Units and conventions

Unit systems make every change of nondimensionalisation an explicit, checked call.

Published values are written in many nondimensionalisations: a plane channel alone has three Reynolds numbers (centreline, bulk, friction), and wavenumbers are scaled by the half-height or the full height depending on the paper. Silent factors of \(2\) or \(3/2\) are among the most common errors when comparing with the literature. The rule: the mechanics is generic, a study’s conventions are presets, and every conversion is an explicit call.

Unit systems and convert

A UnitSystem(name, family, scales, reynolds) lists reference scales (length, time, velocity) with their definition and value in the family’s base units, and its Reynolds group. convert is the only way to move a number between systems:

from conatus.expert import CHANNEL_SYSTEMS, convert

half, full = CHANNEL_SYSTEMS["centreline"], CHANNEL_SYSTEMS["bulk"]
print(convert(1.020547, "wavenumber", half, full))   # 2.041094: alpha per h -> per 2h
print(convert(2.0, "length", half, full))            # 1.0: two half-heights = one height

kind is one of length, time, velocity, wavenumber, rate, frequency, frequency squared, energy density, reynolds; the factor is the product of scale ratios to the power of the dimension. A conversion that needs a scale the system does not define is refused (the bulk system of a channel has no velocity scale until a flow gives one), as are a conversion between different families and an unknown kind.

Channel presets

Preset	Conventions	Source
ChannelUnits(Re, based_on), CHANNEL_SYSTEMS	\(Re_c = U_c h/\nu\), \(Re_b = U_b\,2h/\nu\), \(Re_\tau = u_\tau h/\nu\)	laminar Poiseuille relations only

from conatus.expert import ChannelUnits

print(ChannelUnits(5772.22, "centreline").laminar())
# {'Re_c': 5772.22, 'Re_b': 7696.29, 'Re_tau': 107.45, 'relations': 'U_b = 2/3 U_c, ...'}
try:
    ChannelUnits(180.0, "friction").turbulent()
except NotImplementedError as err:
    print(err)
# turbulent conversions between Re_c, Re_b and Re_tau need the measured
#   u_tau or U_b of the run; no empirical correlation is applied implicitly

ChannelUnits has no default convention: based_on is required. laminar_poiseuille(Re_c=...) gives the exact laminar relations.