Spectral/hp element technology for global flow instability and control

The objective of our paper is to demonstrate the use of spectral/ hp element technology in unravelling global flow instability mechanisms. Understanding these mechanisms is central to devising flow control approaches based on theoretically-founded physical principles. Global instability theory is concerned with prediction and control of linear and nonlinear disturbances developing in flows that are inhomogeneous in more than one spatial direction. As such, this theory encompasses the classic analysis of Tollmien which is valid for simple geometries of academic interest (e.g. a flat-plate) and therefore broadens the scope of this well-established but simplified methodology to include realistic problems encountered in aeronautical engineering. Compared with a direct numerical simulation approach, global instability theory can be used to explore efficiently far wider parameters ranges and deliver physical information to be used as handle for effective flow control.

[1]  V.Theofilis.  Global Instabilities in Trailing-Edge Laminar Separated Flow on a NACA 0012 Aerofoil , 2001 .

[2]  R. Henderson,et al.  Three-dimensional Floquet stability analysis of the wake of a circular cylinder , 1996, Journal of Fluid Mechanics.

[3]  Vassilios Theofilis,et al.  On linear and nonlinear instability of the incompressible swept attachment-line boundary layer , 1998, Journal of Fluid Mechanics.

[4]  George Em Karniadakis,et al.  A triangular spectral element method; applications to the incompressible Navier-Stokes equations , 1995 .

[5]  Cyrus K. Aidun,et al.  Transition to unsteady nonperiodic state in a through‐flow lid‐driven cavity , 1992 .

[6]  W. Arnoldi.  The principle of minimized iterations in the solution of the matrix eigenvalue problem , 1951 .

[7]  G. Karniadakis,et al.  Spectral/hp Element Methods for CFD , 1999 .

[8]  G. B. Schubauer,et al.  Laminar Boundary-Layer Oscillations and Stability of Laminar Flow , 1947 .

[9]  Vassilios Theofilis,et al.  Spatial stability of incompressible attachment-line flow , 1995 .

[10]  S. Newman,et al.  Pressurized aerosols inhaled through extension devices , 1983 .

[11]  T. Herbert.  PARABOLIZED STABILITY EQUATIONS , 1994 .

[12]  Mutsuto Kawahara,et al.  Linear Stability of Incompressible Flow Using a Mixed Finite Element Method , 1998 .

[13]  D. Poll,et al.  Transition in the Infinite Swept Attachment Line Boundary Layer , 1979 .

[14]  George Em Karniadakis,et al.  A NEW TRIANGULAR AND TETRAHEDRAL BASIS FOR HIGH-ORDER (HP) FINITE ELEMENT METHODS , 1995 .

[15]  Cyrus K. Aidun,et al.  Global stability of a lid‐driven cavity with throughflow: Flow visualization studies , 1991 .

[16]  Neil D. Sandham,et al.  Simulation and Modelling of a Skewed Turbulent Channel Flow , 2000 .

[17]  Ray-Sing Lin,et al.  On the stability of attachment-line boundary layers. Part 1. The incompressible swept Hiemenz flow , 1996, Journal of Fluid Mechanics.

[18]  D. I. A. Poll,et al.  On the stability of an infinite swept attachment line boundary layer , 1984 .