Figure 4

Comparison of the equivalent source terms between the previous and present formulations. (a) The magnitudes of equivalent source in the previous formulation⁷. (b) The magnitudes of equivalent source in the present formulation. (c) Comparison of directivity plots along the surface of the acoustic cloak (r = R₂). In all figures, the Helmholtz numbers are set as kR₁ = 3. As shown in (a), the magnitude of the equivalent source in the previous formulation increases as the Mach number increases and the polarity shows the quadrupole patterns. As shown in (b), the magnitude of the equivalent source in the present formulation also increases as the Mach number increases, and the polarity shows the hexapole patterns. As shown in (c), the different polarities and magnitudes of the equivalent sources are more clearly seen. The magnitude of the previous formulation is much larger than the one of the present formulation. It is because the previous formulation introduced the velocity difference term v = u₀ − u_∞ in the equivalent source term in order to make the uniform wave operator. On the other hand, the present formulation has non-uniform wave operator, and all the equivalent sources are due to the fluid compressibility and flow non-uniformity by themselves.