Xiao-Dong Niu

An improved momentum exchanged-based immersed boundary-lattice Boltzmann method by using an iterative technique

A novel immersed boundary-lattice Boltzmann method (IB-LBM) is proposed for incompressible viscous flows in complex geometries. Based on the momentum exchanged-based IB-LBM, an iterative technique is introduced to enforce the non-slip boundary condition at the boundary points. Moreover, the proposed IB-LBM overcomes the drawback that the numerical results of the previous work (Wu and Shu, 2009) which is affected by the distribution of Lagrangian points. A simple theoretical analysis is developed to obtain the optimal iteration parameters. Numerical results show that the present scheme has second-order accuracy and is not affected by the distribution of Lagrangian points. It also shows that the non-slip boundary condition is satisfied on the boundary. This verifies that our IB-LBM is capable of simulating flow problems with complex boundaries.

Full Eulerian lattice Boltzmann model for conjugate heat transfer.

In this paper a full Eulerian lattice Boltzmann model is proposed for conjugate heat transfer. A unified governing equation with a source term for the temperature field is derived. By introducing the source term, we prove that the continuity of temperature and its normal flux at the interface is satisfied automatically. The curved interface is assumed to be zigzag lines. All physical quantities are recorded and updated on a Cartesian grid. As a result, any complicated treatment near the interface is avoided, which makes the proposed model suitable to simulate the conjugate heat transfer with complex interfaces efficiently. The present conjugate interface treatment is validated by several steady and unsteady numerical tests, including pure heat conduction, forced convection, and natural convection problems. Both flat and curved interfaces are also involved. The obtained results show good agreement with the analytical and/or finite volume results.

A mass-conserved diffuse interface method and its application for incompressible multiphase flows with large density ratio

In this work a mass-conserved diffuse interface method is proposed for simulating incompressible flows of binary fluids with large density ratio. In the method, a mass correction term is introduced into the Cahn-Hilliard equation to compensate the mass losses or offset the mass increases caused by the numerical and modeling diffusion. Since the mass losses or increases are through the phase interfaces and at each time step, their values are very small, to keep mass conservation, mass sources or sinks are introduced and uniformly distributed in the volume of diffuse layer. With the uniform distribution, the mass correction term representing mass sources or sinks is derived analytically by applying mass conservation principle. By including the mass correction, the modified Cahn-Hilliard equation is solved by the fifth-order upwind scheme to capture the phase field of the bindery fluids. The flow field is simulated by the newly-developed multiphase lattice Boltzmann flux solver 20]. The proposed approach is validated by simulating the Laplace law, the merging of two bubbles, Rayleigh-Taylor instability and bubble rising under gravity with density ratio of 1000 and viscosity ratio of 100. Numerical results of interface shapes and flow properties agree well with both analytical solutions and benchmark data in the literature. Numerical results also show that the mass is well-conserved in all cases considered. In addition, it is demonstrated that the mass correction term at each time step is in the order of 10 - 4 ~ 10 - 5 , which is a small number compared with the magnitude of order parameter.

Natural Convection in a Concentric Annulus: A Lattice Boltzmann Method Study with Boundary Condition-Enforced Immersed Boundary Method

In this paper, a boundary condition-enforced IBM is introduced into the LBM in orderto satisfy the non-slip and temperatureboundary conditions, and natural convections in a concentric isothermal annulus between a square outer cylinder and a circular inner cylinder are simulated. The obtained results show that the boundary condition-enforced method gives a better solution for the flow field and the compli- cated physics of the natural convections in the selected case is correctly captured. The calculated average Nusselt numbers agree well with the previous studies. AMS subject classifications: 76R10

Damping characteristics and flow behaviors of an ER fluid with a piston sine vibration in a viscous damper

The damping characteristics and flow behaviors of ER fluids inside a piston–cylinder viscous damper subjected to external electric fields are studied based on experiment, theoretical analysis and numerical simulation. The viscous damper is a closed system with an inner piston and an outer cylinder, which is designed and constructed in our laboratory. In the experiment, the test ER fluid is enclosed in the gap of a piston–cylinder system. To examine the damping characteristics of the test ER fluid, a piston sine vibration experiment is performed with accompanying theoretical analyses. In addition, in order to investigate the ER flow behaviors inside the damper, a numerical simulation is carried out. The present study discloses the damping characteristics and the fluid mechanism of the ER fluid in the piston–cylinder damper with an applied external electric field.

Investigation of Impulse Response of an ER Fluid Viscous Damper

The electrorheological (ER) fluid is a fluid that shows non-Newtonian fluid characteristics when the electrical field is applied. In this study, an experiment of an ER fluid viscous damper, in which an ER fluid is enclosed in the gap of a piston—cylinder system, is carried out to investigate the performances of the ER fluids and the effects of the electric field on the impulse response of the damper when an impulsive force is applied to it. To validate the experimental observations, a theoretical cylinder displacement formula of the damper is derived based on the Bingham approximation and the Stokes flow assumption of the test ER fluids in the damper. The present study shows that, when strength of the applied electric field and concentration of the ER fluids increase, the oscillation amplitudes of the cylinder displacement reduce. In other words, the ER damping effect is improved when the strength of the electric field increases.

Finite-volume method with lattice Boltzmann flux scheme for incompressible porous media flow at the representative-elementary-volume scale.

Based on the Darcy-Brinkman-Forchheimer equation, a finite-volume computational model with lattice Boltzmann flux scheme is proposed for incompressible porous media flow in this paper. The fluxes across the cell interface are calculated by reconstructing the local solution of the generalized lattice Boltzmann equation for porous media flow. The time-scaled midpoint integration rule is adopted to discretize the governing equation, which makes the time step become limited by the Courant-Friedricks-Lewy condition. The force term which evaluates the effect of the porous medium is added to the discretized governing equation directly. The numerical simulations of the steady Poiseuille flow, the unsteady Womersley flow, the circular Couette flow, and the lid-driven flow are carried out to verify the present computational model. The obtained results show good agreement with the analytical, finite-difference, and/or previously published solutions.

A free energy-based surface tension force model for simulation of multiphase flows by level-set method

In this paper, a free energy-based surface tension force (FESF) model is presented for accurately resolving the surface tension force in numerical simulation of multiphase flows by the level set method. By using the analytical form of order parameter along the normal direction to the interface in the phase-field method and the free energy principle, FESF model offers an explicit and analytical formulation for the surface tension force. The only variable in this formulation is the normal distance to the interface, which can be substituted by the distance function solved by the level set method. On one hand, as compared to conventional continuum surface force (CSF) model in the level set method, FESF model introduces no regularized delta function, due to which it suffers less from numerical diffusions and performs better in mass conservation. On the other hand, as compared to the phase field surface tension force (PFSF) model, the evaluation of surface tension force in FESF model is based on an analytical approach rather than numerical approximations of spatial derivatives. Therefore, better numerical stability and higher accuracy can be expected. Various numerical examples are tested to validate the robustness of the proposed FESF model. It turns out that FESF model performs better than CSF model and PFSF model in terms of accuracy, stability, convergence speed and mass conservation. It is also shown in numerical tests that FESF model can effectively simulate problems with high density/viscosity ratio, high Reynolds number and severe topological interfacial changes. A free energy-based surface tension force (FESF) model is proposed for simulation of multiphase flows by level set method.The proposed model computes the surface tension force by an explicit form.The proposed model outperforms the existing models in terms of accuracy, stability, convergence speed and mass conservation.The proposed model can effectively simulate multiphase flows.

Lattice Boltzmann flux scheme for the convection-diffusion equation and its applications

In this work a lattice Boltzmann flux scheme for the convection-diffusion equation (CDE) is proposed. In this scheme, the fluxes across the cell interface are calculated by using the local solution of the multiple-relaxation-time lattice Boltzmann equation for CDE. The present method is suitable for simulating both isotopic and anisotropic diffusion processes. Meanwhile, through applying the midpoint time integration technique, the present method relaxes the time step constraint in the original lattice Boltzmann flux scheme. Four convection-diffusion problems are simulated to validate the present scheme. The obtained results agree well with the analytical or previous published solutions.

Solid-Liquid Two-Phase Flow Measurement Using an Electromagnetically Induced Signal Measurement Method

An electromagnetically induced signal measurement method is presented to measure solid-liquid two-phase flows in the present study. The method is validated by comparing visualization results for three flow patterns of “pseudo-homogenous flow,” “heterogeneous flow” and “heterogeneous and sliding-bed flow.” The present method has demonstrated a promising capability of measuring concentration and velocity of solid particles simultaneously with good accuracy.