Numerical Simulation for Abrupt Contraction Flow of Fiber Suspensions in Polymeric Fluid Kazunori Yasuda, Taro Nishimura* and Kiyoji Nakamura Departme

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1 Numerical Simulation for Abrupt Contraction Flow of Fiber Suspensions in Polymeric Fluid Kazunori Yasuda, Taro Nishimura* and Kiyoji Nakamura Department of Mechanical Engineering, Osaka University, Suita, Osaka *Kyoto Institute of Technology, Sakyo-ku, Kyoto Abstract Flow pattern and fiber orientation of fiber suspensions in polymeric fluid through a two-dimensional abrupt contraction are calculated using the Giesekus model and the Dinh-Armstrong model. The flow pattern of fiber suspensions in polymeric fluid is different from that of polymeric fluid ; a vortex near the salient corner in the suspension flow becomes larger than that in the polymeric fluid flow. The dependence of the vortex length on a mobility parameter a in the Giesekus model and a characteristic parameter of fiber suspensions in the Dinh-Armstrong model are discussed.

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4 繊 維 機 械 学 会 誌 50 Fig. 1 Abrupt contraction non-uniform finite geometry difference (in mm) and mesh. 5.急 絞 り流れの数値計算結果 5.1急 絞 り流 れ の流 れ 模 様 と繊 維 配 向 急 絞 り流 路 に お け る 流 線 と繊 維 配 向 の 数 値 計 算 結 果 の 例 を 図3に の場 合 と,ニ 示 す.(a)は ニ ュ ー ト ン流 体(β=0) ュ ー ト ン流 体 を 分 散 媒 と し た繊 維 懸 濁 液 の 場 合(β=5)で あ る.繊 維 懸 濁 液 で は,流 路 の 下半 分 に は 流 線 を,上 半 分 に は 繊 維 配 向 を示 す.(b) は高 分 子 流 体 の 場 合(α=0.1,λ=1.0,We=1.0,β= 0)と,繊 維 懸 濁 高 分 子流 体 の 場 合(β=5)で あ る. 流 れ 模 様 を 比 較 す る と,角 部 の 循 環 二 次 流 れ が,ニ (a) ュ ー ト ン流 体 よ り も高 分 子流 体 の 方 が,ま た,分 散 媒 に か か わ らず 繊 維 が な い場 合 よ り も繊 維 懸 濁 液 の 方 が 大 き く な っ て い る こ と が 分 か る.こ の 循 環 二 次 流 れ に よ っ て 流 線 は よ り ゆ る や か に 曲 が り,そ 後,加 の 速 さ れ な が ら狭 い 流 路 に 流 れ 込 む. 次 に 繊 維 の配 向 状 態 に つ い て み る と,主 流 部 で は 繊 維 が ほ ぼ 流 線 方 向 を 向 い て お り,Lipscomb2)や Chibaら3)が 計 算 に 用 い た.繊 維 配 向 方 向 と流 線 方 向 と が 一 致 して い る と い う仮 定 を 満 足 して い る こ と が 分 か る. 5.2急 絞 り部 にお ける 循 環 二 次 流 れ の長 さ 数 値 計 算 結 果 か ら,急 絞 り流 れ に お い て,ニ ュー ト ン流 体 と 比 べ て 高 分 子 流 体 や 繊 維 懸 濁 液 で は 循 環 二 次 流 れ が 長 く な る こ と が 分 か っ た.そ (b) Fig. 2 Steady mode =4.5 viscometric Giesekus (Pa functions model with ƒås,=0.45 of a (Pa one に示 す 循 環 二 次 流 れ の 長 さLvと s), ƒåp We,Giesekusモ こ で 図3(a) ワ イ セ ンベ ル ク 数 デルの流動 パ ラ メー タ αおよ び繊 s). (a) Shear (b) Elongational 維 の無 次 元 パ ラ メ ー タ β と の 関 係 を 調 べ た.た viscosity. 以 下 で は,渦 の 長 さを,広 い 方 の 流 路 幅Hで viscosity. T4 だ し 無次元

5 Fig. 3 Streamlines and fiber orientations. Lv de notes vortex length. (a) Newtonian fluid ([ƒà=0) and fiber sus pension in Newtonian fluid (ƒà=5). (b) Polymeric fluid (ƒ =0.1, We=1) and fiber suspension in polymeric fluid (ƒ = 0.1, We=1, ƒà=5). Fig. 4 Dependence of vortex length L * on We for various values of ƒà. œ shows Lv* of Newto nian fluid, ; fiber suspension in Newtoni an fluid with ƒà=1, ; ƒà=5, ; ƒà=10. (a) Mobility parameter ƒ =0.1 in Giesekus model. (b) Mobility parameter ƒ =0.4 in Giesekus model.

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7 Fig. 6 Normal stress difference along the center line for various values of ƒà (ƒ = 0.2, We= 2). (a) Newtonian term of normal stress difference in fiber suspension in polymeric fluid. (b) Viscoelastic term of normal stress difference in fiber suspension in polymeric fluid. (c) Fiber suspension term of normal stress difference in fiber suspension in polymeric fluid. (d) Normal stress difference in fiber suspension in polymeric fluid. Fig. 7 Velocity profile along the center line for fiber suspension in polymeric fluid for various values of ƒà (ƒ =0.2, We=2). T7

8 1) R. C. Givler, M. J. Crochet and R. B. Pipes ; J. Composit Materials, 17, 330 (1983) 2) G. G. Lipscomb II, M. M. Denn, D. U. Hur and D. V. Boger ; J. Non-Newtonian Fluid Mech., 26, 297 (1988) 3) K. Chiba, K. Nakamura and D. V. Boger ; J. Non-Newtonian Fluid Mech., 35, 1 (1990) 4) S. M. Dinh and R. C. Armstrong ; J. Rheol., 28, 207 (1984) 7) H. Giesekus ; J. Non-Newtonian Fluid Mech., 11, 69 (1982) 8) B. Debbaut, J. M. Marchal and M. J. Crochet ; J. Non- Newtonian Fluid Mech., 29, 119 (1988) 9) H. Ch. Choi, J. H. Son and J. Y. Yoo ; J. Non-Newtonian Fluid Mech., 29, 347 (1988) 10) J. Y. Yoo and H. Ch. Choi ; Rheol. Acta, 28, 13 (1989) 11) M. A. Hulsen and J. V. D. Zanden ; J. Non-Newtonian Fluid Mech., 38, 183 (1991) 12) G. Schleiniger and R. J. Weinacht ; J. Non-Newtonian Fluid Mech., 40, 79 (1991) 13) G. Ausias ç ¼5 ¼; J. Rheol., 36, 525 (1992) 16) S. G. Advani and C. L. Tucker III ; J. Rheol., 34, 367 (1990)

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