Fluid dynamic turbulence is one of the most challenging computational physics problems because of the extremely wide range of time and space scales involved, the strong nonlinearity of the governing equations, and the many practical and important applications. While most linear fluid instabilities are well understood, the nonlinear interactions among them makes even the relatively simple limit of homogeneous isotropic turbulence difficult to treat physically, mathematically, and computationally. Turbulence is modeled computationally by a two-stage bootstrap process. The first stage, direct numerical simulation, attempts to resolve the relevant physical time and space scales but its application is limited to diffusive flows with a relatively small Reynolds number (Re). Using direct numerical simulation to provide a database, in turn, allows calibration of phenomenological turbulence models for engineering applications. Large eddy simulation incorporates a form of turbulence modeling applicable when the large-scale flows of interest are intrinsically time dependent, thus throwing common statistical models into question. A promising approach to large eddy simulation involves the use of high-resolution monotone computational fluid dynamics algorithms such as flux-corrected transport or the piecewise parabolic method which have intrinsic subgrid turbulence models coupled naturally to the resolved scales in the computed flow. The physical considerations underlying and evidence supporting this monotone integrated large eddy simulation approach are discussed.

New insights into large eddy simulation

A flux splitting scheme is proposed for the general nonequilibrium flow equations with an aim at removing numerical dissipation of Van-Leer-type flux-vector splittings on a contact discontinuity. The scheme obtained is also recognized as an improved Advection Upwind Splitting Method (AUSM) where a slight numerical overshoot immediately behind the shock is eliminated. The proposed scheme has favorable properties: high-resolution for contact discontinuities; conservation of enthalpy for steady flows; numerical efficiency; applicability to chemically reacting flows. In fact, for a single contact discontinuity, even if it is moving, this scheme gives the numerical flux of the exact solution of the Riemann problem. Various numerical experiments including that of a thermo-chemical nonequilibrium flow were performed, which indicate no oscillation and robustness of the scheme for shock/expansion waves. A cure for carbuncle phenomenon is discussed as well.

A Flux Splitting Scheme with High-Resolution and Robustness for Discontinuities(Proceedings of the 12th NAL Symposium on Aircraft Computational Aerodynamics)

Heat transfer augmentation using a magnetic fluid under the influence of a line dipole

Hydrogen production using methane: Techno-economics of decarbonizing fuels and chemicals

Geometric conservation law and applications to high-order finite difference schemes with stationary grids

Two phases produced through the liquid-liquid separation gravitationally segregate during solidification of the monotectic alloys. This paper examined reduction of the gravity segregation for the Cu-Pb monotectic alloys by imposing a static magnetic field up to 10 T. The Cu-Pb alloys with compositions ranging from 15.5 to 84.5 at% Pb solidified at a cooling rate of 10 K/s under a magnetic field. The effect of the magnetic field on the macrosegregation was clearly recognized for the Cu-Pb alloys with compositions ranging from 65 to 70 at% Pb, while the magnetic field did not become a dominant factor of the segregation behavior in the other compositions. Furthermore, diameter of the Cu-rich liquid drops under 10 T was smaller than that under 0 T. The static magnetic field reduced not only the rising velocity of the Cu-rich drops but also the coalescence rate of the liquid drops, resulting in the reduction of the macrosegregation. The magnetohydrodynamic estimation suggested that the terminal velocity of the Cu-rich particles with typical diameters is significantly reduced by the imposed static magnetic field. The difficulty of the particle movement due to the electromagnetic force resulted in the homogenous solidified structure for the Cu-Pb alloys.

Effect of Magnetic Field on Solidification in Cu-Pb Monotectic Alloys

A set of new theoretical equations for apparent contact angles is proposed. The equations are derived from an equilibrium of interfacial tensions of a three-phase contact line pinned at the edges of a fine structure. These equations are validated by comparison with contact-angle measurement results for 2 μL water droplets on poly(methyl methacrylate) microstructured samples with square pillars or holes. The equilibrium contact angles predicted by the new equations reasonably agree with the experimental results. In contrast, the values predicted by the Cassie–Baxter equation or the Wenzel equation do not qualitatively agree with the experimental results in pillar pattern cases because the Cassie–Baxter equation and the Wenzel equation do not account for the pinning effect.

Apparent Contact Angle Calculated from a Water Repellent Model with Pinning Effect

For the aim of computing compressible turbulent flowfield involving shock waves, an implicit large eddy simulation (LES) code has been developed based on the idea of monotonically integrated LES. We employ the weighted compact nonlinear scheme (WCNS) not only for capturing possible shock waves but also for attaining highly accurate resolution required for implicit LES. In order to show that WCNS is a proper choice for implicit LES, a two-dimensional homogeneous turbulence is first obtained by solving the Navier―Stokes equations for incompressible flow. We compare the inertial range in the computed energy spectrum with that obtained by the direct numerical simulation (DNS) and also those given by the different LES approaches. We then obtain the same homogeneous turbulence by solving the equations for compressible flow. It is shown that the present implicit LES can reproduce the inertial range in the energy spectrum given by DNS fairly well. A truncation of energy spectrum occurs naturally at high wavenumber limit indicating that dissipative effect is included properly in the present approach. A linear stability analysis for WCNS indicates that the third order interpolation determined in the upwind stencil introduces a large amount of numerical viscosity to stabilize the scheme, but the same interpolation makes the scheme weakly unstable for waves satisfying kΔx ≈ 1. This weak instability results in a slight increase in the energy spectrum at high wavenumber limit. In the computed result of homogeneous turbulence, a fair correlation is shown to exist between the locations where the magnitude of ∇ × ω becomes large and where the weighted combination of the third order interpolations in WCNS deviates from the optimum ratio to increase the amount of numerical viscosity. Therefore, the numerical viscosity involved in WCNS becomes large only at the locations where the subgrid-scale viscosity can arise in ordinary LES. This suggests the reason why the present implicit LES code using WCNS can resolve turbulent flow field reasonably well.

Implicit Large Eddy Simulation of Two-Dimensional Homogeneous Turbulence Using Weighted Compact Nonlinear Scheme

Three-dimensional numerical computations for a single bubble rising in a liquid metal within a rectangular enclosure in a uniform vertical magnetic field are carried out In this study, the bubble shape, the velocity field and the electric current density field interact with one another under the influence of the vertical magnetic field This is a triple simultaneous problem The pressure and the electric potential fields are obtained with an iterative procedure by the HSMAC method The numerical results exhibit that the rising velocity of the bubble for the range of Hartmann number 0 75 owing to deceleration effect on the fluid flow by the magnetic field The bubble elongates in the direction of the uniform magnetic field because of the modification of the pressure distribution by the Lorentz force

Kazuyuki Ueno

Papers

Effect of Magnetic Field on Solidification in Cu-Pb Monotectic Alloys

Apparent Contact Angle Calculated from a Water Repellent Model with Pinning Effect

Implicit Large Eddy Simulation of Two-Dimensional Homogeneous Turbulence Using Weighted Compact Nonlinear Scheme

Computation of a Rising Bubble in an Enclosure Filled with Liquid Metal under Vertical Magnetic Fields

Numerical simulation of deformed single bubbles rising in magnetic fluid