unclassified ad 269 927 · 2018-11-08 · ethylene c^l^ and methane ch^ are the two fuels...
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UNCLASSIFIED
AD 269 927 Repsiaduced
ARMED SERVICES TECHNICAL INFORMAnON AGENCY ARLINGTON HALL STATIC ARLINGTON 12, VIRGINIA
UNCLASSIFIED
NOTICE: When government or other drawings, speci- fications or other data are used for any purpose other than In connection with a definitely related government procurement operation, the U. S. Government thereby Incurs no responsibility, nor any obligation whatsoever; and the fact that the Govern- ment may have formulated, furnished, or In any way supplied the said drawings, specifications, or other data is not to be regarded by implication or other- wise as in any manner licensing the holder or any other person or corporation, or conveying any rights or permission to manufacture, use or sell any patented invention that may in any way be related thereto.
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NASA TN D-914
MÄ^A XEROX
TECHNICAL NOTE
D-914
CALCULATION PROCEDURE FOR THERMODYNAMIC,
TRANSPORT, AND FLOW PROPERTIES OF THE COMBUSTION PRODUCTS
OF A HYDROCARBON FUEL MIXTURE BURNED IN AIR WITH RESULTS
FOR ETHYLENE-AIR AND METHANE-AIR MIXTURES
By E. W. Leyhe and R. R. Howell
Langley Research Center Langley Air Force Base, Va.
•JJ» w-*m, A S T r A EC" ^
JAN 1 9 t9S2
• '08
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION
WASHINGTON January 1962
1R
1 NATIONAL AERONAUTICS AMD SPACE ADMINISTRATION
L 1 5 9 6
TECHNICAL NOOE D-9lk
CALCULATION PROCEDURE FOR THERMODYNAMIC,
TRANSPORT, AND FLOW PROPERTIES OF THE COMBUSTION PRODUCTS
OF A HYDROCARBON FUEL MIXTURE BURNED Hi AIR WITH RESULTS
FOR ETHYLENE-AIR AND METHANE-AIR MIXTURES
By E. W. Leyhe and R. R. Howell
SUMMARY
A procedure is presented whereby the composition, thermodynamic properties, and transport properties of the dissociated combustion products of a fuel consisting of a mixed hydrocarbon compound burned in air may be calculated. Equations and procedures for determining super- sonic nozzle ordinates and flov properties for the dissociated combus- tion products are presented in an appendix. Results are presented for the respective hydrocarbon fuels, methane and ethylene, at the equiva- lence ratios of 1.0, 0.9, 0.8, and 0.7 for pressures varying between 10-^ and 8 X 102 atmospheres and temperatures from 200° K to 3,000° K.
INTRODUCTION
The determination of the equilibrium composition and the corre- sponding thermodynamic, transport, and flow properties for a gaseous chemical reaction is necessary for certain problems in thermodynamics. Typical examples of such problems are (l) the expansion of combustion gases through a nozzle to obtain thrust as in the case of turbojet and ram-jet engines and (2) the utilization of combustion gases as the test medium in a wind tunnel for simulating combined heating and loading such as that obtained in hypersonic flight. In the latter case, the combus- tion generally takes place under very high pressure in order to achieve the desired velocity for simulation. Consequently, it is desirable to know the properties of such gases over ranges of pressures much greater than those for which information is presently available. (See refs. 1 and 2.)
In the present paper, procedures whereby computations of the com- position, thermodynamic, transport, and flow properties for the products of combustion of two hydrocarbon fuels burning in air are presented.
Ethylene C^l^ and methane CH^ are the two fuels considered. The
properties of the combustion products are defined for a range of pres-
sures hetween 10"^ and 8 X 10^ atmospheres and for a range of tempera- tures "between 200° K and 5*000° K. The properties have been computed for fuel-air equivalence ratios of 1.0, 0,9, 0.8, and 0.7- For these com- putations it is assumed that the combustion takes place at constant pressure, that the combustion efficiency is 100 percent, and that the gas is in chemical equilibrium.
SYMBOLS
A cross-sectional area, sq ft
a sonic velocity, ft/sec
BT proportion by volume of Cn H- in total fuel 1 1
B2 proportion by volume of Cn H_ in total fuel
B, proportion by volume of Cn Hgj in total fuel
Bj^ proportion by volume of H2O possibly mixed In fuel
Cjjl^ hydrocarbon fuel containing n atoms of carbon to m atoms of hydrogen
Cp specific heat at constant pressure, Btu/lb-0!*
D]^ ratio by volume of N2 to O2 in air
©2 ratio by volume of Ar to O2 in air
D» ratio by volume of CO2 to O2 in air
Di^ ratio by volume of H2O to ©2 in air
E moles of O2 available for combustion
E^ excess of moles of O2 above that needed for stoichiometrlc case
P ratio by volume of fuel to air
f ratio ty velght of fuel to air
gravitational conversion factor, 52.171+ lb"mass £t lb-force sec2
H total enthalpy, sensible plus chemical, Btu/lb
h sensible enthalpy, Btu/lb
J mechanical equivalent of heat
K thermal conductivity, Btu/ft-sec-4^
Ki to Kj chemical equilibrium constants based on partial pressures
k Boltzmann's constant (gas constant for one molecule)
1^,1^,1^,1^ defined by equations (k), (5), (6), and (7), respectively
M molecular weight, lb/lb-mole
m^,m2,m« number of atoms of hydrogen in fuels Cn ^ , Cn H_ , and cn,Hm,> respectively
5 5
Nj^ Mach number
Npr Prandtl niimber
n n\imber of moles
n^,nj n\mber of moles of specie
nl'n2'n3 number of atoms of carbon in fuels Cn 1^ , ^«^BL , and
CnjHmy respectively
Pi'Pj
Q
q
pressure, atm
partial pressure, atm
heat of formation, Btu/lb
dynamic pressure, atm
.-, . : .-. ■ ■ ■■ ■ : :, ■ ■ . ■
P \inlversal gas constant, 1.98588 Btu/lb-mol-PR
^eq equivalence ratio, equals f/fs and F/Fs
Rsp specific gas constant, Btu/lb-0!*
r radius from cone vertex, ft
s entropy, Btu/lb-0^
T temperature, ^ or ^ as required
V velocity, ft/sec
W total weight of gas, lb
X mole fraction
x distance along center line measured from nozzle throat, ft
y cross-sectional radius of nozzle measured from center line, ft
ß
/a log M\ " Vö log TJp
m /a log M\ \ä log p/T
7 isentropic exponent
^,6^ numerical step procedvire constants
e Lennard-Jones force constant
e^ arbitrary criterion of accuracy for L1/L2
€2 arbitrary criterion of accuracy for p
9 flow angle, deg
|a viscosity, slugs/ft-sec
H- viscosity of ith specie
p density, slugs/ft5
...
a collision diameter of molecule, angstroms
0 defined by equation (4})
if stream function
ü collision integral (called f^2»2^ in ref. 15
Subscripts:
c calculated value
F flame temperature
i post-combustion specie
j precombustion specie
L lower limit
h,k,m,n numerical indices in block diagram
1 post-combustion specie, dummy index
o reference temperature, 0° K
p constant pressure
r reference temperature, 500° K
S stoichiometric
s constant entropy
T constant temperature
t stagnation or total
U upper limit
w wall condition
Superscript:
* throat
For convenience, parentheses will be used when referring to specific species. For example, p. for partial pressure of CO is
«L
written p(CO), r^ for number of moles of CO2, n(C02), ^ for viscosity of H2O, n^HgO).
FROCEIXJRE
The procedure for the computation of the gas properties of the com- "bustion product la sufficiently general to include any combination of three hydrocarbon fuels together with an equivalence ratio Req which is less than or equal to one. The term "stoichiometric" refers to the condition of R^n ss 1 •
In order to determine the gas properties of the combustion product, real gas effects, which may be considerable at the extreme conditions of high pressures and low temperatures, are omitted and the product gas is considered to be a calorically perfect gas with variable molecular weight. The equations employed for the calculations make use of the following assumptions: (l) the ideal gas equation of state is valid; (2) the prop- erties of the species are functions of the temperature only; (3) the process is adiabatic; {k) the precombustion and post-combustion pressures are equal; (5) the gas is in chemical equilibrium; and (6) there is no phase change.
The development of the gas properties is divided into three sec- tions: the composition, the thermodynamlc properties, and the transport properties. The units are listed with the symbols and consistency is maintained by including conversion factors where necessary. The one excep- tion is temperature for which T denotes both Kelvin and Ranklne tempera- tures. Kelvin temperatures are used in the text; whereas both Kelvin and Ranklne temperatures are used on the figures.
L 1 5 9 6
Gas Composition
The composition of the combustion product gas is obtained by using the equation for chemical reaction along with the equations expressing the chemical equilibrium constants. The equation for chemical reaction requires that the mass of each element in the initial constituents be equal to the mass of each element in the final constituents. As the mass of each element in the reaction is independent of dissociation, the mass of each element present can be obtained from the equation for chemical reaction in which there is no dissociation of the constituents. The final constituents are then allowed to dissociate and their relative proportions by volume are obtained from the equations expressing the chemical equilibrium constants.
In the chemical equation for combustion as used here, the initial constituents are the fuel and oxidlzer. The fuel is assumed to consist
of an arbitrary mixture of three hyärocarbon fuels with possible vater vapor present while the oxidizer, air, is assumed to consist of oxygen, nitrogen, argon, carbon dioxide, and water vapor. The choice of an equivalence ratio indicates the proportion of fuel to oxidizer while the constituents of each are left arbitrary.
The chemical equation for the burning of the fuel mixture in air when there is no dissociation is
^(SJ^j) + ^fngHmg) * ^(S^j) + E(02) + D1E(N2) + *&(**)
+ D^(C02) + (Bi^ + Di+E)(H20)—»-(3^3^ + B2n2 + B^n^ + DjE^COg)
+ -(B^j^ + Bgmg + Bxmj) + B^ + D^E (HgO) + Ejl^Sg) + DgE (Ar) + E-^Og)
(1)
where
1 - R r~ —
= R ^ B^! + B2n2 + B5n3 + ^»j, + B2m2 + Bjmj) (2)
and
E = Bini + B2n2 + Bjnj + i(Bimi + Bgmg + Bjmjj + E^ (5)
The equations for conservation of mass for each element are obtained from equation (l). The masses are transformed into moles and the equa- tions are expressed as ratios of two particular elements in their standard molecular state.
*a - n(02) E + DjE + |(B^ + DI^E)
n(C) B-jn-L + B2n2 + B^nx + DxE (M
L2 = n(N2) _ D^E n(C) B1n1 + B2n2 + B^n* + DxE
(5)
8
n(H2) _ 1^^ + B2m2 * B3m3) •f B^ •'• D^E
n(C) ^lnl + ^2^2 + B5n5 + ^^ (6)
n(N2) Di
The constants L-^, Lg, L^, and L^ are therefore known quantities determined from the input values.
The constituents of the dissociated combustion product gas are next substituted into equations {h) to (7) in place of the input values and are now expressed in terms of partial pressures in order to utilize the equations for the chemical equilibrium constants. The definition of partial pressure leads to the relation:
L 1 5 9 6
p = Pi = Pj + Px n n^ ni + nZ
(8)
where
n n. (9)
and
P = 2_ Pi i
(10)
By restricting the constituents of the dissociated combustion prod- uct gas to the species Ng, O2, H2, CO2, J^O, CO, OH, NO, 0, H, N, and Ar, equations {h) to (7) can be rewritten as:
p(02) + p(C02) + I^HgO) + p(C0) + p(N0) + p(0H) + p(0)]
P(N2) + i(p(N0) + p(N)) (11)
9
L5 p(H20) + p(H2) + ||i>(OH) + p(H)]
T P(N2)
+ |IP(N0) + P(N11
P(N2) + |[p(NO) + p(NJ]
T = p(C02) + p(CO)
(12)
Dp p(Ar) Dl p(N2) + |[p(NO) + p(N)]
(15)
(110
Independent equations for the chemical equilihrium constants, which are functions of temperature, and their values were obtained from refer- ence 3- These equations are:
K = p(C0)p(H20) 1 = p^O^p^)
K2 = p(N0)p(H2)
p^^p^o)
K-, p2(H2)p(02)
P2(H20)
K,, = p(H2)p(0)
p(H20)
P(H) K5 = ^i7^ P1/2^
(15)
(16)
(17)
(18)
(19)
10
«6 = 4/2 (Hg)p(OH)
P(H20) (20)
K7 = pg(N)
P(N2) (21)
Equations (10) to (21) represent 12 unknowns in 12 equations. The •unknowns are the partial pressures of the 12 species previously listed. The 12 equations are nonlinear and must be solved hy a numerical step procedure. As a result, it was found to be more convenient to put equations (12) and (15) into the following form by substituting equa- tions (15) to (21) into equations (12) and (l5).
P^O) =
^3 L2 P(N2) + § fifP (N2) " P(%) " ^5 fi(*2)
1 + K6
m) L
3K
2 yp(N2) L2 2 p^H2)
(22)
L 1 5 9 6
p(C0) = ^ K1P( H- J {P(N2) + |[P(N0)
[p(H20) + KlP(H2)]
P(N)][ (25)
The equations are now solved as follows: For a particular reacting mixture select the temperature and pressure for the combus-cion products, and then assume values for p(N2) and p^I^). Solve the equations in
the following order:
(a) equation (22) for p(H30)
(b) equation (l6) for p(N0)
(c) equation (21) for p(N)
(d) equation (25) for p(C0)
(e) equation (15) for p(C02)
(f) equation (17) for p(02x.
(g) equation (l8) for p(0)
(h) equation (19) for p(H)
(i) equation (20) for p(0H)
(j) equation {lh) for p(Ar)
(k) equation (ll) for LWL2
(l) equation (10) for p
11
This procedure follows that of appendix B of reference k-, which is for specific fuel and air compositions.
As the calculated value of LWl^ ^S*
in general, different from
the known value, a new value of p(H2) is assumed and the equations are
recalculated. This procedure is continued until the desired accuracy is obtained. The calculated total pressure is also, in general, different from the desired total pressure, in vhich case a new p(N2) must he
assumed and the entire procedure retraced.
After a few trial calculations, it was noted that physically signif- icant partial pressures were obtained only when both the numerator and denominator of equation (22) were positive. Compatibility with this restriction is obtained by confining p(H2) within limits which are
established by setting both the numerator and denominator, respectively, equal to zero and by solving for pfHp) • These limits are
pte»^ - m 3 ^2
p(N2) + |^K7p(N2) (21+)
P(H2)L- <| ■T+ IT) *&*f&) (25)
In order to provide an ordered sequence for the selection of the assumed values of p(N2) and p(H2), a numerical step procedure was
devised. This procedure is shown in the block diagram in figure 1.
The number of moles of each specie is computed from the equation
n(C02) + n(CO)
111 = p(C02) + p(CO)Pi (26)
which is obtained from equation (8). This form was chosen because the sum of the numbers of moles of CO2 and CO is equal to the number of
moles of carbon entering into the reaction. Therefore, equation (26) can be rewritten in terms of known quantities. Thus,
12
B^n-L + B2n2 + Bxn» + DxE 111 = p(C02) + p(CO) Pi (2?)
In order to complete the Identification of the gas, the mole frac- tion and the molecular weight of the mixture are obtained from the equations
xl = nl/n
and
"\
(28)
Xi "I J
L 1
9 6
M = ^ X^ 1
(29)
The mole fractions of the species are shown in figures 2 sind 5 as functions of temperature for the combustion products of CgR^-a-lr and CHij.-air mixtures, respectively. Because of the preponderance of data, these figures were selected at the equivalence ratios of 1.0 and 0.8
for the pressures of 10-\ lO-2, and 10° atmospheres in order to Illus- trate the pressure effects on dissociation. Figures k and 5 show curves of molecular weight against temperature for lines of constant entropy, which is calculated in the section on thermodynamic properties, for the combustion products of C/jH^-air and CH^-air mixtures, respectively, both
presented for the equivalence ratios of 1.0, 0.9, 0.8, and 0.7.
Thermodynamic Properties
The thermodynamic properties of the product gas when dissociation is considered are calculated from the equations to follow. (See refs. 1, 5, 6, 7> and 8.) Data for the pure species were obtained from refer- ences 5> 1, 9, 10, and 11. (Note that conversion factors are included where necessary to maintain consistency in units.)
Enthalpy, entropy, and density, example, refs. 1 and 2):
Enthalpy is defined as (see, for
13
H -1 M (^ - hifT) + ^ (50)
where
and Q^ r, the heat of formation of the -pure specie, is referenced to
Tr = 500° K. Values of Qi r are presented in tahle I, along vith
references.
Entropy is defined as (see, for example, refs. 1 and 2):
= ]r Ä ( rT c . f^ + s R. ! . R_ lo^ x ) (51)
where Si r is the reference value of the specie entropy at Tr = 500° K
and p = 1 atmosphere. Values of s^ r are also presented in table I
with references.
The density may he expressed as
= 2116.8 pM = 1176 pM 1.8 gcJRT gcJBT
(52)
The three thermodynamlc properties, enthalpy, entropy, and density, have "been combined to form Mollier charts which are presented in fig- ures 6 and 7 for the combustion products of C^R^-alr and CHij.-air mixtures,
respectively, for the equivalence ratios of 1.0, 0.9, 0.8, and 0.7. These Mollier charts are plotted with enthalpy, in the form H - H0, as
the ordinate, pressure as the abscissa, and for lines of constant entropy, density and temperature.
Specific heat at constant pressure.- The equation for specific heat is obtained from equation (50) by taking the derivative of H with respect to T with p held constant. By rewriting Xi/M as ni/W where W is the weight of the gas
Ik
or
(i)P ■ ^ fe&l ^ - ^)+«^](li)3 <«>
cp - v ^"ir^P'1 + CT M" ir ipr) (3^)
The equations that express the specific heats of the species as func- tions of temperature are listed in table I, together with their references. Unfortunately, no values or equations for the specific heats of OH and NO had been found at the time of the programing. As a result, equations were written for these specific heats based on equations of similar compounds. Any Inaccuracies introduced by these equations are felt to be small as the percentages of these species in the product gas are very low. These equations are also listed in table I. (Since the programing, values of these specific heats have been found (ref. 12) and the values compare favorably with those used in this report.)
The specific heats for the combustion products of CjgH^-air and CHij.-alr mixtures are shown in figures 8 and 9> respectively, again for the equivalence ratios of 1.0, 0.9, 0.8, and 0.7- In these figures, the specific heat is plotted against temperature for lines of constant pressure.
Isentropic exponent.- The exponent (ref. 1) used to describe an isentropic change in state of a dissociating gas is no longer defined as the ratio of specific heats as for the case of an ideal gas. The defi- nition is taken from the sonic velocity equation:
L 1 5 9 6
y = E-fQ) - ß l0g V\ V\bpJB ~ Vö log P)B
By using the basic thermodynamlc relations (see ref. 6)
8cJcp
D2\ÖTL
and
UTI \äp/T
M P2gcJc
I
1176T
.Y
V^P/'T.
(35)
(36)
(37)
15
together with equation (52) and hy defining
_ /a log M\ " ^ log TL
and
\d log pyT
equation (55) may ^e rewritten as
(58)
(59)
7 = cp(l + ß) - g(l - a)
(^0)
The Isentroplc exponents for the combustion products of CgHl^-alr and CHl^-air mixtures for the equivalence ratios of 1.0, 0.9, 0.8, and 0.7 are shown in figures 10 and 11, respectively. In these figures, the isentroplc exponent is plotted against temperature for lines of constant entropy.
Specific gas constant.- The specific gas constant is defined as
vsp R M
(ia)
The specific gas constants were computed and tabulated but no figures were prepared as the values can be determined from the values of M given in the figures.
Flame temperature.- The flame temperature at a given pressure (ref. 7)* which is fixed for a given fuel and oxidizer, equivalence ratio, and initial temperature of the precombustion species, is defined as the temperature at which
nMH = ^TriiMi ^hi - hj^r) + Qi,r = ^^j -hJ,: + Q •J,r (te)
where the right-hand side refers to the precombustion species. The left- hand side refers to the combustion gas mixture. In order to obtain the flame temperature, the left-hand side of the equation is plotted from the data for a few temperatures, at constant pressure, against temperature, and the flame temperature Is picked off the curve at the value equal to the right-hand side of the equation.
The flame temperature is shown in figure 12 as a function of equiv- alence ratio for the combustion of CgHl^-air and CHl^-air mixtures with the
■
16
initial temperatures of the precombustion gas species chosen at 500° K. The flame temperature is plotted for lines of constant pressure of 1, 10, and 100 atmospheres to illustrate the effects of pressure.
Transport Properties
Because available data for the transport properties is extremely limited and in order to maintain as simple a procedure as possible, general equations are again used.
Viscosity.- From references 9^ 13^ and Ik the viscosities for all L species except H2O are represented by the equation: 1
5 m O.O^lksJw x io.6 9
1 a2ü
where a is the collision diameter of the molecule and Ü is the colli- sion integral. Values of Ü were obtained from reference 15 where Q is tabulated as a function of kT/e. The symbol k represents the Boltzmann's constant and e, the Lennard-Jones force constant. Values of a and e/k for the species were obtained from references ih- and 15 and are reproduced in tahle II. The values of a and e/k for the specie N were not found at the time of programing. However, the lack of these values should have little effect inasmuch as the percentage of N in the product gas is small.
The viscosity of the remaining specie H2O is represented by the equations (see ref. 16)
U(H2O) = 0.0535^9 \/T
l + 1511 x 10 57.^
x 10-6 (T < 15000 K) (M0
.(HgO) = 0'0*L286 ^ . x 10-6 (T > 1500o K) (lH5)
1 g^.51 x 10^
T2
For the gas mixture, reference 15 gives the equation
xi
2R
17
where
^M-
i ^7 1+ ^ t±
1/2/MI^1/1,■'
Hi * ^ * w ihl)
The viscosity of the combustion products of C2Hi4.-air and CHi|.-air mixtures for the equivalence ratios of 1.0, 0.9, 0.8, and 0.7 are shown in fig- ures 15 and 1^, respectively. In these figures, the viscosity is plotted against temperature for lines of constant pressure.
Thermal conductivity.- From reference lh, an approximate relation for thermal conductivity of gaseous mixtures is the Eucken equation
K Sc (cp + ^Sp) m
The thermal conductivity Is plotted against temperature for lines of constant pressure In figures 15 and 16 for the combustion products of C^i^-air and CH^-alr mixtures, respectively, and the equivalence ratios of 1.0, 0.9, 0.8, and 0.7.
Prandtl number.- A useful parameter In heat-transfer studies is the Prandtl number which Is presented In this section on transport properties because the equation requires the values of the viscosity and thermal conductivity. This equation Is
Npr - Sc CpU
K (^9)
The Prandtl number Is plotted against temperature for lines of constant pressure In figures 17 and l8 for the combustion products of C2Hl4.-alr and CHi^-air mixtures, respectively, with the equivalence ratios of 1.0, 0.9, 0.8, and 0.7.
RESULTS AND DISCUSSION
The preceding equations have "been programed for the IBM 70^ electronic data processing machine at the Langley Research Center. The required experimental data that are listed in tables I and II together with the data that related Q. to kT/e have been stored in the program In proper order for the computation of the equations. In addition,
18
curve-fitting subroutines have been incorporated Into the program in order to obtain the partial derivatives a., ß, and (öni/äT) . The
present arrangement covers a range of pressures from 0.0001 atmosphere to 800 atmospheres in steps denoted by the relation p = 2n X lO01 where n = 0, 1, 2, 3 and m is zero or any positive or negative integer. The temperature range is from 200° K to 5,000° K in intervals of 100° K. The composition of air vas taken as 0.7809 mole of N2, 0.2089 mole of O2, 0.0095 mole of Ar, and 0.0005 mole of COg per mole of air.
The output of the IBM 704 is in the form of two tables, one of which tabulates X^, n, and M against T and the other tabulates the thermodynamic and transport properties against T, both at a constant pressure for a given fuel and equivalence ratio. Examples of the tabula- tion eure presented in tables Ill(a) and Ill(b). The accuracy of the data listed can be no more than four significant figures when based on the input data. However, the five to seven significant figures shown were retained as representative of the original printout. In addition to the tabular form, the data were also stored on magnetic tapes in an ordered sequence in order to utilize machine plotting. The plotting machines are programed to plot Cp, 7, n, K, and Npr against T for lines of constant pressure.
Because the chemical equilibrium constants obtained from reference 5 were listed for every 100° K, the gas composition was also calculated and tabulated for every 100° K. Later, when the thermodynamic and transport properties were Included In the program. It was desired to have these values in units of the English gravitational system for engineering use. Thus Cp, for example, is in BTU/lb-0^ while tabulated against 0K. In addition, the figures obtained from machine plotting were originally to be engineering work plots only with the abscissa in units of 0R. However, because of the large amount of plotting to be done for this paper, it was decided to retain these plots and incorporate double temperature scales on the figures.
The product gas composition and the thermodynamic and transport prop- erties of the combustion products of air with the hydrocarbon fuels ethy- lene Cj^H^ and methane CH^ have been calculated for the equivalence ratios of 1.0, 0.9> 0,8, and 0.7. Because the tabular form is Inconvenient to use for wind-tunnel or rocket work and also because of its bulklness, the data have been reduced to a series of charts which are shown in figures 2 to 18. Regions in which comparison can be made between the present paper and ref- erence 1 show agreement, in general, to within better than 1 percent.
19
CONCLUSION
A calculation procedure is presented from which the composition, thermodynamlc properties and transport properties of a dissociated com- hustion product gas may he obtained vhen fuel consisting of a mixed hydrocarbon compound is burned in air. Calculations vere made for the respective hydrocarbon fuels methane and ethylene and results are pre- sented at the equivalence ratios of 1.0, 0.9, 0.8, and 0.7 for pressures
varying between 10"^ and 8 x 102 atmospheres and temperatures from 200° K to 3^000° K.
Langley Research Center, National Aeronautics and Space Administration,
Langley Air Force Base, Va., September 27, 1961.
20
APPENDIX A
CALCULATION OF FLOW CHARACTERISTICS AND
SUPERSONIC NOZZLE ORDINATES FOR CALORICALLY PERFECT GASES
WITH VARIABLE MOLECULAR WEIGHT
Mollier charts for gases are generally difficult to read accurately and are laborious to use, especially if they are to he used to compute nozzle ordinates and to determine flow properties along streamlines. In the following sections, equations to he used for the calculation of nozzle ordinates and flow properties are listed with explanations where necessary.
I 1 j
s 6
Flow Characteristics
Equations for flow properties with specific heat as a function of temperature and no dissociation have been developed in reference 17. These equations are here extended to Include dissociation as a function of temperature only, that is, ß = 0, together with the assumption of chemical equillhrlum during expansion. On the Mollier charts (figs. 5 and 6), the condition ß = 0 is restricted to the regions in which the constant-temperature lines are approximately parallel to the ordinates. Furthermore, it can he seen from these charts that, for any pair of stagnation pressures and temperatures in these regions, the flow properties during an expansion along a line of constant entropy will also lie in these regions.
The basic relations for the development of the flow properties along an isentrope are Bernoulli's equation and equations (52), (36), (37)> an,3- (^0) of the text. By solving for the partial derivatives of the right-hand side of equations (56) and (57) of the text and by writing a obtained:
in terms of 7j Cp, and xsp* the following equations are
2. Pt -«- = exp
-c. = exp
(Al)
(A2)
21
= (l.87gcJRBpT):
V = 5.6gcj
cJRBpT»1/2
^/2 1/2
(A3)
(A*)
L 1 5 9 6
TL - JT \7 - 1 /
^Tte ^RspT
11/2
(A5)
Pt RspT Pt ^T V^ - 1 / (A6)
m* _
7^Ip T^
^ sp> 1/2
dT (A?)
A 1 (y*V ^1/2 T exp
CV7
Hsp(y " 1).
1/2. dT T
(A8)
In equation (A7), T IS not an explicit function as the Integral also contains T* as the lover limit. Furthermore, the equation is not amenable to the process of direct Iteration, as the results diverge in an oscillatory manner. The scheme used here for the solution is to reduce successively the value of the lower limit by a constant decrement, say 5 K0, from a value knovn to be greater than the actual solution. Each time a value for the lower limit is chosen, the equation is calcu- lated and the difference between the lower limit and the calculated
is noted. The process is continued until this difference The calculated value of T*" is then within 5 K0 of the If greater accuracy is desired, a smaller decrement is
value of T* changes sign, actual value.
used. A good starting value for the lower limit is T* = 7t + 1
22
In order to solve these equations, a stagnation temperature is specified, together with the temperatures for which the equations are to he solved. Furthermore, tables of RSp, Cp, and 7 against T, such
as are presented in this paper, must he available. The values of Rsp, Cp, and y can he chosen at any pressure compatihle with the assumption ß = 0.
Plow properties of CgH^-air and CHi^-air combustion products at the
equivalence ratios of 1.0 and 0.7 and for stagnation temperatures approxi- mately that of the respective flame temperatures are presented in tables IV and V, respectively. The flow properties for these gases were computed on the IBM 70^ electronic computer for temperatures at intervals of 5 K0 from 200° K to 500° K and at 25 K0 intervals from 500° K up to the stagnation temperature. The representative values of RSp, 7 against T were chosen at the pressure of ^0 atmospheres.
-p.» and
Supersonic Nozzles
A calorically perfect gas with variable molecular weight also requires modifications in the equations hy which the wall coordinates and the distrihution of flow properties are calculated for supersonic nozzles. These modifications are discussed here for the truncated conical nozzle and the contoured nozzle, again subject to the condition ß = 0.
The truncated conical nozzle wall coordinates are completely speci- fied once a cone angle and a throat diameter are chosen. Any radial line from the cone vertex through the nozzle is a streamline along which the flow properties are functions of the radius only. By combining the radial flow equations and the equations of continuity, motion, and state, the radius is written as a function of the temperatures. Thus,
(*)" ]RBpT
"sp1
KW)- _JT \7 - 1 /
1/2
^X (i sp?'
>v
1/2 dT
1/2
(A9)
-/
where r is the radius from the vertex to the sonic line. The ratio r/r* may be converted to x and y coordinates with x = 0 at the throat by the relations
x _ r cos 9 r^ sin 9
cos 6 w w sin 9, (A10)
25
and
y = r sin 9
r* sin 9 (All)
w
L 1 5 9 6
vhere ew 1B the wall angle and y Is the throat radius from the center line. By using the same Input data In equation (A9) that Is used for equations (Al) to (A8), the distribution of the flow properties In the truncated conical nozzle Is obtained.
The contoured nozzle wall and streamlines are designed by the usual method of characteristic networks. (See ref. 18.) The only modifica- tion to the characteristic method is that, once the velocity is found at a point, the Mach number is interpolated from data tabulated from equa- tions (Al) to (A8) In order to determine the Mach angle. Further details are available in reference 19«
The stream function to be used in conjunction with the characteristic network system is developed from the equation of continuity across a Mach line and Is made nondlmenslonal by dividing through by the mass flow at the throat. Thus
d^ = 2 6« sp
T*^1/2
/XpT, exp
1/2
f)#+©2] 1/2
dx (A12)
In order to evaluate ^ and the corresponding flow properties, the velocity Is obtained from the characteristic network equations, the properties are interpolated from the tables and substituted into equa- tion (A12) . The integration Is along a Mach line and \|f = 1 at the nozzle wall.
Other flow regions which use radial flow or characteristic network equations Incorporate these same modifications.
■
2k
REFERENCES
1. Anon.: Properties of Combustion Gases/System: CnH^-Air. Vol. I -
Thermodynamic Properties. McGraw-Hill Book Co., Inc., c.1955. Vol. II - Chemical Composition of Equilibrium Mixtures. Gen. Elec. Co., c.1955.
2. Huff, Vearl N., and Calvert, Clyde S.: Charts for the Computation of Equilibrium Composition of Chemical Reactions in the Carbon-Hydrogen- Oxygen-Nitrogen System at Temperatures From 2000° to 5000° K. NACA TN 1655, 19^8.
J. Martinez, J. S., and Elverum, G. W., Jr.: A Method of Calculating the Performance of Liquid-Propellant Systems Containing the Species C, H, 0, N, F, and One Other Halogen - With Tables of Required Thermo- chemical Properties to 6000° K. Memo. No. 20-121 (Contract No. DA-Olv-14-95-Ord l8). Jet Propulsion Lab., C.I.T., Dec. 6, 1955-
k. Hershey, R. L., Eberhardt, J. E., and Hottel, H. C: Thermodynamic Properties of the Working Fluid in Internal-Combustion Engines. 3AE Jour., vol. 59, no. k, Oct. 1956, pp. k09-k2h.
5. Taylor, Hugh S.: Elementary Physical Chemistry. D. Van Nostrand Co., Inc., 1927.
6. Zemansky, Mark W.: Heat and Thermodynamics. McGraw-Hill Book Co., Inc., IShj.
7. Glasstone, Samuel: Textbook of Physical Chemistry. Second ed., D. Van Nostrand Co., Inc., C.I9U6.
8. Slater, J. C: Introduction to Chemical Physics. First ed., McGraw- Hill Book Co., Inc., 1959.
9. Hilsenrath, Joseph, Beckett, Charles W., et al.: Tables of Thermal Properties of Gases. NBS Cir. %k, U.S. Dept. Commerce, 1955.
10. Faires, Virgil Moring: Applied-Thermodynamics. The MacMillan Co., 1958.
L 1 3 9 6
11. Perry, John H., ed.: Chemical Engineers' Handbook. Third ed., McGraw-Hill Book Co., Inc., 1950.
25
12. Huff, Vearl N., Gordon, Sanford, and Morrell, Virginia E.: General Method and Thermodynamic Tables for Computation of Equilibrium Composition and Temperature of Chemical Reactions. NACA Rep. 1057, 1951. (Supersedes NACA TN 2113 by Huff and Morrell and NACA TN 2l6l by Huff and Gordon.)
15. Liley, P. E.: Survey of Recent Work on the Viscosity, Thermal Con- ductivity and Diffusion of Gases and Gas Mixtures. Thermodynamics and Transport Properties of Gases, Liquids, and Solids. McGraw-Hill Book Co., Inc., c.1959.
L L Ik, Gordon, Sanford, and McBrlde, Bonnie, J.: Theoretical Performance 5 of Liquid Hydrogen With Liquid Oxygen as a Rocket Propellant. NASA 9 MEMO 5-21-59E, 1959. 5
15. Reld, Robert C, and Sherwood, Thomas K.: The Properties of Gases and Liquids. McGraw-Hill Book Co., Inc., 1958.
16. Kestin, J., and Moszynski, J. R.: Review of Available Experimental Data on the Viscosity of Steam. Thermodynamic and Transport Properties of Gases, Liquids, and Solids. McGraw-Hill Book Co., Inc., c.1959.
17. Gelssler, Ernest D., and Reisig, Gerhard: Calculations for a Super- sonic Nozzle With Specific Heats Dependent on Temperature. Rep. 65, Ord. Guided Missile Center, Redstone Arsenal (Huntsville, Ala.) Sept. 1950.
18. Ferri, Antonio: Elements of Aerodynamics of Supersonic Flows. The MacMlllan Co., 1914-9.
19. Guentert, Eleanor Costllow, and Neumann, Harvey E.: Design of Axi- symmetric Exhaust Nozzles by Method of Characteristics Incorporating a Variable Isentroplc Exponent. NASA TR R-55, 1959.
26
iii in» mamiimm
TABI£ I.- HEAT OF FORMATION AMD EMTKOPY REFERENCE VALUES
AM) SPECIFIC HEAT E«IATIOHS
Specie Btu/lb v Btu/lb-OR 0>)
Op,!' Btu/lb-1*
(c)
Ref^rencfes1
(d) 1
»2 0 1.63591 Cp - 0.2U81
cp . 0.338 - 66f + I'** ^
(0° K 5 T < 300° K)
(300° K < T < 3000° K) 3, 9 9
* 10
02 0 1.53201 Op . 0.2171
„ «: 1*.006 . 26.56 •T» 0-36 • Tl/2 ' T
(0° K < T < 300° K)
(300° K S T S 5000° K) 3, 9 9
9' 10
=2 0 15A9105 Cp - 2.1*63 + O.OO325T (0° K < T < 300° K)
(300° K < T $ 3000° K) 3, 9 9 i'' 10
HgO -5,771.29 2.50I465 Cp - O.U1*09 (0° K S T < 500° K)
(300° K 5 T S 5000° K) 5, 9 9 y' 10
CO2 -3,8lA.i9 1.16091 Cp - 0.1579 + 0.000ll*5T
cp . 0.368 - ** ♦ 0-988 x XO» T fp2
(0° K 5 T < 300° K)
(300° K i T S 3000° K) 3, ^id
CO -1,696.29 1.68612 Cp = 0.21*81
op . 0.338 - £^8 + 1-179 x ioU
T i]i2
(0° K < T < 300° K)
(300° K < T S 3000° K) 3, ^'j
NO 1,291* .81 1.67792 Cp - 0.2316
cp. 0.338 -SIJU1-^^
(0° K < T < 300° K)
(300° K S T S 3000° K) 3, ^
OH l,o6i*.50 2.58079 Cp = 0.1*119
cp , 0.1*55 + Sä/Qr - 0^2 106 TI/2
(0° K < T < 500° K)
(300° K < T < 3000° K) 3, 3.9
e
N liv,iv^.57 2.6llt29 Cp - 0.551*6 (0° K < T < 3000° K) 3, 9, 9 1
0 6,651.37 2.1*01*73 Op . 0.3103 (0° K < T < 3000° K) 3, 9, 9 |
H 92,960.61 27.18801* cp = i*.9255 (0° K < T < 3000° K) 3, 9, 9
Ar 0 0.92607 Op - 0.121*3 (0° K < T ^ 3000° K) 3, 9, 9 :
CH1* -2,007.50 3
c^k 600.1*0 3 1
"Referenced to T - 300° K. ^Referenced to T = 300° K and p = 1 atmosphere. cEquatlonB contain conversion factors from ^ to ^ in constants.
"The references refer to Q^ r, s^ T, and Cp ^, respectively.
eSee text.
H
1
, ■!!■ -»i
27
TABLE II.- LENNARD-JONES FORCE CONSTANTS
[Taken from refs. Ik and 15]
L 1 5 9 6
Specie a, angstroms e/k, OK
N2 5.681 91.5
02 5. ^55 115.0
H2 2.968 55.5
H20
COg 5.996 190.0 |
CO 5.590 110.0
NO 5.1+70 119.0
OH 5.110 95.8 1
N
0 5.068 102.2 i
H 2.497 99.8., j
Ar 5A18 12^.0 i
■
28
?8 00 03 03 00 CVI <M CM CVJ
cp Cp 03 03 00 CM CO <M CM CQ
oococooooo oocpcpt-t- CQOJCMCMCM CMCÜSJCMCM
1MB 8 O IAO ONIO
<S <M CM CM CM
O £\H CM ! .
O OvOOC . 1^ CM 8 CM W W
CO ^ CQ GOCQ ON 0> 0\ ON ON
fo KNKN »O P»
iTSITvirMTN irNirMTMAUTN « . . . . ir\ ir\ in U"N U"N
rOKN K\
^8 NI-
CO CM
ir>ir> ir>iAvo
-4" •_ CM ö KSi, 11 f»{ HOO CMVO t-
WS M R CM CM CM CM CM
0\t 100 VO CM. % oovp JS ir\ CM « CM CM
il ^l^ü ICO f-PNCM
■ toco &sir\
CO rHCO t-CO CMJ t-QJ.3 J- CM J- Ö CM CM ir\\D t— t- 00 CO Cö 00 00 H H H H H
| CO
g
i
s
o II
p.
I o
V
6 I 0 I 3 'öa
g
o^ u
^
^
^
J^fl iT'-l-l^OC) CM CM HOO t— )H ä3q\>2)KSir\ CMVOCMPPN
0\F-lACMCO CM lf\ <3MO t" ;8;
( u \
ISS'r t-ooco S co H H H rH H
ICO K~>M3 < Scu b-iAo > r-i CM ir\c
;8
ilß 8888
O O H
ONrH o Jt b-mo in ri ri ri !=! S o o o o o
^ä*i CM t—V KSO < CM m ( \C-CO
H CM
88
Qvß OCO H ^«IfWO CT\
r-| H K^V CM
8S rl rH
88
Q Ö H<J3CO CO IAO O KS O CQ IAH 0\ H »A O •A rA
tr-1 H o\o\
SS RSBSRS
Um H r-| H H d
fTN ITN KS tTN ITN fill < H H H H
i iA ON<Ö H ON
O^ CQVO 1A
ISÖ88 &RS.5
rAJAtAtA fAfASSrAtA HS fA HS JA OJ HHHH HHHHH r-tHHHH
0\CQ a\t-t OJ O Jf t-i H CM 1A CM r CO IA&\^<
IA t-H lA-J* 00 lACOCO IA
«&ä88 ^§88:
KN »TN rr\ KN H H H rH O Q O Q
KNKN»OrOi»r\ »AVp t—t-lTN OJb-r-ilPvCJ
§8§i
^ rA IA ir\ IA
fc-CM IAH S\ o CM F-o -i CM CM H H Q o o o o o
00 t~CMNO i SP^C CM^- CJ ö IA OJ i
8888: CM O VQOO 0\ Oy} VQ O H
CO co KS t—\n co Ha3 CT\iA iiiii
lA^B t—-3- Q ON^^O rf-3 • - o
H t—Q ob IA
x R S § S o o o o o
IA-* tA t—IA
is m\ 1 CM CM CM (
C—t—t^t— t—t—t-t-t
p\P>rH IAO t-t—^ \b C CMCO CM IAO t~-IA t—lAU
O 0
t—t—03 r-l I ^O IA P-rJ L l7SlACr>00 Jt
-^ iSr ■ ' -. 1 l-U .
VO VD IA IA IA
mi
888 88888 88888 88888 88888 8888^ 1 iA^t US vo t^cO ONO rH CM lA^ IA VO t—CO CT\ O H CM IA^ ir\ \0 t—CO CA C
■-( rH H rH H HHHrHCM CMOICMCMCM CMCMCMOJIA
29
I w
a o
no o
00 O O J* t-- ^»5 Si rovo Si HOO 00«) ONC"
0O H O CVJOQ ^- CT\Q r?N OJ
^ KM- VDVO t-t-« OOOTONOH ^tiröx^iö vit-^soiTNQJ t—lAöNöSF-
-ff so rr\ cy Os t—rH H so ir\ H Cy SO i^l^
ITMA irsr
3
ITvOS-d- ITS
88 . iH H H O O O O O
ir\SO ITNOp CM SO HCO ff>SD
K>0 V£>CQ (?s QD^l- WOT H-\
CO ITNSOOO 00 SSOSrH t-H rH rH CSI H H
00 H H (
\00 OS
ITS
o
BsfSM o o o o o csi KS &\^S P
rH H OJ IOv^ f-l r-l H rH rH
Q t--4-S0 OS
irv ös irssß u^v K% csi v^ra ir\ 1A t—ONrH to H rH rHCM OJ
P-p CO Q\G\ . . ■ CU Ö ITS -SD J- rH f-
CSI OJ OJ CSI C\J
p^
8888 8888Ö t-t—t—t- t—t—F-t-t- co co og co co oo oo co oo
o ' '
H CSI CTsOJ J- O O O K^O\ t-t-t-t^t- co CO CO CO co
CO O SO OJ OS rA mso Q so OS OJ CO O OS 00 OSOsrH OJ
OS CSI CO o o
o o '&
^- so in so K"s
O i^-* ITS irs irsirsirs
OJ rH 1ASO so t-so iTS SO CSI t--*
so
t—
^t rH 0\0
Os OS00 ON CSI S- ost^ rsosoj
CSI OJ OJ K> t<S I o t~-so o
UTS rHSO 00 OsoO CO OJ os oj ir\ os
KS KN J- ^t ^t
csi so ITV irscp ITNH rH Oj3 OJ CO ITS ITN ITS KN t— OJ SO OS iA ir\so so so
O OSrH tfSQ - t—osco O
t—-* OSO
SO so SO SO sot—^t—t— t^f-t—C—t^ h-1—t-C—t- t—t—t—t—t- t—t-1—t—t— t I I I I
KNt—irsco KN CSJ OS OS cogsOJt<S sotrcios
OO CO SQ OJ ISO ( I iA-
K> Ö« C~- rH Q-NOT rH -d- ITMJA lASO
HCO CSI rHCO r-l rAH O H
SOSO t—t— t~-
SO OSCO-* -* -3F co t— rH ir> S O OJ O Q t~Ci JArH OS t-CO 00 OS Os
OS-if- 1A O rH 00 t-A 1A.4- rH ITNQ ^t rH 0-=t Q OJ o rH OJ J mso
CO SO OS KSso OsifN^; rHJF j* H Q VO O -3- t-OSO Oi SOSO SO t~- t—
OJOJOJOJ OJOJOIOJOJ OJCSICSJOIOJ OJOICJOJOI KSKSKNIOKN K^^f^K^K^r<^
00 ■ t—SO OS CSJ CO t—Ä o KN rH Q OS 0\ KN KN f?s OJ OJ
H H O rH O J- KStPvCO OS . IpvC
■ C^ r psp ITS .,
I OJ OJ CSI 0J «
CO O KNSO CO -? ITS OSOÖ H ir\ os!fN3 -* OS lA O) O OS rH H H rH O
■ IA OJ rH 1A -oj§fcy
1A-* OS IA-4 -* OJ CSI OJC0 1A OJ 03 OJ t- C0-* «5 rH rH H CSJ CSI KNrA
rH H H H H rH rH H H H H H rH H
O 1A t ■ lA rH CO OS (A r-i CO KS IA O CASO IA IA lAlAsp OJ OJ CSI a
CSI OJ
ad rA^J- o OJ rH SD P OS0Ö
lA^h OJOO^F t—CO OS OSÖ oj csi oj oj KS
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t-fASp t- rH OsO f- OS C-- so oo lAco rA t—so oj KS OJ SO rj t^OO O J1 SO CO OJ Os
OS H tA lA OS t— LA »AO rA H rH IA IA OJ
CO IA OS OS so OslAOsQ-d- rH Q rH rH J lAOOSOIArH t-J? rA^l-^f COlA^-*-*
Ol rA rA oj H
OJ IAO OS SO OJ-* j-
-* OsrA rA t-- co ^t so-d- O
O CO CO H rA I^-OJ rAOsoj
IA IA rAsO OS O so 1AOI Ol
[A CSI IA O-d- t—lASDOCO t—OJ-d-t^OJ rAOJOsOJOJ
lAOS Ol _ rACO^- Os-. ,. OJ OJ H H OP ÖSOSC s rA rA rH co -
~s^ OvrAc
•> ~ i i i
00 OJ-* rACQ OJ t—rH lAOS CO f—"
rH OS SO H H O 1ACO H IA
C^SO IA lA-d- OJ i rH SO rH t—rASO
OJ IA rA OJ p r-1 rHOp OS OS
HCO rH OJ00 IA t— b—IAOJ CO OSO H Ol
rHHOjoj ojoirArArA
8888 88888 88888 OJ rA-it- IA SO t—cO 0\0 H 0J rA.* IA SD t-O
o < o < OS<
88888 rH CSI rA J- IA IA
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OJ ol OJ oi rA
30 TABLE IV.- FLOW PROPERTIES OF CgH^-AIR COMBUSTION PRODUCTS
Letter E denotes that number to left of E is to be multiplied by 10 to the power indicated by number to right; for example,
0.10V79975E 01 = 0.10^79925 x 101]
(a) Req = 1.0; Tt - 2,500° K; T* = 2,271.7° K
3273668SE-00 «63»592'.E-00 56822821E 00 65691037E 00 73637856E 00 e06&;'>33E 00 87251703E 00 93»1908JE 00
992ke33<>E 00 10'>79973E 01 1101172«E 01 U»2426iE 01 12020222E 01 1290196SE 01 12971216E 01 13li30l.05E 01 13880703E 01 1<>323'>02E 01
1»759»25E 01 l»190*2eE 01 1S6170»7E 01 160'>0120E 01 16<|60360E 01 168787286 01
,17295370E 01 177U081E 01 18126487E 01 le>'>200<>E 01
189i81»<lE 01 19375»13E 01 19794S8I.E 01 20215185E 01
>20638002E 01 21063446E
.21*91639E 21923827E 22360081E 01 22800837E 01
01 01 01
.232»7*63E 01
.236977*7E 01
.24143155E 01
.24614Ü71E 01
.25080931E 01
.liiiUOiSE 01
.26033926E 01
.26920988E 01
.270160956 01
.27518675E 01
,28029677E 01 ,28»'>9636E 01 ,290788056 01 ,296186906 01 ,301695e6E 01 .30732208E 01 ,31307571E 01 ,318957756 01 ,32*979876 01 .3311SK.16 01
.337496186 01
.3<i398'>976 01 •35064570E 01 .357490366 01 .36453056E 01 .371785106 01 .37926829E 01 .3e6997e5E 01 .395001026 01 .403277116 01
P/Pt
00
0.099999996 01 0.938076446 00 0.880142726 00 0.825926886 00 O.77516310E 0.72760946E 0.683043686 00 0.64126431E 00 0.60207519E 00
0.565297e0E 00 0.53076809E 00 0.49833364E-00 0.46785571E-00 0.43920550E-00 0.41226359E-0O 0.386920916-00 0.36307272E-00 0.34062304E-00 0.31948331E-00
0.299571086-00 0.280810866-00 0.26313236E-00 0.24647022E-00 0.23076153E-0Ü 0.21595311E-00 0.201993916-00 0.188835706-00 0.I7643201E-O0 0.16474260E-00
0.153728826-00 0.14335397E-00 0.13358216E-00 0.12438293E-00 0.11672659E-00 0.10758465E-00 0.999304146-01 0.92737798E-01 0.e5982301E-01 0.79640776E-01
0.73689 0.68110 0.62885 0.57995 0.53423 0.49152 0.45166 0.41451 0.37990 0.34770
604E-01 4426-01 0556-01 1336-01 1706-01 444E-01 8996-01 133E-01 073E-01 074E-01
0.317778096-01 0.29000416E-O1 0.26425775E-01 0.240417316-01 0.218368376-01 0.198002276-01 0.17921441E-01 0.161907916-01 0.14696962E-Ü1 0.13137054E-01
0.117962616-01 0.10569064E-01 0.944801736-02 0.642591266-02 0.749593016-02 0.665142516-02 0.588613286-02 0.519413346-02 0.456977346-02 0.400785276-02
T/Tt
0.099999996 01 0.989999996 00 0.980000006 00 0.97000000E 00 0.95999999E 00 Ü.95000000E 00 0.94000000E 00 0.93000000E 00 0.91999999E 00
U.910O0000E 00 U.9O00O000E 00 0.889999996 00 0.880000006 00 0.870000006 00 0.86000000E 00 0.849999996 00 0,940000006 00 0.83000000E 00 0.81999999E 00
0,80199999E 00 0.8O:<OO000E 00 0.79TO00O0E 00 0.77'<99999E 00 0.77)000006 00 O.76"000006 00 0.75^000006 00 0.730999996 00 0.73O0O000E 00 0.72000000E 00
0.70999999E 00 &.70000000E 00 0.69000000E 00 0.68000000E 00 0.66999999E 00 0.66000000E 00 0.65000000E 00 0.63999999E 00 U.63000000E 00 0.62000000E 00
0.610 0.599 0.590 0.580 0,569 0.559 O.S50 0,640 0.529 0.520
00O00E 00 99999E 00 00000E 00 000006 00 99999E 00 99999E 00 00000E 00 00000E 00 99999E 00 O0O00E 00
0,51000000E 00 0.50000000E 00 0,489999996-00 0,480000006-00 0.47'J000006-00 ü.45O999996-00 0.451000006-00 ü,44nOÜOOOE-00 Ö.43C100000E-00 0.41">99999E-00
0.4iri 000006-00 0.400000006-00 0.38O99999E-00 0.3euOOOOOE-00 0.37000000E-00 0,360000006-00 0.349999996-00 0.340000006-00 0.330000006-00 0.31999999E-00
*h 0.325930576-00 0.45939400E-00 0.56076721E 00 a.64539229E 00 0,71923582E 00 0.78537094E 00 0.84562713E 00 0.90121395E 00
0.95297407E 00 0.10015238E 01 0.10473332E 01 0.10907659E 01 0.113211396 01 0.117161566 01 0.120946746 01 0.124583856 01 0.128067266 01 0.131469296 01
0.134740756 01 0.137910876 01 0.140987906 01 0.143979136 01 0.146891566 01 0.149730446 01 0.152600776 01 0.155207146 01 0,15785407E 01 0^160444946 01
0.1629 0.1654 0.1679 0.1703 0.1726 0.1749 0.1772 0.1794 0.1817 0.1838
0.1860 0.1881 0.1902 0.1922 0.1942 0.1962 0.1982 0.2002 0.2021 0.2040
0.2059 0.2077 0.2096 0.2114 0,2131 0.2149 0.2166 0.2184 0.2201 0.221S
83046 01 71436 01 13326 01 10826 01 66096 01 81216 01 58046 01 96516 01 04396 01 77306 01
19486 01 31386 01 1384E 01 6775E 01 9397E 01 93306 01 66496 01 14276 01 37496 01 36636 01
1187E 01 6397E 01 93136 01 0003E 01 8621E 01 49176 01 9249E 01 1646E 01 1843E 01 01766 01
0.223466206 01 0.226111456 01 0.22673746E 01 0.22834424E 01 0.22993175E 01 0.23150018E 01 0,23304965E 01 0,23468029E 01 0.236092316 01 0.237585666 01
0,602863106-01 0,11358106E-P0 0.160533646-00 0.201749666-00 0.237770486-00 0.269087486-00 0.29614120E-00 0.31934687E-00
O.339O68116-O0 0.366636666-00 0,369360196-00 0,380489956-00 0,38929826E-00 0.39599886E-00 0,40079228E-00 0.40387121E-00 0.40639e98E-00 0.40562726E-00
0.404390666-00 0.402123906-00 0.398836886-00 0,394633336-00 0,389605026-00 0,383846126-00 0,377432036-00 0,370439436-00 0,362931286-00 0,354976816-00
0,346637236-00 0,337960226-00 0,326995196-00 0,319791406-00 0.310392696-00 0.300839516-00 0,291168646-00 0,28141785E-00 0,27161682E-00 0,261794786-00
0,251974146-00 0,242187226-00 0,232460226-00 0,222816786-00 0,213278796-00 0,203865646-00 0,194595596-00 0.186466466-00 0.176548696-00 0.16780099E-00
0.15925496E-OO 0.15092152E-00 0.14281133E-00 0.13493077E-00 Q,12728626E-00 0,1198a316E-00 0,11272467E-0O 0,10561640E-00 0,99160072E-01 0,92757632E-01
0.86607555E-01 0.80713009E-01 0.750748756-01 0.69692446E-01 0,64564663E-0l 0,6968e063E-01 0,65069432E-01 0.50674579E-01 0.465283366-01 0.426162746-01
A/A«
19238102t 01 143924666 01 124300366 01 113832696 01 107638896 0! 103867346 01 101609876 01 100420206 01
100011516 01 100209696 01 100902616 01 102010366 01 103461696 01 105260296 01 107381796 01 10976773E 01 112429216 01 115361306 01
118564266 01 122037646 01 125768926 01 12962599E 01 13416158E 01 138806566 01 143776916 01 14909064E 01 16477017E 01 160834606 01
167310456 01 174226136 01 181614696 01 169509656 01 197948166 01 20697241E 01 216629326 01 22696824E 01 230046066 01 249932696 01
262696956 01 276417746 01 291171836 01 307063776 01 324166076 01 342623826 01 362563606 01 384097136 01 407416396 01 432682496 01
460091616 01 489863376 01 622240186 01 567506536 01 596979646 01 638018806 01 684037636 01 734490666 01 789906146 01 e5088661E 01
918146516 01 992463026 01 10746'>346 02 116669726 02 12672454E 02 13801292E 02 16061663E 02 164724166 02 180659466 02 196381276 02
Pf«t 099999996 01 948US6eE 00 89914436E 00 852893846 00 809206156 00 767908486 00 728849686 00 691686966 00 65690260E 00
623761966 00 69234968L 00 662552066 00 63428D52L 00 507463646 00 48196744t-00 46774665C-00 434723916-00 412823956-00 391961456-00
37213219C-00 353229526-00 335216796-00 318045146-00 301666026-00 286042066-00 271137006-00 2669140ac-00 243336336-00 230379B6E-00
216014086-00 206211866-00 194945596-00 104194416-00 173936816-00 164151996-00 164819916-00 145923116-00 137442166-00 129369656-00
12165 11432 10733 10069 94369 88394 82704 77306 72187 67339
5926-00 0176-00 9256-00 9926-00 3876-01 8686-01 3736-01 1346-01 9406-01 9446-01
627515296-01 584123666-01 543128596-01 504423156-01 467909136-01 433491666-01 401075526-01 370578626-01 341914976-01 315002036-01
289761856-01 266098546-01 243973266-01 223306646-01 204029286-01 166071116-01 169367066-01 163851336-01 139459456-01 126133126-01
31
TABLE IV.- FLOW PROPERTIES OP 02%-AIR COMBUSTION PRODUCTS - Continued
(a) Req - 1.0; Tt = 2,500° K; T* = 2,271.7° K - Concluded
1 - P/Pt T/Tt *h «/'t A/A* »K 1 1 0.MHS953E 01 0.35034U0E-02 0.30999999E-00 0.23906031E 01 0.389330636-01 0.218496676 02 0.113814646T01
0.*20TT*aSE 01 0.30517855E-02 0.900000C0E-00 0.24091629E 01 0.354727786-01 0.241271066 02 0.102447266-01 0.430060T9E 01 0.264e5234E-02 0.29000000E-00 0.24195J73E 01 0.322287926-01 0.267143256 02 0.919757916-02 0.*39T27*9E 01 0.22e9J36JE-02 0.27999999E-00 0.24337253E 01 0.291948536-01 0.296634176 02 0.823486116-02 0.«*9a22>2E 01 0.19709404E-02 0.2700OO00E-O0 0.24477265E 01 0.263641446-01 0.330373476 02 0.736160266-02 0,<.603S841E 01 0.16e917lOE-02 0.26000000E-00 0.24615409E 01 0.237294796-01 0.369126126 02 0.654286886-02 0.<.711.7»99t 01 0.14407928E-U2 0.2S000Ü00E-00 0.24751680E 01 0.212835836-01 0.413824176 02 0.580402816-02 0.4O13403E 01 0.12226563E-02 0.23999999E-00 0.248e6087E 0! 0.190186746-01 0.465620736 02 0.61306172E-02 0.»9>*31'.2E 01 0.10318242E-02 O,23OOO0O0E-OO 0.2iül8635E 01 0.169269626-01 0.62594523E 02 0.461799696-02 U-SCSHHiE 01 0.86557692E-03- 0.22000000E-00 0.25149332E 01 0.150006416-01 0.596585286 02 0.396233376-02
O.S2220196E 01 0.72147156E-C3 0.20999999E-00 0.25278113E 01 0.132331486-01 0.679731506 02 0.345993556-02 0.53695865E 01 0.597C6429E-03 0.2000ÜUOOE-00 0.23403090E 01 0.116146606-01 0.778341466 02 0.300648616-02 0.51.003267E 01 C.57435194E-03 0,19800000E-00 0.26430275E 01 0.113080836-01 0.800235846 02 0.29213326E-02 0.5<i31'.993E 01 0,55232409E-03 0.19599999E-00 0.25455391E 01 0.110070626-01 0.822932606 02 0.283795836-02 CSOtSllBOE 01 0.530964eiE-03 0.19400000E-00 0.2S4eo«38E 01 0.107115366-01 0.8464^9016 02 0.27563357E-02 C.54951935E 01 0.51025e44E-03 0.19199999E-00 0.23509418E 01 0.10421442E-01 0.87088446E 02 0.267643736-02 Ü.55277379E SI 0,49018964E-C3 0.190OOO00E-00 0.255303296 01 0.101367176-01 0.896220776 02 0.269823636-02 0.55607637E 01 0.47074345E-03 0.18799999E-00 0.25555173E 01 0.985730186-02 0.922521896 02 0.252170666-02 0.i59l.2B*0E 01 0.451905C2E-03 0.ie600000E-00 C.25579949E 01 0.958313396-02 0.949834746 02 0.244682186-02 0.562S3126E 01 0.4336b987E-03 0.18399999E-00 0.25604659E 01 0.931415366-02 0.978208736 02 0.237355626-02
0.5662a635E 01 0.41599382E-03 O.lBrOOOOOE-OO 0.25629303E 01 0.905030166-02 0.100769626 03 0.230188496-02 0.569795UE 01 0,398e92e6E-03 0.16''0Ü000E-C0 0.25653B80E 01 0.87915179E-02 0.10383532E 03 0.223178266-02 0,5729*7'.1E 01 0,38239487E-03 0.17'IOOOOOE-OO 0.256783146 01 0.85388437E-02 0.107009756 03 0.216351626-02 0.37657(>2eE 01 0.36643971E-03 0.17iOOOOOE-00 0.25702670E 01 0.829125646-02 0.110309736 03 0.209680466-02 0.580272I2E 01 0.35100269E-03 0.17-<99999E-00 0.25726965E 01 0.e0484512E-02 0.113744966 03 0.203155846-02 0.5e'.036e6E 01 0.336C7018E-03 0.17<OOOOOE-00 0.25751202E 01 0.7fll03507E-02 0.117322936 03 0.19677487E-02 0.597B72»7E 01 0.32162e94E-03 0.16',99999E-00 0.25775382E 01 0.75768800E-02 0.121051626 03 0.190534796-02 0.5917810U 01 0.30766615E-03 O.ltuOOOOOE-OO 0.25799508E 01 0.734796a6E-02 0.124939606 03 0.184432966-02 0.59576462E 01 0,29416926E-03 0.16:.99999E-00 0.25823583E 01 0.712354526-02 0.128996016 03 0.178466766-02 0.59982556E 01 0.2eil2617E-03 0*16<*0OO00E-00 0.25e47607E 01 0.690354426-02 0.133230676 03 0.172633696-02
0.60396615E 01 a.26832499E-03 0.16199999E-00 0.25871584E 01 0.66e78991E-02 0.137654146 03 0.166931326-02 0.608188ei£ 01 0.25635427E-03 0.16000000E-aO 0.25895514E 01 0.647654906-02 0.142277736 03 0.161357336-02 0.612096&9E 01 0.244602e0E-03 0.158OOO00E-0O 0.25919402E 01 0.626943316-02 0.147113586 03 0.15590946E-O2 0.616S9064e 01 0.23325963E-03 0.15(>0OO0OE-00 0.25943247E 01 0.606649206-02 0.152174796 03 0.150686476-02 0.62137S23E 01 0.22231414E-C3 0.1S400000E-00 0.25967053E 01 0.586767016-02 0.157476506 03 0.1453832eE-02 0.62595274E 01 0.21175601E-C3 0.1S200000E-00 0.25990B21E 01 0.567291396-02 0.163030896 03 0.140300856-02 0.63062620E 01 0.20157511E-03 0.15000000E-00 0.26014554E 01 0.548216926-02 0.168857376 03 0.135336136-02 0.63539879E 01 0.19176164E-03 0.14799999E-00 0.26038254E 01 0.529538746-02 0.174972686 03 0.130487266-02 0.6'>027381E 01 0.18230593E-03 0.14600000E-00 0.26O61922E 01 0.51125178E-02 0.181396006 03 0.12676234E-02 0.6«525'.75E 01 0.17319B66E-03 0.14399999E-00 0.26085561E 01 0.49335144E-02 0.188148106 03 0.121129566-02
C.66C3*52'.E 01 0.16443068E-03 0.14200000E-00 0.26109172E 01 0.4758331^6-02 0.195261546 03 0.116617206-02 0.6S55490BE 01 0.16599305E-03 0.13999999E-00 0.26132757E 01 0.458692566-02 0.202730756 03 0.112213566-02 0.66166152E 01 0.14783340E-03 O.138OOO0OE-OO 0.2615t449E 01 0.441799326-02 0.210673456 03 0.107885136-02 0.66709U65E 01 0.1399e3S3E-03 0.13600O00E-00 0.261B0142E 01 0.425261486-02 0.219064516 03 0.103668806-02 0.t7262927E 01 0.13244 <,91E-03 0.13400000E-00 0.2620380eE 01 0.409103606-02 0.227922616 03 0.995402226-03 0.6782Sli3E 01 0.12S20978E-03 O,132OO000E-O0 0.26227447E 01 0.393323936-02 0.237280326 03 0.956283896-03 O.eS'.OSlBSE 01 0.11B270t>lE-03 0.1300ÜO00E-00 0.262510586 01 0.377920756-02 0.247173646 03 0.916223096-03 0.68994<.79E 01 0.11161944E-03 0.12800000E-00 0.26274639E 01 0.362891986-02 0.257641286 03 0.878209236-03 0.69596S30E 01 0.10S24899E-03 0.12599999E-00 0.262981BeE 01 0.348235526-02 0.268725476 03 0.841231496-03 0.7021ie5'.E 01 0,99151604E-U4 0.12400000E-00 0.26321706E 01 0.333948986-02 0.280472336 03 0.80527862E-03
O.70840997E 01 0.93319793E-04 0.12199999E-00 0.263451916 01 0.320029946-02 0.292932OO6 03 0.770339285-03 0.71<.84536E 01 0,87746107E-04 0.12000O00E-00 0.263686416 01 0.30647574E-02 0.30616949E 03 0.736401606-03 0.72143087E 01 0.82423190E-04 0.11799999E-00 0.263920566 01 0.293283666-02 0.320214856 03 0.703453716-03 0.72817297E 01 0.77343708E-04 0.11600000E-00 0.26415434E 01 0.28045068E-02 0.335164006 03 0.671483146-03 0.73507857E 01 0.725O0i.l8E-Oi. 0.11399999E-00 0.2643B776E 01 0.267973796-02 0.36107919E 03 0.640477346-03 0.74213302E 01 0.678B6163E-0» 0.11200000E-00 0.26462077E 01 0.255B4981E-02 0.368039946 03 0.610423666-03 0.74941006E 01 0.63493837E-04 0.11"OOOOOE-00 0.26485340E 01 0.24407537E-02 0.396133696 03 0.581308936-03 0.756e5208E 01 O.S9316<.13e-04 O-IO-IOOOOOE-OO 0.2650B561E 01 0.232646976-02 0.405457006 03 0.653119846-03 0.7644B988E 01 0.55346977E-04 0.10ftOOOOOE-00 0.26531740E 01 0.221561096-02 0.426116506 03 0.52584307E-03 0.77233294E 01 0.51578673E-0«. 0«10~99999E-00 0.265548766 01 0.210813966-02 0.448230056 03 0.49946487E-03
0.7B039133E 01 0.48O04749E-04 0.10t00000E-0C 0.265779686 01 0.200401786-02 0.471928576 03 0.473971406-03 0.78867589E 01 0»44618&33E-04 0.99"99999E-01 0.2&601015E 01 0.190320656-02 0.497357416 03 0.44934862E-03 0.79719816E 01 0.41413466E-04 0.97y99999E-01 0.26624015E 01 0.180566266-02 0.524678196 03 0.425682366-03 Ü,8Ü597U62E 01 0.38383070E-0'4 0.95''99999E-01 0.26646969E 01 0.171134706-02 0.66407149E 03 0.402658236-03 0.81500654E ai 0.35520984E-01. 0.93i99999E-01 0.26669873E 01 0.162021646-02 0.68673879E 03 0.38066ie6E-03 0.e2«32035E 01 0.32B20942E-04 0.91999999E-01 0.266927296 01 0.153222726-02 0.61990607E 03 0.36927857E-03 0.83392750E 01 0.30276784E-04 0.90000000E-ai 0.267155356 01 0.144733476-02 0.66682702E 03 0.33879372E-03 0.e43a4466E 01 0.278824^2E-04 o.eeooooooE-oi 0.2673B289E 01 0.136549316-02 0.696787216 03 0.31909236E-03 0.95408992E 01 0.25632014E-04 0.e5999999E-01 0.26760991E 01 0.128665666-02 0.74010888E 03 0.300159716-03 1 0.86466284E 01 0.23M9t37E-04 0.84000000E-01 0.267836396 01 0.121077796-02 0.787156636 03 0.28198074E-03
0.87564465E 01 0.21539606E-04 0.81999999E-01 0.268062346 01 0.113780936-02 0.838344306 03 0.264640416-03 0.88699836E 01 0.19686317E-O4 0.79999999E-01 0.26B2B7736 01 0.10677O206-02 0.894142626 03 0.24782367E-03
| 0.a9876920E 01 0.17954290E-04 0.77999999E-01 0.268512556 01 0.100040726-02 0.955089086 03 0.231815116-03
■ ..
32
TABLE IV.- FLOW PROPERTIES OF CgH^-AIR COMBUSTION PRODUCTS
(b) Re(1 = O.Tj Tt = 1,900° Kj T* = 1,678.6° K
Continued
- n p/»t T/Tt "1 "IH I/Pt */*« »K j 0. 0.099999996 01 0,09V99999E 01 0. 0. 0. 0.09999999E 01 1 0.32103197E 00 0.937563856 00 0,9ai-.84210E 00 O.31904475E 00 0.606479066 01 0. 19433614E 01 0,950079656 00 1 0.«9t47ai6E 00 O.S7S<l6262E 00 0,97s68421E 00 O.45060835E-OO 0.115367676 00 0.144828956 01 0,902231216 00 1 0.96212U3E 00 0.8225M.51E 00 0,96052631E 00 0.55163272F 00 0.163966396-00 0,124693206 01 0,856391626 00 1 0.65J73906E 00 O.76968094E 00 0,94f36V>2E 00 0.63641495E 00 0.207050526-00 0,113923066 01 0.81248054t 00 0.73397953E 00 0.71969621E 00 0,934210526 00 0.710927466 00 0.244997996-00 0,107549996 01 0,770423666 00 0.eOS73652E 00 0.67246319E 00 0.921052636 00 0.778132536 00 0.276164566 00 0,103661046 01 0.73015029- 00 1 0.67881906!: 00 0.627e»547E 00 0.90789473E 00 0,83979981E 00 0.306889096 00 0,101424266 01 0.69168610E 00 1 0.9<>>2*368E 00 0.5B572642E 00 0.894736646 00 0,897067306 00 0.3314a538E-00 0.100301686 01 0,65466432E 00 1
0,100a826SE 01 0.J4599036E 00 o,aai57a946 00 0,950729636 00 0.362252e4E 00 0.100034576 01 0,619381246 00 1 0.10701400E 01 O.30832493E 00 0,868421056 00 0,10013672? 01 0.369476616 00 0.100460976 01 0,566622396 00 0.1129616<>E 01 0.47322256E-00 0,855263156 00 0,104941646 01 0,363426296 00 0.10144120E 01 0,653352856 00 1 0.11e76083E 01 O.43997917E-00 0,842106266 00 0,109622466 01 0,394359366-00 0.102933966 01 0,522520506 00 1 0.124*38875 01 O.li086951OE-O0 0.82894737E 00 0,113905796 01 O.40251763E-00 0.104863776 01 0,493072896 00 1 0.1300166<.t 01 O.37927479E-00 0.815789476 00 0,118113656 01 0,408130976-00 0.107262756 01 0,464959876 00 1 0.13SS1936E 01 0.35162652E-00 0.802631576 00 0,122164856 01 0,411415696-00 0.110056836 01 0,4381329U 00 1 0.1<>09%787E 01 0.32 566249E-00 0.789473666 00 0,126073996 01 0,412576706-00 0.113267666 01 0,412544916 00 1 0.1<.63«e60E 01 O.30129a42E-0C 0.77631579E 00 0,129854166 01 0,411807566-00 0.116671656 01 0,366150486 00 0.1S170442E 01 0.27e453i6E-00 0,763157696 00 0,133616386 01 0,409290766-00 0.120906676 01 0,364905516 00 1
0.1570395eE 01 0.257048SOE-00 0,750 000006 00 0,137070466 01 0,405197136-00 0.126379126 01 0,342764676 00 1 0.1623i7ilE 01 O.23701212E-00 0,736842106 00 0,140524286 01 0,399690366 00 0.130309276 01 0,321690716 00 1 0.167670iOE 01 0.2ie27462E-00 0.723684216 00 0,143884786 01 0,392924196-00 0.135723086 01 0,301645366 00 1 0.n2987»6E 01 0.20076850E-00 0,710526316 00 0,147158226 01 0,385043136-00 0.141652036 01 0,282590726 00 0.17S31714E 01 0.18442B7IE-00 0,69736842E 00 0,150350206 01 0,376162766-00 0.148133326 01 0,264489536 00 1 0.18366703t 01 0.16919324E-U0 0,66421052E 00 0,153465616 01 0,366471366-00 0.165209636 01 0,247306476 00 1 a.le90*332E 01 0.15500241E-00 0,67105263E 00 0,156508866 01 0,356026306-00 0.162930396 01 0,231006476 00 0.19»'.S979E 01 0.14179e94E-00 0,65789473E 00 0,159483986 01 0,344965406-00 0.171352006 01 0,21555543t 00 0.19991B45E 01 0.12952788E-00 0.644736846 00 0,162394656 01 0,333367026-00 0.180536746 01 0,200920086 00 0.20i'>282l.E 01 0.118136706-00 0.631578946 00 0,166243856 01 0,321390406-00 0.190663656 01 0,167068166 00 1
0,21099733E 01 O.1O757507E-00 0.61n42105E 00 0,168034846 01 0,309066006-00 0.201609696 01 0,17396632t 00 0.21663371E 01 0.97794ei6E-01 0,605263156 00 0,170770246 01 0,296497666-00 0.213470836 01 0,161590006 00 1 0.22236931E 01 0.88749O91E-01 0,59-10526E 00 0,173452826 01 0,263761326-00 0.226556126 01 0,149902226 00 0.22814205E 01 0.8039308SE-01 0,571947376 00 0,176064506 01 0,270930666-00 0.240866466 01 0,138678016 00 0.23kC2*80E 01 0.72691241E-01 0,56-478947E 00 0,176667226 01 0,256072916-00 0.256596136 01 0,128490276 00 0.24000691E 01 0.65597609E-01 0,55;63157E 00 0,181202826 01 0,24624916E-00 0.27364617E 01 0,116712166-00 0.2*610O31>E 01 0.59075452E-01 0.53"4736eE 00 0,18369322E 01 0,23261336E-00 0.292814696 01 0,109516426 00 0.23230581E 01 0,530891956-01 0.52^31579E 00 0,186139666 01 0,219916636-00 0.31370696E 01 0,100679336 00 0.25863 76<.t 01 0,476043976-01 0,51-157896 00 0.186643446 01 0,207512286-00 0.336756956 01 0,927766206 01 1 0.26510703E 01 0.42688033E-01 0,50^000006 00 0.190905606 01 0,195336366-00 0,362231236 01 0,651844306 01
0.271726'.0E 01 0.3e0ü8709E-0l 0,46o64210E •00 0.193227846 01 0,163426716-00 0,390442566 01 0,780797436-01 1 O.2765077eE 01 0.33836244E-01 0,473684216 ■00 0.195610766 01 0,17181464E-00 0,421752966 01 0,714391756-01 1 0.285«660<.E 01 0,3OO«2O33E-01 0,46052631E -00 0,197755626 01 0,160530546-00 0,456582026 01 0,652405496 01 0.2926168»E 01 0,26598955E-01 0,447368426 -00 0,19996343E 01 0,149597676-00 0,495419836 01 0,594622426 01 1 0.29998310E 01 0.234810346-01 0,43421052E -00 1 0,202135336 01 0.139034996-00 0,538847366 01 0,540825576-01 1 0.307567146 01 0.206643956-01 0,42105263E -00 0,204271936 01 0,12886234E-00 0,667530406 01 0.490824446 01 0.316396»'.E 01 0.iai26211E-01 0,40769473E -00 O.20637390E 01 0,11909416E-00 0,64226156E 01 0.444425046 01 1 0.32349379E 01 0.1584481BE-01 0,394736e4E •00 0,206441916 01 0,109741706-00 0,703961166 01 0,401438636 01 1 0.33189549E 01 0.13799469E-01 0,3ei57894E -00 0,2104 76936 01 0,100611376-00 0,773824636 01 0,361574656 01 0.34039 844E 01 0.11971378E-01 0.368421056 -00 0,212479136 01 0,92311291E-01 0,86311606E 01 0,324967436 01
0.36964735E 01 0,103«2564E-01 0,355263156 -00 0,214448846 01 0,842467716-01 0,943459516 01 0.291151016 01 1 0.35907775E 01 0,88960221E-02 0,342105266 -00 0,216386446 01 0,76615e95E-01 0,104678626 02 0.260061676-01 1 0.36892678E 01 0.76158877E-02 0,328947376 -00 0.218292136 01 0.694213366-01 0,116644776 02 0.231544466-01 1 0.379Z5040E 01 0,646696426-02 0,316789476 »00 0.220166576 01 0,626569606-01 0,130235606 02 0.205439606-01 0.39009852E 01 0,549517186-02 0,302631576 ■00 0.222010266 01 0.563165416-01 0,146111636 02 0,181596466-01 1 0.40153336E 01 0,462743016-02 0.2894736eE -00 0,22382376E 01 0.503925006-01 0,164622036 02 0,159871536-01 0.41358662E 01 0,387196446-02 0.276315796 -00 0,22560647E 01 0.44879864E-01 0,18631495E 02 0,140141266-01 1 0.42646277E 01 0,3216859eE-02 0.26315789E -00 0,227360296 01 0.397619566-01 0.211931036 02 0,122252036-01 0.42913955E 01 0.3O969311E-02 0.260526316 -00 0,227707716 01 0.387645026-01 0,217604166 02 0,118663166-01 1 0.43165227E 01 0,298ü6H5E-02 0.26789473E ■00 0.226054036 01 0.376221666-01 0,223480086 02 0,115561606-01 1
1
H
3R
53
TABLE IV.- FLOW PROPERTIES OF CgH^-AIR COMBUSTION PRODUCTS - Concluded
("b) Req = 0.7; Tt = 1,900° K; T* = 1,678.6° K - Concluded
to«
1 - 1 P/Pt T/Tt VH «/Pt A/A« PJOt 0.<.3'.601B*E 01 0.2e675220E-O2 0>2äS26316E-00 0.22839926E 01 0.36874896E-01 0.22956812E 02 0.11234636E-01 o.myaizoE 01 0.27578e66E-02 0.2S263157E-00 0.22874341E 01 0.35942540E-01 0.23667804E 02 0.10917649t-01 0.<>«021»61E 01 0.26516297E-02 0.25000000E-00 0.22908649E 01 0.35025008E-01 0.24242027E 02 0. 10607105E-01 0,«<.30ei87F 01 0.25»83770E-02 0.24736842E-00 0.22942850E 01 0.34122194E-01 0.24920677E 02 0.103O29O7E-01 0.'><>>9a9i:E 01 O.2»'.83560E-02 0.24473«84E-a0 0.22976945E 01 0.33233999E-01 0.25624616E 02 0.10004965E-01 0.44893661E 01 0.23513953E-02 0.24210626E-00 0.230I0936E 01 0.32360318E-01 0.26365375E 02 0.97131883E-02 0.<>51931«2E 01 0.22574246E-02 0.23''47368E-00 0.23044822E 01 0.31601046E-01 0.27114155E 02 O.94274B60E-02 1 0.'.5'.96eB0E 01 0.216637I.9E-02 O.238e4210E-O0 0.2307e604£ 01 0.30666078E-01 0.27902340E 02 0.91477672E-02 0.<.S772097E 01 0.207B44e'.E-02 0.23'-21052E-00 0.23112179E 01 0.29828911E-01 0.28717B01E 02 0.8e75099iE-02 1 0.<.608b69U[ 01 0,19933344E-02 0.23\57895E-00 0.23145633E 01 0.29O16300E-01 0.29664783E 02 0.86083811t-02 1
0.'>6'>0<>S27E 01 0.191O9076E-02 0.22394736E-00 0.23178992E 01 0.28217331E-01 0.30446724E 02 0.83472694t-02 0.46729672E 01 0.ie310998E-02 0.22-31579E-00 0.23212269E 01 0.27431829E-01 0.31362475E 02 0.e0916684t-U2 0t47060393E 01 0.1753e462E-02 0.22i6S421E-00 0.232..5436E 01 0.26669630E-O1 0.32317016E 02 0.7e414491E-02 0.»7397161E 01 0.16790795E-02 0.22:.05262E-00 0.23278526E 01 0.259O0673E-O1 0.33311471E 02 0.75965426t-02 a.<>77«0162E 01 0.1606740&E-02 0.21o4210bE-00 0.23311534E 01 0.25154503E-01 0.34348106E 02 0.73568455E-02 0.<>8089J8SE 01 0.1S367672E-02 0.21i78947E-00 0.23344461E 01 0.24421276E-01 0.36429352E 02 0.71222665E-02 0«<*84AS624E 01 0,14691004E-02 0.213l57fl9E-00 0.73377311E 01 0.2370074I.E-01 0.366578ieE 02 0.63927171E-0? O.'.ÖHOH'.Hfaf; 01 0.14O36826E-02 O.210e.2631E-0O 0.23'.10086E 01 0.22992774E-01 0.37736299E 02 0.66681127E-02 0.491783B6E 01 0.13404577E-02 0.207a9474E-00 0.23442791E 01 0.22297239E-01 0.3e967B04E 02 0.644e3712t-02 0.49555549E 01 0.12793709E-02 O.20526315E-0O 0.23475428E 01 O.2I6140O7E-01 0.40265664E 02 0.62334124E-02
0.49940207E 01 0*122036e8E-02 0.20263158E-00 0.23507998E 01 0.209429*1E-01 0.41603066E 02 0.6C23l596t-02 0,6U332603E 01 0.11633996E-02 0.20000000E-00 0.23640607t 01 0.202839fl6E-01 0.'.3014036t 02 0.tei76389L-02 0.50732993E 01 0.110e4121E-02 0.19736842E-00 0.23672966E 01 0.19636970E-01 0.44i.92646E 02 0.66164774E-02 o.-jii'.iDi.-i: 01 0.10553672E-O2 O.194736B4E-00 0.23606347E 01 0.19001807E-01 0.46042963E 02 0.54199067E-02 0.51558837E 01 0.10041862E-O2 0.19210526E-00 0.236376B4E 01 0.18378398E-01 0.'.7669981E 02 0.5227766eE-02 0.519e»863E 01 0.954e6204E-03 0.1B947368E-00 0.23669971E 0 1 0.17766644E-01 0.49378739E 0? 0.60399664E-02 0.52'.2002eE 01 0.90730853E-03 0.186e4210E-00 0.23702209E 31 0.17166457E-01 0.61174764E 02 0.43564691E-02 0,5286»666E 01 0.86161052E-03 Ü.18421052E-00 0.23734401E 01 0.16577746E-01 0.63064059E 02 0.45772063E-02 0.533e2670E 01 0.81718349E-03 0.18157e94E-00 0.23766723E 01 0.16996151E-01 0.5506827eE 02 0.»5OO3494t-02 0.938<>6329E 01 ■0.77449667E-03 0.17e94737E-00 0.23799033E 01 0.15425373E-01 0.57183574E 02 0.43284722E-02
0.5'.319179E 01 0,73345955E-03 0.17631S.78E-00 0.23831299E 01 0.14866310E-01 0.69414466E OJ 0.41603068t-02 1 ü.i".eüi569F 01 0a69403318e-03 0.17368421E-00 0.23B63616E 01 0.14318963E-01 0.(,17(!e999t 02 0.39963204t-02 1 0.55293863E 01 0.65617674E-03 O.1710S263E-O0 0.23Ö96684E 01 0.13783329E-01 0.64266902t 02 0.3S3647B6t-02 I 0,55796«'.7E 01 0.61985760E-03 0.16S42105E-00 0.23927802E 01 0.13259403E-01 0.66ea4661E 02 0.36a07469£-02 1 0.56309729E 01 0.!>85O3125E-03 0.16578947E-00 0.23959e68E 01 0.12747169E-01 0.69666690E 0 2 0.35290881£-02 0.56834139E 01 0.55166136E-03 0.163157B9E-00 0.23991B81t Ci 0.12246609E-01 0.72609947E 02 0.33814648t-02 0.57370132E 01 0.51970974E-Ü3 0.16062631E-OÜ 0,24023840E Cl 0.11767696E-01 0.75729977E 0 2 0.32378373t-02 0.67916191E 01 0.48913851E-03 0.15789473E-00 0.24056742E :i 0.112a0401E-01 0.7903908aE 0 2 0.309ei664t-02 0.58478826E 01 0.45991000E-03 ü,15i526316E-00 0#24087688E Cl 0.!0ei4685E-01 0.82661912E 0 2 0.29624077t-02 0.59052679E 01 0.43198673E-03 O.15263157E-00 0.24119376E 01 0.10360605E-01 0.862B4509E 02 0.28305212E-02 1
O.S96«0023E 01 0.40533159E-03 0.15000ÜOOE-00 0.24161103E 01 0.9917B133E-02 0.90264474E 02 0.27024619£-02 I3.60241771E 01 0.37990776E-03 0.14''3(.842E-00 0.24182770E 01 0.94a66671£-02 0.94481130t 0 2 0.26781853t-02 1 0.60868473E 01 0.355)67e72E-03 0. 14473&84E-00 0.24214374E 01 0.90666766E-02 0.939a6783E 02 0.24576462t-02 0.&1'>90820E 01 0.3326Ü83&E-03 0.i4rl0526E-00 0.24246914E 01 0.a6681068E-02 0.10379ia6E O;, 0.23407950t-02 0.62139»0E 01 0.31O&6081E-O3 0.13"47368E-00 0.24277390E 01 0.82607788E-02 0.1089252aE 03 0.22276866t-02 0.62805448E 01 0.289e0072E-03 0.13f.e4210E-00 0.24308799E Cl 0.78746ia6E-02 0.11441467t 0 3 0.21179714E-02 0,63'>S9360E 01 0.269993Ü1E-03 0.13i21052E-00 0.24340142E 01 Q.7A996467E-02 0.12029176E 03 0.20118996t-02 0.6<>192183E 01 0.2512O310E-O3 0.13'.b7e94E-00 0.24371415E .11 0.71364751E-02 0.12659180E 03 0.19093211E-02 1 0.649H.885E 01 0.23339684E-03 0,12^94736E-00 0,24402620E 3! 0.67823ie7E-02 0.13335398E 03 0.13101846E-02 0.6S658496E 01 0.21654049E-03 0.12l'.31679E-00 0.24433763E 01 0.64399816E-02 0.14062200E 03 0.171443e3£-02
0.66»2'.132E 01 0.20060081E-03 0.12Ü68421E-00 0t2446 4814E 01 0.61083660E-02 0.14844466E 03 0.16220297E-02 1 0.672129e5E 01 0.1B554500E-03 0. 12i0&263£-00 0.24495801E 01 0.578736a5E-02 0.15687664t 03 0.16329056t-02 (1.68026347E 01 0.17134078E-03 0.11842106E-00 0.24626714E 01 0.54768B09E-02 0.16597926E 03 0.14(,70121E-02 0.&8eb!i&09E 01 0.1S796831E-03 0.1157B947E-00 0.24667661E 01 0.61767931E-02 0.17582160E 03 0.13642960t-02 0.6973227'.E 01 0.14536034E-03 0.1131i>789E-00 0.24688311E 01 0.48869883E-02 0.18648124E 03 0. 12846991E-02 0.70627972E 01 0.133b2211E-03 0.110i2631E-00 0.2461Ö994E 01 0.'.6073467E-02 0.19804648t 03 0.12081695t-02 0.7155»'.70E 01 0.12241139E-03 0.107e9473E-00 0.24649698E 01 0.43377462E-02 0.21061704E 03 0.11346601E-02 0,72513688E 01 0.11199851E-03 0.1062631bE-00 O^iöBüliOt 01 0.407aü66'4E-02 0.22430646E 03, 0.l0640a4Bt-02 1 0.73507720E 01 0.10225433E-03 0. 102631&8E-00 0.24710663E 01 0.38281486E-02 0.23924430E 03 0.99641693E-03 1
Ik
TABLE V.- FLOW PROPERTIES OF CH^-AIR COMBUSTION PRODUCTS
Letter E denotes that number to left of E is to be multiplied by 10 to the power Indicated by number to right; for example,
0.10V79973E 01 = 0.101+79925 X 101]
(a) Rgq = 1.0; Tt = 2,200° K; T* = 1,969.1° K
p/i>t T/Tt V/H '"t A/A« »/"t
0.»5<.2119*E-00 0.557866&9E 00 ü.6<i60S930E 00 0.72»t0299E 00 0,79635032E 00 0.(16305806t 00 0.92593609E 00
0.98677103E 00 0.i04315«7E 01 0.1098S625E 01 0.115229B3E 01 0.120*6519E 01 0.1255e533E 01 0.13061035E 01 0.13555'>e6E 01 0.14043356E 01 0.1'.525a87E 01
0.1500<i28SE 01 0,15'>79290E 01 0.15951881E 01 0.16*22873E 01 0.168931908 01 0.17363139E 01 0.17833509E 01 0.1B301.919E 01 0,18778231E 01 0.19253296E 01
0.1973093eE 01 0.20211688E 01 0,20696<>18E 01 Ca211846B5E 01 0.21677390E 01 0.22175008 01 0.2267808'.E 01 0.2316729bE 01 0.237031'.5E 01 0.2'.226227E 01
0.2'.757e»3E 01 0.25296669E 01 0.258'>'il22E 01 0«26'.00854E 01 0,2696716*.E 01 0.275'.4916E 01 0.2813'.'.85E 01 0.28736766E 01 0.29352937E 01 0.29983395E 01
0.30629507E 01 0.31292*67E 01 0.31974963E 01 0.32674368E 01 0,33393e33E 01 0.3'*13*i960E 01 0.34899'.69E 01 0.35689^.598 01 0.36507087E 01 0.3736*81'.E 01
0.38236051E 01 0.39151945E 01 0.40106788E 01 0,4110**998 01 0."■21493708 01 0.43247030E 01 0.444031958 01 Ü.45624713E 01 0,469144998 01 0.482968578 01
0.09999999E 01 0.93925402E 00 0.882068128 00 0.82821533E 00 0.77749030E 00 0.729700B6E 00 0,684667848 00 0,642230288 00 0.60222399E 00
0.56450021E 00 0.52892207E 00 0,49535378E-00 0,463690308-00 0,43382770E-00 0.40566651E-0C 0,37911163E-00 0.35407785E-00 0,33048386E-00 0.30825257E-00
0.287309 0.267589 0.249027 0.231562 0.215135 0.199696 0.185191 0.171575 0,158799 0.146822
91E-00 38E-00 14E-00 47E-00 e4E-00 76E-00 86E-00 76E-00 95E-00 65E-00
0.135602908-00 0.125101238-00 0.11527887E-0C 0.10610U8E-00 0.97534245E-01 0.39545276E-01 0.Ü2103066E-01 O.75177081E-O1 0.68738278E-01 0.62758942E-01
0,57211502E-01 0,520723718-01 0.47318092E-01 0,429258848-01 0.388744038-01 0,361419038-01 0,317080368-01 0.286536618-01 0,256600438-01 0.230103258-01
0.205879958-01 0.183774428-01 0.163633558-01 0,146326148-01 0,12e71936E-01 0,113691418-01 0,100123628-01 0,879021938-02 0,769208228-02 0,670791048-02
0,582821568-02 0.604422398-02 0.434766058-02 0.373076348-02 0,318631798-02 0.27o76019E-ü2 0,22880080E-02 0,192l9989E-02 0.16042613E-02 0.132947728-02
0.09999999E 01 0.98863636E 00 0.97727273E 00 0.96690909E 00 0,954549458 00 0.943181818 00 0.931818188 00 0.92045454E 00 0.90709091E 00
0.89"72727E 00 0.a8'i36363E 00 0.S7'*00000E 00 0.36-636368 00 0.85.-'27273E 00 0.84-I90909E 00 0.82"54646E 00 0.81i>18181E 00 0.80u81818E 00 0.79345454E 00
0.78409091E 00 0.77272727E 00 0.76136363E 00 0.760000008 00 0.738636368 00 0.72727273E 00 0.715909098 00 0.70454646E 00 0.693iei81E 00 0.68181BieE 00
0,b7046464E 00 0.659090918 00 0.647727278 00 0.636363638 00 0.626000008 00 0.613636368 00 0.60227273E 00 0.59090909E 00 0,579546468 00 0,568181818 00
0,656818188 00 0,545464648 00 0,53409091E 00 0.52272727E 00 0.511363638 00 0,500000008 00 0,48r.636368-00 0.477272738-00 0.46^909098-00 0.45^645458-00
0.44 118181E-00 0,43:818188-00 ü,42w46454E-00 0,40909091E-00 0,39/72727E-00 0,36636363E-00 0,376000008-00 0,363636368-00 0,362272738-00 0.340909098-00
0.329545458-00 0,318181818-00 0,306818188-00 0,296454548-00 0,284090918-00 0.272727278-00 0.261363638-00 Ü.260000008-OC 0.238636368-00 0.227272738-00
0.3ie72664E-00 0.449696948-00 0.5*9517888 00 0.633127868 00 0.70633470E 00 0.77212B33E 00 0.83228403E 00 0.88798021E 00
0.9400357BE 00 0.989O48608 00 0.10364847E 01 0.1O796BO1E 01 0.11219089E 01 0.11623970E 01 0.120133398 01 0.123887258 01 0.12751***8 01 0.131026308 01
0.13443288E 01 0.13774243E 01 0.14096231E 01 0.144099098 01 0.14715900E 01 0.15014676E 01 0.15306679E 01 0.155923178 01 0.15B71992E 01 0.16145996E 01
0.16414607E 01 0.1667ao94E 01 0.16936728E 01 0.17190693E 01 0.174401778 01 0.176863578 01 0.179263918 01 0.181634458 01 0.1B3966678 01 0.186261978 01
0.188622108 01 0.190747618 01 0.19293926E 01 0.196097838 01 0.197223838 01 0.199318388 01 0.201382398 01 0.203416688 01 0.206422108 01 0.207399268 01
0.20934872E 01 0.21127110E 01 0.21316746E 01 0.21603761E 01 0.216881668 01 0.21869981E 01 0.220492168 01 0.222259048 01 0.224000768 01 0,225717528 01
0,227409728 01 0,229077428 01 0.230720778 01 0.232339968 01 0.233935048 01 0.235606368 01 0.23705421E 01 Ü.23867881E 01 0.240079628 01 0.241557928 01
0.592069eiE-01 0.111996098-00 0,15890032E-00 0,200404468-00 0.23695260E-00 0.268952908-00 0.296774868-00 0.32077403E-00
0.3*126* 0.358637 0.372866 0.38**71 0.393601 0.400466 0.405228 0.408098 0.409233 0.408788
B9E-00 30E-00 87E-00 13E-00 288-00 008-00 208-00 688-00 498-00 21E-00
0.406.90456E-00 0.40372410E-00 0.39936978E-00 0.39396892E-00 0.3fl769912E-00 0.38039670E-C0 0.37244616E-00 0.36383791E-00 0.35465590E-00 0.34498314E-00
O.33439367E-0O 0.324467638-00 0.31373B70E-00 0.30279914E-00 0.29169766E-00 0.28048762E-00 0.26921868E-00 0.26793753E-00 0.2466B603E-00 0.23549951E-00
0.224412e8E-00 0.213461B6E-0O 0.20267795E-00 0.192088898-00 0.181721608-00 0.171594498-00 0.161726698-00 O.15213110E-00 0.14282329E-00 0.13381682E-00
0.12611805E-00 0.1 1673780E-00 0.10867840E-00 0.1OO948O8E-0O 0.9356ie93E-01 0.86492167E-01 0.797700378-01 0.73383772E-01 0.67330632E-01 0.616067308-01
0.562066028-01 0.611249198-01 0.463650528-01 0.418893928-01 0.377199868-01 0.33837225E-01 0.30231311E-01 0.268921888-01 0.238119708-01 0.209761348-01
195532468 01 1*68*4648 01 12561180E 01 114751268 01 10B273678 01 104276658 01 101863328 01 1006489*8 01
10O06210E 01 100197*68 01 100873018 01 10200109E 01 10363199E 01 10543217E 01 107660608 01 11026*318 01 113177908 01 116*21608 01
120001*38 01 12392*318 01 12820390E 01 132856798 01 13790*208 01 1*3368538 01 1*9276738 01 156669708 01 16266*028 01 169996668 01
178031668 01 186707628 01 19608071E 01 20621118E 01 21716586E 01 229020198 01 241858398 01 25677**68 01 270875578 01 287261608 01
132168 01 572948 01 770208 01 912738 01 20860E 01 90776E 01 288908 01 67063E 01 42216E 01 95439E 01
6077*8*0E 01 66735B20E 01 712***67E 01 7737307*8 01 8*2061368 01 918*28008 01 100398418 02 110010188 02 12083988E 02 13307934E 02
146958668 02 16276080E 02 18078531E 02 20146210E 02 22626682E 02 262802548 02 28481589E 02 322239868 02 366212698 02 4182B217E 02
0.099999998 01 0.960268028 00 0.902959678 00 0.867958928 00 0.816136618 00 0.77*365068 00 0.735533778 00 0.698636908 00 0.663281668 00
0.6296630*8 00 0.697691638 00 0.666970018 00 0.6377*8098 00 0.50986*918 00 0.483226968-00 0.457801898-00 0.433628068-00 0.410353168-00 0.3ea22793E-O0
0.367102098-00 0.3*69*0118-00 0.327698568-00 0.309338*08-00 0.291819598-00 0.275111658-00 0.269182618-00 0.2**001208-00 0.229635398-00 0.216761338-00
0.202652 0.190182 0.178325 0,167060 0.166363 0.14621* 0.136691 0.127*7* 0.1188*1 0.11067*
198-00 408-00 908-00 298-00 868-00 768-00 858-00 548-00 978-00 348-00
0.10296052E-OO 0.9666*9*18-01 0.887709118-01 0.822816018-01 0.761716088-01 0.70*229128-01 0.650191658-01 0.599»»62*8-01 0.551836018-01 0.607222*18-01
0.465*62488-01 0.426419118-01 0.3699*8088-01 0.365938168-01 0.32*274098-01 0.294839268-01 0.267621608-01 0.242206898-01 0.218786788-01 0.197152798-01
0.177204458-01 0.158844958-01 0.1*1980608-01 0.126520698-01 0.112379308-01 0.99*706098-02 0.877136138-02 0.77O31393E-02 0.673681958-02 0.586122288-02
H
55
TABLE V.- FLOW PROPERTIES OF CH^-AIR COMBUSTION PRODUCTS - Continued
(a) Re(1 = 1.0; Tt = 2,200° K; T* = 1,969.1° K - Concluded
0,465846636 01 0.488764S2E 01 0.A9172361E 01 0.»9»72»«7C 01 0.«97769'.2E 01 O.S00896<>3E 01 0.50399310E 01 0,50717'i73E 01 0.51040459E 01 0.5136a<>01iE 01
C.S1663169E 01 a.S2002161E 01 0.523*73'>9E 01 0.5269«907E 01 0.53057024E 01 0.5342ia86E 01 0.5379370'.e 01 0.5<.172675E 01 0.5I.559022E 01 0.5'.96297;t 31
0.!>ä35'.7L>,t 01 0.54764631^ Ü1 Ü.66182846E 01 J,i660967^E -1 ;J.57045392E Ul 0.5749029-,t 01 C.5794470JE ul u.5640892oE ..1 w58683SüiE Jl i,.593682-Cd .1
0.59940V0VE 01 J.6044674iE Ul v,60962651E «1 J,61489022E ^1 J.62C26253E Jl
J.6^57477VE .1 1.63135034E Ul C.63707501E 01 «,64292660E 01 ^•64891ü9eE 01
0.65503322E 01 Ü.&6129944E 01 0.66,,71600E 01 0,67428962E 01 0.68102745E 01 0.6e793711E 01 0.69502673E 01 0.70230497E 01 0.7097aillE 01 0,717465ü7E 01
Ü.72536748E 01 0.73349971E 01 0.74187405E 01 0.75050365E 01 0.75940274E 01 0.76858660E 01 0.77807184E 01 Ü.78787640E 01 C.79801977E 01 0.e0852312E 01
0.819409b2E 01
P/Pt
0.12792696E-02 0.12305379E-02 0.11832779E-02 0.11374462E-02 0.10930094E-02 0,104993S4E-02 0.10081924E-02 0.96774911E-03 0.928574e4E-03 0.89063957E-03
0.854O3U83E-C3 0,aia61375E-03 0.7843336CE-03 0.76116111E-03 0.71906762E-!J3 0.6880252iE-J3 C.65800697E-C3 ^.t2üVä65';E-v3 u.oOi,93e51E--3 0.137383782E--3
D,54766CJ5E-v-,3 -.■J2238246E-;-3 c.*v7«aiiac-03 ,.47»4341i£-03 -.4517194(E-C3 ..'.2vei59iE-i.3 -.'.■-87C274E-03 ..38d3396^E-03 C.i6d76b81E-03 C • 3499Ü49:E-C3
^.331651i;..E-03 -.31408262E-1.3 v.2972C54oE —3 u.26100241E-^3 C.26545711E-03 -.25I.55311E-03 J.i36273aoE-03 0.t'2260300E-03 C.20952439E-03 C.1970216CE-03
0.18507858E-03 0.17367933E-03 G.16280800E-03 0.152448eiE-03 0.14258617E-03 0.13320462E-03 D.124288a7E-03 0.115e23eCE-03 0.10779445E-03 O.1O018607E-O3
C.929a4091E-04 0<a6174139E-04 0.79742057E-04 0.73673906E-Ü4 0.67955940E-04 0,62574684E-Ü4 0.57516854E-04 O.52769422E-04 G,483l960eE-04 0.441548blE-04
0.40262891E-04
T/Tt
0,22499999E-C0 0.22272727E-OO 0.22045464E-00 0.218ieieiE-00 0.21590TO9E-00 0.21363636E-00 0.2U3t3&'.E-00 0,209C9090E-00 0.;068181eE-00 0.20454645E-00
0.2022727;E-00 3#2G','0000GE-00 0.19,72727E-00 0.19><45465E-00 0,19-iaiaiE-oo 0.19''90909E-00 -.18-.6363eE-00 C.19C.36363E-00 J.ie-.09090E-00 0« 181bl818E-0Q
0.17944b4tE-00 G.17727272E-00 (■.17500OOCE-00 G.1727272(E-00 'J»17045454E-00 -.'. 68181B1E-00 C.16i90909E-00 0.16363636E-00 0.16136363E-00 0.1590909IE-0O
u.l56ai818E-00 0.15454545E-00 0.15227272E-00 0.150OO0O0E-O0 0.14772727E-00 0.14545454E-00 0.14318ia2E-00 C.i4090909E-00 0.13863636E-00 0.13636363E-00
0.13409O91E-OO 0.13181818E-00 0.12954645E-00 0.12727273E-0O 0.12500000E-00 C.12.,72727E-00 0.12J45464E-00 o.ii'-.ieie2E-oo 0.11^90906E-00 0.11->63636E-00
0.1l\36363E-OO Ü.10909090E-00 0.10C>818ieE-00 0.10..64545E-00 0.10.':27273E-00 0,99999999E-01 0.97727273E-01 0.95454645E-01 0.93iaiB17E-01 0.909090'nE-Cl
0.88636363E-01
V/H
0.24ie5102E 01 0.24214327E 01 0.24243468E 01 0.24272526E 01 0.24301501E 01 0.24330395E 01 0.243592O7E 01 0.243a7936E 01 0.244165886 01 0.244451606 01
0.244735586 01 C.24501864E 01 0.24530096E 01 0.24558257E 01 0.24586351E 01 0.2461438rE 01 0.2464234eE 01 0.24670255E 01 0.2469al05E 01 0.24725901E 01
0.24753645E 01 0.247813406 01 0.248089886 01 0.24a36592E 01 0.248641556 01 0.24a91677E 01 0.24919164E 01 0.24946617E 01 0.24974036E 01 0.2500142eE 01
0.25028952E 01 0,250564816 01 0.250a3978E 01 C.25111445E 01 0.25138a79E 01 0.25166276E 01 0.251936416 01 0.25220966E 01 0.25248253E 01 0.25275499E 01
0.253027O4E 01 0.25329866E 01 0.25366984E 01 0.253a4057E 01 C.254110816 01 0.25438056E 01 0.25464986E 01 0.254918626 01 0.2551B6a6E 01 0.25545456E 01
0.25572171E 01 0.2559a830E 01 0.25625432E 01 0.25651975E 01 0.256784566 01 0.257048806 01 0.25731239E 01 0.25757536E 01 0.257e3767E 01 0.258099326 01
0.25636030E 01
«P.
204371946-01 199074526-01 •9386aieE-01 188752006-01 183725116-01 178786646-01 173935716-01 16917146E-01 164493026-01 159899546-01
15541029E-01 15100683E-01 14668376E-01 142439926-01 13827414E-01 134185266-01 130172296-01 12623413E-01 122369816-01 118578356-01
11465 11121 10763 10412 10068 97310 94005 90766 67693 84465
8876-01 044E-01 2226-01 3406-01 siae-oi eiiE-02 5796-02 7656-02 7196-02 7a3E-02
ai417e45E-02 784110756-02 754704336-02 725956046-02 697870446-02 670439796-02 643663726-02 61753975E-02 592065026-02 567236366-02
543050266-02 519502676-02 496590166-02 474307566-02 45265052E-02 431613916-02 411192546-02 39138065E-02 372172976-02 353562866-02
33554422E-02 31811046E-02 30125479E-02 28497022E-02 26924944E-02 2540a507E-02 23946943E-02 22539468E-02 21185263E-02 19e63565E-02
0.1B633478E-02
A/A*
429e3340E 02 44160459E 02 454215296 02 467086086 02 48043a79E 02 494296556 02 508663796 02 523626346 02 53915172E 02 555289096 02
571993216 02 589353766 02 607422236 02 626237636 02 645642536 02 666261136 02 «87601816 02 70985612E 02 733099376 02 757391086 02
78279521E 02 609380526 02 837221306 02 866397446 02 69699543E 02 929108756 02 962836336 02 996293666 02 103559346 03 107486686 03
111659726 03 116066996 03 120723676 03 125641686 03 130641236 03 136342986 03 142169166 03 148344156 03 154894346 03 161848736 03
169239036 03 177100006 03 185*69766 03 194390306 03 20390776E 03 214073126 03 224942656 03 236576686 03 249050316 03 26243431E 03
27661619E 03 0 292291246 03 0 30696612E 03 0 32696026E 03 0 346407B8E 03 0 36746000E 03 0 39028715E 03 0 415082376 03 0 442064586 03 0 471483226 03 0
0.503622936 03
5»967977E-02 553574706-02 53780195E-02 522356446-02 507233186-02 49242727E-02 47793388E-C2 463748266-02 449865676-02 436261526-02
42304920E-02 410115166-0? 397455666-02 385072056-02 372956466-02 361104096-02 349510116-02 336169646-02 32707877E-02 31623251E-02
305626886-02 29525777E-02 265121226-02 27521345E-02 26553079E-02 25606965E-02 246626636-02 23779639E-02 22»9ei73E-02 22O37350E-O2
211904226-02 20363040E-02 19556419E-02 18770397E-02 180048026-02 17259*566-02 165341746-02 156287586-02 151*30066-02 1**767116-02
138296606-02 132016286-02 12592392E-02 120017166-02 11*2936*6-02 10B75090E-02 103386*7E-02 981978116-03 931823336-03 88337*186-03
636603956-03 791*85676-03 747991936-03 706095106-03 66576700E-03 626979496-03 569703926-03 553911516-03 519573376-03 48666025E-03
0.455142826-03
56
TABLE V.- FLOW PROPERTIES OF CH^-AIR COMBUSTION PROHJCTS - Continued
(b) Req = 0.7; Tt = 1,900° K; T* = 1,678.7° K
! ^ rJH I/Tt *K '/*t A/A* P/Pt I
Oa 0.09999999E 01 0.09CI99999E 01 0. 0. 0. 0.09999999t 01 1
O.32109787E-OO 0.93754268E 00 0.98o84210E 00 0.31911445E- 00 0.60867B75E-01 0.1944312eE 01 0.95005909E 00 1
0•456&47^4E-0Ü 0.87843052E 00 0.97368421E 00 0.46089149E- 00 0.11539616E-00 0.14490671E 01 0.90219977E 00 1
p.A6216787E 00 0.62252496E 00 0.960b2631E 00 0.66170766E 00 0.16399109E-00 0.12476609E 01 0.B5636253E 00 1
0.6&273763E 00 0.76966388E 00 0.94736842E 00 0.63647024E 00 0.20706444E-00 0.11399357t 01 0.61246519E 00
0.7339Z2O3E 00 0.71969981E 00 0.93421052E 00 0.71095433E 00 0.24499729E-00 0.1076iee2E 01 0.77043020t 00
0.80862929E 00 0.67249451E 00 0.92105263E 00 0.77ei230'.E 00 0.27814776E-00 0.1037481BE 01 0.7301B760E 00
0.87839&38E 00 0.62791334E 00 0.90789473E 00 0.83974269E 00 0.306e5«lE-00 0.10148926E 01 0.69166676E 00
0.94493074E 00 0.58583426E 00 0.B9473684E 00 0.a969b764E oo 0.33143866E-00 0.10036366E 01 0.654B0915t 00 1
0.10OB4242E 01 0.^461386&E 00 0.881S789kE 00 0.96056b39E 00 0.35219872E-00 0.10009261E 01 0.61955407E 00 1
0.10696S07E 01 0.5O871235E 00 0.8684210SE 00 0.100n479E 01 0.36942167E-00 O.lOObOiOBE 01 0.58564306t 00 1
0.11290588E 01 0.47344424E-00 0.e!)626315E 00 0.10491476E 01 0.3e337B14E-00 0.1014aB5bE 01 0.5&361722E 00 1
0.1186963&E 01 0.44023228E-00 0.84210526E 00 0.10949029E 01 0.39432399E-00 0.10297463t 01 0.52282624E 00 1
0.12436561E 01 0.40897737E-00 0.82B94737E 00 0.113B6846E 01 0.<.0250091E-O0 0.10491665E 01 0.49341844E-00 1
0.12993iB7E 01 0.3795840'.E-00 0.8157e947E 00 0.11B07127E 01 0.4081379SE-00 0.1072B6b0£ 01 0.46334375L-00
0.13542663E 01 0.35196014E-00 0.80263167E 00 0.12211698E 01 0.41146151E-00 0.Ii00690b£ 01 0.43a65287E-00
0.1408S440E 01 0.32601862E-00 0.78947368E 00 0.12602065E 01 0.41264654E-00 0.11326e64t 01 0.41300014E-00
0.14623316t 01 0.30167560E-00 0.77631579E oo 0.12979508E 01 0.41191621E-00 0.11685766E 01 0.3BB64030t-00 1
0.15157i8eE 01 0.278a5047E-00 0.763157fl9E 00 0.13346126E 01 0.40944296E-00 0.12087bl6E 01 0.36542945E-00 1
0.1S6894eOE 01 0,26746531E-00 0.7iO00000E 00 0.13699872E 01 0.40J39B36E-00 0.12632634E 01 0.34332415E-00 1
0.162198!>1E 01 0.23744692E-00 0.73684210E 00 0,14044660E 01 0.39994497E-00 0.13023141E 01 0.32228446E-00 1
0.16749739^ 01 0.172800ä4E Cl
0.21872462E-00 0.72368421E 00 0.14379904E 01 0.39323650E-00 0.1356160bE 01 0.30227076E-OO
0.20123060E-00 0.71O52631E 00 0.14706636E 01 0.38541353E-00 0. !41f,1136E 01 0.2b324451E-00 1
0.17811822E 01 0.184e9B67E-00 0.69736842E Ü0 0.1i025038E 01 0,37661306E-00 0.14795446t 01 O.265167O9t-0O 1
0.18345410E 01 0.16966791E-00 0.6B421052E 00 0.15335887E 01 0.36696165E-00 0.1549a731E 01 0.24800372e-00
0.18e81792E 01 0.15547B90E-00 0.67I0i263E cc 0.15639521E 01 0.356i7B13E-00 0.16265e43E 01 0.23171984E-00
| 0.19421742E 01 0.14227459E-00 0.63789473E 00 0.15936340E 01 0.34657401E-00 0.17102333E 01 0.21628146E-00
0.19966121E 01 0.12999994E-00 C.644736B4E 00 0.16226713E 01 0.33405243E-00 0.18014564E 01 0.20165498t-00
0.20515455E 01 0,11860309E-0C 0.63157B94E 00 0.16510954E 0] 0.32211102E-00 0.19009664E Cl 0.ie780910E-O0 1
0,21070615E 01 0.10803409E-00 0.61II42105E 00 0.16789357E 01 0.30984005E-00 0.20095756E 01 0.17471284E-00
0.216323e9E 01 0.98245>031E-01 0.60''2631!)E 00 0.17062190E 01 0.29732316E-00 0.21282069E 01 0.16233592t-00
0.22201672E 01 0,89ie9i26E-01 0.b9.-'10526E 00 0.17329716E 0] 0.28463667E-00 0.22579201E o; 0.15064796E-00
0.22779090E 01 0.e0824607E-01 0.57M94737E 00 0.17592137E 01 0.271B5323E-00 0.23998933t 01 0.13962164t-00 1
0.23365229E 01 0.7310e734E-01 0.56-.78947E ÜÜ 0.17849649E 01 0.25903978E-00 0.25654716E 01 0.12922975t-00
0,2396U63E 01 0.66002056E-01 0.55.~b3157E CO 0.18102437E 01 0.246256e7E-00 0.27261925E 01 0. 11944347t-00 1
0.24S68308E 01 0.i9465B49E-01 0.53/47368E 00 0.18350697E 01 0.233557B9E-00 0.29138410t 01 0.11024143E-00
0.25ie6434E 01 0.53464773E-01 0.52«'131579E 00 0.18594551E 01 0.22099616E-00 0.31203894E 01 0. 101594i6E-00 1
0.25817075E 01 0,47964657E-C1 0.61316789E 00 C.18834126E 01 0.20861831E-00 0.33481189t Cl 0.93479621E-01 I
0.26461346E 01 0.42932306E-01 O.^ÜOOOOOOE 00 0,19069^44E 01 0.196'.6588E-00 0.35996t.61E o; 0.85B74047E-01 1
0.27120339E 01 0.38336883E-01 0.«.8681.2 10E -00 0.19300911E 01 0.1B4&7697E-00 0.367B0026E o; 0.7875485aE-01 1
0.27795647E 01 0.34148001E-01 0,4736e421E -00 0,1952e352E 01 0.1729B186E-00 0.41B6709BE 0! 0.72098263E-01
0.284a8597E 01 O.30337082E-01 0,«6052631E -00 0.19751982E Cl 0.16170860E-00 0.4529B664E 0! 0.65882059E-01 1
0,29200760E 01 0.26877083E-01 0.^4736862E -00 0.1997190bE Cl 0.1i078121E-00 0.49122459E 01 0.60084672E-01
0.29934424E 01 0.23742124E-01 ü,i.34210i)2E -00 0.i018B238t Cl 0.14021848E-00 0.!j33950<.9t 01 0.54664453E-01
0.30689833E 01 0.209Ü6411E-01 Ü,4210&263E -00 0.20401044E ■Jl 0.13004031E-00 0.SB181144E 0! 0.49662505E-01
0,31469733E 01 O.18353208E-O1 0.407e9473E -00 0.20610396E 01 0.12026097E-00 0.b3557869t 01 0.44999479E-01
0.322764Q7E 01 0.16054955E-01 0.3g473684E -00 0.20816363E 01 0.11089174E-00 0.69616704E 01 0.40676627E-01
0,33113547E 01 0.13992973E-01 0.38157e94E -00 0.21O19Ü5OE 01 0.10193903E-00 0.7646ai21t 01 0.36674970E-01
0.33980672E 01 0.12148626E-01 0.36842105E -00 0.2121B471E Cl 0.93411373E-01 0.a4240741t 01 O.3297e2O5t-01
0.348e2317E 01 0. 105040&i.E-01 0,35526315E -00 0.21414659E m 0.85313536E-01 0.930895B3E 01 0.295699ÖOE-01 1
0.35822029E 01 0.90423306E-02 0,34210526E -00 0.216076!>5E 01 0.776'.7014E-01 0.J0320263E 0.' 0.26434123E-01 [
0.36803231E 01 0.77477228E-02 0.32894737E -00 0.21797471E Cl O.70412332E-O1 0.114B0617E 02 0.23556479E-01
0.37832339E 01 0.66060129E-02 0.31578947E -00 0.21984184E 01 0.63604170E-01 0.12BlB36bt a: 0.20918009t-01 i
0.38914008E 01 0.56001471E-02 0.30263157E -00 0.22167B!,4E 01 0.57216biaE-01 0.143684bbt OS 0.18506723E-01
0.40054467E 01 0.472Ü0821E-02 0.289i.7368E -00 0.22348536E 01 0.51242172E-01 0.16174446E OS 0.16307402E-01
0,41256493E 01 0.39b31127E-O2 0.27631579E -00 0.22^26174E 01 0.45676970E-01 0. 182a9339t 0,' 0.14307965t-01
0.42541748E 01 0.32672922E-02 0.263157B9E -00 0.22700971E 01 0.40504166E-01 0.207Bt)123t 02 0.12492986E-01
0.42809010E 01 ü<31653152E-02 0.26052631E -00 0.22735602E Cl 0.39515475E-01 0.21337677E OJ 0.12150936E-01
0.43079Bä4E 01 0.30468764E-02 0.26769473E -00 0.2277012t.E 01 0.38541939E-01 0.21909925E 02 0.11815634t-01 I
37
TABLE V.-
(b)
FLOW PROPERTIES OF CHl^-AIR COMBUSTION PRODUCTS - Concluded
Req, = O.Tj Tt = 1,900° K; T* = 1,678.7° K - Concluded
\Q ON
1 - ^ P/Pt ! T/Tt V/H 1 »i*t .A« 1 D/0t
0.<>33»'><>6Se 01 0.293190'.0E-O2 1 0.2^526316E-00 0.2280<.i'.3E 01 0,37583160E-Ol 0.22502767E 02 0. 114e69e3E-'Ol| 0.436328&2E 01 0.282C315t.E- 2 0-25263157E-00 0.2283885. *.£ 01 0.36639340E-O1 0.23117164E 02 0.ni648e9E-01 1 0,'»39l5l*7E 1 0.27120378E- 2 O.250O00O0E-00 0.22B73061E 01 0.35710280E-O1 0.2375.4n8E 02 0.10S49260E-01 1 O-'i^JOlOSSE 1 0.26069966E- 2 0.2<t-'368A?E-00 1 0.22907161.E SI 0,34795B77E-01 0.24414701E 02 0.10539999E-01 0.<.'.'.91«9UI 1 0.260M192E- 2 0.24*736a'.E-00 0.229<.llb4E = 1 0.33896O33t-01 0.2bl00040L 02 0.10237017E-01 O.'.tTSÖSöSE 1 O.2'.0633'17E- 2 0.2*.riO&26E-00 0.22975061E 01 O.33O10652E-O1 0.«4611334E 0, 0.99402242E-02 1 0.<.50e5593E 01 0.23105725E- 2 O.23,'*t7368E-O0 0.2300Ba57t 01 0.32139628E-01 0.26549850L 02 0.96495305t-02 0.453B9102E 01 0.2217761.0E- 2 U.23^8'.210E-O0 0.230'.2i52E 01 0.31282866E-01 0.27316932E 02 0.9364B49SE-02 0.'.5663»77E 01 0.21281213E- 2 0.23-21052E-00 0.230760*.1E 01 0.30443987E-01 0.28110440E Ü, 0.90872B92E-02 1 0.<ib976a98E 1 0.20'.13250E-02' 0.231 S.789^E-00 0.23109H3E Ci 0.29619645E-O1 0.2B934!>62E »2 O.BBlb7135t-02 1
0.'.6295901E 1 0.19572<.7/.E- 2 0,22n9'.736E-00 0.23K.2692E 01 0.2B80B906E-01 0.29791678E 02 0.86497703E-02 1 0.06620650E 01 0.1875e205E- 2 0<22w31579E-00 0.231758B1E 01 0.?B0J159eE-01 0.30683596E J2 O.B2893561E-02 1 0.»6951313E 01 0.179697B0E- 2 O,22:.68'.21E-O0 0.2320B9B6E 01 0.27227557E-01 0.31612246E 02 0.80343700E-02 1 0.<.72e8066E 1 0.172065>ii7E- 2 0.22i0i262E-00 0.232'.2OOtiE 01 0.26456624E-01 0.32b79695E 0^ 0.77fl47143E-O2 1 0.47631090E 1 0.16".67912E- 2 O.216'.2lO^E-00 0.23274945E 11 Ü.25698654E-01 0. 33&8eibe.E 02 0.754O297U-02 1 0.'.7980577E 1 0.157!>3237E-O2 O,21b7B9'*7E-00 0.23307810E 01 0.249^3497E-01 0.34640004E 02 0.73010267E-02 0.<.833t726E 1 0.1506i937E- 2 0.213157Ö9E-00 0«233A0600E 11 0.24221017E-O1 0.35737773E 02 0.70668168E-02 0.il86997<>lE ul 0.1'.393'.36E- 2 0.210i2631E-0Ü 0.23373320E 01 0.23501083E-01 0.366b4202E -2 0.6a376811E-02 1 0.<t90fa9B^lE I 0.137'.717»E- 2 O.2O78ya7**E-O0 0.23'.05973t 01 0.22793i66E-01 0.3B062226E 02 0.66132402E-02 0.1.9«*7250E 1 0.13122S99E-J2 0.20526315E-00 0.23'»38i61E 01 0.22098342E-01 0.39334998E 0 2 0.63937142E-02 1
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MD
H
1200 1400 1600 I80O 2000 2200 2400 2600 2800 3000 3200
JL Temperature,!, "K
I l LJ L 2160 2520 2880 3240 3600 3960 4320
Temperature,!, 0R
4 4680 5040 5400 5760
(a) Rpo = 1.0; R. 'eq p,r 0.068700,
Figure h,- Molecular weight for C2Hj+-air combustion products against
temperature for constant entropy.
52
s/R.
*
dl
1200 1400 1600 1800 2000 2200 2400 I | | | . Temperotufe,T,°K|
2600 2800 3000 3200 J_
2160 2520 2880 3240 3600 3960 4320 Temperature, T, 0R
_L 4680 5040 5400 5760
(b) Req = 0.9; RSpjr = 0.06868T.
Figure k-.- Continued.
55
1200 WOO 1600 1800 2000 2200 2400 2600 2800 3000 3200 J I I Temperature.T,°K J
2160 2520 2880 3240 3600 3960 4320 4680 5040 5400 5760 Temperature, T^R
(c) Req = 0.8; Rsp^r = 0.068675.
Figure 1+.- Continued.
54
mil l nimMr)
s/**m
1200 L
1400 1600 1800 I
2160 2520 2880 3240
2000 2200 2400 Temperqture.T, "K
"3600 3^60 4^20" Temperature, T, "R
2600 2800 3000 3200 J I I . I
4680 5040 5400 5760
tr1
i
H
(d) Req = 0.7; REp,r = 0.068659.
Figure k.- Concluded,
55
VD
H
1400 1600 1800 2000 2200 2400 2600 2800 3000 3200 __j |_ i LTemperoture1Vl<J , , , ,
2160 2520 2880 3240 3600 3960 4320 4680 5040 5400 5760 Temperature, T,0R
(a) Req = 1.0; Rspjr = O.O71587.
Figure 5-- Molecular weight for CH^-alr combustion products against
temperature for constant entropy.
56
2
28
27
26
25
24
23
22
21
20
19
[iiiiiiiniiiiiitiitTniiiiitt ntiniintnfiiin »f•*••■••• }SM*!tu!ittsiiiiiiMtti*ii*i iifiiiiitnitiiniiiiiiiiiiiiiiiiiiiiiii mil s/R.
18 1200 1400
l_
1600 1800 2000 2200 2400 2600 2800 3000 _l | , Temperqfiire,T,0K;
3200 _L _L J_
2160 2520 2880 3240 3600 3960 4320 4680 5040 5400 Temperature, T,0R
5760
V H
(b) Req = 0.9; RSp^r = 0.071500.
Figure 5.- Continued.
57
o 5
1200 1400 1600 1800 E000 2200 2400 ■ | Temperature, T,0K,
2600
2I6Ö 2^0 ^80" 3240 3600 3960 4320 Temperature, T,0R
2800 _l_
3000 3200 _L. J
4680 5040 5400 5760
(c) Req = 0.8; Rsp;r = 0.071008.
FiRure 5.- Continued,
58
200 1400 1600 1800 2000 2200 2400 2600 2800 3000 3200 J I , Temperature, T,°K, i i I i X
2160 2520 2880 3240 3600 3960 4320 4680 5040 5400 5760 Temperature,!",0??
H
(d) Req = 0.7; RSp,r == 0.0T071U
Fif^ure 5-- Concluded.
t^§ S § s S 8 ? §as s?sgs
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