Calculated Velocity Distributions Research Articles

傾斜樋における粒子群流動挙動のシミュレーション

Chute flow of spherical particles is numerically simulated by applying a particle element method, PEM. The calculated velocity distributions of flowing particles agree well with the measured ones, and it is confirmed that the particle element method is a useful tool for the simulation of the flow of granular materials. The microscopic state variables, porosity and dissipation energy distributions in the flow of granular materials, can be obtained by this simulation. The relationships between the velocity distributions and these state variables are discussed. These state variables are important factors in understanding the mechanical behavior of granular materials.

Finite element analysis of turbulent forced convection in lid‐driven rectangular cavities

AbstractTurbulent fluid flow and heat transfer in lid‐driven rectangular cavities are analysed by a finite element procedure for the prediction of the turbulent forced convection in two‐dimensional recirculating flows. The (k–ε) model is used to compute effective viscosities and thermal conductivities. The fluid flow and turbulence model parabolic equations are solved sequentially, one after the other. Then, the calculated velocity distribution is used in the solution of the steady state energy equation to yield the temperature field. Aspect ratios e=0·75, 1·0 and 1·5 and Reynolds numbers ranging from 5 × 104 to 4 × 105 are considered in the numerical examples.

Numerical study on the laminar pulsatile flow of slurries

The laminar pulsatile flow of slurries is studied numerically. A slurry is usually described as a Bingham plastic fluid, but since the apparent viscosity coefficient of a Bingham plastic fluid diverges if the velocity gradient becomes zero, a modified Bingham model (bi-viscosity model) is used in this calculation. As one of the characteristics of the pulsatile flow of non-Newtonian fluids is the flow enhancement (the increase in the mean flow rate due to pulsation), the calculated flow enhancement rates are compared with the experimental results of Kajiuchi and Saito and good agreements are obtained. Finally, the extra power required to pulsate the flow and the characteristics of the calculated velocity distribution and the shear stress at the wall are investigated.

Theoretical investigation of laser-sustained argon plasmas

A theoretical model has been developed for laser-sustained argon plasmas in a forced convective axisymmetric pipe flow. The two-dimensional model based on Navier–Stokes equations was solved using a finite difference algorithm, and included geometric optics, temperature-dependent thermodynamic, transport, and optical properties, as well as radiation-induced thermal conductivity. The results showed good agreement with existing experimental data on temperature distribution, shape, and size of the plasma. The calculated velocity distribution revealed the complexity of the flow field and indicated that the constant axial mass flux (product of axial velocity and density) assumption adopted by existing one-dimensional and semi-two-dimensional models is not adequate. The radiation transfer was found to have a significant influence on the predicted temperature distribution and peak temperature of laser-sustained plasmas.

Equilibrium velocities of a planetesimal population

The random velocities v( m) of planetesimal populations specified by maximum and minimum masses and a number density n( m) ∝ m − q are calculated interatively based on two different physical models involving ratios of rates: (1) excitation of kinetic energy by gravitational perturbation and elastic collision equal to damping of kinetic energy by inelastic collisions; and (2) excitation of kinetic energy a ratio b (∼3 usually) to doubling of mass. Model (2) follows the theory of Safronov closely. Both physical models are developed approximately, using averaged factors for collision dissipation and velocity ratios, and then more precisely, allowing for reference orbit differences and for plausible variations in collisional energy dissipation with impact velocity and planetesimal mass ratios. The approximate model (2) agrees reasonably well with the results of Safronov. Both precise models are applied to populations approximating those generated by the calculations of Greenberg, Cox, and Wetherill, producing qualitatively similar velocities v( m). These results encourage analytic models of planetesimal population growth, incrementing masses and calculating velocity distributions in alternate steps. The principal improvement needed in the models is more realistic collision energy partitioning.

Turbulent Flow in Very Noncircular Conduit

Measurements of the friction factor variation with Reynolds number, and the mean streamwise velocity and boundary shear distributions, are presented for a smooth conduit having a cross section similar to that formed between circular rods stacked in a “square” pattern. This conduit shape was chosen because it displays a large shape effect. Head loss measurements confirmed the significant difference between the friction factor in this conduit shape and that in a pipe. The velocity distributions along normals to the wall followed the “universal distribution” reasonably well. The velocity and boundary shear distributions are compared with those calculated for this conduit shape using a finite element algorithm described in a previous paper, neglecting secondary flow effects. This comparison illustrates the secondary flow effects, and the difference between the measured and calculated velocity distributions is used to estimate the magnitude of the secondary flow in this conduit shape.

Calculation of Velocity Distributions in Ship Wake (2 nd Report)

Before the calculation of velocity distributions in ship wake, three kinds of experiments are carried out in order to get theoretical models as to the separation phenomena and the diffusivity coefficient; (a) observation of the limiting streamlines by the oil film method, (b) the velocity measurement near the separation position and (c) the vorticity measurement in ship wake. The separation position is determined experimentally which can be predicted roughly using some suitable parameters of the boundary layer calculation.It has been made clear from the velocity measurements that the velocity near the seperation position makes remarkable changes and the newly-generated-vorticity affects very much the down stream pattern.It has also been made clear that not only the x-axis vorticity but also the y- and z-axis vorticity compose the stern vortex.Using the measured velocity and vorticity distributions the diffusivity coefficient is determined, which amounts to about 300 times of the molecular one.The velocity calculation of a tanker model is carried out after these experimental considerations, which shows a fairly well agreements with the measured one.

Energetics of ions in quadrupole fields

The phase-space dynamics approach is used to calculate velocity distributions and mean kinetic energies of ions contained by quadrupole fields and to examine their dependence on the phase of the rf field.

Energetics of ions in quadrupole fields

The phase-space dynamics approach is used to calculate velocity distributions and mean kinetic energies of ions contained by quadrupole fields and to examine their dependence on the phase of the rf field.

Calculation of Velocity Distributions in Ship Wake

To know the velocity distributions in ship wake is one of the most essential problems in ship design. Here a method is proposed to estimate them and some results of numerical calculations are shown compared with those of experiments.The velocity is assumed to consist of the potential and the viscous components. The former is calculated from the source distributions which are obtained from the wave analysis and the hull surface condition. The latter is calculated as induced velocity of vorticity distributed in the two. regions, one is the boundary layer on ship surface and the other is the ship wake. For the boundary layer, the three dimensional turbulent boundary layer calculations are carried out and the vorticity distribution and the separation position are determined. On the other hand, the vorticity in ship wake is assumed that it is diffused from the boundary layer which can be estimated by solving the diffusion equation.The estimated vorticity and velocity distributions show fairly well agreements with those of measurements. As an application of this method, the viscous resistance is calculated from the estimated velocity distributions, which shows a little smaller resistance coefficients than those of the wake survey.

Calculation of Velocity Distributions in Rod Clusters

A method of calculating velocity distributions in rod cluster flow passages is described and shown to be in good agreement with experiment in two particular cases. The method is compatible with that of Deissler and Taylor and, because of its greater simplicity, is to be preferred.

Flow in a Pipe Following an Abrupt Increase in Surface Roughness

Measurements of velocity, turbulence intensity, and Reynolds stress distributions following a sudden increase in surface roughness of a pipe are reported. The wall shear stress increases abruptly to its final value and the pressure gradient is very nearly constant throughout the transition region. Reynolds stresses throughout much of the transition region reach values exceeding those in fully developed flow in the rough pipe. The need for knowledge of shear stress distributions for use in the calculation of velocity distributions is pointed out. A flow model is suggested.

Studies on the Characteristics of Radial-Flow Nozzles : 2nd Report, Theoretical Analysis of Inward Flow

The inward flow characteristics of radial-flow nozzles are studied by the similar procedure to the 1st report. As a parameter, R= Vh2/vr2 should be used to calculate velocity distributions in the clearance and pressure losses, etc., where r2 is the outer radius of a nozzle and V is a radial mean velocity at r2. When R is over 5.42, boundary layers cannot fill up the clearance, and if R is less than 5.42, the velocity distribution in the clearance becomes perfectly parabolic, that is, Poiseuille's flow will be established. In either case, the thickness of the boundary layer reduces to zero at the center of the nozzle. Therefore, the pressure loss of the nozzle should be expressed by one of the three different equations according to the combination of R and the diameter ratio of the nozzle.

Application of the Thin-Wing-Expansion Method to the Compressible Flow past Profiles of Arbitrary Shape

The formulae for the velocity distribution over the surface of an obstacle of arbitrary shape are given to the transonic third approximation by the use of Imai's thin-wing-expansion method. These formulae are applied to the flow past an elliptic cylinder and it has been found that the results are in accord with the other authors's results within the order of the approximation used. Further, these formulae, together with the \(\varPsi\)- and the \(\varPhi\varPsi\)-procedures, are applied to the flow past Tomotika-Tamada's profiles. Calculated velocity distributions are compared with Tomotika-Tamada's exact solutions as well as with Takami's numerical results obtained by various approximate methods. These formulae seem to be very useful, because their convergency and accuracy are very good up to considerably high Mach numbers.

The Cavitation Theory of Homogenization

Summary The valve clearances in a Manton-Gaulin homogenizing valve operating with both water and milk were determined for various pressures and used in the calculation of velocity distribution, Reynolds number, and minimum theoretical pressure in the valve crevice. The analysis showed that cavitation could occur. Results obtained in homogenization of milk with several commercial and experimental valves are discussed with reference to theories of homogenization. Effective homogenization was accomplished in the Manton-Gaulin and a rounded-entrance valve even when sufficient back pressure was applied to prevent cavitation. The correlation between valve clearance and the U.S.P.H.S. index indicates that the mechanism of homogenization involves velocity or velocity gradient. Tests with Venturi tubes provided conditions where cavitation occurred, yet homogenization was relatively ineffective in comparison with that accomplished by commercial valves. The results reported do not support either the cavitation or the impact theories of homogenization.