Calculation of \( u^\star \), \( k \) and \(\varepsilon \) from a diameter \( D_H \) and the reference velocity \( U_{ref} \) for a circular duct flow with smooth wall (use for inlet boundary conditions). More...
Public Member Functions | |
subroutine | turbulence_bc_ke_hyd_diam (uref2, dh, rho, mu, ustar2, k, eps) |
Calculation of \( u^\star \), \( k \) and \(\varepsilon \) from a diameter \( D_H \) and the reference velocity \( U_{ref} \) for a circular duct flow with smooth wall (use for inlet boundary conditions).
Both \( u^\star \) and \( (k,\varepsilon )\) are returned, so that the user may compute other values of \( k \) and \( \varepsilon \) with \( u^\star \).
We use the laws from Idel'Cik, i.e. the head loss coefficient \( \lambda \) is defined by:
\[ |\dfrac{\Delta P}{\Delta x}| = \dfrac{\lambda}{D_H} \frac{1}{2} \rho U_{ref}^2 \]
then the relation reads \(u^\star = U_{ref} \sqrt{\dfrac{\lambda}{8}}\). \(\lambda \) depends on the hydraulic Reynolds number \( Re = \dfrac{U_{ref} D_H}{ \nu} \) and is given by:
\[ \lambda = \dfrac{64}{Re} \]
\[ \lambda = \dfrac{1}{( 1.8 \log_{10}(Re)-1.64 )^2} \]
\[ \lambda = 0.021377 + 5.3115. 10^{-6} Re \]
From \( u^\star \), we can estimate \( k \) and \( \varepsilon\) from the well known formulae of developped turbulence
\[ k = \dfrac{u^{\star 2}}{\sqrt{C_\mu}} \]
\[ \varepsilon = \dfrac{ u^{\star 3}}{(\kappa D_H /10)} \]
[in] | uref2 | square of the reference flow velocity |
[in] | dh | hydraulic diameter \( D_H \) |
[in] | rho | mass density \( \rho \) |
[in] | mu | dynamic viscosity \( \nu \) |
[out] | ustar2 | square of friction speed |
[out] | k | calculated turbulent intensity \( k \) |
[out] | eps | calculated turbulent dissipation \( \varepsilon \) |
subroutine turbulence_bc_ke_hyd_diam | ( | real(c_double), value | uref2, |
real(c_double), value | dh, | ||
real(c_double), value | rho, | ||
real(c_double), value | mu, | ||
real(c_double) | ustar2, | ||
real(c_double) | k, | ||
real(c_double) | eps | ||
) |