Reduced-order models of wall-bounded turbulence

The Challenge

Wall turbulence is pervasive in engineered systems, as well as in nature. As an object moves through a fluid, the no-slip condition at the solid boundary generates a thin region of shear close to the surface where the fluid is pulled along with the object. The velocity gradients within this thin region (the boundary layer) give rise to tangential shear stresses (skin-friction drag), against which any propulsion system must work. In the overwhelming majority of cases the flow within this boundary layer is highly chaotic and turbulent (as opposed to laminar), and is therefore referred to as a turbulent boundary layer or a turbulent wall-bounded flow. The viscous drag resulting from this turbulent motion accounts for a large proportion of the mechanical losses that are suffered. For a passenger aircraft, for example, approximately 50% of the overall drag is due to turbulent skin-friction drag. For a large crude tanker, this rises to approximately 90%. For flow in a large pipe or duct, all of the mechanical losses (and therefore pumping costs) are due to turbulent skin-friction drag.

The Solution

Aim 1: We will investigate the estimation of a flow using limited measurements. Work to date (described in the report) has looked at estimation using individual sensor locations, chosen in a relatively ad-hoc fashion. The particular focus will therefore be on a systematic identification of the best sensor types and locations to achieve the best possible flow estimate. High-fidelity simulations will allow a detailed comparison between the model-based estimate and the true flow. Understanding this estimation problem is crucial to the control problem, which forms aim 2 of the study.
• Aim 2: Closed-loop control of high Re turbulence Progressing naturally from aim 1: with a reliable estimate of the flow available, closed-loop control actions based on that estimate will be introduced in high-fidelity numerical simulations (DNS) to control the flow. The particular focus will be on the efficacy of model-based control when using a wall-based actuation strategy. This will require quite an extensive set of high-fidelity simulations to be performed.

The Outcome

The computational requirements of the project are large for two reasons: First, direct numerical solution will be used to resolve the Navier–Stokes equations at all scales, which is an inherently expensive approach. Second, the simulations become more expensive as Reynolds number increases, and our specific interest in high-Reynolds-number flows therefore makes for expensive simulations. To give an example: at a Reynolds number of Reτ =1000 (which sits right at the lower end of what one might deem a ‘high’ Reynolds number) and for one flow-through time, one requires of the order of 1.6 billion cells and 20,000 time steps. For the Chanfast code used—rated at approximately 2 ×10−9 CPU core hours per cell per time step—this requires 64 kSU per flow-through time. At a fundamental scientific level, this proposal will significantly advance the state of the art in the modelling and control of turbulence, and therefore relates to Socio-Economic Objective (SEO) 970102: Expanding Knowledge in the Physical Sciences. The results of the estimation problem in aim 1 are important not only for effective control of wall- bounded turbulent flows: they could also be used in any application where flow field information is desired using only a limited set of measurements. By providing relatively simple dynamical models of high Reynolds number turbulence, the model-based estimators will also provide much-needed physical insight into the dynamical processes at play. At an operational level, a specific and timely benefit to Australia is in the area of skin-friction drag reduction, making it highly relevant to Socio-Economic Objective (SEO) 850702: Energy Conservation and Efficiency in Transport. This relates to the disproportionate effect that rising crude oil prices have on transportation to and from Australia—including, for example, air travel and shipping. The potential benefits would therefore extend well beyond fundamental academic achievement. The benefits of cheaper and more efficient long-haul transportation would permeate many aspects of Australia’s economy, society and its environment.

List of Publications

S. J. Illingworth, Streamwise-constant large-scale structures in Couette and Poiseuille flows, J. Fluid Mech. (2020), vol. 889, A13.

B. Jin, S. J. Illingworth & R. D. Sandberg, Feedback control of vortex shedding using a resolvent-based modelling approach, J. Fluid Mech. (2020), vol. 897, A26.

J. Gong , J. P. Monty & and S. J. Illingworth, Model-based estimation of vortex shedding in unsteady cylinder wakes, Phys. Rev. Fluids (2020) 5, 023901.