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Register a new userUniversal Model of Finite-Reynolds Number Turbulent Flow in Channels and Pipes
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In this Letter we suggest a simple and physically transparent analytical model of the pressure driven turbulent wall-bounded flows at high but finite Reynolds numbers Re. The model gives accurate qualitative description of the profiles of the mean-velocity and Reynolds-stresses (second order correlations of velocity fluctuations) throughout the entire channel or pipe in the wide range of Re, using only three Re-independent parameters. The model sheds light on the long-standing controversy between supporters of the century-old log-law theory of von-K`arm`an and Prandtl and proposers of a newer theory promoting power laws to describe the intermediate region of the mean velocity profile.
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We present a collection of eight data sets, from state-of-the-art experiments and numerical simulations on turbulent velocity statistics along particle trajectories obtained in different flows with Reynolds numbers in the range $R_lambda in [120:740]$. Lagrangian structure functions from all data sets are found to collapse onto each other on a wide range of time lags, revealing a universal statistics, and calling for a unified theoretical description. Parisi-Frisch Multifractal theory, suitable extended to the dissipative scales and to the Lagrangian domain, is found to capture intermittency of velocity statistics over the whole three decades of temporal scales here investigated.
Modeling the effect of complex terrain on high Reynolds number flows is important to improve our understanding of flow dynamics in wind farms and the dispersion of pollen and pollutants in hilly or mountainous terrain as well as the flow in urban areas. Unfortunately, simulating high Reynolds number flows over complex terrain is still a big challenge. Therefore, we present a simplified version of the wall modeled immersed boundary method by Chester et al. (J. Comput. Phys. 2007; 225: 427-448). By preventing the extrapolation and iteration steps in the original method, the proposed approach is much easier to implement and more computationally efficient. Furthermore, the proposed method only requires information that is available to each processor and thus is much more efficient for simulations performed on a large number of cores. These are crucial considerations for algorithms that are deployed on modern supercomputers and will allow much higher grid resolutions to be considered. We validate our method against wind tunnel measurements for turbulent flows over wall-mounted cubes, a two dimensional ridge, and a three-dimensional hill. We find very good agreement between the simulation results and the measurement data, which shows this method is suitable to model high Reynolds number flows over complex terrain.
A shear-improved Smagorinsky model is introduced based on recent results concerning shear effects in wall-bounded turbulence by Toschi et al. (2000). The Smagorinsky eddy-viscosity is modified subtracting the magnitude of the mean shear from the magnitude of the instantaneous resolved strain-rate tensor. This subgrid-scale model is tested in large-eddy simulations of plane-channel flows at two different Reynolds numbers. First comparisons with the dynamic Smagorinsky model and direct numerical simulations, including mean velocity, turbulent kinetic energy and Reynolds stress profiles, are shown to be extremely satisfactory. The proposed model, in addition of being physically sound, has a low computational cost and possesses a high potentiality of generalization to more complex non-homogeneous turbulent flows.
We address the Additive Equivalence discovered by Virk and coworkers: drag reduction affected by flexible and rigid rodlike polymers added to turbulent wall-bounded flows is limited from above by a very similar Maximum Drag Reduction (MDR) asymptote. Considering the equations of motion of rodlike polymers in wall-bounded turbulent ensembles, we show that although the microscopic mechanism of attaining the MDR is very different, the macroscopic theory is isomorphic, rationalizing the interesting experimental observations.
A new approach to turbulence simulation, based on a combination of large-eddy simulation (LES) for the whole flow and an array of non-space-filling quasi-direct numerical simulations (QDNS), which sample the response of near-wall turbulence to large-scale forcing, is proposed and evaluated. The technique overcomes some of the cost limitations of turbulence simulation, since the main flow is treated with a coarse-grid LES, with the equivalent of wall functions supplied by the near-wall sampled QDNS. Two cases are tested, at friction Reynolds number Re$_tau$=4200 and 20,000. The total grid node count for the first case is less than half a million and less than two million for the second case, with the calculations only requiring a desktop computer. A good agreement with published DNS is found at Re$_tau$=4200, both in terms of the mean velocity profile and the streamwise velocity fluctuation statistics, which correctly show a substantial increase in near-wall turbulence levels due to a modulation of near-wall streaks by large-scale structures. The trend continues at Re$_tau$=20,000, in agreement with experiment, which represents one of the major achievements of the new approach. A number of detailed aspects of the model, including numerical resolution, LES-QDNS coupling strategy and sub-grid model are explored. A low level of grid sensitivity is demonstrated for both the QDNS and LES aspects. Since the method does not assume a law of the wall, it can in principle be applied to flows that are out of equilibrium.
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