OPEN ACCESS
The present study shows new results from the recently proposed method for numerical simulations of the spray break-up of cavitating liquid jets. A three-component system consisting of liquid, vapor and gas is applied for the volume-of-fluid simulation of the liquid disintegration in order to track the liquid–gas interface. To keep the numerical effort moderate, the liquid–vapor interface is not resolved by the computational grid, there mass and momentum transfer are described within the Eulerian-Eulerian framework. The numerical method is applied on a simplified injector-like geometry from the literature operated with gasoline at low pressure difference. For quantification of the detached spray ligaments, a new evaluation algorithm has been developed and implemented into the applied CFD code. It scans the liquid volume fraction field for separated ligaments, and determines their position, size and velocity. Additionally the ligament extensions along the principal axes of inertia are determined in order to evaluate the non-sphericity of each ligament after break-up. The presented simulation technique allows detailed numerical investigations of the spray formation process on the micro-scale by taking into account nozzle cavitation, turbulence and aerodynamic forces.
cavitation, droplet size distribution, liquid disintegration, non-spherical droplets, spray break-up, surface-tracking, volume-of-fluid
[1] Menard, T., Tanguy, S. & Berlemont A., Coupling level set/VOF/ghost fluid methods: validation and application to 3D simulation of the primary break-up of a liquid jet. International Journal of Multiphase Flow, 33, pp. 510–524, 2007. https://doi.org/10.1016/j.ijmultiphaseflow.2006.11.001
[2] Shinjo, J. & Umemura, A., Simulation of liquid jet primary breakup: Dynamics of ligament and droplet formation. International Journal of Multiphase Flow, 36(7), pp. 513–532, 2010. https://doi.org/10.1016/j.ijmultiphaseflow.2010.03.008
[3] Hermann, M., Detailed numerical simulations of the primary atomization of a turbulent liquid jet in crossflow. Journal of Engineering for Gas Turbines and Power, 132(6), 2010. https://doi.org/10.1115/1.4000148
[4] Ishimoto, J., Sato, F. & Sato, G., Computational prediction of the effect of microcavitation on an atomization mechanism in a gasoline injector nozzle. Journal of Engineering for Gas Turbines and Power, 132(6), 2010. https://doi.org/10.1115/1.4000264
[5] Schmidt, D.P., Ruland, C.J. & Corradini, M.L., A fully compressible model of small, high speed cavitating nozzle flows. Atomization and Sprays, 9, pp. 255–276, 1999. https://doi.org/10.1615/atomizspr.v9.i3.20
[6] Lu, N.X., Demoulin, F.X., Reveillon, J. & Chesnel, J., Large Eddy simulation of a cavitating multiphase flow for liquid injection. Proceeding of : ILASS, Bremen, Germany, 2014.
[7] Sauer, J., Winkler, G. & Schnerr, G. H., Cavitation and condensation common aspects of physical modeling and numerical approach. Chemical Engineering & Technology, 23, pp. 663–666, 2000.
[8] Cailloux, M., Helie, J., Reveillon, J. & Demoulin, F.X., Large Eddy simulation of a cavitating multiphase flow with OpenFoam. Journal of Physics: Conference Series, 656(1), 2015. https://doi.org/10.1088/1742-6596/656/1/012081
[9] Yu, H., Goldsworthy, L, Brandner, P.A. & Garanijy, V., Development of a compressible multiphase cavitation approach for diesel spray modelling. Applied Mathematical Modelling, 45, pp. 705–727, 2017. https://doi.org/10.1016/j.apm.2017.01.035
[10] Edelbauer, W., Numerical simulation of cavitating injector flow and liquid spray break-up by combination of Eulerian-Eulerian and volume-of-fluid methods. Computers and Fluids, 144, pp. 19–33, 2017. https://doi.org/10.1016/j.compfluid.2016.11.019
[11] Sou, A., Bicer, B. & Tomiyama, A., Numerical simulation of incipient cavitation flow in a nozzle of fuel injector. Computers & Fluids, 103, pp. 42–48, 2014. https://doi.org/10.1016/j.compfluid.2014.07.011
[12] Biçer, B. & Sou, A., Application of the improved cavitation model to turbulent cavitating flow in fuel injector nozzle. Applied Mathematical Modelling, 40(7–8), pp. 4712–4726, 2015. https://doi.org/10.1016/j.apm.2015.11.049
[13] AVL FIRETM, user manual of version v2017, 2017.
[14] Alajbegovic, A., Greif, D., Basara, B. & Iben, U., Cavitation calculation with the twofluid model. Proceeding of 3rd European-Japanese Two-Phase Flow Group Meeting, Italy, 2003.
[15] Greif, D. & Srinivasan, V., Numerical prediction of erosive cavitating flows in injection equipment, SAE 2011-24-0004, 2011.
[16] Greif, D., Sampl, P. & Edelbauer, W., Cavitating injector flow simulations considering longitudinal and lateral needle displacement. International Journal of Automotive Engineering, 5, pp. 85–90, 2014. https://doi.org/10.20485/jsaeijae.5.2_85
[17] Kobayashi, H., The subgrid-scale models based on coherent structures for rotating homogeneous turbulence and turbulent channel flow. Physics of Fluids, 17, 2005. https://doi.org/10.1063/1.1874212
[18] Kobayashi, H., Hama, F. & Wu, X., Application of a local SGS model based on coherent structures to complex geometries. International Journal of Heat and Fluid Flow, 29, pp. 640–653, 2008. https://doi.org/10.1016/j.ijheatfluidflow.2008.02.008
[19] Ubbink, O. & Issa, R.I., A method for capturing sharp fluid interfaces on arbitrary meshes. Journal of Computational Physics, 153, pp. 26–50, 1999. https://doi.org/10.1006/jcph.1999.6276
[20] Walz, K., Die Betonstraße, 11, pp. 27–36, 1936 (German).
[21] Gaskell, P.H. & Lau, A.K.C., Curvature-compensated convective Transport: SMART, a new boundedness-preserving transport algorithm. International Journal for Numerical Methods in Fluids, 8, pp. 617–641, 1988. https://doi.org/10.1002/fld.1650080602
[22] Patankar, S.V. & Spalding, D.B., A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows. International Journal of Heat and Mass Transfer, 15(10), pp. 1510–1520, 1972.
[23] Ferziger, J.H. & Peric M., Computational methods for fluid dynamics, Springer, New York, 1996.