Comparison of numerical methods and combustion models for LES of a ramjet

Ramjets are very sensitive to instabilities and their numerical predictions can only be addressed adequately by Large Eddy Simulation (LES). With this technique, solvers can be implicit or explicit and handle structured, unstructured or hybrid meshes, etc. Turbulence and combustion models are other sources of differences. The impact of these options is here investigated for the ONERA ramjet burner. To do so, two LES codes developed by ONERA and CERFACS compute one stable operating condition. Preliminary LES results of the two codes underline the overall robustness of LES. Mean flow features at the various critical sections are reasonably well predicted by both codes. Disagreement mainly appear in the chamber where combustion positions differ pointing to the importance of the combustion and subgrid mixing models. The two LES produce different energy containing motions. With CEDRE, a low frequency dominates while AVBP produces different ranges of low frequencies that can be linked with acoustic modes of the configuration. To cite this article: A. Roux et al., C. R. Mecanique 337 (2009).     

Large-Eddy Simulation of transcritical flows

The present study uses the LES code AVBP, developed at CERFACS, to simulate transcritical flows. Real gas effects are accounted for by the use of a cubic equation of state, in conjunction with appropriate viscosity and thermal conductivity coefficients. First a single nitrogen round jet at supercritical pressure injected in a gaseous reservoir is simulated. Two cases are considered, one demonstrating a transcritical injection (high density injection), the other being directly injected at supercritical temperature (lower density injection). Comparison with available measurements shows good agreement. Finally, the simulation of a reacting case from the Mascotte bench (ONERA) is performed, consisting in a single coaxial injector injecting transcritical oxygen and supercritical hydrogen in a 60 bar chamber. Mean flow characteristics are in good agreement with the experimental observations of OH^* emission, whereas temperature comparisons are more difficult to interpret. To cite this article: T. Schmitt et al., C. R. Mecanique 337 (2009).     

DNS of premixed turbulent V-flame: coupling spectral and finite difference methods

To allow for a reliable examination of the interaction between velocity fluctuations, acoustics and combustion, a novel numerical procedure is discussed in which a spectral solution of the Navier–Stokes equations is directly associated to a high-order finite difference fully compressible DNS solver (sixth order PADE). Using this combination of high-order solvers with accurate boundary conditions, simulations have been performed where a turbulent premixed V-shape flame develops in grid turbulence. In the light of the DNS results, a sub-model for premixed turbulent combustion is analyzed. To cite this article: R. Hauguel et al., C. R. Mecanique 333 (2005).     

Direct numerical simulation and global stability analysis of three-dimensional instabilities in a lid-driven cavity

The first bifurcation in a lid-driven cavity characterized by three-dimensional Taylor–Görtler-Like instabilities is investigated for a cubical cavity with spanwise periodic boundary conditions at Re=1000. The modes predicted by a global linear stability analysis are compared to the results of a direct numerical simulation. The amplification rate, and the shape of the three-dimensional perturbation fields from the direct numerical simulation are in very good agreement with the characteristics of the steady S1 mode from the stability analysis, showing that this mode dominates the other unstable unsteady modes. To cite this article: J. Chicheportiche et al., C. R. Mecanique 336 (2008).     

Computing Green's function of elasticity in a half-plane with impedance boundary condition

This Note presents an effective and accurate method for numerical calculation of the Green's function G associated with the time harmonic elasticity system in a half-plane, where an impedance boundary condition is considered. The need to compute this function arises when studying wave propagation in underground mining and seismological engineering. To theoretically obtain this Green's function, we have drawn our inspiration from the paper by Durán et al. (2005), where the Green's function for the Helmholtz equation has been computed. The method consists in applying a partial Fourier transform, which allows an explicit calculation of the so-called spectral Green's function. In order to compute its inverse Fourier transform, we separate as a sum of two terms. The first is associated with the whole plane, whereas the second takes into account the half-plane and the boundary conditions. The first term corresponds to the Green's function of the well known time-harmonic elasticity system in (cf. J. Dompierre, Thesis). The second term is separated as a sum of three terms, where two of them contain singularities in the spectral variable (pseudo-poles and poles) and the other is regular and decreasing at infinity. The inverse Fourier transform of the singular terms are analytically computed, whereas the regular one is numerically obtained via an FFT algorithm. We present a numerical result. Moreover, we show that, under some conditions, a fourth additional slowness appears and which could produce a new surface wave. To cite this article: M. Durán et al., C. R. Mecanique 334 (2006).     

Eulerian and Lagrangian Large-Eddy Simulations of an evaporating two-phase flow

Large-Eddy Simulations (LES) of an evaporating two-phase flow in an experimental burner are performed using two different solvers, CDP from CTR-Stanford and AVBP from CERFACS, on the same grid and for the same operating conditions. Results are evaluated by comparison with experimental data. The CDP code uses a Lagrangian particle tracking method (EL) while the code AVBP can be coupled either with a mesoscopic Eulerian approach (EE) or with a Lagrangian method (EL). After a validation of the purely gaseous flow in the burner, liquid-phase dynamics, droplet dispersion and fuel evaporation are qualitatively and quantitatively evaluated for three two-phase flow simulations. They are respectively referred as: CDP-EL, AVBP-EE and AVBP-EL. The results of the three simulations show reasonable agreement with experiments for the two-phase flow case. To cite this article: J.M. Senoner et al., C. R. Mecanique 337 (2009).     

Numerical analysis of a quasistatic piezoelectric problem with damage

The quasistatic evolution of the mechanical state of a piezoelectric body with damage is numerically studied in this paper. Both damage and piezoelectric effects are included into the model. The variational formulation leads to a coupled system composed of two linear variational equations for the displacement field and the electric potential, and a nonlinear parabolic variational equation for the damage field. The existence of a unique weak solution is stated. Then, a fully discrete scheme is introduced by using a finite element method to approximate the spatial variable and an Euler scheme to discretize the time derivatives. Error estimates are derived on the approximate solutions, from which the linear convergence of the algorithm is deduced under suitable regularity conditions. Finally, a two-dimensional example is presented to demonstrate the behaviour of the solution. To cite this article: J.R. Fernández et al., C. R. Mecanique 336 (2008).     

Apparent viscosity of a mixture of a Newtonian fluid and interacting particles

We investigate the behavior of fluid–particle mixtures subject to shear stress, by mean of direct simulation. This approach is meant to give some hints to explain the influence of interacting red cells on the global behavior of the blood. We concentrate on the apparent viscosity, which we define as a macroscopic quantity which characterizes the resistance of a mixture against externally imposed shear motion. Our main purpose is to explain the non-monotonous variations of this apparent viscosity when a mixture of fluid and interacting particles is submitted to shear stress during a certain time interval. Our analysis of these variations is based on preliminary theoretical remarks, and some computations for some well-chosen static configurations. To cite this article: A. Lefebvre, B. Maury, C. R. Mecanique 333 (2005).     

Using data assimilation in numerical simulations of experimental geophysical flows

Data assimilation is used to couple numerical simulations and laboratory experiments of unsteady fluid flows in a stratified, rotating fluid. The experiments are performed on the large Coriolis turntable (Grenoble) and the simulations are performed with a multi-layer shallow water model. Sequential assimilation of high-resolution CIV (Correlation Image Velocimetry) measurements drives the numerical model close to the experimental flow and provides an estimation of all the flow variables at each time and each point. It is then possible (i) to analyse the flow dynamics in details, (ii) to determine the model errors starting from a realistic initial condition and (iii) to test the assimilation scheme when a reduced set of data is assimilated. To illustrate this, some results on the baroclinic instability of a two-layer vortex are presented. To cite this article: M. Galmiche et al., C. R. Mecanique 331 (2003).     

Numerical and analytical investigation of the indirect combustion noise in a nozzle

Analytical and numerical assessments of the indirect noise generated through a nozzle are presented. The configuration corresponds to an experimental setup operated at DLR by Bake et al. (2008) where an entropy wave is generated upstream of the nozzle by means of an electrical heating device. Both 3-D and 2-D axisymmetric simulations are performed to demonstrate that the experiment is mostly driven by linear acoustic phenomena, including pressure wave reflection at the outlet and entropy-to-acoustic conversion in the accelerated regions. Results show that the acoustic impedance downstream of the nozzle must be accounted for appropriately in order to recover the experimental pressure signal. A good agreement is also obtained with a purely analytical assessment based on the Marble and Candel compact nozzle approximation. To cite this article: M. Leyko et al., C. R. Mecanique 337 (2009).     

Liquid sheet disintegration at high pressure: An experimental approach

The primary atomization was studied in a 300 μm thickness water sheet, generated by a planar airblast atomizer. The research novelty consisted in increasing the airflow absolute pressure from atmospheric conditions to 6 bar. The experimental techniques employed included Oscillometry by Laser Intensity Reflexion (ORIL), Laser Doppler Velocimetry (LDV) and flow visualization by fast video camera. The atomization mechanisms, described in the literature at atmospheric environments, were observed at high pressure conditions, for a constant momentum flux ratio. Furthermore, a new atomization mechanism was observed at high values of this ratio. Finally, dimensionless relations have been proposed for the global oscillation frequency, minimum air oscillation velocity, break-up distance and transversal wavelength. To cite this article: V.G. Fernandez et al., C. R. Mecanique 337 (2009).     

Homogenization of an elasticity problem in domains with a net of slender bars near surface

We consider an elasticity problem in a domain Ω⁽⁾=ΩF⁽⁾, where Ω is an open bounded domain in R³, F⁽⁾ is a connected nonperiodic set in Ω like a net of slender bars, and is a parameter characterizing the microstructure of the domain. We consider the case of a surface distribution of the set F⁽⁾, i.e., for sufficiently small , the set F⁽⁾ is concentrated in arbitrary small neighbourhood of a surface Γ. Under a hypothesis on the asymptotic behaviour of the energy functional, we obtain the macroscopic (homogenized) model. To cite this article: M. Goncharenko, L. Pankratov, C. R. Mecanique 331 (2003).     

A criterion of the continuous spectrum for elasticity and other self-adjoint systems on sharp peak-shaped domains

The spectra of the elasticity and piezo-electricity systems for a solid with a sharp peak point on the boundary, which is free of traction, are not discrete. An algebraic criterion of non-empty continuous spectrum is found for the Neumann problem for rather arbitrary formally self-adjoint elliptic systems of second-order differential equations on a sharp peak-shaped domain. To cite this article: S.A. Nazarov, C. R. Mecanique 335 (2007).     

Continuous thermodynamics for droplet vaporization: Comparison between Gamma-PDF model and QMoM

The Continuous Thermodynamics Model (CTM) (Cotterman et al., 1985) is a suitable method to reduce computational cost of multi-component vaporization models. The droplet composition is described by a probability density function (PDF) rather than tens of components in the classical Discrete Component Model (DCM). In the first CTM method developed for this application, the PDF was assumed to be a Γ-function (Hallett, 2000), but some problems had appeared in the case of vapor condensation at the droplet surface (Harstadt et al., 2003). The method put forward in this article, the Quadrature Method of Moments (QMoM), enables one to avoid any assumption on the PDF mathematical form. Following Lage who has developed this method for phase equilibria (Lage, 2007), this article widens the scope of QMoM to the modelling of multi-component droplet vaporization. The different CTM approaches are presented in the first part and the results obtained for a vapor condensation test case are then compared and analysed to illustrate improvements made by QMoM. To cite this article: C. Laurent et al., C. R. Mecanique 337 (2009).     

Resolution of linear viscoelastic equations in the frequency domain using real Helmholtz boundary integral equations

Boundary integral equations are well suitable for the analysis of seismic waves propagation in unbounded domains. Formulations in elastodynamics are well developed. In contrast, for the dynamic analysis of viscoelastic media, there are very seldom formulations by boundary integral equations. In this Note, we propose a new and simple formulation of time harmonic viscoelasticity with the Zener model, which reduces to classical elastodynamics if a compatibility condition is satisfied by boundary conditions. Intermediate variables which satisfy the classical elastodynamic equations are introduced. It makes it possible to utilize existing numerical tools of time harmonic elastodynamics. To cite this article: S. Chaillat, H.D. Bui, C. R. Mecanique 335 (2007).     

Transition of unsteady flows of evaporation to steady state

We investigate the half-space problem of evaporation and condensation in the scope of discrete kinetic theory. Exact solutions are found to the boundary value problem and the initial boundary value problems of the flow in the half space for a discrete velocity model. The results are used to analyze the transition of the unsteady solutions towards steady states. To cite this article: A. d'Almeida, C. R. Mecanique 336 (2008).     

Asymptotics of eigenfrequencies of an elastic body with a heavy and hard peak-shaped inclusion

A heavy and hard peak-shaped inclusion in an elastic body provokes to concentration of eigenvalues in the low-frequency range of the spectrum and localization of the corresponding eigenmodes near the peak tip. To cite this article: S.A. Nazarov, C. R. Mecanique 335 (2007).     

Random-field model for the elasticity tensor of anisotropic random media

This Note deals with the construction of a non-Gaussian positive definite matrix-valued random field whose mathematical properties allow the fourth-order elasticity tensor of random non homogeneous anisotropic three dimensional elastic media to be modelled. If the usual parametric probabilistic approach was used, then 21 mutually dependent random fields should be modelled and identified by using experimental data. Such an approach would be very difficult because the systems of the marginal probability distributions of these random fields have to be identified due to the fact that, for a boundary value problem, the displacement field of the random medium is a non-linear mapping of the random elasticity tensor. The theory presented in this paper allows such a probabilistic model of the fourth-order elasticity tensor field to be constructed and depends only of four scalar parameters: three spatial correlation lengths and one parameter allowing the level of the random fluctuations to be controlled. To cite this article: C. Soize, C. R. Mecanique 332 (2004).

Résumé

On présente la construction d'un champ aléatoire à valeurs dans les matrices définies positives dont les propriétés mathématiques permettent de modéliser le tenseur d'élasticité du quatrième ordre des mileux élastiques anisotropes tridimensionnels aléatoires. Si l'approche probabiliste paramétrique usuelle était utilisée, alors il serait nécessaire de modéliser et d'identifier à l'aide de données expérimentales 21 champs aléatoires mutuellement dépendants. Une telle approche serait très difficile de part le fait que le système de lois marginales de ces champs aléatoires doit être identifié parce que, pour un problème aux limites, le champ de déplacement est une transformation non linéaire du tenseur d'élasticité. La théorie présentée dans ce papier permet de construire une modélisation probabiliste du champ de tenseur d'élasticité qui ne dépend que de quatre paramètres scalaires : trois échelles de corrélation spatiale et un paramètre permettant de contrôler le niveau des fluctuations aléatoires. Pour citer cet article : C. Soize, C. R. Mecanique 332 (2004).