Gas Turbine_Error in fuel composition analysis

[MikeSennis]

Hello,
I've modeled a gas turbine (Brayton Cycle), with the same topology as the one given in TESPy documentation. The model seems to work fine, because the occurring net electric power output is equal to 47.18 MWe, as expected (compared with the results given for a similar model from software for gas turbines' simulation and analysis). In the next step (after the Brayton cycle design), I've tried to evaluate the effect of hydrogen's volume (molar) fraction in fuel mixture in the gas turbine performance (power output and efficiency). To be more specific, the volume fraction range of H2 for this analysis will be from 0 to 75 vol.% in the mixture. The fuel mixture consists of natural gas (assumed of constant composition in every case: 96 % CH4 and 4 % C2H6 by mass) and hydrogen.
The thing is that the following error message occurs after code execution:

"if mass_fraction_sum > 1 + ERR:
       ^^^^^^^^^^^^^^^^^^^^^^^^^^^
ValueError: The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()"

Any help or suggestion for this problem would be much appreciated!
Thank you very much in advance.

Topology:

Code:

from tespy.networks import Network
from tespy.components import (
    DiabaticCombustionChamber, Turbine, Source, Sink, Compressor
)
from tespy.connections import Connection, Ref, Bus

nw = Network(p_unit="bar", T_unit="C", h_unit="kJ / kg")

cp = Compressor("Compressor")
cc = DiabaticCombustionChamber("combustion chamber")
tu = Turbine("turbine")
air = Source("air source")
fuel = Source("fuel source")
fg = Sink("flue gas sink")

c2 = Connection(air, "out1", cc, "in1", label="2")
c3 = Connection(cc, "out1", fg, "in1", label="3")
c5 = Connection(fuel, "out1", cc, "in2", label="5")
nw.add_conns(c2, c3, c5)

cc.set_attr(pr=0.97, eta=1, lamb=1.5, ti=None) # or ti=132.778e6 W (LHV = 49.736 MJ/kg for natural gas)

c2.set_attr(
    p=0.93194, T=13.5,
    fluid={"Ar": 0.0129, "N2": 0.7553, "CO2": 0.0004, "O2": 0.2314}
) # fluid: air -> composition by mass fractions, m=122.415
c5.set_attr(m=0.0001, p=Ref(c2, 1.05, 0), T=13.5, fluid={"CH4": 0.96, "ETHANE": 0.04, "H2": 0}) # fluid: natural gas -> composition by mass fractions

nw.solve(mode="design")

#cc.set_attr(ti=None)
c5.set_attr(m=None)
c5.set_attr(m=1) 
nw.solve(mode="design")

c5.set_attr(m=None)
c5.set_attr(m=2.66966) 
nw.solve(mode="design")

cc.set_attr(lamb=None)
c3.set_attr(T=1306.85)
nw.solve(mode="design")
nw.print_results()
print(nw.results["Connection"])

nw.del_conns(c2, c3)
c1 = Connection(air, "out1", cp, "in1", label="1")
c2 = Connection(cp, "out1", cc, "in1", label="2")
c3 = Connection(cc, "out1", tu, "in1", label="3")
c4 = Connection(tu, "out1", fg, "in1", label="4")
nw.add_conns(c1, c2, c3, c4)

generator = Bus("generator")
generator.add_comps(
    {"comp": tu, "char": 0.98, "base": "component"},
    {"comp": cp, "char": 1, "base": "bus"},
)
nw.add_busses(generator)

cp.set_attr(eta_s=0.82, pr=21.1)
tu.set_attr(eta_s=0.87) 
c1.set_attr(
    m=None, p=0.93194, T=13.5,
    fluid={"Ar": 0.0129, "N2": 0.7553, "CO2": 0.0004, "O2": 0.2314}
) # fluid: air -> composition by mass fractions, m=122.415 
c3.set_attr(m=125.085) 
c4.set_attr(p=Ref(c1, 1.03, 0))
c5.set_attr(p=None)
c5.set_attr(p=Ref(c2, 1.05, 0))
nw.solve("design")

c3.set_attr(m=None, T=1306.85) # or m=125.085 
nw.solve("design")
nw.print_results()

# fuel composition analysis
hyd = np.linspace(0, 0.75, 16), # hydrogen volume (molar) fraction in fuel mixture

# Brayton cycle net power output
power = []
# Brayton cycle efficiency
eta = []

MW_CH4 = 16 # [g/mol]
MW_C2H6 = 30 # [g/mol]
MW_H2 = 2 # [g/mol]

for x_H2 in hyd:
    x_NG = 1-x_H2 # natural gas volume (molar) fraction in fuel mixture
    x_CH4 = 0.9782*x_NG  # methane volume (molar) fraction in fuel mixture (for 96 mass% CH4 and 4 mass% C2H6 in natural gas)
    x_C2H6 = 0.0218*x_NG  # ethane volume (molar) fraction in fuel mixture (for 96 mass% CH4 and 4 mass% C2H6 in natural gas)
    c5.set_attr(fluid={"CH4": (MW_CH4*x_CH4)/((MW_CH4*x_CH4)+(MW_C2H6*x_C2H6)+(MW_H2*x_H2)),
                "ETHANE": (MW_C2H6*x_C2H6)/((MW_CH4*x_CH4)+(MW_C2H6*x_C2H6)+(MW_H2*x_H2)),
    "H2": (MW_H2*x_H2)/((MW_CH4*x_CH4)+(MW_C2H6*x_C2H6)+(MW_H2*x_H2))}) # fluid: natural gas-hydrogen mixture -> composition by mass fractions
    #c5.set_attr(fluid_balance=True)
    #print(c5.fluid_data)
    nw.solve('design')
    power += [abs(generator.P.val) / 1e6] # [MWe]
    eta += [(abs(generator.P.val) / cc.ti.val) * 100]

# reset to base fuel composition
c5.set_attr(fluid={"CH4": 0.96, "ETHANE": 0.04, "H2": 0})

# plotting
fig, ax = plt.subplots(2, 1, figsize=(16, 8), sharex='col')

ax = ax.flatten()
[a.grid() for a in ax]

i = 0
for key in hyd:
    ax[i].scatter(hyd[key] * 100, eta[key], s=100, color="#1f567d")
    ax[i + 1].scatter(hyd[key] * 100, power[key], s=100, color="#18a999")
    i += 1

ax[0].set_ylabel('Efficiency (%)')
ax[1].set_ylabel('Net electric power output [MWe]')
ax[1].set_xlabel('Hydrogen volume fraction in fuel mixture (%)')

plt.tight_layout()
fig.savefig('Gas Turbine_fuel composition analysis.svg')
plt.close()

[fwitte]

Hi!

The issue is, that you are passing an array to all the fluid mass fractions, that cannot work. You do not iterate over the values of the numpy array but over the values of the tuple (first is numpy array, there are no other values in there.

hyd = np.linspace(0, 0.75, 16), # hydrogen volume (molar) fraction in fuel mixture
                           # ^ Due to this comma, python saves the numpy array in a tuple.
for x_H2 in hyd:
    x_NG = 1-x_H2 # natural gas volume (molar) fraction in fuel mixture

[MikeSennis]

Hello @fwitte,
Yes, you're right! That was an oversight on my part. I was trying for hours to understand what I was doing wrong, but I couldn't find it. Thank you for the support and for sharing your time!
Best regards