FK^{3} is an in-house flow and flame analysis code, whose development was initiated at the Komori and Kurose laboratory and has been continued at the Kurose laboratory at Kyoto University. The FK^{3} has been originally developed based on a pressure-based semi-implicit solver for compressible flows and recently expanded to a density-based solver. Some achievements obtained using the FK^{3} are as follows.

K. Kinuta, R. Kai, R. Kurose, “FGM modeling considering preferential diffusion, flame stretch and non-adiabatic effects for hydrogen-air premixed flame wall flashback”, Combustion and Flame, 269, 113718 (2024). | |

K. Kinuta, R. Kai, R. Kurose, “Effects of considering preferential diffusion and flame stretch in FGM method for numerical simulations of hydrogen/air flames”, Journal of Thermal Science and Technology, 19, 24-00087 (2024). | |

S. Suzuki, K. Iwata, R. kai, R. Kurose, “A DNS study of detonation in H2/O2 mixture with variable-intensity turbulences, Proceedings of the Combustion Institute”, 40, 105337 (2024). | |

M. Kawai, J. Nagao, A. L. Pillai, R. Kurose, “Effect of temporal increase in equivalence ratio on combustion instability of a lean-premixed low-swirl hydrogen jet flame: An LES study”, Physics of Fluids, 36, 044119 (2024). | |

R. Kai, H. Watanabe, R. Kurose, “A study on precise estimation of laminar burning velocity of lean hydrogen-air premixed flame (Effect of species diffusion models)”, Mechanical Engineering Journal, 11, 23-00400 (2024). | |

R. Kai, S. Ayukawa, K. Kinuta, R. Kurose, “Effects of preferential diffusion and flame stretch on FGM method for numerical simulations of ammonia/air premixed combustion”, Applications in Energy and Combustion Science, 17, 100253 (2024). | |

S. Wada, R. Kai, R. Kurose, “A semi-implicit pressure-based solver considering real gas effect”, Journal of Computational Physics, 501, 112782 (2024). | |

J. Nagao, A. L. Pillai, T. Shoji, S. Tachibana, T. Yokomori, R. Kurose, “Large-eddy simulation of a lean-premixed hydrogen flame in a low-swirl combustor under combustion instability”, Physics of Fluids, 35, 105124 (2023). | |

M. Saito, J. Xing, J. Nagao, R. Kurose,"Data-driven simulation of ammonia combustion using Neural Ordinary Differential Equations (NODE)", Applications in Energy and Combustion Science,16, 100196 (2023). | |

U. Ahmed, S. P. Malkeson, A. L. Pillai, N. Chakraborty, R. Kurose, “Flame self interaction during turbulent boundary layer flashback of hydrogen-rich premixed combustion”, Physical Review Fluids, 8, 023202 (2023). | |

K. Iwata, S. Suzuki, R. Kai, R. Kurose, Direct numerical simulation of detonation-turbulence interaction in hydrogen/oxygen/argon mixtures with a detailed chemistry, Physics of Fluids, 35, 046107 (2023). | |

J. Nagao, A. L. Pillai, T. Shoji, S. Tachibana, T. Yokomori, R. Kurose, “Investigation of wall effects on combustion noise from a low-swirl flame using hybrid LES/APE-RF approach”, Physics of Fluids, 35, 014109 (2023). | |

R. Kai, T. Tokuoka, J. Nagao, A. L. Pillai, R. Kurose, “LES flamelet modeling of hydrogen combustion considering preferential diffusion effect”, International Journal of Hydrogen Energy, 48, 11086-11101 (2023). | |

P. Yu, R. Kurose, H. Watanabe, “Investigation of the derivation and consistency of the quasi-two-dimensional flamelet models for non-premixed flames”, Physics of Fluids, 35, 0151116 (2023). | |

R. Kai, A. L. Pillai, U. Ahmed, N. Chakraborty, R. Kurose, “Numerical investigation of premixed V-shaped flame-wall interaction in a turbulent channel flow at Reτ= 395”, Combustion Science and Technology, accepted. | |

S. Wada, R. Kai, R. Kurose, “LES study on the breakup mechanism of LOX core in LOX/GH2 supercritical combustion”, Proceedings of the Combustion Institute, 39, 2737-2745 (2023). | |

H. Shehab, H. Watanabe, Y. Minamoto, R. Kurose, T. Kitagawa, "rphology and structure of spherically propagating premixed turbulent hydrogen-air flames", Combustion and Flame, 238, 111888 (2022). | |

T. Ikeda, Y. Tsuruda, H. Watanabe, R. Kurose, T. Kitagawa, "Numerical study on soot formation in spherically propagating, iso-octane, rich, cellular flames", Fuel, 305, 121520 (2021). | |

K. Yunoki, R. Kai, S. Inoue, R. Kurose, "Numerical simulation of CO formation/reduction on flame propagation in the vicinity of cooled wall", Energy, 236, 121352 (2021). | |

R. Kai, R. Masuda, T. Ikedo, R. Kurose, "Conjugate heat transfer analysis of methane/air premixed flame - wall interaction: A study on effect of wall material", Applied Thermal Engineering, 181, 115947 (2020). | |

R. Kai, A. Takahashi, R. Kurose, "Numerical investigation of premixed flame-wall interaction: Effectiveness of insulation wall on heat loss reduction", Journal of Thermal Science and Technology, 15, Paper No.20-00390 (2020). | |

K. Yunoki, R. Kai, S. Inoue, R. Kurose, "Numerical simulation of CO concentration on flame propagation in the vicinity of the wall -Validity of non-adiabatic FGM approach-", International Journal of Gas Turbine, Propulsion and Power Systems, 20(13), 8-15 (2020). | |

U. Ahmed, A. L. Pillai, N. Chakraborty, R. Kurose, "Surface density function evolution and the influence of strain rates during turbulent boundary layer flashback of hydrogen-rich premixed combustion", Physics of Fluids, 32, 055112 (2020). | |

H. Shehab, H. Watanabe, R. Kurose, T. Kitagawa, "Numerical study on the effects of turbulence scale on spherically propagating hydrogen flames within multiple flame radii", International Journal of Automotive Engineering, 10, 292-298 (2019). | |

U. Ahmed, A. L. Pillai, N. Chakraborty, R. Kurose, "Statistical behavior of turbulent kinetic energy transport in boundary layer flashback of hydrogen-rich premixed combustion", Physical Review Fluids, 4, 103201 (2019). | |

P. Yu, H. Watanabe, W. Zhang, R. Kurose, T. Kitagawa, "Flamelet model for a three-feed non-premixed combustion system with diluent stream: Analysis and validation of quasi-two-dimensional flamelet (Q2DF) models", Energy & Fuels, 33, 4640-4650 (2019). | |

Y. Hu, R. Kurose, "Large-eddy simulation of turbulent autoigniting hydrogen lifted jet flame with a multi-regime flamelet approach", International Journal of Hydrogen Energy, 44, 6313-6324 (2019). | |

R. N. Roy, M. Muto, R. Kurose, "Direct numerical simulation of ignition of syngas (H2/CO) mixtures with temperature and composition stratifications relevant to HCCI conditions", International Journal of Hydrogen Energy, 42, 26152-26161 (2017). | |

T. Kitano, H. Iida, R. Kurose, "Effect of chemical reactions of H2/O2 combustion gas on heat transfer on a wall in a turbulent channel flow", Journal of Heat Transfer, 139, 044501 (2017). | |

T. Kitano, T. Tsuji, R. Kurose, S. Komori, "Effect of pressure oscillations on flashback characteristics in a turbulent channel flow", Energy & Fuels, 29, 6815-6822 (2015). |

K. Kato, H. Hashiba, J. Nagao, H. Gotoda, Y. Nabae, R. Kurose, “Dynamic behavior and driving region of spray combustion instability in a backward facing step combustor”, Physical Review E, 110, 0242024 (2024). | |

Y. Hu, R. Kai, J. Wen, T. Murakami, Y. Jiang, R. Kurose, “LES study of stabilization mechanism in lifted ethanol spray flames”, Proceedings of the Combustion Institute, 39, 2609-2620 (2023). | |

A. L. Pillai, T. Murata, R. Kai, R. Masuda, T. Ikedo, R. Kurose, "Numerical analysis of heat transfer characteristics of spray flames impinging on a wall under CI engine-like conditions", Combustion and Flame, 239, 111615 (2022). | |

J. Wen, Y. Hu, R. Kurose, "Numerical simulation of kerosene jet in crossflow atomization and evaporation under the elevated pressure and oscillating air-flow condition", Atomization and Sprays, 31, 73-87 (2021). | |

S.P. Malkeson, U. Ahmed, A.L. Pillai, N. Chakraborty, R. Kurose, “Flame self-interactions in an open turbulent jet spray flame", Physics of Fluids, 33, 035114 (2021). | |

K. Konishi, R. Kai, R. Kurose, “Unsteady flamelet modelling for N2H4/N2O4 flame accompanied by hypergolic ignition and thermal decomposition", Applications in Energy and Combustion Science, 5, 100022 (2021). | |

S. P. Malkeson, U. Ahmed, C. T. d'Auzay, A. L. Pillai, N. Chakraborty, R. Kurose, “Displacement speed statistics in an open turbulent jet spray flame", Fuel, 286, 119242 (2021). | |

S. P. Malkeson, U. Ahmed, A. L. Pillai, N. Chakraborty, R. Kurose, "Evolution of surface density function in an open turbulent jet spray flame", Flow, Turbulence and Combustion, 106, 207-229 (2021). | |

J. Nagao, A. L. Pillai, R. Kurose, " Investigation of lean spray combustion instability in a back step combustor using LES", Journal of Thermal Science and Technology, 15, Paper No.20-00330 (2020). | |

A. L. Pillai, J. Nagao, R. Awane, R. Kurose, “Influences of liquid fuel atomization and flow rate fluctuations on spray combustion instabilities", Combustion and Flame, 220, 337-356 (2020). | |

Y. Hu, R. Kai, R. Kurose, E. Gutheil, H. Olguin, “Large eddy simulation of a partially pre-vaporized ethanol reacting spray using the multiphase DTF/flamelet model", International Journal of Multiphase Flow, 125, 103216 (2020). | |

J. Wen, Y. Hu, A. Nakanishi, R. Kurose, “Atomization and evaporation process of liquid fuel jets in crossflows: A numerical study using Eulerian/Lagrangian method", International Journal of Multiphase Flow, 129, 103331 (2020). | |

C.T. d'Auzay, U. Ahmed, A. L. Pillai, N. Chakraborty, R. Kurose, "Statistics of progress variable and mixture fraction gradients in an open turbulent jet spray flame", Fuel, 247, 198-207 (2019). | |

A.L. Pillai, R. Kurose, "Combustion noise analysis of a turbulent spray flame using a hybrid DNS/APE-RF approach", Combustion and Flame, 200, 168-191 (2019). | |

Y. Hu, R. Kurose, "Partially premixed flamelet in LES of acetone spray flames ", Proceedings of The Combustion Institute, 37, 3327-3334 (2019). | |

Y. Haruki, A. L. Pillai, T. Kitano, R. Kurose, "Numerical investigation of flame propagation in fuel droplet arrays", Atomization and Sprays, 28, 357-388 (2018). | |

A. L. Pillai, R. Kurose, "Numerical investigation of combustion noise in an open turbulent spray flame", Applied Acoustics, 133, 16-27 (2018). | |

Y. Hu, R. Kurose, "Nonpremixed and premixed flamelets LES of partially premixed spray flames using a two-phase transport equation of progress variable", Combustion and Flame, 188, 227-242 (2018). | |

T. Kitano, K. Kaneko, R. Kurose, S. Komori, "Large-eddy simulations of gas- and liquid-fueled combustion instabilities in back-step flows", Combustion and Flame, 170, 63-78 (2016). | |

T. Kitano, J. Nishio, R. Kurose, S. Komori, "Evaporation and combustion of multicomponent fuel droplets", Fuel, 136, 219-225 (2014). | |

T. Kitano, J. Nishio, R. Kurose, S. Komori, "Effects of ambient pressure, gas temperature and combustion reaction on droplet evaporation", Combustion and Flame, 161, 551-564 (2014). | |

T. Kitano, R. Kurose, S. Komori, "Effects of internal pressure and inlet velocity disturbances of air and fuel droplets on spray combustion field", Journal of Thermal Science and Technology, 8, 269-280 (2013). |

U. Ahmed, C.T. d'Auzay, M. Muto, N. Chakraborty, R. Kurose, "Statistics of reaction progress variable and mixture fraction gradients of a pulverised coal jet flame using Direct Numerical Simulation data", Proceedings of The Combustion Institute, 37, 2821-2830 (2019). | |

M. Muto, K. Yuasa, R. Kurose, "Numerical simulation of soot formation in pulverized coal combustion with detailed chemical reaction mechanism", Advanced Powder Technology, 29, 1119-1127 (2018). | |

M. Muto, K. Yuasa, R. Kurose, "Numerical simulation of ignition in pulverized coal combustion with detailed chemical reaction mechanism", Fuel, 190, 136-144 (2017). | |

M. Muto, K. Tanno, R. Kurose, "A DNS study on effect of coal particle swelling due to devolatilization on pulverized coal jet flame", Fuel, 184, 749-752 (2016). | |

T. Hara, M. Muto, T. Kitano, R. Kurose, S. Komori, "Direct numerical simulation of a pulverized coal jet flame employing a global volatile matter reaction scheme based on detailed reaction mechanism", Combustion and Flame, 162, 4391-4407 (2015). |

K. Kitada, R. Kurose, “High-fidelity numerical simulations in Eulerian/Lagrangian framework for liquid fuel jets in crossflow with atomization and evaporation: Effect of aerodynamic Weber number”, International Journal of Multiphase Flow, 174, 104762 (2024). | |

H Muramatsu, AL Pillai, K Kitada, R Kurose, "Numerical simulation of bi-component fuel droplet evaporation using Level Set method", Fuel 318, 123331 (2022). | |

Z. Yuan, M. Matsumoto, R. Kurose, "Numerical study of droplet impingement on surfaces with hierarchical structures", International Journal of Multiphase Flow 147, 103908 (2022). | |

Z. Yuan, M. Matsumoto, R. Kurose, "Stability of the non-wetting state in a droplet impinging on surfaces with multiple holes", Physics of Fluids 33, 123315 (2022). | |

Z. Yuan, M. Mtaumoto, R. Kurose, "Directional rebounding of a droplet impinging hydrophobic surfaces with roughness gradients", International Journal of Multiphase Flow, 138, 103611 (2021). | |

Z. Yuan, M. Matsumoto, R. Kurose, "Directional migration of an impinging droplet on a surface with wettability difference", Physical Review Fluids, 5, 113605 (2020). | |

Z. Yuan, J. Wen, M. Matsumoto, R. Kurose, "Anti-wetting ability of the robust hydrophobic surface decorated by submillimeter grooves", International Journal of Multiphase Flow, 131, 103404 (2020). |

M. Saito, J. Nagao, T. Yamada, A. L. Pillai, R. Kurose, "Large-eddy simulation of blade-turbulence interaction in a cyclorotor system", Aerospace Science and Technology, 146, 108921 (2024). |