1. Univ logo Robust Control of Wall-bounded Turbulent Fluid Flows Peter H. Heins Dr Bryn Jones University of Sheffield UKACC PhD Presentation Showcase

2. Univ logo Turbulence UKACC PhD Presentation Showcase Slide 2 Chaotic system Multi-scale interactions Dynamics governed by nonlinear PDAEs High Highskin-friction drag drag Estimation/actuation difficult away from wall Regeneration mechanisms still unknown

3. Univ logo Modeling UKACC PhD Presentation Showcase Slide 3 Navier-Stokes Equations

4. Univ logo Control For Drag Reduction UKACC PhD Presentation Showcase Slide 4 Passivity-basedH ∞ loop-shaping Control methodologies Restricts upper bound on system energy production Only linear system needs to be controlled 11% reduction in energy 13% reduction in drag Minimizes wall-shear stresses Coprime factor uncertainty model used Low-order controllers with a priori robustness guarantees ≈ 20% reduction in drag

5. Univ logo Passivity-Based Control of Channel Flow UKACC PhD Presentation Showcase Slide 5 Fourier mode α=0,β=2Total flow

6. Univ logo Conclusions and Future Work  Turbulent flows are complex systems which exhibit high skin-friction drag  Justifiable to control the linear dynamics only, as long as the nonlinearity is modeled appropriately as a source of uncertainty  Passivity-based and H ∞ loop-shaping controllers tested using DNS  Future work  LQR/LQG control of FIK identity  Investigate new forms of actuation UKACC PhD Presentation Showcase Slide 6