Acoustic Circulation Effects and the Nonlinear Impedance of Orifices

In his theory of streaming caused by sound waves, Eckart shows that time independent streams necessarily follow as part of the solution of the complete wave equatoin, taking into account viscosity and second-order terms. His treatment is mainly valid for liquids and it proves that the driving force of the streams is proportional to frequency squared. The effect, therefore, is especially important in the ultrasonic region (crystal winds). However, he suggests that slow streams might also be carried in air at audio frequencies. Studies of acoustical streaming phenomena around orifices have been made by the use of smoke particles in a 3-in. diameter circular tube. These studies covered a range of orifices from thicknesses of 0.5 mm to 19 mm and diameters of 3.5 mm to 20 mm. The frequency lay between 150 to 1000 c.p.s. Velocities in the orifice cover the range of 0 to 700 cm/sec. Close studies of the flow patterns have disclosed that there exist four definite regions of flow as the particle velocity in the orifice is increased. These regions have been represented by “phase diagrams.” Photographs of the various flow patterns in each region of the “phase diagram” have been taken for a number of orifices. Under each observed condition, the acoustic impedance of the orifice is determined by a conventional standing-wave measurement in the tube. It is shown that the nonlinear properties of the acoustic impedance of an orifice is closely connected with the circulation effects. Quantitative check in one of the circulation regions and a good qualitative over-all agreement indicate that the nonlinear properties of the impedance is due to the interaction between the sound field and the circulatory effects.