Gas-kinetic unified algorithm for computable modeling of Boltzmann equation and application to aerothermodynamics for falling disintegration of uncontrolled Tiangong-No.1 spacecraft

How to solve the hypersonic aerothermodynamics around large-scale uncontrolled spacecraft during falling disintegrated process from outer space to earth,is the key to resolve the problems of the uncontrolled Tiangong-No.1 spacecraft reentry crash.To study aerodynamics of spacecraft reentry covering various flow regimes,a Gas-Kinetic Unified Algorithm(GKUA)has been presented by computable modeling of the collision integral of the Boltzmann equation over tens of years.On this basis,the rotational and vibrational energy modes are considered as the independent variables of the gas molecular velocity distribution function,a kind of Boltzmann model equation involving in internal energy excitation is presented by decomposing the collision term of the Boltzmann equation into elastic and inelastic collision terms.Then,the gas-kinetic numerical scheme is constructed to capture the time evolution of the discretized velocity distribution functions by developing the discrete velocity ordinate method and numerical quadrature technique.The unified algorithm of the Boltzmann model equation involving thermodynamics non-equilibrium effect is presented for the whole range of flow regimes.The gas-kinetic massive parallel computing strategy is developed to solve the hypersonic aerothermodynamics with the processor cores 500~45,000 at least 80%parallel efficiency.To validate the accuracy of the GKUA,the hypersonic flows are simulated including the reentry Tiangong-1 spacecraft shape with the wide range of Knudsen numbers of 220~0.00005 by the comparison of the related results from the DSMC and N-S coupled methods,and the low-density tunnel experiment etc.For uncontrolling spacecraft falling problem,the finite-element algorithm for dynamic thermalforce coupling response is presented,and the unified simulation of the thermal structural response and the hypersonic flow field is tested on the Tiangong-1 shape under reentry aerodynamic environment.Then,the forecasting analysis platform of end-of-life largescale spacecraft flying track is established on the basis of ballistic computation combined with reentry aerothermodynamics and deformation failure/disintegration.

A Gas-Kinetic Unified Algorithm for Non-Equilibrium Polyatomic Gas Flows Covering Various Flow Regimes

In this paper,a gas-kinetic unified algorithm(GKUA)is developed to investigate the non-equilibrium polyatomic gas flows covering various regimes.Based on the ellipsoidal statistical model with rotational energy excitation,the computable modelling equation is presented by unifying expressions on the molecular collision relaxing parameter and the local equilibrium distribution function.By constructing the corresponding conservative discrete velocity ordinate method for this model,the conservative properties during the collision procedure are preserved at the discrete level by the numerical method,decreasing the computational storage and time.Explicit and implicit lower-upper symmetric Gauss-Seidel schemes are constructed to solve the discrete hyperbolic conservation equations directly.Applying the new GKUA,some numerical examples are simulated,including the Sod Riemann problem,homogeneous flow rotational relaxation,normal shock structure,Fourier and Couette flows,supersonic flows past a circular cylinder,and hypersonic flow around a plate placed normally.The results obtained by the analytic,experimental,direct simulation Monte Carlo method,and other measurements in references are compared with the GKUA results,which are in good agreement,demonstrating the high accuracy of the present algorithm.Especially,some polyatomic gas non-equilibrium phenomena are observed and analysed by solving the Boltzmann-type velocity distribution function equation covering various flow regimes.

Convergence proof of the DSMC method and the Gas-Kinetic Unified Algorithm for the Boltzmann equation

This paper investigates the convergence proof of the Direct Simulation Monte Carlo(DSMC) method and the Gas-Kinetic Unified Algorithm in simulating the Boltzmann equation.It can be shown that the particle velocity distribution function obtained by the DSMC method converges to a modified form of the Boltzmann equation,which is the equation of the gas-kinetic unified algorithm to directly solve the molecular velocity distribution function.Their convergence is derived through mathematical treatment.The collision frequency is presented using various molecular models and the local equilibrium distribution function is obtained by Enskog expansion using the converged equation of the DSMC method.These two expressions agree with those used in the unified algorithm.Numerical validation of the converging consistency between these two approaches is illustrated by simulating the pressure driven Poiseuille flow in the slip transition flow regime and the two-dimensional and three-dimensional flows around a circular cylinder and spherical-cone reentry body covering the whole flow regimes from low speed micro-channel flow to high speed non-equilibrium aerothermodynamics.

A unified gas-kinetic scheme for multiscale and multicomponent flow transport

Compressible flows exhibit a diverse set of behaviors, where individual particle transports and their collective dynamics play different roles at different scales. At the same time, the atmosphere is composed of different components that require additional degrees of freedom for representation in computational fluid dynamics. It is challenging to construct an accurate and efficient numerical algorithm to faithfully represent multiscale flow physics across different regimes. In this paper, a unified gas-kinetic scheme(UGKS) is developed to study non-equilibrium multicomponent gaseous flows. Based on the Boltzmann kinetic equation, an analytical space-time evolving solution is used to construct the discretized equations of gas dynamics directly according to cell size and scales of time steps, i.e., the so-called direct modeling method. With the variation in the ratio of the numerical time step to the local particle collision time(or the cell size to the local particle mean free path), the UGKS automatically recovers all scale-dependent flows over the given domain and provides a continuous spectrum of the gas dynamics. The performance of the proposed unified scheme is fully validated through numerical experiments.The UGKS can be a valuable tool to study multiscale and multicomponent flow physics.

Optimal Power Flow Using Firefly Algorithm with Unified Power Flow Controller

Firefly algorithm is the new intelligent algorithm used for all complex engineering optimization problems. Power system has many complex optimization problems one of which is the optimal power flow (OPF). Basically, it is minimizing optimization problem and subjected to many complex objective functions and constraints. Hence, firefly algorithm is used to solve OPF in this paper. The aim of the firefly is to optimize the control variables, namely generated real power, voltage magnitude and tap setting of transformers. Flexible AC Transmission system (FACTS) devices may used in the power system to improve the quality of the power supply and to reduce the cost of the generation. FACTS devices are classified into series, shunt, shunt-series and series-series connected devices. Unified power flow controller (UPFC) is shunt-series type device that posses all capabilities to control real, reactive powers, voltage and reactance of the connected line in the power system. Hence, UPFC is included in the considered IEEE 30 bus for the OPF solution.

An Efficient Task Scheduling Method for the Unified Interface Platform of the Electric Information Acquisition System

Due to the large and frequent static data interaction between the Electric Information Acquisition System and the external business systems,researching on using limited server sources to do an efficient task scheduling is becoming one of the key technologies of the unified interface platform.The information interaction structure of the unified interface platform is introduced.Task scheduling has been decomposed into two stages,task decomposition and task combination,based on the features(various types and dispersed)of large static data.The principle of the minimum variance of the subtasks data quantity is used to do the target task resolving in the decomposition stage.The thought of the Greedy Algorithm is used in the task combination.Breaking the target task with large static data into serval composed tasks with roughly same data quantity is effectively realized.Meanwhile,to avoid the situation of the GA falling into the local optimal solution,an improved combination method has been put forward.Moreover,the new method creates more average composed tasks and making the task scheduling more effective.Ultimately,the effectiveness of the proposed method is verified by the experimental data.

轴对称Boltzmann模型方程统一算法与空天飞行环境喷管流动模拟

拦截机动飞行器周围大范围区域存在主喷/侧喷流/羽流影响,而传统的纳维-斯托克斯(Navier-Stokes,N-S)方程不能很好模拟发动机喷管扩张段出口附近流动情况,需要一种新的方法来处理这种全流域流动问题。为解决该问题,针对特定轴对称喷管内流动,本文通过数学推导确立描述不同克努森数稀薄环境条件下的轴对称喷管内流动Boltzmann模型方程,初步建立适于该模型方程的数值格式与气体动理论统一算法。通过开展同轴圆筒间的定常/非定常旋转流动以及轴对称喷管内流动数值计算研究,发现统一算法计算流场与其他途径得到的结果吻合较好,验证了统一算法在全局克努森数喷管流动模拟的适应性和可靠性。通过与低密度风洞实验对比,喷管出口核心区羽流结构一致,羽流轴线压力分布一致,表明统一算法可以有效解决喷管入口压缩段到扩张段多流域混合,尤其是出口附近稀薄气体真空低压环境流动问题。

含多类型直流的交直流混联电网潮流计算方法适用性分析

作为电网发展的新阶段,交直流混联电网呈现多类型直流参与、大规模交直流互联的特点,而关于统一迭代和交替迭代2种潮流计算方法的适用性尚未得到深入分析。为此基于含多类型直流的交直流混联电网对2种潮流计算方法的运算性能进行对比研究。推导了含常规直流、柔性直流、混合直流的交直流混联电网潮流模型,进而提出了相应的统一迭代法和交替迭代法。通过3个交直流混联电网测试系统和南方电网实际系统数据验证了潮流模型的有效性和潮流算法的准确性,结合系统负荷水平、系统强度、直流嵌入规模等因素对2种潮流计算方法的收敛性能和计算速度进行对比分析。研究结果表明,在含多类型直流的交直流混联电网中进行潮流计算时,统一迭代法的计算效率比交替迭代法高。

计及购电需求不确定性的微电网能源竞价交易模型

微电网可以将发电高峰期盈余的可再生能源出售来促进可再生能源消纳并获取最大收益。采用拍卖机制确定交易价格,但交易过程中购电需求的变化也会对可再生能源消纳及微电网收益产生影响,为此,提出一种计及购电需求不确定性的微电网能源竞价交易模型。首先采用统一价格同步向上叫价拍卖机制进行定价,并提出了拍卖机制的改进方案来平衡用能消费者的对不同时段的拍卖需求;考虑到用能消费者的购电需求不确定性,采用鲁棒线性优化算法来规避不确定性参数对最优解的影响。最后通过MATLAB软件仿真分析,证明了该模型能够最大限度地提高可再生能源的出售率及微电网的收益。

基于改进类电磁机制算法的UPFC多目标优化配置

统一潮流控制器(UPFC)能在不改变线路拓扑结构的条件下有效地改善电力系统潮流,从而提高输电能力与电压稳定性。针对系统可用输电能力、电压偏差和L指标等目标,建立了UPFC的多目标优化配置模型,采用结合差分进化算法(DE)的改进差分类电磁机制算法(DEEM)对所建模型进行求解,通过对算法中粒子的带电量、合力计算方式进行改进,同时添加自适应因子,进一步平衡算法的全局搜索与局部搜索能力。配置后的结果表明UPFC对增强系统输电能力、电压质量及电压稳定性的性能均有提高,且改进算法寻优效率的提升也得到了验证。

基于mRMR-SOM的异步电机轴承故障诊断研究

针对异步电机轴承故障诊断问题,提出了一种融合最大相关最小冗余特征选择算法(mRMR)和自组织映射神经网络(SOM)的故障诊断方法,并将其应用于轴承故障诊断的不同阶段。首先,在实验室环境下搭建了异步电机故障诊断试验平台,在不同电机状态下分别采集振动、电流和电压信号,利用统计学方法获取了高维混合特征集;然后,以互信息为背景,利用mRMR根据特征与状态标签间的相关性和特征间的冗余性,筛选了具备强区分能力的特征,以避免计算冗余和后验诊断性能下降;最后,采用SOM对异步电机健康和轴承故障状态进行了分类识别,验证了SOM对异步电机轴承故障诊断的有效性,以及mRMR对故障诊断结果的影响。研究结果表明:基于mRMR-SOM的异步电机轴承故障诊断方法能够准确地区分健康和故障状态,测试集分类准确率达到89%;使用mRMR特征筛选能够将154维特征降低至17维,缩短23.5%的网络收敛时间,并将分类准确率由89%提升至98%;试验结果验证了基于mRMR-SOM的异步电机轴承故障诊断方法对于异步电机轴承故障诊断问题的有效性,且证实其具备良好的诊断效果。

基于多源异构数据的能源电力碳排放监测诊断服务系统研究

针对我国碳排放工业类型多、碳排放监测数据源多样的问题,设计了一个基于多源异构数据的能源电力碳排放监测诊断服务系统。系统由非分光红外探测技术、改进型微分粒子群算法(particle swarm optimization,PSO)、云计算、对象链接与嵌入统一架构(OLE for process control-unified architecture,OPC-UA)技术等构成。通过改进PSO算法来提高收敛速度,进一步提高数据监测和处理效率。采取OPC-UA技术实现对碳排放多源异构数据进行统一传输和反馈,极大地缓解了系统主机的计算压力。试验结果表明,经系统技术核算的数据误差率在可接受范围内,为其他技术研究奠定基础。

DESIGN AND IMPLEMENTATION OF DUAL-FIELD MODULAR INVERSION ALGORITHM

Modular inverse arithmetic plays an important role in elliptic curve cryptography. Based on the analysis of Montgomery modular inversion algorithm, this paper presents a new dual-field modular inversion algorithm, and a novel scalable and unified architecture for Montgomery inverse hardware in finite fields GF(p) and GF(2n) is proposed. Furthermore, this architecture based on the new modular inversion algorithm has been verified by modeling it in Verilog-HDL, and accomplished it under 0.18 μm CMOS technology. The result indicates that our work has better performance and flexibility than other works.

A multi-objective gravitational search algorithm based approach of power system stability enhancement with UPFC

On the basis of the theoretical analysis of a single-machine infinite-bus (SMIB),using the modified linearized Phillips-Heffron model installed with unified power flow controller (UPFC),the potential of the UPFC supplementary controller to enhance the dynamic stability of a power system is evaluated by measuring the electromechanical controllability through singular value decomposition (SVD) analysis.This controller is tuned to simultaneously shift the undamped electromechanical modes to a prescribed zone in the s-plane.The problem of robust UPFC based damping controller is formulated as an optimization problem according to the eigenvalue-based multi-objective function comprising the damping factor,and the damping ratio of the undamped electromechanical modes to be solved using gravitational search algorithm (GSA) that has a strong ability to find the most optimistic results.The different loading conditions are simulated on a SMIB system and the rotor speed deviation,internal voltage deviation,DC voltage deviation and electrical power deviation responses are studied with the effect of this flexible AC transmission systems (FACTS) controller.The results reveal that the tuned GSA based UPFC controller using the proposed multi-objective function has an excellent capability in damping power system with low frequency oscillations and greatly enhances the dynamic stability of the power systems.

Unified Gas-Kinetic Wave-Particle Methods VI:Disperse Dilute Gas-Particle Multiphase Flow

A coupled gas-kinetic scheme(GKS)and unified gas-kinetic wave-particle(UGKWP)method for the disperse dilute gas-particle multiphaseflow is proposed.In the two-phaseflow,the gas phase is always in the hydrodynamic regime and is fol-lowed by GKS for the Navier-Stokes solution.The particle phase is solved by UGKWP in all regimes from particle trajectory crossing to the hydrodynamic wave interac-tion with the variation of particle’s Knudsen number.In the intensive particle colli-sion regime,the UGKWP gives a hydrodynamic wave representation for the particle phase and the GKS-UGKWP for the two-phaseflow reduces to the two-fluid Eulerian-Eulerian(EE)model.In the rarefied regime,the UGKWP tracks individual particle and the GKS-UGKWP goes back to the Eulerian-Lagrangian(EL)formulation.In the tran-sition regime for the solid particle,the GKS-UGKWP takes an optimal choice for the wave and particle decomposition for the solid particle phase and connects the EE and EL methods seamlessly.The GKS-UGKWP method will be tested in allflow regimes with a large variation of Knudsen number for the solid particle transport and Stokes number for the two-phase interaction.It is confirmed that GKS-UGKWP is an efficient and accurate multiscale method for the gas-particle two-phaseflow.

Unified gas-kinetic wave-particle methods IV: multi-species gas mixture and plasma transport

In this paper,we extend the unified gas-kinetic wave-particle(UGKWP)methods to the multi-species gas mixture and multiscale plasma transport.The construction of the scheme is based on the direct modeling on the mesh size and time step scales,and the local cell’s Knudsen number determines the flow physics.The proposed scheme has the multiscale and asymptotic complexity diminishing properties.The multiscale property means that according to the cell’s Knudsen number the scheme can capture the non-equilibrium flow physics when the cell size is on the kinetic mean free path scale,and preserve the asymptotic Euler,Navier-Stokes,and magnetohydrodynamics(MHD)when the cell size is on the hydrodynamic scale and is much larger than the particle mean free path.The asymptotic complexity diminishing property means that the total degrees of freedom of the scheme reduce automatically with the decreasing of the cell’s Knudsen number.In the continuum regime,the scheme automatically degenerates from a kinetic solver to a hydrodynamic solver.In the UGKWP,the evolution of microscopic velocity distribution is coupled with the evolution of macroscopic variables,and the particle evolution as well as the macroscopic fluxes is modeled from a time accumulating solution of kinetic scale particle transport and collision up to a time step scale.For plasma transport,the current scheme provides a smooth transition from particle-in-cell(PIC)method in the rarefied regime to the magnetohydrodynamic solver in the continuum regime.In the continuum limit,the cell size and time step of the UGKWP method are not restricted by the particle mean free path and mean collision time.In the highly magnetized regime,the cell size and time step are not restricted by the Debye length and plasma cyclotron period.The multiscale and asymptotic complexity diminishing properties of the scheme are verified by numerical tests in multiple flow regimes.

A Coupled Discrete Unified Gas-Kinetic Scheme for Convection Heat Transfer in Porous Media

In this paper,the discrete unified gas-kinetic scheme(DUGKS)is extended to the convection heat transfer in porous media at representative elementary volume(REV)scale,where the changes of velocity and temperature fields are described by two kinetic equations.The effects from the porous medium are incorporated into the method by including the porosity into the equilibrium distribution function,and adding a resistance force in the kinetic equation for the velocity field.The proposed method is systematically validated by several canonical cases,including the mixed convection in porous channel,the natural convection in porous cavity,and the natural convection in a cavity partially filled with porous media.The numerical results are in good agreement with the benchmark solutions and the available experimental data.It is also shown that the coupled DUGKS yields a second-order accuracy in both temporal and spatial spaces.

A Computational Comparison of Basis Updating Schemes for the Simplex Algorithm on a CPU-GPU System

The computation of the basis inverse is the most time-consuming step in simplex type algorithms. This inverse does not have to be computed from scratch at any iteration, but updating schemes can be applied to accelerate this calculation. In this paper, we perform a computational comparison in which the basis inverse is computed with five different updating schemes. Then, we propose a parallel implementation of two updating schemes on a CPU-GPU System using MATLAB and CUDA environment. Finally, a computational study on randomly generated full dense linear programs is preented to establish the practical value of GPU-based implementation.

Dimensional Complexity and Algorithmic Efficiency

This paper uses the concept of algorithmic efficiency to present a unified theory of intelligence. Intelligence is defined informally, formally, and computationally. We introduce the concept of dimensional complexity in algorithmic efficiency and deduce that an optimally efficient algorithm has zero time complexity, zero space complexity, and an infinite dimensional complexity. This algorithm is used to generate the number line.

基于统一屈服准则超固结土的应力诱导各向异性下负荷面模型

为了描述中主应力对超固结土力学行为的影响,提出了一种表征土体超固结和应力诱导各向异性新的弹塑性本构模型。采用统一表述Mohr-Coulomb、Drucker-Prager、Lade-Duncan和Matsuoka-Nakai 4种屈服准则的形状函数g(θ),将其引入到下负荷面模型中修改临界状态破坏线的斜率M值,从而实现新模型中M值能随洛德角θ改变而变化;选择塑性偏应变增量为迭代变量,利用Newton-Raphson迭代开发了新模型的应力积分算法,编写了UMAT子程序,成功将新模型嵌入大型商业有限元软件ABAQUS中。结果表明:新模型能同时表征土体的超固结、剪胀和应力诱导各向异性,预测结果与试验数据吻合良好;新模型物理意义明确表述简单,便于工程推广应用;新模型的应力积分算法收敛速度快,每个增量步所需的迭代次数少,收敛精度高,算法运行稳定可靠。