An immersed boundary-lattice Boltzmann flux solver in a moving frame to study three-dimensional (3D LBFS) freely falling rigid bodies

Significance Statement

Free falling objects are of great importance in both engineering principles and theoretical research. This has led to near-exhaustive studies at both empirical and theoretical levels, of the topic. Fluid-structure interactions flow problems, which involve complicated dynamic characteristics and also a wide range of applications are usually involved here.

Researchers under the leadership of Professor Chang Shu from the Department of Mechanical Engineering at National University of Singapore proposed an immersed boundary -lattice Boltzmann flux solver in moving frame, to study three-dimensional freely falling rigid bodies in unbounded domains. Their work is now published in Journal of Fluids and Structures.

The team used an immersed boundary lattice Boltzmann flux solver which includes a predictor and corrector steps. Lagrangian markers were applied for the application of boundary conditions while the poignant Eulerian grid was used to calculate the flow field. No rotational motion was allowed in the Eulerian grid but instead a unique translational motion was applied.

Finite volume discretization followed closely where the fractional-step method was applied so as to divide the solution process into two steps; predictor and corrector steps. For the predictor step, intermediate flow field was predicted by solving equations obtained without considerations of the solid boundary present. Velocity corrections were then made, for the flow field, in the corrector step by using the improved boundary condition-enforced immersed boundary method.

Prediction of the transitional flow field was tested as proposed in the 3D-LBFS in a moving frame, in the immovable Cartesian coordinate system which is efficient for non-uniform fields. The numerical fluxes at cell interface between two adjacent cells were evaluated physically from the local solution of lattice Boltzmann equation. Both viscous and inviscid fluxes at each interface were reconstructed simultaneously by local application of the lattice Boltzmann method. Convective flux that was caused by the grid motion was evaluated directly by utilizing the speed of the moving grid. The team then conducted rigid body motion prediction using two accepted co-ordinate systems. A computational sequence finalized the process.

It was necessary that the team validated their numerical method by simulating three incompressible flows with a dynamic sphere, sole particle sedimentation in a rectangular vessel and flows with spontaneously falling disks of varying aspect ratios. Phase illustrations of the different falling patterns were developed.

Regardless of the success of empirical and theoretical studies, numerical investigations of this matter, which may yield more physical data about various instantaneous flow parameters and vortical structures, are still minimal due to its geometrical and dynamical intricates.

Empirical findings yield a classification of varying modes of a free-falling disk. The results obtained here synchronize well with theoretical and empirical data. This research demonstrates the capability of the proposed solver to capture intricate modes of a falling body.

Tumbling_Gray - An immersed boundary-lattice Boltzmann flux solver in a moving frame to study three-dimensional (3D LBFS) freely falling rigid bodies - advances in engineering

Steady_Black - An immersed boundary-lattice Boltzmann flux solver in a moving frame to study three-dimensional (3D LBFS) freely falling rigid bodies - Advances in engineering

spiral_gray1 - An immersed boundary-lattice Boltzmann flux solver in a moving frame to study three-dimensional (3D LBFS) freely falling rigid bodies - Advances in engineering

3D_Tumbling_Gray - An immersed boundary-lattice Boltzmann flux solver in a moving frame to study three-dimensional (3D LBFS) freely falling rigid bodies - Advances in engineering

About The Author

Dr. Wang Yan now is research scientist at Temasek Laboratories, National University of Singapore. He obtained his PhD degree at National University of Singapore in 2014 and received BEng degrees from Nanjing University of Aeronautics and Astronautics (NUAA), China in 2009.

His research interests include Flow-Structures-Interaction problems, Multiphase flows and computational methods in fluid mechanics, such as the lattice Boltzmann method, immersed boundary method, diffuse interface method. He currently conducts research on the use of dispersed multiphase flow models to predict the degradation of aerodynamic performances of aircrafts under rain. 

About The Author

Dr. Shu Chang is a Professor at Department of Mechanical Engineering, National University of Singapore (NUS). He obtained his PhD degree at University of Glasgow in 1991, and received MEng and BEng degrees from Nanjing University of Aeronautics and Astronautics (NUAA), China, respectively in 1986 and 1983. Dr Shu has been working in the Computational Fluid Dynamics (CFD) for more than 30 years.

His major interest is to develop efficient numerical methods to solve flow problems, which are governed by a set of partial differential equations. Recently, he developed a series of flux solvers, which are based on the lattice Boltzmann model and gas kinetic scheme. These solvers can be well applied to simulate fluid flows from incompressible regime to hypersonic regime. He also made effort to develop some efficient models for simulation of multiphase flows and flows around moving boundaries.

So far, he has authored 2 monographs and published about 300 articles in the international referred journals (SCI indexed). The details of his publication can be referred to  (ResearchGate Profile) or  (Google Scholar Profile). So far, his work has been cited more than 11600 times in Google Scholar Profile. Currently, he is the Editor-in-Chief of Advances in Applied Mathematics and Mechanics (AAMM), and the book series of Advances in Computational Fluid Dynamics. He is also the editorial board member of International Journal for Numerical Methods in Fluids.  

About The Author

Dr. YANG Liming received the B.Eng, M.Eng and Ph.D. degrees from Department of Aerodynamics, Nanjing University of Aeronautics and Astronautics, Nanjing, P.R. China. Since Nov. 2016, he has been appointed as a Research Staff in Department of Mechanical Engineering, National University of Singapore, Singapore.

His research interests include lattice Boltzmann method, gas kinetic scheme, discrete velocity method and immersed boundary method. He and his group has developed the lattice Boltzmann flux solver, the simplified gas kinetic scheme and the discrete velocity method with streaming and collision processes. The simplified gas kinetic scheme has been successfully applied to solve many flow problems. This method inherits the merits of the conventional gas kinetic scheme and, at the same time, improves the computational efficiency markedly. 

About The Author

Dr. TEO Chiang Juay received his B. Eng. and M. Eng. degrees in Mechanical Engineering from the National University of Singapore (NUS), and his Ph. D. in Aeronautics and Astronautics from the Massachusetts Institute of Technology (MIT). He is currently an Associate Professor at the NUS Department of Mechanical Engineering. He teaches core modules, technical electives and General Education Modules related to Fluid Mechanics.

His research interests include thermal-fluids, microfluidics, hydrodynamics, aerodynamics and aerospace propulsion. He currently conducts research on the use of superhydrophobic surfaces for reducing flow resistance in microfluidic applications, the use of chaotic advection for heat transfer augmentation in microchannel heat sinks, Wing-In-Ground craft aerodynamics, flow cavitation, Pulse Detonation Engines and Cross-Flow-Fans for Unmanned Air Vehicles. 

Reference

Y. Wang1, C. Shu, L.M. Yang2, C.J. Teo1. An immersed boundary-lattice Boltzmann flux solver in a moving frame to study three-dimensional freely falling rigid bodies. Journal of Fluids and Structures 68 (2017) 444–465.

Show Affiliations
  1. Department of Mechanical Engineering, National University of Singapore, 10 Kent Ridge Crescent, 119260, Singapore
  2. Department of Aerodynamics, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Yudao Street, Nanjing 210016, Jiangsu, China

 

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