Direct numerical simulation of wall-bounded and buoyancy-driven turbulent flows

The aim of this project is to improve our understanding and prediction of turbulent fluid flows. Turbulence is the chaotic swirling fluid motion generated at the interface between fast- and slow-moving streams. Fluid here refers to gasses or liquids. One example is the flow close to the surface of aircraft, and another example is the buoyant rise of hot air in the atmosphere. These turbulent flows transport momentum, heat and mass, and thus profoundly impact energy efficiency and the climate. An improved understanding and prediction of turbulence informs the design and operation of engineering systems, and sustainable management of the environment.

Principal investigator

Daniel Chung
Magnifying glass

Area of science

Turbulent Flows Fluidisation and Fluid Mechanics Aerodynamics (excl. Hypersonic Aerodynamics)

Systems used


Applications used

Chanfast, Cascade
Partner Institution: The University of Melbourne| Project Code: fb2

The Challenge

Intuitively, the smoother a surface, the more slippery it is. However, a meticulously roughened surface, such as small grooves aligned with fluid flow called riblets, can be more slippery, or less draggy. This drag reduction is achieved by manipulating the chaotic swirls of turbulent fluid motion. The concept of riblets is inspired by textures found on sharkskin and they are now finding application on freight aircraft, leading to substantial fuel savings and emissions reductions. However, not all grooves reduce drag. Drag reduction is highly sensitive to groove cross-sectional geometry, but important details of this sensitivity remain unresolved even today, owing to limited access to high-fidelity flow data for developing physical theories, both from laboratory experiments and from computer simulations. However, University of Melbourne researchers have been making progress.

When hot (buoyant) air rises with sufficient intensity, turbulence develops. Turbulence is an efficient transporter of momentum, heat and mass. For example, it leads to enhance cooling. A complicating factor is rotation, found in aircraft engines and, of course, Earth. A classic illustration is how hurricanes rotate anticlockwise in the northern hemisphere but clockwise in the southern hemisphere. Although buoyancy-driven turbulence has been studied in laboratory experiments and in numerical simulations for decades, the effect of rotation is less understood, with consequences on engine efficiencies and climate prediction. In an aircraft engine, too much cooling leads to unnecessary waste of thrust, but too little cooling leads to engine failure. The effect of rotation is less understood because it is not only challenging to set up and observe in a laboratory but also challenging to numerically simulate on a computer at realistic rotation and heating. Thus, current design practices are based on extrapolation from data at lower heating. However, it has been long cautioned in the non-rotating setup that the behaviour at lower heating does not resemble that at higher heating. This extrapolation risk is expected to carry over to rotating systems.

The Solution

In order to develop robust riblet designs and fabrication tolerances, access to high-fidelity data is crucial, allowing us to observe the subtle changes to the turbulent flow. Even with supercomputers, the cost of direct numerical simulation is prohibitively expensive. To tackle this challenge, University of Melbourne researchers devised a novel strategy to simulate the turbulent flow in a restricted region very close to the riblets in flight conditions, along with an upscaling rule to describe the unresolved part of the flow. This strategy enabled the researchers to focus Pawsey’s supercomputing resources on the parts of the flow that mattered and across an unprecedented variety of riblet cross sections and sizes. With this data set, the researchers are able to develop and test physical theories regarding drag-reduction and drag-degradation mechanisms, which determine the optimal size and shape of riblets.

A challenge has been the availability of high-fidelity data that describes the interaction between heat transfer, turbulence, and rotation in a systematic way. On the one hand, previous laboratory experiments were constrained in parameter spaces that entangle the effects of heating and rotation rates. On the other hand, previous numerical simulations were limited in coverage of the parameter space owing to the high cost of large simulation domains. To mitigate this challenge, University of Melbourne researchers devised a strategy for simulating only a limited spatial domain that approximates conditions in a large domain. In such an idealisation, the number of essential parameters is minimised, focussing Pawsey’s supercomputing resources on a systematic investigation of the heating and rotation rates, varied independently and across meaningful ranges.

The Outcome

Research outcomes are reported in two papers, Endrikat et al. (2021) and Modesti et al. (2021), published in the prestigious Journal of Fluid Mechanics. The physical findings are based on the unprecedented high-fidelity data, generated using Pawsey supercomputing resources. The simulations would have taken at least 170 years to run on a laptop, but Pawsey’s Magnus was a lot faster. The papers transform the way we think about riblet design and optimisation. Previously, only one flow mechanism was presumed to be relevant for all riblets, but these papers show how the optimal size and shape of riblets is, in fact, set by (at least) two distinct flow mechanisms. One is the so-called Kelvin-Helmholtz mechanism also commonly seen above plant canopies (figure 1a), and the other is associated with cross-stream flow also seen near corners of cross sections (figure 1b). The relevant mechanism for a given riblet shape remains an open question and is the subject of ongoing research.

The research was conducted during the course of Dr Sebastian Endrikat’s PhD studies at the University of Melbourne, in collaboration with postdocs Dr Davide Modesti (now assistant professor at Delft University of Technology) and Dr Michael MacDonald (now lecturer at University of Auckland), Discovery Project partner investigator Dr Ricardo García-Mayoral (University of Cambridge) and Discovery Project chief investigators Professor Nicholas Hutchins and Associate Professor Daniel Chung (University of Melbourne). Now supported by the Asian Office of Aerospace Research and Development (AOARD), the team is continuing their research on riblets towards developing robust design strategies. This study highlights the importance of high-fidelity systematic turbulent flow datasets as enabled by Pawsey’s supercomputing resources in developing the theory that underpins practical drag-reduction applications.

The character of buoyancy-driven turbulence subject to rotation with systematically varied parameters is reported in Rouhi et al. (2021), led by University of Melbourne researchers, in collaboration with Prof Chao Sun (Tsinghua University, China) and Prof Detlef Lohse (University of Twente, The Netherlands). The study shows that the effect of rotation is not trivial. For small rotations, the cooling is enhanced with increasing rotation, but the trend is surprisingly reversed for high rotations. Another non-trivial effect is the earlier onset of turbulence near the wall at lower heating owing to the organising effect of rotation, with consequences on how we extrapolate cooling to operating conditions. Overall, this study highlights the importance of systematic studies that isolates the relevant physics and cautions against uninformed extrapolation of laboratory measurements to operating conditions.

List of Publications

A. Rouhi, D. Lohse, I. Marusic, C. Sun & D. Chung (2021)
Coriolis effect on centrifugal buoyancy-driven convection in a thin cylindrical shell.
Journal of Fluid Mechanics 910:A32 DOI:10.1017/jfm.2020.959

D. Modesti, S. Endrikat, N. Hutchins & D. Chung (2021)
Dispersive stresses in turbulent flow over riblets.
Journal of Fluid Mechanics 917:A55 DOI:10.1017/jfm.2021.310

S. Endrikat, D. Modesti, R. García-Mayoral, N. Hutchins & D. Chung (2021)
Influence of riblet shapes on the occurrence of Kelvin—Helmholtz rollers.
Journal of Fluid Mechanics 913:A37 DOI:10.1017/jfm.2021.2


Figure 1: Flow over riblets, micron-sized surface grooves used for aircraft drag reduction. The optimal size and shape are determined by two factors: (a) the Kelvin-Helmholtz mechanism, visualised by spanwise-coherent reversed-flow shaded regions (mean flow is into the page), occurring over the 30-degree-angle triangular riblets (left) but puzzlingly not over the 90-degree-angle triangular riblets (right); and (b) the cross-stream turbulent flow (indicated by the arrows), occurring near corners of the cross section (mean flow into the page is fast if red and slow if blue). Understanding and predicting the relevant physical mechanisms are key to robust riblet design and fabrication.
Figure 2: Heat transfer driven by buoyancy (red is hot fluid, blue is cold fluid) in a rotating thin shell. The green outline indicates a small representative domain containing the turbulence that is simulated in a doubly periodic box. The flow visualisation shows the onset of the near-wall streaky structures in grey scale heralding the onset of near-wall turbulence that changes the heat-transfer behaviour away from that extrapolated from lower levels of heating. Understanding this regime transition and its sensitivity to rotation rates are key to engineering design and climate prediction.