Numerical Investigation of Reynolds number effect on Lock-in

Ability of an Aeroacoustic Field in Ducted

Flows

Dept. of Mechanical and Manufacturing EngineeringTrinity College Dublin

Cristina Paduano Dr.Craig Meskell

Aeroacoustic Resonance Overview Noise intensification It can occur when a Gas Flow in a duct/cavity exhibits Periodic Vortices

Vortex shedding Duct acoustic mode

HYDRODYNAMIC

Vortex shedding at acoustic frequency

=

Tonal noise is emitted

Vo

rte

x sh

ed

din

g f

req

ue

ncy

LOCK-IN

Flow velocity

flow

𝒇 𝒂𝒅𝒖𝒄𝒕

Off resonance

Off resonance

NOISE SELF-SUSTAINS and

ENHANCES

Physics behind the phenomenonAeroacoustic resonance

Flow induces an Acoustic field

Flow-Acoustics exchange energy

Howe’s reformulation of Lightill’s analogy

Vorticity as a source of sound

Homogeneous Wave Equation Source of Sound

1𝑐2

𝜕2𝑝 ′

𝜕𝑡 2 −𝛻2𝑝 ′=𝜌𝛻 ∙ (�⃗�×𝑉 )

Vortices need to deform(interact-impact body)

Unbalanced Sound: flow compresses and

decompresses

Physics behind the phenomenonAeroacoustic resonance

Flow induces an Acoustic field

Flow-Acoustics exchange energy

Vorticity

Acoustic particles velocity

Velocity

Howe’s Integral Acoustic power, localisation of sources

Not organized vortices Organized

vortices

Flow induces an Acoustic field

Flow-Acoustics exchange energy

Vo

rte

x sh

ed

din

g f

req

ue

ncy

LOCK- IN

Flow velocity

Not organized vortices

Aeroacoustic resonance

Motivation

HOW THE ACOUSTIC FIELD

INITIATES RESONANCE ?

Low pressure vortices

Low energy induced acoustics

Acoustic pressures << flow pressures

Aeroacoustic Resonance behavior

10 15 20 25 300

100

200

300

400

500

V (m/s)

Freq

uenc

y (H

z)

10 15 20 25 300

500

1000

1500

2000

V (m/s)

Pa (

Pa)

PROBLEM OF NOISE ,VIBRATIONS (FATIGUE FAILURE)

UPPER LIMIT TO THE PRACTICABLE FLOW VELOCITIES ACROSS A SYSTEM

(REDUCED EFFICIENCY)

Pressure measurements (heat exchanger)

UNPREDICTABLE VELOCITYEXTENTS OF LOCK IN RANGE UNKNOWN

NO TOOLS AVAILABLE TO DESIGN AGAINST

AEROACOUSTIC RESONANCE

Velocity measurements (heat exchanger)

140 dB

An industrial design concern Heat exchangers Corrugated pipes Heat Ventilation Air Conditioning systems (HVAC) Aircrafts Environmental Control Systems (ECS) Aircrafts cavities

flow

Sound wavepropagation

Sound wavepropagation

Our research: Two cylinders in cross flow

Test cases for resonanceCylinders in cross flow : good model for aeroacoustic resonance of ducted flows

Flow separationFlow instabilitiesVortex shedding (well known)

• Minimal 3D effects if cylinder is long (Length > >Diameter)

TYPICAL OF NOISE

GENERATING FLOWS

flow

Cylinders Pitch L/D

D

L

Conditions for resonance

(Hall, Ziada, Weaver data -2003)

Lock-in map (EXPERIMENTAL DATA)CO

ND

ITIO

NS

for R

ESO

NAN

CE

Amplitude of the acoustic wave

Frequency of vortex shedding approaches natural

frequency of duct/cavity

OUR RESEARCH:REYNOLDS NUMBER

HAS AN EFFECT ON LOCK-IN!

CFD simulation of resonance

ACOUSTICS IS

“ COMPRESSIBLE”

INCOMPRESSIBLEFLOW

(uRANS, SST) += OSCILLATING VELOCITY (BOUNDARY CONDITION)

Hydrodynamic Analogy (Tan ,Thompson, Hourigan-2003)

TRASVERSAL ACOUSTIC WAVE replaced by the Flow OSCILLATION which it causesRESONANCE: fa chosen to be in LOCK-IN ratio with fv

Uacs=Asin(2fat)

Hydrodynamic analogy response: Lock-in maps

EXPERIMENTAL LOCK-IN MAP

(Mohany and Ziada data-2009)-Single cylinder

(Reyes,Finnegan, Meskell data -2010)-Two cylinders L/D=2.5

(Hall, Ziada, Weaver data -2003)

NUMERICAL LOCK-IN MAP

Simulations parameters

𝑓 𝑎𝑓 𝑣

=𝟎 .𝟖𝟓𝑓 𝑎𝑓 𝑣

=𝟏 .𝟐

12 flow velocities(from 12m/s to 40m/s)

Reynolds n.10000-36000

Vo

rte

x sh

ed

din

g f

req

ue

ncy

Flow velocity

1

Flows excitation:Uacs=Asin(2fat)

fa=1.2 fv

fa=0.85 fv

Pre-coinc. resonance

Coinc. resonance

fv

A=10% Vinlet

Vortex shedding frequencies

Oscillating Lift (verse changes at each shed )

FFT of oscillating of the downstream cylinder

Each simulation has shown a clear vortex shedding (example v=12 m/s )

Strouhal simulated against experimental

CONSIDERATIONS:

Simulated Strouhal higher (20%)

Model is 2D

No boundaries

Experiments in wind tunnel (side walls effects)

STROUHAL n. of 0.18 similar to experimental one (Finnegan, Ziada,Meskell-2010)

Normalized frequencies, f/fv Reynolds numbers

Pre

ssu

re,

Pasc

als

Excitation frequency 2

Acoustics has LOCKED the frequency of vortex shedding JUST for simulations run at Reynolds above 27000

Vortex shedding

frequencies

Results pre-coincidence 2 Acoustic

frequencies

Results coincidence

Normalized frequencies, f/fv Reynolds numbers

Pre

ssu

re,

Pasc

als

Acousticfrequencies Vortex

shedding frequencies

Excitation frequency 85

Acoustics has LOCKED the frequency of vortex shedding JUST for simulations run at Reynolds above 27000

Reynolds number Normalized frequency f/fv

Normalized frequency f/fvReynolds number

Pre

ssure

, Pa

scals

Pre

ssure

, Pa

scals

PreCoincidence /=1.2

Reynolds number dependency of Lock-in

Coincidence /=0.85

Lock-in map at Reynolds 27000

EXPERIMENTAL LOCK-IN MAP

Lock-in map of tandem cylinders obtained numerically well compare with the experimental one(L/D=2.5)

(Hall, Ziada, Weaver data -2003)

NUMERICAL LOCK-IN MAP

LOCK-IN and Velocity contours

% V inlet

Normalized velocity WITHOUT EXCITATION

% V inlet

Normalized velocity case NOT LOCKED IN (Re=10000)

Normalized velocitycase LOCKED IN (Re=36000)

Normalized velocity WITHOUT EXCITATION

% V inlet% V inlet

ConclusionsHOW THE ACOUSTIC FIELD INITIATES RESONANCE ?

Condition for resonance : Frequency ratioAmplitude

• Lock-in only occurred at the higher Reynolds n.(above 27000) for both pre-coincidence and coincidence situations

• Vorticity appears to be reduced in the 2D model at lock-in

Higher Reynolds n. (turbulence higher, flow stronger) flow more prone to be controlled by acoustics ?

Could Turbulence be a source of energy for the Acoustic field?

Lock-in

Pre

ssure

, Pa

scals

Reynolds number Normalized frequency f/fv