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Advanced fluid mechanics (II)Course content:1.Compressible Fluid
Mechanics Textbook: Modern Compressible Flow, 2nd ed. , by John D
Anderson, Jr. Reference Book1. Gas Dynamics, 2nd ed., by James. E.
A. John2. Compressible Fluid Dynamics by Philip A. Thompson3.
Elements of Gasdynamics by H. W. Liepmann and A. Roshko4.
Compressible Fluid Flow. , 2nd ed. , by Michel A. SaadGrading: 1.
Homework 60% 2. Final Project 40%
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Chapter I1. Introduction and Review of ThermodynamicsWhat is
Compressible Flow?1. 2. Energy transformation and temperature
change are important considerations Importance of Thermodynamics
e.q Flow of standard sea level conditions, Specific internal
energy
Specific kinetic energy
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1.1 Definition of Compressible Flow Incompressible flow
compressibility effect can be ignored.
is the specific volume &
Compressibility of the fluid
Physical meaning: the fractional change in volume of the fluid
element per unit change in pressureChapter INote: dp(+) dv(-)
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. Isothermal compressibility ..isentropic compressibility (speed
of sound)Compressibility is a property of the fluidLiquids have
very low values of
e.g for water = at 1atm Gases have high e.g for air =10-5 m2/N
at 1 atm, Alternate form of
Chapter I
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Chapter IGeneral speakingMa >0.3 Compressible effect can not
be ignoredMa < 0.3 Incompressible flowFor most practical problem
compressible
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1.2. Regimes of compressible flow
Streamline deflected far upstream of the bodyFlow is forewarned
of the presence of the body
Subsonic flowChapter I
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Chapter ITransonic flow is less than 1 , but high enough to
produce a pocket of locally supersonic slow
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LooselyDefined as the Transonic regimeIf is increased to
slightly above 1 , the shock will move to the trailing edge of the
airfoil , and bow shock appears upstream of the leading
edge.(Highly unstable)
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Chapter I Supersonic FlowEverywhere Behind the shock+ Parallel
the free stream flow is not forewarned of presence of the body
until the shock is encountered+ Both flow of upstream of the shock
and downstream of the shock are supersonic+ Dramatic physical and
mathematical difference between subsonic and supersonic flows.(We
will mostly focus on this regimes)
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High enough to excite the internal modes of energy dissociate or
even ionize the gas.
Chapter IHypersonic FlowReal gas effect !!! Chemistry comes
in
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Chapter IIncompressible flow is a special case of subsonic flow
limiting case Trivial , no flowFor incompressibilityFlow can be
also be classified as ViscousinviscidViscous flow: + Dissipative
effects : Viscosity, thermal conduction, mass diffusion.+ Important
in regions of large gradients of V, T and Ci e.g. Boundary
layerFlows
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Chapter IInviscid flows: - ignore dissipative effects outside of
B.L
(We will treat this kind of flow )Also consider the gas to be
Continuum Mean free path
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R - specific gas constant 1.3 A Review of Thermodynamics 1.3.1
Ideal gas intermolecular force are negligible 8314
(J/kg.mole.k)Molecular weightsFor air at standard
conditionsBoltzmann constant =
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Isothermal compressibilityLdL > 10d , for most compressible
flows
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Chapter I-Translational-Rotational No of collisions > 5
equilibrium-Vibration : No of collisions > 0 (100 ) equilibrium
Add one more time scale or length scale-Electronic excitation +
nuclear1.3.2. Internal Energy and EnthalpyIf the particles of the
gas (called the system) are rattling about their state of maximum
disorder, the system of particle will be in equilibrium.Statistical
Thermodynamics +Quantum mechanics
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Let be specific internal energyLet be specific enthalpy
For both a real gas and a chemically reacting mixture of perfect
gases.
Thermally perfect gas
Chapter IReturn to macroscopic view continuum
- Chapter ICalorically perfect gasare const Will be assumed in
the discussion of this classRatio of specific heat , =1.4 for a
diatomic gas =5/3 for a monatoinic gas Air, T
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Consider caloriacally perfect gas + thermally perfect gas Note:
specific heat at constant pressure specific heat at constant
volume
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Chapter IIdeal gas Perfect gas
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Conservation of EnergyConsider a system, which is a fixed mass
of gas separated from the surroundings by a flexible boundary. For
the time being, assume the system is stationary, i.e., it has no
directed kinetic energy
e is state variable, de is an exact differential depends only on
the initial and final states of the system1.3.3. First law of the
thermodynamicsAn incremental amount of heat added to the system
across the boundary The work done on the system by the
surrondings
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Chapter IFor a given , there are in general an infinite
different ways (processes) of We will be primarily concerned with 3
types of processes:Adiabatic processReversible process no
dissipative phenomena occur, i.e,. Where the effects of viscosity,
thermal conductivity, and mass diffusion are absent (see any text
on thermodynamic)3. Isentropic process - both adiabatic &
reversible2nd law of thermodynamic
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A contribution from the irreversible dissipative phenomena of
viscosity thermal conductivity, and mass diffusion occurring within
the systemChapter I Define a new state variable, the entropy,
The actual heat added/T, These dissipative phenomena always
increase the entropyFor a reversible processIf the process is
adiabatic, 2nd lawIn summary, the concept of entropy in combination
with the 2nd law allow us to predict the direction that nature
takes.1.3.4 Entropy and the Second Law of Thermodynamic or
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Chapter IAssume the heat is reversible, 1st law becomes For a
thermally perfect gas, If the gas also obey the ideal gas equation
of stateIntegrate Note
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1.3.5. Isentropic realtionsFor an adiabatic process and for a
reversible process Hence, from eq ,i.e.,
the entropy is constant. Chapter IIf we further assume a
calorically perfect gas,
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Chapter I
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Outside B.L-Isentropic relations prevaile.g. T=1350KP=?T=2500
KP=15atmM=12, Cp=4157 J/kg.K
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Chapter I1.3.6. Aerodynamic forces on a BodyMain concerns : Lift
& dragForces on a body of airfoil-Surface forces: pressure
shear stress-Body forces : gravity ; electric-magneticSources of
aerodynamic force, resultant force and its resolution into lift and
drag
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Drag D is the component of parallelIn our plot. L// , D//Lift L
is the component of perpendicular to the relative wind Chapter ILet
be unit vectors perpendicular and parallel, respectively to the
element ds,inviscid
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Chapter IPressure drag -> wave drag, e.g slender supersonic
shapes with shock wavesSkin friction drag-We consider only inviscid
flows and both pressure and skin-friction drags are important-In
the most cases, we can not predict the drag accuratelyFor blunt
bodies, Dp dominatesFor streamlined bodies, Dskin dominateswith
shock wave, Dwave drag dominate and Dskin can be neglectedD can be
predicted reasonably
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