## Unsteady separated flows Large Eddy Simulation and Wing Flows

Many flows of practical importance are governed by viscous near-wall phenomena that have a major influence on the flow properties. Among those, unsteady flow separation currently poses one of the greatest challenges for numerical simulations. It appears in a wide range of applications pertinent not only to external flows but also to internal flows, such as flows around turbomachinery blades, in divergent channels and nozzles. The flow over curved surfaces has to overcome an adverse pressure gradient as it travels along the surface. Consequently, kinetic energy is transformed into internal energy. In addition to this retarding force, the viscous shear continuously slows the fluid down as it progresses along the surface until, ultimately, the slope of the velocity profile becomes zero. Under the perpetual influence of the adverse pressure gradient the flow begins to reverse its direction and separates from the surface. These phenomena are inherently unstable; thus a well-defined point of separation cannot be accounted for. It rather results in a separation area with a downstream recirculation zone. The unsteady free shear-layer between the main-stream and the separated boundary layer rolls up into KelvinHelmholtz-type vortices that transfer momentum between the free-flow and the recirculation zone. The instability of this unsteady system manifests itself in the breakdown of the Kelvin Helmholtz structures. Thus, for massively separated flow, a highly turbulent wake region dominated by the small-scale dynamics of the secondary vortices develops. To date, no theoretical models have been developed that can deal with the complexity of this type of flow. The boundary-layer equations, a simplification of the NavierStokes equations, are only valid up to the point of separation. Downstream of this point, however, the separation zone thickens quickly and the approximations made in the boundary-layer equations are no longer valid.

To address the above issues we have developed Implicit Large Eddy Simulation (ILES) methods and applied them to the study of transitional and turbulent separated flows. The ILES methods include second, third, and fifth order MUSCL and third and ninth-order WENO methods. Indicative examples from ILES are shown below:

#### References

- D. Drikakis, M. Hahn, A. Mosedale, B. Thornber, Large Eddy Simulation Using High Resolution and High Order Methods, Philosophical Transactions Royal Society A, 367, 2985-2997, 2009.
- M. Hahn, D. Drikakis, Implicit Large-Eddy Simulation of Swept Wing Flow using High-Resolution Methods, AIAA Journal, Vol. 47, 3, 618-629, 2009.
- M. Hahn, D. Drikakis, Assessment of Large-Eddy Simulation of Internal Separated Flow, Journal of Fluids Engineering, Vol. 131, 071201-071215, 2009.
- B. Thornber, D.Drikakis, Implicit Large Eddy Simulation of a Deep Cavity Using High-Resolution Methods, AIAA Journal, Vol. 46, 10, 2634-2685, 2008.
- D. Drikakis, M. Hahn, Z. Malick, E. Shapiro, Implicit Large Eddy Simulations of Wall-Bounded Turbulent Flows, ERCOFTAC Bulletin, Special Issue on Wall Modelling in LES, 72, 61-66, 2007.
- D. Drikakis, Advances in turbulent flow computations using high-resolution methods, Progress in Aerospace Science, 39, 405-424, 2003.
- Z.A. Rana, B. Thornber, D. Drikakis, On the importance of generating accurate turbulent boundary condition for unsteady simulations, Journal of Turbulence, Vol. 12, 2011.
- P. Tsoutsanis, A.F. Antoniadis, D. Drikakis, WENO schemes on arbitrary unstructured meshes for laminar, transitional and turbulent flow, Journal of Computational Physics, 256, 254-276, 2014.
- M. Hahn, D. Drikakis, Large eddy simulation of compressible turbulence using high-resolution methods, International Journal for Numerical Methods in Fluids, 47, 971-977, 2005.