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Abstract
This article presents results from a systematic study to establish whether computational fluid dynamics techniques are capable of predicting pressure drop in close-coupled five-gore elbows having nominal diameters of 203 mm (8 in.) and turning radii r/D = 1.5. The close-coupled elbow combinations comprised either a Z-shape or a U-shape. In every instance the duct length separating the center-points of the elbows was systematically varied. An experimental program was likewise conducted to verify the computational fluid dynamics predictions, and data from the measurements are included. Zero-length pressure loss coefficients were predicted using five two-equations Eddy Viscosity Models including the standard k-ϵ, the Realizable k-ϵ, RNG k-ϵ, standard k-ω, and SST k-ω models, as well as the Reynolds Stress Model, and compared to the experimental data. The two-equation turbulence models predicted incorrect trends when applied to flow in U- and Z-configuration ducts. However, the Reynolds Stress Models with enhanced wall treatment was generally able to correctly predict elbow loss coefficients with less than 15% of error.
Nomenclature
| C | = | elbow pressure loss coefficient, dimensionless |
| Cf | = | friction coefficient, dimensionless |
| D | = | duct diameter, m (ft) |
| De | = | Dean number, dimensionless |
| f | = | friction factor, dimensionless |
| ks | = | equivalent sand roughness height m (ft) |
| k+ | = |
|
| L | = | length of ductwork between specified planes, m(ft) |
| Lint | = | intermediate duct length from elbow center-point to center-point, m (ft) |
| pv | = | velocity pressure, Pa (in. wg) |
| pt | = | total pressure, Pa (in. wg) |
| ps | = | static pressure, Pa (in. wg) |
| Δpf | = | duct pressure loss, Pa (in. wg) |
| Δps | = | static pressure loss, Pa (in. wg) |
| Δpt | = | total pressure loss, Pa (in. wg) |
| Q | = | volumetric flow rate, |
| R | = | elbow turning radius, m (ft) |
| Re | = | Reynolds number, dimensionless |
| uτ | = | friction velocity, m/s (ft/min) |
| u+ | = | dimensionless velocity |
| V | = | velocity, |
| x | = | length from outlet plane of upstream elbow to inlet plane of downstream elbow, m (ft) |
| y | = | distance from duct wall, m (ft) |
| Yn | = | nozzle expansion factor, dimensionless |
| y+ | = | dimensionless wall distance (y plus), y+ = ρ uτ y / μ |
Greek symbols
| ϵ | = | relative surface roughness, m (ft) |
| ρ | = | density, |
| μ | = | dynamic viscosity, |
| v | = | kinematic viscosity, m2/s (ft2/s) |
| τij | = | Reynolds stresses, N/m2 (lbf/ft2) |
Subscripts
| e | = | exit plane |
| x | = | plane 1, 2, - - -, n, as applicable |
| z | = | upstream plane |