It is well known that acoustic cavitation is the root of most sonomechanical and sonochemical processes conducted in liquids under the influence of ultrasound. It is also known that the specific acoustic power radiated by a horn into a liquid load can be expressed as follows:
w = 0.5 rV2 [W/m2].
Here, r is the effective acoustic resistance of the liquid at cavitation and V is the amplitude of the oscillation velocity of the horn’s radiating output surface. The total acoustic power radiated into the liquid is:
W= wS [W].
Here S is the area of the radiating surface of the horn.
Thus, it is evident that an increase in the total radiated acoustic power at a constant load and frequency can be achieved by increasing either of the following two factors: the horn’s output vibration amplitude or the area of the horn’s output radiating surface. The output vibration amplitude cannot be increased above a certain value that corresponds to the fatigue strength of the horn material. Increasing the amplitude above this level causes the horn to break down. Furthermore, considerable increase in the amplitude of vibrations is not always justified from the technological point of view.
On the other hand, it is possible to increase total radiated power by enlarging the output diameter of a horn up to a certain value (about λ/4, where λ is the wavelength of ultrasound waves in the material of a horn). When the horn diameter is larger than this value, radiation via the horn’s side surfaces begins to have a strong effect, and the horn’s acoustic properties become difficult to predict. Nevertheless, increasing the horn’s output diameter up to a value close to λ/4 gives an opportunity to increase the radiated power several times, as compared to the currently used designs, as explained below.
The commonly used ultrasonic horns have converging (tapering) shapes towards their output ends, in contact with the load. This shape ensures that the gain factor of the amplitude of the ultrasonic vibrations in the horn is higher than unity in the direction of the load. The best performing version of this design, in our opinion, is the three-element stepped horn with a transitional element of variable cross-section. This horn has the maximum possible gain factor among the converging horns, for a given ratio of their output to input diameters. The transitional element, located between to cylindrical elements, is needed to reduce and distribute the deformation hot spots appearing at the junction of the cylindrical elements.
Figure 1 shows the schematic of such stepped horn with a catenoidal transitional element. Plots of the vibration amplitude distribution and the deformation along the horn’s length are also given. Here: V(z) – amplitude of vibration velocity; e(z) – deformation amplitude; k – wave number; Ln – vibration node position; L – vibration antinode position; L1, L2, L3 – corresponding element lengths; D0, D1 – input and output diameters.
FIGURE 1
Figure 2 gives a better idea on what this horn looks like in real life.
FIGURE 2
