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The Synthetic Scale-up Data Generated by the Austin model and Their Estimation by the Kotake–Kanda Model

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posted on 22.04.2022, 11:47 authored by Ecevit Bilgili

The Excel spreadsheet contains the synthetic scale-up data generated by the Austin model and their estimation using the Kotake–Kanda (KK) model, which overall yields the information presented in Table 2 of the manuscript. In view of all scale-up (SU) cases in Table 2, the Austin model, via Eqn. (12) of the manuscript, was used to produce the synthetic scale-up data, i.e., the specific breakage rate Si*, to which the Si* generated by the KK model, via Eqn. (13) of the manuscript, were compared (SU1–SU4 in Table 2). In SU1–SU4, standard values of the scale-up correction exponents, i.e., N1 = 0.5 and N2 = 0.2, were used. In SU5–SU8, N1 and N2 were estimated by fitting Eqn. (13) to the synthetic scale-up data for each diameter ratio D/DT separately. In SU9–SU12, they were fitted to the synthetic scale-up data for all D/DT data together. These two separate types of fits are presented in the Excel spreadsheet, which contains two separate spreadsheets entitled “Separately fitted” and “Simultaneously fitted.” For simplicity, Si* was replaced by Si in the Excel spreadsheet. Columns A and B yield, respectively, the ball size dB values and the particle size xi values from which the artificial Si values were calculated using the Austin model for different values of D/DT. A summary table is included at the far right side of the Excel spreadsheet, which presents the values used in Table 2 of the manuscript. 

Nomenclature
Si,A and Si,K: Si* calculated by the Austin model and estimated by the KK model
Si,Kmod: Si* estimated by the KK model with modified (fitted) N1 and N2
Sqrt(Si,A) and Sqrt(Si,K): Square root of Si,A and Si,K
Sqrt(Si,Kmod): Square root of Si,Kmod
SE original: square error between the Austin and the KK model for N1 = 0.5 and N2 = 0.2
SE modified: square error between the Austin and the KK model for fitted N1 and N2

 

History

Manuscript title

On the Similarity of Austin Model and Kotake–Kanda Model and Implications for Tumbling Ball Mill Scale-up

Article DOI

https://doi.org/10.14356/kona.2023005

Corresponding author email address

bilgece@njit.edu

Copyright

© 2022 The Author(s)