基于界面跟踪方法的汽蚀模型和算法的有效性验证

针对两相附着汽蚀流动机理,基于界面跟踪方法发展了新的汽蚀模型和算法。所发展的汽蚀模型和算法不仅考虑了液相／气相界面处的压力差,而且考虑了耦合Reynolds-Averaged Navier-Stokes方程求解技术得到的流场压力梯度信息来迭代计算附着汽蚀形状。采用具有试验数据的半球形头部圆柱体汽蚀绕流作为算例来验证所提出的汽蚀模型和算法的有效性。采用不同的网格数和松弛因子数值验证了发展的汽蚀模型和算法的有效性。三种汽蚀数下的数值计算结果得到的压力系数分布与试验数据完全吻合。结果表明所提出的汽蚀模型和算法能够准确模拟出汽蚀发生点和汽蚀长度。     

A Dynamic Analysis and Numerical Simulation of Explosive Development of an Extratropical Cyclone Over Land

The present paper has made a dynamic and diagnostic study of the process of explosive deepening of an extratropical cyclone over North China on April 25-26, 1983, in order to gain an insight into the physical mechanism of explosive development of cyclone over land. It turns out that this cyclone occurred in the strong baroclinic zone, and the vorticity and thermal advection triggered the initial development of the cyclone. Subsequently, as the rainfall increased, the effect of condensational heating became more and more important. During the time period of rapid intensification (from 1200GMT 25 to 0000GMT 26 April, 1983, the central surface pressure fell down from 998. 2 to 988. 3 hPa), the peak of diabatic heating profile continuously descended, leading to a rapid increase in heating amount in the lower troposphere. This condition is favorable to the explosive development of rotational circulation or vortex. The numerical simulations have further demonstrated the importance of the lowering of heating p     

Mass transport in gas channels of electrochemical cells with a solid-oxide electrolyte: Allowing for the electrode reaction rates in numerical calculations

The concentration fields, Nusselt number distributions along the electrode, and ratios of concentrations of electrochemically active components at the entrance into and exit out of an electrochemical cell are determined by numerical integration of the convective-diffusion equation for a broad range of rate constants of electrode reactions, Peclet numbers, and geometrical parameters of channels. Three regions of parameter values are revealed. At low reaction rates (K _l < 0.5), mass transfer is completely determined by electrode kinetics; at high rates (K _l > 20), it is completely determined by the diffusion in the gas phase; and in the intermediate region of values of K _l it is necessary to allow for both the diffusion processes and the electrode reactions.Translated from Elektrokhimiya, Vol. 41, No. 3, 2005, pp. 317–324.Original Russian Text Copyright © 2005 by Ezin, Somov.     

大型液相色谱分离过程FAD－SMT数学模型及其数值解

提出大型液相色谱分离过程ＦＡＤ－ＳＭＴ数学模型，把色谱分离连续性方程转变为对流扩散方程和常微分方程组，并提出模型的数值方法，分析了数值解的稳定条件和收敛条件以及空间和时间步长的选取。实验结果表明，ＦＡＤ－ＳＭＴ数学模型计算的液相色谱分离葡萄糖、果糖和分离甘露醇、山梨醇理论与实验流出曲线相吻合。灵敏度分析结果表明：相平衡常数比轴向扩散系数和总传质系数对色谱分离有较大的影响。     

Topological and fractal properties of turbulent passive scalar fluctuations at small scales

Corrections of Batchelor's spectral law –1 of passive scalar-fluctuations are obtained by taking into account the topological instabilities of small-scale vortex sheets: –4/3 for supercritical and –5/4 for subcritical regimes. The corresponding fractal dimensions of the scalar interface areD =8/3 for supercritical andD =11/4 for subcritical regimes. Good agreement with experimental data is established.     

The Padé-Rayleigh-Ritz method for solving large hermitian eigenproblems

We make use of the Padé approximants and the Krylov sequencex, Ax,,...,A ^m–1 x in the projection methods to compute a few Ritz values of a large hermitian matrixA of ordern. This process consists in approaching the poles ofR _x()=((I–A)^–1 x,x), the mean value of the resolvant ofA, by those of [m–1/m]_Rx(), where [m–1/m]_Rx() is the Padé approximant of orderm of the functionR _x(). This is equivalent to approaching some eigenvalues ofA by the roots of the polynomial of degreem of the denominator of [m–1/m]_Rx(). This projection method, called the Padé-Rayleigh-Ritz (PRR) method, provides a simple way to determine the minimum polynomial ofx in the Krylov subspace methods for the symmetrical case. The numerical stability of the PRR method can be ensured if the projection subspacem is sufficiently small. The mainly expensive portion of this method is its projection phase, which is composed of the matrix-vector multiplications and, consequently, is well suited for parallel computing. This is also true when the matrices are sparse, as recently demonstrated, especially on massively parallel machines. This paper points out a relationship between the PRR and Lanczos methods and presents a theoretical comparison between them with regard to stability and parallelism. We then try to justify the use of this method under some assumptions.     

Vortex rings interacting with a wall

Accurate numerical simulations of vortex rings impinging on flat boundaries have revealed the same features observed in the experiment of Walkeret al. (1987). They observed atRe _v >1250 the formation of azimuthal instabilities in the secondary ring during its compression within the primary ring. In the present numerical simulation the number of waves agrees very well with those observed in the experiment. The distributions of the vorticities together with the distribution of each term in the vorticity equations give insights on the formation of azimuthal instabilities.     

On the Landau-Teller approximation for energy exchanges with fast degrees of freedom

We revisit the Landau-Teller heuristic approach to adiabatic invariants and, following Rapp, use it to investigate the energy exchanges between the different degrees of freedom, in simple Hamiltonian systems describing the collision of fast rotating or vibrating molecules with a fixed wall. We critically compare the theoretical results with particularly accurate numerical computations (quite small energy exchanges, namely of one part over 10³⁰, are measured).     

Influence of operational parameters on retention of ultra-high molecular weight polystyrenes in thermal field-flow fractionation

Summary The influence of various parameters (concentration of the injected polymer solution, flow rate, temperature gradient, relaxation conditions) on the retention and shape of the fractogram of ultra-high molecular weight polystyrenes in thermal field-flow fractionation was investigated. Under the operating conditions adopted, reproducible oscillations in the peak shape are observed for molecular weights larger than a few millions, especially at relatively high polymer concentration. They are attributed to some hydrodynamic instabilities. The retention of ultra-high molecular weight polystyrenes at high flow rate is strongly dependent on the initial relaxation period. All of the investigated operational variables have a complex effect on the resulting shape of the fractogram. Consequently, the confirmation of the shear-induced focusing of macromolecules across the channel thickness requires further study. Experiments on reinjection of fractions collected after an initial high speed pass through the separation system leads to the conclusion that shear degradation of the ultra-high molecular weight polymers did not occur under the investigated experimental conditions even at the highest flow rates.     

Polymer crystallization dynamics,as reflected by differential scanning calorimetry. Part 2: Numerical simulations

With the aid of a model for the kinetics of polymer crystallization, as put forward in previous publications, the shape of DSC-curves and their position on the temperature scale were simulated for various conditions of heat transfer in the apparatus. It turns out that the outcome is very dependent on the assumptions made with respect to these heat transfer conditions. For the ideal condition — no temperature differences between sample, pan and furnace — an invariable shape is predicted for the DSC-curves. They only shift to lower temperatures with increasing cooling rates. For more realistic conditions, the curves not only shift but become broader and their maxima decrease. They show a more familiar appearance. These calculations are very involved, however, A simple balance equation is shown to yield equivalent results, if a dimensionless characteristic number like the Nusselt number remains considerably smaller than one. This number contains an effective heat transfer coefficient between sample and furnace which, surprisingly, should not be too high. Apparently, the heat capacity of the pan does not play an important role under these conditions. This is investigated in Appendix II. Appendix I describes the procedure of the numerical simulations.