Fundamental Concepts of Real Gasdynamics
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Fundamentals of mechanical engineering [email protected] MOHAMMED ABASS ALI What is thermodynamics Thermodynamics is the branch of physics that studies the effects of temperature and heat on physical systems at the macroscopic scale. In addition, it also studies the relationship that exists between heat, work and energy. Thermal energy is found in many forms in today’s society including power generation of electricity using gas, coal or nuclear, heating water by gas or electric. THE BASICS OF THERMODYNAMICS Basic concepts Properties are Features of a system which include mass, volume, energy, pressure and temperature. Thermodynamics also considers other quantities that are not physical properties, such as mass flow rates and energy transfers by work and heat. Energy forms Fluids and solids can possess several forms of energy. All fluids possess energy due to their temperature and this is referred to as ‘internal energy’. They will also possess ‘ potential energy’ (PE) due to distance (z) above a datum level and if the fluid is moving at a velocity (v), it will also possess ‘kinetic energy’. If the fluid is pressurised, it will possess ‘flow energy’ (FE). Pressure and temperature are the two governing factors and internal energy can be added to FE to produce a single property called ‘enthalpy’. Internal energy The molecules of a fluid possess both kinetic energy (KE) and PE relative to an internal datum. Generally, this is regarded simply as the energy due to its temperature and the change in internal energy in a fluid that undergoes a temperature change is given by ΔU = mcΔT The total internal energy is denoted by the symbol ‘U’, which has values of J, kJ or MJ; also the specific internal energy ‘u’ has the values of kJ/kg. -
Aerodynamic Heating at Hypersonic Speed
10 Aerodynamic Heating at Hypersonic Speed Andrey B. Gorshkov Central Research Institute of Machine Building Russia 1. Introduction At designing and modernization of a reentry space vehicle it is required accurate and reliable data on the flow field, aerodynamic characteristics, heat transfer processes. Taking into account the wide range of flow conditions, realized at hypersonic flight of the vehicle in the atmosphere, it leads to the need to incorporate in employed theoretical models the effects of rarefaction, viscous-inviscid interaction, flow separation, laminar-turbulent transition and a variety of physical and chemical processes occurring in the gas phase and on the vehicle surface. Getting the necessary information through laboratory and flight experiments requires considerable expenses. In addition, the reproduction of hypersonic flight conditions at ground experimental facilities is in many cases impossible. As a result the theoretical simulation of hypersonic flow past a spacecraft is of great importance. Use of numerical calculations with their relatively small cost provides with highly informative flow data and gives an opportunity to reproduce a wide range of flow conditions, including the conditions that cannot be reached in ground experimental facilities. Thus numerical simulation provides the transfer of experimental data obtained in laboratory tests on the flight conditions. One of the main problems that arise at designing a spacecraft reentering the Earth’s atmosphere with orbital velocity is the precise definition of high convective heat fluxes (aerodynamic heating) to the vehicle surface at hypersonic flight. In a dense atmosphere, where the assumption of continuity of gas medium is true, a detailed analysis of parameters of flow and heat transfer of a reentry vehicle may be made on the basis of numerical integration of the Navier-Stokes equations allowing for the physical and chemical processes in the shock layer at hypersonic flight conditions. -
Real Gases – As Opposed to a Perfect Or Ideal Gas – Exhibit Properties That Cannot Be Explained Entirely Using the Ideal Gas Law
Basic principle II Second class Dr. Arkan Jasim Hadi 1. Real gas Real gases – as opposed to a perfect or ideal gas – exhibit properties that cannot be explained entirely using the ideal gas law. To understand the behavior of real gases, the following must be taken into account: compressibility effects; variable specific heat capacity; van der Waals forces; non-equilibrium thermodynamic effects; Issues with molecular dissociation and elementary reactions with variable composition. Critical state and Reduced conditions Critical point: The point at highest temp. (Tc) and Pressure (Pc) at which a pure chemical species can exist in vapour/liquid equilibrium. The point critical is the point at which the liquid and vapour phases are not distinguishable; because of the liquid and vapour having same properties. Reduced properties of a fluid are a set of state variables normalized by the fluid's state properties at its critical point. These dimensionless thermodynamic coordinates, taken together with a substance's compressibility factor, provide the basis for the simplest form of the theorem of corresponding states The reduced pressure is defined as its actual pressure divided by its critical pressure : The reduced temperature of a fluid is its actual temperature, divided by its critical temperature: The reduced specific volume ") of a fluid is computed from the ideal gas law at the substance's critical pressure and temperature: This property is useful when the specific volume and either temperature or pressure are known, in which case the missing third property can be computed directly. 1 Basic principle II Second class Dr. Arkan Jasim Hadi In Kay's method, pseudocritical values for mixtures of gases are calculated on the assumption that each component in the mixture contributes to the pseudocritical value in the same proportion as the mol fraction of that component in the gas. -
Fundamentals of Hypersonic Flow - Aerothermodynamics
FUNDAMENTALSOFHYPERSONICFLOW- AEROTHERMODYNAMICS D. G. Fletcher von Karman Institute, Belgium 1. Introduction To aid in understanding the different topics discussed in the current Lecture Series and to provide background material for interested participants who may not have specialized training in this field, a brief summary of the fundamental attributes of hypersonic flows is given. Many of the topics that are introduced in this section will be elaborated further in contributions related to specific subjects related to sustained hypersonic flight. The differencesbetweenthethermalandchemicalaspectsofhypersonicflowandsupersonic flow are therefore highlighted. The age of some of the figures used in the subsequent discussion reflect the fact that the problems of hypersonic flight are not newly discovered! Fig. 1.1 Flight trajectories for different hypersonic vehicles comparing sustained atmo- spheric flight with re-entry. The hypersonic flight regime includes atmospheric entry and re-entry, ground testing, and flight for both powered and unpowered vehicles. In the present Lecture Series, the main interest is on sustained and controlled hypersonic flight, whether for military or civil transport application. Even though it is not currently certified for flight, there is one operational hypersonic vehicle: the space shuttle of NASA. At least 20 years before the development of the shuttle a significant activity in hypersonic flight research was conducted by the US Air Force in their X-15 program. This vehicle has reached a flight Mach number of 6.7 on its final flight, which also used to test a hypersonic ramjet engine. Direct shock impingement on the pylon holding a dummy engine caused severe heating and structural damage, and this was one of many lessons learned from the program. -
Experimental Investigation Into Shock Waves Formation and Development Process in Transonic Ow
Scientia Iranica B (2017) 24(5), 2457{2465 Sharif University of Technology Scientia Iranica Transactions B: Mechanical Engineering www.scientiairanica.com Experimental investigation into shock waves formation and development process in transonic ow M. Farahani and A. Jaberi Department of Aerospace Engineering, Sharif University of Technology, Tehran, Iran. Received 11 May 2016; received in revised form 12 August 2016; accepted 8 October 2016 KEYWORDS Abstract. An extensive experimental investigation was performed to explore the shock waves formation and development process in transonic ow. Shadowgraph visualization Shock waves technique was employed to provide visual description of the ow eld features. Based on formation process; the visualization, the formation process was categorized into two intrinsically di erent Transonic ow; phases, namely, subsonic and supersonic. The characteristics of subsonic phase are well Shadowgraphy known; however, those of the supersonic one are far less studied. The supersonic phase visualization; itself is made up of two consecutive phases, namely, approaching and sweeping. The e ects Splitting of shock of each phase on the ow eld characteristics and on shaping the supersonic regime were waves; studied in details. In order to generalize the results, three di erent models were tested. A Zeh shock. special terminology is suggested by authors to ease the process description and pave a way for future studies. Above all, as the transition from transonic regime to the supersonic one is a vague concept in terms of physical reasoning, a new explanation is proposed that can be used as a criterion for distinguishing between transonic and supersonic regimes. © 2017 Sharif University of Technology. -
Bifurcating Mach Shock Reflections with Application to Detonation Structure
BIFURCATING MACH SHOCK REFLECTIONS WITH APPLICATION TO DETONATION STRUCTURE Philip Mach A thesis submitted to the Faculty of Graduate and Postdoctoral Studies in partial fulfillment of the requirements for the degree of MASTER OF APPLIED SCIENCE in Mechanical Engineering Ottawa-Carleton Institute for Mechanical and Aerospace Engineering University of Ottawa Ottawa, Canada August 2011 © Philip Mach, Ottawa, Canada, 2011 ii Abstract Numerical simulations of Mach shock reflections have shown that the Mach stem can bifurcate as a result of the slip line jetting forward. Numerical simulations were conducted in this study which determined that these bifurcations occur when the Mach number is high, the ramp angle is high, and specific heat ratio is low. It was clarified that the bifurcation is a result of a sufficiently large velocity difference across the slip line which drives the jet. This bifurcation phenomenon has also been observed after triple point collisions in detonation simulations. A triple point reflection was modelled as an inert shock reflecting off a wedge, and the accuracy of the model at early times after reflection indicates that bifurcations in detonations are a result of the shock reflection process. Further investigations revealed that bifurcations likely contribute to the irregular structure observed in certain detonations. iii Acknowledgements Firstly, I would like to thank my supervisor, Matei Radulescu, who guided me through the complicated task of learning about the detonation phenomenon, provided me with most of the scripts for the numerical simulations, answered my questions (no matter how dumb they were), and was patient with my progress. I would have obviously been lost without him. -
Investigation of Shock Wave Interactions Involving Stationary
Investigation of Shock Wave Interactions involving Stationary and Moving Wedges Pradeep Kumar Seshadri and Ashoke De* Department of Aerospace Engineering, Indian Institute of Technology Kanpur, Kanpur, 208016, India. *Corresponding Author: [email protected] Abstract The present study investigates the shock wave interactions involving stationary and moving wedges using a sharp interface immersed boundary method combined with a fifth-order weighted essentially non- oscillatory (WENO) scheme. Inspired by Schardin’s problem, which involves moving shock interaction with a finite triangular wedge, we study influences of incident shock Mach number and corner angle on the resulting flow physics in both stationary and moving conditions. The present study involves three incident shock Mach numbers (1.3, 1.9, 2.5) and three corner angles (60°, 90°, 120°), while its impact on the vorticity production is investigated using vorticity transport equation, circulation, and rate of circulation production. Further, the results yield that the generation of the vorticity due to the viscous effects are quite dominant compared to baroclinic or compressibility effects. The moving cases presented involve shock driven wedge problem. The fluid and wedge structure dynamics are coupled using the Newtonian equation. These shock driven wedge cases show that wedge acceleration due to the shock results in a change in reflected wave configuration from Single Mach Reflection (SMR) to Double Mach Reflection (DMR). The intermediary state between them, the Transition Mach Reflection (TMR), is also observed in the process. The effect of shock Mach number and corner angle on Triple Point (TP) trajectory, as well as on the drag coefficient, is analyzed in this study. -
Real Gas Behavior Pideal Videal = Nrt Holds for Ideal
Real gas behavior Pideal Videal = nRT holds for ideal gas behavior. Ideal gas behavior is based on KMT, p. 345: 1. Size of particles is small compared to the distances between particles. (The volume of the particles themselves is ignored) So a real gas actually has a larger volume than an ideal gas. Vreal = Videal + nb n = number (in moles) of particles Videal = Vreal - nb b = van der Waals constant b (Table 10.5) Pideal (Vreal - nb) = nRT But this only matters for gases in a small volume and with a high pressure because gas molecules are crowded and bumping into each other. CHEM 102 Winter 2011 Ideal gas behavior is based on KMT, p. 345: 3. Particles do not interact, except during collisions. Fig. 10.16, p. 365 Particles in reality attract each other due to dispersion (London) forces. They grab at or tug on each other and soften the impact of collisions. So a real gas actually has a smaller pressure than an ideal gas. 2 Preal = Pideal - n a n = number (in moles) 2 V real of particles 2 Pideal = Preal + n a a = van der Waals 2 V real constant a (Table 10.5) 2 2 (Preal + n a/V real) (Vreal - nb) = nRT Again, only matters for gases in a small volume and with a high pressure because gas molecules are crowded and bumping into each other. 2 CHEM 102 Winter 2011 Gas density and molar masses We can re-arrange the ideal gas law and use it to determine the density of a gas, based on the physical properties of the gas. -
The Perfect Gas
LANDMARK UNIVERSITY, OMU-ARAN LECTURE NOTE 2 COLLEGE: COLLEGE OF SCIENCE AND ENGINEERING DEPARTMENT: MECHANICAL ENGINEERING ALPHA 2016-17 ENGR. ALIYU, S.J. Course code: MCE 211 Course title: INTRODUCTION TO MECHANICAL ENGINEERING. Course Units: 2 UNITS. Course status: compulsory THE PERFECT GAS. The characteristic equation of state. At temperatures that are considerably in excess of the critical temperature of a fluid, and also at very low pressures, the vapour of the fluid tends to obey the equation; . No gases in practice obey this law rigidly, but many gases tend towards it. An imaginary ideal gas which obey the law is called a perfect gas, and the equation , pv/T = R, is called the characteristic of state of a perfect gas. The constant R, is called the gas constant. The unit of R are N m/kg K or kJ/kg K. Each perfect gas has a different gas constant. The characteristic equation is usually written; pv = RT……1 or for m kg. occupying V m3, pV = mRT ……………..2 Another form of the characteristic equation can be derived using the kilogram-mole as a unit. The kilogram-mole is defined as a quantity of gas equivalent to M kg. of the gas, where M is the molecular weight of the gas (e.g since the molecular weight of oxygen is 32, then 1 kg. mole of oxygen is equivalent 32 kg of oxygen). From the definition of kilogram-mole, for m kg of a gas we have, m = nM ………………3 (where n is the number of moles) Note: Since the standard of mass is the kg. -
Chapter 5 the Laws of Thermodynamics: Entropy, Free
Chapter 5 The laws of thermodynamics: entropy, free energy, information and complexity M.W. Collins1, J.A. Stasiek2 & J. Mikielewicz3 1School of Engineering and Design, Brunel University, Uxbridge, Middlesex, UK. 2Faculty of Mechanical Engineering, Gdansk University of Technology, Narutowicza, Gdansk, Poland. 3The Szewalski Institute of Fluid–Flow Machinery, Polish Academy of Sciences, Fiszera, Gdansk, Poland. Abstract The laws of thermodynamics have a universality of relevance; they encompass widely diverse fields of study that include biology. Moreover the concept of information-based entropy connects energy with complexity. The latter is of considerable current interest in science in general. In the companion chapter in Volume 1 of this series the laws of thermodynamics are introduced, and applied to parallel considerations of energy in engineering and biology. Here the second law and entropy are addressed more fully, focusing on the above issues. The thermodynamic property free energy/exergy is fully explained in the context of examples in science, engineering and biology. Free energy, expressing the amount of energy which is usefully available to an organism, is seen to be a key concept in biology. It appears throughout the chapter. A careful study is also made of the information-oriented ‘Shannon entropy’ concept. It is seen that Shannon information may be more correctly interpreted as ‘complexity’rather than ‘entropy’. We find that Darwinian evolution is now being viewed as part of a general thermodynamics-based cosmic process. The history of the universe since the Big Bang, the evolution of the biosphere in general and of biological species in particular are all subject to the operation of the second law of thermodynamics. -
Ideal Gas and Real Gases
2013.09.11. Ideal Gas and Real Gases Lectures in Physical Chemistry 1 Tamás Turányi Institute of Chemistry, ELTE State properties state property: determines the macroscopic state of a physical system state properties of single component gases: amount of matter, pressure, volume, temperature n, p, V, T amount of matter denoted by n name of the unit: mole (denoted by mol ) 23 1 mol matter contains NA = 6,022 ⋅ 10 particles, Avogadro constant pressure definition p = F/A, (force F acting perpendicularly on area A) SI unit pascal (denoted by: Pa): 1 Pa = 1 N m -2 1 bar= 10 5 Pa; 1 atm=760 Hgmm=760 torr=101325 Pa 1 2013.09.11. State properties 2 state properties of single component gases: n, p, V, T volume denoted by V, SI unit: m 3 volume of one mole matter Vm molar volume temperature characterizes the thermal state of a body many features of a matter depend on their thermal state: e.g. volume of a liquid, colour of a metal 3 Temperature scales 1: Fahrenheit Fahrenheit scale (1709): 0 F (-17,77 °C) the coldest temperature measured in the winter of 1709 Daniel Gabriel Fahrenheit 100 F (37,77 ° C) temperature measured in the (1686-1736) rectum of Fahrenheit’s cow physicists, instrument maker between these temperatures the scale is linear (measured by an alcohol thermometer) Problem: Fahrenheit personally had to make copies from his original thermometer lower and upper reference temperature arbitrary lower and upper reference temperature not reproducible an „original” thermometer was needed for making further copies 4 2 2013.09.11. -
University of London
UNIVERSITY COLLEGE LONDON J University of London EXAMINATION FOR INTERNAL STUDENTS For The Following Qualifications:- B.Sc. M.Sci. Physics 1B28: Thermal Physics COURSE CODE : PHYSIB28 UNIT VALUE : 0.50 DATE : 18-MAY-04 TIME : 10.00 TIME ALLOWED : 2 Hours 30 Minutes 04-C1074-3-140 © 2004 Universi~ College London TURN OVER Answer ALL SIX questions from Section A and THREE questions from Section B. The numbers in square brackets in the right-hand margin indicate the provisional allocations of maximum marks per sub-section of a question. The gas constant R = 8.31 J K -1 molq Boltzmann's constant k = 1.38 x I0 -23 J K -~ Avogadro's number NA = 6.02 x 10 23 mol q Acceleration due to gravity g = 9.81 m s -2 Freezing point of water 0°C = 273.15 K SECTION A [Part marks] 1. (a) Explain what is meant by an ideal gas in classical thermodynamics. [4] Under what physical conditions do the assumptions underlying the ideal gas model fail? (b) Write down the equation of state for an ideal gas and one for a real gas. [4] Explain the meaning of any symbols used. (a) Write down an expression for the average translational kinetic energy of a [2] mole of an ideal classical gas at temperature T. Explain how this expression is related to the principle of equipartition of energy. (b) Calculate the root-mean-square speed of oxygen molecules at T = 300°C. [2] The molar mass of oxygen is equal to 32 g-mo1-1. (c) Sketch the Maxwell-Boltzmann distribution of molecular speeds, and [2] indicate the positions of both the most probable and the root-mean-square speeds on the diagram.