ARF#

Examples using this class are:

Acoustofluidics 2022: ARF Comparison

Hasegawa (1979) Figure 3

class osaft.solutions.hasegawa1969.arf.ARF(f, R_0, rho_s, E_s, nu_s, rho_f, c_f, p_0, wave_type, position=None, N_max=5)[source]#

Bases: ScatteringField, BaseARF

ARF class for Hasegawa & Yosioka (1969)

Parameters:

f (Frequency | float | int) – Frequency [Hz]
R_0 (Sphere | float | int) – Radius of the sphere [m]
rho_s (float) – Density of the solid sphere [kg/m^3]
E_s (float) – Young’s modulus [Pa]
nu_s (float) – Poisson’s ratio of the solid sphere [-]
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]
position (None | float, optional) – Position in the standing wave field [rad]
Default: None
wave_type (WaveType) – Either standing or progressive wave
N_max (int, optional) –
Default: 5

Public Data Attributes:

Inherited from BaseHasegawa

`supported_wavetypes`
`x_f`	dimensionless wave number in the fluid [-]
`x_s_l`	dimensionless wave number in the particle, longitudinal direction [-]
`x_s_t`	dimensionless wave number in the particle, transversal direction [-]
`lambda_rho`	ratio of densities [-]
`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.ElasticSolid.rho_s`
`E_s`	Wraps to `osaft.core.solids.ElasticSolid.E_s`
`nu_s`	Wraps to `osaft.core.solids.ElasticSolid.nu_s`
`rho_f`	Wraps to `osaft.core.fluids.InviscidFluid.rho_f`
`c_f`	Wraps to `osaft.core.fluids.InviscidFluid.c_f`
`k_s_l`	Wraps to `osaft.core.solids.ElasticSolid.k_l`
`k_s_t`	Wraps to `osaft.core.solids.ElasticSolid.k_t`
`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 BaseScattering

N_max

Cutoff mode number for infinite sums

Public Methods:

`compute_arf`()	Acoustic radiation force [N]
`U_n`(n)	Coefficient \(U_n\) [-]
`V_n`(n)	Coefficient \(V_n\) [-]
`d_U_n`(n)	Coefficient \(U_n'\) [-]
`d_V_n`(n)	Coefficient \(V_n'\) [-]

Inherited from ScatteringField

`radial_particle_velocity`(r, theta, t[, mode])	Radial particle velocity [m/s]
`tangential_particle_velocity`(r, theta, t[, mode])	Tangential particle velocity [m/s]
`potential_coefficient`(n)	Wrapper to the fluid scattering coefficients for an inviscid fluid
`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
`c_n`(n)	Coefficient \(c_n\) [-]
`c_n_A`(n)	Coefficient \(c_n\) [m]
`a_n`(n)	Coefficient \(a_n\) [m]
`b_n`(n)	Coefficient \(b_n\) [m]

Inherited from BaseHasegawa

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 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_in(n)#

Wraps to osaft.core.backgroundfields.BackgroundField.A_in

Return type:: complex

U_n(n)[source]#

Coefficient \(U_n\) [-]

(Eq. 19)

Parameters:: n (int) – mode [-]
Return type:: complex
Returns:: coefficient [m^2/s]

V_n(n)[source]#

Coefficient \(V_n\) [-]

(Eq. 19)

Parameters:: n (int) – mode [-]
Return type:: complex
Returns:: coefficient [m^2/s]

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)#

Radial scattering field velocity term of mode n without Legendre coefficients

Returns radial scattering field velocity in [m/s]

Parameters:

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

Return type:

complex | Sequence[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)#

Tangential scattering field velocity term of mode n without Legendre coefficients

Returns tangential scattering field velocity in [m/s]

Parameters:

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

Return type:

complex | Sequence[complex]

a_n(n)#

Coefficient \(a_n\) [m]

(determined by boundary conditions)

Parameters:: n (int) – mode [-]
Return type:: complex

b_n(n)#

Coefficient \(b_n\) [m]

(determined by boundary conditions)

Parameters:: n (int) – mode [-]
Return type:: complex

c_n(n)#

Coefficient \(c_n\) [-]

(Eq. 7)

Parameters:: n (int) – mode [-]
Return type:: complex

c_n_A(n)#

Coefficient \(c_n\) [m]

(Eq. 7)

Parameters:: n (int) – mode [-]
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 force [N]

Computes the ARF, based on the general solution (Eq. 13)

Raises:: WrongWaveTypeError – if wrong wave_type
Return type:: float

copy()#

Returns a copy of the object

Return type:: BaseSolution

d_U_n(n)[source]#

Coefficient \(U_n'\) [-]

(Eq. 19)

Parameters:: n (int) – mode [-]
Return type:: complex
Returns:: coefficient [m^2/s]

d_V_n(n)[source]#

Coefficient \(V_n'\) [-]

(Eq. 19)

Parameters:: n (int) – mode [-]
Return type:: complex
Returns:: coefficient [m^2/s]

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]

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

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)#

Radial particle velocity [m/s]

Parameters:

r (float | Sequence[float]) – radial coordinate [m]
theta (float | Sequence[float]) – tangential coordinate [rad]
t (float | Sequence[float]) – time [s]
mode (None | int, optional) – mode
Default: None

Return type:

float | Sequence[float]

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)#

Tangential particle velocity [m/s]

Parameters:

r (float | Sequence[float]) – radial coordinate [m]
theta (float | Sequence[float]) – tangential coordinate [rad]
t (float | Sequence[float]) – time [s]
mode (None | int, optional) – mode
Default: None

Return type:

float | Sequence[float]

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:

complex

property E_s: float#: Wraps to osaft.core.solids.ElasticSolid.E_s

property N_max#

Cutoff mode number for infinite sums

Getter:: returns number of infinite sum term
Setter:: automatically invokes osaft.core.variable.BaseVariable.notify()

property R_0: float#: Wrapper for osaft.core.geometries.Sphere.R_0

property area: float#: Wrapper for osaft.core.geometries.Sphere.area

property c_f: float#: Wraps to osaft.core.fluids.InviscidFluid.c_f

property f: float#: wrapper for osaft.core.frequency.Frequency.f

property k_f: float#: Wraps to osaft.core.fluids.InviscidFluid.k_f

property k_s_l: float#: Wraps to osaft.core.solids.ElasticSolid.k_l

property k_s_t: float#: Wraps to osaft.core.solids.ElasticSolid.k_t

property kappa_f: float#: Wraps to osaft.core.fluids.InviscidFluid.kappa_f

property lambda_rho: float#: ratio of densities [-]

property nu_s: float#: Wraps to osaft.core.solids.ElasticSolid.nu_s

property omega: float#: wrapper for osaft.core.frequency.Frequency.omega

property p_0: float#: Wraps to osaft.core.backgroundfields.BackgroundField.p_0

property position: float#: Wraps to osaft.core.backgroundfields.BackgroundField.position

property rho_f: float#: Wraps to osaft.core.fluids.InviscidFluid.rho_f

property rho_s: float#: Wraps to osaft.core.solids.ElasticSolid.rho_s

property volume: float#: Wrapper for osaft.core.geometries.Sphere.volume

property wave_type: WaveType#: Wraps to osaft.core.backgroundfields.BackgroundField.wave_type

property x_f: float#: dimensionless wave number in the fluid [-]

property x_s_l: float#: dimensionless wave number in the particle, longitudinal direction [-]

property x_s_t: float#: dimensionless wave number in the particle, transversal direction [-]