1.Introduction

With a high speed camera and a high repetition laser, velocity measurements can be performed at high-temporal and high-spatial resolutions, e.g., 1000x1000 pixels spatial resolution at 5000 Hz. Although huge amount of data, e.g., 5GB per 1 second, can be obtained, the extracted information remains have been limited to some statistical information, i.e., turbulence intensity, power spectrum and so on (Natrajan et al 2007, Wernet 2000, Son et al 2001 etc.). The development of advanced algorithms and analysis methods are still a necessity for the extraction of the advanced information from the huge amount of TR-PIV data to comprehend the dynamics of fluids.

In this study, three new techniques will be proposed to extract the improved information from the huge amount of TR-PIV data. These techniques are the extraction of fluctuation transfer velocity, out-of-plane velocity extraction for the micro TR-PIV and two kinds of vector extraction from the overlapped micro TR-PIV images. With these new techniques, the measurable information by the TR-PIV will be greatly extended.

2.Fluctuation transfer in turbulent flow

2.1.Background

The spatio-temporal velocity correlation analysis was used for measuring the large-scale structure transfer velocities of a two-dimensional backward-facing step flow utilizing Laser Doppler Velocimetry (LDV) by Furuichi et al (2004).

2.2.Experimental setup

Figure 2.1 illustrate the schematic of the target area. A high-speed Photron camera and a Nd:YLF double-pulse laser were used. For this experiment frame straddling technique was utilized, the double pulse interval is arranged as 2 μs and 10 μs. The flow channel has a 10 mm × 10 mm cross-section and a length of 1 m. Two flow cases were studied with Reynolds numbers of 34,000 and 11,000. Nitrogen gas seeded with oil particles using Laskine nozzle.

2.3.Methods

The instantaneous velocity vector maps are calculated using a recursive PIV analysis technique. Figure 2.2 shows sample images and the time-serial relative velocity vector maps. The fluctuation creation on the vortex path occurs with a time delay between two different spatial positions. The measure of the degree of correlation between the two velocity fluctuations is defined as a function of space and time delay in equation (2.1).

C(x,y,z)k=∫u(xk,yk,t)u(x,y,t+z)dt/√∫u(xk,yk,t)2dt√∫u(x,y,z)2dt (2.1)

C(x,y,z)k is the correlation value. k represents the reference point index and u(x,y,z) is the downstream component of the fluctuation velocity. With the delay time of the reference point fixed as zero, the value of z was changed in the interval of [-2, 2] ms with an increment of 0.1 ms, and the correlations were calculated at every discrete z values; then the same procedure was applied to all points in the flow field. In the delay time interval of [-2, 2] ms, the correlation value between two points takes a highest value at a particular delay.

Correlations and time delay spatial distributions were plotted in figures 2.3 for an arbitrary reference point. Figures 2.3 (b) depicts time delay distribution contour map, where reference point location is marked by a black circle. Fluctuating events on the right-hand side occur earlier than the reference point, and fluctuating events on the left-hand side occur after the reference point. Time delay versus x-axis graphs (streamwise axes) are plotted as in figure 2.4 for the Reynolds numbers of 11 000 at all chosen reference points.

The inverse of the slope of the delay curve, which is obtained by linear curve fitting in figure 2.4, gives the average transfer velocity of the fluctuations at this point due to equation (2.2).

∂z/∂x=1/u(tr) (2.2)

2.4.Results and discussions

Two-point velocity correlation was applied, and the normalized fluctuation transfer velocity distribution was obtained in the flow area and depicted in figure 2.5 as a two-dimensional contour map. The green regions in colored maps correspond to approximately half of the average flow velocity in the boundary layer. That result is in good agreement with those from Furuichi et al (2004) and Hijikata et al (1991). It can be seen that when the average flow velocity is higher, the fluctuation transfer velocity decreases to smaller values in the boundary layer region.

Spatial and temporal relations of the fluctuating velocities were measured using the time dependent multi-point velocity correlation. That method is not limited to the only two spatial locations in the flow field, but provides full-field fluctuation transfer velocity distribution that differs from the former hot-wire anemometer measurements and that of LDV measurements.

3.Development of 3C velocity field measurement in micro-scales using single high speed camera

3.1.Background

The small working distances associated with microfluidic devices and microscopes provide limited optical access and small spaces to set up experimental apparatus like two cameras to determine the three-component (3C) velocity field.

In this section, simulation of a new 3C velocity measurement technique based on the PIV and performing the correlation peak height tracking inside the small ensembles of the dynamic PIV images in the bounded time intervals will be investigated.

3.2.Synthetic images generation

Several sets of synthetic micro TR-PIV images having different out-of-plane velocities are generated. Every set composed of 12 time sequential images, which all have the same uniform out-of-plane and in-plane velocity in one set, with 512x512 pixels in size. Particle locations are defined randomly within an arbitrary measurement volume. Particle diameters and intensity distributions are defined as proposed by Olsen et al (2000).

Synthetic images consisting of 1μm diameter particles were generated as visualized from an optical system having M = 40, NA=0.8. The depth of field δz of the optical system would be ~7.1μm.

3.3.PIV analysis and correlation peak tracking

Evaluation procedure composed of two essential parts. First one is instantaneous in-plane velocity measurement using recursive PIV analysis technique, the other one is the CC peak value tracking in the time sequential images with respect to a reference image.

Instantaneous velocity vector maps are calculated using window deformation iterative multi grid image distortion interrogation algorithm (Scarano 2002). Description of the cross-correlation function described initially as;

C(f,g)(m,n)=(M)Σ(i=0)(N)Σ(j=0)[f(i,j)-μ(f)][g(i-m,j-n)-μ(g)(m,n)]/√δ(f)(m,n)√δ(g)(m,n) (3.1)

δ(f)(m,n)=(M)Σ(i=0)(N)Σ(j=0)[f(i,j)-μ(f)](2) (3.1)

δ(g)(m,n)=(M)Σ(i=0)(N)Σ(j=0)[g(i-m,j-n)-μ(g)(m,n)](2) (3.1)

C(f,g)(m,n) is the correlation value at a point m, n in search window between the first image's intensity distribution f and the second image's intensity distribution g over the interrogation window. μis the average intensity of the interrogation window. The particle image displacement is obtained as the distance of the maximum from the origin of the correlation map. When iterative PIV evaluation is applied, the particle displacements evaluated from CC are used to obtain a displacement predictor field at each pixel position. The displacement predictor is used to deform the original images to eliminate the in-plane displacements and make them virtually similar. These regenerated images are re-correlated with each other with a reduced interrogation window size and the displacement results are added to the previous displacements.

When the above evaluation procedure is performed by taking one median image as a reference image, correlate it with the forward and backward images by shifting in the time domain, it would be seen that CC peak height is changing with respect to the time.

Maximum value of C(k,k+r) ,which is defined in Equation 3.1, for an interrogation area is calculated for ∀t∈[-5,5] at an arbitrary spatial position, and then alteration of C(k, k+r) versus the discrete time shift value of t is plotted in Figure 3.1. CC value changes almost linearly. In the next section, these correlation curves including both left and right side are going to be fitted to a linear curve with a particular deviation i.e. , then inclination of that curve would give us the rate of change of the CC peak height with respect to the time. That rate and particle's out-of-plane velocity would be associated.

3.4.Results and Discussions

Above method is repeated for all synthetic image sets which have different out-of-plane velocities. And finally, evolution of time gradient of CC peak height with respect to the out-of-plane velocity is plotted in Figure 3.2. Horizontal axis is taken as the ratio of the out-of-plane velocity to the depth of field of the simulated optical system. The CC gradient values were chosen for relatively well linear fitted spatial locations.

Rate of decrease in CC peak height is linearly dependent to the out-of-plane velocity. It can be detected with a chi-square (EPS) less then 0.0008 if the out-of-plane displacement is less than around 10% of depth of field of the optical system.

4.Measurement of complex flow fields in micro-scales

The mixing is achieved in chaotic mixers (Stroock et al 2002) with mainly transverse velocity components of the flow that causes sensors to capture complicated PIV images which have particle images moving in the different directions with different velocities on the same image plain.

In this section, two kinds of velocity extraction method for the complex flows in the micro-channels having grooved inner surfaces is investigated by making use of the huge amount of time-resolved PIV data.

4.1.Experimental setup and Methodology

Flow images were recorded via an epiflourescence microscope with a water-immersion objective lens (M=40, NA=0.8). A schematic view of the rectangular micro channel with obliquely oriented ridges is shown in Figure 4.1.

4.2.Method of analysis

If depth of the bottom groove is 5-10 μm, it is almost equivalent to the thickness of the measurement plane of the micro PIV system. Therefore, measurement of the velocity field near the groove is very difficult due to the existence of the tracing particles which have different velocities in the same measurement volume that they are placed on the same image plane (Figure 4.1).

Unlike the classical PIV images, there are two different velocity vector fields in our measurement plane. Dynamic ensemble correlation method (Equation 4.1) is proposed to extract these velocity vectors.

R(t)(m,n)=1/Z(Z)Σ(k=1)C(k,k+t)((m,n)) (4.1)

C(k,k+t)((m,n)) defined in Equation 3.1 is the correlation value. t is the time interval i.e. skipping image number. R(t) is the final average cross-correlation value at a point (m, n). A contour map of the ensemble correlation function R(t)(m,n) for t=25,Z=3000 value in an interrogation area is plotted in Figure 4.2.

4.3Results

Water inside the channel flows with a Reynolds number of 0.32 and average velocity of 1.5 mm/s in laminar mode. Overlapped velocity vectors are presented in Figure 4.3. Fast describes the velocity vectors obtained from the particles moving above the grooves and Slow describes the velocity vectors obtained from the particles moving inside of the grooves. Because of the high reflections and background noise, overlapped velocity vectors could not be detected in every grid positions. Also 1 μm diameter fluorescent flow tracing particles were used. That size is quite big as much as not to be able to detect chaotic velocity fluctuations in such a small length scales.

5.Conclusion

Three evaluation methods have been proposed in order to extract the advanced information from the huge amount of Dynamic-PIV data. These methods make use of the huge amount of temporal data for the evaluation of the fluid flow covering wide dynamic range and spatial range i.e. laminar flow inside the micro-channels and high-speed turbulent flow in macro scales.

It is demonstrated that high-time resolved information acquired by dynamic-PIV is not used only for temporally fine resolved instantaneous velocity vector field realizations, but also extraction of advanced information including 3C velocity, full-field turbulent large structure transfer velocity and two different overlapped vector fields from the same image of micro-scale chaotic flow.

Figure 2.1: Enlarged test section

Figure 2.2 Original flow images and instantaneous velocity vectors (Re=34 000).

Figure 2.3: (a) Spatial distribution of correlation values, (b) time delay (in s) distribution of correlation values. (Re=11000)

Figure 2.4: Position-time graphs of fluctuation transfers.

Figure 2.5: Normalized fluctuation transfer velocity distribution. (u(tr)(x, y)/U(av)(x, y)) (Re = 11 000).

Figure 3.1: Cross-correlation peak height change versus image number at an arbitrary spatial

Figure 3.2: Cross-correlation gradient evolution with respect to Δz/δz.

Figure 4.1 Target flow area near to the grooves.

Figure 4.2 Dynamic ensemble correlation maps. A sample interrogation window on the groove.

Figure 4.3 Velocity vector map.

本論文は、高空間解像度かつ高時間分解能で速度分布情報を取得することができる高時間分解粒子画像流速測定法(TR-PIV)を応用した、新しい計測システムの提案を行い、その有効性について論じたものである。具体的な計測システムとしては、多地点速度相関を用いた変動輸送速度分布計測システム、面外速度分布を含むマイクロ3成分速度分布計測システム、マイクロチャネル内グルーブ近傍における2速度ベクトル検出システムの3種類である。本論文は5章で構成されている。

第1章では、本研究の動機と目的について述べている。粒子画像流速測定法(PIV)から発展した、高速度ビデオカメラと高速度パルスレーザを用いた高時間分解PIV(TR-PIV)の現状と問題点についてまとめている。高時間分解PIVは従来のPIVに比べて3桁程度高時間分解情報が得られるのに対して、現状のデータ解析は従来のPIVと同様にとどまっており、その高時間分解というメリットを生かしきれていない事を示している。そこで、高時間分解のメリットを生かした新しい計測システムの提案を行うと共に、その評価を目的とすることを述べている。

第2章では、高時間分解PIV手法を応用した、変動輸送速度分布計測システムについて述べている。TR-PIVをエッジからの乱流境界層に適用し、10kHzのサンプリング周波数で境界層における速度分布情報を取得している。2点速度相関を得られた全ての点に適用し、任意の2点間で計測される変動の時間遅れと相関を求める。全ての計測点における時間遅れデータから変動輸送速度を求め、2次元分布情報として示している。また、このシステムにより求められた乱流境界層における変動輸送速度が平均流速の約50%であることを示すと共に、従来得られなかった変動輸送速度の分布情報を取得することに成功したことを示している。

第3章では、高時間分解PIV手法を応用し、マイクロ流動場における奥行き方向の速度を含む3成分速度分布を求めるシステムについて述べている。時間方向に大量に得られる情報には、2次元の平面方向の移動量に加えて、面外方向に移動する粒子の情報も含まれている。これらの画像相互相関を統計的に処理することで、面外方向移動量情報を抽出するシステムである。人工的に作成した模擬画像を用いて、その抽出アルゴリズムの有効性を確認すると共に、100μmのマイクロチューブを傾けた流速場の計測実験を行っている。ポアズイユフローから、理論的な面外方向速度が求められるので、実験データと比較することで、提案システムの有効性を実験的に確認している。さらに、実験結果からシステムの限界と計測の不確かさについて議論を行っている。

第4章は、マイクロチャネル下部にグルーブを形成した、カオティックミキサーと呼ばれるマイクロ複雑流路内における2速度情報の抽出システムについて述べている。マイクロ流動場では、対物レンズの被写界深度が比較的大きいため、グルーブ内速度とグルーブ外速度情報が同時に画像に記録される。この2速度情報を、時間間隔を変更した相関係数のアンサンブル平均を応用することで、分割して求めるシステムを提案し、その有効性を実験的に確認している。

第5章は結論であり、本論文で得られた成果をまとめている。

以上のように、本論文は、高時間分解PIVを用いて得られる多量情報の中から、今まで得られなかった計測データを取得することを目的とした、3種類の新計測システムを提案すると共に、乱流境界層やマイクロ流動場に適用することでその有効性を評価した論文であり、システム量子工学、特に流体可視化工学の発展に寄与することが少なくない。よって、本論文は博士(工学)の学位請求論文として合格と認められる。