Aerodynamicsimulation_省略_eBoltzmannMetho
Science in China Series E: Technological Sciences© 2008 SCIENCE IN CHINA PRESSReceived December 25, 2007; accepted February 3, 2008doi: 10.1007/s11431-008-0063-3†Corresponding author (email: chenys@)Sci China Ser E-Tech Sci | Jun. 2008 | vol. 51 | no. 6 | Aerodynamic simulation of high-speed trains based on the Lattice Boltzmann Method (LBM)WANG YiWei, WANG Yang , AN YiRan & CHEN YaoSong†Department of Mechanics and Engineering, Peking University, Beijing 100871, ChinaAerodynamic simulation of high-speed trains has been carried out by using Lattice Boltzmann Method (LBM). Non-simplified train model was used and the number ofspace grids reached tens of millions. All results under different working conditions reflected the actual situation.Lattice Boltzmann Method (LBM), aerodynamic simulation, engineering applicationBoltzmann equation describes the kinetics of gas based on theory of molecular motion. But be-cause of the complexity of the equation, it is almost incapable of dealing with practical gas ki-netic except deducing a few thermodynamic relations. However, due to the emergence of giant computer, a method of practical value―the Lattice-Boltzmann Method (LBM)[1—3]―has been developed with the help of earlier lattice algorithm since the end of 1980s, which made fluid me-chanics from continuum level to molecular level and has become an advanced method of compu-tational fluid dynamics. After decades’ effort, excellent computational software has been given birth from theoretical LBM, which is now widely applied to the research and development of new products in some main pillar industries[4]. For instance, this computation software of fluid me-chanics is adopted by almost all the automobile manufacturing companies to optimize the aero-dynamic performance of their new models. Nowadays, China’s development of high-speed trains has just started, and the aerodynamic influence plays an important role in this field considering the high speed of trains. In this paper, LBM is used to study the aerodynamic performance of trains running in open air, in tunnel and in strong crosswind, respectively, which provides a tech-nological basis for the design of high-speed trains.Recently, with great development of the high-speed trains, it becomes quite urgent to obtain their aerodynamic performance. For high-speed trains at speed of over 200 km/h, their air drag reaches more than 75% of the total drag[5], which produces a direct impact on the power equip-ment of engines and the collocation of power grid. And what is more, high-speed trains running774 WANG YiWei et al. Sci China Ser E-Tech Sci | Jun. 2008 | vol. 51 | no. 6 | 773-783under strong crosswind are very likely to be turned over. As a result, it is both necessary and im-portant to study the aerodynamic performance and evaluate the running safety of high-speed trains.As a key method to study aerodynamic problems, Computational Fluid Dynamics (CFD) has been paid more and more attention to due to its advantage of saving time and money compared to experiment. Nowadays, the most common approach of CFD is solving Navier-Stocks equation based on continuum theory by discretizing it. However, due to the limited capabilities of modern computers, a great number of physical phenomena of fluids, such as turbulence, cannot be real-ized using the direct numerical simulation (DNS) approach. Various physical approximations have to be added. But these physical approximative models are not applicable to practical engi-neering problems concerning flow around cars, trains or other bluff body due to low accuracy of results (such as RANS model [6]) or tremendous quantity of solution process (such as LES/DES models [6]). However, in some area, LBM has an advantage over the computation methods based on Navier-Stocks equations.1 Governing equationsBoltzmann equation is more basic than N-S equation to reflect fluid mechanism [7, 8], from which the LBM method is developed with the help of the progress in computing technologies and the success in lattice algorithms. A standard Boltzmann equation can be described mathematically as follows:(,)(,)(),i i i i f t t t f t C f +∆+∆=+x c x (1) where i f represents the particle distribution function, i C represents the collision term, and i c represents the particle velocity along the direction i [9]. The most common form of the collision term is the so called BGK [10, 11] model: eq(),i f f C f τ−=− (2)where eq f represents equilibrium distribution function, and τ is the relaxation time for the particle distribution to converge to the equilibrium state by collision. It can be proved that the system described by eq. (1) basically satisfies the N-S equation at the macroscopic level under condition that the discrete velocity set satisfies certain symmetry requirements.And the hydrodynamic variables can be obtained by simple summations given below:(,)(,),b i i t f t ρ=∑x x (3)(,)(,),b i i i t f t ρ=∑u x c x (4) 2(,)()(,),b i i i e t f t ρ=−∑x c u x (5) where ρ is fluid density, (,)t u x is fluid velocity, and (,)e t x is energy density.Turbulence is simulated based on the principle of performing very large eddy simulations (VLES)[12] that directly simulate resolvable flow scales while model unresolved scales by using an RNG form of k-epsilon equations with proprietary extensions to achieve VLES time accurate physics.WANG YiWei et al. Sci China Ser E-Tech Sci | Jun. 2008 | vol. 51 | no. 6 | 773-783 7752 Numerical model2.1 Vehicle geometryA three-department train model (including the head vehicle, tail vehicle and an intermediate ve-hicle) is considered, which comes from the CAD (computer aided design) data of a real high-speed train (including the bogie and non-simplified doors and windows). The surface gridsgenerated are shown in Figures 1 and 2.Figure 1 Surface grids of the head train.Figure 2 Surface grids of the bogie. 2.2 Computing gridThe Cartesian grid form is adopted to generate the space grid, which comprises nearly 40 million grids when the crosswind is not considered and over 57 million grids when the crosswind is taken into account. Grids near the train, the bogie and the pantograph have been refined, and the mini-mum scale of the grid is 1 cm (see Figure 3).2.3 Computing conditions2.3.1 Working conditionsRunning in open air at speeds of 200, 250 and 300 km/h, respectively. Running in tunnel at speeds of 200, 250 and 300 km/h, respectively.776 WANG YiWei et al. Sci China Ser E-Tech Sci | Jun. 2008 | vol. 51 | no. 6 | 773-783Running at a speed of 200 km/h under a strong crosswind of 364 m/s.Figure 3 Sectional plane of space grids.2.3.2 Boundary Conditions [13]. As shown in Figure 4, among the 5 faces of the most outside cube, the left face represents velocity inlet from which the air blows in at the speed of trains when running in the open air, and a modification of piston wind is considered when the trains running in tunnel. The right face represents pressure outlet with the pressure of 101325 Pa, and the other 3 are referred to as the walls of wind tunnel. The gray area represents the floor, at the top of which and under the train, there is a thin slice that has been set as a conveyor which moves at the same speed as the running train. Above the floor, there are two rail tracks which also move at the speed of running trains.Figure 4 Schematic diagram of the model.The wheels are set as rotating walls, which rotate around their corresponding center with their outside edge line speed equal to the speed of running trains.The surface of the train, the pantograph and the bogie part excluding the wheels are set as sta-tionary walls.2.3.3 Modification of piston wind. While the train is running in the tunnel, its piston effect will produce piston wind that moves in the same direction as the train. And the inlet velocity should be set as the speed of the train deducting that of the piston wind. According to the wave propaga-tion theory, the equation that the one-dimensional piston wind must obey can be deduced as 1,2cu p ρ=∆ (6) where ρ is air density, c is the local Mach number, u is the speed of piston wind and p ∆WANG YiWei et al. Sci China Ser E-Tech Sci | Jun. 2008 | vol. 51 | no. 6 | 773-783 777is pressure difference of wave source located near the surface of the train. And u can be ob-tained by repeatedly calculating flow field starting with an assumed u and revising it using eq.(6). But in practice, considering the enormous amount of computation, u is attained by using the Dynamic Mesh Method of software FLUENT.3 Computation results3.1 Aerodynamic resultThe drag, lift and lateral force arise from the resultant forces of the corresponding directions. For convenience of analyzing, a dimensionless force coefficient is defined as 2,2F C V S ρ= (7) where F is the resultant force of a direction, ρ is density, V is the speed of the train and S is the reference area. The largest vertical projection, horizontal projection and lateral projection areas are referred to as reference areas for drag, lift and lateral force, respectively.Force conditions of trains under different working conditions are addressed as in Figure 5.Figure 5 The force coefficients and the distribution of force.The study of flow around a Smooth cylinder with high Reynolds number indicates that when the Reynolds number is larger than 5×105, it can be considered that the flow has evolved into a state of self similarity, thus the flow characteristics will become irrelevant to Reynolds number. Flow around a train is much more complicated than around a cylinder, and its critical Reynolds number is smaller as well. The Reynolds number of flow around a train at the speed of 200 km/h has an order of 107, which means the flow has already entered its self similarity state. As a result, Cp, the surface dimensionless pressure coefficient of the train, will not change with the increase in speed, which makes the dimensionless force coefficients of trains at different speeds very close to each other.3.2 Aerodynamic analysis of trains running in the open airThe coefficient of air drag which consists of pressure drag and friction drag is one of the most important characters to measure the aerodynamic performance of trains [14]. The pressure drag arises from pressure difference between the front and back surfaces of every component of the train, as shown in Figure 6. When the surface flow of the train encounters a protruding, the veloc-778 WANG YiWei et al. Sci China Ser E-Tech Sci | Jun. 2008 | vol. 51 | no. 6 | 773-783ity of the flow will decrease, which results in the increase of surface pressure. For example, when the flow hits the nose of the train, the highest pressure is produced due to stagnation which makes the velocity of flow nearly zero, and when the flow encounters pantograph and bogie, the pres-sure will also rise under the influence of stagnation. At the contact points of the wheels and tracks, the rotation of wheels gives rise to high pressure in front of these points and low pressure behind them. Near the doors and windows, flow separation and reattachment are noticeable as well, which lead to apparent pressure gradient in these areas, as shown in Figure 7. At the tail of the train, there occurs obvious boundary layer separation as shown in Figure 7 that produces reflux area to form a low pressure that causes pressure difference.Figure 6 Surface pressure distribution curve of train axis.Figure 7 Friction curves and separation points at the tail of the train.When the viscous air is moving along the train, a boundary layer is produced near train surface within which the velocity of flow will increase rapidly from zero on the surface to almost the same as inlet flow at the top of the layer. The thickness of boundary lay is zero at the stationary point and will grow thicker gradually from head to downstream, as shown in Figure 8. Viscous shear stress on train surface is produced due to different velocity layers in boundary layer, the integral force of which in the direction opposite to running train forms the total friction drag of the train.WANG YiWei et al. Sci China Ser E-Tech Sci | Jun. 2008 | vol. 51 | no. 6 | 773-783 779Figure 8 Surface boundary layer distribution of the train.Overall, facing the wind directly, the head vehicle is the main drag resource of the train which accounts for half of its total drag. And the drag of tail vehicle is the second important part. Being designed very scientifically, the train in our study has a weak separation at its tail, as shown in Figure 9, while running in open air, because the separation point is postponed to a very later posi-tion as shown in Figure 7, which lessens the drag of tail vehicle to the same level as intermediate vehicle and pantograph. Also facing the wind, the strip-structure pantograph impedes the flow seriously, which makes considerable contribution to total drag and leaves much possibility to im-prove. The direct component of drag from wheels and bogie is relatively small, but their exis-tence can impact the aerodynamic force of body and lead to an indirect influence on the total drag,too.Figure 9 Space streamlines at the tail of the train.Aerodynamic lift is another important aspect to measure the aerodynamic performance of trains. Considering the wheel-rail train system, a positive lift will decrease the friction between wheels and tracks, which can make them “float” in air; the train will even be derailed if the lift is too big. By contrast, a negative lift will increase dynamic axle load of trains, intensify shocks between the train and tracks and fasten the wear of wheels and tracks. According to these, a zero lift of the train is desired. And the lift in this case performs quite well, for all the lift coefficients780 WANG YiWei et al. Sci China Ser E-Tech Sci | Jun. 2008 | vol. 51 | no. 6 | 773-783under different conditions have an order of 10―3 or lower (see Figure 5).3.3 Aerodynamic analysis of trains running in tunnelWhile running in tunnel, the train is just like a piston moving in a cylinder, generating a strong piston wind. Restricted by the tunnel, the air in front of train head is compressed intensely to produce a great positive pressure gradient (shown in Figure 10), while the air behind the train rearexpands to produce a great negative pressure gradient (see Figure 10).Figure 10 Pressure contours on the surface of the train and tunnel.The interaction between tunnel and train makes the whole field much more complicated com-pared to the situation when the train runs in open air: Not only the friction lines go upward, but they also curl in large area; the separation phenomena reflected by iso-surface of total pressure coefficient (see Figure 11) is more notable as well; and the wake also performs apparently un-steady and asymmetric, accompanied by the break and shedding of vortexes (see Figure 12).Figure 11 Contrast of zero valued total pressure coefficient iso-surface between running in open air (upper) and in tunnel (lower).It is conspicuous that the drag coefficient will fluctuate with time due to the great chaos of flow field, and the average value of drag coefficient is 1.5 times as much as that in the situation when the train runs in open air (as shown in Figure 5, and the pantograph is not considered in the condition of trains running in tunnel).3.4 Aerodynamic analysis of trains running under strong crosswindThe aerodynamic performance of the train deteriorates greatly while it runs under strong cross-wind [15]. The aerodynamic drag, lift and lateral force increases promptly, with a high rolling mo-ment which brings serious impact on the stability of the train. When the train is running in strongWANG YiWei et al. Sci China Ser E-Tech Sci | Jun. 2008 | vol. 51 | no. 6 | 773-783 781crosswind, the coupled wind leads to a quite different result compared to the condition of running in open air. The air flows around the train to its side rear and produces huge vortexes. In the area near rear and the area between two departments, vortex shedding occurs continuously to result inthe similar cyclical change of some variables (see Figures 13(a) and (d).Figure 12 Velocity-time diagram of wake on a horizontal cross section.Figure 13 (a) Space streamlines; (b) friction lines and velocity distribution of head vehicle; (c) pressure curves on symmetric face and horizontal cross section; (d) velocity-time diagram on the horizontal cross section.The stagnation points which are usually at the nose and at the top of the plate move to the up-wind side. On top surface of the train, the air velocity is the fastest in the fuscous area shown in Figure 13(b), where the surface pressure is quite small and notable separation area can be ob-782 WANG YiWei et al. Sci China Ser E-Tech Sci | Jun. 2008 | vol. 51 | no. 6 | 773-783 served. When the air is passing through the bogie, due to its complicated structure, the flow field behind it exhibits very unstable, and the iso-surface of vorticity seems quite chaos, too. Overall, the pressure on the bottom is much higher than that on the top, which gives birth to a large lift on the train (see Figure 13(c)).Most of the friction lines flow around the train from above, while a small number of them go through from below. In the wake zone near the leeward side of the train, a great deal of separation and reattachment occur and even second or higher order vortices appear (see Figure 14) which make the pressure on the leeward side very low. While on the windward side, the pressure is high because of the stagnation of air. Both of them are the cause of the big lateral force and rollingmoment (see Figure 13(c)).Figure 14 Streamlines and vortexes on vertical cross section of head and rear. 4 ConclusionCompared with traditional CFD method [16, 17] which deals with N-S equation, LBM has a serial of advantages such as saving memory, high efficiency of parallel computation and convenience of using complex geometry, all necessary for dealing with computation of high-speed trains. Pow-erFLOW, the only commercial software that is based on LBM, is adopted in this paper, which, limited to the low-speed aerodynamic area (Mach number <0.5)[18] at present, will soon be appli-cable to more fields such as high-speed, multiphase flow, etc. Not only should the LBM be adopted widely, but it is also necessary to develop new LBM algorithm that can be applied to new fields.We would like to thank EXA Corporation for freely providing the software used in this paper. Also, sincere thanks to Academi-cian Qiang Lu and Professor Yanhua Qin, for the instruction and encouragement during the whole process of both computationand paper writing.1 Chen Y S, Shan X W, Chen H D. New direction of computational fluid dynamics and its applications in industry. SciChina Ser E-Tech Sci, 2007, 50(5): 521―5332 Chen S, Chen H, Martinez D, et al. Lattice Boltzmann Model for simulation of magnetohydrodynamics. Phys Rev Lett,1991, 67(27): 3776―37793 Li Y, Shock R, Zhang R, et al. Numerical study of flow past an impulsively started cylinder by the lattice-BoltzmannMethod. J Fluid Mech, 2004, 519: 273―3004 Chen H, Chen S, Matthaeus W H. Recovery of Navier-Stokes Equations Using a Lattice-Gas Boltzmann Method. PhysRev A, 1992, 45(8): R5339―53425 Raghu S, Raghunathan H-D Kim, Setoguchi T. Aerodynamics of high-speed railway train.Progress in Aerospace Sci, 2002,38(6-7): 469―5146 Wilcox D. Turbulence Modeling for CFD. DCW Industries Inc, 19937 Chen S, Doolen G. Lattice Boltzmann Method for fluid flows. Ann Rev Fluid Mech, 1998, 30: 329―3648 Exa Corporation. PowerFLOW User’s Guide, Release 4.0. 9 Shan X, He X. Discretization of the velocity space in solution of the Boltzmann Equation. Phys Rev Lett, 1998, 80(1):65―6810 Qian Y H, d’Humieres D, Lallemand P. Lattice BGK Models for Navier-Stokes Equation. Europhys Lett, 1992, 17: 479―48411 Bhatnagar P, Gross E, Krook M. A model for collision processes in gases. I: Small amplitude processes in charged andneutral one-component system. Phys Rev, 1954, 94: 511―52512 Chen Y S, Kim S W. Computation of turbulent flows using an extended κ-εt urbulence closure model. NASA CR-179204,198713 Chen H, Teixeira C, Molvig K. Realization of fluid boundary conditions via discrete Boltzmann Dynamics. Intl J ModPhys C, 1998, 9(8): 1281―129214 Brockie N J W, Baker C J. The aerodynamic drag of high speed trains. J Wind Eng Indust Aerodyn, 1990, 34(3): 273―29015 Suzuki M, Tanemoto K, Maeda T. Aerodynamic characteristics of train/vehicles under cross winds. J Wind Eng IndustAerodyn, 2003, 91(1-2): 209―21816 Anderson J D. Computational Fluid Dynamics: The Basics with Applications. Beijing: Tsinghua University Press, 200217 Patankar S V. Numerical Heat Transfer and Fluid Flow. New York: McGraw Hill, 198018 Du T, Li X, Zhang X, et al. Lattice Boltzmann Method used for the aircraft characteristics computation with high angle ofattack. Eng Appl Comput Fluid Mech, acceptedWANG YiWei et al. Sci China Ser E-Tech Sci | Jun. 2008 | vol. 51 | no. 6 | 773-783783。
浸没边界格子Boltzmann方法的改进及转动圆柱绕流模拟
浸没边界格子Boltzmann方法的改进及转动圆柱绕流模拟王露;李天匀;朱翔;郭文杰【摘要】Based on Suzuki's immersed boundary lattice Boltzmann method, an improved approach is pro⁃posed. By adopting the force model of the lattice Boltzmann method and improving the technique of fluid structure interaction force calculation, the process of calculating the force of fluid structure interaction is simplified. Moreover,its calculation time is over 50%shorter than that of the original method, which means that efficiency is greatly improved. Based on the improved method, such features as lift coefficient, drag co⁃efficient,pressure coefficient and flow field are discussed under different conditions of flow over a rotating cylinder. Compared with the related results, this new improved method is shown to be accurate and reliable.%针对浸没边界格子Boltzmann方法计算效率不足的问题，提出一种改进浸没边界格子Boltzmann方法。
涡轮螺旋桨发动机建模与控制仿真
26 00
航 空动力学报
第 25 卷
动机的动态加速性能.
1 建模过程
1. 1 涡轮螺旋桨发动机核心模型建模
航空涡桨发动机一体化模型由发动机核心模 型、燃油调节器模型和螺旋桨及其负载调节机构 模型组成. 系统框图如图 1 所示[ 1-3] . 将负载信号 和燃油量信号传递给 发动机核心模 型计算出转 速, 螺旋桨负载调节器和燃油调节器同时接受转 速信号, 计算出新的负载信号和燃油量信号, 形成 闭环控制系统.
1. 4 发动机转速影响螺旋桨负载的建模分析
使用笛卡尔右手系规定扭矩方向. 发动机输
入给螺旋桨机构扭矩为 M 1, 弹性轴 上的扭矩为
Ms , 传递到减速器轴上扭矩是 M 2 , 扭矩经过减速
器传到螺旋桨( 参看图 3) . 在负载桨距角不变时,
发动机的转速 n1 是主动输入量. 列出方程组
M1( t) - M s( t) =
T IA N Chao1 , H U AN G Xiang- hua1 , DENG Zh-i w ei1, 2
( 1. Co lleg e of Ener gy and P ow er Eng ineering , Nanjing U niversit y of Aeronaut ics and Ast ronaut ics, N anjing 210016, China;
第 25 卷 第 11 期 2010 年 11 月
航空动力学报
Journal of Aerospace Power
Vo l. 25 No . 11 Nov . 2010
文章编号: 1000- 8055( 2010) 11-2599- 07
18基于CFD方法的电控旋翼气动特性建模与验证-王超(6)
第二十八届（2012）全国直升机年会论文基于CFD 方法的电控旋翼气动特性建模与验证王 超 陆 洋 王 伟（南京航空航天大学直升机旋翼动力学重点实验室，南京，210016）摘 要：首先建立了基于CFD 方法的带襟翼翼型定常气动力模型，继而结合电控旋翼动力入流模型以及电控旋翼桨叶挥舞响应与桨叶变距和襟翼操纵量的关系，建立了电控旋翼气动特性分析模型。
之后通过与国外试验数据对比，验证带襟翼翼型气动力模型的正确性。
最后以改进型电控旋翼试验系统为平台进行了风洞试验，测量了不同操纵条件下的电控旋翼气动力、桨距、襟翼偏角及旋翼挥舞角的变化情况。
通过理论计算与试验数据的对比分析，验证了所建立电控旋翼气动特性分析模型的正确性和有效性。
关键词：电控旋翼；后缘襟翼；气动力；风洞试验1 引言电控旋翼是美国NASA 于本世纪初提出的一种新概念旋翼。
近十余年来，国外针对电控旋翼技术开展了广泛的研究。
从2002年开始，美国Maryland 大学的Chopra ，Falls 等人[1]对电控旋翼进行较为深入的理论研究，建立了电控旋翼气弹动力学分析模型，研究了襟翼偏转对旋翼性能的影响，验证了后缘襟翼用于旋翼主操纵的可行性。
2009年，美国Boeing 直升机公司将MD900直升机的旋翼改造为电控旋翼，在NASA 的Ames 研究中心对该电控旋翼系统进行了风洞吹风试验，评估了电控旋翼的气动特性，经过长达60小时的持续吹风验证了电控旋翼操纵系统的可靠性[2]。
2009年，美国Sikorsky 直升机公司将S434直升机的旋翼改造成全尺寸电控旋翼，并于2010年在美国全尺寸气动试验中心进行了风洞试验，测试了旋翼气动响应与稳定性，并检验了硬件系统的可靠性[3]。
国内，陆洋等人从2003年开始对电控旋翼技术进行研究，建立了电控旋翼气弹动力学分析模型，研制了专用的电磁作动器和原理性电控旋翼试验系统，并进行了初步的试验研究，验证了电控旋翼用于旋翼主操纵的可行性[4]。
仿生飞行动力稳定发展模型优化及模拟计算
仿生飞行动力稳定发展模型优化及模拟计算随着科学技术的不断发展，仿生学作为一种研究自然界中生物的结构、功能和行为的理论和方法，被广泛应用于工程设计与优化领域。
在航空航天工程中，仿生学的应用可以提供有益的灵感，帮助我们设计更加高效、稳定和节能的飞行器。
飞行力学作为研究飞机飞行原理和特性的学科，对于仿生飞行动力稳定发展模型的优化和模拟计算具有重要意义。
本文将重点介绍如何利用仿生学原理优化飞行器的动力系统以实现稳定发展，并通过模拟计算验证设计的可行性。
1. 仿生学原理在飞行器动力系统优化中的应用1.1 生物翼型的仿生设计生物界存在着许多以高效飞行为目的的生物翼型，例如猎隼的长翼和雨燕的削尖翅膀。
通过对生物翼型结构和气动力学特性的深入研究，可以优化飞行器的翼型设计，提升升力和减少阻力，从而提高飞行效率。
1.2 生物推进系统的仿生组织生物界中有许多具有高效推进系统的生物，例如鳐鱼的尾鳍和鸟类的翅膀。
通过仿生设计，可以将生物的推进系统应用于飞行器中，实现更加高效、稳定的推进力。
2. 仿生飞行动力稳定发展模型的优化过程2.1 动力系统结构优化通过仿生学原理分析生物界中具有优秀动力系统的生物，优化飞行器动力系统的结构，提高系统的可靠性和稳定性。
比如，利用仿生学原理设计具有高效推进和低噪声的飞行器发动机。
2.2 动力系统参数优化根据仿生学研究的结果，优化飞行器动力系统的各项参数，包括推力、气流控制、燃料效率等，以提高飞行器的性能。
通过模拟计算和实验验证，确定最佳参数组合，使飞行器能够在不同环境下保持稳定的发展。
3. 仿生飞行动力稳定发展模型的模拟计算3.1 建立仿真模型根据飞行器的实际结构和参数，建立仿真模型。
模型应包括飞行器的动力系统、控制系统、气动外形等，以尽可能真实地模拟飞行器在不同工况下的运行状态。
3.2 进行仿真计算通过使用计算流体力学（CFD）和多体动力学（MD）等模拟计算方法，对飞行器在不同工况下的动力学特性进行分析和优化。
宇航员训练机器人卧推模式建模与控制
宇航员训练机器人卧推模式建模与控制张立勋;邹宇鹏【摘要】针对微重力环境下宇航员的训练问题,设计了一种基于柔索驱动的宇航员训练机器人,帮助宇航员在失重状态下完成卧推训练.在对卧推训练运动特性进行分析的基础上,完成了机器人的构型设计.在该机器人构型的基础上,给出了机器人的可控工作空间并建立了柔索牵引力规划数学模型.针对控制系统的力控制任务,将基于位置的力外环控制策略应用于并联柔索机器人控制系统的设计.最后对人机系统模型进行了仿真分析,仿真结果表明,该控制策略能够有效地跟踪卧推运动并完成动态负载力的控制.%In order to solve the training problems of astronauts within a microgravity environment, an astronaut-training robot based on a parallel wire driven robot was designed to help astronauts complete bench press training. The robot configuration was designed based on a motion characteristics analysis of bench press. Furthermore, the controllable workspace and the mathematical model of tension distribution were studied. To complete the task of force control, an explicit force control strategy based on position inner loop control was proposed. Finally, the man-machine system was simulated and analyzed. The simulation results verify that the control strategy can effectively track bench press and control the dynamic load.【期刊名称】《哈尔滨工程大学学报》【年(卷),期】2011(032)009【总页数】6页(P1179-1184)【关键词】宇航员训练;力控制;并联柔索机器人;卧推【作者】张立勋;邹宇鹏【作者单位】哈尔滨工程大学机电工程学院,黑龙江哈尔滨150001;哈尔滨工程大学机电工程学院,黑龙江哈尔滨150001【正文语种】中文【中图分类】TE2机器人辅助运动功能康复训练技术是机器人研究领域的前沿和热点，其目的一方面是为患者提供安全、高强度和以任务为导向的训练;另一方面有助于减轻医疗人员的负担，降低卫生成本［1］.现有各种康复器械虽然能够在一定程度上满足了包括残疾人、伤病人及老年人的需求，但是对于失重环境下的宇航员而言却没有合适安全和以任务为导向的康复训练机器人.因此，为宇航员研制适用于失重环境的训练机器人，提高宇航员心理及生理的稳定性，保证宇航员的工作效率，对于我国载人航天事业的发展具有重要的意义.目前，在国际空间站中宇航员对上身部分肌肉群的锻炼主要采用拉力器和抗阻力训练器(advanced resistance exercise device，ARED).拉力器结构简单、质量轻，但是功能相对单一，效果不明显［2］;抗阻力训练器是利用真空产生负压的原理模拟自由负重器械对宇航员进行锻炼，但ARED体积和质量大，给原本空间有限的空间站带来很大的压力［3］.卧推是仰卧推举的简称，主练胸部和臂部肌肉群.卧推参与的骨肉多，尤其对发展上肢伸肌和胸大肌有显著作用，是其他动作无法比拟的［4］.卧推对于全面锻炼宇航员上肢力量，提高上肢作业能力具有重要作用.但是在太空失重环境下采用普通的杠铃进行训练将失去效果.因此，本文提出了一种基于柔索驱动的宇航员训练机器人，通过模拟真实负载实现航天员在太空微重力环境下进行卧推训练.文中通过分析卧推运动特性设计了机器人构型;研究了其可控工作空间及牵引力规划数学模型;针对人机系统的特性，提出基于位置内环的力外环控制策略;最后对人机系统进行仿真研究.1 机器人构型研究1.1 卧推运动的特性人体在进行卧推训练过程中，上肢和横杠可能有的运动形式有:1)根据需要训练部位的不同，卧推有斜上推、斜下推和平推3种训练方式.但是斜推对人体力量要求较高，在力量不足的情况下容易出现横杠脱落和肌肉拉伤等情况，不适宜用于失重状态下宇航员的训练.项目采取平推的方式，因此存在一个横杠沿人体矢状轴(见图1)移动的自由度.图1 卧推训练自由度示意Fig.1 DOF of bench press training2)考虑到人体双臂力量的不均衡，在平推的过程中可能出现横杠的倾斜，即存在一个横杠绕人体垂直轴转动的自由度.3)在手部握紧横杠和臂部坚挺的状态下，不存在横杠绕自身轴线、冠状轴及矢状轴转动的自由度.同时，为了避免人体受到损伤，应通过机器人构型设计和控制避免横杠沿垂直轴和冠状轴2个方向的移动自由度.综上所述，为了完成对人体上肢肌肉群的训练，同时避免人体受到损伤，人在卧推过程中横杠具有2个自由度，即沿矢状轴的移动和绕垂直轴的转动.按照文献［5］的分类，卧推模型的自由度类型为1R1T型，属于空间机构.1.2 机器人结构模型根据文献［6］，1R1T柔索牵引并联机构不存在.因为对于任意给定的位姿，动平台(横杠)都无法满足力封闭的条件，机构是不可控的.机械人构型如图2所示.图2 机器人构型Fig.2 Robot configuration图2中，设固定坐标系为Oxyz，横杠坐标系为Pxpypzp.不考虑人体上肢对横杠的约束，根据螺旋理论，横杠所受的力螺旋平衡方程可以表示为式中:F∈R6×1表示横杠在失重状态下所受的包括惯性力在内的力螺旋(不包括重力);T∈R6×1表示柔索张力矢量;W(X)∈R6×6为柔索矩阵，柔索矩阵可以表示为式中:r1=PP1，r2=PP2;Li=PmBi(m=1，i=1，2，3;m=2，i=4，5，6)为柔索矢量;li= ‖Li‖表示第 i根柔索的长度;l0i=Li/li为第i根柔索的正规化柔索矢量.由卧推的运动特性可知，横杠在工作空间内有绕z轴(垂直轴)转动的非零力矩，即柔索矩阵W(X)的第6行与柔索张力矢量T的乘积非零，则必然无法保证W(X)的第3行与T的乘积在任意时刻都为零，即运动过程中存在沿z轴的横向力，整个机构失控.所以，单纯通过柔索牵引并联机构实现1R1T构型设计是不可能的.宇航员训练机器人主要用来实现失重环境下宇航员卧推过程中的负载力控制.据此目的得出了机器人机构模型如图2所示.对本项目而言，虽然机器人是具有并联特征的不完整约束系统，但是人提供了系统的部分约束，人与柔索驱动机构共同组成了宇航员训练人机系统.从整个人机系统的角度考虑，系统具有完整约束的特性，整个系统是可控的.因此，在建模时只有将人机系统共同建模，模型才有意义.由于项目采用平推作为宇航员卧推的基本训练形式，因此在训练过程中，宇航员的上肢仅在xoy平面内运动，人体的肩关节和腕关节也由原来复杂的多自由度关节简化为仅有一个自由度的转动关节［7］.为了保证卧推训练的基本形式，简化控制系统，在该机构模型中，动平台(横杠)由6根对称分布的柔索牵引，柔索的一端按照3根一组的方式铰接在横杠的两端 P1和 P2上，横杠长度 lP1P2=1.5 m.柔索的另外一端连接在6组带有万向轮的柔索驱动单元Bi(i=1，2，…，6)上，6组柔索驱动单元均匀地分布在直径d=2 m的圆形机架上.在固定坐标系 Oxyz中，6组柔索驱动单元的坐标为在每根柔索中间分别安装一个拉力传感器来检测柔索张力，利用光电编码器检测直流力矩电机转速来计算柔索长度.1.3 机器人可控工作空间定义:对于6根柔索牵引的2自由度宇航员训练机器人，对于xoy平面内给定一个位姿X，如果存在柔索张力矢量T(T＞0)，满足W(X)T=F，则X属于可控工作空间.其中，F=F1+F2，F1和F2分别为横杠两端 P1、P2上柔索牵引力的合力，大小F1=F2，方向沿y轴负方向.在不考虑卧推形式及人体各关节运动能力和范围对机器人限制的前提下，机器人的可控工作空间为2个三棱柱，其下限为机架平面，棱柱的横截面为ΔB1B2B3和ΔB4B5B6，如图2虚线三角形所示.在所要求的1R1T运动形式下，工作空间为xoy平面内2个矩形平面，其边界受三棱柱边界以及人体上肢卧推运动范围限制.较大的工作空间保证了机器人在面对不同使用者以及训练过程中特殊情况时具有较强的适应能力，增强了机器人的适用性.2 柔索牵引力规划柔索牵引力规划问题可叙述为:当给定的横杠的位姿X时，可确定柔索矩阵W(X)，通过规划柔索张力矢量T，使得W(X)T=F.在本文中，各个柔索张力之间不存在耦合，对于给定的负载力，各个柔索张力的解唯一.因此在计算绳索张力时不需要利用Moore-Penrose逆的办法［8］.柔索张力矢量T可表示为以横杠一端P1点的柔索牵引力规划为例，如图3所示.F1=F/2，l1=l3，t1=t3，P1P1'⊥ B1B2B3O'，P1'B2=R/4.则单侧柔索张力矢量T1表示为卧推过程中拟加载的负载力F可以表示为式中:G为重力项，其大小固定不变;Fi为惯性力，其大小与横杠的加速度成正比. 对于本文所设计的机器人构型，虽然柔索张力之间不存在耦合，但是运动学上却是相互耦合的.由于机器人自由度类型为1R1T型，横杠仅会在xoy平面内运动，这就简化了机器人的运动学解算.横杠上柔索铰接点的运动可以表示为式中:li、lyi和分别为第i根柔索的长度、伸缩速度和加速度;J(li)是一个与机器人几何形状有关的函数表达式.图3 柔索牵引力规划Fig.3 Wire tension distribution3 基于位置的力外环控制策略宇航员训练机器人控制器的主要目标是在跟随人体卧推训练姿态的同时，实现失重环境下卧推过程中的动态负载力控制.目前，基于力外环的方法已经成功应用到机器人的力跟踪控制中［9］.本文基于力外环的思想，控制器采用基于位置内环的力外环控制策略.基于位置的力外环控制原理图如图4所示.如图4中，该方法是通过安装在柔索中间的拉力传感器测量柔索张力，力控制器的输出作为位置控制器的输入值，通过检测电机转速来计算柔索的长度和速度，在完成对横杠运动跟踪的前提下实现对人体的负载力控制.图4 基于位置的力外环控制Fig.4 Position based explicit force control该控制策略的优点是实现简单.但是其控制精度依赖于机器人位置控制器的精度，因此本文位置控制器采用基于速度内环的位置控制器，这样提高了位置控制器的精度，并且避免了因为换向速度变化造成力的波动.由于机器人采用柔索作为传动元件，控制对象为人体，人机系统刚度较小，因此避免了该控制策略在以往的使用过程中因为环境刚度较大而造成的系统不稳定.4 人机系统的建模与仿真4.1 人机系统建模宇航员训练机器人主要是用于失重状态下的宇航员的体育锻炼，失重环境对人机系统模型的建立及其控制系统的设计都有重要影响.本文利用Matlab SimMechanics 工具箱建立人机系统模型，通过设置Machine Environment模块，完成无重力环境的建立.人机系统模型分为人体上肢(包括横杠)模型和并联柔索机器人模型2部分.人机系统控制框图如图5所示.图5 人机系统控制框图Fig.5 Control system of man-machine system机器人模型包括电机模型和柔索模型2部分.电机模型按照式(8)建立直流力矩电机的数学模型.其中，Ia、Ua、La、Ra、Ce分别为直流力矩电机的电流、电压、电枢回路电感、电阻和反电动势常数，θ·m为电机转速.柔索模型是利用SimMechanics工具箱中的Body、Body Spring＆Damper等模块建立柔索实物模型:人体在进行卧推时，主要是上肢及胸部的肌肉发挥作用.因此，在建立人体模型时将其简化为如图2所示的包括上肢、胸部及横杠在内的封闭六连杆机构.按照实际人体各部位的参数完成对杆件变量的设置［10］.在卧推训练过程中，为了保证训练效果，预防训练伤害，卧推速度不能太快，同时避免急起急停.设定横杠在一个周期内(0～6 s)的速度变化规律函数为其运动轨迹变化曲线如图6所示.图6 卧推轨迹曲线Fig.6 Curve of bench press4.2 仿真分析为了验证牵引力规划器和控制器的有效性，检验控制系统的性能，对图5所示的人机系统模型进行仿真研究.模拟负载的质量设定为为60 kg，模拟的重力加速度值为10 m/s2.利用SimMechanics工具箱中的传感器模块，检测柔索模型的运动状态，按照式(5)～(7)完成对动态负载力的计算.在一个周期内动态负载力变化曲线如图7所示.由图7可以看出，人体在卧推过程中，相对于恒定负载，人体所受的实际负载力波动是比较大的.因此，为了真实的模拟重力环境下的负载特性，实时优化负载力是很必要的.图7 动态负载力曲线Fig.7 Curve of dynamic load按照式(4)所确定的柔索牵引力规划数学模型，在卧推训练过程中，给定的柔索牵引力变化曲线如图8中实线所示.图8 各柔索牵引力曲线Fig.8 Curves of wire tension将人机系统模型、柔索力控制器及牵引力规划模型进行联合仿真.仿真过程中，虚拟拉力传感器实际测到的柔索牵引力如图8中虚线所示.从图中可以看出，在卧推训练过程中，柔索实际的牵引力基本上能够跟随规划牵引力，这说明控制器是有效的，能够很好地跟随横杠位姿变化并完成运动过程中动态负载力的控制.观察可发现:在横杠上升阶段，柔索实际牵引力略大于规划牵引力;横杠下降阶段，柔索实际牵引力小于规划牵引力.这与实际情况是吻合的，因为宇航员训练机器人需要根据训练对象的姿态和运动状态把期望负载力施加到人体上，人做主动运动，而机器人处于被动运动状态.机器人在做被动运动的同时要实现动态负载力控制，是被动方式下的力控制.图9所示为各个柔索的实际牵引力与规划的牵引力的误差曲线.从图9的误差曲线可以看出，在训练开始后，力控制器能很快响应，误差迅速变小.在正常工作过程中，无论柔索牵引力如何波动，都能将误差控制在5 N以内，这说明力控制器性能良好，响应速度快并且对力干扰有很强的鲁棒性.控制器满足系统力控制要求. 图9 柔索张力误差曲线Fig.9 Curves of wire tension deviation5 结束语针对太空失重的恶劣环境，为了实现宇航员的卧推训练，设计了一种柔索驱动的宇航员训练机器人.通过分析卧推的运动特性，设计了具有不完整约束特性的机器人构型，考虑人体上肢的约束作用，系统是一个具有完整约束特性的人机系统，这是对并联柔索机器人机构学理论和控制的大胆探索.针对所设计的机器人构型，给出了机器人的可控工作空间，并建立了牵引力规划数学模型.鉴于柔索及人体的刚度小，本文采用了基于位置内环的力外环控制策略.仿真研究表明:该控制策略能够有效地跟踪卧推过程中横杠的运动，并能够完成运动过程中动态负载力的控制.本文的研究为基于并联柔索机器人的宇航员训练机器人力控制系统的设计提供了理论依据，研究内容具有重要意义.本文初步设计了机器人的构型，在理论上研究了机器人的力控制策略，下一步研究将进一步优化机器人构型并通过实验验证控制策略的有效性.参考文献:【相关文献】［1］叶晓勤，季林红，谢雁鸣，等.康复训练机器人与传统中医康复方法相结合的探讨［J］.中国康复医学杂志，2010，25(8):781-784.YE Xiaoqing，JI Linheng，XIE Yanming，etal.Discussion on combination of rehabilitation robot and rehabilitation methods of traditional Chinese medicine［J］.Chinese Journal of Rehabilitation Medicine，2010，25(8):781-784.［2］张立勋，刘攀，王克义.基于绳索牵引的航天员机能训练机器人虚拟重力控制［J］.机器人，2010，32(4):454-458.ZHANG Lixun，LIU Pan，WANG Keyi.Virtual-gravity control of a wire-driven cosmonaut-enginery-training robot［J］.Robot，2010，32(4):454-458. ［3］KIRK L，JAMES A.Reliability of strength testing using the advanced resistive exercise device and free weights［R］.NASA，2008.［4］付海峰.平板卧推动作肌肉工作特征的研究［D］.北京:北京体育大学，2006:6-11.FUHaifeng.Research on characteristics of muscles during the flat bench press［D］.Beijing:Beijing Sport Univesity，2006:6-11.［5］张波，战红春，赵明扬，等.柔索驱动三自由度球面并联机构运动学与静力学研究［J］.机器人，2003，25(3):198-200.ZHANG Bo，ZHAN Hongchun，ZHAO Mingyang，eta1.Kinematics and statics analysis of a 3-DOF sphere parallel wire driven mechanism ［J］.Robot，2003，25(3):198-200.［6］郑亚青.绳牵引并联机构若干关键理论问题及其在风洞支撑系统中的应用研究［D］.福建:华侨大学，2004:31-38.ZHENG Yaqing.Research on key theoretical issues of wiredriven parallel kinematic manipulators and the application to wind tunnel support systems［D］.Fujian:Huaqiao Univesity，2004:31-38.［7］李庆玲，叶腾茂，杜志江，等.外骨骼式上肢康复机器人力辅助控制［J］.哈尔滨工程大学学报，2009，30(2):166-170.LI Qingling，YE Tengmao，DU Zhijiang，et al.Controlled assistance by an exoskeletal rehabilitation robot for upper limbs［J］.Journal of Harbin Engineering University，2009，30(2):166-170.［8］GOUTTEFARDE M，DANEY D，MERLET J P.Interval-analysis-based determination of the wrench feasible workspace of parallel cable-driven robots［J］.IEEE Transactions on Robotics，2011，27(1):1-13.［9］蒋再男，刘宏，黄剑斌，等.基于阻抗内环的新型力外环控制策略［J］.航空学报，2009，30(8):1515-1520.JIANG Zainan，LIU Hong，HUANG Jianbin，et al.Novel explicit force control strategy based on impedance inner control［J］.Journal of Astronautics，2009，30(8):1515-1520.［10］张大威，李浩，石岫昆，等.计算中国男性人体体段转动惯量的多元回归方程的研究［J］.医用生物力学，2005，20(2):85-87.ZHANG Dawei，LI Hao，SHI Xiukun，et al.Study on multiple regression equation for calculating segmental move inertia of segments of Chinese young male bodies［J］.Journal of Medical Biomechanics，2005，20(2):85-87.。
空气动力学CH9
c = λRT∞ = 1.4× 287 × 216.78 = 295m / s
飞机飞行速度为：
V∞ = Ma∞ ⋅ c = 2× 295 = 590m / s 飞机升力为：
L = 9400× 9.8 = 9.212 ×104 N
24
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2011/5/11
空气动力学 Aerodynamics
ρV∞ 2c
= ( C pl
− C pu
)d (
x c
)
Cp =
2θ
Ma
2 ∞
−
1
θu
=
dz u dx
−α
θu
=
−
dz l dx
+α
带入线化后的压强系数表达式及翼面局部折角公式，得：
dC l =
2
( 2α − dz l − dz u )d ( x )
Ma
2 ∞
−
1
dx dx c
14
空气动力学 Aerodynamics
16
空气动力学 Aerodynamics
9.2.3 激波阻力
上、下翼面的压强在来流方向的合力，即为阻力：
d d = pl ds l sin θ l + pu ds u sin θ u = plθ l dx + puθ u dx
ds l sin θ l ≈ dx ⋅ θ l ds u sin θ u ≈ dx ⋅ θ u
空气动力学 Aerodynamics
上、下翼面上不同 点的气流折角为：
θu
=
dz u dx
−α
θl
=
−
dz l dx
+α
基于非定常气动力辨识技术的气动弹性数值模拟
[ 5~ 8]
580
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第 27 卷
1 计算方法 Dow ell 依据非定常气 动力特性 将之分为 3 类 : ( a) 全线性模型, 如亚、 超声速小扰动小振 幅非定常流动 ; ( b) 动态线性 模型, 如跨 声速、 厚 翼等作小振幅非定常流动 ; ( c) 全非线性模型, 如 大迎角、 深失速等流动。动态线性模型描述的流 动也就是指空间表现为非线性, 而时间上表现为 线性的非定常流动。而在气动弹性研究中最重要 的颤振边界的计算就是研究弹性体在小振幅振动 下的影响。这就成为运用线性模型进行诸如跨声 速气动弹性研究的依据。 图 1 给出了基于气动力辨识技术的气动弹性 仿真流程图。对于非定常流场求解器 , 输入激励 信号 ( 结构的广义位移) , 得到对应的输出信号 ( 广 义气动力 ) 。运用辨识 技术, 进 行参数辨 识。这 样, 1 个计算状态只用进行 1 个激励信号的计算 ( 通常激励响应的计算量小于直接模拟时气动弹 性 1 个响应的计算量 ) 便可得到降阶的辨识模型。 而后寻找颤振临界点的若干个响应的气动力计算 就可运用辨识出的降阶气动力模型, 这一过程的 计算量和非定常 Euler 方程的求解过程相比可以 忽略不计。
第4期
张伟伟等 : 基于非定常气动力辨识技术的气动弹性数值模拟
大密度比双气泡在孔板结构微通道内上升行为的格子Boltzmann方法模拟
大密度比双气泡在孔板结构微通道内上升行为的格子Boltzmann方法模拟严裕;娄钦【期刊名称】《空气动力学学报》【年(卷),期】2022(40)3【摘要】基于格子Boltzmann两相流大密度比模型模拟了孔板结构微通道内双气泡在浮力作用下的上升过程,主要研究E?tv?s数(Eo)、气泡相对大小、气泡之间的距离以及气泡和孔板间的距离对气泡变形、合并的动力学行为以及气泡上升速度和气泡剩余质量的运动特性的影响。
研究发现,随着Eo数的增大,气泡在通过孔板通道时形变越严重,表现为上部气泡和下部气泡在合并过程中所夹带的液泡数量和质量同时增加,且气泡在通过通道的过程中会发生多次接触、合并与破裂;数值结果还表明,随着Eo数的增大,气泡达到顶端的时间增加而气泡穿过孔板的质量减小。
另一方面,当上方气泡的尺寸大于下方气泡的尺寸时,两气泡在合并的过程中夹带的液泡数量更少,气泡穿过孔板时更迟缓但能够穿过孔板的气泡质量增多。
此外,对于不同的气泡间距离和不同的气泡与孔板之间的距离,发现上下气泡之间的距离过大或者过小时,在气泡的合并过程中都不容易夹带液泡,且气泡穿过孔板的质量随着两气泡之间距离以及上方气泡与孔板之间距离的减小而增加。
【总页数】11页(P120-129)【作者】严裕;娄钦【作者单位】上海理工大学能源与动力工程学院;上海市动力工程多相流动与传热重点实验室【正文语种】中文【中图分类】O359【相关文献】1.利用格子Boltzmann方法模拟单个气泡在复杂流道内的运动特性2.分叉微通道内液滴动力学行为的格子Boltzmann方法模拟3.复杂微通道内气泡在浮力作用下上升行为的格子Boltzmann方法模拟4.大密度比气泡在含非对称障碍物微通道内的运动行为5.T型微通道内的幂律流体液滴破裂行为的格子Boltzmann方法模拟因版权原因，仅展示原文概要，查看原文内容请购买。
封闭方腔自然对流的格子-Boltzmann方法动态模拟
4.504 4.519 4.510 4.510 0.199%
8.767 8.800 8.806 8.805 0.056%
从表 1 中可以发现，采用本文所介绍的不可压缩双分布函数 TLBM 模型进行数值计算，得 到了比较精确的结果。相对误差
5. 方腔内自然对流的动态模拟
封闭方腔自然对流是热流耦合的经典问题，通过对其进行数值模拟而获得不同 Ra 情况
2. 物理模型
本文所计算的封闭方腔自然对流的物理模型如图 1 所示。封闭方腔高为 H ，上、下壁
1
本课题得到国家杰出青年科学基金资助项目（50425620）及高等学校博士学科点专项科研基金资助项目 -1（20050698036）资助。
Th + Tc ⎞ 面绝热，腔内充满 ρ = 3 ， Pr = 0.71 ，温度 T = ⎛ ⎜ ⎟ 的均质 ⎝ 2 ⎠
p i x + ei dt , t + dt − p x, t = −
(
) ( )
dtτ p Fi dt p i − pieq + τ p + 0.5dt τ p + 0.5dt
(
)
（6）
g i x + ei dt , t + dt − g x, t = −
(
) ( )
p dt dt g i − gieq − Z i 2i τ g + 0.5dt τ g + 0.5dt cs
(
)
（7）
图 2. D2Q9 模型
。 其中 τ p ，τ g 分别为运动和热方程的松弛时间； cs 为声速（ cs = 1/ 3 ） 流体的宏观参量（包括压力，速度，温度及热流等）可按下列各式计算：
常用物理词汇中英文对照
常用物理词汇中英文对照Aa.c. generator 交流发电机aberration 光行差，像差absolute index of refraction 绝对折射率absolute refractive index 绝对折射率absolute temperature scale 绝对温标absolute zero 绝对零度absorber 吸收体absorbing power 吸收能力，吸收本领absorptance 吸收比absorption 吸收absorption coefficient 吸收系数absorption line 吸收谱线absorption spectrum 吸收光谱，吸收谱accelerate 加速acceleration 加速度acceleration due to gravity 重力加速度acceleration-time graph 加速度—时间关系线图accelerator 加速器acceptor 接受体acceptor doping 受体掺杂acceptor impurity 受体杂质accommodation 调节，视觉调节accumulator 蓄电池accuracy 准确度acetate strip 醋酸酯条片achromatic 消色差的achromatic aberration 消色差achromatic condenser 消色差聚光透镜achromatic light 消色差光，白光acoustic blur 声响模糊acoustic board 吸音板，吸声板acoustic navigation 声响导航acoustic pressure 声压acoustics 声学act on 施于action 作用量，作用，作用力action of point 尖端作用activation 激活，活化activation energy 激活能，活化能active nucleus 活性核，放射性核activity 放射强度，放射性adapter 接合器adder 加法器adhesion 附着力，附着，黏附adhesive force 附着力adiabatic 绝热的adiabatic expansion 绝热膨胀adiabatic process 绝热过程aerial 天线??aerial induction 天线调谐电感aerial network 天线网络aerodynamic force 气动力，空气动力aerodynamics 气体动力学，空气动力学aerofoil 机翼agent 剂air blower 吹风器air column 空气柱，气柱air cushion 气垫air damping 空气阻尼air film 气膜air track 气垫导航air wedge 气楔alignment 对准，校整alpha decay α衰变alpha particle α粒子alpha particle scattering analogue α粒子放射模拟alternating current 交流电alternating voltage 交变电压，交流电压alternator 交流发电机altimeter 高度计，测高仪americium ?宝?ammeter 安培计amorphous 非结晶的，无定形的ampere 安培，安ampere-hour 安培小时，安时amplification 放大，放大率amplifier 放大器amplify 放大amplitude 振幅amplitude modulation 调幅，振幅调剂amyl acetate 醋酸戊酯anaemia 贫血analogue 模拟analogue experiment 模拟实验analogue signal 仿真讯号，非数字讯号analogue-to-digital conversion 模拟转换analyser 检偏振器AND gate 「与」门anemometer 风速计aneroid barometer 无液气压计，空盒气压计angle of contact 接触角angle of deviation 偏向角angle of diffraction 衍射角，绕射角angle of dip 倾角angle of elevation 仰角angle of emergence 出射角angle of incidence 入射角angle of inclination 倾角angle of minimum deviation 最小偏向角angle of projection 投射角angle of reflection 反射角angle of refraction 折射角angle of twist 扭转角angstrom 埃angular acceleration 角加速度angular aperture 孔径张角angular displacement 角位移angular frequency 角频率angular impulse 角冲量angular magnification 角度放大，角放大率angular momentum 角动量，动量矩angular motion 角向运动，角运动angular seed 角速率angular velocity 角速度angular width 角宽度annealing 退火，韧化anode 阳极，正极anomalous expansion 反常膨胀antenna 天线??anticlockwise moment 逆时针力矩antifreeze 防冻剂antinodal line 腹线??antinode 波腹antiparticle 反粒子antiphase 反相，逆相aperture 孔径，口径，孔apparent depth 视深apparent expansion 表观膨胀，视膨胀apparent frequency 表观频率，视频率apparent loss in weight 表观失重apparent weight 表观重量Appleton layer 阿普顿层，F电离层aqueous layer 水层Archimedes' principle 阿基米得原理area 面积argon 氩armature 电枢artificial disintegration 人工蜕变artificial radioactivity 人工放射astable 非稳态的astable circuit 非稳态电路astable multivibrator 非态多谐振荡器astigmatism 像散，散光astronomical telescope 天文望远镜at infinity 在无穷远处at rest 静止atmosphere 大气，大气层，大气压atmospheric pressure 大气压强atom 原子atomic bomb 原子弹atomic bond 原子键atomic density 原子密度atomic diameter 原子直径atomic energy 原子能atomic mass 原子质量atomic mass unit 原子质量单位atomic model 原子模型atomic nucleus 原子核atomic number 原子序数atomic radius 原子半径atomic separation 原子间距atomic spacing 原子间距atomic structure 原子结构atomic theory 原子论atomizer 喷雾器attenuation 衰减attraction 吸引attractive force 吸力audible frequency range 听频范围audible signal 可听讯号audio frequency 声频autofocus 自动聚焦，自动对焦avalanche 电子雪崩average acceleration 平均加速度average power 平均功率average speed 平均速率average velocity 平均速度Avogadro constant 阿佛加德罗常数，阿佛加德罗常量Avogadro number 阿佛加德罗数Avogadro's law 阿佛加德罗定律axial 轴向的，沿轴的axial field 轴向场axial search coil 轴向探察线图axis 轴axis of rotation 转轴Bback e.m.f. 反电动势background radiation 本底辐射Bainbridge mass spectrometer 班布里奇质谱仪balance 天平，秤，平衡balance arm 秤杆，平衡臂balance point 平衡点balance bridge 平衡电桥balanced force 平衡力ball bearing 球轴承，滚珠轴承ballistic galvanometer 冲击电流计，冲击检流计ballistic pendulum 冲击摆Balmer series 巴耳末系，巴耳末光谱band spectrum 带状光谱，带状谱bandwidth 带宽bar code 条形码bar magnet 磁棒bare wire 裸线??barium 钡barometer 气压计barrier 障碍物barrier layer 阻档层，耗尽层barrier potential difference 阻档层电势差，阻档层电位差Barton's pendulums 巴尔通摆base 基极base current 基极电流battery 电池组battery charger 电池充电器battery holder 电池座beaker 烧杯beam splitter 分束器，射束分离器beat 拍beat frequency 拍频becquerel 贝克勒耳，贝克bel 贝尔，贝bell jar 钟形罩bench mat 实验台垫Bernoulli's theorem 伯努利定律beryllium 铍beta decay β衰变beta particle β粒子biasing circuit 偏压电路biasing voltage 偏压biconcave lens 双凹透镜biconvex lens 双凸透镜bicycle dynamo 自行车发电机，脚踏车发电机bifilar pendulum 双线摆bifocal lens 双焦距透镜big bang model 大爆炸模型bimetallic strip 双层金属片，双金属片binary adder 二进加法器binary system 二进制binding 结合binding energy 结合能binoculars 双筒望远镜Biot-Savart law 毕奥—萨伐尔定律bipolar 双极的birefraction 双折射bistable 双稳态的，双稳器bistable circuit 双稳电路bistable multivibrator 双稳态多谐振荡器bit 二进制制，位black body radiation 黑体辐射block and tackle 滑轮组block diagram 方框图blocking capacitor 隔直流电器容blooming 敷霜，表面加膜Bohr atom 玻尔原子Bohr radius 玻尔半径Bohr theory 玻尔理论boil 沸腾，煮沸boiler 锅炉boiling point 沸点bolometer 辐射热计Boltzmann constant 玻耳兹曼常数，玻耳兹曼常量bombardment 轰击bond energy 键能bonding 键合Bourdon gauge 布尔登气压计bow wave 弓形波，舷波Boyle's law 博伊尔定律Brackett series 布喇开系，布喇开光谱Bragg angle 布喇格角Bragg diffraction 布喇格衍射，布喇格绕射Bragg plane 布喇格平面Bragg's law 布喇格定律brake 制动器breakdown potential 击穿电势，击穿电位breaking point 断点breaking strength 抗断强度breaking stress 致断应力breeder reactor 增殖反应堆bremsstrahlung 轫致辐射Brewster's law 布鲁斯特定律bridge circuit 桥式电路bridge rectifier 桥式整流器bright fringe 亮纹brightness 亮度brittle 脆的，易碎的bromine 溴Brownian movement 布朗运动brush 电刷bubble chamber 气泡室bubble raft model 泡筏模型buffer 缓冲器buffer circuit 缓冲电路bulk modulus 体积弹性模量Bunsen burner 本生灯buoyancy 浮力burette 滴定管burette stand 滴定管架burglar alarm 防盗警报器，防盗警钟buzzer 蜂鸣器by-pass 旁路byte 二进制组，字节Ccable 电缆cadmium sulphide 硫化镉caesium 铯calcite 方解石calibrate 校准，标上刻度calipers 测径器，卡钳calorie 卡路里，卡calorimeter 量热器camera 照相机cancer cell 癌细胞candela 坎德拉cantilever 悬臂capacitance 电容capacitance substitution box 换值电容箱capacitive circuit 电容电路capacitive component 电容性分量capacitive coupling 电容耦合capacitive discharge 电容性放电capacitive reactance 容抗capacitor 电容器capacitor-input filter 电容输入滤波器capacity 容量，载量capillarity 毛细现象，毛细作用capillary depression 毛细下降capillary rise 毛细上升capillary tube 毛细管capsule 囊capture 俘获carbon 碳carbon granule 碳颗粒carbon paper disc 圆形碳纸carbon-14 dating 碳14年代测定法carburettor 化油器，汽化器carrier wave 载波carry 进位castor oil 蓖麻油cataract 白内障cathode 阴极，负极cathode ray 阴极射线??cathode ray deflection tube 阴极射线偏转管cathode-ray oscilloscope 阴极射线示波器，示波器cathode-ray tube 阴极射线管cavity resonator 空腔共振器celestial telescope 天体望远镜cell 电池，细胞Celsius temperature scale 摄氏温标centimetre 厘米centralized low voltage power supply unit 中央控制低压电源箱centre of curvature 曲率中心centre of gravity 重心centre of mass 质心centre of oscillation 振荡中心centre-tapped transformer 中心抽头变压器centrifugal force 离心力centrifuge 离心机centripetal acceleration 向心加速度centripetal force 向心力Chadwick 查德威克chain reaction 连锁反应change of state 物态变化change-over switch 换向开关characteristic 特性，特征characteristic curve 特性曲线??characteristic line 特征线，特征谱??characteristic spectrum 特征光谱，特征谱charge 电荷，充电，起电charge carrier 载荷子charge conservation 电荷守恒charge density 电荷密度charge distribution 电荷分布charge to mass ratio 荷质比charged particle 带电粒子charging by contact 接触起电charging by friction 摩擦生电charging by induction 感应起电charging by sharing 授受起电charging time constant 充电时间常数，充电时间常量Charles's law 查理定律choke 扼流，抗流，扼流圈，抗流圈choke circuit 扼流电路，抗流电路chromatic aberration 色差chromatic dispersion 色散cinefilm soundtrack 电影胶片声迹circle of least confusion 最少模糊圈，明晰圈circuit 电路circuit board 电路板circuit breaker 断路器circuit symbol 电路符号circular coil 环形线圈circular motion 圆周运动circular orbit 圆周轨道circular pulse 圆形脉冲circular wave 圆形波circular wavefront 圆形波阵面，圆形波前clamp 夹钳，夹紧clap-echo method 「拍掌—回声」法cleave 裂开clinical thermometer 体温计clip 夹子clockwise moment 顺时针力矩closed circuit 闭合电路closed pipe 闭管closed tube 闭管closed-loop control system 死循环控制系统closed-loop gain 死循环增益closed-loop voltage gain 死循环电压增益closely packed 密堆积的cloud chamber 云室cloud chamber track 云室径迹coaxial 共轴，同轴coaxial cable 同轴电缆，同轴??cobalt 钴code 编码coder 编码器coefficient of dynamic friction 动摩擦系数coefficient of friction 摩擦系数coefficient of restitution 恢复系数coefficient of static friction 静摩擦系数coefficient of viscosity 黏滞系数coherent 相干的cohesion 内聚力，内聚cohesive force 内聚力coil 线圈collector 集电极，集极collector current 集电极电流，集极电流collimator 准直管，准直仪collision 碰撞colour 颜色colour code 色码，色标combinational logic 组合逻辑common emitter 共发射极common-mode voltage 共模电压commutator 换向器compass 指南针，罗盘complete circuit 完整电路component 组件，分量，组分component of force 分力compound microscope 复式显微镜compound pendulum 复摆compressed gas 压缩气体compressibility 可压缩性，压缩系数，压缩率compressible fluid 可压缩性流体compression 密部，压缩compression spring balance 压缩弹簧天平concave 凹concave lens 凹透镜concave mirror 凹镜，凹面镜concentric capacitor 同心电容器condensation 凝结，凝聚condensation nucleus 凝结核，凝聚核condensation point 凝点，凝结点condenser 聚光器，电容器，冷凝器conductance 电导conductivity 传导性，传导率conductor 导体conical pendulum 锥摆conjugate foci 共轭焦点conservation of angular momentum 角动量守恒conversation of charge 电荷守恒conservation of energy 能量守恒conservation of mechanical energy 机械能守恒conservation of momentum 动量守恒conservative force 守恒力，保守力conserved 守恒constant acceleration 恒加速度constant angular acceleration 恒角加速度constant angular velocity 恒角速度constant force 恒力constant motion 恒速运动constant pressure 定压constant speed 恒速率constant temperature 定温constant velocity 恒速度constant volume 定容constant volume gas thermometer 定容气体温度计constantan 康铜constriction 颈缩constructive interference 相长干涉contact angle 接触角contact area 接触面积contact force 接触力continuity equation 连续性方程continuous spectrum 连续光谱，连续谱continuous wave 连续波contract 收缩control experiment 对照实验，比对实验control grid 控制栅极control rod 控制棒control system 控制系统convection 对流converge 会聚converging lens 会聚透镜converging mirror 会聚镜convex 凸convex lens 凸透镜convex mirror 凸镜，凸面镜coolant 冷却剂cooling by evaporation 蒸发致冷cooling correction 冷却修正cooling curve 冷却曲线??cooling effect 冷却效应cooling system 冷却系统，散热系统coplanar forces 共面力core 心，核心Coriolis force 科里奥利力corkscrew rule 螺旋法则cornea 角膜corona discharge 电晕放电corpuscular theory of light 光的微粒学说correction 矫正，修正cosmic radiation 宇宙辐射coulomb 库伦Coulomb's law 库伦定律count rate 计数率counter 计数器counter weight 平衡锤，配重couple 力偶coupled oscillation 耦合振荡coupling 耦合covalent bond 共价键crane magnet 起重磁铁creep 蠕变crest 波峰critical angle 临界角critical damping 临界阻尼critical mass 临界质量critical point 临界点critical temperature 临界温度critical velocity 临界速度crocodile clip 鳄鱼夹cross hairs 十字丝，叉丝cross-sectional area 截面积Crova's disc 克罗瓦盘crystal 晶体crystal diffraction 晶体衍射，晶体绕射crystal lattice 晶体点阵，晶体格子，晶格crystal planes 晶面crystalline 结晶的crystallization 结晶crystallography 晶体学cubical expansivity 体积膨胀系数，体积膨胀率curie 居里current 电流current amplification 电流放大current amplification factor 电流放大因素current amplifier 电流放大器current balance 电流天平current density 电流密度current gain 电流增益current intensity 电流强度current pulse 电流脉冲current sensitivity 电流灵敏度current stabilizer 稳流器current transfer characteristic 电流转移特性current-carrying conductor 载电流导体current-voltage characteristic curve 电流—电压特性曲线?? curved mirror 曲面镜cyclotron 回旋加速器cylindrical concave lens 柱面凹透镜cylindrical concave mirror 柱面凹镜cylindrical convex lens 柱面凸透镜cylindrical convex mirror 柱面凸镜cylindrical lens 柱面透镜cylindrical mirror 柱面镜Ff-number f数，光圈数f-stop f制光圈far point 远点farad 法拉Faraday constant 法拉第常数，法拉第常量Faraday's law of electromagnetic induction 法拉第电磁感应定律fast breeder reactor 快中子增殖反应堆feedback 反馈feedback amplifier 反馈放大器feedback resistance 反馈电阻ferromagnetic substance 铁磁性物质ferromagnetism 铁磁性fictitious force 假力，伪力fidelity 保真性，保真度field coil 场线圈field effect transistor 场效应晶体管field intensity 场强field lines 场力线??field magnet 场磁铁，场磁体field of view 视场，视野field strength 场强figure of merit 优值，灵敏值filament 灯丝，丝极filter capacitor 滤波电容器filter circuit 滤波电路filter pump 滤泵final state 终态，末态final velocity 末速度fine-adjustment 微调，细调fire alarm 火警警报器，火警钟first law of thermodynamics 热力学第一定律first order spectrum 第一级光谱，第一级谱fission 裂变fission reactor 裂变反应堆fixed point 定点fixed pulley 定滑轮fixed resistor 定值电阻器flat coil 扁平线圈flat solenoid 扁平螺线管flat-bottomed flask 平底烧瓶Fleming's left hand rule 弗林明左手定则Fleming's right hand rule 弗林明右手定则floating body 浮体fluid 流体fluid dynamics 流体动力学fluorescence 荧光fluorescent screen 荧光屏，荧光幕flux 通量flux density 通量密度fly-back 回扫flywheel 飞轮focal length 焦距focal plane 焦平面focus 焦点，聚焦，对焦focus control 聚焦控制follower circuit 跟随电路foot pump 脚踏泵force 力force constant 力常数，力常量force polygon 力多边形force resolution 力的分解force triangle 力三角形force-extension curve 施力—伸长关系曲线?? forced oscillation 受迫振荡former 框forward biased 正向偏压forward current 正向电流fossil fuel 化石燃料Foucault's rotating mirror method 傅科旋转镜法frame of reference 参考坐标系，参考系Franck-Hertz experiment 弗兰克—赫兹实验Fraunhofer diffraction 夫琅和费衍射，夫琅和费绕射Fraunhofer lines 夫琅和费谱线??free electron 自由电子free fall 自由下坠，自由下落free falling body 自由落体free oscillation 自由振荡free path 自由程free space 自由空间freeze 凝固freezing point 凝固点freon 氟利昂，二氯二氟甲烷frequency 频率frequency modulation 调频，频率调制frequency response 频率响应Fresnel diffraction 菲涅耳衍射，菲涅耳绕射Fresnel's biprism 菲涅耳双棱镜friction 摩擦，摩擦力friction compensated 补偿摩擦作用frictionless motion 无摩擦运动fringe 条纹fringe pattern 条纹图形fuel rod 燃料棒fulcrum 支点full adder 全加法器full-scale deflection 满标偏转full-wave rectification 全波整流full-wave rectifier 全波整流器fundamental frequency 基频fundamental mode of vibration 基谐振动模式fundamental note 基音fundamental quantity 基本量fundamental unit 基本单位fuse 保险丝fuse rating 保险丝额定值fusion 熔解，聚变fusion point 熔点fusion reactor 聚变反应堆GG - clamp G-形钳gain 增益gain control 增益控制galaxy 星系Galilean telescope 伽利略望远镜Galileo's thought experiment 伽利略假想实验galvanometer 电流计，检流计gamma radiation 伽玛辐射gamma ray 伽玛射线??gap 隙gas 气，气体gas pressure 气体强压，气压gaseous phase 气相gaseous state 气态gauge 规，计Gauss theorem 高斯定理Geiger counter 盖革计数器Geiger-Marsden scattering experiment 盖革—马斯登散射实验Geiger-Muller counter 盖革—弥勒计数器Geiger-Muller tube 盖革—弥勒管general gas equation 普适气体方程general gas law 普适气体定律generator 发电机genetic effect 遗传效应geometrical optics 几何光学germanium 锗ghost effect 迭影效应glancing angle 掠射角glass fibre 玻璃纤维glycerine 甘油gold foil 金箔fold leaf electroscope 金箔验电器gradient 斜率，梯度graduated cylinder 量筒Graham's law of diffusion 格拉哈姆散定律grain 粒，晶粒gramophone record 唱片，唱碟graph 图，线图，图表graphical method 图解法grating 光栅grating spectrometer 光栅光谱仪，光栅分光计gravitational acceleration 重力加速度gravitational attraction 引力，重力gravitational constant 引力常数，引力常量gravitational field 引力场，重力场gravitational force 引力，重力gravitational mass 引力质量gravitational potential 引力势，重力势gravitational potential difference 引力势差，重力势差gravitational potential energy 引力势能，重力势能gravity 重力grazing incidence 掠入射，切入射greenhouse effect 温室效应grid 栅极grid control 栅极控制grid system 电力网groove 纹道，针槽，开槽ground 接地ground state 基态guinea and feather experiment 「硬币与羽毛」实验Hhair spring 游丝half adder 半加法器half-life 半衰期half-silvered mirror 半镀银镜half-wave rectification 半波整流half-wave rectifier 半波整流器Hall effect 霍耳效应Hall probe 霍耳探测器Hall voltage 霍耳电压hand stroboscope 手动式频闪观测器harmonic 谐音harmonic motion 谐运动harmonic oscillation 谐振荡head-on collision 对正碰撞，正碰heat 热，热量，加热，热学heat absorbent 吸热剂heat absorber 吸热器heat absorption 吸热，热吸收heat capacity 热容量heat conduction 热传导heat exchange 热交换heat flow 热流heat gain 热增益，得热heat insulation 热绝缘，隔热heat loss 热损耗，失热heat proof 耐热的，隔热的heat pump 热泵heat radiation 热辐射heat reservoir 热库，储热器heat sink 热壑heat transfer 热传递，热转移heater 发热器，加热器heating effect 热效应heating element 发热组件Helmholtz coils 亥姆霍兹线圈henry 亨利，亨hertz 赫兹，赫high dispersion prism 高色散棱镜high tension 高电压hole 空穴，空子hollow plastic lens 空心塑料透镜hollow plastic prism 空心塑料棱镜hologram 全息图holography 全息术，全息学Hooke's law 虎克定律horizontal 水平horizontal component 水平分量horizontal deflection 水平偏转horseshoe magnet 蹄形磁铁hot cathode 热阴极hour 小时Huygens' principle 惠更斯原理hydraulic press 水压机hydroelectric power 水力发电hydrogen bomb 氢弹hygrometer 湿度计hyperbolic orbit 双曲线轨道hypodermic needle 皮下注射针头hypodermic syringe 皮下注射针筒hypothesis 假说，假设hysteresis 滞后现象Iideal gas 理想气体ideal gas equation 理想气体方程ideal gas temperature scale 理想气体温标ideal machine 理想机械illuminate 照明，照亮image 像image distance 像距immerse 浸没immersion heater 浸没式电热器impact 碰撞impedance 阻抗impulse 冲量impurity 杂质in focus 焦点对准in parallel 并联in phase 同相in series 串联incident ray 入射线??incident wavefront 入射波阵面，入射波前inclined plane 斜面incoherent 不相干的incompressible fluid 非压缩性流体indicator 指示器indirectly heated cathode 旁热式阴极induced charge 感生电荷induced current 感生电流induced e.m.f. 感生电动势induced voltage 感生电压??inducing charge 施感电荷inducing current 施感电流inductance 电感inductance capacitance coupled circuit 感容耦合电路inductance coil 电感线圈induction 感应induction heating 感应生热inductive circuit 电感电路inductive component 电感性分量inductive reactance 感抗inductor 电感器，感应器inelastic collision 非弹性碰撞inert gas 惰性气体inertia 惯性，惯量inertia balance 惯性秤inertial frame 惯性坐标系，惯性系inertial mass 惯性质量infra-red detector 红外线探测器infra-red radiation 红外辐射infra-red ray 红外线??initial state 初态initial velocity 初速度input 输入input bias current 输入偏压电流input characteristic 输入特性input current 输入电流input offset current 输入补偿电流input power 输入功率input resistance 输入电阻input voltage 输入电压input-output voltage characteristic 输入—输出电压特性instantaneous acceleration 瞬时加速度instantaneous angular velocity 瞬时角速度instantaneous current 瞬时电流instantaneous power 瞬时功率instantaneous speed 瞬时速率instantaneous velocity 瞬时速度instantaneous voltage 瞬时电压insulation 绝缘insulator 绝缘体integrated circuit 集成电路intensity 强度intensity control 强度控制intensity of current 电流强度interaction 相互作用interatomic force 原子间力interatomic potential 原子间势，原子间位interatomic separation 原子间距intercept 截距，截段interconversion 互换interference 干涉interference pattern 干涉图形internal energy 内能internal force 内力internal resistance 内电阻internal work 内功international system of units 国际单位制，公制，十进制interval 间隔intrinsic semiconductor 纯半导体，本征半导体inverse-square law 平方反比定律inverted 倒立的inverter 反相器，倒换器inverting input 反相输入ion 离子ion-pair 离子偶，离子对ionic bond 离子键ionic structure 离子结构ionization 电离作用ionization chamber 电离室ionization current 电离电流ionization energy 电离能ionization potential 电离电势，电离电位ionization voltage 电离电压ionize 电离ionized atom 离子ionized layer 电离层ionizing power 致电离能力，致电离本领ionizing radiation 致电离辐射ionosphere 电离层iris 虹膜，可变光阑iron core 铁心iron filings 铁粉irreversible process 不可逆过程isobar 等压线，同质异序素isobaric expansion 等压膨胀isobaric process 等压过程isochronous oscillation 等时振荡isotherm 等温线??isothermal process 等温过程isotope 同位素isovolumetric process 等容过程JJaegers method 耶格法jet propulsion 喷气推进jockey 滑动触头joule 焦耳joulemeter 焦耳计junction 连接，接头junction diode 面结型二极管junction transistor 面结型晶体管KKaleidoscope 万花筒Kelvin 开尔文，开Kelvin temperature scale 开氏温标Kepler's law 开普勒定律key 电键kilogram 千克kilowatt 千瓦特，千瓦kilowatt-hour 千瓦小时，千瓦时kilowatt-hour meter 电表，千瓦时计kinematics 运动学kinetic energy 动能kinetic friction 动摩擦kinetic theory 分子运动论kinetic theory model 分子运动模型kinetic theory of gases 气体分子运动论Kirchhoff's law 基尔霍夫定律kit 套件knife-edge 刃形支承，刀刃，刀边kryton 氪Kundt's tube 孔脱管Llagging 保温套laminar flow 层流laminated 分层的，迭片的laser 激光，激光器laser beam 激光束laser material 激光材料latch 闩锁latent heat 潜热lateral 横向，侧向，旁向lateral inversion 横向倒置lateral magnification 横向放大，横向放大率lateral search coil 横向探察线圈lattice 点阵，晶格lattice spacing 点阵间隔，点阵间距law 定律law of conservation of momentum 动量守恒定律law of reflection 反射定律law of refraction 折射定律lead 导线，铅lead-acid accumulator 铅酸蓄电池leakage current 漏泄电流least distance of distinct vision 最小明视距离Leclanche cell 勒克朗谢电池length 长度lens 透镜，晶体，晶状体lens formula 透镜公式lens holder 透镜座lens marker's formula 透镜制造者公式Lenz's law 楞次定律leukaemia 白血病lever 杠杆light 光，光学light beam 光束，光柱light dependent resistor 光敏电阻器light emitting diode 发光二极管light guide 光导light pipe 光导管light ray 光线??light sensitive resistor 光敏电阻器light source 光源lightning 闪电lightning conductor 避雷针limiting angle 极限角limiting friction 极限摩擦line of action 作用线??line of force 力线??line spectrum 线状光谱，线状谱linear air track 线性气垫导航linear electronics 线性电子学linear expansivity 线性膨胀系数，线性胀率linear flow 线流linear momentum 线动量linear voltage amplification 线性电压放大率linearly polarized wave 线偏振波liquefaction 液化liquid 液体liquid crystal 液晶体liquid phase 液相liquid pressure 液体压强liquid-in-glass thermometer 玻管液体温度计Lissajous figure 利萨如图形live 载电，活线，火线Lloyd's mirror 洛埃镜load 负荷lodestone 磁石logic gate 逻辑门logic level 逻辑电平，逻辑级logic level indicator 逻辑电平指示器，逻辑级指示器logic value 逻辑值long sight 远视long wave 长波longitudinal magnification 纵向放大，纵向放大率longitudinal wave 纵波loop 回路，圈Lorentz force 洛兰兹力Lorentz rotating disc 洛兰兹旋转盘loudness 响度loudspeaker 扬声器low frequency a.c. generator 低频交流发电机low voltage 低电压low voltage immersion heater 低压浸没式电热器lower limit 下限lycopodium powder 石松粉Lyman series 赖曼系，赖曼光谱MMach number 马赫数machine 机械macroscopic 宏观的magnadur magnet 玛格纳多尔磁铁magnet 磁铁，磁体magnet keeper 永久磁铁衔铁magnetic domain 磁畴，磁域magnetic effect 磁效应magnetic field 磁场magnetic field board 磁场板magnetic field intensity 磁场强度magnetic field strength 磁场强度magnetic flux 磁通量magnetic flux density 磁通量密度magnetic flux linkage 磁链，磁键，磁通匝数magnetic force 磁力magnetic hysteresis 磁滞magnetic induction 磁感应强度，磁感应magnetic line of force 磁力线?? magnetic material 磁性材料magnetic meridian 磁子午线??magnetic moment 磁矩magnetic north pole 磁北极magnetic permeability 磁导率magnetic pole 磁极magnetic screen 磁屏magnetic shield 磁屏magnetic south pole 磁南极magnetic susceptibility 磁化率magnetic tape 磁带magnetic tape recorder 磁带录音机magnetic torque 磁矩magnetic track 磁迹magnetism 磁学，磁性magnetization 起磁，磁化作用magnetize 磁化magnetizing current 磁化电流magnification 放大，放大率magnified 放大的magnifying glass 放大镜magnifying power 放大率magnitude 量，量值mains frequency 市电频率mains immersion heater 市电浸没式热器mains supply 市电电源majority carriers 多数载流子malleable 展性的，韧性的Maltese cross tube 马尔塔十字管manometer 流体压强计mass 质量mass defect 质量亏损mass number 质量数mass spectrometer 质谱仪mass-energy relation 质能关系matter wave 物质波maximum error 最大误差mean free path 平均自由程measurement 测量mechanical advantage 机械利益mechanical efficiency 机械效率mechanical energy 机械能mechanical oscillation 机械振荡mechanical wave 机械波mechanism 机制，机理medium 介质medium wave 中波Melde's experiment 迈尔德实验melt 熔化melting point 熔点meniscus 弯液面，弯月面meniscus lens 凹凸透镜，弯月形透镜mercury 汞，水银metal fatigue 金属疲劳fetal grid 金属珊metallic bond 金属键metastable 亚稳态的，介稳态的method of dimensions 维量法，因次法method of no-parallax 无视差法metre 米metre bridge 滑线电桥，米尺电桥metre rule 米尺mica 云母mica capacitor 云母电容器microammeter 微安培计，微安计microelectronics 微电子学micrometer 测微计micrometer screw gauge 螺旋测微计microphone 微音器，传声器microscope 显微镜microscopic 微观的microwave 微波microwave apparatus 微波仪器microwave receiver 微波接收器microwave transmitter 微波发送器milliammeter 毫安计，毫安计Millikan experiment 密立根实验millimetre 毫米minimum deviation 最小偏向minority carrier 少数载流子minute 分，分钟mirage 海市蜃楼，蜃景mirror 镜mirror formula 球面镜公式mobility 动性，迁移率mode 模式model eye 眼球模型model power line 输电线模型moderator 减速剂，缓和剂modulation 调制，调节module 组件modulus of elasticity 弹性模量modulus of rigidity 刚性模量molar gas constant 摩尔气体常数，摩尔气体常量molar heat capacity 摩尔热容量molar volume 摩尔体积mole 摩尔molecular bombardment 分子撞击molecular force 分子力molecular motion 分子运动molecular polarization 分子极化molecular separation 分子间距molecular structure 分子结构molecule 分子moment 矩moment arm 矩臂，力臂moment of couple 力偶矩moment of dipole 偶极矩moment of force 力矩moment of inertia 转动惯量moment of momentum 动量矩momentum 动量monatomic molecule 单原子分子monochromatic light 单色光motion 运动motor 电动机motor rule 电动机法则movable pulley 动滑轮moving-coil galvanometer 动圈式电流计，动圈式检流计moving-coil loudspeaker 动圈式扬声器moving-coil meter 动圈式电表multiflash photography 多闪照相法multimeter 万用电表，多用电表multiple image 复像multiple reflection 多次反射multiplication process 倍增过程multiplier 倍加器multivibrator 多谐振荡器musical instrument 乐器mutation 突变multiple-slit interference 多缝干涉mutual inductance 互感mutual induction 互感应mutually perpendicular 互相垂直的Nn-type semiconductor n型半导体NAND gate 「与非」门，「非与」门naphthalene ???natural frequency 固有频率，自然频率nature 本质near point 近点necking 颈缩negater 反相器，倒换器negative charge 负电荷negative feedback 负反馈negative ion 负离子negative supply rail 负供电轨negative terminal 负端钮，负接线柱net force 净力network 网络，网络neutral 中性，中线??neutral equilibrium 中性平衡，随遇平衡neutral point 中和点neutrino 中微子neutron 中子neutron number 中子数newton 牛顿Newton's first law of motion 牛顿运动第一定律Newton's law of gravitation 牛顿万有引力定律Newton's ring 牛顿环Newton's second law of motion 牛顿运动第二定律Newton's third law of motion 牛顿运动第三定律Newtonian fluid 牛顿流体Newtonian mechanics 牛顿力学nichrome wire 镍铬线，镍铬合金线??Nicol prism 尼科尔棱镜nitrogen 氮no-parallax 无视差nodal line 节线??node 节点，波节noise 噪音noise level 噪音级noise pollution 噪音污染non-conservative force 非守恒力，非保守力non-inertial frame 非惯性坐标系，非惯性系non-inverting input 非反相输入non-Newtonian fluid 非牛顿流体non-ohmic conductor 非奥姆导体non-ohmic resistor 非奥姆电阻器NOR gate 「或非」门，「非或」门normal 法线??normal incidence 正入射normal reaction 法向反作用力normal stress 法向应力north pole 北极NOT gate 「非」门note 音，乐音，律音nozzle 喷嘴nuclear 原子核的nuclear energy 核能nuclear energy level 核能级nuclear fission 核裂变nuclear force 核力nuclear fusion 核聚变nuclear pile 核反应堆nuclear radiation 核辐射nuclear reaction 核反应nuclear rector 核反应堆nuclear waste 核废料nuclear weapon 核武器nucleon 核子nucleon number 核子数，质量数nucleus 原子核nuclide 核素Oobject 物，物体object distance 物距objective 接物镜，物镜。