60 research outputs found
Evolution of isolated turbulent trailing vortices
In this work, the temporal evolution of a low swirl-number turbulent Batchelor vortex is studied using pseudospectral direct numerical simulations. The solution of the governing equations in the vorticity-velocity form allows for accurate application of boundary conditions. The physics of the evolution is investigated with an emphasis on the mechanisms that influence the transport of axial and angular momentum. Excitation of normal mode instabilities gives rise to coherent large scale helical structures inside the vortical core. The radial growth of these helical structures and the action of axial shear and differential rotation results in the creation of a polarized vortex layer. This vortex layer evolves into a series of hairpin-shaped structures that subsequently breakdown into elongated fine scale vortices. Ultimately, the radially outward propagation of these structures results in the relaxation of the flow towards a stable high-swirl configuration. Two conserved quantities, based on the deviation from the laminar solution, are derived and these prove to be useful in characterizing the polarized vortex layer and enhancing the understanding of the transport process. The generation and evolution of the Reynolds stresses is also addressed
Data-driven Balanced Truncation for Predictive Model Order Reduction of Aeroacoustic Response
Rapid prediction of the aeroacoustic response is a key component in the
design of aircraft and turbomachinery. While it is possible to achieve accurate
predictions using direct solution of the compressible Navier-Stokes equations,
applications of such solvers is not feasible in design optimization due to the
high cost of resolving wave phenomena in an Eulerian setting. In this work, we
propose a technique for highly accelerated predictions of aeroacoustic response
using a data-driven model reduction approach based on the eigensystem
realization algorithm (ERA), as a non-intrusive balanced truncation method.
Specifically, we create and compare ERA ROMs based on the training data
generated by solving the linearized and nonlinear Euler equations with Gaussian
pulse inputs, and use them for prediction of the aeroacoustic response of an
airfoil subject to different types of gust loading. The results show that both
ROMs are in good agreement with the full-order model (FOM) solution in a purely
predictive setting, while achieving orders of magnitude reduction in the online
computation time. Using ERA for prediction of the acoustic response requires
activating each input channel separately in the FOM for training ROMs, and
operating on a large Hankel matrix, that can become computationally infeasible.
We address this bottleneck in two steps: first, we propose a multi-fidelity
gappy POD method to identify the most impactful input channels based on a
coarser grid. Therefore, we reduce the computation cost on the FOM and ROM
levels as we build the Markov sequence by querying the high-resolution FOM only
for the input channels identified by gappy POD. Second, we use tangential
interpolation at the ROM level to reduce the size of the Hankel matrix. The
proposed methods enable application of ERA for highly accurate online acoustic
response prediction and reduce the offline computation cost of ROMs
Extracting Koopman Operators for Prediction and Control of Non-linear Dynamics Using Two-stage Learning and Oblique Projections
The Koopman operator framework provides a perspective that non-linear
dynamics can be described through the lens of linear operators acting on
function spaces. As the framework naturally yields linear embedding models,
there have been extensive efforts to utilize it for control, where linear
controller designs in the embedded space can be applied to control possibly
nonlinear dynamics. However, it is challenging to successfully deploy this
modeling procedure in a wide range of applications. In this work, some of the
fundamental limitations of linear embedding models are addressed. We show a
necessary condition for a linear embedding model to achieve zero modeling
error, highlighting a trade-off relation between the model expressivity and a
restriction on the model structure to allow the use of linear systems theories
for nonlinear dynamics. To address these limitations, neural network-based
modeling is proposed based on linear embedding with oblique projection, which
is derived from a weak formulation of projection-based linear operator
learning. We train the proposed model using a two-stage learning procedure,
wherein the features and operators are initialized with orthogonal projection,
followed by the main training process in which test functions characterizing
the oblique projection are learned from data. The first stage achieves an
optimality ensured by the orthogonal projection and the second stage improves
the generalizability to various tasks by optimizing the model with the oblique
projection. We demonstrate the effectiveness of the proposed method over other
data-driven modeling methods by providing comprehensive numerical evaluations
where four tasks are considered targeting three different systems
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