SIMULTANEOUS FINITE ELEMENT COMPUTATION OF DIRECT … · Guasch et al. Acta Acust. United Ac.. 2016. SIMULTANEOUS FEM COMPUTATION DIRECT AND DIFFRACTED FLOW NOISE FLINOVIA II A methodology

SIMULTANEOUS FEM COMPUTATION DIRECT AND DIFFRACTED FLOW NOISE

SIMULTANEOUS FINITE ELEMENT COMPUTATION OF DIRECT ANDDIFFRACTED FLOW NOISE IN DOMAINS WITH STATIC AND MOVING

BOUNDARIES

ORIOL GUASCH1, ARNAU PONT2, JOAN BAIGES2 AND RAMON CODINA21GTM Grup de recerca en Tecnologies Mèdia – La Salle, Universitat Ramon Llull – Barcelona, Catalonia

2CIMNE Centre Internacional de Mètodes Numèrics en Enginyeria ‐ Universitat Politècnica de Catalunya – Barcelona, Catalonia

FLINOVIA II


FLINOVIA II

INTRODUCTION

CURLE’S ANALOGY AS A DIFFRACTION PROBLEM

PROPOSED APPROACH

FINITE ELEMENT FORMULATION

NUMERICAL EXAMPLES:

– AEOLIAN TONE IN 2D

– PRODUCTION OF SIBILANT /S/

– TEETH‐SHAPED MOVING DOMAIN

CONCLUSIONS

2

OUTLINE


FLINOVIA II

Hybrid approach to compute aerodynamic noise at low Mach numbers

3

FLOW NOISE PROBLEM

INTRODUCTION

1. Solve the incompressibleNavier‐Stokes equations toobtain the velocity andpressure fields. Compute theacoustic source terms.

2. Solve an acoustic waveoperator equation to obtainthe acoustic pressure and/oracoustic particle velocity .


FLINOVIA II

Common procedure for the hybrid approach:

1. The first step is usually carried out resorting to the finite elementmethod (FEM) due to the non‐linearity of the problem and thecomplexity of the geometry.Numerical issues: turbulence modelling and numerical stability(closely related)

2. The second step may involve solving the wave equation (e.g., inacoustic analogies), the linearized Euler equations or the acousticperturbation equations. FEM can be used but one often resorts tointegral formulations for far field propagation.Numerical issues: depending on the integral/differential formulationand on the involved wave operator

4

SOLVING THE AEROACOUSTIC PROBLEM

INTRODUCTION


FLINOVIA II

The three goals in this work are:

Goal A: Avoid using two codes and obtain the results from steps1 and 2 with the sole use of FEM in a single computational run.This solves the low Mach inconsistency of Curle’s analogy whenperforming incompressible CFD.

Goal B: Obtain the separate contributions of the quadrupolar(turbulent) and dipolar (body) noise to the total acousticpressure from this sole (FEM) computational run.

Goal C: Achieve goal B in the case of domains with movingboundaries.

5

THREE GOALS

INTRODUCTION


FLINOVIA II

6

CURLE’S ANALOGY


Differential formulation

Lighthill’s analogy

Curle’s analogy (Integral formulation)

Integral formulation

Tailored Green function!

We would like to use the free space Green function:

Quadrupolar flow contribution Dipolar body contribution


FLINOVIA II

Curle’s analogy as a diffraction problem:Decompose:

Substitute in Lighthill’s integral formulation:

Comparing (A) and (B):

7

DIPOLAR CONTRIBUTION AND DIFFRACTED FIELD


Problem: This term contains both, aerodynamic and acoustic fluctuations! It cannot be obtained from theincompressible Navier‐Stokes equations

Free field Diffracted

(A)

(B)

Doak, Proc. R. Soc. Lond. 1960, Crighton Prog. Aerosp. Sci. 1975, Gloerfelt et al. J. Sound Vib. 2005


FLINOVIA II

Given that Curle’s surface term corresponds to the aerodynamicquadrupolar sound diffracted by the body we split intoLighthill’s equation. Therefore

8

PROPOSED APPROACH I

PROPOSED APPROACH

Total acoustic pressure

Incident pressure field (quadrupolar contribution)

Diffracted pressure field (dipolar contribution)

Body absent


FLINOVIA II

The proposed approach to determine the incident (quadrupolar)and diffracted (dipolar) contributions to aerodynamic soundconsists in:

9

PROPOSED APPROACH II

PROPOSED APPROACH

1. Solve the Navier‐Stokes equations to obtain theincompressible velocity and pressure fields

2. Solve Lighthill’sacoustic analogy in free‐field to obtain theincident acoustic field

3. Solve the acousticwave equation to obtainthe diffracted acousticfield

Guasch et al. Comput. & Fluids. 2016


FLINOVIA II

The method can be generalized to any linear wave operator

10

PROPOSED APPROACH III

PROPOSED APPROACH

1. Solve the Navier‐Stokes equations to obtain theincompressible velocity and pressure fields

2. Solve the acousticsfor the direct incidentfield

3. Solve the acousticsfor the diffracted field

can stand for the convected wave equation, the wave equation in mixed form, the wave equation inmixed form in a moving domain, the acoustic perturbation equations for low Mach, etc. denotes theacoustic source term which depends on the incompressible velocity and pressure.


FLINOVIA II

FEM is used to discretize the spatial weak formulations of problems 1 to 3 and a secondorder back difference (BDF2) is used for the time discretization. For each time step of thesimulation, the final scheme consists in (notation ):

11



1. Solve the discrete weak formulation of the Navier‐Stokes equations:

Galerkin terms

2. Solve the discrete weak formulation of Lighthill’s equation for the incidentacoustic pressure in free field

3. Solve the discrete weak formulation of the wave equation forthe diffracted field

With this procedure we obtain the quadrupolar (flow) and dipolar (body)contributions to the total aerodynamic sound at the end of a single computationalrun.

Subgrid scale stabilizationterms (they can account forturbulence)

Guasch et al. Comput. & Fluids. 2016, Codina et al. Comput. Meth. Appl. Mech. Eng.2007, Guasch and Codina , Comput. Meth. Appl. Mech. Eng. 2013


FLINOVIA II

12

AEOLIAN TONE IN 2D

NUMERICAL EXAMPLES

Total acoustic pressure

Diffracted pressure (dipolar contribution)

Incident pressure (quadrupolar contribution)


FLINOVIA II

13

PRODUCTION OF SIBILANT /S/

NUMERICAL EXAMPLES

Computational domain

• # elements: 46 million elements• Mesh size: from 0.025mm to 2.5 mm• Maximum captured wavelength: 30mm (12

kHz)• Computational resources: 256 processors (30

hours) BSC: Barcelona Supercomputing Centre

Arnau et al. J. Acoust. Soc. Am . 2017 (Submitted)


FLINOVIA II

14


NUMERICAL EXAMPLES

CFD results

Flow jet Lighthill’s acoustic term


FLINOVIA II

15


NUMERICAL EXAMPLES

Acoustic results

Radiated front waves


FLINOVIA II

16

NUMERICAL EXAMPLES

Acoustic spectra at a point non‐influenced by the mouth outflow


Direct and diffracted contributions Validation with measured data from literature


FLINOVIA II

17

NUMERICAL EXAMPLES

Evolving 2D and 3F geometries

TEETH‐SHAPED MOVING DOMAIN


FLINOVIA II

18

NUMERICAL EXAMPLES

To get the acoustic field we now need to solve the waveequation in mixed form in an ALE framework


Incident pressure field (quadrupolar contribution)

Diffracted pressure field (dipolar contribution)


FLINOVIA II

19

NUMERICAL EXAMPLES

CFD results



FLINOVIA II

20

NUMERICAL EXAMPLES

Acoustic results



FLINOVIA II

21

NUMERICAL EXAMPLES


Input glottal pulses

Output acoustic pressure

+

-0

From diphthongs to syllables

Guasch et al. Acta Acust. United Ac.. 2016


FLINOVIA II

A methodology has been presented to carry out low Mach number CAAcomputations that allow one to obtain, in a single finite elementcomputational run,– The incompressible velocity and incompressible pressure fields– The total acoustic pressure field– The individual contributions of the incident (quadrupolar) acoustic

pressure and the diffracted (dipolar) pressure field

The performance of the methodology has been tested by means of abenchmark 2D case consisting of aeolian tones and applied to find thesound sources in the production of sibilant /s/.

Preliminary results have also been presented to extend the method todomains with moving boundaries with the aim to generate syllablesounds in the future.

22

CONCLUSIONSCONCLUSIONS


FLINOVIA II

THANK YOU FOR YOUR ATTENTION

23

THIS IS THE END

CONCLUSIONS

Documents

SIMULTANEOUS FINITE ELEMENT COMPUTATION OF DIRECT … · Guasch et al. Acta Acust. United Ac.. 2016. SIMULTANEOUS FEM COMPUTATION DIRECT AND DIFFRACTED FLOW NOISE FLINOVIA II A methodology