Homogeneous Shear Turbulence

We study the generation and self-sustaining mechanisms of turbulence in homogeneous shear turbulence. Simple uniform shear flow is easy to use in theoretical analysis. My previous research revealed it to be a good model for high-Reynolds-number wall-bounded turbulence used in engineering. It has been used to analyze micro-/macroscopic phenomena in molecules and powders, atmospheric stratified turbulence, and turbulence in accretion disks around black holes.

The figure on the left shows the interaction between density fluctuations (red and blue) and small-scale vortices (gray) in turbulent flows. We are expanding the scope of application to stratified turbulence (see below), which plays an essential part in atmospheric turbulence and turbulent mixing in chemical engineering, to study heat and mass transport at high Prandtl numbers.

Turbulent Channel Flow

We investigate the fundamental mechanism of maintaining and generating coherent structures near the wall and the heat transfer at the wall. A wall surface causes a sudden increase in the velocity gradient near the wall, which generates three-dimensional coherent vortex structures (longitudinal vortices elongated in the flow direction and low-velocity streaks). At high Reynolds numbers, they form a hierarchical self-generating mechanism.

Turbulent Duct Flow

For turbulent flow in a rectangular duct surrounded by walls on four sides, the behavior of the coherent structure of turbulent flow near the walls changes significantly near the corners (left figure below). This causes a secondary flow in the mean flow toward the corner, as shown in the right figure below. This is called Prandtl's secondary flow. We investigate the effect of the mean secondary flow on the wall heat transfer coefficient and wall frictional drag and explore its relationship to the coherent structures in turbulent flows. The relationship between the hierarchical structure of eddies at higher Reynolds numbers and mean secondary flow and turbulence statistics and their modeling is a challenge. We also develop technologies to improve the performance of production processes by controlling complex flows such as secondary flows.

Reinforcement learning and Bayesian optimization for flow control

The ability to control unsteady, engineering-critical turbulence can contribute to efficient energy use and a sustainable society. We are researching methods to automate various trial-and-error processes using numerical fluid simulations with AI and machine learning methods. The figure on the right shows an image of thermal control of turbulent flow in a square duct using reinforcement learning. As the agent learns, it can successfully control the amount of heating on the duct wall and the ever-changing turbulent flow conditions. Faster numerical simulations and larger truth-learning models will likely be the key to success.

Turbulent Multiphase Flow

We study mixing and interfacial phenomena of two-phase flow, such as mixing of water and oil. When two or more immiscible fluids come into contact with each other, an interface is created. Because these phenomena are on the nanoscale, they are very difficult to deal with in macro-scale numerical fluid dynamics simulations.

Turbulent Boundary Layer

My research focuses on understanding and modeling turbulent boundary layers around curved airfoil geometries such as aircraft wings and turbine blades. A thin layer, called the boundary layer, exists between the wall and the fluid flowing at high velocities on the wall, where highly complex eddy interactions occur. The separation phenomenon, especially on curved surfaces, reduces the prediction accuracy of conventional turbulence models. Therefore, it is essential to use highly accurate numerical simulation data to elucidate the underlying physics. Suppose a precise (fast and lean) turbulence model can be constructed. In that case, improving the prediction accuracy of fluid simulations and shortening the trial-and-error design process is possible. We will also clarify the details of the flow separation mechanism and propose new control methods.

(left) Visualization on the Reynolds stress isosurface reveals large-scale structure, while (right) visualization on the vorticity enstrophy reveals fine-scale vortices in turbulent flow.

Dynamical system and Data-driven approach for self-sustaining mechanism of turbulent shear flow

We conduct fundamental research to understand turbulence dynamics and control fluid flow using dynamical-system approaches and data-driven methods. Turbulence is not a random phenomenon but a nonlinear mechanism by which eddy structures are created and maintained, which affects turbulence statistics and other parameters. Statistical physics methods have not yet been applied to understand turbulent phenomena, and numerical simulations are used to study them. We are interested in understanding and modeling the generation and maintenance mechanisms of turbulent eddies embedded in the Navier-Stokes, which are the governing equations. The left figure shows turbulence activation in phase space and an unstable periodic orbit embedded in turbulence (red line). The right panel shows the eddy structure (flow-directed vorticity, red for positive and blue for negative) and velocity streaks (isosurfaces of flow-directed velocity colored by height) of turbulence approaching an active periodic solution. These solutions correspond to saddle points; turbulent conditions often come and leave the unstable solution. At relatively low Reynolds numbers, the role of these unstable periodic solutions in turbulence is becoming clear. At high Reynolds numbers, however, the interaction of eddies of various sizes is a challenge for understanding the dynamics of turbulence. A new approach is needed to understand the dynamics of turbulence.

High-performance computing with GPUs

Accelerators such as GPUs accelerate fluid analysis and optimize the design. The efficient use of GPU computation chips for machine learning and other applications is a fundamental technology for IT and environmental harmony, leading to green computing. The figure shows speed-up of Poisson solver for square duct turbulence, details in Super Computing News, Tokyo University, Vol23(1) P.57 (2021.8)

Adjoint variational method and data-assimilation

One of the data assimilation methods is an inverse analysis using the variational method. The following is an example of thermal convection in a two-dimensional cavity. The associated sensitivity analysis estimates the boundary conditions necessary to control the temperature in a set target area. To convey the information from the boundary to the target area, a simulation with inverted causality (right) is performed. It can be seen that the information flows almost in the opposite direction of the actual airflow on the left and arrives at the boundary. This sensitivity analysis is not only used in simulations but in interpreting machine learning models, i.e. explainable machine learning techniques.