شبیه‌سازی عددی تلاطم غیر‌خطی درون یک مخزن تحت اثر شتاب‌های انتقالی و زاویه‌ای

نوع مقاله: مقالة‌ تحقیقی‌ (پژوهشی‌)

نویسندگان

1 دانشکده مهندسی مکانیک و انرژی، دانشگاه شهید بهشتی

2 عضو هیئت علمی دانشکده فنی مهندسی دانشگاه خوارزمی

چکیده

در مقالة حاضر،  پدیدة تلاطم سیال در یک مخزن نیمه‌پر تحت اثر شتاب‌های جانبی (سرج) و زاویه‌ای (پیچ) به‌صورت عددی مورد بررسی قرار گرفته است. یک الگوریتم عددی براساس تکنیک کسر حجمی استفاده شده تا رفتار غیر‌خطی تلاطم سیال و درنتیجه تعقیب سطح آزاد سیال و نحوة اثر شتاب‌های جانبی و زاویه‌ای بر روی آن شبیه‌سازی شود. به منظور بهبود کیفیت تسخیر سطح مشترک دو فاز از روش افزایش انسجام THINC در کد عددی موجود بهره گرفته شده است. ضمناً، به منظور اعتبار سنجی حل عددی، جابجایی سطح آزاد برای تلاطم سیال تحت اثر شتاب جانبی با در نظر گرفتن فرکانس ارتعاشات در دو حالت تشدید و دور از تشدید با نتایج آزمایشگاهی و حل تحلیلی مقایسه شده است. ضمناً، فشار بر روی دیواره برای تلاطم سیال تحت اثر شتاب زاویه‌ای برای دو حالت با و بدون صفحات میراکننده با نتایج آزمایشگاهی مقایسه شده‌اند. 

کلیدواژه‌ها


عنوان مقاله [English]

Numerical Simulation of Sloshing in a Container under Translational and Angular Accelerations

نویسندگان [English]

  • sahand majidi 1
  • Mostafa Esmaili 2
1 Faculty of Mechanical and Energy Systems Engineering, shahid beheshti university
2 PhD of mechanical Engineering Faculty of kharazmi University
چکیده [English]

Liquid sloshing of a partially filled container subject to surge and pitch motions is
numerically investigated using a sophisticated numerical algorithm. The algorithm is
developed based on the finite volume methodology and volume of fluid (VOF) technique is
utilized to capture the interface evolution and deformation. Also, the interface capturing
quality of the developed flow solver is enhanced due to its coupling to THINC interface
sharpening technique. The numerical results are validated through the comparison of the
interface deformation amplitude and the frequency with the available experimental and
analytical data for liquid sloshing caused by lateral sinusoidal accelerations with
resonance and non-resonance frequencies. Moreover, liquid sloshing due to angular
excitations are studied for two different tank geometries with and without damping
baffles. The resulting pressure oscillations of the pressure exerted on the side walls are
monitored and compared to the experimental data.

کلیدواژه‌ها [English]

  • Non-linear sloshing
  • Container
  • Volume of fluid technique
  • Resonance
  • Damping baffles

[1]     Abramson, H.N., The Dynamic Behavior of Liquids in Moving Containers, with Applications to Space Vehicle Technology, NASA SP. 106, 1966.

[2]     Faltinsen, O.M. “A Numerical Nonlinear Method of Sloshing in Tanks with Two-Dimensional Flow,” Journal of  Ship Research, Vol. 22, 1978, pp. 193-202.

[3]     Faltinsen, O.M., Rognebakke, O.F., Lukovsky, I.A. and Timokha, A.N., “Multidimensional Modal Analysis of Nonlinear Sloshing in a Rectangular Tank with Finite Water Depth,” Journal of Fluid Mechanics, Vol. 407, 2000, pp. 201-234.

[4]     Hill, D. F., “Transient and Steady-State Amplitudes of Forced Waves in Rectangular Basins,” Physics of Fluids, Vol. 15, 2003, pp. 1576-1587.

[5]     Pal P. and Bhattacharyya, S., “Sloshing in Partially Filled Liquid Containers—Numerical and Experimental Study for 2-D Problems,” Journal of Sound and Vibration, Vol. 329, 2010, pp. 4466-4485.

[6]     Zhang, T., Ren, Y.-F., Fan, C.M. and Li, P.W., “Simulation of Two-Dimensional Sloshing Phenomenon by Generalized Finite Difference Method,” Engineering Analysis with Boundary Elements, Vol. 63, 2016, pp. 82-91.

[7]     Wang, J., Lo, S. and Zhou, D., “Liquid Sloshing in Rigid Cylindrical Container with Multiple Rigid Annular Baffles: Free Vibration,” Journal of Fluids and Structures, Vol. 34, 2012, pp. 138-156.

[8]     Wu, N.J., Hsiao, S.C. and Wu, H.L., “Mesh-Free Simulation of Liquid Sloshing Subjected to Harmonic Excitations,” Engineering Analysis with Boundary Elements, Vol. 64, 2016, pp. 90-100.

[9]     Nakayama, T. and Washizu, K., “Nonlinear Analysis of Liquid Motion in a Container Subjected to Forced Pitching Oscillation,” International Journal for Numerical Methods in Engineering, Vol. 15, 1980, pp. 1207-1220.

[10]  Cho, J. and Lee, H., “Non‐Linear Finite Element Analysis of Large Amplitude Sloshing Flow in Two‐Dimensional Tank,” International Journal for Numerical Methods in Engineering, vol. 61, 2004, pp. 514-531,.

[11]  Chen, B. F. and Nokes, R. “Time-Independent Finite Difference Analysis of Fully Non-Linear and Viscous Fluid Sloshing in a Rectangular Tank,” Journal of Computational Physics, Vol. 209, 2005, pp. 47-81.

[12]  De Chowdhury, S. and Sannasiraj, S., “Numerical Simulation of 2D Sloshing Waves Using SPH with Diffusive Terms,” Applied Ocean Research, Vol. 47, 2014, pp. 219-240.

[13]  Safarzade A., Maghsod N., “Investigation of the Excitation Frequency Effect on Liquid Sloshing Phenomenon using Three-Dimensional Numerical Model,” Presented at the International Conference in Civil Engineering, Architecture and Urban Sustainable Development, Tabriz, 1392.

[14]   Javanshir, A., “Numerical Investigation of Three-  Dimensional Sloshing in a Liquid Container,” (Thesis Ms.c.) Ferdowsi university Mashhad, 1392.

[15]    Gharaee R., “Numerical Simulation and Experimental Investigation of the Liquid Sloshing in  a Partially Filled Container with Damping Baffle,” (Thesis Ms.c.), Shahroud University of Thecnology, 1390.

[16]  Liu, D. and Lin, P., “A Numerical Study of Three-Dimensional Liquid Sloshing in Tanks,” Journal of Computational physics, Vol. 227, 2008, pp. 3921-3939.

[17]  Zhao, Y. and Chen, H.C., “Numerical Simulation of 3D Sloshing Flow in Partially Filled LNG Tank Using a Coupled Level-Set and Volume-of-Fluid Method,” Ocean Engineering, Vol. 104, 2015, pp. 10-30.

[18]  Gibou, F., Chen, L., Nguyen, D. and Banerjee, S., “A Level Set Based Sharp Interface Method for the Multiphase Incompressible Navier–Stokes Equations with Phase Change,” Journal of Computational Physics, Vol. 222, 2007, pp. 536-555.

[19]  Prosperetti, A. and Tryggvason, G., Computational Methods for Multiphase Flow, Cambridge University Press, 2009.

[20]  Chern, I. L., Glimm, J., McBryan, O., Plohr, B. and Yaniv, S. “Front Tracking for Gas Dynamics,” Journal of Computational Physics, Vol. 62, 1986, pp. 83-110.

[21]  Tryggvason, G., Bunner, B., Esmaeeli, A. and  et al., “A Front-Tracking Method for The Computations of Multiphase Flow,” Journal of Computational Physics, Vol. 169, 2001, pp. 708-759.

[22]  Unverdi, S.O. and Tryggvason, G., “A Front-Tracking Method for Viscous, Incompressible, Multi-Fluid Flows,” Journal of Computational Physics, Vol. 100, 1992, pp. 25-37.

[23]  Renardy, Y. and Renardy, M., “PROST: a Parabolic Reconstruction of Surface Tension for The Volume-of-Fluid Method,” Journal of Computational Physics, Vol. 183, 2002, pp. 400-421.

[24]  Rudman, M., “Volume-Tracking Methods for Interfacial Flow Calculations,” International Journal for Numerical Methods in Fluids, Vol. 24, 1997, pp. 671-691.

[25]  Scardovelli, R. and Zaleski, S., “Direct Numerical Simulation of Free-surface and Interfacial Flow,” Annual Review of Fluid Mechanics, Vol. 31, 1999, pp. 567-603.

[26]  Xiao, F., Honma, Y. and Kono, T., “A Simple Algebraic Interface Capturing Scheme using Hyperbolic Tangent Function,” International Journal for Numerical Methods in Fluids, Vol. 48, 2005, pp. 1023-1040.

[27]  Aulisa, E., Manservisi, S. and Scardovelli, R. “A Mixed Markers and Volume-of-Fluid Method for the Reconstruction and Advection of Interfaces in Two-Phase and Free-Boundary Flows,” Journal of Computational Physics, Vol. 188, 2003, pp. 611-639.

[28]  Manservisi, C.S. and Scardovelli, R., “An Optimal Constrained Approach for Divergence-Free Velocity Interpolation and Multilevel VOF Method,” Computers & Fluids, Vol. 47, 2011, pp. 101-114.

[29]  Cassidy, D. A., Edwards, J.R. and Tian, M., “An Investigation of Interface-Sharpening Schemes for Multi-phase Mixture Flows,” Journal of Computational Physics, Vol. 228, 2009, pp. 5628-5649.

[30]  So, K., Hu, X. and Adams, N., “Anti-diffusion Method for Interface Steepening in Two-Phase Incompressible Flow,” Journal of Computational Physics, Vol. 230, 2011, pp. 5155-5177.

[31]  Yokoi, K., “Efficient Implementation of THINC Scheme: a Simple and Practical Smoothed VOF Algorithm,” Journal of Computational Physics, Vol. 226, 2007, pp. 1985-2002,.

[32]  Ubbink, O. and Issa, R., “A Method for Capturing Sharp Fluid Interfaces on Arbitrary Meshes,” Journal of Computational Physics, Vol. 153, 1999, pp. 26-50.

[33]  Ii, S., Sugiyama, K., Takeuchi, S., Takagi, S., Matsumoto, Y. and Xiao, F., “An Interface Capturing Method with a Continuous Function: The THINC Method with Multi-Dimensional Reconstruction,” Journal of Computational Physics, Vol. 231, 2012, pp. 2328-2358.

[34]  Shyue, K..M. and Xiao, F., “An Eulerian Interface Sharpening Algorithm for Compressible Two-Phase Flow: The Algebraic THINC Approach,” Journal of Computational Physics, Vol. 268, 2014, pp. 326-354.

[35]  Ménard, T., Tanguy, S. and 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, Vol. 33, 2007, pp. 510-524.

[36]  Liu, D. and Lin, P., “Three-Dimensional Liquid Sloshing in a Tank with Baffles,” Ocean Engineering, Vol. 36, 2009, pp. 202-212.

[37]  Jeong, S.m., Hwang, S.C. and Park, J.C., “Numerical Simulation of Impact Loads Caused by Sloshing in a Rectangular Tank Using Eulerian and Lagrangian Approaches,” International Journal of Offshore and Polar Engineering, Vol. 24, 2014, pp. 174-180.

[38]  Ibrahim, R.A., Liquid Sloshing Dynamics: Theory and Applications: Cambridge University Press, 2005.

[39]  Nakayama, T. and Washizu, K., “The Boundary Element Method Applied to the Analysis of Two‐Dimensional Nonlinear Sloshing Problems,” International Journal for Numerical Methods in Engineering, Vol. 17, 1981, pp. 1631-1646.

[40]  Akyildiz, H. and Ünal, E., “Experimental Investigation of Pressure Distribution on a Rectangular Tank Due to the Liquid Sloshing,” Ocean Engineering, Vol. 32, 2005, pp. 1503-1516.