| 1 | MODULE lpm_collision_kernels_mod |
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| 2 | |
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| 3 | !--------------------------------------------------------------------------------! |
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| 4 | ! This file is part of PALM. |
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| 5 | ! |
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| 6 | ! PALM is free software: you can redistribute it and/or modify it under the terms |
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| 7 | ! of the GNU General Public License as published by the Free Software Foundation, |
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| 8 | ! either version 3 of the License, or (at your option) any later version. |
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| 9 | ! |
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| 10 | ! PALM is distributed in the hope that it will be useful, but WITHOUT ANY |
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| 11 | ! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR |
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| 12 | ! A PARTICULAR PURPOSE. See the GNU General Public License for more details. |
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| 13 | ! |
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| 14 | ! You should have received a copy of the GNU General Public License along with |
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| 15 | ! PALM. If not, see <http://www.gnu.org/licenses/>. |
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| 16 | ! |
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| 17 | ! Copyright 1997-2014 Leibniz Universitaet Hannover |
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| 18 | !--------------------------------------------------------------------------------! |
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| 19 | ! |
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| 20 | ! Current revisions: |
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| 21 | ! ----------------- |
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| 22 | ! |
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| 23 | ! |
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| 24 | ! Former revisions: |
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| 25 | ! ----------------- |
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| 26 | ! $Id: lpm_collision_kernels.f90 1347 2014-03-27 13:23:00Z witha $ |
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| 27 | ! |
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| 28 | ! 1346 2014-03-27 13:18:20Z heinze |
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| 29 | ! Bugfix: REAL constants provided with KIND-attribute especially in call of |
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| 30 | ! intrinsic function like MAX, MIN, SIGN |
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| 31 | ! |
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| 32 | ! 1322 2014-03-20 16:38:49Z raasch |
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| 33 | ! REAL constants defined as wp_kind |
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| 34 | ! |
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| 35 | ! 1320 2014-03-20 08:40:49Z |
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| 36 | ! ONLY-attribute added to USE-statements, |
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| 37 | ! kind-parameters added to all INTEGER and REAL declaration statements, |
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| 38 | ! kinds are defined in new module kinds, |
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| 39 | ! revision history before 2012 removed, |
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| 40 | ! comment fields (!:) to be used for variable explanations added to |
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| 41 | ! all variable declaration statements |
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| 42 | ! |
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| 43 | ! 1092 2013-02-02 11:24:22Z raasch |
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| 44 | ! unused variables removed |
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| 45 | ! |
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| 46 | ! 1071 2012-11-29 16:54:55Z franke |
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| 47 | ! Bugfix: collision efficiencies for Hall kernel should not be < 1.0E-20 |
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| 48 | ! |
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| 49 | ! 1036 2012-10-22 13:43:42Z raasch |
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| 50 | ! code put under GPL (PALM 3.9) |
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| 51 | ! |
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| 52 | ! 1007 2012-09-19 14:30:36Z franke |
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| 53 | ! converted all units to SI units and replaced some parameters by corresponding |
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| 54 | ! PALM parameters |
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| 55 | ! Bugfix: factor in calculation of enhancement factor for collision efficencies |
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| 56 | ! changed from 10. to 1.0 |
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| 57 | ! |
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| 58 | ! 849 2012-03-15 10:35:09Z raasch |
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| 59 | ! routine collision_efficiency_rogers added (moved from former advec_particles |
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| 60 | ! to here) |
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| 61 | ! |
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| 62 | ! 835 2012-02-22 11:21:19Z raasch $ |
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| 63 | ! Bugfix: array diss can be used only in case of Wang kernel |
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| 64 | ! |
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| 65 | ! 828 2012-02-21 12:00:36Z raasch |
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| 66 | ! code has been completely reformatted, routine colker renamed |
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| 67 | ! recalculate_kernel, |
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| 68 | ! routine init_kernels added, radius is now communicated to the collision |
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| 69 | ! routines by array radclass |
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| 70 | ! |
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| 71 | ! Bugfix: transformation factor for dissipation changed from 1E5 to 1E4 |
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| 72 | ! |
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| 73 | ! 825 2012-02-19 03:03:44Z raasch |
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| 74 | ! routine renamed from wang_kernel to lpm_collision_kernels, |
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| 75 | ! turbulence_effects on collision replaced by wang_kernel |
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| 76 | ! |
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| 77 | ! 790 2011-11-29 03:11:20Z raasch |
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| 78 | ! initial revision |
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| 79 | ! |
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| 80 | ! Description: |
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| 81 | ! ------------ |
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| 82 | ! This module calculates collision efficiencies either due to pure gravitational |
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| 83 | ! effects (Hall kernel, see Hall, 1980: J. Atmos. Sci., 2486-2507) or |
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| 84 | ! including the effects of (SGS) turbulence (Wang kernel, see Wang and |
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| 85 | ! Grabowski, 2009: Atmos. Sci. Lett., 10, 1-8). The original code has been |
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| 86 | ! provided by L.-P. Wang but is substantially reformatted and speed optimized |
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| 87 | ! here. |
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| 88 | ! |
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| 89 | ! ATTENTION: |
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| 90 | ! Physical quantities (like g, densities, etc.) used in this module still |
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| 91 | ! have to be adjusted to those values used in the main PALM code. |
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| 92 | ! Also, quantities in CGS-units should be converted to SI-units eventually. |
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| 93 | !------------------------------------------------------------------------------! |
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| 94 | |
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| 95 | USE constants, & |
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| 96 | ONLY: pi |
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| 97 | |
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| 98 | USE kinds |
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| 99 | |
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| 100 | USE particle_attributes, & |
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| 101 | ONLY: collision_kernel, dissipation_classes, particles, radius_classes |
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| 102 | |
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| 103 | USE pegrid |
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| 104 | |
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| 105 | |
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| 106 | IMPLICIT NONE |
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| 107 | |
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| 108 | PRIVATE |
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| 109 | |
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| 110 | PUBLIC ckernel, collision_efficiency_rogers, init_kernels, & |
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| 111 | rclass_lbound, rclass_ubound, recalculate_kernel |
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| 112 | |
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| 113 | REAL(wp) :: epsilon !: |
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| 114 | REAL(wp) :: eps2 !: |
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| 115 | REAL(wp) :: rclass_lbound !: |
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| 116 | REAL(wp) :: rclass_ubound !: |
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| 117 | REAL(wp) :: urms !: |
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| 118 | REAL(wp) :: urms2 !: |
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| 119 | |
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| 120 | REAL(wp), DIMENSION(:), ALLOCATABLE :: epsclass !: |
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| 121 | REAL(wp), DIMENSION(:), ALLOCATABLE :: radclass !: |
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| 122 | REAL(wp), DIMENSION(:), ALLOCATABLE :: winf !: |
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| 123 | |
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| 124 | REAL(wp), DIMENSION(:,:), ALLOCATABLE :: ec !: |
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| 125 | REAL(wp), DIMENSION(:,:), ALLOCATABLE :: ecf !: |
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| 126 | REAL(wp), DIMENSION(:,:), ALLOCATABLE :: gck !: |
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| 127 | REAL(wp), DIMENSION(:,:), ALLOCATABLE :: hkernel !: |
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| 128 | REAL(wp), DIMENSION(:,:), ALLOCATABLE :: hwratio !: |
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| 129 | |
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| 130 | REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: ckernel !: |
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| 131 | |
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| 132 | SAVE |
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| 133 | |
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| 134 | ! |
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| 135 | !-- Public interfaces |
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| 136 | INTERFACE collision_efficiency_rogers |
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| 137 | MODULE PROCEDURE collision_efficiency_rogers |
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| 138 | END INTERFACE collision_efficiency_rogers |
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| 139 | |
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| 140 | INTERFACE init_kernels |
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| 141 | MODULE PROCEDURE init_kernels |
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| 142 | END INTERFACE init_kernels |
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| 143 | |
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| 144 | INTERFACE recalculate_kernel |
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| 145 | MODULE PROCEDURE recalculate_kernel |
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| 146 | END INTERFACE recalculate_kernel |
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| 147 | |
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| 148 | |
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| 149 | CONTAINS |
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| 150 | |
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| 151 | |
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| 152 | SUBROUTINE init_kernels |
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| 153 | !------------------------------------------------------------------------------! |
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| 154 | ! Initialization of the collision efficiency matrix with fixed radius and |
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| 155 | ! dissipation classes, calculated at simulation start only. |
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| 156 | !------------------------------------------------------------------------------! |
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| 157 | |
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| 158 | IMPLICIT NONE |
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| 159 | |
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| 160 | INTEGER(iwp) :: i !: |
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| 161 | INTEGER(iwp) :: j !: |
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| 162 | INTEGER(iwp) :: k !: |
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| 163 | |
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| 164 | |
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| 165 | ! |
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| 166 | !-- Calculate collision efficiencies for fixed radius- and dissipation |
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| 167 | !-- classes |
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| 168 | IF ( collision_kernel(6:9) == 'fast' ) THEN |
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| 169 | |
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| 170 | ALLOCATE( ckernel(1:radius_classes,1:radius_classes, & |
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| 171 | 0:dissipation_classes), epsclass(1:dissipation_classes), & |
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| 172 | radclass(1:radius_classes) ) |
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| 173 | |
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| 174 | ! |
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| 175 | !-- Calculate the radius class bounds with logarithmic distances |
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| 176 | !-- in the interval [1.0E-6, 2.0E-4] m |
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| 177 | rclass_lbound = LOG( 1.0E-6_wp ) |
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| 178 | rclass_ubound = LOG( 2.0E-4_wp ) |
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| 179 | radclass(1) = 1.0E-6 |
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| 180 | DO i = 2, radius_classes |
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| 181 | radclass(i) = EXP( rclass_lbound + & |
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| 182 | ( rclass_ubound - rclass_lbound ) * ( i-1.0 ) /& |
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| 183 | ( radius_classes - 1.0 ) ) |
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| 184 | ! IF ( myid == 0 ) THEN |
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| 185 | ! PRINT*, 'i=', i, ' r = ', radclass(i)*1.0E6 |
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| 186 | ! ENDIF |
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| 187 | ENDDO |
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| 188 | |
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| 189 | ! |
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| 190 | !-- Set the class bounds for dissipation in interval [0.0, 0.1] m**2/s**3 |
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| 191 | DO i = 1, dissipation_classes |
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| 192 | epsclass(i) = 0.1 * REAL( i, KIND=wp ) / dissipation_classes |
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| 193 | ! IF ( myid == 0 ) THEN |
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| 194 | ! PRINT*, 'i=', i, ' eps = ', epsclass(i) |
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| 195 | ! ENDIF |
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| 196 | ENDDO |
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| 197 | ! |
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| 198 | !-- Calculate collision efficiencies of the Wang/ayala kernel |
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| 199 | ALLOCATE( ec(1:radius_classes,1:radius_classes), & |
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| 200 | ecf(1:radius_classes,1:radius_classes), & |
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| 201 | gck(1:radius_classes,1:radius_classes), & |
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| 202 | winf(1:radius_classes) ) |
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| 203 | |
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| 204 | DO k = 1, dissipation_classes |
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| 205 | |
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| 206 | epsilon = epsclass(k) |
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| 207 | urms = 2.02 * ( epsilon / 0.04_wp )**( 1.0_wp / 3.0_wp ) |
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| 208 | |
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| 209 | CALL turbsd |
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| 210 | CALL turb_enhance_eff |
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| 211 | CALL effic |
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| 212 | |
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| 213 | DO j = 1, radius_classes |
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| 214 | DO i = 1, radius_classes |
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| 215 | ckernel(i,j,k) = ec(i,j) * gck(i,j) * ecf(i,j) |
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| 216 | ENDDO |
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| 217 | ENDDO |
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| 218 | |
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| 219 | ENDDO |
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| 220 | |
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| 221 | ! |
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| 222 | !-- Calculate collision efficiencies of the Hall kernel |
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| 223 | ALLOCATE( hkernel(1:radius_classes,1:radius_classes), & |
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| 224 | hwratio(1:radius_classes,1:radius_classes) ) |
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| 225 | |
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| 226 | CALL fallg |
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| 227 | CALL effic |
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| 228 | |
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| 229 | DO j = 1, radius_classes |
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| 230 | DO i = 1, radius_classes |
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| 231 | hkernel(i,j) = pi * ( radclass(j) + radclass(i) )**2 & |
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| 232 | * ec(i,j) * ABS( winf(j) - winf(i) ) |
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| 233 | ckernel(i,j,0) = hkernel(i,j) ! hall kernel stored on index 0 |
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| 234 | ENDDO |
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| 235 | ENDDO |
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| 236 | |
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| 237 | ! |
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| 238 | !-- Test output of efficiencies |
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| 239 | IF ( j == -1 ) THEN |
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| 240 | |
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| 241 | PRINT*, '*** Hall kernel' |
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| 242 | WRITE ( *,'(5X,20(F4.0,1X))' ) ( radclass(i)*1.0E6, & |
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| 243 | i = 1,radius_classes ) |
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| 244 | DO j = 1, radius_classes |
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| 245 | WRITE ( *,'(F4.0,1X,20(F8.4,1X))' ) radclass(j), & |
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| 246 | ( hkernel(i,j), i = 1,radius_classes ) |
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| 247 | ENDDO |
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| 248 | |
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| 249 | DO k = 1, dissipation_classes |
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| 250 | DO i = 1, radius_classes |
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| 251 | DO j = 1, radius_classes |
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| 252 | IF ( hkernel(i,j) == 0.0 ) THEN |
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| 253 | hwratio(i,j) = 9999999.9 |
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| 254 | ELSE |
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| 255 | hwratio(i,j) = ckernel(i,j,k) / hkernel(i,j) |
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| 256 | ENDIF |
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| 257 | ENDDO |
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| 258 | ENDDO |
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| 259 | |
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| 260 | PRINT*, '*** epsilon = ', epsclass(k) |
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| 261 | WRITE ( *,'(5X,20(F4.0,1X))' ) ( radclass(i)*1.0E6, & |
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| 262 | i = 1,radius_classes ) |
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| 263 | DO j = 1, radius_classes |
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| 264 | ! WRITE ( *,'(F4.0,1X,20(F4.2,1X))' ) radclass(j)*1.0E6, & |
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| 265 | ! ( ckernel(i,j,k), i = 1,radius_classes ) |
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| 266 | WRITE ( *,'(F4.0,1X,20(F8.4,1X))' ) radclass(j)*1.0E6, & |
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| 267 | ( hwratio(i,j), i = 1,radius_classes ) |
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| 268 | ENDDO |
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| 269 | ENDDO |
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| 270 | |
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| 271 | ENDIF |
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| 272 | |
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| 273 | DEALLOCATE( ec, ecf, epsclass, gck, hkernel, winf ) |
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| 274 | |
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| 275 | ELSEIF( collision_kernel == 'hall' .OR. collision_kernel == 'wang' ) & |
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| 276 | THEN |
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| 277 | ! |
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| 278 | !-- Initial settings for Hall- and Wang-Kernel |
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| 279 | !-- To be done: move here parts from turbsd, fallg, ecoll, etc. |
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| 280 | ENDIF |
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| 281 | |
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| 282 | END SUBROUTINE init_kernels |
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| 283 | |
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| 284 | |
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| 285 | !------------------------------------------------------------------------------! |
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| 286 | ! Calculation of collision kernels during each timestep and for each grid box |
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| 287 | !------------------------------------------------------------------------------! |
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| 288 | SUBROUTINE recalculate_kernel( i1, j1, k1 ) |
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| 289 | |
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| 290 | USE arrays_3d, & |
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| 291 | ONLY: diss |
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| 292 | |
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| 293 | USE particle_attributes, & |
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| 294 | ONLY: prt_count, prt_start_index, radius_classes, wang_kernel |
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| 295 | |
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| 296 | IMPLICIT NONE |
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| 297 | |
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| 298 | INTEGER(iwp) :: i !: |
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| 299 | INTEGER(iwp) :: i1 !: |
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| 300 | INTEGER(iwp) :: j !: |
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| 301 | INTEGER(iwp) :: j1 !: |
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| 302 | INTEGER(iwp) :: k1 !: |
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| 303 | INTEGER(iwp) :: pend !: |
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| 304 | INTEGER(iwp) :: pstart !: |
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| 305 | |
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| 306 | |
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| 307 | pstart = prt_start_index(k1,j1,i1) |
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| 308 | pend = prt_start_index(k1,j1,i1) + prt_count(k1,j1,i1) - 1 |
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| 309 | radius_classes = prt_count(k1,j1,i1) |
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| 310 | |
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| 311 | ALLOCATE( ec(1:radius_classes,1:radius_classes), & |
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| 312 | radclass(1:radius_classes), winf(1:radius_classes) ) |
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| 313 | |
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| 314 | ! |
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| 315 | !-- Store particle radii on the radclass array |
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| 316 | radclass(1:radius_classes) = particles(pstart:pend)%radius |
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| 317 | |
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| 318 | IF ( wang_kernel ) THEN |
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| 319 | epsilon = diss(k1,j1,i1) ! dissipation rate in m**2/s**3 |
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| 320 | ELSE |
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| 321 | epsilon = 0.0 |
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| 322 | ENDIF |
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| 323 | urms = 2.02 * ( epsilon / 0.04_wp )**( 0.33333333333_wp ) |
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| 324 | |
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| 325 | IF ( wang_kernel .AND. epsilon > 1.0E-7 ) THEN |
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| 326 | ! |
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| 327 | !-- Call routines to calculate efficiencies for the Wang kernel |
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| 328 | ALLOCATE( gck(1:radius_classes,1:radius_classes), & |
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| 329 | ecf(1:radius_classes,1:radius_classes) ) |
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| 330 | |
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| 331 | CALL turbsd |
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| 332 | CALL turb_enhance_eff |
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| 333 | CALL effic |
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| 334 | |
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| 335 | DO j = 1, radius_classes |
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| 336 | DO i = 1, radius_classes |
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| 337 | ckernel(pstart+i-1,pstart+j-1,1) = ec(i,j) * gck(i,j) * ecf(i,j) |
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| 338 | ENDDO |
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| 339 | ENDDO |
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| 340 | |
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| 341 | DEALLOCATE( gck, ecf ) |
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| 342 | |
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| 343 | ELSE |
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| 344 | ! |
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| 345 | !-- Call routines to calculate efficiencies for the Hall kernel |
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| 346 | CALL fallg |
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| 347 | CALL effic |
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| 348 | |
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| 349 | DO j = 1, radius_classes |
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| 350 | DO i = 1, radius_classes |
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| 351 | ckernel(pstart+i-1,pstart+j-1,1) = pi * & |
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| 352 | ( radclass(j) + radclass(i) )**2 & |
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| 353 | * ec(i,j) * ABS( winf(j) - winf(i) ) |
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| 354 | ENDDO |
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| 355 | ENDDO |
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| 356 | |
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| 357 | ENDIF |
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| 358 | |
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| 359 | DEALLOCATE( ec, radclass, winf ) |
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| 360 | |
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| 361 | END SUBROUTINE recalculate_kernel |
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| 362 | |
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| 363 | |
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| 364 | !------------------------------------------------------------------------------! |
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| 365 | ! Calculation of gck |
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| 366 | ! This is from Aayala 2008b, page 37ff. |
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| 367 | ! Necessary input parameters: water density, radii of droplets, air density, |
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| 368 | ! air viscosity, turbulent dissipation rate, taylor microscale reynolds number, |
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| 369 | ! gravitational acceleration --> to be replaced by PALM parameters |
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| 370 | !------------------------------------------------------------------------------! |
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| 371 | SUBROUTINE turbsd |
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| 372 | |
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| 373 | USE control_parameters, & |
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| 374 | ONLY: g, molecular_viscosity |
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| 375 | |
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| 376 | USE particle_attributes, & |
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| 377 | ONLY: radius_classes |
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| 378 | |
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| 379 | IMPLICIT NONE |
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| 380 | |
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| 381 | LOGICAL, SAVE :: first = .TRUE. !: |
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| 382 | |
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| 383 | INTEGER(iwp) :: i !: |
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| 384 | INTEGER(iwp) :: j !: |
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| 385 | |
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| 386 | REAL(wp) :: ao !: |
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| 387 | REAL(wp) :: ao_gr !: |
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| 388 | REAL(wp) :: bbb !: |
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| 389 | REAL(wp) :: be !: |
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| 390 | REAL(wp) :: b1 !: |
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| 391 | REAL(wp) :: b2 !: |
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| 392 | REAL(wp) :: ccc !: |
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| 393 | REAL(wp) :: c1 !: |
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| 394 | REAL(wp) :: c1_gr !: |
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| 395 | REAL(wp) :: c2 !: |
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| 396 | REAL(wp) :: d1 !: |
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| 397 | REAL(wp) :: d2 !: |
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| 398 | REAL(wp) :: eta !: |
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| 399 | REAL(wp) :: e1 !: |
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| 400 | REAL(wp) :: e2 !: |
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| 401 | REAL(wp) :: fao_gr !: |
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| 402 | REAL(wp) :: fr !: |
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| 403 | REAL(wp) :: grfin !: |
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| 404 | REAL(wp) :: lambda !: |
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| 405 | REAL(wp) :: lambda_re !: |
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| 406 | REAL(wp) :: lf !: |
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| 407 | REAL(wp) :: rc !: |
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| 408 | REAL(wp) :: rrp !: |
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| 409 | REAL(wp) :: sst !: |
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| 410 | REAL(wp) :: tauk !: |
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| 411 | REAL(wp) :: tl !: |
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| 412 | REAL(wp) :: t2 !: |
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| 413 | REAL(wp) :: tt !: |
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| 414 | REAL(wp) :: t1 !: |
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| 415 | REAL(wp) :: vk !: |
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| 416 | REAL(wp) :: vrms1xy !: |
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| 417 | REAL(wp) :: vrms2xy !: |
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| 418 | REAL(wp) :: v1 !: |
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| 419 | REAL(wp) :: v1v2xy !: |
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| 420 | REAL(wp) :: v1xysq !: |
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| 421 | REAL(wp) :: v2 !: |
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| 422 | REAL(wp) :: v2xysq !: |
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| 423 | REAL(wp) :: wrfin !: |
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| 424 | REAL(wp) :: wrgrav2 !: |
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| 425 | REAL(wp) :: wrtur2xy !: |
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| 426 | REAL(wp) :: xx !: |
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| 427 | REAL(wp) :: yy !: |
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| 428 | REAL(wp) :: z !: |
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| 429 | |
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| 430 | REAL(wp), DIMENSION(1:radius_classes) :: st !: |
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| 431 | REAL(wp), DIMENSION(1:radius_classes) :: tau !: |
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| 432 | |
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| 433 | ! |
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| 434 | !-- Initial assignment of constants |
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| 435 | IF ( first ) THEN |
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| 436 | |
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| 437 | first = .FALSE. |
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| 438 | |
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| 439 | ENDIF |
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| 440 | |
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| 441 | lambda = urms * SQRT( 15.0_wp * molecular_viscosity / epsilon ) ! in m |
|---|
| 442 | lambda_re = urms**2 * SQRT( 15.0_wp / epsilon / molecular_viscosity ) |
|---|
| 443 | tl = urms**2 / epsilon ! in s |
|---|
| 444 | lf = 0.5 * urms**3 / epsilon ! in m |
|---|
| 445 | tauk = SQRT( molecular_viscosity / epsilon ) ! in s |
|---|
| 446 | eta = ( molecular_viscosity**3 / epsilon )**0.25_wp ! in m |
|---|
| 447 | vk = eta / tauk |
|---|
| 448 | |
|---|
| 449 | ao = ( 11.0 + 7.0 * lambda_re ) / ( 205.0 + lambda_re ) |
|---|
| 450 | tt = SQRT( 2.0 * lambda_re / ( SQRT( 15.0_wp ) * ao ) ) * tauk ! in s |
|---|
| 451 | |
|---|
| 452 | CALL fallg ! gives winf in m/s |
|---|
| 453 | |
|---|
| 454 | DO i = 1, radius_classes |
|---|
| 455 | tau(i) = winf(i) / g ! in s |
|---|
| 456 | st(i) = tau(i) / tauk |
|---|
| 457 | ENDDO |
|---|
| 458 | |
|---|
| 459 | ! |
|---|
| 460 | !-- Calculate wr (from Aayala 2008b, page 38f) |
|---|
| 461 | z = tt / tl |
|---|
| 462 | be = SQRT( 2.0_wp ) * lambda / lf |
|---|
| 463 | bbb = SQRT( 1.0 - 2.0 * be**2 ) |
|---|
| 464 | d1 = ( 1.0 + bbb ) / ( 2.0 * bbb ) |
|---|
| 465 | e1 = lf * ( 1.0 + bbb ) * 0.5 ! in m |
|---|
| 466 | d2 = ( 1.0 - bbb ) * 0.5 / bbb |
|---|
| 467 | e2 = lf * ( 1.0 - bbb ) * 0.5 ! in m |
|---|
| 468 | ccc = SQRT( 1.0 - 2.0 * z**2 ) |
|---|
| 469 | b1 = ( 1.0 + ccc ) * 0.5 / ccc |
|---|
| 470 | c1 = tl * ( 1.0 + ccc ) * 0.5 ! in s |
|---|
| 471 | b2 = ( 1.0 - ccc ) * 0.5 / ccc |
|---|
| 472 | c2 = tl * ( 1.0 - ccc ) * 0.5 ! in s |
|---|
| 473 | |
|---|
| 474 | DO i = 1, radius_classes |
|---|
| 475 | |
|---|
| 476 | v1 = winf(i) ! in m/s |
|---|
| 477 | t1 = tau(i) ! in s |
|---|
| 478 | |
|---|
| 479 | DO j = 1, i |
|---|
| 480 | rrp = radclass(i) + radclass(j) |
|---|
| 481 | v2 = winf(j) ! in m/s |
|---|
| 482 | t2 = tau(j) ! in s |
|---|
| 483 | |
|---|
| 484 | v1xysq = b1 * d1 * phi_w(c1,e1,v1,t1) - b1 * d2 * phi_w(c1,e2,v1,t1) & |
|---|
| 485 | - b2 * d1 * phi_w(c2,e1,v1,t1) + b2 * d2 * phi_w(c2,e2,v1,t1) |
|---|
| 486 | v1xysq = v1xysq * urms**2 / t1 ! in m**2/s**2 |
|---|
| 487 | vrms1xy = SQRT( v1xysq ) ! in m/s |
|---|
| 488 | |
|---|
| 489 | v2xysq = b1 * d1 * phi_w(c1,e1,v2,t2) - b1 * d2 * phi_w(c1,e2,v2,t2) & |
|---|
| 490 | - b2 * d1 * phi_w(c2,e1,v2,t2) + b2 * d2 * phi_w(c2,e2,v2,t2) |
|---|
| 491 | v2xysq = v2xysq * urms**2 / t2 ! in m**2/s**2 |
|---|
| 492 | vrms2xy = SQRT( v2xysq ) ! in m/s |
|---|
| 493 | |
|---|
| 494 | IF ( winf(i) >= winf(j) ) THEN |
|---|
| 495 | v1 = winf(i) |
|---|
| 496 | t1 = tau(i) |
|---|
| 497 | v2 = winf(j) |
|---|
| 498 | t2 = tau(j) |
|---|
| 499 | ELSE |
|---|
| 500 | v1 = winf(j) |
|---|
| 501 | t1 = tau(j) |
|---|
| 502 | v2 = winf(i) |
|---|
| 503 | t2 = tau(i) |
|---|
| 504 | ENDIF |
|---|
| 505 | |
|---|
| 506 | v1v2xy = b1 * d1 * zhi(c1,e1,v1,t1,v2,t2) - & |
|---|
| 507 | b1 * d2 * zhi(c1,e2,v1,t1,v2,t2) - & |
|---|
| 508 | b2 * d1 * zhi(c2,e1,v1,t1,v2,t2) + & |
|---|
| 509 | b2 * d2* zhi(c2,e2,v1,t1,v2,t2) |
|---|
| 510 | fr = d1 * EXP( -rrp / e1 ) - d2 * EXP( -rrp / e2 ) |
|---|
| 511 | v1v2xy = v1v2xy * fr * urms**2 / tau(i) / tau(j) ! in m**2/s**2 |
|---|
| 512 | wrtur2xy = vrms1xy**2 + vrms2xy**2 - 2.0 * v1v2xy ! in m**2/s**2 |
|---|
| 513 | IF ( wrtur2xy < 0.0 ) wrtur2xy = 0.0 |
|---|
| 514 | wrgrav2 = pi / 8.0_wp * ( winf(j) - winf(i) )**2 |
|---|
| 515 | wrfin = SQRT( ( 2.0_wp / pi ) * ( wrtur2xy + wrgrav2) ) ! in m/s |
|---|
| 516 | |
|---|
| 517 | ! |
|---|
| 518 | !-- Calculate gr |
|---|
| 519 | IF ( st(j) > st(i) ) THEN |
|---|
| 520 | sst = st(j) |
|---|
| 521 | ELSE |
|---|
| 522 | sst = st(i) |
|---|
| 523 | ENDIF |
|---|
| 524 | |
|---|
| 525 | xx = -0.1988 * sst**4 + 1.5275 * sst**3 - 4.2942 * sst**2 + & |
|---|
| 526 | 5.3406 * sst |
|---|
| 527 | IF ( xx < 0.0 ) xx = 0.0 |
|---|
| 528 | yy = 0.1886 * EXP( 20.306_wp / lambda_re ) |
|---|
| 529 | |
|---|
| 530 | c1_gr = xx / ( g / vk * tauk )**yy |
|---|
| 531 | |
|---|
| 532 | ao_gr = ao + ( pi / 8.0_wp) * ( g / vk * tauk )**2 |
|---|
| 533 | fao_gr = 20.115 * SQRT( ao_gr / lambda_re ) |
|---|
| 534 | rc = SQRT( fao_gr * ABS( st(j) - st(i) ) ) * eta ! in cm |
|---|
| 535 | |
|---|
| 536 | grfin = ( ( eta**2 + rc**2 ) / ( rrp**2 + rc**2) )**( c1_gr*0.5 ) |
|---|
| 537 | IF ( grfin < 1.0 ) grfin = 1.0 |
|---|
| 538 | |
|---|
| 539 | gck(i,j) = 2.0 * pi * rrp**2 * wrfin * grfin ! in cm**3/s |
|---|
| 540 | gck(j,i) = gck(i,j) |
|---|
| 541 | |
|---|
| 542 | ENDDO |
|---|
| 543 | ENDDO |
|---|
| 544 | |
|---|
| 545 | END SUBROUTINE turbsd |
|---|
| 546 | |
|---|
| 547 | |
|---|
| 548 | !------------------------------------------------------------------------------! |
|---|
| 549 | ! phi_w as a function |
|---|
| 550 | !------------------------------------------------------------------------------! |
|---|
| 551 | REAL(wp) FUNCTION phi_w( a, b, vsett, tau0 ) |
|---|
| 552 | |
|---|
| 553 | IMPLICIT NONE |
|---|
| 554 | |
|---|
| 555 | REAL(wp) :: a !: |
|---|
| 556 | REAL(wp) :: aa1 !: |
|---|
| 557 | REAL(wp) :: b !: |
|---|
| 558 | REAL(wp) :: tau0 !: |
|---|
| 559 | REAL(wp) :: vsett !: |
|---|
| 560 | |
|---|
| 561 | aa1 = 1.0 / tau0 + 1.0 / a + vsett / b |
|---|
| 562 | phi_w = 1.0 / aa1 - 0.5 * vsett / b / aa1**2 ! in s |
|---|
| 563 | |
|---|
| 564 | END FUNCTION phi_w |
|---|
| 565 | |
|---|
| 566 | |
|---|
| 567 | !------------------------------------------------------------------------------! |
|---|
| 568 | ! zhi as a function |
|---|
| 569 | !------------------------------------------------------------------------------! |
|---|
| 570 | REAL(wp) FUNCTION zhi( a, b, vsett1, tau1, vsett2, tau2 ) |
|---|
| 571 | |
|---|
| 572 | IMPLICIT NONE |
|---|
| 573 | |
|---|
| 574 | REAL(wp) :: a !: |
|---|
| 575 | REAL(wp) :: aa1 !: |
|---|
| 576 | REAL(wp) :: aa2 !: |
|---|
| 577 | REAL(wp) :: aa3 !: |
|---|
| 578 | REAL(wp) :: aa4 !: |
|---|
| 579 | REAL(wp) :: aa5 !: |
|---|
| 580 | REAL(wp) :: aa6 !: |
|---|
| 581 | REAL(wp) :: b !: |
|---|
| 582 | REAL(wp) :: tau1 !: |
|---|
| 583 | REAL(wp) :: tau2 !: |
|---|
| 584 | REAL(wp) :: vsett1 !: |
|---|
| 585 | REAL(wp) :: vsett2 !: |
|---|
| 586 | |
|---|
| 587 | aa1 = vsett2 / b - 1.0 / tau2 - 1.0 / a |
|---|
| 588 | aa2 = vsett1 / b + 1.0 / tau1 + 1.0 / a |
|---|
| 589 | aa3 = ( vsett1 - vsett2 ) / b + 1.0 / tau1 + 1.0 / tau2 |
|---|
| 590 | aa4 = ( vsett2 / b )**2 - ( 1.0 / tau2 + 1.0 / a )**2 |
|---|
| 591 | aa5 = vsett2 / b + 1.0 / tau2 + 1.0 / a |
|---|
| 592 | aa6 = 1.0 / tau1 - 1.0 / a + ( 1.0 / tau2 + 1.0 / a) * vsett1 / vsett2 |
|---|
| 593 | zhi = (1.0 / aa1 - 1.0 / aa2 ) * ( vsett1 - vsett2 ) * 0.5 / b / aa3**2 & |
|---|
| 594 | + (4.0 / aa4 - 1.0 / aa5**2 - 1.0 / aa1**2 ) * vsett2 * 0.5 / b /aa6& |
|---|
| 595 | + (2.0 * ( b / aa2 - b / aa1 ) - vsett1 / aa2**2 + vsett2 / aa1**2 )& |
|---|
| 596 | * 0.5 / b / aa3 ! in s**2 |
|---|
| 597 | |
|---|
| 598 | END FUNCTION zhi |
|---|
| 599 | |
|---|
| 600 | |
|---|
| 601 | !------------------------------------------------------------------------------! |
|---|
| 602 | ! Calculation of terminal velocity winf following Equations 10-138 to 10-145 |
|---|
| 603 | ! from (Pruppacher and Klett, 1997) |
|---|
| 604 | !------------------------------------------------------------------------------! |
|---|
| 605 | SUBROUTINE fallg |
|---|
| 606 | |
|---|
| 607 | USE cloud_parameters, & |
|---|
| 608 | ONLY: rho_l |
|---|
| 609 | |
|---|
| 610 | USE control_parameters, & |
|---|
| 611 | ONLY: g |
|---|
| 612 | |
|---|
| 613 | USE particle_attributes, & |
|---|
| 614 | ONLY: radius_classes |
|---|
| 615 | |
|---|
| 616 | |
|---|
| 617 | IMPLICIT NONE |
|---|
| 618 | |
|---|
| 619 | INTEGER(iwp) :: i !: |
|---|
| 620 | INTEGER(iwp) :: j !: |
|---|
| 621 | |
|---|
| 622 | LOGICAL, SAVE :: first = .TRUE. !: |
|---|
| 623 | |
|---|
| 624 | REAL(wp), SAVE :: cunh !: |
|---|
| 625 | REAL(wp), SAVE :: eta !: |
|---|
| 626 | REAL(wp), SAVE :: phy !: |
|---|
| 627 | REAL(wp), SAVE :: py !: |
|---|
| 628 | REAL(wp), SAVE :: rho_a !: |
|---|
| 629 | REAL(wp), SAVE :: sigma !: |
|---|
| 630 | REAL(wp), SAVE :: stb !: |
|---|
| 631 | REAL(wp), SAVE :: stok !: |
|---|
| 632 | REAL(wp), SAVE :: xlamb !: |
|---|
| 633 | |
|---|
| 634 | REAL(wp) :: bond !: |
|---|
| 635 | REAL(wp) :: x !: |
|---|
| 636 | REAL(wp) :: xrey !: |
|---|
| 637 | REAL(wp) :: y !: |
|---|
| 638 | |
|---|
| 639 | REAL(wp), DIMENSION(1:7), SAVE :: b !: |
|---|
| 640 | REAL(wp), DIMENSION(1:6), SAVE :: c !: |
|---|
| 641 | |
|---|
| 642 | ! |
|---|
| 643 | !-- Initial assignment of constants |
|---|
| 644 | IF ( first ) THEN |
|---|
| 645 | |
|---|
| 646 | first = .FALSE. |
|---|
| 647 | b = (/ -0.318657E1, 0.992696E0, -0.153193E-2, -0.987059E-3, & |
|---|
| 648 | -0.578878E-3, 0.855176E-4, -0.327815E-5 /) |
|---|
| 649 | c = (/ -0.500015E1, 0.523778E1, -0.204914E1, 0.475294E0, & |
|---|
| 650 | -0.542819E-1, 0.238449E-2 /) |
|---|
| 651 | |
|---|
| 652 | ! |
|---|
| 653 | !-- Parameter values for p = 1013,25 hPa and T = 293,15 K |
|---|
| 654 | eta = 1.818E-5 ! in kg/(m s) |
|---|
| 655 | xlamb = 6.6E-8 ! in m |
|---|
| 656 | rho_a = 1.204 ! in kg/m**3 |
|---|
| 657 | cunh = 1.26 * xlamb ! in m |
|---|
| 658 | sigma = 0.07363 ! in kg/s**2 |
|---|
| 659 | stok = 2.0 * g * ( rho_l - rho_a ) / ( 9.0 * eta ) ! in 1/(m s) |
|---|
| 660 | stb = 32.0 * rho_a * ( rho_l - rho_a) * g / (3.0 * eta * eta) |
|---|
| 661 | phy = sigma**3 * rho_a**2 / ( eta**4 * g * ( rho_l - rho_a ) ) |
|---|
| 662 | py = phy**( 1.0_wp / 6.0_wp ) |
|---|
| 663 | |
|---|
| 664 | ENDIF |
|---|
| 665 | |
|---|
| 666 | DO j = 1, radius_classes |
|---|
| 667 | |
|---|
| 668 | IF ( radclass(j) <= 1.0E-5 ) THEN |
|---|
| 669 | |
|---|
| 670 | winf(j) = stok * ( radclass(j)**2 + cunh * radclass(j) ) |
|---|
| 671 | |
|---|
| 672 | ELSEIF ( radclass(j) > 1.0E-5 .AND. radclass(j) <= 5.35E-4 ) THEN |
|---|
| 673 | |
|---|
| 674 | x = LOG( stb * radclass(j)**3 ) |
|---|
| 675 | y = 0.0 |
|---|
| 676 | |
|---|
| 677 | DO i = 1, 7 |
|---|
| 678 | y = y + b(i) * x**(i-1) |
|---|
| 679 | ENDDO |
|---|
| 680 | ! |
|---|
| 681 | !-- Note: this Eq. is wrong in (Pruppacher and Klett, 1997, p. 418) |
|---|
| 682 | !-- for correct version see (Beard, 1976) |
|---|
| 683 | xrey = ( 1.0 + cunh / radclass(j) ) * EXP( y ) |
|---|
| 684 | |
|---|
| 685 | winf(j) = xrey * eta / ( 2.0 * rho_a * radclass(j) ) |
|---|
| 686 | |
|---|
| 687 | ELSEIF ( radclass(j) > 5.35E-4 ) THEN |
|---|
| 688 | |
|---|
| 689 | IF ( radclass(j) > 0.0035 ) THEN |
|---|
| 690 | bond = g * ( rho_l - rho_a ) * 0.0035**2 / sigma |
|---|
| 691 | ELSE |
|---|
| 692 | bond = g * ( rho_l - rho_a ) * radclass(j)**2 / sigma |
|---|
| 693 | ENDIF |
|---|
| 694 | |
|---|
| 695 | x = LOG( 16.0 * bond * py / 3.0_wp ) |
|---|
| 696 | y = 0.0 |
|---|
| 697 | |
|---|
| 698 | DO i = 1, 6 |
|---|
| 699 | y = y + c(i) * x**(i-1) |
|---|
| 700 | ENDDO |
|---|
| 701 | |
|---|
| 702 | xrey = py * EXP( y ) |
|---|
| 703 | |
|---|
| 704 | IF ( radclass(j) > 0.0035 ) THEN |
|---|
| 705 | winf(j) = xrey * eta / ( 2.0 * rho_a * 0.0035_wp ) |
|---|
| 706 | ELSE |
|---|
| 707 | winf(j) = xrey * eta / ( 2.0 * rho_a * radclass(j) ) |
|---|
| 708 | ENDIF |
|---|
| 709 | |
|---|
| 710 | ENDIF |
|---|
| 711 | |
|---|
| 712 | ENDDO |
|---|
| 713 | |
|---|
| 714 | END SUBROUTINE fallg |
|---|
| 715 | |
|---|
| 716 | |
|---|
| 717 | !------------------------------------------------------------------------------! |
|---|
| 718 | ! Calculation of collision efficiencies for the Hall kernel |
|---|
| 719 | !------------------------------------------------------------------------------! |
|---|
| 720 | SUBROUTINE effic |
|---|
| 721 | |
|---|
| 722 | USE particle_attributes, & |
|---|
| 723 | ONLY: radius_classes |
|---|
| 724 | |
|---|
| 725 | IMPLICIT NONE |
|---|
| 726 | |
|---|
| 727 | INTEGER(iwp) :: i !: |
|---|
| 728 | INTEGER(iwp) :: iq !: |
|---|
| 729 | INTEGER(iwp) :: ir !: |
|---|
| 730 | INTEGER(iwp) :: j !: |
|---|
| 731 | INTEGER(iwp) :: k !: |
|---|
| 732 | |
|---|
| 733 | INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: ira !: |
|---|
| 734 | |
|---|
| 735 | LOGICAL, SAVE :: first = .TRUE. !: |
|---|
| 736 | |
|---|
| 737 | REAL(wp) :: ek !: |
|---|
| 738 | REAL(wp) :: particle_radius !: |
|---|
| 739 | REAL(wp) :: pp !: |
|---|
| 740 | REAL(wp) :: qq !: |
|---|
| 741 | REAL(wp) :: rq !: |
|---|
| 742 | |
|---|
| 743 | REAL(wp), DIMENSION(1:21), SAVE :: rat !: |
|---|
| 744 | |
|---|
| 745 | REAL(wp), DIMENSION(1:15), SAVE :: r0 !: |
|---|
| 746 | |
|---|
| 747 | REAL(wp), DIMENSION(1:15,1:21), SAVE :: ecoll !: |
|---|
| 748 | |
|---|
| 749 | ! |
|---|
| 750 | !-- Initial assignment of constants |
|---|
| 751 | IF ( first ) THEN |
|---|
| 752 | |
|---|
| 753 | first = .FALSE. |
|---|
| 754 | r0 = (/ 6.0, 8.0, 10.0, 15.0, 20.0, 25.0, 30.0, 40.0, 50.0, 60., & |
|---|
| 755 | 70.0, 100.0, 150.0, 200.0, 300.0 /) |
|---|
| 756 | rat = (/ 0.00, 0.05, 0.10, 0.15, 0.20, 0.25, 0.30, 0.35, 0.40, 0.45, & |
|---|
| 757 | 0.50, 0.55, 0.60, 0.65, 0.70, 0.75, 0.80, 0.85, 0.90, 0.95, & |
|---|
| 758 | 1.00 /) |
|---|
| 759 | |
|---|
| 760 | ecoll(:,1) = (/0.001, 0.001, 0.001, 0.001, 0.001, 0.001, 0.001, & |
|---|
| 761 | 0.001, 0.001, 0.001, 0.001, 0.001, 0.001, 0.001, 0.001/) |
|---|
| 762 | ecoll(:,2) = (/0.003, 0.003, 0.003, 0.004, 0.005, 0.005, 0.005, & |
|---|
| 763 | 0.010, 0.100, 0.050, 0.200, 0.500, 0.770, 0.870, 0.970/) |
|---|
| 764 | ecoll(:,3) = (/0.007, 0.007, 0.007, 0.008, 0.009, 0.010, 0.010, & |
|---|
| 765 | 0.070, 0.400, 0.430, 0.580, 0.790, 0.930, 0.960, 1.000/) |
|---|
| 766 | ecoll(:,4) = (/0.009, 0.009, 0.009, 0.012, 0.015, 0.010, 0.020, & |
|---|
| 767 | 0.280, 0.600, 0.640, 0.750, 0.910, 0.970, 0.980, 1.000/) |
|---|
| 768 | ecoll(:,5) = (/0.014, 0.014, 0.014, 0.015, 0.016, 0.030, 0.060, & |
|---|
| 769 | 0.500, 0.700, 0.770, 0.840, 0.950, 0.970, 1.000, 1.000/) |
|---|
| 770 | ecoll(:,6) = (/0.017, 0.017, 0.017, 0.020, 0.022, 0.060, 0.100, & |
|---|
| 771 | 0.620, 0.780, 0.840, 0.880, 0.950, 1.000, 1.000, 1.000/) |
|---|
| 772 | ecoll(:,7) = (/0.030, 0.030, 0.024, 0.022, 0.032, 0.062, 0.200, & |
|---|
| 773 | 0.680, 0.830, 0.870, 0.900, 0.950, 1.000, 1.000, 1.000/) |
|---|
| 774 | ecoll(:,8) = (/0.025, 0.025, 0.025, 0.036, 0.043, 0.130, 0.270, & |
|---|
| 775 | 0.740, 0.860, 0.890, 0.920, 1.000, 1.000, 1.000, 1.000/) |
|---|
| 776 | ecoll(:,9) = (/0.027, 0.027, 0.027, 0.040, 0.052, 0.200, 0.400, & |
|---|
| 777 | 0.780, 0.880, 0.900, 0.940, 1.000, 1.000, 1.000, 1.000/) |
|---|
| 778 | ecoll(:,10)= (/0.030, 0.030, 0.030, 0.047, 0.064, 0.250, 0.500, & |
|---|
| 779 | 0.800, 0.900, 0.910, 0.950, 1.000, 1.000, 1.000, 1.000/) |
|---|
| 780 | ecoll(:,11)= (/0.040, 0.040, 0.033, 0.037, 0.068, 0.240, 0.550, & |
|---|
| 781 | 0.800, 0.900, 0.910, 0.950, 1.000, 1.000, 1.000, 1.000/) |
|---|
| 782 | ecoll(:,12)= (/0.035, 0.035, 0.035, 0.055, 0.079, 0.290, 0.580, & |
|---|
| 783 | 0.800, 0.900, 0.910, 0.950, 1.000, 1.000, 1.000, 1.000/) |
|---|
| 784 | ecoll(:,13)= (/0.037, 0.037, 0.037, 0.062, 0.082, 0.290, 0.590, & |
|---|
| 785 | 0.780, 0.900, 0.910, 0.950, 1.000, 1.000, 1.000, 1.000/) |
|---|
| 786 | ecoll(:,14)= (/0.037, 0.037, 0.037, 0.060, 0.080, 0.290, 0.580, & |
|---|
| 787 | 0.770, 0.890, 0.910, 0.950, 1.000, 1.000, 1.000, 1.000/) |
|---|
| 788 | ecoll(:,15)= (/0.037, 0.037, 0.037, 0.041, 0.075, 0.250, 0.540, & |
|---|
| 789 | 0.760, 0.880, 0.920, 0.950, 1.000, 1.000, 1.000, 1.000/) |
|---|
| 790 | ecoll(:,16)= (/0.037, 0.037, 0.037, 0.052, 0.067, 0.250, 0.510, & |
|---|
| 791 | 0.770, 0.880, 0.930, 0.970, 1.000, 1.000, 1.000, 1.000/) |
|---|
| 792 | ecoll(:,17)= (/0.037, 0.037, 0.037, 0.047, 0.057, 0.250, 0.490, & |
|---|
| 793 | 0.770, 0.890, 0.950, 1.000, 1.000, 1.000, 1.000, 1.000/) |
|---|
| 794 | ecoll(:,18)= (/0.036, 0.036, 0.036, 0.042, 0.048, 0.230, 0.470, & |
|---|
| 795 | 0.780, 0.920, 1.000, 1.020, 1.020, 1.020, 1.020, 1.020/) |
|---|
| 796 | ecoll(:,19)= (/0.040, 0.040, 0.035, 0.033, 0.040, 0.112, 0.450, & |
|---|
| 797 | 0.790, 1.010, 1.030, 1.040, 1.040, 1.040, 1.040, 1.040/) |
|---|
| 798 | ecoll(:,20)= (/0.033, 0.033, 0.033, 0.033, 0.033, 0.119, 0.470, & |
|---|
| 799 | 0.950, 1.300, 1.700, 2.300, 2.300, 2.300, 2.300, 2.300/) |
|---|
| 800 | ecoll(:,21)= (/0.027, 0.027, 0.027, 0.027, 0.027, 0.125, 0.520, & |
|---|
| 801 | 1.400, 2.300, 3.000, 4.000, 4.000, 4.000, 4.000, 4.000/) |
|---|
| 802 | ENDIF |
|---|
| 803 | |
|---|
| 804 | ! |
|---|
| 805 | !-- Calculate the radius class index of particles with respect to array r |
|---|
| 806 | !-- Radius has to be in µm |
|---|
| 807 | ALLOCATE( ira(1:radius_classes) ) |
|---|
| 808 | DO j = 1, radius_classes |
|---|
| 809 | particle_radius = radclass(j) * 1.0E6_wp |
|---|
| 810 | DO k = 1, 15 |
|---|
| 811 | IF ( particle_radius < r0(k) ) THEN |
|---|
| 812 | ira(j) = k |
|---|
| 813 | EXIT |
|---|
| 814 | ENDIF |
|---|
| 815 | ENDDO |
|---|
| 816 | IF ( particle_radius >= r0(15) ) ira(j) = 16 |
|---|
| 817 | ENDDO |
|---|
| 818 | |
|---|
| 819 | ! |
|---|
| 820 | !-- Two-dimensional linear interpolation of the collision efficiency. |
|---|
| 821 | !-- Radius has to be in µm |
|---|
| 822 | DO j = 1, radius_classes |
|---|
| 823 | DO i = 1, j |
|---|
| 824 | |
|---|
| 825 | ir = ira(j) |
|---|
| 826 | rq = radclass(i) / radclass(j) |
|---|
| 827 | iq = INT( rq * 20 ) + 1 |
|---|
| 828 | iq = MAX( iq , 2) |
|---|
| 829 | |
|---|
| 830 | IF ( ir < 16 ) THEN |
|---|
| 831 | IF ( ir >= 2 ) THEN |
|---|
| 832 | pp = ( ( radclass(j) * 1.0E06_wp ) - r0(ir-1) ) / & |
|---|
| 833 | ( r0(ir) - r0(ir-1) ) |
|---|
| 834 | qq = ( rq- rat(iq-1) ) / ( rat(iq) - rat(iq-1) ) |
|---|
| 835 | ec(j,i) = ( 1.0-pp ) * ( 1.0-qq ) * ecoll(ir-1,iq-1) & |
|---|
| 836 | + pp * ( 1.0-qq ) * ecoll(ir,iq-1) & |
|---|
| 837 | + qq * ( 1.0-pp ) * ecoll(ir-1,iq) & |
|---|
| 838 | + pp * qq * ecoll(ir,iq) |
|---|
| 839 | ELSE |
|---|
| 840 | qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) ) |
|---|
| 841 | ec(j,i) = (1.0-qq) * ecoll(1,iq-1) + qq * ecoll(1,iq) |
|---|
| 842 | ENDIF |
|---|
| 843 | ELSE |
|---|
| 844 | qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) ) |
|---|
| 845 | ek = ( 1.0 - qq ) * ecoll(15,iq-1) + qq * ecoll(15,iq) |
|---|
| 846 | ec(j,i) = MIN( ek, 1.0_wp ) |
|---|
| 847 | ENDIF |
|---|
| 848 | |
|---|
| 849 | IF ( ec(j,i) < 1.0E-20 ) ec(j,i) = 0.0 |
|---|
| 850 | |
|---|
| 851 | ec(i,j) = ec(j,i) |
|---|
| 852 | |
|---|
| 853 | ENDDO |
|---|
| 854 | ENDDO |
|---|
| 855 | |
|---|
| 856 | DEALLOCATE( ira ) |
|---|
| 857 | |
|---|
| 858 | END SUBROUTINE effic |
|---|
| 859 | |
|---|
| 860 | |
|---|
| 861 | !------------------------------------------------------------------------------! |
|---|
| 862 | ! Calculation of enhancement factor for collision efficencies due to turbulence |
|---|
| 863 | !------------------------------------------------------------------------------! |
|---|
| 864 | SUBROUTINE turb_enhance_eff |
|---|
| 865 | |
|---|
| 866 | USE particle_attributes, & |
|---|
| 867 | ONLY: radius_classes |
|---|
| 868 | |
|---|
| 869 | IMPLICIT NONE |
|---|
| 870 | |
|---|
| 871 | INTEGER(iwp) :: i !: |
|---|
| 872 | INTEGER(iwp) :: iq !: |
|---|
| 873 | INTEGER(iwp) :: ir !: |
|---|
| 874 | INTEGER(iwp) :: j !: |
|---|
| 875 | INTEGER(iwp) :: k !: |
|---|
| 876 | INTEGER(iwp) :: kk !: |
|---|
| 877 | |
|---|
| 878 | INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: ira !: |
|---|
| 879 | |
|---|
| 880 | LOGICAL, SAVE :: first = .TRUE. !: |
|---|
| 881 | |
|---|
| 882 | REAL(wp) :: particle_radius !: |
|---|
| 883 | REAL(wp) :: pp !: |
|---|
| 884 | REAL(wp) :: qq !: |
|---|
| 885 | REAL(wp) :: rq !: |
|---|
| 886 | REAL(wp) :: y1 !: |
|---|
| 887 | REAL(wp) :: y2 !: |
|---|
| 888 | REAL(wp) :: y3 !: |
|---|
| 889 | |
|---|
| 890 | REAL(wp), DIMENSION(1:11), SAVE :: rat !: |
|---|
| 891 | |
|---|
| 892 | REAL(wp), DIMENSION(1:7), SAVE :: r0 !: |
|---|
| 893 | |
|---|
| 894 | REAL(wp), DIMENSION(1:7,1:11), SAVE :: ecoll_100 !: |
|---|
| 895 | REAL(wp), DIMENSION(1:7,1:11), SAVE :: ecoll_400 !: |
|---|
| 896 | |
|---|
| 897 | ! |
|---|
| 898 | !-- Initial assignment of constants |
|---|
| 899 | IF ( first ) THEN |
|---|
| 900 | |
|---|
| 901 | first = .FALSE. |
|---|
| 902 | |
|---|
| 903 | r0 = (/ 10.0, 20.0, 30.0, 40.0, 50.0, 60.0, 100.0 /) |
|---|
| 904 | rat = (/ 0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0 /) |
|---|
| 905 | ! |
|---|
| 906 | !-- for 100 cm**2/s**3 |
|---|
| 907 | ecoll_100(:,1) = (/1.74, 1.74, 1.773, 1.49, 1.207, 1.207, 1.0 /) |
|---|
| 908 | ecoll_100(:,2) = (/1.46, 1.46, 1.421, 1.245, 1.069, 1.069, 1.0 /) |
|---|
| 909 | ecoll_100(:,3) = (/1.32, 1.32, 1.245, 1.123, 1.000, 1.000, 1.0 /) |
|---|
| 910 | ecoll_100(:,4) = (/1.250, 1.250, 1.148, 1.087, 1.025, 1.025, 1.0 /) |
|---|
| 911 | ecoll_100(:,5) = (/1.186, 1.186, 1.066, 1.060, 1.056, 1.056, 1.0 /) |
|---|
| 912 | ecoll_100(:,6) = (/1.045, 1.045, 1.000, 1.014, 1.028, 1.028, 1.0 /) |
|---|
| 913 | ecoll_100(:,7) = (/1.070, 1.070, 1.030, 1.038, 1.046, 1.046, 1.0 /) |
|---|
| 914 | ecoll_100(:,8) = (/1.000, 1.000, 1.054, 1.042, 1.029, 1.029, 1.0 /) |
|---|
| 915 | ecoll_100(:,9) = (/1.223, 1.223, 1.117, 1.069, 1.021, 1.021, 1.0 /) |
|---|
| 916 | ecoll_100(:,10)= (/1.570, 1.570, 1.244, 1.166, 1.088, 1.088, 1.0 /) |
|---|
| 917 | ecoll_100(:,11)= (/20.3, 20.3, 14.6 , 8.61, 2.60, 2.60 , 1.0 /) |
|---|
| 918 | ! |
|---|
| 919 | !-- for 400 cm**2/s**3 |
|---|
| 920 | ecoll_400(:,1) = (/4.976, 4.976, 3.593, 2.519, 1.445, 1.445, 1.0 /) |
|---|
| 921 | ecoll_400(:,2) = (/2.984, 2.984, 2.181, 1.691, 1.201, 1.201, 1.0 /) |
|---|
| 922 | ecoll_400(:,3) = (/1.988, 1.988, 1.475, 1.313, 1.150, 1.150, 1.0 /) |
|---|
| 923 | ecoll_400(:,4) = (/1.490, 1.490, 1.187, 1.156, 1.126, 1.126, 1.0 /) |
|---|
| 924 | ecoll_400(:,5) = (/1.249, 1.249, 1.088, 1.090, 1.092, 1.092, 1.0 /) |
|---|
| 925 | ecoll_400(:,6) = (/1.139, 1.139, 1.130, 1.091, 1.051, 1.051, 1.0 /) |
|---|
| 926 | ecoll_400(:,7) = (/1.220, 1.220, 1.190, 1.138, 1.086, 1.086, 1.0 /) |
|---|
| 927 | ecoll_400(:,8) = (/1.325, 1.325, 1.267, 1.165, 1.063, 1.063, 1.0 /) |
|---|
| 928 | ecoll_400(:,9) = (/1.716, 1.716, 1.345, 1.223, 1.100, 1.100, 1.0 /) |
|---|
| 929 | ecoll_400(:,10)= (/3.788, 3.788, 1.501, 1.311, 1.120, 1.120, 1.0 /) |
|---|
| 930 | ecoll_400(:,11)= (/36.52, 36.52, 19.16, 22.80, 26.0, 26.0, 1.0 /) |
|---|
| 931 | |
|---|
| 932 | ENDIF |
|---|
| 933 | |
|---|
| 934 | ! |
|---|
| 935 | !-- Calculate the radius class index of particles with respect to array r0 |
|---|
| 936 | !-- Radius has to be in µm |
|---|
| 937 | ALLOCATE( ira(1:radius_classes) ) |
|---|
| 938 | |
|---|
| 939 | DO j = 1, radius_classes |
|---|
| 940 | particle_radius = radclass(j) * 1.0E6_wp |
|---|
| 941 | DO k = 1, 7 |
|---|
| 942 | IF ( particle_radius < r0(k) ) THEN |
|---|
| 943 | ira(j) = k |
|---|
| 944 | EXIT |
|---|
| 945 | ENDIF |
|---|
| 946 | ENDDO |
|---|
| 947 | IF ( particle_radius >= r0(7) ) ira(j) = 8 |
|---|
| 948 | ENDDO |
|---|
| 949 | |
|---|
| 950 | ! |
|---|
| 951 | !-- Two-dimensional linear interpolation of the collision efficiencies |
|---|
| 952 | !-- Radius has to be in µm |
|---|
| 953 | DO j = 1, radius_classes |
|---|
| 954 | DO i = 1, j |
|---|
| 955 | |
|---|
| 956 | ir = ira(j) |
|---|
| 957 | rq = radclass(i) / radclass(j) |
|---|
| 958 | |
|---|
| 959 | DO kk = 2, 11 |
|---|
| 960 | IF ( rq <= rat(kk) ) THEN |
|---|
| 961 | iq = kk |
|---|
| 962 | EXIT |
|---|
| 963 | ENDIF |
|---|
| 964 | ENDDO |
|---|
| 965 | |
|---|
| 966 | y1 = 0.0001 ! for 0 m**2/s**3 |
|---|
| 967 | |
|---|
| 968 | IF ( ir < 8 ) THEN |
|---|
| 969 | IF ( ir >= 2 ) THEN |
|---|
| 970 | pp = ( radclass(j)*1.0E6 - r0(ir-1) ) / ( r0(ir) - r0(ir-1) ) |
|---|
| 971 | qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) ) |
|---|
| 972 | y2 = ( 1.0-pp ) * ( 1.0-qq ) * ecoll_100(ir-1,iq-1) + & |
|---|
| 973 | pp * ( 1.0-qq ) * ecoll_100(ir,iq-1) + & |
|---|
| 974 | qq * ( 1.0-pp ) * ecoll_100(ir-1,iq) + & |
|---|
| 975 | pp * qq * ecoll_100(ir,iq) |
|---|
| 976 | y3 = ( 1.0-pp ) * ( 1.0-qq ) * ecoll_400(ir-1,iq-1) + & |
|---|
| 977 | pp * ( 1.0-qq ) * ecoll_400(ir,iq-1) + & |
|---|
| 978 | qq * ( 1.0-pp ) * ecoll_400(ir-1,iq) + & |
|---|
| 979 | pp * qq * ecoll_400(ir,iq) |
|---|
| 980 | ELSE |
|---|
| 981 | qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) ) |
|---|
| 982 | y2 = ( 1.0-qq ) * ecoll_100(1,iq-1) + qq * ecoll_100(1,iq) |
|---|
| 983 | y3 = ( 1.0-qq ) * ecoll_400(1,iq-1) + qq * ecoll_400(1,iq) |
|---|
| 984 | ENDIF |
|---|
| 985 | ELSE |
|---|
| 986 | qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) ) |
|---|
| 987 | y2 = ( 1.0-qq ) * ecoll_100(7,iq-1) + qq * ecoll_100(7,iq) |
|---|
| 988 | y3 = ( 1.0-qq ) * ecoll_400(7,iq-1) + qq * ecoll_400(7,iq) |
|---|
| 989 | ENDIF |
|---|
| 990 | ! |
|---|
| 991 | !-- Linear interpolation of dissipation rate in m**2/s**3 |
|---|
| 992 | IF ( epsilon <= 0.01 ) THEN |
|---|
| 993 | ecf(j,i) = ( epsilon - 0.01 ) / ( 0.0 - 0.01 ) * y1 & |
|---|
| 994 | + ( epsilon - 0.0 ) / ( 0.01 - 0.0 ) * y2 |
|---|
| 995 | ELSEIF ( epsilon <= 0.06 ) THEN |
|---|
| 996 | ecf(j,i) = ( epsilon - 0.04 ) / ( 0.01 - 0.04 ) * y2 & |
|---|
| 997 | + ( epsilon - 0.01 ) / ( 0.04 - 0.01 ) * y3 |
|---|
| 998 | ELSE |
|---|
| 999 | ecf(j,i) = ( 0.06 - 0.04 ) / ( 0.01 - 0.04 ) * y2 & |
|---|
| 1000 | + ( 0.06 - 0.01 ) / ( 0.04 - 0.01 ) * y3 |
|---|
| 1001 | ENDIF |
|---|
| 1002 | |
|---|
| 1003 | IF ( ecf(j,i) < 1.0 ) ecf(j,i) = 1.0 |
|---|
| 1004 | |
|---|
| 1005 | ecf(i,j) = ecf(j,i) |
|---|
| 1006 | |
|---|
| 1007 | ENDDO |
|---|
| 1008 | ENDDO |
|---|
| 1009 | |
|---|
| 1010 | END SUBROUTINE turb_enhance_eff |
|---|
| 1011 | |
|---|
| 1012 | |
|---|
| 1013 | |
|---|
| 1014 | SUBROUTINE collision_efficiency_rogers( mean_r, r, e) |
|---|
| 1015 | !------------------------------------------------------------------------------! |
|---|
| 1016 | ! Collision efficiencies from table 8.2 in Rogers and Yau (1989, 3rd edition). |
|---|
| 1017 | ! Values are calculated from table by bilinear interpolation. |
|---|
| 1018 | !------------------------------------------------------------------------------! |
|---|
| 1019 | |
|---|
| 1020 | IMPLICIT NONE |
|---|
| 1021 | |
|---|
| 1022 | INTEGER(iwp) :: i !: |
|---|
| 1023 | INTEGER(iwp) :: j !: |
|---|
| 1024 | INTEGER(iwp) :: k !: |
|---|
| 1025 | |
|---|
| 1026 | LOGICAL, SAVE :: first = .TRUE. !: |
|---|
| 1027 | |
|---|
| 1028 | REAL(wp) :: aa !: |
|---|
| 1029 | REAL(wp) :: bb !: |
|---|
| 1030 | REAL(wp) :: cc !: |
|---|
| 1031 | REAL(wp) :: dd !: |
|---|
| 1032 | REAL(wp) :: dx !: |
|---|
| 1033 | REAL(wp) :: dy !: |
|---|
| 1034 | REAL(wp) :: e !: |
|---|
| 1035 | REAL(wp) :: gg !: |
|---|
| 1036 | REAL(wp) :: mean_r !: |
|---|
| 1037 | REAL(wp) :: mean_rm !: |
|---|
| 1038 | REAL(wp) :: r !: |
|---|
| 1039 | REAL(wp) :: rm !: |
|---|
| 1040 | REAL(wp) :: x !: |
|---|
| 1041 | REAL(wp) :: y !: |
|---|
| 1042 | |
|---|
| 1043 | REAL(wp), DIMENSION(1:9), SAVE :: collected_r = 0.0 !: |
|---|
| 1044 | |
|---|
| 1045 | REAL(wp), DIMENSION(1:19), SAVE :: collector_r = 0.0 !: |
|---|
| 1046 | |
|---|
| 1047 | REAL(wp), DIMENSION(1:9,1:19), SAVE :: ef = 0.0 !: |
|---|
| 1048 | |
|---|
| 1049 | mean_rm = mean_r * 1.0E06_wp |
|---|
| 1050 | rm = r * 1.0E06_wp |
|---|
| 1051 | |
|---|
| 1052 | IF ( first ) THEN |
|---|
| 1053 | |
|---|
| 1054 | collected_r = (/ 2.0, 3.0, 4.0, 6.0, 8.0, 10.0, 15.0, 20.0, 25.0 /) |
|---|
| 1055 | collector_r = (/ 10.0, 20.0, 30.0, 40.0, 50.0, 60.0, 80.0, 100.0, & |
|---|
| 1056 | 150.0, 200.0, 300.0, 400.0, 500.0, 600.0, 1000.0, & |
|---|
| 1057 | 1400.0, 1800.0, 2400.0, 3000.0 /) |
|---|
| 1058 | |
|---|
| 1059 | ef(:,1) = (/0.017, 0.027, 0.037, 0.052, 0.052, 0.052, 0.052, 0.0, & |
|---|
| 1060 | 0.0 /) |
|---|
| 1061 | ef(:,2) = (/0.001, 0.016, 0.027, 0.060, 0.12, 0.17, 0.17, 0.17, 0.0 /) |
|---|
| 1062 | ef(:,3) = (/0.001, 0.001, 0.02, 0.13, 0.28, 0.37, 0.54, 0.55, 0.47/) |
|---|
| 1063 | ef(:,4) = (/0.001, 0.001, 0.02, 0.23, 0.4, 0.55, 0.7, 0.75, 0.75/) |
|---|
| 1064 | ef(:,5) = (/0.01, 0.01, 0.03, 0.3, 0.4, 0.58, 0.73, 0.75, 0.79/) |
|---|
| 1065 | ef(:,6) = (/0.01, 0.01, 0.13, 0.38, 0.57, 0.68, 0.80, 0.86, 0.91/) |
|---|
| 1066 | ef(:,7) = (/0.01, 0.085, 0.23, 0.52, 0.68, 0.76, 0.86, 0.92, 0.95/) |
|---|
| 1067 | ef(:,8) = (/0.01, 0.14, 0.32, 0.60, 0.73, 0.81, 0.90, 0.94, 0.96/) |
|---|
| 1068 | ef(:,9) = (/0.025, 0.25, 0.43, 0.66, 0.78, 0.83, 0.92, 0.95, 0.96/) |
|---|
| 1069 | ef(:,10)= (/0.039, 0.3, 0.46, 0.69, 0.81, 0.87, 0.93, 0.95, 0.96/) |
|---|
| 1070 | ef(:,11)= (/0.095, 0.33, 0.51, 0.72, 0.82, 0.87, 0.93, 0.96, 0.97/) |
|---|
| 1071 | ef(:,12)= (/0.098, 0.36, 0.51, 0.73, 0.83, 0.88, 0.93, 0.96, 0.97/) |
|---|
| 1072 | ef(:,13)= (/0.1, 0.36, 0.52, 0.74, 0.83, 0.88, 0.93, 0.96, 0.97/) |
|---|
| 1073 | ef(:,14)= (/0.17, 0.4, 0.54, 0.72, 0.83, 0.88, 0.94, 0.98, 1.0 /) |
|---|
| 1074 | ef(:,15)= (/0.15, 0.37, 0.52, 0.74, 0.82, 0.88, 0.94, 0.98, 1.0 /) |
|---|
| 1075 | ef(:,16)= (/0.11, 0.34, 0.49, 0.71, 0.83, 0.88, 0.94, 0.95, 1.0 /) |
|---|
| 1076 | ef(:,17)= (/0.08, 0.29, 0.45, 0.68, 0.8, 0.86, 0.96, 0.94, 1.0 /) |
|---|
| 1077 | ef(:,18)= (/0.04, 0.22, 0.39, 0.62, 0.75, 0.83, 0.92, 0.96, 1.0 /) |
|---|
| 1078 | ef(:,19)= (/0.02, 0.16, 0.33, 0.55, 0.71, 0.81, 0.90, 0.94, 1.0 /) |
|---|
| 1079 | |
|---|
| 1080 | ENDIF |
|---|
| 1081 | |
|---|
| 1082 | DO k = 1, 8 |
|---|
| 1083 | IF ( collected_r(k) <= mean_rm ) i = k |
|---|
| 1084 | ENDDO |
|---|
| 1085 | |
|---|
| 1086 | DO k = 1, 18 |
|---|
| 1087 | IF ( collector_r(k) <= rm ) j = k |
|---|
| 1088 | ENDDO |
|---|
| 1089 | |
|---|
| 1090 | IF ( rm < 10.0 ) THEN |
|---|
| 1091 | e = 0.0 |
|---|
| 1092 | ELSEIF ( mean_rm < 2.0 ) THEN |
|---|
| 1093 | e = 0.001 |
|---|
| 1094 | ELSEIF ( mean_rm >= 25.0 ) THEN |
|---|
| 1095 | IF( j <= 2 ) e = 0.0 |
|---|
| 1096 | IF( j == 3 ) e = 0.47 |
|---|
| 1097 | IF( j == 4 ) e = 0.8 |
|---|
| 1098 | IF( j == 5 ) e = 0.9 |
|---|
| 1099 | IF( j >=6 ) e = 1.0 |
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| 1100 | ELSEIF ( rm >= 3000.0 ) THEN |
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| 1101 | IF( i == 1 ) e = 0.02 |
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| 1102 | IF( i == 2 ) e = 0.16 |
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| 1103 | IF( i == 3 ) e = 0.33 |
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| 1104 | IF( i == 4 ) e = 0.55 |
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| 1105 | IF( i == 5 ) e = 0.71 |
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| 1106 | IF( i == 6 ) e = 0.81 |
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| 1107 | IF( i == 7 ) e = 0.90 |
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| 1108 | IF( i >= 8 ) e = 0.94 |
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| 1109 | ELSE |
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| 1110 | x = mean_rm - collected_r(i) |
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| 1111 | y = rm - collector_r(j) |
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| 1112 | dx = collected_r(i+1) - collected_r(i) |
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| 1113 | dy = collector_r(j+1) - collector_r(j) |
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| 1114 | aa = x**2 + y**2 |
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| 1115 | bb = ( dx - x )**2 + y**2 |
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| 1116 | cc = x**2 + ( dy - y )**2 |
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| 1117 | dd = ( dx - x )**2 + ( dy - y )**2 |
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| 1118 | gg = aa + bb + cc + dd |
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| 1119 | |
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| 1120 | e = ( (gg-aa)*ef(i,j) + (gg-bb)*ef(i+1,j) + (gg-cc)*ef(i,j+1) + & |
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| 1121 | (gg-dd)*ef(i+1,j+1) ) / (3.0*gg) |
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| 1122 | ENDIF |
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| 1123 | |
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| 1124 | END SUBROUTINE collision_efficiency_rogers |
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| 1125 | |
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| 1126 | END MODULE lpm_collision_kernels_mod |
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