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source: palm/trunk/SOURCE/lpm_collision_kernels.f90 @ 1787

Last change on this file since 1787 was 1777, checked in by hoffmann, 9 years ago
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[1682]	1	!> @file lpm_collision_kernels.f90
[1036]	2	!--------------------------------------------------------------------------------!
	3	! This file is part of PALM.
	4	!
	5	! PALM is free software: you can redistribute it and/or modify it under the terms
	6	! of the GNU General Public License as published by the Free Software Foundation,
	7	! either version 3 of the License, or (at your option) any later version.
	8	!
	9	! PALM is distributed in the hope that it will be useful, but WITHOUT ANY
	10	! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	11	! A PARTICULAR PURPOSE. See the GNU General Public License for more details.
	12	!
	13	! You should have received a copy of the GNU General Public License along with
	14	! PALM. If not, see <http://www.gnu.org/licenses/>.
	15	!
[1310]	16	! Copyright 1997-2014 Leibniz Universitaet Hannover
[1036]	17	!--------------------------------------------------------------------------------!
	18	!
[790]	19	! Current revisions:
	20	! -----------------
[1777]	21	!
[1347]	22	!
[1321]	23	! Former revisions:
	24	! -----------------
	25	! $Id: lpm_collision_kernels.f90 1777 2016-03-02 17:56:37Z raasch $
	26	!
[1777]	27	! 1776 2016-03-02 17:54:58Z hoffmann
	28	! Bugfix: Collection efficiencies must be calculated for the larger droplet.
	29	!
[1683]	30	! 1682 2015-10-07 23:56:08Z knoop
	31	! Code annotations made doxygen readable
	32	!
[1520]	33	! 1519 2015-01-08 10:20:42Z hoffmann
	34	! Bugfix: Using the new particle structure, particles are not sorted by size.
	35	! Hence, computation of collision efficiencies must ensure that the ratio of
	36	! two colliding droplets is < 1.
	37	!
[1360]	38	! 1359 2014-04-11 17:15:14Z hoffmann
	39	! New particle structure integrated.
	40	! Kind definition added to all floating point numbers.
	41	!
[1347]	42	! 1346 2014-03-27 13:18:20Z heinze
	43	! Bugfix: REAL constants provided with KIND-attribute especially in call of
	44	! intrinsic function like MAX, MIN, SIGN
	45	!
[1323]	46	! 1322 2014-03-20 16:38:49Z raasch
	47	! REAL constants defined as wp_kind
	48	!
[1321]	49	! 1320 2014-03-20 08:40:49Z
[1320]	50	! ONLY-attribute added to USE-statements,
	51	! kind-parameters added to all INTEGER and REAL declaration statements,
	52	! kinds are defined in new module kinds,
	53	! revision history before 2012 removed,
	54	! comment fields (!:) to be used for variable explanations added to
	55	! all variable declaration statements
[1008]	56	!
[1093]	57	! 1092 2013-02-02 11:24:22Z raasch
	58	! unused variables removed
	59	!
[1072]	60	! 1071 2012-11-29 16:54:55Z franke
	61	! Bugfix: collision efficiencies for Hall kernel should not be < 1.0E-20
	62	!
[1037]	63	! 1036 2012-10-22 13:43:42Z raasch
	64	! code put under GPL (PALM 3.9)
	65	!
[1008]	66	! 1007 2012-09-19 14:30:36Z franke
[1007]	67	! converted all units to SI units and replaced some parameters by corresponding
	68	! PALM parameters
	69	! Bugfix: factor in calculation of enhancement factor for collision efficencies
	70	! changed from 10. to 1.0
[829]	71	!
[850]	72	! 849 2012-03-15 10:35:09Z raasch
	73	! routine collision_efficiency_rogers added (moved from former advec_particles
	74	! to here)
	75	!
[836]	76	! 835 2012-02-22 11:21:19Z raasch $
	77	! Bugfix: array diss can be used only in case of Wang kernel
	78	!
[829]	79	! 828 2012-02-21 12:00:36Z raasch
[828]	80	! code has been completely reformatted, routine colker renamed
	81	! recalculate_kernel,
	82	! routine init_kernels added, radius is now communicated to the collision
	83	! routines by array radclass
[790]	84	!
[828]	85	! Bugfix: transformation factor for dissipation changed from 1E5 to 1E4
	86	!
[826]	87	! 825 2012-02-19 03:03:44Z raasch
	88	! routine renamed from wang_kernel to lpm_collision_kernels,
	89	! turbulence_effects on collision replaced by wang_kernel
	90	!
[791]	91	! 790 2011-11-29 03:11:20Z raasch
	92	! initial revision
[790]	93	!
	94	! Description:
	95	! ------------
[1682]	96	!> This module calculates collision efficiencies either due to pure gravitational
	97	!> effects (Hall kernel, see Hall, 1980: J. Atmos. Sci., 2486-2507) or
	98	!> including the effects of (SGS) turbulence (Wang kernel, see Wang and
	99	!> Grabowski, 2009: Atmos. Sci. Lett., 10, 1-8). The original code has been
	100	!> provided by L.-P. Wang but is substantially reformatted and speed optimized
	101	!> here.
	102	!>
	103	!> @attention Physical quantities (like g, densities, etc.) used in this module
	104	!> still have to be adjusted to those values used in the main PALM code.
	105	!> Also, quantities in CGS-units should be converted to SI-units eventually.
[790]	106	!------------------------------------------------------------------------------!
[1682]	107	MODULE lpm_collision_kernels_mod
	108
[790]	109
[1320]	110	USE constants, &
	111	ONLY: pi
	112
	113	USE kinds
	114
	115	USE particle_attributes, &
	116	ONLY: collision_kernel, dissipation_classes, particles, radius_classes
	117
[828]	118	USE pegrid
[790]	119
[828]	120
[790]	121	IMPLICIT NONE
	122
	123	PRIVATE
	124
[849]	125	PUBLIC ckernel, collision_efficiency_rogers, init_kernels, &
[1007]	126	rclass_lbound, rclass_ubound, recalculate_kernel
[790]	127
[1682]	128	REAL(wp) :: epsilon !<
	129	REAL(wp) :: eps2 !<
	130	REAL(wp) :: rclass_lbound !<
	131	REAL(wp) :: rclass_ubound !<
	132	REAL(wp) :: urms !<
	133	REAL(wp) :: urms2 !<
[790]	134
[1682]	135	REAL(wp), DIMENSION(:), ALLOCATABLE :: epsclass !<
	136	REAL(wp), DIMENSION(:), ALLOCATABLE :: radclass !<
	137	REAL(wp), DIMENSION(:), ALLOCATABLE :: winf !<
[1320]	138
[1682]	139	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: ec !<
	140	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: ecf !<
	141	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: gck !<
	142	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: hkernel !<
	143	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: hwratio !<
[1320]	144
[1682]	145	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: ckernel !<
[792]	146
[828]	147	SAVE
[792]	148
[790]	149	!
	150	!-- Public interfaces
[849]	151	INTERFACE collision_efficiency_rogers
	152	MODULE PROCEDURE collision_efficiency_rogers
	153	END INTERFACE collision_efficiency_rogers
	154
[828]	155	INTERFACE init_kernels
	156	MODULE PROCEDURE init_kernels
	157	END INTERFACE init_kernels
[790]	158
[828]	159	INTERFACE recalculate_kernel
	160	MODULE PROCEDURE recalculate_kernel
	161	END INTERFACE recalculate_kernel
[790]	162
	163
[828]	164	CONTAINS
[790]	165
[792]	166
[828]	167	!------------------------------------------------------------------------------!
[1682]	168	! Description:
	169	! ------------
	170	!> Initialization of the collision efficiency matrix with fixed radius and
	171	!> dissipation classes, calculated at simulation start only.
[828]	172	!------------------------------------------------------------------------------!
[1682]	173
	174	SUBROUTINE init_kernels
[792]	175
[828]	176	IMPLICIT NONE
[792]	177
[1682]	178	INTEGER(iwp) :: i !<
	179	INTEGER(iwp) :: j !<
	180	INTEGER(iwp) :: k !<
[790]	181
[828]	182
	183	!
	184	!-- Calculate collision efficiencies for fixed radius- and dissipation
	185	!-- classes
	186	IF ( collision_kernel(6:9) == 'fast' ) THEN
	187
	188	ALLOCATE( ckernel(1:radius_classes,1:radius_classes, &
	189	0:dissipation_classes), epsclass(1:dissipation_classes), &
	190	radclass(1:radius_classes) )
	191
	192	!
	193	!-- Calculate the radius class bounds with logarithmic distances
	194	!-- in the interval [1.0E-6, 2.0E-4] m
[1322]	195	rclass_lbound = LOG( 1.0E-6_wp )
	196	rclass_ubound = LOG( 2.0E-4_wp )
[1359]	197	radclass(1) = 1.0E-6_wp
[828]	198	DO i = 2, radius_classes
	199	radclass(i) = EXP( rclass_lbound + &
[1359]	200	( rclass_ubound - rclass_lbound ) * &
	201	( i - 1.0_wp ) / ( radius_classes - 1.0_wp ) )
[828]	202	ENDDO
	203
	204	!
[1007]	205	!-- Set the class bounds for dissipation in interval [0.0, 0.1] m2/s3
[828]	206	DO i = 1, dissipation_classes
[1359]	207	epsclass(i) = 0.1_wp * REAL( i, KIND=wp ) / dissipation_classes
[828]	208	ENDDO
	209	!
	210	!-- Calculate collision efficiencies of the Wang/ayala kernel
	211	ALLOCATE( ec(1:radius_classes,1:radius_classes), &
	212	ecf(1:radius_classes,1:radius_classes), &
	213	gck(1:radius_classes,1:radius_classes), &
	214	winf(1:radius_classes) )
	215
	216	DO k = 1, dissipation_classes
	217
	218	epsilon = epsclass(k)
[1359]	219	urms = 2.02_wp * ( epsilon / 0.04_wp )**( 1.0_wp / 3.0_wp )
[828]	220
	221	CALL turbsd
	222	CALL turb_enhance_eff
	223	CALL effic
	224
	225	DO j = 1, radius_classes
	226	DO i = 1, radius_classes
	227	ckernel(i,j,k) = ec(i,j) * gck(i,j) * ecf(i,j)
	228	ENDDO
	229	ENDDO
	230
	231	ENDDO
	232
	233	!
	234	!-- Calculate collision efficiencies of the Hall kernel
	235	ALLOCATE( hkernel(1:radius_classes,1:radius_classes), &
	236	hwratio(1:radius_classes,1:radius_classes) )
	237
	238	CALL fallg
	239	CALL effic
	240
	241	DO j = 1, radius_classes
	242	DO i = 1, radius_classes
	243	hkernel(i,j) = pi * ( radclass(j) + radclass(i) )**2 &
	244	* ec(i,j) * ABS( winf(j) - winf(i) )
	245	ckernel(i,j,0) = hkernel(i,j) ! hall kernel stored on index 0
	246	ENDDO
	247	ENDDO
	248
	249	!
	250	!-- Test output of efficiencies
	251	IF ( j == -1 ) THEN
	252
	253	PRINT, '** Hall kernel'
[1359]	254	WRITE ( ,'(5X,20(F4.0,1X))' ) ( radclass(i)1.0E6_wp, &
[1007]	255	i = 1,radius_classes )
[828]	256	DO j = 1, radius_classes
[1007]	257	WRITE ( *,'(F4.0,1X,20(F8.4,1X))' ) radclass(j), &
	258	( hkernel(i,j), i = 1,radius_classes )
[828]	259	ENDDO
	260
	261	DO k = 1, dissipation_classes
	262	DO i = 1, radius_classes
	263	DO j = 1, radius_classes
[1359]	264	IF ( hkernel(i,j) == 0.0_wp ) THEN
	265	hwratio(i,j) = 9999999.9_wp
[828]	266	ELSE
	267	hwratio(i,j) = ckernel(i,j,k) / hkernel(i,j)
	268	ENDIF
	269	ENDDO
	270	ENDDO
	271
	272	PRINT, '** epsilon = ', epsclass(k)
[1359]	273	WRITE ( ,'(5X,20(F4.0,1X))' ) ( radclass(i) 1.0E6_wp, &
[1007]	274	i = 1,radius_classes )
[828]	275	DO j = 1, radius_classes
[1359]	276	WRITE ( ,'(F4.0,1X,20(F8.4,1X))' ) radclass(j) 1.0E6_wp, &
[1007]	277	( hwratio(i,j), i = 1,radius_classes )
[828]	278	ENDDO
	279	ENDDO
	280
	281	ENDIF
	282
	283	DEALLOCATE( ec, ecf, epsclass, gck, hkernel, winf )
	284
	285	ELSEIF( collision_kernel == 'hall' .OR. collision_kernel == 'wang' ) &
	286	THEN
	287	!
	288	!-- Initial settings for Hall- and Wang-Kernel
	289	!-- To be done: move here parts from turbsd, fallg, ecoll, etc.
	290	ENDIF
	291
	292	END SUBROUTINE init_kernels
	293
	294
[790]	295	!------------------------------------------------------------------------------!
[1682]	296	! Description:
	297	! ------------
	298	!> Calculation of collision kernels during each timestep and for each grid box
[790]	299	!------------------------------------------------------------------------------!
[828]	300	SUBROUTINE recalculate_kernel( i1, j1, k1 )
[790]	301
[1320]	302	USE arrays_3d, &
	303	ONLY: diss
[790]	304
[1320]	305	USE particle_attributes, &
[1359]	306	ONLY: prt_count, radius_classes, wang_kernel
[1320]	307
[790]	308	IMPLICIT NONE
	309
[1682]	310	INTEGER(iwp) :: i !<
	311	INTEGER(iwp) :: i1 !<
	312	INTEGER(iwp) :: j !<
	313	INTEGER(iwp) :: j1 !<
	314	INTEGER(iwp) :: k1 !<
	315	INTEGER(iwp) :: pend !<
	316	INTEGER(iwp) :: pstart !<
[790]	317
	318
[1359]	319	pstart = 1
	320	pend = prt_count(k1,j1,i1)
[828]	321	radius_classes = prt_count(k1,j1,i1)
[792]	322
[828]	323	ALLOCATE( ec(1:radius_classes,1:radius_classes), &
	324	radclass(1:radius_classes), winf(1:radius_classes) )
[790]	325
[828]	326	!
[1007]	327	!-- Store particle radii on the radclass array
	328	radclass(1:radius_classes) = particles(pstart:pend)%radius
[790]	329
[835]	330	IF ( wang_kernel ) THEN
[1007]	331	epsilon = diss(k1,j1,i1) ! dissipation rate in m2/s3
[835]	332	ELSE
[1359]	333	epsilon = 0.0_wp
[835]	334	ENDIF
[1359]	335	urms = 2.02_wp * ( epsilon / 0.04_wp )**( 0.33333333333_wp )
[790]	336
[1359]	337	IF ( wang_kernel .AND. epsilon > 1.0E-7_wp ) THEN
[828]	338	!
	339	!-- Call routines to calculate efficiencies for the Wang kernel
	340	ALLOCATE( gck(1:radius_classes,1:radius_classes), &
	341	ecf(1:radius_classes,1:radius_classes) )
[790]	342
[828]	343	CALL turbsd
	344	CALL turb_enhance_eff
	345	CALL effic
[790]	346
[828]	347	DO j = 1, radius_classes
	348	DO i = 1, radius_classes
	349	ckernel(pstart+i-1,pstart+j-1,1) = ec(i,j) * gck(i,j) * ecf(i,j)
[790]	350	ENDDO
[828]	351	ENDDO
[790]	352
[828]	353	DEALLOCATE( gck, ecf )
[790]	354
	355	ELSE
[828]	356	!
	357	!-- Call routines to calculate efficiencies for the Hall kernel
[790]	358	CALL fallg
	359	CALL effic
	360
[828]	361	DO j = 1, radius_classes
	362	DO i = 1, radius_classes
	363	ckernel(pstart+i-1,pstart+j-1,1) = pi * &
	364	( radclass(j) + radclass(i) )**2 &
	365	* ec(i,j) * ABS( winf(j) - winf(i) )
[790]	366	ENDDO
	367	ENDDO
	368
	369	ENDIF
	370
[828]	371	DEALLOCATE( ec, radclass, winf )
[790]	372
[828]	373	END SUBROUTINE recalculate_kernel
[790]	374
[828]	375
[790]	376	!------------------------------------------------------------------------------!
[1682]	377	! Description:
	378	! ------------
	379	!> Calculation of gck
	380	!> This is from Aayala 2008b, page 37ff.
	381	!> Necessary input parameters: water density, radii of droplets, air density,
	382	!> air viscosity, turbulent dissipation rate, taylor microscale reynolds number,
	383	!> gravitational acceleration --> to be replaced by PALM parameters
[790]	384	!------------------------------------------------------------------------------!
[792]	385	SUBROUTINE turbsd
[799]	386
[1320]	387	USE control_parameters, &
	388	ONLY: g, molecular_viscosity
	389
	390	USE particle_attributes, &
	391	ONLY: radius_classes
[790]	392
	393	IMPLICIT NONE
[1320]	394
[1682]	395	LOGICAL, SAVE :: first = .TRUE. !<
[790]	396
[1682]	397	INTEGER(iwp) :: i !<
	398	INTEGER(iwp) :: j !<
[790]	399
[1682]	400	REAL(wp) :: ao !<
	401	REAL(wp) :: ao_gr !<
	402	REAL(wp) :: bbb !<
	403	REAL(wp) :: be !<
	404	REAL(wp) :: b1 !<
	405	REAL(wp) :: b2 !<
	406	REAL(wp) :: ccc !<
	407	REAL(wp) :: c1 !<
	408	REAL(wp) :: c1_gr !<
	409	REAL(wp) :: c2 !<
	410	REAL(wp) :: d1 !<
	411	REAL(wp) :: d2 !<
	412	REAL(wp) :: eta !<
	413	REAL(wp) :: e1 !<
	414	REAL(wp) :: e2 !<
	415	REAL(wp) :: fao_gr !<
	416	REAL(wp) :: fr !<
	417	REAL(wp) :: grfin !<
	418	REAL(wp) :: lambda !<
	419	REAL(wp) :: lambda_re !<
	420	REAL(wp) :: lf !<
	421	REAL(wp) :: rc !<
	422	REAL(wp) :: rrp !<
	423	REAL(wp) :: sst !<
	424	REAL(wp) :: tauk !<
	425	REAL(wp) :: tl !<
	426	REAL(wp) :: t2 !<
	427	REAL(wp) :: tt !<
	428	REAL(wp) :: t1 !<
	429	REAL(wp) :: vk !<
	430	REAL(wp) :: vrms1xy !<
	431	REAL(wp) :: vrms2xy !<
	432	REAL(wp) :: v1 !<
	433	REAL(wp) :: v1v2xy !<
	434	REAL(wp) :: v1xysq !<
	435	REAL(wp) :: v2 !<
	436	REAL(wp) :: v2xysq !<
	437	REAL(wp) :: wrfin !<
	438	REAL(wp) :: wrgrav2 !<
	439	REAL(wp) :: wrtur2xy !<
	440	REAL(wp) :: xx !<
	441	REAL(wp) :: yy !<
	442	REAL(wp) :: z !<
[790]	443
[1682]	444	REAL(wp), DIMENSION(1:radius_classes) :: st !<
	445	REAL(wp), DIMENSION(1:radius_classes) :: tau !<
[1320]	446
[799]	447	!
[828]	448	!-- Initial assignment of constants
[799]	449	IF ( first ) THEN
[790]	450
[799]	451	first = .FALSE.
[790]	452
[1007]	453	ENDIF
[790]	454
[1322]	455	lambda = urms * SQRT( 15.0_wp * molecular_viscosity / epsilon ) ! in m
	456	lambda_re = urms*2 SQRT( 15.0_wp / epsilon / molecular_viscosity )
[828]	457	tl = urms**2 / epsilon ! in s
[1359]	458	lf = 0.5_wp * urms**3 / epsilon ! in m
[1007]	459	tauk = SQRT( molecular_viscosity / epsilon ) ! in s
[1322]	460	eta = ( molecular_viscosity3 / epsilon )0.25_wp ! in m
[1007]	461	vk = eta / tauk
[790]	462
[1359]	463	ao = ( 11.0_wp + 7.0_wp * lambda_re ) / ( 205.0_wp + lambda_re )
	464	tt = SQRT( 2.0_wp * lambda_re / ( SQRT( 15.0_wp ) * ao ) ) * tauk ! in s
[799]	465
[1007]	466	CALL fallg ! gives winf in m/s
[790]	467
[828]	468	DO i = 1, radius_classes
[1007]	469	tau(i) = winf(i) / g ! in s
[828]	470	st(i) = tau(i) / tauk
[790]	471	ENDDO
	472
[828]	473	!
	474	!-- Calculate wr (from Aayala 2008b, page 38f)
	475	z = tt / tl
[1322]	476	be = SQRT( 2.0_wp ) * lambda / lf
[1359]	477	bbb = SQRT( 1.0_wp - 2.0_wp * be**2 )
	478	d1 = ( 1.0_wp + bbb ) / ( 2.0_wp * bbb )
	479	e1 = lf * ( 1.0_wp + bbb ) * 0.5_wp ! in m
	480	d2 = ( 1.0_wp - bbb ) * 0.5_wp / bbb
	481	e2 = lf * ( 1.0_wp - bbb ) * 0.5_wp ! in m
	482	ccc = SQRT( 1.0_wp - 2.0_wp * z**2 )
	483	b1 = ( 1.0_wp + ccc ) * 0.5_wp / ccc
	484	c1 = tl * ( 1.0_wp + ccc ) * 0.5_wp ! in s
	485	b2 = ( 1.0_wp - ccc ) * 0.5_wp / ccc
	486	c2 = tl * ( 1.0_wp - ccc ) * 0.5_wp ! in s
[790]	487
[828]	488	DO i = 1, radius_classes
[790]	489
[1007]	490	v1 = winf(i) ! in m/s
[828]	491	t1 = tau(i) ! in s
[790]	492
[828]	493	DO j = 1, i
[1007]	494	rrp = radclass(i) + radclass(j)
	495	v2 = winf(j) ! in m/s
[828]	496	t2 = tau(j) ! in s
[790]	497
[1007]	498	v1xysq = b1 * d1 * phi_w(c1,e1,v1,t1) - b1 * d2 * phi_w(c1,e2,v1,t1) &
	499	- b2 * d1 * phi_w(c2,e1,v1,t1) + b2 * d2 * phi_w(c2,e2,v1,t1)
	500	v1xysq = v1xysq * urms2 / t1 ! in m2/s**2
	501	vrms1xy = SQRT( v1xysq ) ! in m/s
[790]	502
[1007]	503	v2xysq = b1 * d1 * phi_w(c1,e1,v2,t2) - b1 * d2 * phi_w(c1,e2,v2,t2) &
	504	- b2 * d1 * phi_w(c2,e1,v2,t2) + b2 * d2 * phi_w(c2,e2,v2,t2)
	505	v2xysq = v2xysq * urms2 / t2 ! in m2/s**2
	506	vrms2xy = SQRT( v2xysq ) ! in m/s
[790]	507
[828]	508	IF ( winf(i) >= winf(j) ) THEN
[799]	509	v1 = winf(i)
[790]	510	t1 = tau(i)
[799]	511	v2 = winf(j)
[790]	512	t2 = tau(j)
	513	ELSE
[799]	514	v1 = winf(j)
[790]	515	t1 = tau(j)
[799]	516	v2 = winf(i)
[790]	517	t2 = tau(i)
	518	ENDIF
	519
[828]	520	v1v2xy = b1 * d1 * zhi(c1,e1,v1,t1,v2,t2) - &
	521	b1 * d2 * zhi(c1,e2,v1,t1,v2,t2) - &
	522	b2 * d1 * zhi(c2,e1,v1,t1,v2,t2) + &
	523	b2 * d2* zhi(c2,e2,v1,t1,v2,t2)
	524	fr = d1 * EXP( -rrp / e1 ) - d2 * EXP( -rrp / e2 )
[1359]	525	v1v2xy = v1v2xy * fr * urms2 / tau(i) / tau(j) ! in m2/s**2
	526	wrtur2xy = vrms1xy2 + vrms2xy2 - 2.0_wp * v1v2xy ! in m2/s2
	527	IF ( wrtur2xy < 0.0_wp ) wrtur2xy = 0.0_wp
[1322]	528	wrgrav2 = pi / 8.0_wp * ( winf(j) - winf(i) )**2
	529	wrfin = SQRT( ( 2.0_wp / pi ) * ( wrtur2xy + wrgrav2) ) ! in m/s
[790]	530
[828]	531	!
	532	!-- Calculate gr
	533	IF ( st(j) > st(i) ) THEN
	534	sst = st(j)
[790]	535	ELSE
[828]	536	sst = st(i)
[790]	537	ENDIF
	538
[1359]	539	xx = -0.1988_wp * sst*4 + 1.5275_wp sst*3 - 4.2942_wp &
	540	sst*2 + 5.3406_wp sst
	541	IF ( xx < 0.0_wp ) xx = 0.0_wp
	542	yy = 0.1886_wp * EXP( 20.306_wp / lambda_re )
[790]	543
[1007]	544	c1_gr = xx / ( g / vk * tauk )**yy
[790]	545
[1322]	546	ao_gr = ao + ( pi / 8.0_wp) * ( g / vk * tauk )**2
[1359]	547	fao_gr = 20.115_wp * SQRT( ao_gr / lambda_re )
[828]	548	rc = SQRT( fao_gr * ABS( st(j) - st(i) ) ) * eta ! in cm
[790]	549
[1359]	550	grfin = ( ( eta2 + rc2 ) / ( rrp2 + rc2) )*( c1_gr0.5_wp )
	551	IF ( grfin < 1.0_wp ) grfin = 1.0_wp
[790]	552
[1359]	553	gck(i,j) = 2.0_wp * pi * rrp*2 wrfin * grfin ! in cm**3/s
[790]	554	gck(j,i) = gck(i,j)
	555
	556	ENDDO
	557	ENDDO
	558
[828]	559	END SUBROUTINE turbsd
[790]	560
[828]	561
[790]	562	!------------------------------------------------------------------------------!
[1682]	563	! Description:
	564	! ------------
	565	!> phi_w as a function
[790]	566	!------------------------------------------------------------------------------!
[1320]	567	REAL(wp) FUNCTION phi_w( a, b, vsett, tau0 )
[790]	568
	569	IMPLICIT NONE
	570
[1682]	571	REAL(wp) :: a !<
	572	REAL(wp) :: aa1 !<
	573	REAL(wp) :: b !<
	574	REAL(wp) :: tau0 !<
	575	REAL(wp) :: vsett !<
[790]	576
[1359]	577	aa1 = 1.0_wp / tau0 + 1.0_wp / a + vsett / b
	578	phi_w = 1.0_wp / aa1 - 0.5_wp * vsett / b / aa1**2 ! in s
[790]	579
[1007]	580	END FUNCTION phi_w
[792]	581
[790]	582
	583	!------------------------------------------------------------------------------!
[1682]	584	! Description:
	585	! ------------
	586	!> zhi as a function
[790]	587	!------------------------------------------------------------------------------!
[1320]	588	REAL(wp) FUNCTION zhi( a, b, vsett1, tau1, vsett2, tau2 )
[790]	589
	590	IMPLICIT NONE
	591
[1682]	592	REAL(wp) :: a !<
	593	REAL(wp) :: aa1 !<
	594	REAL(wp) :: aa2 !<
	595	REAL(wp) :: aa3 !<
	596	REAL(wp) :: aa4 !<
	597	REAL(wp) :: aa5 !<
	598	REAL(wp) :: aa6 !<
	599	REAL(wp) :: b !<
	600	REAL(wp) :: tau1 !<
	601	REAL(wp) :: tau2 !<
	602	REAL(wp) :: vsett1 !<
	603	REAL(wp) :: vsett2 !<
[790]	604
[1359]	605	aa1 = vsett2 / b - 1.0_wp / tau2 - 1.0_wp / a
	606	aa2 = vsett1 / b + 1.0_wp / tau1 + 1.0_wp / a
	607	aa3 = ( vsett1 - vsett2 ) / b + 1.0_wp / tau1 + 1.0_wp / tau2
	608	aa4 = ( vsett2 / b )2 - ( 1.0_wp / tau2 + 1.0_wp / a )2
	609	aa5 = vsett2 / b + 1.0_wp / tau2 + 1.0_wp / a
	610	aa6 = 1.0_wp / tau1 - 1.0_wp / a + ( 1.0_wp / tau2 + 1.0_wp / a) * &
	611	vsett1 / vsett2
	612	zhi = (1.0_wp / aa1 - 1.0_wp / aa2 ) * ( vsett1 - vsett2 ) * 0.5_wp / &
	613	b / aa32 + ( 4.0_wp / aa4 - 1.0_wp / aa52 - 1.0_wp / aa1**2 ) &
	614	* vsett2 * 0.5_wp / b /aa6 + ( 2.0_wp * ( b / aa2 - b / aa1 ) - &
	615	vsett1 / aa22 + vsett2 / aa12 ) * 0.5_wp / b / aa3 ! in s**2
[799]	616
[828]	617	END FUNCTION zhi
[790]	618
[828]	619
[790]	620	!------------------------------------------------------------------------------!
[1682]	621	! Description:
	622	! ------------
	623	!> Calculation of terminal velocity winf following Equations 10-138 to 10-145
	624	!> from (Pruppacher and Klett, 1997)
[790]	625	!------------------------------------------------------------------------------!
[828]	626	SUBROUTINE fallg
[1320]	627
	628	USE cloud_parameters, &
	629	ONLY: rho_l
	630
	631	USE control_parameters, &
	632	ONLY: g
[790]	633
[1320]	634	USE particle_attributes, &
	635	ONLY: radius_classes
[790]	636
[1320]	637
[828]	638	IMPLICIT NONE
[790]	639
[1682]	640	INTEGER(iwp) :: i !<
	641	INTEGER(iwp) :: j !<
[790]	642
[1682]	643	LOGICAL, SAVE :: first = .TRUE. !<
[790]	644
[1682]	645	REAL(wp), SAVE :: cunh !<
	646	REAL(wp), SAVE :: eta !<
	647	REAL(wp), SAVE :: phy !<
	648	REAL(wp), SAVE :: py !<
	649	REAL(wp), SAVE :: rho_a !<
	650	REAL(wp), SAVE :: sigma !<
	651	REAL(wp), SAVE :: stb !<
	652	REAL(wp), SAVE :: stok !<
	653	REAL(wp), SAVE :: xlamb !<
[790]	654
[1682]	655	REAL(wp) :: bond !<
	656	REAL(wp) :: x !<
	657	REAL(wp) :: xrey !<
	658	REAL(wp) :: y !<
[799]	659
[1682]	660	REAL(wp), DIMENSION(1:7), SAVE :: b !<
	661	REAL(wp), DIMENSION(1:6), SAVE :: c !<
[799]	662
	663	!
[828]	664	!-- Initial assignment of constants
	665	IF ( first ) THEN
[799]	666
[828]	667	first = .FALSE.
[1359]	668	b = (/ -0.318657E1_wp, 0.992696E0_wp, -0.153193E-2_wp, &
	669	-0.987059E-3_wp, -0.578878E-3_wp, 0.855176E-4_wp, &
	670	-0.327815E-5_wp /)
	671	c = (/ -0.500015E1_wp, 0.523778E1_wp, -0.204914E1_wp, &
	672	0.475294E0_wp, -0.542819E-1_wp, 0.238449E-2_wp /)
[790]	673
[1007]	674	!
	675	!-- Parameter values for p = 1013,25 hPa and T = 293,15 K
[1359]	676	eta = 1.818E-5_wp ! in kg/(m s)
	677	xlamb = 6.6E-8_wp ! in m
	678	rho_a = 1.204_wp ! in kg/m**3
	679	cunh = 1.26_wp * xlamb ! in m
	680	sigma = 0.07363_wp ! in kg/s**2
	681	stok = 2.0_wp * g * ( rho_l - rho_a ) / ( 9.0_wp * eta ) ! in 1/(m s)
	682	stb = 32.0_wp * rho_a * ( rho_l - rho_a) * g / (3.0_wp * eta * eta)
[1007]	683	phy = sigma*3 rho_a2 / ( eta4 * g * ( rho_l - rho_a ) )
[1322]	684	py = phy**( 1.0_wp / 6.0_wp )
[790]	685
[828]	686	ENDIF
[790]	687
[828]	688	DO j = 1, radius_classes
[790]	689
[1359]	690	IF ( radclass(j) <= 1.0E-5_wp ) THEN
[799]	691
[1007]	692	winf(j) = stok * ( radclass(j)*2 + cunh radclass(j) )
[790]	693
[1359]	694	ELSEIF ( radclass(j) > 1.0E-5_wp .AND. radclass(j) <= 5.35E-4_wp ) THEN
[790]	695
[828]	696	x = LOG( stb * radclass(j)**3 )
[1359]	697	y = 0.0_wp
[790]	698
[828]	699	DO i = 1, 7
	700	y = y + b(i) * x**(i-1)
	701	ENDDO
[1007]	702	!
	703	!-- Note: this Eq. is wrong in (Pruppacher and Klett, 1997, p. 418)
	704	!-- for correct version see (Beard, 1976)
[1359]	705	xrey = ( 1.0_wp + cunh / radclass(j) ) * EXP( y )
[790]	706
[1359]	707	winf(j) = xrey * eta / ( 2.0_wp * rho_a * radclass(j) )
[790]	708
[1359]	709	ELSEIF ( radclass(j) > 5.35E-4_wp ) THEN
[790]	710
[1359]	711	IF ( radclass(j) > 0.0035_wp ) THEN
	712	bond = g * ( rho_l - rho_a ) * 0.0035_wp**2 / sigma
[828]	713	ELSE
[1007]	714	bond = g * ( rho_l - rho_a ) * radclass(j)**2 / sigma
[828]	715	ENDIF
[790]	716
[1359]	717	x = LOG( 16.0_wp * bond * py / 3.0_wp )
	718	y = 0.0_wp
[790]	719
[828]	720	DO i = 1, 6
	721	y = y + c(i) * x**(i-1)
	722	ENDDO
[790]	723
[828]	724	xrey = py * EXP( y )
[790]	725
[1359]	726	IF ( radclass(j) > 0.0035_wp ) THEN
	727	winf(j) = xrey * eta / ( 2.0_wp * rho_a * 0.0035_wp )
[828]	728	ELSE
[1359]	729	winf(j) = xrey * eta / ( 2.0_wp * rho_a * radclass(j) )
[828]	730	ENDIF
[790]	731
[828]	732	ENDIF
[790]	733
[828]	734	ENDDO
[790]	735
[828]	736	END SUBROUTINE fallg
[790]	737
[828]	738
[790]	739	!------------------------------------------------------------------------------!
[1682]	740	! Description:
	741	! ------------
	742	!> Calculation of collision efficiencies for the Hall kernel
[790]	743	!------------------------------------------------------------------------------!
[828]	744	SUBROUTINE effic
[1320]	745
	746	USE particle_attributes, &
	747	ONLY: radius_classes
[790]	748
[828]	749	IMPLICIT NONE
[790]	750
[1682]	751	INTEGER(iwp) :: i !<
	752	INTEGER(iwp) :: iq !<
	753	INTEGER(iwp) :: ir !<
	754	INTEGER(iwp) :: j !<
	755	INTEGER(iwp) :: k !<
[790]	756
[1682]	757	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: ira !<
[790]	758
[1682]	759	LOGICAL, SAVE :: first = .TRUE. !<
[790]	760
[1682]	761	REAL(wp) :: ek !<
	762	REAL(wp) :: particle_radius !<
	763	REAL(wp) :: pp !<
	764	REAL(wp) :: qq !<
	765	REAL(wp) :: rq !<
[790]	766
[1682]	767	REAL(wp), DIMENSION(1:21), SAVE :: rat !<
[1320]	768
[1682]	769	REAL(wp), DIMENSION(1:15), SAVE :: r0 !<
[1320]	770
[1682]	771	REAL(wp), DIMENSION(1:15,1:21), SAVE :: ecoll !<
[790]	772
[792]	773	!
[828]	774	!-- Initial assignment of constants
	775	IF ( first ) THEN
[790]	776
[792]	777	first = .FALSE.
[1359]	778	r0 = (/ 6.0_wp, 8.0_wp, 10.0_wp, 15.0_wp, 20.0_wp, 25.0_wp, &
	779	30.0_wp, 40.0_wp, 50.0_wp, 60.0_wp, 70.0_wp, 100.0_wp, &
	780	150.0_wp, 200.0_wp, 300.0_wp /)
[790]	781
[1359]	782	rat = (/ 0.00_wp, 0.05_wp, 0.10_wp, 0.15_wp, 0.20_wp, 0.25_wp, &
	783	0.30_wp, 0.35_wp, 0.40_wp, 0.45_wp, 0.50_wp, 0.55_wp, &
	784	0.60_wp, 0.65_wp, 0.70_wp, 0.75_wp, 0.80_wp, 0.85_wp, &
	785	0.90_wp, 0.95_wp, 1.00_wp /)
	786
	787	ecoll(:,1) = (/ 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, &
	788	0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, &
	789	0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp /)
	790	ecoll(:,2) = (/ 0.003_wp, 0.003_wp, 0.003_wp, 0.004_wp, 0.005_wp, &
	791	0.005_wp, 0.005_wp, 0.010_wp, 0.100_wp, 0.050_wp, &
	792	0.200_wp, 0.500_wp, 0.770_wp, 0.870_wp, 0.970_wp /)
	793	ecoll(:,3) = (/ 0.007_wp, 0.007_wp, 0.007_wp, 0.008_wp, 0.009_wp, &
	794	0.010_wp, 0.010_wp, 0.070_wp, 0.400_wp, 0.430_wp, &
	795	0.580_wp, 0.790_wp, 0.930_wp, 0.960_wp, 1.000_wp /)
	796	ecoll(:,4) = (/ 0.009_wp, 0.009_wp, 0.009_wp, 0.012_wp, 0.015_wp, &
	797	0.010_wp, 0.020_wp, 0.280_wp, 0.600_wp, 0.640_wp, &
	798	0.750_wp, 0.910_wp, 0.970_wp, 0.980_wp, 1.000_wp /)
	799	ecoll(:,5) = (/ 0.014_wp, 0.014_wp, 0.014_wp, 0.015_wp, 0.016_wp, &
	800	0.030_wp, 0.060_wp, 0.500_wp, 0.700_wp, 0.770_wp, &
	801	0.840_wp, 0.950_wp, 0.970_wp, 1.000_wp, 1.000_wp /)
	802	ecoll(:,6) = (/ 0.017_wp, 0.017_wp, 0.017_wp, 0.020_wp, 0.022_wp, &
	803	0.060_wp, 0.100_wp, 0.620_wp, 0.780_wp, 0.840_wp, &
	804	0.880_wp, 0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
	805	ecoll(:,7) = (/ 0.030_wp, 0.030_wp, 0.024_wp, 0.022_wp, 0.032_wp, &
	806	0.062_wp, 0.200_wp, 0.680_wp, 0.830_wp, 0.870_wp, &
	807	0.900_wp, 0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
	808	ecoll(:,8) = (/ 0.025_wp, 0.025_wp, 0.025_wp, 0.036_wp, 0.043_wp, &
	809	0.130_wp, 0.270_wp, 0.740_wp, 0.860_wp, 0.890_wp, &
	810	0.920_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
	811	ecoll(:,9) = (/ 0.027_wp, 0.027_wp, 0.027_wp, 0.040_wp, 0.052_wp, &
	812	0.200_wp, 0.400_wp, 0.780_wp, 0.880_wp, 0.900_wp, &
	813	0.940_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
	814	ecoll(:,10) = (/ 0.030_wp, 0.030_wp, 0.030_wp, 0.047_wp, 0.064_wp, &
	815	0.250_wp, 0.500_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
	816	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
	817	ecoll(:,11) = (/ 0.040_wp, 0.040_wp, 0.033_wp, 0.037_wp, 0.068_wp, &
	818	0.240_wp, 0.550_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
	819	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
	820	ecoll(:,12) = (/ 0.035_wp, 0.035_wp, 0.035_wp, 0.055_wp, 0.079_wp, &
	821	0.290_wp, 0.580_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
	822	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
	823	ecoll(:,13) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.062_wp, 0.082_wp, &
	824	0.290_wp, 0.590_wp, 0.780_wp, 0.900_wp, 0.910_wp, &
	825	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
	826	ecoll(:,14) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.060_wp, 0.080_wp, &
	827	0.290_wp, 0.580_wp, 0.770_wp, 0.890_wp, 0.910_wp, &
	828	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
	829	ecoll(:,15) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.041_wp, 0.075_wp, &
	830	0.250_wp, 0.540_wp, 0.760_wp, 0.880_wp, 0.920_wp, &
	831	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
	832	ecoll(:,16) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.052_wp, 0.067_wp, &
	833	0.250_wp, 0.510_wp, 0.770_wp, 0.880_wp, 0.930_wp, &
	834	0.970_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
	835	ecoll(:,17) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.047_wp, 0.057_wp, &
	836	0.250_wp, 0.490_wp, 0.770_wp, 0.890_wp, 0.950_wp, &
	837	1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
	838	ecoll(:,18) = (/ 0.036_wp, 0.036_wp, 0.036_wp, 0.042_wp, 0.048_wp, &
	839	0.230_wp, 0.470_wp, 0.780_wp, 0.920_wp, 1.000_wp, &
	840	1.020_wp, 1.020_wp, 1.020_wp, 1.020_wp, 1.020_wp /)
	841	ecoll(:,19) = (/ 0.040_wp, 0.040_wp, 0.035_wp, 0.033_wp, 0.040_wp, &
	842	0.112_wp, 0.450_wp, 0.790_wp, 1.010_wp, 1.030_wp, &
	843	1.040_wp, 1.040_wp, 1.040_wp, 1.040_wp, 1.040_wp /)
	844	ecoll(:,20) = (/ 0.033_wp, 0.033_wp, 0.033_wp, 0.033_wp, 0.033_wp, &
	845	0.119_wp, 0.470_wp, 0.950_wp, 1.300_wp, 1.700_wp, &
	846	2.300_wp, 2.300_wp, 2.300_wp, 2.300_wp, 2.300_wp /)
	847	ecoll(:,21) = (/ 0.027_wp, 0.027_wp, 0.027_wp, 0.027_wp, 0.027_wp, &
	848	0.125_wp, 0.520_wp, 1.400_wp, 2.300_wp, 3.000_wp, &
	849	4.000_wp, 4.000_wp, 4.000_wp, 4.000_wp, 4.000_wp /)
[828]	850	ENDIF
[790]	851
[792]	852	!
[828]	853	!-- Calculate the radius class index of particles with respect to array r
[1007]	854	!-- Radius has to be in Âµm
[828]	855	ALLOCATE( ira(1:radius_classes) )
	856	DO j = 1, radius_classes
[1322]	857	particle_radius = radclass(j) * 1.0E6_wp
[828]	858	DO k = 1, 15
	859	IF ( particle_radius < r0(k) ) THEN
	860	ira(j) = k
	861	EXIT
	862	ENDIF
	863	ENDDO
	864	IF ( particle_radius >= r0(15) ) ira(j) = 16
	865	ENDDO
[790]	866
[792]	867	!
[828]	868	!-- Two-dimensional linear interpolation of the collision efficiency.
	869	!-- Radius has to be in Âµm
	870	DO j = 1, radius_classes
	871	DO i = 1, j
[792]	872
[828]	873	ir = ira(j)
[1519]	874	rq = MIN( radclass(i) / radclass(j), radclass(j) / radclass(i) )
[828]	875	iq = INT( rq * 20 ) + 1
	876	iq = MAX( iq , 2)
[792]	877
[828]	878	IF ( ir < 16 ) THEN
	879	IF ( ir >= 2 ) THEN
[1776]	880	pp = ( ( MAX(radclass(j),radclass(i)) * 1.0E06_wp ) - r0(ir-1) ) / &
[828]	881	( r0(ir) - r0(ir-1) )
[1359]	882	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
	883	ec(j,i) = ( 1.0_wp - pp ) * ( 1.0_wp - qq ) &
	884	* ecoll(ir-1,iq-1) &
	885	+ pp * ( 1.0_wp - qq ) * ecoll(ir,iq-1) &
	886	+ qq * ( 1.0_wp - pp ) * ecoll(ir-1,iq) &
[828]	887	+ pp * qq * ecoll(ir,iq)
	888	ELSE
	889	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	890	ec(j,i) = ( 1.0_wp - qq ) * ecoll(1,iq-1) + qq * ecoll(1,iq)
[828]	891	ENDIF
	892	ELSE
	893	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	894	ek = ( 1.0_wp - qq ) * ecoll(15,iq-1) + qq * ecoll(15,iq)
[1346]	895	ec(j,i) = MIN( ek, 1.0_wp )
[1071]	896	ENDIF
[792]	897
[1359]	898	IF ( ec(j,i) < 1.0E-20_wp ) ec(j,i) = 0.0_wp
[1071]	899
[828]	900	ec(i,j) = ec(j,i)
[792]	901
[828]	902	ENDDO
	903	ENDDO
[792]	904
[828]	905	DEALLOCATE( ira )
[792]	906
[828]	907	END SUBROUTINE effic
[792]	908
	909
[790]	910	!------------------------------------------------------------------------------!
[1682]	911	! Description:
	912	! ------------
	913	!> Calculation of enhancement factor for collision efficencies due to turbulence
[790]	914	!------------------------------------------------------------------------------!
[828]	915	SUBROUTINE turb_enhance_eff
[790]	916
[1320]	917	USE particle_attributes, &
	918	ONLY: radius_classes
[790]	919
[828]	920	IMPLICIT NONE
[790]	921
[1682]	922	INTEGER(iwp) :: i !<
	923	INTEGER(iwp) :: iq !<
	924	INTEGER(iwp) :: ir !<
	925	INTEGER(iwp) :: j !<
	926	INTEGER(iwp) :: k !<
	927	INTEGER(iwp) :: kk !<
[790]	928
[1682]	929	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: ira !<
[1320]	930
[1682]	931	LOGICAL, SAVE :: first = .TRUE. !<
[790]	932
[1682]	933	REAL(wp) :: particle_radius !<
	934	REAL(wp) :: pp !<
	935	REAL(wp) :: qq !<
	936	REAL(wp) :: rq !<
	937	REAL(wp) :: y1 !<
	938	REAL(wp) :: y2 !<
	939	REAL(wp) :: y3 !<
[790]	940
[1682]	941	REAL(wp), DIMENSION(1:11), SAVE :: rat !<
[1320]	942
[1682]	943	REAL(wp), DIMENSION(1:7), SAVE :: r0 !<
[1320]	944
[1682]	945	REAL(wp), DIMENSION(1:7,1:11), SAVE :: ecoll_100 !<
	946	REAL(wp), DIMENSION(1:7,1:11), SAVE :: ecoll_400 !<
[799]	947
	948	!
[828]	949	!-- Initial assignment of constants
	950	IF ( first ) THEN
[799]	951
[828]	952	first = .FALSE.
[799]	953
[1359]	954	r0 = (/ 10.0_wp, 20.0_wp, 30.0_wp, 40.0_wp, 50.0_wp, 60.0_wp, &
	955	100.0_wp /)
	956
	957	rat = (/ 0.0_wp, 0.1_wp, 0.2_wp, 0.3_wp, 0.4_wp, 0.5_wp, 0.6_wp, &
	958	0.7_wp, 0.8_wp, 0.9_wp, 1.0_wp /)
[828]	959	!
[1007]	960	!-- for 100 cm2/s3
[1359]	961	ecoll_100(:,1) = (/ 1.74_wp, 1.74_wp, 1.773_wp, 1.49_wp, &
	962	1.207_wp, 1.207_wp, 1.0_wp /)
	963	ecoll_100(:,2) = (/ 1.46_wp, 1.46_wp, 1.421_wp, 1.245_wp, &
	964	1.069_wp, 1.069_wp, 1.0_wp /)
	965	ecoll_100(:,3) = (/ 1.32_wp, 1.32_wp, 1.245_wp, 1.123_wp, &
	966	1.000_wp, 1.000_wp, 1.0_wp /)
	967	ecoll_100(:,4) = (/ 1.250_wp, 1.250_wp, 1.148_wp, 1.087_wp, &
	968	1.025_wp, 1.025_wp, 1.0_wp /)
	969	ecoll_100(:,5) = (/ 1.186_wp, 1.186_wp, 1.066_wp, 1.060_wp, &
	970	1.056_wp, 1.056_wp, 1.0_wp /)
	971	ecoll_100(:,6) = (/ 1.045_wp, 1.045_wp, 1.000_wp, 1.014_wp, &
	972	1.028_wp, 1.028_wp, 1.0_wp /)
	973	ecoll_100(:,7) = (/ 1.070_wp, 1.070_wp, 1.030_wp, 1.038_wp, &
	974	1.046_wp, 1.046_wp, 1.0_wp /)
	975	ecoll_100(:,8) = (/ 1.000_wp, 1.000_wp, 1.054_wp, 1.042_wp, &
	976	1.029_wp, 1.029_wp, 1.0_wp /)
	977	ecoll_100(:,9) = (/ 1.223_wp, 1.223_wp, 1.117_wp, 1.069_wp, &
	978	1.021_wp, 1.021_wp, 1.0_wp /)
	979	ecoll_100(:,10) = (/ 1.570_wp, 1.570_wp, 1.244_wp, 1.166_wp, &
	980	1.088_wp, 1.088_wp, 1.0_wp /)
	981	ecoll_100(:,11) = (/ 20.3_wp, 20.3_wp, 14.6_wp, 8.61_wp, &
	982	2.60_wp, 2.60_wp, 1.0_wp /)
[828]	983	!
[1007]	984	!-- for 400 cm2/s3
[1359]	985	ecoll_400(:,1) = (/ 4.976_wp, 4.976_wp, 3.593_wp, 2.519_wp, &
	986	1.445_wp, 1.445_wp, 1.0_wp /)
	987	ecoll_400(:,2) = (/ 2.984_wp, 2.984_wp, 2.181_wp, 1.691_wp, &
	988	1.201_wp, 1.201_wp, 1.0_wp /)
	989	ecoll_400(:,3) = (/ 1.988_wp, 1.988_wp, 1.475_wp, 1.313_wp, &
	990	1.150_wp, 1.150_wp, 1.0_wp /)
	991	ecoll_400(:,4) = (/ 1.490_wp, 1.490_wp, 1.187_wp, 1.156_wp, &
	992	1.126_wp, 1.126_wp, 1.0_wp /)
	993	ecoll_400(:,5) = (/ 1.249_wp, 1.249_wp, 1.088_wp, 1.090_wp, &
	994	1.092_wp, 1.092_wp, 1.0_wp /)
	995	ecoll_400(:,6) = (/ 1.139_wp, 1.139_wp, 1.130_wp, 1.091_wp, &
	996	1.051_wp, 1.051_wp, 1.0_wp /)
	997	ecoll_400(:,7) = (/ 1.220_wp, 1.220_wp, 1.190_wp, 1.138_wp, &
	998	1.086_wp, 1.086_wp, 1.0_wp /)
	999	ecoll_400(:,8) = (/ 1.325_wp, 1.325_wp, 1.267_wp, 1.165_wp, &
	1000	1.063_wp, 1.063_wp, 1.0_wp /)
	1001	ecoll_400(:,9) = (/ 1.716_wp, 1.716_wp, 1.345_wp, 1.223_wp, &
	1002	1.100_wp, 1.100_wp, 1.0_wp /)
	1003	ecoll_400(:,10) = (/ 3.788_wp, 3.788_wp, 1.501_wp, 1.311_wp, &
	1004	1.120_wp, 1.120_wp, 1.0_wp /)
	1005	ecoll_400(:,11) = (/ 36.52_wp, 36.52_wp, 19.16_wp, 22.80_wp, &
	1006	26.0_wp, 26.0_wp, 1.0_wp /)
[799]	1007
[828]	1008	ENDIF
[790]	1009
[828]	1010	!
	1011	!-- Calculate the radius class index of particles with respect to array r0
[1007]	1012	!-- Radius has to be in Âµm
[828]	1013	ALLOCATE( ira(1:radius_classes) )
[790]	1014
[828]	1015	DO j = 1, radius_classes
[1322]	1016	particle_radius = radclass(j) * 1.0E6_wp
[828]	1017	DO k = 1, 7
	1018	IF ( particle_radius < r0(k) ) THEN
	1019	ira(j) = k
	1020	EXIT
	1021	ENDIF
	1022	ENDDO
	1023	IF ( particle_radius >= r0(7) ) ira(j) = 8
	1024	ENDDO
[799]	1025
	1026	!
[828]	1027	!-- Two-dimensional linear interpolation of the collision efficiencies
[1007]	1028	!-- Radius has to be in Âµm
[828]	1029	DO j = 1, radius_classes
	1030	DO i = 1, j
[799]	1031
[828]	1032	ir = ira(j)
[1519]	1033	rq = MIN( radclass(i) / radclass(j), radclass(j) / radclass(i) )
[799]	1034
[828]	1035	DO kk = 2, 11
	1036	IF ( rq <= rat(kk) ) THEN
	1037	iq = kk
	1038	EXIT
	1039	ENDIF
	1040	ENDDO
[790]	1041
[1359]	1042	y1 = 0.0001_wp ! for 0 m2/s3
[1007]	1043
[828]	1044	IF ( ir < 8 ) THEN
	1045	IF ( ir >= 2 ) THEN
[1776]	1046	pp = ( MAX(radclass(j),radclass(i))*1.0E6_wp - r0(ir-1) ) / &
	1047	( r0(ir) - r0(ir-1) )
[828]	1048	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	1049	y2 = ( 1.0_wp - pp ) * ( 1.0_wp - qq ) * ecoll_100(ir-1,iq-1) + &
	1050	pp * ( 1.0_wp - qq ) * ecoll_100(ir,iq-1) + &
	1051	qq * ( 1.0_wp - pp ) * ecoll_100(ir-1,iq) + &
	1052	pp * qq * ecoll_100(ir,iq)
	1053	y3 = ( 1.0-pp ) * ( 1.0_wp - qq ) * ecoll_400(ir-1,iq-1) + &
	1054	pp * ( 1.0_wp - qq ) * ecoll_400(ir,iq-1) + &
	1055	qq * ( 1.0_wp - pp ) * ecoll_400(ir-1,iq) + &
	1056	pp * qq * ecoll_400(ir,iq)
[828]	1057	ELSE
	1058	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	1059	y2 = ( 1.0_wp - qq ) * ecoll_100(1,iq-1) + qq * ecoll_100(1,iq)
	1060	y3 = ( 1.0_wp - qq ) * ecoll_400(1,iq-1) + qq * ecoll_400(1,iq)
[828]	1061	ENDIF
	1062	ELSE
	1063	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	1064	y2 = ( 1.0_wp - qq ) * ecoll_100(7,iq-1) + qq * ecoll_100(7,iq)
	1065	y3 = ( 1.0_wp - qq ) * ecoll_400(7,iq-1) + qq * ecoll_400(7,iq)
[828]	1066	ENDIF
	1067	!
[1007]	1068	!-- Linear interpolation of dissipation rate in m2/s3
[1359]	1069	IF ( epsilon <= 0.01_wp ) THEN
	1070	ecf(j,i) = ( epsilon - 0.01_wp ) / ( 0.0_wp - 0.01_wp ) * y1 &
	1071	+ ( epsilon - 0.0_wp ) / ( 0.01_wp - 0.0_wp ) * y2
	1072	ELSEIF ( epsilon <= 0.06_wp ) THEN
	1073	ecf(j,i) = ( epsilon - 0.04_wp ) / ( 0.01_wp - 0.04_wp ) * y2 &
	1074	+ ( epsilon - 0.01_wp ) / ( 0.04_wp - 0.01_wp ) * y3
[828]	1075	ELSE
[1359]	1076	ecf(j,i) = ( 0.06_wp - 0.04_wp ) / ( 0.01_wp - 0.04_wp ) * y2 &
	1077	+ ( 0.06_wp - 0.01_wp ) / ( 0.04_wp - 0.01_wp ) * y3
[828]	1078	ENDIF
[790]	1079
[1359]	1080	IF ( ecf(j,i) < 1.0_wp ) ecf(j,i) = 1.0_wp
[790]	1081
[828]	1082	ecf(i,j) = ecf(j,i)
[790]	1083
[828]	1084	ENDDO
	1085	ENDDO
[790]	1086
[828]	1087	END SUBROUTINE turb_enhance_eff
[790]	1088
[849]	1089
	1090
	1091	!------------------------------------------------------------------------------!
[1682]	1092	! Description:
	1093	! ------------
	1094	!> Collision efficiencies from table 8.2 in Rogers and Yau (1989, 3rd edition).
	1095	!> Values are calculated from table by bilinear interpolation.
[849]	1096	!------------------------------------------------------------------------------!
[1682]	1097
	1098	SUBROUTINE collision_efficiency_rogers( mean_r, r, e)
[849]	1099
	1100	IMPLICIT NONE
	1101
[1682]	1102	INTEGER(iwp) :: i !<
	1103	INTEGER(iwp) :: j !<
	1104	INTEGER(iwp) :: k !<
[849]	1105
[1682]	1106	LOGICAL, SAVE :: first = .TRUE. !<
[849]	1107
[1682]	1108	REAL(wp) :: aa !<
	1109	REAL(wp) :: bb !<
	1110	REAL(wp) :: cc !<
	1111	REAL(wp) :: dd !<
	1112	REAL(wp) :: dx !<
	1113	REAL(wp) :: dy !<
	1114	REAL(wp) :: e !<
	1115	REAL(wp) :: gg !<
	1116	REAL(wp) :: mean_r !<
	1117	REAL(wp) :: mean_rm !<
	1118	REAL(wp) :: r !<
	1119	REAL(wp) :: rm !<
	1120	REAL(wp) :: x !<
	1121	REAL(wp) :: y !<
[1320]	1122
[1682]	1123	REAL(wp), DIMENSION(1:9), SAVE :: collected_r = 0.0_wp !<
[1320]	1124
[1682]	1125	REAL(wp), DIMENSION(1:19), SAVE :: collector_r = 0.0_wp !<
[1320]	1126
[1682]	1127	REAL(wp), DIMENSION(1:9,1:19), SAVE :: ef = 0.0_wp !<
[849]	1128
[1322]	1129	mean_rm = mean_r * 1.0E06_wp
	1130	rm = r * 1.0E06_wp
[849]	1131
	1132	IF ( first ) THEN
	1133
[1359]	1134	collected_r = (/ 2.0_wp, 3.0_wp, 4.0_wp, 6.0_wp, 8.0_wp, &
	1135	10.0_wp, 15.0_wp, 20.0_wp, 25.0_wp /)
	1136	collector_r = (/ 10.0_wp, 20.0_wp, 30.0_wp, 40.0_wp, 50.0_wp, &
	1137	60.0_wp, 80.0_wp, 100.0_wp, 150.0_wp, 200.0_wp, &
	1138	300.0_wp, 400.0_wp, 500.0_wp, 600.0_wp, 1000.0_wp, &
	1139	1400.0_wp, 1800.0_wp, 2400.0_wp, 3000.0_wp /)
[849]	1140
[1359]	1141	ef(:,1) = (/ 0.017_wp, 0.027_wp, 0.037_wp, 0.052_wp, 0.052_wp, &
	1142	0.052_wp, 0.052_wp, 0.0_wp, 0.0_wp /)
	1143	ef(:,2) = (/ 0.001_wp, 0.016_wp, 0.027_wp, 0.060_wp, 0.12_wp, &
	1144	0.17_wp, 0.17_wp, 0.17_wp, 0.0_wp /)
	1145	ef(:,3) = (/ 0.001_wp, 0.001_wp, 0.02_wp, 0.13_wp, 0.28_wp, &
	1146	0.37_wp, 0.54_wp, 0.55_wp, 0.47_wp/)
	1147	ef(:,4) = (/ 0.001_wp, 0.001_wp, 0.02_wp, 0.23_wp, 0.4_wp, &
	1148	0.55_wp, 0.7_wp, 0.75_wp, 0.75_wp/)
	1149	ef(:,5) = (/ 0.01_wp, 0.01_wp, 0.03_wp, 0.3_wp, 0.4_wp, &
	1150	0.58_wp, 0.73_wp, 0.75_wp, 0.79_wp/)
	1151	ef(:,6) = (/ 0.01_wp, 0.01_wp, 0.13_wp, 0.38_wp, 0.57_wp, &
	1152	0.68_wp, 0.80_wp, 0.86_wp, 0.91_wp/)
	1153	ef(:,7) = (/ 0.01_wp, 0.085_wp, 0.23_wp, 0.52_wp, 0.68_wp, &
	1154	0.76_wp, 0.86_wp, 0.92_wp, 0.95_wp/)
	1155	ef(:,8) = (/ 0.01_wp, 0.14_wp, 0.32_wp, 0.60_wp, 0.73_wp, &
	1156	0.81_wp, 0.90_wp, 0.94_wp, 0.96_wp/)
	1157	ef(:,9) = (/ 0.025_wp, 0.25_wp, 0.43_wp, 0.66_wp, 0.78_wp, &
	1158	0.83_wp, 0.92_wp, 0.95_wp, 0.96_wp/)
	1159	ef(:,10) = (/ 0.039_wp, 0.3_wp, 0.46_wp, 0.69_wp, 0.81_wp, &
	1160	0.87_wp, 0.93_wp, 0.95_wp, 0.96_wp/)
	1161	ef(:,11) = (/ 0.095_wp, 0.33_wp, 0.51_wp, 0.72_wp, 0.82_wp, &
	1162	0.87_wp, 0.93_wp, 0.96_wp, 0.97_wp/)
	1163	ef(:,12) = (/ 0.098_wp, 0.36_wp, 0.51_wp, 0.73_wp, 0.83_wp, &
	1164	0.88_wp, 0.93_wp, 0.96_wp, 0.97_wp/)
	1165	ef(:,13) = (/ 0.1_wp, 0.36_wp, 0.52_wp, 0.74_wp, 0.83_wp, &
	1166	0.88_wp, 0.93_wp, 0.96_wp, 0.97_wp/)
	1167	ef(:,14) = (/ 0.17_wp, 0.4_wp, 0.54_wp, 0.72_wp, 0.83_wp, &
	1168	0.88_wp, 0.94_wp, 0.98_wp, 1.0_wp /)
	1169	ef(:,15) = (/ 0.15_wp, 0.37_wp, 0.52_wp, 0.74_wp, 0.82_wp, &
	1170	0.88_wp, 0.94_wp, 0.98_wp, 1.0_wp /)
	1171	ef(:,16) = (/ 0.11_wp, 0.34_wp, 0.49_wp, 0.71_wp, 0.83_wp, &
	1172	0.88_wp, 0.94_wp, 0.95_wp, 1.0_wp /)
	1173	ef(:,17) = (/ 0.08_wp, 0.29_wp, 0.45_wp, 0.68_wp, 0.8_wp, &
	1174	0.86_wp, 0.96_wp, 0.94_wp, 1.0_wp /)
	1175	ef(:,18) = (/ 0.04_wp, 0.22_wp, 0.39_wp, 0.62_wp, 0.75_wp, &
	1176	0.83_wp, 0.92_wp, 0.96_wp, 1.0_wp /)
	1177	ef(:,19) = (/ 0.02_wp, 0.16_wp, 0.33_wp, 0.55_wp, 0.71_wp, &
	1178	0.81_wp, 0.90_wp, 0.94_wp, 1.0_wp /)
[849]	1179
	1180	ENDIF
	1181
	1182	DO k = 1, 8
	1183	IF ( collected_r(k) <= mean_rm ) i = k
	1184	ENDDO
	1185
	1186	DO k = 1, 18
	1187	IF ( collector_r(k) <= rm ) j = k
	1188	ENDDO
	1189
[1359]	1190	IF ( rm < 10.0_wp ) THEN
	1191	e = 0.0_wp
	1192	ELSEIF ( mean_rm < 2.0_wp ) THEN
	1193	e = 0.001_wp
	1194	ELSEIF ( mean_rm >= 25.0_wp ) THEN
	1195	IF( j <= 2 ) e = 0.0_wp
	1196	IF( j == 3 ) e = 0.47_wp
	1197	IF( j == 4 ) e = 0.8_wp
	1198	IF( j == 5 ) e = 0.9_wp
	1199	IF( j >=6 ) e = 1.0_wp
	1200	ELSEIF ( rm >= 3000.0_wp ) THEN
	1201	IF( i == 1 ) e = 0.02_wp
	1202	IF( i == 2 ) e = 0.16_wp
	1203	IF( i == 3 ) e = 0.33_wp
	1204	IF( i == 4 ) e = 0.55_wp
	1205	IF( i == 5 ) e = 0.71_wp
	1206	IF( i == 6 ) e = 0.81_wp
	1207	IF( i == 7 ) e = 0.90_wp
	1208	IF( i >= 8 ) e = 0.94_wp
[849]	1209	ELSE
	1210	x = mean_rm - collected_r(i)
	1211	y = rm - collector_r(j)
	1212	dx = collected_r(i+1) - collected_r(i)
	1213	dy = collector_r(j+1) - collector_r(j)
	1214	aa = x2 + y2
	1215	bb = ( dx - x )2 + y2
	1216	cc = x2 + ( dy - y )2
	1217	dd = ( dx - x )2 + ( dy - y )2
	1218	gg = aa + bb + cc + dd
	1219
	1220	e = ( (gg-aa)ef(i,j) + (gg-bb)ef(i+1,j) + (gg-cc)*ef(i,j+1) + &
[1359]	1221	(gg-dd)ef(i+1,j+1) ) / (3.0_wp gg)
[849]	1222	ENDIF
	1223
	1224	END SUBROUTINE collision_efficiency_rogers
	1225
[825]	1226	END MODULE lpm_collision_kernels_mod

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