Development of a suitable numerical solution algorithm for the two-phase Euler-Lagrange approach with four way coupling in spray simulation

Authors

1 Energy Conversion Department .Mechanical Engineering Faculty. Tarbiat Modares University

2 Energy Conversion Department. Mechanical Engineering Faculty. Tarbiat Modares University

Abstract

The most common method of simulating liquid spray in a gaseous environment is the Eulerian Lagrangian approach where the gas phase is solved by the Euler method and the liquid phase by the Lagrange method. In the dense regime, the effect of the liquid phase on the gas phase and also the effect of the droplets on each other are of great importance. Due to the strong coupling between the gas phase and liquid phase, numerical solution of these equations is one of the main challenges of this approach. In this study, two SIMPLE based algorithms for solving these equations are presented. To do this task, a Lagrangian-Eulerian computer code was developed for the two-phase flow equations. To evaluate the proposed approaches, the diesel fuel spray was solved and by comparing results, the appropriate algorithm was selected. The results showed solving the liquid phase equations at the beginning of the SIMPLE iteration loop and then making two corrections in the appropriate position inside the algorithm, provides a suitable method for solving governing equations of the spray with the assumption of four-way coupling in the Eulerian-Lagrangian approach.

Keywords

Main Subjects

References

  • Zhou, Q., Lucchini, T., D’Errico, G., Novella, R.,  García-Oliver, J. M., & Lu, X. (2021). CFD analysis of combustion and emission characteristics of primary reference fuels: from transient Diesel spray to heavy-duty engine. Fuel, 301, 120994.
  • Benavides-Morán, A., Cubillos, A., & Gómez, A. (2021). Spray drying experiments and CFD simulation of guava juice formulation. Dry. Technol, 39(4), 450-465..
  • Ali, A. M., Dena, A. S. A., Yacoub, M. H., & El-Sherbiny, I. M. (2022). Drag-minimizing spore/pollen-mimicking microparticles for enhanced pulmonary drug delivery: CFD and experimental studies. J. Drug. Deliv. Sci. Technol, 67, 102960.
  • Farivar, F., Zhang, H., Tian, Z. F., & Gupte, A. (2020). CFD-DEM-DDM model for spray coating process in a Wurster coater. J. Pharm. Sci., 109(12), 3678-3689.
  • Desjardins, O., Fox, R. O., & Villedieu, P. (2008). A quadrature-based moment method for dilute fluid-particle flows. J. Comput. Phys, 227(4), 2514-2539.
  • Ejtehadi, O., Rahimi, A., Karchani, A., & Myong, R. S. (2018). Complex wave patterns in dilute gas–particle flows based on a novel discontinuous Galerkin scheme. Int. J. Multiph. Flow, 104, 125-151.
  • Ferry, J., & Balachandar, S. (2001). A fast Eulerian method for disperse two-phase flow. Int. J. Multiph. Flow, 27(7), 1199-1226.
  • Williams, F. A. (1958). Spray combustion and atomization. Phys. Fluids, 1(6), 541-545.
  • Koch, D. L. (1990). Kinetic theory for a monodisperse gas–solid suspension. Phys. Fluids, 2(10), 1711-1723.
  • Zhang, D. Z., & Prosperetti, A. (1994). Ensemble phase‐averaged equations for bubbly flows. Phys. Fluids, 6(9), 2956-2970.
  • O 'Rourke , P. J. (1985). The KIVA computer program for multidimensional chemically reactive fluid flows with fuel sprays. In Numerical Simulation of Combustion Phenomena (pp. 74-89). Springer, Berlin, Heidelberg.
  • Amsden, A. A. (1989). A computer program for chemically reactive flows with sprays. Report of Los Alamos National Laboratory.
  • Torres, D. J., & Trujillo, M. F. (2006). KIVA-4: An unstructured ALE code for compressible gas flow with sprays. J. Comput. Phys, 219(2), 943-975.
  • Duan, X., Xu, Z., Sun, X., Deng, B., & Liu, J. (2021). Effects of injection timing and EGR on combustion and emissions characteristics of the diesel engine fuelled with acetone–butanol–ethanol/diesel blend fuels. Energy, 231, 121069.
  • Ghayoumi, M. (2022). An Investigation of Applied Techniques to Improve Grid Generation in ICEs Simulations by KIVA. Fluid. Mech. Aerodyn. J, 10(2).
  • Liu, J., Guo, Q., Guo, J., & Wang, F. (2021). Optimization of a diesel/natural gas dual fuel engine under different diesel substitution ratios. Fuel, 305, 121522.
  • Lungu, J., Siwale, L., & Luwaya, E. (2018). Numerical Accuracy of the Kiva4 Code under Different Ignition Timing on the Combustion Characteristics of Gasoline in a Spark Ignition Engine. J. Power. Energy, 6(11), 87.
  • Elghobashi, S. (1994). On predicting particle-laden turbulent flows. Appl.   Res, 52(4), 309-329.
  • Capecelatro, J., & Desjardins, O. (2013). An Euler–Lagrange strategy for simulating particle-laden flows. J. Comput. Phys, 238, 1-31.
  • Jacobs, G. B., & Don, W. S. (2009). A high-order WENO-Z finite difference based particle-source-in-cell method for computation of particle-laden flows with shocks. J. Comput. Phys, 228(5), 1365-1379.
  • Zhu, H. P., Zhou, Z. Y., Yang, R. Y., & Yu, A. B. (2007). Discrete particle simulation of particulate systems: theoretical developments. Chem. Eng. Sci, 62(13), 3378-3396.
  • Amsden, A. A., Butler, T. D., O'rourke, P. J., & Ramshaw, J. D. (1985). KIVA—a comprehensive model for 2-D and 3-D engine simulations. SAE trans, 1-15.
  • Watkins, A. P. (1989). Three-dimensional modelling of gas flow and sprays in diesel engines. Computer simulation of fluid flow, heat and mass transfer and combustion in reciprocating engines, (ed. N. C. Markatos). Washington, DC: Hemisphere Publishing Corporation. 193-237.
  • Watkins, A. P., Khaleghi, H., & Wang, D. M. (1991). Modelling spray phenomena in direct-injection diesel engines. Internal Combustion Engine Research in Universities, Polytechnics and Colleges, 131-142.
  • Khaleghi, H., Farani Sani, H., Ahmadi, M., & Mohammadzadeh, F. (2021). Effects of turbulence on the secondary breakup of droplets in diesel fuel sprays. Proceedings of the Institution of Mechanical Engineers, Part D: J. Automot. Eng, 235(2-3), 387-399.
  • Khaleghi, H., Ahmadi, M., & Farani Sani, H. (2019). Effects of two-way turbulence interaction on the evaporating fuel sprays. Appl. Fluid Mech., 12(5), 1407-1415.
  • Khaleghi, H., Yazdanparast, S., Keshtkar, M., & Firouznia, Z. (2018). DEVELOPMENT OF A SPREAD SUBMODEL FOR SPRAY/WALL IMPACTION. At. Sprays , 28(10).
  • Issa, R. I., Gosman, A. D., & Watkins, A. P. (1986). The computation of compressible and incompressible recirculating flows by a non-iterative implicit scheme. J. Comput. Phys, 62(1), 66-82.
  • Ling, Y., Zaleski, S., & Scardovelli, R. (2015). Multiscale simulation of atomization with small droplets represented by a Lagrangian point-particle model. Int. J. Multiph. Flow, 76, 122-143.
  • Zhou, L., Xia, J., Shinjo, J., Cairns, A., Cruff, L., & Blaxill, H. (2015). Towards high-fidelity multi-scale simulation of spray atomization. Energy. Procedia, 66, 309-312.
  • Ström, H., Sasic, S., Holm-Christensen, O., & Shah, L. J. (2016). Atomizing industrial gas-liquid flows–development of an efficient hybrid vof-lpt numerical framework. Int. J. Heat. Fluid. Flow, 62, 104-113
  • Hsiang, L. P., & Faeth, G. M. (1992). Near-limit drop deformation and secondary breakup. Int. J. Multiph. Flow, 18(5), 635-652.
  • Pilch, M., & Erdman, C. A. (1987). Use of breakup time data and velocity history data to predict the maximum size of stable fragments for acceleration-induced breakup of a liquid drop.  Int. J. Multiph. Flow, 13(6), 741-757.
  • Omidvar, A., & Khaleghi, H. (2012). An analytical approach for calculation of critical weber number of droplet breakup in turbulent gaseous flows. Arab. J. Sci. Eng, 37(8), 2311-2321.
  • Reitz, R. D., & Diwakar, R. (1986). Effect of drop breakup on fuel sprays. SAE trans, 218-227.
  • Munnannur, A., & Reitz, R. D. (2007). Droplet collision modeling in multi-dimensional spray computations. In SAE World Congress.
  • Launder, B.E., Spalding, D.B., (1974). Numerical computation of turbulent flows. Comput. Methods. Appl. Mech. Eng. 3 (2), 269–289

 

  • Versteeg, H. K., & Malalasekera, W. (1995). Computational fluid dynamics. The finite volume method, Harlow, England: Longman Scientific & Technical
  • Yule, A. J., Mo, S. L., Tham, S. Y., & Aval, S. M. (1985). Diesel spray structure. Proc. ICLASS-85, 1-1.
Journal of Solid and Fluid Mechanics
Volume 12, Issue 4
September and October 2022
Pages 133-144

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