Direct computation of the sound generated by vortex pairing in an axisymmetric jet

1999 ◽  
Vol 383 ◽  
pp. 113-142 ◽  
Author(s):  
BRIAN E. MITCHELL ◽  
SANJIVA K. LELE ◽  
PARVIZ MOIN
Keyword(s):  
Mach Number ◽  
Stokes Equations ◽  
Near Field ◽  
Prediction Method ◽  
Axial Direction ◽  
Navier Stokes ◽  
Far Field ◽  
Source Terms ◽  
Vortex Pairing ◽  
Field Sound

The sound generated by vortex pairing in axisymmetric jets is determined by direct solution of the compressible Navier–Stokes equations on a computational grid that includes both the near field and a portion of the acoustic far field. At low Mach number, the far-field sound has distinct angles of extinction in the range of 60°–70° from the jet's downstream axis which can be understood by analogy to axisymmetric, compact quadrupoles. As the Mach number is increased, the far-field sound takes on a superdirective character with the dominant sound directed at shallow angles to the jet's downstream axis. The directly computed sound is compared to predictions obtained from Lighthill's equation and the Kirchhoff surface method. These predictions are in good agreement with the directly computed data. The Lighthill source terms have a large spatial distribution in the axial direction necessitating the introduction of a model to describe the source terms in the region downstream of the last vortex pairing. The axial non-compactness of the quadrupole sources must be adequately treated in the prediction method.

scholarly journals Sound generation in a mixing layer

1997 ◽  
Vol 330 ◽  
pp. 375-409 ◽  
Author(s):  
TIM COLONIUS ◽  
SANJIVA K. LELE ◽  
PARVIZ MOIN
Keyword(s):  
Acoustic Field ◽  
Stokes Equations ◽  
Near Field ◽  
Mixing Layer ◽  
Navier Stokes ◽  
Far Field ◽  
Source Terms ◽  
Acoustic Analogy ◽  
Navier Stokes Equations ◽  
Acoustic Sources

The sound generated by vortex pairing in a two-dimensional compressible mixing layer is investigated. Direct numerical simulations (DNS) of the Navier–Stokes equations are used to compute both the near-field region and a portion of the acoustic field. The acoustic analogy due to Lilley (1974) is also solved with acoustic sources determined from the near-field data of the DNS. It is shown that several commonly made simplifications to the acoustic sources can lead to erroneous predictions for the acoustic field. Predictions based on the quadrupole form of the source terms derived by Goldstein (1976a, 1984) are in excellent agreement with the acoustic field from the DNS. However, despite the low Mach number of the flow, the acoustic far field generated by the vortex pairings cannot be described by considering compact quadrupole sources. The acoustic sources have the form of modulated wave packets and the acoustic far field is described by a superdirective model (Crighton & Huerre 1990). The presence of flow–acoustic interactions in the computed source terms causes the acoustic field predicted by the acoustic analogy to be very sensitive to small changes in the description of the source.

ANALYSIS OF A HETEROGENEOUS DOMAIN DECOMPOSITION FOR COMPRESSIBLE VISCOUS FLOW

2001 ◽  
Vol 11 (04) ◽  
pp. 565-599 ◽  
Author(s):  
CRISTIAN A. COCLICI ◽  
WOLFGANG L. WENDLAND
Keyword(s):  
Domain Decomposition ◽  
Stokes Equations ◽  
Domain Decomposition Method ◽  
Near Field ◽  
Outer Region ◽  
Navier Stokes ◽  
Far Field ◽  
Computational Domain ◽  
Linearized Euler Equations ◽  
Naca0012 Airfoil

We analyze a nonoverlapping domain decomposition method for the treatment of two-dimensional compressible viscous flows around airfoils. Since at some distance to the given profile the inertial forces are strongly dominant, there the viscosity effects are neglected and the flow is assumed to be inviscid. Accordingly, we consider a decomposition of the original flow field into a bounded computational domain (near field) and a complementary outer region (far field). The compressible Navier–Stokes equations are used close to the profile and are coupled with the linearized Euler equations in the far field by appropriate transmission conditions, according to the physical properties and the mathematical type of the corresponding partial differential equations. We present some results of flow around the NACA0012 airfoil and develop an a posteriori analysis of the approximate solution, showing that conservation of mass, momentum and energy are asymptotically attained with the linear model in the far field.

scholarly journals Analytical Equations for Thermoacoustic Instability Sources and Acoustic Radiation from Reacting Turbulence

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
S. A. E. Miller
Keyword(s):  
Stokes Equations ◽  
Acoustic Radiation ◽  
Prediction Method ◽  
Combustion Noise ◽  
Navier Stokes ◽  
Reacting Flow ◽  
Source Terms ◽  
Navier Stokes Equations ◽  
Thermoacoustic Instability ◽  
Aerodynamic Interaction

We seek to ascertain and understand source terms that drive thermoacoustic instability and acoustic radiation. We present a new theory based on the decomposition of the Navier-Stokes equations coupled with the mass fraction equations. A series of solutions are presented via the method of the vector Green’s function. We identify both combustion-combustion and combustion-aerodynamic interaction source terms. Both classical combustion noise theory and classical Rayleigh criterion are recovered from the presently developed more general theory. An analytical spectral prediction method is presented, and the two-point source terms are consistent with Lord Rayleigh’s instability model. Particular correlations correspond to the source terms of Lighthill, which represent the noise from turbulence and additional terms for the noise from reacting flow.

Analytical and Numerical Investigations on the Aeroacoustical Oscillation of Flow Past the Cavity

2015 ◽  
Author(s):  
Weidong Shao ◽  
Jun Li
Keyword(s):  
Stokes Equations ◽  
Near Field ◽  
Navier Stokes ◽  
Far Field ◽  
Navier Stokes Equations ◽  
Flow Past ◽  
Tonal Frequency ◽  
Number Flow ◽  
Unsteady Characteristics ◽  
Flow Flux

Noise radiated by aeroacoustical oscillation of low Mach number flow past a two-dimensional cavity has been investigated analytically and numerically using electro-acoustical analogy and a hybrid scheme combining CFD with an implementation of the porous Ffowcs Williams-Hawkings equation. The noise generation mechanism is illustrated and the interaction between flow and cavity as well as key factors of resonant frequency is discussed. The 2D compressible unsteady Reynolds averaged Navier-Stokes equations (URANS) are solved to obtain near field acoustic source and unsteady characteristics of cavity flow. A buffer domain is exerted along all external boundaries to suppress boundary wave reflection. Computed tonal frequency and amplitude of pressure oscillations demonstrate good agreement with previous computational simulations and experiments. The influences of the length and shape of the neck and porous inserts on the noise radiated to the far field are also investigated. The 3D far field numerical results show that at a certain incoming flow velocity and shear layer thickness the frequency of the dominant oscillation increases with the length of the neck and the magnitude in the downstream far field is 8dB greater than that in the upstream far field. The increasing chamfer decreases the resonance frequency and changes the effective streamwise opening length resulting in significant differences in acoustic pressure fluctuation. The porous inserts on the floor of the cavity reduce the mass flow flux through the cavity neck and accordingly suppress the amplitude of dominant oscillation. The preliminary simulations reveal promising methods for sound radiation control.

Computational Analysis of Tonal Noise Generated High-Bypass Ratio Fan Stage

2005 ◽  
Author(s):  
Aleksey M. Sipatov ◽  
Michail V. Usanin ◽  
Valery G. Avgustinovich ◽  
Natalia O. Chuhlantseva
Keyword(s):  
Pressure Distribution ◽  
Acoustic Analysis ◽  
Stokes Equations ◽  
Near Field ◽  
Hybrid Approach ◽  
Leading Edge ◽  
Navier Stokes ◽  
Far Field ◽  
Unsteady Pressure ◽  
Acoustic Contribution

The paper shows the procedure of estimating different fan stage geometries from the point of the fan stage aerodynamic and acoustic efficiency by using CFX v.5.6 gas dynamics software. Two different fan stages were examined. The acoustic analysis was made based on unsteady pressure distribution along exit guide vanes. The unsteady pressure distribution was determined from 3-D calculations of rotor-stator interactions. An improved approach is suggested to estimate acoustic sources with the leading edge geometry considered. Three various grid models were analyzed to estimate the grid discretization influence on computational results. The hybrid approach was used to evaluate the acoustic contribution of fan stage rotor–stator interaction to a turbo-jet engine total noise level on first harmonic in a far field. This approach consists of three steps. The first step includes the solving of Navier-Stokes equations in fan stage, the second step includes the solving of linearized Euler’s equations (LEE) in a near field and, then, the third covers the calculation of Ffowcs Williams–Hawkings (FWH) integral in a far field. The first step marked the effect of strong attenuation of acoustics modes in the fan passage. The results of calculations in the far field were compared with experiment data.

Spin-up from rest of a compressible fluid in a rapidly rotating cylinder

1992 ◽  
Vol 237 ◽  
pp. 413-434 ◽  
Author(s):  
Jae Min Hyun ◽  
Jun Sang Park
Keyword(s):  
Mach Number ◽  
Compressible Fluid ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Axial Direction ◽  
Ekman Layer ◽  
Infinite Cylinder ◽  
Full Time ◽  
Viscous Effects ◽  
Initial State

Spin-up flows of a compressible gas in a finite, closed cylinder from an initial state of rest are studied, The flow is characterized by small reference Ekman numbers, and the peripheral Mach number is O(1). Comprehensive numerical solutions have been obtained for the full, time-dependent compressible Navier-Stokes equations. The details of the flow, temperature, and density evolution are described. In the early phase of spin-up, owing to the thermoacoustic disturbances caused by the compressible Rayleigh effect, the flows are oscillatory, and this oscillatory behaviour is pronounced at higher Mach numbers. The principal dynamical role of the Ekman layer is dominant over moderate times of orders of the homogeneous spin-up timescales. Owing to the density stratification in the radial direction, the Ekman layer is thicker in the central region of the interior. The interior azimuthal flows are mainly uniform in the axial direction. As the Mach number increases, the rate of spin-up in the interior becomes slower, and the propagating shear front is more diffusive. Explicit comparisons with the results for an infinite cylinder are made to ascertain the contributions of the endwall disks. In contrast to the usual incompressible spin-up from rest, the viscous effects are relatively more important for the case of a compressible fluid.

scholarly journals Implicit MAC scheme for compressible Navier–Stokes equations: low Mach asymptotic error estimates

2020 ◽  
Author(s):  
David Maltese ◽  
Antonín Novotný
Keyword(s):  
Mach Number ◽  
Initial Data ◽  
Error Estimate ◽  
Strong Solution ◽  
Stokes Equations ◽  
Main Tool ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Low Mach Number ◽  
Mac Scheme

Abstract We investigate the error between any discrete solution of the implicit marker-and-cell (MAC) numerical scheme for compressible Navier–Stokes equations in the low Mach number regime and an exact strong solution of the incompressible Navier–Stokes equations. The main tool is the relative energy method suggested on the continuous level in Feireisl et al. (2012, Relative entropies, suitable weak solutions, and weak–strong uniqueness for the compressible Navier–Stokes system. J. Math. Fluid Mech., 14, 717–730). Our approach highlights the fact that numerical and mathematical analyses are not two separate fields of mathematics. The result is achieved essentially by exploiting in detail the synergy of analytical and numerical methods. We get an unconditional error estimate in terms of explicitly determined positive powers of the space–time discretization parameters and Mach number in the case of well-prepared initial data and in terms of the boundedness of the error if the initial data are ill prepared. The multiplicative constant in the error estimate depends on a suitable norm of the strong solution but it is independent of the numerical solution itself (and of course, on the discretization parameters and the Mach number). This is the first proof that the MAC scheme is unconditionally and uniformly asymptotically stable in the low Mach number regime.

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