IMMERSED BOUNDARY-FINITE DIFFERENCE LATTICE BOLTZMANN METHOD USING TWO RELAXATION TIMES

ABSTRACT It is known that velocity fields computed by using an immersed boundary-lattice Boltzmann method (IB-LBM) with a single-relaxation time (SRT) show unphysical distortion when the relaxation time, τ, is high. The authors proposed an immersed boundary-finite difference lattice Boltzmann method (IB-FDLBM) using SRT to predict liquid-solid flows. In simulations with IB-FDLBM, numerical errors in the velocity fields appear as in IBLBMs when τ is high. A two-relaxation time (TRT) collision operator is therefore implemented into IB-FDLBM in this study to reduce numerical errors at high τ. Simulations of circular Couette flows show that the proposed method gives accurate predictions at high τ, provided that the magic parameter, which is a function of the relaxation times, is less than unity. In addition, predicted drag coefficients of a circular cylinder and a sphere at low Reynolds numbers show reasonable agreements with theoretical solutions and measured data

A coupled 3-dimensional bonded discrete element and lattice Boltzmann method for fluid-solid coupling in cohesive geomaterials

This paper presents a 3D bonded discrete element and lattice Boltzmann method for resolving the fluid‐solid interaction involving complicated fluid‐particle coupling in geomaterials. In the coupled technique, the solid material is treated as an assembly of bonded and/or granular particles. A bond model accounting for strain softening in normal contact is incorporated into the discrete element method to simulate the mechanical behaviour of geomaterials, whilst the fluid flow is solved by the lattice Boltzmann method based on kinetic theory and statistical mechanics. To provide a bridge between theory and application, a 3D algorithm of immersed moving boundary scheme was proposed for resolving fluid‐particle interaction. To demonstrate the applicability and accuracy of this coupled method, a benchmark called quicksand, in which particles become fluidised under the driving of upward fluid flow, is first carried out. The critical hydraulic gradient obtained from the numerical results matches the theoretical value. Then, numerical investigation of the performance of granular filters generated according to the well‐acknowledged design criteria is given. It is found that the proposed 3D technique is promising, and the instantaneous migration of the protected soils can be readily observed. Numerical results prove that the filters which comply with the design criteria can effectively alleviate or eliminate the appearance of particle erosion in dams

An immersed boundary-lattice-boltzmann method for the simulation of the flow past an impulsively started cylinder

We present a lattice-Boltzmann method coupled with an immersed boundary technique for the simulation of bluff body flows. The lattice-Boltzmann method for the modeling of the Navier-Stokes equations, is enhanced by a forcing term to account for the no-slip boundary condition on a non-grid conforming boundary. We investigate two alternatives of coupling the boundary forcing term with the grid nodes, namely the direct and the interpolated forcing techniques. The present LB-IB methods are validated in simulations of the incompressible flow past an impulsively started cylinder at low and moderate Reynolds numbers. We present diagnostics such as the near wall vorticity field and the drag coefficient and comparisons with previous computational and experimental works and assess the advantages and drawbacks of the two techniques

An experimental investigation of the flow around impulsively started cylinders

A study of impulsively started flow over cylindrical objects is made using the particle image velocimetry (PIV) technique for Reynolds numbers of Re = 200, 500 and 1000 in an X-Y towing tank. The cylindrical objects studied were a circular cylinder of diameter, D = 25.4 mm, and square and diamond cylinders each with side length, D = 25.4 mm. The aspect ratio, AR (= L/D) of the cylinders was 28 and therefore they were considered infinite. The development of the recirculation zone up to a dimensionless time of t* = 4 following the start of the motion was examined. The impulsive start was approximated using a dimensionless acceleration parameter, a*, and in this research, the experiments were conducted for five acceleration parameters, a* = 0.5, 1, 3, 5 and 10. The study showed that conditions similar to impulsively started motion were attained once a* ¡Ý 3. A recirculation zone was formed immediately after the start of motion as a result of flow separation at the surface of the cylinder. It contained a pair of primary eddies, which in the initial stages (like in this case) were symmetrical and rotating in opposite directions. The recirculation zone was quantified by looking at the length of the zone, LR, the vortex development, both in terms of the streamwise location and the cross-stream spacing of the vortex centers, a and b, respectively, as well as the circulation (strength) of the primary vortices, ¦£. For all types of cylinders examined, the length of the recirculation zone, the streamwise location of the primary eddies and the circulation of the primary eddies increase as time advances from the start of the impulsive motion. They also increase with an increase in the acceleration parameter, a*, until a* = 3, beyond which there is no more change, since the conditions similar to impulsively started conditions have been achieved. The cross-stream spacing of the primary vortices is relatively independent of Re, a* and t* but was different for different cylinders. Irrespective of the type of cylinder, the growth of the recirculation zone at Re = 500 and 1000 is smaller than at Re = 200. The recirculation zone of a diamond cylinder is much larger than for both square and circular cylinders. The square and diamond cylinders have sharp edges which act as fixed separation points. Therefore, the cross-stream spacing of the primary vortex centers are independent of Re, unlike the circular cylinder which shows some slight variation with changes in Reynolds number. The growth of the recirculation is more dependent on the distance moved following the start of the impulsive motion; that is why for all types of cylinders, the LR/D, a/D and ¦£/UD profiles collapse onto common curves when plotted against the distance moved from the start of the motion

Immersed Boundary Methods in the Lattice Boltzmann Equation for Flow Simulation

In this dissertation, we explore direct-forcing immersed boundary methods (IBM) under the framework of the lattice Boltzmann method (LBM), which is called the direct-forcing immersed boundary-lattice Boltzmann method (IB-LBM). First, we derive the direct-forcing formula based on the split-forcing lattice Boltzmann equation, which recovers the Navier-Stokes equation with second-order accuracy and enables us to develop a simple and accurate formula due to its kinetic nature. Then, we assess the various interface schemes under the derived direct-forcing formula. We consider not only diffuse interface schemes but also a sharp interface scheme. All tested schemes show a second-order overall accuracy. In the simulation of stationary complex boundary flows, we can observe that the sharper the interface scheme is, the more accurate the results are. The interface schemes are also applied to moving boundary problems. The sharp interface scheme shows better accuracy than the diffuse interface schemes but generates spurious oscillation in the boundary forcing terms due to the discontinuous change of nodes for the interpolation. In contrast, the diffuse interface schemes show smooth change in the boundary forcing terms but less accurate results because of discrete delta functions. Hence, the diffuse interface scheme with a corrected radius can be adopted to obtain both accurate and smooth results. Finally, a direct-forcing immersed boundary method (IBM) for the thermal lattice Boltzmann method (TLBM) is proposed to simulate non-isothermal flows. The direct-forcing IBM formulas for thermal equations are derived based on two TLBM models: a double-population model with a simplified thermal lattice Boltzmann equation (Model 1) and a hybrid model with an advection-diffusion equation of temperature (Model 2). The proposed methods are validated through natural convection problems with stationary and moving boundaries. In terms of accuracy, the results obtained from the IBMs based on both models are comparable and show a good agreement with those from other numerical methods. In contrast, the IBM based on Model 2 is more numerically efficient than the IBM based on Model 1. Overall, this study serves to establish the feasibility of the direct-forcing IB-LBM as a viable tool for computing various complex and/or moving boundary flow problems

Development of a flexible forcing immersed boundary-lattice Boltzmann method and its applications in thermal and particulate flows

Ph.DDOCTOR OF PHILOSOPH