基于多重分形的离心压缩机出口动态压力非线性特征研究及其在喘振识别中的应用

以800 kW离心压缩机系统的工作状态从平稳到喘振阶段的出口动态压力为分析对象,从多重分形角度研究了多重分形谱参数与出口动态压力之间的关系,着重研究了系统在喘振状态表现出的复杂非线性特征。通过控制系统出口防喘振阀的开度得到离心压缩机在不同工况下的出口动态压力。研究系统出口动态压力的结构函数在不同权重因子下的尺度特征和多重分形谱参数与离心压缩机出口动态压力的关系。研究结果显示,系统稳态时,动态压力结构函数的曲线线性特征较为明显,而随着系统从过渡状态进入喘振时,表现出明显的非线性和多重分形特征。从多重分形谱的形状可以看出,当离心压缩机在稳态时,多重分形谱的宽度Δα最小,接近于零。随着系统进入喘振状态,宽度明显增加,而且在过渡过程时Δα的变化量较大,系统的不稳定性增加。从出口动态压力的多重分形谱参数的变化可以看出,多重分形谱参数在离心压缩机的过渡状态均出现了突变特征,参数Δα、αmax和Δf(α)随着系统从稳态进入失稳时增大,但参数αmin和f(αmax)则反方向变化,并且参数Δα、αmin、αmax的突变最为明显,这些特征可以作为系统进入过渡过程的判断依据。参数Δα、αmin、αmax在喘振时的波动量远大于稳态时的波动量,表明在喘振时动态压力的分布不如稳态时均匀。参数f(αmin)在喘振初期出现了短暂的峰值平台,说明此阶段的动态压力峰值出现的概率最大,而且Δf(α)的峰值也出现在喘振初期,这一特征可以用于初始喘振预测。研究结果能够为离心压缩机初始喘振的识别和预测提供新的依据,并可进一步用于压缩机喘振的主动控制中。     

On the geometric factors in fractured media

Abstract

In double‐porosity and multiple continuum models the fractured rock domain can be simplified as two overlapping continua, one for the matrix block system and the other for the fracture network. In this case, it is necessary to define an exchange term accounting for the transfer of fluid and solute masses between the two continua. A newly derived geometric parameter appears in the fluid exchange term, and is valid for any point‐centered block. The geometric parameter is more general and has a clear physical meaning. It is a function of both the shape and the size of the matrix block and agrees well with the double porosity model. The geometric center and conductance of the element is different under the quasi‐steady state compared to the steady state. Quasi‐steady condition is more suitable than steady state condition for modeling fractured media.     

Constrained pseudo‐transient continuation

This paper addresses the problem of finding a stationary point of a nonlinear dynamical system whose state variables are under inequality constraints. Systems of this type often arise from the discretization of PDEs that model physical phenomena (e.g., fluid dynamics) in which the state variables are under realizability constraints (e.g., positive pressure and density). We start from the popular pseudo‐transient continuation method and augment it with nonlinear inequality constraints. The constraint handling technique does not help in situations where no steady‐state solution exists, for example, because of an under‐resolved discretization of PDEs. However, an often overlooked situation is one in which the steady‐state solution exists but cannot be reached by the solver, which typically fails because of the violation of constraints, that is, a non‐physical state error during state iterations. This is the shortcoming that we address by incorporating physical realizability constraints into the solution path from the initial condition to steady state. Although we focus on the DG method applied to fluid dynamics, our technique relies only on implicit time marching and hence can be extended to other spatial discretizations and other physics problems. We analyze the sensitivity of the method to a range of input parameters and present results for compressible turbulent flows that show that the constrained method is significantly more robust than a standard unconstrained method while on par in terms of cost. Copyright © 2015 John Wiley & Sons, Ltd.     

An NTU-ε model for alternative refrigerants: Un modèle NTU-ε pour les frigorigènes de remplacement

This paper presents a steady state simulation model to predict the performance of alternative refrigerants in vapour compression refrigeration/heat pump systems. The model is based on the NTU-ε method in analysing the heat exchangers following an elemental approach. The model extends its applicability to new refrigerants including hydrocarbons and uses a large database of REFPROP package for refrigerant properties. The main inputs to the model include the physical details of the heat exchangers, compressor efficiency, mass flow rates of heat transfer fluids and their inlet temperatures to the evaporator and the condenser, the pressure drops across the heat exchangers and the capacity of either the evaporator or condenser (in kW). The model results are validated with a wide range of experimental data of HCFC22 and propane (HC290) on a heat pump test facility for a number of parameters, e.g. coefficient of performance, condenser capacity, mass flow rate of the refrigerant and compressor discharge temperature. Although the model is currently tested for pure refrigerants using compact brazed plate (counter flow type) heat exchangers, it can also be applied to mixture of refrigerants as well as to other types of heat exchangers.     

Fluidization of a granular bed (theory)

On the basis of a simple physical model, it is shown that four basic mechanisms are possible for the conversion of a granular bed into the fluidized state in apparatuses of constant cross section. Conditions for the practical realization of these mechanisms are discussed as functions of bed parameters.     

Dynamic testing and modeling of a diffusion absorption refrigeration system

This paper presents experimental investigations and modeling in dynamic or transient mode of a commercial diffusion-absorption refrigerator powered by an electric heater. The instantaneous cooling capacity is experimentally determined for different electric heater inputs. A first order transfer function with delay is found to be an adequate model of the refrigerator behavior for each heat input. The fitting quality of the model ranges between 93% and 97%. The three parameters of the model are expressed in a further step as functions of energy input to the machine in order to construct a generalized model for the machine. The steady state performances of the refrigerator are quite good predicted, with deviations in cooling capacity not exceeding 8%. The proposed generalized model could be very useful for the prediction of the transient behavior of the commercial diffusion-absorption refrigerator.     

Small-signal perturbation technique used for DSP-based identification of a three-phase three-level boost-type Vienna rectifier

New small-signal-modelling technique and validation procedures are applied to a three-phase three-level boost-type AC/DC Vienna converter. The adopted methodology consists of three steps: the first one is to elaborate the converter steady state and dynamic models that are derived by means of a local linearisation around the nominal operating point from the state space-averaged model, initially expressed in abc physical variables and then transformed into dqo synchronous reference frame. Twenty transfer functions relating the inputs to the outputs of the system are therefore obtained. The second step is the numerical verification using the averaged state space model and the converter model built in SIMULINK/MATLAB. Finally, an experimental validation of the transfer functions is carried out using a 1.5 kW laboratory prototype on the basis of the DS 1104 real-time controller board of dSPACE. The results are quantified and compared as magnitude and phase Bode graphs. It is confirmed that the proposed new small-signal model represents rather accurately the real system and is therefore reliable for further tasks such as dynamic characteristic analysis, numerical simulation as well as controller design purposes     

Exploiting intrinsic fluctuations to identify model parameters

Parameterisation of kinetic models plays a central role in computational systems biology. Besides the lack of experimental data of high enough quality, some of the biggest challenges here are identification issues. Model parameters can be structurally non‐identifiable because of functional relationships. Noise in measured data is usually considered to be a nuisance for parameter estimation. However, it turns out that intrinsic fluctuations in particle numbers can make parameters identifiable that were previously non‐identifiable. The authors present a method to identify model parameters that are structurally non‐identifiable in a deterministic framework. The method takes time course recordings of biochemical systems in steady state or transient state as input. Often a functional relationship between parameters presents itself by a one‐dimensional manifold in parameter space containing parameter sets of optimal goodness. Although the system''s behaviour cannot be distinguished on this manifold in a deterministic framework it might be distinguishable in a stochastic modelling framework. Their method exploits this by using an objective function that includes a measure for fluctuations in particle numbers. They show on three example models, immigration‐death, gene expression and Epo‐EpoReceptor interaction, that this resolves the non‐identifiability even in the case of measurement noise with known amplitude. The method is applied to partially observed recordings of biochemical systems with measurement noise. It is simple to implement and it is usually very fast to compute. This optimisation can be realised in a classical or Bayesian fashion.Inspec keywords: biochemistry, physiological models, stochastic processes, measurement errors, fluctuations, parameter estimationOther keywords: model parameter identification, deterministic framework, biochemical system, steady state, transient state, stochastic modelling framework, objective function, immigration‐death model, gene expression, Epo–EpoReceptor interaction, stochastic fluctuations, measurement noise     

Oxidation of Alloying Elements during ESR of Stainless Steel

The oxidation of alloying elements duringthe ESR of stainless steel has been studied.The model previously developed by WEI and Mitchellfor the chemical reactions and mass transferprocesses during ESR was applied to the remeltingof the high Cr steel 1Cr18Ni9(Ti).The laboratorydata for the unsteady state A.C.ESR were analyzedand dealt with by the model.When the remeltingprocess reached a steady state,an oxidant(Fe_2O_3powder)or a deoxidant(Ca-Si powder or metallicCa)was added to the slag bath.The resultsshowed that this model is applicable to theremelting of stainless steel rather precisely,and it is expected that the model may offera reliable basis for the control of compositionduring practical ESR of high alloy steel.Also,the oxidation of Cr in the steel mustbe noticed when its content is high;but itis entirely possible to adjust the Cr contentof ingot within a considerable range,usinga special technique by means of the slag-metalreactions during the remelting.     

Parameter identification of the observed citation distribution

Based on the transfer function model of the observed citation distribution and the expression of the cumulative citation probability distribution, parameters of 12 citation distributions are identified from statistical data of age distributions of references of 10 journals in JCR using the parameter optimization fitting method. At same time, based on the steady state solution of differential equations of the publication delay process and data of publication delays of 10 journals, the publication delay parameters of every journal are identified using the fitting method. Identified parameters of every journal citation distribution are compared with the journal’s publication delay parameters and some valuable conclusions are deduced.     

The structure of gasdynamic flow in a supersonic separator of natural gas

Results are given of calculations of flow within the two-dimensional Euler model of supersonic swirling flow of gas in a supersonic separator of natural gas. The formulation of the problem is given, numerical experiment is performed, and the basic parameters of gas flow (velocity components, pressure, and so on) are obtained as functions of radius. The process of relaxation of flow to steady state with the formation of shock wave is considered, and the shock wave structure is determined. The behavior of gasdynamic parameters is analyzed under conditions of separation in the region of shock wave and behind it.     

Unsteady‐ and steady‐state gas permeation through active packaging walls

Steady‐ and unsteady‐state gas permeation rates through packaging walls containing active (scavenger) materials are determined as functions of the system's physical parameters and the scavenger load. With the simplifying assumptions of constant scavenger concentration and first‐order reaction kinetics, steady‐state analysis shows that there is a minimum quantity of scavenger that must be added to the packaging wall if any reduction of gas permeation is to be achieved. Unsteady‐state studies have established the dependence of the time needed to reach stationary behaviour on the system's physical parameters. Copyright © 2007 John Wiley & Sons, Ltd.     

A simulation for the bulk polymerization of acrylonitrile

Abstract

In this paper, referring to the experimental observation of Thomas and Pellon, the authors consider the possible features of the development of the inter‐ and intra‐molecular forces of polymer and monomer molecules in the reaction mixture. Then, a critical chain length is proposed to be a criterion for the loci of polymerization for the polymer molecules. The polymer molecules formed initially exist and react in the solution phase. As soon as they attain a chain length longer than the critical chain length, they will separate from the solution phase, and continue their reaction in the precipitation phase by the diffusion‐controlled process. The chain transfer to monomer reaction is suggested as the deactivation reaction for the precipitated polymer radicals. In the kinetic treatment, the unsteady‐state condition is applied for the precipitation phase, while the steady‐state assumption is used for the solution phase.

Using the kinetic model proposed above, the authors provide the kinetic parameters for this acrylonitrile polymerization. The simulations of conversion‐time, rate‐conversion, and molecular weight‐conversion obtained fit excellently with the data of Hamielec et al. The critical chain length for this acrylonitrile system is found to be a function of the reaction temperature and the conversion.     

一种测量光学滤波器参数的低相干方法

在光纤通信网络中, 以微环为代表的光学滤波器是实现在波长频段选择功能的重要器件。测量该器件的物理参数不仅是实际应用的需求更有利于设计更加复杂的滤波器结构。本文基于低相干干涉测量技术, 给出一种通用数学方法, 可获得复杂结构微环滤波器的物理参数。该方法引入数字滤波器概念以及 Z变换分析法来对光学滤波器进行建模, 并用简洁的线性方程组将干涉图中峰值以及传输函数的系数关联起来。对于一个给定的滤波器结构, 根据传输函数与物理参数的内在关联, 物理参数就能被准确地计算出来, 从而为器件的激光修正提供关键参数。实验结果表明, 该方法实现了低成本并且准确可行。     

Value of a statistical life in road safety: A benefit-transfer function with risk-analysis guidance based on developing country data

We model a value of statistical life (VSL) transfer function for application to road-safety engineering in developing countries through an income-disaggregated meta-analysis of scope-sensitive stated preference VSL data. The income-disaggregated meta-analysis treats developing country and high-income country data separately. Previous transfer functions are based on aggregated datasets that are composed largely of data from high-income countries. Recent evidence, particularly with respect to the income elasticity of VSL, suggests that the aggregate approach is deficient because it does not account for a possible change in income elasticity across income levels. Our dataset (a minor update of the OECD database published in 2012) includes 123 scope-sensitive VSL estimates from developing countries and 185 scope-sensitive estimates from high-income countries. The transfer function for developing countries gives VSL = 1.3732E−4 × (GDP per capita)^∧2.478, with VSL and GDP per capita expressed in 2005 international dollars (an international dollar being a notional currency with the same purchasing power as the U.S. dollar). The function can be applied for low- and middle-income countries with GDPs per capita above $1268 (with a data gap for very low-income countries), whereas it is not useful above a GDP per capita of about $20,000. The corresponding function built using high-income country data is VSL = 8.2474E+3 × (GDP per capita)^∧.6932; it is valid for high-income countries but over-estimates VSL for low- and middle-income countries. The research finds two principal significant differences between the transfer functions modeled using developing-country and high-income-country data, supporting the disaggregated approach. The first of these differences relates to between-country VSL income elasticity, which is 2.478 for the developing country function and .693 for the high-income function; the difference is significant at p < 0.001. This difference was recently postulated but not analyzed by other researchers. The second difference is that the traffic-risk context affects VSL negatively in developing countries and positively in high-income countries. The research quantifies uncertainty in the transfer function using parameters of the non-absolute distribution of relative transfer errors. The low- and middle-income function is unbiased, with a median relative transfer error of −.05 (95% CI: −.15 to .03), a 25th percentile error of −.22 (95% CI: −.29 to −.19), and a 75th percentile error of .20 (95% CI: .14 to .30). The quantified uncertainty characteristics support evidence-based approaches to sensitivity analysis and probabilistic risk analysis of economic performance measures for road-safety investments.     

计算二维矩形声腔传递矩阵及传递函数的声源模型探讨

计算二维矩形声腔传递矩阵的点源模型已在实际工程中取得了广泛应用，但是点源模型本身的奇异性使得传递矩阵的计算不精确。首先全面分析了线声源和面声源模型的声压收敛情况，证明线源和面源可以用来计算传递矩阵。然后详细讨论了点源和面源模型计算传递函数的区别，得出结论：面源模型更适合用于二维模型计算传递矩阵，收敛更快，可以消除点源模型计算的奇异性；点源模型可以计算体积流量的传递函数，但是计算压力传递函数会引起较大误差，这时需要用到面源模型。     

Isothermal two-phase flow of a vapor-liquid system with non-negligible inertial effects

In this paper we consider the problem of gas/liquid extraction near the bottom well in the context of geothermal energy exploitation. In particular we develop a mathematical model for the isothermal two-phase flow of a mono-component fluid in an undeformable porous media taking into account inertial effects. We use the so-called Forchheimer’s equation to model the relation between the fluid velocity and the pressure gradient in the region of co-existence of the two phases.We formulate the problem in cylindrical geometry assuming steady state and isothermal conditions. We take into account capillary pressure and we study its influence on the whole system. We derive important formulas that allow to predict the main thermodynamical quantities in the region of co-existence of the liquid and gaseous phase and we determine constraints on the physical parameters in order to predict the behavior of the fluid in the domain of the problem. Finally, we perform some numerical simulations to investigate the dependence on the physical parameters involved in the model.     

Symmetry in Partially Coherent Imaging of Semi-transparent Edges

Abstract

The extended linear approximation [1] is applied to defocused imaging of semi-transparent edges. The approximated intensity distributions are given and the influence of the following parameters are studied: edge transparency and phase shift, coherence parameter and defocusing. For an opaque edge and a phase edge approximated intensity curves are compared to curves obtained by the exact calculation with the ‘bilinear transfer function’. It is shown that characteristic effects of the image intensity can be referred to the two transfer functions of the extended linear approximation and that it is possible to separate the influence of the object and the system, which is the principal advantage of the use of transfer functions.     

An equivalent pressure source for the heart

A technique is described for the representation of the left ventricle as a one-port source characterized by a generator pressure and an internal impedance. The Fourier components of the pressure and impedance are determined from phasor analysis performed on recorded time-domain functions of pressure and flow under two conditions of loading. One condition is the quiescent state corresponding to normal operation of the circulatory system, and the other is obtained by use of a phase-shift balloon pump situated in the descending thoracic aorta. The use of the balloon pump for determining source parameters is novel. The Fourier components of pressure and impedance are determined for the first five harmonics of the quiescent pulse rate. Heart failure is simulated by ligation of all branches of the anterior descending coronary artery. The source parameters have been found to vary considerably between normal and failing hearts. Valve impedance and the impedance at the root of the aorta were also measured. The generator time-domain pressure waveforms were determined from the Fourier components. Effects of long duration pumping, upon the source parameters were found. The ratio of the calculated magnitudes of internal to external or load impedance indicates the possibility of considering the heart as a pressure source.     

Stabilized finite element method for viscoplastic flow: formulation with state variable evolution

A stabilized, mixed finite element formulation for modelling viscoplastic flow, which can be used to model approximately steady‐state metal‐forming processes, is presented. The mixed formulation is expressed in terms of the velocity, pressure and state variable fields, where the state variable is used to describe the evolution of the material's resistance to plastic flow. The resulting system of equations has two sources of well‐known instabilities, one due to the incompressibility constraint and one due to the convection‐type state variable equation. Both of these instabilities are handled by adding mesh‐dependent stabilization terms, which are functions of the Euler–Lagrange equations, to the usual Galerkin method. Linearization of the weak form is derived to enable a Newton–Raphson implementation into an object‐oriented finite element framework. A progressive solution strategy is used for improving convergence for highly non‐linear material behaviour, typical for metals. Numerical experiments using the stabilization method with hierarchic shape functions for the velocity, pressure and state variable fields in viscoplastic flow and metal‐forming problems show that the stabilized finite element method is effective and efficient for non‐linear steady forming problems. Finally, the results are discussed and conclusions are inferred. Copyright © 2002 John Wiley & Sons, Ltd.