Resistance of a Flow through an Annulus with an Inner Rotating Cylinder

Abstract

In this paper, the resistance of a water flow through co-axial cylinders when the inner cylinder rotates, is studied experimentally. The resistances are measured for six gap sizes (s/r_1=0.0136〜0.115,s : gap, r_1 : radius of inner cylinder) and for various combinations of axial and rotational flows. Results obtained are as follows : 1. When the axial flow is laminar, the resistance of a flow is unaffected up to a certain rotating speed (R_ : critical rotating Reynolds number), but beyond this speed the flow resistance increases as the R_ω increases. 2. The value of critical Taylor number R_ (s/r_1)^<1/2> increases as the axial Reynolds number (R_e=v_ms/ν) increases up to a certain value (R_e=600), beyond this value R_ (s/r_1)^<1/2> decreases to zero with the increase of R_e. When the axial flow is turbulent, such a critical rotating Reynolds number cannot be recognized. 3. When R_ω>10 000,the resistance coefficient of a flow λ can be expressed by λ= 0.26 R_e^ ×{1+(7/8)^2(R_ω/2Re)^2}^<0.38> even for small R_e.