SlowGuess/NeurIPS_2023_OCR huggingface dataset:
All data is generated by the present authors and licensed via CC BY-NC-SA 4.0. The present authors bear responsibility in case of violation of rights.
C Maintenance Plan and Long Term Preservation
The contributors to BLASTNet 2.0 are committed to maintaining and preserving this dataset. Maintenance of this dataset will largely involve tracking and fixing issues that might be discovered after release. To facilitate this, we host an issues webpage (https://github.com/blastnet/blastnet.github.io/issues) for user feedback. All data is shared via Kaggle, ensuring that the data will be preserved and available in the long-term. In addition, our maintenance plan involves adhering to the FAIR principles [71] for scientific data management, with the specific details as follows:
Findable All data are indexed and can be easily searched via both Kaggle and BLASTNet platforms. To ensure that the data is findable, a http://schema.org structured metadata is employed, as detailed in Appendices D and E. All BLASTNet datasets share a global and persistent DOI at Zenodo: https://doi.org/10.5281/zenodo.7242864.
Accessible Both data and descriptive metadata are retrievable via the Kaggle command-line API. This protocol is free and available at https://github.com/Kaggle/kaggle-api, with authentication and authorization provided through a Kaggle account. We provide a bash script for users to download all data (shared in multiple repositories) at once with this API. Users can also download the data directly from Kaggle repositories.
Interoperable The data and descriptive metadata use accessible formats that can be read by standard python numpy and json packages. BLASTNet's http://schema.org structured metadata also references the structured metadata of each separate BLASTNet repository (providing information on specific contributors and Kaggle URLs). We have attempted to use accessible language when generating these metadata.
Reusable The descriptive metadata contains information on the flow configuration (initial conditions, chemistry, numerics, source publication, etc.). In addition, all Kaggle repositories employ a CC BY-SA NC 4.0 license. The structured http://schema.org metadata provides rich information that passes the rich results test (https://search.google.com/test/ rich-results). All data and descriptive metadata are presented in consistent little-endian single-precision binaries and . json files, guaranteeing acceptable standards for fast I/O, sufficient floating-point precision, and broad accessibility via widely-used python packages.
D Additional BLASTNet 2.0 Details
BLASTNet 2.0 contains pre-processed DNS data shared via a network of Kaggle repositories, with links consolidated at the landing page https://blastnet.github.io.
D.1 Data Format and Directory Structure
Data, generated from different numerical solvers (as detailed in Appendix D.2), initially exists in a range of formats (.vtk, .vtu, .tec, and .dat) that are not readily formatted for training ML models. Thus, we pre-process all generated data into a consistent and convenient format consisting of physical and chemical data (Appendix D.1.1), descriptive metadata (Appendix D.1.2), and web metadata (Appendix D.1.3), along with instructions for reading the data in Appendix D.1.4. This information is summarized in Figure 7.
Figure 7: Directory structure and reading instructions for an instance of a BLASTNet configuration.
D.1.1 Files on Flow Physics and Chemistry
All flowfield data are processed into a consistent format - little-endian single-precision binaries that can be read with np.fromfile(np.memmap, as shown in Figure 7. The choice of this data format enables high I/O speed in loading arrays. As also shown in Figure 7, we also provide .json files (see Appendix D.1.2) that store additional information on configurations, contributors, solvers, and corresponding source publications. Chemical mechanisms and transport properties are shared through Cantera [88]. .cti/.xml/.yaml or Chemkin [89] fortran files. Thus BLASTNet data contains
all information needed to reconstruct any derived auxiliary quantities (such as vorticity, viscosity, turbulence closure terms, along with heat and chemical transport coefficients) from the conservation equations.
D.1.2 Descriptive Metadata
The binary data described in Appendix D.1.1 contains information on physical and chemical data, without much context. Details involving global information such as configuration, boundary/initial conditions, solvers, related publications, and spatial grid information, as well as local temporal information (if any) are provided through an info.json file in each Kaggle repository. Listings 1 and 2 present the python code used to generate global and local information in one example of info.json.
metadata['global'] = { "dataset_id": "waitongchung/inert-ch4o2-hit-dns", "Nxyz": [129,129,129], "snapshots": 98, "variables": ["UX-ms-1","UY-ms-1","UZ-ms-1", "P_Pa", "T_K", "RHO_kgm-3", "YO2", "YCH4"], "compression": "None", "grid": {"x": "/grid/X_m.dat", "y": "/grid/Y_m.dat", "z": "/grid/Z_m.dat"}, "numerics": {"spatial": "4th order central-differencing with 2nd order ENO", "temporal": "3rd-order SSP-RK3 (non-stiff) and semi-implicit ROWPLUS (stiff)", "solver": "CharlesX"}, "bc": "Periodic in x-, y-, and z-directions.", "ic": {"U": "HIT Von Karman Pao with Re_t = 80 and integral lengthscale of 62.5E-6m", "T [K]": 300, "P [Pa]": 101325, "Mixture": "CH4-O2 inert branch from 1D cantera counterflow calculations.", "doi": "https://doi.org/10.1016/jcombustflame.2021.111758", "contributors": "Wai Tong Chung and Matthias Ihme", "description": "Compressible Inert CH4-O2 Homogeneous Isotropic Turbulence DNS", "chem_thermo_tran": {"description": "FRC and Mixture-Averaged Transport with constant lewis number", "cantera_xml": "/chem_thermo_tran/bfer.xml"} }
Listing 1: Python command for generating global metadata for a BLASTNet Kaggle repository.
metadata['local'] = [ {"id": 0, "time [s]: 6.88389e-06, "UX-ms-1 filename": "./data/UX-ms-1_id000.dat", "UY-ms-1 filename": "./data/UY-ms-1_id000.dat", "UZ-ms-1 filename": "./data/UZ-ms-1_id000.dat", "P_Pa filename": "./data/P_Pa_id000.dat", "T_K filename": "./data/T_K_id000.dat", "RHO_kgm-3 filename": "./data/RHO_kgm-3_id000.dat", "YO2 filename": "./data/YO2_id000.dat", "YCH4 filename": "./data/YCH4_id000.dat"], {"id": 1, ..., }, {"id": 97, ...}]
Listing 2: Python command for generating local metadata for a BLASTNet Kaggle repository.
D.1.3 Structured Web Metadata
A http://schema.org metadata has been added to https://blastnet.github.io/datasets, and tested with https://search.google.com/test/rich-results.
D.1.4 Reading Data
As shown in Figure 7, BLASTNet data can be read by (i) loading the descriptive metadata with the json package on python, and (i) using np.fromfile/np.memmap to load and reshape the data. Links to tutorials to perform this are also shared in Appendix A.
D.2 DNS Configurations
BLASTNet 2.0 contains data from 34 different DNS configurations. The Kaggle link of all configurations are provided in Table 4. The details of each DNS configuration are provided in this section as well.
D.2.1 Non-reacting homogeneous isotropic turbulence (HIT)
The HIT DNS simulation [20] is performed on a 3D cubic domain of length  $L$ , where a spherical gaseous-oxygen core of radius  $r = 0.25L$  at  $300\mathrm{K}$  is initialized in gaseous methane environment of  $300\mathrm{K}$  at 1 atm pressure, providing an idealized representation of an inert gaseous fuel-air mixture in a rocket engine. The simulation setup is shown in Figure 8. Periodic boundary conditions are used at all boundaries. A synthetic turbulence generator by Saad et al. [90] based on von Kármán-Pao energy spectrum with zero mean velocity is used to generate the initial velocity profile. Ideal gas law is used as the equation of state (EoS) to relate pressure, temperature and density.
The simulation is performed in an unstructured compressible finite-volume solver [64]. The solver uses a fourth-order accurate central spatial finite difference scheme. For the time integration, a stable third-order Runge-Kutta scheme is employed. As mentioned before in Section 3, mixture-averaged transport properties are used in the DNS.
D.2.2 Reacting forced homogeneous isotropic turbulence
The DNS study [67] involves a statistically steady, isotropic, and homogeneous turbulent flow in an unconfined space. The schematic of the simulation setup is presented in Figure 9. The flame is initialized by a planar surface separating half of the domain containing methane/air mixture at
$t = t_{I}$
Figure 8: Schematic of the DNS configuration of inert HIT.  $t_I$  denotes large-eddy timescale, while  $l_I$  denotes integral lengthscale. Adapted from [20], Copyright 2022, with permission from Elsevier.
$700\mathrm{K}$  and  $3.04\times 10^{7}\mathrm{ergcm}^{-3}$  pressure, and another half with hot products, and is immersed in a high-intensity turbulent flow field with Kolmogorov type spectrum. The idea is to investigate the process of flame interaction with steady homogeneous isotropic turbulence. However, the flow needs to be constantly stirred at the largest scale to ensure a steady energy cascade to smaller scales so that the turbulence-flame interaction at the quasi-steady state can be studied. A spectral turbulencedriving method is used in the study, the details of which are available in Poludnenko and Oran [67]. This driving method produces statistically steady forced-HIT flows with arbitrarily complex energy spectra. In particular, it is possible to achieve Kolmogorov type turbulence with inertial range of energy cascade extending up to energy injection scale. The other advantage of this method is that it does not introduce any artificial large-scale anisotropy, compression, or rarefaction. Prior to ignition, all domain boundaries are periodic. At ignition, boundary conditions along the left and right  $z$  -boundaries (as shown in Figure 9) are switched to zero-order extrapolation to prevent any non-physical pressure build-up in the domain and the formation of artificial large-scale rarefaction waves at the boundaries.
Figure 9: Schematic of the DNS configuration of reacting forced HIT [67]. The top and bottom contour plots correspond to the magnitude of velocity and  $\mathrm{CH}_2\mathrm{O}$  species mass fractions, respectively.
The computational domain aspect ratio is  $1 \times 1 \times 16$ , with a grid size of  $257 \times 257 \times 4097$ , including 16 grid points per unit laminar flame thermal thickness. The cell size is  $2.62 \times 10^{-4} \mathrm{~cm}$ . The turbulent velocity at energy injection scale ( $L = 0.067 \mathrm{~cm}$ ) length scale is  $213.92 \mathrm{~cm} \mathrm{s}^{-1}$  with turbulent root-mean-squared (RMS) velocity of  $245.83 \mathrm{~cm} \mathrm{s}^{-1}$ , resulting in an eddy turnover time of  $3.14 \times 10^{-4} \mathrm{~s}$ . The same velocity quantities corresponding to the integral length scale ( $l = 0.0196 \mathrm{~cm}$ ) are  $141.93 \mathrm{~cm} \mathrm{s}^{-1}$  and  $132.2 \mathrm{~cm} \mathrm{s}^{-1}$ . The ignition delay time of the mixture is three times the eddy turn-over time, and the total simulation runtime is 16 times the eddy turn-over time. The Damkohler and Karlovitz numbers are 0.66 and 9.97, respectively.
The DNS calculation is performed using the code Athena-RFX [67], which implements higher-order fully conservative Godunov-type methods for integration of fluid equations. The numerics in this work are third-order accurate in space and second-order accurate in time. More details are available in the original paper [67]. The foundational fuel chemistry model (FFCM-1) [91] with 22 species and 107 reactions is used as the chemical mechanism.
D.2.3 Reacting jet flows
The DNS configurations by Brouzet et al. [29] involve two parametric variations of 3D reacting turbulent premixed methane/air round-jet flames with high-fidelity acoustics to investigate the effect of different chemical mechanisms on flame dynamics. The setup is initialized with methane/air combustion products at adiabatic flame temperature and at atmospheric pressure. The jet Reynolds and Mach numbers are 5300 and 0.36, respectively. A schematic representation of the DNS configuration is shown in Figure 10. The two variations of the reacting jet correspond to two different chemical mechanisms: (i) a semi-global  $\mathrm{CH}_4$ -BFER mechanism with 2 reactions [92], and (ii) a skeletal COFFEE mechanism [93] with 14 species and 38 reactions. In both configurations, the domain size is  $20D \times 16D \times 16D$ . The grid sizes are  $1811 \times 721 \times 721$  and  $1546 \times 676 \times 676$  for the BFER and COFFEE cases, respectively. These meshes correspond to 10 and 12 grid points per unit thermal flame thickness in the streamwise direction, and 12 and 16 points in the transverse and spanwise directions.
Figure 10: Schematic of the DNS configuration of reacting jet flows. Reprinted from [29], Copyright 2021, with permission from Cambridge University Press.
The DNS is performed using the code NTMIX-CHEMKIN [94], which solves fully compressible Navier-Stokes equations along with energy and species conservation equations in Cartesian coordinates. The solver uses an eight-order explicit central spatial difference scheme and a third-order Runge-Kutta time integration scheme. Ideal gas law and mixture-averaged species-specific properties are used for the simulations. Further details of the DNS configuration and solver are provided in Brouzet et al. [29].
D.2.4 Non-reacting transcritical channel flow
The study by Guo et al. [69] involves six different configurations of wall-bounded DNS in the transcritical regime. The schematic of the DNS setup is shown in Figure 11. They used nitrogen  $\mathrm{N}_2$  as the working fluid with a critical pressure and temperature of  $p_c = 3.39\mathrm{MPa}$  and  $T_{c} = 126.19\mathrm{K}$ . These studies consider the flow of  $\mathbf{N}_2$  inside a channel with a hot top and a cold bottom wall with temperatures  $T_{\mathrm{hot}}$  and  $T_{\mathrm{cold}}$ , respectively. The six variations correspond to different temperature ratio (TR) between the two walls. The channel is periodic in streamwise and spanwise direction, while the wall boundary conditions are enforces at two walls. The domain dimensions are  $L_{x}\times 2L_{y}\times L_{z}$ , where  $L_{x} / L_{y} = 2\pi$ ,  $L_{z} / L_{y} = 4\pi /3$  and the channel height is  $2L_{y} = 9.0132\times 10^{-5}\mathrm{m}$ . A Cartesian grid (with mesh size  $384\times 256\times 384$ ) is used for all six configurations.
Figure 11: Schematic of the DNS configuration of non-reacting transcritical channel flows. The contour plots correspond to the  $c_p$  for configurations TR3 and TR1.9. Adapted from [69], Copyright 2022, with permission from Cambridge University Press.
A summary of the individual configurations is provided here in Table 5, with more details being available in the original paper [69]. The operating conditions are chosen such that they cover the range of density ratio,  $\Omega = \rho_{\mathrm{hot}} / \rho_{\mathrm{cold}}$ , between 1 and 20, where  $\rho$  is the density of the fluid at the wall. The name of the configurations are based on different TRs. Configurations TR3, TR1.9, TR1.4 and TR1.3 are transcritical, whereas the other two configurations are sub-critical. The pressure for all configurations is set to be  $3.87\mathrm{MPa}$ , which is higher than  $p_c$ . The bulk Reynolds number is  $3.5\times 10^{4}$ . Table 5 also reports the friction Reynolds number  $(Re_{\tau})$  for two walls using the channel half-height  $L_{y}$  as the length scale.
A compressible finite-volume solver [64] is used for these DNS. The governing equations are solved using a strong stability-preserving Runge-Kutta scheme with third-order accuracy in time stepping, and a fourth-order accurate central spatial finite difference, which reduces to third-order for non-uniform meshes. As the conditions of these simulations are in the transcritical regime, the Peng-Robinson EoS is used, which provides better accuracy in predicting thermodynamic variables than ideal gas in the investigated regime. To avoid the pressure oscillations and to obtain physically realizable solutions, an entropy-stable double-flux model [64] is used along with second-order accurate essentially non-oscillatory (ENO) scheme and Harten-Lax-Van Leer contact (HLLC) Riemann flux computations.
D.2.5 Reacting channel flow
This DNS configuration by Jiang et al. [28] investigates the flame-wall interaction for methane/air flames diluted by hot combustion products in a 3D turbulent V-flame configuration inside a channel with isothermal hot and cold walls. The simulation setup is shown in Figure 12. At the inlet of the channel, the reactant mixture consists of a mixture of cold reactants (30%) and hot combustion products from 1D premixed freely-propagating flame simulation (70%), resulting in an inlet temperature of  $T_{\mathrm{in}} = 1705 \mathrm{~K}$  at 2 atm pressure. The hot and cold wall temperatures are fixed at 1200 and  $400 \mathrm{~K}$ , respectively. The inlet turbulence is generated with a non-reacting simulation of the same channel. Then, the results collected at a sampling plane of  $x / H = 4$  are fed into the reacting simulation. This turbulence generation allows coupling of the velocity and temperature fluctuations at the inlet.
Table 5: Summary of the operating conditions of six different DNS configurations of non-reacting transcritical channel flows [69].  $T_{r,\mathrm{cold}} = T_{\mathrm{cold}} / T_c$ ,  $T_{r,\mathrm{hot}} = T_{\mathrm{hot}} / T_c$  and  $\rho_{r,0} = \rho_0 / \rho_c$ , where subscript 0 and  $c$  indicate volume averaged and critical quantity, respectively.
Configs.	Tr,cold	Tr,hot	ρr,0	Ω	Reτ,cold	Reτ,hot
TR3	0.79	2.38	1.16	17.84	430	300
TR1.9	0.79	1.51	1.60	10.05	440	610
TR1.4	0.79	1.11	1.92	5.24	500	1370
TR1.3	0.79	1.03	2.09	2.89	570	1530
TR1.25	0.79	0.99	2.19	1.60	590	1290
TR1	0.79	0.79	2.36	1.00	700	700
Figure 12: Schematic of the 3D DNS domain of reacting channel flow. The bottom figure shows a snapshot of 2D normalized heat release rate contour along with the black dashed line, which is an iso-line of methane progress variable at a particular value. Reprinted from [28], Copyright 2021, with permission from Elsevier.
Velocity fluctuations are first produced using the Passot-Pouquet spectrum for the turbulent kinetic energy. The inlet turbulence for the non-reacting simulation was then generated by rescaling these fluctuations with the RMS profiles of a fully developed channel flow at a Reynolds number of 3200. Next, this is fed into the domain with a convection velocity  $25\%$  lower than the mean inlet velocity at the centerline. This accounts for a correction to the Taylor's hypothesis due to the high near-wall shear stress. Non-reflecting Navier-Stokes Characteristic Boundary Condition (NSCBC) is used for the outlet boundary, and a periodic boundary condition is used in the  $z$ -direction. For the reacting case to ignite, a cylindrical hot patch is imposed at  $y / H = 0$  and  $x / H = 1$  with a diameter of  $0.03H$ , which creates two branches of the V-flame that interact with two walls.
The domain size is  $12H \times 2H \times 3H$ , with a grid size of  $1000 \times 250 \times 250$ , which stretches from  $5\mu \mathrm{m}$  at the wall to  $30\mu \mathrm{m}$  at the centerline in the  $y$ -direction, and  $30\mu \mathrm{m}$  uniform grid in both  $x$ - and  $z$ -direction, and ensures at least one grid point within one wall unit and a mean grid size less than 1.4 times the Kolmogorov length scale. There are around 20 grid points inside the flame thickness as well.
The numerical solver used for the DNS study is NTMIX-CHEMKIN [94]. Similar to the study of Brouzet et al. [29], this solver features an eighth-order central finite difference scheme for spatial derivatives and a third-order Runge-Kutta time integrator. A tenth-order explicit filter is also used to eliminate spurious oscillations at high wave numbers. Ideal gas law is used as the EoS. A reduced mechanism for methane/air combustion with 23 species, 12 quasi-steady species and 205 reactions is developed for this study.
D.2.6 Partially-premixed slot burner
This DNS configuration [27] involves a turbulent lifted hydrogen jet flame in heated co-flow air. Figure 13 shows the schematic of the simulation setup. A diluted fuel mixture (65% H $_2$  and 35% N $_2$  by volume) is issued from the central slot at an inlet temperature of 400 K. This central jet is surrounded on either side by co-flowing heated air streams with an inlet temperature of 850 K, at atmospheric pressure. The mean inlet axial velocity  $U_{\mathrm{in}}$  is given by:
$$
U _ {\mathrm {i n}} = U _ {c} + \frac {U _ {\mathrm {j e t}} - U _ {c}}{2} \left[ \tanh  \left(\frac {y + H / 2}{0 . 1 H}\right) - \tanh  \left(\frac {y - H / 2}{0 . 1 H}\right) \right], \tag {7}
$$
where the mean inlet jet  $(U_{\mathrm{jet}})$  and co-flow  $(U_{c})$  velocities are 240 and  $2\mathrm{ms}^{-1}$ , respectively. The jet width at the inlet is  $2\mathrm{mm}$ . The other quantities, such as temperature and species mass fractions also follow the same profile (Equation (7)). The jet Reynolds number is 8000. Velocity fluctuations,  $u^{\prime}$ , which is  $10\%$  of  $U_{\mathrm{jet}}$ , is obtained by generating an auxiliary homogeneous isotropic turbulence field. These fluctuations are then fed from the inlet using Taylor's hypothesis. This  $2000\times 1600\times 400$  computational domain is  $15H\times 20H\times 3H$  in the streamwise  $x-$ , transverse  $y-$ , and spanwise  $z-$  directions, respectively, resulting in a total of 1.28 billion cells. A uniform grid size of  $15\mu \mathrm{m}$  is placed in the  $x-$  and  $z$ -directions, while the  $y$ -directional grid is algebraically stretched outside the flame and shear zones. Improved non-reflecting boundary conditions [95, 96] are adopted in the  $x-$  and  $y$ -directions, while periodic boundary conditions are applied in the  $z$ -direction. The data is collected after four jet flow-through times after the flame becomes statistically stationary.
Figure 13: Schematic of the DNS of slot-burner setup. The contours correspond to OH and  $\mathrm{HO}_2$  species. Reprinted from [27], Copyright 2021, with permission from Elsevier.
The Sandia DNS code, S3D [65], is employed for solving the compressible Navier-Stokes, species conservation, and total energy equations. Spatial derivatives are approximated with an eighth-order central difference scheme, and a tenth-order filter is used to remove any spurious high-frequency fluctuations in the solution. For time integration, a fourth-order explicit Runge-Kutta method is used. The employed detailed hydrogen-air chemical mechanism composed of 9 species and 21 elementary reaction steps was developed by Li et al. [97]
D.2.7 Freely-propagating flame
This DNS configuration [70] presents a statistically-planar, freely-propagating flame. BLASTNet contains 22 parametric variations of this configuration that differ by three essential parameters involving turbulence: (i) turbulence intensity, characterized by the RMS velocity  $u'$ , (ii) inflow velocity,  $U_{\mathrm{in}}$ , and (iii) integral length scale,  $l_I$ . A schematic diagram of the setup is shown in Figure 14. These configurations represent a series of hydrogen-premixed turbulent flames in autoignitive reheat combustion conditions that provide rich information on regimes of turbulent spontaneous ignition and turbulent deflagration.