Empirical fuel manipulation
Evaluating mean fluid properties
In this note we show how to use Cantera to retrieve mixture properties for use in external simulations. This approach should be used only when composition dependency may be neglected or real-time evaluation becomes to expensive.
using WallyToolbox
using PyCanteraTools
using CairoMakie
using Polynomials
using PythonCall
const ct = pyimport("cantera")
const np = pyimport("numpy") CondaPkg Found dependencies: /home/runner/.julia/packages/PythonCall/Nr75f/CondaPkg.toml
CondaPkg Found dependencies: /home/runner/work/WallyToolbox.jl/WallyToolbox.jl/CondaPkg.toml
CondaPkg Resolving changes
+ cantera
+ libstdcxx-ng
+ matplotlib
+ numpy
+ openssl
+ pandas
+ python
+ pyvista
+ scipy
+ seaborn
CondaPkg Creating environment
│ /home/runner/.julia/artifacts/7973f2c7725e2d0eef7a95159454c4145f0945a2/bin/micromamba
│ -r /home/runner/.julia/scratchspaces/0b3b1443-0f03-428d-bdfb-f27f9c1191ea/root
│ create
│ -y
│ -p /home/runner/work/WallyToolbox.jl/WallyToolbox.jl/docs/.CondaPkg/env
│ --override-channels
│ --no-channel-priority
│ cantera[version='*']
│ libstdcxx-ng[version='>=3.4,<13.0']
│ matplotlib[version='*']
│ numpy[version='*']
│ openssl[version='>=3, <3.1']
│ pandas[version='*']
│ python[version='>=3.8,<4',channel='conda-forge',build='*cpython*']
│ pyvista[version='*']
│ scipy[version='*']
│ seaborn[version='*']
└ -c conda-forge
Transaction
Prefix: /home/runner/work/WallyToolbox.jl/WallyToolbox.jl/docs/.CondaPkg/env
Updating specs:
- cantera=*
- libstdcxx-ng[version='>=3.4,<13.0']
- matplotlib=*
- numpy=*
- openssl[version='>=3, <3.1']
- pandas=*
- conda-forge::python[version='>=3.8,<4',build=*cpython*]
- pyvista=*
- scipy=*
- seaborn=*
Package Version Build Channel Size
──────────────────────────────────────────────────────────────────────────────────────────────
Install:
──────────────────────────────────────────────────────────────────────────────────────────────
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Summary:
Install: 253 packages
Total download: 157kB
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Transaction finished
To activate this environment, use:
micromamba activate /home/runner/work/WallyToolbox.jl/WallyToolbox.jl/docs/.CondaPkg/env
Or to execute a single command in this environment, use:
micromamba run -p /home/runner/work/WallyToolbox.jl/WallyToolbox.jl/docs/.CondaPkg/env mycommand
/home/runner/work/WallyToolbox.jl/WallyToolbox.jl/docs/.CondaPkg/env/lib/python3.11/site-packages/h5py/__init__.py:36: UserWarning: h5py is running against HDF5 1.14.2 when it was built against 1.14.0, this may cause problems
_warn(("h5py is running against HDF5 {0} when it was built against {1}, "Since Cantera is not yet available from Julia (I am working on that!), we wrap the interfacing with Python code in function fit_gas_properties provided below. There is a slight possibility that this function or a more generic variant of it will at some point be integrated into PyCanteraTools.
function fit_gas_properties(sol; orders = Dict())
T = pyconvert(Vector{Float64}, sol.T)
mu = pyconvert(Vector{Float64}, sol.viscosity)
kg = pyconvert(Vector{Float64}, sol.thermal_conductivity)
cp = pyconvert(Vector{Float64}, sol.cp_mass)
poly_mu = Polynomials.fit(T, mu, get(orders, :mu, 4))
poly_kg = Polynomials.fit(T, kg, get(orders, :kg, 4))
poly_cp = Polynomials.fit(T, cp, get(orders, :cp, 4))
return (mu, kg, cp, poly_mu, poly_kg, poly_cp)
endFor display of results, we also provide a standardized plotting function plot_gas_properties.
function plot_gas_properties(
T, mu, kg, cp, poly_mu, poly_kg, poly_cp;
every = 10
)
Ts = T[begin:every:end]
f = Figure(size = (700, 800))
ax1 = Axis(f[1, 1]; xgridstyle=:dash, ygridstyle=:dash)
ax2 = Axis(f[2, 1]; xgridstyle=:dash, ygridstyle=:dash)
ax3 = Axis(f[3, 1]; xgridstyle=:dash, ygridstyle=:dash)
lines!(ax1, T, mu; color = :red)
lines!(ax2, T, kg; color = :red)
lines!(ax3, T, cp; color = :red)
scatter!(ax1, Ts, poly_mu.(Ts); color = :black)
scatter!(ax2, Ts, poly_kg.(Ts); color = :black)
scatter!(ax3, Ts, poly_cp.(Ts); color = :black)
ax1.ylabel = "Viscosity [Pa.s]"
ax2.ylabel = "Conductivity [W/(m.K)]"
ax3.ylabel = "Specific heat [J/(kg.K)]"
ax3.xlabel = "Temperature [K]"
return f, (ax1, ax2, ax3)
endFor illustration purposes we make use of a typical composition of air over a broad range of temperatures. Evaluation of the properties table is performed with Cantera SolutionArray class.
T = LinRange(200, 3000, 200)
X = "N2: 0.768, O2: 0.21, H2O: 0.006, Ar: 0.012, CO2: 0.004"
gas = ct.Solution("gri30.yaml")
sol = ct.SolutionArray(gas, shape=length(T))
sol.TPX = pylist(T), ct.one_atm, XFinally we visualize the results; verification is performed against values proposed in the literature by Mujumdar2006i [8]. As one can inspect below, values diverge from those evaluated from Gri-MECH 3.0 database.
with_theme() do
rets = fit_gas_properties(sol)
μmuj = AirViscosityMujumdar2006()
kmuj = AirHeatConductivityMujumdar2006()
f, ax = plot_gas_properties(T, rets...)
lines!(ax[1], T, μmuj.(T); color = :blue)
lines!(ax[2], T, kmuj.(T); color = :blue)
ax[1].yticks = 1.0e-05:3.0e-05:1.0e-04
ax[2].yticks = 0.0:0.05:0.2
ax[3].yticks = 900:100:1400
xlims!(ax[1], 300, 3000)
xlims!(ax[2], 300, 3000)
xlims!(ax[3], 300, 3000)
ylims!(ax[1], 1.0e-05, 10.0e-05)
ylims!(ax[2], 0.0, 0.2)
ylims!(ax[3], 900.0, 1400)
f
end
Another application case is the fitting of flue gases properties. One often needs to simulate the post-combustion flow in a segregated manner, i.e. not as an integral part of the combusting system. To that end, fitting properties and simply ignoring species transport can be an alternative to speed up calculations if the physics allows to do so.
Below we evaluate acetylene equilibrium adiabatic combustion products and then inspect the fitted polynomals.
fuel = "C2H2: 1.0"
oxid = "O2: 1.0"
nums = 100
gas = ct.Solution("gri30.yaml")
gas.set_equivalence_ratio(1.0, fuel=fuel, oxidizer=oxid, basis="mole")
gas.equilibrate("HP")
sol = ct.SolutionArray(gas, shape=(nums,))
sol.TP = np.linspace(200, 3800, nums), ct.one_atm
rets = fit_gas_properties(sol)
for p in rets[end-2:end]
println(repr(p))
endPolynomial(3.081205307347277e-6 + 5.4247558010721024e-8*x - 1.6613184369737246e-11*x^2 + 3.9677505080811406e-15*x^3 - 3.8013623932160725e-19*x^4)
Polynomial(0.006242391591397946 + 0.00013276848768928543*x - 2.3751176359017937e-8*x^2 + 4.471623756383515e-12*x^3 - 3.9917579021139404e-16*x^4)
Polynomial(1103.403676383008 + 0.41428156929065896*x - 0.00010655706152057004*x^2 + 8.222293810551883e-9*x^3 + 4.4544721879115824e-13*x^4)As a final validation step, one can again inspect properties graphically.
with_theme() do
T = pyconvert(Vector{Float64}, sol.T)
f, ax = plot_gas_properties(T, rets...)
f
end
Computing an equivalent species
In this tutorial we discuss an approach to unify species in a chemical system for simplified representation in CFD simulations; a typical use case would be simulating a system where energy aspects are more important than actual kinetics features and a major combusting species is present.
We start by importing the required tools:
using WallyToolbox
using PyCanteraTools
using PythonCall
const ct = pyimport("cantera")In what follows let's assume that the molar composition of the reference fuel is given by the following composition string (in Cantera format). This is a typical natural gas composition where we find methane as major species, other minor hydrocarbons, and residual inert species.
X = "CH4: 0.9194, C2H6: 0.0302, C3H8: 0.0059, CO2: 0.0078, N2: 0.0367"Assume we want to get a single equivalent hydrocarbon representing all those details in fuel composition; other species remain as they are. For this we can filter the selected species from the provided composition string with functionalities exported by PyCanteraTools.
hydrocarbons = ["CH4", "C2H6", "C3H8"]
ishydrocarbon(x) = x[1] in hydrocarbons
X_dict = filter(ishydrocarbon, cantera_string_to_dict(X))
X_hydr = cantera_dict_to_string(X_dict)"C3H8: 0.005900000000, CH4: 0.919400000000, C2H6: 0.030200000000"Next we load a solution with the reference mechanism and set the gas composition to the filtered (relative molar fractions) composition.
gas = ct.Solution("gri30.yaml")
gas.TPX = nothing, nothing, X_hydrThe elemental mass fractions of CHONS can be recoved from Cantera using the wrapper function chons_get_fractions.
Y = chons_get_fractions(gas; basis = :mass)5-element Vector{Float64}:
0.7526577798064804
0.2473422201935198
0.0
0.0
0.0For preserving the flow characteristics of the simplified fuel, it is important to ensure the new artificial composition preserves the mean molecular mass. Doing so will keep constant inlet flow rate if using mass flow boundary conditions, as it is usual in combustion simulations.
mw = pyconvert(Float64, gas.mean_molecular_weight)
mw16.659571428571425Below we compute the stoichiometric coefficient of carbon in the target artificial species; it is simply a mass to mole fraction conversion, as one might promptly recognize.
scaler = :C => Y[1]*mw/1000atomicmass(:C):C => 1.043956043956044Using the mass fractions and the scaler one can easily compute the new hypothetical species using hfo_empirical_formula. It must be emphasized that although this function was initially conceived for handling heavy-fuel oils (HFOs) it is can also be used for any species in the CHONS chemistry family.
empirical_fuel = hfo_empirical_formula(Y; scaler)
String(empirical_fuel)"C(1.043956)H(4.087912)O(0.000000)N(0.000000)S(0.000000)"To wrap-up we verify that the new species really matches the target molecular mass; because of round-off errors and possible differences in atomic masses between Cantera and our database [1].
1000ChemicalCompound(Dict(zip("CHONS", empirical_fuel.X))).M ≈ mwtrueThere are a few extra steps that one must be aware; with the newly created species we need to create (by some means not described here) a new mechanism containing the hypothetical species. Once that is done, one needs to compute the heating values related to that fuel, e.g. using mixture_heating_value, what will lead to unphysical values at first. The formation enthalpy of the referred species needs to be corrected in mechanism data (generally NASA7 polynomials, for which it is done in the fifth coefficient) to match the reference fuel energy release.
- 1There should not be any difference because the database used internally by WallyToolbox is an extraction of Cantera source code.