ARF

Examples using this class are:

Acoustofluidics 2022: ARF Comparison

Acoustofluidics 2022: ARF Comparison

Hasegawa (1979) Figure 3

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 (Union[Frequency, float, int]) – Frequency [Hz]

  • R_0 (Union[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 (Optional[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

field

omega

R_0

rho_f

k_f

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 (Union[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 (Union[float, Sequence[float]]) – radial coordinate [m]

Return type:

Union[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 (Union[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 (Union[float, Sequence[float]]) – radial coordinate [m]

Return type:

Union[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 (Union[float, Sequence]) – radial coordinate [m]

  • theta (Union[float, Sequence]) – tangential coordinate [rad]

  • t (Union[float, Sequence]) – time [s]

  • scattered (bool) – add scattered field

  • incident (bool) – add incident

  • mode (Optional[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 (Union[float, Sequence]) – radial coordinate [m]

  • theta (Union[float, Sequence]) – tangential coordinate [rad]

  • t (Union[float, Sequence]) – time [s]

  • scattered (bool) – scattered field contribution

  • incident (bool) – incident field contribution

  • mode (Optional[int], optional) – specific mode number of interest; if None then all modes until N_max

    Default: None

Return type:

Union[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 (Union[float, Sequence]) – radial coordinate [m]

  • theta (Union[float, Sequence]) – tangential coordinate [rad]

  • t (Union[float, Sequence]) – time [s]

  • mode (Optional[int], optional) – specific mode number of interest; if None then all modes until N_max

    Default: None

Return type:

Union[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 (Union[float, Sequence]) – radial coordinate [m]

  • theta (Union[float, Sequence]) – tangential coordinate [rad]

  • t (Union[float, Sequence]) – time [s]

  • mode (Optional[int], optional) – specific mode number of interest; if None that all modes until N_max

    Default: None

Return type:

Union[complex, ndarray]

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

Radial particle velocity [m/s]

Parameters:

  • r (Union[float, Sequence[float]]) – radial coordinate [m]

  • theta (Union[float, Sequence[float]]) – tangential coordinate [rad]

  • t (Union[float, Sequence[float]]) – time [s]

  • mode (Optional[int], optional) – mode

    Default: None

Return type:

Union[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 (Union[float, Sequence]) – radial coordinate [m]

  • theta (Union[float, Sequence]) – tangential coordinate [rad]

  • t (Union[float, Sequence]) – time [s]

  • scattered (bool) – scattered field contribution

  • incident (bool) – incident field contribution

  • mode (Optional[int], optional) – specific mode number of interest; if None then all modes until N_max

    Default: None

Return type:

Union[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 (Union[float, Sequence]) – radial coordinate [m]

  • theta (Union[float, Sequence]) – tangential coordinate [rad]

  • t (Union[float, Sequence]) – time [s]

  • mode (int) – specific mode number of interest; if None then all modes until N_max

Return type:

Union[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 (Union[float, Sequence]) – radial coordinate [m]

  • theta (Union[float, Sequence]) – tangential coordinate [rad]

  • t (Union[float, Sequence]) – time [s]

  • mode (Optional[int], optional) – specific mode number of interest; if None that all modes until N_max

    Default: None

Return type:

Union[complex, ndarray]

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

Tangential particle velocity [m/s]

Parameters:

  • r (Union[float, Sequence[float]]) – radial coordinate [m]

  • theta (Union[float, Sequence[float]]) – tangential coordinate [rad]

  • t (Union[float, Sequence[float]]) – time [s]

  • mode (Optional[int], optional) – mode

    Default: None

Return type:

Union[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 (Union[float, Sequence]) – radial coordinate [m]

  • theta (Union[float, Sequence]) – tangential coordinate [rad]

  • t (Union[float, Sequence]) – time [s]

  • scattered (bool) – add scattered field

  • incident (bool) – add incident

  • mode (Optional[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 [-]