文件名称:
Computer Program for combustion
开发工具:
文件大小: 2mb
下载次数: 0
上传时间: 2019-07-20
详细说明：航空发动机燃烧室计算，这里面包含了如何具体的计算燃烧室里的各种污染物排放，在详细计算航空发动机污染物排放的时候，需要对发动机燃烧室建模，建立燃烧室火焰模型，以及燃油雾化模型，并且在具体的计算中还涉及到燃烧室化学平衡，需要计算化学平衡过程中各种污染物的摩尔分数，需要对燃油雾化过程进行建模，并且建立燃烧液滴模型，换需要考虑回流的影响，这篇文章中主要讲了具体实现的原理和方法。Preface
This report presents the latest in a number of versions of chemical
quilibrium and applications programs developed at the NASa Lewis research
Center over more than 40 years. These programs have changed over the years to
include additional features and improved calculation techniques and to take
advantage of constantly improving computer capabilities. The minimization-of
free-energy approach to chemical equilibrium calculations has been used in all
versions of the program since 1967
The two principal purposes of this report are presented in two parts. The
first purpose, which is accomplished here in part L, is to present in detail a
number of topics of general interest in complex equilibrium calculations. These
topics include mathematical analyses and techniques for obtaining chemical
equilibrium; formulas for obtaining thermodynamic and transport mixture
properties and thermodynamic derivatives; criteria for inclusion of condensed
phases; calculations at a triple point; inclusion of ionized species, and various
applications, such as constant-pressure or constant-volume combustion, rocket
performance based on either a finite-or infinite-chamber-area model, shock wave
calculations, and Chapman Jouguet detonations
The second purpose of this report, to facilitate the use of the computer
code, is accomplished in part II, entitledUsers Manual and Program
Description. Various aspects of the computer code are discussed, and a number
of examples are given to illustrate its versatility
X PAGE PLANK NOT FNMED
PAGE二帐 TENTIONAL:!"
k;”x着
Contents
1. Introduction,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
e1
2. Equations Describing Chemical equilibrium
2.1 Units
2.2 Equation of State .,,,..
2.3 Minimization of Gibbs Energy
即■p■
2.3. 1 Gibbs Iteration equations
2.3.2 Reduced Gibbs Iteration Equations
2.4 Minimization of Helmholtz Energy ........... 8
2.4.1 Helmholtz Iteration equations
2.5 Thermodynamic Derivatives From Matrix Solution
2.4.2 Reduced helmholtz Iteration equations
....10
2.5.1 Derivatives With respect to Temperature
10
2.5.2 Derivatives with respect to Pressure
2.6 Other Thermodynamic derivatives
12
3. Procedure for Obtaining Equilibrium Compositions
13
3.1 Initial estimates
13
3.2 Magnitude of Species Used During Iteration
13
3.3 Convergence
昏■■■章■
,,,,,,,14
3. 4 Tests for Condensed Phases
15
3.5 Phase Transitions and Special derivatives
.16
3.6 Singularities
3.7 Iteration Procedure and Tests for ions
17
4, Thermodynamic Data
.,,,19
4. 1 Assigned Enthalpies
4.2 Least-Squares coefficients
19
5. Thermal Transport Property Data
21
5. 1 Data for Individual Species
21
5.2 Mixture Property Data
21
5.2.1 Viscosity and Frozen Thermal Conductivity ..... 21
5.2.2 Reaction Thermal Conductivity
22
5.2.3 Specific Heat for Gases OnI
23
5.2.4 Prandtl number
6. Theoretical rocket Performance
曾甲··圈【■■■●b鲁·鲁鲁●
25
6. 1 Assumptions
25
PRIOMDi\s PAG五 ANK NOT FILMED
PAGE
iNTENTIONALLY BLANK
6.2 Parameters
鲁·,●4
26
6.2.1 Conservation Equations
26
6.2.2 Velocity of Flow
6.2. 3 Force
6. 2. 4 Specific Impuls
26
6.2.5 Mach Number
6.2.6 Characteristic Velocity
27
6
2.7 Area per Unit Mass Flow Rate
.27
6.2.8 Coefficient of Thrust
,,,,,,27
6.2.9 Area ratio
6.3 Procedure for Obtaining Equilibrium Rocket Performance
for IAc model
6.3. 1 Combustion Conditions
。自
28
6.3.2 Exit Conditions
28
6.3. 3 Throat Conditions
28
6.3.4 Discontinuities at Throat
28
6.3.5 Assigned Subsonic or Supersonic Area Ratios ..... 29
6.3.6 Empirical Formulas for Initial Estimates of PinP
29
6.3.7 Analytic Expression for Improved Estimates
29
6. 4 Procedure for Obtaining Equilibrium Rocket Performance
for fac model
30
6.4.1 Initial Estimates for Pf and aJa
30
642 Improved Estimates for Pinf and A!A∵………31
6.5 Procedure for Obtaining Frozen Rocket Performance
31
6.5.1 Exit conditions,.,,,,,,,,,,,,,,,,,,,,,.31
6.5.2 Throat Conditio
6.5.3 Thermodynamic Derivatives for Frozen Composition
7. Incident and reflected shocks
3
7.1 Incident Shocks
7. 1.1 Iteration Equations
34
7. 1.2 Corrections and convergence
35
7.1.3 Initial Estimates of T2/T1 and P2Pl
1 and
35
7.2 Reflected Shocks
36
7.2.1 Iteration Equations .,,..,,,.....
36
7.2.2 Corrections and Convergence
37
7. 2.3 Initial Estimates of Ts/T2 and Ps/p2
37
8. Chapman-Jouguet Detonations..…………………3
8. 1 Iteration equations
8.2 Corrections and Convergence
40
8.3 Initial Estimates of T2/Ti and P2/PI
40
9
Input Calculations
Appendix- Symbols
Reference
Chapter 1
Introduction
Knowing the chemical equilibrium compositions of
(a) Temperature and pressure, tp
a chemical system permits one to calculate theoretical
(b)Enthalpy and pressure, hp
thermodynamic properties for the system. These proper
(c) Entropy and pressure, sp
ties can be applied to a wide variety of problems in
(d) Temperature and volume(or density),tv
chemistry and chemical engineering. Some applications
(e) Internal energy and volume(or density),uv
are the design and analysis of equipment such as
f) Entropy and volume (or density),sY
compressors, turbines, nozzles, engines, shock tubes, heat
2)Calculating theoretical rocket performance for
exchangers, and chemical processing equipment
a finite- or infinite-area combustion chamber
For more than 40 ycars the NaSa Lewis research
(3)Calculating Chapman-Jouguet detonations
Center has been involved in developing methods and
(4) Calculating shock tube parameters for both inci-
computer programs for calculating complex chemical dent and reflected shocks
equilibrium compositions and thermodynamic properties
of the equilibrium mixtures and in applying these Some problems handled by the program use just one
properties to a number of problems(Gordon et al., 1959, combination of assigned states--namely the tp, hp, sp
1962, 1963, 1970, 1976, 1984, 1988; Huff et al., 1951; tv, uv, and sv problems. For example, the tp problem,
Svehla and McBride, 1973 and Zeleznik and Gordon, which consists of a schedule of one or more assigned
1960,1962a, b, 1968) Earlier versions of the chemical temperatures and pressures, might be used to construct
equilibrium computer program(Zeleznik and Gordon, Mollier diagrams. The hp problem gives constant
1962a; and Gordon and McBride, 1976 have had wide
pressure combustion properties and the uv problem gives
acceptance. Since the last publication this program has constant-volume combustion properties. Other problems
been under continuous revision and updating, including make use of more than one combination of assigned
several substantial additions. One addition is an option thermodynamic states. For example, the shock and
for obtaining the transport properties of complex detonation problems use hp and tp; the rocket problem
mixtures(Gordon et al 1984)by methods simpler than uses hp or tp and also sp
those of Svehla and McBride(1973). A second addition
This report consists of two parts. Part I, containing
is an option to calculate rocket performance for a rocket the analysis, includes
motor with a finite-area combustor (Gordon and
McBride, 1988). The present report documents these and
(1)The equations describing chemical equilibriun
other additions and revisions to the program since 1976. and the applications previously mentioned (i.e, rocket
The revised program is called CEA (Chemical performance, shocks, and Chapman-Jouguet detonations
Equilibrium and Applications
2)The reduction of these equations to forms
pro. The program can now do the following kinds of suitable for mathematical solution by means of iterative
es.
procedures
() Equations for obtaining thermodynamic and
(1)Obtaining chemical equilibrium compositions transport properties of mixtures
for assigned thermodynamic states These states may be
specified by assigning two thermodynamic state func- Part II, a program description and users manual,
tions as follows
discusses the modular form of the program and briefly
describes each subroutine. It also discusses the prepara- Svehla (1962), and Zeleznik and gordon (1961). In
tion of input, various permitted options, output tables, addition to data calculated by us, other thermodynamic
and error messages. A number of examples are also data included in our files are taken from sources such as
given to illustrate the versatility of the program
Chase et al.(1985), Garvin et al .(1987), Gurvich et al
In addition to the work in chemical equilibrium ( 1989), and Marsh et al.(1988). Files distributed with
calculations and applications over the past 40 years, the computer program are described in part ll
progress in computer programs, data generation, and data
Various versions of the equilibrium program or
fitting has also been made at NASA Lewis for the ther- modifications of the program have been incorporated
modynamic and thermal transport properties of indi- into a number of other computer codes. An example
vidual species required for the equilibrium calculations. is Radhakrishnan and Bittker (1994) for kinetics cal
Some examples of this effort are Burcat et al.(1985), culations
McBride et al..(196l,1963,1967,1992,1993ab),
2
Chapter 2
Equations Describing Chemical Equilibrium
Chemical equilibrium is usually described by either
of two equivalent formulations--equilibrium constants or
Symbol
minimization of free energy. Reports by Zeleznik and
quantity
Gordon(1960, 1968)compare the two formulations
ength
meter
Zeleznik and Gordon(1960)shows that, if a generalized
method of solution is used, the two formulations reduce
Mass
kilogram
to the same number of iteration equations. However,
Time
with the minimization-of-free-energy method each
species can be treated independently without specifying
Tet
kelvin
K
a set of reactions a priori, as is required with equilibrium
Force
newton
constants. Therefore the minimization-of-free-energy
Pressure
formulation is used in the CEA program
newton per
Nm
square meter
The condition for equilibrium can be stated in terms
of any of several thermodynamic functions, such as the
Work, energy
」ou
minimization of Gibbs or Helmholtz energy or the
maximization of entropy. If one wishes to use tempera
ture and pressure to characterize a thermodynamic state,
he numerical values of a number of fundament
contants are taken from Cohen and Taylor(1987).For
Gibbs energy is most easily minimized inasmuch as
temperature and pressure are its natural variables
example, the value of the gas constant R taken from this
Similarly, Helmholtz energy is most easily minimized if reference is 8314.51 J/(kg-mole)(K). In those sections
dealing with the computer program, other units are used
the thermodynamic state is characterized by temperature
in addition to or instead of si units
and volume(or density)
Zeleznik and Gordon(1960) presents equations
based on minimization of Gibbs energy. Some of thes
2.2 Equation of State
equations are repeated and expanded herein for
convenience. In addition, a set of equations based on
In this report we assume that all gases are ideal and
minimization of Helmholtz energy is also presented. that interactions among phases may be neglected. The
However, because only ideal gases and pure condensed equation of state for the mixture is
hases are being considered, the general notation of
Zeleznik and Gordon(1960)is not used
PV= NRT
(2.1a)
2.1 Units
The International System of Units(SI)used in this
nRT
(21b)
p
report Is
3
where p is pressure(in newtons per square meter),V
specific volume (in cubic meters per kilogram), n moles
per unit mass of mixture (in kilograms-mole per
MW=
kilogram), T temperature (in kelvin), and p density (in
kilograms per cubic meter). Symbols used in this report
are defined in the appendix. For a reacting chemical
system the number of moles n is generally not constant.
Equation (2. 1) is assumed to be correct even when
small amounts of condensed species (up to several
Molecular weight is given the symbol MW in equa
percent by weight) are present. In this event the
tion( 2.4a)to differentiate it from M. The two different
condensed species are assumed to occupy a negligible
definitions of molecular weight, M and mw, give differ
volume relative to the gaseous species. An example
ent results only in mixtures of products containing con-
given in part I of this report illustrates the validity of
densed as well as gaseous species. only M
is given in
this assumption. In the variables V, n, and p the volume
he output, but Mw may be obtained from m by means
and mole number refer to gases only, but the mass is for of
the entire mixture including condensed species. The
wordmixture"is used in this report to refer to mixtures
MW=M I
of reaction products as distinguished from mixtures of
2引
24b)
reactants, which are referred to as"total reactants
On the basis of this definition, n can be written as where x; is the mole fraction of species j relative to all
species in the mixture. Some additional discussion of the
G
differences in these molecular weights is given in part II
(22)
f this report
where n; is the number of kilogram-moles of species j 2.3 Minimization of Gibbs Energy
per kilogram of mixture and the index Ng refers to the
number of gases in the mixture. The molecular weight of
the mixture M is defined as
For a mixture of NS species the Gibbs energy per
kilogram of mixture g is given by
1
∑
(2
or equivalently as
where the chemical potential per kilogram-mole of
species i is defined to be
NS
∑
M
(23b)
NG
an
(2.6)
∑
TP
The condition for chemical equilibrium is the minimiza-
tion of free energy. This minimization is usually subject
where M, is the molecular weight of species j and the to certain constraints, such as the following mass-balance
index NS refers to the number of species in the mixture. constraints
In the CEa computer program, among the NS species
gases are indexed from I to NG and condensed species
from ng+I to Ns
NS
More conventionally, molecular weight is defined
∑q
0(i=1,,0(2.7a)
(系统自动生成,下载前可以参看下载内容)
下载文件列表
相关说明
- 本站资源为会员上传分享交流与学习,如有侵犯您的权益,请联系我们删除.
- 本站是交换下载平台，提供交流渠道，下载内容来自于网络，除下载问题外，其它问题请自行百度。
- 本站已设置防盗链，请勿用迅雷、QQ旋风等多线程下载软件下载资源，下载后用WinRAR最新版进行解压.
- 如果您发现内容无法下载，请稍后再次尝试；或者到消费记录里找到下载记录反馈给我们.
- 下载后发现下载的内容跟说明不相乎，请到消费记录里找到下载记录反馈给我们，经确认后退回积分.
- 如下载前有疑问，可以通过点击"提供者"的名字，查看对方的联系方式，联系对方咨询.
