The interaction of near-wall turbulence with compliant tensegrity fabrics: Modeling, simulation, and optimization

This work focuses on the modeling, simulation, and optimization of a novel type of compliant surface, a tensegrity fabric, for the possible reduction of the drag caused by an overlying turbulent flow.; The spatially-periodic tensegrity fabric is modeled with an extension of the tensegrity dynamics software developed by Skelton et al., who also designed the plate-class tensegrity structures used in this work. To account for the skin friction and pressure forces on the tensegrity structure, a simple tessellation is used.; The spatially-periodic turbulent flow is modeled with direct numerical simulation. To account for the effect of the interface motion on the flow, a 3D time-dependent coordinate transformation is adopted to map the deformed flow domain to a regular domain. When formulating the Navier-Stokes equation governing the flow in moving coordinates, both the contravariant form and the Cartesian form are considered. The former needs special care in the time differentiation of the momentum vector, and is discussed separately in the tensor framework. The latter is computationally less expensive and is thus used in the bulk of our simulations.; A significant influence of the compliant surface on the statistics of the near-wall turbulence is found in simulations at Re tau = 150, which show that, when the structure's stiffness and damping are low, the interface forms streamwise-traveling waves which significantly increase both drag and turbulent kinetic energy.; To exploit the (yet unexplored) large design flexibility of the tensegrity fabric, we have significantly refined a recently-developed direct search method, called the surrogate management framework (SMF), which is suitable for static optimization problems such as the present, in which the cost function is both non-differentiable and expensive to evaluate. Our refinements of the SMF focus on the use of n-dimensional extrapolations of the body-centered cubic (BCC) and face-centered cubic (FCC) crystalline structures as the underlying lattice during the optimization, rather than the default Cartesian mesh. These lattices both cover the parameter space and distribute the vectors of the minimal positive basis more uniformly than the Cartesian mesh, thus provide significantly improved convergence when used as the underlying lattice in pattern search algorithms.