22 research outputs found
Thermoacoustic instability - a dynamical system and time domain analysis
This study focuses on the Rijke tube problem, which includes features
relevant to the modeling of thermoacoustic coupling in reactive flows: a
compact acoustic source, an empirical model for the heat source, and
nonlinearities. This thermo-acoustic system features a complex dynamical
behavior. In order to synthesize accurate time-series, we tackle this problem
from a numerical point-of-view, and start by proposing a dedicated solver
designed for dealing with the underlying stiffness, in particular, the retarded
time and the discontinuity at the location of the heat source. Stability
analysis is performed on the limit of low-amplitude disturbances by means of
the projection method proposed by Jarlebring (2008), which alleviates the
linearization with respect to the retarded time. The results are then compared
to the analytical solution of the undamped system, and to Galerkin projection
methods commonly used in this setting. This analysis provides insight into the
consequences of the various assumptions and simplifications that justify the
use of Galerkin expansions based on the eigenmodes of the unheated resonator.
We illustrate that due to the presence of a discontinuity in the spatial
domain, the eigenmodes in the heated case, predicted by using Galerkin
expansion, show spurious oscillations resulting from the Gibbs phenomenon. By
comparing the modes of the linear to that of the nonlinear regime, we are able
to illustrate the mean-flow modulation and frequency switching. Finally,
time-series in the fully nonlinear regime, where a limit cycle is established,
are analyzed and dominant modes are extracted. The analysis of the saturated
limit cycles shows the presence of higher frequency modes, which are linearly
stable but become significant through nonlinear growth of the signal. This
bimodal effect is not captured when the coupling between different frequencies
is not accounted for.Comment: Submitted to Journal of Fluid Mechanic
A Conservative Cartesian Cut Cell Method for the Solution of the Incompressible Navier-Stokes Equations on Staggered Meshes
The treatment of complex geometries in Computational Fluid Dynamics
applications is a challenging endeavor, which immersed boundary and cut-cell
techniques can significantly simplify by alleviating the meshing process
required by body-fitted meshes. These methods however introduce new challenges,
as the formulation of accurate and well-posed discrete operators becomes
nontrivial. Here, a conservative cartesian cut cell method is proposed for the
solution of the incompressible Navier--Stokes equation on staggered Cartesian
grids. Emphasis is set on the structure of the discrete operators, designed to
mimic the properties of the continuous ones while retaining a nearest-neighbor
stencil. For convective transport, a divergence is proposed and shown to also
be skew-symmetric as long as the divergence-free condition is satisfied,
ensuring mass, momentum and kinetic energy conservation (the latter in the
inviscid limit). For viscous transport, conservative and symmetric operators
are proposed for Dirichlet boundary conditions. Symmetry ensures the existence
of a sink term (viscous dissipation) in the discrete kinetic energy budget,
which is beneficial for stability. The cut-cell discretization possesses the
much desired summation-by-parts (SBP) properties. In addition, it is fully
conservative, mathematically provably stable and supports arbitrary geometries.
The accuracy and robustness of the method are then demonstrated with flows past
a circular cylinder and an airfoil
A Comprehensive Study of Adjoint-Based Optimization of Non-Linear Systems with Application to Burgers' Equation
In the context of adjoint-based optimization, nonlinear conservation laws
pose significant problems regarding the existence and uniqueness of both direct
and adjoint solutions, as well as the well-posedness of the problem for
sensitivity analysis and gradient-based optimization algorithms. In this paper
we will analyze the convergence of the adjoint equations to known exact
solutions of the inviscid Burgers' equation for a variety of numerical schemes.
The effect of the non-differentiability of the underlying approximate Riemann
solver, complete vs. incomplete differentiation of the discrete schemes and
inconsistencies in time advancement will be discussed.Comment: 28 pages, 6 figures, published 10 Jun 201
Adjoint-based sensitivity analysis of steady char burnout
Simulations of pulverised coal combustion rely on various models, required in
order to correctly approximate the flow, chemical reactions, and behavior of
solid particles. These models, in turn, rely on multiple model parameters,
which are determined through experiments or small-scale simulations and contain
a certain level of uncertainty. The competing effects of transport, particle
physics, and chemistry give rise to various scales and disparate dynamics,
making it a very challenging problem to analyse. Therefore, the steady
combustion process of a single solid particle is considered as a starting point
for this study. As an added complication, the large number of parameters
present in such simulations makes a purely forward approach to sensitivity
analysis very expensive and almost infeasible. Therefore, the use of
adjoint-based algorithms, to identify and quantify the underlying sensitivities
and uncertainties, is proposed. This adjoint framework bears a great advantage
in this case, where a large input space is analysed, since a single forward and
backward sweep provides sensitivity information with respect to all parameters
of interest. In order to investigate the applicability of such methods, both
discrete and continuous adjoints are considered, and compared to the
conventional approaches, such as finite differences, and forward sensitivity
analysis. Various quantities of interest are considered, and sensitivities with
respect to the relevant combustion parameters are reported for two different
freestream compositions, describing air and oxy-atmospheres. This study serves
as a benchmark for future research, where unsteady and finally turbulent cases
will be considered.Comment: Submitted to Combustion Theory and Modellin
A monotonicity preserving conservative sharp interface flow solver for high density ratio two-phase flows
A 3D Unsplit Forward/Backward Volume-of-Fluid Approach and Coupling to the Level Set Method
Monolithic Solvers for Incompressible Two-Phase Flows at Large Density and Viscosity Ratios
International audienc
Navier-Stokes Solvers for Incompressible Single- and Two-Phase Flows
International audienc
Control and Optimization of Interfacial Flows Using Adjoint-Based Techniques
International audienc
Navier-Stokes solvers for incompressible single-and two-phase flows
The presented work is dedicated to the mathematical and numerical modeling of unsteady single-and two-phase flows using finite volume and penalty methods. Two classes of Navier-Stokes solvers are considered in order to compare their accuracy and robustness, as well as to highlight their limitations. Exact (or monolythic) solvers such as the Augmented Lagrangian and the Fully Coupled methods address the saddle-point structure on the pressure-velocity couple of the discretized system by means of a penalization term or even directly, whereas the approximate (or segregated) solvers such as the Standard Projection method rely on operator splitting to break the problem down into decoupled systems. The objective is to compare all approaches in the context of two-phase flows at high viscosity and density ratios. To characterize the interface location, a volume of fluid (VOF) approach is used based on a Piecewise Linear Interface Construction (PLIC). Various 2D simulations are performed on single-and two-phase flows to characterize the behavior and performances of the various solvers