Power Number and Mixing Drag Coefficient of Koch Fractal Impellers used by Koch Curve

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  • コッホ曲線を用いたフラクタル翼の動力数と撹拌抗力係数
  • コッホ キョクセン オ モチイタ フラクタルヨク ノ ドウリョクスウ ト カクハン コウリョク ケイスウ

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Abstract

<p>In this study, we evaluated the power characteristics of various impeller blades incorporating the Koch curve, which is a typical self-similar fractal shape. The experiment was performed in a turbulent region with standard baffles. We chose a six-flat-blade Rushton turbine impeller and a four-flat-blade paddle impeller as basic impellers. To evaluate hydrodynamically the blade shape of fractal impellers incorporating the Koch curve into the blades of the basic impellers, we proposed the mixing drag coefficient CDM as a new simple index, which consists of drag coefficient and proportional coefficient of a model that assumes a simple velocity distribution. Thus, the power number NP can be expressed as NP=4π3npCDMSf* by using the number of blades np and the dimensionless blade area factor Sf*. This factor represents the effects of projected area and rotational moment of blades. The results showed that the NP of Koch fractal impellers ranged widely from 40 to 97% of the basic impeller in the six-bladed Rushton impeller system and from 46 to 87% in the four-bladed flat paddle impeller system. On the other hand, in the evaluation using the CDM, each Koch fractal impeller had a value in a narrow range from 86 to 97% of the basic impeller, although the blade area was different. Especially for some fractal impellers, the CDM decreases as the iteration number of Koch curve increased, so we confirmed the drag reduction effect by incorporating the Koch curve. The CDM can be easily derived from the Np, and become a basic and practical index of fluid drag coefficient in a special rotating flow field, namely, a stirring tank.</p>

Journal

  • KAGAKU KOGAKU RONBUNSHU

    KAGAKU KOGAKU RONBUNSHU 47 (3), 57-63, 2021-05-20

    The Society of Chemical Engineers, Japan

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