Date of Award

Spring 5-2020

Author's School

McKelvey School of Engineering

Author's Department

Mechanical Engineering & Materials Science

Degree Name

Master of Science (MS)

Degree Type



Metamaterials are rationally designed artificial materials composed of tailored functional building blocks densely packed into an effective material. While metamaterials historically are primarily thought to be associated with negative index of refraction and invisibility cloaking in electromagnetism or optics, it turns out that the simple metamaterial concept also applies to many other areas of physics namely the thermodynamics, classical mechanics including elastostatics, acoustics, fluid dynamics and elastodynamics, and in principle also to the quantum mechanics. The goal of this thesis is to introduce and evaluate the potential of a hydrodynamic metamaterial cloak for drag reduction of objects in viscous flow. In recent years, the hydrodynamic metamaterial cloak has been created in very low Reynolds number Stokes flow by changing the viscosity tensor distribution in the cloak around the object. In practice, the spatially varying viscosity distribution is achieved by introducing a large number of micro-pillars in the cloak domain. In this thesis, the hydrodynamic cloaks for 2D objects of complex shapes such as airfoil are created by coordinate transformation using the Stokes equations for low Reynolds number flows. First, the viscosity tensor for a circular cylinder cloak is derived by coordinate transformation based on the Stokes equations. Then the viscosity tensors for an elliptic-cylinder cloak and an airfoil cloak are obtained by stretching the circular cylinder cloak. The effect of the cloaks is simulated using the commercially available software ANSYS FLUENT 2019R2. The unstructured meshes for all cases are generated by the software ICEM. By comparing the velocity fields, pressure fields, streamlines and wall skin friction coefficient in flow about various geometries without and with cloak, the potential of a hydrodynamic metamaterial cloak for drag reduction is evaluated. The cloak changes the velocity field and pressure field in the cloak region such that the velocity distribution in the region outside the cloak becomes more uniform, and the pressure difference between the upstream and downstream regions of the object becomes smaller; this produces the hydrodynamic hiding effect and drag reduction. These effects are reduced at higher Reynolds numbers. The results for a cloak around a circular cylinder, an elliptic-cylinder, an airfoil and a flat plate (normal to the flow) show that a hydrodynamic cloak has the effect of hiding the object and reduces the drag, although these effects are reduced at high Reynolds numbers.


English (en)


Ramesh K. Agarwal

Committee Members

Ramesh K. Agarwal, Chair David Peters Swami Karunamoorthy