×

A hybrid smoothed particle hydrodynamics coupled to a fictitious domain method for particulate flows and its application in a three-dimensional printing process. (English) Zbl 07536796

Summary: A hybrid smoothed particle hydrodynamics (SPH) coupled to a direct-forcing fictitious domain (FD) scheme is proposed for the simulation of particulate flows. The new method is effective in calculating the particle-fluid interaction forces and uses a kernel interpolation function to realize the momentum exchange between fluids and particles. A higher-order interpolation scheme is applied to preserve the consistency and accuracy of the kernel function. We first test our method by simulating the benchmark of flow past a cylinder at Reynolds number ranging from 20 to 200 and obtain the convergent results, including accurate lift and drag coefficients, Strouhal number, length of the recirculation bubble, and separation angle. Subsequently, we verify our new method for the typical particulate flows, including the motion of a neutrally-buoyant cylinder in Couette flow, the motion of a neutrally-buoyant cylinder in a planar Poiseuille flow, the sedimentation of a circular cylinder in a channel, and the motion of a neutrally-buoyant slender particle in Couette flow. A good agreement with the existing experimental data, with other numerical results, and with available theoretical solutions is obtained indicating the accuracy and the robustness of the new method. Subsequently, our SPH-FD is applied to simulate a slender fiber in a three-dimensional (3D) printing process, showing a good potential and advantages in simulating particulate flows of some industrial processes.

MSC:

76Mxx Basic methods in fluid mechanics
76Dxx Incompressible viscous fluids
65Mxx Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems

Software:

DualSPHysics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Lai, M.; Peskin, C. S., An immersed boundary method with formal second-order accuracy and reduced numerical viscosity, J. Comput. Phys., 160, 2, 705-719 (2000) · Zbl 0954.76066
[2] Kim, J.; Kim, D.; Choi, H., An immersed-boundary finite-volume method for simulations of flow in complex geometries, J. Comput. Phys., 171, 1, 132-150 (2001) · Zbl 1057.76039
[3] Uhlmann, M., An immersed boundary method with direct forcing for the simulation of particulate flows, J. Comput. Phys., 209, 2, 448-476 (2005) · Zbl 1138.76398
[4] Glowinski, R.; Pan, T.; Periaux, J., A fictitious domain method for Dirichlet problem and applications, Comput. Methods Appl. Mech. Eng., 111, 3-4, 283-303 (1994) · Zbl 0845.73078
[5] Glowinski, R.; Pan, T.; Hesla, T.; Joseph, D., A distributed Lagrange multiplier/fictitious domain method for particulate flows, Int. J. Multiph. Flow, 25, 5, 755-794 (1999) · Zbl 1137.76592
[6] Glowinski, R.; Pan, T.; Hesla, T.; Joseph, D.; Périaux, J., A fictitious domain approach to the direct numerical simulation of incompressible viscous flow past moving rigid bodies: application to particulate flow, J. Comput. Phys., 169, 2, 363-426 (2001) · Zbl 1047.76097
[7] Yu, Z.; Shao, X.; Wachs, A., A fictitious domain method for particulate flows with heat transfer, J. Comput. Phys., 217, 2, 424-452 (2006) · Zbl 1160.76382
[8] Yu, Z.; Shao, X., A direct-forcing fictitious domain method for particulate flows, J. Comput. Phys., 227, 1, 292-314 (2007) · Zbl 1280.76052
[9] Mittal, R.; Iaccarino, G., Immersed boundary methods, Annu. Rev. Fluid Mech., 37, 1, 239-261 (2005) · Zbl 1117.76049
[10] Nasar, A.; Rogers, B.; Revell, A.; Stansby, P.; Lind, S., Eulerian weakly compressible smoothed particle hydrodynamics (SPH) with the immersed boundary method for thin slender bodies, J. Fluids Struct., 84, 263-282 (2019)
[11] Dupuis, A.; Chatelain, P.; Koumoutsakos, P., An immersed boundary-lattice-Boltzmann method for the simulation of the flow past an impulsively started cylinder, J. Comput. Phys., 227, 9, 4486-4498 (2008) · Zbl 1136.76041
[12] Lucy, L. B., A numerical approach to the testing of the fission hypothesis, Astron. J., 82, 1013 (1977)
[13] Gingold, R. A.; Monaghan, J. J., Smoothed particle hydrodynamics: theory and application to non-spherical stars, Mon. Not. R. Astron. Soc., 181, 3, 375-389 (1977) · Zbl 0421.76032
[14] Altomare, C.; Domínguez, J.; Crespo, A.; González-Cao, J.; Suzuki, T.; Gómez-Gesteira, M.; Troch, P., Long-crested wave generation and absorption for SPH-based DualSPHysics model, Coast. Eng., 127, 37-54 (2017)
[15] Tafuni, A.; Domínguez, J.; Vacondio, R.; Crespo, A., A versatile algorithm for the treatment of open boundary conditions in smoothed particle hydrodynamics GPU models, Comput. Methods Appl. Mech. Eng., 342, 604-624 (2018) · Zbl 1440.76125
[16] Bertevas, E.; Férec, J.; Khoo, B. C.; Ausias, G.; Phan-Thien, N., Smoothed particle hydrodynamics (SPH) modeling of fiber orientation in a 3D printing process, Phys. Fluids, 30, 10, Article 103103 pp. (2018)
[17] Ouyang, Z.; Bertevas, E.; Parc, L.; Khoo, B. C.; Phan-Thien, N.; Férec, J.; Ausias, G., A smoothed particle hydrodynamics simulation of fiber-filled composites in a non-isothermal three-dimensional printing process, Phys. Fluids, 31, 12, Article 123102 pp. (2019)
[18] Ouyang, Z.; Bertevas, E.; Wang, D.; Khoo, B. C.; Férec, J.; Ausias, G.; Phan-Thien, N., A smoothed particle hydrodynamics study of a non-isothermal and thermally anisotropic fused deposition modeling process for a fiber-filled composite, Phys. Fluids, 32, 5, Article 053106 pp. (2020)
[19] Antoci, C.; Gallati, M.; Sibilla, S., Numerical simulation of fluid-structure interaction by SPH, Comput. Struct., 85, 11-14, 879-890 (2007)
[20] Domínguez, J. M.; Crespo, A. J.; Hall, M.; Altomare, C.; Wu, M.; Stratigaki, V.; Troch, P.; Cappietti, L.; Gómez-Gesteira, M., SPH simulation of floating structures with moorings, Coast. Eng., 153, Article 103560 pp. (2019)
[21] Tran-Duc, T.; Phan-Thien, N.; Khoo, B. C., A smoothed particle hydrodynamics (SPH) study of sediment dispersion on the seafloor, Phys. Fluids, 29, 8, Article 083302 pp. (2017)
[22] Tran-Duc, T.; Phan-Thien, N.; Khoo, B. C., A smoothed particle hydrodynamics (SPH) study on polydisperse sediment from technical activities on seabed, Phys. Fluids, 30, 2, Article 023302 pp. (2018)
[23] Tran-Duc, T.; Phan-Thien, N.; Khoo, B. C., A three-dimensional smoothed particle hydrodynamics dispersion simulation of polydispersed sediment on the seafloor using a message passing interface algorithm, Phys. Fluids, 31, 4, Article 043301 pp. (2019)
[24] Hieber, S.; Koumoutsakos, P., An immersed boundary method for smoothed particle hydrodynamics of self-propelled swimmers, J. Comput. Phys., 227, 19, 8636-8654 (2008) · Zbl 1227.76052
[25] Liu, G. R.; Liu, M. B., Smoothed particle hydrodynamics, (A Meshfree Particle Method (2003)) · Zbl 1046.76001
[26] Antuono, M.; Colagrossi, A.; Marrone, S., Numerical diffusive terms in weakly-compressible SPH schemes, Comput. Phys. Commun., 183, 12, 2570-2580 (2012) · Zbl 1507.76152
[27] Morris, J. P.; Fox, P. J.; Zhu, Y., Modeling low Reynolds number incompressible flows using SPH, J. Comput. Phys., 136, 1, 214-226 (1997) · Zbl 0889.76066
[28] Adami, S.; Hu, X.; Adams, N., A generalized wall boundary condition for smoothed particle hydrodynamics, J. Comput. Phys., 231, 21, 7057-7075 (2012)
[29] Liu, M.; Liu, G., Restoring particle consistency in smoothed particle hydrodynamics, Appl. Numer. Math., 56, 1, 19-36 (2006) · Zbl 1329.76285
[30] Peskin, C. S., Numerical analysis of blood flow in the heart, J. Comput. Phys., 25, 3, 220-252 (1977) · Zbl 0403.76100
[31] Chen, J. K.; Beraun, J. E.; Carney, T. C., A corrective smoothed particle method for boundary value problems in heat conduction, Int. J. Numer. Methods Eng., 46, 2, 231-252 (1999) · Zbl 0941.65104
[32] Verlet, L., Computer “Experiments” on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules, Phys. Rev., 159, 1, 98-103 (1967)
[33] Monaghan, J. J., Smoothed particle hydrodynamics, Annu. Rev. Astron. Astrophys., 30, 1, 543-574 (1992)
[34] Tritton, D. J., Experiments on the flow past a circular cylinder at low Reynolds numbers, J. Fluid Mech., 6, 4, 547-567 (1959) · Zbl 0092.19502
[35] Marrone, S.; Colagrossi, A.; Antuono, M.; Colicchio, G.; Graziani, G., An accurate SPH modeling of viscous flows around bodies at low and moderate Reynolds numbers, J. Comput. Phys., 245, 456-475 (2013) · Zbl 1349.76715
[36] Hu, Y.; Yuan, H.; Shu, S.; Niu, X.; Li, M., An improved momentum exchanged-based immersed boundary-lattice Boltzmann method by using an iterative technique, Comput. Math. Appl., 68, 3, 140-155 (2014) · Zbl 1369.76045
[37] Lima, E.; Silva, A.; Silveira-Neto, A.; Damasceno, J., Numerical simulation of two-dimensional flows over a circular cylinder using the immersed boundary method, J. Comput. Phys., 189, 2, 351-370 (2003) · Zbl 1061.76046
[38] Le, D.; Khoo, B.; Lim, K., An implicit-forcing immersed boundary method for simulating viscous flows in irregular domains, Comput. Methods Appl. Mech. Eng., 197, 25-28, 2119-2130 (2008) · Zbl 1158.76407
[39] Negi, P.; Ramachandran, P.; Haftu, A., An improved non-reflecting outlet boundary condition for weakly-compressible SPH, Comput. Methods Appl. Mech. Eng., 367, Article 113119 pp. (2020) · Zbl 1442.76088
[40] Feng, J.; Hu, H. H.; Joseph, D. D., Direct simulation of initial value problems for the motion of solid bodies in a Newtonian fluid. Part 2. Couette and Poiseuille flows, J. Fluid Mech., 277, 271-301 (1994) · Zbl 0876.76040
[41] Feng, Z.; Michaelides, E. E., The immersed boundary-lattice Boltzmann method for solving fluid-particles interaction problems, J. Comput. Phys., 195, 2, 602-628 (2004) · Zbl 1115.76395
[42] Nie, D.; Lin, J., Behavior of three circular particles in a confined power-law fluid under shear, J. Non-Newton. Fluid Mech., 221, 76-94 (2015)
[43] Ouyang, Z.; Lin, J.; Ku, X., The hydrodynamic behavior of a squirmer swimming in power-law fluid, Phys. Fluids, 30, 8, Article 083301 pp. (2018)
[44] Segre, G.; Silberberg, A., Radial particle displacements in Poiseuille flow of suspensions, Nature, 189, 4760, 209-210 (1961)
[45] Chen, S.; Pan, T.; Chang, C., The motion of a single and multiple neutrally buoyant elliptical cylinders in plane Poiseuille flow, Phys. Fluids, 24, 10, Article 103302 pp. (2012)
[46] Aidun, C. K.; Lu, Y.; Ding, E., Direct analysis of particulate suspensions with inertia using the discrete Boltzmann equation, J. Fluid Mech., 373, 287-311 (1998) · Zbl 0933.76092
[47] Feng, J.; Hu, H. H.; Joseph, D. D., Direct simulation of initial value problems for the motion of solid bodies in a Newtonian fluid Part 1. Sedimentation, J. Fluid Mech., 261, 95-134 (1994) · Zbl 0800.76114
[48] Huang, H.; Yang, X.; Lu, X., Sedimentation of an ellipsoidal particle in narrow tubes, Phys. Fluids, 26, 5, Article 053302 pp. (2014)
[49] Jeffery, G. B., The motion of ellipsoidal particles immersed in a viscous fluid, Proc. R. Soc. Lond. Ser. A, Contain. Pap. Math. Phys. Character, 102, 715, 161-179 (1922) · JFM 49.0748.02
[50] Harris, J.; Pittman, J., Equivalent ellipsoidal axis ratios of slender rod-like particles, J. Colloid Interface Sci., 50, 2, 280-282 (1975)
[51] Ku, X. K.; Lin, J. Z., Inertial effects on the rotational motion of a fibre in simple shear flow between two bounding walls, Phys. Scr., 80, 2, Article 025801 pp. (2009)
[52] A. Colagrossi, 0 0 0 0. Benchmark Test 6: 2D Incompressible flow around a moving square inside a rectangular box, SPHERIC.
[53] Lind, S.; Xu, R.; Stansby, P.; Rogers, B., Incompressible smoothed particle hydrodynamics for free-surface flows: a generalised diffusion-based algorithm for stability and validations for impulsive flows and propagating waves, J. Comput. Phys., 231, 4, 1499-1523 (2012) · Zbl 1286.76118
[54] Cao, W. J.; Yang, D. Z.; Lu, X. W.; He, Y.; Zhou, Z. Y., Numerical simulation of flow and heat transfer during filling process based on SPH method, Adv. Mater. Res., 658, 276-280 (2013)
[55] Ren, J.; Ouyang, J.; Jiang, T., An improved particle method for simulation of the non-isothermal viscoelastic fluid mold filling process, Int. J. Heat Mass Transf., 85, 543-560 (2015)
[56] Xu, X.; Yu, P., Modeling and simulation of injection molding process of polymer melt by a robust SPH method, Appl. Math. Model., 48, 384-409 (2017) · Zbl 1480.76092
[57] Xu, X.; Yu, P., Extension of SPH to simulate non-isothermal free surface flows during the injection molding process, Appl. Math. Model., 73, 715-731 (2019) · Zbl 1481.76165
[58] Zhong, W.; Li, F.; Zhang, Z.; Song, L.; Li, Z., Short fiber reinforced composites for fused deposition modeling, Mater. Sci. Eng. A, 301, 2, 125-130 (2001)
[59] Tekinalp, H. L.; Kunc, V.; Velez-Garcia, G. M.; Duty, C. E.; Love, L. J.; Naskar, A. K.; Blue, C. A.; Ozcan, S., Highly oriented carbon fiber-polymer composites via additive manufacturing, Compos. Sci. Technol., 105, 144-150 (2014)
[60] Ning, F.; Cong, W.; Hu, Y.; Wang, H., Additive manufacturing of carbon fiber-reinforced plastic composites using fused deposition modeling: effects of process parameters on tensile properties, J. Compos. Mater., 51, 4, 451-462 (2016)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.