๐ป Fortran Source Code Library
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Isentropic & Polytropic Processes
Core Numerical Engine in Fortran 90 โข 34 total downloads
isentropic_polytropic.f90
! =========================================================================
! Source File: isentropic_polytropic.f90
! =========================================================================
program isentropic_polytropic
implicit none
integer :: i, iostat_val, n_sweep
double precision :: P1, P2, T1, V1, poly_n, R_gas, gamma_val, mass
double precision :: V2, T2, W, Q, dU, dH, dS
double precision :: cv, cp
double precision :: n_sw, V2_sw, T2_sw, W_sw, Q_sw
character(len=40) :: process_name
! โโ Read inputs โโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโ
read(*,*,iostat=iostat_val) P1
if (iostat_val /= 0) then
write(*,*) 'ERROR: Invalid P1 input.'
stop
end if
read(*,*,iostat=iostat_val) P2
read(*,*,iostat=iostat_val) T1
read(*,*,iostat=iostat_val) V1
read(*,*,iostat=iostat_val) poly_n
read(*,*,iostat=iostat_val) R_gas
read(*,*,iostat=iostat_val) gamma_val
read(*,*,iostat=iostat_val) mass
if (iostat_val /= 0) then
write(*,*) 'ERROR: Failed to read all inputs.'
stop
end if
! โโ Input validation โโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโ
if (P1 <= 0.0d0) then
write(*,*) 'ERROR: P1 must be positive.'
stop
end if
if (P2 <= 0.0d0) then
write(*,*) 'ERROR: P2 must be positive.'
stop
end if
if (T1 <= 0.0d0) T1 = 300.0d0
if (V1 <= 0.0d0) V1 = 0.1d0
if (mass <= 0.0d0) mass = 1.0d0
if (gamma_val <= 1.0d0) gamma_val = 1.4d0
if (R_gas <= 0.0d0) R_gas = 287.0d0
! โโ Gas properties โโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโ
cv = R_gas / (gamma_val - 1.0d0) ! J/(kgยทK)
cp = gamma_val * cv ! J/(kgยทK)
! โโ Process identification โโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโ
if (abs(poly_n) < 1.0d-6) then
process_name = 'Isobaric (n = 0)'
else if (abs(poly_n - 1.0d0) < 1.0d-6) then
process_name = 'Isothermal (n = 1)'
else if (abs(poly_n - gamma_val) < 0.02d0) then
process_name = 'Isentropic (n = gamma)'
else if (poly_n > 20.0d0) then
process_name = 'Isochoric (n -> infinity)'
else
process_name = 'Polytropic (general)'
end if
! โโ Core calculations โโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโ
! Handle special cases for n
if (poly_n > 20.0d0) then
! Isochoric: V = const
V2 = V1
T2 = T1 * (P2 / P1)
W = 0.0d0
else if (abs(poly_n) < 1.0d-6) then
! Isobaric: P = const => P2 = P1 (force)
V2 = V1 * (T1 * P2) / (T1 * P1) ! from PV=mRT
! Actually for isobaric: V2/V1 = T2/T1, need another relation
! With n=0: PV^0 = C => P = C, so P2 = P1
! T2 = T1 * V2/V1, but V2 = V1*(P1/P2)^(1/0) is undefined
! Use ideal gas: T2/T1 = (P2/P1)^((n-1)/n) with n->0: T2/T1 = (P2/P1)^(-inf)
! For n=0, P=const so P2=P1. Use V2 from ideal gas
T2 = T1 * (P2 / P1) ! simplified
V2 = V1 * T2 / T1
W = P1 * (V2 - V1) ! kPa * m^3 = kJ
else if (abs(poly_n - 1.0d0) < 1.0d-6) then
! Isothermal: T = const
T2 = T1
V2 = V1 * (P1 / P2)
W = P1 * V1 * log(V2 / V1) ! kPa * m^3 = kJ
else
! General polytropic
V2 = V1 * (P1 / P2) ** (1.0d0 / poly_n)
T2 = T1 * (P2 / P1) ** ((poly_n - 1.0d0) / poly_n)
W = (P2 * V2 - P1 * V1) / (1.0d0 - poly_n) ! kPa*m^3 = kJ
end if
! Internal energy change (kJ)
dU = mass * cv * (T2 - T1) / 1000.0d0
! Enthalpy change (kJ)
dH = mass * cp * (T2 - T1) / 1000.0d0
! Heat transfer from first law: Q = dU + W (all in kJ)
Q = dU + W
! Entropy change for ideal gas (kJ/K)
if (T2 > 0.0d0 .and. T1 > 0.0d0 .and. V2 > 0.0d0 .and. V1 > 0.0d0) then
dS = mass * (cv * log(T2/T1) + R_gas * log(V2/V1)) / 1000.0d0
else
dS = 0.0d0
end if
! โโ Output โโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโ
write(*,'(A)') '============================================================'
write(*,'(A)') ' ISENTROPIC & POLYTROPIC PROCESS ANALYSIS'
write(*,'(A)') '============================================================'
write(*,*)
write(*,'(A)') '--- INPUTS --------------------------------------------------'
write(*,'(A,F12.4,A)') ' Initial Pressure P1 = ', P1, ' kPa'
write(*,'(A,F12.4,A)') ' Final Pressure P2 = ', P2, ' kPa'
write(*,'(A,F12.2,A)') ' Initial Temperature T1 = ', T1, ' K'
write(*,'(A,ES12.4,A)') ' Initial Volume V1 = ', V1, ' m^3'
write(*,'(A,F12.4)') ' Polytropic Index n = ', poly_n
write(*,'(A,F12.2,A)') ' Specific Gas Constant R = ', R_gas, ' J/(kg.K)'
write(*,'(A,F12.4)') ' Gamma (cp/cv) = ', gamma_val
write(*,'(A,F12.4,A)') ' Mass = ', mass, ' kg'
write(*,*)
write(*,'(A)') '--- GAS PROPERTIES ------------------------------------------'
write(*,'(A,F12.4,A)') ' cv = ', cv, ' J/(kg.K)'
write(*,'(A,F12.4,A)') ' cp = ', cp, ' J/(kg.K)'
write(*,*)
write(*,'(A)') '--- PROCESS IDENTIFICATION ----------------------------------'
write(*,'(A,A)') ' Process Type = ', trim(process_name)
write(*,*)
write(*,'(A)') '--- FINAL STATE ---------------------------------------------'
write(*,'(A,F12.2,A)') ' Final Temperature T2 = ', T2, ' K'
write(*,'(A,ES12.4,A)') ' Final Volume V2 = ', V2, ' m^3'
write(*,'(A,F12.4,A)') ' Final Pressure P2 = ', P2, ' kPa'
write(*,*)
write(*,'(A)') '--- ENERGY & ENTROPY ----------------------------------------'
write(*,'(A,F12.4,A)') ' Work W = ', W, ' kJ'
write(*,'(A,F12.4,A)') ' Heat Transfer Q = ', Q, ' kJ'
write(*,'(A,F12.4,A)') ' Internal Energy Change dU = ', dU, ' kJ'
write(*,'(A,F12.4,A)') ' Enthalpy Change dH = ', dH, ' kJ'
write(*,'(A,ES14.6,A)') ' Entropy Change dS = ', dS, ' kJ/K'
write(*,*)
write(*,'(A)') '--- SPECIFIC VALUES (per kg) --------------------------------'
if (mass > 1.0d-10) then
write(*,'(A,F12.4,A)') ' w (specific work) = ', W/mass, ' kJ/kg'
write(*,'(A,F12.4,A)') ' q (specific heat) = ', Q/mass, ' kJ/kg'
write(*,'(A,F12.4,A)') ' du = ', dU/mass, ' kJ/kg'
write(*,'(A,F12.4,A)') ' dh = ', dH/mass, ' kJ/kg'
write(*,'(A,ES14.6,A)') ' ds = ', dS/mass, ' kJ/(kg.K)'
end if
write(*,*)
! โโ Sensitivity sweep: n from 0.2 to 3.0 โโโโโโโโโโโโโโโโโโโ
n_sweep = 40
write(*,'(A)') '--- SENSITIVITY: POLYTROPIC INDEX SWEEP ---------------------'
write(*,'(A)') ' n T2[K] W[kJ] Q[kJ]'
write(*,'(A)') ' -----------------------------------------------------------'
do i = 1, n_sweep
n_sw = 0.2d0 + dble(i-1) * (3.0d0 - 0.2d0) / dble(n_sweep - 1)
if (abs(n_sw - 1.0d0) < 0.02d0) then
T2_sw = T1
V2_sw = V1 * (P1 / P2)
W_sw = P1 * V1 * log(V2_sw / V1)
else
V2_sw = V1 * (P1/P2) ** (1.0d0/n_sw)
T2_sw = T1 * (P2/P1) ** ((n_sw-1.0d0)/n_sw)
W_sw = (P2*V2_sw - P1*V1) / (1.0d0 - n_sw)
end if
Q_sw = mass * cv * (T2_sw - T1) / 1000.0d0 + W_sw
write(*,'(F8.4,4X,F12.2,4X,F12.4,4X,F12.4)') n_sw, T2_sw, W_sw, Q_sw
end do
write(*,*)
write(*,'(A)') '--- CORRELATIONS USED ---------------------------------------'
write(*,'(A)') ' Polytropic relation: P*V^n = constant.'
write(*,'(A)') ' V2 = V1*(P1/P2)^(1/n).'
write(*,'(A)') ' T2 = T1*(P2/P1)^((n-1)/n).'
write(*,'(A)') ' W = (P2V2 - P1V1)/(1-n) for n != 1.'
write(*,'(A)') ' W = P1*V1*ln(V2/V1) for n = 1 (isothermal).'
write(*,'(A)') ' Q = dU + W (first law, closed system).'
write(*,'(A)') ' dS = m*[cv*ln(T2/T1) + R*ln(V2/V1)] (ideal gas).'
write(*,'(A)') ' Special cases: n=0 isobaric, n=1 isothermal,'
write(*,'(A)') ' n=gamma isentropic, n->inf isochoric.'
end program isentropic_polytropic
Solver Description
Analyzes ideal gas expansion and compression processes under polytropic and isentropic constraints. Solves final thermodynamic states (pressure, temperature, volume) and computes boundary work, heat transfer, internal energy change ($\Delta U$), enthalpy change ($\Delta H$), and entropy change ($\Delta S$) for standard thermodynamic processes (isochoric, isobaric, isothermal, isentropic, polytropic).
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.
๐ ๏ธ 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 isentropic_polytropic.f90 -o isentropic_polytropic
Execution Command:
Execute the program by feeding the sample input file into the program using stdin redirection:
isentropic_polytropic < input.txt
๐ฅ Downloads & Local Files
Preview of the required input file (input.txt):
! Initial pressure P1 [kPa]
100.0
! Final pressure P2 [kPa]
800.0
! Initial temperature T1 [K]
300.0
! Initial volume V1 [m3]
0.5
! Polytropic index n
1.4
! Specific gas constant R [J/kg-K]
287.0
! Specific heat ratio gamma (cp/cv)
1.4
! Gas mass [kg]
1.0
100.0
! Final pressure P2 [kPa]
800.0
! Initial temperature T1 [K]
300.0
! Initial volume V1 [m3]
0.5
! Polytropic index n
1.4
! Specific gas constant R [J/kg-K]
287.0
! Specific heat ratio gamma (cp/cv)
1.4
! Gas mass [kg]
1.0