A Variational Gradient Descent Method for Reducing Resistance in Building Transmission and Distribution Systems and its Application to Guide Tees

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. The flow field and pressure loss of the optimized tee are compared with those of the traditional tee in this paper, in which the performance improvement and energy-saving potential of the optimized tee are assessed. The reduction rate of the bypass pipe resistance of the optimized diverter tee ranges from 9% to 94% under different area ratios and flow rates. This method offers greater accuracy, flexibility, and universality, providing a new approach to resistance optimization design for building distribution systems.

Keywords: Ventilation, Guide tee, Shape optimization, Resistance