(537g) Mixing Improvement of Fluid Flow Using Lagrangian Coherent Structures

Considering fluid flow problem as a dynamical system, there are emergent patterns that influence the transport phenomena in the flow. These patterns are known as coherent structures [1]. When studied in terms of the velocity field of a fluid flow in a Lagrangian framework, these structures are called Lagrangian Coherent Structures (LCSs). Relating LCSs to the ridges of finite-time Lyapunov exponent (FTLE) (or Direct Lyapunov Exponent (DLE) [2]), Shadden et al. developed the theory  and computation procedure of LCSs [3,4]. These structures are known as dynamically driven barriers to transport processes in a fluid flow and they can help reveal the mixing properties and transport mechanisms in the system. Today, identification of these structures have become an important tool for studying transport phenomena in fluid mechanics.

Moving LCSs can improve mixing by inducing transport mechanisms causing material stretching and folding [5]. In this study, it is intended to move the LCSs present in the fluid domain of a rectangular geometry to enhance mixing properties of the flow. To this end, Navier-Stockes equations with Boussinesq approximation are considered along with continuity as governing equations of fluid flow. These equations can be projected to a divergence-free space to obtain the input-output behaviour of the fluid flow. By Boussimesq approximation, the velocity field of fluid domain can be manipulated by the boundary actuation in terms of temperature distribution or heat flux to the boundary.

Finally, we are going to provide the input function (temperature distribution or heat flux on the boundary) to bring the velocity field to a desired state for which the mixing properties of the flow has been enhanced.

References

1. S. Wiggins, Chaotic transport in dynamical systems, Springer-Verlak, 1992.
2. G. Haller, Distinguished material surfaces and coherent structures in 3d fluid flows, Physica D 149 (2001) 248-277.
3. S.C. Shadden, F. Lekien, J.E. Marsden, Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows, Physica D 212 (2005) 271-304.
4. F. Lekien, S.C. Shadden, J.E. Marsden, Lagrangian coherent structures in n-dimensional systems, Journal of Mathematical Physics 48 (2007) 065404.
5. Y. Wang, G. Haller, A. Banaszuk, G. Tadmor, Closed-loop Lagrangian separation control in a bluff body shear flow model, Physics of Fluids 15 (2003) 2251-2266.