Linear Stability Analysis of Compressible Channel Flow over Porous Walls

Rahbari, Iman; Scalo, Carlo

doi:10.1007/978-3-319-41217-7_24

Cited by 8 publications

(8 citation statements)

References 25 publications

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“…Finally, the phase speed of the most amplified instability is given as a function of resistance in 17(d) for case AC01. The phase speed decreases with decreasing R. It would appear that this is opposite to the observations by Rahbari and Scalo [57] (see their Fig. 6) that the phase velocity increases when R decreases, at a fixed wavenumber.…”

Section: Link Between Resistance Growth Rate and Observed Drag Incrcontrasting

confidence: 63%

“…In particular, the frequency of the most amplified instability saturates to a value slightly larger than K/M when R → 0. This would not be the case for a purely resistive system (such as considered by Jimenez et al [23] or Rahbari and Scalo [57]), in which the frequency of the most amplified instability (as well as the corresponding wavenumber) would increase importantly as R → 0. Finally, the phase speed of the most amplified instability is given as a function of resistance in 17(d) for case AC01.…”

Section: Link Between Resistance Growth Rate and Observed Drag Incrmentioning

confidence: 97%

“…In the present case, since the computational domain is periodic in the flow direction, a temporal analysis is more relevant: the (real) wavenumber k x is given, and the spectrum of the (complex) angular frequency ω = ω r + iω i is computed. Temporal analyses have been performed by Jimenez et al [23] for a purely resistive surface, by Tilton and Cortelezzi [55] for a model of porous surface, and by Rahbari and Scalo [57], again for a purely resistive surface.…”

Section: Stability Analysismentioning

confidence: 99%

See 2 more Smart Citations

Numerical simulation of a turbulent channel flow with an acoustic liner

Sebastian

Marx

Fortuné

2019

Journal of Sound and Vibration

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Numerical simulations of a compressible turbulent channel flow with an acoustic impedance boundary condition are performed to assess how the flow is modified compared with a channel flow with rigid walls. When the liner resonance frequency is not too large and the resistance sufficiently small, turbulent statistics deviate from those obtained with rigid walls and surface waves are found traveling along the liner surface. For small resonance frequencies these waves are two-dimensional, they have a large wavelength compared to the turbulent structures and modulate these structures. As a result, they transport momentum toward the impedance wall, causing a drag increase. When the resonance frequency increases, the waves along the liner surface progressively lose their spanwise coherence while their streamwise wavelength decreases to get close to the flow typical length scales, which may also result in a drag increase when the resistance is sufficiently small. In the cases in which the surface waves are twodimensional, a connection is established between them and the unstable modes computed by using a linear stability analysis. Given the streamwise periodicity of the channel, a temporal stability analysis is performed rather than a spatial analysis, the latter being more frequently encountered in acoustic mode computations. This temporal analysis shows that the unstable mode in the vicinity of an acoustic liner arises from the A-branch of wall modes.

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Section: Link Between Resistance Growth Rate and Observed Drag Incrcontrasting

confidence: 63%

Section: Link Between Resistance Growth Rate and Observed Drag Incrmentioning

confidence: 97%

Section: Stability Analysismentioning

confidence: 99%

See 1 more Smart Citation

Numerical simulation of a turbulent channel flow with an acoustic liner

Sebastian

Marx

Fortuné

2019

Journal of Sound and Vibration

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“…To this end, we first performed linear stability analysis of compressible turbulent and laminar channel flow over purely real impedance in a range of subsonic to transonic Mach numbers. 6 For sufficiently high wall permeability, two unstable modes show up: one representing a bulk pressure mode and another is a standing-wave like mode. They both generate additional Reynolds shear stresses concentrated in the viscous sublayer region.…”

Section: Ia Backgroundmentioning

confidence: 99%

Quasi-Spectral Sparse Bi-Global Stability Analysis of Compressible Channel Flow over Complex Impedance

Rahbari

Scalo

2017

55th AIAA Aerospace Sciences Meeting

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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).

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“…Equation (8) with appropriate boundary conditions would yield a conventional Helmholtz problem, which is essentially an eigenvalue problem that is typically considered in linear acoustic analysis. 11 Solving this problem returns a finite set of frequencies (eigenvalues) and wave forms (eigenvectors). Note that homogeneous boundary conditions (b = 0) are required by an eigenvalue solver.…”

Section: Iib Numerics and Algebraic Formulationmentioning

confidence: 99%

Towards Impedance Characterization of Carbon-Carbon Ultrasonically Absorptive Coatings via the Inverse Helmholtz Problem

Patel

Gupta

Scalo

et al. 2017

55th AIAA Aerospace Sciences Meeting

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We present a numerical method to determine the complex acoustic impedance at the open surface of an arbitrarily shaped cavity, associated to an impinging planar acoustic wave with a given wavenumber vector and frequency. We have achieved this by developing the first inverse Helmholtz Solver (iHS), which implicitly reconstructs the complex acoustic waveform-at a given frequency-up to the unknown impedance boundary, hereby providing the spatial distribution of impedance as a result of the calculation for that given frequency. We show that the algebraic closure conditions required by the inverse Helmholtz problem are physically related to the assignment of the spatial distribution of the pressure phase over the unknown impedance boundary. The iHS is embarassingly parallelizable over the frequency domain allowing for the straightforward determination of the full broadband impedance at every point of the target boundary. In this paper, we restrict our analysis to two-dimensions only. We first validate our results against Rott's quasi one-dimensional thermoacoustic theory for viscid and inviscid constant-area rectangular ducts, test our iHS in a fully unstructured fashion with a geometrically complex cavity, and finally, present a simplified, two-dimensional analysis of a sample of carbon-carbon ultrasonically absorptive coatings (C/C UACs) manufactured in DLR-Stuttgart, and used in the hypersonic transition delay experiments by Wagner et al. in AIAA 2012-5865. The final goal is to model C/C UACs with multi-oscillator Time Domain Impedance Boundary Conditions (TDIBC) developed by Lin et al. in JFM (2016) to be applied in direct numerical simulations (DNS) focused on the overlying boundary layer, eliminating the need to simultaneously resolve the microscopic porous structure of the C/C UACs.

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Linear Stability Analysis of Compressible Channel Flow over Porous Walls

Cited by 8 publications

References 25 publications

Numerical simulation of a turbulent channel flow with an acoustic liner

Numerical simulation of a turbulent channel flow with an acoustic liner

Quasi-Spectral Sparse Bi-Global Stability Analysis of Compressible Channel Flow over Complex Impedance

Towards Impedance Characterization of Carbon-Carbon Ultrasonically Absorptive Coatings via the Inverse Helmholtz Problem

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