Open horn configuration (left) and illustration of the superposition approach (right) showing throat and mouth variables at x 1 and x 2, respectively.
(Color online) Numerically modeled particle velocity fields (absolute value) within a double, axisymmetrical, conical horn at frequencies from 1 Hz to 5000 Hz. Horn dimensions: l = 20 cm, R 1 = 1 cm, R 2 = 10 cm. Horn’s first resonance occurs at 2650 Hz.
Frequency dependence of acoustic particle velocity amplification factor for pipe having a radius R = 0.01 m and length l = 0.2 m in water. Dashed line: numerical solution, solid line: analytical solution, as per Eqs. (13) and (18).
Axial velocity amplification factors (at the axis of the horn) vs frequency at the throat of single conical, Eqs. (13) and (19); double conical, Eqs. (29) and (19); horns and exponential single horn, Eqs. (13) and (20). For all horns: throat radius R 1 = 1 cm, single horn length l = 20 cm, mouth radius R 2 = 10 cm. Dashed lines: numerical solutions, solid lines: analytical solutions.
Conical AVH geometrical parameters.
Velocity amplification vs throat radius R 1 [per Fig. 6(a)] for cone with fixed lengths l and a fixed radii ratio K = R 2/R 1 = 10.
Horn amplification vs length [per Fig. 6(b)] for fixed radii ratios K = R 2/R 1, and a fixed throat radius R 1 = 1 cm. Dashed lines show cone angles α corresponding to the length and radii.
Horn amplification vs mouth-to-throat radii ratio K [per Fig. 6(c)] for fixed lengths and a fixed throat radius R 1 = 1 cm.
Axial particle velocity distribution, in water, in a single AVH (upper) and double AVH (lower). AVH dimensions are l = 20 cm, R 1 = 1 cm, K = 10, and the frequency was 50 Hz.
Frequency responses (in water) of single (dashed line) and double (solid line) horns with the same overall length of 20 cm, and a throat and mouth radii of 1 cm and 10 cm, respectively.
COMSOL computed AVH polar directionality patterns for 1 Hz, 600 Hz, and 1 kHz single conical horn, L = 10 cm, R throat = 1 cm, K = 5. Gray dashed line is scaled to A = 4 corresponding to the computed amplification (radial division represents velocity amplification factor).
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