scholarly journals An improved lumped model for freezing of a freely suspended supercooled water droplet in air stream

2021 ◽  
Vol 130 (1) ◽  
Author(s):  
Emerson B. dos Anjos ◽  
Carolina P. Naveira-Cotta ◽  
Manish K. Tiwari ◽  
Renato M. Cotta ◽  
Igor S. Carvalho
Keyword(s):  
Water Droplet ◽  
Supercooled Water ◽  
Freezing Process ◽  
Partial Differential ◽  
Interface Position ◽  
Spherical Droplet ◽  
Differential Model ◽  
Differential Formulation ◽  
Air Stream ◽  
Freely Suspended

AbstractThis work deals with the mathematical modeling of the transient freezing process of a supercooled water droplet in a cold air stream. The aim is to develop a simple yet accurate lumped-differential model for the energy balance for a freely suspended water droplet undergoing solidification, that allows for cost effective computations of the temperatures and freezing front evolution along the whole process. The complete freezing process was described by four distinct stages, namely, supercooling, recalescence, solidification, and cooling. At each stage, the Coupled Integral Equations Approach (CIEA) is employed, which reduces the partial differential equation for the temperature distribution within the spherical droplet into coupled ordinary differential equations for dimensionless boundary temperatures and the moving interface position. The resulting lumped-differential model is expected to offer improved accuracy with respect to the classical lumped system analysis, since boundary conditions are accounted for in the averaging process through Hermite approximations for integrals. The results of the CIEA were verified using a recently advanced accurate hybrid numerical-analytical solution through the Generalized Integral Transform Technique (GITT), for the full partial differential formulation, and comparisons with numerical and experimental results from the literature. After verification and validation of the proposed model, a parametric analysis is implemented, for different conditions of airflow velocity and droplet radius, which lead to variations in the Biot numbers that allow to inspect for their influence on the accuracy of the improved lumped-differential formulation.

IMPROVED LUMPED-DIFFERENTIAL ANALYSIS OF THE FREEZING PROCESS IN A SUPERCOOLED WATER DROPLET

2020 ◽  
Author(s):  
Emerson Barbosa dos Anjos ◽  
Carolina Palma Naveira Cotta ◽  
Renato Machado Cotta ◽  
Igor Soares Carvalho ◽  
Manish Tiwari
Keyword(s):  
Water Droplet ◽  
Supercooled Water ◽  
Freezing Process ◽  
Differential Analysis

Numerical investigation of the impacting and freezing process of a single supercooled water droplet

2021 ◽  
Vol 33 (4) ◽  
pp. 042114
Author(s):  
Yongkui Wang ◽  
Lei Ju ◽  
Duanfeng Han ◽  
Qing Wang
Keyword(s):  
Numerical Investigation ◽  
Water Droplet ◽  
Supercooled Water ◽  
Freezing Process

scholarly journals Freezing of water droplets colliding with kaolinite particles

2009 ◽  
Vol 9 (13) ◽  
pp. 4295-4300 ◽  
Author(s):  
E. A. Svensson ◽  
C. Delval ◽  
P. von Hessberg ◽  
M. S. Johnson ◽  
J. B. C. Pettersson
Keyword(s):  
Water Vapor ◽  
Relative Humidity ◽  
Water Droplet ◽  
Supercooled Water ◽  
Dust Particles ◽  
Freezing Process ◽  
Water Droplets ◽  
Electrodynamic Balance ◽  
Dry Conditions

Abstract. Contact freezing of single supercooled water droplets colliding with kaolinite dust particles has been investigated. The experiments were performed with droplets levitated in an electrodynamic balance at temperatures from 240 to 268 K. Under relatively dry conditions (when no water vapor was added) freezing was observed to occur below 249 K, while a freezing threshold of 267 K was observed when water vapor was added to the air in the chamber. The effect of relative humidity is attributed to an influence on the contact freezing process for the kaolinite-water droplet system, and it is not related to the lifetime of the droplets in the electrodynamic balance. Freezing probabilities per collision were derived assuming that collisions at the lowest temperature employed had a probability of unity. Mechanisms for contact freezing are briefly discussed.

Cascade Freezing of Supercooled Water Droplet Collectives

ACS Nano ◽  
2018 ◽  
Vol 12 (11) ◽  
pp. 11274-11281 ◽  
Author(s):  
Gustav Graeber ◽  
Valentin Dolder ◽  
Thomas M. Schutzius ◽  
Dimos Poulikakos
Keyword(s):  
Water Droplet ◽  
Supercooled Water

Transient Conjugated Conduction: External Convection With Front Face Imposed Wall Heat Flux

2007 ◽  
Author(s):  
Carolina P. Naveira ◽  
Renato M. Cotta ◽  
Mohammed Lachi ◽  
Jacques Padet
Keyword(s):  
Heat Flux ◽  
Integral Transform ◽  
Heat Conduction Problem ◽  
Solid Wall ◽  
Method Of Lines ◽  
Wall Heat Flux ◽  
Front Face ◽  
Flat Plates ◽  
Partial Differential ◽  
Differential Formulation

This work presents hybrid numerical-analytical solutions for transient laminar forced convection over flat plates of non-negligible thickness, subjected to arbitrary time variations of applied wall heat flux at the interface fluid-solid wall. This conjugated conduction-convection problem is first simplified through the employment of the Coupled Integral Equations Approach (CIEA) to reformulate the heat conduction problem on the plate by averaging the related energy equation in the transversal direction. As a result, a partial differential formulation for the average wall temperature is obtained, while a third kind boundary condition is achieved for the fluid in the heat balance at the solid-fluid interface. From the available velocity distributions, the solution method is then proposed for the coupled partial differential equations, based on the Generalized Integral Transform Technique (GITT) under its partial transformation mode, combined with the method of lines implemented in the Mathematica 5.2 routine NDSolve.

Effect of nucleation and icing evolution on run-back freezing of supercooled water droplet

2019 ◽  
Vol 2 (2) ◽  
pp. 147-153
Author(s):  
Mingming Sun ◽  
Weiliang Kong ◽  
Fuxin Wang ◽  
Hong Liu
Keyword(s):  
Water Droplet ◽  
Supercooled Water

Experimental Researches on Micro-Droplet Freezing on a Solid Surface Under Atmospheric Conditions: Part I

2008 ◽  
Author(s):  
Heyun Liu ◽  
Xiaohui Ma
Keyword(s):  
Transmission Lines ◽  
Power Transmission ◽  
Electrostatic Force ◽  
Droplet Diameter ◽  
Ccd Camera ◽  
Freezing Process ◽  
Ice Accretion ◽  
Power Transmission Lines ◽  
Atmospheric Conditions ◽  
Air Stream

Atmospheric ice accretion on structures is a problem of fundamental importance to a number of industries. Examples of engineering problems caused by ice accretion involving aircraft, power transmission lines, telecommunication towers, electrical railway contact-wires, and other structures. Under atmospheric icing conditions two basic types of ice may form; rime or glaze. The supercooled micro-droplets in clouds are an important factor in icing. The objective of this study was to develop a new experimental method to investigate a single supercooled micro-droplet freezing process, in order to better understand the mechanism of rime or glaze ice accretion. The experimental device and principles are described in this paper. The experimental set has two small cold rooms, which is separated by a board with a central hole. A droplet with diameter of 15∼40 μm, temperature of 0∼−5°C was levitated in the cold air stream by electrostatic force. A CCD camera tracked its trace. The air temperature is from 0∼−10°C, the micro-droplet diameter is from 15∼40μm, and its temperature is from 0∼−5°C in the experimental study. This article focused on the experimental set and the experimental principles, and the next article will focus on the experimental data analysis.

The Combustion of a Liquid Fuel Droplet during Forced Convection

1994 ◽  
Vol 12 (1) ◽  
pp. 44-61
Author(s):  
Andrzej Teodorczyk ◽  
Stanislaw Wójcicki
Keyword(s):  
Reynolds Number ◽  
Forced Convection ◽  
Droplet Diameter ◽  
Fuel Droplet ◽  
Combus Tion ◽  
Air Stream ◽  
Freely Suspended ◽  
High Reynolds ◽  
Additional Support ◽  
Physical And Mathematical Models

A new experimental technique was used to investigate single fuel droplet combustion during forced convection: the burning droplet was freely suspended in the controlled air stream, without any additional support. Based on the photo-records of the burning process, the characteristics of the change of square of droplet diameter with time were made and the actual values of burning constants were determined for four hydrocarbon fuels: ben zene, n-heptane, iso-octane and toluene. The experiments were also carried out under micro-gravity and free convection conditions for the same set of fuels. The investigations have allowed the comparison of the burning mechanism of a single droplet for the three different external conditions and have compared quantitatively the burning constants. On the basis of the color pictures of the droplet burning under forced convection conditions and the temperature and gas concentration measurements within the flame, the mechanism of combus tion of fuel droplet was explained. The physical and mathematical models of the process have been proposed which included the aerodynamics of the droplet located in the high Reynolds number air stream, the energy balance of the evaporating droplet and the chemical reaction in the flow. The models have made it possible to determine the quantitative dependence of the burning con stant of different kinds of fuels on Reynolds number, the flow field parameters and the physical and chemical parameters of the liquid and its close surround ings. The calculated values of the parameters describing the burning pro cess have been compared to the experimental data and to the results reported by other investigators. The model has revealed the importance of the feed back mechanism between physical processes involved during droplet combus tion.

Experimental Study of Droplet Evaporation in a High-Temperature Air Stream

1983 ◽  
Vol 105 (2) ◽  
pp. 384-388 ◽  
Author(s):  
M. Renksizbulut ◽  
M. C. Yuen
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Liquid Droplets ◽  
Transfer Number ◽  
Number Range ◽  
Transfer Rates ◽  
Hot Air ◽  
Air Stream ◽  
Stream Density ◽  
Freely Suspended

Heat transfer rates to simulated and freely suspended liquid droplets were measured in an atmospheric hot air tunnel. The experiments were limited to water, methanol, and heptane droplets in a Reynolds number range of 25 to 2000, and a mass transfer number range of 0.07 to 2.79. The present experimental data together with data by others can best be correlated by Nuf(1+Bf).7 = 2 + 0.57 ReM1/2 Prf1/3, where properties are evaluated at film conditions except for the density in the Reynolds number which is the free-stream density. Thus the data shows that at higher temperatures, evaporation reduces heat transfer rates directly by a factor of (1 + Bf).7. Indirectly, evaporation affects heat transfer rates through the changes in both the composition and temperature of the surrounding gaseous medium.

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