8.0
general documentation
turbulence_bc_ke_hyd_diam Interface Reference

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...

+ Collaboration diagram for turbulence_bc_ke_hyd_diam:

Public Member Functions

subroutine turbulence_bc_ke_hyd_diam (uref2, dh, rho, mu, ustar2, k, eps)
 

Detailed Description

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:

  • for \( Re < 2000 \)

    \[ \lambda = \dfrac{64}{Re} \]

  • for \( Re > 4000 \)

    \[ \lambda = \dfrac{1}{( 1.8 \log_{10}(Re)-1.64 )^2} \]

  • for \( 2000 < Re < 4000 \), we complete by a straight line

    \[ \lambda = 0.021377 + 5.3115. 10^{-6} Re \]

From \( u^\star \), we can estimate \( k \) and \( \varepsilon\) from the well known formulae of developped turbulence

\[ k = \dfrac{u^{\star 2}}{\sqrt{C_\mu}} \]

\[ \varepsilon = \dfrac{ u^{\star 3}}{(\kappa D_H /10)} \]

Parameters
[in]uref2square of the reference flow velocity
[in]dhhydraulic diameter \( D_H \)
[in]rhomass density \( \rho \)
[in]mudynamic viscosity \( \nu \)
[out]ustar2square of friction speed
[out]kcalculated turbulent intensity \( k \)
[out]epscalculated turbulent dissipation \( \varepsilon \)

Constructor & Destructor Documentation

◆ turbulence_bc_ke_hyd_diam()

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 
)

The documentation for this interface was generated from the following file: