The effect of wall roughness on heat transport in turbulent natural thermal convection

• Applicant: Privatdozentin Dr. Olga Shishkina
• Subject Area: Fluid Mechanics
• Term: from 2010 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 191894326

• Final Report Year: 2020

Final Report Abstract

The regular wall roughness effects were studied by means of DNS, in a box-shaped domain, for Pr = 0.786 and Ra between 106 and 108 . The surface roughness was introduced by parallelepiped equidistantly distributed obstacles attached to the bottom and top plates. In particular, it was shown that for a fixed Ra, the change in the value of Nu is determined not only by the covering area of the surface, i.e. the obstacle height, but also by the distance between the obstacles. The heat flux enhancement was found to be the largest for wide cavities between the obstacles which can be “washed out” by the flow. Theoretical limiting cases for very wide and very narrow obstacles were studied and a simple model for the heat flux enhancement due to the wall roughness was suggested, without introducing any free parameters. This model predicts well the general trends and the order of magnitude of the heat flux enhancement obtained in the DNS. The above study was extended to the case of a cylindrical convection cell of the aspect ratio one. The roughness was introduced by a set of isothermal obstacles, which are attached to the plates and have a form of concentric rings of the same width. The choice of the geometry was motivated by the following reasons. In cylindrical domains with ring-shaped roughness elements, the turbulent wind, or LSC, that develops in RBC cells for sufficiently large Ra, unavoidably goes across the roughness elements, independently from the LSC orientation. Also the geometry choice is motivated by a reduced influence of the sidewall effects compared to the previously studied case of convection in box-shaped containers with small widths. The considered Pr = 1 and Ra varied from 106 to 108 , the considered number of the rings on each plate is 1, 2, 4, 8 or 10, the height of the rings was varied from 1.5% to 49% of the cylinder height and the gap between the rings was varied from 1.5% to 18.8% of the cell diameter (totally, 135 different cases). The DNS showed that by small Ra and wide roughness rings, a small reduction of the mean heat transport (Nu) is possible, but in the most cases, the presence of the heated and cooled obstacles generally leads to an increase of Nu, compared to the case of classical RBC with smooth plates. When the rings are very tall and the gaps between them are sufficiently wide, the effective mean heat flux can be several times (more than 7 times for the studied cases) larger than in the smooth case. For a fixed geometry of the obstacles, the scaling exponent in the Nu vs. Ra scaling first increases with growing Ra up to approximately 0.5, but then smoothly decreases back towards the exponent in the no-obstacle case. To prevent the saturation of the above scaling exponent, multiscale roughness was employed. Multiple 2D DNS of RBC using an immersed boundary method to capture the plate roughness were conducted. It was found that for rough boundaries that contain three distinct length scales, a scaling exponent of about 0.49 can be sustained for at least three decades of Ra. The Ra-threshold at which the scaling exponent saturates back to the smoothwall value is pushed to larger Ra, when the smaller roughness elements protrude through the thermal BL.

Publications

• (2016). Heat flux enhancement by regular surface roughness in turbulent thermal convection. J. Fluid Mech. 763, 109–135
  S. Wagner & O. Shishkina
  
• (2017). Scaling relations in large-Prandtlnumber natural thermal convection. Phys. Rev. Fluids 2, 103502
  O. Shishkina, M. Emran, S. Grossmann, D. Lohse
  
• (2018). Effect of Prandtl number on heat transport enhancement in Rayleigh–Bénard convection under geometrical confinement. Phys. Rev. Fluids 3, 013501
  K.L. Chong, S. Wagner, M. Kaczorowski, O. Shishkina, K.-Q. Xia
  
• (2019). Nu ∼ Ra1/ 2 scaling enabled by multiscale wall roughness in Rayleigh–Bénard turbulence. J. Fluid Mech. 869, R4
  X. Zhu, R.J.A.M Stevens, O. Shishkina, R. Verzicco & D. Lohse
  
• (2020). Natural convection in cylindrical containers with isothermal ring-shaped obstacles. J. Fluid Mech. 882, A3
  M. Emran & O. Shishkina