!> @file lpm_droplet_condensation.f90 !------------------------------------------------------------------------------! ! This file is part of the PALM model system. ! ! PALM 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. ! ! PALM 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 ! PALM. If not, see . ! ! Copyright 1997-2018 Leibniz Universitaet Hannover !------------------------------------------------------------------------------! ! ! Current revisions: ! ------------------ ! ! ! Former revisions: ! ----------------- ! $Id: lpm_droplet_condensation.f90 3049 2018-05-29 13:52:36Z kanani $ ! Error messages revised ! ! 3045 2018-05-28 07:55:41Z Giersch ! Error messages revised ! ! 3039 2018-05-24 13:13:11Z schwenkel ! bugfix for lcm with grid stretching ! ! 2718 2018-01-02 08:49:38Z maronga ! Corrected "Former revisions" section ! ! 2696 2017-12-14 17:12:51Z kanani ! Change in file header (GPL part) ! ! 2608 2017-11-13 14:04:26Z schwenkel ! Calculation of magnus equation in external module (diagnostic_quantities_mod). ! ! 2375 2017-08-29 14:10:28Z schwenkel ! Changed ONLY-dependencies ! ! 2312 2017-07-14 20:26:51Z hoffmann ! Rosenbrock scheme improved. Gas-kinetic effect added. ! ! 2000 2016-08-20 18:09:15Z knoop ! Forced header and separation lines into 80 columns ! ! 1890 2016-04-22 08:52:11Z hoffmann ! Some improvements of the Rosenbrock method. If the Rosenbrock method needs more ! than 40 iterations to find a sufficient time setp, the model is not aborted. ! This might lead to small erros. But they can be assumend as negligible, since ! the maximum timesetp of the Rosenbrock method after 40 iterations will be ! smaller than 10^-16 s. ! ! 1871 2016-04-15 11:46:09Z hoffmann ! Initialization of aerosols added. ! ! 1849 2016-04-08 11:33:18Z hoffmann ! Interpolation of supersaturation has been removed because it is not in ! accordance with the release/depletion of latent heat/water vapor in ! interaction_droplets_ptq. ! Calculation of particle Reynolds number has been corrected. ! eps_ros added from modules. ! ! 1831 2016-04-07 13:15:51Z hoffmann ! curvature_solution_effects moved to particle_attributes ! ! 1822 2016-04-07 07:49:42Z hoffmann ! Unused variables removed. ! ! 1682 2015-10-07 23:56:08Z knoop ! Code annotations made doxygen readable ! ! 1359 2014-04-11 17:15:14Z hoffmann ! New particle structure integrated. ! Kind definition added to all floating point numbers. ! ! 1346 2014-03-27 13:18:20Z heinze ! Bugfix: REAL constants provided with KIND-attribute especially in call of ! intrinsic function like MAX, MIN, SIGN ! ! 1322 2014-03-20 16:38:49Z raasch ! REAL constants defined as wp-kind ! ! 1320 2014-03-20 08:40:49Z raasch ! ONLY-attribute added to USE-statements, ! kind-parameters added to all INTEGER and REAL declaration statements, ! kinds are defined in new module kinds, ! comment fields (!:) to be used for variable explanations added to ! all variable declaration statements ! ! 1318 2014-03-17 13:35:16Z raasch ! module interfaces removed ! ! 1092 2013-02-02 11:24:22Z raasch ! unused variables removed ! ! 1071 2012-11-29 16:54:55Z franke ! Ventilation effect for evaporation of large droplets included ! Check for unreasonable results included in calculation of Rosenbrock method ! since physically unlikely results were observed and for the same ! reason the first internal time step in Rosenbrock method should be < 1.0E02 in ! case of evaporation ! Unnecessary calculation of ql_int removed ! Unnecessary calculations in Rosenbrock method (d2rdt2, drdt_m, dt_ros_last) ! removed ! Bugfix: factor in calculation of surface tension changed from 0.00155 to ! 0.000155 ! ! 1036 2012-10-22 13:43:42Z raasch ! code put under GPL (PALM 3.9) ! ! 849 2012-03-15 10:35:09Z raasch ! initial revision (former part of advec_particles) ! ! ! Description: ! ------------ !> Calculates change in droplet radius by condensation/evaporation, using !> either an analytic formula or by numerically integrating the radius growth !> equation including curvature and solution effects using Rosenbrocks method !> (see Numerical recipes in FORTRAN, 2nd edition, p. 731). !> The analytical formula and growth equation follow those given in !> Rogers and Yau (A short course in cloud physics, 3rd edition, p. 102/103). !------------------------------------------------------------------------------! SUBROUTINE lpm_droplet_condensation (ip,jp,kp) USE arrays_3d, & ONLY: dzw, hyp, pt, q, ql_c, ql_v USE cloud_parameters, & ONLY: l_d_rv, l_v, molecular_weight_of_solute, & molecular_weight_of_water, rho_l, rho_s, r_v, vanthoff USE constants, & ONLY: pi USE control_parameters, & ONLY: dt_3d, dz, message_string, molecular_viscosity, rho_surface USE cpulog, & ONLY: cpu_log, log_point_s USE diagnostic_quantities_mod, & ONLY: magnus USE grid_variables, & ONLY: dx, dy USE lpm_collision_kernels_mod, & ONLY: rclass_lbound, rclass_ubound USE kinds USE particle_attributes, & ONLY: curvature_solution_effects, hall_kernel, number_of_particles, & particles, radius_classes, use_kernel_tables, wang_kernel IMPLICIT NONE INTEGER(iwp) :: ip !< INTEGER(iwp) :: jp !< INTEGER(iwp) :: kp !< INTEGER(iwp) :: n !< REAL(wp) :: afactor !< curvature effects REAL(wp) :: arg !< REAL(wp) :: bfactor !< solute effects REAL(wp) :: ddenom !< REAL(wp) :: delta_r !< REAL(wp) :: diameter !< diameter of cloud droplets REAL(wp) :: diff_coeff !< diffusivity for water vapor REAL(wp) :: drdt !< REAL(wp) :: dt_ros !< REAL(wp) :: dt_ros_sum !< REAL(wp) :: d2rdtdr !< REAL(wp) :: e_a !< current vapor pressure REAL(wp) :: e_s !< current saturation vapor pressure REAL(wp) :: error !< local truncation error in Rosenbrock REAL(wp) :: k1 !< REAL(wp) :: k2 !< REAL(wp) :: r_err !< First order estimate of Rosenbrock radius REAL(wp) :: r_ros !< Rosenbrock radius REAL(wp) :: r_ros_ini !< initial Rosenbrock radius REAL(wp) :: r0 !< gas-kinetic lengthscale REAL(wp) :: sigma !< surface tension of water REAL(wp) :: thermal_conductivity !< thermal conductivity for water REAL(wp) :: t_int !< temperature REAL(wp) :: w_s !< terminal velocity of droplets REAL(wp) :: re_p !< particle Reynolds number ! !-- Parameters for Rosenbrock method (see Verwer et al., 1999) REAL(wp), PARAMETER :: prec = 1.0E-3_wp !< precision of Rosenbrock solution REAL(wp), PARAMETER :: q_increase = 1.5_wp !< increase factor in timestep REAL(wp), PARAMETER :: q_decrease = 0.9_wp !< decrease factor in timestep REAL(wp), PARAMETER :: gamma = 0.292893218814_wp !< = 1.0 - 1.0 / SQRT(2.0) ! !-- Parameters for terminal velocity REAL(wp), PARAMETER :: a_rog = 9.65_wp !< parameter for fall velocity REAL(wp), PARAMETER :: b_rog = 10.43_wp !< parameter for fall velocity REAL(wp), PARAMETER :: c_rog = 0.6_wp !< parameter for fall velocity REAL(wp), PARAMETER :: k_cap_rog = 4.0_wp !< parameter for fall velocity REAL(wp), PARAMETER :: k_low_rog = 12.0_wp !< parameter for fall velocity REAL(wp), PARAMETER :: d0_rog = 0.745_wp !< separation diameter REAL(wp), DIMENSION(number_of_particles) :: ventilation_effect !< REAL(wp), DIMENSION(number_of_particles) :: new_r !< CALL cpu_log( log_point_s(42), 'lpm_droplet_condens', 'start' ) ! !-- Absolute temperature t_int = pt(kp,jp,ip) * ( hyp(kp) / 100000.0_wp )**0.286_wp ! !-- Saturation vapor pressure (Eq. 10 in Bolton, 1980) e_s = magnus( t_int ) ! !-- Current vapor pressure e_a = q(kp,jp,ip) * hyp(kp) / ( q(kp,jp,ip) + 0.622_wp ) ! !-- Thermal conductivity for water (from Rogers and Yau, Table 7.1) thermal_conductivity = 7.94048E-05_wp * t_int + 0.00227011_wp ! !-- Moldecular diffusivity of water vapor in air (Hall und Pruppacher, 1976) diff_coeff = 0.211E-4_wp * ( t_int / 273.15_wp )**1.94_wp * & ( 101325.0_wp / hyp(kp) ) ! !-- Lengthscale for gas-kinetic effects (from Mordy, 1959, p. 23): r0 = diff_coeff / 0.036_wp * SQRT( 2.0_wp * pi / ( r_v * t_int ) ) ! !-- Calculate effects of heat conductivity and diffusion of water vapor on the !-- diffusional growth process (usually known as 1.0 / (F_k + F_d) ) ddenom = 1.0_wp / ( rho_l * r_v * t_int / ( e_s * diff_coeff ) + & ( l_v / ( r_v * t_int ) - 1.0_wp ) * rho_l * & l_v / ( thermal_conductivity * t_int ) & ) new_r = 0.0_wp ! !-- Determine ventilation effect on evaporation of large drops DO n = 1, number_of_particles IF ( particles(n)%radius >= 4.0E-5_wp .AND. e_a / e_s < 1.0_wp ) THEN ! !-- Terminal velocity is computed for vertical direction (Rogers et al., !-- 1993, J. Appl. Meteorol.) diameter = particles(n)%radius * 2000.0_wp !diameter in mm IF ( diameter <= d0_rog ) THEN w_s = k_cap_rog * diameter * ( 1.0_wp - EXP( -k_low_rog * diameter ) ) ELSE w_s = a_rog - b_rog * EXP( -c_rog * diameter ) ENDIF ! !-- Calculate droplet's Reynolds number re_p = 2.0_wp * particles(n)%radius * w_s / molecular_viscosity ! !-- Ventilation coefficient (Rogers and Yau, 1989): IF ( re_p > 2.5_wp ) THEN ventilation_effect(n) = 0.78_wp + 0.28_wp * SQRT( re_p ) ELSE ventilation_effect(n) = 1.0_wp + 0.09_wp * re_p ENDIF ELSE ! !-- For small droplets or in supersaturated environments, the ventilation !-- effect does not play a role ventilation_effect(n) = 1.0_wp ENDIF ENDDO IF( .NOT. curvature_solution_effects ) then ! !-- Use analytic model for diffusional growth including gas-kinetic !-- effects (Mordy, 1959) but without the impact of aerosols. DO n = 1, number_of_particles arg = ( particles(n)%radius + r0 )**2 + 2.0_wp * dt_3d * ddenom * & ventilation_effect(n) * & ( e_a / e_s - 1.0_wp ) arg = MAX( arg, ( 0.01E-6 + r0 )**2 ) new_r(n) = SQRT( arg ) - r0 ENDDO ELSE ! !-- Integrate the diffusional growth including gas-kinetic (Mordy, 1959), !-- as well as curvature and solute effects (e.g., Köhler, 1936). ! !-- Curvature effect (afactor) with surface tension (sigma) by Straka (2009) sigma = 0.0761_wp - 0.000155_wp * ( t_int - 273.15_wp ) ! !-- Solute effect (afactor) afactor = 2.0_wp * sigma / ( rho_l * r_v * t_int ) DO n = 1, number_of_particles ! !-- Solute effect (bfactor) bfactor = vanthoff * rho_s * particles(n)%aux1**3 * & molecular_weight_of_water / ( rho_l * molecular_weight_of_solute ) dt_ros = particles(n)%aux2 ! use previously stored Rosenbrock timestep dt_ros_sum = 0.0_wp r_ros = particles(n)%radius ! initialize Rosenbrock particle radius r_ros_ini = r_ros ! !-- Integrate growth equation using a 2nd-order Rosenbrock method !-- (see Verwer et al., 1999, Eq. (3.2)). The Rosenbrock method adjusts !-- its with internal timestep to minimize the local truncation error. DO WHILE ( dt_ros_sum < dt_3d ) dt_ros = MIN( dt_ros, dt_3d - dt_ros_sum ) DO drdt = ddenom * ventilation_effect(n) * ( e_a / e_s - 1.0 - & afactor / r_ros + & bfactor / r_ros**3 & ) / ( r_ros + r0 ) d2rdtdr = -ddenom * ventilation_effect(n) * ( & (e_a / e_s - 1.0) * r_ros**4 - & afactor * r0 * r_ros**2 - & 2.0 * afactor * r_ros**3 + & 3.0 * bfactor * r0 + & 4.0 * bfactor * r_ros & ) & / ( r_ros**4 * ( r_ros + r0 )**2 ) k1 = drdt / ( 1.0 - gamma * dt_ros * d2rdtdr ) r_ros = MAX(r_ros_ini + k1 * dt_ros, particles(n)%aux1) r_err = r_ros drdt = ddenom * ventilation_effect(n) * ( e_a / e_s - 1.0 - & afactor / r_ros + & bfactor / r_ros**3 & ) / ( r_ros + r0 ) k2 = ( drdt - dt_ros * 2.0 * gamma * d2rdtdr * k1 ) / & ( 1.0 - dt_ros * gamma * d2rdtdr ) r_ros = MAX(r_ros_ini + dt_ros * ( 1.5 * k1 + 0.5 * k2), particles(n)%aux1) ! !-- Check error of the solution, and reduce dt_ros if necessary. error = ABS(r_err - r_ros) / r_ros IF ( error .GT. prec ) THEN dt_ros = SQRT( q_decrease * prec / error ) * dt_ros r_ros = r_ros_ini ELSE dt_ros_sum = dt_ros_sum + dt_ros dt_ros = q_increase * dt_ros r_ros_ini = r_ros EXIT ENDIF END DO END DO !Rosenbrock loop ! !-- Store new particle radius new_r(n) = r_ros ! !-- Store internal time step value for next PALM step particles(n)%aux2 = dt_ros ENDDO !Particle loop ENDIF DO n = 1, number_of_particles ! !-- Sum up the change in liquid water for the respective grid !-- box for the computation of the release/depletion of water vapor !-- and heat. ql_c(kp,jp,ip) = ql_c(kp,jp,ip) + particles(n)%weight_factor * & rho_l * 1.33333333_wp * pi * & ( new_r(n)**3 - particles(n)%radius**3 ) / & ( rho_surface * dx * dy * dzw(kp) ) ! !-- Check if the increase in liqid water is not too big. If this is the case, !-- the model timestep might be too long. IF ( ql_c(kp,jp,ip) > 100.0_wp ) THEN WRITE( message_string, * ) 'k=',kp,' j=',jp,' i=',ip, & ' ql_c=',ql_c(kp,jp,ip), '&part(',n,')%wf=', & particles(n)%weight_factor,' delta_r=',delta_r CALL message( 'lpm_droplet_condensation', 'PA0143', 2, 2, -1, 6, 1 ) ENDIF ! !-- Check if the change in the droplet radius is not too big. If this is the !-- case, the model timestep might be too long. delta_r = new_r(n) - particles(n)%radius IF ( delta_r < 0.0_wp .AND. new_r(n) < 0.0_wp ) THEN WRITE( message_string, * ) '#1 k=',kp,' j=',jp,' i=',ip, & ' e_s=',e_s, ' e_a=',e_a,' t_int=',t_int, & '&delta_r=',delta_r, & ' particle_radius=',particles(n)%radius CALL message( 'lpm_droplet_condensation', 'PA0144', 2, 2, -1, 6, 1 ) ENDIF ! !-- Sum up the total volume of liquid water (needed below for !-- re-calculating the weighting factors) ql_v(kp,jp,ip) = ql_v(kp,jp,ip) + particles(n)%weight_factor * new_r(n)**3 ! !-- Determine radius class of the particle needed for collision IF ( use_kernel_tables ) THEN particles(n)%class = ( LOG( new_r(n) ) - rclass_lbound ) / & ( rclass_ubound - rclass_lbound ) * & radius_classes particles(n)%class = MIN( particles(n)%class, radius_classes ) particles(n)%class = MAX( particles(n)%class, 1 ) ENDIF ! !-- Store new radius to particle features particles(n)%radius = new_r(n) ENDDO CALL cpu_log( log_point_s(42), 'lpm_droplet_condens', 'stop' ) END SUBROUTINE lpm_droplet_condensation