Everything about The Dean Number totally explained
The
Dean number 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 studied such flows in the 1920's (Dean, 1927, 1928).
Definition
The Dean number is typically denoted by the symbol
D, and is defined as
»
is the
convective derivative.
The Dean number
D is the only parameter left in the system, and encapsulates the leading order curvature effects. Higher-order approximations will involve additional parameters.
Another parameter, similar to Dean Number is the
Germano Number, which is an extension of the first Number and it considers the effect of torsion where curvature and pitch of
curved pipes have a substantial value.
The expression of the
Germano Number will be the following:
»
where
Re is the
Reynolds Number and
η is the product of torsion
τ by the pipe radius
a, which the same value
a already defined.
For weak curvature effects (small
D), the Dean equations can be solved as a series expansion in
D. The first correction to the leading-order axial
Poiseuille flow is a pair of vorticies in the cross-section carrying flow form the inside to the outrside of the bend across the centre and back around the edges. This solution is stable up to a critical Dean number
(Dennis & Ng 1982). For larger
D, there are multiple solutions, many of which are unstable.
Further Information
Get more info on 'Dean Number'.
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