Variables = "x", "T", "P", "N", "Y", "r"
0.0000000E+00 1.0000000E+03 5.0000000E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00
2.0202020E-02 1.0000000E+03 4.9898375E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00
4.0404040E-02 1.0000000E+03 4.9795496E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00
6.0606062E-02 1.0000000E+03 4.9691359E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00
8.0808081E-02 1.0000000E+03 4.9585922E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00
1.0101010E-01 1.0000000E+03 4.9479172E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00
1.2121212E-01 1.0000000E+03 4.9371070E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00
1.4141414E-01 1.0000000E+03 4.9261602E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00
1.6161616E-01 1.0000000E+03 4.9150742E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00
1.8181819E-01 1.0000000E+03 4.9038465E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00
2.0202020E-01 1.0000000E+03 4.8924727E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00
2.2222222E-01 1.0000000E+03 4.8809523E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00
2.4242425E-01 1.0000000E+03 4.8692809E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00
2.6262626E-01 1.0000000E+03 4.8574566E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00
2.8282827E-01 1.0000000E+03 4.8454746E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00
3.0303031E-01 1.0000000E+03 4.8333336E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00
3.2323232E-01 1.0000000E+03 4.8210289E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00
3.4343433E-01 1.0000000E+03 4.8085586E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00
3.6363637E-01 1.0000000E+03 4.7959184E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00
3.8383839E-01 1.0000000E+03 4.7831051E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00
4.0404040E-01 1.0000000E+03 4.7701148E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00
4.2424244E-01 1.0000000E+03 4.7569445E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00
4.4444445E-01 1.0000000E+03 4.7435898E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00
4.6464646E-01 1.0000000E+03 4.7300473E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00
4.8484850E-01 1.0000000E+03 4.7163125E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00
5.0505048E-01 1.0000000E+03 4.7023812E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00
5.2525252E-01 1.0000000E+03 4.6882492E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00
5.4545456E-01 1.0000000E+03 4.6739133E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00
5.6565654E-01 1.0000000E+03 4.6593668E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00
5.8585858E-01 1.0000000E+03 4.6446074E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00
6.0606062E-01 1.0000000E+03 4.6296297E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00
6.2626261E-01 1.0000000E+03 4.6144281E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00
6.4646465E-01 1.0000000E+03 4.5989980E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00
6.6666669E-01 1.0000000E+03 4.5833336E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00
6.8686867E-01 1.0000000E+03 4.5674297E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00
7.0707071E-01 1.0000000E+03 4.5512820E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00
7.2727275E-01 1.0000000E+03 4.5348836E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00
7.4747473E-01 1.0000000E+03 4.5182293E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00
7.6767677E-01 1.0000000E+03 4.5013121E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00
7.8787881E-01 1.0000000E+03 4.4841266E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00
8.0808079E-01 Infinity Infinity Infinity NaN NaN
8.2828283E-01 NaN NaN NaN NaN 0.0000000E+00
8.4848487E-01 NaN NaN NaN NaN 0.0000000E+00
8.6868685E-01 NaN NaN NaN NaN 0.0000000E+00
8.8888890E-01 NaN NaN NaN NaN 0.0000000E+00
9.0909094E-01 NaN NaN NaN NaN 0.0000000E+00
9.2929292E-01 NaN NaN NaN NaN 0.0000000E+00
9.4949496E-01 NaN NaN NaN NaN 0.0000000E+00
9.6969700E-01 NaN NaN NaN NaN 0.0000000E+00
9.8989898E-01 NaN NaN NaN NaN 0.0000000E+00
1.0101010E+00 NaN NaN NaN NaN 0.0000000E+00
1.0303030E+00 NaN NaN NaN NaN 0.0000000E+00
1.0505050E+00 NaN NaN NaN NaN 0.0000000E+00
1.0707071E+00 NaN NaN NaN NaN 0.0000000E+00
1.0909091E+00 NaN NaN NaN NaN 0.0000000E+00
1.1111112E+00 NaN NaN NaN NaN 0.0000000E+00
1.1313131E+00 NaN NaN NaN NaN 0.0000000E+00
1.1515151E+00 NaN NaN NaN NaN 0.0000000E+00
1.1717172E+00 NaN NaN NaN NaN 0.0000000E+00
1.1919192E+00 NaN NaN NaN NaN 0.0000000E+00
1.2121212E+00 NaN NaN NaN NaN 0.0000000E+00
1.2323233E+00 NaN NaN NaN NaN 0.0000000E+00
1.2525252E+00 NaN NaN NaN NaN 0.0000000E+00
1.2727273E+00 NaN NaN NaN NaN 0.0000000E+00
1.2929293E+00 NaN NaN NaN NaN 0.0000000E+00
1.3131313E+00 NaN NaN NaN NaN 0.0000000E+00
1.3333334E+00 NaN NaN NaN NaN 0.0000000E+00
1.3535353E+00 NaN NaN NaN NaN 0.0000000E+00
1.3737373E+00 NaN NaN NaN NaN 0.0000000E+00
1.3939394E+00 NaN NaN NaN NaN 0.0000000E+00
1.4141414E+00 NaN NaN NaN NaN 0.0000000E+00
1.4343435E+00 NaN NaN NaN NaN 0.0000000E+00
1.4545455E+00 NaN NaN NaN NaN 0.0000000E+00
1.4747474E+00 NaN NaN NaN NaN 0.0000000E+00
1.4949495E+00 NaN NaN NaN NaN 0.0000000E+00
1.5151515E+00 NaN NaN NaN NaN 0.0000000E+00
1.5353535E+00 NaN NaN NaN NaN 0.0000000E+00
程序输出结果如上，修改程序module constants
implicit none
! 物理常数
real, parameter :: pi = 3.141592653589793
real, parameter :: R_univ = 8.314462618 ! 通用气体常数 [J/(mol·K)]
real, parameter :: k_B = 1.380649e-23 ! 玻尔兹曼常数 [J/K]
real, parameter :: N_A = 6.02214076e23 ! 阿伏伽德罗常数 [1/mol]
! 水物性参数
real, parameter :: M_H2O = 0.018015 ! 水的摩尔质量 [kg/mol]
real, parameter :: rho_l = 1000.0 ! 液态水密度 [kg/m³]
real, parameter :: sigma_H2O = 0.072 ! 表面张力 [N/m]
real, parameter :: h_fg = 2.257e6 ! 汽化潜热 [J/kg]
real, parameter :: cp_v = 1410.0 ! 水蒸气比热 [J/(kg·K)]
! 发动机参数
real, parameter :: De = 0.2 ! 喷口直径 [m]
real, parameter :: T0 = 1000.0 ! 喷口温度 [K]
real, parameter :: P0 = 50000.0 ! 喷口压力 [Pa]
real, parameter :: U0 = 2000.0 ! 喷口速度 [m/s]
real, parameter :: X_H2O = 0.22 ! 水蒸气摩尔分数
! 数值参数
integer, parameter :: nx = 100 ! 空间网格数
integer, parameter :: nt = 1000 ! 时间步数
real, parameter :: dt = 1e-5 ! 时间步长 [s]
real, parameter :: L_domain = 10.0 * De ! 计算域长度 [m]
! 共享变量
real, allocatable :: P_g(:) ! 压力场
end module constants
program condensation_model
use constants
implicit none
! 场变量定义
real :: x(nx), dx
real :: T_g(nx), U_g(nx), rho_g(nx)
real :: N_d(nx), Y_d(nx), r_d(nx) ! 液滴数密度、质量分数、半径
real :: m_v(nx), J_nuc(nx), dr_dt(nx) ! 凝结速率、成核率、半径增长率
! 辅助变量
real :: S(nx), r_c(nx), P_sat(nx)
integer :: i, t_step
! 分配共享数组
allocate(P_g(nx))
! 初始化网格
dx = L_domain / (nx - 1)
do i = 1, nx
x(i) = (i - 1) * dx
end do
! 初始化流场 (简化线性分布)
do i = 1, nx
P_g(i) = P0 * (1.0 - 0.8 * x(i)/L_domain)
T_g(i) = T0 * (1.0 - 0.6 * x(i)/L_domain)
U_g(i) = U0 * (1.0 - 0.3 * x(i)/L_domain)
rho_g(i) = P_g(i) / (287.0 * T_g(i)) ! 空气气体常数
end do
! 初始化液相变量
N_d = 0.0
Y_d = 0.0
r_d = 0.0
! 时间迭代循环
do t_step = 1, nt
! 计算过饱和比和临界半径
call calculate_saturation_ratio(P_g, T_g, S, P_sat, r_c)
! 初始化成核和生长参数
J_nuc = 0.0
dr_dt = 0.0
! 应用Schmidt-Appleman冷凝判据 (显式循环代替where)
do i = 1, nx
if (S(i) > 1.0) then
call nucleation_model_element(T_g(i), rho_g(i), S(i), r_c(i), J_nuc(i))
call droplet_growth_model_element(T_g(i), rho_g(i), r_d(i), r_c(i), S(i), dr_dt(i))
end if
end do
! 计算凝结质量速率
do i = 1, nx
if (r_d(i) > 0.0) then
m_v(i) = 4.0 * pi * r_d(i)**2 * rho_l * dr_dt(i) * N_d(i)
else
m_v(i) = 0.0
endif
end do
! 更新液相控制方程
call update_liquid_phase(N_d, Y_d, r_d, J_nuc, m_v, dr_dt, U_g, dx)
! 更新气相控制方程
call update_gas_phase(T_g, P_g, U_g, rho_g, m_v, dx)
! 输出数据
if (mod(t_step, 100) == 0) then
call output_data(t_step, x, T_g, P_g, N_d, Y_d, r_d)
end if
end do
! 输出最终结果
call output_data(nt, x, T_g, P_g, N_d, Y_d, r_d)
deallocate(P_g)
contains
! 计算饱和比和临界半径
subroutine calculate_saturation_ratio(P, T, S, P_sat, r_c)
real, intent(in) :: P(:), T(:)
real, intent(out) :: S(:), P_sat(:), r_c(:)
integer :: i
do i = 1, nx
P_sat(i) = 611.0 * exp(5423.0 * (1.0/273.0 - 1.0/T(i))) ! 简化Antoine方程
S(i) = (X_H2O * P(i)) / P_sat(i)
r_c(i) = merge(2.0 * sigma_H2O / (rho_l * (R_univ/M_H2O) * T(i) * log(S(i))), &
1e-9, S(i) > 1.0)
end do
end subroutine
! 单元素成核模型
subroutine nucleation_model_element(T, rho_g, S, r_c, J_nuc)
use constants, only: pi, sigma_H2O, k_B
real, intent(in) :: T, rho_g, S, r_c
real, intent(out) :: J_nuc
real :: A, B, DeltaG
if (S > 1.0) then
DeltaG = 4.0 * pi * r_c**2 * sigma_H2O / 3.0
A = 1e30 ! 指前因子
B = 4.0 * pi * r_c**2 * sigma_H2O / (3.0 * k_B * T)
J_nuc = A * exp(-B)
else
J_nuc = 0.0
end if
end subroutine
! 单元素液滴生长模型
subroutine droplet_growth_model_element(T, rho_g, r, r_c, S, dr_dt)
use constants, only: M_H2O, R_univ, rho_l, h_fg, sigma_H2O, pi, P_g
real, intent(in) :: T, rho_g, r, r_c, S
real, intent(out) :: dr_dt
real :: lambda_v, Kn, Pr_v, T_sat
if (S > 1.0 .and. r > 0.0) then
lambda_v = 0.026 ! 导热系数
Kn = sqrt(pi * M_H2O / (2.0 * R_univ * T)) / r
Pr_v = 0.71 ! 普朗特数
T_sat = 373.0 - (P_g(i) - 101325.0) * 0.00025 ! 简化计算
dr_dt = lambda_v * (T_sat - T) * (1.0 - r_c/r) &
/ (rho_l * h_fg * r * (1.0 + 3.78*(1.0 - 0.82*Kn)/Pr_v * Kn))
else
dr_dt = 0.0
end if
end subroutine
! 更新液相变量
subroutine update_liquid_phase(N_d, Y_d, r_d, J_nuc, m_v, dr_dt, U, dx)
use constants, only: dt, rho_l, pi
real, intent(inout) :: N_d(:), Y_d(:), r_d(:)
real, intent(in) :: J_nuc(:), m_v(:), dr_dt(:), U(:), dx
integer :: i
do i = 2, nx-1
! 数密度守恒
N_d(i) = N_d(i) + dt*(J_nuc(i) - U(i)*(N_d(i)-N_d(i-1))/dx)
! 质量分数守恒
Y_d(i) = Y_d(i) + dt*(m_v(i)/rho_l - U(i)*(Y_d(i)-Y_d(i-1))/dx)
! 更新液滴半径
if (N_d(i) > 0.0) then
r_d(i) = (3.0 * Y_d(i) / (4.0 * pi * rho_l * N_d(i)))**(1.0/3.0)
else
r_d(i) = 0.0
end if
end do
end subroutine
! 更新气相变量
subroutine update_gas_phase(T, P, U, rho, m_v, dx)
use constants, only: dt, h_fg, cp_v
real, intent(inout) :: T(:), P(:), U(:), rho(:)
real, intent(in) :: m_v(:), dx
integer :: i
do i = 2, nx-1
! 连续方程
rho(i) = rho(i) - dt * m_v(i)
! 动量方程
U(i) = U(i) - dt * U(i) * (U(i)-U(i-1))/dx - dt*(P(i)-P(i-1))/(dx*rho(i))
! 能量方程
T(i) = T(i) - dt * U(i) * (T(i)-T(i-1))/dx + dt * m_v(i) * h_fg / (rho(i)*cp_v)
! 状态方程
P(i) = rho(i) * 287.0 * T(i)
end do
end subroutine
! 数据输出
subroutine output_data(step, x, T, P, N, Y, r)
integer, intent(in) :: step
real, intent(in) :: x(:), T(:), P(:), N(:), Y(:), r(:)
character(len=50) :: filename
integer :: i
write(filename, '(a,i6.6,a)') 'output_', step, '.dat'
open(unit=10, file=filename, status='replace')
write(10, '(A)') 'Variables = "x", "T", "P", "N", "Y", "r"'
do i = 1, nx
write(10, '(6ES16.7)') x(i), T(i), P(i), N(i), Y(i), r(i)
end do
close(10)
end subroutine
end program condensation_model
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