研 究 発 表 等 (Research Papers and Patents)

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工 業 所 有 権 (Patents)

(1) 中林功一，土田陽一，科学技術振興事業団 多段分級装置, 特許出願中 特願2002-061141, 出願 平成14年3月6日

本発明は，広い粒度分布をもつ原料の微粒子群から狭い複数の微粒子群を同時に分収できる効率的な多段分級装置を提供するものである．分級範囲の異なる複数の分級ユニットを同一回転軸上に縦続配設して回転させ，各分級ユニットで準剛体回転成層流を実現して，同時に複数の粒度範囲の分級が高精度に行なわれるようにした．特に各段の分級ユニットの寸法を，各段の分級性能と微粒子の条件，運転条件などから普遍的なスケール則に基づいて簡単に決定できるようにした．

(2) 中林功一, 土田陽一, 積水化学工業(株) 分級装置, 特許 第3542382号,平成16年4月9日

本発明は，湿式の分級装置において，微粒産物への粗大粒子の混入を完全に防止することにより高精度な分級を達成することを目的として，準剛体回転成層流内で原料スラリを分級する装置を提供するものである．この目的のために，ロータの外周面とこのロータと同一軸芯上に配設されたハウジングの内周面との間に分級室を形成し，この分級室内に水及び原料スラリを供給すると共に，このロータ及びハウジングを一体的に高速回転させて，この分級室内で準剛体回転成層流を生成させ，この流れ中で高精度の分級を可能ならしめた．

発 表 論 文 (Research papers)

(1) K. NAKABAYASHI, W. Sha and Y. Tsuchida Relaminarization phenomena and external-disturbance effects in spherical
Couette flow, *JFM*, in press.

*Key words**: Relaminarization, Chaos, Transition, Spherical Couette flow, External
disturbance, Bifurcation*

(2) Y. TSUCHIDA and K. NAKABAYASHI New wettype centrifugal classification using an almost rigidly rotating flow (Double-stage
system) *Proceedings of PARTEC 2004* (*International Congress for Particle Technology*), CD-ROM, 4 pages, 2004.

In our previous study (WCPT3 in 1998), we proposed a new accurate wet-type centrifugal classification system (single stage) that employs a perfectly laminar almost-rigidly-rotating-through-flow and classifies feed particles into fine and coarse products. In the present study, we have extended this system into a double-stage system that classifies feed particles into coarse, medium and fine products all at once, and have experimentally shown that the double-stage system works well as both semi-continuous and batch types.

(3) K. NAKABAYASHI and Y. TSUCHIDA Accurate wettype centrifugal classification using an almost rigidly rotating flow Classification principle and performance of the batchtype classification *Advanced Powder Technology*, **15**-1, pages 109-129, 2004.

We have proposed a new system for an accurate wettype centrifugal classification to which an almost rigidly rotating throughflow is applied. This flow can be produced within a highly rotating doublewalled container, without any turbulent fluctuation. In the present paper, we have employed the batchtype classification with a cylindersphereshaped container in classification experiments, theoretical and numerical flow analyses and flowvisualization measurements. Consequently, we have obtained the following main conclusions; (1) with decreasing Ekman number (i.e. increasing rotation rate) at a constant Rossby number or with decreasing Rossby number (decreasing throughflow rate) at a constant Ekman number, the cut size and fine yield decrease and the classification accuracy increases, (2) for the occurrence of the rigidrotation region which is indispensable to collect the coarse product, it is necessary to make the flow field inverseCshaped towards the rotation axis.

(4) 中林功一, 土田陽一，森西洋平，木村一成，軸対称回転容器内流れのスチュワートソン層と微粒子軌道, 日本機械学会論文集(B編), **69**-682, pp1364-1371, 2003.

K. NAKABAYASHI, Y. TSUCHIDA, Y. MORINISHI and K. KIMURA: Study on the Stewartson Layer and Particle Trajectory in Rotating Fluid Flow within an Axisymmetric Container (in Japanese)

* *

*Key Words**:** **Viscous Flow, Internal Flow, Axisymmetric Flow, Almost Rigidly Rotating
Flow, Stewartson Layer, Interior Region, Ekman Layer, Centrifugal Classification*

In order to consider the rotating source-sink flow, which is applicable to an accurate wet-type centrifugal classification system, we numerically studied the structure of through-flow within a rotating
axisymmetric container, focusing on the almost rigidly rotating flow developing with decreasing Ekman number for a very small Rossby number.
Consequently, in the almost rigidly rotating flow in a rotating squarish doughnut-shaped container with the source and sink at corners of outer and inner walls, an axial velocity component was found
to singularly increase in magnitude near the source and sink. Also, the axial-transport thickness defined by an axial velocity component and the displacement thickness defined by an angular momentum were found to correspond to E^{1/3}-and E^{1/4}-Stewartson layers, respectively. Next, we numerically studied particle motions in the almost rigidly rotating flow in a radially-inward-expanding axisymmetric container, and obtained the result that the cut size can be controlled by angles of walls with hardly decreasing the classification
accuracy in this flow field.

(5) K. NAKABAYASHI and Y. TSUCHIDA New Multi-stage Centrifugal Classification in Almost Rigidly Rotating Flow, *Proceedings of the 15th International Congress of Chemical and Process
Engineering*, CD-ROM, 11 pages, 2002.

We have proposed a new double-stage classification system, and have considered its classification performance by making the classification test. Consequently, we have obtained the following conclusions. (1) We have verified that the present double-stage classifier can classify the feed powder into fine, medium and coarse particles all at once, as estimated by the scale law, although the measured performance is a little different from the estimated one. (2) With increasing centrifugal-effect parameters at the first and second stages, the partial fractional efficiency of the medium product tends to have a narrower distribution and a larger maximum value, i.e. we can obtain a more uniform powder. (3) The present double-stage classifier exhibits better classification accuracy in smaller particle diameters than Okuda’s dry cyclone.

(6) K. NAKABAYASHI and Y. TSUCHIDA Scaling Law of Centrifugal Classification by Almost Rigidly Rotating Flow, *Proceedings of the World Congress on Particle Technology 4*, CD-ROM, 8 pages, 2002.

** **

In order to clarify the scaling law in the centrifugal system, which classifies accurately fine particles suspended in a liquid (water) with a low concentration by applying an almost rigidly rotating throughflow between the housing and corewalls of a rotating doublewalled container, we performed classification experiments under various conditions. Consequently, we found that the scaling law is such that the ratio of the cutoff size to the length scale of the fluid and particle motions (characteristic length of the classifier) is determined as a function only of the centrifugaleffect parameter that characterizes the ratio of the centrifugal force to the drag force exerting on the particle.

(7) K. NAKABAYASHI, Y. TSUCHIDA and Z. ZHENG, Characteristics of disturbances in the laminar-turbulent transition of
spherical Couette flow. Part 1, Spiral Taylor-Görtler vortices and traveling waves for narrow gaps, *Physics of Fluids*, **14**-10, pp3963-3972, 2002.

The fundamental frequencies of velocity fluctuations caused by disturbances (vortices and waves) in the laminar-turbulent transition of spherical Couette flow (SCF) between two concentric spheres with only the inner sphere rotating
are investigated by simultaneous and flow-visualization measurements for two small ratios, 0.06 and 0.024, of the clearance to inner-sphere radius for which spiral Taylor-Görtler (TG) vortices and traveling waves on TG vortices play an important role. As the Reynolds number* Re* is increased for both clearance ratios, firstly toroidal TG vortices occur at the equator, but the flow is steady. Secondly, spiral TG vortices
(fundamental frequency *f*_{S1}) occur next to the toroidal ones, so that the flow becomes singly periodic. Thirdly, in addition to these spiral TG vortices, new spiral TG vortices
occur between them at the different colatitude *q*, so that the pair number of spiral TG vortices around the spherical annulus
differs by *q*. Therefore, plural fundamental frequencies *f*_{Si} (*i*=1, 2, . . .) of spiral TG vortices are detected, corresponding to the
different pair numbers. However, the flow is not quasi-periodic, because ratios of the different frequencies *f*_{Si} are in rational. Fourthly, traveling waves (fundamental frequency *f*_{W}) occur on TG vortices, so that the flow becomes quasi-periodic (*f*_{Si} and *f*_{W}). Fifthly, the plural frequencies *f*_{Si} change to a broadband frequency *f*_{B}, which indicates the onset of chaos. Sixthly, *f*_{W} disappears, so that the flow becomes chaotic spiral TG vortex-flow with
only *f*_{B}. The rotation frequency (wave speed) of traveling waves is larger than that of spiral TG vortices, and the
value of* f*_{B} exists about between the two rotation frequencies.

(8) K. NAKABAYASHI, Z. ZHENG and Y. TSUCHIDA, Characteristics of disturbances in the laminar-turbulent transition of
spherical Couette flow. Part 2. New disturbances observed for a medium
gap, *Physics of Fluids*, **14**-10, 3973-3982), 2002.

Supercritical flow in spherical Couette system with a rotating inner sphere and a fixed outer sphere has been investigated
for a medium gap of the clearance ratio 0.206 in terms of the structure, wavenumber, fundamental and rotational frequencies of disturbances. Consequently, ring vortices and traveling letter-x-like waves were found within the Ekman-type secondary flow as new disturbances, in addition to Stuart vortices and shear waves. Also, interior waves were found within toroidal Taylor-Görtler (TG) vortices as a new disturbance, in addition to twists. Further,
the wavy outflow boundary at the equator of the turbulent basic flow was found. Each ring vortex
occurring successively around the pole moves toward the pole for one wavelength
in the meridian direction (*q*=10°) while it rotates for one wavelength in the azimuthal direction (*φ*=90°), because it has four traveling waves. The rotational direction of
Stuart vortices is opposite to that of the inner sphere. The wave speed
(rotation frequency) of interior waves or twists is the same as that of
oscillating inflow boundary between two toroidal TG vortex cells, and the wave speed of shear waves is the same as that of the oscillating outflow boundary
between the toroidal TG vortex cell and the Ekman-type secondary flow.
Also, the wave speed of the oscillating outflow boundary is about two times
the oscillating inflow boundary.

(9) K. NAKABAYASHI, Z. ZHENG and Y. TSUCHIDA, Evolution of Fluctuating Velocity Components in the Laminar-turbulent Transition
of Spherical Couette Flow, *Physics of Fluids*, **14**-8, pp2839-2846, 2002.

In the laminar-turbulent transition of spherical Couette flow with only the inner sphere rotating in the case of gap ratio 0.14, we
have studied experimentally the evolution of mean and fluctuating velocities with increasing Reynolds number at two meridian angles, θ=60゜ and 90゜ (the equator), respectively. For a reduced Reynolds number, *R*^{＊}=1.2, the phase of a fluctuating velocity component in the main-flow direction advances radially inward from the outer to
the inner sphere at θ=90゜, but delays radially inward at θ=60゜. When *R*^{＊} is 4.2 and 6.0, the phase slightly advances radially inward at θ=90゜, but does not change so much at θ=60゜. The phase-averaged profile of fluctuating velocity in the presence of spiral Taylor-Görtler (TG) vortices differs from that in the presence of traveling azimuthal waves. Spiral TG vortices make the amplitude of fluctuating velocity large in
the central part of the gap. But traveling azimuthal waves make it large
somewhat near the inner sphere. For the flow with spiral TG vortices and/or
traveling waves at low *R*^{＊}, the rms value of fluctuating velocity tends to be large on the outer-sphere side at θ=60゜, while on the inner-sphere side at θ=90゜. In the fully turbulent flow for *R*^{＊}≧20, the rms value of fluctuation velocity becomes large near the fixed
outer sphere at both θ=60゜ and 90゜, and log-laws on mean azimuthal velocity profiles hold there.

(10)中林功一, 余偉明，足立尚史，土田陽一, ２球間クエット流の遷移過程で生じる速度 変動消滅現象, 日本機械学会論文集(B編), **68**-668, pp972-978, 2002.

Koichi NAKABAYASHI, Weiming SHA, Naofumi ADACHI and Yoichi TSUCHIDA Disappearance Phenomena of Velocity Fluctuation in the Transition of Spherical Couette Flow (in Japanese)

*Key Words**: Chaos, Transition, Vortex, Spherical Couette Flow, Correlation Dimension,
** **Maximum Lyapunov Exponent, Power Spectrum, Taylor-G**ö**rtler Vortex*

In order to study on disappearance phenomena of velocity fluctuation in the laminar-turbulent transition of spherical Couette flow with only an inner sphere rotating, we measured azimuthal component of velocity
fluctuation at the equator for various clearance ratios β=0.06〜0.206, and considered the evolution of correlation dimension *d*, maximum Lyapunov exponent λ and power spectra of the azimuthal velocity component with an increase of the rotating Reynolds
number *Re* for each β. Consequently, the following conclusions were obtained. The disappearance phenomena occur only for β≒0.13〜0.17. Even though *d*≒2, no T^{2} torus appears in the case of λ>0. The kinetic energy of disturbance increases with *Re* in the range of higher frequencies in the case of βwhere the disappearance phenomena do not occur, but decreases to almost
zero in the case where they occur.

(11) 中林功一, 余偉明，土田陽一，菅原里志, ２球間クエット流の遷移過程における逆分 岐, 日本機械学会論文集(B編), **68**-668, pp979-986, 2002.

K. NAKABAYASHI, W. SHA, Y. TSUCHIDA and Satoshi SUGAWARA, Reverse-Bifurcation in the Transition Process of Spherical Couette Flow (In Japanese).

*Key Words**: Chaos, Transition, Vortex, Spherical Couette Flow, Bifurcation Diagram,
Disappearance*

* *

In the spherical Couette flow with only an inner sphere rotating, relaminarizing flow in the laminar-turbulent transition process has been investigated by the introduction of infinitesimal disturbances from the external into the supercritical flow modes with a pair of toroidal
Taylor-Görtler (TG) vortices. Normal and reverse bifurcations are discussed. The onset Reynolds numbers of toroidal TG vortices, spiral TG vortices and traveling waves as well as the onset Reynolds number of the relaminarization are influenced by the external disturbances, although the critical *R*e of the primary instability is not influenced. Influence of the external disturbances on rms values
of velocity fluctuations is greater in the relaminarizing *R*e-region than in the lower *R*e-region. Fundamental frequencies of disturbances are not influenced by the external disturbances.

of Disturbance, Taylor-Görtler Vortex, External Infinitesimal Disturbance, Critical Reynolds Number

(12)中林功一, 土田陽一，本多敦, 独立に回転する同心二球間の流れ, 日本機械学会論文 集(B編), **68**-668, pp1008-1015, 2002.

K. NAKABAYASHI, Y. TSUCHIDA and A. Honda, Flow between Two Independently Rotating Concentric Spheres (In Japanese).

*Key Words: **Transition, Vortex, Wave, Turbulence, Spherical Couette Flow, Taylor Instability,
Flow
Regime, Periodic Disturbance, Phase Velocity*

The laminar-turbulent transition of spherical Couette flow between two independently rotating concentric spheres for the gap ratio 0.14 where the Taylor instability occurs for the fixed outer sphere has been investigated by simultaneous spectral and flowvisualization measurements. Rotation frequencies (phase velocities) of periodic disturbances do not so much depend on the ratio of the outer- to the inner-sphere rotating Reynolds number if they are non-dimensionalized by the mean rotation frequency of both spheres. Traveling azimuthal waves on only an inflow boundary of toroidal Taylor-Görtler (TG) vortices and herring-bone waves appear for the case of co-rotating spheres, while spiral vortices and twists in toroidal TG vortices appear for the case of counter-rotating spheres. Flow regimes and their occurrence-regions in the plane of the inner- and outer-sphere rotating Reynolds numbers differ depending on the Reynolds-number history.

(13) K. NAKABAYASHI and Y. TSUCHIDA, Accurate Wet-type Centrifugal Classification Using an Almost Rigidly Rotating
Flow, *KONA (Powder and Particle)*, **19**, pp197-212, 2001.

The authors propose a new system for accurate wet-type centrifugal classification that employs an almost rigidly rotating through-flow. This flow can be produced within a rapidly rotating double-walled container, without producing any turbulent fluctuation. We have conducted both batch and continuous classification using a double-walled cylinder-sphere container in classification experiments and in theoretical and numerical flow analyses. The batch type exhibited decreasing cut size and increasing classification accuracy when the Ekman number decreased (i.e., rotation rate increased) while the Rossby number remained constant, or when the Rossby number decreased (i. e. , through-flow rate decreased) and the Ekman number remained constant. With the continuous type, achieved by extracting the coarse product continuously, the cut size decreased as the extraction rate increased, but the sharpness index was almost as high as that for the batch type when the extraction rate was below the threshold value, which was reduced when the Ekman and Rossby numbers decreased.

(14) K. NAKABAYASHI and Y. TSUCHIDA, Accurate Wet-type Centrifugal Classification Using an Almost Rigidly Rotating Flow, Proc. of First Asian Particle Technology Symposium, (6 pages), 2000.

We developed a new wet-type centrifugal classification system, which can accurately^{ }classify fine powder particles suspended in a liquid (water) with a low
massconcentration by the difference between centrifugal and drag forces acting
on the particles due to the particlesize difference. An axisymmetric through-flow applied to the present system
is steady and almost rigidly rotating, within a rotating double-walled
container, so that we can increase the centrifugal force arbitrarily without
turbulence. Hence, we can manage the centrifugal and drag forces well and
can lower the cut-size into a very fine size with an excellent accuracy. Also, the present system works very well not only as a batch-type but also as a continuous-type. We verified a high quality performance for both types experimentally, revealing the flow characteristics theoretically
and numerically.

(15) 中林功一，土田陽一, 準剛体回転中の微粒子分級のスケール則 粉体工学会誌・37-11, pp800-8007, 2000．

Koichi NAKABAYASHI, Yoichi TSUCHIDA, Scale Law of Fine Particle Classification in Almost Rigidly Rotating Flow (In Japanese)

*Key Words**: Wet****type Centrifugal Classification, Almost Rigid Rotation, Cut Size, Scale
Up, Particle Motion*

In order to clarify the scale law in the centrifugal system which classifies accurately fine particles suspended in a liquid (water) with a low concentration by applying an almost rigidly rotating throughflow between the housing and corewalls of a rotating doublewalled container, we made classification experiments under various testconditions distinguished by classifiers with different sizes and feeders, feed powders with different true relative densities and particle sizes, and Ekman and Rossby numbers. Consequently, we found the scale law that the ratio of the cutsize to the length scale of the fluid and particle motions (characteristic length of the classifier) is determined as a function of only the centrifugaleffect parameter which is a dimensionless parameter characterizing the ratio of the centrifugal to the dragforce acting on the particle.

問い合わせ先 (Contact address)

Do not hesitate to contact us if you take interests in our study.

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Yoichi Tsuchida

Associate Professor

Engineering Physics, Electronics and Mechanics

Graduate School of Engineering

Nagoya Institute of Technology

Gokiso-cho, Showa-ku, Nagoya 466-8555, Japan

TEL +81-52-735-5341

FAX +81-52-735-5503

E-MAIL tsuchida.yoichi@nitech.ac.jp

tsuchida@nitech.ac.jp

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土田陽一

名古屋工業大学大学院（おもひ領域）准教授

工学研究科 機能工学専攻

工学部 機械工学教育類 担当

〒466-8555 名古屋市昭和区御器所町(ごきそちょう)

名古屋工業大学 おもひ領域

TEL 052-735-5341 (ダイアルイン)

FAX 052-735-5503 (おもひ領域事務室)

TEL 052-735-5521 (おもひ領域事務室)

E-MAIL tsuchida.yoichi@nitech.ac.jp

tsuchida@nitech.ac.jp

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