Ind. Eng. Chem. ProcessDes. Dev. lQ84, 23,861
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Response to Comments on “Estimation of the Drag Coefficient of Regularly Shaped Particles In Slow Flows from Morphologlcai Descriptors”
Sic I thank Mr. Soszyski for his comments regarding my proposed correlation for the estimate of drag coefficients of regularly shaped particles in slow flows using morphological descriptors. Most of the questions raised by Mr. Soszyski are related to the values of the shape parameters E L 2 and EL3. For circular profiles the theoretical value for these parameters is zero as I have listed them in Table IV in my paper. However, our image analyzing system (PIAS) has a resolution that calculates a value of 1 X 10-lofor E L 2 and EL3 for circular profiles. The values of Kprdin eq 9 in my paper were calculated using 1 X 10-loinstead of zero. We chose to use the machine values instead of the theoretical ones so that the analysis could be done directly from PIAS generated values. Predictions with eq 9 using EL, and EL3equal to zero are meaningless since the smallest possible value predicted by PIAS is 1 X 10-lo. Therefore, the curve of predicted values for spheroids calculated by Mr. Soszyski by use of eq 9 using only nonzero terms is a misrepresentation of the prediction capability of these descriptors. Indeed if eq 9 is used with the 1X 10-lovalues then the predictions
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follow the solid curves quite well (compare my Figure 2 with his Figure 1). Rather, his results demonstrate the restriction of a correlation that is cast in a form that is limited by the resolution of the instrument. This resolution problem can be eliminated if the following correlation form is used
K
A(dC/ds)B(LoN/Lor)c(l - CL2N)D(1- CL2qE(1 CLsT)*
A repeat analysis of data in Table IV yields A = 0.95, B = 0.268, C = -1.69, D = 1.42, E = -0.21, and F = -0.13. The regression coefficient for this correlation is 0.93. This correlation allows for the use of zero values. Finally, I should like to call to the reader’s attention that K,, values for particles 40 and 41 in Table I in my paper should be 0.92 and 0.84, respectively. Chemical & Materials Engineering Program University of Iowa Iowa City, Iowa 52242
0 1984 American Chemical Society
Gregory R. Carmichael
