Energy balance analysis of HVAC divided flow fittings

Abstract

Energy balances are performed on selected converging and diverging flow tees and laterals to calculate the net energy loss in order to quantify the total energy loss expected for a particular application. The goal is to identify those divided flow fittings that exhibit the minimum total energy loss so that the least fan power consumption will be required when such fittings are installed in an air duct system. Loss coefficient correlations previously published in literature are employed in the analysis. The total energy dissipation is expressed in terms of branch and main loss coefficients. It is shown that the total energy loss is positive within the limited accuracy of the published correlations for loss coefficient data. A physically realistic explanation is provided for previously reported negative main and branch loss coefficients. A range of branch-to-common flow rate ratios is identified for converging flow straight-body flat oval 45° laterals in order to minimize energy loss.

Nomenclature

a	=	flat oval main/common minor dimension, mm (in.)
A	=	flat oval main/common major dimension, mm (in.)
Ab	=	branch cross-sectional area, m2 (ft2)
Ac	=	common cross-sectional area, m2 (ft2)
c	=	flat oval branch minor dimension, mm (in.)
C	=	flat oval branch major dimension, mm (in.)
Cb	=	branch pressure loss coefficient, dimensionless
Cs	=	straight pressure loss coefficient, dimensionless
D	=	round diameter, mm (in.)
E	=	total fitting energy loss, dimensionless
g	=	acceleration of gravity, m/s2 (ft/s2)
hL	=	head loss, m (ft)
	=	mass flow rate, kg/s (lbm/s)
p	=	static pressure, Pa (in. wg)
Q	=	flow rate, L/s (cfm)
V	=	average velocity, m/s (ft/min)
ρ	=	air density, kg/m3 (lbm/ft3)

Subscripts

b	=	branch section
c	=	common section
s	=	straight (main) section