The mixing of solid particles in a motionless mixer—a stochastic approach

AIChE Journal ◽  
1972 ◽  
Vol 18 (5) ◽  
pp. 984-989 ◽  
Author(s):  
S. J. Chen ◽  
L. T. Fan ◽  
C. A. Watson
Keyword(s):  
Stochastic Approach ◽  
Solid Particles ◽  
Motionless Mixer

scholarly journals Heterogeneous freezing of water droplets containing kaolinite particles

2011 ◽  
Vol 11 (9) ◽  
pp. 4191-4207 ◽  
Author(s):  
B. J. Murray ◽  
S. L. Broadley ◽  
T. W. Wilson ◽  
J. D. Atkinson ◽  
R. H. Wills
Keyword(s):  
Cooling Rate ◽  
Surface Area ◽  
Clay Mineral ◽  
Constant Temperature ◽  
Hydrophobic Surface ◽  
Supercooled Liquid ◽  
Stochastic Approach ◽  
Solid Particles ◽  
Rate Coefficients ◽  
Water Droplets

Abstract. Clouds composed of both ice particles and supercooled liquid water droplets exist at temperatures above ~236 K. These mixed phase clouds, which strongly impact climate, are very sensitive to the presence of solid particles that can catalyse freezing. In this paper we describe experiments to determine the conditions at which the clay mineral kaolinite nucleates ice when immersed within water droplets. These are the first immersion mode experiments in which the ice nucleating ability of kaolinite has been determined as a function of clay surface area, cooling rate and also at constant temperatures. Water droplets containing a known amount of clay mineral were supported on a hydrophobic surface and cooled at rates of between 0.8 and 10 K min−1 or held at constant sub-zero temperatures. The time and temperature at which individual 10–50 μm diameter droplets froze were determined by optical microscopy. For a cooling rate of 10 K min−1, the median nucleation temperature of 10–40 μm diameter droplets increased from close to the homogeneous nucleation limit (236 K) to 240.8 ± 0.6 K as the concentration of kaolinite in the droplets was increased from 0.005 wt% to 1 wt%. This data shows that the probability of freezing scales with surface area of the kaolinite inclusions. We also show that at a constant temperature the number of liquid droplets decreases exponentially as they freeze over time. The constant cooling rate experiments are consistent with the stochastic, singular and modified singular descriptions of heterogeneous nucleation; however, freezing during cooling and at constant temperature can be reconciled best with the stochastic approach. We report temperature dependent nucleation rate coefficients (nucleation events per unit time per unit area) for kaolinite and present a general parameterisation for immersion nucleation which may be suitable for cloud modelling once nucleation by other important ice nucleating species is quantified in the future.

Effects of Applying a Stochastic Rebound Model in Erosion Prediction of Elbow and Plugged Tee

2002 ◽  
Author(s):  
Xianghui Chen ◽  
Brenton S. McLaury ◽  
Siamack A. Shirazi
Keyword(s):  
Prediction Model ◽  
Oil And Gas ◽  
Oil And Gas Industry ◽  
Outer Wall ◽  
Stochastic Approach ◽  
Solid Particles ◽  
Gas Industry ◽  
Erosion Prediction ◽  
Before And After ◽  
Experimental Findings

Solid particle erosion is a complex phenomenon that depends on many factors such as particle and fluid characteristics, type of material being eroded, and flow geometry. Fittings used in the oil and gas industry such as elbows are susceptible to erosion when solid particles are present in the flow. The momentum of particles carries them across streamlines and the particles impinge the outer wall of the elbow resulting in erosion damage. In an erosive environment, plugged tees are commonly used instead of elbows to reduce the erosion especially where space considerations are important and long-radius elbows can not be used. However, it is unclear how much of a reduction in erosion occurs by replacing an elbow with a plugged tee. In order to compare the erosion in an elbow and a plugged tee exposed to the same flow conditions, a CFD-based erosion prediction model is applied. The model has three primary steps: flow modeling, particle tracking, and applying erosion equations. The results from the model agree with experimental findings for the elbow geometry. However, the simulation results for erosion rate generated for the plugged tee requires a stochastic approach. Results obtained with the erosion prediction model before and after this modification are shown.

Abrasive wear of polymer/steel gear drives

2008 ◽  
Vol 4 (1) ◽  
pp. 1-26
Author(s):  
Gábor Kalácska
Keyword(s):  
Wear Resistance ◽  
Abrasive Wear ◽  
Material Selection ◽  
Solid Particles ◽  
Soil Types ◽  
General View ◽  
Modern Engineering ◽  
Clean Environment ◽  
Engineering Polymers ◽  
Plastic Gears

Research was performed on the friction, wear and efficiency of plastic gears made of modern engineering polymers and their composites both in a clean environment (adhesive sliding surfaces) and in an environment contaminated with solid particles and dust (abrasive), with no lubrication at all. The purpose is to give a general view about the results of abrasive wear tests including seven soil types as abrasive media. At the first stage of the research silicious sand was applied between the meshing gears and the wear of plastic and steel gears was evaluated and analyzed from the point of different material properties (elongation at break, hardness, yield stress, modulus of elasticity) and its combinations. The different correlations between the experienced wear and material features are also introduced. At the second stage of the project the abrasive sand was replaced with different physical soil types. The abrasive wear of gears is plotted in the function of soil types. The results highlight on the considerable role of physical soil types on abrasive wear resistance and the conclusions contain the detailed wear resistance. The results offer a new tribology database for the operation and maintenance of agricultural machines with the opportunity of a better material selection according to the dominant soil type. This can finally result longer lifetime and higher reliability of wearing plastic/steel parts.

LIMITATIONS OF THE STOCHASTIC APPROACH IN TWO-PHASE TURBULENT FLOW CALCULATIONS

1996 ◽  
Vol 6 (2) ◽  
pp. 211-225 ◽  
Author(s):  
Keh-Chin Chang ◽  
Wen-Jing Wu ◽  
Muh-Rong Wang
Keyword(s):  
Turbulent Flow ◽  
Stochastic Approach ◽  
Two Phase

INVERSE PROBLEMS METHOD FOR STUDY OF HEAT TRANSFER IN SOLIDS INTERACTED WITH GAS FLOWS LOADED BY SOLID PARTICLES

Equipment ◽  
2006 ◽  
Author(s):  
Aleksey V. Nenarokomov ◽  
O. M. Alifanov ◽  
E. A. Artioukhine ◽  
I. V. Repin
Keyword(s):  
Heat Transfer ◽  
Inverse Problems ◽  
Solid Particles ◽  
Gas Flows
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