Control Theory for Flow Management

Module aims

The purpose of the course is to provide an overview of a rapidly expanding area involving novel ways in which fluid flow may be controlled through sensing (e.g. velocity, temperature, pressure) and its subsequent control via actuation to produce a controlled disturbance (e.g. blowing, suction, vortex generator deployment) in order to achieve a desired effect (e.g. drag reduction, mixing enhancement, noise reduction). The ideas may generally be expressed as “flow management” or “flow control”.  The course is multi-disciplinary, beginning with the introduction of basic ideas from linear algebra and control theory, their application to data-driven flow modelling, new advances in materials and some fundamentals of fluid mechanics.  Key flow control strategies relating to drag reduction will be discussed.  

Learning outcomes

Upon completing this course you will be able to: 1. Assess what modern technology permits in terms of flow control 2. Describe novel open- and closed-loop control schemes from theoretical origins to the development of technology platforms 3. Apply concepts from linear algebra and control theory to fluid flow modelling and control 4. Apply matrix-valued optimisation to extract flow models from numerical or experimental data thereby developing a clear understanding of modern methods for data-driven flow modelling 5. Appraise a diverse range of methods for flow control, including those that represent mature technologies as well as those that are at the cutting edge AHEP Learning Outcomes: SM7M, EA6M, EA5m, EA7M, D9M, E11M, P12M, G1 

Module syllabus

Reduced-order models for flow control. Data-driven modelling techniques, including Proper Orthogonal Decomposition and Dynamic Mode Decomposition. Linear Algebra: matrix-vector manipulation, matrix-valued optimziation, solution of finite-dimensional ordinary differential equations. Application of linear control to fluid modelling and control in both the time domain and frequency domain. Laplace transforms. Linear control systems with delays. Stabilization of nonlinear systems. Extremum-seeking control.    Identification of control goals.  An assessment of the key requirements for effective flow control, observability, controllability. Why feedback control?  Receptivity, stability.  Review of sensors, need for wall-mounted sensors and actuators including pressure sensors and shear-stress sensors. Review of actuators, and explanation by use of vorticity flux. Application of new materials (e.g. electro-active polymers). State estimation and model reduction. Applications to flow control and drag reduction: full domain forcing of turbulent channel flow, separation and direct–wake control. 

Pre-requisites

Mathematics, including linear algebra and calculus (ordinary differential equations)

Teaching methods

The module will be delivered primarily through large-class lectures introducing the key concepts and methods, supported by a variety of delivery methods combining the traditional and the technological.  The content is presented via a combination of slides, whiteboard and visualizer.Learning will be reinforced through tutorial question sheets, featuring analytical tasks representative of those carried out by practising engineers. 

Assessments

Exam - Written examination (100%)