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Multidimensional Modeling of Mixture Formation in a Hydrogen-Fueled Heavy-Duty Optical Engine With Direct Injection

Hydrogen (H 2 ), as a carbon-free fuel, is considered as one of the most promising solutions to reduce the carbon footprint of hard-to-decarbonize energy and transportation sectors. As such, hydrogen-fueled internal combustion engines (H 2 ICEs) have recently been receiving increasing attention, particularly in applications such as on-road/off-road heavy-duty transport and combined heat and power. The direct injection (DI) of gaseous hydrogen into the combustion chamber offers great potential for achieving high power density and high engine efficiency, while mitigating the risk of backfire and reducing pre-ignition. However, the numerical simulation of H 2 DI system remains a formidable challenge associated with the high computational cost of reproducing compressible supersonic flow and shocks in narrow injector passages and in near-nozzle regions. In general, there is a lack of well-established and validated practices for the modeling of high-pressure H 2 DI in large-bore engines. Here, to this end, this study focuses on computational fluid dynamics (CFD) modeling of the mixture formation process in a heavy-duty optical engine employing a medium-pressure H 2 DI system. Both large eddy simulations (LES) and Reynolds Averaged Navier–Stokes (RANS) simulations are performed and evaluated against optical data. Gaseous hydrogen is injected into the combustion chamber via a centrally located outward opening hollow-cone injector at a pressure of 40 bar. Simulations are carried out for two injection timings, namely, −120 and −60 °CA. The numerical predictions for H 2 distribution in different horizontal and vertical planes during the compression stroke are systematically compared against optical data obtained through planar laser-induced fluorescence (PLIF) measurements. Overall, the LES approach using the Dynamic Structure model is found to have good predictive capabilities for the early jet penetration in terms of length and shape, as well as the later H 2 distributions. However, the unsteady RANS approach with the renormalization group $k - ϵ$ model, which is widely used by industry to model heavy-duty ICEs, significantly underpredicts the H 2 mixing, even at similar mesh resolution to that used in LES. These results indicate that there is a need for the improvement of mixing submodels within the RANS approach when applied to H 2 DI simulations.

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Materials Data on NdAl3Pd2 by Materials Project

NdPd2Al3 crystallizes in the hexagonal P6/mmm space group. The structure is three-dimensional. Nd is bonded in a distorted hexagonal planar geometry to six equivalent Pd and twelve equivalent Al atoms. All Nd–Pd bond lengths are 3.17 Å. All Nd–Al bond lengths are 3.47 Å. Pd is bonded in a 9-coordinate geometry to three equivalent Nd and six equivalent Al atoms. All Pd–Al bond lengths are 2.64 Å. Al is bonded in a 12-coordinate geometry to four equivalent Nd and four equivalent Pd atoms.

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Materials Data on ThAl3Ni2 by Materials Project

ThNi2Al3 crystallizes in the hexagonal P6/mmm space group. The structure is three-dimensional. Th is bonded in a distorted hexagonal planar geometry to six equivalent Ni and twelve equivalent Al atoms. All Th–Ni bond lengths are 3.07 Å. All Th–Al bond lengths are 3.35 Å. Ni is bonded in a 9-coordinate geometry to three equivalent Th and six equivalent Al atoms. All Ni–Al bond lengths are 2.55 Å. Al is bonded in a 12-coordinate geometry to four equivalent Th and four equivalent Ni atoms.

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Materials Data on LaAl3Pd2 by Materials Project

LaPd2Al3 crystallizes in the hexagonal P6/mmm space group. The structure is three-dimensional. La is bonded in a distorted hexagonal planar geometry to six equivalent Pd and twelve equivalent Al atoms. All La–Pd bond lengths are 3.20 Å. All La–Al bond lengths are 3.49 Å. Pd is bonded in a 9-coordinate geometry to three equivalent La and six equivalent Al atoms. All Pd–Al bond lengths are 2.66 Å. Al is bonded in a 12-coordinate geometry to four equivalent La and four equivalent Pd atoms.

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Materials Data on BPb7Br3O7 by Materials Project

BPb7O7Br3 crystallizes in the monoclinic C2/c space group. The structure is three-dimensional. B3+ is bonded in a trigonal planar geometry to three O2- atoms. There is one shorter (1.38 Å) and two longer (1.39 Å) B–O bond length. There are seven inequivalent Pb2+ sites. In the first Pb2+ site, Pb2+ is bonded in a 2-coordinate geometry to three O2- and three Br1- atoms. There are a spread of Pb–O bond distances ranging from 2.33–2.94 Å. There are a spread of Pb–Br bond distances ranging from 2.97–3.42 Å. In the second Pb2+ site, Pb2+ is bonded in a 4-coordinate geometry to four O2- and three Br1- atoms. There are a spread of Pb–O bond distances ranging from 2.28–2.71 Å. There are a spread of Pb–Br bond distances ranging from 3.53–3.57 Å. In the third Pb2+ site, Pb2+ is bonded in a 4-coordinate geometry to four O2- and three Br1- atoms. There are a spread of Pb–O bond distances ranging from 2.39–2.46 Å. There are a spread of Pb–Br bond distances ranging from 3.63–3.77 Å. In the fourth Pb2+ site, Pb2+ is bonded in a 4-coordinate geometry to four O2- and two Br1- atoms. There are a spread of Pb–O bond distances ranging from 2.37–2.59 Å. There are one shorter (3.54 Å) and one longer (3.66 Å) Pb–Br bond lengths. In the fifth Pb2+ site, Pb2+ is bonded in a 3-coordinate geometry to three O2- and three Br1- atoms. There are a spread of Pb–O bond distances ranging from 2.24–2.55 Å. There are a spread of Pb–Br bond distances ranging from 3.23–3.73 Å. In the sixth Pb2+ site, Pb2+ is bonded in a 3-coordinate geometry to three O2- and two Br1- atoms. There are a spread of Pb–O bond distances ranging from 2.27–2.38 Å. There are one shorter (3.47 Å) and one longer (3.53 Å) Pb–Br bond lengths. In the seventh Pb2+ site, Pb2+ is bonded in a 2-coordinate geometry to four O2- and two equivalent Br1- atoms. There are a spread of Pb–O bond distances ranging from 2.23–2.80 Å. There are one shorter (3.27 Å) and one longer (3.86 Å) Pb–Br bond lengths. There are seven inequivalent O2- sites. In the first O2- site, O2- is bonded in a distorted single-bond geometry to one B3+ and three Pb2+ atoms. In the second O2- site, O2- is bonded to four Pb2+ atoms to form a mixture of distorted edge and corner-sharing OPb4 tetrahedra. In the third O2- site, O2- is bonded to four Pb2+ atoms to form a mixture of edge and corner-sharing OPb4 tetrahedra. In the fourth O2- site, O2- is bonded in a distorted single-bond geometry to one B3+ and three Pb2+ atoms. In the fifth O2- site, O2- is bonded to four Pb2+ atoms to form a mixture of edge and corner-sharing OPb4 tetrahedra. In the sixth O2- site, O2- is bonded in a distorted single-bond geometry to one B3+ and three Pb2+ atoms. In the seventh O2- site, O2- is bonded to four Pb2+ atoms to form a mixture of edge and corner-sharing OPb4 tetrahedra. There are four inequivalent Br1- sites. In the first Br1- site, Br1- is bonded in a 1-coordinate geometry to six Pb2+ atoms. In the second Br1- site, Br1- is bonded in a distorted L-shaped geometry to two equivalent Pb2+ atoms. In the third Br1- site, Br1- is bonded in a 8-coordinate geometry to eight Pb2+ atoms. In the fourth Br1- site, Br1- is bonded in a 7-coordinate geometry to seven Pb2+ atoms.

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Materials Data on LiAgC2 by Materials Project

LiAgC2 crystallizes in the hexagonal P-6m2 space group. The structure is three-dimensional. Li1+ is bonded in a distorted hexagonal planar geometry to six equivalent C1- atoms. All Li–C bond lengths are 2.30 Å. Ag1+ is bonded in a linear geometry to two equivalent C1- atoms. Both Ag–C bond lengths are 2.05 Å. C1- is bonded to three equivalent Li1+, one Ag1+, and one C1- atom to form a mixture of distorted face and corner-sharing CLi3AgC trigonal bipyramids. The C–C bond length is 1.25 Å.

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Materials Data on Ba3LiTi5Nb3O21 by Materials Project

LiBa3Ti5Nb3O21 crystallizes in the orthorhombic Cmc2_1 space group. The structure is three-dimensional. Li1+ is bonded in a trigonal planar geometry to four O2- atoms. There are a spread of Li–O bond distances ranging from 1.85–2.67 Å. There are two inequivalent Ba2+ sites. In the first Ba2+ site, Ba2+ is bonded in a 12-coordinate geometry to twelve O2- atoms. There are a spread of Ba–O bond distances ranging from 2.79–3.27 Å. In the second Ba2+ site, Ba2+ is bonded in a 12-coordinate geometry to twelve O2- atoms. There are a spread of Ba–O bond distances ranging from 2.74–3.23 Å. There are three inequivalent Ti4+ sites. In the first Ti4+ site, Ti4+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with two TiO6 octahedra, corners with three NbO6 octahedra, and edges with two TiO6 octahedra. The corner-sharing octahedra tilt angles range from 26–42°. There are a spread of Ti–O bond distances ranging from 1.89–2.15 Å. In the second Ti4+ site, Ti4+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with two equivalent NbO6 octahedra, corners with three TiO6 octahedra, an edgeedge with one TiO6 octahedra, and an edgeedge with one NbO6 octahedra. The corner-sharing octahedra tilt angles range from 26–42°. There are a spread of Ti–O bond distances ranging from 1.89–2.15 Å. In the third Ti4+ site, Ti4+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with two equivalent TiO6 octahedra, corners with three NbO6 octahedra, and edges with two equivalent TiO6 octahedra. The corner-sharing octahedra tilt angles range from 27–42°. There are a spread of Ti–O bond distances ranging from 1.91–2.13 Å. There are two inequivalent Nb5+ sites. In the first Nb5+ site, Nb5+ is bonded to six O2- atoms to form NbO6 octahedra that share a cornercorner with one NbO6 octahedra and corners with five TiO6 octahedra. The corner-sharing octahedra tilt angles range from 37–43°. There are a spread of Nb–O bond distances ranging from 1.99–2.06 Å. In the second Nb5+ site, Nb5+ is bonded to six O2- atoms to form NbO6 octahedra that share corners with two equivalent NbO6 octahedra, corners with three TiO6 octahedra, and edges with two equivalent TiO6 octahedra. The corner-sharing octahedra tilt angles range from 27–43°. There are a spread of Nb–O bond distances ranging from 1.95–2.11 Å. There are twelve inequivalent O2- sites. In the first O2- site, O2- is bonded in a 5-coordinate geometry to one Li1+, one Ba2+, two equivalent Ti4+, and one Nb5+ atom. In the second O2- site, O2- is bonded in a 3-coordinate geometry to one Ba2+ and three Ti4+ atoms. In the third O2- site, O2- is bonded in a 3-coordinate geometry to one Li1+, two equivalent Ba2+, one Ti4+, and one Nb5+ atom. In the fourth O2- site, O2- is bonded in a 3-coordinate geometry to one Ba2+ and three Ti4+ atoms. In the fifth O2- site, O2- is bonded in a 4-coordinate geometry to one Ba2+, two Ti4+, and one Nb5+ atom. In the sixth O2- site, O2- is bonded in a 3-coordinate geometry to one Li1+, two Ba2+, and two Ti4+ atoms. In the seventh O2- site, O2- is bonded in a 2-coordinate geometry to two Ba2+, one Ti4+, and one Nb5+ atom. In the eighth O2- site, O2- is bonded in a distorted bent 150 degrees geometry to two Ba2+, one Ti4+, and one Nb5+ atom. In the ninth O2- site, O2- is bonded in a 2-coordinate geometry to two Ba2+, one Ti4+, and one Nb5+ atom. In the tenth O2- site, O2- is bonded in a 2-coordinate geometry to two Ba2+ and two Nb5+ atoms. In the eleventh O2- site, O2- is bonded in a 2-coordinate geometry to two equivalent Ba2+, one Ti4+, and one Nb5+ atom. In the twelfth O2- site, O2- is bonded in a 2-coordinate geometry to two equivalent Ba2+, one Ti4+, and one Nb5+ atom.

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Materials Data on Ba3LiTi5(SbO7)3 by Materials Project

LiBa3Ti5(SbO7)3 is Orthorhombic Perovskite-derived structured and crystallizes in the orthorhombic Cmc2_1 space group. The structure is three-dimensional. Li1+ is bonded in a trigonal planar geometry to four O2- atoms. There are three shorter (1.88 Å) and one longer (2.66 Å) Li–O bond lengths. There are two inequivalent Ba2+ sites. In the first Ba2+ site, Ba2+ is bonded in a 12-coordinate geometry to twelve O2- atoms. There are a spread of Ba–O bond distances ranging from 2.79–3.23 Å. In the second Ba2+ site, Ba2+ is bonded in a 12-coordinate geometry to twelve O2- atoms. There are a spread of Ba–O bond distances ranging from 2.70–3.19 Å. There are three inequivalent Ti4+ sites. In the first Ti4+ site, Ti4+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with two equivalent SbO6 octahedra, corners with three TiO6 octahedra, an edgeedge with one TiO6 octahedra, and an edgeedge with one SbO6 octahedra. The corner-sharing octahedra tilt angles range from 26–43°. There are a spread of Ti–O bond distances ranging from 1.88–2.18 Å. In the second Ti4+ site, Ti4+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with two TiO6 octahedra, corners with three SbO6 octahedra, and edges with two TiO6 octahedra. The corner-sharing octahedra tilt angles range from 26–44°. There are a spread of Ti–O bond distances ranging from 1.90–2.18 Å. In the third Ti4+ site, Ti4+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with two equivalent TiO6 octahedra, corners with three SbO6 octahedra, and edges with two equivalent TiO6 octahedra. The corner-sharing octahedra tilt angles range from 24–42°. There are a spread of Ti–O bond distances ranging from 1.90–2.16 Å. There are two inequivalent Sb5+ sites. In the first Sb5+ site, Sb5+ is bonded to six O2- atoms to form SbO6 octahedra that share a cornercorner with one SbO6 octahedra and corners with five TiO6 octahedra. The corner-sharing octahedra tilt angles range from 38–49°. There are a spread of Sb–O bond distances ranging from 1.99–2.02 Å. In the second Sb5+ site, Sb5+ is bonded to six O2- atoms to form SbO6 octahedra that share corners with two equivalent SbO6 octahedra, corners with three TiO6 octahedra, and edges with two equivalent TiO6 octahedra. The corner-sharing octahedra tilt angles range from 24–49°. There are a spread of Sb–O bond distances ranging from 1.99–2.04 Å. There are twelve inequivalent O2- sites. In the first O2- site, O2- is bonded in a 5-coordinate geometry to one Li1+, one Ba2+, two equivalent Ti4+, and one Sb5+ atom. In the second O2- site, O2- is bonded in a 3-coordinate geometry to one Ba2+ and three Ti4+ atoms. In the third O2- site, O2- is bonded in a 3-coordinate geometry to one Li1+, two equivalent Ba2+, one Ti4+, and one Sb5+ atom. In the fourth O2- site, O2- is bonded in a 4-coordinate geometry to one Ba2+, two Ti4+, and one Sb5+ atom. In the fifth O2- site, O2- is bonded in a 3-coordinate geometry to one Ba2+ and three Ti4+ atoms. In the sixth O2- site, O2- is bonded in a 3-coordinate geometry to one Li1+, two Ba2+, and two Ti4+ atoms. In the seventh O2- site, O2- is bonded in a 2-coordinate geometry to two Ba2+, one Ti4+, and one Sb5+ atom. In the eighth O2- site, O2- is bonded in a 2-coordinate geometry to two Ba2+, one Ti4+, and one Sb5+ atom. In the ninth O2- site, O2- is bonded in a 2-coordinate geometry to two Ba2+, one Ti4+, and one Sb5+ atom. In the tenth O2- site, O2- is bonded in a 2-coordinate geometry to two Ba2+ and two Sb5+ atoms. In the eleventh O2- site, O2- is bonded in a 2-coordinate geometry to two equivalent Ba2+, one Ti4+, and one Sb5+ atom. In the twelfth O2- site, O2- is bonded in a 2-coordinate geometry to two equivalent Ba2+, one Ti4+, and one Sb5+ atom.

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Materials Data on LaSb2Au by Materials Project

LaAuSb2 crystallizes in the tetragonal P4/nmm space group. The structure is three-dimensional. La3+ is bonded in a distorted hexagonal planar geometry to six Sb3- atoms. There are a spread of La–Sb bond distances ranging from 3.24–3.27 Å. Au3+ is bonded in a distorted hexagonal planar geometry to six Sb3- atoms. There are four shorter (3.24 Å) and two longer (3.25 Å) Au–Sb bond lengths. There are two inequivalent Sb3- sites. In the first Sb3- site, Sb3- is bonded in a 6-coordinate geometry to two equivalent La3+ and four equivalent Au3+ atoms. In the second Sb3- site, Sb3- is bonded in a 6-coordinate geometry to four equivalent La3+ and two equivalent Au3+ atoms.

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Materials Data on BaPrO3 by Materials Project

BaPrO3 crystallizes in the trigonal R-3c space group. The structure is three-dimensional. Ba2+ is bonded in a distorted trigonal planar geometry to nine equivalent O2- atoms. There are three shorter (2.68 Å) and six longer (3.25 Å) Ba–O bond lengths. Pr4+ is bonded to six equivalent O2- atoms to form corner-sharing PrO6 octahedra. The corner-sharing octahedral tilt angles are 28°. All Pr–O bond lengths are 2.35 Å. O2- is bonded in a 5-coordinate geometry to three equivalent Ba2+ and two equivalent Pr4+ atoms.

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Materials Data on BaNdO3 by Materials Project

BaNdO3 crystallizes in the trigonal R-3c space group. The structure is three-dimensional. Ba is bonded in a distorted trigonal planar geometry to nine equivalent O atoms. There are three shorter (2.69 Å) and six longer (3.23 Å) Ba–O bond lengths. Nd is bonded to six equivalent O atoms to form corner-sharing NdO6 octahedra. The corner-sharing octahedral tilt angles are 27°. All Nd–O bond lengths are 2.34 Å. O is bonded in a 5-coordinate geometry to three equivalent Ba and two equivalent Nd atoms.

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Materials Data on CsAu3Se2 by Materials Project

CsAu3Se2 crystallizes in the trigonal P-3m1 space group. The structure is three-dimensional. Cs1+ is bonded in a distorted hexagonal planar geometry to six equivalent Se2- atoms. All Cs–Se bond lengths are 3.94 Å. Au1+ is bonded in a distorted linear geometry to two equivalent Se2- atoms. Both Au–Se bond lengths are 2.47 Å. Se2- is bonded to three equivalent Cs1+ and three equivalent Au1+ atoms to form a mixture of distorted edge and corner-sharing SeCs3Au3 octahedra. The corner-sharing octahedra tilt angles range from 0–70°.

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Materials Data on UInPt2 by Materials Project

UPt2In crystallizes in the orthorhombic Cmcm space group. The structure is three-dimensional. U3+ is bonded in a distorted hexagonal planar geometry to six equivalent Pt2- atoms. There are four shorter (2.86 Å) and two longer (2.89 Å) U–Pt bond lengths. Pt2- is bonded in a 8-coordinate geometry to three equivalent U3+, one Pt2-, and four equivalent In1+ atoms. The Pt–Pt bond length is 2.68 Å. There are a spread of Pt–In bond distances ranging from 2.96–3.08 Å. In1+ is bonded in a 8-coordinate geometry to eight equivalent Pt2- atoms.

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Materials Data on LaGa3Pd2 by Materials Project

LaPd2Ga3 crystallizes in the hexagonal P6/mmm space group. The structure is three-dimensional. La is bonded in a distorted hexagonal planar geometry to six equivalent Pd and twelve equivalent Ga atoms. All La–Pd bond lengths are 3.16 Å. All La–Ga bond lengths are 3.49 Å. Pd is bonded in a 9-coordinate geometry to three equivalent La and six equivalent Ga atoms. All Pd–Ga bond lengths are 2.68 Å. Ga is bonded to four equivalent La and four equivalent Pd atoms to form a mixture of distorted edge, face, and corner-sharing GaLa4Pd4 cuboctahedra.

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Materials Data on BaNaSc(BO3)2 by Materials Project

ScBaNa(BO3)2 crystallizes in the trigonal R-3 space group. The structure is three-dimensional. Na1+ is bonded in a distorted hexagonal planar geometry to six equivalent O2- atoms. There are three shorter (2.48 Å) and three longer (2.86 Å) Na–O bond lengths. Ba2+ is bonded in a 9-coordinate geometry to nine O2- atoms. There are six shorter (2.81 Å) and three longer (2.85 Å) Ba–O bond lengths. There are two inequivalent Sc3+ sites. In the first Sc3+ site, Sc3+ is bonded in an octahedral geometry to six equivalent O2- atoms. All Sc–O bond lengths are 2.13 Å. In the second Sc3+ site, Sc3+ is bonded in an octahedral geometry to six equivalent O2- atoms. All Sc–O bond lengths are 2.11 Å. There are two inequivalent B3+ sites. In the first B3+ site, B3+ is bonded in a trigonal planar geometry to three equivalent O2- atoms. All B–O bond lengths are 1.39 Å. In the second B3+ site, B3+ is bonded in a trigonal planar geometry to three equivalent O2- atoms. All B–O bond lengths are 1.38 Å. There are two inequivalent O2- sites. In the first O2- site, O2- is bonded in a 2-coordinate geometry to two equivalent Ba2+, one Sc3+, and one B3+ atom. In the second O2- site, O2- is bonded in a 1-coordinate geometry to two equivalent Na1+, one Ba2+, one Sc3+, and one B3+ atom.

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Materials Data on BaNaY(BO3)2 by Materials Project

BaNaY(BO3)2 crystallizes in the trigonal R-3 space group. The structure is three-dimensional. Na1+ is bonded in a distorted hexagonal planar geometry to six equivalent O2- atoms. There are three shorter (2.68 Å) and three longer (2.83 Å) Na–O bond lengths. Ba2+ is bonded in a 9-coordinate geometry to nine O2- atoms. There are three shorter (2.84 Å) and six longer (2.87 Å) Ba–O bond lengths. There are two inequivalent Y3+ sites. In the first Y3+ site, Y3+ is bonded in an octahedral geometry to six equivalent O2- atoms. All Y–O bond lengths are 2.27 Å. In the second Y3+ site, Y3+ is bonded in an octahedral geometry to six equivalent O2- atoms. All Y–O bond lengths are 2.26 Å. There are two inequivalent B3+ sites. In the first B3+ site, B3+ is bonded in a trigonal planar geometry to three equivalent O2- atoms. All B–O bond lengths are 1.39 Å. In the second B3+ site, B3+ is bonded in a trigonal planar geometry to three equivalent O2- atoms. All B–O bond lengths are 1.39 Å. There are two inequivalent O2- sites. In the first O2- site, O2- is bonded in a 1-coordinate geometry to two equivalent Ba2+, one Y3+, and one B3+ atom. In the second O2- site, O2- is bonded in a 1-coordinate geometry to two equivalent Na1+, one Ba2+, one Y3+, and one B3+ atom.

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Materials Data on CuO by Materials Project

CuO crystallizes in the monoclinic C2/c space group. The structure is three-dimensional. Cu2+ is bonded in a square co-planar geometry to four equivalent O2- atoms. There is two shorter (1.94 Å) and two longer (1.96 Å) Cu–O bond length. O2- is bonded to four equivalent Cu2+ atoms to form a mixture of edge and corner-sharing OCu4 tetrahedra.

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Materials Data on CuO by Materials Project

CuO crystallizes in the monoclinic C2/c space group. The structure is three-dimensional. Cu2+ is bonded in a square co-planar geometry to four equivalent O2- atoms. There is two shorter (1.95 Å) and two longer (1.96 Å) Cu–O bond length. O2- is bonded to four equivalent Cu2+ atoms to form a mixture of corner and edge-sharing OCu4 tetrahedra.

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