scholarly journals Modelling the Hindered Settling Velocity of a Falling Particle in a Particle-Fluid Mixture by the Tsallis Entropy Theory

Entropy ◽  
2019 ◽  
Vol 21 (1) ◽  
pp. 55 ◽  
Author(s):  
Zhongfan Zhu ◽  
Hongrui Wang ◽  
Dingzhi Peng ◽  
Jie Dou
Keyword(s):  
Experimental Data ◽  
Settling Velocity ◽  
Concentration Function ◽  
Tsallis Entropy ◽  
Entropy Theory ◽  
Clear Fluid ◽  
Deterministic Models ◽  
Fluid Mixture ◽  
Hindered Settling ◽  
Hindered Settling Velocity

The settling velocity of a sediment particle is an important parameter needed for modelling the vertical flux in rivers, estuaries, deltas and the marine environment. It has been observed that a particle settles more slowly in the presence of other particles in the fluid than in a clear fluid, and this phenomenon has been termed ‘hindered settling’. The Richardson and Zaki equation has been a widely used expression for relating the hindered settling velocity of a particle with that in a clear fluid in terms of a concentration function and the power of the concentration function, and the power index is known as the exponent of reduction of the settling velocity. This study attempts to formulate the model for the exponent of reduction of the settling velocity by using the probability method based on the Tsallis entropy theory. The derived expression is a function of the volumetric concentration of the suspended particle, the relative mass density of the particle and the particle’s Reynolds number. This model is tested against experimental data collected from the literature and against five existing deterministic models, and this model shows good agreement with the experimental data and gives better prediction accuracy than the other deterministic models. The derived Tsallis entropy-based model is also compared with the existing Shannon entropy-based model for experimental data, and the Tsallis entropy-based model is comparable to the Shannon entropy-based model for predicting the hindered settling velocity of a falling particle in a particle-fluid mixture. This study shows the potential of using the Tsallis entropy together with the principle of maximum entropy to predict the hindered settling velocity of a falling particle in a particle-fluid mixture.

scholarly journals Evaluating Different Methods for Determining the Velocity-Dip Position over the Entire Cross Section and at the Centerline of a Rectangular Open Channel

Entropy ◽  
2020 ◽  
Vol 22 (6) ◽  
pp. 605
Author(s):  
Zhongfan Zhu ◽  
Pengfei Hei ◽  
Jie Dou ◽  
Dingzhi Peng
Keyword(s):  
Experimental Data ◽  
Cross Section ◽  
Shannon Entropy ◽  
Open Channel ◽  
Lateral Distribution ◽  
Tsallis Entropy ◽  
The Other ◽  
Deterministic Models ◽  
Entire Cross Section ◽  
General Index

The velocity profile of an open channel is an important research topic in the context of open channel hydraulics; in particular, the velocity-dip position has drawn the attention of hydraulic scientists. In this study, analytical expressions for the velocity-dip position over the entire cross section and at the centerline of a rectangular open channel are derived by adopting probability methods based on the Tsallis and general index entropy theories. Two kinds of derived entropy-based expressions have the same mathematical form as a function of the lateral distance from the sidewall of the channel or of the aspect ratio of the channel. Furthermore, for the velocity-dip position over the entire cross section of the rectangular open channel, the derived expressions are compared with each other, as well as with two existing deterministic models and the existing Shannon entropy-based expression, using fifteen experimental datasets from the literature. An error analysis shows that the model of Yang et al. and the Tsallis entropy-based expression predict the lateral distribution of the velocity-dip position better than the other proposed models. For the velocity-dip position at the centerline of the rectangular open channel, six existing conventional models, the derived Tsallis and general index entropy-based expressions, and the existing Shannon entropy-based models are tested against twenty-one experimental datasets from the literature. The results show that the model of Kundu and the Shannon entropy-based expression have superior prediction accuracy with respect to experimental data compared with other models. With the exception of these models, the Tsallis entropy-based expression has the highest correlation coefficient value and the lowest root mean square error value for experimental data among the other models. This study indicates that the Tsallis entropy could be a good addition to existing deterministic models for predicting the lateral distribution of the velocity-dip position of rectangular open channel flow. This work also shows the potential of entropy-based expressions, the Shannon entropy and the Tsallis entropy in particular, to predict the velocity-dip position at the centerline of both narrow and wide rectangular open channels.

On constitutive functions for hindered settling velocity in 1-D settler models: Selection of appropriate model structure

2017 ◽  
Vol 110 ◽  
pp. 38-47 ◽  
Author(s):  
Elena Torfs ◽  
Sophie Balemans ◽  
Florent Locatelli ◽  
Stefan Diehl ◽  
Raimund Bürger ◽  
...  
Keyword(s):  
Settling Velocity ◽  
Model Structure ◽  
Hindered Settling ◽  
Hindered Settling Velocity ◽  
Selection Of

scholarly journals Hindered Settling Velocity of Irregular Shaped Particles

1988 ◽  
Vol 104 (1206) ◽  
pp. 505-512
Author(s):  
Hiroshi SATO ◽  
Karoku NODA ◽  
Kazuo OTSUKA ◽  
Toshio KAWASHIMA
Keyword(s):  
Settling Velocity ◽  
Hindered Settling ◽  
Hindered Settling Velocity

On-line quantification of settling properties with in-sensor-experiments in an automated settlometer

1996 ◽  
Vol 33 (1) ◽  
pp. 37-51 ◽  
Author(s):  
P. Vanrolleghem ◽  
D. Van der Schueren ◽  
G. Krikilion ◽  
K. Grijspeerdt ◽  
P. Willems ◽  
...  
Keyword(s):  
Settling Velocity ◽  
Practical Experience ◽  
Identifiability Analysis ◽  
Hindered Settling ◽  
Dilution Step ◽  
On Line ◽  
Hindered Settling Velocity ◽  
External Light Source ◽  
Maintenance Requirements ◽  
Initial Results

An on-line settlometer has been developed. Batch settling experiments lasting 40 min are performed in a model clarifier incorporated in the sensor (“In-Sensor-Experiment”). The descent of the sludge blanket interface is monitored and the settling characteristics are deduced. The hardware consists of a 10 litre Pyrex decanter, a stirring/wall-scraping mechanism, an external light source and a moving light-intensity scanner. Either stirred or non-stirred settling curves can be recorded. Processing of the raw data readily produces the zone or hindered settling velocity (Vs) and the (stirred) sludge volume ([S]SV). The latter can be combined with a sludge concentration measurement to determine SVI-values, and dSVIs if a dilution step is included. Initial results are reported on a more elaborate interpretation of the data based on sedimentation models. The Takács et al. and Cho et al. models described the settling curves equally well. However, an identifiability analysis showed that not all parameters can be given unique values on the basis of the simple batch settling experiments applied in the work. More elaborate “In-Sensor-Experiments” are required to obtain complete identification. Two years of practical experience with the device on pilot- and full-scale treatment plants revealed its robustness, low maintenance requirements and reproducible monitoring of settling curves.

Sign in / Sign up

Export Citation Format

Share Document