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Functions/Subroutines
turent.f90 File Reference

Calculation of turbulent inlet conditions for a circular duct flow with smooth wall. More...

Functions/Subroutines

subroutine keendb (uref2, dh, xrho, xmu, cmu, xkappa, ustar2, xk, xeps)
 
subroutine keenin (uref2, xintur, dh, cmu, xkappa, xk, xeps)
 Calculation of $ u^\star$, $ k $ and $\varepsilon$ from a diameter $ D_H $, a turbulent intensity $ I $ and the reference velocity $ U_{ref} $ for a circular duct flow with smooth wall (use for inlet boundary conditions). More...
 

Detailed Description

Calculation of turbulent inlet conditions for a circular duct flow with smooth wall.

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 the $ u^\star $.

We use the laws coming for Idel'Cik, i.e. the head losses 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:

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

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

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

Function/Subroutine Documentation

subroutine keendb ( double precision  uref2,
double precision  dh,
double precision  xrho,
double precision  xmu,
double precision  cmu,
double precision  xkappa,
double precision  ustar2,
double precision  xk,
double precision  xeps 
)
Parameters
[in]uref2square of the flow speed of reference
[in]dhhydraulic diameter $ D_H $
[in]xrhomass density $ \rho $
[in]xmudynamic viscosity $ \nu $
[in]cmuconstant $ C_\nu $
[in]xkappaconstant $ \kappa $
[out]ustar2square of friction speed
[out]xkcalculated turbulent intensity $ k $
[out]xepscalculated turbulent dissipation $ \varepsilon $
subroutine keenin ( double precision  uref2,
double precision  xintur,
double precision  dh,
double precision  cmu,
double precision  xkappa,
double precision  xk,
double precision  xeps 
)

Calculation of $ u^\star$, $ k $ and $\varepsilon$ from a diameter $ D_H $, a turbulent intensity $ I $ and the reference velocity $ U_{ref} $ for a circular duct flow with smooth wall (use for inlet boundary conditions).

\[ k = 1.5 I {U_{ref}}^2 \]

\[ \varepsilon = 10 \dfrac{{C_\mu}^{0.75} k^{1.5}}{ \kappa D_H} \]

Parameters
[in]uref2square of the flow velocity of reference
[in]xinturturbulent intensity $ I $
[in]dhhydraulic diameter $ D_H $
[in]cmuconstant $ C_\mu $
[in]xkappaconstant $ \kappa $
[out]xkcalculated turbulent intensity $ k $
[out]xepscalculated turbulent disspation $ \varepsilon $