 |
|||||||||||||||||||||||||||||||
|
Cavity Aeroacoustics |
|||||||||||||||||||||||||||||||
|
________________________________________________________________________________________
Work performed under a subcontract to Craft Tech. who are supported by the Air Force Office of Scientific Research. ________________________________________________________________________________________ |
|||||||||||||||||||||||||||||||
| The problems associated with cavity aeroacoustics are some of the more pressing problems facing the aeroacoustics community today. They are driven by the militaries weapons bay applications but are crucial to many applications in commercial aircraft and programs such as NASA's aircraft based telescope. The problems stem from the acoustic loads on objects in the cavities being extremely large causing failures in the payloads. Here at the University of Mississippi we have embarked on a joint experimental/numerical to understand and control the underlying phenomena in this class of flows. The approach will use data from numerical simulations to generate low-dimensional models which can be used to help develop control strategies that will eventually be validated in the experimental phases of this study. | |||||||||||||||||||||||||||||||
| The numerical
simulations are being conducted at CRAFT
Tech. and are based on VLES techniques. The figure to the right shows
a series of snapshots of Mach number contours at various time intervals
for supersonic flow over a cavity. Mach Number Contours for Mach 1.5, L/D=6 Cavity The simulations have been run for several different scenarios and validated versus experimental measurements of the wall pressure spectra. The simulations are being used to generate a data set from which two-point statistical quantities can be calculated. Once sufficient statistical quantities have been calculated the Proper Orthogonal Decomposition (POD) is used to extract a basis set of orthogonal functions that can be |
|||||||||||||||||||||||||||||||
 |
|||||||||||||||||||||||||||||||
| used to represent
the flow field. The POD is an unbiased technique for decomposing a flow
field, especially one with directions of non-homogeneities, into an optimal
basis set of orthogonal functions. The POD was introduced to the turbulence
community by Lumley and has been used extensively for studying many incompressible
flows. Those interested in other applications can either contact us
or search current fluid mechanic literature. The plots below show how rapid the convergence of POD modes for applications to both the density and velocity fields. |
|||||||||||||||||||||||||||||||
 |
|||||||||||||||||||||||||||||||
|
Convergence of POD Modes
|
|||||||||||||||||||||||||||||||
| From
these figures it is quite evident that the first POD mode is dominant
in both applications, over 20% for density and just under 20% for the
velocity field. It is also apparent that for both cases there is over
70% of the mean square properties represented with the first 8 modes.
This result is quite encouraging because a low-dimensional model with
only 8 modes would be quite representative of the flow. The figure to the right displays the eigenfunctions from the first eight density modes. These modes highlight two typical organizations. The first, prominent in the lower modes, is streamwise aligned waves. The second is associated with events propagating out of the cavity at an angle prescribed by the leading edge shock. |
|||||||||||||||||||||||||||||||
 |
|||||||||||||||||||||||||||||||
| The following two figures display the eigenfunctions for the first eight velocity modes for both the streamwise and normal velocities. | |||||||||||||||||||||||||||||||
 |
|||||||||||||||||||||||||||||||
 |
|||||||||||||||||||||||||||||||
| As with the density
modes the streamwise velocity modes highlight two types of the flow organizations.
The first being a periodicity in the streamwise direction across the cavity.
The second, a phenomenon only observed in the streamwise velocity modes,
is an opposition in the sign of the eigenfunction inside and outside of
the cavity. This opposition in sign is across the shear layer that sits
on top of the cavity which has been shown to consist of spanwise aligned
vortical structures. Using simple geometrical arguments, on the fluctuating
velocity field, spanwise aligned vortical structures are represented by
an opposition in sign across the shear layer. The wall-normal velocity modes have similar characteristics to the density modes, i.e., the streamwise aligned waves and events being propagated out of the cavity at the shock angle. The streamwise organization of these modes is also consistent with the geometrical construct used in discussing the streamwise velocity and are representative of the vortical structure in the shear layer. For the v component of velocity an opposition in sign in the streamwise direction is representative of a spanwise aligned structure. Examination of the modes show how well the POD modes capture the vortical structures which have been shown to exist in the shear layer above the cavity along with highlighting the structure at the downstream corner of the cavity. The figure below displays contour plots of the spanwise vorticity field for a series of snapshots from the original simulations and a reconstruction using the first eight POD modes. Each of the plots represent an area chosen to highlight the shear layer above the cavity and have the same contour values which run from red being approximately zero through blue being a large negative value. The five plots are from evenly spaced intervals over 2 milliseconds which represents one oscillation cycle of the shear layer. This cycle was described in Sinha et al. and consists of the periodically shed vorticity impinging on the real wall of the cavity which through a feedback mechanisms causes the shear layer to oscillate up and down. From these plots it is quite apparent that the eight POD mode reconstruction is representative of the large scale features of the spanwise vorticity field, although the finer details of pairing and individual structures appear to be smeared out. In terms of the time dependence, the sequence of events appear to be well represented. This is especially clear from observing the vorticity propagating upstream across the bottom of the cavity. The consistencies between the full simulation results and those from the direct POD projection using 8 modes hint that the low-dimensional model under development will provide the correct dynamics on which to attempt control applications. |
|||||||||||||||||||||||||||||||
 |
|||||||||||||||||||||||||||||||
| Comparison of
Original Vorticity Field and the First Eight POD Modes The evidence presented here indicates that using 8 POD modes from each the density and velocity provide a detailed low-dimensional description of the resonating cavity flow. The next phase of work, which is currently underway, involves the time integration of a low-dimensional model derived from projecting the eigenfunctions discussed here onto the conservation of mass and momentum equations using a Galerkin method. The model currently being investigated has 16 equations, eight derived from Navier-Stokes and from continuity, respectively. Results from this model and one derived for the coupled, density and velocity modes will be compared to the simulations and serve as a test bed for control applications. |
|||||||||||||||||||||||||||||||
| __________________________________________________________________________________________ | |||||||||||||||||||||||||||||||
| PUBLICATIONS TO DATE | |||||||||||||||||||||||||||||||
| Ukeiley, L., Seiner,
J., Arunajatesan, Sinha, N. and Dash, S. (2000) "Low-Dimensional Description
of Resonating Cavity Flow" AIAA Paper 2000-2459. Sinha, N. Arunajatesan, S. and Ukeiley, L. (2000) "High Fidelity Simulation of Weapons Bay Aeroacoustics and Active Flow Control" AIAA Paper 2000-1968. |
|||||||||||||||||||||||||||||||
| ___________________________________________________________________________________________ | |||||||||||||||||||||||||||||||
 |
|||||||||||||||||||||||||||||||
 |
|||||||||||||||||||||||||||||||
|
About
UM Web............... UM
Home
Last Modified: Monday, 14-May-2001 2:27:13 CDT Copyright © 1999-2001 The University of Mississippi. All rights reserved. Comments, Suggestions and Assistance |
|||||||||||||||||||||||||||||||
 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|