ENGINEERING AND CFD

The efficient design and performance of many engineering systems rely on turbulent boundary layers (TBL) remaining attached to aerodynamic surfaces in regions of adverse pressure gradient (APG); for example in wind turbine blades and aircraft wings. The boundary layer is the region where the mean flow velocity increases from zero at the wall to its maximum value at some relatively short distance away from the wall. If the near mean wall velocity points in the direction opposing the bulk fluid flow, then the flow is deemed to have separated. Separation occurs in the presence of an APG, and can potentially result in catastrophic consequences, such as for example an aircraft losing lift or at best sub-optimal performance, such as for example wind turbines producing less energy.

There has been a long history of theoretical, experimental and numerical research into TBL. The vast majority of the research, however, has been centred on the zero pressure gradient (ZPG) case, while many aspects of the complex turbulent structure and appropriate scaling of APG TBL remain largely unresolved. The study of APG TBL in an appropriate canonical form is, therefore, of utmost importance to understand the influence of the local pressure gradient. Adverse pressure gradients typically arise due to the presence of convex curved surfaces, such as on a wind turbine blade. This type of configuration is difficult to systematically study, since the pressure gradient applied to the TBL is constantly changing. Here we study a self-similar APG TBL, in which the non-dimensional pressure gradient (β) is constant, and each of the terms in the governing equations have the same proportionality with position in the streamwise bulk-flow direction.

Specifically direct numerical simulation (DNS) is used to investigate the structure and dynamics of a self-similar TBL in a strong APG environment such that the flow is statistically maintained immediately prior to separation. The maximum momentum thickness based Reynolds number is Re_δ2=10⁴. The results are also compared and contrasted to an associated ZPG TBL.

This project had to overcome a number of challenges, which without the supercomputer facilities made available by the Gauss Centre for Supercomputing could not have been addressed. One, which is pivotal to the simulation of the self-similar APG TBL, and any TBL in general, is in this case the correct far field boundary conditions which leads to the desired strong APG environment that will lead to a self-similar TBL at the verge of mean boundary layer separation. No exact theoretical far field boundary condition can be derived for a TBL. What was necessary was the derivation of a far field boundary condition based on a theoretical idea from laminar boundary layer theory. The testing of the boundary condition could only be undertaken using DNS of the TBL itself and then testing if the required conditions for self-similarity were indeed obtained [1].

This process, ultimately after having undergone a number of optimisations and fine-tuning, as well as domain independence studies, resulted in the DNS of the self-similar TBL in a strong APG environment at the verge of separation up to a Reynolds number based on the momentum thickness of 10⁴. This DNS of this turbulent flow at the desired Reynolds number is the first of its kind and has only been possible because of the availability of the Leibniz Supercomputer Centre SuperMUC Petascale System through the Gauss Centre for Supercomputing.

The numerical computer code used for the DNS, originally developed by Professor Jimenez and his group at Universidad Politécnica de Madrid, Spain utilises hybrid MPI/openMP parallelisation to decompose the domain [2]. All input and output is parallelised using the parallel HDF5 library and associated file format.

17 million CPU-hours were used in the course of this project. The code has been parallelised up to 32,768 cores, with typical jobs using 4096 cores. For a single instant in time, one set of restart files requires 168Gb of disk space. Statistics have been accumulated over millions of instances in time. Hundreds of restart files have been written to disk for further post-processing of the results.

Figure 1 compares instantaneous vortex structures from the APG TBL (red) and ZPG TBL (green), illustrating the vast complexity and size of such flows. The APG TBL also clearly expands more rapidly in streamwise direction due to the stronger farfield BC suction velocity.