Shintaro Takeuchi

An interface capturing method with a continuous function: The THINC method with multi-dimensional reconstruction

An interface capturing method with a continuous function is proposed within the framework of the volume-of-fluid (VOF) method. Being different from the traditional VOF methods that require a geometrical reconstruction and identify the interface by a discontinuous Heaviside function, the present method makes use of the hyperbolic tangent function (known as one of the sigmoid type functions) in the tangent of hyperbola interface capturing (THINC) method [F. Xiao, Y. Honma, K. Kono, A simple algebraic interface capturing scheme using hyperbolic tangent function, Int. J. Numer. Methods Fluids 48 (2005) 1023-1040] to retrieve the interface in an algebraic way from the volume-fraction data of multi-component materials. Instead of the 1D reconstruction in the original THINC method, a multi-dimensional hyperbolic tangent function is employed in the present new approach. The present scheme resolves moving interface with geometric faithfulness and compact thickness, and has at least the following advantages: (1) the geometric reconstruction is not required in constructing piecewise approximate functions; (2) besides a piecewise linear interface, curved (quadratic) surface can be easily constructed as well; and (3) the continuous multi-dimensional hyperbolic tangent function allows the direct calculations of derivatives and normal vectors. Numerical benchmark tests including transport of moving interface and incompressible interfacial flows are presented to validate the numerical accuracy for interface capturing and to show the capability for practical problems such as a stationary circular droplet, a drop oscillation, a shear-induced drop deformation and a rising bubble.

A consistent direct discretization scheme on Cartesian grids for convective and conjugate heat transfer

A new discretization scheme on Cartesian grids, namely, a consistent direct discretization scheme, is proposed for solving incompressible flows with convective and conjugate heat transfer around a solid object. The Navier-Stokes and the pressure Poisson equations are discretized directly even in the immediate vicinity of a solid boundary with the aid of the consistency between the face-velocity and the pressure gradient. From verifications in fundamental flow problems, the present method is found to significantly improve the accuracy of the velocity and the wall shear stress. It is also confirmed that the numerical results are less sensitive to the Courant number owing to the consistency between the velocity and pressure fields. The concept of the consistent direct discretization scheme is also explored for the thermal field; the energy equations for the fluid and solid phases are discretized directly while satisfying the thermal relations that should be valid at their interface. It takes different forms depending on the thermal boundary conditions: Dirichlet (isothermal) and Neumann (adiabatic/iso-heat-flux) boundary conditions for convective heat transfer and a fluid-solid thermal interaction for conjugate heat transfer. The validity of these discretizations is assessed by comparing the simulated results with analytical solutions for the respective thermal boundary conditions, and it is confirmed that the present schemes also show high accuracy for the thermal field. A significant improvement for the conjugate heat transfer problems is that the second-order spatial accuracy and numerical stability are maintained even under severe conditions of near-practical physical properties for the fluid and solid phases.

A numerical method for mass transfer by a thin moving membrane with selective permeabilities

We propose a numerical method for mass transfer by membrane movement in the framework of the non-conforming mesh with respect to the membrane. The method treats the discontinuity at the membrane by incorporating the concentration jump into the finite element discretization. Through coupling the weak forms of the unsteady convection-diffusion equation and membrane permeability equation, an implicit treatment of the jump value is derived, which is capable of handling both permeable and non-permeable membranes. Through some comparisons of the numerical tests with analytical solutions, the validity of the proposed method is established. The analytical solutions include the steady concentration distributions as well as transient state during the movement of the membrane. The method is applied to the mass transfer with a membrane of curved geometry, and the applicability for the membrane with arbitrary shape is demonstrated.

Interaction between fluid and flexible membrane structures by a new fixed-grid direct forcing method

A fixed-grid direct forcing method is newly developed to study interaction between a fluid and flexible thin membrane structure. The method is to undertake a consistency between the velocity and pressure fields by directly discretising the Navier-Stokes equation in the vicinity of the object, rather than interpolating the velocity from the ambient fluid. The method is validated through comparisons with the analytical and independent numerical solutions of several 2-D flow fields including moving membrane and objects. The result shows that the present method exhibits convergence at a rate of approximately first order with respect to the grid spacings. Also, the simulation result of a flapping flag in a uniform flow suggests that the predicted flapping criterion is similar to that by a stability theory, and that the tight momentum conservation due to the consistent discretisation enables a strong interaction of snapping behaviour of a heavier flag.

Wake Structures of a Particle in Straight and Curved Flows

To investigate the effect of non-axisymmetric shear on the wake structure of a particle, the flows around a single spherical particle in the following two kinds of shear flows are simulated: parallel (streamwise) shear and curved (cross-streamwise) shear flows. The ranges of the particle Reynolds number and the shear Reynolds number are determined by assuming that the particle size is comparable to the Kolmogorov length scale in a turbulent flow. The effect of the parallel shear on the perturbation velocity is small. For the curved shear, the wake region is deflected in space. However, the width of the wake is almost unchanged near the particle. For the fixed and translating particle cases, even if the streamlines of the undisturbed flow relative to the particle translation are similar to each other, the difference of the ambient pressure gradient makes the difference of the velocity distributions.

Numerical study of heat transfer problems in two-phase flows involving temperature distribution within dispersed solid particles

Heat transfer in solid-dispersed two-phase flow is simulated, and the effects of temperature distribution within the finite-sized particles on the flow structure, particle behaviour and heat transfer are studied. Temperature distribution within the particles is solved by an interfacial heat flux model with the discrete temperature field. The interfacial heat conduction model is validated through a comparison with the analytical solution of the heat conduction through eccentric cylinders of constant temperature difference. The method is applied to 2-D and 3-D natural convection problems in a confined container under relatively low Rayleigh numbers (104 ∼ 106). Particle behaviours are studied for different heat conductivity ratios (solid to fluid) ranging between 10−3 and 102. With particles of relatively low heat conductivity ratios ( 101), particulate flow structure shows a transition ...

Effect of Solid And Liquid Heat Conductivities on Two-Phase Heat and Fluid Flows

Liquid-solid two-phase flow with heat transfer is simulated, and the effects of temperature gradient within a solid object and particle mobility on heat transfer are studied. The interaction between fluid and particles is considered with our original immersed solid approach on a rectangular grid system. A discrete element model with soft-sphere collision is applied for particle-particle interaction. Governing equation of temperature is time-updated with an implicit treatment for the diffusion term, which enables stable simulation with particles of very high/low ratios of heat conductivity (from 1/1000 to 1000) to fluid. The local heat flux at the fluid-solid interface is carefully discretised and incorporated into the implicit scheme of temperature. The method is applied to a 2-D confined flow including multiple particles under a high Rayleigh number condition. Heat transfer and particle behaviours are studied for different ratios of heat conductivity (solid to liquid) and solid volume fractions. For a relatively low solid volume fraction, a transition of particulate flow pattern is observed depending on the heat conductivity ratio; the cases with high ratios of heat conductivities exhibit simple (single or double) circulating flows, whereas low heat conductivity ratio causes complicated flow patterns involving multiple circulation of particles, resulting in low Nusselt number. The above simulation results, together with the heat transfer properties under a near-packed condition, highlight the effect of temperature distributions within the particles and liquid.

Numerical Simulation of Unsteady Flow Through a Two-Dimensional Channel With a Vocal Cord Model

For the understanding of the phonation mechanism and for the design of an artificial vocal cord, we developed a computational method for the fluid-structure interaction, including the elastic walls and membranes. A robust and efficient method is required to deal with large deformation of biological materials and high frequency vibration. To this end, we apply an immersed boundary method. The flow through a two-dimensional channel including a pair of flexible structures, which is a simplification of a vocal cord, is simulated. The elastic solid is modeled by the St. Venant-Kirchhoff constitutive equation and its motion is simulated by a finite-element method, where the contact of the vocal cord is taken into account by a Lagrange multiplier method. The incompressible fluid flow is computed by a finite-difference method. Then the immersed-boundary method of a body-force type developed by the authors is successfully applied for the fluid-structure interaction. In the present results, the deformation of the structure and the frequency of the pulsating flow are reasonably reproduced. The obtained frequency is within the measured range of the data for a human vocal cord. Also, two velocity peaks are observed when the vocal cord is in the opening and closing phases in each period of the vocal cord vibration, and the velocity of the closing phase is larger than that of the opening phase.Copyright