Acoustic resonances in a high-lift configuration

2007 ◽  
Vol 582 ◽  
pp. 179-202 ◽  
Author(s):  
STEFAN HEIN ◽  
THORSTEN HOHAGE ◽  
WERNER KOCH ◽  
JOACHIM SCHÖBERL
Keyword(s):  
Leading Edge ◽  
Absorbing Boundary Conditions ◽  
Computational Domain ◽  
Mean Flow ◽  
Coherent Noise ◽  
Absorbing Boundary ◽  
High Lift ◽  
Complex Scaling Method ◽  
Temporal Decay ◽  
Acoustic Resonances

Low- and high-frequency acoustic resonances are computed numerically via a high-order finite-element code for a generic two-dimensional high-lift configuration with a leading-edge slat. Zero mean flow is assumed, approximating the low-Mach-number situation at aircraft landing and approach. To avoid unphysical reflections at the boundaries of the truncated computational domain, perfectly matched layer absorbing boundary conditions are implemented in the form of the complex scaling method of atomic and molecular physics. It is shown that two types of resonance exist: resonances of surface waves which scale with the total airfoil length and longitudinal cavity-type resonances which scale with the slat cove length. Minima exist in the temporal decay rate which can be associated with the slat cove resonances and depend on the slat cove geometry. All resonances are damped owing to radiation losses. However, if coherent noise sources exist, as observed in low-Reynolds-number experiments, these sources can be enhanced acoustically by the above resonances if the source frequency is close to a resonant frequency.

Acoustic resonances and trapped modes in annular plate cascades

2009 ◽  
Vol 628 ◽  
pp. 155-180 ◽  
Author(s):  
WERNER KOCH
Keyword(s):  
Axial Flow ◽  
Radiation Condition ◽  
Absorbing Boundary Conditions ◽  
Radiation Damping ◽  
Resonance Problem ◽  
Trapped Modes ◽  
Mean Flow ◽  
Absorbing Boundary ◽  
Complex Scaling Method ◽  
Acoustic Resonances

As a stepping stone towards understanding acoustic resonances in axial flow compressors, acoustic resonances are computed numerically in fixed single and tandem plate cascades in an infinitely long annular duct. Applying perfectly matched layer absorbing boundary conditions in the form of the complex scaling method of atomic and molecular physics to approximate the radiation condition the resonance problem is transformed into an eigenvalue problem. Of particular interest are resonances with zero radiation damping (trapped modes) or very small radiation damping (nearly trapped modes). Such resonances can be excited by wakes from compressor cascades or struts. If the shedding frequency is sufficiently close to an acoustic resonant frequency, the latter may control the vortex shedding causing high-intensity tonal noise or occasionally even blade failure. All resonances are computed for zero mean flow approximating low-Mach-number flows. The influence of various cascade parameters on the resonant frequencies is studied and, whenever possible, our numerical results are compared with published experimental findings.

Acoustic resonances and trapped modes in pipes and tunnels

2008 ◽  
Vol 605 ◽  
pp. 401-428 ◽  
Author(s):  
STEFAN HEIN ◽  
WERNER KOCH
Keyword(s):  
Cross Sections ◽  
High Speed ◽  
Hard Spheres ◽  
Cutoff Frequency ◽  
Three Dimensional ◽  
Absorbing Boundary Conditions ◽  
Trapped Modes ◽  
Absorbing Boundary ◽  
Complex Scaling Method ◽  
Acoustic Resonances

Acoustic resonances of simple three-dimensional finite-length structures in an infinitely long cylindrical pipe are investigated numerically by solving an eigenvalue problem. To avoid unphysical reflections at the finite grid boundaries placed in the uniform cross-sections of the pipe, perfectly matched layer absorbing boundary conditions are applied in the form of the complex scaling method of atomic and molecular physics. Examples of the structures investigated are sound-hard spheres, cylinders, cavities and closed side branches. Several truly trapped modes with zero radiation loss are identified for frequencies below the first cutoff frequency of the pipe. Such trapped modes can be excited aerodynamically by coherent vortices if the frequency of the shed vortices is close to a resonant frequency. Furthermore, numerical evidence is presented for the existence of isolated embedded trapped modes for annular cavities above the first cutoff frequency and for closed side branches below the first cutoff frequency. As applications of engineering interest, the acoustic resonances are computed for a ball-type valve and around a simple model of a high-speed train in an infinitely long tunnel.

LONG-TERM STABILITY ANALYSIS OF ACOUSTIC ABSORBING BOUNDARY CONDITIONS

2013 ◽  
Vol 23 (11) ◽  
pp. 2129-2154 ◽  
Author(s):  
HÉLÈNE BARUCQ ◽  
JULIEN DIAZ ◽  
VÉRONIQUE DUPRAT
Keyword(s):  
Stability Analysis ◽  
Boundary Conditions ◽  
Absorbing Boundary Conditions ◽  
Computational Domain ◽  
Acoustic Wave Equation ◽  
Absorbing Boundary ◽  
Term Stability ◽  
Long Term Stability ◽  
The Stability

This work deals with the stability analysis of a one-parameter family of Absorbing Boundary Conditions (ABC) that have been derived for the acoustic wave equation. We tackle the problem of long-term stability of the wave field both at the continuous and the numerical levels. We first define a function of energy and show that it is decreasing in time. Its discrete form is also decreasing under a Courant–Friedrichs–Lewy (CFL) condition that does not depend on the ABC. Moreover, the decay rate of the continuous energy can be determined: it is exponential if the computational domain is star-shaped and this property can be illustrated numerically.

An Absorbing Boundary Condition Based on Perfectly Matched Layer Technique Combined with Discontinuous Galerkin Boltzmann Method for Low Mach Number Flow Noise

2018 ◽  
Vol 26 (04) ◽  
pp. 1850011 ◽  
Author(s):  
Weidong Shao ◽  
Jun Li
Keyword(s):  
Boundary Condition ◽  
Discontinuous Galerkin ◽  
Perfectly Matched Layer ◽  
Absorbing Boundary Condition ◽  
Time Behavior ◽  
Computational Domain ◽  
Mean Flow ◽  
Absorbing Boundary ◽  
Flow Noise ◽  
Boltzmann Method

For flow noise simulations, the nonreflecting boundary condition (NRBC) is significant to confine the computational domain to a small domain. Lattice Boltzmann method (LBM) has advantages for noise because of its low dissipation, but is limited to the uniform grid. In this paper, an absorbing boundary condition (ABC) based on perfectly matched layer (PML) technique is introduced to LBM. Then PML stability is analyzed and a new strategy is developed to achieve robustness. Invoking the decoupling time integration, the underlying equation for streaming is solved with the nodal discontinuous Galerkin method. Benchmark acoustic problems were used to demonstrate the PML absorption. Moreover, PML parameters, long time behavior and inhomogeneous pseudo mean flow are discussed. The methodology appears to work very well and would be hoped for practical flow noise computation.

Towards a General-Purpose Open Boundary Condition for Wave Simulations

2011 ◽  
Author(s):  
Bulent Duz ◽  
Rene H. M. Huijsmans ◽  
Peter R. Wellens ◽  
Mart J. A. Borsboom ◽  
Arthur E. P. Veldman
Keyword(s):  
Boundary Condition ◽  
Three Dimensional ◽  
General Purpose ◽  
Absorbing Boundary Conditions ◽  
Design Stage ◽  
Open Boundary ◽  
Computational Domain ◽  
Absorbing Boundary ◽  
Scaled Model ◽  
Artificial Boundaries

For the design of FPSO’s in harsh environments an accurate assessment of the ability of the platform to survive in extreme sea conditions is of prime importance. Next to scaled model tests on the FPSO in waves also CFD capabilities are at the disposal of the designer. However even with the fastest computers available it is still a challenge to use CFD in the design stage because of the large computational resources they require. In that respect to use a small computational domain will improve the turn around time of the computations, however at the expense of various numerical artifacts, like reflection on artificial boundaries in the computational domain. In order to mitigate the reflection properties new absorbing boundary conditions have been developed. The work in this paper is constructed on the previous study about the generating and absorbing boundary condition (GABC) in the ComFLOW project. We present a method to apply the GABC on all the boundaries in a three dimensional domain. The implementation of the GABC in ComFLOW is explained in detail.

Stability of wide‐angle absorbing boundary conditions for the wave equation

Geophysics ◽  
1989 ◽  
Vol 54 (9) ◽  
pp. 1153-1163 ◽  
Author(s):  
R. A. Renaut ◽  
J. Petersen
Keyword(s):  
Wave Equation ◽  
Boundary Conditions ◽  
Least Squares ◽  
Absorbing Boundary Conditions ◽  
Computational Domain ◽  
Wide Angle ◽  
Courant Number ◽  
Absorbing Boundary ◽  
Wide Range ◽  
Artificial Boundaries

Numerical solution of the two‐dimensional wave equation requires mapping from a physical domain without boundaries to a computational domain with artificial boundaries. For realistic solutions, the artificial boundaries should cause waves to pass directly through and thus mimic total absorption of energy. An artificial boundary which propagates waves in one direction only is derived from approximations to the one‐way wave equation and is commonly called an absorbing boundary. Here we investigate order 2 absorbing boundary conditions which include the standard paraxial approximation. Absorption properties are compared analytically and numerically. Our numerical results confirm that the [Formula: see text] or Chebychev‐Padé approximations are best for wide‐angle absorption and that the Chebychev or least‐squares approximations are best for uniform absorption over a wide range of incident angles. Our results also demonstrate, however, that the boundary conditions are stable for varying ranges of Courant number (ratio of time step to grid size). We prove that there is a stability barrier on the Courant number specified by the coefficients of the boundary conditions. Thus, proving stability of the interior scheme is not sufficient. Furthermore, waves may radiate spontaneously from the boundary, causing instability, even if the stability bound on the Courant number is satisfied. Consequently, the Chebychev and least‐squares conditions may be preferred for wide‐angle absorption also.

Generating and Absorbing Boundary Conditions for Free-Surface Flow Simulations in Offshore Applications

2015 ◽  
Author(s):  
Bülent Düz ◽  
René H. M. Huijsmans ◽  
Peter R. Wellens ◽  
Mart J. A. Borsboom ◽  
Arthur E. P. Veldman ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Cfd Simulation ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Absorbing Boundary Conditions ◽  
Computational Domain ◽  
Wave Impact ◽  
Absorbing Boundary ◽  
Floating Structures ◽  
Hydrodynamic Wave

Numerical simulations of wave phenomena necessarily have to be carried out in a limited computational domain. This implies that incoming waves should be prescribed properly, and the outgoing waves should leave the domain without causing reflections. In this paper we will present an enhanced type of such generating and absorbing boundary conditions (GABC). The new approach is applied in studies of extreme hydrodynamic wave impact on rigid and floating structures in offshore and coastal engineering, for which the VOF-based CFD simulation tool ComFLOW has been developed.

scholarly journals Performance advantages of CPML over UPML absorbing boundary conditions in FDTD algorithm

2017 ◽  
Vol 68 (1) ◽  
pp. 47-53 ◽  
Author(s):  
Branko D. Gvozdic ◽  
Dusan Z. Djurdjevic
Keyword(s):  
Boundary Conditions ◽  
Electromagnetic Waves ◽  
Fdtd Method ◽  
Absorbing Boundary Conditions ◽  
Numerical Code ◽  
Computational Domain ◽  
Absorbing Boundary ◽  
Simulation Performance ◽  
Efficient Type ◽  
Computer Resources

Abstract Implementation of absorbing boundary condition (ABC) has a very important role in simulation performance and accuracy in finite difference time domain (FDTD) method. The perfectly matched layer (PML) is the most efficient type of ABC. The aim of this paper is to give detailed insight in and discussion of boundary conditions and hence to simplify the choice of PML used for termination of computational domain in FDTD method. In particular, we demonstrate that using the convolutional PML (CPML) has significant advantages in terms of implementation in FDTD method and reducing computer resources than using uniaxial PML (UPML). An extensive number of numerical experiments has been performed and results have shown that CPML is more efficient in electromagnetic waves absorption. Numerical code is prepared, several problems are analyzed and relative error is calculated and presented.

scholarly journals Equivalent Boundary Conditions for Heterogeneous Acoustic Media

2014 ◽  
Vol 15 (3) ◽  
pp. 301
Author(s):  
Manuela Longoni De Castro ◽  
Julien Diaz ◽  
Victor Perón
Keyword(s):  
Boundary Conditions ◽  
Seismic Waves ◽  
Heterogeneous Media ◽  
Absorbing Boundary Conditions ◽  
Computational Domain ◽  
Absorbing Boundary ◽  
Equivalent Boundary ◽  
Artificial Boundaries ◽  
Acoustic Media ◽  
Propagation Of Waves

In this work, we have worked on possibilities to model artificial boundaries needed in the simulation of wave propagation in acoustic heterogeneous media.  Our motivation is to restrict the computational domain in the simulation of seismic waves that are propagated from the earth and transmitted to the stratified heterogeneous media composed by ocean and atmosphere. Two possibilities were studied and compared in computational tests: the use of absorbing boundary conditions on an artificial boundary in the atmosphere layer and the elimination of the atmosphere layer using an equivalent boundary condition that mimics the propagation of waves through the atmosphere. <br />

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