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Numerical simulations are used to investigate the self-sustained oscillating flows past an open cavity. The two-dimensional incompressible Navier-Stokes equations are solved directly by using the finite difference method for cavities with an upstream laminar boundary layer. A series of simulations are performed for a variety of cavity length-to-depth ratio. The results show the switching among some flow modes including non-oscillation mode, shear layer mode and wake mode. The variation of the Strouhal number is in favorable agreement with available experimental data. The results of flow fields in the cavity reveal the relationship between the cavity shear layer oscillation modes and recirculating vortices in the cavity.

Flows over open cavities occur in a wide variety of aerospace and engineering applications, for example, the landing systems of aircrafts, sunroofs and windows of automobiles, and spaces between bullet train cars. A schematic of the cavity model and the cavity flow is illustrated in

the acoustic wavelength is much longer than the length of the cavity, so that pressure fluctuations propagate instantaneously to the upstream leading edge of the cavity. The feedback mechanism can be regarded as purely hydrodynamic. The self-sustaining cavity oscillations in compressible flows at high Mach numbers are classified as fluid- resonant oscillations. The acoustic wavelength is of the same order of magnitude as the cavity length. The acoustic pressure disturbances radiate and propagate toward the upstream edge with acoustic speed and there is an acoustic delay. The flow-acoustic resonance arises from this feedback loop. This feedback mechanism can regard as acoustic.

It is well known that the primary frequency of shear layer oscillations varies with cavity length. Many experimental studies have been carried out to reveal the characteristics of the frequency variation (Sarohia [

Unlike the experimental studies, the numerical studies of mode switching among the mode II and mode III and the wake mode so far have been limited to few papers. Rowley et al. [

subsonic flow for L/D = 1, 2, 3, 4, 5 using the two-dimensional direct numerical simulation. Rubio et al. [

In this paper, we investigate numerically the mode switching in the two-dimensional incompressible flow over a rectangular open cavity. We perform the two-dimensional incompressible Navier-Stokes direct numerical simulations using the finite difference method. We also reveal the relationship between the cavity shear layer oscillations and recirculating vortices in the cavity.

Schematic of the computation domain is shown in

In

The computational results are validated by performing systematic grid refinement studies to ensure that the results are independence of grid resolution. The case of L/D = 2.0 is calculated with five grids shown in

Grid points in the cavity | Total grid points | |
---|---|---|

Grid 1 | ||

Grid 2 | ||

Grid3 | ||

Grid 4 | ||

Grid 5 |

y velocity component v near the downstream edge of cavity (x = 6.9, y = 0.0). The results of grids finer than Grid 3 are almost identical.

A series of two-dimensional simulations for varying the length-to-depth ratio L/D from 1.0 to 4.0 at 0.1 interval have been conducted. The shear layer mode is characterized by periodic oscillations of separated shear layer. The Strouhal number is defined by St =

the wake mode. The numerically obtained Strouhal number at 3.7 ≤ L/D ≤ 4.0 is smaller than that in the mode III. As will be discussed in sec. 3.2 about the difference between the mode III and the wake mode predicted in the present study, the shear layer in the mode III oscillats on the multiple recirculating vortices in the cavity, while the flow in the wake mode has a vortex that expands to nearly entire cavity and sheds from the cavity in a long time period. Therefore, the Strouhal number in the wake mode becomes very low. It might be suggested that Knisely and Rockwell [

showed a strong two-dimensional coherency for a wide range of the length-to-depth ratio. The experiment of Gharib and Roshko [

Time-averaged streamlines for different values of the length-to-depth ratio are shown in

2.0, the counterclockwise vortex on the upstream side of the cavity becomes large and has similar scale as that of the clockwise vortex on downstream side of the cavity. The third clockwise thin vortex appears near the upstream edge of cavity. The third vortex becomes larger as the ratio is longer for L/D = 2.3 in

Two-dimensional incompressible flows over an open cavity are numerically investigated. The mode switching between non-oscillations, mode II, mode III and wake mode are simulated. The minimum length for initiation of self-sustained oscillations is L/D = 1.7. The mode switching from mode II to mode III occurs between L/D = 3.1 and L/D = 3.2. The Strouhal number variation is consistent with the experimental results of Knisely and Rockwell [

This research was partly supported by JSPS KAKENHI Grant Number 18560160.

Yoshida, T. and Watanabe, T. (2016) Numerical Simulation of Flow over an Open Cavity with Self- Sustained Oscillation Mode Switching. Open Journal of Fluid Dynamics, 6, 361-370. http://dx.doi.org/10.4236/ojfd.2016.64027