CALTECH

My thesis research investigates the global instabilities and control of flows over open cavities. Direct numerical simulations (DNS) of three-dimensional compressible flow past a cavity are performed to study the flow physics and the basic mechanisms underlying the cavity oscillations.

The understanding of flow over open cavities is relevant for a wide range of applications, from automobile sunroof to aircraft weapon bay and landing gear well. Noise control in open cavities on aircraft has been one of the main motivation for recent works on cavity flow: self-sustained oscillation inside the cavity generate intense pressure fluctuations that can lead to structural damage and failure of aircraft components.

Shear-layer mode

The goal of the present work is to develop a framework for predicting and understanding the global instabilities of compressible flow over open cavities, which can ultimately be used to design robust cavity noise suppression devices. The transition between stable flow and unstable shear-layer mode oscillations will be studied for different cavity geometries and flow conditions. The influence of three-dimensionality and flow control are also of particular interest.

Krishnamurty (1955)

Rowley, Colonius & Basu (2002) [1]

A schematic diagram of the rectangular cavity configuration is shown below. The full compressible viscous Navier-Stokes equations are solved (no turbulence model required) using a sixth-order compact finite-difference scheme in the x and y-direction, with a fourth-order Runge-Kutta scheme for time marching [2]. 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 and runs on a Caltech cluster.

The following animation is representative of our 2D numerical simulations. The subsonic flow over a cavity of aspect ratio length over depth equal 1 is computed at moderate Reynolds number (L / D = 1, M = 0.3, Re = U D / ν = 15 050, L / θ = 106). The cavity lies between 1 > x > 0, and 0 > y > -1, and the mean flow is from left to right, with a Blasius boundary layer spanning the cavity as initial condition. The vorticity contours are plotted to visualize the flow in shear-layer mode, with a shedding frequency corresponding to the first Rossiter's mode.

To study the stability of the 3D cavity flow, we used the biglobal linear stability theory [3]. For some cavity geometry under particular conditions, the flow develops a three-dimensional instability of wavelength about one cavity depth, before even becoming 2D unstable.

These results were confirmed by our full 3D nonlinear simulations. A visualization of two wavelengths of the 3D instability is given here, where the isosurface represent vorticity. The shear-layer oscillations are also present.

We found that this instability was hydrodynamic in nature, and mainly dependent on the two-dimensional steady flow and the Reynolds number (Re). The instability appears to arise from a generic centrifugal instability [4] associated with the large recirculating flow in the downstream half of the cavity . The unstable 3D modes are reminiscent of 3D cellular patterns found in previous experiments [5,6,7].

For more details, please go to

http://hermite.caltech.edu/CFPG/CavityFlow.htm

References:

[1] On self-sustained oscillations in two dimensional compressible flow over rectangular cavities.

C. W. Rowley, T. Colonius, and A.J. Basu; J. Fluid Mech., 455:315–346, 2002.

[2] Compact finite difference scheme with spectral-like resolution.

S. K. Lele; J. Comput. Phys., 103:16–42, 1992.

[3] An algorithm for the recovery of 2- and 3-D biglobal instabilities of compressible flow over 2-D open cavities.

V. Theofilis and T. Colonius; AIAA Paper, 2003-4143, 2003.

[4] Hydrodynamic stability.

P. G. Drazin and W. H. Reid; Cambridge, New York, 1981.

[5] Three-dimensional flow in cavities.

D. J. Maull and L. F. East; J. Fluid Mech., 16:620–632, 1963.

[6] Observations of the three-dimensional nature of unstable flow past a cavity.

D. Rockwell and C. Knisely; Phys. Fluids, 23:425–431, 1980.

[7] Visualizations of the flow inside an open cavity at medium range Reynolds numbers.

T. M. Faure, P. Adrianos, F. Lusseyran & L . Pastur, Experiments in Fluids 42:169-184, 2007

CONFERENCES & PUBLICATIONS:

- AFOSR Annual Meeting, Denver, CO (August 2004)

- AFOSR Annual Meeting, Long Beach, CA (August 2005)

- APS Division of Fluid Dynamics 58th Annual Meeting, Chicago, IL (November 2005)

- 1st Southern California Symposium on Flow Physics, Pasadena, CA (April 2007)

- APS Division of Fluid Dynamics 60th Annual Meeting, Salt Lake City, UT (November 2007)

A Unified View of Global Instability in Compressible Flow over Open Cavities

T. Colonius & G. A. Brès

Final Report AFOSR F49620-02-1-0362 (March 2006)

Three-Dimensional Linear Stability Analysis of Cavity Flows

G. A. Brès & T. Colonius - AIAA paper 2007-1126

45th AIAA Aerospace Sciences Meeting and Exhibit, Reno - NV (January 2007)

Numerical Simulations of Three-Dimensional Instabilities in Cavity Flows

G. A. Brès

Ph.D. Thesis, California Institute of Technology (Avril 2007)

Direct Numerical Simulations of Three-Dimensional Cavity Flows

G. A. Brès & T. Colonius - AIAA paper 2007-3405

13th AIAA/CEAS Aeroacoustics Conference, Rome - Italy (May 2007)

Three-Dimensional Instabilities in Compressible Flow over Open Cavities

G. A. Brès & T. Colonius

Journal of Fluid Mechanics, Vol. 599, pp. 309-339, 2008

Work supported by AFOSR, in collaboration in part with Pr. V. Theofilis, School of Aeronautics, Universidad Politecnica de Madrid

Last update:November 2009