# Physical Mechanics

Eduard Son
Joint Institute for High Temperature RAS

## Description

Physical mechanics is based on the microstructure of matter, using the achievements of modern physics, physical chemistry, quantum chemistry and other sciences to describe the motion of the real media used in engineering practice. The term "physical mechanics" was introduced by one of the greatest engineers of our time, a PhD student of Prandtl, the father of China's space and nuclear programs, Qian Xue-sen. Physical mechanics in the modern sense is from one side the part of continuum mechanics, in which the properties of the medium can be changed under the influence of applied forces or energy impacts. On the other hand, the physical mechanics objects are not described by the continuum equations. These include, for example, low-density gas, plasma, rheology media, multi-phase flows consisting of droplets in a gas or bubbles in liquids, and the intermediate states with different gas content, dusty gas and plasma, foams, nano-sized objects. For description of objects in physical mechanics it is not enough equations of continuum mechanics, but kinetic description is necessary, i.e. use of the kinetic Boltzmann equation, or other classical kinetic equations, and in some cases quantum equations. The physical state of matter in physical mechanics can be liquid, gas, plasma, single-and multi-phase, the medium may consist of mixtures of different components, among which chemical reactions occur, it may be under the influence of various bulk and surface forces of the gravitational, electromagnetic and inertial forces nature. As an example, studied the physical mechanics, we consider the motion of the plasma in an electromagnetic field when the external magnetic field acts on the flow and the moving medium generates electric currents that create magnetic fields, resulting in a need of self-consistent solution of problems. Another example of the need of self-consistent solution of nonlinear problems, are the processes of combustion and detonation occurs when the shock wave compression of the gas temperature rises so much that dissociation and ionization of the gas occur, which lead to a change in medium compressibility, i.e. changing the medium reaction to the external influences. Another example of necessity self-consistent solution is the turbulent flow, which are studied in continuum mechanics of classical fluids and gas, and for media with chemical reactions in a conducting medium in electromagnetic fields, in the presence of electromagnetic radiation in nonequilibrium gases and plasma, takes additional methods of solution. The book is based on a course of lectures delivered at the Moscow Institute of Physics and Technology at the Department of Physical Mechanics, Faculty of Aerophysics and space research and is intended as a textbook for teaching the subject, and so the author sought to concisely as possible and clearly articulate key concepts and provisions. The course sets out the basic concepts of technical thermodynamics, classical continuum mechanics, mechanics of an deformed solid, fluid dynamics, gas dynamics and stability of the theory and the turbulence necessary to study the fundamentals and the subsequent examination of the physical mechanics. The proposed course is enough strict, ie does not require other textbooks to get the results cited. The manual is accompanied by qualitative explanations that take into account at the initial level of knowledge in mathematics - differential equations and mathematical physics. The course consists of theoretical lectures and seminars that address practical problems and laboratory training. Laboratory workshop represented a separate publication. Numerical simulation is now of instruments used not only for the construction of settlements, necessary for comparison with experiments, but also an effective method of design new complex technological objects. This course provides examples of numerical solutions of simple problems that are available by using software packages such as MAPLE, MATHCAD, MATHEMATICA, and the numerical simulation of near-real physical mechanics problems are presented by separate edition. In the textbook are used the experimental results and obtained by numerical simulation at the Department of Physical Mechanics, Faculty of Aerophysics and Space Research of the Moscow Institute of Physics and Technology.

395 pages,
© 2012

## Table des matières:

1. Measurement of Flame Temperature by the Spectral-Line Reversal Method

1.2. Some Information on Radiation

1.3. Emission and Absorption of Real Media

1.4. Optical Methods of Measuring the Temperature of Real Media

1.5. Description of the Laboratory Work

1.5.1. Assignment to carry out the experimental part of the work

1.5.2. Assignment to process experimental data

1.6. Technical Characteristics of the LOP-72 Optical Pyrometer. Construction of the Pyrometer. Order of Performing the Work

1.7. Gas Dynamic Parameters

1.8. Radiative Properties of Metals

2. Probe Methods of Plasma Research

2.1. Diagnostics of the Electric Parameters of Plasma

2.2. The Purpose of the Work

2.3. Current-Voltage Characteristic of a Single Probe

2.4. The Range of Validity of the Probe Methods

2.5. The Theory of a Single Electric Probe

2.6. The Theory of Double Electric Probe

2.7. Experimental Part of the Work

2.7.1. Assignment to carry out the laboratory work

2.7.2. Description of the setup

2.7.3. Carrying out measurements with the aid of a single probe

2.7.4. Carrying out measurements with the aid of a double probe

2.7.5. Processing of the data of the laboratory work

2.8. A Criterion of Space Charge Layer Formation at Great Negative Probe Potentials

2.9. Determination of the Plasma Potential from Measurements of the Floating Potential

2.10. Measurement of the Energy Distribution Function

2.11. The Theory of Electron Current in the Case of a Thick Space Layer

2.12. Determination of the Electron Temperature

3. Study of a Glow Discharge in Helium

3.2. Qualitative Description of a Glow Discharge

3.3. Assignment to Carry out Laboratory Work

3.3.1. Processing of data

3.3.2. Comparison between theory and experiment

3.4. Elementary Theory of the Cathode Part of the Glow Discharge

3.5. Positive Column of a Glow Discharge

3.6. Nonequilibrium State of a Weakly Ionized Plasma

4. Study of the Oscillations of a Fluid in a Channel

4.2. Experimental Technique

4.2.1. Experimental setup

4.2.2. Probe of the fluid level displacement

4.2.4. Determination of the spectral components of oscillations

4.3. Measurement Technique

4.5. Elements of the Theory of Oscillations and Waves in a Fluid

4.5.2. Linearization of equations

4.5.3. Natural oscillations of a liquid

5. Determination of the Reynolds Number in Transition to Turbulence in a Boundary Layer

5.2. Justification of the Experimental Technique

5.3. Description of the Experimental Setup

5.4. Guidelines for Carrying out the Work

5.5. Elements of the Boundary Layer Theory

5.6. Boundary Layer Thickness on a Flat Plate

5.7. Inferences of the Linear Theory of Hydrodynamic Stability for a Boundary Layer on a Flat Plate

6. Laminar Liquid Flow Over the Starting Length of a Plane Channel

6.2. The Procedure of Measuring Flow Velocity

6.3. Principle of Doppler Signal Processing by a 55α90 Counter

6.5. Operational Procedure for the Setup

6.6. Operating Controls of the 55α90 Block

6.7. Operational Procedure for a 55α90 Counter

6.9. Laminar Flow Development in a Plane Channel

7. Investigation of a Laminar Boundary Layer on a Plate by a Doppler Laser Velocimeter

7.1. Elements of the Theory of the Doppler Laser Method of Velocity Measuring

7.3. Elements of the Theory of a Boundary Layer on a Flat Plate

8. Methods of Generation and Registration of Shock Waves

8.1. The Purpose of the Work

8.2. Briefly on the Processes Occurring in Starting of Sock Tubes

8.3. Operation of a Shock Tube with the Cross Section Constant along the Length

8.4.1. General description

8.4.2. Pneumatic diagram of the setup

8.4.3. Methods of measuring the shock wave parameters and instrumentation

8.4.4. System of optical recording of a shock wave

8.4.6. High-speed photographic recorder

8.4.7. Lighting source and synchronization block

8.6. Calculation of the Shock Wave Intensity for a Shock Tube of Variable Cross Section

9. Study of the Characteristics of the Ballistic Installation

9.2. Ballistic Installation

9.3. Estimation of the Shell Velocity

9.5. Basic Relations for Unsteady Gas Flows

10. Investigation of the Supersonic Rarefied Gas Flow

10.2. Generation of the Rarefied Gas Flow

10.3. Investigation of the Rarefied Gas Flow Parameters by a Pitot Tube

10.4. Measuring Instruments and Experimental Technique

10.6. Elements of the Boundary-Layer Theory

10.7. Velocity and Temperature Jumps at a Wall in a Slip Gas Flow

11. Structure of a Shock Wave in a Low-Density Gas Flow Past a Cylinder

11.2. Application of a Free-Molecular Thermal Probe to Investigate the Flow Field Near a Cylinder Immersed in a Transverse Flow

11.3. Application of a Glow Discharge to Visualize the Flow Pattern

11.5. Structure of a Shock Wave

11.6. Shock Wave Withdrawal

12. Study of the Regimes of Gas Outflow from a Laval Nozzle

12.2. One-Dimensional Theory of the Supersonic Nozzle

12.3. Gas Outflow with Overexpansion

12.4. Gas Outflow with Underexpansion

12.6. Experimental Procedure

13. Determination of the Time of the Vibrational Relaxation of CO2

13.2. Determination of the Time of the VT Relaxation of the Deformation Mode of CO2

13.3. Description of the Setup

13.4. The Order of Performing the Work

13.5. Processing of Results

13.7. Vibrational Relaxation of Molecules (the Landau–Teller Theory)

13.8. Entropy Increment in the Process of Retardation and Vibrational Relaxation of a Flow

14. Atmospheric-Vacuum Supersonic Wind Tunnel

14.1. The Bernoulli–St. Venant Equation

14.2. Measurement of the Reduced Flow Velocity or of the M Number

14.3. Principles of Calculation of the Atmospheric-Vacuum Supersonic Wind Tunnel

14.4. Arrangement of the ST-4 Wind Tunnel

14.5. The Order of the Start-up and Shut-down of the Wind Tunnel

14.6. Study of Flow in the Laval Nozzle

14.6.1. Static pressure along the nozzle length

14.6.2. Nonuniformity of the profiles of gasdynamic quantities at the nozzle cut

14.7. Study of Some Characteristics of the Wind Tunnel

14.7.1. Flow field in the working chamber

14.7.2. Compression degree and time of wind tunnel operation

14.8.1. Operational procedure

14.8.2. Students’ report structure

15. Supersonic Flow Past a Plate

15.1. Supersonic Flow past a Plate

15.3. Elements of Gas Dynamics

15.3.2. The Prandtl–Mayer flow

16. Measurement of Averaged And Pulsation Characteristics of a Turbulent Flow by a Constant Temperature Anemometer

16.2. Brief Information on Turbulent Motion

16.3. Thermoanemometric Method

16.4. Measurement of Average and Pulsation Velocities in a Flow

16.6. Description of the Laboratory Setup

16.7. Order of the Fulfillment of the Work

16.8. Representation of Results

17. Investigation of a Free Turbulent Jet

17.2. Some Information on Turbulent Flows

17.3. Scheme and Basic Laws Governing the Development of a Free Turbulent Jet

17.4. Description of the Laboratory Setup and of the System of Measurements

17.5. The Order of the Fulfillment of the Work

17.6. Processing of the Results of Experiments and Drawing up of the Laboratory Work

18. Generation of a Low-Temperature Plasma by Electric-Arc Plasmatrons

18.2. General Information on Arc Discharges and Plasmatrons

18.3. Construction of the DCP-2 Plasmatron

18.4. Methods of Measuring the Plasmatron Characteristics

18.4.1. Measurement of the arc current and voltage

18.4.2. Measurement of the working substance flow rate

18.4.3. Measurement of the cooling liquid flow rate

18.4.4. Measurement of the heating of water

18.4.5. Measurement of pressure in the working chamber

18.4.6. Measurement of heat flows

18.4.7. Measurement of the plasmatron characteristics

18.5. Instructions for Carrying out the Work and Assignment

18.5.1. Order of the fulfillment of the work

18.5.2. Program of the experimental part of the laboratory work

18.6. The Thermophysical Properties of Helium

19. Interaction of Concentrated Electron Beams with a Solid Body

19.2. Production of Electron Beams

19.3. Experimental Setup and Procedures

19.4. Subject-Matter of the Work

19.6. Interaction of Electron Beams with a Substance

19.6.1. Elastic collisions

19.6.2. Inelastic collisions

19.6.3. Thermal effect of electrons on solid bodies

19.7. Calculation of Electron Beam Trajectories

19.8. Calculation of the Concentration of Secondary Electrons in a Residual Gas

19.9. Neutralization of the Electron Beam Space Charge

19.10. Electron Beam Scattering

19.11. Inelastic Energy Losses by Electrons and Electron Beam Stopping Range

20. Hydrodynamic Stability of the Rotational Couette Flow

20.2. Brief Information on the Cylindrical Couette Flow

20.5. The Order of the Fulfillment of the Work

20.6. Processing of Results

20.8. Stationary Distribution of Velocities in the Couette Flow

20.9. Stability of Motion of an Inviscid Fluid

20.10. Stability of Motion of a Viscous Fluid

20.11. Stability of the Couette Flow for a Narrow Gap

20.12. The stability of the Couette Flow for a Gap of Finite Thickness

21. Measurement of the Temperature of Heavy Particles in a Gas Discharge by the Radiation Spectrum of the Second Positive System of N2

21.1. The Aim of the Work

21.2. Temperature and Temperature-Measurement Methods

21.2.1.Temperature measurement by contact methods

21.2.2. Optical methods of the measurement of temperature

21.2.3. Spectral methods of the measurement of temperature

21.3.1. Means of creation and sustainment of a glow discharge

21.4. Processing of Experimental Data

21.6. Determination of Gas Temperature from the Radiation Intensity Distribution in the Electronic-Vibrational-Rotational Bands of Molecular Transitions

21.6.1. Introduction to the theory of molecular spectra

21.6.2. Designations of the electronic terms of diatomic molecules

21.6.3. Measurement of the rotational temperature from the relative intensity of the rotational structure of the electronic-vibrational spectrum

21.6.4. Relationship between rotational and translational temperatures

21.6.5. Structure and principal characteristics of a glow discharge

22. Propagation of Sound Waves in a Microbubble Medium

22.2. Experimental Procedure

22.2.1. Experimental setup

22.2.2. A set of devices for measuring the speed of sound in a heterogeneous medium

22.2.3. A set of devices for creating a micorbubble medium

22.2.4. Technical characteristics

22.2.5. Determination of the speed of sound and of volumetric gas content

22.3. Measurement Procedure

22.5. Elements of the Theory of Propagation of Sonic Waves in a Heterogeneous Medium