# Fundamental Physics of Turbulence

## Numerical simulation of particle-laden turbulent channel flow

수치해석 방법을 이용하여 Particle-laden turbulent channel flow의 특성을 연구한다.

• Motivation

The study on the behavior of inertial particles suspended in wall-bounded turbulence has a wide range of applications, from industrial devices to environmental systems, and is expected to resolve most of the practical problems involving walls (e.g., transport of contaminants in urban area and deposition of fine dust in a human respiratory system). From an engineering perspective, it is very important to accurately predict the particle motion and understand particle dynamics in wall-bounded turbulence.

• Lagrangian particle tracking
• Particles near the wall moving in the x-direction

Particles are concentrated in the low speed streaks (blue regions in the right figure).

• Y-Z plane views of particle distribution

Particles are transferred towards the wall, interacting with turbulence.

## Geometric nature of particle trajectories

입자의 궤적을 통해 알수있는 곡률(curvature) 및 비틀림률(torsion)의 성질을 조사함으로써, 난류의 회전구조 및 헬리시티와의 상관성을 조사하였다.

The geometric nature of particle trajectory is investigated using direct numerical simulation of isotropic turbulence. Probability density functions and autocorrelations along a fluid particle trajectory associated with geometric quantities such as curvature and torsion of the Lagrangian trajectory are provided. We proposed the ratio of torsion to curvature as parameter to identify the particle trajectory and it is found to play crucial role in understanding the geometric shape of particle trajectory. The relationship between Lagrangian helicity and the ratio of torsion to curvature is investigated where Lagrangian helicity is defined as dot product of velocity and vorticity at the point of fluid particle. We found that probability density functions of torsion and torsion normalized by curvature clearly show well-established slope in log–log plots. Lagrangian helicity is intermittently distributed and high Lagrangian helicity is always found, where high acceleration is observed. Regarding the relationship between coherent structure and acceleration, coherent structure can be understood in terms of Lagrangian helicity, curvature, and torsion. Geometric characteristics for solid particles are also investigated and its results are varied according to Stokes number.

## Acceleration model in Turbulent flows

난류에서 나타나는 가속도의 간헐성을 회전에 의해 나타나는 가속도와 소산에 의해 나타나는 가속도로 분리함으로써 해석하고자 하였다.

Compare the Lamb vortex model and real turbulent flow

It is well known that fluid acceleration in turbulence is highly intermittent. Source of the intermittency was found to be closely related to the rotational motion of coherent vortical structures. From the Poisson equation for pressure, acceleration, which is mostly the negative of pressure gradient, can be expressed as a sum of acceleration-like below.
$$\frac{\partial u}{\partial t} + u\cdot\nabla u = -\frac{1}{\rho} \nabla P + \nu \nabla^{2}u = a^{I} + a^{S}$$
$$a=-(\nabla^2)^{-1} \nabla \Omega + (\nabla^2)^{-1} \frac{\nabla \epsilon}{2\nu} =a^{\Omega} + a^{\epsilon}$$

They are acceleration due to rotational motion of eddy and acceleration due to irrotational strain field, respectively. We investigated the statistical characteristics of those accelerations by using direct numerical simulation of isotropic turbulence. Flatness of acceleration is of order of 10 but flatness of new defined acceleration terms are 3~5 which represents less intermittency in the range of moderate Reynolds number. Numerical and experimental results do not show clear slope since the Reynolds number is relatively low, but an asymptotic behavior is observed.