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!**********************************************************************
! Copyright 1998,1999,2000,2001,2002,2005,2007,2008,2009,2010 *
! Andreas Stohl, Petra Seibert, A. Frank, Gerhard Wotawa, *
! Caroline Forster, Sabine Eckhardt, John Burkhart, Harald Sodemann *
! *
! This file is part of FLEXPART. *
! *
! FLEXPART 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 3 of the License, or *
! (at your option) any later version. *
! *
! FLEXPART 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 FLEXPART. If not, see <http://www.gnu.org/licenses/>. *
!**********************************************************************
subroutine get_settling(itime,xt,yt,zt,nsp,settling)
! i i i i i o
!*****************************************************************************
! *
! This subroutine calculates particle settling velocity. *
! *
! Author: A. Stohl *
! *
! May 2010 *
! *
! Improvement over traditional settling calculation in FLEXPART: *
! generalize to higher Reynolds numbers and also take into account the *
! temperature dependence of dynamic viscosity. *
! *
! Based on: *
! Naeslund E., and Thaning, L. (1991): On the settling velocity in a *
! nonstationary atmosphere, Aerosol Science and Technology 14, 247-256. *
! *
!*****************************************************************************
! *
! Variables: *
! itime [s] current temporal position *
! xt,yt,zt coordinates position for which wind data shall be cal- *
! culated *
! *
! Constants: *
! *
!*****************************************************************************
use par_mod
use com_mod
implicit none
integer :: itime,indz
real :: xt,yt,zt
! Auxiliary variables needed for interpolation
real :: dz1,dz2,dz
real :: rho1(2),tt1(2),temperature,airdens,vis_dyn,vis_kin,viscosity
real :: settling,settling_old,reynolds,c_d
integer :: i,n,nix,njy,indzh,nsp
!*****************************************************************************
! 1. Interpolate temperature and density: nearest neighbor interpolation sufficient
!*****************************************************************************
nix=int(xt)
njy=int(yt)
! Determine the level below the current position for u,v
!*******************************************************
do i=2,nz
if (height(i).gt.zt) then
indz=i-1
goto 6
endif
end do
6 continue
! Vertical distance to the level below and above current position
!****************************************************************
dz=1./(height(indz+1)-height(indz))
dz1=(zt-height(indz))*dz
dz2=(height(indz+1)-zt)*dz
! Bilinear horizontal interpolation
!**********************************
! Loop over 2 levels
!*******************
do n=1,2
indzh=indz+n-1
rho1(n)=rho(nix,njy,indzh,1)
tt1(n)=tt(nix,njy,indzh,1)
end do
! Linear vertical interpolation
!******************************
temperature=dz2*tt1(1)+dz1*tt1(2)
airdens=dz2*rho1(1)+dz1*rho1(2)
vis_dyn=viscosity(temperature)
vis_kin=vis_dyn/airdens
reynolds=dquer(nsp)/1.e6*abs(vsetaver(nsp))/vis_kin
! Iteration to determine both Reynolds number and settling velocity
!******************************************************************
settling_old=vsetaver(nsp) ! initialize iteration with Stokes' law, constant viscosity estimate
do i=1,20 ! do a few iterations
if (reynolds.lt.1.917) then
c_d=24./reynolds
else if (reynolds.lt.500.) then
c_d=18.5/(reynolds**0.6)
else
c_d=0.44
endif
settling=-1.* &
sqrt(4*ga*dquer(nsp)/1.e6*density(nsp)*cunningham(nsp)/ &
(3.*c_d*airdens))
if (abs((settling-settling_old)/settling).lt.0.01) goto 11 ! stop iteration
reynolds=dquer(nsp)/1.e6*abs(settling)/vis_kin
settling_old=settling
end do
11 continue
end subroutine get_settling
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