Table of unit conversions: Difference between revisions
mNo edit summary |
No edit summary |
||
| (7 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
{{latexPreamble}} | {{latexPreamble}} | ||
To convert the value of a dimensionless variable in 'code' units to 'lab' units, multiply by $C$ from the following table | |||
('code' units are based on $R$ and $U_{cl}$, 'lab' units are based on $D$ and $U_b$). | |||
$ | |||
E.g. for the variable $z$: $~~z_\mathrm{lab} \,(D) = z_\mathrm{code} \,(R) = z_\mathrm{code} \,(\frac{1}{2}D) | |||
~~\Rightarrow~~z_\mathrm{lab} = z_\mathrm{code} \times \frac{1}{2},~~$ | |||
i.e. $~z_\mathrm{lab} = z_\mathrm{code} \times C$ with $C=\frac{1}{2}$. | |||
Note: For consistent streamwise wavenumber $\alpha$, papers using the length scale $R$ write $L=2\pi/\alpha$, while papers using $D$ usually write $L=\pi/\alpha$. | |||
| Line 13: | Line 19: | ||
\vec{u} & U_{cl} & U_b & 2 & \mbox{speed} \\ | \vec{u} & U_{cl} & U_b & 2 & \mbox{speed} \\ | ||
t & R/U_{cl} & D/U_b & \frac{1}{4} & \mbox{time} \\ | t & R/U_{cl} & D/U_b & \frac{1}{4} & \mbox{time} \\ | ||
\sigma & U_{cl}/R & U_b/D & 4 & \mbox{growth rate} \\ | |||
E & \rho\,U_{cl}^2\, R^3 & \rho\,U_b^2\,D^3 & \frac{1}{2} & \mbox{kinetic energy} \\ | E & \rho\,U_{cl}^2\, R^3 & \rho\,U_b^2\,D^3 & \frac{1}{2} & \mbox{kinetic energy} \\ | ||
D & \rho\,U_{cl}^3\, R^2 & \rho\,U_b^3\,D^2 & 2 & \mbox{dissipation rate} \\ | D & \rho\,U_{cl}^3\, R^2 & \rho\,U_b^3\,D^2 & 2 & \mbox{dissipation rate} \\ | ||
E' & \rho\,U_{cl}^2\, R^2 & \rho\,U_b^2\,D^2 & 1 & \mbox{energy per unit length} \\ | E' & \rho\,U_{cl}^2\, R^2 & \rho\,U_b^2\,D^2 & 1 & \mbox{energy per unit length} \\ | ||
\ | \tilde{E} & \rho\,U_{cl}^2 & \rho\,U_b^2 & 4 & \mbox{energy density} | ||
\end{array}$ | \end{array}$ | ||
Latest revision as of 06:39, 5 November 2024
$ \renewcommand{\vec}[1]{ {\bf #1} } \newcommand{\bnabla}{ \vec{\nabla} } \newcommand{\Rey}{Re} \def\vechat#1{ \hat{ \vec{#1} } } \def\mat#1{#1} $
To convert the value of a dimensionless variable in 'code' units to 'lab' units, multiply by $C$ from the following table ('code' units are based on $R$ and $U_{cl}$, 'lab' units are based on $D$ and $U_b$).
E.g. for the variable $z$: $~~z_\mathrm{lab} \,(D) = z_\mathrm{code} \,(R) = z_\mathrm{code} \,(\frac{1}{2}D)
~~\Rightarrow~~z_\mathrm{lab} = z_\mathrm{code} \times \frac{1}{2},~~$
i.e. $~z_\mathrm{lab} = z_\mathrm{code} \times C$ with $C=\frac{1}{2}$.
Note: For consistent streamwise wavenumber $\alpha$, papers using the length scale $R$ write $L=2\pi/\alpha$, while papers using $D$ usually write $L=\pi/\alpha$.
$\begin{array}{ccccl}
variable & \mbox{'code' units} & \mbox{'lab' units} & \mbox{conversion factor}~C & \mbox{comment}\\
\hline
r,z & R & D & \frac{1}{2} & \mbox{length}\\
\vec{u} & U_{cl} & U_b & 2 & \mbox{speed} \\
t & R/U_{cl} & D/U_b & \frac{1}{4} & \mbox{time} \\
\sigma & U_{cl}/R & U_b/D & 4 & \mbox{growth rate} \\
E & \rho\,U_{cl}^2\, R^3 & \rho\,U_b^2\,D^3 & \frac{1}{2} & \mbox{kinetic energy} \\
D & \rho\,U_{cl}^3\, R^2 & \rho\,U_b^3\,D^2 & 2 & \mbox{dissipation rate} \\
E' & \rho\,U_{cl}^2\, R^2 & \rho\,U_b^2\,D^2 & 1 & \mbox{energy per unit length} \\
\tilde{E} & \rho\,U_{cl}^2 & \rho\,U_b^2 & 4 & \mbox{energy density}
\end{array}$