Measurements of the Solid-body Rotation of Anisotropic Particles in 3D Turbulence

We introduce a new method to measure Lagrangian vorticity and the rotational dynamics of anisotropic particles in a turbulent fluid flow. We use 3D printing technology to fabricate crosses (two perpendicular rods) and jacks (three mutually perpendicular rods). Time-resolved measurements of their orientation and solid-body rotation rate are obtained from stereoscopic video images of their motion in a turbulent flow between oscillating grids with $R_\lambda$=$91$. The advected particles have a largest dimension of 6 times the Kolmogorov length, making them a good approximation to anisotropic tracer particles. Crosses rotate like disks and jacks rotate like spheres, so these measurements, combined with previous measurements of tracer rods, allow experimental study of ellipsoids across the full range of aspect ratios. The measured mean square tumbling rate, $\langle \dot{p}_i \dot{p}_i \rangle$, confirms previous direct numerical simulations that indicate that disks tumble much more rapidly than rods. Measurements of the alignment of crosses with the direction of the solid-body rotation rate vector provide the first direct observation of the alignment of anisotropic particles by the velocity gradients of the flow.Comment: 15 pages, 7 figure

관성입자의 침 강속도에 난류가 미치는 영향에 대한 실험연구

학위논문(석사) -- 서울대학교대학원 : 공과대학 건설환경공학부, 2023. 2. 박용성.Existing particle tracking models predict the vertical velocity of particles using the linear summation of carrier fluid velocity, the settling velocity in still fluid, and the random value following normal distribution to represent the effect of diffusion and dispersion. However, it has been reported that the terminal settling velocity of inertial particles changed in a turbulent flow. Therefore, it is necessary to investigate the interactions between advection by carrier fluid, settling velocity in stagnant water, and changes of settling velocity in a turbulent flow to improve the performance of predicting particle transport in particle tracking models. To this end, numerical simulations and laboratory experiments were conducted in the present study. First of all, the numerical simulations for the particle settlement in a steady uniform flow have been carried out to evaluate the effect of a parallel advection on the settling velocity. The resultant settling velocity was the same as the velocity calculated by superposing the advection by carrier fluid and the settling velocity in still fluid because the particles relative velocity has to be consistent according to the particle and fluid characteristics. To investigate the turbulence effect on the settling velocity, two kinds of experiments, namely, the open-channel flow experiments and experiments using the Vertical Recirculation Tube (VeRT), were conducted. In both of the experiments, the velocity of inertial particles was measured using particle tracking velocimetry (PTV), and fluid velocity and turbulence were measured using particle image velocimetry (PIV). In the present study, the PTV algorithm, which can track multiple settling particles, has been constructed. The experimental results showed that the settling velocity of the particles was generally larger in turbulent flow than in stagnant water. Then, several parameters representing particle and turbulence characteristics, such as Stokes number (St) and Rouse number (Sv) were investigated to determine which parameter depends on settling velocity change. As a result, the combination of Stokes and Rouse number, SvSt, which can be seen as a length scale parameter, appears to show a more evident correlation with the settling velocity change than other parameters. Thus, it is maintained that SvSt can be used as a defining parameter to describe the turbulence effect on the settling velocity change of inertial particles in a turbulent flow. In conclusion, through the experiments conducted in the present study and preceding studies, it was evident that the settling velocity generally increases with increasing level of turbulence. Hence, the existing particle tracking model could overestimate the transport distance, which is mainly determined by the ratio of the settling distance to vertical velocity of particles. Thus, it is important to take into account the turbulence effect on the settling velocity of inertial particles in order to improve the performance of particle transport.기존의 입자추적모델은 주변 유체의 유속과 입자의 정지 수체에서의 침강속도 그리고 분산과 확산 효과를 나타내기 위해 정규 분포를 따르는 임의 값의 선형 합으로 입자의 연직 방향 속도를 예측한다. 하지만 많은 선행 연구들은 난류 흐름에서 입자의 최종 침강속도가 변한다는 것을 제시해왔다. 따라서 입자추적모델의 입자 수송(particle transport)에 대한 정확도 향상을 위해, 주변 유체에 의한 이송(advection), 정지 수체에서의 입자 침강속도, 그리고 난류 흐름에서의 침강속도 변화 간의 상호작용에 대해 조사할 필요가 있다. 이를 위해, 본 연구에서는 수치 모의와 실험실 실험이 수행되었다. 먼저, 입자의 침강 방향과 평행한 이송이 작용할 때 침강속도에 미치는 영향을 평가하기 위해, 정상류에서 입자의 침강 거동에 대한 수치 모의가 수행되었다. 그 결과, 이송의 영향을 받은 침강 속도는 정지 수체에서의 침강속도와 주변 유체의 유속의 중첩을 통해 계산된 것과 같았으며, 이는 유체 내의 관성입자의 거동에 대한 운동방정식을 통해, 유체에 대한 입자의 상대속도가 입자 조건에 따라 일정하기 때문임을 확인하였다. 다음으로, 침강 속도에 난류가 미치는 영향을 조사하기 위해 입자의 침강과 수직 방향으로 유체가 이동하는 개수로 흐름에서의 실험과 침강과 평행한 방향으로 유체가 이동하는 연직순환수로(Vertical Recirculation Tube; VeRT) 실험을 진행하였다. 두 가지 실험에서, 실험 입자의 속도는 PTV(Particle Tracking Velocimetry) 기법을 통해 측정되었으며, 유체의 속도와 난류는 PIV(Particle Image Velocimetry) 기법을 통해 측정되었다. 특히, 본 연구에서는 여러 개의 입자를 함께 추적 가능한 PTV 알고리즘을 구축하여 사용하였다. 실험 결과는 입자의 침강속도가 일반적으로 정지 수체보다 난류 흐름에서 더 빠르다는 것을 보여주었고, 그 침강속도 변화에 어떤 인자가 종속적인지를 Stokes 수, Rouse 수 등 입자 및 난류 특성을 함께 나타내는 몇 가지 인자들을 대상으로 조사하였다. 그 결과, Stokes 수와 Rouse 수를 곱하여 입자와 난류 특성의 길이 차원 비를 나타내는 가 해당 값이 증가함에 따라 침강 속도 변화율이 감소하는 형태를 다른 인자들에 비해 명확하게 보여주었다. 따라서 가 난류 흐름에서 관성입자의 침강속도 변화에 난류가 미치는 영향을 설명할 수 있는 가장 지배적인 인자로 사용될 수 있음을 확인하였다. 결론적으로, 본 연구에서 수행된 실험들과 선행 연구의 결과로부터 난류 흐름에서 침강 속도는 대체로 증가함을 관측하였다. 따라서 기존의 입자추적모델은 입자의 연직방향 유속을 과소산정할 수 있으며, 이에 따라 입자의 수송 거리를 과대산정할 수 있다. 그러므로, 특정한 입자 및 흐름 조건에서 침강 속도의 변화를 예측할 수 있도록 추가적인 연구를 수행하고, 이를 입자추적모델의 정확도 향상을 위해 입자 거동 해석에 반영할 필요가 있다.1. Introduction 1 1.1 Background and necessities of study 1 1.2 Research objectives 3 2. Theoretical background 7 2.1 Inertial particles in a viscous fluid 7 2.1.1 Equation of motion 7 2.1.2 Numerical integration scheme for the MRE 12 2.2 Settling velocity of inertial particles 16 2.2.1 Terminal settling velocities in Stokes regime 16 2.2.2 Settling velocity changes in turbulence 17 2.3 Estimating turbulent kinetic energy (TKE) dissipation rate for turbulence analysis 22 2.3.1 Particle Image Velocimetry (PIV) 22 2.3.2 TKE dissipation rate 22 2.3.3 The method estimating TKE dissipation rate from PIV data suggested by Sheng et al. (2000) 25 2.4 Empirical Mode Decomposition (EMD) 32 3. Experimental setup and instrumentations 34 3.1 Experimental setup 34 3.1.1 Experiment 1: Open-channel flume 34 3.1.2 Experiment 2: Vertical Recirculation Tube (VeRT) 44 3.2 Particle Tracking Velocimetry (PTV) 57 4. Results and discussion 63 4.1 Effect of parallel advection on the settling velocity 63 4.1.1 Modified drag force in MRE 63 4.1.2 Validation of the numerical scheme 65 4.1.3 Numerical simulation in a steady uniform flow 70 4.2 Experimental results 73 4.2.1 Experiment 1: Open-channel flume 73 4.2.2 Experiment 2: VeRT 88 4.3 Effect of turbulence on settling velocity change 101 5. Conclusion 113 REFERENCES 116 APPENDIX 121 국문초록 131석

Turbulent channel flow of dense suspensions of neutrally-buoyant spheres

Dense particle suspensions are widely encountered in many applications and in environmental flows. While many previous studies investigate their rheological properties in laminar flows, little is known on the behaviour of these suspensions in the turbulent/inertial regime. The present study aims to fill this gap by investigating the turbulent flow of a Newtonian fluid laden with solid neutrally-buoyant spheres at relatively high volume fractions in a plane channel. Direct Numerical Simulation are performed in the range of volume fractions Phi=0-0.2 with an Immersed Boundary Method used to account for the dispersed phase. The results show that the mean velocity profiles are significantly altered by the presence of a solid phase with a decrease of the von Karman constant in the log-law. The overall drag is found to increase with the volume fraction, more than one would expect just considering the increase of the system viscosity due to the presence of the particles. At the highest volume fraction here investigated, Phi=0.2, the velocity fluctuation intensities and the Reynolds shear stress are found to decrease. The analysis of the mean momentum balance shows that the particle-induced stresses govern the dynamics at high Phi and are the main responsible of the overall drag increase. In the dense limit, we therefore find a decrease of the turbulence activity and a growth of the particle induced stress, where the latter dominates for the Reynolds numbers considered here.Comment: Journal of Fluid Mechanics, 201

Accurate direct numerical simulation of two-way coupled particle-laden flows through the nonuniform fast Fourier transform

The ability of the non-uniform Fast Fourier Transform (NUFFT) to predict the particle feedback on the flow in particle-laden flows in the two-way coupling regime is examined. In this regime, the particle back-reaction on the fluid phase can substantially modify the flow statistics across all the scales, when particle loading is significant. While many works in the literature focus on the direct B-spline interpolation, which is now a well-established method for the one-way coupling, only a few methods are available for the computation of particle back-reaction, which are often lower order and reduce the overall accuracy of the simulation. In our implementation, particle momentum and temperature back-reactions on the fluid flow are computed by means of the forward NUFFT with B-spline basis, while the B-spline interpolation is performed as a backward NUFFT. An application of the NUFFT to the simulation of a statistically steady and isotropic turbulent flow, laden with inertial particles is presented. The effect of particle feedback on velocity and temperature structure functions and on particle clustering is discussed as a function of the Stokes number, together with the spectral characterization of the particle phase

Bias in particle tracking acceleration measurement

We investigate sources of error in acceleration statistics from Lagrangian Particle Tracking (LPT) data and demonstrate techniques to eliminate or minimise bias errors introduced during processing. Numerical simulations of particle tracking experiments in isotropic turbulence show that the main sources of bias error arise from noise due to position uncertainty and selection biases introduced during numerical differentiation. We outline the use of independent measurements and filtering schemes to eliminate these biases. Moreover, we test the validity of our approach in estimating the statistical moments and probability densities of the Lagrangian acceleration. Finally, we apply these techniques to experimental particle tracking data and demonstrate their validity in practice with comparisons to available data from literature. The general approach, which is not limited to acceleration statistics, can be applied with as few as two cameras and permits a substantial reduction in the spatial resolution and sampling rate required to adequately measure statistics of Lagrangian acceleration