ARF#

Examples using this class are:

Doinikov Rigid (1994): Sandstone in Glycerin

class osaft.solutions.king1934.arf.ARF(f, R_0, rho_s, rho_f, c_f, p_0, wave_type, position=None, N_max=5, small_particle_limit=False)[source]#

Bases: ScatteringField, BaseARF

ARF class for King (1934)

Parameters:

f (Frequency | float | int) – Frequency [Hz]
R_0 (Sphere | float | int) – Radius of the sphere [m]
rho_s (float) – Density of the fluid-like sphere [kg/m^3]
rho_f (float) – Density of the fluid [kg/m^3]
c_f (float) – Speed of sound of the fluid [m/s]
p_0 (float) – Pressure amplitude of the field [Pa]
wave_type (WaveType) – Type of incident wave (traveling/standing)
position (None | float, optional) – Position in the standing wave field [rad]
Default: None
N_max (int, optional) – Highest order mode
Default: 5
small_particle_limit (bool, optional) – compute ARF based on small particle limit
Default: False

Public Data Attributes:

`f_2`	Dipole scatting coefficient \(f_2\) [-]
`Phi`	Acoustic contrast factor \(\Phi\) [-]
`small_particle_limit`	ARF for the small particle limit

Inherited from BaseKing

`supported_wavetypes`
`alpha`	Wave number times radius of the particle (\(kR\)) [-]
`rho_tilde`	Density ratio `rho_s`/ `rho_f` [-]
`position`	Wraps to `osaft.core.backgroundfields.BackgroundField.position`
`p_0`	Wraps to `osaft.core.backgroundfields.BackgroundField.p_0`
`wave_type`	Wraps to `osaft.core.backgroundfields.BackgroundField.wave_type`
`rho_s`	Wraps to `osaft.core.solids.RigidSolid.rho_s`
`rho_f`	Wraps to `osaft.core.fluids.InviscidFluid.rho_f`
`c_f`	Wraps to `osaft.core.fluids.InviscidFluid.c_f`
`kappa_f`	Wraps to `osaft.core.fluids.InviscidFluid.kappa_f`
`k_f`	Wraps to `osaft.core.fluids.InviscidFluid.k_f`

Inherited from BaseSphereFrequencyComposite

`R_0`	Wrapper for `osaft.core.geometries.Sphere.R_0`
`area`	Wrapper for `osaft.core.geometries.Sphere.area`
`volume`	Wrapper for `osaft.core.geometries.Sphere.volume`

Inherited from BaseFrequencyComposite

`f`	wrapper for `osaft.core.frequency.Frequency.f`
`omega`	wrapper for `osaft.core.frequency.Frequency.omega`

Inherited from BaseSolution

`supported_wavetypes`
`wave_type`	returns the wave type of the solution

Inherited from BaseScatteringRigidParticle

R_0

Inherited from BaseScattering

`N_max`	Cutoff mode number for infinite sums
`field`
`omega`
`R_0`
`rho_f`
`k_f`

Public Methods:

`compute_arf`()	Acoustic radiation fore in [N]
`FFGG`(n)	Returns the coefficient \(F_{n+1}F_{n}+G_{n+1}G_{n}\) for n.
`FGFG`(n)	Returns the coefficient \(F_{n+1}G_{n}-G_{n+1}F_{n}\) for n.
`HH`(n)	Returns the coefficient \(H_{n}^2(n)H_{n}^2(n+1)\) for n of (56) and (57).

Inherited from ScatteringField

`particle_velocity`(t)	Particle velocity
`potential_coefficient`(n)	Wrapper to the fluid scattering coefficients for an inviscid fluid
`phi_n`(n, arg)	From King equation (22)
`psi_n`(n, arg)	From King equation (22)
`F_n`(n, arg)	From King equation (30) and (31)
`G_n`(n, arg)	From King equation (30) and (31)
`A_dash_n`(n)	From King equation (21), (28) potential from 28 to form of 21
`Phi_scattering`(r, theta, t)	King equation (28) for scattering potential \(\Phi_{\mathrm{scattering}}\)
`Phi_incident`(r, theta, t)	King equation (28) for scattering potential \(\Phi_{\mathrm{incident}}\)
`V_r_sc`(n, r)	Implements `osaft.solutions.base_scattering.BaseScattering.V_r_sc()`
`V_theta_sc`(n, r)	Implements `osaft.solutions.base_scattering.BaseScattering.V_theta_sc()`

Inherited from BaseKing

A_in(n)

Wraps to osaft.core.backgroundfields.BackgroundField.A_in

Inherited from BaseFrequencyComposite

input_variables()

Returns all properties that are settable.

Inherited from BaseSolution

`copy`()	Returns a copy of the object
`check_wave_type`()	Checks if `wave_type` is in `supported_wavetypes`

Inherited from BaseScatteringRigidParticle

`particle_velocity`(t)	Particle velocity
`radial_particle_velocity`(r, theta, t[, mode])	Particle velocity in radial direction
`tangential_particle_velocity`(r, theta, t[, mode])	Particle velocity in tangential direction

Inherited from BaseScattering

`radial_acoustic_fluid_velocity`(r, theta, t, ...)	Returns the value for the radial acoustic velocity in [m/s].
`tangential_acoustic_fluid_velocity`(r, theta, ...)	Returns the value for the tangential acoustic velocity in [m/s].
`pressure`(r, theta, t, scattered, incident[, ...])	Returns the acoustic pressure [Pa].
`potential_coefficient`(n)	Wrapper to the fluid scattering coefficients for an inviscid fluid
`velocity_potential`(r, theta, t, scattered, ...)	Returns the velocity potential of the fluid in [m^2/s].
`radial_particle_velocity`(r, theta, t[, mode])	Returns the value for the radial particle velocity in [m/s].
`tangential_particle_velocity`(r, theta, t[, mode])	Returns the value for the tangential particle velocity in [m/s].
`radial_particle_displacement`(r, theta, t[, mode])	Particle displacement in radial direction
`tangential_particle_displacement`(r, theta, t)	Particle displacement in tangential direction
`radial_mode_superposition`(radial_func, r, ...)	Returns either a single mode (`mode=int`) or a the sum until `N_max` (`mode=None`).
`tangential_mode_superposition`(...)	Returns either a single mode (`mode=int`) or a the sum until `N_max` (`mode=None`).
`V_r_i`(n, r)	Radial incident field velocity term of mode n without Legendre coefficients
`V_theta_i`(n, r)	Tangential incident field velocity term of mode n without Legendre coefficients
`V_r_sc`(n, r)	Radial scattering field velocity term of mode n without Legendre coefficients
`V_theta_sc`(n, r)	Tangential scattering field velocity term of mode n without Legendre coefficients
`V_r`(n, r, scattered, incident)	Superposition of `V_r_sc()` and `V_r_i()` depending on `scattered` and `incident`
`V_theta`(n, r, scattered, incident)	Superposition of `V_theta_sc()` and `V_theta_i()` depending on `scattered` and `incident`

Inherited from BaseARF

compute_arf()

Returns the value for the ARF in Newton [N].

A_dash_n(n)#

From King equation (21), (28) potential from 28 to form of 21

Returns Scattering field coefficient \(A^{\prime}_{n}\)

Parameters:: n (int) – mode number
Return type:: complex

A_in(n)#

Wraps to osaft.core.backgroundfields.BackgroundField.A_in

Parameters:: n (int) –
Return type:: complex

FFGG(n)[source]#

Returns the coefficient \(F_{n+1}F_{n}+G_{n+1}G_{n}\) for n.

Parameters:: n (int) – order
Return type:: complex

FGFG(n)[source]#

Returns the coefficient \(F_{n+1}G_{n}-G_{n+1}F_{n}\) for n.

Parameters:: n (int) – order
Return type:: complex

F_n(n, arg)#

From King equation (30) and (31)

Returns \(F_n\)

Parameters:

n (int) – mode
arg (float) – argument for spherical Bessel function

Return type:

float

G_n(n, arg)#

From King equation (30) and (31)

Returns \(G_n\)

Parameters:

n (int) – mode
arg (float) – argument for spherical Bessel function

Return type:

complex

HH(n)[source]#

Returns the coefficient \(H_{n}^2(n)H_{n}^2(n+1)\) for n of (56) and (57).

Parameters:: n (int) – order
Return type:: float

Phi_incident(r, theta, t)#

King equation (28) for scattering potential \(\Phi_{\mathrm{incident}}\)

Parameters:

r (float | NDArray | list[float]) – radial coordinate [m]
theta (float | NDArray | list[float]) – tangential coordinate [rad]
t (float | NDArray | list[float]) – time [s]

Return type:

complex

Phi_scattering(r, theta, t)#

King equation (28) for scattering potential \(\Phi_{\mathrm{scattering}}\)

Parameters:

r (float | NDArray | list[float]) – radial coordinate [m]
theta (float | NDArray | list[float]) – tangential coordinate [rad]
t (float | NDArray | list[float]) – time [s]

Return type:

complex

V_r(n, r, scattered, incident)#

Superposition of V_r_sc() and V_r_i() depending on scattered and incident

At least one of the two must be True.

Parameters:

n (int) – mode
r (float) – radial coordinate [m]
scattered (bool) – add scattered field
incident (bool) – add incident

Return type:

complex

V_r_i(n, r)#

Radial incident field velocity term of mode n without Legendre coefficients

Returns radial incident field velocity in [m/s]

Parameters:

n (int) – mode
r (float | Sequence) – radial coordinate [m]

Return type:

complex

V_r_sc(n, r)#

Implements osaft.solutions.base_scattering.BaseScattering.V_r_sc()

Parameters:

n (int) –
r (float | NDArray | list[float]) –

Return type:

complex

V_theta(n, r, scattered, incident)#

Superposition of V_theta_sc() and V_theta_i() depending on scattered and incident

At least one of the two must be True.

Parameters:

n (int) – mode
r (float) – radial coordinate [m]
scattered (bool) – add scattered field
incident (bool) – add incident

Return type:

complex

V_theta_i(n, r)#

Tangential incident field velocity term of mode n without Legendre coefficients

Returns tangential incident field velocity in [m/s]

Parameters:

n (int) – mode
r (float | Sequence) – radial coordinate [m]

Return type:

complex

V_theta_sc(n, r)#

Implements osaft.solutions.base_scattering.BaseScattering.V_theta_sc()

Parameters:

n (int) –
r (float | NDArray | list[float]) –

Return type:

complex

check_wave_type()#

Checks if wave_type is in supported_wavetypes

Raises:: WrongWaveTypeError – If wave_type is not supported
Return type:: None

compute_arf()[source]#

Acoustic radiation fore in [N]

Raises:

WrongWaveTypeError – if wrong wave_type
AssumptionWarning – if the used parameters might not be valid for the chosen limiting case

Return type:

float

copy()#

Returns a copy of the object

Return type:: BaseSolution

classmethod input_variables()#

Returns all properties that are settable.

Returns a list of the names of all properties that are settable, i.e. all properties that wrap a PassiveVariable.

Return type:: list[str]

particle_velocity(t)#

Particle velocity

Returns the value of the particle velocity in the direction of the axis of rotational symmetry of the radiation field in [m/s]

Parameters:: t (float) – time [s]
Return type:: float

static phi_n(n, arg)#

From King equation (22)

Returns \(\phi_n\)

Parameters:

n (int) – mode
arg (float) – argument for spherical Bessel function

Return type:

complex

potential_coefficient(n)#

Wrapper to the fluid scattering coefficients for an inviscid fluid

This method must be implemented by every theory to have a common interface for other modules.

Parameters:: n (int) – mode
Return type:: complex

pressure(r, theta, t, scattered, incident, mode=None)#

Returns the acoustic pressure [Pa].

Parameters:

r (float | Sequence) – radial coordinate [m]
theta (float | Sequence) – tangential coordinate [rad]
t (float | Sequence) – time [s]
scattered (bool) – add scattered field
incident (bool) – add incident
mode (None | int, optional) – specific mode number of interest; if None then all modes until N_max
Default: None

Return type:

complex

static psi_n(n, arg)#

From King equation (22)

Returns \(\psi_n\)

Parameters:

n (int) – mode
arg (float) – argument for spherical Bessel function

Return type:

complex

radial_acoustic_fluid_velocity(r, theta, t, scattered, incident, mode=None)#

Returns the value for the radial acoustic velocity in [m/s].

This method must be implemented by every theory to have a common interface for other modules.

Parameters:

r (float | Sequence) – radial coordinate [m]
theta (float | Sequence) – tangential coordinate [rad]
t (float | Sequence) – time [s]
scattered (bool) – scattered field contribution
incident (bool) – incident field contribution
mode (None | int, optional) – specific mode number of interest; if None then all modes until N_max
Default: None

Return type:

complex | NDArray

radial_mode_superposition(radial_func, r, theta, t, mode=None)#

Returns either a single mode (mode=int) or a the sum until N_max (mode=None).

If mode=int the formula is

\[e^{-i\omega t}\, f_{\text{mode}}(r) \,P_{\text{mode}}(\cos\theta)\]

If mode=None the formula is

\[e^{-i\omega t} \sum_{n=0}^{\text{N}_{\text{max}}} \,f_n(r) \,P_n(\cos\theta)\]

where \(f_\text{n}(r)\) is the radial_func(n, r) passed to the method.

Parameters:

radial_func (Callable[[int, float], complex]) – radial function dependent on r
r (float | Sequence) – radial coordinate [m]
theta (float | Sequence) – tangential coordinate [rad]
t (float | Sequence) – time [s]
mode (int, optional) – specific mode number of interest; if None then all modes until N_max
Default: None

Return type:

complex | NDArray

radial_particle_displacement(r, theta, t, mode=None)#

Particle displacement in radial direction

Returns the value of the particle displacement in radial direction in [m]

Parameters:

r (float | Sequence) – radial coordinate [m]
theta (float | Sequence) – tangential coordinate [rad]
t (float | Sequence) – time [s]
mode (None | int, optional) – specific mode number of interest; if None that all modes until N_max
Default: None

Return type:

complex | NDArray

radial_particle_velocity(r, theta, t, mode=None)#

Particle velocity in radial direction

Returns the value of the particle velocity in radial direction in [m/s]

Parameters:

r (float | Sequence) – radial coordinate [m]
theta (float | Sequence) – tangential coordinate [rad]
t (float | Sequence) – time [s]
mode (None | int, optional) – specific mode number of interest; if None that all modes until N_max
Default: None

Return type:

complex | NDArray

tangential_acoustic_fluid_velocity(r, theta, t, scattered, incident, mode=None)#

Returns the value for the tangential acoustic velocity in [m/s].

This method must be implemented by every theory to have a common interface for other modules.

Parameters:

r (float | Sequence) – radial coordinate [m]
theta (float | Sequence) – tangential coordinate [rad]
t (float | Sequence) – time [s]
scattered (bool) – scattered field contribution
incident (bool) – incident field contribution
mode (None | int, optional) – specific mode number of interest; if None then all modes until N_max
Default: None

Return type:

complex | NDArray

tangential_mode_superposition(tangential_func, r, theta, t, mode)#

Returns either a single mode (mode=int) or a the sum until N_max (mode=None).

If mode=int the formula is

\[e^{-i\omega t}\, f_\text{mode}(r) \,P^1_{\text{mode}}(\cos\theta)\]

If mode=None the formula is

\[e^{-i\omega t}\sum_{n=0}^{\text{N}_{\text{max}}} \,f_n(r) \,P^1_n(\cos\theta)\]

where \(f_n(r)\) is the tangential_func(n, r) passed to the method.

Parameters:

tangential_func (Callable[[int, float], complex]) – tangential function dependent on r
r (float | Sequence) – radial coordinate [m]
theta (float | Sequence) – tangential coordinate [rad]
t (float | Sequence) – time [s]
mode (int) – specific mode number of interest; if None then all modes until N_max

Return type:

complex | NDArray

tangential_particle_displacement(r, theta, t, mode=None)#

Particle displacement in tangential direction

Returns the value of the particle displacement in tangential direction in [m]

Parameters:

r (float | Sequence) – radial coordinate [m]
theta (float | Sequence) – tangential coordinate [rad]
t (float | Sequence) – time [s]
mode (None | int, optional) – specific mode number of interest; if None that all modes until N_max
Default: None

Return type:

complex | NDArray

tangential_particle_velocity(r, theta, t, mode=None)#

Particle velocity in tangential direction

Returns the value of the particle velocity in tangential direction in [m/s]

Parameters:

r (float | Sequence) – radial coordinate [m]
theta (float | Sequence) – tangential coordinate [rad]
t (float | Sequence) – time [s]
mode (None | int, optional) – specific mode number of interest; if None that all modes until N_max
Default: None

Return type:

complex | NDArray

velocity_potential(r, theta, t, scattered, incident, mode=None)#

Returns the velocity potential of the fluid in [m^2/s].

Parameters:

r (float | Sequence) – radial coordinate [m]
theta (float | Sequence) – tangential coordinate [rad]
t (float | Sequence) – time [s]
scattered (bool) – add scattered field
incident (bool) – add incident
mode (None | int, optional) – specific mode number of interest; if None then all modes until N_max
Default: None

Return type: