Accounting for convective effects in zero-Mach-number thermoacoustic models

This paper presents a methodology to account for some mean-flow effects on thermo-acoustic instabilities when using the zero-Mach-number assumption. It is shown that when a computational domain is represented under the M=0 assumption, a nonzero-Mach-number element can simply be taken into account by imposing a proper acoustic impedance at the boundaries so as to mimic the mean flow effects in the outer, not computed flow domain. A model that accounts for the coupling between acoustic and entropy waves is presented. It relies on a “delayed entropy coupled boundary condition” (DECBC) for the Helmholtz equation satisfied by the acoustic pressure. The model proves able to capture low-frequency entropic modes even without mean-flow terms in the fluctuating pressure equation

A high-order numerical algorithm for DNS of low-Mach-number reactive flows with detailed chemistry and quasi-spectral accuracy

A novel and efficient algorithm is presented in this paper to deal with DNS of turbulent reacting flows under the low-Mach-number assumption, with detailed chemistry and a quasi-spectral accuracy. The temporal integration of the equations relies on an operating-split strategy, where chemical reactions are solved implicitly with a stiff solver and the convection-diffusion operators are solved with a Runge-Kutta-Chebyshev method. The spatial discretisation is performed with high-order compact schemes, and a FFT based constant-coefficient spectral solver is employed to solve a variable-coefficient Poisson equation. The numerical implementation takes advantage of the 2DECOMP&FFT libraries developed by [1], which are based on a pencil decomposition method of the domain and are proven to be computationally very efficient. An enhanced pressure-correction method is proposed to speed up the achievement of machine precision accuracy. It is demonstrated that a second-order accuracy is reached in time, while the spatial accuracy ranges from fourth-order to sixth-order depending on the set of imposed boundary conditions. The software developed to implement the present algorithm is called HOLOMAC, and its numerical efficiency opens the way to deal with DNS of reacting flows to understand complex turbulent and chemical phenomena in flames

Navier-Stokes characteristic boundary conditions using ghost cells

Solution methods for the compressible Navier-Stokes equations based on finite volume discretizations often implement boundary conditions using ghost cells outside of the computational domain. Filling the ghost cells using straightforward zeroth-or first-order extrapolation, although computationally expedient, is well known to fail even for some simple flows, especially when turbulent structures interact with the boundaries or if time-varying inflow conditions are imposed. The Navier-Stokes characteristic boundary condition approach provides more accurate boundary conditions, but requires the use of special discretizations at boundaries. The present paper develops a new technique based on the Navier-Stokes characteristic boundary condition approach to derive values for ghost cells that significantly improve the treatment of boundaries over simple extrapolation, but retain the ghost cell approach. It is demonstrated in the context of a Godunov integration procedure that the new method provides accurate results, while allowing the use of the same stencil and numerical methodology near the boundaries as in the interior

Effects of equivalence ratio variations on turbulent flame speed in lean methane/air mixtures under lean-burn natural gas engine operating conditions

Direct numerical simulations of turbulent premixed CH4/air flames were carried out using an inflow-outflow configuration to study the effects of equivalence ratio on the turbulent flame speed in lean mixtures. The inflow velocity was dynamically adjusted at a run-time to stabilize the flame brush location within the computational domain. Linear forcing was applied to maintain the turbulent intensities at desired levels. Numerous equivalence ratios near the lean limit were selected for the same turbulence properties and the normalized turbulent flame speed was shown to be a function of the equivalence ratio. Simulations were performed for over 80 eddy turnover times with the turbulent flame speed obtained by averaging the inflow velocity. Results revealed that the equivalence ratio does not have an explicit effect on the normalized turbulent flame speed over the lean limit. Analysis of flame surface area showed that the surface wrinkling produced by eddies of varying scales was not influenced by the change in equivalence ratios when the Karlovitz and Damkohler numbers are fixed. Finally based on the flame surface statistics flame surface normal is preferentially parallel to the most compressive strain rate direction for all equivalence ratios

A hybrid adaptive low-Mach number/compressible method: Euler equations

Flows in which the primary features of interest do not rely on high-frequency acoustic effects, but in which long-wavelength acoustics play a nontrivial role, present a computational challenge. Integrating the entire domain with low-Mach-number methods would remove all acoustic wave propagation, while integrating the entire domain with the fully compressible equations can in some cases be prohibitively expensive due to the CFL time step constraint. For example, simulation of thermoacoustic instabilities might require fine resolution of the fluid/chemistry interaction but not require fine resolution of acoustic effects, yet one does not want to neglect the long-wavelength wave propagation and its interaction with the larger domain. The present paper introduces a new multi-level hybrid algorithm to address these types of phenomena. In this new approach, the fully compressible Euler equations are solved on the entire domain, potentially with local refinement, while their low-Mach-number counterparts are solved on subregions of the domain with higher spatial resolution. The finest of the compressible levels communicates inhomogeneous divergence constraints to the coarsest of the low-Mach-number levels, allowing the low-Mach-number levels to retain the long-wavelength acoustics. The performance of the hybrid method is shown for a series of test cases, including results from a simulation of the aeroacoustic propagation generated from a Kelvin–Helmholtz instability in low-Mach-number mixing layers. It is demonstrated that compared to a purely compressible approach, the hybrid method allows time-steps two orders of magnitude larger at the finest level, leading to an overall reduction of the computational time by a factor of 8

A fourth-order adaptive mesh refinement algorithm for the multicomponent, reacting compressible Navier–Stokes equations

In this paper, we present a fourth-order in space and time block-structured adaptive mesh refinement algorithm for the compressible multicomponent reacting Navier–Stokes equations. The algorithm uses a finite-volume approach that incorporates a fourth-order discretisation of the convective terms. The time-stepping algorithm is based on a multi-level spectral deferred corrections method that enables explicit treatment of advection and diffusion coupled with an implicit treatment of reactions. The temporal scheme is embedded in a block-structured adaptive mesh refinement algorithm that includes subcycling in time with spectral deferred correction sweeps applied on levels. Here we present the details of the multi-level scheme paying particular attention to the treatment of coarse–fine boundaries required to maintain fourth-order accuracy in time. We then demonstrate the convergence properties of the algorithm on several test cases including both non-reacting and reacting flows. Finally we present simulations of a vitiated dimethyl ether jet in 2D and a turbulent hydrogen jet in 3D, both with detailed kinetics and transport

A mixed acoustic-entropy combustion instability in a realistic gas turbine

A combustion instability in a combustor typical of aero-engines is analyzed and modeled thanks to a low order Helmholtz solver. A Dynamic Mode Decomposition is first applied to the Large Eddy Simulation (LES) database. The mode with the highest amplitude shares the same frequency of oscillation as the experiment (approx. 350 Hz) and it 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 650-700 Hz, it is postulated that the instability observed around 350 Hz stems from a mixed entropy/acoustic mode where the acoustic generation associated by the entropy spots being convected throughout the choked nozzle plays a key role. A Delayed Entropy Coupled Boundary Condition is then derived in order to account for this interaction in the framework of a Helmholtz solver where the baseline flow is assumed at rest. When fed by appropriate transfer functions to model the entropy generation and convection from the flame to the exit, the Helmholtz solver proves able to predict the presence of an unstable mode around 350 Hz, in agreement with both the LES and the experiments. This finding supports the idea that the instability observed in the combustor is indeed driven by the entropy/acoustic coupling.E. Motheau, L. Selle, Y. Mery, T. Poinsot, F. Nicou