Tetsu-to-Hagane Vol. 87 (2001) No. 1 Fig. 1. Experimental apparatus for PIV measurement. Fig. 2. Detail of A.

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Tetsu-to-Hagane Vol. 87 (2001) No. 1 Analysis of the Stirring Process of Water Bath Contained in a Rotating Cylindrical Vessel with Particle Imaging Velocimetry Tomoyuki SHIMIZU, fin YOSHIDA, Norihisa TSUDA, Tsuneo KOSEKI, Shin-ichiro YOKOYA and Manabu IGUCHI Synopsis : The instantaneous velocity of laminar flow in a water bath contained in a cylindrical vessel, being initially at rest and then suddenly set in rotation, was measured with particle imaging velocimetry (PIV). The period from the start of rotation to the moment at which the flow in the bath reaches steady state is defined as the flow establishment time. The results for the establishment timewere compared with previous empirical equations derived on the basis of velocity measurements with laser Doppler velocimetry (LDV), and an applicable range of the equations was evaluated. The measured values of the flow establishment time were underestimated by the equations. This is because the equations were obtained in a higher Reynolds number range. An empirical equation for the flow establishment time was newly proposed. Key words : unsteady flow; rotating laminar flow; flow establishment time; PIV; cylindrical vessel.

Tetsu-to-Hagane Vol. 87 (2001) No. 1 Fig. 1. Experimental apparatus for PIV measurement. Fig. 2. Detail of A.

粒 子画像流速計 を用 いた回転円筒容 器内部の撹拌過程の解析 (a) Image of visualized particles. (b) Scheme of (a) Fig. 5. Velocity vectors. HL/D= (Re=36.6, ƒö=2.36 rad/s, t= 10 s. 2.61) (c) Fundamental algorithm of PIV system. Fig. 3. Explanation of P1V system. (a) Image of visualized particles. (b) Scheme of (a). (c) Fundamental algorithm of PIV system. Fig. 6. Distribution 2.36 3. of rad/s, t=10 tangential velocity. s, HL/D= (Re =36.6, ƒö= 2.61) 実 験 結 果 と考 察 3 1 速 度 ベ ク トル と 接 線 方 向 速 度 の 分 布,過 渡時間の定 義 測 定 結 果 の 一 例 と し てRe=36.6,ω=2.36rad/s,t=10s, HL/D=2.61に お け る 速 度 ベ ク トル をFig,5に 示 す.な お, 円 筒 容 器 中 心 近 傍 に お け る 速 度 ベ ク トル は 繁 雑 さ を 避 け る た め10mm/sを し き い 値 と し て,そ れ 以 下 の 速 度 ベ ク トル は 削 除 し て 表 記 し て あ る.Fig.6は 半 径 方 向 に お け る接 線 方 向 速 度νθの 分 布 を 表 して い る.容 お け る 接 線 方 向 速 度ν θは54.3mm/sと 器 の 側 壁(R=23mm)に な っ た.速 度 の 大 き い 領 域 は 容 器 側 壁 か ら 中 心 へ と 徐 々 に 遷 移 して い き,充 分 時 間 が 経 過 す る と 速 度 分 布 は ほ ぼ 直 線 と な る.(Fig.7)こ れ は 容 器 内 の 流 れ が 定 常 状 態 に 達 し た こ と を 意 味 して い る. そ こで 容 器 内 の 流 れ が定 常 状 態 に 至 る ま で の 過 渡 時 間 を Fig. 4. Estimation of PIV measurement 求 め る た め に,半 error. 行 っ た.ξ,τ,φ 径 方 向 座 標r,時 れ 次 式 で 定 義 され る 渦. 9 間t,速 度νθの 無 次 元 化 を はr,t,νθ に 対 す る 無 次 元 数 で あ り,そ れぞ 9

Tetsu-to-Hagane Vol. 87 (2001) No. 1 Fig. 9. Relationship between Ė and ė. (HL/D=2.61) Fig. 7. Transition of the distribution of tangential velocity. (Re=36.6, Ě=2.36 rad/s, HL/D=2.61) (a) Relationship between Ė and ė. (b) Relationship between Ėē and ē.

Fig. 11. Comparison of previous equation and experimentally measured values of Ėt,s. Fig. 12. Relationship between Reynolds number and nondimensionalized flow establishment time. Fig. 13. Relationship between Reynolds number and nondimensionalized flow establishment time.

Tetsu-to-Hagan6 Vol. 87 (2001) No. 1 Fig. 14. Relationship between aspect ratio and values of Fig. 16. Comparison of previous equation and experimentally measured values of flow establishment time Ts. Fig. 15. Comparison of empirical equation and experimentally measured values of Ėt,s.

1 ) Y.Kato, S.Hiraoka, Y.Tada, S.Shirai, T.Ue, S.-T.Koh and T. Yamaguchi: Kagaku Kogaku Ronbunshu, 21 (1995), 365. 2 ) Y.Kato, S.Hiraoka, Y.Tada, T.Mori, S.Shirai, T.Ue and S.-T.Koh: Ka- gaku Kogaku Ronbunshu, 20 (1994), 437. 3 ) G.Kawashima and W.J.Yang: Exp. Fluids, 6 (1988), 165. 4 ) G.Kawashima and W.J.Yang: Proc. Measuring and Metering of Unsteady Flows, vol. 106, ASME, New York, (1991), 41. 5 ) G.Kawashima and W.J.Yang: Flow Visualization, vol. V, Hemisphere, New York, (1989), 633. 7 ) S.Yokoya, M.Iguchi, S.Takagi and M.Sakamoto: ISIJ Int., 38 (1998), 421. 8 ) M.Iguchi, M.Sakamoto, H.Kawabata and S.Yokoya: ISIJ Int., 38 (1998), 1180. 9 ) M.Kawashima, H.Ogami and W.J.Yang: Trans. Jpn. Soc. Mech. Eng., 61B (1995), 2918. 10) X.Song, F.Yamamoto, M.Iguchi and Y.Murai: Exp. Fluids, 26 (1999), 371. 11) X.Song, F.Yamamoto, M.Iguchi, M.Koketsu and G.Chen: 1511 Int., 36 (1996), S54. 12) Y.Sada, K.Sato, N.Kasagi and N.Takamura: Trans. Jpn. Soc. Mech. Eng., 60B (1994), 865. 14) N.Tsuda, T.Kobayashi, T.Saga and S.Segawa: Preprint of Jpn. Soc. Mech. Eng., 910 (1991), 316. 15) H.P.Greenspan: The Theory of Rotating Fluids, Cambridge Univ. Press, Cambridge, (1980), 275.

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