The understanding
of flow over open cavities is relevant for a wide range of applications,
from car sunroof to aircraft weapon bay, landing gear well and instrumentation/optical
cavities. Self-sustained oscillations inside the cavity generate
intense pressure fluctuations that can lead to structural damage
and failure of components.
Direct numerical
simulations (DNS) of two- and three-dimensional compressible flow
over open cavities are performed to study the flow physics and the
basic mechanisms underlying the cavity oscillations.
Sponsored by the Air Force Office
of Scientific Research (AFOSR)
Work done in part in collaboration
with Pr. V. Theofilis, School of Aeronautics, Universidad Politecnica
de Madrid
A schematic diagram of the rectangular
cavity configuration is shown above. The full three-dimensional compressible
viscous Navier-Stokes equations are solved (no turbulence model used)
using a sixth-order compact finite-difference scheme in the x and y-direction,
with a fourth-order Runge-Kutta scheme for time marching[1]. The cavity
is supposed homogeneous (periodic) in the spanwise direction (z-direction)
and the z-derivatives are computed using Fast Fourier Transform (FFT)
method. The domain is discretized into a stretched cartesian grid, with
clustering of points near the walls and in the shear layer spanning the
cavity. The code is fully parallelized using MPI and runs on clusters
at Caltech and ARL.
First a
linear stability analysis[2] is conducted to search for three-dimensional
global instabilities of the two-dimensional mean flow for cavities that
are homogeneous in the spanwise direction. The presence of such instabilities
is reported for a range of flow conditions and cavity aspect ratios. For
cavities of aspect ratio (length to depth) of 2 and 4, the three-dimensional
mode has a spanwise wavelength of approximately one cavity depth and oscillates
with a frequency about one order of magnitude lower than two-dimensional
Rossiter (flow/acoustics) instabilities. A steady mode of smaller spanwise
wavelength is also identified for square cavities. The linear results
indicate that the instability is hydrodynamic (rather than acoustic) in
nature and arises from a generic centrifugal instability mechanism associated
with the mean recirculating vortical flow in the downstream part of the
cavity. These three-dimensional instabilities are related to centrifugal
instabilities previously reported in flows over backward facing steps,
lid-driven cavity flows and Couette flows.
Results from three-dimensional
simulations of the nonlinear compressible Navier-Stokes equations are
also reported. The formation of oscillating (and, in some cases, steady)
spanwise structures is observed inside the cavity. The spanwise wavelength
and oscillation frequency of these structures agree with the linear analysis
predictions. When present, the shear-layer (Rossiter) oscillations experience
a low-frequency modulation that arises from nonlinear interactions with
the three-dimensional mode. The results are consistent with observations
of low-frequency modulations and spanwise structures in previous experimental
and numerical studies on open cavity flows[3].
[1]
Lele S. K., “Compact
finite difference scheme with spectral-like resolution,”
J. Comput. Phys., 103:16-42, 1992.
[2] Theofilis V.
and Colonius T., “An
algorithm for the recovery of 2- and 3-D biglobal instabilities of compressible
flow over 2-D open cavities,”
AIAA Paper 2003-4143, 2003.
[3] Faure T. M.,
Adrianos P., Lusseyran F. and Pastur L., “Visualizations of the
flow inside an open cavity at medium range Reynolds numbers, ” Experiments
in Fluids 42:169-184, 2007.
PUBLICATIONS &
CONFERENCES
APS Division
of Fluid Dynamics 60th Annual Meeting
