Ab initio hydrodynamic rough surface characterisation with applications

Turbulent flow over rough surfaces is common in nature and in many technological applications, yet the methods used to predict it are based on a limited experimental database and on correlations that are known to give contradictory predictions. There is much still to learn about how particular surface features lead to certain drag increases and it is widely accepted that the standard measure of equivalent sand grain roughness is no longer sufficient, since surfaces with the same roughness on this scale have different behaviour in the transitionally rough flow regime. We propose a research programme based on numerical simulation to study rough surface flow, particularly in the high speed flight regime where we have an immediate requirement from our project partners in government and industry. With the proposed development of high-order implementations of immersed boundary conditions, numerical simulation of flow over regular or random rough surfaces will be feasible, resolving the scales of roughness that interact with turbulent flow near a wall. A programme of work is proposed to develop such a capability, initially based on parameteric studies and high resolution studies requiring the use of national supercomputer facilities. However, with the rapidly decreasing cost of computing power, the technique we will use for this work is believed to be more widely useful, and by the end of the project we propose to develop a rough surface characterisation workflow, whereby samples can be scanned, using for example a confocal microscope, surface data interpolated into a boundary condition for numerical simulation and then simulations run for a range of scales (surface scale relative to flow scale) to build a hydrodynamic characterisation map of the surface.

The more academic aspects will be reported to conferences and journals as appropriate. Several aspects have a good chance for high academic impact. The development of a high-order immersed boundary treatment is currently absent from the numerical literature. We think we are well on the road to demonstrate how this can be done and, with the workplan proposed, we would expect to be able to publish in a top journal, for example the Journal of Computational Physics. The algorithms developed will be incorporated in the Southampton SBLI code which is the most widely used code in the UK Turbulence Consortium, thus making the advances available to a small but active high performance computing community. The proposed simulations of high speed flow over roughness elements are novel and we expect to be able to publish two papers in the Journal of Fluid Mechanics on more fundamental aspects of the fluid mechanics. Beyond these, we expect to be able to use the simulation capability to do calculations that will develop synthetic rough wall conditions for large eddy simulation (LES) that can have a large impact as LES becomes more widely used for engineering applications. Summary data from calculations will be published online in a standardised format, including the surface morphology alongside the simulation data. The proposed rough-surface characterisation service, to be developed during the project and then continued as a consultancy venture via our research institute for industry (Rifi), will provide industrial impact. The basic components of such a process are in place and we anticipate that computer costs will reduce in a three year time frame to the point where a practical service can be offered. The project partners (Dstl and FGE) will have early access to the service for high speed material selection for space access and sustained high speed flight applications. Partners and clients will ultimately be able to submit surface samples and have these characterised in terms of hydrodynamic roughness, providing valuable data for clients to obtain commercial advantage for their products.