Influence of Blade Number on the Performance of Hydraulic Turbines in the Transition Stage

To analyze the effect of blade number on the performance of hydraulic turbines during the transient stage in which theflow rate is not constant,six hydraulic turbines with different blade numbers are considered.The instantaneous hydraulic performance of the turbine and the pressure pulsation acting on the impeller are investigated numerically by using the ANSYS CFX software.The ensuing results are compared with the outcomes of experimental tests.It is shown that thefluctuation range of the pressure coefficient increases with time,but the corresponding range for the transient hydraulic efficiency decreases gradually when theflow velocity transits to larger values.During the transition to smallflow velocity,thefluctuation range of the pressure coefficient gradually decreases as time passes,but the correspondingfluctuation range of its transient hydraulic efficiency gradually becomes larger.Thefluctuation range in the Z9 case is small during the transition.The main frequency of transient hydraulic efficiency pulsation is equal to the blade frequency.At the main frequency,Z7 has the largest amplitude of the hydraulic efficiency pulsation,Z10 has the smallest amplitude,and the difference between Z7 and Z9 is limited.As the number of blades grows,the pressure pulsation during the transition process gradually decreases,but the pressure pulsation of Z10 at the volute tongue is larger.In the steady state,Z9 has the highest efficiency and in the transient stage,the pressure coefficientfluctuation range is small.Accordingly,for the hydraulic turbine Z9,the performance is optimal.

Effect of non-uniform swelling on coal multiphysics during gas injection: The triangle approach

In current dual porosity/permeability models,there exists a fundamental assumption that the adsorption-induced swelling is distributed uniformly within the representative elementary volume (REV),irrespective of its internal structures and transient processes.However,both internal structures and transient processes can lead to the non-uniform swelling.In this study,we hypothesize that the non-uniform swelling is responsible for why coal permeability in experimental measurements is not only controlled by the effective stress but also is affected by the adsorption-induced swelling.We propose a concept of the swelling triangle composed of swelling paths to characterize the evolution of the non-uniform swelling and serve as a core link in coupled multiphysics.A swelling path is determined by a dimensionless volumetric ratio and a dimensionless swelling ratio.Different swelling paths have the same start and end point,and each swelling path represents a unique swelling case.The swelling path as the diagonal of the triangle represents the case of the uniform swelling while that as the two perpendicular boundaries represents the case of the localized swelling.The paths of all intermediate cases populate inside the triangle.The corresponding relations between the swelling path and the response of coal multiphysics are established by a non-uniform swelling coefficient.We define this method as the triangle approach and corresponding models as swelling path-based ones.The proposed concept and models are verified against a long-term experimental measurement of permeability and strains under constant effective stress.Our results demonstrate that during gas injection,coal multiphysics responses have a close dependence on the swelling path,and that in both future experiments and field predictions,this dependence must be considered.

Ionization process and distinctive characteristic of atmospheric pressure cold plasma jet driven resonantly by microwave pulses

In the present study,a coaxial transmission line resonator is constructed,which is always capable of generating cold microwave plasma jet plumes in ambient air in spite of using argon,nitrogen,or even air,respectively.Although the different kinds of working gas induce the different discharge performance,their ionization processes all indicate that the ionization enhancement has taken place twice in each pulsed periods,and the electron densities measured by the method of microwave Rayleigh scattering are higher than the amplitude order of 10^(18)m^(-3).The tail region of plasma jets all contain a large number of active particles,like NO,O,emitted photons,etc,but without O_(3).The formation mechanism and the distinctive characteristics are attributed to the resonance excitation of the locally enhanced electric fields,the ionization wave propulsion,and the temporal and spatial distribution of different particles in the pulsed microwave plasma jets.The parameters of plasma jet could be modulated by adjusting microwave power,modulation pulse parameters(modulation frequency and duty ratio),gas type and its flow rate,according to the requirements of application scenarios.

Transient numerical simulation of annealing process in a conjugate combined radiation conduction heat transfer

The annealing time is an important affecting factor in the performance of many furnaces.The present work deals with the transient simulation of annealing process in a cubic furnace in which a solid element is placed in its center.As the working gas can have some radiating features,a set of governing equations including the energy balance with the radiative transfer equation(RTE)for the gray radiating medium and the conduction equation inside the solid product are numerically solved with progressing in time.Numerical results which are validated against both analytical and theoretical findings in the literature demonstrate that during the starting period,a high rate of radiant energy transfers into the solid body even at small optical thickness.This behavior which hastens the rate of heat transfer at low values of the radiation conduction parameter,causes a fast annealing process in which the solid body warms up to its maximum temperature.Moreover,it is revealed that the rate of heat transfer is an increasing function of radiation-conduction parameter.

Finite Element Method for the Transient Process of the Separation of External Stores from Aircraft

The adjustment and the regeneration of the flow field unstructuredmesh as well as the fi- nitelement solutions for the Euler equationsin the transient process of the separation o external stores form anaircraft at a predetermined downward translation and rotation areinvestigated. It is shown that the adjustment or regeneration ofgrids needed for moving store can be confined within a small regionaround the store and the finite element numerical solution method ofEuler equations for fixed grids can also be used for moving grids ifthe conservative fluxes F_k of fixed grids are replaced by E_k ofmoving grids. The relation-ships between F_k and E_k are alsoestablished. The numerical results For practical examples of aircraftwith external stores are shown.

Arranging transient process used in iterative learning control system

Considering the same initial state error in each repetitive operation in the iterative learning system, a method of arranging the transient process is given. During the current iteration, the system will track the transient function firstly, and then the expected trajectory. After several iterations, the learning system output will trend to the arranged curve, which has avoided the effect of the initial error on the controller. Also the transient time can be changed as you need, which makes the designing simple and the operation easy. Then the detailed designing steps are given via the robot system. At last the simulation of the robot system is given, which shows the validity of the method.

1/3 PURE SUB-HARMONIC SOLUTION AND FRACTAL CHARACTERISTIC OF TRANSIENT PROCESS FOR DUFFING'S EQUATION

The 1/3 sub-harmonic solution for the Duffing＇s with damping equation was investigated by using the methods of harmonic balance and numerical integration. The assumed solution is introduced, and the domain of sub-harmonic frequencies was found. The asymptotical stability of the subharmonic resonances and the sensitivity of the amplitude responses to the variation of damping coefficient were examined. Then, the subharmonic resonances were analyzed by using the techniques from the general fractal theory. The analysis indicates that the sensitive dimensions of the system time-field responses show sensitivity to the conditions of changed initial perturbation, changed damping coefficient or the amplitude of excitation, thus the sensitive dimension can clearly describe the characteristic of the transient process of the subharmonic resonances.

Effect of Carried-Envelope Phase on Transient Process in a Cascade-Type System

This paper investigates the effect of carried-envelope phase on transient process in a cascade-type atomic system, which is driven by two ultrashort laser pulses （probe and signal laser）. It is found that the one- and two-photon processes corresponding to pathway ｜0〉→｜1〉and ｜0〉→｜1〉→｜2〉 can be enhanced or ,suppressed by modulating the carried-envelope phases of probe laser pulse. Our numerical results also show that the transient populations of two excited states can be periodically affected by the carried-envelope phase of probe laser pulse. With certain time, the partial population transfer between two exited states can be realized just by adjusting the carried-envelope phase of probe laser pulse.

A 1/3 PURE SUBHARMONIC SOLUTION AND TRANSIENT PROCESS FOR THE DUFFING'S EQUATION

The 1/3 subharmonic solution for the Duffing’s equation is investigated by using the methods of harmonic balance and numerical integration. The sensitivity of parameter variation for the transient process and the transient process for the perturbance initial conditions are studied. Over and above, the precision of numerical integration method is discussed and the numerical integration method is compared with the harmonic balance method. Finally, asymptotical stability of the pure subharmonic oscillations element is inspected.

Initial transient process in a simple helical flux compression generator

An analytical scheme on the initial transient process in a simple helical flux compression generator, which includes the distributions of both the magnetic field in the hollow of an armature and the conducting current density in the stator, is developed by means of a diffusion equation. A relationship between frequency of the conducting current, root of the characteristic function of Bessel equation and decay time in the armature is given. The skin depth in the helical stator is calculated and is compared with the approximate one which is widely used in the calculation of magnetic diffusion. Our analytical results are helpful to understanding the mechanism of the loss of magnetic flux in both the armature and stator and to suggesting an optimal design for improving performance of the helical flux compression generator.

High-Accuracy Pneumatic Position Control by Applying Nonlinear Control and Arranging Transient Process

By applying a nonlinear control and arranging a transient process, the initiative error of the pneumatic servo positioning system is reduced largely, and a larger gain of the controller is used to improve the responding speed of the system at the same damping ratio. Therefore, a compromise is made among the responding speed, overshoot, robustness, adaptability and stability. In addition, a dynamic output feedback controller, including position velocity and acceleration （PVA） feedback, is designed to improve the performance of the system. And a nonlinear controller is reconstructed based on the linear output feedback controller to decrease noises and disturbances. The dynamic responses of the system are simulated and tested. Results show that the error is kept within 0.02 mm under different mass loads and the positioning transient process is smooth, without overshoot and speedy.

Analysis Process of Finite Element Method in Heat Transfer through Fabrics

According to heat transfer principle and the process of solving engineering problems by finite element method, examples were given to demonstrate how finite element analysis can be used to describe transient heat transfer through fabrics. Details were given to describe how conduction and convection affect temperature distribution and heat loss during heat transfer processes by taking advantage of the quick calculation of FEA software MSC.Marc. Experimental results show good agreement with the theoretical results.

Transient flameout process of boron-magnesium agglomerates during combustion in oxygen-rich atmospheres

In this study,boron–magnesium agglomerates with varying mass ratios were prepared by drying a micron-sized boron–magnesium mixed suspension,and the combustion process of these agglomerates under different oxygen-rich concentrations were investigated using a laser ignition system.The test results showed that when the mass fraction of magnesium powder in boron-magnesium agglomerates exceeded a certain threshold(between 2%and 5%),flame extinction and reignition occurred after a significant reduction in the agglomerate volume during combustion.This process is referred to as the transient flameout process,which is affected by the magnesium content of the agglomerate and the oxygen concentration in the ambient atmosphere.An increase in the magnesium content or oxygen concentration makes this phenomenon more pronounced.During weakening of the flame intensity,a dark film gradually covered the particle surfaces.X-ray diffraction and elemental analyses of the cross-section and outer surface of the condensed combustion product suggested that the dark film is primarily composed of Mg-B-O ternary oxides.This film prevents direct contact between boron and oxygen,thereby inhibiting surface and gas-phase reactions and leading to the occurrence of the transient flameout phenomenon.

Intensity Correlation Function and Associated Relaxation Time of a Saturation Laser Model with Correlated Noises

We investigate the intensity correlation function C（s） and its associated relaxation time Tc for a saturation model of single-mode laser with correlated noises. The expressions of O（s） and Tc are derived by means of the projection operator method, and effects of correlations between an additive noise and a multiplicative noise are discussed by numerical calculation. Based on the calculated results, it is found that the correlation strength A between the additive noise and the multiplicative noise can enhance the fluctuation decay of the laser intensity.

Numerical study and acceleration of LBM-RANS simulation of turbulent flow

The coupled models of LBM （Lattice Boltzmann Method） and RANS （Reynolds-Averaged Navier-Stokes） are more practical for the transient simulation of mixing processes at large spatial and temporal scales such as crude oil mixing in large-diameter storage tanks. To keep the efficiency of parallel computation of LBM, the RANS model should also be explicitly solved; whereas to keep the numerical stability the implicit method should be better for PANS model. This article explores the numerical stability of explicit methods in 2D cases on one hand, and on the other hand how to accelerate the computation of the coupled model of LBM and an implicitly solved RANS model in 3D cases. To ensure the numerical stability and meanwhile avoid the use of empirical artificial lim- itations on turbulent quantities in 2D cases, we investigated the impacts of collision models in LBM （LBGK, MRT） and the numerical schemes for convection terms （WENO, TVD） and production terms （FDM, NEQM） in an explic- itly solved standard k-e model. The combination of MRT and TVD or MRT and NEQM can be screened out for the 2D simulation of backward-facing step flow even at Re = 107. This scheme combination, however, may still not guarantee the numerical stability in 3D cases and hence much finer grids are required, which is not suitable for the simulation of industrial-scale processes.Then we proposed a new method to accelerate the coupled model of LBM with RANS （implicitly solved）. When implemented on multiple GPUs, this new method can achieve 13.5-fold accelera- tion relative to the original coupled model and 40-fold acceleration compared to the traditional CFD simulation based on Finite Volume （FV） method accelerated by multiple CPUs. This study provides the basis for the transient flow simulation of larger spatial and temporal scales in industrial applications with LBM-RANS methods.

The Drift of Dust Grains Induced by Transient Magnetic Field

Our experiment shows that the dust grains, suspended on the edge of the sheath of a radio-frequency discharge, undergo a contraction when switching a vertical magnetic field on, and an expansion when switching the magnetic field off. We call this kind of magnetic field "transient magnetic field". A primary analysis is proposed for the phenomenon.

A Basis for Causal Scattering Waves, Relativistic Diffraction in Time Functions

Relativistic diffraction in time wave functions can be used as a basis for causal scattering waves. We derive such exact wave function for a beam of Dirac and Klein-Gordon particles. The transient Dirac spinors are expressed in terms of integral defined functions which are the relativistic equivalent of the Fresnel integrals. When plotted versus time the exact relativistic densities show transient oscillations which resemble a diffraction pattern. The Dirac and Klein-Gordon time oscillations look different, hence relativistic diffraction in time depends strongly on the particle spin.

Optimization of the co-closing law of guide vanes and blades for bulb turbines based on CFD

The load rejection transient process of bulb turbine units is critical to safety of hydropower stations,and determining appropriate closing laws of guide vanes(GVs)and runner blades(RBs)for this process is of significance.In this study,we proposed a procedure to optimize the co-closing law of GVs and RBs by using computational fluid dynamics(CFD),combined with the design of experiment(DOE)method,approximation model,and genetic optimization algorithm.The sensitivity of closing law parameters on the histories of head,speed,and thrust was analyzed,and a two-stage GVs’closing law associating with a linear RBs’closing law was proposed.The results show that GVs dominate the transient characteristics by controlling the change of discharge.Speeding GVs’first-stage closing speed while shortening first-stage closing time can not only significantly reduce the maximum rotational speed but also suppress the water hammer pressure;slowing GVs’second-stage closing speed is conducive to controlling the maximum reverse axial force.RBs directly affect the runner force.Slowing RBs’closing speed can further reduce the rotational speed and the maximum reverse axial force.The safety margin of each control parameter,flow patterns,and pressure pulsations of a practical hydropower station were all improved after optimization,demonstrating the effectiveness of this method.

On the Joint Distribution of the Future Infimum and Its Location for a Transient Bessel Process

For a transient Bessel process X let I(t) = in fs＞tX(s) and§(t) = inf{u≥ 2 t: X(u) = I(t)}. In this note we compute the joint distribution of I(t),§(t) and Xt.

EFFECTS OF NONLINEARITY ON TRANSIENT PROCESSES IN AT-CUT QUARTZ THICKNESS-SHEAR RESONATORS

We study the effects of mechanical nonlinearity arising from large thickness-shear deformation on the transient process of an AT-cut quartz plate resonator. Mindlin＇s two-dimensional plate equation is used, from which a system of first-order nonlinear differential equations governing the evolution of the vibration amplitude is obtained. Numerical solutions by the Runge-Kutta method show that in common operating conditions of quartz resonators the nonlinear effect varies from noticeable to significant. As resonators are to be made smaller and thinner in the future with about the same power requirement, nonlinear effects will become more important and need more understanding and consideration in resonator design.