24 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
Fundamental and subharmonic transition to turbulence in zero-pressure-gradient flat-plate boundary layers
In this fluid dynamics video, recent simulations of transition to turbulence
in compressible (M = 0.2), zero-pressure-gradient flat-plate boundary layers
triggered by fundamental (Klebanoff K-type) and subharmonic (Herbert H-type)
secondary instabilities of Tollmien-Schlichting waves are highlighted.Comment: Two fluid dynamics videos are included for the 64th Annual APS DFD
Gallery of Fluid Motion in Baltimore, Maryland 201
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
Reduced-order representation of near-wall structures in the late transitional boundary layer
International audienceDirect numerical simulations (DNS) of controlled H- and K-type transitions to turbulence in an M=0.2 (where M is the Mach number) nominally zero-pressure-gradient and spatially developing flat-plate boundary layer are considered. Sayadi, Hamman & Moin (J. Fluid Mech., vol. 724, 2013, pp. 480-509) showed that with the start of the transition process, the skin-friction profiles of these controlled transitions diverge abruptly from the laminar value and overshoot the turbulent estimation. The objective of this work is to identify the structures of dynamical importance throughout the transitional region. Dynamic mode decomposition (DMD) (Schmid, J. Fluid Mech., vol. 656, 2010, pp. 5-28) as an optimal phase-averaging process, together with triple decomposition (Reynolds & Hussain, J. Fluid Mech., vol. 54 (02), 1972, pp. 263-288), is employed to assess the contribution of each coherent structure to the total Reynolds shear stress. This analysis shows that low-frequency modes, corresponding to the legs of hairpin vortices, contribute most to the total Reynolds shear stress. The use of composite DMD of the vortical structures together with the skin-friction coefficient allows the assessment of the coupling between near-wall structures captured by the low-frequency modes and their contribution to the total skin-friction coefficient. We are able to show that the low-frequency modes provide an accurate estimate of the skin-friction coefficient through the transition process. This is of interest since large-eddy simulation (LES) of the same configuration fails to provide a good prediction of the rise to this overshoot. The reduced-order representation of the flow is used to compare the LES and the DNS results within this region. Application of this methodology to the LES of the H-type transition illustrates the effect of the grid resolution and the subgrid-scale model on the estimated shear stress of these low-frequency modes. The analysis shows that although the shapes and frequencies of the low-frequency modes are independent of the resolution, the amplitudes are underpredicted in the LES, resulting in underprediction of the Reynolds shear stress
RONAALP: Reduced-Order Nonlinear Approximation with Active Learning Procedure
Many engineering applications rely on the evaluation of expensive, non-linear
high-dimensional functions. In this paper, we propose the RONAALP algorithm
(Reduced Order Nonlinear Approximation with Active Learning Procedure) to
incrementally learn a fast and accurate reduced-order surrogate model of a
target function on-the-fly as the application progresses. First, the
combination of nonlinear auto-encoder, community clustering and radial basis
function networks allows to learn an efficient and compact surrogate model with
limited training data. Secondly, the active learning procedure overcome any
extrapolation issue when evaluating the surrogate model outside of its initial
training range during the online stage. This results in generalizable, fast and
accurate reduced-order models of high-dimensional functions. The method is
demonstrated on three direct numerical simulations of hypersonic flows in
chemical nonequilibrium. Accurate simulations of these flows rely on detailed
thermochemical gas models that dramatically increase the cost of such
calculations. Using RONAALP to learn a reduced-order thermodynamic model
surrogate on-the-fly, the cost of such simulation was reduced by up to 75%
while maintaining an error of less than 10% on relevant quantities of interest.Comment: 38 pages, 16 figure
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
Control and Optimization of Interfacial Flows Using Adjoint-Based Techniques
International audienc