Rotating cylindrical acoustic invisibility cloak: Solution using perturbation method

• In view of real-world applications of an acoustic invisibility cloak, the effect of rotation on cloaking is evaluated. • A rotating anisotropic fluid region is modelled using linearised equations of motion with convective terms. • A new differential equation describing acoustic wave propagation in a rotating anisotropic fluid region is derived. • The equation is solved using a new perturbation method which can calculate the scattering at low computational cost. • Results are compared to a numerical solution and show good agreement within the valid range of input values. Transformation Acoustics initiated a new paradigm of metamaterial designs in the mid-2000s. Using this approach, an invisibility cloak can be created, and this holds promise for stealth and noise reduction applications in aviation. However, adapting this design to meet the demands of realistic conditions has proven challenging. The work below focusses on the design of a stationary 2D cylindrical cloak and its performance whilst rotating, a result not yet reported in the literature. The study utilises linearised equations of motion with convective terms. A differential equation for acoustic pressure in an anisotropic rotating fluid is formulated assuming radial dependence of its effective density components and bulk modulus. For a slowly rotating cloak the corresponding solution and scattering coefficients for the acoustic incident plane wave are derived using a perturbation method and compared with a numerical solution. These scattering coefficients are used to evaluate the performance of the rotating cloak. Results show that rotation causes a reduction in cloaking performance with greater scattering observed for increasing rotational speeds, with a reasonable agreement (within 1.7%) between the methods within the range of applicability. The perturbation method used in this study provides a fast and computationally inexpensive approach to evaluating wave scattering from a rotating, radially graded anisotropic fluid region. The methodology and results presented lay a foundation for designing rotating acoustic cloaks, with potential applications in stealth technology and noise reduction in aviation.