This article presents fully three-dimensional conjugate heat transfer analysis and a multi-objective, constrained optimization to find sizes of pin-fins, inlet water pressure, and average speed for arrays of micro pin-fins used in the forced convection cooling of an integrated circuit with a uniformly heated 4 × 3 mm footprint and a centrally located 0.5 × 0.5 mm hot spot. Sizes of micro pin-fins having cross sections shaped as circles, symmetric airfoils, and symmetric convex lenses are optimized to completely remove heat due to a steady, uniform heat flux of 500 W cm⁻² imposed over the entire footprint (background heat flux) and a steady, uniform heat flux of 2000 W cm⁻² imposed on the hot spot area only (hot spot heat flux). The two simultaneous objectives are to minimize maximum substrate temperature and minimize pumping power, while keeping the maximum temperature constrained below 85°C and removing all of input thermal energy by convection. The design variables are the inlet average velocity and size of the pin-fins. A response surface is generated for each of the objectives and coupled with a genetic algorithm to arrive at a Pareto frontier of the best trade-off solutions. Numerical results show that, for a specified maximum temperature, optimized arrays with pin-fins having symmetric convex lens shapes create the lowest pressure drop, followed by the symmetric airfoil and circular cross-section pin-fins. An a posteriori three-dimensional stress–deformation analysis incorporating hydrodynamic and thermal loads shows that Von-Mises stress for each pin-fin array is significantly below the yield strength of silicon, thus, confirming structural integrity of such arrays of micro pin-fins.

The wing tip device in this study was to mimic the wing tips of a soaring bird, featuring three smoothly blended elements. Each such multi-element winglet was integrated into a complete wing–tail–body aircraft configuration. The geometry of each of the three elements in the multi-element winglet was defined using 11 parameters, totaling 33 parameters for a complete multi-element winglet geometry. This design methodology used a three-dimensional geometry generation algorithm based on locally analytical smoothly connected surface patches, allowing for the creation of vastly diverse three-dimensional geometries with a minimal number of specified design parameters. A three-dimensional, compressible, turbulent flow, steady-state analysis was performed using a Reynolds-averaged Navier–Stokes solver on each configuration to obtain the objective function values. Each configuration was analyzed at a freestream Mach number of 0.25 and at an angle of attack of 11 deg to mimic the takeoff conditions of a passenger aircraft. Multi-objective optimization was carried out using modeFRONTIER, using a radial basis function response surface approximation coupled with a genetic algorithm. Maximizing coefficients of the lift and lift-to-drag ratio and minimizing the coefficients of drag and the magnitude of the coefficient of the moment were the four simultaneous objectives. The Pareto-optimized multi-element winglet concept demonstrated superior performance at subsonic and transonic speeds.

The work presented in this paper used rigorous 3D flow-field analysis combined with multi-objective constrained shape design optimization for the design of complete blade + bladelet configurations for a three-blade propeller type wind turbine. The fluid flow analysis in this work was performed using OpenFOAM software. The 3D, steady, incompressible, turbulent flow Reynolds-Averaged Navier-Stokes equations were solved in the rotating frame of reference for each combination of wind turbine blade and bladelet geometry. The free stream uniform wind speed in all cases was assumed to be 9 m s^-1. The three simultaneous design optimization objectives were: a) maximize the coefficient of power, b) minimize the coefficient of thrust, and c) minimize twisting moment around the blade axis. The bladelet geometry was fully defined by using a small number of parameters. The optimization was carried out by creating a multi-dimensional response surface for each of the simultaneous objectives. The response surfaces were based on radial basis functions, where the support points were designs analyzed using the high fidelity CFD analysis of the full blade + bladelet geometry. The response surfaces were then coupled to an optimization algorithm in modeFRONTIER software. The predicted values of the objective functions for the optimum designs were then again validated using OpenFOAM high fidelity analysis code.