Global Stability Analysis and Control of Compressible Flows over Rectangular Cavities

• Other Authors: Sun, Yiyang (author)
• Format: Others
• Language: English; English
• Published: Florida State University
• Subjects: Mechanical engineering
• Online Access: http://purl.flvc.org/fsu/fd/FSU_FALL2017_Sun_fsu_0071E_14244

The present numerical investigation aims to uncover the inherent instability in compressible cavity flows and aid designs of effective flow control to alter undesirable flow features. Two-dimensional (2D) and three-dimensional (3D) global stabilities of compressible open-cavity flows are examined in detail, which provides insights into designs of active flow control to reduce the pressure fluctuations over the cavity. The stability characteristics of compressible spanwise-periodic open-cavity flows are investigated with direct numerical simulation (DNS) and biglobal stability analysis for rectangular cavities with length-to-depth ratios of $L/D=2$ and 6. This study examines the behavior of instabilities with respect to stable and unstable steady states in the laminar regimes for subsonic as well as transonic conditions where compressibility plays an important role. It is observed that an increase in Mach number destabilizes the flow in the subsonic regime and stabilizes the flow in the transonic regime. Biglobal stability analysis for spanwise-periodic flows over rectangular cavities with large aspect ratio is closely examined in this study due to its importance in aerodynamic applications. Moreover, biglobal stability analysis is conducted to extract 2D and 3D eigenmodes for prescribed spanwise wavelengths $\lambda/D$ about the 2D steady state. The properties of 2D eigenmodes agree well with those observed in the 2D DNS. In the analysis of 3D eigenmodes, it is found that an increase of Mach number stabilizes dominant 3D eigenmodes. For a short cavity with $L/D=2$, the 3D eigenmodes primarily stem from centrifugal instabilities. For a long cavity with $L/D=6$, other types of eigenmodes appear whose structures extend from the aft-region to the mid-region of the cavity, in addition to the centrifugal stability mode located in the rear part of the cavity. A selected number of 3D DNS are performed at $M_\infty=0.6$ for cavities with $L/D=2$ and 6. For $L/D=2$, the properties of 3D structures present in the 3D nonlinear flow correspond closely to those obtained from linear stability analysis. However, for $L/D=6$, the 3D eigenmodes cannot be clearly observed in the 3D DNS, due to the strong nonlinearity that develops over the length of the cavity. In addition, it is noted that three-dimensionality in the flow helps alleviate violent oscillations for the long cavity. The analysis performed in this paper can provide valuable insights for designing effective flow control strategies to suppress undesirable aerodynamic and pressure fluctuations in compressible open-cavity flows. Three-dimensional nonlinear simulations (DNS and LES) are also conducted to examine influence of cavity width, sidewall boundary conditions, free stream Mach numbers, and Reynolds numbers on open-cavity flows. DNS and large eddy simulations (LES) are performed with $L/D=6$, width-to-depth ratios of $W/D$=1 and 2 for Reynolds number of $Re_D = 502$ and $10^4$. To numerically study the effects of cavity width on the flows, we consider (1) 2D cavities with spanwise periodicity and (2) finite-span cavities with no-slip adiabatic walls. Furthermore, the analyses are conducted for subsonic ($M_\infty=0.6$) and supersonic ($M_\infty=1.4$) speeds to reveal compressibility effects. It is found that, at low $Re_D=502$, widening the cavity can decrease the velocity fluctuations of the flow by introducing spanwise variations in the shear layer to reduce the kinetic energy from spanwise vortices associated with Rossiter modes. Both velocity and pressure fluctuations decrease in the finite-span cavity compared to those with spanwise periodic boundary conditions. With the characteristics of base flows revealed, flow control is implemented for turbulent cavity flows where steady blowing is introduced along the leading edge of the cavity for both subsonic ($M_\infty=0.6$) and supersonic ($M_\infty=1.4$) flows. We examine how the actuations interact with the flows and reduce the velocity and pressure fluctuations with and without sidewalls. From the control study, we find that pressure reduction on the cavity surfaces can be achieved in an effective manner by taking advantage of 3D flow physics. === A Dissertation submitted to the Department of Mechanical Engineering in partial fulfillment of the requirements for the degree of Doctor of Philosophy. === Fall Semester 2017. === November 3, 2017. === Compressible cavity flow, Flow control of cavity flows, Global stability analysis === Includes bibliographical references. === Kunihiko Taira, Professor Directing Dissertation; Weikuan Yu, University Representative; Louis N. Cattafesta, III, Committee Member; Lawrence S. Ukeiley, Committee Member; Shangchao Lin, Committee Member.