Elias Balaras

An embedded-boundary formulation for large-eddy simulation of turbulent flows interacting with moving boundaries

A non-boundary-conforming formulation for simulating complex turbulent flows with dynamically moving boundaries on fixed Cartesian grids is proposed. The underlying finite-difference solver for the filtered incompressible Navier-Stokes equations is based on a second-order fractional step method on a staggered grid. To satisfy the boundary conditions on an arbitrary immersed interface, the velocity field at the grid points near the interface is reconstructed using momentum forcing without smearing the sharp interface. The concept of field-extension is also introduced to treat the points emerging from a moving solid body to the fluid. Laminar flow cases and large-eddy simulations (LES) are presented to demonstrate the formal accuracy and range of applicability of the method. In particular, simulations of laminar flow induced by the harmonic in-line oscillation of a circular cylinder in quiescent fluid, and from a transversely oscillating cylinder in a free-stream are presented and compared to reference simulations and experiments. LES of turbulent flow over a traveling wavy wall and transitional flow through a bileaflet prosthetic heart valve are also shown. All results are in very good agreement with reference results in the literature.

Modeling complex boundaries using an external force field on fixed Cartesian grids in large-eddy simulations

Abstract In the present study a methodology to perform large-eddy simulations around complex boundaries on fixed Cartesian grids is presented. A novel interpolation scheme which is applicable to boundaries of arbitrary shape, does not involve special treatments, and allows the accurate imposition of the desired boundary conditions is introduced. A method to overcome the problems associated with the computation of the subgrid scale terms near solid boundaries is also discussed. A detailed study on the accuracy and efficiency of the method is carried out for the cases of Stokes flow around a cylinder in the vicinity of a moving plate, the three-dimensional flow around a circular cylinder, and fully developed turbulent flow in a plane channel with a wavy wall. It is demonstrated that the method is second-order accurate, and that the solid boundaries are mimicked “exactly” on the Cartesian grid within the overall accuracy of the scheme. For all cases under consideration the results obtained are in very good agreement with analytical and numerical data.

The inner-outer layer interface in large-eddy simulations with wall-layer models

The interaction between the inner and outer layer in large-eddy simulations (LES) that use approximate near-wall treatments is studied.In hybrid Reynolds-averaged Navier–Stokes (RANS)/LES models a transition layer exists between the RANS and LES regions, which has resulted in incorrect prediction of the velocity profiles, and errors of up to 15% in the prediction of the skin friction.Several factors affect this transition layer, but changes we made to the formulation had surprisingly little effect on the mean velocity.In general, it is found that the correct prediction of length- and time-scales of the turbulent eddies in the RANS region is important, but is not the only factor affecting the results.The inclusion of a backscatter model appears to be effective in improving the prediction of the mean velocity profile and skin-friction coefficient.

A priori and a posteriori tests of inflow conditions for large-eddy simulation

Comparisons of inflow conditions for large-eddy simulations of turbulent, wall-bounded flows are carried out. Consistent with previous investigations, it is found that the spectral content of the inflow velocity is important. Inflow conditions based on random-noise, or small-scale eddies only, dissipate quickly. Temporal and spatial filtering of a time series obtained from a separate calculation indicates that it is important to capture eddies of dimensions equal to or larger than the integral length scale of the flow. Three methods for generating inflow velocity fields are tested in a simulation of spatially developing turbulent channel flow. Synthetic turbulence generation methods that introduce realistic length scales are more suitable than uncorrelated random noise, but still require fairly long development lengths before realistic turbulence is established. A recycling method based on the use of turbulent data obtained from a separate calculation, in different flow conditions, was found to result in more rapid transition. A forcing method that includes a control loop also appears to be effective by generating turbulence with the correct Reynolds stresses and correlations within less than ten channel half heights.

Influence of flexibility on the aerodynamic performance of a hovering wing

SUMMARY In the present study, a computational investigation was carried out to understand the influence of flexibility on the aerodynamic performance of a hovering wing. A flexible, two-dimensional, two-link model moving within a viscous fluid was considered. The Navier–Stokes equations governing the fluid dynamics were solved together with the equations governing the structural dynamics by using a strongly coupled fluid–structure interaction scheme. Harmonic kinematics was used to prescribe the motions of one of the links, thus effectively reducing the wing to a single degree-of-freedom oscillator. The wings flexibility was characterized by the ratio of the flapping frequency to the natural frequency of the structure. Apart from the rigid case, different values of this frequency ratio (only in the range of 1/2 to 1/6) were considered at the Reynolds numbers of 75, 250 and 1000. It was found that flexibility can enhance aerodynamic performance and that the best performance is realized when the wing is excited by a non-linear resonance at 1/3 of the natural frequency. Specifically, at Reynolds numbers of 75, 250 and 1000, the aerodynamic performance that is characterized by the ratio of lift coefficient to drag coefficient is respectively increased by 28%, 23% and 21% when compared with the corresponding ratios of a rigid wing driven with the same kinematics. For all Reynolds numbers, the lift generated per unit driving power is also enhanced in a similar manner. The wake capture mechanism is enhanced, due to a stronger flow around the wing at stroke reversal, resulting from a stronger end of stroke vortex at the trailing edge. The present study provides some clues about how flexibility affects the aerodynamic performance in low Reynolds number flapping flight. In addition, it points to the importance of considering non-linear resonances for enhancing aerodynamic performance.

Scale-similar models for large-eddy simulations

Scale-similar models employ multiple filtering operations to identify the smallest resolved scales, which have been shown to be the most active in the interaction with the unresolved subgrid scales. They do not assume that the principal axes of the strain-rate tensor are aligned with those of the subgrid-scale stress (SGS) tensor, and allow the explicit calculation of the SGS energy. They can provide backscatter in a numerically stable and physically realistic manner, and predict SGS stresses in regions that are well correlated with the locations where large Reynolds stress occurs. In this paper, eddy viscosity and mixed models, which include an eddy-viscosity part as well as a scale-similar contribution, are applied to the simulation of two flows, a high Reynolds number plane channel flow, and a three-dimensional, nonequilibrium flow. The results show that simulations without models or with the Smagorinsky model are unable to predict nonequilibrium effects. Dynamic models provide an improvement of the re...

A general reconstruction algorithm for simulating flows with complex 3D immersed boundaries on Cartesian grids

In the present note a general reconstruction algorithm for simulating incompressible flows with complex immersed boundaries on Cartesian grids is presented. In the proposed method an arbitrary three-dimensional solid surface immersed in the fluid is discretized using an unstructured, triangular mesh, and all the Cartesian grid nodes near the interface are identified. Then, the solution at these nodes is reconstructed via linear interpolation along the local normal to the body, in a way that the desired boundary conditions for both pressure and velocity fields are enforced. The overall accuracy of the resulting solver is second-order, as it is demonstrated in two test cases involving laminar flow past a sphere.

Turbulent structures in accelerating boundary layers

The vortical structures in spatially developing turbulent boundary layers subjected to streamwise acceleration are studied. Two cases are examined: one in which the acceleration is insufficient to cause reversion to the laminar state of the initially turbulent flow, and another in which the acceleration is stronger and relaminarization begins to take place; the pressure gradient, however, is not maintained long enough for full reversion to occur. The turbulent statistics show the expected trends: the mean velocity profile deviates significantly from the logarithmic law-of-the-wall and shows, in the strongly accelerated case, a tendency to approach the laminar profile; the turbulent kinetic energy increases less rapidly than the energy of the mean flow. The structure of the inner layer is also significantly altered. In the near-wall region, the streaks become more elongated and show fewer undulations, owing to a significant decrease of the spanwise fluctuations relative to the streamwise ones. The coherent...

Direct numerical simulation of the pulsatile flow through an aortic bileaflet mechanical heart valve

This work focuses on the direct numerical simulation of the pulsatile flow through a bileaflet mechanical heart valve under physiological conditions and in a realistic aortic root geometry. The motion of the valve leaflets has been computed from the forces exerted by the fluid on the structure both being considered as a single dynamical system. To this purpose the immersed boundary method, combined with a fluid–structure interaction algorithm, has shown to be an inexpensive and accurate technique for such complex flows. Several complete flow cycles have been simulated in order to collect enough phase-averaged statistics, and the results are in good agreement with experimental data obtained for a similar configuration. The flow analysis, strongly relying on the data accessibility provided by the numerical simulation, shows how some features of the leaflets motion depend on the flow dynamics and that the criteria for the red cell damages caused by the valve need to be formulated using very detailed analysis. In particular, it is shown that the standard Eulerian computation of the Reynolds stresses, usually employed to assess the risk of haemolysis, might not be adequate on several counts: (i) Reynolds stresses are only one part of the solicitation, the other part being the viscous stresses, (ii) the characteristic scales of the two solicitations are very different and the Reynolds stresses act on lengths much larger than the red cells diameter and (iii) the Eulerian zonal assessment of the stresses completely misses the information of time exposure to the solicitation which is a fundamental ingredient for the phenomenon of haemolysis. Accordingly, the trajectories of several fluid particles have been tracked in a Lagrangian way and the pointwise instantaneous viscous stress tensor has been computed along the paths. The tensor has been then reduced to an equivalent scalar using the von Mises criterion, and the blood damage index has been evaluated following Grigioni et al . ( Biomech. Model Mechanobiol ., vol. 4, 2005, p. 249).

Modeling the interaction of coils with the local blood flow after coil embolization of intracranial aneurysms.

Aneurysmal recanalization and coil compaction after coil embolization of intracranial aneurysms are seen in as many as 40% of cases. Higher packing density has been suggested to reduce both coil compaction and recanalization. Basilar bifurcation aneurysms remain a challenge due possibly to the hemodynamics of this specific aneurysm/parent vessel architecture, which subjects the coil mass at the aneurysm neck to elevated and repetitive impingement forces. In the present study, we propose a new modeling strategy that facilitates a better understanding of the complex interactions between detachable coils and the local blood flow. In particular, a semiheuristic porous media set of equations used to describe the intra-aneurysmal flow is coupled to the incompressible Navier-Stokes equations governing the dynamics of the flow in the involved vessels. The resulting system of equations is solved in a strongly coupled manner using a finite element formulation. Our results suggest that there is a complex interaction between the local hemodynamics and intra-aneurysmal flow that induces significant forces on the coil mass. Although higher packing densities have previously been advocated to reduce coil compaction, our simulations suggest that lower permeability of the coil mass at a given packing density could also promote faster intra-aneurysmal thrombosis due to increased residence times.