Franck Nicoud

An approach to wall modeling in large-eddy simulations

Channel flow with friction Reynolds number Reτ as high as 80 000 is treated by large-eddy simulation at a moderate cost, using the subgrid-scale model designed for detached-eddy simulations. It includes wall modeling, and was not adjusted for this flow. The grid count scales with the logarithm of the Reynolds number. Three independent codes are in fair agreement with each other. Reynolds-number variations and grid refinement cause trades between viscous, modeled, and resolved shear stresses. The skin-friction coefficient is too low, on the order of 15%. The velocity profiles contain a “modeled” logarithmic layer near the wall and some suggest a “resolved” logarithmic layer farther up, but the two layers have a mismatch of several units in U+.

Acoustic modes in combustors with complex impedances and multidimensional active flames

two approaches for solving the corresponding nonlinear eigenvalue problem are proposed. The first one is based on an asymptotic expansion of the solution, the baseline being the acoustic modes and frequencies for a steady (or passive) flame and appropriate boundary conditions. This method allows a quick assessment of any acoustic mode stabilitybutisvalidonlyforcaseswherethecouplingbetweenthe flameandtheacousticwavesissmallinamplitude. The second approach is based on an iterative algorithm where a quadratic eigenvalue problem is solved at each subiteration. It is more central processing unit demanding but remains valid even in cases where the response of the flametoacousticperturbationsislarge.Frequency-dependentboundaryimpedancesareaccountedforinbothcases. A parallel implementation of the Arnoldi iterative method is used to solve the large eigenvalue problem that arises fromthespacediscretization ofthe Helmholtzequation.Several academicandindustrial testcasesareconsideredto illustrate the potential of the method.

Using singular values to build a subgrid-scale model for large eddy simulations

An eddy-viscosity based, subgrid-scale model for large eddy simulations is derived from the analysis of the singular values of the resolved velocity gradient tensor. The proposed σ-model has, by construction, the property to automatically vanish as soon as the resolved field is either two-dimensional or two-component, including the pure shear and solid rotation cases. In addition, the model generates no subgrid-scale viscosity when the resolved scales are in pure axisymmetric or isotropic contraction/expansion. At last, it is shown analytically that it has the appropriate cubic behavior in the vicinity of solid boundaries without requiring any ad-hoc treatment. Results for two classical test cases (decaying isotropic turbulence and periodic channel flow) obtained from three different solvers with a variety of numerics (finite elements, finite differences, or spectral methods) are presented to illustrate the potential of this model. The results obtained with the proposed model are systematically equivalent...

Compact finite difference schemes on non-uniform meshes. Application to direct numerical simulations of compressible flows

In this paper, the development of a fourth- (respectively third-) order compact scheme for the approximation of first (respectively second) derivatives on non-uniform meshes is studied. A full inclusion of metrics in the coefficients of the compact scheme is proposed, instead of methods using Jacobian transformation. In the second part, an analysis of the numerical scheme is presented. A numerical analysis of truncation errors, a Fourier analysis completed by stability calculations in terms of both semi- and fully discrete eigenvalue problems are presented. In those eigenvalue problems, the pure convection equation for the first derivative, and the pure diffusion equation for the second derivative are considered. The last part of this paper is dedicated to an application of the numerical method to the simulation of a compressible flow requiring variable mesh size: the direct numerical simulation of compressible turbulent channel flow. Present results are compared with both experimental and other numerical (DNS) data in the literature. The effects of compressibility and acoustic waves on the turbulent flow structure are discussed.

Large-eddy simulation and acoustic analysis of a swirled staged turbulent combustor

The analysis of self-excited combustion instabilies encountered in a laboratory-scale, swirl-stabilized combustion system is presented. The instability is successfully captured by reactive large-eddy simulation (LES) and analyzed by using a global acoustic energy equation. This energy equation shows how the source term due to combustion (equivalent to the Rayleigh criterion) is balanced by the acoustic fluxes at the boundaries when reaching the limit cycle. Additionally, an Helmholtz-equation solver including flame-acoustics interaction modeling is used to predict the stability characteristics of the system. Feeding the flame-transfer function from the LES into this solver allows to predict an amplification rate for each mode. The unstable mode encountered in the LES compares well with the mode of the highest amplification factor in the Helmholtz-equation solver, in terms of mode shape as well as in frequency.

Flow forcing techniques for numerical simulation of combustion instabilities

Investigation of combustion instabilities in gas turbine combustors require the knowledge of flame transfer functions. Those can be obtained by experimental measurement or by Large Eddy Simulations (LES). Because calculations are usually limited to a portion of the whole combustor, boundary conditions are of crucial importance. It is common practice to inject acoustic perturbations for the flame transfer function measurement in form of velocity perturbations (u(t)). We present an alternative method based on a characteristic treatment of the Euler Equations. It consists of injecting sound waves traveling into the computational inlet while letting outgoing waves leave the domain without reflection. This method has several advantages concerning the study of flame transfer functions compared to injecting velocity perturbations. Both techniques are compared for cases where analytical solutions may be derived (a duct without flame and a planar laminar flame) and for one case where a CFD code is necessary (a laminar Bunsen-type flame).

Large eddy simulation wall-modeling based on suboptimal control theory and linear stochastic estimation

The cost of large eddy simulation (LES) in the near-wall region of attached turbulent boundary layers scales as the square of the friction Reynolds number, thus limiting LES to moderate Reynolds numbers. Wall stress boundary conditions are frequently used to alleviate this resolution requirement, but commonly used models are shown to perform poorly at high Reynolds numbers even in turbulent channel flow. Techniques from optimal control theory are used to find wall stresses that yield much better results in turbulent channel flow at high Reynolds numbers than existing models even on extremely coarse grids. In this approach, a suboptimal control strategy is used in which the objective is to force the outer LES towards a desired solution by using the wall stress boundary conditions as control. The suboptimal wall stresses are not necessarily physical, rather they are whatever is necessary to overcome the numerical and modeling errors present in the near-wall region to yield the correct mean velocity profile....

Large-eddy simulation of a bi-periodic turbulent flow with effusion

Large-eddy simulations of a generic turbulent flow with discrete effusion are reported. The computational domain is periodic in both streamwise and spanwise directions and contains both the injection and the suction sides. The blowing ratio is close to 1.2 while the Reynolds number in the aperture is of order 2600. The numerical results for this fully developed bi-periodic turbulent flow with effusion are compared to available experimental data from a large-scale spatially evolving isothermal configuration. It is shown that many features are shared by the two flow configurations. The main difference is related to the mean streamwise velocity profile, which is more flat for the bi-periodic situation where the cumulative effect of an infinite number of upstream jets is accounted for. The necessity of considering both sides of the plate is also established by analysing the vortical structure of the flow and some differences with the classical jet-in-crossflow case are highlighted. Finally, the numerical results are analysed in terms of wall modelling for full-coverage film cooling. For the operating point considered, it is demonstrated that the streamwise momentum flux is dominated by non-viscous effects, although the area where only the viscous shear stress contributes is very large given the small porosity value (4%).

Biomechanical wall properties of human intracranial aneurysms resected following surgical clipping (IRRAs Project)

BACKGROUND AND PURPOSE Individual rupture risk assessment of intracranial aneurysms is a major issue in the clinical management of asymptomatic aneurysms. Aneurysm rupture occurs when wall tension exceeds the strength limit of the wall tissue. At present, aneurysmal wall mechanics are poorly understood and thus, risk assessment involving mechanical properties is inexistent. Aneurysm computational hemodynamics studies make the assumption of rigid walls, an arguable simplification. We therefore aim to assess mechanical properties of ruptured and unruptured intracranial aneurysms in order to provide the foundation for future patient-specific aneurysmal risk assessment. This work also challenges some of the currently held hypotheses in computational flow hemodynamics research. METHODS A specific conservation protocol was applied to aneurysmal tissues following clipping and resection in order to preserve their mechanical properties. Sixteen intracranial aneurysms (11 female, 5 male) underwent mechanical uniaxial stress tests under physiological conditions, temperature, and saline isotonic solution. These represented 11 unruptured and 5 ruptured aneurysms. Stress/strain curves were then obtained for each sample, and a fitting algorithm was applied following a 3-parameter (C(10), C(01), C(11)) Mooney-Rivlin hyperelastic model. Each aneurysm was classified according to its biomechanical properties and (un)rupture status. RESULTS Tissue testing demonstrated three main tissue classes: Soft, Rigid, and Intermediate. All unruptured aneurysms presented a more Rigid tissue than ruptured or pre-ruptured aneurysms within each gender subgroup. Wall thickness was not correlated to aneurysmal status (ruptured/unruptured). An Intermediate subgroup of unruptured aneurysms with softer tissue characteristic was identified and correlated with multiple documented risk factors of rupture. CONCLUSION There is a significant modification in biomechanical properties between ruptured aneurysm, presenting a soft tissue and unruptured aneurysms, presenting a rigid material. This finding strongly supports the idea that a biomechanical risk factor based assessment should be utilized in the to improve the therapeutic decision making.

Red cells' dynamic morphologies govern blood shear thinning under microcirculatory flow conditions

Significance Our work reveals rich RBCs’ dynamic morphologies which govern blood shear thinning under microcirculatory flow conditions, contrary to the current paradigm assuming steady RBC orientation and membrane circulation. Our results suggest that any pathological change in RBCs’ local rheology will impact the onset of these morphological transitions and should play a key role in pathological blood flow. Blood viscosity decreases with shear stress, a property essential for an efficient perfusion of the vascular tree. Shear thinning is intimately related to the dynamics and mutual interactions of RBCs, the major component of blood. Because of the lack of knowledge about the behavior of RBCs under physiological conditions, the link between RBC dynamics and blood rheology remains unsettled. We performed experiments and simulations in microcirculatory flow conditions of viscosity, shear rates, and volume fractions, and our study reveals rich RBC dynamics that govern shear thinning. In contrast to the current paradigm, which assumes that RBCs align steadily around the flow direction while their membranes and cytoplasm circulate, we show that RBCs successively tumble, roll, deform into rolling stomatocytes, and, finally, adopt highly deformed polylobed shapes for increasing shear stresses, even for semidilute volume fractions of the microcirculation. Our results suggest that any pathological change in plasma composition, RBC cytosol viscosity, or membrane mechanical properties will affect the onset of these morphological transitions and should play a central role in pathological blood rheology and flow behavior.