Hi Brad, hi community,
I'm simulating the thermo-acoustic field of an annular transducer, in a heterogeneous medium (a water tank and a small piece of fat in the focal region, in order to evaluate the thermal lesion). The source pressure is 175 kPa, the frequency is 1.5 MHz. The problem is that I obtain an extremely high (wrong) field of temperature, up to 1000 °C with a heating period of 5 s. I obtain a max intensity of 4691.1406 W/cm^2 and a max heat volume rate Q of 1212.9214 W/cm^3. Thus, maybe Q is excessive but I cannot explain why. This is the formula that I have considered:
alpha_np = db2neper(medium.alpha_coeff, medium.alpha_power) .* (2 * pi * freq).^medium.alpha_power;
Q = alpha_np .* amp.^2 ./ (medium.density .* medium.sound_speed);
Briefly, these are some parameters that I'm considering:
% water medium parameters
c0 = 1500; % sound speed [m/s]
rho0 = 1000; % density [kg/m^3]
BonA = 5.2; % non linear parameter of the medium (B over A)
alpha_0 = 0; % frequency-dependent absorption coefficient
alpha_y = 2; % power-law exponent of water
% tissue medium parameters (fat tissue)
c0_t = 1450; % sound speed of tissue [m/s]
rho0_t = 911; % density of tissue [kg/m^3]
BonA_t = 10; % non linear parameter of tissue (B over A)
alpha_0_t = 0.6; % frequency-dependent absorption coefficient of tissue [dB/cm*MHz]
alpha_y_t = 1.0861; % power-law exponent of tissue
axial_size = 100e-3; % total grid size in the axial dimension [m]
lateral_size = 120e-3; % total grid size in the lateral dimension [m]
x_tissue = 30e-3; % tissue dimension along x coordinate [m]
y_tissue = 120e-3; % tissue dimension along y coordinate [m]
z_tissue = 120e-3; % tissue dimension along z coordinate [m]
distance_t = 70e-3; % tissue distance from the transducer external surface [m]
% thermal parameters
T0 = 20; % water initial temperature [°C]
thermal_conductivity = 0.6045; % water thermal conductivity [W/(m.K)]
specific_heat = 4178; % water specific heat [J/(kg.K)]
T0_t = 20; % tissue initial temperature [°C]
thermal_conductivity_t = 0.211; % tissue thermal conductivity [W/(m.K)]
specific_heat_t = 2348.33; % tissue specific heat [J/(kg.K)]
on_time = 5; % source on time [s]
off_time = 20; % source off time [s]
dt_thermal = 0.1; % time step size of thermal simulation
I thank you in advance for your attention!