PhD Defence Xiaojue Zhu

Taylor-couette and Rayleigh-Bénard turbulence: the role of the boundaries 

Xiaojue Zhu is PhD-Student in the Physics of Fluids Research Group. His supervisors are Detlef Lohse and Roberto Verzicco from the Faculty of Science and Technology. 

The ubiquity of turbulent flows with surface roughness in nature and technology makes it important to study them. This thesis covers mainly the broad topic of Taylor-Couette (TC) and Rayleigh-Bénard (RB) turbulence with wall roughness. The roughness elements vary from the shape, size, sparseness, and alignment. The studies were mainly done by means of direct numerical simulations, with the code AFiD, which is a highly parallelized, efficient code, in combination with an immersed boundary method to track the roughness surfaces.  

We first extended the AFiD code to the GPU clusters (Chapter 2). The GPU porting has been carried out in CUDA Fortran with the extensive use of kernel loop directives (CUF kernels) in order to have a source code as close as possible to the original CPU version; just a few routines have been manually rewritten. Further, we introduced a new transpose scheme to improve the scaling of the Poisson solver. The resulting GPU version can reduce the wall clock time by an order of magnitude compared to the CPU version for large meshes. The good scaling of the code can be sustained up to 4096 GPU cards.  

As a next step, we studied TC turbulence with grooved wall roughness, parallel to the flow direction (Chapter 3). With increasing Ta, we start to observe a sharp increase of the torque and thus the effective scaling law for the torque Nuω vs. the Taylor number Ta becomes much steeper. However, with further increasing Ta, the effective scaling law saturates to the ``ultimate'' regime effective exponents seen for smooth walls. 

In Chapter 4 and Chapter 5, we tried a different type of wall roughness, namely square bars perpendicular to the flow direction. We found Nuω vs. Ta scaling exponent is enhanced greatly with wall roughness. We showed that the dominant torque at the rough boundary stems from the pressure forces on the side faces of the rough element, rather than from viscous stresses. We observed that the system becomes bulk dominant, thus increasing the effective torque scaling exponent. Specifically, when wall roughness exists on both cylinders, we have demonstrated that the asymptotic ultimate regime scaling exponent 1/2, corresponding to the upper limit of transport, can be realized. For different roughness heights, we showed a Moody-like diagram for TC turbulence. We further showed that different numbers of roughness elements could tune the scaling exponents and optimal transport properties extensively. 

In Chapter 6, we focused on the effects of wall roughness in 2D RB turbulence. With increasing Rayleigh number Ra, we revealed the existence of two regimes. In the first one, the local effective scaling exponent for Nusselt number Nu vs. Rayleigh number Ra can reach up to 1/2. However, a further increase in Ra leads to the second regime, in which the scaling exponent saturates back to a value close to the smooth wall case. This is very similar to the case of Chapter 3. In Chapter 7, we further pushed Ra to Ra=1014 in 2D RB convection with smooth walls. We revealed that the transition to the ultimate regime starts at Ra=1013 for Prandtl number Pr=1 in 2D RB turbulence, similar to the 3D counterpart.   

In Chapter 8, in 3D RB turbulence, we showed that asymmetric roughness (ratchet surfaces) can help to lock the orientation of the Large Scale Circulation Roll (LSCR) to a preferred direction even when the cell is perfectly leveled out. By introducing a small tilt to the system, we showed that the LSCR orientation can be tuned and controlled. The two different orientations of LSCR gave two quite different heat transport efficiencies, indicating that heat transport is sensitive to the LSCR direction over the asymmetric roughness structure.

Last but not least, in Chapters 9, we extended the immersed boundary method to study the interaction of multiple surface nanobubbles. We developed a finite difference scheme for the diffusion equation coupled with the immersed boundary method for the deformable and moving boundaries. With the code, we found that pinning and oversaturation can stabilize the nanobubbles against Ostwald ripening, even when the bubbles are very close to each other.