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 $u^\star$ , and $\varepsilon$ from a diameter , a turbulent intensity 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:

for
$\lambda = \dfrac{64}{Re}$
for
$\lambda = \dfrac{1}{( 1.8 \log_{10}(Re)-1.64 )^2}$
for , 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

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

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

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]	uref2	square of the flow speed of reference
[in]	dh	hydraulic diameter
[in]	xrho	mass density $\rho$
[in]	xmu	dynamic viscosity $\nu$
[in]	cmu	constant $C_\nu$
[in]	xkappa	constant $\kappa$
[out]	ustar2	square of friction speed
[out]	xk	calculated turbulent intensity
[out]	xeps	calculated 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]	uref2	square of the flow velocity of reference
[in]	xintur	turbulent intensity
[in]	dh	hydraulic diameter
[in]	cmu	constant $C_\mu$
[in]	xkappa	constant $\kappa$
[out]	xk	calculated turbulent intensity
[out]	xeps	calculated turbulent disspation $\varepsilon$

Functions/Subroutines

Detailed Description

Function/Subroutine Documentation