program main_NR_total
implicit none
Double Precision :: G_GHI, G_DNI, u_Air, T_a, T_sky, T_in_HTF, T_PVi
Double Precision :: T_abs, T_sub, T_out_HTF, T_PTC, T_PV
Double Precision :: R_cond_abs, R_cond_PV, R_cond_sub
Double Precision :: R_conv_abs, R_conv_PV, R_conv_PTC
!Double Precision :: W_PV, W_abs, L, A_PV, A_abs, A_ap, A_PTC
!Double Precision :: CR_PTC, alpha_PV, alpha_abs, epsilon_PV, epsilon_abs
!Double Precision :: IAM_elec, IAM_th, eta_opt, sigma
!Double Precision :: m_dot_HTF, C_p_HTF, U, A_hx, P_PV, T_PV
!Double Precision :: alpha_PTC, epsilon_PTC
Double Precision :: C_p_HTF, rho_Water
Double Precision :: D,W_PV,W_abs,W_PTC, L_PTC,L_SRC_PVT ! Geometry of the PTC and SRC-PVT (Definir en el Type)
Double Precision :: A_PV,A_abs,A_sub,A_ap,A_PTC, CR_PTC
Double Precision :: alpha_PV,alpha_abs,alpha_PTC ! Design parameters
Double Precision :: epsilon_PV,epsilon_abs,epsilon_PTC
Double Precision :: IAM_elec,IAM_th,eta_opt,sigma
Double Precision :: P_Air,P_HTF,m_dot_HTF, th_PV,th_abs,th_sub,k_PV,k_abs,k_sub
Double Precision :: r_pipe,h_triangle,h_inscribed, th_min,th_max ! Thickness of the substrate
Double Precision :: A_cs_pipe,u_Water, A_hx,NTU,E, U ! Water (HTF) velocity and NTU number
Double Precision :: eta_PV,P_PV, q_dot_HTF,eta_elec,eta_th !
Double Precision :: h_abs, h_PTC, h_PV, h_HTF
integer :: iter
! ===== Inicialización de constantes =====
! ---- ---- ---- ---- Boundary conditions
G_GHI = 1000.0d0
G_DNI = 800.0d0
u_Air = 5.0d0
T_a = 25.0d0 + 273.15d0
T_sky = 25.0d0 + 273.15d0
T_in_HTF = 70.0d0 + 273.15d0
T_PVi = 355.45d0
! ---- ---- ---- ---- Geometry of the PTC and SRC-PVT
D = 0.03d0
W_PV = 0.12d0
W_abs = 0.06d0
W_PTC = 1.2d0
L_PTC = 10.0d0
L_SRC_PVT = L_PTC
A_PV = W_PV * L_SRC_PVT !1.2d0
A_abs = W_abs * L_SRC_PVT !0.6d0
A_sub = A_PV + A_abs !OJO aquí
A_ap = 1.2d0 * L_PTC
A_PTC = 3.0d0 * L_PTC !30.0d0
CR_PTC = A_ap / A_PV
! ---- ---- ---- ---- Design parameters
alpha_PV = 0.97d0
alpha_abs = 0.90d0
alpha_PTC = 0.03d0
epsilon_PV = 0.2d0
epsilon_abs = 0.2d0
epsilon_PTC = 0.3d0
IAM_elec = 0.72d0
IAM_th = 0.86d0
eta_opt = 0.83d0
sigma = 5.67d-8 !5.670374d-8
m_dot_HTF = 0.15d0
C_p_HTF = 4187.0d0
h_HTF = 1665.0d0
P_Air = 1.01325
P_HTF = 0.3119
m_dot_HTF = 0.15
th_PV = 0.003d0
th_abs = 0.003d0
!th_sub = 0.02541d0
k_PV = 50.0d0
k_abs = 205.0d0
k_sub = 250.0d0
!U = 780.1d0
!A_hx = 0.9425d0
!P_PV = 1723.0d0
!R_cond_abs = 0.00002439d0
!R_cond_PV = 0.00005d0
!R_cond_sub = 0.00008472d0
!R_conv_abs = 0.4848d0
!R_conv_PV = 0.3428d0
!R_conv_PTC = 0.04336d0
h_abs = 35.22d0 !3.438d0 !35.22d0
h_PTC = 7.87d0 !0.7687d0 !7.87d0
h_PV = 24.90d0 !2.431d0 !24.90d0
h_HTF = 1684.90d0 !835.3d0 !1684.90d0
!h_HTF = hh_HTF
rho_Water = 977.7d0
! ======================= Thickness of the substrate using a circle inscribed in a triangle
r_pipe = D/2.0d0
h_triangle = (sqrt(3.0d0)/3.0d0) * W_abs
h_inscribed = (sqrt(3.0d0)/6.0d0) * W_abs
th_min = h_inscribed - r_pipe
th_max = h_triangle - r_pipe
th_sub = (th_min + 2.0d0 * th_max)/3.0d0 !Substrate thickness
! ======================= Calculation of thermal resistances
R_cond_abs = th_abs/(k_abs * A_abs)
R_cond_sub = th_sub/(k_sub * A_sub)
R_cond_PV = th_PV/(k_PV * A_PV)
R_conv_abs = 1.0d0/(h_abs * A_abs)
R_conv_PTC = 1.0d0/(h_PTC * A_PTC)
R_conv_PV = 1.0d0/(h_PV * A_PV)
! ======================= Water (HTF) velocity
A_cs_pipe = (3.1416d0 * (D/2.0d0)**(2)) !Pipe cross-sectional area
u_Water = (m_dot_HTF)/(rho_Water * A_cs_pipe) !Water velocity
! ======================= Calculation of heat transfer efficiency (NTU number)
A_hx = 3.1416d0 * D * 10.0d0 ! Heat exchanger area
NTU = ((1.0d0/((1.0d0/h_HTF) + R_cond_sub)) * A_hx)/(m_dot_HTF * (C_p_HTF)) ! NTU number
E = 1.0d0 - exp(- NTU)
! ======================= Calculation of the electrical power of the PV
eta_PV = 0.298d0 + 0.0142d0 * (log(CR_PTC)) + (- 0.000715d0 +0.0000697d0 * (log(CR_PTC))) * (T_PV - 298.0d0)
P_PV = G_DNI * A_PV * CR_PTC * eta_opt * IAM_elec * eta_PV !1723.0d0
! ======================= Calculation of electrical and thermal efficiency
q_dot_HTF = (T_out_HTF - T_in_HTF) * m_dot_HTF * C_p_HTF
eta_elec = (P_PV)/(G_DNI * A_ap)
eta_th = (q_dot_HTF)/(G_DNI * A_ap)
! ======================= LMTD
U = 1d0/((1d0/h_HTF) + R_cond_sub)
! ==== Paso 1: Calcular T_PTC ====
call calc_T_PTC(T_a, T_sky, T_PVi, T_PTC, sigma, G_GHI, A_PTC, alpha_PTC, &
epsilon_PV, A_PV, epsilon_PTC, R_conv_PTC, iter)
print *, "--------------------------------------"
print *, "Cálculo de T_PTC"
print *, "Iteraciones: ", iter
print *, "T_PTC [K]: ", T_PTC
! ==== Paso 2: Calcular T_abs, T_sub, T_out_HTF ====
call solve_NR_3x3(T_abs, T_sub, T_out_HTF, &
G_GHI, G_DNI, T_a, T_sky, T_in_HTF, T_PVi, T_PTC, &
A_PV, A_abs, CR_PTC, alpha_PV, alpha_abs, epsilon_PV, epsilon_abs, &
sigma, m_dot_HTF, C_p_HTF, U, A_hx, P_PV, &
R_cond_abs, R_cond_sub, R_conv_abs, R_conv_PV)
print *, "--------------------------------------"
print *, "Resultados Newton–Raphson 3x3:"
print *, "T_abs [K]: ", T_abs
print *, "T_sub [K]: ", T_sub
print *, "T_out_HTF [K]: ", T_out_HTF
print *, "--------------------------------------"
! ==== Paso 3: Calcular T_PV ====
call calc_T_PV(T_abs, T_sub, T_out_HTF, T_in_HTF, R_cond_PV, R_cond_sub, R_cond_abs, &
m_dot_HTF, C_p_HTF, T_PV)
print *, "--------------------------------------"
print *, "Cálculo de T_PV:"
print *, "T_PV [K]: ", T_PV
print *, "--------------------------------------"
end program main_NR_total
!===============================================================
subroutine calc_T_PTC(T_a, T_sky, T_PVi, T_PTC, sigma, G_GHI, A_PTC, alpha_PTC, &
epsilon_PV, A_PV, epsilon_PTC, R_conv_PTC, iter)
implicit none
Double Precision, intent(out) :: T_PTC
Double Precision, intent(in) :: T_a, T_sky, T_PVi
Double Precision, intent(in) :: sigma, G_GHI, A_PTC, alpha_PTC
Double Precision, intent(in) :: epsilon_PV, A_PV, epsilon_PTC, R_conv_PTC
integer, intent(out) :: iter
Double Precision :: f_T_PTC, df_T_PTC, T_PTCe, tol
integer :: max_iter
T_PTC = 320.0d0
tol = 1.0d-6
max_iter = 100
do iter = 1, max_iter
f_T_PTC = G_GHI * A_PTC * alpha_PTC &
- (T_PTC**4 - T_sky**4) * A_PTC * epsilon_PTC * sigma &
+ (T_PVi**4 - T_PTC**4) * A_PV * epsilon_PV * sigma &
- ((T_PTC - T_a)/(R_conv_PTC))
df_T_PTC = - 4.0d0 * T_PTC**3 * A_PTC * epsilon_PTC * sigma &
- 4.0d0 * T_PTC**3 * A_PV * epsilon_PV * sigma &
- 1.0d0/R_conv_PTC
T_PTCe = T_PTC - f_T_PTC/df_T_PTC
if (abs(T_PTCe - T_PTC) < tol) then
T_PTC = T_PTCe
exit
endif
T_PTC = T_PTCe
end do
end subroutine calc_T_PTC
!===============================================================
subroutine solve_NR_3x3(T_abs, T_sub, T_out_HTF, &
G_GHI, G_DNI, T_a, T_sky, T_in_HTF, T_PV, T_PTC, &
A_PV, A_abs, CR_PTC, alpha_PV, alpha_abs, epsilon_PV, epsilon_abs, &
sigma, m_dot_HTF, C_p_HTF, U, A_hx, P_PV, &
R_cond_abs, R_cond_sub, R_conv_abs, R_conv_PV)
implicit none
Double Precision, intent(out) :: T_abs, T_sub, T_out_HTF
Double Precision, intent(in) :: G_GHI, G_DNI, T_a, T_sky, T_in_HTF, T_PV, T_PTC
Double Precision, intent(in) :: A_PV, A_abs, CR_PTC, alpha_PV, alpha_abs
Double Precision, intent(in) :: epsilon_PV, epsilon_abs, sigma
Double Precision, intent(in) :: m_dot_HTF, C_p_HTF, U, A_hx, P_PV
Double Precision, intent(in) :: R_cond_abs, R_cond_sub, R_conv_abs, R_conv_PV
Integer :: it, maxit
Double Precision :: tol, normF
Double Precision :: F(3), dx(3), J(3,3)
tol = 1.0d-8
maxit = 100
T_abs = 355.0d0
T_sub = 355.0d0
T_out_HTF = 355.0d0
do it = 1, maxit
call residual_and_jacobian(T_abs, T_sub, T_out_HTF, F, J, &
G_GHI, G_DNI, T_a, T_sky, T_in_HTF, T_PV, T_PTC, &
A_PV, A_abs, CR_PTC, alpha_PV, alpha_abs, epsilon_PV, epsilon_abs, &
sigma, m_dot_HTF, C_p_HTF, U, A_hx, P_PV, &
R_cond_abs, R_cond_sub, R_conv_abs, R_conv_PV)
normF = max( max(abs(F(1)),abs(F(2))), abs(F(3)) )
if (normF < tol) exit
call solve_3x3(J, -F, dx)
T_abs = T_abs + dx(1)
T_sub = T_sub + dx(2)
T_out_HTF = T_out_HTF + dx(3)
end do
print *, "Iteraciones: ", it-1
print *, "||F||_inf : ", normF
end subroutine solve_NR_3x3
!===============================================================
subroutine residual_and_jacobian(T_abs, T_sub, T_out_HTF, F, J, &
G_GHI, G_DNI, T_a, T_sky, T_in_HTF, T_PV, T_PTC, &
A_PV, A_abs, CR_PTC, alpha_PV, alpha_abs, epsilon_PV, epsilon_abs, &
sigma, m_dot_HTF, C_p_HTF, U, A_hx, P_PV, &
R_cond_abs, R_cond_sub, R_conv_abs, R_conv_PV)
implicit none
Double Precision, intent(in) :: T_abs, T_sub, T_out_HTF
Double Precision, intent(out):: F(3), J(3,3)
Double Precision, intent(in) :: G_GHI, G_DNI, T_a, T_sky, T_in_HTF, T_PV, T_PTC
Double Precision, intent(in) :: A_PV, A_abs, CR_PTC, alpha_PV, alpha_abs
Double Precision, intent(in) :: epsilon_PV, epsilon_abs, sigma
Double Precision, intent(in) :: m_dot_HTF, C_p_HTF, U, A_hx, P_PV
Double Precision, intent(in) :: R_cond_abs, R_cond_sub, R_conv_abs, R_conv_PV
Double Precision :: q_solar_abs, q_solar_ptc
Double Precision :: rad_abs, rad_pv, conv_pv, conv_abs
Double Precision :: DT, eps_log, denom, Lmtd, Rcond_sum
Rcond_sum = R_cond_abs + R_cond_sub
q_solar_abs = G_GHI*A_abs*alpha_abs
q_solar_ptc = G_DNI*A_PV*alpha_PV*CR_PTC*0.83d0*0.86d0
rad_abs = epsilon_abs*sigma*A_abs*(T_abs**4 - T_sky**4)
rad_pv = epsilon_PV *sigma*A_PV*(T_PV**4 - T_PTC**4)
conv_pv = (T_PV - T_a)/R_conv_PV
conv_abs= (T_abs - T_a)/R_conv_abs
DT = T_out_HTF - T_in_HTF
eps_log = 1.0d-9
denom = max( (T_sub - T_out_HTF), eps_log )
Lmtd = log( max( (T_sub - T_in_HTF), eps_log ) / denom )
F(1) = q_solar_abs + q_solar_ptc - P_PV - rad_abs - rad_pv - conv_pv - conv_abs - m_dot_HTF*C_p_HTF*DT
F(2) = q_solar_abs - rad_abs - conv_abs - (T_abs - T_sub)/Rcond_sum
F(3) = m_dot_HTF*C_p_HTF*DT - U*A_hx * ( DT / Lmtd )
J(1,1) = -4.0d0*epsilon_abs*sigma*A_abs*(T_abs**3) - 1.0d0/R_conv_abs
J(1,2) = 0.0d0
J(1,3) = - m_dot_HTF*C_p_HTF
J(2,1) = -4.0d0*epsilon_abs*sigma*A_abs*(T_abs**3) - 1.0d0/R_conv_abs - 1.0d0/Rcond_sum
J(2,2) = 1.0d0/Rcond_sum
J(2,3) = 0.0d0
J(3,1) = 0.0d0
J(3,2) = U*A_hx * DT / (Lmtd*Lmtd) * ( 1.0d0/(max(T_sub - T_in_HTF,eps_log)) - 1.0d0/(denom) )
J(3,3) = m_dot_HTF*C_p_HTF - U*A_hx * ( ( Lmtd - DT/(denom) ) / (Lmtd*Lmtd) )
end subroutine residual_and_jacobian
!===============================================================
subroutine solve_3x3(A, b, x)
implicit none
Double Precision, intent(in) :: A(3,3), b(3)
Double Precision, intent(out) :: x(3)
Double Precision :: M(3,3), det
M = A
det = M(1,1)*(M(2,2)*M(3,3)-M(2,3)*M(3,2)) &
- M(1,2)*(M(2,1)*M(3,3)-M(2,3)*M(3,1)) &
+ M(1,3)*(M(2,1)*M(3,2)-M(2,2)*M(3,1))
if (abs(det) < 1.0d-16) then
print *, "Jacobiano casi singular."
end if
x(1) = ( b(1)*(M(2,2)*M(3,3)-M(2,3)*M(3,2)) &
- b(2)*(M(1,2)*M(3,3)-M(1,3)*M(3,2)) &
+ b(3)*(M(1,2)*M(2,3)-M(1,3)*M(2,2)) ) / det
x(2) = ( - b(1)*(M(2,1)*M(3,3)-M(2,3)*M(3,1)) &
+ b(2)*(M(1,1)*M(3,3)-M(1,3)*M(3,1)) &
- b(3)*(M(1,1)*M(2,3)-M(1,3)*M(2,1)) ) / det
x(3) = ( b(1)*(M(2,1)*M(3,2)-M(2,2)*M(3,1)) &
- b(2)*(M(1,1)*M(3,2)-M(1,2)*M(3,1)) &
+ b(3)*(M(1,1)*M(2,2)-M(1,2)*M(2,1)) ) / det
end subroutine solve_3x3
!===============================================================
subroutine calc_T_PV(T_abs, T_sub, T_out_HTF, T_in_HTF, R_cond_PV, R_cond_sub, R_cond_abs, &
m_dot_HTF, C_p_HTF, T_PV)
implicit none
Double Precision, intent(in) :: T_abs, T_sub, T_out_HTF, T_in_HTF
Double Precision, intent(in) :: R_cond_PV, R_cond_sub, R_cond_abs
Double Precision, intent(in) :: m_dot_HTF, C_p_HTF
Double Precision, intent(out) :: T_PV
Double Precision :: term1, term2
term1 = m_dot_HTF*C_p_HTF*(T_out_HTF - T_in_HTF) ! q_dot_HTF
term2 = (T_abs - T_sub)/(R_cond_abs + R_cond_sub) ! q_dot_cond_abs_x_sub
T_PV = T_sub + (term1 - term2)*(R_cond_PV + R_cond_sub)
end subroutine calc_T_PV
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