Continuous extrusion and rolling forming velocity of copper strip

A new copper strip production technology combined with continuous extrusion and rolling technology was proposed. The roll velocity must first be matched with the continuous extrusion velocity to achieve continuous extrusion and roll forming. The bite condition of continuous extrusion was determined, and the compatibility equation between the roll velocity and parameters such as the extrusion wheel velocity, reduction, and strip size was established through mechanical by plastic theoretical calculations. The finite element model of continuous extrusion and rolling was then established by using the TLJ400 continuous extrusion machine with a roll diameter of 200 mm. The relationship between the continuous extrusion and rolling velocities was determined through numerical simulations by software DEFORM-3D, and the accuracy of compatibility equation of velocity was verified.

MOTION VELOCITY SMOOTH LINK IN HIGH SPEED MACHINING

To deal with over-shooting and gouging in high speed machining, a novel approach for velocity smooth link is proposed. Considering discrete tool path, cubic spline curve fitting is used to find dangerous points, and according to spatial geometric properties of tool path and the kinematics theory, maximum optimal velocities at dangerous points are obtained. Based on method of velocity control characteristics stored in control system, a fast algorithm for velocity smooth link is analyzed and formulated. On-line implementation results show that the proposed approach makes velocity changing more smoothly compared with traditional velocity control methods and improves productivity greatly.

A NOVEL METHOD FOR CALCULATING VERTICAL VELOCITY:A RELATIONSHIP BETWEEN HORIZONTAL VORTICITY AND VERTICAL MOVEMENT

The present work provides a novel method for calculating vertical velocity based on continuity equations in a pressure coordinate system.The method overcomes the disadvantage of accumulation of calculating errors of horizontal divergence in current kinematics methods during the integration for calculating vertical velocity,and consequently avoids its subsequent correction.In addition,through modifications of the continuity equations,it shows that the vorticity of the vertical shear vector(VVSV) is proportional to-ω,the vertical velocity in p coordinates.Furthermore,if the change of ω in the horizontal direction is neglected,the vorticity of the horizontal vorticity vector is proportional to-ω.When ω is under a fluctuating state in the vertical direction,the updraft occurs when the vector of horizontal vorticity rotates counterclockwise;the downdraft occurs when rotating clockwise.The validation result indicates that the present method is generally better than the vertical velocity calculated by the ω equation using the wet Q-vector divergence as a forcing term,and the vertical velocity calculated by utilizing the kinematics method is followed by the O'Brien method for correction.The plus-minus sign of the vertical velocity obtained with this method is not correlated with the intensity of d BZ,but the absolute error increases when d BZ is >=40.This method demonstrates that it is a good reflection of the direction of the vertical velocity.

Gas-kinetic numerical method for solving mesoscopic velocity distribution function equation

A gas-kinetic numerical method for directly solving the mesoscopic velocity distribution function equation is presented and applied to the study of three-dimensional complex flows and micro-channel flows covering various flow regimes. The unified velocity distribution function equation describing gas transport phenomena from rarefied transition to continuum flow regimes can be presented on the basis of the kinetic Boltzmann-Shakhov model equation. The gas-kinetic finite-difference schemes for the velocity distribution function are constructed by developing a discrete velocity ordinate method of gas kinetic theory and an unsteady time-splitting technique from computational fluid dynamics. Gas-kinetic boundary conditions and numerical modeling can be established by directly manipulating on the mesoscopic velocity distribution function. A new Gauss-type discrete velocity numerical integra- tion method can be developed and adopted to attack complex flows with different Mach numbers. HPF paral- lel strategy suitable for the gas-kinetic numerical method is investigated and adopted to solve three-dimensional complex problems. High Mach number flows around three-dimensional bodies are computed preliminarilywith massive scale parallel. It is noteworthy and of practical importance that the HPF parallel algorithm for solving three-dimensional complex problems can be effectively developed to cover various flow regimes. On the other hand, the gas-kinetic numerical method is extended and used to study micro-channel gas flows including the classical Couette flow, the Poiseuillechannel flow and pressure-driven gas flows in twodimensional short micro-channels. The numerical experience shows that the gas-kinetic algorithm may be a powerful tool in the numerical simulation of microscale gas flows occuring in the Micro-Electro-Mechanical System （MEMS）.

General formulas for drag coefficient and settling velocity of sphere based on theoretical law

The settlement of particles is of great importance in many areas. The accurate determination of drag coefficient and settling velocity in wide Reynolds number （Re） range remains a problem. In this paper, a series of new formulas for drag coefficient of spherical particles based on theoretical laws, such as the Stokes law, the Oseen law, and the Goldstein law, were developed and fitted using 480 groups of experimental data （Re 〈 2 × 10^5）. The results show that the 2nd approximation of a rational function containing only one parameter can describe Co-Re relationship accurately over the whole Re range of 0-2× 10^5. The new developed formulas containing five parameters show higher goodness over wide Re range than presently existing equations. The introduction of the Oseen law is helpful for improving the fitting goodness of the empirical formulas. On the basis of one of the Oseen-based Co-Re formulas giving the lowest sum of squared relative errors Qover the whole Re range （Re 〈 2 × 10^5）, a general formula for settling velocity ut based on dimensionless parameters was proposed showing high goodness.

THE EVOLUTION EQUATION OF JOINT PDF OF TURBULENT VELOCITY AND DISSIPATION

According to the hypothesis that the dissipation of turbulent kinetic energy satisfies log-normal distribution, a stochastic model of dissipation is provided and the Langevin modef[6] of velocity is modified. Then a joint Pdf equation of turbulent velocity and dissipation is derived. We solve numerically the joint Pdf equation using Monte Carlo method and obtain satisfactory results for decaying turbulence and homogeneous turbulent shear flow. The preliminary results show that the model is well working.

Correction of seabed layer thickness in processing subbottom profile data

The subbottom profiling is an important means of marine engineering survey, hazardous geology study and continental shelf scientific research. The accuracy of subbottom profile data interpretation has a direct impact on the research and investigation results. Because some of profilers’ transducer and hydrophone are separately installed, when the survey area is very shallow, distortion of shallow layers will be caused if it is seen as a self-excited and self-collected single-channel seismic system. According to the principle of subbottom profiler, the distortion correction formula is deduced and analyzed, providing actual value to using C-View software to interpret such subbottom profile data more accurately. In addition, the seabed sediments sound velocity is one of the key parameters when acquiring and processing the subbottom profile data. On the basis of comparing some sound velocity forecasting empirical equations, the LU Bo’s equation was considered the most appropriate to predict the seabed sediments, sound velocity at near-shore of China. In a survey of an artificial island site, the LU Bo’s equation and the porosity data obtained from geological drilling were utilized to predict the sediments sound velocity, and the sound velocity structure profile was plotted, which was applied in processing the subbottom profile data of the artificial island investigation. The method of using porosity data to predict sediments sound velocity in processing subbottom profile data can improve the interpretation accuracy and it’s of practical significance.

Numerical Study on Forming Process of the PET/PA6 Component Melt in Micro Hole in Composite Spinning

The forming mechanism of the multi-component polymer melt is always the difficult problem in the study on the composite fiber, due to the difference of the material properties. The study simulated the flow of PET/PA6 composite melt on the influence law for the velocity distribution and the micro hole＇s structure on the influence law for extrusion swelling based on the theory of the rheology and the spinning process and the structure of the spinning components by Polyflow. In addition by comparison with the previous experiments about extrusion swelling, the results show that the value of the swell ratio decreases rapidly at low values of length/ diameter and then levels off as length/diameter is increased further, whereas increases with the die exit angle increasing. The veincity distribution of the composite melt and the micro hole＇s structure have a significant influence on the extrusion swelling, which has very good guidance function for studying the forming mechanism of the composite melt and preparation of the high performance fiber.

Error Analysis of A New Higher Order Boundary Element Method for A Uniform Flow Passing Cylinders

A higher order boundary element method(HOBEM)is presented for inviscid flow passing cylinders in bounded or unbounded domain.The traditional boundary integral equation is established with respect to the velocity potential and its normal derivative.In present work,a new integral equation is derived for the tangential velocity.The boundary is discretized into higher order elements to ensure the continuity of slope at the element nodes.The velocity potential is also expanded with higher order shape functions,in which the unknown coefficients involve the tangential velocity.The expansion then ensures the continuities of the velocity and the slope of the boundary at element nodes.Through extensive comparison of the results for the analytical solution of cylinders,it is shown that the present HOBEM is much more accurate than the conventional BEM.

Blowup Criteria for Full Compressible Navier-Stokes Equations with Vacuum State

This paper deals with the global strong solution to the three-dimensional(3D)full compressible Navier-Stokes systems with vacuum. The authors provide a sufficient condition which requires that the Sobolev norm of the temperature and some norm of the divergence of the velocity are bounded, for the global regularity of strong solution to the 3D compressible Navier-Stokes equations. This result indicates that the divergence of velocity fields plays a dominant role in the blowup mechanism for the full compressible Navier-Stokes equations in three dimensions.

Hydrodynamic behavior of liquid-solid micro-fluidized beds determined from bed expansion

The bed-expansion characteristics of liquid-solid micro-fluidized beds were experimentally studied. Bed columns with inner diameters of 0.8, 1.45, and 2.3 mm were fabricated based on capillaries. Five parti- cle sizes in a range of 22-58 t^m were investigated. Bed-expansion curves were plotted using visually recorded bed-expansion heights. The bed expansion and initial fluidization behavior were compared with predictions for conventional-scale beds, Evident differences are reflected in lower expansion ratios and higher minimum fluidization velocities for micro-fluidized beds. These were attributed to the increase in the internal surface area of the particle beds and specific surface area of wall contact. The wall effect for micro-fluidized beds at higher particle/bed diameter ratios caused higher local voidage and an increase in expansion ratio. Correlations for the exponent and proportional coefficient in the Richardson-Zaki equation for micro-fluidized beds were proposed. The minimum fluidization velocities were correlated using a modification of the Ergun equation.

Data-Domain Wave Equation Reflection Traveltime Tomography

Estimation of an accurate macro velocity model plays an important role in seismic imag- ing and model parameter inversion. Full waveform inversion （FWI） is the classical data-domain inver- sion method. However, the misfit function of FWI is highly nonlinear, and the local optimization cannot prevent convergence of the misfit function toward local minima. To converge to the global minimum, FWI needs a good initial model or reliable low frequency component and long offset data. In this article, we present a wave-equation-based reflection traveltime tomography （WERTT） method, which can pro- vide a good background model （initial model） for FWI and （least-square） pre-stack depth migration （LS-PSDM）. First, the velocity model is decomposed into a low-wavenumber component （background velocity） and a high-wavenumber component （reflectivity）. Second, the primary reflection wave is pre- dicted by wave-equation demigration, and the reflection traveltime is calculated by an automatic picking method. Finally, the misfit function of the 12-norm of the reflection traveltime residuals is mini- mized by a gradient-based method. Numerical tests show that the proposed method can invert a good background model, which can be used as an initial model for LS-PSDM or FWI.