No abstract

We have investigated the effects of permeable walls, modeled by linear acoustic impedance with zero reactance, on compressible channel flow via linear stability analysis (LSA). Base flow profiles are taken from impermeable isothermal-wall laminar and turbulent channel flow simulations at bulk Reynolds number, Re b = 6900 and Mach numbers, M b = 0.2, 0.5, 0.85. For a sufficiently high value of permeability, Two dominant modes are made unstable: a bulk pressure mode, causing symmetric expulsion and suction of mass from the porous walls (Mode 0); a standing-wavelike mode, with a pressure node at the centerline (Mode I). In the case of turbulent mean flow profiles, both modes generate additional Reynolds shear stresses augmenting the (base) turbulent ones, but concentrated in the viscous sublayer region; the trajectories of the two modes in the complex phase velocity space follow each other closely for values of wall permeability spanning two orders of magnitude, suggesting their coexistence. The transition from subcritical to supercritical permeability does not alter the structure of the two modes for the range of wavenumbers investigated, suggesting that wall permeability simply accentuates pre-existing otherwise stable modes. Results from the present investigation will inform the design of new compressible turbulent boundary layer control strategies via assigned wallimpedance.

No abstract

No abstract

We have developed a fully sparse, compact-scheme based biglobal stability analysis numerical solver applied, for the scope of the current paper, to the investigation of the effects of impedance boundary conditions (IBCs) on the structure of a fully developed compressible turbulent channel flow. A sixth-order compact finite difference scheme is used to discretize the linearized Navier-Stokes equations leading to a Generalized Eigenvalue Problem (GEVP). Sparsity is retained by explicitly introducing derivatives of the perturbation as additional unknowns, increasing the overall problem size (number of columns × number of rows) while significantly reducing the number of non-zeros and the computational cost with respect to traditional implementations yielding otherwise dense matrix blocks. The resulting GEVP is coded in Python and solved employing an Message Passing Interface (MPI) parallelized PETSc-based sparse eigenvalue solver adopting a modified Arnoldi algorithm. Base flow is taken from impermeable isothermal-wall turbulent channel flow simulations at bulk Reynolds number, Re b = 6900 and Mach number, M b = 0.85. The eigenvalue spectrum calculated in the biglobal stability analysis shows distinct groups of modes associated with a discrete set of streamwise wave numbers accommodated by computational domain. An iterative strategy for the imposition of the complex IBCs, which are a nonlinear function of the real-valued (Fourier) frequency in the GEVP, has been devised. The adopted IBC specifically represents an array of sub-surface-mounted Helmholtz cavities with resonant frequency, fres, covered by a porous sheet with permeability inversely proportional to the impedance resistance R. The tunable resonant frequency has been shown to be an attractor for the instability, yielding a single unstable mode at that frequency. Future work is focused on companion Direct Numerical Simulation (DNS) calculations using a high order compact scheme for the same flow configuration investigating the effects of variable resonant frequency in the streamwise direction fres = fres(x).