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

Abstract

In this paper, a local component optimization method is proposed for reducing resistance and consumption in building transmission and distribution systems. The gradient descent method is used to investigate energy dissipation minimization constrained by the Navier‒Stokes equation with nonlinear boundary conditions, and the optimality conditions of the shape are derived from the shape optimization problem using the function space parameterization method. The shape of the upper wall of the transition tee is iteratively optimized until the optimal shape with the minimum energy dissipation is obtained. The derivative of the free boundary shape of the transition tee and the objective function are proposed, and the normalized wall height of the transition tee with different area ratios are provided; these results can enable the adaptation of various sizes of transition tees in engineering to achieve air supply conditions that meet the engineering requirements. In this paper, the flow field and pressure loss of the optimized and conventional tees are compared, and the optimized tee performance improvement and energy saving potential are evaluated. The optimized transition tee has a resistance reduction rate of 6∼99% for the straight duct and 2–98% for the branch duct under different area ratios and flow ratios. Our method has the advantages of being more accurate, flexible and general and provides a novel method for the resistance optimization design of building transmission and distribution systems.