Flow topology and loss analysis of a square-to-square sudden expansion relevant to HVAC systems: A case study

Abstract

Mechanical ventilation of buildings contributes significantly to the world's overall energy consumption, therefore, it is important to consider and control the fluid mechanics losses of air duct components. The current investigation aims to investigate the Borda-Carnot sudden expansion, which is often used in ventilation systems in place of diffusers when the flow cross-section needs to be increased. While a significant amount of research has been carried out on axisymmetric sudden expansions, expansions of square or rectangular cross-sections are seldom discussed in the literature. As rectangular air ducts are widely used in ventilation systems, a claim on the research of the flow topology and the loss characteristics of rectangular expansions is raised and is assessed in the present study. In a first step, the Borda-Carnot loss was examined for uniform and fully developed inlet velocity profiles by means of semi-empirical methods. It was concluded that the classic loss formula derived for uniform inlet underestimates the losses and may cause a 2–3% error for each sudden expansion in the calculation of losses in a ventilation system. In a second step, the flow details and the loss characteristics of a square-to-square sudden expansion of an area ratio of 2.78 were examined by experimental means. The investigated Reynolds number range was (0.36–1.8)·105, being representative of ventilation systems. Detailed velocity and turbulence-related measurements were carried out with a laser Doppler anemometer. The downstream effects of the square-to-square expansion were found to extend significantly farther downstream than that of an axisymmetric expansion, resulting in a 1.5–2.5 times larger flow reattachment length and a 1.5–2 times longer path to reach a fully developed state. The elongated downstream effect gains importance when there is a need to place control or measurement devices downstream of the expansion. As revealed by wall static pressure measurements, the semi-empirical formula derived for the Borda-Carnot loss for fully developed upstream flow approximates the losses more accurately than the classic formula derived for a uniform inlet. Therefore, a methodology has been proposed herein for calculating the Borda-Carnot loss in ventilation systems, incorporating the loss formula for fully developed inflow.