scholarly journals Isotropic polarization of compressible flows

2015 ◽  
Vol 787 ◽  
pp. 440-448 ◽  
Author(s):  
Jian-Zhou Zhu
Keyword(s):  
Compressible Flows ◽  
Large Scale ◽  
Negative Temperature ◽  
Acoustic Mode ◽  
Positive Definite ◽  
Helmholtz Decomposition ◽  
Adiabatic Flow ◽  
Acoustic Modes

The helical absolute equilibrium of a compressible adiabatic flow presents not only polarization between two purely helical modes of opposite chiralities but also that between vortical and acoustic modes, deviating from the equipartition predicted by Kraichnan (J. Acoust. Soc. Am., vol. 27, 1955, pp. 438–441). Owing to the existence of the acoustic mode, even if all the Fourier modes of one chiral sector in the sharpened Helmholtz decomposition (Moses, SIAM J. Appl. Maths, vol. 21, 1971, pp. 114–130) are thoroughly truncated, leaving the system with positive-definite helicity and energy, negative temperature and the corresponding large-scale concentration of vortical modes are not allowed, unlike in the incompressible case.

scholarly journals Scalability of OpenFOAM Density-Based Solver with Runge–Kutta Temporal Discretization Scheme

2020 ◽  
Vol 2020 ◽  
pp. 1-11 ◽  
Author(s):  
Sibo Li ◽  
Roberto Paoli ◽  
Michael D’Mello
Keyword(s):  
Compressible Flows ◽  
Large Scale ◽  
National Laboratory ◽  
Time Integration ◽  
Argonne National Laboratory ◽  
Euler Scheme ◽  
Third Order ◽  
Runge Kutta ◽  
Unsteady Problems ◽  
Large Scale Simulations

Compressible density-based solvers are widely used in OpenFOAM, and the parallel scalability of these solvers is crucial for large-scale simulations. In this paper, we report our experiences with the scalability of OpenFOAM’s native rhoCentralFoam solver, and by making a small number of modifications to it, we show the degree to which the scalability of the solver can be improved. The main modification made is to replace the first-order accurate Euler scheme in rhoCentralFoam with a third-order accurate, four-stage Runge-Kutta or RK4 scheme for the time integration. The scaling test we used is the transonic flow over the ONERA M6 wing. This is a common validation test for compressible flows solvers in aerospace and other engineering applications. Numerical experiments show that our modified solver, referred to as rhoCentralRK4Foam, for the same spatial discretization, achieves as much as a 123.2% improvement in scalability over the rhoCentralFoam solver. As expected, the better time resolution of the Runge–Kutta scheme makes it more suitable for unsteady problems such as the Taylor–Green vortex decay where the new solver showed a 50% decrease in the overall time-to-solution compared to rhoCentralFoam to get to the final solution with the same numerical accuracy. Finally, the improved scalability can be traced to the improvement of the computation to communication ratio obtained by substituting the RK4 scheme in place of the Euler scheme. All numerical tests were conducted on a Cray XC40 parallel system, Theta, at Argonne National Laboratory.

scholarly journals Helmholtz’s decomposition for compressible flows and its application to computational aeroacoustics

2020 ◽  
Vol 1 (6) ◽  
Author(s):  
Stefan Schoder ◽  
Klaus Roppert ◽  
Manfred Kaltenbacher
Keyword(s):  
Flow Velocity ◽  
Compressible Flows ◽  
Base Flow ◽  
Computational Aeroacoustics ◽  
Helmholtz Decomposition ◽  
The Finite Element Method ◽  
Main Challenge ◽  
Source Data ◽  
Flow Domain ◽  
Definition Of

Abstract The Helmholtz decomposition, a fundamental theorem in vector analysis, separates a given vector field into an irrotational (longitudinal, compressible) and a solenoidal (transverse, vortical) part. The main challenge of this decomposition is the restricted and finite flow domain without vanishing flow velocity at the boundaries. To achieve a unique and $$L_2$$ L 2 -orthogonal decomposition, we enforce the correct boundary conditions and provide its physical interpretation. Based on this formulation for bounded domains, the flow velocity is decomposed. Combining the results with Goldstein’s aeroacoustic theory, we model the non-radiating base flow by the transverse part. Thereby, this approach allows a precise physical definition of the acoustic source terms for computational aeroacoustics via the non-radiating base flow. In a final simulation example, Helmholtz’s decomposition of compressible flow data using the finite element method is applied to an overflowed rectangular cavity at Mach 0.8. The results show a reasonable agreement with the source data and illustrate the distinct parts of the Helmholtz decomposition.

Azimuthal Behaviour of Self-Excited Diametral Modes of Internal Cavities

2009 ◽  
Author(s):  
K. Aly ◽  
S. Ziada
Keyword(s):  
Acoustic Mode ◽  
Free Shear Layer ◽  
Complex Flow ◽  
Complex Behaviour ◽  
Pressure Transducers ◽  
Acoustic Modes ◽  
Mode Amplitude ◽  
Temporal Phase ◽  
Internal Cavities ◽  
Shallow Cavities

The aerodynamic excitation of ducted cavity diametral modes, which are inherently antisymmetric acoustic modes, by the oscillation of the axisymmetric free shear layer gives rise to complex flow-sound interaction mechanisms, in which the acoustic diametral modes do not possess a preferred azimuthal orientation. The azimuthal behaviour of this self-excitation mechanism is investigated experimentally. The study is performed for axisymmetric shallow cavities in a duct for a range of cavity length to depth ratio of L/d = 1 to 4, and for Mach numbers up to 0.4. Three pressure transducers flush mounted to the cavity floor are used to determine the acoustic mode amplitude and orientation. The excited acoustic modes are classified into spinning, partially spinning and stationary diametral modes. An analytical model based on the superposition of two orthogonal modes with 90° temporal phase shift is developed to reproduce the spinning and the partially spinning diametral modes. The developed model clarifies the observed complex behaviour of the azimuthal modes.

Finite-wavelength scattering of incident vorticity and acoustic waves at a shrouded-jet exit

2008 ◽  
Vol 612 ◽  
pp. 407-438 ◽  
Author(s):  
ARNAB SAMANTA ◽  
JONATHAN B. FREUND
Keyword(s):  
Mach Number ◽  
Acoustic Waves ◽  
Vortex Sheet ◽  
Acoustic Mode ◽  
Uniform Flow ◽  
Sharp Edge ◽  
Potential Mechanism ◽  
Ambient Flow ◽  
Acoustic Modes ◽  
Cylindrical Vortex

As the vortical disturbances of a shrouded jet pass the sharp edge of the shroud exit some of the energy is scattered into acoustic waves. Scattering into upstream-propagating acoustic modes is a potential mechanism for closing the resonance loop in the ‘howling’ resonances that have been observed in various shrouded jet configurations over the years. A model is developed for this interaction at the shroud exit. The jet is represented as a uniform flow separated by a cylindrical vortex sheet from a concentric co-flow within the cylindrical shroud. A second vortex sheet separates the co-flow from an ambient flow outside the shroud, downstream of its exit. The Wiener–Hopf technique is used to compute reflectivities at the shroud exit. For some conditions it appears that the reflection of finite-wavelength hydrodynamic vorticity modes on the vortex sheet defining the jet could be sufficient to reinforce the shroud acoustic modes to facilitate resonance. The analysis also gives the reflectivities for the shroud acoustic modes, which would also be important in establishing resonance conditions. Interestingly, it is also predicted that the shroud exit can be ‘transparent’ for ranges of Mach numbers, with no reflection into any upstream-propagating acoustic mode. This is phenomenologically consistent with observations that indicate a peculiar sensitivity of resonances of this kind to, say, jet Mach number.

Excitation of geodesic acoustic mode continuum by drift wave turbulence

2012 ◽  
Vol 78 (6) ◽  
pp. 651-655 ◽  
Author(s):  
JUN YU ◽  
J. Q. DONG ◽  
X. X. LI ◽  
D. DU ◽  
X. Y. GONG
Keyword(s):  
Growth Rate ◽  
Acoustic Mode ◽  
Kinetic Approach ◽  
Wave Turbulence ◽  
Ion Temperature ◽  
Drift Wave Turbulence ◽  
Acoustic Modes ◽  
Drift Wave ◽  
Radial Structure ◽  
Geodesic Acoustic Mode

AbstractExcitation of the geodesic acoustic mode continuum by drift wave turbulence is studied using the wave kinetic approach. For a model profile of weak non-uniform ion temperature, the forms of growth rate and radial structure of geodesic acoustic modes are obtained analytically. The growth rate is analyzed for several conditions for present-day tokamaks and compared with that for uniform ion temperature, as well as that given by the coherent mode approach for non-uniform ion temperature.

Modelling a Structural-Acoustic Coupled System with an Equivalent Lumped Parameter Mechanical System

1999 ◽  
Vol 121 (4) ◽  
pp. 453-459 ◽  
Author(s):  
S. M. Kim ◽  
M. J. Brennan
Keyword(s):  
Coupled System ◽  
Acoustic Mode ◽  
Physical Parameters ◽  
Acoustic System ◽  
Acoustic Modes ◽  
Lumped Parameter ◽  
Resonance Frequencies ◽  
Mechanical Models ◽  
Equivalent Mass ◽  
Physical Insight

This paper describes the way in which a structural acoustic coupled system can be modelled using an equivalent lumped parameter mechanical model. The impedance-mobility approach is first used to model the system, and by relating the physical parameters to equivalent mass and stiffness, lumped parameter models can be derived provided that damping in the acoustic system is neglected in all modes, but the first (zero order) mode. A limitation of this approach, however, is that these simple mechanical models formulated in terms of the uncoupled structural and acoustic modes are only possible for either a single structural mode coupled to many acoustic modes, or a single acoustic mode coupled to many structural modes. These models facilitate physical insight into the dynamic behavior of a lightly-damped structural-acoustic system at frequencies close to the resonance frequencies of the coupled system.

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