H. W. Zheng

A lattice Boltzmann model for multiphase flows with large density ratio

a lattice Boltzmann model for simulating multiphase flows with large density ratios is described in this paper. The method is easily implemented. It does not require solving the Poisson equation and does not involve the complex treatments of derivative terms. The interface capturing equation is recovered without any additional terms as compared to other methods [M.R. Swift, W.R. Osborn, J.M. Yeomans, Lattice Boltzmann simulation of liquid-gas and binary fluid systems, Phys. Rev. E 54 (1996) 5041-5052; T. Inamuro, T. Ogata, S. Tajima, N. Konishi, A lattice Boltzmann method for incompressible two-phase flows with large density differences, J. Comput. Phys. 198 (2004) 628-644; T. Lee, C.-L. Lin, A stable discretization of the lattice Boltzmann equation for simulation of incompressible two-phase flows at high density ratio, J. Comput. Phys. 206 (2005) 16-47]. Besides, it requires less discrete velocities. As a result, its efficiency could be greatly improved, especially in 3D applications. It is validated by several cases: a bubble in a stationary flow and the capillary wave. The numerical surface tension obtained from the Laplace law and the interface profile agrees very well with the respective analytical solution. The method is further verified by its application to capillary wave and the bubble rising under buoyancy with comparison to other methods. All the numerical experiments show that the present approach can be used to model multiphase flows with large density ratios.

An object-oriented and quadrilateral-mesh based solution adaptive algorithm for compressible multi-fluid flows

In this paper, an object-oriented and quadrilateral-mesh based solution adaptive algorithm for the simulation of compressible multi-fluid flows is presented. The HLLC scheme (Harten, Lax and van Leer approximate Riemann solver with the Contact wave restored) is extended to adaptively solve the compressible multi-fluid flows under complex geometry on unstructured mesh. It is also extended to the second-order of accuracy by using MUSCL extrapolation. The node, edge and cell are arranged in such an object-oriented manner that each of them inherits from a basic object. A home-made double link list is designed to manage these objects so that the inserting of new objects and removing of the existing objects (nodes, edges and cells) are independent of the number of objects and only of the complexity of O(1). In addition, the cells with different levels are further stored in different lists. This avoids the recursive calculation of solution of mother (non-leaf) cells. Thus, high efficiency is obtained due to these features. Besides, as compared to other cell-edge adaptive methods, the separation of nodes would reduce the memory requirement of redundant nodes, especially in the cases where the level number is large or the space dimension is three. Five two-dimensional examples are used to examine its performance. These examples include vortex evolution problem, interface only problem under structured mesh and unstructured mesh, bubble explosion under the water, bubble-shock interaction, and shock-interface interaction inside the cylindrical vessel. Numerical results indicate that there is no oscillation of pressure and velocity across the interface and it is feasible to apply it to solve compressible multi-fluid flows with large density ratio (1000) and strong shock wave (the pressure ratio is 10,000) interaction with the interface.

NUMERICAL STUDY OF 2D MULTIPHASE FLOWS OVER GROOVED SURFACE BY LATTICE BOLTZMANN METHOD

In this paper, the effects of surface wettability and topography on a droplet, which is driven by a body force to pass through grooved walls, are studied by using the multiphase lattice Boltzmann model. At small scale, the shape and velocity of the droplet were found to be strongly affected by the wettability and configuration of the wall. The drag on the droplet moving over grooved surfaces was found to decrease as the wall hydrophobicity increases. It was also found that the wettability decides whether the droplet fills or does not fill the whole grooves.

A PLATFORM FOR DEVELOPING NEW LATTICE BOLTZMANN MODELS

This paper presents a platform to develop new lattice Boltzmann models. It gives a general framework for different applications. It also presents basic velocity models and a set of basic conditions to construct new models which can recover Navier–Stokes equations. Besides, the equilibrium function can be easily obtained through a set of equations. By using the platform, we can easily recover the existing models. Some new models are derived from the platform and validated by their application to simulate the two-dimensional driven cavity flow. The obtained numerical results agree very well with available data in the literature.

Assessment of DES on the Flow after a Snow-Flake Orifice

To understand the mechanism of the multi-scale nature of turbulent flows, the interaction between the turbulence flow and the two special multi-scale fractal shaped geometries (SF2 and SF3) with high Reynolds numbers in a pipe is investigated by detached-eddy simulation (DES). As compared to the circular orifice, more mixing structures are generated after the fractal shape orifice. The numerical mean velocity profiles along the pipe show a good agreement with the experiment values obtained by hotwire anemometry. These show the feasibility of DES to be applied to study the problem.

Detached Eddy Simulation for Turbulent Flows in a Pipe with a Snowflake Fractal Orifice

Turbulent flows in a pipe with a snowflake fractal shape (SF2) orifice are investigated using the parallelized, density-based, dynamic mesh and detached eddy simulation code (DG-DES) (Xia, PhD thesis, 2005; Xia and Qin, AIAA 2005-106, 2005). For comparison with the laboratory experiment, the flow is essentially a low Mach number flow. In order to tackle the low speed problem of the density based method, the SLAU (Simple Low dissipation AUSM) (Shima and Kitamura in 47th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, AIAA 2009-136, 2009) is adopted in this paper. The scheme exhibits low numerical dissipations for low speeds and needs no problem-dependent “cut-off Mach number”. The results for the flows after the orifice are compared with those of the corresponding experiment (Chong, PhD thesis, 2008). Comparisons show good agreements in the mean velocity profiles at the different holes.

NEW LATTICE KINETIC SCHEMES FOR INCOMPRESSIBLE VISCOUS FLOWS

A new two-dimensional lattice kinetic scheme on the uniform mesh was recently proposed by Inamuro, based on the standard lattice Boltzmann method (LBM). Compared with the standard LBM, this scheme can easily implement the boundary condition and save computer memory. In order to remove the shortcoming of a relatively large viscosity at a high Reynolds number, a first-order derivative term is introduced in the equilibrium density distribution function. However, the parameter associated with the derivative term is very sensitive and was chosen in a narrow range for a high Reynolds number case. To avoid the use of the derivative term while removing the shortcoming of a relatively large viscosity, new lattice kinetic schemes are proposed in this work following the original lattice kinetic scheme. In these new lattice kinetic schemes, the derivative term is dropped out and the difficulty of the relatively large viscosity is eased by controlling the time step δt or sonic speed cs. To validate these new lattice kinetic schemes, the numerical simulations of the two-dimensional square driven cavity flow at Reynolds numbers from 100 to 1000 are carried out. The results using the new lattice kinetic schemes are compared with the benchmark data.

Investigation of Aerodynamic Performance of High-Speed Train by Detached Eddy Simulation

The detached eddy simulation (DES) is employed to study the flows around the high speed train at speed of 500km/h. Its object is to evaluate the aerodynamic performance. As we know, for high speed trains at speeds bigger than 250 km/h, most (about 75–80%) of the total resistance is caused by aerodynamic drag. Hence, it is important to accurately predict the aerodynamic drag for the designer of new shape of train. To achieve this goal, one of the challenge problems is to capture the massively separations in the wake region which are rarely explored in the literature. To further simplified the problem, the study is only applied to the simplified modelling train which does not include items like bogies, pantographs etc. The results show that DES can capture the separation as well as the small scales of eddies in the wake region.

EVALUATION OF THE PERFORMANCE OF THE HYBRID LATTICE BOLTZMANN BASED NUMERICAL FLUX

It is well known that the numerical scheme is a key factor to the stability and accuracy of a Navier-Stokes solver. Recently, a new hybrid lattice Boltzmann numerical flux (HLBFS) is developed by Shus group. It combines two different LBFS schemes by a switch function. It solves the Boltzmann equation instead of the Euler equation. In this article, the main object is to evaluate the ability of this HLBFS scheme by our in-house cell centered hybrid mesh based Navier-Stokes code. Its performance is examined by several widely-used bench-mark test cases. The comparisons on results between calculation and experiment are conducted. They show that the scheme can capture the shock wave as well as the resolving of boundary layer.

Implementation and Verification of High-Order Accurate Discontinuous Galerkin Method on 2-D Unstructured Grids

In this paper, the discontinuous Galerkin method (DG) is applied to solve the 2D Euler equation. DG can be easily used in the unstructured girds, which has advantages in dealing with problems with complex boundaries. High order accuracy is achieved by higher order polynomial approximations within elements. In order to capture the shock without oscillation, the limiter is also applied. The performance of DG is illustrated by three numerical experimental tests, which show the potential of DG in engineering applications. The vortex propagation problem is to verify high-order accuracy of DG, while Sob problem and forward step problem are used to illustrate the ability to capture shock.