## Overview

**Synthesis of flow controllers to minimise the transient energy growth of perturbations**

The objective of this work is the suppression of unstable flow perturbations with the aid of optimal and robust controllers. If these perturbations are not controlled, they grow and can lead to transition to turbulence. Suppressing (or even delaying) transition to turbulence has many beneficial effects, especially in the aerospace industry as significant savings in propulsive power can be made. In particular, the flow perturbations that develop in the flow between parallel flat plates have been studied. Current work focuses on the control of perturbations developing in boundary layers due to free stream turbulence.

**Fluid structure interaction (focus on flows inside flexible vessels)**

Fluid structure interaction (FSI) occurs in many areas of engineering (aerospace, civil or mechanical) as well as other scientific disciplines including medicine, biomechanics etc. During this interaction, the forces from the fluid flow act on the structure and cause it to deform which in turn affects the fluid flow and consequently the forces of the fluid. Thus, the response of the system can be determined only if the coupled problem is solved. A solution method for solving coupled fluid structure interaction problems has been formulated: the same discretisation method (finite volume) and solution algorithm (SIMPLE or PISO) are used for the solution of the equations that describe both media (fluid and solid). The solution method can handle both compressible and incompressible solids. For incompressible solids an equation for pressure is solved. The pressure field is discontinuous across the interface but the wall normal stress is continuous and this allows the derivation of a condition that links the pressures on either side.

**Turbulent mixing **

Mixing operations comprise a substantial part of the total process industry costs and stirred tanks is one of the main mechanical devices to perform this type of operations. Large Eddy Simulations (LES)ï»¿ of the turbulent flow inside a vessel stirred by a Rushton impeller have been performed. The interaction between the moving impeller and static baffles was accounted for explicitly using a sliding mesh methodology between the rotating and static grids.

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**PANTARHEI CODE**

For the numerical simulations a computer code developed by G. Papadakis and his group at King's and Imperial College, called** PANTARHEI**, is used. The main features of the code are listed below:

- finite volume discretisation method in fully unstructured grids.
- 2nd order accurate discretisations in space and time (up to 4th order accurate in space for structured meshes), standard or limited central schemes.
- SIMPLE or PISO algorithms for pressure/velocity coupling.
- local mesh refinement
- Explicit Algebraic Reynolds Stress Model that accounts explicitly for the non-local wall-blocking effect using elliptic relaxation
- standard Smagorinsky and dynamic sub-grid scale models for LES simulations
- sliding interfaces (for example interaction between static/rotating meshes)
- fluid-structure-interaction (solution of linear elastodynamic equations coupled with fluid flow).
- coupling with feedback controlers designed off-line using a linear model of the flow (actuation based on blowing and suction, sensing based on shear stress measurements).
- global stability analysis (coupling with the ARPACK eigensolver)

Current funding (PI): "Control of boundary layer streaks induced by free-stream turbulence using a novel velocity-pressure control framework", EPSRC, EP/I016015/1.

## Collaborators

Dr J. Whidborne, Cranfield University, Flow control

Dr P. Ricco, Sheffield University, Klebanoff modes, flow control

## Research Staff

Lu,L