The local and global stability of confined planar wakes at intermediate Reynolds number

At high Reynolds numbers, wake flows become more globally unstable when they are confined within a duct or between two flat plates. At Reynolds numbers around 100, however, global analyses suggest that such flows become more stable when confined, while local analyses suggest that they become more unstable. The aim of this paper is to resolve this apparent contradiction by examining a set of obstacle-free wakes. In this theoretical and numerical study, we combine global and local stability analyses of planar wake flows at $\mathit{Re}= 100$ to determine the effect of confinement. We find that confinement acts in three ways: it modifies the length of the recirculation zone if one exists, it brings the boundary layers closer to the shear layers, and it can make the flow more locally absolutely unstable. Depending on the flow parameters, these effects work with or against each other to destabilize or stabilize the flow. In wake flows at $\mathit{Re}= 100$ with free-slip boundaries, flows are most globally unstable when the outer flows are 50 % wider than the half-width of the inner flow because the first and third effects work together. In wake flows at $\mathit{Re}= 100$ with no-slip boundaries, confinement has little overall effect when the flows are weakly confined because the first two effects work against the third. Confinement has a strong stabilizing effect, however, when the flows are strongly confined because all three effects work together. By combining local and global analyses, we have been able to isolate these three effects and resolve the apparent contradictions in previous work.

Verifying stability of approximate explicit MPC

Several authors have proposed algorithms for approximate explicit MPC [1],[2],[3]. These algorithms have in common that they develop a stability criterion for approximate explicit MPC that require the approximate cost function to be within a certain distance from the optimal cost function. In this paper, stability is instead ascertained by considering only the cost function of the approximate MPC. If a region of the state space is found where the cost function is not decreasing, this indicates that an improved approximation (to the optimal control) is required in that region. If the approximate cost function is decreasing everywhere, no further refinement of the approximate MPC is necessary, since stability is guaranteed. ©2009 IEEE.

Moment asymptotic stability of stochastic hybrid delay systems

in this paper we investigate the moment asymptotic stability for the nonlinear stochastic hybrid delay systems. Sufficient criteria on the stabilization and robust stability are also established for linear stochastic hybrid delay systems. Copyright © 2005 IFAC.

Enhancing the stability of subsonic compressors using casing grooves

Casing grooves are known to increase the stable operating range of axial compressors. The mechanism by which this stability enhancement occurs is poorly understood. This paper develops a better understanding of the behavior of casing grooves through analysis of new data. An experimental parametric study is used to demonstrate the effect of varying the axial location of a single casing groove on the stability and efficiency of the compressor. The effect that the groove has on rotor outflow blockage, blade loading, and the near-casing flow field is then investigated using both experimental and computational methods. It is found that the interaction of the groove with the flow field is different when the groove is positioned forward or aft relative to the blade. The interaction of the groove with the flow in the tip region in both of these positions is presented in detail. Finally, the implications of these findings for the design of casing grooves of different depths are discussed. © 2011 American Society of Mechanical Engineers.

Enhancing the stability of subsonic compressors using casing grooves

Casing grooves are known to increase the stable operating range of axial compressors. The mechanism by which this stability enhancement occurs is poorly understood. This paper develops a better understanding of the behaviour of grooves through analysis of new data. An experimental parametric study is used to demonstrate the effect of varying the axial location of a single casing groove on the stability and efficiency of the compressor. The effect that the groove has on rotor outflow blockage, blade loading and the near-casing flow field is then studied using both experimental and computational methods. It is found that the interaction of the groove with the flow field is different when the groove is positioned forward or aft relative to the blade. The interaction of the groove with the flow in the tip region in both of these positions is presented in detail. Finally, the implications of these findings for the design of casing grooves of different depths are discussed. Copyright © 2009 Rolls-Royce plc.

On the stability of a rod adhering to a rigid surface: Shear-induced stable adhesion and the instability of peeling

Using variational methods, we establish conditions for the nonlinear stability of adhesive states between an elastica and a rigid halfspace. The treatment produces coupled criteria for adhesion and buckling instabilities by exploiting classical techniques from Legendre and Jacobi. Three examples that arise in a broad range of engineered systems, from microelectronics to biologically inspired fiber array adhesion, are used to illuminate the stability criteria. The first example illustrates buckling instabilities in adhered rods, while the second shows the instability of a peeling process and the third illustrates the stability of a shear-induced adhesion. The latter examples can also be used to explain how microfiber array adhesives can be activated by shearing and deactivated by peeling. The nonlinear stability criteria developed in this paper are also compared to other treatments. © 2012 Elsevier Ltd. All rights reserved.