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Entropy & Exergy Analysis
Core Numerical Engine in Fortran 90 • 35 total downloads
entropy_exergy.f90
! =========================================================================
! Source File: entropy_exergy.f90
! =========================================================================
program entropy_exergy
implicit none
integer :: i, iostat_val, n_sweep
double precision :: T_sys, T0, P_sys, P0, mdot, cp_val
double precision :: h_in, h_out, s_in, s_out, h0, s0
double precision :: Q_dot_in, Q_dot_out, T_source, T_sink
double precision :: S_gen, X_dest, psi_in, psi_out
double precision :: X_in, X_out, eta_ex, X_Q_in, X_Q_out
double precision :: dH, dS, W_rev, W_act, eta_2nd
double precision :: T0_sweep, S_gen_sw, X_dest_sw, eta_sw
! ── Read inputs ─────────────────────────────────────────────
read(*,*,iostat=iostat_val) T_sys
if (iostat_val /= 0) then
write(*,*) 'ERROR: Invalid system temperature input.'
stop
end if
read(*,*,iostat=iostat_val) T0
read(*,*,iostat=iostat_val) P_sys
read(*,*,iostat=iostat_val) P0
read(*,*,iostat=iostat_val) mdot
read(*,*,iostat=iostat_val) cp_val
read(*,*,iostat=iostat_val) h_in
read(*,*,iostat=iostat_val) h_out
read(*,*,iostat=iostat_val) s_in
read(*,*,iostat=iostat_val) s_out
read(*,*,iostat=iostat_val) h0
read(*,*,iostat=iostat_val) s0
read(*,*,iostat=iostat_val) Q_dot_in
read(*,*,iostat=iostat_val) Q_dot_out
read(*,*,iostat=iostat_val) T_source
read(*,*,iostat=iostat_val) T_sink
if (iostat_val /= 0) then
write(*,*) 'ERROR: Failed to read all inputs.'
stop
end if
! ── Input validation ────────────────────────────────────────
if (T0 <= 0.0d0) T0 = 298.15d0
if (T_source <= 0.0d0) T_source = 1000.0d0
if (T_sink <= 0.0d0) T_sink = T0
if (mdot <= 0.0d0) mdot = 1.0d0
if (cp_val <= 0.0d0) cp_val = 1.005d0
! ── Core calculations ───────────────────────────────────────
! Entropy generation (general entropy balance for open system)
S_gen = mdot * (s_out - s_in)
if (T_source > 0.0d0 .and. Q_dot_in > 0.0d0) then
S_gen = S_gen - Q_dot_in / T_source
end if
if (T_sink > 0.0d0 .and. Q_dot_out > 0.0d0) then
S_gen = S_gen + Q_dot_out / T_sink
end if
if (S_gen < 0.0d0) S_gen = 0.0d0 ! cannot be negative (2nd law)
! Exergy destruction (Gouy-Stodola theorem)
X_dest = T0 * S_gen
! Flow exergy (specific)
psi_in = (h_in - h0) - T0 * (s_in - s0)
psi_out = (h_out - h0) - T0 * (s_out - s0)
! Exergy rates
X_in = mdot * psi_in
X_out = mdot * psi_out
! Heat exergy (Carnot factor)
X_Q_in = 0.0d0
if (T_source > 0.0d0) X_Q_in = Q_dot_in * (1.0d0 - T0 / T_source)
X_Q_out = 0.0d0
if (T_sink > 0.0d0) X_Q_out = Q_dot_out * (1.0d0 - T0 / T_sink)
! Exergy efficiency
if (abs(X_in) > 1.0d-10) then
eta_ex = X_out / X_in
else
eta_ex = 0.0d0
end if
! Enthalpy and entropy changes
dH = mdot * (h_out - h_in)
dS = mdot * (s_out - s_in)
! Reversible work and second-law efficiency
W_rev = X_in - X_out + X_Q_in - X_Q_out
W_act = dH
if (abs(W_rev) > 1.0d-10) then
eta_2nd = W_act / W_rev
else
eta_2nd = 0.0d0
end if
! ── Output ──────────────────────────────────────────────────
write(*,'(A)') '============================================================'
write(*,'(A)') ' ENTROPY & EXERGY ANALYSIS'
write(*,'(A)') '============================================================'
write(*,*)
write(*,'(A)') '--- INPUTS --------------------------------------------------'
write(*,'(A,F12.2,A)') ' System Temperature = ', T_sys, ' K'
write(*,'(A,F12.2,A)') ' Dead State Temperature T0 = ', T0, ' K'
write(*,'(A,F12.2,A)') ' System Pressure = ', P_sys, ' kPa'
write(*,'(A,F12.2,A)') ' Dead State Pressure P0 = ', P0, ' kPa'
write(*,'(A,F12.4,A)') ' Mass Flow Rate = ', mdot, ' kg/s'
write(*,'(A,F12.4,A)') ' cp = ', cp_val, ' kJ/(kg.K)'
write(*,'(A,F12.2,A)') ' h_in = ', h_in, ' kJ/kg'
write(*,'(A,F12.2,A)') ' h_out = ', h_out, ' kJ/kg'
write(*,'(A,F12.6,A)') ' s_in = ', s_in, ' kJ/(kg.K)'
write(*,'(A,F12.6,A)') ' s_out = ', s_out, ' kJ/(kg.K)'
write(*,'(A,F12.2,A)') ' h0 (dead state) = ', h0, ' kJ/kg'
write(*,'(A,F12.6,A)') ' s0 (dead state) = ', s0, ' kJ/(kg.K)'
write(*,'(A,F12.4,A)') ' Q_dot_in = ', Q_dot_in, ' kW'
write(*,'(A,F12.4,A)') ' Q_dot_out = ', Q_dot_out, ' kW'
write(*,'(A,F12.2,A)') ' T_source = ', T_source, ' K'
write(*,'(A,F12.2,A)') ' T_sink = ', T_sink, ' K'
write(*,*)
write(*,'(A)') '--- ENTROPY RESULTS -----------------------------------------'
write(*,'(A,ES14.6,A)') ' Entropy Generation Sgen = ', S_gen, ' kW/K'
write(*,'(A,F12.4,A)') ' Entropy Change dS = ', dS, ' kW/K'
write(*,*)
write(*,'(A)') '--- EXERGY RESULTS ------------------------------------------'
write(*,'(A,F12.4,A)') ' Exergy Destruction Xdest = ', X_dest, ' kW'
write(*,'(A,F12.4,A)') ' Flow Exergy In psi_in = ', psi_in, ' kJ/kg'
write(*,'(A,F12.4,A)') ' Flow Exergy Out psi_out = ', psi_out, ' kJ/kg'
write(*,'(A,F12.4,A)') ' Exergy Rate In X_in = ', X_in, ' kW'
write(*,'(A,F12.4,A)') ' Exergy Rate Out X_out = ', X_out, ' kW'
write(*,'(A,F12.4,A)') ' Heat Exergy In X_Q_in = ', X_Q_in, ' kW'
write(*,'(A,F12.4,A)') ' Heat Exergy Out X_Q_out = ', X_Q_out, ' kW'
write(*,'(A,F12.4,A)') ' Irreversibility Rate = ', X_dest, ' kW'
write(*,*)
write(*,'(A)') '--- EFFICIENCY ----------------------------------------------'
write(*,'(A,F10.6)') ' Exergy Efficiency eta_ex = ', eta_ex
write(*,'(A,F10.2,A)') ' Exergy Efficiency = ', eta_ex*100.0d0, ' percent'
write(*,'(A,F12.4,A)') ' Reversible Work W_rev = ', W_rev, ' kW'
write(*,'(A,F12.4,A)') ' Actual Energy Change dH = ', dH, ' kW'
write(*,'(A,F10.6)') ' Second Law Efficiency = ', eta_2nd
write(*,'(A,F10.2,A)') ' Second Law Efficiency = ', eta_2nd*100.0d0, ' percent'
write(*,*)
! ── Sensitivity sweep: T0 from 273 to 323 K ────────────────
n_sweep = 50
write(*,'(A)') '--- SENSITIVITY: EXERGY VS DEAD-STATE TEMPERATURE ----------'
write(*,'(A)') ' T0[K] Sgen[kW/K] Xdest[kW] eta_ex'
write(*,'(A)') ' -----------------------------------------------------------'
do i = 0, n_sweep
T0_sweep = 273.0d0 + dble(i) * (323.0d0 - 273.0d0) / dble(n_sweep)
S_gen_sw = mdot * (s_out - s_in)
if (T_source > 0.0d0 .and. Q_dot_in > 0.0d0) then
S_gen_sw = S_gen_sw - Q_dot_in / T_source
end if
if (T_sink > 0.0d0 .and. Q_dot_out > 0.0d0) then
S_gen_sw = S_gen_sw + Q_dot_out / T_sink
end if
if (S_gen_sw < 0.0d0) S_gen_sw = 0.0d0
X_dest_sw = T0_sweep * S_gen_sw
! recompute exergy with swept T0
psi_in = (h_in - h0) - T0_sweep * (s_in - s0)
psi_out = (h_out - h0) - T0_sweep * (s_out - s0)
if (abs(mdot * psi_in) > 1.0d-10) then
eta_sw = (mdot * psi_out) / (mdot * psi_in)
else
eta_sw = 0.0d0
end if
write(*,'(F10.2,4X,ES14.6,2X,F12.4,4X,F10.6)') &
T0_sweep, S_gen_sw, X_dest_sw, eta_sw
end do
write(*,*)
write(*,'(A)') '--- CORRELATIONS USED ---------------------------------------'
write(*,'(A)') ' Gouy-Stodola theorem: X_dest = T0 * S_gen'
write(*,'(A)') ' Flow exergy: psi = (h-h0) - T0*(s-s0)'
write(*,'(A)') ' Heat exergy: X_Q = Q*(1 - T0/T_boundary)'
write(*,'(A)') ' Exergy efficiency: eta_ex = X_out / X_in'
end program entropy_exergy
Solver Description
Performs thermodynamic second-law analysis for open control volumes under steady-state conditions. Calculates entropy generation rate, exergy destruction rate, flow exergy at inlet and outlet states, reversible power, dead-state reference availability, and exergetic (second-law) efficiency using the Gouy-Stodola theorem.
Key Numerical Methods & Architecture
- Input Redirection: Reads parameters sequentially from standard input (`stdin`) using Fortran sequential read (`read(*,*)`), ensuring modular integration.
- Modular Design: Formulated using pure mathematical routines, separation of equations from output formatting, and precise numerical solvers (e.g. bisection, Newton-Raphson).
- Standard Compliant: Written in clean, standards-compliant Fortran 90 to ensure cross-compiler compatibility.
🛠️ Local Compilation
To test this code on your machine, compile the source code file(s) using a standard Fortran compiler (e.g., `gfortran`).
Compilation Command:
gfortran -O3 entropy_exergy.f90 -o entropy_exergy
Execution Command:
Execute the program by feeding the sample input file into the program using stdin redirection:
entropy_exergy < input.txt
📥 Downloads & Local Files
Preview of the required input file (input.txt):
! System temperature [K]
773.15
! Dead state temperature T0 [K]
298.15
! System pressure [kPa]
8000.0
! Dead state pressure P0 [kPa]
101.325
! Mass flow rate [kg/s]
50.0
! Specific heat cp [kJ/kg-K]
2.1
! Inlet enthalpy h_in [kJ/kg]
3400.0
! Outlet enthalpy h_out [kJ/kg]
2600.0
! Inlet entropy s_in [kJ/kg-K]
6.85
! Outlet entropy s_out [kJ/kg-K]
7.50
! Dead state enthalpy h0 [kJ/kg]
104.9
! Dead state entropy s0 [kJ/kg-K]
0.367
! Heat inlet rate Qin [kW]
0.0
! Heat outlet rate Qout [kW]
0.0
! Heat source temperature Tsrc [K]
1200.0
! Heat sink temperature Tsnk [K]
298.15
773.15
! Dead state temperature T0 [K]
298.15
! System pressure [kPa]
8000.0
! Dead state pressure P0 [kPa]
101.325
! Mass flow rate [kg/s]
50.0
! Specific heat cp [kJ/kg-K]
2.1
! Inlet enthalpy h_in [kJ/kg]
3400.0
! Outlet enthalpy h_out [kJ/kg]
2600.0
! Inlet entropy s_in [kJ/kg-K]
6.85
! Outlet entropy s_out [kJ/kg-K]
7.50
! Dead state enthalpy h0 [kJ/kg]
104.9
! Dead state entropy s0 [kJ/kg-K]
0.367
! Heat inlet rate Qin [kW]
0.0
! Heat outlet rate Qout [kW]
0.0
! Heat source temperature Tsrc [K]
1200.0
! Heat sink temperature Tsnk [K]
298.15