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Wet dam-break simulation using the SPS-LES turbulent contribution on the WCMPS method to evaluate green water events

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The paper analyzes the contribution of the sub-particle-scale large-eddy simulation (SPS-LES) turbulent model on the dynamic behavior of the weakly compressible moving-particle semi-implicit (WCMPS) method. To search a robust WCMPS method configuration, the next models are tested: two pressure gradient models, two Laplacian models and the constrained stabilization technique through the control adjustment of the particle velocity by Xu and Jin (Comput Fluids 137:1–14, 2016. https://doi.org/10.1016/j.compfluid.2016.07.014). Then, for these combinations the influence of the SPS-LES turbulent dynamic contributions on the WCMPS method is analyzed. The WCMPS resultant configurations are applied to represent the physics of two different isolated green water events, produced by incoming bores that were generated with the two-dimensional wet dam-break approach. Numerical results captured well the evolution of the green water events, indicating that the WCMPS method can be suitable tool to represent the complex physics of these phenomena, including the breaking features of flow. Moreover, it is shown that even though turbulence is a three-dimensional phenomenon, turbulent contribution can be observable on the velocity field in two dimensions, having a considerable contribution on the adequate representation of green water amounts.

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Acknowledgements

The author Sanchez-Mondragon J. would like to thank Dirección de Cátedras CONACyT for the support given during the creation of this manuscript. The author Hernández-Fontes J.V. thanks the support provided by DGAPA-UNAM postdoctoral fellowship.

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Authors and Affiliations

  1. CONACYT Research Fellow-Instituto Mexicano del Petróleo, Eje Central Lázaro Cárdenas 152, Gustavo A. Madero, 07730, Mexico City, Mexico

    J. Sanchez-Mondragon

  2. Instituto de Ingeniería, Universidad Nacional Autónoma de México Edificio 17, Ciudad Universitaria, 04510, Mexico City, Mexico

    J. V. Hernández-Fontes

  3. Lloyds Register, Lago Zurich 219, Floor 12. Col. Granada, 11529, Mexico City, Mexico

    A. O. Vázquez-Hernández

  4. LABOCEANO (Ocean Technology Laboratory), Ocean Engineering Program, Federal University of Rio de Janeiro, Parque Tecnológico do Rio, Rio de Janeiro, 21941-907, Brazil

    P. T. T. Esperança

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Appendix: Reduced parameter on constrained stabilization technique

Appendix: Reduced parameter on constrained stabilization technique

To adjust the constrained stabilization technique, as shown in Eq. (18), by the reduced parameter values on the CWCMPS method by Xu and Jin [48], we tested the following constant values: \( rpv = 0.0005 \), \( 0.0010 \), \( 0.0020 \) and \( 0.0050 \), on the parameter \( \Delta r_{i} = rpv l_{i} \). This test is developed on the same conditions of the wet dam-break of the case A (Table 2 and Fig. 2). This test is independent on the two pressure gradient models probed, because the global behavior is similar to every case. Then, from the pressure gradient models by Lee et al. [25] [Eq. (9)] and Sanchez-Mondragon [34] [Eq. (10)], in this appendix the results from the Lee et al. [25] pressure gradient model [Eq. (9)] are shown, because they had the best performance to stabilize the velocity vector behavior. Moreover, because results are also independent from Laplacian model, we decided to present the results from the Koshizuka et al. [23] Laplacian model, as shown in Eq. (12).

Thus, pressure distributions are compared with experimental snapshots and the WCMPS case configured without constrained stabilization technique [Eq. (18)], as shown in figures for \( t1 \), \( t2 \) and \( t3 \) snapshots from Table 3. Results are shown in Fig. 23. From this figure, at \( t1 \) snapshots, it is shown that the free-surface particles are more stable when the \( rpv \) parameter increases, and then, at \( rpv = 0.0020 \) and \( rpv = 0.0050 \), there are less unstable particles. Also, at \( t2 \) snapshots, when green water collides against the wall step, the height of water jet tends to decrease as the \( rpv \) parameter increases. This shows the oversuppressed forces by high \( rpv \) values, as \( rpv = 0.0050 \). Moreover, from \( t3 \) time figures, the water jet from green water event decreases when the \( rpv \) parameter increases; then, for the \( rpv = 0.0020 \) value, water column is highly suppressed. Furthermore, for time figures at \( t3 \) snapshots, results from parameter values \( rpv = 0.0005 \) and \( rpv = 0.0010 \) present similar behavior compared to experimental snapshots and the WCMPS case configured without the constrained stabilization technique [Eq. (18)]. From this analysis, and by considering the major contribution of the \( rpv \) parameter without affecting physical behavior, we decided to use the value of \( rpv = 0.0010 \) for all numerical calculations.

Fig. 23
figure 23

Comparison of experimental results with the numerical pressure field distribution at the green water development for case A, as shown in Table 2. Numerical calculations configured with the Lee et al. [25] pressure gradient model [Eq. (9)], by the standard WCMPS case and the CWCMPS case by Xu and Jin [48] using the reduced parameter values \( rpv = 0.0005 \), \( rpv = 0.0010 \), \( rpv = 0.0020 \) and \( rpv = 0.0050 \) on the CWCMPS1 to the CWCMPS4 cases, respectively

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Sanchez-Mondragon, J., Hernández-Fontes, J.V., Vázquez-Hernández, A.O. et al. Wet dam-break simulation using the SPS-LES turbulent contribution on the WCMPS method to evaluate green water events. Comp. Part. Mech. 7, 705–724 (2020). https://doi.org/10.1007/s40571-019-00302-8

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