INFLUENCE OF UPSTREAM TURBULENCE ON SELF-SUSTAINED OSCILLATIONS IN AN OPEN CAVITY

Abstract

Direct numerical and large eddy simulations of incompressible turbulent flows over deep and shallow cavities were performed in the range of 600≤ReD≤12000 to investigate the influence of the incoming turbulent boundary layer on self-sustained oscillations of the shear layer. When the turbulent boundary layer of Reθ=300 approached the open cavity with ReD=3000, the energy spectra of the pressure fluctuations showed energetic frequencies in the range of 0.15≤ ωθ ≤0.3. Conditionally averaged flow fields disclosed that the energetic frequencies arise from the separation of high speed streaky structures rather than from a geometric peculiarity of the cavity. The same energetic frequencies were observed in a backward-facing step flow as well as in deep and shallow cavity flows, despite the different geometries of these systems. In the turbulent cavity flow of ReD=12000, however, the peak frequencies of the energy spectra at cavity lengths of L/D = 1 and 2 were found to correspond to the N th modes with N = 2 and 3 respectively. These N th modes were very similar to the frequency characteristics of self-sustained oscillations reported for laminar cavity flows. Inspection of instantaneous pressure fluctuations as well as spanwiseaveraged pressure fluctuations revealed that regular shedding of quasi two-dimensional vortical structures was responsible for the peak frequency in the energy spectra. INTRODUCTION Flows over open cavities occur in many engineering applications, for example landing gear wells and bomb bays in aircraft and sunroofs in automobiles. The presence of the open cavity generates strong self-sustained oscillations of velocity, pressure and, occasionally, density. To understand the mechanism underlying such oscillations and prevent undesirable effects, numerous experimental and numerical studies have been carried out since Norton (1952) investigated the buffeting of bomber airplanes due to air flow over their bomb bays. Nevertheless it is unclear whether the turbulent incoming boundary layer can give rise to self-sustained oscillations in incompressible turbulent cavity flows (Rockwell 1998). Pereira & Sousa (1994, 1995) observed periodically oscillating shear layers in the flow of a turbulent incoming boundary layer over an open cavity. Lin & Rockwell (2001) also observed self-sustained oscillations in water-tunnel experiments, and suggested that the oscillations are related to large-scale vortical structures. In contrast, Grace, Dewar & Wroblewski (2004) found no evidence of self-sustained oscillations in velocity and pressure data from their experiment with a turbulent incoming boundary layer. Chatellier, Laumonier & Gervais (2004) observed self-sustained oscillations of the mixing layer in their experiments, and theoretically analyzed the fluctuating behaviors of turbulent cavity flows at low Mach number. They suggested that the oscillating process is not governed by periodic shedding of coherent structures but by convective waves of naturally unstable mixing layer. However, Ashcroft & Zhang (2005) observed the shedding of large-scale vortical structures by Galilean decomposition of the instantaneous and fluctuating velocity fields. The coherent vortical structures were present in the majority of PIV images, although well-defined structures were not always observed. The authors pointed out small peaks in the pressure spectra as evidence of weak tonal components; however strong self-sustained oscillations were not observed. The main objective of the present study was to elucidate whether a fully turbulent boundary layer can give rise to self-sustained oscillations and, if such oscillations exist, whether they are related to coherent vortex formation. To achieve this, we performed DNSs and LESs of incompressible turbulent flows over deep and shallow cavities for a wide range of Reynolds number (600≤ ReD ≤12000), where ReD is the Reynolds number based on the cavity depth. The present simulations used L/θ values of up to 80, which is sufficiently large to identify the existence of self-sustained oscillations. The turbulent flow over a backward-facing step was also simulated for comparison. Turbulence statistics and frequency spectra of fluctuating quantities were obtained to analyze the fluctuating behaviors of the turbulent cavity flows. Conditionalaveraging and spanwise-averaging were employed to extract spatial maps of the pressure fluctuations. Figure 1: Schematic diagram of computational domain. NUMERICAL METHOD A schematic diagram of the computational domain is shown in Figure 1. For all of the present simulations, the turbulent boundary layer was provided at the inlet with the realistic velocity fluctuations of Reθ =300. DNSs of incompressible flows over an open cavity were performed for two Reynolds numbers, ReD =600 and 3000. The cavity flows at high Reynolds number (ReD =12000) were simulated using a LES with a dynamic sub-grid scale model. The simulation conditions used in the present study are summarized in Table 1. Table 1: Simulation conditions. D Re D L / , θ / L z y x N N N × × 1, 2 289×95×129 600 2, 4 321×95×129