Fluid: Acoustic velocity plots with arrows

This example shows how to plot the acoustic velocity and also add arrows within In this example we illustrate how we can use arrow plots to illustrate both magnitude and direction of the acoustic particle velocity.

In this example we study a glass sphere in a viscous fluid.

from matplotlib import pyplot as plt

import osaft

# --------
# Geometry
# --------
# Radius
R_0 = 50e-6  # [m]

# -------------------
# Properties of Glass
# -------------------
# Speed of sound
c_1_glass = 4_521  # [m/s]
c_2_glass = 2_226  # [m/s]
# Density
rho_glass = 2_240  # [kg/m^3]

# ---------------------------
# Properties of Viscous Fluid
# ---------------------------
# Speed of sound
c_oil = 1_400  # [m/s]
# Density
rho_oil = 900  # [kg/m^3]
# Viscosity
eta_oil = 0.04  # [Pa s]
zeta_oil = 0  # [Pa s]

# --------------------------------
# Properties of the Acoustic Field
# --------------------------------
# Frequency
f = 10e5  # [Hz]
# Pressure
p_0 = 1e5  # [Pa]
# Wave type
wave_type = osaft.WaveType.STANDING
# Position of the particle in the field
position = osaft.pi / 4  # [rad]

Here, we are given the primary and the secondary wave speed of glass only. The model doinikov2021viscous, however, takes the Young’s modulus and the Poisson’s ratio as input parameters. We therefore have to convert the properties. The ElasticSolid class offers such conversion methods.

E_s = osaft.ElasticSolid.E_from_wave_speed(c_1_glass, c_2_glass, rho_glass)
nu_s = osaft.ElasticSolid.nu_from_wave_speed(c_1_glass, c_2_glass)

sol = osaft.doinikov2021viscous.ScatteringField(
    f=f,
    R_0=R_0,
    rho_s=rho_glass,
    E_s=E_s,
    nu_s=nu_s,
    rho_f=rho_oil,
    c_f=c_oil,
    eta_f=eta_oil,
    zeta_f=zeta_oil,
    p_0=p_0,
    wave_type=wave_type,
    position=position,
)

The next step is to initialise the plotter for the fluid. The option n_quiver_points let’s use decide how many arrows along the z-direction and x-direction shall be plotted. If you chose the plotting option symmetric=False then the arrows along the x-direction will be halved. It is set in the constructor of the plotter, because the solution for the quiver arrows is stored within the class and it depends on the number of points. A change of this parameter will invoke new computation of the quiver directions. Per default it is set to n_quiver_points=21. It is advisable to use an odd number if you like to change the parameter because this ensures that have a point at z=0, x=0.

plotter = osaft.FluidScatteringPlot(sol, r_max=3 * sol.R_0, cmap="Oranges")

Let’s start by simply plotting the acoustic velocity for phase=0. In order to also show the arrows within the plot we need to add the option quiver_color='____'. Per default quiver_color = None such that no arrows will be overlayed.

fig, ax = plotter.plot_velocity(quiver_color="black", symmetric=False)
ax.set_title("Acoustic Velocity Magnitude + Quiver")
fig.tight_layout()
plt.show()

We can also have a look at first four modes and look how the velocity behaves for each of them individually. We start by creating a plt.subplots(...) with two rows and two columns.

fig, Axes = plt.subplots(2, 2, figsize=(12, 10))

# Now we loop over each of the ``plt.Axes`` within the ``Axes`` array and
# depict a different mode.

for i, ax in enumerate(Axes.flatten()):
    plotter.plot_velocity(mode=i, ax=ax, quiver_color="black")
    ax.set_title(f"Mode #{i}")

fig.tight_layout()
plt.show()

The quiver_color=... option is also available for the plotter.plot_velocity_evolution(quiver_color=...). Let’s check first if the incident acoustic field is depicted right. Therefore, we set incident=True and scattered=False.

plotter.plot_velocity_evolution(
    quiver_color="black",
    mode=None,
    incident=True,
    scattered=False,
    symmetric=False,
    layout=(3, 3),
    figsize=(12, 12),
)
plt.show()

And also for plotter.animate_velocity(quiver_color=...).

anim = plotter.animate_velocity(
    frames=100,
    interval=50,
    quiver=True,
    quiver_color="black",
    mode=None,
    incident=False,
    scattered=True,
)
plt.show()

Once Loop Reflect

Estimated memory usage: 9 MB