We propose a new algorithm for producing computer graphics of melting and evaporation process of matter. Such a computation becomes possible by a universal solver for solid, liquid and gas based on the CIP (Cubic-Interpolated Propagation / Constrained Interpolation Profile) method proposed by one of the authors. This method can also be applied to the movement, deformation and even break up of solid, liquid and gas in one simple algorithm. Therefore seamless computation of all the phases of matter becomes possible. This enables us to reproduce natural phenomena in some instances by computation. In order to demonstrate this reality, we show how precisely the computational result replicates the movies of real phenomena. The flattering motions of metal disk in water and thin name card in air are treated showing accuracy of force calculation on the surface of sub-grid scale. Although the CIP uses semi-Lagrangian form algorithm, the exact mass conservation is guaranteed by additional tool. By using this scheme, separation of a bubble in bifurcation tube and splashing of water surface are successfully simulated.
This paper presents a practical numerical method for incompressible flows by combining the concept of the CIP method and the finite volume formulation. The method, namely VSIAM3 (Volume/Surface Integrated Average based Multi-Moment Method), employs two integrated averages, i.e. Volume Integrated Average (VIA) and Surface Integrated Average (SIA) which are generically called integrated moments of the dependent variable herein. Using both VIA and SIA as the model variables, VSIAM3 is different from any existing conventional finite volume method and can be interpreted as the simplest finite volume method of the CIP type. Previous studies show that VSIAM3 has accurate numerical dispersion, compact mesh stencil and flexibility for various fluid problems. In this paper, the author will briefly introduce the general framework of VSIAM3 and its implementation to incompressible flows.
This paper concerns the cubic interpolation with volume/area coordinates (CIVA) method, which is an extension of the cubic interpolation profile (CIP) to a triangular or tetrahedral mesh system, implemented in an unstructured and fixed (Eulerian) mesh-based finite-volume solver. First, we briefly explain the accuracy of and the results of stability analysis by CIVA. Then, to demonstrate the accuracy and robustness of the algorithm, we solve two-dimensional benchmark problems of incompressible lid-driven recirculating flow in square and triangular cavities. In addition, a two-dimensional vortex-driven flow is solved in order to analyze the conservative property of CIVA. Finally, an example of an industrial application of CIVA method is described. These numerical experiments demonstrate the high capability of the method and that it is sufficiently robust for complex industrial applications.
An Interpolated Differential Operator (IDO) scheme using a new interpolation function is proposed. The gradient of the dependent variable is calculated at the position shifted by a half grid size from that of the physical value. A fourth-order Hermite-interpolation function is constructed locally using both the value and the gradient defined at staggered positions. The numerical solutions for the Poisson, diffusion, advection and wave equations have fourth-order accuracy in space. In particular, for the Poisson and diffusion equations, the Gradient-Staggered (G-S) IDO scheme shows better accuracy than the original IDO scheme. As a practical application, the Direct Numerical Simulation (DNS) for two-dimensional isotropic homogeneous turbulence is examined and a comparable result with that of the original IDO scheme is obtained. The G-S IDO scheme clearly contributes to high-accurate computations for solving partial differential equations in computational mechanics.
A new numerical method for solving a flow with a free water surface and an arbitrary topography is described. The method is based on the constrained interpolation profile (CIP) scheme and the finite-element method (FEM). Although advection terms are accurately solved using the conventional CIP scheme, nonadvection terms are solved by FEM. To solve nonadvection terms, the reversed weighted residual method (RWRM) based on FEM is proposed. Using the RWRM, surface boundary conditions can be imposed on an arbitrarily curved water surface appropriately even if a simple Cartesian mesh system is employed and the surface is not fitted to the boundaries of a computational mesh. Furthermore, in this paper, an algorithmic improvement in the pressure acceleration phase is proposed. By using the improved numerical procedure, the computational cost due to a matrix-solution can be reduced efficiently. The improved CIP-RWRM solver is applied to 2-D solutions to examine its efficiency and accuracy. The computational results show good agreements with the results calculated by other numerical methods for a multiphase flow.
The algorithm for mold-filling simulation with consideration of surface tension has been developed based on the CIP method. As a test problem, a squeeze casting simulation was taken up. As an application to a practical casting problem, we also applied this scheme to a die-casting simulation and compared the numerical results with the experimental data on the size and the position of blow holes. Numerical results both with and without surface tension indicated the existence of blow holes. However, the simulation without surface tension tended to underestimate the size of blow holes. Through these numerical results, it is confirmed that the consideration of surface tension is very important for predicting the size and the position of gas trapped in mold cavities. Furthermore, we propose a criterion for estimating whether the gas remaining in the cavity is compressed or expanded during mold filling, and adopt it to a practical die-casting problem.
For the prediction of sloshing in the propellant tank of a rocket vehicle, the preliminary investigation was conducted. The flow field in the propellant tank during the ballistic flight of the vehicle was experimentally reproduced with the sub-scale model. The lateral acceleration as large as about 0.8G was provided with a mechanical exciter and the deformation of the liquid surface in the small vessel was visualized with a high-speed camera. The sloshing phenomena were also simulated with the CFD code, called CIP-LSM. The important features of surface deformation and wave breaking were successfully reproduced in the computation.
For atmospheric and oceanic modeling, the equations of motion are numerically solved in either momentum form or vorticity form. Since vorticity is a conservative quantity in the Lagrangian sense, it has been considered that the vorticity form discretization scheme is more appropriate for the simulation of atmospheric and oceanic flows. However, it requires a Poisson solver to obtain the streamfunction from the vorticity: the use of a Poisson solver is thought to be a drawback for high-resolution atmospheric and oceanic modeling. In contrast, a Poisson solver is not required if the momentum form discretization scheme is applied to compressible flows. In this study, we propose a new advection scheme which possesses the advantages of both schemes: conservation of vorticity and no need for a Poisson solver. Both velocity components and vorticity are temporally integrated using the semi-Lagrangian method by constructing a unified interpolation function for velocity components and vorticity. We apply this scheme to a two-dimensional shear instability problem, and have found that this scheme gives a result competitive with the vorticity form scheme and is more accurate than the momentum form scheme.
In order to improve the model representation, we have implemented the CIP-CSLR in meteorological models. Real-case simulations and idealized tests were carried out on the Earth Simulator with atmospheric general circulation models that only the watervapor and liquid water were transported with the CIP-CSLR method. Numerical experiments show that the CIP-CSLR scheme substantially improved the model outputs for both pure advection tests and the long-term climate simulations. Reasonable tropical precipitation is shown with the CIP-CSLR scheme, which is largely improved in comparison with the original spectral method. Using the CIP-CSLR on a new grid (Yin-Yang) system, we also achieved conservative and more accurate results of passive tracer advection with relatively fewer grid points compared with the latitude-longitude grid. Without polar singularity, the splitting procedure of CIP-CSLR achieves promising transport in spherical geometry even if large Courant number is specified.
A numerical method is developed for prediction of large deformations associated with a geomaterial flow. The geomaterial is modeled as a viscous fluid, where a Bingham type constitutive model is proposed based on Mohr-Coulomb's failure criterion and the equivalent Newtonian viscosity is derived from the cohesion and friction angle. These two parameters are very important factors for the behavior of geomaterials. In solving Navier-Stokes's equations, a constrained interpolated profile (CIP) scheme is utilized. The numerical method developed in this paper is used to simulate a 2-dimensional gravitational flow in order to check the performance of the constitutive model. The method is also applied to two real slope failures. One is due to heavy rain and the other due to earthquake. In the analysis of the slope failure due to earthquake, simulated velocity of ground flow, displacement and elapsed time are compared with observed results. In the case of the analysis of the slope failure due to heavy rain, a previous study about the slope failure using finite element method (FEM) is firstly introduced. The method used in the previous study, however, could not describe the subsequent ground flow after the initiation of slope failure. Therefore, the method developed in this paper is applied to simulate the ground flow.
This paper demonstrates the usefulness of the CIP-combined unified procedure (C-CUP) to perform numerical simulations of a compressible flow of a suspension. As a conspicuous example of such a flow, we present three-dimensional numerical simulations of a pyroclastic surge, which spreads laterally over the ground surface during some volcanic eruptions as occurred at Unzen Volcano in 1991-1995. Since a pyroclastic surge suspends numerous solid particles, the density of a pyroclastic surge cannot be approximated by the equation of state for an ideal gas. On the other hand, a pyroclastic surge greatly changes its density as it heats and expands the air mixed from the calm surroundings. The above characteristics bring unique features into the motion of a pyroclastic surge. The features are successfully simulated by C-CUP with a slight modification owing to the fact that C-CUP can incorporate the equation of state of an arbitrary form.
The numerical methods of CIP (Cubic Interpolation Pseudo-particle/Propagation) and C-CUP (CIP Combined Unified Procedure) are appropriate and numerically robust even in the direct simulation of turbulent combustible flows. Although these methods have many advantages in the numerical procedure, their accuracy and characteristics have not been evaluated in detail. In the present study, the ability of CIP was firstly examined by comparing it with classical methods in a direct numerical simulation of incompressible turbulent flow. Secondly, C-CUP was evaluated by direct simulations of a compressible-fluid, single-vortex convection problem and of the Aeolian tone. In the first cases, CIP was inferior to the classical method in the vortex shape reproduction. In the latter case, C-CUP showed an advantage in suppressing unrealistic pressure increase and satisfactorily simulated the sound pressure distribution. Furthermore, CIP and C-CUP were applied to numerical simulation of spray combustion in conjunction with applying classical methods in order to compensate the inferior points of CIP.
In this paper, we show that a new numerical method, the Constrained Interpolation Profile - Basis Set (CIP-BS) method, can solve partial differential equations (PDEs) with high accuracy and can be a universal solver by presenting examples for the solutions of typical parabolic, hyperbolic, and elliptic equations. Here, we present the numerical errors caused by this method, and illustrate that the solutions by the CIP-BS2 method, in which fifth order polynomials are used to constrain the values and first and second order spatial derivatives, are highly refined compared to those by the CIP-BS1 method, in which third order polynomials are used to constrain the values and first order spatial derivatives. The fact that this method can unambiguously solve PDEs with an one-to-one correspondence to analytical requirements is also shown for PDEs including singular functions like the Dirac delta function with Dirichet or Neumann boundary conditions. This method is straightforwardly applicable to PDEs describing complex physical and engineering problems.
In this paper, we show that a new numerical method, the Constrained Interpolation Profile - Basis Set (CIP-BS) method, can solve general hyperbolic equations efficiently. This method uses a simple polynomial basis set that is easily extendable to any desired higher-order accuracy. The interpolating profile is chosen so that the subgrid scale solution approaches the local real solution owing to the constraints from the spatial derivatives of the master equations. Then, introducing scalar products, the linear and nonlinear partial differential equations are uniquely reduced to the ordinary differential equations for values and spatial derivatives at the grid points. The method gives stable, less diffusive, and accurate results. It is successfully applied to the continuity equation, the Burgers equation, the Korteweg-de Vries equation, and one-dimensional shock tube problems.
The present research deals with turbulent friction reduction for bypass transition on a flat plate with a textile surface. Unique boundary layers such as those found in swimsuits, sail wings, or skiwear, where certain boundary layer trip structure-like folded edges or masts of a sailboat exist, contain limited turbulence level in the boundary layer even under laminar conditions. A turbulent transition delay in such boundary layers is observed for textile surfaces.
A solid oxide fuel cell (SOFC) is expected to be applied to the distributed energy systems because of its high thermal efficiency and exhaust gas utilization. The exhaust heat from the SOFC can be transferred to the electric power by a gas turbine and the high efficiency power generation can be achieved. In this paper, the local processes in electrodes and electrolyte of unit SOFC are analyzed taking into account the heat conduction, mass diffusion, electrode reactions and transport of electron and oxygen ion. The temperature and concentration distributions in electrodes and electrolyte membrane are investigated. The effects of operating conditions on the cell performance are also shown. Furthermore, the entropy generation and exergy loss of each process are analyzed and the reason for generating the exergy loss in the SOFC is clarified. It is noted that two electrode reactions are responsible for the major exergy loss.
A Y-junction made of transparent acrylic resin was placed vertically downward. One side of the Y-junction was coated with repellent to change its wettability. As a result, the wettability of that side became poor, while the wettability of the other side was originally good. Straight pipes were connected to the main pipe and two branches of the Y-junction. A downward air-water two-phase flow was introduced into the main pipe. The air attached preferably to the poorly wetted side of the main pipe and entered into the poorly wetted branch. When the superficial velocities of air and water, jg and jw, were less than their respective critical values, air was completely distributed into the poorly wetted branch, and thus, the gas separation efficiency was 100%. An empirical equation was proposed for predicting the critical values of jg and jw.
Circumferential grooves over a rotor blade tips are used for improving axial flow compressor performances. Such casing treatment facility extends a stable operation range in most cases, but decreases compressor efficiency as a rule. There are presented results of parametric investigation of grooves of traditional and new configurations. Development of new groove constructions must permit combining of stable operation range extension with efficiency increase. Model on basis of Group Method of Data Handling may help designing groove configurations with improved performances.