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This archive contains data that describes a dummy medium to run htrdr for a combustion application, in the general case of an heterogeneous medium. It also proposes a program to validate htrdr-combustion.

The provided combustion medium is an axis aligned cube of 0.2 m side length. The (x=0, y=0) position is the center of the bottom face of the cube, meaning that x and y coordinates vary in the [-0.1, 0.1] m range, while the z coordinate varies in the [0, 0.2] m range.

The laser sheet is 1 mm thick, is horizontal, and splits the medium at half height: the altitude of the laser sheet therefore varies in the [0.0995, 0.105] m range, while x and y coordinates vary in the [-0.1, 0.1] m range. The laser sheet is emitted from the y=0 plane, and propagates in the direction of positive y. Its wavelength is 532 nm, and its surface power density is 1000 W/m².

The sensor on which the flux will be computed is located in the center of the bottom limit of the combustion medium. It is a square of 5 cm side length: x and y coordinates over the sensor vary in the [-0.025, 0.025] m range, and z=0.

Boundaries of the combustion chamber are black, and the sensor is also a blackbody: whenever radiation reaches a boundary, it is fully absorbed. Only the flux that reaches the sensor is accounted for.

Soot aggregates absorb and scatter radiation within the limits of the combustion chamber. Their optical cross-sections are computed according to the RDG-FA theory, using the following data:

• refraction index: 1.60+0.75.i
• fractal dimension: 1.80
• fractal prefactor: 1.30
• primary particles diameter: 20 nm
• number of primary particles per aggregate: 100

The soot volume fraction follows the following inhomogeneous axisymmetric profile:

fv(x,y,z)=fv_max*(1/2-x/L)*(1-sqrt(2*((y/L-1/2)²+(z/L-1/2)²)))

with fv_max the maximum soot volumic fraction, reached at x=-L/2, y=0, z=L/2, L the length of the cubic combustion chamber, x and y in [-L/2, L/2] and z in [0, L]. fv_max is set at 10^-6 m³ of soot per m³.

Content

Illustration of the combustion medium provided in the Starter Pack. This medium is illuminated by a laser sheet whose surface of emission is here represented in red. The image on the left shows the entire medium. In the image on the right, the medium is clipped along the y axis to emphasize the axisymmetric profile of its soot volume fraction.

Dummy medium

The dummy_medium directory contains all the data necessary to describe the aforementioned medium within htrdr-combustion. The available files are:

• tetra_mesh.sth: it stores the tetrahedral mesh that represents the heterogeneous medium (12 millions of tetrahedra).
• refraction_index.atrri: this file defines the spectrally varying refractive indices of the medium.
• thermodynamic_conditions.atrtp: it saves the per node physical properties of the tetrahedral mesh.

This directory also contains two Bash scripts that run the htrdr-combustion program to compute a flux density map on this combustion medium (compute_flux_density_map.sh) or to draw an image of it (draw_image.sh). These scripts can be a good starting point to study how to run htrdr for a combustion application. Assuming that htrdr-combustion is correctly installed and registered into the current Bash shell, simply run the desired script. You can finally use htpp to convert the computed images into a PPM image that can be then displayed with a regular image viewer.

~ $ bash htrdr-Combustion-Starter-Pack-0.0.0/dummy_medium/draw_image.sh
~ $ htpp -vm default -o dummy_image.ppm dummy_image_800x600x128.txt

Validation program

The sw_flux directory contains a simple program, written in Fortran, that was designed to solve the problem of interest only (fixed geometric configuration and analytical thermodynamic properties fields). However, two separate Monte-Carlo algorithms have been implemented in order to compute the required flux:

• a direct Monte-Carlo algorithm: optical trajectories are followed from the laser emission surface, until they reach the sensor (or are lost).
• a reverse Monte-Carlo algorithm: this is actually the one that was implemented into htrdr-combustion. Optical paths start from the sensor, and a first-scattering contribution increases the weight of the realization at each scattering position in the medium.

To compile the executable simply invoke make into the sw_flux directory. Note that the build procedure assumes that the GNU Fortran compiler (gfortran) is installed. Once built, run the generated executable named sw_flux. Both algorithms (direct and reverse) must agree, within the limits of the statistical uncertainty. Furthermore, these results should also agree with the flux computed by htrdr-combustion via the script dummy_medium/compute_flux_density_map.sh.

~ $ cd htrdr-Combustion-Starter-Pack-0.0.0/sw_flux
sw_flux $ make
sw_flux $ ./sw_flux
sw_flux $ cd ../dummy_medium/
dummy_medium $ bash compute_flux_density_map.sh

The result should be, in terms of surface power density:

1.028e-2 +/- 1e-5 W/m²

Copyright notice

Copyright © 2021 |Méso|Star> (contact@meso-star.com)
Copyright © 2021 CNRS/RAPSODEE

License

htrdr: Combustion Starter Pack is released under the GPLv3+ license: GNU GPL version 3 or later. You can freely study, modify or extend it. You are also welcome to redistribute it under certain conditions; refer to the license for details.