Numerical simulation of gas-particle flows behind a backward-facing step using an improved stochastic separated flow model

An improved stochastic separated flow (ISSF) model developed by the present authors is tested in gas-particle flows behind a backward-facing step, in this paper. The gas phase of air and the particle phase of 150 μm glass and 70 μm copper spheres are numerically simulated using the k–ɛ model and the ISSF model, respectively. The predicted mean streamwise velocities as well as streamwise and transverse fluctuating velocities of both phases agree well with experimental data reported by Fessler. The reattachment length of 7.6H matches well with the experimental value of 7.4H. Distributions of particle number density are also given and found to be in good agreement with the experiment. The sensitivity of the predicted results to the number of calculation particles is studied and the improved model is shown to require much less calculation particles and less computing time for obtaining reasonable results as compared with the traditional stochastic separated flow model. It is concluded that the ISSF model can be used successfully in the prediction of backward-facing step gas-particle flows, which is characterised by having recirculating regions and anisotropic fluctuating velocities. Received 20 June 2000     

An improved perturbation method for stochastic finite element model updating

In this paper, an improved perturbation method is developed for the statistical identification of structural parameters by using the measured modal parameters with randomness. On the basis of the first‐order perturbation method and sensitivity‐based finite element (FE) model updating, two recursive systems of equations are derived for estimating the first two moments of random structural parameters from the statistics of the measured modal parameters. Regularization technique is introduced to alleviate the ill‐conditioning in solving the equations. The numerical studies of stochastic FE model updating of a truss bridge are presented to verify the improved perturbation method under three different types of uncertainties, namely natural randomness, measurement noise, and the combination of the two. The results obtained using the perturbation method are in good agreement with, although less accurate than, those obtained using the Monte Carlo simulation (MCS) method. It is also revealed that neglecting the correlation of the measured modal parameters may result in an unreliable estimation of the covariance matrix of updating parameters. The statistically updated FE model enables structural design and analysis, damage detection, condition assessment, and evaluation in the framework of probability and statistics. Copyright © 2007 John Wiley & Sons, Ltd.     

Approximate method for calculating turbulent two-phase flow in a channel with permeable walls

Based on a model of a double-velocity and two-temperature medium the authors constructed a system of equations that describes plane or axisymmetric turbulent flow of a gas suspension in a channel with permeable walls. The system of equations of motion and heat transfer reduces to a system of ordinary differential equations, whose integration is much less difficult than solution of the initial system. The authors obtained the distribution of the velocity and local characteristics of turbulence in the channel with injection with allowance for the inverse effect of a condensed phase.     

An Oseen-type model for swirling internal separated flows

The viscous, laminar, separated flow downstream of a sudden expansion in a pipe is studied. The flow is modeled by an Oseen-type equation, but with the additional feature that the nonlinearity in the swirl is retained. Exact solutions are obtained for a high-Reynolds-number limit and for arbitrary Reynolds number by use of an eigenfunction-expansion procedure, in the presence of swirl. This leads to a non-standard eigenvalue problem. When the swirl is sufficiently large, a central recirculating region is observed. The effect of the pressure gradients on the velocity profiles and the central recirculating eddy is discussed. The low-Reynolds-number solutions go over smoothly to the large Reynolds number solution as the Reynolds number increases. Good agreement is obtained with the numerically computed value of the reattachment length.     

Magnetic fluid model for two-phase pulsatile flow of blood

Summary A two-phase magnetic fluid model for pulsatile flow of blood has been investigated by using realistic input data (pressure gradient). Closed form analytic solutions have been obtained. It is observed that the existing analysis could be improved by including driving force profiles (this could help in detecting the numerical, algebraic or formulation error to some extent) and two types of velocity profiles. Further, a new nondimensional numberS _N is introduced which can be used to control the flow and its behavior. It is possible to make the flow stable or unstable with a proper choice ofS _N. This could be exploited for many interesting applications, e.g. in bloodless surgery, in designing magnetic band aids for first aid box (for snake bites and to stop the blood loss from injuries in accidents and wars).     

An approximate mathematical model of heat and mass transfer in two-phase flow

We propose an approximate method for studying transport processes in one-dimensional two-phase flow which permits the determination of the system output as a function of input and the system parameters. The error of the method is estimated.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 34, No. 4, pp. 673–683, April, 1978.     

Fluctuation model of a nonequilibrium two-phase channel flow

An ill-posed Cauchy problem for a model of a nonequilibrium two-phase flow in the barotropic approximation is transformed into a well-posed problem by changing the type of the initial hyperbolic equations. Approximation of fluctuations of the phase velocities by a random delta-correlated process and averaging of the equations over its realizations generate a system of parabolic equations. Results of numerical integration of this system are compared with experiment and calculations by well-known models.Notation a velocity of propagation of acoustic perturbations - frozen velocity of sound - b dimensionless constant - h enthalpy - L tube length, scale of velocity fluctuations - p pressure - R complex - T temperature - t time - velocity - x coordinate - step of the difference scheme - fluctuating component of the velocity, delta-function - dimensionless variable - phase density - ² variance of the velocity - characteristic correlation time - volume phase concentration Institute of Engineering Thermophysics, Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 66, No. 6, pp. 651–656, June, 1994.     

Statistical model of turbulent flow with polymer additives

A closed equation is obtained for the function describing the length scale distribution of the turbulent velocity fluctuation energy in an isotropic flow of dilute linear high-molecular polymer solution.Translated from Inzhenerno-fizicheskii Zhurnal, Vol. 61, No. 6, pp. 895–904, December, 1991.     

An improved model for simulating impedance spectroscopy

A numerical method for simulating the frequency-dependent impedance response of multi-phase composite materials has been developed. The algorithm takes as input 1) a digital image of a microstructure, in two or three dimensions, of any specified composite material, and 2) the frequency-dependent electrical properties of the individual phases of the composite. An impedance spectrum of any frequency range can then be computed using a conjugate gradient algorithm operating on a finite difference solution scheme of Laplace's equation. Examples are given of the impedance of analytically solvable microstructures, to validate the algorithm, and of a random system, to test the usefulness of two different effective medium theories.     

A finite difference calculation procedure for three-dimensional turbulent separated flows

A general finite difference scheme has been proposed along with a three-dimensional co-ordinate transformation procedure for the prediction of three-dimensional fully elliptic flows. This numerical scheme has been successfully employed for the calculations of the three-dimensional turbulent separated flow in a rectangular diffuser. The complexity of the phenomena is seen to increase tremendously for the three-dimensional flows of this class.     

An electrical arc in a turbulent gas flow

The self-similar solution of the equations describing an axisymmetric electrical arc in a turbulent gas flow is presented.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 48, No. 2, pp. 272–278, February, 1985.     

An improved explicit finite element method for tidal flow

A weighting function by which the mass matrix is made to be diagonal is deduced on the two-dimensional simplex element. Adopting the weighted residual method with the deduced weighting function for spatial domain and the two-step Lax–Wendroff method for time differentiation, the two-dimensinoal tidal flow in a model basin is calculated by means of the explicit finite element method. The water mass transport integrated over one tidal period at some cross-sections of the basin is also estimated, in order to verify the water mass conservation. It is found that the water mass is nearly conserved in the present method, although the usual lumped mass matrix technique fails to conserve. The present explicit finite element method with the conservative form of governing equations is also investigated and the water mass conservation is found to be a little more improved in this case than in the case of non-conservative forms. Application to a real bay indicates that the method with the conservative form of equations could be used for the estimation of tidal residual flow.     

桥梁断面气动导数识别的改进随机子空间法

随机子空间算法在桥梁断面气动导数识别中表现出了良好的适应性,已能较好地识别出系统的频率和阻尼比,但在低风速条件下模态振型的识别精度尚无法令人满意.气动导数对模态振型相对变化的敏感性分析表明,模态振型对气动导数识别结果影响显著.在传统的基于输出协方差的随机子空间方法(SSI)基础上,引入一种新的稳定图,同时将频率、阻尼比和振型这3种模态参数的相对误差作为形成稳定轴的标准来获取气动导数.为验证该方法的可行性,进行了平板节段模型的数值仿真,结果表明该方法有助于提高模态振型的识别精度,进而提高气动导数的识别精度.     

An improved MCDM DEA model for technology selection

This paper presents an Improved MCDM Data Envelopment Analysis (DEA) model in order to evaluate the best efficient DMUs in Advanced Manufacturing Technology (AMT). This model is capable of ranking the next most efficient DMUs after removing the previous best one.     

一种改进的扬声器Volterra模型研究

在研究扬声器振膜的非线性振动时,通常使用Volterra模型进行建模分析。然而受到误差的影响,该模型仅适用于微弱的非线性现象。增大激励电压,频响预测结果的误差逐渐增大。针对这一问题,一种改进的扬声器Volterra模型被提出。该模型引入了振膜平衡位置偏移量对非线性参数的影响,并且在计算位移响应时引入高阶核函数的互调项,使位移响应预测结果更为精确。为了验证模型,搭建了一套可以测量振膜瞬时位移的激光测量系统。实验中测量并计算了振膜平衡位置偏移量和位移的基频响应。结果表明,改进的扬声器Volterra模型与实验结果的一致性较传统模型更好。     

Soil deposit stochastic settlement simulation using an improved autocorrelation model

Soil parameters are spatially random variables. Thus, the spatial correlation relationship, besides the mean and variance, of a specific soil site is needed for any realistic stochastic modeling. In this regard, an improved autocorrelation model involving a linear, an exponential and cosine terms, named linear-exponential-cosine (LNCS), is adopted here to capture the spatial properties of the soil deposits. Further, a random field of the soil deposit is simulated using a two-dimensional Karhunen–Loéve expansion based on the new autocorrelation model. Furthermore, two cases for the soil settlement are calculated with the random field of the soil deposits. One case is the stochastic settlement from a reference paper. Some comparisons are undertaken, and it is found that the mean value agrees well with the reference. The other case involves the differential settlement analysis of a real engineering project. The settlement is calculated with the random field, the uniform field respectively, and is compared with the on-site measured values. The results show that the random field model can capture the differential settlement better than the corresponding uniform field model.     

An improved Navier-Stokes flow computation of AGARD case-10 flow over RAE2822 airfoil using Baldwin-Lomax model

Summary Transonic flow over the RAE2822 airfoil has been solved for flow coditions corresponding to the AGARD test case 10. An extensively tested steady Navier-Stokes flow solver based on the finitevolume cell-centered explicit Runge-Kutta time stepping scheme has been used to simulate the flow. The experiment has shown a zone of separated flow after the foot of the shock. Under the conditions of considerable shock-boundary layer interaction, the Baldwin-Lomax eddy viscosity model has been found to produce unsatisfactory results. But, at the same time, efforts using different schemes and the turbulence/eddy viscosity models do not seem to lead to any significantly improved simulation of this flow even when computations have been made with marginally adjusted mach number and/or angle of attack. Interestingly, when the present code was used to study the above case, significantly improved result has been obtained (with marginally adjustedM and ) that is as good as and even better than the computations seen in the literature using various improved turbulence models. This computation appears to be the first of its kind where Baldwin-Lomax model has been used to produce such good quality result for this flow. This may even point towards a need to have another look at the wind tunnel interference correction used in AGARD test.     

Numerical calculation of fully developed turbulent flow in curved channels: An extended algebraic Reynolds-stress model

The primary objective of the paper is to extend an algebraic Reynolds-stress model including a new expression for the turbulent shear stress, in order to describe the negative production of turbulent kinetic energy appearing in curved channel flows in a region between the points of maximum velocity and vanishing shear stress. This so-called energy reversal cannot be captured by the majority of turbulence models with conventional eddy-viscosity formulation. Computations are made for fully developed flows in channels of rectangular cross section and large aspect ratio with mild and strong curvature. The results are compared with different model predictions and experimental data reported in the literature. In the cases considered, the accuracy of present model predictions is comparable to that of a Reynolds-stress model. The latter, however, requires much more computing time and is thus more costly than the model here proposed.     

Two-fluid model of refrigerant two-phase flow through short tube orifice

Pronounced hydrodynamic and thermodynamic non-equilibrium exist in the flow of refrigerant through a short tube orifice under typical operating conditions. A non-equilibrium two-fluid model (TFM) for refrigerant two-phase critical flow inside the short tube orifice is developed. Both inter-phase velocity slip and inter-phase temperature difference are taken into account in the model. The mass flow rate, the two-phase velocity and temperature distributions in a short tube orifice are simulated. Comparisons among the experimental data of refrigerants R134a, R12, R22, R410A and R407C flowing through short tubes, the predictions by the TFM and by the homogeneous equilibrium model (HEM) show that the TFM gives acceptable predictions with the deviations of ±20%, while the HEM underestimates the flow rate by 20% or so.