A variable gradient descent shape optimization method for guide tee resistance reduction

Abstract

This article introduces an optimization method for local components in building distribution systems aimed at reducing resistance and energy consumption. The method employs gradient descent to minimize the energy dissipation governed by the Navier‒Stokes equations under nonlinear boundary conditions. Starting from the shape optimization problem, the optimality conditions for the steady-state shape optimization problem are derived in the paper using a functional space parameterization approach. Taking a diverter tee as an example, the guide vane shape of the tee is iteratively optimized until the optimal shape with the least energy dissipation is obtained. A revised mixed-length model for the diverter tee is proposed, along with normalized wall heights for diverter tees with various area ratios to accommodate diverter tees of all sizes in engineering projects and thus achieve air supply conditions that meet engineering standards. In this paper, the pressure, velocity, energy dissipation rate and local resistance coefficients of the optimized tee and the conventional tee are analyzed and investigated and the performance improvement and energy saving potential of the optimized tee are evaluated. The optimized flow-guiding tee has a branch duct resistance reduction rate of 6–96 % at different area ratios and flow ratios. The shape of the globally optimal solution for the guide vanes within the distribution system is given iteratively using the gradient descent method, thus realizing the low-resistance self-optimization and self-design of the building fluid distribution system. This method offers greater accuracy, flexibility, and universality, providing a new approach to resistance optimization design for building distribution systems.