19 research outputs found
Investigation of finite-volume methods to capture shocks and turbulence spectra in compressible flows
The aim of the present paper is to provide a comparison between several
finite-volume methods of different numerical accuracy: second-order Godunov
method with PPM interpolation and high-order finite-volume WENO method. The
results show that while on a smooth problem the high-order method perform
better than the second-order one, when the solution contains a shock all the
methods collapse to first-order accuracy. In the context of the decay of
compressible homogeneous isotropic turbulence with shocklets, the actual
overall order of accuracy of the methods reduces to second-order, despite the
use of fifth-order reconstruction schemes at cell interfaces. Most important,
results in terms of turbulent spectra are similar regardless of the numerical
methods employed, except that the PPM method fails to provide an accurate
representation in the high-frequency range of the spectra. It is found that
this specific issue comes from the slope-limiting procedure and a novel hybrid
PPM/WENO method is developed that has the ability to capture the turbulent
spectra with the accuracy of a high-order method, but at the cost of the
second-order Godunov method. Overall, it is shown that virtually the same
physical solution can be obtained much faster by refining a simulation with the
second-order method and carefully chosen numerical procedures, rather than
running a coarse high-order simulation. Our results demonstrate the importance
of evaluating the accuracy of a numerical method in terms of its actual
spectral dissipation and dispersion properties on mixed smooth/shock cases,
rather than by the theoretical formal order of convergence rate.Comment: This paper was previously composed of 2 parts, and this submission
was part 1. It is now replaced by the combined pape
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
On the numerical accuracy in finite-volume methods to accurately capture turbulence in compressible flows
The goal of the present paper is to understand the impact of numerical
schemes for the reconstruction of data at cell faces in finite-volume methods,
and to assess their interaction with the quadrature rule used to compute the
average over the cell volume. Here, third-, fifth- and seventh-order WENO-Z
schemes are investigated. On a problem with a smooth solution, the theoretical
order of convergence rate for each method is retrieved, and changing the order
of the reconstruction at cell faces does not impact the results, whereas for a
shock-driven problem all the methods collapse to first-order. Study of the
decay of compressible homogeneous isotropic turbulence reveals that using a
high-order quadrature rule to compute the average over a finite volume cell
does not improve the spectral accuracy and that all methods present a
second-order convergence rate. However the choice of the numerical method to
reconstruct data at cell faces is found to be critical to correctly capture
turbulent spectra. In the context of simulations with finite-volume methods of
practical flows encountered in engineering applications, it becomes apparent
that an efficient strategy is to perform the average integration with a
low-order quadrature rule on a fine mesh resolution, whereas high-order schemes
should be used to reconstruct data at cell faces.Comment: arXiv admin note: text overlap with arXiv:1902.0666
Accounting for mean flow effects in a zero-Mach number thermo-acoustic solver: application to entropy induced combustion instabilities
Pratiquement toutes les chambres de combustion présentent des instabilités. Par conséquent, il est nécessaire de mieux les comprendre afin de les contrôler. Une possibilité est de simuler l’écoulement réactif à l’intérieur d’une chambre de combustion grâce à la Simulation aux Grandes Echelles (SGE). Cependant la SGE est très coûteuse en terme de capacité de calcul. Une autre possibilité est de réduire la complexité du problème à une simple équation d’onde thermoacoustique (équation dite de Helmholtz), qui peut être résolue en fréquence comme un problème aux valeurs propres. Le couplage entre l’acoustique et la flamme est alors prise en compte au travers des modèles appropriés. Le principal problème de cette méthode est qu’elle repose sur l’hypothèse d’un nombre de Mach nul. Tous les phénomènes liés à l’écoulement moyen sont donc négligés. La présente thèse propose une nouvelle stratégie pour prendre en compte certains effets de l’écoulement dans un contexte à Mach nul. Dans une première partie, la manière la plus judicieuse d’imposer un élément présentant un écoulement très rapide est étudiée. La seconde partie se focalise sur le couplage entre l’acoustique et les hétérogénéités de température qui sont générées par la flamme et naturellement convectées par l’écoulement moyen. Ce phénomène est important car il est responsable du bruit indirect de combustion qui peut conduire à une instabilité thermoacoustique. Un nouveau type de condition limite (DECBC) est proposé afin de prendre en compte ce mécanisme dans un contexte de résolution de l’équation de Helmholtz à Mach nul. Dans la dernière partie, une chambre de combustion aéronautique présentant une instabilité mixte acoustique/entropique est étudiée. Le bénéfice des méthodes développées dans la présente thèse est testé et comparé à des calculs avec la SGE. Il est montré que les calculs avec un solveur de Helmholtz peuvent reproduire une instabilité de combustion complexe, et que cet outil s’avère avoir le potentiel pour prédire les instabilités afin de concevoir de nouvelles chambres de combustion. ABSTRACT : Virtually all combustion chambers are subject to instabilities. Consequently there is a need to better understand them so as to control them. A possibility is to simulate the reactive flow within a combustor with the Large-Eddy Simulation (LES) method. However LES results come at a tremendous computational cost. Another route is to reduce the complexity of the problem to a simple thermoacoustic Helmholtz wave equation, which can be solved in the frequency domain as an eigenvalue problem. The coupling between the flame and the acoustics is then taken into account via proper models. The main drawback of this latter methodology is that it relies on the zero-Mach number assumption. Hence all phenomena inherent to mean flow effects are neglected. The present thesis aims to provide a novel strategy to introduce back some mean flow effects within the zero-Mach number framework. In a first part, the proper way to impose high-speed elements such as a turbine is investigated. The second part focuses on the coupling between acoustics and temperature heterogeneities that are naturally generated at the flame and convected downstream by the flow. Such phenomenon is important because it is responsible for indirect combustion noise that may drive a thermoacoustic instability. A Delayed Entropy Coupled Boundary Condition (DECBC) is then derived in order to account for this latter mechanism in the framework of a Helmholtz solver where the baseline flow is assumed at rest. In the last part, a realistic aero-engine combustor that features a mixed acoustic/entropy instability is studied. The methodology developed in the present thesis is tested and compared to LES computations. It is shown that computations with the Helmholtz solver can reproduce a complex combustion instability, and that this latter methodology is a potential tool to design new combustors so as to predict and avoid combustion instabilities
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
Using boundary conditions to account for mean flow effects in a zero mach number acoustic solver
The present study is devoted to the modeling of mean flow effects while computing thermoacoustic modes under the zero Mach number assumption. It is first recalled that the acoustic impedance modeling of a compressor or a turbine must be prescribed under an energetical form instead of the classical acoustic variables. Then we demonstrate the feasibility to take into account the coupling between acoustic and entropy waves in a zero Mach number framework to capture a family of low frequency entropic modes. The proposed approach relies on a new delayed entropy coupled boundary condition (DECBC) and proves able to capture a family of low frequency entropic mode even though no mean flow term is included in the fluctuating pressure equation
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 discretization 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 nonreacting 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