Dean number
The Dean number (D) is a dimensionless group in fluid mechanics, which occurs in the study of flow in curved pipes and channels. It is named after the British scientist W. R. Dean, who was the first to provide a theoretical solution of the fluid motion through curved pipes for laminar flow by using a perturbation procedure from a Poiseuille flow in a straight pipe to a flow in a pipe with very small curvature.
If a fluid is moving along a straight pipe that after some point becomes curved, the bend will cause the fluid particles to change their main direction of motion. There will be an adverse pressure gradient generated from the curvature with an increase in pressure, therefore a decrease in velocity close to the convex wall, and the contrary will occur towards the outer side of the pipe. This gives rise to a secondary motion superposed on the primary flow, with the fluid in the centre of the pipe being swept towards the outer side of the bend and the fluid near the pipe wall will return towards the inside of the bend. This secondary motion is expected to appear as a pair of counter-rotating cells, which are called Dean vortices.
The Dean number is typically denoted by De (or Dn). For a flow in a pipe or tube it is defined as:
where
The Dean number is therefore the product of the Reynolds number (based on axial flow through a pipe of diameter ) and the square root of the curvature ratio.
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