| 1 | subroutine n_acethylene(ngrid,nq,nbin, |
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| 2 | * dt,pl,tl,aerad, |
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| 3 | * q,qprime) |
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| 4 | |
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| 5 | implicit none |
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| 6 | #include "dimensions.h" |
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| 7 | #include "microtab.h" |
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| 8 | #include "varmuphy.h" |
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| 9 | |
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| 10 | c Arguments |
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| 11 | c --------- |
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| 12 | |
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| 13 | integer ngrid,nq,nbin |
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| 14 | |
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| 15 | REAL dt ! physical time step (s) |
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| 16 | REAL pl(ngrid,nz) ! pressure at each level (mbar) |
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| 17 | REAL tl(ngrid,nz) ! temperature at each level (K) |
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| 18 | REAL aerad(nbin) ! Radius array |
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| 19 | |
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| 20 | c Tracers : |
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| 21 | REAL q(ngrid,nz,nq) ! tracer (kg/kg) |
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| 22 | REAL qprime(ngrid,nz,nbin) ! tracer (kg/kg) |
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| 23 | |
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| 24 | |
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| 25 | c Local variables |
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| 26 | c --------------- |
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| 27 | |
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| 28 | integer ntyp |
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| 29 | parameter (ntyp=3) |
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| 30 | |
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| 31 | real n_aer(nz,nbin,ntyp) |
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| 32 | real c2h2vap(nz) |
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| 33 | |
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| 34 | integer itrac |
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| 35 | integer ig,i,j,k,l,n ! Loop integers |
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| 36 | integer ilay,iq |
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| 37 | |
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| 38 | c Treatment |
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| 39 | c --------- |
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| 40 | |
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| 41 | DO ig = 1 , NGRID |
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| 42 | |
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| 43 | c Set up the aerosol array |
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| 44 | do j = 1, ntyp |
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| 45 | do k = 1, nbin |
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| 46 | itrac = (j-1) * nbin + k |
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| 47 | do l = 1, nz |
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| 48 | n_aer(l,k,j) = max(q(ig,l,itrac),0.) |
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| 49 | enddo |
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| 50 | enddo |
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| 51 | enddo |
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| 52 | |
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| 53 | c Set up the methane vapor array |
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| 54 | do l = 1, nz |
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| 55 | c2h2vap(l) = q(ig,l,nq) |
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| 56 | enddo |
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| 57 | |
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| 58 | call nucleacond3(ngrid,nbin,dt,ig,pl,tl,aerad, |
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| 59 | & n_aer,qprime,c2h2vap) |
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| 60 | |
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| 61 | c Update q arrays |
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| 62 | do j = 1, ntyp |
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| 63 | do k = 1, nbin |
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| 64 | itrac = (j-1) * nbin + k |
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| 65 | do l = 1, nz |
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| 66 | q(ig,l,itrac) = n_aer(l,k,j) |
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| 67 | enddo |
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| 68 | enddo |
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| 69 | enddo |
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| 70 | |
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| 71 | c Update methane vapor array |
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| 72 | do l = 1, nz |
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| 73 | q(ig,l,nq) = c2h2vap(l) |
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| 74 | enddo |
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| 75 | |
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| 76 | ENDDO |
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| 77 | |
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| 78 | return |
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| 79 | END |
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| 80 | |
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| 81 | **************************************************************** |
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| 82 | subroutine nucleacond3(ngrid,nbin,dt,ig, |
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| 83 | * pl,tl,aerad,n_aer,qprime,c2h2vap) |
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| 84 | * * |
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| 85 | * This routine updates species concentrations due * |
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| 86 | * to both nucleation and condensation-induced variations. * |
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| 87 | * Gain and loss rates associated to each one of these * |
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| 88 | * processes are computed separately in other routines. * |
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| 89 | * * |
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| 90 | **************************************************************** |
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| 91 | |
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| 92 | implicit none |
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| 93 | #include "dimensions.h" |
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| 94 | #include "microtab.h" |
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| 95 | #include "varmuphy.h" |
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| 96 | |
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| 97 | integer ng,nalt |
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| 98 | parameter(ng=1,nalt=llm) |
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| 99 | |
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| 100 | |
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| 101 | real lv |
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| 102 | |
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| 103 | common/lheat/lv |
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| 104 | |
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| 105 | |
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| 106 | |
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| 107 | c Arguments |
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| 108 | c --------- |
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| 109 | |
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| 110 | integer ngrid,nbin |
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| 111 | integer ig |
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| 112 | integer ntyp |
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| 113 | parameter (ntyp=3) |
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| 114 | |
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| 115 | real dt ! Global time step |
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| 116 | real pl(ngrid,nz),tl(ngrid,nz) |
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| 117 | real aerad(nbin) |
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| 118 | real c2h2vap(nz) ! Methane vapor mass mixing ratio (kg/m3) |
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| 119 | real c2h2vap_old |
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| 120 | real n_aer(nz,nbin,ntyp) ! number concentrations of particle/each size bin |
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| 121 | real qprime(ngrid,nz,nbin) ! tracer (kg/kg) |
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| 122 | REAL total1(nz),total11(nz),total2(nz),total22(nz) |
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| 123 | REAL dmsm,mtot |
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| 124 | |
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| 125 | |
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| 126 | |
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| 127 | |
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| 128 | |
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| 129 | c Local |
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| 130 | c ----- |
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| 131 | |
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| 132 | integer i,j,k,l,n,iindice,iselec |
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| 133 | |
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| 134 | real dQc ! Amount of condensed methane (kg/m3) during timestep |
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| 135 | real*8 sat_ratio ! Methane saturation ratio over liquid |
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| 136 | real*8 sat_ratmix ! Methane saturation ratio over liquid |
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| 137 | real*8 pc2h2 ! Methane partial pressure (Pa) |
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| 138 | real qsat ! Methane mass mixing ratio at saturation (kg/kg of air) |
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| 139 | real qsatmix ! Methane mass mixing ratio at saturation (kg/kg of air) |
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| 140 | real*8 rate(nbin) ! Heterogeneous Nucleation rate (s-1) |
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| 141 | real*8 elim |
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| 142 | |
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| 143 | real nsav(nbin,ntyp) |
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| 144 | real dn(nbin,ntyp) |
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| 145 | real rad(nbin) ! Radius of droplets in each size bin |
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| 146 | real*8 gr(nbin) ! Growth rate in each bin |
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| 147 | real radius ! Radius of droplets after growth |
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| 148 | real Qs ! Mass of condensate required to reach saturation |
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| 149 | real newsat |
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| 150 | real vol(nbin) |
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| 151 | |
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| 152 | real press |
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| 153 | real sig3,temp,seq(nbin) |
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| 154 | real Ctot,up,dwn,newvap,gltot |
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| 155 | |
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| 156 | real temp0,temp1,temp2,last_temp |
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| 157 | real qsat1,sat_ratio1,tempf(0:10),sat_ratiof(0:10) |
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| 158 | real rho_a,cap |
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| 159 | real tempref |
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| 160 | real xtime,xtime_prime |
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| 161 | |
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| 162 | |
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| 163 | c Variables for latent heat release |
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| 164 | real lw |
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| 165 | data lw / 581.e+3/ |
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| 166 | save lw |
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| 167 | |
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| 168 | |
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| 169 | c Treatment |
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| 170 | c --------- |
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| 171 | do i = 1, nbin |
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| 172 | vol(i) = 4./3. * pi * aerad(i)**3. |
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| 173 | enddo |
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| 174 | |
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| 175 | do l = 1, nz |
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| 176 | total1(l)=0. !solide |
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| 177 | do k = 1, nbin |
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| 178 | total1(l)=total1(l)+n_aer(l,k,2)*rhoi_c2h2 |
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| 179 | enddo |
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| 180 | total2(l)=c2h2vap(l) |
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| 181 | enddo |
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| 182 | |
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| 183 | |
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| 184 | c Start loop over heights |
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| 185 | DO 100 l = 1, nz |
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| 186 | |
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| 187 | iindice=0 ! mettre l'indice à 0 |
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| 188 | |
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| 189 | temp = tl(ig,l) |
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| 190 | press = pl(ig,l) |
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| 191 | tempref=temp |
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| 192 | |
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| 193 | c Save the values of the particle arrays before condensation |
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| 194 | do j = 1, ntyp |
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| 195 | do i = 1, nbin |
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| 196 | nsav(i,j) = n_aer(l,i,j) |
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| 197 | enddo |
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| 198 | enddo |
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| 199 | |
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| 200 | |
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| 201 | 99 continue |
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| 202 | |
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| 203 | |
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| 204 | call c2h2sat(temp,press,qsat) |
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| 205 | qsatmix=qsat |
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| 206 | |
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| 207 | c quantité pmixc2h2(l) déjà calculé dans cnuages.F et passé dans un common |
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| 208 | |
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| 209 | c Get the partial presure of methane vapor and its saturation ratio |
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| 210 | pc2h2 = c2h2vap(l) * (Mn2/Mc2h2) * press |
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| 211 | sat_ratio = c2h2vap(l) / qsat |
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| 212 | sat_ratmix = c2h2vap(l) / qsatmix |
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| 213 | |
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| 214 | c Get the rates of nucleation |
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| 215 | call nuclea3(nbin,aerad,pc2h2,temp,sat_ratio,rate) |
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| 216 | |
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| 217 | c Get the growth rates of condensation/sublimation |
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| 218 | up = c2h2vap(l) |
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| 219 | dwn = 1. |
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| 220 | Ctot = c2h2vap(l) |
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| 221 | DO i = 1, nbin |
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| 222 | |
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| 223 | if (n_aer(l,i,3).eq.0) then |
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| 224 | rad(i) = aerad(i) |
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| 225 | else |
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| 226 | rad(i) = ((n_aer(l,i,2)/n_aer(l,i,3) + |
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| 227 | & qprime(ig,l,i)/n_aer(l,i,3) |
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| 228 | & +vol(i))*0.75/pi)**(1./3.) |
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| 229 | endif |
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| 230 | |
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| 231 | |
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| 232 | * Equilibrium saturation ratio (due to curvature effect) |
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| 233 | seq(i) = exp( 2.*sig3(temp)*Mc2h2 /(rhoi_c2h2*rgp*temp*rad(i))) |
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| 234 | |
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| 235 | call growthrate3(dt,temp,press,pc2h2, |
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| 236 | & sat_ratmix,seq(i),rad(i),gr(i)) |
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| 237 | |
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| 238 | up = up + dt * gr(i) * 4. * pi * rhoi_c2h2 * rad(i) * seq(i) |
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| 239 | * * nsav(i,3) |
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| 240 | dwn= dwn+ dt * gr(i) * 4. * pi * rhoi_c2h2 * rad(i) / qsat |
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| 241 | * * nsav(i,3) |
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| 242 | Ctot= Ctot + rhoi_c2h2 * nsav(i,2) |
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| 243 | |
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| 244 | ENDDO |
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| 245 | |
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| 246 | newvap = min(up/dwn,Ctot) |
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| 247 | newvap = max(newvap,0.) |
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| 248 | |
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| 249 | gltot = 0. |
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| 250 | DO i = 1, nbin |
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| 251 | gr(i) = gr(i) * ( newvap/qsat - seq(i) ) |
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| 252 | if(nsav(i,2).le.0. .and. gr(i).le.0.) then |
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| 253 | n_aer(l,i,2) = 0. |
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| 254 | else |
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| 255 | n_aer(l,i,2) = nsav(i,2) + dt * gr(i) * 4. * pi * rad(i) |
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| 256 | * * n_aer(l,i,3) |
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| 257 | if (n_aer(l,i,2).le.0.) then |
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| 258 | n_aer(l,i,1) = n_aer(l,i,1) + n_aer(l,i,3) |
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| 259 | n_aer(l,i,2) = 0. |
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| 260 | n_aer(l,i,3) = 0. |
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| 261 | endif |
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| 262 | gltot=n_aer(l,i,2)*rhoi_c2h2+gltot |
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| 263 | endif |
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| 264 | |
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| 265 | ENDDO |
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| 266 | |
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| 267 | c Determine the mass of exchanged methane |
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| 268 | |
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| 269 | dQc = 0. |
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| 270 | DO i = 1, nbin |
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| 271 | dQc = dQc - rhoi_c2h2 * ( n_aer(l,i,2) - nsav(i,2) ) |
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| 272 | ENDDO |
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| 273 | |
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| 274 | c Update the methane vapor mixing ratio implied by |
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| 275 | c the cond/eva processes. |
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| 276 | |
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| 277 | |
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| 278 | c Arrays resetted to their initial value before condensation |
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| 279 | do j = 1, ntyp |
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| 280 | do i = 1, nbin |
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| 281 | dn(i,j) = n_aer(l,i,j) - nsav(i,j) |
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| 282 | n_aer(l,i,j) = nsav(i,j) |
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| 283 | enddo |
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| 284 | enddo |
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| 285 | |
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| 286 | c Update the c arrays. |
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| 287 | c nucleation & cond/eva tendencies added together. |
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| 288 | |
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| 289 | do i=1,nbin |
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| 290 | elim = dt * rate(i) |
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| 291 | n_aer(l,i,1) = n_aer(l,i,1) / (1.+elim) |
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| 292 | n_aer(l,i,3) = n_aer(l,i,3) + elim * n_aer(l,i,1) + dn(i,3) |
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| 293 | n_aer(l,i,1) = n_aer(l,i,1) + dn(i,1) |
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| 294 | n_aer(l,i,2) = n_aer(l,i,2) + dn(i,2) |
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| 295 | if(n_aer(l,i,2).lt.0.) n_aer(l,i,2)=0. |
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| 296 | enddo |
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| 297 | |
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| 298 | dQc = 0. |
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| 299 | DO i = 1, nbin |
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| 300 | dQc = dQc - rhoi_c2h2 * ( n_aer(l,i,2) - nsav(i,2) ) |
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| 301 | ENDDO |
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| 302 | |
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| 303 | |
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| 304 | c2h2vap(l) = c2h2vap(l) + dQc |
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| 305 | |
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| 306 | 100 CONTINUE |
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| 307 | |
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| 308 | do l = 1, nz |
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| 309 | total11(l)=0. |
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| 310 | do k = 1, nbin |
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| 311 | total11(l)=total11(l)+n_aer(l,k,2)*rhoi_c2h2 |
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| 312 | enddo |
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| 313 | total22(l)=c2h2vap(l) |
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| 314 | enddo |
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| 315 | |
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| 316 | return |
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| 317 | end |
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| 318 | |
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| 319 | |
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| 320 | ******************************************************* |
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| 321 | * * |
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| 322 | subroutine nuclea3(nbin,aerad,pc2h2,temp,sat,nucrate) |
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| 323 | * This subroutine computes the nucleation rate * |
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| 324 | * as given in Pruppacher & Klett (1978) in the * |
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| 325 | * case of water ice forming on a solid substrate. * |
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| 326 | * Definition refined by Keese (jgr,1989) * |
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| 327 | * * |
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| 328 | ******************************************************* |
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| 329 | |
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| 330 | implicit none |
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| 331 | #include "dimensions.h" |
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| 332 | #include "microtab.h" |
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| 333 | #include "varmuphy.h" |
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| 334 | |
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| 335 | integer nbin |
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| 336 | real aerad(nbin) |
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| 337 | |
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| 338 | real*8 nucrate(nbin) |
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| 339 | real*8 pc2h2 |
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| 340 | real temp |
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| 341 | real*8 sat |
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| 342 | |
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| 343 | integer l,i |
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| 344 | real*8 nc2h2 |
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| 345 | real sig3 ! Water-ice/air surface tension (N.m) |
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| 346 | real*8 rstar ! Radius of the critical germ (m) |
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| 347 | real*8 gstar ! # of molecules forming a critical embryo |
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| 348 | real*8 x ! Ratio rstar/radius of the nucleating dust particle |
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| 349 | real fistar ! Activation energy required to form a critical embryo (J) |
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| 350 | real*8 zeldov ! Zeldovitch factor (no dim) |
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| 351 | real*8 fshape3 ! function defined at the end of the file |
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| 352 | real*8 deltaf |
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| 353 | |
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| 354 | real nus |
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| 355 | data nus/1.e+13/ ! Jump frequency of a molecule (s-1) |
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| 356 | real m0 |
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| 357 | data m0/4.31894e-26/ ! Weight of a methane molecule (kg) |
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| 358 | real vo1 |
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| 359 | data vo1/4.22764e-5/ ! Volume molaire (masse molaire/masse volumique = MolWt/LDEN) |
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| 360 | real desorp |
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| 361 | data desorp/0.288e-19/ ! Activation energy for desorption of water on a dust-like substrate (J/molecule) |
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| 362 | real surfdif |
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| 363 | data surfdif/0.288e-20/! Estimated activation energy for surface diffusion of water molecules (J/molecule) |
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| 364 | |
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| 365 | IF (sat .GT. 1.) then ! minimum condition to activate nucleation |
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| 366 | |
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| 367 | nc2h2 = pc2h2 / kbz / temp |
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| 368 | rstar = 2. * sig3(temp) * vo1 / (rgp*temp*log(sat)) |
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| 369 | gstar = 4. * nav * pi * (rstar**3) / (3.*vo1) |
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| 370 | c Loop over size bins |
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| 371 | do i=1,nbin |
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| 372 | x = aerad(i) / rstar |
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| 373 | x = aerad(imono) / rstar ! r(5)=monomere |
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| 374 | fistar = (4./3.*pi) * sig3(temp) * (rstar**2.) |
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| 375 | & *fshape3(mtetac2h2,x) |
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| 376 | deltaf = min( max((2.*desorp-surfdif-fistar)/(kbz*temp) |
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| 377 | & , -100.), 100.) |
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| 378 | if (deltaf.eq.-100.) then |
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| 379 | nucrate(i) = 0. |
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| 380 | else |
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| 381 | zeldov = sqrt ( fistar / (3.*pi*kbz*temp*(gstar**2.)) ) |
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| 382 | nucrate(i) = zeldov * kbz* temp * rstar**2. |
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| 383 | & * 4. * pi * ( nc2h2*aerad(i) )**2. |
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| 384 | & / ( fshape3(mtetac2h2,x) * nus * m0 ) |
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| 385 | & * dexp(deltaf) |
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| 386 | |
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| 387 | |
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| 388 | if(i.gt.imono) nucrate(i)= zeldov * kbz* temp * rstar**2. |
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| 389 | & * 4. * pi * vrat_e**(i-imono)*(nc2h2*aerad(imono) )**2. |
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| 390 | & / (fshape3(mtetac2h2,x) * nus * m0 ) |
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| 391 | & * dexp(deltaf) |
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| 392 | |
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| 393 | endif |
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| 394 | enddo |
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| 395 | ELSE |
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| 396 | do i=1,nbin |
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| 397 | nucrate(i) = 0. |
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| 398 | enddo |
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| 399 | |
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| 400 | ENDIF |
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| 401 | |
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| 402 | return |
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| 403 | end |
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| 404 | |
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| 405 | ****************************************************************** |
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| 406 | subroutine c2h2sat(t,p,qsat) |
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| 407 | * * |
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| 408 | * cette fonction calcule la pression de vapeur saturante de l' * |
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| 409 | * ethane a une altitude donnee z par Reid et al., p657 * |
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| 410 | * * |
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| 411 | * Compatible avec Barth et al., dans l'intervalle 30-90K * |
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| 412 | * * |
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| 413 | * * |
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| 414 | ****************************************************************** |
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| 415 | |
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| 416 | real rgp |
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| 417 | data rgp/8.3143/ |
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| 418 | |
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| 419 | * declaration des variables internes |
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| 420 | * ---------------------------------- |
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| 421 | |
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| 422 | real qsat,t,p |
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| 423 | |
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| 424 | |
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| 425 | a=-6.90128 |
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| 426 | b=1.26873 |
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| 427 | c=-2.09113 |
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| 428 | d=-2.75601 |
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| 429 | pc=61.4*1.013e5 |
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| 430 | tc=308.3 |
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| 431 | |
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| 432 | x=(1.-t/tc) |
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| 433 | if(x.gt. 0.) qsat=(1-x)**(-1)*(a*x+b*x**1.5+c*x**3.+d*x**6.) |
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| 434 | if(x.le. 0.) qsat=a*x/abs(1.-x) ! approx pour t > tc |
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| 435 | qsat=pc*exp(qsat) |
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| 436 | |
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| 437 | qsat=qsat* 26.0 / (28.0*p) ! kg/kg |
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| 438 | |
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| 439 | return |
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| 440 | end |
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| 441 | |
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| 442 | c======================================================================= |
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| 443 | subroutine growthrate3(timestep,temp,press,pc2h2,sat,seq,r,Cste) |
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| 444 | c |
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| 445 | c Determination of the droplet growth rate |
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| 446 | c |
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| 447 | c======================================================================= |
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| 448 | |
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| 449 | IMPLICIT NONE |
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| 450 | #include "dimensions.h" |
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| 451 | #include "microtab.h" |
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| 452 | #include "varmuphy.h" |
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| 453 | |
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| 454 | c----------------------------------------------------------------------- |
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| 455 | C DECLARATIONS: |
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| 456 | c ------------- |
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| 457 | |
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| 458 | common/lheat/Lv |
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| 459 | |
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| 460 | c |
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| 461 | c arguments: |
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| 462 | c ---------- |
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| 463 | |
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| 464 | REAL timestep |
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| 465 | REAL temp ! temperature in the middle of the layer (K) |
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| 466 | REAL press ! pressure in the middle of the layer (K) |
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| 467 | REAL*8 pc2h2 ! Methane vapor partial pressure (Pa) |
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| 468 | REAL*8 sat ! saturation ratio |
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| 469 | REAL r ! crystal radius before condensation (m) |
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| 470 | REAL seq ! Equilibrium saturation ratio |
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| 471 | |
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| 472 | c local: |
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| 473 | c ------ |
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| 474 | |
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| 475 | REAL psat |
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| 476 | REAL moln2,molc2h2 |
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| 477 | REAL To,tc2h2,wc2h2 ! Reid et al., (eq 7-9.4 + Appendix compound [168]) |
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| 478 | REAL fte |
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| 479 | |
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| 480 | c Effective gas molecular radius (m) |
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| 481 | data moln2/1.75e-10/ ! N2 |
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| 482 | c Effective gas molecular radius (m) |
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| 483 | data molc2h2/2.015e-10/ ! C2H2 |
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| 484 | c Temperature critique + omega |
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| 485 | data tc2h2/308.3/ |
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| 486 | data wc2h2/19.0e-2/ |
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| 487 | |
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| 488 | REAL k,Lv |
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| 489 | REAL knudsen ! Knudsen number (gas mean free path/particle radius) |
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| 490 | REAL a,Dv,lambda,Rk,Rd ! Intermediate computations for growth rate |
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| 491 | REAL*8 Cste |
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| 492 | |
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| 493 | c----------------------------------------------------------------------- |
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| 494 | c Ice particle growth rate by diffusion/impegement of molecules |
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| 495 | c r.dr/dt = (S-Seq) / (Seq*Rk+Rd) |
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| 496 | c with r the crystal radius, Rk and Rd the resistances due to |
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| 497 | c latent heat release and to vapor diffusion respectively |
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| 498 | c----------------------------------------------------------------------- |
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| 499 | |
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| 500 | psat = pc2h2 / sat |
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| 501 | |
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| 502 | c - Thermal conductibility of N2 |
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| 503 | |
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| 504 | k = ( 2.857e-2 * temp - 0.5428 ) * 4.184e-3 |
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| 505 | |
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| 506 | |
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| 507 | c - Latent heat of c2h2 (J.kg-1) |
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| 508 | Lv =581.e3 ! eq (7-9.4) Reid et al. |
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| 509 | fte=(1.-temp/tc2h2) |
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| 510 | if (fte.le.1.e-3) fte=1.e-3 |
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| 511 | Lv=8.314*tc2h2*(7.08*fte**0.354+10.95*wc2h2*fte**0.456)/26.e-3 |
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| 512 | |
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| 513 | |
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| 514 | |
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| 515 | c - Constant to compute gas mean free path |
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| 516 | c l= (T/P)*a, with a = ( 0.707*8.31/(4*pi*molrad**2 * avogadro)) |
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| 517 | |
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| 518 | a = 0.707*rgp/(4 * pi* (moln2*1.e10)**2 * (nav*1.e-20)) |
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| 519 | |
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| 520 | c - Compute Dv, methane vapor diffusion coefficient |
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| 521 | c accounting for both kinetic and continuum regime of diffusion, |
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| 522 | c the nature of which depending on the Knudsen number. |
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| 523 | |
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| 524 | Dv = 1./3. * sqrt( 8*rgp*temp/(pi*Mc2h2) )* (kbz*1.e20) * temp/ |
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| 525 | & (pi*press*(moln2*1.e10+molc2h2*1.e10)**2 * sqrt(1.+Mc2h2/Mn2)) |
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| 526 | |
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| 527 | knudsen = temp / press * a / r |
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| 528 | lambda = (1.333+0.71/knudsen) / (1.+1./knudsen) |
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| 529 | Dv = Dv / (1. + lambda * knudsen) |
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| 530 | |
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| 531 | c - Compute Rk |
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| 532 | Rk = Lv**2 * rhoi_c2h2 * Mc2h2 / (k*rgp*temp**2.) |
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| 533 | * print*,'Cste Rk :',Lv,k,rgp,t |
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| 534 | |
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| 535 | c - Compute Rd |
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| 536 | Rd = rgp * temp *rhoi_c2h2 / (Dv*psat*Mc2h2) |
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| 537 | * print*,'Cste Rd :',Dv,psat,Mc2h2 |
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| 538 | |
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| 539 | c - Compute: rdr/dt = Cste * (S-Seq) |
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| 540 | Cste = 1. / (seq*Rk+Rd) |
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| 541 | * print*,'Cste Cste :',seq,Rk,Rd |
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| 542 | |
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| 543 | |
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| 544 | RETURN |
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| 545 | END |
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| 546 | |
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| 547 | |
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| 548 | ********************************************************* |
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| 549 | real function sig3(t) |
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| 550 | * this function computes the surface tension (N.m) * |
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| 551 | * between acethylene and air as a function of temp. * |
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| 552 | ********************************************************* |
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| 553 | |
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| 554 | real t |
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| 555 | pc=61.4*1.01325e5 |
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| 556 | tc=308.3 |
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| 557 | tb=188.4 |
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| 558 | tr=t/tc |
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| 559 | tbr=tb/tc |
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| 560 | if(t.gt.308.0) then |
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| 561 | tr=308./tc |
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| 562 | endif |
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| 563 | |
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| 564 | |
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| 565 | |
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| 566 | sig3=0.1196*(1.+(tbr*alog(pc/1.01325))/(1.-tbr))-0.279 |
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| 567 | sig3=pc**(2./3.)*tc**(1./3.)*sig3*(1.-tr)**(11./9.) |
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| 568 | sig3=sig3*1.e-8 |
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| 569 | |
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| 570 | return |
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| 571 | end |
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| 572 | |
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| 573 | ********************************************************* |
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| 574 | real*8 function fshape3(cost,rap) |
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| 575 | * function computing the f(m,x) factor * |
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| 576 | * related to energy required to form a critical embryo * |
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| 577 | ********************************************************* |
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| 578 | |
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| 579 | implicit none |
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| 580 | |
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| 581 | real cost |
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| 582 | real*8 rap |
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| 583 | real*8 phi |
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| 584 | real*8 a,b,c |
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| 585 | |
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| 586 | |
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| 587 | phi = sqrt( 1. - 2.*cost*rap + rap**2 ) |
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| 588 | a = 1. + ( (1.-cost*rap)/phi )**3 |
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| 589 | b = (rap**3) * (2.-3.*(rap-cost)/phi+((rap-cost)/phi)**3) |
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| 590 | c = 3. * cost * (rap**2) * ((rap-cost)/phi-1.) |
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| 591 | |
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| 592 | fshape3 = 0.5*(a+b+c) |
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| 593 | |
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| 594 | if (rap.gt.3000.) fshape3 = ((2.+cost)*(1.-cost)**2)/4. |
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| 595 | |
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| 596 | return |
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| 597 | end |
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| 598 | |
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