Effect of multiperforated plates on the acoustic modes in combustors

The analytical model derived by Howe assessing the acoustic effect of perforated plates has been implemented in a 3D Helmholtz solver. This solver allows one to compute the acoustic modes of industrial chambers taking into account the multiperforated plates present for the cooling of the walls. An academic test case consisting of two coaxial cylinders, with the inner one being perforated is used to validate the implementation in the general purpose AVSP code. This case is also used to show the effects of the presence of the plates. In particular, the sensitivity of the acoustic damping to the bias flow speed will be studied. A maximum absorption speed is shown, and the behaviour towards an infinite speed will be illustrated by the academic case. Computations are also conducted in the case of an industrial helicopter chamber. The value of the maximum absorption speed is discussed to explain why the modes are in fact not much absorbed by the perforated plates, and that the frequencies are the same as for walls. To cite this article: E. Gullaud et al., C. R. Mecanique 337 (2009).     

Conjugate heat transfer with Large Eddy Simulation for gas turbine components

CHT (Conjugate Heat Transfer) is a main design constraint for GT (gas turbines). Most existing CHT tools are developed for chained, steady phenomena. A fully parallel environment for CHT has been developed and applied to two configurations of interest for the design of GT. A reactive Large Eddy Simulations code and a solid conduction solver exchange data via a supervisor. A flame/wall interaction is used to assess the precision and the order of the coupled solutions. A film-cooled turbine vane is then studied. Thermal conduction in the blade implies lower wall temperature than adiabatic results and CHT reproduces the experimental cooling efficiency. To cite this article: F. Duchaine et al., C. R. Mecanique 337 (2009).     

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).     

A DES method applied to a Backward Facing Step reactive flow

Hybrid Reynolds Averaged Navier Stokes–Large Eddy Simulation is a trend which is becoming of common use in aerodynamics but has seldom been employed to simulate reactive flows. Such methods, like the Delayed Detached Eddy Simulation (DDES) presented in this article, have been created to treat near wall flows with a RANS approach while switching to LES in the separated flow region. It is indeed an affordable solution to simulate complex and unsteady compressible flows and to have access to accurate skin friction and wall thermal fluxes. In order to validate this technique in combustion, we chose a simple and well documented Backward Facing Step combustor. To account for turbulent combustion a Dynamic Thickened Flame was used. The results obtained on this case show a good agreement with the experimental database and are of the same quality as LES in the separated region for both inert and reactive flows. To cite this article: B. Sainte-Rose et al., C. R. Mecanique 337 (2009).     

The structure of multidimensional strained flames under transcritical conditions

Strained flames are commonly used to study the structure of reactive layers and describe the local properties of turbulent combustion. This model is attractive because constant strain rate flames only depend on a transverse coordinate and can be treated as a one-dimensional problem. This configuration is considered in a multidimensional context in which the strained flow is obtained by two counterflowing streams of reactants. It is used to examine the structure of transcritical strained flames in which one or two reactants are injected at a high pressure exceeding the critical value while their temperature is below the critical value. Calculations are carried out in a two-dimensional domain to test numerical models developed for multidimensional simulations and test thermodynamic and transport models devised to deal with high pressure real gas effects. Multidimensional strained flame calculations carried out in this study serve to check the validity of a new version of a Navier–Stokes flow solver (AVBP) conceived to deal with transcritical combustion of interest to liquid propellant rocket applications. This article describes the basic elements of such simulations and discusses results of calculations. It is shown that the calculated multidimensional strained flames have the expected features in terms of structure and response to the imposed strain rate. To cite this article: L. Pons et al., C. R. Mecanique 337 (2009).     

Injection coupling with high amplitude transverse modes: Experimentation and simulation

High frequency combustion instabilities have technical importance in the design of liquid rocket engines. These phenomena involve a strong coupling between transverse acoustic modes and combustion. They are currently being investigated by combining experimentation and numerical simulations. On the experimental level, the coupling is examined in a model scale system featuring a multiple injector combustor (MIC) comprising five coaxial injectors fed with liquid oxygen and gaseous methane. This system is equipped with a novel VHAM actuator (Very High Amplitude Modulator) which comprises two nozzles and a rotating toothed wheel blocking the nozzles in an alternate fashion. This device was designed to obtain the highest possible levels of transverse oscillation in the MIC. After a brief review of the VHAM, this article reports cold flow experiments using this modulator. Velocity maps obtained under resonant conditions using the VHAM are examined at different instants during a cycle of oscillation. Experimental data are compared with numerical pressure and velocity fields obtained from an acoustic solver. The good agreement observed in the nozzle vicinity indicates that numerical simulations can be used to analyze the complex flow field generated by the VHAM. To cite this article: Y. Mery 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).     

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).     

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).     

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).     

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).     

Missing boundary data recovering for the Helmholtz problem

This Note is dedicated to the numerical treatment of the ill-posed Cauchy–Helmholtz problem. Resorting to the domain decomposition tools, these missing boundary data are rephrased through an ‘interfacial’ equation. This equation is solved via a preconditioned Richardson algorithm with dynamic relaxation. The efficiency of the proposed method is illustrated by some numerical experiments. To cite this article: R. Ben Fatma et al., C. R. Mecanique 335 (2007).     

Stabilization of non-premixed flames in supersonic reactive flows

A Lagrangian framework is set out to describe turbulent non-premixed combustion in high speed coflowing jet flows. The final aim is to provide a robust computational methodology to simulate, in various conditions, the underexpanded GH2/GO2 torch jet that is used to initiate combustion in an expander cycle engine. The proposed approach relies on an early modelling proposal of Borghi and his coworkers. The model is well suited to describe finite rate chemistry effects and its recent extension to high speed flows allows one to take the influence of viscous dissipation phenomena into account. Indeed, since the chemical source terms are highly temperature sensitive, the influence of viscous phenomena on the thermal runaway is likely to be all the more pronounced since the Mach number values are high. The validation of the extended model has been recently performed through the numerical simulation of two distinct well-documented experimental databases. Only a brief summary of this preliminary validation step is provided here. The main purpose of the present work is to proceed with the numerical simulation of geometries that bring together the essential peculiarities of the underexpanded GH2/GO2 torch. The behavior of the corresponding supersonic coflowing jet flames for various conditions is discussed in the light of computational results. To cite this article: J.-F. Izard, A. Mura, 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).     

Use of Faraday instabilities to enhance fuel pulverisation in air-blast atomisers

The atomization of liquids into a spray is an important process in many industrial applications and particularly in the aero-engine sector. Conventional air-blast injectors in aircraft engines today use aerodynamic shearing effects to atomize the liquid fuel. However, at operating conditions where the air velocity is below 30 m/s (such as ground start and high altitude restart) the atomization quality is poor. Consequently combustion is less efficient with high pollutant emissions. The objective of this study is to validate a new concept of injector which couples the shearing effects with the principle of ultrasonic atomization. The latter consists of using piezoelectric actuators to generate the oscillations of a wall in contact with the liquid film. This excitation perpendicular to the liquid film surface creates Faraday instabilities at the liquid/air interface. Amplitudes higher than a defined threshold value induce the break-up of ligaments and the formation of droplets. To cite this article: M. Boukra et al., C. R. Mecanique 337 (2009).     

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).     

Weighted Korn inequalities for thin-walled elastic structures

Appropriate weighted norms in H¹ are presented such that the Korn type inequality is asymptotically sharp with respect to relative thickness and stiffness of the elastic plates. The weights depend crucially on the geometric structure of the plates' junction. To cite this article: O.V. Izotova et al., C. R. Mecanique 334 (2006).     

Chemical kinetics modeling and LES combustion model effects on a perfectly premixed burner

Chemical kinetics modeling and coupling with turbulent combustion models for compressible Large Eddy Simulations (LES) is a critical issue. Accurate flow predictions can only be guaranteed if the coupling is well mastered. In a first attempt to qualify the effect of each model, the case of a lean premixed swirled combustor with comprehensive measures is targeted (species mass fractions and temperature fields). For the investigation, two turbulent combustion models are considered. The first model relies on a presumed PDF approach coupled to a look-up chemistry table obtained with a reduced chemical scheme. The second model makes use of the thickened flame approach using the same reduced chemical scheme but with reaction rates computed explicitly as the computation advances. Then, to estimate kinetic schemes reduction effects, the first model is compared to a third one, with the same PDF approach, but coupled to a look-up chemistry table obtained with a complete chemical scheme. All LES are very close to each other. The main difference between the different predictions relies on CO mass fractions. Although they are all able to return good outlet mass fractions, CO values inside the flame are different depending on the model used. To cite this article: G. Albouze et al., C. R. Mecanique 337 (2009).     

Impact of a bead on a rotating wall

We study experimentally the impact of a plastic bead on a rotating wall made of steel (velocity Ω; radial position x₀). The results show that the restitution coefficient is directly function of the impact velocity x₀Ω and is invariant by changing frame reference. The influence of the height of release of the particle on its angular velocity after impact is also studied. We observe an increase of the angular velocity with height followed by a saturation. We propose an interpretation for this evolution considering that the particle may roll without sliding during all the impact. This physical feature is not always taken into account in existing models of impact between rigid bodies. To cite this article: F. Rioual et al., C. R. Mecanique 336 (2008).