Expression for turbulent power draw of an in-line Silverson high shear mixer

Abstract

We report the validation of an expression to accurately describe the power draw of an in-line rotor–stator mixer over a range of flow rates and rotor speeds. The expression consists of a term which reflects the power required to rotate the shaft in response to the liquid resistance and a term to reflect the power convected away from the mixing chamber. A specially commissioned high speed (12,000rpm), instrumented 150/250 MS Silverson mixer has been developed with power draw determined from both torque and calorimetric measurements. Experiments are carried out using water over a range of independently controlled flow rates and rotor speeds with losses for both techniques carefully accounted for. For the torque measurement the value of the constants for the two terms above are Poz=0.197 and k1=9.35, respectively. For the calorimetric technique the measured temperature rise was similar to some of the corrections and losses over a significant range of the experimental space but nevertheless with careful experimentation constants similar to those for the torque technique were obtained, Poz=0.229 and k1=7.46. Allowing the calibration of the temperature probes to be a fit parameter in the regression routine increased the value of k1=8.10 but did not affect the value of Poz. A simple graphical method is also proposed using a dimensionless form of the expression which yielded slightly higher value of Poz but a slightly lower value of k1. The accuracy of both measurement techniques improves with rotor speed and the differences between the constants is attributed to the better accuracy of the torque technique at higher flow rates whereas the calorimetric technique is more accurate at low flow rates where the temperature rise is larger. Several repeats of the calorimetric technique with a reduced set of experimental points show good reproducibility. Finally at low flow rates (<10% of the maximum) the power unexpectantly increases and a modification to the expression is proposed by considering the pumping efficiency.