2 research outputs found
Stability of a jet in crossflow
We have produced a fluid dynamics video with data from Direct Numerical
Simulation (DNS) of a jet in crossflow at several low values of the velocity
inflow ratio R. We show that, as the velocity ratio R increases, the flow
evolves from simple periodic vortex shedding (a limit cycle) to more
complicated quasi-periodic behavior, before finally exhibiting asymmetric
chaotic motion. We also perform a stability analysis just above the first
bifurcation, where R is the bifurcation parameter. Using the overlap of the
direct and the adjoint eigenmodes, we confirm that the first instability arises
in the shear layer downstream of the jet orifice on the boundary of the
backflow region just behind the jet.Comment: Two fluid dynamics videos, high-resolution 1024x768 (~80MB), and low
resolution 320x240 (~10MB), included in the ancillary file
Modeling of Transitional Channel Flow Using Balanced Proper Orthogonal Decomposition
We study reduced-order models of three-dimensional perturbations in
linearized channel flow using balanced proper orthogonal decomposition (BPOD).
The models are obtained from three-dimensional simulations in physical space as
opposed to the traditional single-wavenumber approach, and are therefore better
able to capture the effects of localized disturbances or localized actuators.
In order to assess the performance of the models, we consider the impulse
response and frequency response, and variation of the Reynolds number as a
model parameter. We show that the BPOD procedure yields models that capture the
transient growth well at a low order, whereas standard POD does not capture the
growth unless a considerably larger number of modes is included, and even then
can be inaccurate. In the case of a localized actuator, we show that POD modes
which are not energetically significant can be very important for capturing the
energy growth. In addition, a comparison of the subspaces resulting from the
two methods suggests that the use of a non-orthogonal projection with adjoint
modes is most likely the main reason for the superior performance of BPOD. We
also demonstrate that for single-wavenumber perturbations, low-order BPOD
models reproduce the dominant eigenvalues of the full system better than POD
models of the same order. These features indicate that the simple, yet accurate
BPOD models are a good candidate for developing model-based controllers for
channel flow.Comment: 35 pages, 20 figure