Yoichi Tsuchida

Flow-history effect on higher modes in the spherical Couette system

Our flow-visualization and spectral studies of spherical Couette flow between two concentric spheres with only the inner sphere rotating for the clearance ratio (or gap ratio) 0.14 where the Taylor instability occurs have been pursued to systematically explore how and why a variety of wavenumbers and rotation frequencies of the non-axisymmetric periodic disturbances occurs at the same supercritical Reynolds number. The observed periodic disturbances constitute six kinds of disturbances: spiral TG (Taylor–Gortler) vortices, twists developing within toroidal TG vortices, both unmodulated and modulated waves travelling on the TG vortices, and both Stuart vortices and shear waves developing within the Ekman-type secondary flow. Development of these disturbances depends strongly on the flow mode at the initial Reynolds number (initial flow mode) and on the Reynolds-number evolution process approaching the final Reynolds number (acceleration rate and history of the Reynolds number). In our previous studies (Nakabayashi 1983; Nakabayashi & Tsuchida 1988 a, b ), we clarified the structures, wavenumbers and rotation frequencies of the periodic disturbances caused by a quasi-static increasing of the Reynolds number. In the present study, we consider how the characteristics of periodic disturbances depend on the following three factors: (i) the rate of increase of the Reynolds number; (ii) the number of toroidal vortices in an initial flow mode; and (iii) the quasi-static Reynolds-number history. The flow modes observed in the present study are all stable to small perturbations, and the transitions among the flow modes are reproducible.

Modulated and unmodulated travelling azimuthal waves on the toroidal vortices in a spherical Couette system

We have investigated the modulated and unmodulated travelling azimuthal waves appearing on the toroidal Taylor–Gortler (TG) vortices in a fluid contained between two concentric spheres with the inner sphere rotating. For smaller-clearance cases, toroidal TG vortices appear at the equator, just as in the flow between two concentric cylinders with the inner cylinder rotating. When the Reynolds number of the flow increases quasi-statically, spiral TG vortices appear in addition to toroidal TG vortices, and no modulation occurs, even if the Reynolds number further increases quasi-statically. However, when the Reynolds number is increased from zero to a particular value with a specific acceleration of the inner sphere, modulated wavy toroidal TG vortices appear. We found that the necessary condition for occurrence of modulation is the prevention of spiral TG vortices. Using simultaneous flow-visualization and spectral techniques, and measuring the fluctuation of sinks and sources of vortex boundaries, we obtained the frequency f 1 of travelling azimuthal waves passing a fixed point in the laboratory and the modulation frequencies f 2 and f ′ 2 of these waves, as determined by an observer in the laboratory and an observer fixed in a reference frame that rotates in phase with the travelling azimuthal waves, respectively. The relationship among the characteristic frequencies, f 1 , f 2 and f ′ 2 , obtained by modal analysis and the experimental results, is ( f ′ 2 + kf 1 / m )/ f 2 = − 1, where k and m are a modulation parameter and the wavenumber of travelling azimuthal waves, respectively.

Relaminarization phenomena and external-disturbance effects in spherical Couette flow

The relaminarization phenomenon in the laminar turbulent transition process of spherical Couette flow with the inner sphere rotating and the outer sphere fixed has been experimentally investigated for 0.06≤β≤0.206, where β is the ratio of the clearance to the inner-sphere radius. The relaminarization occurs for 0.13 < β < 0.17, and is observed as a reverse Hopf bifurcation from the limit cycle to the fixed point. The kinetic energy in the high-frequency region of the fluctuating azimuthal velocity component continues to increase with Reynolds number Re in the case without relaminarization, but in the case with relaminarization it first increases and then decreases with increasing Re and finally vanishes with the onset of the relaminarization. For β=0.14 with relaminarization, a small artificial disturbance introduced externally into the spherical Couette flow has no influence on the lowest critical Reynolds number of the first instability that can be defined universally and uniquely

Characteristics of disturbances in the laminar–turbulent transition of spherical Couette flow. 2. New disturbances observed for a medium gap

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, wave-number, 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–Gortler (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 (θ=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 ...

Transition phenomena in a spherical Couette flow between independently rotating spheres

The quasistatic laminar-turbulent transition of spherical Couette flow between two independently rotating concentric spheres for a gap ratio (ratio of the gap between two spheres to the inner-sphere radius) of 0.14 for which the Taylor instability occurs in the case of the inner sphere rotating and the outer sphere fixed has been investigated by simultaneous spectral and flow-visualization measurements. Rotation frequencies (phase velocities), scaled by the mean rotation frequency of both spheres, of various periodic disturbances do not depend much on the ratio Ro*∕Ri* of the outer-sphere rotating Reynolds number Ro* to the inner-sphere rotating Reynolds number Ri*, although the phase velocity differs by the kind of disturbance. As disturbances unobserved in the case of the fixed outer sphere, traveling azimuthal waves only on an inflow boundary of toroidal Taylor-Gortler (TG) vortices and herringbone waves are observed in the case of co-rotating spheres, and spiral vortices and twists in toroidal TG vort...

Evolution of mean and fluctuating velocity components in the laminar-turbulent transition of spherical Couette flow

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–Gortler (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 vor...

531 Numerical Study on Optimization of the Wall Shape in a Centrifugal Classification System Using an Almost Rigidly Rotating Flow

1.緒言 本研究は,一体回転するコアとハウジングからなる二重容 器内に生成させた準剛体回転流を用いた高精度湿式遠心分 級方式の確立を目指した基礎研究の一環である.Fig.1 の FOF-MCWCM 型三産物分級機について,前報の分級実 験では,粒子が数値解析結果のように主要な分級場であるコ ア円柱面に沿うスチュワートソン層に入らないために,良好 な性能が得られなかった.そこで本報では,粒子がスチュワ ートソン層に入りやすくなるように,コアの角部 CC の形状 を円柱形状 Ogから円錐形状 CO,円弧断面形状 Arに変更した ときの分級性能を数値的に考察する. またこのような角部 形状について,コアのアスペクト比 Γが分級性能に及ぼす影 響についても考察する. 主な記号 a* : 長さスケール(コア半径 a*=50.85×10m) [m] CE : 遠心効果パラメータ= (1) / ( E RS) [m] CV : 粒径の変動係数(小さいほど均一度良好) =σ* (標準偏差) / DPA* (平均径) [-] DP*: 球形粒子の直径(球相当径)= DP a* [m] DJPN*: 産物 J の N%分離粒子径 (J(DJPN*) = N/100) [m] E : エクマン数= */(*a*) [-] (i, j, k): 回転円柱座標系の基底ベクトル [-, -, -] p* : 遠心力項を含む圧力 = p * *a* UE* [Pa] [q*,T*]:[エクマン,スチュワートソン]輸送量=[q,T ]QO* [m /s] [QJ*,QW*]: [産物 J,給水 W]の流量 = [QJ,QW]QO* [m /s] QO* : 流量スケール(Feed 流量) [m /s] (r*,, z*): 回転円柱座標系 = (ra*,, za*) [-, -, -] RS : ロスビー数 = UE*/(*a*) [-] t* : 時間= tΩ* [s] [U*,V*]: [流体, 粒子]の速度ベクトル = [U, V] UE* [m/s] UE* : 速度スケール(Feed 供給部の r =aでのエクマン層 内での断面平均流速) = QO*/(4a*(*/*) ) [m/s] ,: 粒子の[仮想質量,動力学的形状]係数 [-,-] J : 産物 J の部分分級効率(粒径 DP における原料粉体に 対する産物 J の質量の比F+M+C=1) [-] J : J 産物の収率(大きいほど処理量大) [-]  粒子の真比重流体密度ρ*に対する 粒子真密度ρP*の比) [-] * : 流体の動粘性係数 [m/s] * : ハウジング・コアの回転角速度 [rad/s] 上付添字*は有次元量,下付添字 O,J(=F,M,C),W はそれぞれ 原料粉体,産物 J(微粉 Fine,中間粉 Medium,粗粉 Coarse), 給水 (Water)に関する量を表す. 2.数値解析条件および数値解析法 Fig.1 は,FOF-MCWCM 型三産物分級機の基本形状(Og) の寸法 L,流量 Q,輸送量 q,T を示す. Fig.2(a), (b)は,Fig.1 のコア角部CCの円柱形状Ogからの変更形状である円錐形状 COと円弧断面形状 Arを示す. 本解析では,粒子が微小,濃度が希薄であるとして粒子運 動から流れへの干渉,粒子同士の干渉を無視し,流れ,粒子 運動の順に数値計算を行って分級性能を求めた.次式は, 回転座標系での流れ,粒子運動の支配方程式である NS 式・ 連続の式,バセット・ブシネスク・オセーン式を示す. ∂U /∂t + U・▽U + 2k×U = -▽p + E▽U, ▽・U = 0 (1) γ (dV / dt + 2k×V / RS r i / RS ) = -18 κ (V U) E / (RS DP ) + (dU / dt + 2k×U / RS r i / RS ) + α (dU / dt + 2k×U / RS dV / dt 2k×V / RS) (2) 解析条件は,粒子を球形(= 1,α = 0.5)のシリカ(γ = 2.2), 流れ条件を E = 10×10-6,RS = 4.0×10 として,遠心効果パ ラメータ CE = 3.0×10 と設定した. また,各流入出部では流 れを二円板間のポアユイズ流れと仮定し,入口部 O では粒子 速度を流体速度と一致させた.さらに,収率の計算に必要な 原料粉体の頻度分布(質量基準)を DP*=0.1~4.0μm での一様 分布と仮定し,コア半径 a*= 50.85×10 m とした.Table 1 は 計算条件を示す.

Accurate wet-type centrifugal classification using an almost rigidly rotating flow — classification principle and performance of the batch-type classification

We have proposed a new system for an accurate wet-type centrifugal classification to which an almost rigidly rotating through-flow is applied. This flow can be produced within a highly rotating double-walled container, without any turbulent fluctuation. In the present paper, we have employed the batch-type classification with a cylinder-sphere-shaped container in classification experiments, theoretical and numerical flow analyses, and flow-visualization measurements. Consequently, we have obtained the following main conclusions: (i) with decreasing Ekman number (i.e. increasing rotation rate) at a constant Rossby number or with decreasing Rossby number (decreasing through-flow rate) at a constant Ekman number, the cut size and fine yield decrease and the classification accuracy increases, and (ii) for the occurrence of the rigid-rotation region which is indispensable to collect the coarse product, it is necessary to make the flow field inverse-C-shaped towards the rotation axis.

Laminar-Turbulent Transition in Spherical Couette Flow

The laminar-turbulent transition of spherical Couette flow with only the inner sphere rotating has been investigated by velocity measurements and simultaneous spectral and flow-visualization measurements for clearance ratios β≤0.20, where Taylor-Gőrtler (TG) vortices are detectable near the equator. The present study has focused on β dependence of the transition phenomena and on relaminarization for β=0.14. We have investigated transition Reynolds numbers, rotation frequencies of travelling waves and spiral TG vortices, the formation mechanism of spiral TG vortices, the law of the wall of mean velocity at the equator, and both the rms value and correlation dimension of fluctuating velocity leading up to the relaminarization.

Method to Analyse Disturbance by Simultaneous Spectral and Flow-visualization Measurements using Tracer Particles.

In the present simultaneous spectral and flow-visualization measurements, the disturbance is visible using a suspension of small aluminium or Kalliroscope polymeric flakes that align with the flow, and the intensity of laser or light-emitting-diode light scattered by the flakes is simultaneously measured. The disturbance structure is clarified and the fundamental frequency of the velocity fluctuation is identified by comparing the results of the visual observation and the spectral analysis of the scattered-light intensity.The present method using simultaneous spectral and flow-visualization measurements is applied to analyse various disturbance appearing in the spherical Couette flow between rotating spheres and the radial flow between two parallel disks with an axial inflow.