The hybrid two-level large eddy simulation (TLS-LES) method is a multi-scale simulation method for high Reynolds number flows, where the two-level simulation (TLS) model is combined with the large-eddy simulation (LES) model in an additive manner through a blending function. The hybridization of TLS and LES models is performed in a manner, which ensures that the TLS model is active in the intense turbulence regions and in other regions LES model is used, thereby providing an efficient and accurate approach for simulating practical high Reynolds number flows. In TLS, the flow field is decomposed into the resolved large-scale (LS) and unresolved small-scale (SS) components through a large-scale function. It does not use the spatial filtering typically used in a large eddy simulation and therefore, many limitations associated with the filtering operation are removed. From this decomposition, a coupled system of large- and small-scale governing equations is derived. In this model, small-scale field is explicitly simulated by solving the SS equations within the LS grid. In contrast to a conventional LES, where the major effort is concentrated on modeling the subgrid scale stresses, in the multi-scale TLS method, the major effort is focused on modeling the SS velocity itself.

The TLS method is computationally expensive compared to a conventional LES due to additional solution step required for small-scale equations. Therefore, a hybrid MPI-OpenMP approach becomes essential for simulation of practical high Reynolds number flows with significant cost reduction. Current effort is generalizing the TLS-LES method to simulate both wall-bounded and complex flows such as free shear layers, wakes, strongly separated flows etc. The generalized implementation utilizes static and dynamic blending functions, a closure model for the terms resulting from hybridization, hybrid programming approach for computational efficiency and an over layered LES and TLS-LS grid topology, which ensures efficient approach to capture large- and small-scale features of a flow.

Personnel Involved: Dr. R. Ranjan, S. Mani

Sponsor: ONR (2012-2014)

**Animations:**

- spectra
- vortical
- cylinder
- airfoil

The animation shows time evolution of the small scale spanwise spectra in comparison to the large scale spanwise energy spectra. The simulation corresponds to turbulent flow in a fully developed periodic channel where TLS is used as a near-wall model. [Paper 1]

The animation shows time evolution of the instantaneous vortical structures in the turbulent flow over a bump in a channel. The vortical structures are identified using iso-values of the second invariant of the velocity gradient tensor and are colored by the instantaneous streamwise velocity. The simulation was performed with the hybrid TLS-LES approach using a static blending function. [Paper 1]

The animation shows time evolution of the magnitude of the spanwise vorticity for flow over a cylinder at a subcritical Reynolds number of 3900. A dynamic bending function is used to perform hybridization of LES and TLS models. [Paper 2]

The animation shows time evolution of the magnitude of the spanwise vorticity for flow over a NACA0015 airfoil at a Reynolds number of 35000. A dynamic bending function is used to perform hybridization of LES and TLS models. [Paper 2, 3]

**Images:**

- umean_Re

Profile of mean streamwise velocity normalized by the wall-shear velocity in the inner coordinate and compared with the DNS data. Solid curve denotes DNS results, dashed curve denotes viscous sublayer relationship and dashed-dotted curve denotes “Law of the Wall” relationship. Symbols denote TLS-LES results at friction Reynolds number = 590, 950, 1200 and 1500, respectively. The curves at different values of Reynolds number are shifted along the y-axis for clarity.

**Publications:**

- Ranjan, R. & Menon, S., 2013, "A multi-scale simulation method for high Reynolds number wall-bounded turbulent flows", Journal of Turbulence, Volume 14, No. 9, 1-39.
- Ranjan, R. & Menon, S., 2013, "A dynamic two-level large-eddy simulation method for high Reynolds number flows", 66th Annual Meeting of the APS Division of Fluid Dynamics, Volume 58, No. 18.
- Ranjan, R. & Menon, S., 2014, "Multi-scale simulations of turbulent wall-bounded and wake flows", AIAA 2014-1447, 52nd AIAA Aerospace Sciences Meeting (SciTech 2014), January 2014.