Scale Interactions in Wall Turbulence: Old Challenges Tackled with New Perspectives

The need to improve the efficiency of fluid-based systems is now of paramount importance. In experimental aerodynamics, one of the most difficult measurements is an accurate determination of surface friction. Our need to predict it accurately is fundamentally important to the design of efficient systems. Reynolds number similarity is an essential concept in describing the fundamental properties of turbulent wall-bounded flow. Unlike the drag coefficient for bluff bodies, that for a turbulent boundary layer continues to decrease indefinitely with increasing Reynolds number because the small-scale motion near the surface is directly affected by viscosity at any Reynolds number. Therefore Reynolds number similarity is very important in design and is a vital tool for the engineer, who, plied with information from either direct numerical simulations or wind-tunnel tests (or both), may well have to extrapolate over several orders of magnitude in order to estimate quantities such as drag at engineering or even meteorological Reynolds numbers. Perhaps the most well-known example of Reynolds number similarity is the region of log velocity variation (the log law) found in wall-bounded flows which, at sufficiently high Reynolds numbers, exists regardless of the nature of the surface boundary condition or the form of the outer imposed length scale.

In wall-bounded flows relevant to practical applications, where the flow is turbulent and the Reynolds number is high, the transport and loss of fluid momentum and energy is not well understood. Consequently, most predictive and modelling methods rely on a variety of assumptions. The two most critical ones are the Law of the Wall (the log law) and Townsend's local-equilibrium hypothesis. Both assumptions implicitly assume that large scales in the flow are weak and that they function independently of the small scales. However, this is clearly not true, especially in flows of engineering importance, such as when the surface is rough or when the flow is not in equilibrium. In fact, there is a multiscale interaction, referred to here as an inner-outer interaction (IOI), where the large scales influence the dynamics of the small scales and vice-versa. These interactions are not well understood and therefore any corrections to the predictive models to include these interactions are essentially achieved through ad-hoc means.

A better understanding of IOI will help explain the apparent non-universality of the constants in the log law and will certainly influence the development of models for both Reynolds-Averaged Navier-Stokes (RANS) calculation methods, Large-Eddy Simulations (LES) and hybrid RANS-LES. It will also be useful in the development of models for the control of wall turbulence, complementing knowledge from Direct Numerical Simulations which, we believe, are inherently incomplete owing to the restriction to low Reynolds numbers. Accurate models for prediction and control at realistic Reynolds numbers typical of practical applications will have to address IOI. Researchers working in specific areas of internal rough-wall flows, rough-wall boundary layers and freestream turbulence effects on boundary layers will also benefit from this fundamental work. All these aspects are abundantly present in a variety of practical applications and natural systems. For example, researchers exploring modelling strategies for practical applications such as oil and natural-gas pipelines, ship hulls and the natural and urban terrains will find the the data obtained from the roughness experiments to be very useful for validation exercises. Similarly, researchers in the area of turbomachinery will find the data from the roughness and freestream turbulence experiments extremely useful.

The understanding developed as a part of this project will enable us to devise new models for both prediction in LES as well as the control of wall turbulence for drag reduction. Both of these will lead to developments in new design technologies. The impact of wall-bounded turbulence in the transportation and energy generation sectors cannot be overstated. For example, 50% of drag in aircraft and ships, about 65% in submarines and over 90% of drag in gas pipelines can be attributed to skin friction. Given that worldwide ocean shipping consumes about 2 billion barrels of oil per year and the airline industry uses 1.5 billion barrels of jet fuel (Kim & Bewley, Annu Rev. Fluid Mech., 39:383-417, 2007), even a few percent reduction in skin-friction drag will have a massive economic and environmental impact. According to the UK Climate Change Programme's report to Parliament in July 2008, the transportation and energy supply sectors are responsible for over 55% of carbon emissions within the UK. Similar trends are observed in various countries around the world. The ability to reduce the drag will translate directly to reductions in fuel consumption and emissions. Moreover, the aircraft industries in Europe have signed up to an ACARE (Advisory Council for Aeronautic Research) agreement which commits to reducing NOx emissions by 80% and halving CO2 emissions by 2020. The proposed project attempts to radicalise our approach to wall-bounded turbulence by devising a new methodology aimed at understanding the impact of scale interactions. This will enable us to realise the commitments made to improving our environment and thereby securing our future.

Apart from contributing to our efforts aimed at addressing climate change, the long-term benefits of the current project to the general public are two-fold. First, this highly novel set of experiments is specifically focussed on generating scale interactions that are deterministic in nature, so providing a rational basis on which they may be categorised. This will help to establishing the UK with world-leading expertise in an area that has direct tangible benefits to emissions reductions and therefore the UK economy. Second, the training of a two researchers in this important research area will help counter the erosion of expertise in the area of experimental fluid mechanics in the UK and enable us to sustain excellence in this field.