Study on Miter-Bend Flow : Part 1-Analysis of Flow based upon Two-Dimensional Potential Theory

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Other Title
  • 屈折管内の流れに関する研究 : 第1報-二次元ポテンシャル理論による流れの解析
  • 屈折管内の流れに関する研究-1-二次元ポテンシャル理論による流れの解析
  • クッセツカンナイ ノ ナガレ ニカンスルケンキュウ 1 2ジゲン ポテンシャル

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Abstract

A miter bend is one of the most general joints of conduits, and it is used in many piping and fluid machinery. So it is very important to industry to clarify flow patterns and mechanisms in a miter bend. Besides, due to the geometrical shape of its conduit the flow in a miter bend separates at the convex corner or the bending corner of the inner wall. So the study of the flow patterns and mechanisms in a miter bend are expected to be useful also in considering general flows with separation. Then, as a basis in considering the flow in the conduit of a miter bend, the authors analyzed the flow with separation at the convex corner of a bending channel in two-dimensional potential flow based upon the hodograph method. The analytical method used in this report can be applied to the bending channel flow with an arbitrary bending angle and an arbitrary crosssectional area ratio. First, for analytical examples of the miter bends with the angles of 45°, 90° and 135°, which are minutely considered in the following reports, the authors analyzed and calculated coefficients of contraction, forms of streamlines and pressure distributions. Next, for those with the angle of 5° and with the angles from 15° to 165° with 15° intervals, the authors calculated the analytical results, and got the relation among bending angles, flow velocities, coefficients of contraction and crosssectional area ratios. Consequently, the following conclusions were obtained-that is, the flow velocities at infinity upstream before bending and cofficients of contraction at the same crosssectional area ratio decrease with the increase of the bending angle; the flow velocities at infinity upstream before bending with the same bending angle decrease but coefficients of contraction increase with the increase of the crosssectional area ratio. In analysis, to suppose potential flow is to ignore the influence of viscous effect. Besides, to suppose two-dimension is to suppose a conduit of rectangular crosssection whose depth is much longer than its width. But it will be clarified in the following reports that with appropriate considerations, the analytical results in two-dimensional potential flow are very useful to the study of the viscous flow in a complicated three-dimensional bend.

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