Lagrangian coherent structures

The most immediate impression of turbulent flow is, probably, that it is an exceedingly complicated, tortuous and chaotic phenomenon. The experimenter equipped with instruments capable of recording the parameters of a turbulent flow will soon conclude that all these parameters fluctuate in an irregular fashion.

Statistical Description of Turbulence

Inflow boundary conditions are developed for hybrid large-eddy simulation (LES)/Reynolds-averaged Navier-Stokes approaches. They are based on an extension of the rescaling-reintroducing method developed for LES to a hybrid scheme. A blending function is used to shift the turbulence closure from a κ-ζ model near the wall to a κ-Δ subgrid-scale model away from the wall. The approach was tested for a flat plate and then applied to the study of a 25-deg compression-expansion ramp for a Mach number of 2.88 and a Reynolds number of 3.24 × 10 7 /m. In general, improvements over the κ-ζ model were noted in the recovery region. The significance of this work is that it provides a way for LES methods to address flows at a high Reynolds number

Inflow boundary conditions for hybrid large eddy/Reynolds averaged Navier-Stokes simulations

We review wall-bounded turbulent flows, particularly high–Reynolds number, zero–pressure gradient boundary layers, and fully developed pipe and channel flows. It is apparent that the approach to an asymptotically high–Reynolds number state is slow, but at a sufficiently high Reynolds number the log law remains a fundamental part of the mean flow description. With regard to the coherent motions, very-large-scale motions or superstructures exist at all Reynolds numbers, but they become increasingly important with Reynolds number in terms of their energy content and their interaction with the smaller scales near the wall. There is accumulating evidence that certain features are flow specific, such as the constants in the log law and the behavior of the very large scales and their interaction with the large scales (consisting of vortex packets). Moreover, the refined attached-eddy hypothesis continues to provide an important theoretical framework for the structure of wall-bounded turbulent flows.

High Reynolds Number Wall Turbulence

Synthetic generation of equilibrium boundary layer turbulence from modeled statistics

The finite-time Lyapunov exponent (FTLE) technique has shown substantial success in analyzing incompressible flows by capturing the dynamics of coherent structures. Recent applications include river and ocean flow patterns, respiratory tract dynamics, and bio-inspired propulsors. In the present work, we extend FTLE to the compressible flow regime so that coherent structures, which travel at convective speeds, can be associated with waves traveling at acoustic speeds. This is particularly helpful in the study of jet acoustics. We first show that with a suitable choice of integration time interval, FTLE can extract wave dynamics from the velocity field. The integration time thus acts as a pseudo-filter separating coherent structures from waves. Results are confirmed by examining forward and backward FTLE coefficients for several simple, well-known acoustic fields. Next, we use this analysis to identify events associated with intermittency in jet noise pressure probe data. Although intermittent events are known to be dominant causes of jet noise, their direct source in the turbulent jet flow has remained unexplained. To this end, a Large-Eddy Simulation of a Mach 0.9 jet is subjected to FTLE to simultaneously examine, and thus expose, the causal relationship between coherent structures and the corresponding acoustic waves. Results show that intermittent events are associated with entrainment in the initial roll up region and emissive events downstream of the potential-core collapse. Instantaneous acoustic disturbances are observed to be primarily induced near the collapse of the potential core and continue propagating towards the far-field at the experimentally observed, approximately 30° angle relative to the jet axis.

Finite-time Lyapunov exponent-based analysis for compressible flows

Localised arc filament plasma actuators are modelled with a validated technique to examine asymmetric control of a perfectly expanded round free jet to deflect its downstream trajectory. The nominal Mach and Reynolds numbers are 1.3 and 1 million, respectively. No-control, symmetrically controlled, and under-expanded jets are also simulated for comparison purposes. Parametric variation of actuation frequency and duty cycle indicate that asymmetric control can alter the trajectory, and, within the confines of the parameters investigated, the optimal forcing scheme was found to correspond to the jet's column-mode frequency and a duty cycle of approximately 60%. Increasing frequency and duty cycle beyond these values have a detrimental effect on control, which is consistent with experimental findings. Asymmetric actuation resulted in significant mixing enhancement on the actuated side, as evidenced by the increased growth rate of the non-dimensional momentum thickness. The effectiveness of control is reduced for under-expanded jet conditions.

David R. Gonzalez

Papers

Synthetic generation of equilibrium boundary layer turbulence from modeled statistics

Finite-time Lyapunov exponent-based analysis for compressible flows

Large-eddy simulations of plasma-based asymmetric control of supersonic round jets

Finite-Time Lyapunov Exponent Analysis of Intermittent Acoustic Events in a Round Jet

Wall-Modeling Strategies for Large-Eddy Simulation of Non-Equilibrium Turbulent Boundary Layers