Roughness in Highly Turbulent Taylor-Couette and Rayleigh-Bénard Flows

**Principal Investigator:**

Detlef Lohse

**Affiliation:**

Max-Planck-Institut für Dynamik und Selbstorganisation, Göttingen (Germany), and Max Planck Center Twente for Complex Fluid Dynamics and Physics of Fluids Group, University of Twente (The Netherlands)

**Local Project ID:**

PRA099

**HPC Platform used:**

JUWELS of JSC

**Date published:**

Many wall-bounded flows in nature and technology are affected by the surface roughness at the wall. In some cases, this has adverse effects, e.g. drag increase leading to higher fuel costs; in others, it is beneficial for mixing enhancement or transfer properties. Computationally, it is notoriously difficult to simulate these flows because of the large scale-separation in highly turbulent flows and the challenging involved in simulating the effect of irregular boundaries. From a physics perspective, many questions are still unanswered, one of the most urgent ones being the effects of roughness topology on local and global flow features. In this research, three specific points are investigated, which contribute to a better understanding of the relationship between roughness topology and flow dynamics.

First, the effect of the mean surface height in the transitionally rough regime of Taylor-Couette flow is investigated [1], see figure 1. Remarkably, it is found that the Hama roughness function appears to be similar for Taylor-Couette and pipe flow (Nikuradse) - in particular, when one considers that Taylor-Couette flow contains a streamwise curvature and strong secondary motions (Taylor rolls), which are absent in the pipe flow. As such, the findings point towards a universal behavior of the roughness function for very different fluid flow systems.

By a superposition of different rough elements with various length scales, a systematical study on the effect of the multi-scale nature on the small scale properties and large scale heat transfer is investigated [2]. It is found that for rough boundaries that contain three distinct length scales, a scaling exponent of β=0.49±0.02 can be sustained for at least three decades of Ra. The physical reason is that the threshold Rayleigh at which the scaling exponent β saturates back to the smooth wall value is pushed to larger Rayleigh when the smaller roughness elements fully protrude through the thermal boundary layer. The multi-scale roughness employed here may better resemble the irregular surfaces that are encountered in geophysical flows and some industrial applications, than typical studies with monodisperse roughness do.

Third, the dynamics of the large scale Taylor-Vortex in Taylor-Couette flow are investigated [3]. It is found that under the generic name of ‘Taylor Vortex,’ there is a wide variety of structures that differ in the vorticity distribution within the cores, the way they are driven, and their effects on the mean flow. The rolls at high Reynolds numbers do not form due to centrifugal instabilities, but to a combination of shear and anti-cyclonic rotation, showing that they are preserved in the limit of vanishing curvature and can be better understood as a pinned cycle which shows similar characteristics as the self-sustained process of shear flows. By analyzing the effect of the computational domain size, we show that the position of the rolls varies with space and time and is determined by a random process.

The studies are carried out for Taylor-Couette and Rayleigh-Bénard flow, i.e., two paradigmatic and complementary systems in turbulence research. In particular, the effects of wall roughness on the flow structures in the vicinity of the wall, higher-order statistics, energy budgets, and large-scale flow features (e.g., plume ejection, Taylor rolls, and the large-scale circulation) are investigated. Direct numerical simulations are carried out with the AFiD code (www.afid.eu). Wall roughness is implemented using the immersed boundary method.

**Project Team**

Detlef Lohse(PI)^{1,2,} Richard Stevens^{2}, Roberto Verzicco^{2,3,4}, Chong Shen Ng^{2}, Xiaojue Zhu^{2}, Alexander Blass^{2}, Pieter Berghout^{2}, Martin Assen^{2}, Vamsi Arza^{2}, Francesco Sacco^{4}

[1] Max-Planck-Institut für Dynamik und Selbstorganisation, Am Fassberg 17, 37077 Göttingen, Germany

[2] Max Planck Center Twente, Physics of Fluids Group, MESA+ Institute, and J. M. Burgers Center for Fluid Dynamics, University of Twente, P.O. Box 217, 7500AE Enschede, Netherlands

[3] Dipartimento di Ingegneria Industriale, University of Rome ‘Tor Vergata’, Via del Politecnico 1,

Roma 00133, Italy

[4] Gran Sasso Science Institute - Viale F. Crispi, 7 67100 L'Aquila, Italy

**References and Links**

[1] P. Berghout, X. Zhu, D. Chung, R. Verzicco, R.J.A.M. Stevens, and D. Lohse. Direct numerical simulations of Taylor–Couette turbulence: the effects of sand grain roughness. J. Fluid Mech. 873, 260–286 (2019)

[2] F. Sacco, R. Verzicco, and R. Ostilla-Mónico. Dynamics and evolution of turbulent Taylor rolls. J. Fluid Mech. 870, 970–987 (2019)

[3] X. Zhu, R.J.A.M. Stevens, O. Shishkina, R. Verzicco, and D. Lohse. Nu~Ra(1/2) scaling enabled by multiscale wall roughness in Rayleigh–Bénard turbulence. J. Fluid Mech. 869, R4 (2019).

**Scientific Contact**

Prof. Dr. Detlef Lohse

Max-Planck-Institut für Dynamik und Selbstorganisation, Göttingen, Germany

Max Planck Center Twente for Complex Fluid Dynamics and Physics of Fluids Group, University of Twente, The Netherlands

e-mail: d.lohse [@] utwente.nl

**NOTE:** This project was made possible by PRACE (Partnership for Advanced Computing in Europe) allocating a computing time grant on GCS HPC system Hazel Hen of the High Performancee Computing Center Stuttgart (HLRS).

*JSC project ID: PRA099*

*December 2019*