Radiation Force Calculations on Apertured Piston Fields

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Radiation Force Calculations on Apertured Piston
Fields
Pierre Gélat, Mark Hodnett and Bajram Zeqiri
3 April 2003
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Background

• The effective radiating area AER is the area at
  or close to the face of the treatment head
  through which the majority of the ultrasonic
  power passes (IEC 61689)
• The NPL aperture method for determining AER was
  developed so that radiation force balances can be
  used to determine AER for physiotherapy treatment
  heads
• Original implementation of method used a
  reflecting target radiation force balance new
  implementation uses an absorbing target
• In both cases, diffraction provides a source of
  systematic measurement uncertainty
• There is a requirement to model and understand
  the way in which a circular absorbing aperture
  modifies the acoustic field Use the Finite
  Element method

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Schematic Representation of Aperture Technique
Using an Absorbing Target
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Schematic Representation of Aperture Technique
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Theory of Acoustic Radiation Force and Radiation
Power on an Absorbing Target

• Acoustic radiation stress tensor

• Where
• ?ij is the Kronecker delta

is the time-averaged acoustic pressure
i and j assume values of 1,2 and 3

• Acoustic radiation force vector

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Acoustic Radiation Force and Power on the Target

• In axisymmetric case, axial component of F is

Where b is the target radius and where ()
denotes the complex amplitude V is the potential
energy density Tx is the kinetic energy density
due to the axial particle velocity TR is the
kinetic energy density due to the radial particle
velocity

• Acoustic power on the target resulting from
  normal acoustic intensity

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Un-Apertured Case

• Consider un-apertured case to validate Finite
  Element approach

• Use velocity potential ? to compute near-field
  pressure and axial particle velocity

Where A1 is the piston surface area
is the maximum piston velocity
r1 is the position vector of a point on the
piston r is the position vector of a point in the
sound field

• Acoustic pressure

• Axial component of particle velocity

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Analytical expression for ratio Fc/P

• Serves as an additional check for Rayleigh
  integral and Finite Element computations in
  un-apertured case (Beissner, Acoustic radiation
  pressure in the near field. JASA 1984 93(4)
  537-548)

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Apertured Field (Aperture Diameter 0 mm)
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Apertured Field (Aperture Diameter 4 mm)
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Apertured Field (Aperture Diameter 6 mm)
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Apertured Field (Aperture Diameter 9 mm)
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Apertured Field (Aperture Diameter 12 mm)
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Apertured Field (Aperture Diameter 16 mm)
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Apertured Field (Aperture Diameter 19 mm)
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Apertured Field (Aperture Diameter 22 mm)
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Apertured Field (Aperture Diameter 24 mm)
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Apertured Field (Aperture Diameter 30 mm)
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Apertured Field (Aperture Diameter ?)
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Fc/P Comparissons
 
 
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Radiation Force on Target, Aperture Front Face
and Rear Face, for ka21, vs. Aperture Diameter
Normalised to Radiation Force on Target in
Absence of Aperture
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Conclusions

• Prediction of apertured transducer pressure field
• Prediction of radiation force and radiation power
  on absorbing target for apertured transducer
  field using the Finite Element method
• Comparison of FE derived Fc/P in absence of
  aperture with analytical expression and Rayleigh
  integral