空气动力学英文PPT(Chapter7)

ds =
δqrev
T
where s is the entropy of the system, δqrev is an incremental amount of heat added reversibly to the system, and T is the system temperature.
3. Isentropic process: this process is both adiabatic and
reversible
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For a reversible process, δw = − pdv , where dv is an incremental change in the volume due to a displacement of the boundary; thus Eq. (7.11) becomes
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7.2 A BRIEF REVIEW OF THERMODYNAMICS
7.2.1 PERFECT GAS A gas is a collection of particles that are in more or less random motion. If these particles are far enough apart, the influence of intermolecular forces can be neglected; this gas is defined as a perfect gas for which p, ρ and T are related through the equation of state:
e = cvT
h = c pT
In this case, the gas is called calorically perfect gas. calorically perfect gas : 量热完全气体 Some explanation for the thermodynamic state variables, and specially for specific heats
or
cv R 1− = cp cp
Define γ ≡ c p cv . For air at standard conditions,
γ = 1.4 . Then we get particularly useful equations:
R 1− = γ cp
1
or
γR cp = γ −1
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δq − pdv = de
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7.2.4 ENTROPY AND THE SECOND LAW OF THERMODYNAMICS Reason for introducing the entropy ???? Let us define a new state variable, the entropy, as follows:
P : pressure
ρ : density
T : temperature e : internal energy
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For a specific gas, we have the following equations:
c p − cv = R
δq + δw = de
This is the first law of thermodynamics.
பைடு நூலகம்
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Hence de is an exact differential, its value depend only on the initial and final states of the system, e is a state variable. In contrast, δq and δw depend on the process in going from the initial to the final states. We consider 3 types of processes:
Similarly, dividing the above equation by
cv
R cv = γ −1
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7.2.3 FIRST LAW OF THERMODYNAMICS Consider a fixed mass of gas called system. The region outside the system is called surroundings, the interface is called boundary.
pv = RT
where mass);
v
is the specific volume (volume per unit
v =1 ρ
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7.2.2 INTERNAL ENERGY AND ENTHALPY
Consider a molecule:
•its velocity and its rotational motion create kinetic energy •its vibration creates vibrational energy •the motion of electrons around the nuclei creates electronic energy
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7.1 Introduction
Giving the main differences between the incompressible and compressible flows with respect to aerodynamic properties . What flow properties should be introduced for the analysis of compressible flow problems. This chapter relates interesting, historical events dating back to the birth of modern aerodynamics; I advice all students to read this chapter carefully.
Chapter 7
Inviscid, Compressible Flow
With the realization of airplane and missile speeds equal to or even surpassing the many times the speed of sound, thermodynamics has entered the scene and will never again leave our consideration.
1. Adiabatic process: no heat is added or taken away
from the system.
2. Reversible process: no dissipative phenomena occur;
effects of viscosity, thermal conductivity, and mass diffusion are absent.
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The energy of a given molecule is the sum of these energies.
Consider a finite volume of gas consisting of a large number of molecules. The sum of the energies of all the molecules in this volume is defined as the internal energy of the gas. Per unit of mass, it is denoted as e . A related quantity is the specific enthalpy, denoted by h and defined as:
p = ρRT
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where R is the specific gas constant ; for air at standard conditions, R = 287 J/(kg.K). This formula can also be written as:
h
,
dh = c p dT
and c p are the specific heats at constant volume and constant pressure, respectively
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For a perfect gas where these specific heats are constants , the above formula become:
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e and h are thermodynamic state variables,
they depend only on the state of the gas and are independent of any process. Now, we have the thermodynamic variables as follows:
h = e + pv
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For a perfect gas, both temperature only:
e
and
h
are functions of
e = e(T )
de = cv dT