In pipe and duct systems, bend losses are usually taken from tables. Those values are correct — for an isolated bend with a uniform approach.
Dean vortices
In a curved duct, centrifugal force pushes the fluid towards the outer wall; continuity balances that with two counter-rotating cells. The result is a secondary circulation superimposed on the axial flow, and it does not decay for tens of diameters after the bend.
It has two consequences:
The loss increases. The secondary circulation consumes energy too; the total loss is above the isolated-bend table value.
The downstream flow is distorted. The flow leaving a bend is not uniform. A flow meter placed just after it reads wrong, a fan suffers system effect, a heat exchanger suffers a distribution problem, and a pump suction is degraded.
Bends in series
If two bends follow one another, the total loss is not the sum of the individual losses. In the same plane the secondary flow may be reinforced or cancelled; in different planes a three-dimensional swirling flow arises and the loss increases markedly. Adding table values systematically misleads here — it is one of the clearest places where CFD earns its keep in system design.
A modelling note
Secondary flow consists of velocity components normal to the axial flow, and those components are small. A coarse mesh or a first-order scheme erases them easily. The mesh must have enough resolution across the section and the solution must be finished at second order.
On the turbulence side, isotropic two-equation models are weak at capturing the anisotropy of swirling flow; where the strength of the secondary flow matters, a Reynolds stress model is more realistic [1]. The same limitation applies in cyclones.
References
- Launder, B. E., Reece, G. J. & Rodi, W. (1975). Progress in the development of a Reynolds-stress turbulence closure. Journal of Fluid Mechanics, 68(3), 537–566.
- Ferziger, J. H., Perić, M. & Street, R. L. (2020). Computational Methods for Fluid Dynamics, 4th ed. Springer. DOI: 10.1007/978-3-319-99693-6