Optimization of economic air velocity for ventilation ducts using the GWO algorithm

The current design of ventilation ducts in China largely adheres to the air velocity standards established in the 1980s. However, owing to fluctuating energy prices, increasing material costs and energy-saving demands, the original design approach fails to balance initial investment with energy-efficient operating costs, resulting in considerable resource waste. In this study, a method for calculating the economic air velocity is proposed to address the economic aspects of ventilation systems. To determine the economic velocities for the four key pipe fittings, we solved the total life cycle cost (TLCC) mathematical model—which incorporates carbon emissions—using both the fminbnd algorithm in MATLAB and an improved gray wolf optimizer (GWO). The improved GWO integrates a nonlinear convergence factor and a dynamic weight position update mechanism to avoid local optima and accelerate convergence. On the basis of the resistance characteristics of typical industrial systems and the application of the weighted average method to quantify segmental resistance contributions, an optimized range of economic air velocities, namely, 4.87–9.00 m/s for main ducts and 4.17–7.31 m/s for branch ducts, is proposed. The experimental results indicate that the system designed with the proposed economic air velocities achieves a total cost reduction of 20.31% and a carbon emission reduction of approximately 19.15% over a 20-year life cycle. This study provides a robust optimization framework and identifies economic airspeeds for the practical design of energy-efficient and sustainable ventilation systems in modern buildings.