A stress tensor discontinuity-based immersed boundary-lattice Boltzmann method

We propose an immersed boundary-lattice Boltzmann method using the discontinuity of the stress tensor. In the immersed boundary method, the body force which is applied to enforce the no-slip boundary condition is equivalent to the discontinuity of the stress tensor across the boundary. In the proposed method, the boundary is expressed by Lagrangian points independently of the background lattice points, and the discontinuity of the stress tensor is calculated on these points from desired particle distribution functions which satisfy the no-slip boundary condition based on the bounce-back scheme. By using this method, we can obtain the force locally acting on the boundary from the stress tensor of one side of the fluids divided by the boundary, and there is no need to consider the internal mass effect in calculating the total force and torque acting on the boundary. To our best knowledge, the present method is the first one which enables us to calculate the stress tensor on the boundary in the class of the diffusive interface method. In order to validate the present method, we apply it to simulations of typical moving-boundary problems, i.e., a Taylor-Couette flow, an oscillating circular cylinder in a stationary fluid, the sedimentation of an elliptical cylinder, and the sedimentation of a sphere. As a result, the present method has the first-order spatial accuracy and has a good agreement with other numerical and experimental results. In addition, we discuss two problems of the present method, i.e., penetration and spurious oscillation of local force, and a possible remedy for them. (C) 2018 Elsevier Ltd. All rights reserved.ArticleCOMPUTERS & FLUIDS.172: 593-608(2018)journal articl

Lattice Boltzmann simulation of motion of red blood cell in constricted circular pipe flow

The lattice Boltzmann method for two-phase flows containing a deformable body with a viscoelastic membrane is improved to simulate circular pipe flows by incorporation of the immersed boundary method. In order to examine the validity of the red blood cell (RBC) model, the method is applied to the motion of a biconcave disk-shaped body in a pressure-driven circular pipe flow. The validation is demonstrated by investigating the relation between the deformation index and terminal axial velocity of the RBC in the pipe flow. In this study, the behavior of a biconcave disk-shaped body in constricted pipe flows is simulated under various geometrical conditions. The square and circular pipes with various lengths and sizes of the constriction are considered, and the flow is induced by the pressure difference between the inlet and outlet. From the results, it is found that as the length of the constriction becomes smaller, the body is deformed larger and accelerated at the entrance and exit in the constriction, although the speed of the body is reduced while passing through the constriction. Also, it is found that as the size of the constriction becomes larger, the deformation index linearly decreases and the axial velocity exponentially increases. These results indicate that the present method has applicability to simulation of the motion of RBCs in microscale capillary blood vessels.ArticleJournal of Fluid Science and Technology.9(3):JFST0031(2014)journal articl

A trapezoidal wing equivalent to a Janatella leucodesma's wing in terms of aerodynamic performance in the flapping flight of a butterfly model

Wing planform is one of the most important factors for lift and thrust generation and enhancement in flapping flight. In a previous study based on a simple numerical model of a butterfly, we found that the wing planform of an actual butterfly (Janatella leucodesma) is more efficient than any rectangular or trapezoidal wing planform. In the present study, we make a hypothesis that the efficient aerodynamic performance of a butterfly's wings can be reproduced by the following four geometrical parameters of wing planform: aspect ratio, taper ratio, position of the rotational axis for the geometric angle of attack, and sweepback angle. In order to test this hypothesis, we explore a trapezoidal wing planform equivalent to an actual butterfly's wing planform in terms of aerodynamic performance in a parameter space consisting of these four parameters. We use a simple butterfly model composed of two rigid thin wings and a rod-shaped body and calculate the aerodynamic performance of the model by an immersed boundary-lattice Boltzmann method to find such a trapezoidal wing planform. As a result, we find a trapezoidal wing planform which gives almost the same lift, thrust, pitching moment, power, and power-loading coefficients as an actual butterfly's wing planform. Furthermore, in the free flight of the butterfly model with pitching motion control, the flight behavior of the model with the resulting trapezoidal wing planform is almost the same as that with an actual butterfly's wing planform.ArticleBIOINSPIRATION & BIOMIMETICS.14(3):036003(2019)journal articl

Aerodynamic comparison of a butterfly-like flapping wing-body model and a revolving-wing model

The aerodynamic performance of flapping- and revolving-wing models is investigated by numerical simulations based on an immersed boundary-lattice Boltzmann method. As wing models, we use (i) a butterfly-like model with a body and flapping- rectangular wings and (ii) a revolving-wing model with the same wings as the flapping case. Firstly, we calculate aerodynamic performance factors such as the lift force, the power, and the power loading of the two models for Reynolds numbers in the range of 50-1000. For the flapping-wing model, the power loading is maximal for the maximum angle of attack of 90 degrees, a flapping amplitude of roughly 45 degrees, and a phase shift between the flapping angle and the angle of attack of roughly 90 degrees. For the revolving-wing model, the power loading peaks for an angle of attack of roughly 45 degrees. In addition, we examine the ground effect on the aerodynamic performance of the revolving-wing model. Secondly, we compare the aerodynamic performance of the flapping- and revolving-wing models at their respective maximal power loadings. It is found that the revolving-wing model is more efficient than the flapping- wing model both when the body of the latter is fixed and where it can move freely. Finally, we discuss the relative agilities of the flapping- and revolving-wing models.ArticleFLUID DYNAMICS RESEARCH.49(3):035512(2017)journal articl

Three-Dimensional Lattice Boltzmann Simulation of Two-Phase Flow Containing a Deformable Body with a Viscoelastic Membrane

First published in Communications in Commun. Comput. Phys. in No. 5, 9 (2011), published by Global Science PressThe lattice Boltzmann method (LBM) with an elastic model is applied to the simulation of two-phase flows containing a deformable body with a viscoelastic membrane. The numerical method is based on the LBM for incompressible two-phase fluid flows with the same density. The body has an internal fluid covered by a viscoelastic membrane of a finite thickness. An elastic model is introduced to the LBM in order to determine the elastic forces acting on the viscoelastic membrane of the body. In the present method, we take account of changes in surface area of the membrane and in total volume of the body as well as shear deformation of the membrane. By using this method, we calculate two problems, the behavior of an initially spherical body under shear flow and the motion of a body with initially spherical or biconcave discoidal shape in square pipe flow. Calculated deformations of the body (the Taylor shape parameter) for various shear rates are in good agreement with other numerical results. Moreover, tank-treading motion, which is a characteristic motion of viscoelastic bodies in shear flows, is simulated by the present method.ArticleCommunications in Computational Physics. 9(5):1397-1413 (2011)journal articl

Effect of wing mass in free flight of a two-dimensional symmetric flapping wing-body model

The effect of wing mass in the free flight of a flapping wing is investigated by numerical simulations based on an immersed boundary-lattice Boltzmann method. We consider a model consisting of two-dimensional symmetric flapping wings with uniform mass density connected by a body represented as a point mass. We simulate free flights of the two-dimensional symmetric flapping wing with various mass ratios of the wings to the body. In free flights without gravity, it is found that the time-averaged lift force becomes smaller as the mass ratio increases, since with a large mass ratio the body experiences a large vertical oscillation in one period and consequently the wing-tip speed relatively decreases. We define the effective Reynolds number Reeff taking the body motion into consideration and investigate the critical value of Reeff over which the symmetry breaking of flows occurs. As a result, it is found that the critical value is Re-eff similar or equal to 70 independently of the mass ratio. In free flights with gravity, the time-averaged lift force becomes smaller as the mass ratio increases in the same way as free flights without gravity. In addition, the unstable rotational motion around the body is suppressed as the mass ratio increases, since with a large mass ratio the vortices shedding from the wing tip are small and easily decay.ArticleFLUID DYNAMICS RESEARCH.49(5):055504(2017)journal articl

Lattice Boltzmann simulation of nucleate pool boiling in saturated liquid

First published in Communications in Commun. Comput. Phys. in No. 5, 9 (2011), published by Global Science PressA thermal lattice Boltzmann method (LBM) for two-phase fluid flows in nucleate pool boiling process is proposed. In the present method, a new function for heat transfer is introduced to the isothermal LBM for two-phase immiscible fluids with large density differences. The calculated temperature is substituted into the pressure tensor, which is used for the calculation of an order parameter representing two phases so that bubbles can be formed by nucleate boiling. By using this method, two-dimensional simulations of nucleate pool boiling by a heat source on a solid wall are carried out with the boundary condition for a constant heat flux. The flow characteristics and temperature distribution in the nucleate pool boiling process are obtained. It is seen that a bubble nucleation is formed at first and then the bubble grows and leaves the wall, finally going up with deformation by the buoyant effect. In addition, the effects of the gravity and the surface wettability on the bubble diameter at departure are numerically investigated. The calculated results are in qualitative agreement with other theoretical predictions with available experimental data.ArticleCommunications in Computational Physics. 9(5):1347-1361 (2011)journal articl