arXiv subjects

Oscar A. Holroyd

Publications and source records attributed to Oscar A. Holroyd.

3 recordsLinked to original sources

arXiv2026

Controlling three-dimensional falling liquid films: from weighted-residual models to direct numerical simulation

We consider the problem of controlling a three-dimensional falling liquid film using same-fluid blowing and suction through the substrate. Building upon recent results for the corresponding two-dimensional problem, we employ a reduced-dimensional weighted-residual model for the film height and downstream flux as the basis for controller design. Linear stability analysis is used to estimate the number of actuators required to stabilise the film, while a linear-quadratic regulator (LQR) framework is used to construct feedback controls for the linearised system. The resulting gain matrix is then combined with observations from direct numerical simulation (DNS) of the three-dimensional Navier-Stokes equations, allowing controls derived from the reduced-dimensional model to be applied directly to the full flow. Through systematic numerical tests, we demonstrate that these controls successfully stabilise the flat-film solution across a physically relevant range of Reynolds numbers and domain configurations. We further show that both the number and placement of actuators play a crucial role in control performance, with spanwise instabilities requiring additional actuator coverage in the cross-stream direction. Although the extension from two to three dimensions substantially increases the cost of controller construction, this cost is incurred entirely offline during the computation of the gain matrix, making the overall framework computationally tractable. Our results demonstrate that LQR feedback controls derived from a three-dimensional weighted-residual model retain predictive value when applied to fully resolved DNS, extending previous two-dimensional control methodologies and helping bridge the gap between theoretical control design and experimentally relevant falling-film flows.

physics.flu-dyn↗

arXiv2024

Stabilisation of falling liquid films with restricted observations

We propose a method to stabilise a solution to equations describing the interface of thin liquid films falling under gravity with a finite number of actuators and restricted observations. As for many complex systems, full observation of the system state is challenging in physical settings, so methods able to take this into account are important. The Navier-Stokes equations modelling the flow are a complex, highly nonlinear set of PDEs, so standard control theoretical results are not applicable. Instead, we chain together a hierarchy of increasingly idealised approximations, developing a control strategy for the simplified model which is shown to be successfully applied to simulations of the full system.

math.OC↗

arXiv2023

Linear quadratic regulation control for falling liquid films

We propose and analyse a new methodology based on linear-quadratic regulation (LQR) for stabilising falling liquid films via blowing and suction at the base. LQR methods enable rapidly responding feedback control by precomputing a gain matrix, but are only suitable for systems of linear ordinary differential equations (ODEs). By contrast, the Navier-Stokes equations that describe the dynamics of a thin liquid film flowing down an inclined plane are too complex to stabilise with standard control-theoretical techniques. To bridge this gap we use reduced-order models - the Benney equation and a weighted-residual integral boundary layer model - obtained via asymptotic analysis to derive a multi-level control framework. This framework consists of an LQR feedback control designed for a linearised and discretised system of ODEs approximating the reduced-order system, which is then applied to the full Navier-Stokes system. The control scheme is tested via direct numerical simulation (DNS), and compared to analytical predictions of linear stability thresholds and minimum required actuator numbers. Comparing the strategy between the two reduced-order models we show that in both cases we can successfully stabilise towards a uniform flat film across their respective ranges of valid parameters, with the more accurate weighted-residual model outperforming the Benney-derived controls. The weighted-residual controls are also found to work successfully far beyond their anticipated range of applicability. The proposed methodology increases the feasibility of transferring robust control techniques towards real-world systems, and is also generalisable to other forms of actuation.

math.OC↗