A stochastic approach to calculate the particle size distribution function of soot particles in laminar premixed flames

We introduce an efficient stochastic approach to solve the population balance equation that describes the formation and oxidation of soot particles in a laminar premixed flame. The approach is based on a stochastic particle system representing the ensemble of soot particles. The processes contributing to the formation and oxidation of soot particles are treated in a probabilistic manner. The stochastic algorithm, which makes use of an efficient majorant kernel and the method of fictitious jumps, resolves the entire soot particle distribution (PSDF) without introducing additional closure assumptions. A fuel-rich laminar premixed acetylene flame is computed using a detailed kinetic soot model. Solutions are obtained for both, the stochastic approach and the method of moments combined with a modified version of the Premix, CHEMKIN code. In this manner, the accuracy of the method of moments in a laminar premixed flame simulation is investigated. It is found that the accuracy for the first moment is excellent (5% error), and mean error for rest of the moments is within 25%. Also the effect of the oxidation of the smallest particles (burnout) has been quantified but was found not to be important in the flame investigated. The time evolution of computed size distributions and their integral properties are compared to experimental measurements and the agreement was found to be satisfactory. Finally, the efficiency of the stochastic method is studied.     

波浪荷载作用下海上新型潜式浮式风力机运动特性研究

以适用于中等水深(50~200 m)的新型潜式浮式风力机为研究对象,该风力机基础综合Spar式、半潜式及张力腿(TLP)3类浮式风力机基础的优点,运行时基础主体淹没在水下,具有较小的水线面(如同Spar平台),受波浪影响较小;平台通过张紧式系泊线与海床相连(如同TLP平台),具有良好的垂荡和摇摆运动特性;拖航状态下,浮式平台处于半潜状态,水线面面积大(如同半潜式平台),具有良好的浮稳性。通过分析不同波况下的潜式浮式风力机耦合动力响应得到潜式浮式基础的横荡、纵荡、垂荡及纵摇运动响应,以及发电功率、叶片根部弯矩、塔筒顶部和底部弯矩、锚链张力时程曲线。研究结果表明:波浪对于结构的纵摇运动的影响最为明显,对发电功率、叶片根部弯矩和塔筒顶部弯矩影响较小,对塔筒底部弯矩和系泊线张力影响较大。     

Net-section limit moments and approximate J estimates for circumferential cracks at the interface between elbows and pipes

This paper firstly presents net-section limit moments for circumferential through-wall and part-through surface cracks at the interface between elbows and attached straight pipes under in-plane bending. Closed-form solutions are proposed based on fitting results from small strain FE limit analyses using elastic–perfectly plastic materials. Net-section limit moments for circumferential cracks at the interface between elbows and attached straight pipes are found to be close to those for cracks in the centre of elbows, implying that the location of the circumferential crack within an elbow has a minimal effect on the net-section limit moment. Accordingly it is also found that the assumption that the crack locates in a straight pipe could significantly overestimate the net-section limit load (and thus maximum load-carrying capacity) of the cracked component. Based on the proposed net-section limit moment, a method to estimate elastic–plastic J based on the reference stress approach is proposed for circumferential cracks at the interface between elbows and attached straight pipes under in-plane bending.     

Wind turbine aerodynamics and loads control in wind shear flow

Wind turbine is subjected to some asymmetrical effects like wind shear, which will lead to unsteady blade airloads and performance. Fatigue loads can lead to damage of turbine components and eventually to failures. It is evident that the variation of the velocity over the rotor disc has an influence on the blade and introduces both flap-wise and edge-wise fatigue damage on the blade as a result of moment fluctuations in the two directions. The flap-wise moments on the blade are the origin of the rotor yaw and tilt moments which transmit to the turbine structure through the drive train to the yaw system and the tower. A lifting surface method with time marching free wake model is used to investigate the periodic unsteady nature in the wind shear. Individual pitch control (IPC) that is applied nowadays is the most advanced active control to reduce the fatigue. The blade airloads and performance of the turbine are also predicted under IPC control. It is found that IPC of the fluctuating blade root flap-wise moment can reduce the flap-wise fatigue damage remarkably while the blade root edge-wise moments are less sensitive to the varying blade pitch than the blade root flap-wise moments.     

Plastic collapse moment of 90° long radius elbows with internal circumferential surface crack at intrados under in-plane bending

Piping elbows under in-plane bending moment are vulnerable to cracking. The crack initiates at the surface and eventually reaches through the thickness and may lead to failure. The structural integrity assessment requires knowledge of the limit load. Limit load solutions for elbows with through-wall crack configurations are available in the open literature. But solutions for surface crack are not available. This paper presents a closed form expression for the plastic collapse moment (PCM) of 90°, long radius elbows with circumferential surface cracks at the intrados, under in-plane bending moment. The expression is derived, based on the results of non-linear (geometric and material) FE analyses covering a wide range of geometries and crack sizes. These plastic collapse moments evaluated herein will help in structural integrity assessment.     

Effects of wind shear on wind turbine rotor loads and planetary bearing reliability

Recent studies suggest that wind shear and the resulting pitch moments increase bearing loads and thereby contribute to premature wind turbine gearbox failure. In this paper, we use momentum‐based modeling approaches to predict the pitch moments from wind shear. The non‐dimensionalized results, which have been validated against accepted aeroelastic results, can be used to determine thrust force, pitch moment and power of a general rotor as a function of the wind shear exponent. Even in extreme wind shear (m = 1), the actual thrust force and power for a typical turbine (R* < 0.5) were within 8% and 20% of the nominal values (those without wind shear), respectively. The mean pitch moment increased monotonically with turbine thrust, rotor radius and wind shear exponent. For extreme wind shear (m = 1) on a typical turbine (R* = 0.5), the mean pitch moment is ~25% the product of thrust force and rotor radius. Analysis of wind shear for a typical 750 kW turbine revealed that wind shear does not significantly affect bearing loads because it counteracts the effects of rotor weight. Furthermore, even though general pitch moments did significantly increase bearing loads, they were found to be unlikely to cause bearing fatigue. Analyses of more common low wind‐speed cases suggest that bearing under‐loading and wear are more likely to contribute to premature bearing failure than overloading and classical surface contact fatigue. Copyright © 2015 John Wiley & Sons, Ltd.     

Assessing the advantages and drawbacks of government trading of guarantees of origin for renewable electricity in Europe

The European Commission has proposed a new Renewable Energy Directive, which includes flexibility provisions allowing the cost-effective attainment of the ambitious target for renewable energy of 20% of energy consumption, which has been set for the year 2020. One of the flexibility provisions currently being considered is to allow countries to reach their individual targets by buying their renewable electricity deployment deficit from other countries with a surplus (i.e., with a renewable electricity deployment above their targets). This trade is likely to take the form of an exchange in guarantees of origin (GOs). GOs are currently implemented in Member States to fulfil the Renewable Electricity Directive requirement that each country has a system that allows the tracing of the source of each kWh of renewable electricity and informs on this source. Although the recent and tiny literature on the analysis of GO trading has focused on trade between firms, the exchange of GOs between governments has not received a comparable attention. This paper analyses the advantages and drawbacks of a system of government trading of GOs with respect to company trading.     

National policies for achieving energy thrift, environmental protection, improved quality of life, and sustainability

For this study, countries are categorised on the basis of their level of economic development (i.e. as being either industrialised or developing) and with respect to their indigenous energy resources (i.e. as being either energy rich or energy poor). A further factor to consider is the growing strength of the emerging regional trading blocs in the world, and the more-effective protectionist measures that these blocs have the potential to administer: a developing country is likely to benefit when it becomes part of such a trading bloc.

Nevertheless not only regionally, but also worldwide, governments are failing to address with sufficient urgency the simultaneous but related problems and consequences of: (i) the major depletion of fossil-fuel reserves that will occur during the next 50 years; and (ii) the rapid environmental degradation occurring as a result of our non-sustainable lifestyles.

The issues that need to be considered when trying to implement sustainable energy policies are discussed.     

Optimal bidding strategy in a competitive electricity market based on agent-based approach and numerical sensitivity analysis

The objective of this study is to present a new method for determination of the optimal bidding strategies among generating companies (GenCo) in the electricity markets using agent-based approach and numerical sensitivity analysis (NSA). While agent-based approach provides for decision making, NSA can help with identifying the critical control points that lead to proper decisions to be taken by GenCos. To achieve the objective, the pricing mechanism used for settling the electricity market and determining the GenCos rewards is locational marginal pricing (LMP) and the sensitivity of each GenCo reward with respect to its bid is analyzed, then, the optimal strategy is determined. An example and a case study are used to illustrate the efficiency of the proposed method. The LMPs and allocated generations of GenCos show that the proposed method leads GenCos to learn a strategic manner and, as a result, increase prices and maximize their rewards. To validate the proposed method, the results from this study are compared with those available in the literature. The comparison of results shows an improved simulation time by 8.16 percent and total reward of market by 2.46 percent.     

Population balance model of heat transfer in gas–solid particulate systems

A population balance model is derived for heat transfer processes in gas–solid systems with intensive motion of particles in order to describe the temperature distribution of particulate phase. The model involves collisional particle–particle and particle–wall heat transfers, and continuous gas–particle, gas–wall and wall–liquid environment heat transfer processes. Collisional heat transfers are characterised by collision frequencies and random heat exchange parameters with general probability distributions with support [0, 1], describing the heat transfer efficiency between the colliding solid bodies. An infinite hierarchy of moment equations, describing the time evolution of moments of the temperature of particle population is derived from the population balance equation, which can be closed at any order of moments. The properties of the model and the effects of parameters are examined by numerical experiments using the second order moment equation model of a spatially homogeneous fluidized bed.     

Airfoil wind tunnel correction for angles of attack from −180° to 180°

Wind tunnel corrections are investigated for two‐dimensional low‐speed wind tunnel tests that are performed for three similar airfoils for angles of attack ranging from ?180° to 180° at Re = 0.75 × 10⁶. Aided by the Blasius theorem, wind tunnel corrections are deduced for the lift, drag and pitching moment of the airfoil at high angles of attack. The wall pressure signature method is applied to determine the strengths of the equivalent singularities. The tunnel wall‐induced force and pitching moment are obtained by calculating the force and moment exerted on the equivalent singularities. The maximum correction for drag is determined to be about 50%. The corrected forces and pitching moments for three similar airfoils are coincident with one another. A method to determine an optimum singularities distribution range is presented. The results indicate that the correction method in the paper is effective for airfoil testing at high angles of attack. Copyright © 2014 John Wiley & Sons, Ltd.     

Comparison between a composition PDF transport equation model and an ASOM model for simulating a turbulent jet flame

A composition PDF transport equation (PDF) model and an algebraic second-order moment (ASOM) model of turbulent combustion are used to simulate a methane–air turbulent jet flame, measured by the Sandia National Laboratory. In most regions, both PDF and ASOM predictions are in agreement with the experimental data with not too much difference. The PDF modeling results give the second-order moments with distributions having a similar trend as those given by the ASOM closure model. Although in general the PDF modeling results are somewhat better than the ASOM results, but considering that the computation time of the ASOM model is almost in two orders of magnitude smaller than that of the PDF model, the ASOM model is suggested for simulating large-size engineering facilities.     

Green's function for infinite thin plate with elliptic hole under bending heat source and interaction between elliptic hole and crack under uniform bending heat flux

Green's function is derived for the bending problem of an infinite thin plate with an elliptic hole under a bending heat source. Then the interaction problem between an elliptic hole and a crack in a thin plate under uniform bending heat flux is analyzed. First, the complex variable method is developed for the thermoelastic problem of bending. Then an exact solution in explicit form is derived for the Green's function by using the complex variable method. Distributions of temperature moment, heat flux moments, bending moments along the hole edge are shown in figures. For solving the interaction problem, a solution for an infinite thin plate with an adiabatic elliptic hole under uniform bending heat flux, and two Green's functions of the plate under a bending heat source couple and a bending dislocation are given. The interaction problem then reduces into singular integral equations using the Green's functions and the principle of superposition. After the equations are solved numerically, the moment intensity factors at crack tips are presented in the figures.     

Parametric survey of upper and lower bound limit in-plane bending moments for single mitred pipe bends of various geometries

The problem of limit analysis for a cylinder–cylinder intersection forming a single mitred pipe bend subject to in-plane bending has been investigated. Lower bound analysis with new equations of force and moment equilibrium together with a higher number of parameters resulted in more stability as compared to a previous analysis of the same problem [PhD Thesis, The University of Manchester, 1991]. Concurrently, abaqus finite element plastic collapse moments were obtained as upper bounds to the problem. Two sets of results were compared, showing good agreement with each other. It could be finally concluded that the true limit moments are bounded in between.     

A stackelberg game approach for heterogeneous energy market in integrated energy system

With the increasing demand of energy and the growing intensity of energy crisis, various smart energy systems are developed on the distribution level, such as integrated energy system (IES). In this article, a trading mechanism among various energy retailers and consumers is designed under the open market environment. The trading problem is formulated as a multi‐leader and multi‐follower Stackelberg game, which is built with the strategy set of energy bidding price and purchasing pattern. In particular, consumer's demand is described with the price elasticity property of demand, and non‐cooperative competition behavior among retailers is analyzed mathematically. To implement the proposed game approach, a distributed algorithm is presented by combining particle swarm optimization (PSO) and interior point method (IPM). Finally, simulation results show that the proposed trading mechanism will contribute to the development of heterogeneous energy market and the overall profit of retailers in the traditional trading mechanism is 37.8% lower than the profit in the proposed mechanism.     

Nonlinear analysis and plastic deformation of pipe elbows subjected to in-plane bending

The purpose of this study is to investigate the large strain and stress analysis for pipe elbows subjected to in-plane bending moments. A finite element model for the bend was constructed and loaded taking geometric and material nonlinearities into account using (ABAQUS) nonlinear finite element code. The initiation of yielding for the opening and closing cases appears at the inside surface of the elbow crown. However, further loading causes a significant difference in strain distribution and deformed shapes. The limit moment for the opening cases is higher than that for closing due to the geometric stiffening effects.     

BUCKLING OF AUTOMATIC TRANSMISSION CLUTCH PLATES DUE TO THERMOELASTIC/PLASTIC RESIDUAL STRESSES

The plates of multidisk automatic transmission are known to buckle under extreme operating conditions. Axisymmetric (coning) and nonaxisymmetric (potato chip) modes can be obtained. It is shown that these modes result from in-plane axisymmetric residual bending moments in the disk and the critical value for each mode is found. A numerical algorithm is then developed to determine the residual moment due to a prescribed axisymmetric thermal history. Allowance is made for the temperature dependence of yield stress, elastic modulus, and coefficient of thermal expansion. The results show that susceptibility to buckling depends on a dimensionless geometric shape factor, the material properties, and the magnitude of the largest thermal excursion. With steel disks and typical design values for the shape parameter, buckling is predicted for temperature differences of about 600°C between inner and outer radii     

水文离散系统矩估计的E变换

研究了应用E变换与水文离散系统模型矩法的关系。示例证明,E变换可被用作为水文离散系统模型矩估计的一种有效方法。     

The influence of carbon dioxide trading scheme on economic dispatch of generators

This paper aims at probing into the topic of power units’ operation and dispatch based on Carbon Dioxide (CO₂) trading scheme. The trading cost of CO₂ emission is embedded into the traditional economic dispatch model, which will be solved by the New Particle Swarm Optimization (NPSO). By considering the CO₂ trading scheme, the influences of the various strategies for unit’s dispatch are simulated and analyzed in this paper. The proposed method, NPSO is developed in such a way that PSO with Constriction Factor (PSO-CF) algorithm is applied as a based level search. NPSO introduces two operators, “Random Particles” and “Fine-Tuning” into the PSO-CF algorithm to improve the drawback of searching global optimum and make the search method more efficient at the end of search. The efficiency and ability of NPSO is demonstrated by the six generating units. Simulation results indicated that reasonable solutions provide a practical and flexible framework for power sectors. They can be also used for generating alternatives and thus help decision makers to obtain the goals of minimal operation cost under their desired emission’s policies.     

Conditional moment closure for turbulent combustion

This paper reviews the fundamentals of conditional moment closure (CMC) methods for the prediction of turbulent reacting flows, with particular emphasis on combustion. It also surveys several of the applications that have been made. CMC methods predict the conditional averages and higher moments of quantities such as species mass fractions and enthalpy, conditional on the mixture fraction or reaction progress variable having a particular value. A brief introduction is given to generalized functions and probability density function (pdf) methods. This is followed by an exposition on the various methods of derivation for the CMC equation and the general characteristics of this equation and its boundary conditions. Simplifications that can be made in slender layer flows such as jets and plumes are outlined and examples of application of the technique to such flows are given. The method allows the definition of a new class of simplified reactors related to the well known perfectly stirred reactor and plug flow reactor: these are outlined. CMC predictions are compared to experiment and direct numerical simulations for flows with homogeneous turbulence. Derivation and modeling of the equations for conditional variances and covariances are outlined and their use in second-order CMC illustrated. Brief review is made of progress on application of the method to problems involving differential diffusion, multiple conditioning, sprays and premixed combustion.