On the damped oscillations of an elastic quasi-circular membrane in a two-dimensional incompressible fluid

We propose a procedure - partly analytical and partly numerical - to find the frequency and the damping rate of the small-amplitude oscillations of a massless elastic capsule immersed in a two-dimensional viscous incompressible fluid. The unsteady Stokes equations for the stream function are decomposed onto normal modes for the angular and temporal variables, leading to a fourth-order linear ordinary differential equation in the radial variable. The forcing terms are dictated by the properties of the membrane, and result into jump conditions at the interface between the internal and external media. The equation can be solved numerically, and an excellent agreement is found with a fully-computational approach we developed in parallel. Comparisons are also shown with the results available in the scientific literature for drops, and a model based on the concept of embarked fluid is presented, which allows for a good representation of the results and a consistent interpretation of the underlying physics.Comment: in press on JF

Use of direct and large eddy simulations for the development of multicomponent reacting compressible turbulent boundary layer wall model

A study of multicomponent reacting channel flows with significant heat transfer and low Mach number has been performed using a set of direct and large eddy simulations. The use of LES computations was needed to analyze accurate and relevant data of such flows at a sufficient Reynolds number and reasonable computational cost. The analysis of these data will be detailed leading to the development of an analytical wall model for predicting the total shear stress and heat flux at the wall

Progress in analytical methods to predict and control azimuthal combustion instability modes in annular chambers

Longitudinal low-frequency thermoacoustic unstable modes in combustion chambers have been intensively studied experimentally, numerically, and theoretically, leading to significant progress in both understanding and controlling these acoustic modes. However, modern annular gas turbines may also exhibit azimuthal modes, which are much less studied and feature specific mode structures and dynamic behaviors, leading to more complex situations. Moreover, dealing with 10–20 burners mounted in the same chamber limits the use of high fidelity simulations or annular experiments to investigate these modes because of their complexity and costs. Consequently, for such circumferential acoustic modes, theoretical tools have been developed to uncover underlying phenomena controlling their stability, nature, and dynamics. This review presents recent progress in this field. First, Galerkin and network models are described with their pros and cons in both the temporal and frequency framework. Then, key features of such acoustic modes are unveiled, focusing on their specificities such as symmetry breaking, non-linear modal coupling, forcing by turbulence. Finally, recent works on uncertainty quantifications, guided by theoretical studies and applied to annular combustors, are presented. The objective is to provide a global view of theoretical research on azimuthal modes to highlight their complexities and potential

Mixed acoustic–entropy combustion instabilities in gas turbines

A combustion instability in a combustor terminated by a nozzle is analysed and modelled based on a low-order Helmholtz solver. A large eddy simulation (LES) of the corresponding turbulent, compressible and reacting flow is first performed and analysed based on dynamic mode decomposition (DMD). The mode with the highest amplitude shares the same frequency of oscillation as the experiment (approximately 320 Hz) and shows the presence of large entropy spots generated within the combustion chamber and convected down to the exit nozzle. The lowest purely acoustic mode being in the range 700–750 Hz, it is postulated that the instability observed around 320 Hz stems from a mixed entropy–acoustic mode, where the acoustic generation associated with entropy spots being convected throughout the choked nozzle plays a key role. The DMD analysis allows one to extract from the LES results a low-order model that confirms that the mechanism of the low-frequency combustion instability indeed involves both acoustic and convected entropy waves. The delayed entropy coupled boundary condition (DECBC) (Motheau, Selle & Nicoud, J. Sound Vib., vol. 333, 2014, pp. 246–262) is implemented into a numerical Helmholtz solver where the baseline flow is assumed at rest. When fed with appropriate transfer functions to model the entropy generation and convection from the flame to the exit, the Helmholtz/DECBC solver predicts the presence of an unstable mode around 320 Hz, in agreement with both LES and experiments

Data assimilation for identification of cardiovascular network characteristics

International audienceA method to estimate the hemodynamics parameters of a network of vessels using an Ensemble Kalman filter is presented. The elastic moduli (Young's modulus) of blood vessels and the terminal boundary parameters are estimated as the solution of an inverse problem. Two synthetic test cases and a configuration where experimental data is available are presented. The sensitivity analysis confirms that the proposed method is quite robust even with a few numbers of observations. The simulations with the estimated parameters recovers target pressure or flow rate waveforms at given specific locations, improving the state of the art predictions available in the literature. This shows the effectiveness and the efficiency of both the parameters estimation algorithm and the blood flow model

The actual impedance of non-reflecting boundary conditions : implications for the computation of resonators

Non-reflecting boundary conditions are essential elements in the computation of many compressible flows: such simulations are very sensitive to the treatment of acoustic waves at boundaries. Non-reflecting conditions allow acoustic waves to propagate through boundaries with zero or small levels of reflection into the domain. However, perfectly non-reflecting conditions must be avoided because they can lead to ill-posed problems for the mean flow. Various methods have been proposed to construct boundary conditions which can be sufficiently non-reflecting for the acoustic field while still making the mean-flow problem well posed. This paper analyses a widely-used technique for non-reflecting outlets (Rudy and Strikwerda, Poinsot and Lele). It shows that the correction introduced by these authors can lead to large reflection levels and non-physical resonant behaviors. A simple scaling is proposed to evaluate the relaxation coefficient used in theses methods for a non-reflecting outlet. The proposed scaling is tested for simple cases (ducts) both theoretically and numerically

Accounting for Acoustic Damping in a Helmholtz Solver

Thermoacoustic Helmholtz solvers provide a cheap and efficient way of predicting combustion instabilities. However, because they rely on the inviscid Euler equations at zero Mach number, they cannot properly describe the regions where aerodynamics may interact with acoustic waves, in the vicinity of dilution holes and injectors, for example. A methodology is presented to incorporate the effect of non-purely acoustic mechanisms into a three- dimensional thermoacoustic Helmholtz solver. The zones where these mechanisms are important are modeled as two-port acoustic elements, and the corresponding matrices, which notably contain the dissipative effects due to acoustic–hydrodynamic interactions, are used as internal boundary conditions in the Helmholtz solver. The rest of the flow domain, where dissipation is negligible, is solved by the classical Helmholtz equation. With this method, the changes in eigenfrequency and eigenmode structure introduced by the acoustic–hydrodynamic effects are captured, while keeping the simplicity and efficiency of the Helmholtz solver. The methodology is successfully applied on an academic configuration, first with a simple diaphragm, then with an industrial swirler, with matrices measured from experiments and large-eddy simulation

Sensitivity analysis of thermo-acoustic eigenproblems with adjoint methods

International audienceThis paper outlines two new applications of adjoint methods in the study of thermoacoustic instability. The first is to calculate gradients for the active subspace method, which is used in uncertainty quantification. The second is to calculate gradients in a nonlinear thermo-acoustic Helmholtz solver. Two methods are presented. The first, which uses the discrete adjoint approach, is specifically for nonlinear Helmholtz eigenvalue problems that are solved iteratively. The second, which uses a hybrid adjoint approach, is more general and can be applied to both problems

Effects of inlet/outlet boundary conditions on acoustic behaviour of a swirled burner

Self-excited acoustic oscillations on an experimental swirled burner are studied both numerically and experimentally. Inlet acoustic impedance is measured experimentally and the sensibility of cavity acoustic mode frequencies to the inlet and outlet boundary conditions is investigated numerically by the use of an Helmholtz solver. Strong effect of the inlet impedance is observed on the frequencies of the acoustic cavity modes, and have to be taken into account for futures compressible LES