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!-------------------------------------------------------------------------------
! This file is part of Code_Saturne, a general-purpose CFD tool.
!
! Copyright (C) 1998-2016 EDF S.A.
!
! This program is free software; you can redistribute it and/or modify it under
! the terms of the GNU General Public License as published by the Free Software
! Foundation; either version 2 of the License, or (at your option) any later
! version.
!
! This program is distributed in the hope that it will be useful, but WITHOUT
! ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
! FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
! details.
!
! You should have received a copy of the GNU General Public License along with
! this program; if not, write to the Free Software Foundation, Inc., 51 Franklin
! Street, Fifth Floor, Boston, MA 02110-1301, USA.
!-------------------------------------------------------------------------------
!===============================================================================
! Function:
! --------
!> \file turent.f90
!> \brief Calculation of turbulent inlet conditions for a circular duct flow
!> with smooth wall.
!>
!> \brief Calculation of \f$ u^\star \f$, \f$ k \f$ and \f$\varepsilon \f$
!> from a diameter \f$ D_H \f$ and the reference velocity \f$ U_{ref} \f$
!> for a circular duct flow with smooth wall
!> (use for inlet boundary conditions).
!>
!> Both \f$ u^\star \f$ and\f$ (k,\varepsilon )\f$ are returned, so that
!> the user may compute other values of \f$ k \f$ and \f$ \varepsilon \f$
!> with the \f$ u^\star \f$.
!>
!> We use the laws coming for Idel'Cik, i.e.
!> the head losses coefficient \f$ \lambda \f$ is defined by:
!> \f[ |\dfrac{\Delta P}{\Delta x}| =
!> \dfrac{\lambda}{D_H} \frac{1}{2} \rho U_{ref}^2 \f]
!>
!> then the relation reads \f$u^\star = U_{ref} \sqrt{\dfrac{\lambda}{8}}\f$.
!> \f$\lambda \f$ depends on the hydraulic Reynolds number
!> \f$ Re = \dfrac{U_{ref} D_H}{ \nu} \f$ and is given by:
!> - for \f$ Re < 2000 \f$
!> \f[ \lambda = \dfrac{64}{Re} \f]
!>
!> - for \f$ Re > 4000 \f$
!> \f[ \lambda = \dfrac{1}{( 1.8 \log_{10}(Re)-1.64 )^2} \f]
!>
!> - for \f$ 2000 < Re < 4000 \f$, we complete by a straight line
!> \f[ \lambda = 0.021377 + 5.3115. 10^{-6} Re \f]
!>
!> From \f$ u^\star \f$, we can estimate \f$ k \f$ and \f$ \varepsilon\f$
!> from the well known formulae of developped turbulence
!>
!> \f[ k = \dfrac{u^{\star 2}}{\sqrt{C_\mu}} \f]
!> \f[ \varepsilon = \dfrac{ u^{\star 3}}{(\kappa D_H /10)} \f]
!-------------------------------------------------------------------------------
!-------------------------------------------------------------------------------
! Arguments
!______________________________________________________________________________.
! mode name role
!______________________________________________________________________________!
!> \param[in] uref2 square of the flow speed of reference
!> \param[in] dh hydraulic diameter \f$ D_H \f$
!> \param[in] xrho mass density \f$ \rho \f$
!> \param[in] xmu dynamic viscosity \f$ \nu \f$
!> \param[in] cmu constant \f$ C_\nu \f$
!> \param[in] xkappa constant \f$ \kappa \f$
!> \param[out] ustar2 square of friction speed
!> \param[out] xk calculated turbulent intensity \f$ k \f$
!> \param[out] xeps calculated turbulent dissipation
!> \f$ \varepsilon \f$
!______________________________________________________________________________!
subroutine keendb &
( uref2, dh, xrho, xmu , cmu, xkappa, ustar2, xk, xeps )
!===============================================================================
! Module files
!===============================================================================
!===============================================================================
implicit none
! Arguments
double precision uref2, dh, xrho, xmu , ustar2, xk, xeps
double precision cmu, xkappa
! Local variables
double precision re, xlmbda
!===============================================================================
re = sqrt(uref2)*dh*xrho/xmu
if (re.lt.2000) then
! in this case we calculate directly \f$u*^2\f$ to avoid an issue with
! \f$ xlmbda= \dfrac{64}{Re} \f$ when Re->0
ustar2 = 8.d0*xmu*sqrt(uref2)/xrho/dh
else if (re.lt.4000) then
xlmbda = 0.021377d0 + 5.3115d-6*re
ustar2 = uref2*xlmbda/8.d0
else
xlmbda = 1/( 1.8d0*log(re)/log(10.d0)-1.64d0)**2
ustar2 = uref2*xlmbda/8.d0
endif
xk = ustar2/sqrt(cmu)
xeps = ustar2**1.5d0/(xkappa*dh*0.1d0)
!----
! End
!----
return
end subroutine
!===============================================================================
! Function:
! --------
!> \brief Calculation of \f$ u^\star\f$, \f$ k \f$ and \f$\varepsilon\f$
!> from a diameter \f$ D_H \f$, a turbulent intensity \f$ I \f$
!> and the reference velocity \f$ U_{ref} \f$
!> for a circular duct flow with smooth wall
!> (use for inlet boundary conditions).
!>
!> \f[ k = 1.5 I {U_{ref}}^2 \f]
!> \f[ \varepsilon = 10 \dfrac{{C_\mu}^{0.75} k^{1.5}}{ \kappa D_H} \f]
!-------------------------------------------------------------------------------
!-------------------------------------------------------------------------------
! Arguments
!______________________________________________________________________________.
! mode name role
!______________________________________________________________________________!
!> \param[in] uref2 square of the flow velocity of reference
!> \param[in] xintur turbulent intensity \f$ I \f$
!> \param[in] dh hydraulic diameter \f$ D_H \f$
!> \param[in] cmu constant \f$ C_\mu \f$
!> \param[in] xkappa constant \f$ \kappa \f$
!> \param[out] xk calculated turbulent intensity \f$ k \f$
!> \param[out] xeps calculated turbulent disspation
!> \f$ \varepsilon \f$
!______________________________________________________________________________!
subroutine keenin &
( uref2, xintur, dh, cmu, xkappa, xk, xeps )
!===============================================================================
! Module files
!===============================================================================
!===============================================================================
implicit none
! Arguments
double precision uref2, xintur, dh, cmu, xkappa, xk, xeps
! Local variables
!===============================================================================
xk = 1.5d0*uref2*xintur**2
xeps = 10.d0*cmu**(0.75d0)*xk**1.5d0/(xkappa*dh)
!----
! End
!----
return
end subroutine
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