for measurement and analysis of precipitation particle charge from an aircraft in the highly variable and harsh environment of a convective cloud. A compromise, practical instrument design enables particle charge and sign to be measured with concentrations up to 5 L−1. The system employs two induction rings in series; it is de-iced both on the electrostatic shield and internally. New techniques are described which enable rapid analysis of sequential charge data over a penetration period of 55 s, with rejection of spurious data pulses resulting from particle impaction.
