 Software

ChamAllard1991.m

Matlab code to calculate the normalised complex impedance and wavenumber for sound propagation in a porous material using the model proposed by the Champoux and Allard in their J. Appl. Phys. paper in 1991 [Journal of Applied Physics 70, 1975 (1991)]. Also calculates the following parameters for a hard-backed layer of thickness d: surface impedance (Zs), reflection coefficient (rfl), absorption coefficient (alpha), dynamic density (Rp) and complex compressibility (Cp).

Input parameters:
freq = array of frequency points [Hz];
sigma = viscous flow resistivity [Pa s /m2];
sigmaprime = thermal flow resistivity [Pa s /m2]
om = open porosity [-]
q = tortuosity (sqrt(alpha_inf)) [-]
Lam, = viscous length [m]
Lamprime = thermal characteristic lengths [m]
d = layer thickness [m]

% function Zs, impd, wnmb, rfl, alpha, Rp, Cp] = ChamAllard1991(freq, sigma, sigmaprime, om, q, Lam, Lamprime, d)
% Used to calculate the normalised impedance and the wavenumber
% for propagation inside a porous material by the Champoux and Allard
% model as described in JAP 1991 paper.
% On Entry:
% freq = frequency points;
% sigma = viscous flow resistivity [N s /m4];
% sigmaprime = thermal flow resistivity [N s /m4]
% om = porosity
% q = tortuosity (sqrt(alpha_inf))
% Lam, Lamd = characteristic lengths, m
% d - layer thickness [m].

% Define the key parameters:
%%%%%
%%%%% Room conditions
%%%%%
T = 20; % Temperature in Celsius degrees
P0 = 101320; % [N.m-2] atmospheric pressure

% Compute air parameters related to room conditions
% (acknowledgment goes to Dominic Pilon,
% dominic.pilon@metafoam.com, for gathering almost all these
% expression from the references below)
%
% References:
% Lide, D. R. and Kehiaian H. V.,
% CRC. Handbook of Thermophysical and Thermochemical Data,
% CRC. Press Inc, 1994
%
% Touloukian, Y. S. and Makita, T.,
% Specific Heat - Non metallic Liquids and gases,
% The TPRC Data Series, Volume 6, IFI/PLENUM, 1970
%
% Pierce, A. D.,
% Acoustics, An Introduction to Its Physical Principles and Applications
% Acoustical Society of America, 2nd edition, 1989

% Convert temperature from Celsius to Kelvin
T = 273.16+T;

% Universal gas constant (J.K-1.kg-1) [also 8.314 J.mol-1.K-1]
R = 287.031;

% Specific heat at constant pressure (J.kg-1.K-1; 260 K < T < 600 K
Cp = 4168.8*(0.249679-7.55179e-5*T+1.69194e-7*T^2-6.46128e-11*T^3);

% Specific heat at constant volume (J.kg-1.K-1; 260 K < T < 600 K
Cv = Cp-R;

% Dynamic viscosity (N.s.m-2; 100 K < T < 600 K
eta = 7.72488e-8*T-5.95238e-11*T^2+2.71368e-14*T^3;

% Ratio of specific heats
gam = Cp/Cv;

% Density of air (kg.m-3)
rho0 = P0/(R*T);

% Velocity of sound (m.s^-1)
c0 = sqrt(gam*R*T);

% Thermal conductivity (W.m-1.K-1) - cf A. D. Pierce p 513
kappa = 2.624e-02 * ( (T/300)^(3/2) * (300+245.4*exp(-27.6/300))/(T+245.4*exp(-27.6/T)) );

% Prandtl's number
Npr = eta*Cp/kappa;

omega = 2*pi*freq;
q2 = q^2;

ko = eta/sigma;
a = sqrt(8*q2*eta/sigma/om);
F = q2/om;
%Lam = sqrt(4*F*ko);
%Lamd = om*b/(3*(1-om));
%Rd = 8*q2*eta/Lamd^2;

% Complex tortuosity:
alp = q2 - i*sigma*om/rho0./omega.*sqrt(1 + 4*i*q2^2*eta*rho0*omega/(sigma*Lam*om)^2);
Rp = alp*rho0/om;
%Cp = om*(gam - (gam-1)./(1-(i*sigmaprime*om./(rho0*q2*Npr*omega).*...
% sqrt(1+4*i*q2^2*eta*rho0*Npr*omega/(sigmaprime*Lamprime*om)^2))));
Cp = om*(gam - (gam-1)./(1-(i*sigmaprime*om./(rho0*Npr*omega).*...
sqrt(1+4*i*eta*rho0*Npr*omega/(sigmaprime*Lamprime*om)^2))))/gam/P0;