Topology optimization of thermal cloaks in euclidean spaces and manifolds using an extended level set method

Thermal cloaks are devices designed to shield an object against thermal detection, which have attracted growing interest in research. This paper proposes to design thermal cloaks using the level-set-based shape and topology optimization in the context of pure heat conduction. The cloaking effect is achieved by optimizing the distribution of two bulk heat conductive materials to eliminate the temperature disturbance induced by the introduction of the insulator (cloaking region) into a homogeneous thermal conduction medium. The optimized thermal cloaks are free of high anisotropy and nonhomogeneity commonly seen in the popular transformation thermotics or scattering cancellation methods. Due to the clear boundary characteristic of the level set representation, no sophisticated filtering techniques are required to suppress the appearance of ”gray regions” as opposed to the density-based topology optimization methods. Considering the fact that the device components that need to be thermally cloaked, e.g., sensors, can take an arbitrary free-form shape, a conformal thermal cloak on the manifold is also topologically optimized using the extended level set method (X-LSM), which has not been reported in the literature. The structural boundary is evolved by solving the (modified) Hamilton-Jacobi equation. The feasibility and robustness of the proposed method to design thermal meta-devices with cloaking functionality are demonstrated through a number of 2D and 3D (solid and shell) numerical examples with different cloaking regions (circular, human-shaped, spherical, and curved circular). This work may shed light on further exploration of the thermal meta-devices in the heat flux manipulation regime.