Effect of grazing flow on the acousdcal behaviour of a porous ...

Experimental setup 50 mm 200 mm 15 mm Flow pr<strong>of</strong>ile 100 mm Fully developed turbulent pr<strong>of</strong>ile Acoustics 2012, Nantes, 26 april 2012 <strong>Effect</strong> <strong>of</strong> <strong>flow</strong> on a porous material in a duct, Y. Renou and Y. Aurégan 0 20 40 60 80 U(m/s) 5

Experimental setup 2 configura4ons for measurement: Downstream source Acous4cal wave in <strong>flow</strong> direc4on M=0.2 Acous9c Upstream source Acous4cal wave against the <strong>flow</strong> M=0.2 AcousticAcoustics 2012, Nantes, 26 april 2012 <strong>Effect</strong> <strong>of</strong> <strong>flow</strong> on a porous material in a duct, Y. Renou and Y. Aurégan 6

Numerical method: finite difference method yP N−1 − P Nh 2 + k 2 myP N =0N pointsM pointshP i+1 + P i−1 − 2P ih 2 + k 2 myP i =03P M − 4P M−1 + P M−2=2hA −3P M +4P M+1 − P M−22hP i+1 + P i−1 − 2P ih 2 + k 2 ayP i =0P 2 − P 1h 2 + k 2 ayP 1 =0Acoustics 2012, Nantes, 26 april 2012 <strong>Effect</strong> <strong>of</strong> <strong>flow</strong> on a porous material in a duct, Y. Renou and Y. Aurégan 11

Finite difference method Con4nuity <strong>of</strong> p∂p∂x = qCon4nuity <strong>of</strong> qVanishing <strong>of</strong> qAcoustics 2012, Nantes, 26 april 2012 <strong>Effect</strong> <strong>of</strong> <strong>flow</strong> on a porous material in a duct, Y. Renou and Y. Aurégan 12

Finite difference method vs Experiments p +Rp + Tp +Porous Transmission coefficient Finite difference method Experiments Acoustics 2012, Nantes, 26 april 2012 <strong>Effect</strong> <strong>of</strong> <strong>flow</strong> on a porous material in a duct, Y. Renou and Y. Aurégan 13

Experimental results without <strong>flow</strong> p(x, ω) p(0, ω) Acous4cal wave Porous material Acoustics 2012, Nantes, 26 april 2012 <strong>Effect</strong> <strong>of</strong> <strong>flow</strong> on a porous material in a duct, Y. Renou and Y. Aurégan 14

Results without <strong>flow</strong> p(x, ω)p(0, ω)Experimental determina4on <strong>of</strong> an equivalent wave number k xAcoustics 2012, Nantes, 26 april 2012 <strong>Effect</strong> <strong>of</strong> <strong>flow</strong> on a porous material in a duct, Y. Renou and Y. Aurégan 15

Results without <strong>flow</strong> Real(k x )Propaga4on Experimental determina4on <strong>of</strong> an equivalent wave number k xImag(k x )Ajenua4on Phase velocity Acoustics 2012, Nantes, 26 april 2012 <strong>Effect</strong> <strong>of</strong> <strong>flow</strong> on a porous material in a duct, Y. Renou and Y. Aurégan 16

Calcula4ons without <strong>flow</strong> Imag(k x /k 0 )f Real(k x /k 0 )f = 2000 HzAcoustics 2012, Nantes, 26 april 2012 <strong>Effect</strong> <strong>of</strong> <strong>flow</strong> on a porous material in a duct, Y. Renou and Y. Aurégan 17

With <strong>flow</strong> M=0.2 Imag(k x /k 0 )Con4nuity <strong>of</strong> displacement β v =0Real(k x /k 0 )Imag(k x /k 0 )Con4nuity <strong>of</strong> velocity β v =1Real(k x /k 0 )Acoustics 2012, Nantes, 26 april 2012 <strong>Effect</strong> <strong>of</strong> <strong>flow</strong> on a porous material in a duct, Y. Renou and Y. Aurégan 18

With <strong>flow</strong> M=0.2 Real(k x )(1/m)Experiments with <strong>flow</strong> Acous4cal wave against the <strong>flow</strong> β v =1 Without <strong>flow</strong> Myers: β v =0 Experiments with <strong>flow</strong> Acous4cal wave in <strong>flow</strong> direc4on Real(k x )(1/m)β v =1 Without <strong>flow</strong> Myers: β v =0 Acoustics 2012, Nantes, 26 april 2012 <strong>Effect</strong> <strong>of</strong> <strong>flow</strong> on a porous material in a duct, Y. Renou and Y. Aurégan 19

With <strong>flow</strong> M=0.2 Imag(k x )(1/m)Experiments with <strong>flow</strong> Acous4cal wave against the <strong>flow</strong> Without <strong>flow</strong> β v =1 Myers: β v =0 Real(k x /k 0 )Imag(k x )(1/m)Experiments with <strong>flow</strong> Acous4cal wave in <strong>flow</strong> direc4on Without <strong>flow</strong> β v =1 Myers: β v =0 Real(k x /k 0 )Acoustics 2012, Nantes, 26 april 2012 <strong>Effect</strong> <strong>of</strong> <strong>flow</strong> on a porous material in a duct, Y. Renou and Y. Aurégan 20

With <strong>flow</strong> M=0.2 Experiments with <strong>flow</strong> Acous4cal wave against the <strong>flow</strong> β v =1 Myers: β v =0 Without <strong>flow</strong> Acoustics 2012, Nantes, 26 april 2012 <strong>Effect</strong> <strong>of</strong> <strong>flow</strong> on a porous material in a duct, Y. Renou and Y. Aurégan 21

With <strong>flow</strong> M=0.2 Experiments with <strong>flow</strong> Acous4cal wave in <strong>flow</strong> direc4on Myers: β v =0 β v =1 Without <strong>flow</strong> Acoustics 2012, Nantes, 26 april 2012 <strong>Effect</strong> <strong>of</strong> <strong>flow</strong> on a porous material in a duct, Y. Renou and Y. Aurégan 22

With <strong>flow</strong> M=0.2 Hydrodynamical modes ? Acoustics 2012, Nantes, 26 april 2012 <strong>Effect</strong> <strong>of</strong> <strong>flow</strong> on a porous material in a duct, Y. Renou and Y. Aurégan 23

With <strong>flow</strong> M=0.2 ωU 0x = nπAcoustics 2012, Nantes, 26 april 2012 <strong>Effect</strong> <strong>of</strong> <strong>flow</strong> on a porous material in a duct, Y. Renou and Y. Aurégan 24

Conclusions and perspec4ves on the effects <strong>of</strong> <strong>flow</strong> on porous • New experiments are needed on rigid frame materials (metallic foam) • The stability problem over porous material need to be inves4gated. • For research purposes, the boundary layer effects had to be taken into account by a shear <strong>flow</strong> and not via a Ingard-­‐Myers condi4on (even a modified condi4on) Acoustics 2012, Nantes, 26 april 2012 <strong>Effect</strong> <strong>of</strong> <strong>flow</strong> on a porous material in a duct, Y. Renou and Y. Aurégan 25