=Paper=
{{Paper
|id=Vol-2964/article_196
|storemode=property
|title=Accelerating High-fidelity Combustion Simulations with Classification Algorithms
|pdfUrl=https://ceur-ws.org/Vol-2964/article_196.pdf
|volume=Vol-2964
|authors=Wai Tong Chung,Aashwin Mishra,Nikolaos Perakis,Matthias Ihme
|dblpUrl=https://dblp.org/rec/conf/aaaiss/ChungMPI21
}}
==Accelerating High-fidelity Combustion Simulations with Classification Algorithms==
https://ceur-ws.org/Vol-2964/article_196.pdf
Accelerating high-fidelity combustion simulations with classification algorithms
Wai Tong Chung,1,* Aashwin Ananda Mishra, 2 Nikolaos Perakis, 1,3 Matthias Ihme, 1
1
Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA
2
SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA
3
Chair of Space Propulsion, Technical University of Munich, 85748 Garching, Germany
*
Corresponding author: wtchung@stanford.edu
Abstract terms (Lapeyre et al. 2019; Henry de Frahan et al. 2019).
However, supervised learning in flow-physics problems are
High-fidelity combustion simulations are useful for optimiz- still in their infancy, and face challenges when extrapolating
ing engineering designs, and can result in reduced design
costs, increased engineering performance, and lower emis-
beyond the training set – resulting in generalization errors
sions. In these simulations, the representation of combustion that arise from numerical predictions that only match spe-
chemistry is a computational bottleneck. In this investigation, cific flow configurations represented by the training data (Wu,
we accelerate unsteady combustion simulations by employing Xiao, and Paterson 2018).
neural networks for dynamic combustion submodel assign- This study ameliorates this issue by employing a ma-
ment. Neural networks, trained with local flow properties as chine learning classification algorithm that selects well-tested
input variables and combustion model errors as training la- physics-based combustion submodels of varying fidelity and
bels, assign three different combustion models – finite-rate complexity, and assigns them to different regions of the sim-
chemistry (FRC), flamelet progress variable (FPV), and inert ulation domain. Thus, the potential approximation errors
mixing (IM) – with high classification accuracy in a priori made by the machine-learning algorithm are limited by the
tests. A priori results are compared with those generated by
random forests. A posteriori simulations, integrating a neural
predictive capability of the lowest performing submodel. Pre-
network model in the computational fluid dynamics solver, vious work (Chung et al. 2020) has investigated the use of
demonstrate that high-fidelity simulations can be performed random forests (Breiman 2001) for combustion submodel
with this approach at significantly reduced cost compared to assignment. While random forests can provide high classifi-
detailed chemistry simulations and simultaneously achieving cation accuracy, the development of deep learning methods
improved accuracy over low-order combustion models. provides advantages to neural networks in learning spatial
and temporal data, commonly seen in flow-physics problems.
To this end, we examine the application of employing
Introduction neural networks for the purpose of local and dynamic
Combustion processes are present in engineering applica- model assignment in large-eddy simulations (LES) of a
tions, such as in rockets, thermal generators, and propulsion gaseous-oxygen/gaseous-methane (GOX/GCH4) rocket com-
engines. Thus, accurate combustion simulation techniques bustor (Silvestri et al. 2015, 2016). Results from an a priori
are useful for optimizing engineering designs, and can re- investigation are assesed and compared with results from
sult in reduced design costs, increased engineering perfor- random foretts. Additionally, an a posteriori neural network-
mance, and substantially lower greenhouse-gas emissions integrated simulation to demonstrate the effectiveness of this
and pollutants. However, commonplace adoption of such approach, and the computational gains achieved.
high-fidelity simulation techniques is restricted by a bottle-
neck that emerges from the high computational expense of Mathematical models
combustion chemistry. Hence, a significant portion of com- Large-eddy simulations in the present study are performed
bustion research has been devoted to the development of by solving the Favre-filtered conservation equations for mass,
cost-efficient models for representing the combustion chem- momentum, energy, and chemical species:
istry (Pope 2013) in large-scale high-fidelity simulations.
∂t ρ + ∇ · (ρeu) =0 (1a)
Alternatively, data-driven methods can be employed for
fast and accurate predictive modeling. In particular, artificial u) + ∇ · (ρe
∂t (ρe uue ) = − ∇ · (pI)
neural networks have been employed for regressing thermo- + ∇ · (τ v + τ t ) (1b)
physical quantities (Christo et al. 1996; Blasco et al. 1999; e) + ∇ · [e
∂t (ρe e + p)] = − ∇ · (q v + q t )
u(ρe
Ihme, Schmitt, and Pitsch 2009; Kempf, Flemming, and Jan-
icka 2005; Sen and Menon 2010), and modeling turbulent + ∇ · [(τ v + τ t ) · u
e ] (1c)
e + ∇ · (ρe
∂t (ρφ) uφ)e = − ∇ · (J v + J t ) + Ṡ (1d)
Copyright © 2021 for this paper by its authors. Use permitted under
Creative Commons License Attribution 4.0 International (CC BY with density ρ, velocity vector u, specific total energy e,
4.0). stress tensor τ , and heat flux vector q; · denotes a filtered
quantity and e· is a Favre-filtered quantity. Subscripts v and and IM quantities of interest Q by interpolating from gener-
t denote viscous and turbulent quantities, respectively. The ated flamelet tables (Pitsch 1998).
pressure p is computed from the ideal gas equation of state. φ, Secondly, we assign labels Y = {IM, FPV, FRC} to the
J , and Ṡ are the transported scalars, scalar diffusive fluxes, training data. We consider FRC as combustion model of
and scalar source terms for the candidate combustion mod- highest fidelity but at the expense of highest computational
els. The dynamic Smagorinsky model (Moin et al. 1991) cost. Therefore, we assign labels in the training set based on
and dynamic thickened-flame model (Colin et al. 2000) are the normalized combustion submodel error yQ of quantities
used to model closure in the turbulent terms. Simulations of interest α ∈ Q between FRC and the models of lower
are performed by employing an unstructured compressible fidelity (Wu et al. 2015):
finite-volume solver (Khalighi et al. 2011; Ma, Lv, and Ihme
1 X |αFRC − αy |
2017; Wu et al. 2019). yQ = with y ∈ {FPV, IM} , (2)
In this work, we employ three different combustion N kαFRC k∞
α∈Q
submodels, namely an inert mixing (IM) model, the
flamelet/progress variable (FPV) model (Pierce and Moin where the error for considering N = |Q| number of quanti-
2004; Ihme, Cha, and Pitsch 2005), and a finite-rate chemistry ties of interest (QoIs) is a normalized linear combination of
(FRC) model. The present framework couples the different each individual submodel error. A model of higher fidelity
combustion models with the approach developed by Wu et al. is assigned when the QoI submodel error yQ exceeds a user-
y
(2019), which ensures the conservation of mass, momen- defined threshold θQ , with FRC chosen when all conditions
tum, and energy. Reconstruction of the chemical state-vector for selecting FPV and IM are not met.
needed for FRC involves interpolation from the chemistry Thirdly, we construct the feature vector x ∈ X . To this
tables that stores all species, whereas the reconstruction of end, we applied the Maximal Information Coefficient (MIC)
the progress variable needed for tabulated chemistry involves (Reshef et al. 2011) to identify the top six (out of fifteen)
the sum of all major combustion product species: CO2 , CO, thermophysical quantities with the strongest relationships
H2 O, and H2 . To ensure consistency between the combustion with the local combustion submodel error. These six features,
submodels, the aforementioned reconstruction is applied for namely mixture fraction, progress variable, density, local
the inactive combustion model at the submodel interface at Prandtl number, and Euclidean norm of the mixture frac-
every timestep. The GRI-3.0 chemical mechanism (Smith tion gradient, viz., x = [Z, e ρ, Te, P r∆ , k∇Zk
e C, e 2 ] are then
et al. 2000), involving 33 chemical species, is used to describe selected for constructing the feature set.
combustion chemistry. Lastly, we train, validate, and test the classification algo-
rithms. In this investigation, we compare the combustion
Experimental configuration and submodel assignment by neural networks and random forests
computational setup in the a priori study. 1 × 104 training points have been ran-
We perform simulations of the gaseous oxygen-gaseous domly sampled from a single simulation snapshot consisting
methane rocket combustor setup by Silvestri et al. (2015, of 2×105 cells. The hyperparameters of a random forest, con-
2016) using an axisymmetric domain. We select this config- sisting of twenty decision trees, and maximum depth of ten
uration to challenge the shortcomings of FPV in represent- nodes, are found using random grid search. Addtionally, the
ing correct wall heat flux, which results in a thicker ther- hyperparameters of a neural network consisting of 4 hidden
mal boundary layer and overprediction of CO mass fraction dense layers with L2 regularization consisting of 36 nodes
shown in fig. 1. are found using Bayesian optimization.
Inlet fuel and oxidizer mass flow rates and temperature,
along with chamber and nozzle wall temperatures are pre- Results
scribed following experimental measurements (Silvestri et al. We first perform an a priori assessment to determine the ac-
2015, 2016; Perakis and Haidn 2019). All remaining bound- curacy of neural network and random forest classification,
aries are defined as adiabatic non-slip walls with the excep- as shown in Table 1, on a monolithic FRC simulation test
tion of the exhaust, which is modeled as a pressure outlet. The dataset from an unseen timestep. Temperature and CO mass
computational domain is discretized by a block-structured fraction fields from the test dataset are shown in fig. 2a. and
mesh consisting of 2 × 105 cells. The wall-normal direction 2b. Temperature Te is chosen as a QoI to describe the combus-
is resolved down to 30 µm, and a wall model (Kawai and tion efficiency and engine performance. CO mass fraction,
Larsson 2013) is employed for the viscous sublayer. A typical YeCO , is chosen to challenge the deficiencies of FPV and IM
timestep is 25 ns, corresponding to a convective CFL number in capturing intermediate species (Wu et al. 2019). Through-
of 1.0. out this study we explore cases that use the same threshold
IM FPV
for both IM and FPV, viz., θQ = θQ = θQ for simplicity.
Data-driven methods Classification accuracy range from approximately 0.7 to 0.8,
In this section, we describe the procedure for incorporating which is comparable to the use of classifiers in other flow
a supervised learning algorithm for combustion submodel physics problems (Maulik et al. 2019). We note that while the
assignment. Firstly, we use the instantaneous flow-field so- combustion submodel assignment accuracy of both classifiers
lutions from the FRC simulation of the combustor as the are comparable, neural networks produce less ‘speckled’ sub-
learning dataset. FRC data are then used to reconstruct FPV model assignment. This is an improvement as it reduces the
Figure 1: Time-averaged temperature and CO mass fraction for monolithic FRC and FPV LES. The location of the stoichiometric
mixture, Zest = 0.2, is shown by black lines.
Table 1: A priori analysis of neural networks, summarizing submodel assignment and assignment accuracy.
Case θ{T,CO} =0.05 θ{T,CO} =0.02 θ{T,CO} =0.05 θ{T,CO} =0.02
Classifier Neural network Neural network Random forest Random forest
IM:FPV:FRC 6:74:20 5:46:49 6:63:31 6:42:52
Classification accuracy 0.773 0.696 0.753 0.734
Figure 2: Instantaneous (a) temperature, (b) CO mass fraction, and (c,d) combustion submodel assignment from test set in the a
priori assessment. The location of the stoichiometric mixture, Z
est = 0.2, is shown by black lines.
reconstruction operations between the different combustion FRC is assigned in fuel-rich regions immediately downstream
submodels at the submodel interface. of the injectors where intermediate species reactions are not
captured well by tabulated chemistry submodels. Employing
Figure 2c. and 2d. demonstrates the a priori combustion
random forest results in 31% FRC assignment within the
submodel assignment on an unseen FRC-simulation snapshot
domain, while neural network results 20% FRC assignment.
for case θ{T,CO} = 0.05 using a neural network and random
forest respectively. For both cases shown, inert mixing (IM) is Figure 2e. and 2f. demonstrates the a priori combustion
assigned in 6% of the domain at the injector and the oxidizer submodel assignment for case θ{T,CO} = 0.02 using a neural
core, where chemical processes are insignificant. In general, network and random forest respectively. Here, the neural
Figure 3: Time-averaged temperature, CO mass fraction, along with time-averaged and instantaneous combustion submodel
assignment for a posteriori data-assisted LES using neural-networks. The location of the stoichiometric mixture, Z
est = 0.2, is
shown by black lines.
network fails to recognize that IM should be applied to the 80NSSC18C0207, and from the Stanford University Harold
fuel injector, resulting in a lower overall IM assignment of and Marcia Wagner Engineering Fellowship. Resources sup-
5%. In addition to the aforementioned fuel rich region, both porting this work are provided by the High-End Computing
classifiers assign FRC to the near wall regions, which are (HEC) Program at NASA Ames Research Center.
essential for accurate thermal and species boundary layer
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