气体动力学第一讲概述.ppt

Course for the GE3 programCourse for the GE3 program Fundamentals Fundamentals ofof Gas Gas DynamicsDynamics Lecture 1Lecture 1 Prof. Yancheng You(尤延铖) Lecture 1: An Introduction p Overview Course syllabus Questions to be answered Review of elementary principles Lecture 1: An Introduction p Course syllabus Textbook: Zucker, Robert D. Fundamentals of Gas Dynamics. 2nd ed. Hoboken, N. J: J. Wiley, 2002. /s/jik368j3u7wxje9emsgo Reference: F. M. White, Fluid Mechanics( with Student DVD). McGraw Hill, ISBN: 9780077422417, 2010. J. Anderson, Fundamentals of Aerodynamics. ISBN: 9780073398105, McGraw-Hill, 2010. M. J. Zucrow, and J. D. Hoffman. Gas Dynamics, Vol. 2: Multidimensional Flow. Wiley, ISBN: 9780471018063, 1977. Liepmann, H. W., and A. Roshko. Elements of Gasdynamics. Dover Publications, ISBN: 0486419630, 2002. F. M. White, Viscous Fluid Flow. McGraw-Hill, ISBN: 9780071244930, 2006. Lecture 1: An Introduction p Course syllabus Course Objectives: This course deals with compressible flow that is encountered in many aerospace and mechanical engineering practices and provides deeper knowledge on the effect of compressibility on a flow much more than aerodynamics, fluid mechanics or thermodynamics. This course has a set of objectives that you need to keep in mind during the course of the semester. You should be able to: Describe assumptions, physical meaning of terms and utilize key relationships for compressible flow, speed of sound, isentropic and non- isentropic flows; Calculate the effect of area change, heat addition, and friction on flow states in a compressible duct flow, including effects on mass flow rate and flow regime; Estimate the lift and drag for basic aerodynamic shapes in compressible, inviscid flows; Perform a numerical simulation of compressible flow through a variable area duct. Lecture 1: An Introduction p Course Contents Control volume analysis Material Derivative, Control volume approach, Conservation laws, The stagnation concept, Momentum equation Introduction to compressible flows Definitions and equations of compressible flow, Sonic velocity and Mach number Varying-area adiabatic flow Isentropic flow, Nozzle operation, diffuser performance, Converging and converging-diverging nozzle Normal shock waves Stationary and moving normal shock wave, Working equations and shocks in nozzles, and application Lecture 1: An Introduction p Course Contents Oblique shock wave Working equations, Oblique shock analysis, Conical shocks Prandtl-Meyer Flow Analysis of Prandtl-Meyer flow, Shock-expansion interaction Propulsion systems General performance parameters, thrust, power and efficiency, Air-breathing propulsion systems, Rocket Propulsion systems, Supersonic diffusers Method of Characteristics 2D MOC for inviscid supersonic flowpath analysis Lecture 1: An Introduction p Homeworks Attending lectures, reading book and solving examples are not sufficient. You must work HWs yourself Doing HWs is your way to a good grade in any course. (cannot emphasize more) Try Solving HWs yourself first and if stuck seek help from your teaching assistant or me, 3 exercises every week. Homeworks are due in class, late homeworks are not accepted. p Exams and Grading Quizzes: 2 quizzes about hour each, on weeks 6, 12 Final exams: the open-book exam will be 2 hours and covers all topics of the course discussed in the class from the first day till the last day. Grading: Homeworks 20%, Quizzes 30%, Final Exam 50% Lecture 1: An Introduction p Questions to be answered What does compressible fluid flow means? Why do we need to study compressible fluid flow? Are all fluids compressible? Are all flows compressible? Is there any relation between compressibility and flow speed? What are the assumptions adopted in the basic analysis of compressible fluids? What are the equations (laws) used in the analysis of compressible fluids? What are the effects of density variation on the design of some aerospace systems? Lecture 1: An Introduction p Questions to be answered What does compressible fluid means? A fluid which experience a variation in density is called compressible fluid. What does compressible flow means? The main sources of density variation are: Pressure, Temperature What are the effects of the density variation (pressure and temperature) on the flow of compressible fluid? Recall from energy equation that temperature is related to kinetic energy ( ). ; where specific heat at constant pressure where stagnation enthalpy static enthalpy flow speed Lecture 1: An Introduction p Questions to be answered If = constant (not function of ) ; or This means that as the difference between static and stagnation temperatures increases, the kinetic energy (velocity) of the flow increases. Recall that for perfect gas, the density, temperature and pressure are related by perfect gas law. ; where gas constant Therefore, the study of a flow in which the variations of density and temperature are important is called compressible fluid flow or gas dynamics. Lecture 1: An Introduction p Questions to be answered Why do we need to study compressible fluid flow? All fluids are compressible. Compressible flow occurs in many systems encountered in aerospace, mechanical and chemical engineering practices such as: High speed flows (M 0.3) Gas turbines (jet engines) Reciprocating engines Combustion chambers When the density in a flow varies, equations used in the analysis of such flow get complicated. Lecture 1: An Introduction p Review of elementary principles Units and notation Dimension: a qualitative definition of a physical entity (such as time, length, force) Unit: an exact magnitude of a dimension (such as seconds, feet, newtons) Lecture 1: An Introduction p Review of elementary principles Units and notation Force and Mass Density and Specific Volume Pressure Lecture 1: An Introduction p Review of elementary principles Units and notation Temperature Viscosity ( ) Equation of State Some mathematical concepts Variables: independent variable, dependent variable For example, y=f(x) Infinitesimal, Infinity Derivative Differential Integral Lecture 1: An Introduction p Review of elementary principles Some mathematical concepts Maximum and Minimum Taylor Series Thermodynamics concepts Microscopic approach Macroscopic approach Control mass: fixed quantity of mass that is being analyzed. It is separated from its surroundings by a boundary. A control mass is also referred to as a closed system. Control volume: a region of space that is being analyzed. The boundary separating it from its surroundings is called the control surface. Matter as well as energy may cross the control surface, and thus a control volume is also referred to as an open system. Lecture 1: An Introduction p Review of elementary principles Thermodynamics concepts Properties Types of properties Observable properties Mathematical properties Derived properties State change Path or process: represents a series of consecutive states that define a unique path from one state to another. Cycle, point functions, path functions Forms of the 1st law The second law p Laws of classical Thermodynamics Lecture 1: An Introduction Lecture 1: An Introduction p First Law of Thermodynamics conservation of energy Heat and work are two extreme types of energy in transit. For a closed system that executes a complete cycle Q = heat transferred into the system W = work transferred from the system For a closed system that executes a process On a unit mass basis Lecture 1: An Introduction p First Law of Thermodynamics The total energy may be broken down into (at least) three types: Lecture 1: An Introduction p First Law of Thermodynamics For an infinitesimal process, Note that since heat and work are path functions, infinitesimal amounts of these quantities are not exact differentials and thus are written as q and w. For a stationary system, The reversible work done by pressure forces Lecture 1: An Introduction p First Law of Thermodynamics define the property enthalpy, Enthalpy is a property since it is defined in terms of other properties. It is frequently used in differential form: the specific heats at constant pressure (cp) and constant volume (cv) Lecture 1: An Introduction p Second Law of Thermodynamics It is impossible for an engine operating in a cycle to produce net work output when exchanging heat with only one temperature source. It leads the way eventually to the establishment of a most important property (entropy). The second law also recognizes the degradation of energy quality by irreversible effects. The integral of Q/T for a reversible process is independent of the path. A property is defined, which is called entropy increase of entropy Lecture 1: An Introduction p Second Law of Thermodynamics on a unit mass basis for a differential process Property Relations Consider the first law for a stationary system If it is a reversible process Lecture 1: An Introduction p Second Law of Thermodynamics Differentiating the enthalpy, we obtained contain only properties and thus are valid relations to use between any end states Lecture 1: An Introduction p Perfect Gases the perfect gas equation of state the internal energy and the enthalpy are functions of temperature only If u = f (T ) only Lecture 1: An Introduction p Perfect Gases Similarly, for the specific heat at constant pressure, In gas dynamics one simplifies calculations by introducing an arbitrary base for internal energy. We let u = 0 when T = 0 absolute. Other frequently used relations in connection with perfect gases are Lecture 1: An Introduction p Entropy Changes Similarly, for the specific heat at constant pressure, Perfect gas: Equation of state For calorically perfect gas Entropy Entropy changes? p Laws of classical Thermodynamics Lecture 1: An Introduction For an