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

Numerical Benchmark for High-Reynolds-Number Supercritical Flows with Large Density Gradients

Because of the extreme complexity of physical phenomena at high pressure, only limited data are available for solver validation at device-relevant conditions such as liquid rocket engines, gas turbines, or diesel engines. In the present study, a two-dimensional direct numerical simulation is used to establish a benchmark for supercritical flow at a high Reynolds number and high-density ratio at conditions typically encountered in liquid rocket engines. Emphasis has been placed on maintaining the flow characteristics of actual systems with simple boundary conditions, grid spacing, and geometry. Results from two different state-of-the-art codes, with markedly different numerical formalisms, are compared using this benchmark. The strong similarity between the two numerical predictions lends confidence to the physical accuracy of the results. The established database can be used for solver benchmarking and model development at conditions relevant to many propulsion and power systems

Using LES to Study Reacting Flows and Instabilities in Annular Combustion Chambers

Great prominence is put on the design of aeronautical gas turbines due to increasingly stringent regulations and the need to tackle rising fuel prices. This drive towards innovation has resulted sometimes in new concepts being prone to combustion instabilities. In the particular field of annular combustion chambers, these instabilities often take the form of azimuthal modes. To predict these modes, one must compute the full combustion chamber, which remained out of reach until very recently and the development of massively parallel computers. Since one of the most limiting factors in performing Large Eddy Simulation (LES) of real combustors is estimating the adequate grid, the effects of mesh resolution are investigated by computing full annular LES of a realistic helicopter combustion chamber on three grids, respectively made of 38, 93 and 336 million elements. Results are compared in terms of mean and fluctuating fields. LES captures self-established azimuthal modes. The presence and structure of the modes is discussed. This study therefore highlights the potential of LES for studying combustion instabilities in annular gas turbine combustors

Modeling Requirements for LES of Fully Multicomponent Fuel Flows

The Large Eddy Simulation (LES) equations for multi-component (MC) fuel two-phase flow are derived from the Direct Numerical Simulation (DNS) equations by filtering the DNS equations using a top-hat filter. The filtered equations contain two categories of subgrid-scale (SGS) terms that must be modeled: (1) SGS terms and (2) terms representing the 'LES assumptions'. In contrast to single-component (SC) fuels, it is shown that two LES formulations, rather than a single one, are possible, and these formulations are not equivalent. Assumptions not present in corresponding SC LES equations are examined and assessed. Criteria are proposed to select the formulation best suited for LES. These criteria are used in conjunction with evaluations based on a DNS database and lead to the final LES equations. This analysis represents the precursor to a future study for modeling the MC LES equations

Direct Numerical Simulation of Transitional Multicomponent-Species Gaseous and Multicomponent-Liquid Drop-Laden Mixing

A model of multicomponent-liquid (MC-liquid) drop evaporation in a three-dimensional mixing layer is here exercised at larger Reynolds numbers than in a previous study, and transitional states are obtained. The gas phase is followed in an Eulerian frame and the multitude of drops is described in a Lagrangian frame. Complete coupling between phases is included with source terms in the gas conservation equations accounting for the drop/flow interaction in terms of drop drag, drop heating and species evaporation. The liquid composition, initially specified as a single-Gamma (SG) probability distribution function (PDF) depending on the molar mass is allowed to evolve into a linear combination of two SGPDFs, called the double-Gamma PDF (DGPDF). The compositions of liquid and vapor emanating from the drops are calculated through four moments of the DGPDFs, which are drop-specific and location-specific, respectively. The mixing layer is initially excited to promote the double pairing of its four initial spanwise vortices into an ultimate vortex in which small scales proliferate. Simulations are performed for four liquids of different compositions and the effect of the initial mass loading and initial free-stream gas temperature are explored. For reference, Simulations are also performed for gaseous multicomponent mixing layers for which the effect of Reynolds number is investigated. The results encompass examination of the global layer characteristics, flow visualizations and homogeneous-plane statistics at transition. Comparisons are performed with previous pre-transitional MC-liquid simulations and with transitional single-component (SC) liquid studies. It is found that MCC flows at transition, the classical energy cascade is of similar strength, but that the smallest scales contain orders of magnitude less energy than SC flows, which is confirmed by the larger viscous dissipation in the former case. Contrasting to pre-transitional MC flows, the vorticity and drop organization depend on the initial gas temperature, this being due to the drop/turbulence coupling. The vapor-composition mean molar mass and standard deviation distributions strongly correlate with the initial liquid-composition PDF; such a correlation only exists for the magnitude of the mean but not for that of the standard deviation. Unlike in pre-transitional situations, regions of large composition standard deviation no longer necessarily coincide with regions of large mean molar mass. The kinetic energy, rotational and composition characteristics, and dissipation are liquid specific and the variation among liquids is amplified with increasing free-stream gas temperature. Eulerian and Lagrangian statistics of gas-phase quantities show that the different. Observation framework may affect the perception of the flow characteristics. The gas composition, of which the first four moments are calculated, is shown to be close to, but distinct from a SGPDF. The PDF of the scalar dissipation rate is calculated for drop-laden layers and is shown to depart more significantly from the typically assumed Gaussian in gaseous flows than experimentally measured gaseous scalar dissipation rates, this being attributed to the increased heterogeneity due to drop/flow interactions

Novel Subgrid Modeling of the LES Equations Under Supercritical Pressure

Transitional states obtained from Direct Numerical Simulation (DNS) of a supercritical mixing layer are analyzed for studying small-scale behavior and assessing the ability of Subgrid Scale (SGS) models to duplicate that behavior. Initially, the mixing layer contains a single chemical species in each of the two streams, and a perturbation promotes rollup and a double pairing of the four spanwise vortices initially present. The database encompasses three combinations of chemical species, several perturbation wavelengths and amplitudes, and several initial Reynolds numbers specifically chosen for the sole purpose of achieving transition. The Large Eddy Simulation (LES) equations are derived from the DNS ones through filtering. This filtering leads to two types of additional terms in the LES compared to the DNS equations : SGS fluxes and other terms for which either assumptions or models are necessary. The magnitude of all terms in the LES conservation equations is analyzed on the DNS database, with special attention to terms that could possibly be neglected. It is shown that in contrast to atmospheric-pressure gaseous flows, there are two new terms that must be modeled: one in each of the momentum and the energy equations. Discussed is a model for the momentum-equation additional term. This model performs well at small filter size but deteriorates as the filter size increases, highlighting the necessity of ensuring appropriate grid resolution in LES

Flame–wall interaction effects on the flame root stabilization mechanisms of a doubly-transcritical LO2/LCH4 cryogenic flame

International audienceHigh-fidelity numerical simulations are used to study flame root stabilization mechanisms of cryogenic flames, where both reactants (O2 and CH4) are injected in transcritical conditions in the geometry of the laboratory scale test rig Mascotte operated by ONERA (France). Simulations provide a detailed insight into flame root stabilization mechanisms for these diffusion flames: they show that the large wall heat losses at the lips of the coaxial injector are of primary importance, and require to solve for the fully coupled conjugate heat transfer problem. In order to account for flame–wall interaction (FWI) at the injector lip, detailed chemistry effects are also prevalent and a detailed kinetic mechanism for CH4 oxycombustion at high pressure is derived and validated. This kinetic scheme is used in a real-gas fluid solver, coupled with a solid thermal solver in the splitter plate to calculate the unsteady temperature field in the lip. A simulation with adiabatic boundary conditions, an hypothesis that is often used in real-gas combustion, is also performed for comparison. It is found that adiabatic walls simulations lead to enhanced cryogenic reactants vaporization and mixing, and to a quasi-steady flame, which anchors within the oxidizer stream. On the other hand, FWI simulations produce self-sustained oscillations of both lip temperature and flame root location at similar frequencies: the flame root moves from the CH4 to the O2 streams at approximately 450 Hz, affecting the whole flame structure

Comparison among Lattice Boltzmann and finite volume solvers for swirled confined flows

International audienceA finite volume and two Lattice-Boltzmann unsteady, flow solvers using LES (Large Eddy Simulation) were compared in a swirling flow configuration, typical of aeronautical combustion chambers. Numerical results were validated against experimental data collected at EM2C laboratory by comparing pressure losses, mean and RMS velocity profiles on multiple planes and axial velocity spectra. Meshes and the overall numerical setups were individually adjusted for each code to obtain the targeted accuracy before comparing CPU efficiencies. Results confirm that the three LES codes provide high fidelity results, much better than usual RANS especially in terms of RMS data. The analysis of CPU performances shows that LBM (Lattice-Boltzmann Method) solvers are faster than the finite volume solver, even if CPU efficiencies remains of the same order of magnitude. In addition, strong scaling tests from 36 to 900 cores show that the finite volume solver scales more efficiently than the LBM codes (specially when the number of grid points per core is not sufficient)