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source: palm/trunk/SOURCE/lpm_collision_kernels.f90 @ 1812

Last change on this file since 1812 was 1777, checked in by hoffmann, 9 years ago
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1	!> @file lpm_collision_kernels.f90
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	!
16	! Copyright 1997-2014 Leibniz Universitaet Hannover
17	!--------------------------------------------------------------------------------!
18	!
19	! Current revisions:
20	! -----------------
21	!
22	!
23	! Former revisions:
24	! -----------------
25	! $Id: lpm_collision_kernels.f90 1777 2016-03-02 17:56:37Z knoop $
26	!
27	! 1776 2016-03-02 17:54:58Z hoffmann
28	! Bugfix: Collection efficiencies must be calculated for the larger droplet.
29	!
30	! 1682 2015-10-07 23:56:08Z knoop
31	! Code annotations made doxygen readable
32	!
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	!
38	! 1359 2014-04-11 17:15:14Z hoffmann
39	! New particle structure integrated.
40	! Kind definition added to all floating point numbers.
41	!
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	!
46	! 1322 2014-03-20 16:38:49Z raasch
47	! REAL constants defined as wp_kind
48	!
49	! 1320 2014-03-20 08:40:49Z
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
56	!
57	! 1092 2013-02-02 11:24:22Z raasch
58	! unused variables removed
59	!
60	! 1071 2012-11-29 16:54:55Z franke
61	! Bugfix: collision efficiencies for Hall kernel should not be < 1.0E-20
62	!
63	! 1036 2012-10-22 13:43:42Z raasch
64	! code put under GPL (PALM 3.9)
65	!
66	! 1007 2012-09-19 14:30:36Z franke
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
71	!
72	! 849 2012-03-15 10:35:09Z raasch
73	! routine collision_efficiency_rogers added (moved from former advec_particles
74	! to here)
75	!
76	! 835 2012-02-22 11:21:19Z raasch $
77	! Bugfix: array diss can be used only in case of Wang kernel
78	!
79	! 828 2012-02-21 12:00:36Z raasch
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
84	!
85	! Bugfix: transformation factor for dissipation changed from 1E5 to 1E4
86	!
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	!
91	! 790 2011-11-29 03:11:20Z raasch
92	! initial revision
93	!
94	! Description:
95	! ------------
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.
106	!------------------------------------------------------------------------------!
107	MODULE lpm_collision_kernels_mod
108
109
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
118	USE pegrid
119
120
121	IMPLICIT NONE
122
123	PRIVATE
124
125	PUBLIC ckernel, collision_efficiency_rogers, init_kernels, &
126	rclass_lbound, rclass_ubound, recalculate_kernel
127
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 !<
134
135	REAL(wp), DIMENSION(:), ALLOCATABLE :: epsclass !<
136	REAL(wp), DIMENSION(:), ALLOCATABLE :: radclass !<
137	REAL(wp), DIMENSION(:), ALLOCATABLE :: winf !<
138
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 !<
144
145	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: ckernel !<
146
147	SAVE
148
149	!
150	!-- Public interfaces
151	INTERFACE collision_efficiency_rogers
152	MODULE PROCEDURE collision_efficiency_rogers
153	END INTERFACE collision_efficiency_rogers
154
155	INTERFACE init_kernels
156	MODULE PROCEDURE init_kernels
157	END INTERFACE init_kernels
158
159	INTERFACE recalculate_kernel
160	MODULE PROCEDURE recalculate_kernel
161	END INTERFACE recalculate_kernel
162
163
164	CONTAINS
165
166
167	!------------------------------------------------------------------------------!
168	! Description:
169	! ------------
170	!> Initialization of the collision efficiency matrix with fixed radius and
171	!> dissipation classes, calculated at simulation start only.
172	!------------------------------------------------------------------------------!
173
174	SUBROUTINE init_kernels
175
176	IMPLICIT NONE
177
178	INTEGER(iwp) :: i !<
179	INTEGER(iwp) :: j !<
180	INTEGER(iwp) :: k !<
181
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
195	rclass_lbound = LOG( 1.0E-6_wp )
196	rclass_ubound = LOG( 2.0E-4_wp )
197	radclass(1) = 1.0E-6_wp
198	DO i = 2, radius_classes
199	radclass(i) = EXP( rclass_lbound + &
200	( rclass_ubound - rclass_lbound ) * &
201	( i - 1.0_wp ) / ( radius_classes - 1.0_wp ) )
202	ENDDO
203
204	!
205	!-- Set the class bounds for dissipation in interval [0.0, 0.1] m2/s3
206	DO i = 1, dissipation_classes
207	epsclass(i) = 0.1_wp * REAL( i, KIND=wp ) / dissipation_classes
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)
219	urms = 2.02_wp * ( epsilon / 0.04_wp )**( 1.0_wp / 3.0_wp )
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'
254	WRITE ( ,'(5X,20(F4.0,1X))' ) ( radclass(i)1.0E6_wp, &
255	i = 1,radius_classes )
256	DO j = 1, radius_classes
257	WRITE ( *,'(F4.0,1X,20(F8.4,1X))' ) radclass(j), &
258	( hkernel(i,j), i = 1,radius_classes )
259	ENDDO
260
261	DO k = 1, dissipation_classes
262	DO i = 1, radius_classes
263	DO j = 1, radius_classes
264	IF ( hkernel(i,j) == 0.0_wp ) THEN
265	hwratio(i,j) = 9999999.9_wp
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)
273	WRITE ( ,'(5X,20(F4.0,1X))' ) ( radclass(i) 1.0E6_wp, &
274	i = 1,radius_classes )
275	DO j = 1, radius_classes
276	WRITE ( ,'(F4.0,1X,20(F8.4,1X))' ) radclass(j) 1.0E6_wp, &
277	( hwratio(i,j), i = 1,radius_classes )
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
295	!------------------------------------------------------------------------------!
296	! Description:
297	! ------------
298	!> Calculation of collision kernels during each timestep and for each grid box
299	!------------------------------------------------------------------------------!
300	SUBROUTINE recalculate_kernel( i1, j1, k1 )
301
302	USE arrays_3d, &
303	ONLY: diss
304
305	USE particle_attributes, &
306	ONLY: prt_count, radius_classes, wang_kernel
307
308	IMPLICIT NONE
309
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 !<
317
318
319	pstart = 1
320	pend = prt_count(k1,j1,i1)
321	radius_classes = prt_count(k1,j1,i1)
322
323	ALLOCATE( ec(1:radius_classes,1:radius_classes), &
324	radclass(1:radius_classes), winf(1:radius_classes) )
325
326	!
327	!-- Store particle radii on the radclass array
328	radclass(1:radius_classes) = particles(pstart:pend)%radius
329
330	IF ( wang_kernel ) THEN
331	epsilon = diss(k1,j1,i1) ! dissipation rate in m2/s3
332	ELSE
333	epsilon = 0.0_wp
334	ENDIF
335	urms = 2.02_wp * ( epsilon / 0.04_wp )**( 0.33333333333_wp )
336
337	IF ( wang_kernel .AND. epsilon > 1.0E-7_wp ) THEN
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) )
342
343	CALL turbsd
344	CALL turb_enhance_eff
345	CALL effic
346
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)
350	ENDDO
351	ENDDO
352
353	DEALLOCATE( gck, ecf )
354
355	ELSE
356	!
357	!-- Call routines to calculate efficiencies for the Hall kernel
358	CALL fallg
359	CALL effic
360
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) )
366	ENDDO
367	ENDDO
368
369	ENDIF
370
371	DEALLOCATE( ec, radclass, winf )
372
373	END SUBROUTINE recalculate_kernel
374
375
376	!------------------------------------------------------------------------------!
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
384	!------------------------------------------------------------------------------!
385	SUBROUTINE turbsd
386
387	USE control_parameters, &
388	ONLY: g, molecular_viscosity
389
390	USE particle_attributes, &
391	ONLY: radius_classes
392
393	IMPLICIT NONE
394
395	LOGICAL, SAVE :: first = .TRUE. !<
396
397	INTEGER(iwp) :: i !<
398	INTEGER(iwp) :: j !<
399
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 !<
443
444	REAL(wp), DIMENSION(1:radius_classes) :: st !<
445	REAL(wp), DIMENSION(1:radius_classes) :: tau !<
446
447	!
448	!-- Initial assignment of constants
449	IF ( first ) THEN
450
451	first = .FALSE.
452
453	ENDIF
454
455	lambda = urms * SQRT( 15.0_wp * molecular_viscosity / epsilon ) ! in m
456	lambda_re = urms*2 SQRT( 15.0_wp / epsilon / molecular_viscosity )
457	tl = urms**2 / epsilon ! in s
458	lf = 0.5_wp * urms**3 / epsilon ! in m
459	tauk = SQRT( molecular_viscosity / epsilon ) ! in s
460	eta = ( molecular_viscosity3 / epsilon )0.25_wp ! in m
461	vk = eta / tauk
462
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
465
466	CALL fallg ! gives winf in m/s
467
468	DO i = 1, radius_classes
469	tau(i) = winf(i) / g ! in s
470	st(i) = tau(i) / tauk
471	ENDDO
472
473	!
474	!-- Calculate wr (from Aayala 2008b, page 38f)
475	z = tt / tl
476	be = SQRT( 2.0_wp ) * lambda / lf
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
487
488	DO i = 1, radius_classes
489
490	v1 = winf(i) ! in m/s
491	t1 = tau(i) ! in s
492
493	DO j = 1, i
494	rrp = radclass(i) + radclass(j)
495	v2 = winf(j) ! in m/s
496	t2 = tau(j) ! in s
497
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
502
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
507
508	IF ( winf(i) >= winf(j) ) THEN
509	v1 = winf(i)
510	t1 = tau(i)
511	v2 = winf(j)
512	t2 = tau(j)
513	ELSE
514	v1 = winf(j)
515	t1 = tau(j)
516	v2 = winf(i)
517	t2 = tau(i)
518	ENDIF
519
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 )
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
528	wrgrav2 = pi / 8.0_wp * ( winf(j) - winf(i) )**2
529	wrfin = SQRT( ( 2.0_wp / pi ) * ( wrtur2xy + wrgrav2) ) ! in m/s
530
531	!
532	!-- Calculate gr
533	IF ( st(j) > st(i) ) THEN
534	sst = st(j)
535	ELSE
536	sst = st(i)
537	ENDIF
538
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 )
543
544	c1_gr = xx / ( g / vk * tauk )**yy
545
546	ao_gr = ao + ( pi / 8.0_wp) * ( g / vk * tauk )**2
547	fao_gr = 20.115_wp * SQRT( ao_gr / lambda_re )
548	rc = SQRT( fao_gr * ABS( st(j) - st(i) ) ) * eta ! in cm
549
550	grfin = ( ( eta2 + rc2 ) / ( rrp2 + rc2) )*( c1_gr0.5_wp )
551	IF ( grfin < 1.0_wp ) grfin = 1.0_wp
552
553	gck(i,j) = 2.0_wp * pi * rrp*2 wrfin * grfin ! in cm**3/s
554	gck(j,i) = gck(i,j)
555
556	ENDDO
557	ENDDO
558
559	END SUBROUTINE turbsd
560
561
562	!------------------------------------------------------------------------------!
563	! Description:
564	! ------------
565	!> phi_w as a function
566	!------------------------------------------------------------------------------!
567	REAL(wp) FUNCTION phi_w( a, b, vsett, tau0 )
568
569	IMPLICIT NONE
570
571	REAL(wp) :: a !<
572	REAL(wp) :: aa1 !<
573	REAL(wp) :: b !<
574	REAL(wp) :: tau0 !<
575	REAL(wp) :: vsett !<
576
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
579
580	END FUNCTION phi_w
581
582
583	!------------------------------------------------------------------------------!
584	! Description:
585	! ------------
586	!> zhi as a function
587	!------------------------------------------------------------------------------!
588	REAL(wp) FUNCTION zhi( a, b, vsett1, tau1, vsett2, tau2 )
589
590	IMPLICIT NONE
591
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 !<
604
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
616
617	END FUNCTION zhi
618
619
620	!------------------------------------------------------------------------------!
621	! Description:
622	! ------------
623	!> Calculation of terminal velocity winf following Equations 10-138 to 10-145
624	!> from (Pruppacher and Klett, 1997)
625	!------------------------------------------------------------------------------!
626	SUBROUTINE fallg
627
628	USE cloud_parameters, &
629	ONLY: rho_l
630
631	USE control_parameters, &
632	ONLY: g
633
634	USE particle_attributes, &
635	ONLY: radius_classes
636
637
638	IMPLICIT NONE
639
640	INTEGER(iwp) :: i !<
641	INTEGER(iwp) :: j !<
642
643	LOGICAL, SAVE :: first = .TRUE. !<
644
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 !<
654
655	REAL(wp) :: bond !<
656	REAL(wp) :: x !<
657	REAL(wp) :: xrey !<
658	REAL(wp) :: y !<
659
660	REAL(wp), DIMENSION(1:7), SAVE :: b !<
661	REAL(wp), DIMENSION(1:6), SAVE :: c !<
662
663	!
664	!-- Initial assignment of constants
665	IF ( first ) THEN
666
667	first = .FALSE.
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 /)
673
674	!
675	!-- Parameter values for p = 1013,25 hPa and T = 293,15 K
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)
683	phy = sigma*3 rho_a2 / ( eta4 * g * ( rho_l - rho_a ) )
684	py = phy**( 1.0_wp / 6.0_wp )
685
686	ENDIF
687
688	DO j = 1, radius_classes
689
690	IF ( radclass(j) <= 1.0E-5_wp ) THEN
691
692	winf(j) = stok * ( radclass(j)*2 + cunh radclass(j) )
693
694	ELSEIF ( radclass(j) > 1.0E-5_wp .AND. radclass(j) <= 5.35E-4_wp ) THEN
695
696	x = LOG( stb * radclass(j)**3 )
697	y = 0.0_wp
698
699	DO i = 1, 7
700	y = y + b(i) * x**(i-1)
701	ENDDO
702	!
703	!-- Note: this Eq. is wrong in (Pruppacher and Klett, 1997, p. 418)
704	!-- for correct version see (Beard, 1976)
705	xrey = ( 1.0_wp + cunh / radclass(j) ) * EXP( y )
706
707	winf(j) = xrey * eta / ( 2.0_wp * rho_a * radclass(j) )
708
709	ELSEIF ( radclass(j) > 5.35E-4_wp ) THEN
710
711	IF ( radclass(j) > 0.0035_wp ) THEN
712	bond = g * ( rho_l - rho_a ) * 0.0035_wp**2 / sigma
713	ELSE
714	bond = g * ( rho_l - rho_a ) * radclass(j)**2 / sigma
715	ENDIF
716
717	x = LOG( 16.0_wp * bond * py / 3.0_wp )
718	y = 0.0_wp
719
720	DO i = 1, 6
721	y = y + c(i) * x**(i-1)
722	ENDDO
723
724	xrey = py * EXP( y )
725
726	IF ( radclass(j) > 0.0035_wp ) THEN
727	winf(j) = xrey * eta / ( 2.0_wp * rho_a * 0.0035_wp )
728	ELSE
729	winf(j) = xrey * eta / ( 2.0_wp * rho_a * radclass(j) )
730	ENDIF
731
732	ENDIF
733
734	ENDDO
735
736	END SUBROUTINE fallg
737
738
739	!------------------------------------------------------------------------------!
740	! Description:
741	! ------------
742	!> Calculation of collision efficiencies for the Hall kernel
743	!------------------------------------------------------------------------------!
744	SUBROUTINE effic
745
746	USE particle_attributes, &
747	ONLY: radius_classes
748
749	IMPLICIT NONE
750
751	INTEGER(iwp) :: i !<
752	INTEGER(iwp) :: iq !<
753	INTEGER(iwp) :: ir !<
754	INTEGER(iwp) :: j !<
755	INTEGER(iwp) :: k !<
756
757	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: ira !<
758
759	LOGICAL, SAVE :: first = .TRUE. !<
760
761	REAL(wp) :: ek !<
762	REAL(wp) :: particle_radius !<
763	REAL(wp) :: pp !<
764	REAL(wp) :: qq !<
765	REAL(wp) :: rq !<
766
767	REAL(wp), DIMENSION(1:21), SAVE :: rat !<
768
769	REAL(wp), DIMENSION(1:15), SAVE :: r0 !<
770
771	REAL(wp), DIMENSION(1:15,1:21), SAVE :: ecoll !<
772
773	!
774	!-- Initial assignment of constants
775	IF ( first ) THEN
776
777	first = .FALSE.
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 /)
781
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 /)
850	ENDIF
851
852	!
853	!-- Calculate the radius class index of particles with respect to array r
854	!-- Radius has to be in Âµm
855	ALLOCATE( ira(1:radius_classes) )
856	DO j = 1, radius_classes
857	particle_radius = radclass(j) * 1.0E6_wp
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
866
867	!
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
872
873	ir = ira(j)
874	rq = MIN( radclass(i) / radclass(j), radclass(j) / radclass(i) )
875	iq = INT( rq * 20 ) + 1
876	iq = MAX( iq , 2)
877
878	IF ( ir < 16 ) THEN
879	IF ( ir >= 2 ) THEN
880	pp = ( ( MAX(radclass(j),radclass(i)) * 1.0E06_wp ) - r0(ir-1) ) / &
881	( r0(ir) - r0(ir-1) )
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) &
887	+ pp * qq * ecoll(ir,iq)
888	ELSE
889	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
890	ec(j,i) = ( 1.0_wp - qq ) * ecoll(1,iq-1) + qq * ecoll(1,iq)
891	ENDIF
892	ELSE
893	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
894	ek = ( 1.0_wp - qq ) * ecoll(15,iq-1) + qq * ecoll(15,iq)
895	ec(j,i) = MIN( ek, 1.0_wp )
896	ENDIF
897
898	IF ( ec(j,i) < 1.0E-20_wp ) ec(j,i) = 0.0_wp
899
900	ec(i,j) = ec(j,i)
901
902	ENDDO
903	ENDDO
904
905	DEALLOCATE( ira )
906
907	END SUBROUTINE effic
908
909
910	!------------------------------------------------------------------------------!
911	! Description:
912	! ------------
913	!> Calculation of enhancement factor for collision efficencies due to turbulence
914	!------------------------------------------------------------------------------!
915	SUBROUTINE turb_enhance_eff
916
917	USE particle_attributes, &
918	ONLY: radius_classes
919
920	IMPLICIT NONE
921
922	INTEGER(iwp) :: i !<
923	INTEGER(iwp) :: iq !<
924	INTEGER(iwp) :: ir !<
925	INTEGER(iwp) :: j !<
926	INTEGER(iwp) :: k !<
927	INTEGER(iwp) :: kk !<
928
929	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: ira !<
930
931	LOGICAL, SAVE :: first = .TRUE. !<
932
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 !<
940
941	REAL(wp), DIMENSION(1:11), SAVE :: rat !<
942
943	REAL(wp), DIMENSION(1:7), SAVE :: r0 !<
944
945	REAL(wp), DIMENSION(1:7,1:11), SAVE :: ecoll_100 !<
946	REAL(wp), DIMENSION(1:7,1:11), SAVE :: ecoll_400 !<
947
948	!
949	!-- Initial assignment of constants
950	IF ( first ) THEN
951
952	first = .FALSE.
953
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 /)
959	!
960	!-- for 100 cm2/s3
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 /)
983	!
984	!-- for 400 cm2/s3
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 /)
1007
1008	ENDIF
1009
1010	!
1011	!-- Calculate the radius class index of particles with respect to array r0
1012	!-- Radius has to be in Âµm
1013	ALLOCATE( ira(1:radius_classes) )
1014
1015	DO j = 1, radius_classes
1016	particle_radius = radclass(j) * 1.0E6_wp
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
1025
1026	!
1027	!-- Two-dimensional linear interpolation of the collision efficiencies
1028	!-- Radius has to be in Âµm
1029	DO j = 1, radius_classes
1030	DO i = 1, j
1031
1032	ir = ira(j)
1033	rq = MIN( radclass(i) / radclass(j), radclass(j) / radclass(i) )
1034
1035	DO kk = 2, 11
1036	IF ( rq <= rat(kk) ) THEN
1037	iq = kk
1038	EXIT
1039	ENDIF
1040	ENDDO
1041
1042	y1 = 0.0001_wp ! for 0 m2/s3
1043
1044	IF ( ir < 8 ) THEN
1045	IF ( ir >= 2 ) THEN
1046	pp = ( MAX(radclass(j),radclass(i))*1.0E6_wp - r0(ir-1) ) / &
1047	( r0(ir) - r0(ir-1) )
1048	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
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)
1057	ELSE
1058	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
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)
1061	ENDIF
1062	ELSE
1063	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
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)
1066	ENDIF
1067	!
1068	!-- Linear interpolation of dissipation rate in m2/s3
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
1075	ELSE
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
1078	ENDIF
1079
1080	IF ( ecf(j,i) < 1.0_wp ) ecf(j,i) = 1.0_wp
1081
1082	ecf(i,j) = ecf(j,i)
1083
1084	ENDDO
1085	ENDDO
1086
1087	END SUBROUTINE turb_enhance_eff
1088
1089
1090
1091	!------------------------------------------------------------------------------!
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.
1096	!------------------------------------------------------------------------------!
1097
1098	SUBROUTINE collision_efficiency_rogers( mean_r, r, e)
1099
1100	IMPLICIT NONE
1101
1102	INTEGER(iwp) :: i !<
1103	INTEGER(iwp) :: j !<
1104	INTEGER(iwp) :: k !<
1105
1106	LOGICAL, SAVE :: first = .TRUE. !<
1107
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 !<
1122
1123	REAL(wp), DIMENSION(1:9), SAVE :: collected_r = 0.0_wp !<
1124
1125	REAL(wp), DIMENSION(1:19), SAVE :: collector_r = 0.0_wp !<
1126
1127	REAL(wp), DIMENSION(1:9,1:19), SAVE :: ef = 0.0_wp !<
1128
1129	mean_rm = mean_r * 1.0E06_wp
1130	rm = r * 1.0E06_wp
1131
1132	IF ( first ) THEN
1133
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 /)
1140
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 /)
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
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
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) + &
1221	(gg-dd)ef(i+1,j+1) ) / (3.0_wp gg)
1222	ENDIF
1223
1224	END SUBROUTINE collision_efficiency_rogers
1225
1226	END MODULE lpm_collision_kernels_mod

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