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Produced by the NASA Center for Aerospace Information (CASI) 5 Final Report January 15, 1976 - August 31, 1978 I NSG 1275

(NASA-CR-158110) A THEORETICAL STUDY OF A N79-16931 LAMINAR DIFFUSION FLAME Final Report, 15 Jan. 1976 - 31 Aug. 1978 (Virginia Polytechnic Inst. and State Univ.) 99 p HC Unclas A05/MF A01 CSCL 21B G3/25 14436

A THEORETICAL STUDY OF A LAMINAR DIFFUSION FLAME

Karen L. Frair Virginia Polytechnic Institute and State University Blacksburg, VA 24061

The NASA Technical Officer for this Grant is

Dr. Howard G. Maahs MS 284 NASA-Langley Hampton, VA 23665

I. ABSTRACT

Theoretical models of an axisymmetric laminar diffusion flame are discussed, with an emphasis on the behavior of such flames at increasing pressures. The flame-sheet or Burke-Schumann model (in terms of BesseI functions) and various boundary-layer numerical solutions are presented and their results compared with experimental data. The most promising theoretical model combines the numerical flow field solution of the

Patankar-Spalding computer code with the Pratt-Wormeck chemical reaction subroutine. The flame shapes for pressures of 1, 5, 10, 20, and 50 atmospheres have been computed and agree remarkably well with exper- imentaI data. There is a noticeable shape change with pressure, believed to be a result of buoyancy effects. The chemical concentration profiles do not exhibit much dependence on pressure, a reflection of the fac, that only one chemical mechanism was utilized at all pressures. 2 F.

II. INTRODUCTION

The problem of pollutant formation in turbine combustors is currently

receiving a great deal of warrented attention, especially the pollution

associated with aircraft turbine engines in and around airports. Of the

various pollutants discharged from these engines, two of the most harmful

are nitric oxide and nitrogen dioxide, commonly referred to as NOx.

Since actual combustors may operate at pressures up to 30 atm, it is of

special interest to consider the effect of pressure on the formation of

NO during the combustion process, which has been done experimentally by

Miller and Maahs [1] at NASA-Langley.

In their experimental investigation, an intentionally simplified

combustion system--a laminar diffusion flame--was chosen to model the

actual combustion process. The diffusion, or non-premixed, flame was

selected over the premixed flame because it is an experimentally simpler

system and because larger NO concentrations are expected with the

diffusion flame. The laminar flow regime was selected in order to

eliminate fluid flow effects as much as possible so as to concentrate on

chemical effects.

The structure of laminar diffusion flames has been the subject of

investigation for a great many years. The first analytical study of

diffusion flames was made by Burke and Schumann [2] in 1926. They

introduced the assumption that the zone of combustion might be approxi-

mated as a surface, i.e. infinitely thin. It would then follow that the

associated reaction rates would be infinite. Burke and Schumann were

concerned with a cylindrical laminar fuel jet discharging into an air

stream moving with the same velocity as the fuel; they proceeded to

calculate the flame shape for various initial conditions. The same

assumption has been utilized to predict the length of both laminar and 3

turbulent open flames. (.Hottel and Hawthorne [3], Wohi, Gasley, and

Knapp [4], Barr [51).

zeldovich [6] was among the first to consider the structure of a reaction zone of finite thickness and hence the effects of finite reaction rates. Similar studies have been done by Spalding [7] with an emphasis on the phenomenon of extinction. Linan [8] has also studied the effects of finite chemical reaction rates by means of a boundary-layer-type solution, while many have applied perturbation techniques to the problem

(Pendell [91, Kassoy and Williams [10], Chung, Fendell, and Holt [11]).

The computer simulation and prediction of chemically reacting flows, an extremely difficult problem because one must describe the interaction of many reacting chemical species with fluctuating temperature and velocity fields, is nevertheless a method of solution that is being used to a greater and greater degree as computer software/hardware facilities become more advanced.

There exist at present two well- defined bodies of literature on the numerical (computer) solution to chemically reacting flows: 1) fluid flow with infinite-rate chemistry (chemical equilibrium), and 2) finite- rate chemically reacting flow without mixing or with infinite-rate mixing. Examples of such works are those by Patankar and Spalding [12] and Pratt [13], respectively. Pratt and Wormeck [14] have then attempted to combine aspects of both bodies of literature to achieve a scheme that could model the phenomena of a diffusion flame-a laminar finite-rate chemically reacting flow field.

It is the purpose of this study to construct an analytical model of the laminar diffusion flame described by Miller and Maahs [1] and to

compare experimental and theoretical results concerning the effects of

high pressure on flame shape, temperature distribution and NO formulation. F

Sections III and IV describe the physical system and experimental results,

Section V introduces the governing equations and Section VI describes various theoretical models and associated results,

^i 5

III. DESCRIPTION OF THE PHYSICAL SYSTEM

For purposes of completeness a summarized description of the physical system employed at NASA-Langley is included. For a more detailed description, Reference Eli should be consulted.

A diagram of the burner and collection sy tam is shown in Figure 1.

Methane gas issues from a cylindrical tube into a concentric cylindrical tube through which air is -Flowing. The fuel tube has an inside diameter of 3.06 mm and the air tube has an inside diameter of 20.5 mm. Fuel and air flow rates are held constant at 41.8 standard cm 3/min (sccm) and

2450 sccm, respectively.

In order to obtain a flat velocity profile in the fuel and air streams as they exit from their respective ducts, porous disks of sintered stainless steel were installed near the duct exits. Ignition is accomplished by means of an electrical hot-wire igniter, During operation the igniter is positioned 10 to 20 mm above the burner; once ignition is attained the igniter is removed from the flow.

The combustion products exit from the top of the quartz chimney and are swept into a total-sample collector by the nitrogen pressurizing gas. The nitrogen flow rate is kept low enough so as not to excessively dilute the gases to be analyzed. The products are analyzed by a continuous infrared CO 2 monitor and a chemiluminescent NO-NO x analyzer.

The measurement of flame temperature is the most difficult and most uncertain of any measurements made. The method of two-color pyrometry was employed (with the carbon in the flame as the radient emitter) Go determine a spatial average temperature near the hottest point in the flame.

i 6

Hot Wire

AC Suppi, yzers

ator

High-Press Chamber Total

Glass Chim ow

Diffusion Fl ame

Fuel Tube (3 mm dia.

Izing Fuel C tas

Figure ! - Schematic diagram of burner and collection system C f

7 n

IV. EXPERIMENTAL RESULTS

A. Flame Shape

A definite change in the shape of the diffusion flame occurred as

pressure was increased from 1 to 50 atm. This is shown in Figure 2,

taken from Reference [1]. At i atm the sides of the flame bow outward,

but this decreased as the pressure was increased above 1 atm. At about

10 atm the flame exhibited a slight concavity and the diameter decreased

considerably. A further decrease in flame diameter occurred as the

pressure increased, the maximum change associated with a pressure of

approximately 20 atm.

An increase in the amount of carbon accompanied the change of flame

shape and at pressures higher than 20 atm only minor changes occurred.

The height of the flame did not change drastically with pressure,

as illustrated in Figure 3. The flames were typically 10 mm in height.

B. Nitrogen Oxide

The molar emission index of NOx , Im, is defined as the number of

moles of NO and NO 2 produced per mole of fuel burned. Figure 4 shows

that this quantity increases rapidly as pressure increases, reaching a

maximum at about 9 atm. Above this pressure the molar emission index

decreases slowly and continuously until it returns to roughly its original

value.

C. Flame Temperature

A plot of the optically--measured peak temperature as a function of

pressure is shown in Figure 5, with data limits shown by vertical lines.

There is a steady decrease of peak temperature with pressure. I

r+ 1 mm

fi 2.2 !l ii 3.1 ji

/Ambient pressure, atm

00 n ;V -U 0 020 b ;^ r CD >^ i" M rr,

i a to 9.7 ii it. 19.8 !i 1i 30 . It 11 ti 49.9 A L-77-167 Figure 2 - Photographs of methane-air diffusion flames for various ambient pressures. Methane flow rate, 41.8 sccm; air flow rate, 2450 sccm; burner diameter, 3.06 mm. See Ref. 1. 4

ORIGINAL PAGE IS OF POOR QUALITY

^.Z

'v 6

Cd W 4

0 Ambient pressure, atm Fizure 3 Flame height as function of pressure. See Ref. 1 xw U w0 m 0 ^ Ok z 0 00 1.0 0 G) o^ ;^

.9 .0a^ .: .,j 0 0

.8 a^

^a 0

.^ 0 4 8 12 16 20 24 28 32 36 40 44 48 52 Pressure, atrn 0 rigure 4- Molar emission index of NOX as function of pressure. See Ref. 1 A

240P

Tad

2200

2000

Cd CL 1800 H Tf

1600 Mr-

M 1400 0 10 20 30 40. 50 Pressure, atm

Figure 1^ -- Flame temperature as function of pressure. Dashed line indicates extrapolation. See Ref. 1 12

V. GOVERNING DIFFERENTIAL EQUATIONS

The equations of motion reflecting the conservation of mass, momen- tum, energy, and mass of each component for a chemically reacting gas mixture are:

Conservation of Mass

+divpV=O where p = density V = velocity vector

Newton's Second Law

DV -^ VP + div z DtW where 2t = substantial derivative = at + V - V

p = pressure

T = viscous stress tensor

Conservation of Energy

Dh 1p + T E -di v q Dt where ORIGINAL PAGE 15 OF POOR QUALITY h = enthalpy

e = rate of strain tensor

q = heat flux vector

Species Conservation Dm PD =-divJ i +Ri where

mi = mass fraction of species i Li p j i = mass flux vector

R i = rate of creation of species i by chemical reactions

In order to close the system the following constitutive relationships

and equations of state are introduced:

T 2ue + Xdiv 11 ^E

where + A are the lst and 2nd coefficient: of viscosity and

R is the unit tensor

e = 1 / 2 (VV + VVT)

j i = PED i,3 Vm

where ji is the mass flux vector and D ii 's are the diffusion coefficients

q = -k0T + Eh iji q is the heat flux vector T = temperature

k = coefficients of conductivity. M. T p = pRT E i i i + W^ h = Eh m hi -- h C dT i i T oS p i where W i = molecular weight of species i.

The above equations are non-linear second order partial differential

equations. The two main types of solutions are analytical and numerical.

Analytical methods are those that express the solution as algebraic . a formulae, power series, etc. Methodologies such as separation of variables,

series expansions, and coordinate transformations are employed to obtain

such solutions. These types of solutions are usually limited to linear

or linearized differential equations.

Numerical methods are those that express the solution in the form

of numbers related to the particular circumstances of the flow. The

differential equations are.transformed to algebraic "finite-difference"

equations and the values of all dependent variables are calculated at

the nodes of a grid covering the domain of interest.

The flow to be considered is in general governed by nonlinear

equations with the rate of chemical production term (R i ) being highly

complex. Simplifying assumptions may be made and various solutions

obtained. A discussion of these solutions and associated assumptions

follows in Section VI. r

VI. THEORETICAL ANALYSES

A. Burke - Schumann Analytical_ Solution

If the following assumptions are made:

1. steady cylindrical flow

2. inviscid flow

3. negligible pressure and thermal diffusion

4. Ficks Diffusion Law

5. single step chemical reaction of fuel and oxidant -} product

6. parallel and equal gas velocities

7. constant mass flux

8. axial diffusion <<< radial diffusion

9. entire chemical reaction occurs at the flame surface then the governing equations may be combined into a single linear partial differential equation with appropriate boundary conditions. The solution is in terms of Bessel functions and a flame shape may be predicted from the analysis. Reference [15] presents a more detailed discussion of this solution.

The predicted flame shape agrees fairly well with the experimental evidence, although the predicted flame height at I atm (3.6 cm) is greater than the experimental. Furthermore, the Burke-Schumann model predicts absolutely no change of shape with pressure, hence it is evident that a more refined theoretical analysis is necessary.

B. Edelman - Fortune - Weilerstein Numerical Solution

The effects of inertia, viscosity, diffusion, gravity, and combustion on an axisymmetric laminar diffusion flame have been investigated via a boundary layer type formulation by Edelman, Fortune, and Weilerstein

[16]. First a von Mises transformation is made in going from axisymmetric physical coordinates (x, r), where x is the axial distance and r the 15 radial distance, to (x,,) coordinates. The stream function, is defined by ^b rp f Vft ° f purdr a ra

The governing equations are then non-dimensionalized by means of an emperical normalization parameter. 11 1t is customary practice to do this (non-dimensionalization) by normalizing the variables directly in terms of the boundary conditions. However . the resulting dimensionless groups do not truly characterize the process and that is due to the large variation in flow properties throughout the domain of interest. Accordingly, the current approach involves the introduction of a set of characteristic quantities which are based upon some state within the flow that more accurately reflects the flame structure." [16]

The equations are then solved numerically by means of an explicit finite difference formulation.

The Burke-Schumann combustion model, or "flame sheet assumption", is that all the heat is released on the suface where the fuel-air ratio is stoichiometric. A more accurate combustion description is offered in this model in terms of a basic equilibrium theory for the combustion in either the fuel-lean or fuel-rich regime.

For a pressure of one atmosphere this program predicted a flame height of .S cm and a flame shape that agrees remarkably well with experimental data. However, the results for pressures greater than one atmosphere could not be substantiated either qualitatively or quantitatively by experimental data. This was due to the fact that the analysis in

Ref. [161 utilizes.a normalization parameter obtained experimentally at one atmosphere of pressure. This does not affect the original work since the problem considered was buoyancy effects of diffusion'flames, all at one atmosphere. The analysis, limited as it is to a pressure of one atmosphere, does not therefore lend itself to the problem at hand. 16

C. Patankar-Spalding Numerical Solution

Patankar and Spalding [I2] likewise utilize a boundary layer formulation and a von Mises coordinate transformation so as to put the conservation equations in the general fora

ate a1 a +(a+bw) = (-C )+d ax aw aw aw where

x and w are the two independent coordinates

a and b are arbitrary functions of x

c and d are arbitrary functions of any dependent and independent variables

stands for any one of a set of variables, each possessing its own differential equation, e.g., -Fluid velocity, stagnation enthalpy, mass fraction, etc.

These differential equations are transformed into finite difference equations and solved by means of the tri-diagonal matrix algorithm

(TDMA).

The chemistry incorporated into this numerical scheme is a very simple fuel-oxidant-product equilibrium model where the rate of genera- tion of fuel by chemical reaction, R f , is assumed to obey an "Arrhenius- u type" relation.

For the case.of negligible chemical reactions this program produces acceptable results in that the diffusional nature of the axial flow of fuel and air is well represented by means of velocity and concentration profiles. With the inclusion of limited equilibrium chemistry a flame shape can be obtained that agrees qualitatively with that obtained experimentally. The theoretical flame height at one atmosphere is 8 cm as opposed to an experimental height of .8 cm however. Since the chemistry of the flow field under consideration is fi t

17 model does indeed limit its ability to accurately describe the flame under investigation.

B. Patankar--Spalding and Pratt-Wormeck Numerical Solution

As stated previously, the hydrodynamic aspects of Spaldings code are well-developed and offer a valid model of the diffusional nature of the flow. A more realistic chemical model is provided by Pratt and

Wormeck [14] in their subroutine for the calculation of chemically complex equilibrium or non-equilibrium stationary states.

The scheme employed by Pratt and Wormeck in their determination of chemical equilibrium states at prescribed temperature and pressure is essentially the same utilized by Gordon and McBride [17]: Gibbs function minimization.

A similiar procedure is employed for the case of non-equilibrium

(kinetic) stationary states. A chemical-kinetic source term is included which takes into account the effects of forward and reverse reaction rates, and reaction contact indices.

A combination of the hydrodynamic code of Spalding and the chemical package of Pratt and Wormeck results in a computer code that is capable of producing a numerical solution to the hydrodynamic equations of motion while taking into account the effects of complex chemical reaction.

This combination computer code was applied to the problem at hand for the two cases of equilibrium and kinetic chemistry. It was found that the kinetic solution proved much too costly in computer time (IBM 370) to even consider, so the following results are limited to the case of equilibrium chemistry.

The thermochemical data were taken from Gordon and McBride [17]. A reaction mechanism consisting of 19 species and 34 reactions was utilized, as given in the actual computer listing found in the Appendix. A 18

cross-stream grid of 21 grid points was used. The results were found

to be fairly sensitive to the input value for the temperature at the

base of the burner. Since the computer solution is for a steady flow,

the actual ignition phase is not considered, but a temperature is chosen

that hopefully represents the physical situation after a steady state

has been achieved. All the results discussed are for a base temperature

of 1000°K.

Figure 6 demonstrates the change in theoretical flame height with

pressure. As can be seen from a comparison of Figures 6 and 3, this agrees

very well with the data obtained experimentally. The average computed

flame height was 8.6 mm, as compared to the value of 10 mm for the

emperical case.

Figures 7 and 8 demonstrate the theoretical flame shapes for pressures

of one and five atmospheres of pressure and ten, twenty, and fifty

atmospheres, respectively. The flame position at a particular height

above the burner was assumed to be at the point of maximum temperature for

that height.

As can be seen from a comparison of these Figures (7 and 8) with the actual flame shapes obtained (Figure 2), there is a remarkable

agreement between the mathematical model and the emperical data. At one

atmosphere the computed flame is fairly bulbous in nature, the sides of

the flame bowing outward away from the burner. As pressure is increased

the outward bowing of the sides of the flame decreases, and at 10 atmo-

spheres there is almost no bowing at all. At 20 and 50 atmospheres the

flame exhibits a concave appearance, which agrees extremely well with

experimental results.

This shape change is believed to be a direct result of buoyancy

effects. As the pressure increases,the difference between the densities 10

g z uj uj

2 F^ '.I I

10 20 30 40 50 ^i AMBIENT PRESSURE, ATM I i FIGURE 6 - THEORETICAL FLAME HEIGHT AS A FUNCTION OF 'I PRESSURE

i PRESSURE = 1 ATM

1, M

PRESSURE = 5 ATM

FIGURE 7 - THEORETICAL FLAME SHAPES 21

CM FIGURE — THEORETICAL FLAME SHAPES r

of methane and air become much more pronounced, hence the behavior of the two now very different gases under the action of gravity, i.e., buoyancy, affects the resulting -Flow field. In addition, the problem at hand is one of fairly low velocities. As the pressure is increased these velocities become even smaller and the -Fluid flow more sensitive to buoyancy effects. Prior to the inclusion of buoyancy effects in the computer program, all flames exhibited a somewhat bulbous shape similar to that found at one atmosphere.

Figure g is a plot of approximate maximum flame temperature as a function of pressure. Since these values are fairly sensitive to the input temperature at the base of the burner, it is difficult to make any general statement concerning this data except to say that in comparison with Figure 5, the computed flame temperature behaves in qualitatively the same manner as the adiabatic flame temperature shown there.

Figures 10-15 demonstrate various species mass fractions as a function of the radial distance outward from the center of the burner.

Figure 10 is for a pressure of I atmosphere at a position of .15 cm above the inlet. Figures 11-15 are for a position of 0.5 cm above the burner, toward the top of the flame, and for pressures of 1, 5, 10, 20, and 50 atmospheres respectively.

At a vertical distance of .15 cm above the burner there still exists some unburned fuel close to the axis of the burner. The maximum

NOx concentration occurs closer to the flame position, as does the maximum concentration of CO2.

At a vertical distance of .5 cm above the burner, there is no CH

present and once again the maximum NO production occurs near the flame x

front. There is essentially no change in the relative magnitude of this maximum concentration with pressure, only a change in where it occurs.

This of course corresponds to the change of flame position with pressure. 2 800 x ^ a &-4 2600 x ^ w ac F- ul z ^ 2400 " W X t-- 0 ray w C. IF—* a. Q 2 200

2000 10 20 30 40 50

PRESSURE, ATM

FIGURE 9 -- MAXIMUM FLAME TEMPERATURE AS A FUNCTION OF PRESSURE

m IO°

10-1

0 10-2 ua

w 10-4 u ur U3 °-

10-5

lfl-e

1 .2 .3 4 .5 .6 ,7 .8 RADIAL DISTANCE OUTWARD f CM

FIGURE 10 - SPECIES MASS FRACTION AS FUNCTION OF PRESSURE 10°

02 f0-i

102

CO2 la-3

104

105

1 U-6

NO2 loo

10-'

I o-2 0

U 4 IV LL.

U) U) ul w io-4 U w a- U

o-5 i

E E

1 101 {

10 I

10=

l0-4

!05

10--11

.I .2 .3 4 .5 .6 .7 .8 E RADIAL DISTANCE OUTWARD, CM

FIGURE 13 -- SPECIES MASS FRACTION AS FUNCTION OF PRESSURE

h 0 r ATKA Ill r%YT^AI T%TnPARI^+ T'11-&& TSSTRI I"'1l — n r -aa

loo

10-1

IV 0

d LL 10

ID q .-a U

u7 10

-6 10

.I .2 .3 .4 .5 .6 ,7 .8 to RADIAL DISTANCE OUTWARD, CM

FIGURE 14 - SPECIES MASS FRACTION AS FUNCTION OF PRESSURE loo

i a-I 0 w F- U Q ICF 2

U) Q

U) q w 4 a- U LL! 0.

5 !0

io, C^

VII. CONCLUSIONS

In order to reflect the physical system under consideration to an acceptable degree, the governing differential equations must be solved numerically. The algorithm utilized by the Patankar-Spalding computer code produces a solution that represents the hydrodynamic nature of the flow field extremely well. It has been found, however, that refinements must be made to the chemical reaction portion of the code in order to produce meaningful results. These refinements take the form of the

Prat:-Wormeck chemical subroutine which has been incorporated into the

Patankar-Spalding computer code.

The flame shapes for pressures of 1, 5, 10, 20, and 50 atm have been computed and agree remarkably well with experimental data. There

is a noticeable shape change that occurs with increasing pressure and believed to be a result of buoyancy effects, which become increasingly

important at higher pressures.

The species concentrations computed for the flow regime at hand seem to reflect the chemical aspect of combustion fairly well. The

concentration profiles do not reflect much dependence on pressure, however, except in so far as position is concerned. Since the chemical mechanism

incorporated into the program did not vary with pressure this is a somewhat expected result. It would be of considerable interest to change

the input chemical mechanism with pressure and to note any resulting

changes in the general shape of the concentration profiles. 32 b

REFERENCES

1. Miller, Irvin M. and Maahs, Howard G., "High-Pressure Flame System for Pollution Studies with Results for Methane-Air Diffusion Flames," NASA TN D-8407, June 1977.

2. Burke, S. P. and Schumann, T. E. W., "Diffusion Flames," Industrial and Chemical Engineering, Vol. 20, No. 10, Oct. 1928.

3. Hottel, H. C. and Hawthorne, W. R., "Diffusion in Laminar Flame Jets," 3rd Symposium on Combustion, Williams and Wilkins, 1969, p. 254-266.

4. Wohl, K., Gasley, C. and Kapp, N., "Diffusion Flames," 3rd Symposium on Combustion, Williams and Wilkins, 1969, p. 258-301.

5. Barr, J., "Length of Cylindrical Laminar Diffusion Flames," Fuel, Jan. 1956, p. 51-59.

6. Zeidovich, Y. B., "On the Theory of Combustion of Initially Unmixed Gases," NACA Tech. Mem. 1296.

7. Spalding, D. B., "A Theory of the Extinction of Diffusion Flames," Fuel, March 1954, p. 255-273.

8. Linan, A., "On the Structure of Laminar Diffusion Flames," Ph.D. Thesis, Calif. Inst. of Tech.

9. Fendell, F. E., "Ignition and Extinction in Combustion of Initially Unmixed Reactants," J. F. M., Vol. 21, 1965, p. 281-303.

10. Kassoy, D. R. and Williams, F. A., "Liquid Droplet Combustion with Finite Rate Chemistry, Paper No. 68-181, AIAA 6th Aerospace Sciences Meeting, New York, Jan. 22-26, 1968.

11. Chung, Fendell and Holt, "Nonequilibrium Anomalies in the Development of Diffusion Flames," AIAA Journal, Vol. 4, 1966, p. 1020-1026.

12. Patankar, S. V. and Spalding, 0. B., "Heat and Mass Transfer in Boundary Layers," Intertext, London, 1970.

13. Pratt, 0. T., "Calculation of Chemically Reacting Flows with Complex Chemistry," Studies in Convection, Vol. II, Pergamon Press, 1976.

14. Pratt, D. T. and Wormeck, J. J., "A Computer Program for Calculation of Combustion Reaction Equilibrium and Kinetics in Laminar or Turbulent Flow," Washington State University Report, ME-TEL-76-1, March 1976.

15. Williams, F. A., Combustion Theory, Addison-Wesley, 1965.

16. Edelman, R. B., Fortune, 0. and Weilerstein, G., "Analytical Study of Gravity Effects on Laminar Diffusion Flames," NASA CR-129021, Feb. 1972.

17. Gordon, S. and McBride, B., "Computer Program for Calculation of Complex Chemical Equilibrium Compositions, NASA SP-273, 1971. 33

APPENDIX

Computer Listing and Sample Output 0

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L,EVtL 2.2 IStPT 7d) uS/.*60 FUKIKAN h tXft.nutU UAit 7S.LV9/1C.3b*lk% REQUtS Tt:u UPTI ISMS : UPTIUMS IN t:i-FCL]; i%..Mtt 'MAlitJ sWuPTIMILe LlNt.-L tusv Tt7 ? 1 S1LtlM ^X1 AUJOURLINONit) ` ,&UURLL LB4.UiL. NU'L1S) NUULtA UVJ t1.1 NUMAP NuFUkal'hT WU6US )M ( NUXkEr NUALC NUAIVSF 7t f(M i-LA ISN U4,) 1 Z:,t,;bKuuliNC StKIJztl^w) GtN{U1470 I.SN 4)L03 IMP L1L1 C K CAL*IJ [ A—h•*L:—Z 1 6LNU1472 1SN UUU" LU6i LrA L LAUTAOiLtWU1LyLKt^Ll •LUI:bWIi*LI U'KN bt1Y11I414 s 15N 0(101 U1Mc4j'S1 UN ASUbJZ( * j) bt:Nti147b 1 SN 0 Uub L OMM014 bLN01478 i/L,1.1y'EM1/[.NSUM * Fal * rt'LN * KGA,^hlipSlN,sMlNYÎK1hVîLN*Lt.UNVbrLNltl, bENL) 1^ray0 1/LINUtX/ ZULU * IUCUL91Urr2.tuntU • IUN2oiUUZ g l nLP59ILC ILngjmAlgjlEks bENU1•► 82 [ J.J*Ni ^N2* ^SrNh * H1yLtit^llV.LU'ts1'*N'LM•lVL!*NSM GrN'01.4&4 1/tVAKAM/AbkabINIvNt*tMY IVAIPQwtWLv?2#Q3q l4*KhUP* btNU14eb c :. M•Stt:. ul * S^:t^-L) * IKsLA UA Abi LUE t>-U tx *L LWtl lL * LKtAI.T b tN[► 1••'t!# ` iJ[l U., iii ^'Vni'7U^V/Llifì../..t-+Sl*AJtl:+l*AJ114L)^bt'*^):L.t+^1,1.SALrA*Ut++31*Uhl,itl.sbtN^^45 ►J • ^x * t^4Ut y :+l * FILt * 43),l ax * l tivu * l l= lir,l t^4LtzZ) P ANUlt.:21*lUui*IUU mv P utNol4yt ^ i^lt.r * i1^^1 * IufKHr * JJ•JAW *JV*,IY*Ktr*K11`.,Kf-Av * At*NJcIRF,NUVtL• N i"1* btNJ i4^Y nt'c * hr':*:i+ilti3?•UrriL'tr^l*VIs^1*!'t1^1'h1G^l•Nhert^2*Y^1*1' Sirsr511 *tct4VtNUi4ya *► ^l^Khtl. l • ^1^hMt^ 'K;4il*htJl •+3)•tJi^l7 * •, .11• I.Ive y l• .cul^tltr3) * X^:tXUtSVI^ * ^,9)*btN'L1 4 ^r h .' rl-s9) lp * Y1 bi`NUi,E:L 151Y J.,ur► :. 4r7r3tJ1Y / 4Lî"tr+ / ^1KlkLMa * I+►K'K4U[^,tMfi+ i.L^fb.fn*tirll * 1NtK7 * MA SSTK * NUUMY* bCNO1^Ci^ a Muuc^. * rJx^rU * rKEtAr * NkkSS * liliAl.,uFtiL. [st:Wul9tl4 ` L4t------twbKUUT'!Nt t-UR PKUUhA.M {atNl! LX wA btNGl^:10 L/ in1S JUbKLU'liAt a tKeU:K Z% iht SAMt U-PtKAi lUN5 as Tnt: UNt IN 6tNMIX4A bcNGl!$0b C bbl MUKE c6UA0MlLALLVw The A g bjL AKKAYS AKt UNt —U1MENSICNAL * b0 ft btNtlibiO L tll- Tch UbLU NUNLTIUNS Ulm UM AKt SIUKCU * AMU A U AKR'AV SAVES toENOI:#IL L. UmNECtSSAKY AK11hMLO11. IN Iht t'UMA 0PvXAT1UN % r 6LNO1514 ISN OGUY ulMr-N4IUN K G(2cI•ANPeIeL ! * U2422) 1 nNP21221 9 CAZ11 LNP 122 1 vu2(22 1v tLN.tll:10Lt 1 wNPLIt2) * hhLrit4s1,bUnT^th3f*Fulrct*rulrlt221t2rtitltr) * l,i122) * (PtNu1520 ` L a+ ISUM1431 * NbuM143)tTHLl+ ft43) * TTi+l^lc[i lat:NU1522 ISW U ,., iu 0UMi491*UMPUfijU1MtNSlUN 43)gdbl-t1) bkNG1514 1$N Uu11 UIhtr4.*1U1* beN01S46 ISN GJ12 uATA a r1A'.CL /l.U— d/*1iNY/1.W— CO/ L 6rNU1y34 15N Uu13 EWUIVALtNGt tuPUXl1) * US( 1) 1 6tNt,1532 1SN 04j14 EUUIVALhWLL tAKKLUNjlLtZfUCLI i2k Ito 1z,34 lsw OG15 toll 70 t1U0U * 4u06I—,*VGuq r4) Ot]) * 1SM 6.ENt11336 L btNL31.3b I C S I K I 1) t 1 * ** ** ***= ^*btNJ194U ISN Uul6 LlUt,u 11-t1SItP) 100S9100-I v L1C0 ueN015►4 1 0 p 1Sw UL 17 1001 UM1 =. a*UMt4) V:tNtll541 ^^ ^ ISN i)ui8 Uf4t =. 7*il •—UMlNel)) 6ENU13y4 "€1 0 IsN oui9 L-101064 l = tvN'Y1 • utNGiti4.8 ISN t]u[u b umlI J= um .tl *1 1—UMt1- 11 utNG155O ® > ISN UE11 bUnT3t1)=3.40UM4I) btNU1552 ;v r- 1 Sft Gu22 umPuMti l=um'll) *UM41*11 tstN01.554 D 1SN Ut.23 L.UG4 U.MUt 1 / =UMI 1 *1)-^11M1 j ) UtNUlS^t+ j— ^ , 1SN OU24 umt.#t1)-d1rMlZ) bEN4L155.11 ISN 0025 art=l. trtNL^l7Fit1 ±:; ^ 1SN tiGcn 111'1=1. btNC 1761 - ^, ISN OLiz t Y(I) =u. t tNG t :. cy t^ ISN 0J.2b 1rtnKAU e tU.li uu IU 11LU btNCLbbb ISN UU -7 U uu 1u41 1=_îrr3 utNutâb

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y _ LEVEL 2.2 lStrl 101 .0KWIL Us/360 raKTKAN M tXFLNUtU DATE 78.19V/10m3b.ld ISN OG31 1001 Kill=i. GEN01570 ISN 8032 K^5=1. GEN01572 ISN UU33 KNi = 1. trtNU15 i^ 1S^V Cili3^ I:Flll'rsT.^vc.u) rfrcllttatNi:•lt:) [k[1)sl=l,rvP3)^KZ9,#tvl y C.r.hllil9'la LALt.U LA)1 U19 Ur KMU*U • S------6tIVll^s711 ISN UUJO 1 1UU U,U 11G, 1 =i,wr_^ bt NU19bG ISN G,U3 Y ll`IKnU (i).61.U.) 6U 1U L101 bENG1 .lit ISN UL31 WK11E(b t1 10 a) KnUll i vivKHU ( 1) 6tN015tY ISN Uu4U 11Ut: rUKMAIl_Orh **** ** ** NrbA'11 Vt OR LtKG khU111=92PULLe3, 6h A7 1 = 9 6tNO1586 1 1: gbAg41h1,:t3 1U AhS Ut- Kht+411 - * LL11. :3si1H •+ M+** S1k1Ut• 1) 6tN0L!Pkfb ISN t]u41 RhU( 1 ) z LUA6siKMU[ 1)) 6EN019.1G ISN 04J44 Li U! KU[ 1 1 =khU11 ! *Ul 1) bENolb9z ISN Ot-t3 RU..=Hsi(311 60VOiti" ISni ;,U" RUN1=,Ku(Net ) urNC19^^b 1SiV UU-t:) U?L llu4L 1=4^9hNl utNf1^YH i S w liu'Fb llu- K%:ll l)+Kull+^ ► ) bt^t'IbL4 JW* u641 irllic:l.iYc.yt) WK11t lbevu1s.) lkUlllrl = lsr+^- ),1x^l1V1,FcU.j *F'trl bknitllbE^^ ------i,AiLt ULA 11LN Or r '.b A(W r{ G ------Y s !b rUK PLAML G^_unLIRV 6EN,-.1bUa ISN 1, t.4v Yi =!'t1-U'M.L/ IGrA4KUi_'11 . btNi.lb(Jb ISN v1.5.: Yln)=Y1 *et Iv UA(-I) I(KU(1)*etUS) LsrN(+161L 151 vJ.')L Y( t- ) = :L.+Y1 -Y4 .s! btNl,lbl4e 1SN Ow5L ub 1111- I ;-ftq p i ILANvIb14 1JN 0U7.^ li ves Yil) = Y 11 -1l +P:LI*UMUl1 -1)/Ru,i i-1) 6LN'U1616 ISN 1` 054 Y 1i119=Y IN,Y1)* rtl*UMu(NPi)/IKU(NI'1)*KUNiI btN01ai8 1SjV Yt=PEL*UMt/tdPt*KwMVi!) btNU1620 ISN 0u50 Y[NF31 = YN1:^*v L btNU16L[ ISty 0057 6kNolb24 ISN 009d ItIKRAU*LU.0) KEIUKN i,E1,80162b Y'S ANU K • S F=UK AXISYMMETRIGAL. GtOnETKY 6tNG162E ISN 006L, 1r 1LbAL1rA.tW.U,) Gq 1'U ili0 btNGlbau C ------LSALFA NE LtRU bt=N41b.32 ISN Ucib[ GENGI634 ISN uU6.i it[kll),IitL,U.) G[l IU 1109 6CN01636 GEN016a i ISN 01:69 UU flub 1 = LfNYa GtNU1640 ISN 00bb 16tNUt642 ISN 000 111.c K l l) =Yl 1 )*4.SALFA btNLlb44 ISN OG68 Y 1 =us WKi [UA6b( Y1 /1.04UL)) GtN01.64a ISN 0:00 i YN15=U^tih1 lUAb3l YWL:# /t.t1SU2)) btNG1648 153+1 0070 6 U lU li L t btNU1650 .._...._..______--- R(L) Nt U. 6eN01052 Isw cull 1109 RIU2=.:,*KI i ) GtN191694 ISN 0472 K1U4Sw-ZALUt*KLU2 btNUlbbb ISA 067J 00 liu,► i=L t NP. GEN01658 ISN U07 •6, Ytl)=Y11 ) / 1 K1Ui*USWK$iuAbJlKiW1SU +LUSVf*Yl1 )))) GEN01660 ISN UU7 !> 11U,* R(1)=RI1!*Y[1)*C*ALFA 6tNUl6b2 INN UIL;U Y 1=Y 1 / (Ki ut +US VK 1 ( UAnS l K lU2SW+(.(JSUt*Y I !)) bt N016 b4 ISN 0074 1PENUlb6b ISN 0078 A.ti, I Ri:5=K 11) *Y 1--l.SALFA Ur.NUibbb ISN 00 Po KNlt1 =Xf i 1 *YN15*LLA1tA 6t NOit>7G ISN oum, Yt= Y(NejI- Y 1v. 9 6tNU1672 1SW Oval RE UK14 16tN( Ib741 U _-^._. ------_-_ ..... __-- — LSac. l-A tQ ZCKU ibEN(tib b ISN 015 llitr UAL. 1i111w = 4jNr_ bEPWIblb

LEVEL 2 .2 t a tP V In 1 NTK I UL US/36U FORMAN M tXTtNUtU UAIt 78.199/10m3belb ISN OUb3 Y 1 1 1= Y 1 l l /K 1 1 I GtNO1680 INN OU8 4 Lill Ftl11 = hll l GENG16B2 ISN 008 Y1=YI / h(0 istNG16t4 ISN aUdo YA1:^=Yn17/ Ki t 1 6ENulbbb ISN 0v81 R D=A t t) bt-NOlbtsEs 1 N uUs b K;rl^=F,111 t, tNuidyi+ ISN GU89 Y^= Y 11vF'.a # – Y'N 19 bt:NU 169[ 1.4N t7.G `iii K k I U1t N 6 EN016V4 , :}#Ft^^^raF^ * zi * z:.=. a: a^ * # y 1 K I U E 2 ##>^#****#*>F#**#'^VtND169b i ____^._._.___^___- ___..-.._ ___ VKtLiM1NA1:1cN FUK CUcFF IA. IcN1S 4JEN0164M I SN O.La 1 .-O0 t vA=Ptl/ux 6tNO1700 ISN G L92- ISN lru 1.3 !' 1, : - F^'kr ^ * F'FJ,a^ V 1-N1'r i 7 C k ISN UVI.+ G=KM1 -mil L vtNblfvu I5h GLv^ Ai%M1=WAM—N,ihM1 1 iscfilua7lib i^N Otrvt .^.itr:t = Urtt Jlhl^c 1 btN`. l 11 ISN Ct.y"l utr4=.[^ ► V btNGL11i' 1 b1V Li.yt r y=rx + ^ uvmoi 1 1144 14N 4L9 1 ISN vivv P60'4=1'L,L. o+rUUL btNU1 71b 1S'V u au1 'KMIu_ = . a^KMI ucNO02C 15N L 1 Gi ut 2Ut;ft 1=4•Nl'L 4acNULIZ2 1 SeV iil U3 PbL'M1 i 1=F'A+bUMi • # ixkwa 124 ISN Utu4 20U 4^ Pt bm i 1 #-ruu4*uMu l 1) UE14017Z6 INN 0iu:^ e4UMN=rUft*b 3M ([ 1 60401128 G --— ------— ukIU NUIN4 1 GENI?1730 L^..._ ------,_... TAul v esPl Ip . Ti Gt:N01732 . ISN 0lot 1r1KDe.Ki:.1# uu ]U 2001 6tNO1734 I NN QLU,d I;:ALL Writ.aipbP191i*TA.Ui1 tsl:Nt117'Jb 1JN (GlUv bu to 40:01 ut:Nit1 738 ISN Ou lu ( 1 =ue VEN01740 IaW till! iriKKAU.^d.01 bF'1=.393j.3+.t,a6o1*itUli!/KUlLI [`sEN017^ 1 ISii u 113 11^(KKAU.cwsll bal l =(K1 i# f I!) * *KU Il#*KUiL1#+3. K27* i tN0174^f► 1 lKUtli+Ruilill/b./iKi11+K2^1/RU121.' GtNt^1746 L dUUNUARY 60tt-1-1L1tNIS tuK VtLOLlfl 6EN01748 ISN 0115 4[►c^ e^L1^ =KM1U-GU+^uMrurFt 2 I 6EN01750 INN 41 1 a AreL1'= u.+n a t rsLV 1 6EN01752 ISN i,i17 Mt.l'-hLN+nLN 6LN0175,&. ISN 011e Th:LPT 4 ,e 1 = f"LF+ GENOL 756 INN G 11v (F'=tM U141 16ENUIl b l 1.%N i;#.Lt) f tF'= f P+AMLP* UAts^ l f V-A"LP # GEN0176U j JiV a3 l s^ 1 A 14 1=1 1 r- 1 htr - 1 l-F'i,U14{ 1 - 6t NO1762 I :N 0122 n t[ 1= 2. + f 1*wtr^ l +AFZl4 i GEN017o4 ISN G12i t.t,^l = P .ruMe; * ut2# +U 3) )-US (41 GEN017be -On iii INN till~ es l4l - Ail1 * ry t21 * F' tsur4t^1 v!

LEVEL 2.2 (5tp l 701 .%IK Ili t U'/3bU fURTKAN H t:XTENUEU UATr 78oLVV/10.3b.1ts ISN 0137 [301 Tir =O. Gi:N0090 ISN 0 13t t=ulF1 411=U. 9-1EN04.792 . ISN Ol:z-) tSu1 A&.ijI=i i rr- IJl - IrrLP - i 1r-Ptsum 21 btNG17y4 ISN Cif%L 021J1=[.+I AI-*KM1*AKM1 t7 NLIIvo iSN x141 0&IJI z-ki.IJl * 6 kiJl+rd' m1,21 btN6.1?vd ISN U 4t 1=-IIF4Fulr11J utNCIbOL . ISN Ov*3 kiu YU 43G2 6E9v01802 ISN ui4 't Z.3 U.. H2IjI - II p1-1J! - InLr-PburiIc1 . iat"v1bo,* ISN 0145 tic1 l=L. btNULUG6 . ISN Oi-rq v21 4 1=A AJJ+PbUM1[I UtNG1tl9d iSN 00647 It i%Mi4rlJv11 + AJlIJ1*RitJ btNf^lll4b ISM 014h I+FiJszs1 ooENG181ii ISN Gi tV c30L 1.21.01 =•N-rL:61r + 1T+2.*1 lftNclb12 bR l u 1 UIM 1 NPL GeNu Is 14 4----__..______..___ IALt, bet * fivN3 btNvidlb . 19:v Ll"n.u L3t+-+ 1r(ncA.Nt.11 bU 1U b rNLl111t ISN v utNu1.6t-3 1 S u1:)3 uL FJ -a.L r-' bi:Nui1112 l5N G,S-► ALL- t4 6tNL I b2r HN C: A L.ta.LJ brN%lL02o 1JrV ii : 7t ^r1 +4i^r.. . ^W.il owtr = lF:LCv!' .^1^• 1^.^F: UI[v131+F^13 { 1Vt^1l1+3.^K^v17 '^ 1sENL<1t1113 1 tKUl +vi'^1+hUl^v^11Ii / b.!{itiivr3i + k1Vlti1 / hvllVrll lykW{1^1{i^0 L ------.. tUuNUAKY CUt:ri"1L.ItNTk rUK OcLULITY btNG18a[ iSW U17 y c^1L^ HLir=KMiuc-bUJt*UMPLMINI' 11 btNGl834 ISN U,ou AnLA=UA619nLMI 1akN{^iti3ls ISN 0j b.L. T nLM=nLM+hLM GENV184fJ ISN U4b2 fri=cM ulNN i I btNG.J1tS^r2 ISN U103 f Tea= fM +A "Lrt +U AhS i To -AnLM 1 GEMOib44 ISN U1b ,t P4uMM =ru%kgUMtNN 2! . Ut:NuLbdtb ISN 0iaS A(NP2l=L.+fivP3-RMt+AK1'tt be NO 1848 ISN J1ao :ilivP Gl = TTI'i+IrnLM-TNi'3-rVUMINPlI 6ENGifSDG F' I3iv iilo7 1. rirr' c1= r4UMM l3. U{NF+ L1+ULNrlll-USTNN21 btWiSDI ISN dints UINV2)=AINr2l+ciNP21+PbOMINP21 bENU1b.>2 L ____------—_r_ bLUNUARY LOU-FIGItNTS tOR F O S btN(Ji8S3 E ' ISN 01 69 UU 232 ,L J.=1 irr bt1V U IUrob ISN 0017 TMi-=Tt1/ PKtt JoNP1I 1lENGttsbb ISN 0171 11Mi~= iAF*AMLM+UAtISI1m,F-AhLM) btNUleb[ 1SN 0112 lrlictx.Nt.11 bU fU !! Sll btNOido4 JbN 0174 L1,:LL ^rr lJ,ivP3st•ulrtl J l,INrir , Gt 1^1I beNultsbc ISN x, 112 1r11NutlJl. tw .,e! uU Tu 2313 6tNvAubs ISN ulll aJ::iJl =bt1J 1{{. 7 {1-1 .1:NN2 l+Fl.J,NrI! ! ♦ FUlrki .l!-rt.JrNl+ j!! btNCJLs7u ISN 0478 Liu IU 4.11c bENG Lib 72 ISN 0 179 [311 TNP3,1= = fl. btNUlb?4 ISN U i 311; rui#~t l .J 1 =++. btNl}l87t+ ISN 0181 c31t 4Ne2l y 1=1.+ INP3r -KMt+AKME btNUib tb ISN 0102 6NPclJI = IIMt-+irWM-'INr3r -rb11M4NPI1 42ENG18au 1,N 0 1 84 urtr2 ( i J =AN'X 2 111 +'bNI'21. 1 frEiOMlNV;r. 1 b1tW01bb4 ISN 0184 T=-TNP.:r+ruIrclJ! ► 6tNUltb4 ISN Ultra tali TO behuibut 1Sii Oltib beNLibbb i5N lil y 1 t7N1'1 { J I= i iMr+ I ritTrl-i'I,UMINri I bElvu16go iSly wl +sts L1Ni'GIJI=utx#^21 .31 +rtr[s MlNr21 I^tN61k;iL 1SN uLu g T=-3 Mt+rlalNrl ! — NJtlJJ 4 K1 P3) UtNOiL94 ISN 01 9 u I I=3.*rl 4 r,vN.: llri.i r[ 1 bcilowic '-, 1SN ui til ^.^y i~GIJJ = r'hL► Nli « IT * ^.+T i.tN..ltt`sts

lk LEVEL 2.1 (Ste1 701 aIr,Iut US/360 rilKiKAN H cx1tNUtU UATt 713.iyb/ 1G..3e,.ltt F ISN 0192 R.t IUR N 6ENlilyuG Lx•**s;******,:.+*f** K I U L 3 *** â*s * ^x*GENOI^ L ISN iJl y .:^ .ji:Ui Uu 3UG!> 1=.1 * f4P1 6cN611vG4 15N 0194 T hLM=J Lr bt-Nt jvbt ISN 01Y!; r1Lr =Rt%iUt"uu-. *UM rUM1 1 J btni JM^d ISN UI g b 1 mLN = h!Le*hL r btN^^ly 111 ISN kii g I fNLVTill=fnLr btNul412 i ISN [ i9 d AhL-PZUO bbl nLr 1 6tNUIli 14 iS14 to L99 AhLeTt1J =Ah LP t.rNLIV16 ISN 0200 TIM= 1Te (AWL, 1918 ISN 04-01 Ir=tM U-111 btNOIV20 ISN 0204 I IP=I P +AhLr+L)Abb U P -AnLN GtN6I9[2 ISN Olu3 AIIJ=*J1P-J"LP - PkxJMiIJ GtNUl924 ISN Liu4 0111 = IIM*lnLA-1'vUM i I- AI c^tN(jl'1s't ISW u 4 u--^ LIII = Y p.ti+t C U'MI3i _11+UiI) *UMUI11 UA1 * iJ+OMUII-11 4U[I-11 -UbIII 6CNG11728 ISN 1)406 u I i 1=J-t1 J t ^111*e bum II J vtWti19,^L ISN j407 :.JL ..Lotilvr6.:^. t1*0A. V 3,e ISN 34ub UL 1U NU'VrL ta' N:.t10, ISN 42vò 3 1r11 1 L-%1 J : y i;ir^'y u5r3YGv btfy:•153t: INA u[-, i btN^1`1=b 1a^Y v^1L vr 1^tc.r^Y^^1 i rsitlrL = [^ IV1s J btiN+. 1`140 1 J^ti ^îL WK11clrr3'y ^^J t V tllrl^-^:^NF' 2J VrNt1`lw;' ISN O..i,s [UI1J*L= 4r Nr21 6tIY1ilY44 ISN u21 -r V(i C tUKMA f l I 1411 J * IPLIu11..;s1 l 7X * 111J11.31 J. 6Ei4Ovj4o ISN 021.,) ;9 %;t runMAI ( i n oil) 6t N:; 15arb ISN 0210 3966 k-LKMAIiIh Lill r 1P AiUil. -I f 1?X*L1UL1a'311 biNisly5il ISN 0217 ::Y G4 rUmfiA I t Ih Ul i 1 vit liull . 3/ 17X * 110,i1.311 bfNU11952 1,N U[18 3"3u^ L.UWiNUt [sENUlb94 L _------b t NG i 5156 ISN 021,9 U111=u111 -UPUX 4 LJ*OX / kUl11 btWulbba ISN U4411 1NtKtA.tN.2.ANU * KUU(N:V31*Nt.Uwk btN'ULVb0 L..._.._ ..____--_-..w____---_ SU,LV'E FUR UUMNSTKtAM V $ b ------btN#i196Z ISN 0.^2 dIzI =i =121+Dill+1.1[1 10, u [I LE11ULV64 ISN Oit 4 A[cJ=At2J./UUJ btNOAV66 ISN ei4L3 UO 304a 1=3 *NPi bENUiVbb ISN U 226 I=ul 1 1-131 I J*Ai i-1 } 6bN01V 11j ISN G ee7 A(i)= A11J / 1 arnlutyi2 iso OZ28 U 1L rst1J = { ti1J*utl - 11 +t:1i11 / I T VtNt.lyl4 ISN 0d-29 UO 1UASh =4f- *Nr4. tarWG1N?G ISN Uk30 l =N +-r-Iu:r,3ia C+rNUlS 7ei i ISN 031 ul1J = k11JUii * lJ+rs111 bl:N^liylsd► l; ------— ------Tr ST J-UR N tt. A 11V c . U r b btNu lv e; ! L'/IU1KA r = Uq-WU AL11UN/ • vi.U,NO I U 1.0-3-0/ * b1 . 1g1FLa= -1/ Ouj. [ g1TES1=1 /6eNGLYb4 1SN OcsG 1r11U1n1;1' . tW .u.UK.I.t U.t.UK.l.tZF . N1'21 bU lU 3U:IU biNJlYbb O ISN QL34 Il=1LI41 Jf 6tNO19ba ISN 0235 :30-to J =ibTcr *L bErvcit9y:: Z ISN G236 W'KIILlo * JU`*l) Ulllrlr .i htNOlyS►2 ISN 0t3! 30-*7 r:U'hMAI (2Sn V [ Lt 4EKU) = •tNUiU . .)*bh Af I = 913 * GENCIVV4 ^ r 1 Un * 15J rF'=*1t•*3,rh * ar •f U fU 1.0-3(., SIRIUt3) bkNUL'r5.6 ISN 023r3 t1i!# =L.0-:^w tytN[.1*^ytS ISN Jt v 1171NZ-1UIKAN/c atnrC'tLiG C^ ISN Gz4u I I La f = IU IKA1'/3 btN::CE1tte At t: ISM Jz% 1 ;W U CUivl IN U.E bt NOZ C: 04 L------tic+vLCauc lJ1 ISN tia4z 1r1 11^l . ^4t.^1 vi1J -. 5+luJ::l+ui 11 btlV..[UL: L..

LEVLL 2.2 (bLVT 7o) bIKlut Ub13bU FUKTKAN H LXTENOW Uw1(k 7b.lyy/lU.3d.1b 0 INN 0444 bkNJ2010 ISN 024b jo} A. IHI ikzfl bt W012 ISN OiYI 31111 WiK1Tt(Gg3L+'11) 1vllirl=l,RN^1 bENU1ir14 1SN 0"-41 J'U1' tUKMA113h u ,bAj &VIAULL.^/ (YA II.LUll..)1f bLNG2Glb L ------btNlr[41t^ ISN :,Gl.a It- 1141-1 ».c:l+•ûc•u, ;L t4 bt;,4i 11r2^+ ISN a45(.# 21114 CONI1Nut btNi:2C'« ISN 0251 uu J=1,Ni btN(^L; k4 ------SULV L FOX UU NNS I KLAM F O J ► ISN 0222 U;c l=ui:1 J bt:,N 1G2b 1SN 0:53 ► 30 ISN 045 + ti 1 4 1 ='rte l J l/U l i UrNWX32 151,4 UCS!) Lt1.r,c1=1,[1Ji/IJ► 141 bENOZiJ34 ISN (i--au a 1 Jl ^tNCPkO.:b INN 0451 A;NY2 = Ai ,WI /UINN11 b=NuZLJt ISN G..Dd bIi111'cl=-a1%Jj► îJ1/uIoW-; I bcNLcl:-t£o 1.%w U L!>, ì "tW-zf,44 ISN tACd1j U!4 zutL 1- 3 TI+It 1 ut%4. e-L at4 1S1V ii^01 T1r1r= 11Vt-1a t-LNL2G4b INN 41'04 I1*r =41'1 U 11 1 /rK► r- IJ,I1 t2tNG264+t ISN .)4n:. TTVt-1J =1Yr*kMe14a ► +uAb-'jiF'I--..nLNl 1111 VtNL-/-L 54 1SN U4u4 x111=I ►lPr1J1- 'IhLPitil-kUUMILI btN::1(i52 INN U2o3 Dil ► =I IMir*+nLrIIA-l ► -YUUM%L-11 btN'bLU^4 1S1A 0[.t)6 61il = PL"4+ltd0h11 .3111+1- Ji l l 1 *UMulil4t 1 j,1*11+(JHU11-1) 4,1, li t 1-11! l^rN1JC[r9b ISN GZC)7 tllil=At11 +0+111+vbuM111 VtNa[05t3 ISN Ocb-ti Al 11 = AII /D(I1 1^tN.fl7GbQ ISN 0409 1311 ! = l l l► /0 1 1 1 L,tNi 20a2 I' 1w UG7'0 CFIJ 1 =,L.iI I/U411 L+thi(t1Q64► I SN 0211 3002 1;UNI INuc► btivUcOdb 1 s O1?;?. 1F;11151.) ^-96693YU7, 54Y06 btNUiubb ISN 0[7,5 390o WKllttb ,jbul! lAII)II =k914P, I 6EN O2070 ISN 027. WKiTc(be3V021 1n11i,1 =L9NV2i btNG2072 1 S 0215 WKilk to,iVW$1 1Lr1J,l), 1=1,111P21 brNu2b 1y ISN Ui: 7w W.KITE4b939041 tU%lJg1=[,NF'ti 1sfENb2o-1b INN 0471 1YU7 LUN T INuc brNo Zc 1 d ISN 0,276 [ 4 ";Ur 1 1Nue 6tNO2080 C ------► -__--..-_..- 6ENO, eok:2 ISN GLIY 11.1=0 btNillGbr INN 02ato UL bl 1=2 9 NP2 btNu2U8h ISN 0 28 1 fSAVEIll = tlnll , l ► btNG20bb I S14 j leb b l u:UN f 1!4ut GLNO20'vU L 1 I LkA f I VE 1.uUY FUR LtiEK bL4O[04l2 ISN 0263 be CONTINuc GENG.Jogd, ISN Urts4 UL .1,4U 1 =4 9 NYL 6cNUZGV4b 1 SN 0 8:i tMY=01 4 1 /S U 1 j ,1 l bENu20yli ISN 013b Uu 3Uo J = 1,N5 btNO2100 ISN 04b1 Ii M=A 111-*F(191*t1*21 1 1 *ti .dsl-1f+4rlJ 9 II 6ENO2LG2 ISN GZ66 it [flM.LI.IINV) 11M=[1fvY► 6tN01104 1SN U29,U z^11J =ff1% btRu[iQb IS14 Ga-0i S 4 i a l► = r I J, 1 1 btw&; -Ioo L INS UK t r1111 LS11MK;t b y S21K1.1>1 * NMALL IShvE UAIA SlAIEMFN11 VI:NUZIIi; INN OZ94 lr 1511J1.t1.i.0-1U1 ^11J1 ,;,NMALL brNc.411t ISN U 'i-r .3C1:, Lui,111Rut ULNC2114 L rt%,-VLNI 10,v-L (UN4,tNIKAI1UN t-KUM L)kLrt1-;13 yb 1NLc 1 VALUL 10 L lL6J ULcU Iu 1UtINI1rY Lrv^.-. li-r:^ tu_ L l.tht:lilzr +:v, ,^rrr.-°`r;°"'1Rr^ ^ , ,;. 'r",s+s x ca. 1, t-it^`:s .R4i'£ch . a.' w; r ' LEVEL 1 . L iStl' t 701 31KIUE US/360 FORIKAN M tATENOW DA Tr 7t!•lyy/lU•96 .1ti i t, AKKCUN U^tU TO bAVL 1NLt1 SIRLAM FiXL MULL NUMULK bENi)1l[.(3 ISN U,^Y5 IF iSlilul.u).61,aiFukL) S14iUt:UI=S2Fu L GkNG2112 ISN GZ9I fisumu=A#I)+FiNF,1*L)+b{11}F-iAr,I-1!*LFiNF III 6ENUJ124 ISN iK= i- fNil11 6tNfJ1l2b rsl.+r,tl^r^ LLATALI 1+A*U.EXrS FINK tLYWAKL ANU RcVtKSt RtAL'iLUN, IF Ur;:IbtNu142d 1. LALL r 1X^ utrI L•21316 INm 0411 ii• L rK.L I.:+bl,.1 Lht•AVT=.r14L.St:. 6EN%t 2132 ISN 0-iol t:ALL LREK 4atNozl34 ISN 0300 I- i LbuKN! Lht Al. I =. 1 KUt • (A lvuelx sb ISN Eiaut Uu - iOb j = LvW% 6ENO213k Is,-4 0iu!) } lbtNG1140 ISN 03ub 3Ub Gu+rI114L-t GrNO2142 ISN l,a.U •i rihrI I J = hsubu uEN4114^ 1 Soa u Gtt ri iy i, l l =1K brN04 146 ISN :}^,;9 F 11,ts Ii =tN 6EM—i4a '1 Ibil tj i L mri.- ( =Kna:i- btNIC2170 1Siv i! :al ^4i t.Liii i I ut 6tW4t152 L JtQ T KJK L ua'y VkKutm&.t t'F= IhzK14!.'LHEMlLAL FitL0 btNL - ItA lW4 (J.; 1L II.; Sr =4. uzsVLC1tic, ISv 1zlz^ UL LL'* J =-,fled. bt14 :;t Ish Gz.s -► kcal =L,Ar,-*-ii:jAVLii it) ikru,.-Ic(, I.NN N-j1:) Lk i t c: l .vi .l. l I q wi T =1 btNuzibi! ISN U-11I iS,%vcil I=F-1wi, 11 t:tNGdIb4 IS1v U.,18 iift L.UniI 1 +auk utrW2lbb 14N uZ,19 lr :iuulT.c4j.41 bU TU 119 6kNf3L1611 ISN 0.>21 ItL i=14.11 +1 GtNO2170 is" 022 Ir (ILI .Lc.20) VU Tu G1. Vtnazk72 IS14 b-124 WHIlt 46991]1 isit r , { riN'IsK ) , K= i,Nr3! b.tNO2174 1Si!t L,31 91.) FUKMAT tih4, 4[:x,a-lh mtj 4UNYtR6cNL. t OF THrRMUGhtMIGAL flELU .••T tMPSGtNU217b lAie:t b1:Ivuz 178 1 S 0-- ZZa 11:^ t, ulv ilN ut 6tN(;&ZLe0 . AUJUS 1 F l J,1) ANU F I J,NF'a 1 ------16tNU 1 b2 ISN 031I uu :3321 J -19Nt btNO21ts4 INN G32d 6u i U l -iclt<,j220 v.*d3U J t K IN bEN0:21tsb 1114 (; SLY 3Lla. It ilj4ut4ji.t w.t 1 FiJ,il = eulFit ij +.:+!F4J!, 2l+F-i .i,3))+AjliJ! /6IiJI 6.tNO2lbti. ISN U3 j L uU Ju 6 b (46 cc yG ISN Clza2 J4 3u F iJ,i l = .:.+t F t .1,4) +ri jv.*lJ b.tNU11Y[ IS;V 03j- 1120 VU Yd 4 3-' 1( , -3 3ca,:33 -lG) # Kt x GLN.U211IY4 ISN 6tNuz1yt. F4.I,NP11 ) -Aat 4 .1! /uti ,^! VtNU214L' mil j SiV V^.'.0 t3,11 1 .a3%0 bEfllU[2ii[I 1 .133i, rtj N4't5 )=.S iFiJ,lar1!* w iJrNi'1!) 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M LEVEL 2.2 4Strj 7b§ LKtK Ub,/3bO I-UKJKAW H kATENutu VATt 7 8.199/ 1U.37.tG 0 ISN OLU5 ASSIVN 191+ lU NLxIGK GEN4JOL6 ISN Click► ASSIUN Z -IU lU NtXIN6 6ENL.Alii ISN u181 bl, iu -Gwv btNU3G2U L bt Nli;012 L4** 44* * IF* 4.0# *4+ LHAP'1 tK 3 4+4 Y4* 6eN.OA'2,% L 44 * 4+4 Y Lm AN i LK 3 sww * art L,tNV.ê.6 i Vt hlj3t)[ti L #**NCN-AulAOA 1 11,4-+• # blrNU3l)a{i L Stl. l iujv hLK N6N--AUlAbAl IC buLuT IUNS F= KLM AblAbATIC cb.TIMAlt.b VtNU3032 t. (MUUt Z ANU 4 ONLY1 6tNO3034 L TAY UIRELILV T U UbTAIN NOW—AUlA dAl1L tOL U71U1rl it NuT Nl4LG.ESSIkUL * GENO303b tr S iAR 1 n LF — lNf tKVAL St.AL1146 tKOM Tnt AUTAHATIL )#JLU I1uN bV 6ENO30s8 L UCl-: lIÌNb A JLAL1.Nb F=AL.Fuk Fw 10,U —l..GI IU MULF1PLY lht OWN--AUlAbAFlL GtNO3U40 L ithNi loll 1;4 the rNthbV c:WUAI IL;i' IN .LVcLt e bLNU,042 L 6tN Li;,,O`r4 I SN t: ldd L L^blAb = .l-MLLE. l,tiV4.SL40 IaN t7,^y ^tÛ=u... btNU:3G4b Ism ul` u Aril=1.L ^tNt,^G50 IbN 419, 1.,E hi. Û9c ISN 6IY2 1A=,^ ttNC^+„^-r 1S1v Ul `do A^jS1 +j'R 34.. IL NrAfL,n t;tlîi^^C>>(^ 1SN ui y•r A-'—, IObA JB;j I NcXTNV 6ttii.^L7t tJN 0 11.1 uL: lu ^vw bLNL :t bi: btNG3Gat► ISN UL9:0 3tL IF li^wscw.i.Ui VU lU 5uG ttitnLl3t+c.4 INN U 196 ALu='F w [rtNG3G oa INN U199 Fw=1.(i 6tNO306b ISN 0ZL4 Ahl = 1.0 bENO3clo ISN GzU1 I %x-u bENGao7t IS^v E,^J2 GO iu z16 bENO313i4 L 6ENU to?b ISN Oz O3 33u iX=1X+t 6bNU;47t ISiv 02uk I V lIA * 61.lU) bU lb .%4i. 61:Ntl30bu Ism 6kua ( K=TS A VE bt NG..sOd2 ISM 0zG J Ulu 1a1 I =a WNS btNU3Ub4 ISN GC-i1t a4i S4ll 1=SSAVL 11 ) bkNU3Gtb ISN 0 ;41.,1 ru-U * Dm (AUj + ,(rill GLNO-0ib i ISN u2i4j Ah,l =Fw L,LNO30S0 ISN 0211 GL: lU AIL 6tN63OV2 L l,tNO3U9k ISN Ucle- 34u t:UNIIivut 6ENG::096 ISw 00.13 1=L=1. 16ENG30yii ISN 021-r tau TU Oat (xtmoalUO L l;LNO3102 L+444 *441 41*44 6hAP i tR 4 ***bCN63IL4 L **—P,: *444 44** L:NAPf tk 4 *++* *4*6ENU3106 L bENO3kG8 L ** T rAlLUKL th1iS*4* r 6tNc311C L rkiLtU L11ulL UK KiNLII-C JULN Uhf CO U1V F.AiIU UVISIUt (foeitl0l 6kNU.^l12 L KLiUKN AuiALA I IL * NUN-KtACTEU MIX'IUKr- i-i.'uPtkllc .^ btNu3114 I.S'N 021: 4uO SM=t1.o tatNU3l'its ISN 021b ub 4U1 1=1r Nb utNJ3120 i I IN U21 ] 5141 1 =mot tl l bt14t.%I k e ISN 0218 6LNLzi, at Y LEVEL 2.2 OPEPI 7a1 IL. RtK US/160 EUK TRAN n tXltNUtU UATt 713.15+9/10.3-1.2U ISN Oc19 401 Guwl1NuE GENO3126 ISN 0,[40 TK= 100u.Lf 6ENO3 ► ib ISN 0,:41 ALU='1 K b tNU i,& 30 ISN OZ22 1nL 1'S=1 6E140.ai1 s2 ISN u223 lr%IN V=I.LU --1 bthU31`s4 1SN U22A+ uL 4U.;^ 1 = t • li [sCNUsl1b ISN 0ZZj CAL L ML Vs b1 Ni731jts ISN GLLb. rlbuM =u.V bt:Nt$j14ti ISN 0221 LIU 4u^ n =a,Na bENv314[ ISN OZ28 h:>u =" WM+rtUiK 1*S L SK I 6ENO31 44 ISN 042.v Lu i11 11Ntc UtN9314r6 1SN 013ko T K- TtL+l1.L:+lhSU36*KGASIN*1K1NV—htSUMI LVbUAI t tNU314es ISN uk-iL G /1A bt N1:31s4 Ibf11 k; Xrsi=uA in—ALUI 4--tNl;s1,>2 ISN G ALU =Ir. titNG:'"!54 LSN 11434 lr lXly t.Ll.t.t.l GU lu -rvv btN o3ti0 1504 u4st^ &r..:, LLN 1 1111th Uk; NC31 too I%- 1 SN U L 37 WKilhlt:lftLJ 1*Ahl1 btNU.AtU ISN j 8 -rv'r %.'ui%it £V.ur- u'I:Nv31tt ISI4 02.sj Kr.Ue= ei, /Ir.uAS*IKIF-bMI (ytNU--1tat I 5 J 4t, ut I u r41 btiVV3 i bb L, t,tNGt^t GL Lz^*T^ ^^^^* +^^^^ ^^^^^ ^^^^ t.rlAt'Ttlr 7 ^^xr^^ '^t tNUj1 /(: t,rt 4r *444 4p.**44 44 * 0 iaF44 LhAPT tR 7 ***w* *6tNV3172► i, bENO3I74 t: *W•:.t KbbLkM t,tLL LA-LL TIC SPt,Lt*** btNO3176 • IAKt irle ES11MAILb 6LNERAiE11 Ih CMAPtERS 1j2 ANU AT 1E MP I A SOLU110N 16tNO317t • WI Fn t-U LL tQuAJAUNS. II= SUGCtSSEUL9 UPUATr TMt S AVt A NSwt: ktS wIln lnt6i:N0slb0 L. SU'LU I IUN ml-w Kc IUKN lV bIATtl r.N 1 N•UM1 j:R NLATUK. IF NU1 w Int ACl IUN . UENO3lbZ L ULP6114u5 Uis~ wMtl'htk Am EQUIL13M UR KlNkTl,L bULN IS SGu6h1Y. rf%lLtu - 6tNu-41b4 4 tQUIL ,ULNe kL]Ukft 7U Sj^jk;MtNT NUMIiEk NEXI'Nb, WhLLt I =AILUkk IN A btNO31bb u Klhlai1L 4ULN WILL tic rULLuwtu b y AN ArTtMPf WiTh LNRb-r -- + kT-O. p 6LNO3188 C ANu SAMt LbIIMAl¢S. Stl)lNb Kl=U.ii IMPLIES InAi A LKANGE IN tEMP GENV31vo L t-1tLu nAS NU trrr.CT UN Srr Clt5 lUISTkit$UTIUN FWk ThA I PAKTiGULAK 6ENO3142 L 1'tcKNliUNj b-Ul' UutS ALLOW fhk: - S:PrLlrb CnAM2 C S 'fU tNrLUtNCt Int IrMr btNO31y4 C L,HAN6:t: ----- VAK11 AL ULLUUPLlhb OF TM: tNthur EuUMIUN. 1t- SuGCESSrUL6ENO3190 L. will LNKu - it KLVLAF WITH LNKb=1 lt=ULL LQUAFlUNS11' i1- ST1LL NU bUUUv 16ENO3LJ6 L. kclUKIY fU 11A1tMEN1 wUMbER NEXINta. btNO3L G0 C t i:NU32Ul ISN t1Z4t Dult GALL SPet t 6tNO320-t 1SN ll[kL it- tLLUNV61 bU TU ^4[1 br.NG32G8 L SULUf LUw rA1LEU TkY KI =OeU 6tNO32'06 0 ISN QZ1*4 It ILNK%aJ 4U Tu DZO 16ENO3210 1SN Gt4o Lllkt.,-.IKUL. bENO321[ .0 ISN 0z,*7 51U Gu IU NtXINb* ILOU91309LI09210r2D0,ZlC*330sbOOI 6ENGi214 ISN GZkti D4G It ILtwUiLl bU tU :*IU 6cNO321b ^..4 ISN u/5u Sat: LN-1tb=.rALbt. 6tNG-12ld ISN G2tii Gu lU : 40J bENO3[[C 0000 L MAVt :.L.LHI DUI W1 Jtl0U F Kf FtAmb, StNU Trt1S btNU3222 C 30 C ZULN A^ tbI 1MAI=S Wl1h K LALCULA I 1 Ulm 6tNV-lL24 ISN U25Z '54t, i t lLNKbl faU TU 55U 6040x2 20 ISN UZ94 LNKt>=.lRUc. btNO3221i H is" OZDD to T u 7AQO 6tmu,-42.^j t. bt.NU3d Ae r. 4_^•^••••1t 1.uf ll:î 15 S,UL UL j. k-` ►J'L= U'rl-A ft jAVL t+il dwl ltKz, ANLI t.Ur%T 1NUt. 6LNua2:+,r 4

LEVEL 2.2 (.S t:P T to) LXLK US /3b0 FOKTKAN P1 tXfCNUtU DAf t 713.199/1G.37.2C - j G ^ GrNC3323b ISN 027b 55C TSAVE=TK brNO32^ri ISN U-] / uU 7bt L^-i^N, btNi^jLyl ISN UL -6),t3 ,^RV.c i► i 1 = Jtl L 1 tat:N{l32w2 c btNl 1SN U.^ yy FU wcA1cKip btN;;.)l40 i. btNG.a.14tf ' t **+f*+ Y**#44 LhA:Pf6K n ****** bLNU32ti0 t:++*+ ,^++,^ s**+^^ *a***s LhAPTER 6e ****** t ENG32')t L bt NW) 2t4 C ***t_i KUA MC -' bAGt S*** tiLN0^4 9b L b tNU 32 bb ISN 02ou 006 WRIftlo*tLl) 6tNO32cO INN ucbI. ova r-AILUttt; TU h1NV t•UU1L SULN...o bt:Nv32o2 AZ"mAV'U INLL i 1'F Urb kL'l l AN—t u/) btIVCf3[bM 1 -S iSN C 6'U &U t:• Du btNiJ:2GQ ISN U Lb;, 04- W-K11 t t II 1 GcNGsôL ISrY U404 oil t-AILUhc IU h]NU NtAK-tIJUIL *>VLN...r br.NU.3[7L A2htiAv u iNLtl NttLPb' Rtiti r(i4r : /1 +3tNO32?2 lstV L o y ^^_ iu u:)t. bt.NU.627y IS;^ ^r4fsb b1v N!r i i t c t L411 tak^VC:^t %d "' ISw uca j o4l rt3nMA1tlMv• 1uA9-1 14n+ *t*1 sal+h FA1LUKt IU Ut$IA I N KI-Nrflt, atILN Hi- lFtKvbt:N(+f,2 ?t3 A-rr-n i LIB 1N 1 Cn VAL nALV1No,:,.. .R Vba INLz i i,#%u b RE I URNLU/ 1 ULNU. Lkbu ISN U26b tab; iU bDL bt:NO32bZ ISN 6409 bû W'kl i t i b, bst l brNO.32b4 1SN aG7(+ o:31 FUK14ATtahko916A9314ri****1pd9H h0N-ÛTAbAT1C SULN FAI.LeDo..f , bENu3lzbb AiVMAUlk-d !WLN RETUkNtU/1 b NU32i38 ISN u[71 GL IU clU bLNO3290 4 bLNtrs^5i1 L.-----KCSTUkc rA1LrU PkUbL?--M M uut: PKIUR TO kkTURiSt Vi:NOj294 (, bt 1+14315x6 Isirl 0272 6>L x r iMU,Ut:-EWe[1 LA0IAd=,FAL"t. GENC.329b I4N 0474 It IMOUc . tWel) LcWlllt:=.Ffi.LSt. bl:NO3300 ISil 1721b 1F 1MULC.c4l . 4) LAULAti= . FÂLSt• b1=NU33U1 ISN 04 Its uu Tu g oti 6ENU^3G4 4 16LNO3306 [.-----Fk1Lt:U N-LN-"UTAbA l IL LULU I f0N... K:t 1 uKN AUTAbA I IL btN^: {3u^1 L.----- tQU1L UK Kai rAti. SUL U110M btNL331G ` t, bt+vu3^x2 ISN 027`! b tv .1 1aAVt btNO.',314 ISN 04dO :, Pi= 1.0 (^klMU.9.310 ISN Ol8t U'U b%l 1=1 * N- [^tNU331ti ISN 0282 x21 11=z bAwr { 1) btNt3337s+ ISN 4LI283 b71 JM=N14 { 1 1 txbX03322 L btNC3324 ISN tl 8k 906 btNG3326 ISN 026:) Kt 1UKN 6LN0642b ISN 0z8b c fit U btNC"x33:3

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A1 iK)) UU I .4'alG bENU.S!^ bG ISN Ot94* ALILtNZ:1 =ALILiiN31*t-6K) GC NO 35 bb L btNV3^bV u-----'tS1AB:Libh MULE1:ULAK 01:16r11 LJF S AE4.1ES btNU35y2 6 GENG3b Y4 ISN WJ9 SUM=Sl1M+AIUMi4tLl*b4K) b1=NG35 96 IJN U (tyo zaU LUNffilut INN 00 ,Y? 24L CuM INut bkNU:3o00 1sw Gu y's SIMw(Wal =tAim lxk Nbbbfj2 INN 0u 10 52iN5)=l.Gls—o bENG36 (A C 61LNO3666 L:_-----ÎUAC nULLtKIIh NAME UF- bPECIEN, GENUsbou L GtNOsa to I'SN OLUG UL 25v I=1 t3 btNO3b 12 1Siv u1Gl 4:i4 A.' .Ld1 :, t 1I =UA1Ai 1 ) beNo'^614 1. bk"03b 1b L-----btU1tt INUtA NUMoLk OF ,PrL1tS clt:14 336 Is L GtNt33620 ISN 31U2 It- ( A :UM1N.4 t ll.tW&ALU) 1W LU=NS GtN0.^b12 ISN 01U4 lt• 1,AJubINSt1).ci,I.ALU2) IULUZ=N'S GtNG3024 ISN GLUb Ik; IANUb4 ft,t 1).EW * AH4 I IUM2=iVN 61:N" 5626 ISN u11It1 1r IAN1oUIR1tI1.tW.Ah[UI 1U112U-1VS bkfflti 36L#f °oa ISN 0111. iF IASUUWZi,tli . cu * ANt) tUt41=NN 61:NG3ti3tj ^r ISN 011L IF IAÛbINSt1).cW.Ali lUUC=NS GEN33b^)2 G (mtNU3b&4 C ISN Olio NN =NS+i UcNV3d3b iSl G11^ bu fu 201 OLNO363U r 16M)36" I SN 13 1 1u ZbU NJ=NS—I Iwq Oli l NSM =NN +1 bENU.Jb44 1514 w11ts NW=Na*2 btNluab4a INN OLLV bkNl^3bkH INN . 0&.:L _ _ _ .. Ulf 1U 10 bt`+ILt^tsû LEVL-L 2 IStrl lb) LKLNG uS/3oU NUKTKAN ti cXTtNUtU UATt Tb.LV9/I0.37.dr3 I G bANU3652 L*** ^ '* LHANT tR 3 oENO3654 L**^ 44* #^Y . V *4 rp T 4 TH ** *, M LMA.P I tK 3 *** v** t7tNUSb9b' b0. lvGs69t! L *4^PMLLHAhlbt *** L. KtAU Vl=CmANISM/ KAIC UAIA LAKU' b -NO3ot2 L, Tht VAKIAbLr ull 11.0LUMNS 7z/7bl 1S UbtU AS A t^LAG: L L6S --'+ l.Lfa UWilSt KA1t CUllbl ANTS IN bM-MULt, t LMt %I:L t7tNk36bb. t. ANU tAL IN MCAL/bM-MOLL) btNO3668 L 6CMM ----s I.UMMZfti LAK0 9 FIR Ni 4tb L h AK.1C1 ERS Pk1Ni LV UUl btNU36?u G Kctla ----• KtVcK.`.L KATt DATA, IN bAMi^ UNiIS AS FUKWAKU UAIA L- EP40.36 72 L GLOO taLUDAL KA l t kAvRcSS iUN UAIA IN b1 UNI I S bt:NO3b 74 L Ulh:cKWlbt Tht '^1 UNAS lKb-MULtbi M t StCJ Alit ASSU.Mtu L..t=iVti3b ?6 L U11 ANU U12 tL.UL $a / 6v) LhN rtAVC ANrfMINI,, Ii`.tlhlMt11A1S1 it AbUV: Ft?UK oEWL: Jb 7b 4 WUKUb AKL NUN t LWIKLO lakNt73b t,0 L TAt. I is HI.11VAi lUN ltMPCKAlUKt t = EAL % /liA :LUNv U'kU K bti^ti^b b.. L. U tN:. 3b t54 14N UL21 3+,Ij JJ=1 L^ k S11 ►i :fib Bb bC^1'V jb tip, L bt:Ni:3o yl+ Ia4v U 2 JIU A-AW:, * , tlJ l Vn i n l l lt a= ltt c l'tCr1IlJJlsTtivf .^,rlsl:^îtJ J1tU'I LtVI^' k2L- biL ISN Uizn .3t1 r^ UKMA I11CA y t:.f b.,,tZA41 GENUjbb4 ISN UL2:, It I JASA l Ll.cat . dLA,1NK * AP4 U * Ui1.I iC . LUMMI '60 lU 37o btNO3696 L-----LMLIC rUK % 1UMMtNI I.AKU 6t NU3b y8 154 0127 il= lula.,Vi=.GUMM) bu TU 3i3 tPL-NO3,1 00 I bw GIZ9 W,Kllkibts121 lUATAlI1ti=1t121 0.,tNO3 1 U[ ISN U1JU 31 1 FCkMA1t 1nUv tAt .2t7 * **tI1.A4v 4h***1 b is NO3704 ISN 0131 60 'IU 31G GENO3706 L------Cht L:K tuh xkvcK.St kATt Uf%T " e * o IKU.tk OF CAKbS MUST bt GUKRtCT 6bNO3 00 L-----UNITS Ut- ktVtKSt UAIA ASSUMCU SAMr AS (-CKWARO UAIA takNG37 La ISN 013.2 31.3 lip tUlaw NL .AtVi:1 tau TU 31 3 60NO3712 14N 013-t J=JJ^1 GLNU3714 ISN 013:, bX4(J)=bX1JJl U ENO 3716 ISN Grab ltN21., 1=it:f4lJ.11 G.LNO371b 15N Ui 3 l fALf2W 1 =]ALl tJJ1 WA03720 15N 0138 WKI Ft t 93L-t1 tillL l J l t Ttnl[ t J J, TALT L I J 1. UT 1,1uT[ bENO3722 1W14 uiS y 314 ruKMATt1 4A, IlnktVtK-l-i7 KAlt UAIA l .2. dXt314-i-w . 3t2A4J vE14037 e4 L----^-LtlWVEKl t:Xt rU'k lfio tKNAL LALLULA IILNS utNG3 17 kb ISN 01-t0 8X2(J'1=mXt(JI*'irNLK 6ENU372b ISN 0141 11- ILSl) sou lU îiU btNU3/30 1414 0-iti3 sXLlJI=liX2lJJ - IteliLiî*9. y 6kNO3732 ISN a144 fACi2tJ1 = 1AL.IZIJJ*LUGU.G/l.9tt7 bkN.03734 ISN UL 't5 I tMUuKIJI . tU.41 bA?-IJJ =tiA2W),-li`NLW43.0 GENU3736 IbN G147 GU 1u -io btNO373b C---- -Chct.K TUK ON115 t, ENOJ 740 ISN UL wd 313 LS 1 =.1 KUt• GENO37 -42 . INN 0149 IF lU il Ll eeW aLbSl L41=.FALbE. btNO374M L: btNU3746 ISIV 0151 WKAlCit•t11b 1 J.JtIUATAII1ti=;-Itl2itbAliJJ)ofr-NIJJI*'IALTIJJJ#Ulltbfz GtN'ii314U ISN 0152 Jib tUK0Al%I"Uv5A s lDv%M & tit A4a3F15.:.t3x.tcA.^+l 6LNU-1 f 50 ISN 0153 it 1.iwT. LbI 1 FACllJJ1=TA(-liJJ1*10000/i.9c7 UE-NIU.37 St I SN G1.77 It tUll.c4.bLUb) Nu Lub=N bLub+t bt: NL 315-r L-----CUNVEs I uX FtlK i mTrRr*AL LAL.LULATlUt,IS ut:Nt'RalD0 ! bN 131! ti?.LJJI^-tiXiJVl^ l t,rLi^ u l

LEVEL 2.2 lbt0l 7b! GKtKO W%1360 FUK IrKAN N tXTtNDt:D UAI E 78.1VV/10o47.4r L-----lL(1 PJ ) 1S Int INUc x NumbtK U1= Th< I -l k 015TINCT SPECIES IN GrNO3762 [.-----KEat;TluN ^ ... 1=1,4 AS NU OlSlImLT 1hIKU bCUItS Alit; CUNSlokktu I,tNU.s$64 t;,ttvL 3 o6 S 1a^v 0lû UU ZtG 1=1.4 GLNO37 6b ISN g15H ^1: IUt191Jl=L btNval7c brNti37 7Z ISN 0:kOv 1VW=1 6tNG3174 1 S+v X31 a 1 Uu -14D N =1 ta bt:NO3776 • 1 SN u 1 o2 bENO3778 I SN G1o3 IF 40A1AIK1LW * BLANK) by TO 32D VENC3780 ISN UloD It iQAlA%N):wEeTnik U! bu lu 421 ISN Glol U A TA(Kf=BLANK VtN0^7t•4 ISN olov UL Ill ^ 2 bt Nt3 J7 be I SN u 1 a'1 .ti Lt:IIJTlivut bt'N^d/bb l- ISN G,l ?U uu a2z 1 = 1 s i!l.: bt:N^^'7SiL I SIv 0.I 1 lh kV, d AlN) . Nr.rIJULI1 s l1l ut TU 34L vlrNv3lYt IBA U11^ it tuAlAtK*lt.nt.AbUbtl,cl! (.,U IU zotr yr:Wu^7yr 15nt u!!:^ i1=4 b t.N C 3 4 srt) IaN.17u uL lu at^ GGNG 37 ^s< 1S+v G 1 7? at& LUNItks- t Lt.; lr lA.uf.$) uu lu --t,* tatfYi. 338 LZ I utl,01JJ 1 vtNG3tiG4 ISN 0161 iV u=IV u t 1 - ISN uA.8;: b:u IU ; 2 b GtNU3wDb ISN Cid 3 31 y It liilt.,t4.[ 1 hU=^ 6k:NC. lb I ISN ulti^ 1L IiYU^J,J J=11 btN.G3812 I SN ld(3 rut.=NUti► 6ENC3814 ISN O.L*7 jZ L ON1IPwf tatNOjti 16 L ` GENU3btb L GkNO3b20 4-'--`--, f L'ErLt I htt t YPE 01: k.tALTIuN...T"KtE TYPES ttNU3b 22 t. MUUK 1 .,. A + 8 ----1 L + U . bkNO3824 L M'GL3KL ... A&► * M ----% A + 8 + M 6bNG3b1a L muuk 3 ... A * d + M ----+ Ad + M GtNU:3bk b 4 btNO36 3U ISN Oi88 M'UuR i .t. l =1 t^LNG38 3Z ISN utby 1t- ► liulm i jil=L btN'(; 3Zs 34 1 , +ow +ây1 It lIvl drrJJ1 . t:U.GI MUuKtJJ1 =,3 btNti:^b 36 L btNU3ts 3ti L bENUsB 40 t L inL tULLLJ4,Il14b S=LllUNj UP *IU :lAItMtNT 3.55 LNi..LUSiVti MAY tt 6tNO3b,*2 t. cL1M1N.4 1tu !r Kcv.EkSt IA4 WELL AS I-OKWAKUI Kroft: DATA 1S SuPPLltu bENv3ib soo A i. r= Uk ++ ALL ** KLAL f lUNS. b ENO38 46 L btNti384d L GA LUL' ftJ K t^VirKS i- kAit i -A& I Ll AN15 FKUM Lld'K1AlA LUN,iAWI$ UfNUjfSSG ^ . 4 AIYU tÙhWAkU KATc LUNSTANIS NUR FltEttN QUINTS btNO3b5Z L UVtK Tht ltMPLRAlUNt KANUL IOUO IU 3000 Utl K 6ENDa854 1561 U 193 dAt1JJJ=0. GH403b56 a ISN UlY4 TtN2i JJ1-t). 4atNG3tl76 IS'll Olti:- 1 Au 12 t u.r)=U. utNtljB b!} ISN 0I Lib It tUil . rk:sGLUfjJ foU IU ZS5 [Êl11v:abtsZ ISN Ut98 Ux = l AKAX-AJ it fu ► / 14. U lstN[13ci t;ti ISN 0IV9 ,,WmA = u 0., t,tt,10386a 1S^v DLGv SLMY=U.0 61-N6.$lJbb ISN ULul 1rrLNJ 'c ts1 v -3is7L : fir'

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LtVtL 2.2 t,tPT 1b) cKrKu US/ IbO FUR TItAN h EX 1 EfAUtU UAI t TB.i^►y/!U. f.4.3 ISN G20c Uu 351 N=1,15 GLNO387t ISN 0203 X(NJ=AMiu+uX*vfLLA1tN -1J 6hNO3874 ISN 0234 SUMX= uMX+X tN1 ISN 0ZGS 1 el1NV=X lir) 1itNO38 Ìt] ISN ozUG t 1c= 1 .G/'IK111Y I sry u2u 7 1 LN=uLu.bt iii 1 I'm CNU3tbz ISN u2Ub LALL Mt:PS btNU ib 84 LSN 0201 sumi=4. V btN^ysT1 tia 1",N Otiu UU 37U Nb=it4 [s LNG38bb 1SN Q24L x= luiNtl,JJ) btNW8 90 ISN 0112 11- 1K.Ld.4) 6U TU 3DO b E".:W 1i_ ISN u2ik yF=MU(&1-SG4K) b tN.G 38 v.t 1 SN U21-b) 11- 1N;U.LT.a0 Sun1=SUMi+6r L`•_ tW;;i8y ISN 43411 It- tNb.6L..:) aUayl= ^ttril-br VtNk^d6k_ 76t 1 ail U.:av u t.UNJ 1Wut L^cNu^ %y jb IaN ( L2ù 1 M,.=C.:. vtNu.^ y c:^ ISN G cL i I1- lIu(^,J.,l.tbl.u! IMi=Tt_1ti -1.L'G3,r tatf`t:: aî L`y I b iV uc[3 if (lUt'+,., .^l.t bl . L1 TMi =2.^tu34-1LiYI btNG3yc.e 1 bN I1Ivl = toil wM1 + 1Lht jj ALIV- ALftJJi} iK1i4V+bytJJ1 ' a trv.J sy ub Ism U2 G ^vi^Y=autK Y +tr 1 it1 btN u3`J IG i >N .i^L 1 iai LLN111.4,t btirv"ilx1C ISN L12u X L AR = bvMX/ &D.4, btNL: Iv 1" i fir Gc19 btNij 3`116 ISN GL3u i>kwO39id ISN SUMI°u. tv Gt N U:39 20 ISN UZjz SUMY=to.0 GtNWvke ISN Uk3s U,U a5[ N =i s t5 L_tM).4!24 ISN Gt34 5-UMX=3u14x+T 1 N 1 I X (N) --AbAK ! Ut: NU3y2b I S iv Oc3..n SuMl = ^<,Mi*'(XtN!- Ar3A1t l ^w1 ISN r7^9d SuMY-,vMY+tviN)-YdAk1**2 bEttU39 30 I sm ii2.2 7 Sic CUNli.lhut to tN W$V 32 I SN i1 L 313 TtNLIJ^)-Li.U, GENO3y's4 ISN o'e3Y I AL Tll j J 1 = -SUMX/ SUM 1 GLNO3936 024U dA24 J41 = 1 YbAK+IAA 12 (JJ S WAbAK 1 /•itNLN tycNO39 38 ISN G j 141 S tiMX=G. b bENU .394u I 5N Oc42 U jDa N=1lp15 GtNO3y42 LSN oz-t3 .iUMA=,ti14X+ 1 Y t W) t I ALI 2 t JJ ) *A t N) -1 LNLW^bî t JJ 1) 442 GENO3ti44 I SN 01_44 35j t.uriit+rut btNGJ9 40 ISN. 024:) SLIMY`=US y k•1 (1.0-5UMX/SUMP) GtNo iv4b G L'e.b bLMA=U: UK? 14.U1 6tNu39n(i I SN 024-! U'[hLL -[AL1R,IJJ) . ^t:NU3y^z ISN 044d IF t.NU1.L:^1) UTh.LL =TALT[(Jj)*1.yb7#.UG1 bi=NO35r 5^r IaN 0ztiU h1K1lt ib * Ja41 bAz4jJ ) ,p 1t~rvL1JJ1 , UIhLL v5UMA9SUMY isENU35rya ISN U451 3]4 1'; UKMA r (_GA*!9i h LALLULA ICu htVtKSt. h A TC uAiaip ST u UtV ANIU L URK CUt f6bN0.39bd 1 - ,'t17.3t4X*2N2U1U.31 btNo3vbo bAe- 1-UK iA LKNAL CALGuLAT IUN5 bEfl1;A9b2 ISN o z:) 2 tbA_'(JJ 1-t1X2 (JJ 1*1 tNLN 6ENO3964 L bLNO396b R ISN U2ti3 3D5 JJ=JJ+1 GLNu3'lbts G-----4;UNVcl.i ALL RAlt DATA i!3 S1 UNITS btNU39 'Ifl ISN 1i1^4 It- tLS11 W TU i tu 1S^Î ti25o J =J,,-1 1 jN i^L7l tix (Jl =tix iJ!-TtNLry#^.0 G:kNV 39 16 I,j1^ U ^.7 t3 #^ 1ls_ I J 1 = t1 x.L I J 1- 1 c ivL1Y+^ ^ . L► btNU3'r Jb ISN Ozt9v 't ^" 1MtluK ( J 1.L^.11 ^-XL(J'j = k3-T^1J)-Ic1VLA ^.J.[^ v r NU .:Sr,^.t': Art r' ` LEVEL 2 . l Cbk PI lb) LKtKU ON/abU NUKTKAN H txTt:NUCU uA'lt f$.19ii/1Lf.31.43 ISN 02bi lF' (MUVKl .i).cW..31 1bX1.11 =1dX(J1 - TENLN*i.G atM{J35►b^ . ISN 04os uls TU jlO btNt33y$%t C. LatNil^'Jbb ISN 13 [ 64 35c JJ=aJ - 1 brNOSylls ISN U2b^ NbL.ub-V=Nk LL b* L l,t N4^'45G L IskNii ^Sr*lc (,--- -kt hllYT LiUI AKKAV Ut' b 'lUllrhlUA,r lKiL LutFr• L't.iENTS bE«1G3y5iti G btNii3Y5►d ISN Gtoo UU 472 J=i*JJ GENG .996 ISN 02b7 l;u ^l'fi N-1 , o GtNo-+Goo ISN 02bb n=N*2 -i btNC+406Z ISN 02 6V L=N 6CM04004 1 N uAzN it lh.u f.3) L-N-1 to EN(-)-tGG.b ISN Ui7 OAIAiKI =-oL.AW& IaF:Nu^rUOt ISN 027 u.AiAi&+I1 = bLANIK frkN^;»G 1U Ism 0 214 11- UL 1U =l : 6tNL-*CL2 I b.% u 2 lc, 11- l:4. cw..b1 tou i t., ^.1^ trtNudruI" ISN 0i.7d 11- ; lulL t J1 • td'.U1 sm) TU 37u btNUdfLit' ISN oec;j . IuLJ= iL.II-,JI otNk,ZZ,it ISN ti - bA u,.IkLKs=A+iUDIIU".Atal bLN,i Ckztp ISN Jcc, KeLU^p A =-K +1 I.,LNU-*ko :^. iSIM u4b;, u.:AA(KVLu:, l1 utiIuLJtci bcNL-rGG4,r 1 S ULts4 j l.. %.L ioI I Nut tatNu tU2b ISN oze.3 1f- llL)tZv,l.LW * U1 WATA01 = T1ll?(U taEr4o,*L2b 1 ,N tic$7 Ir bkrW4Uj30 ISN 0. 13,1 Uti:IAIII) =VA IA4D1 btNG40:L l luAlAtKJ*K 1 * 121 GEN04034 ISN 0[y G W K iTt40,3l l J ► = IS44 Gcy l 311 r4,1.MAl15x,151irs.*-'04vGA4 9 4101--•- wbX9b1441 1 16tNG4036 Ib14 029c C 31z GuN I lnrut 6tN0403b UU] ALL RAft DATA IN Sl UNITS bEN04L4,e L btN",' 044 00 ISN UZV3 WkITt lr•, 3.611 6ENU4046 ISN 0zv-t 38'V r= t,KMAII // intJ , 4lr:X , Ly tlKilVtlll. KAlt UAIA IN SL UN1TV VcND404b à G ALfW,b,M.Xt w oo * -rriMUk)RgI2Xj2hiU o IVXvch6XuX9 ir*rtftNr y Xlp4FiIALI 9 bema4[,:w CZ bENO.60D2 0310 bl.:X , 3n"Xt * YXt4.h1EN2v V X* tint ALT/./1 w r- ` IbN lIZYS U.0 .:tic J=1sJJ btNU405# . 15N @lc90 f Mi=bA l J !/ 1 cNLN tatNG sQb(3 fr^2 = rsxctJlrfttiuv 6EN0405t c a ISN 0297 (AzNG-r0cd0 . p ISN OZ9b btNC34Gb2 1fMc, ftf^:i1.► 1,TAt.T[lJ1 ISN 02 yy 3az GU141INut (A 4Ub4 ISN 04OU 3bt I lUKMAJ oKtIL,in.t18vr ,, A t " 15 1 2i.;sX 9 3rI1 -1AI I GENU4Uob ' c GrN"oass t.---- - Jc'1 t,. t.UNTALT 1Nucx e:, FU UNITY btN04070 ISN 03tji UU j yL J=LtJJ 16tNO407k IS14 03uG xllJl =1.V bF:N4t(i74 IS+11 Us(13 XL 1.11 = I.t, btrwho 7b IS1Y O3 yVU 6©h11NU.t btN04078 L 6ENli4iUbu ISN 030ti Kc iURN GtN'(-ripE2 r L 61` NC'40b4t G+s* +*k + LHAVftK *+*6EN04Ubo ^ 1r •! ^ ^ 3R i' ^ ^ F ^r a. fat +i it ^b ^ 1^ lS 41::1:1'ti t, ê ^r 3f ► ^ M f r + ^ ^ w k.rNx F'' f t K 4 ^'► s

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Vii. LLVLL 2 . 2 { Stf I 761 Ub /460 FORTRAN " t1tTtNUcU UATc itf.lY-s/iG.3t.•f3 y C ***RtAt.TAN rs +^► btNodto y7 t. KLAU KEAE.iANTS DATA LAKLJS Ft3k LALH lIV 'LET STHt;;M trEN1.-40 V4 L b li.w -4.{i li b ISN 0100 4i.0 wS t kM=,.S 1 1+M+1 UtN'i.4to yt ISN u.:U1 LMuLt::= .rALLU b t1vu- 1 00 L-----^S4hub bPeL1cb MULr JVUMtl=k AKRAV 6tN041► C2 ISN u3uti Ou --U::i i=1,Nb . UEN4i41 G4 ISN 0409 4t79 Jclal=u.V %a kN u-• 146 ISN 0 .i1u SuM1. =L.0 b:t N4341 G E. L t=tNO-,l I.0 ISN usll 4I( KtA1^ { ? f41.11 l ti Ttll , tt{1J,1 = 1 *41flUAl.. 111fI =1f1 , I't{;.411,Mt Ltfl'hAZ btMU4i 12 ISN 0312 41 1 1-:l;kMAI{41H.. , hl.^lf^p4 , LX,h7 . 3sAlf ' ^l,All atNt^431ti ^ , 1SN U.^1.1 it {A1l11 . LQ.c.LNKJ aJ TU 4''0 htNt 4i lb I,N U^la Wh,1L { c.,-t1cJ 4HI^iJ, ^ lllfi = l*'fJf1UAIH11 ► * 1=IfL1f^' C1.hfi,CiC:Ltf t:tNG411t ► t'riNL•N^ T1:M t^ tM{14111'i ISoq :ala Yip rt ;1>M.11{1X,^rl X, ^L,f-y.3ls^X , 1A-r,?X , r^.S, ^tr^+ i.[x.A1,2A•15.f ^rNu-tll^ I lr {Mt;LE.-V.r4LLf L1YLULt== .Tt3 I UU J u -+10 biNV4it4 1 4N 0S36 43:, LLN I INt3t 6tNC41tC L 6r-N()4i bti 1S14 O s S y w1t11tib,-:-Gl tpkNvs* i 70 ISN Ga40 4-fU FUKjnA1(1h(e f 1uX,4-*Jn KtALFANT ABO,Vt NuT t-nu U iw rhtkMO LibRARV /J bEN04172 ISN G.s-o-1 U.0 FU 41U GtNG4114 t; Oat 14174 ISN 0342 45u L UJ%Illvut 6:ENU437U L 6tNU41t0 G-----ES1Af3L1bh M1XIURE L14TMALI1V UENu+,la2 L btNG*Lb4 ISN 0343 1nLeS=.L GLNU4166 ISN 0344 LALL nCNS btNG-* 1 f'.ts L b 04041's0 IS14 0345 NSTKM bENO,41 y: 1SN 0.1-to 4bO rUKMAl tLhU•l Vh--+ KL=ALIANf S1Kk-AM,13,4M Vs*/ tAN041 V4 .,11-^t:f^^► fltslt `rJt t71'iSNtLltStlM /tt16bIMULtt,U^L/+h Nftibltl,^Xf bt Ni141 yr, dl^r^rluL^. PU+YI[sCKS , ^x,1Yt+rwASS FrtAi. IIUi^^/.i^d*17niril^rlULf: 11/{1tti iJ* G£NE+4iyL^ C-rn,ilr^lni,M.^t_ I1 / IrCV. xJ * ^!c*1^t^lhU 1)/lxU X1i1

LLVEL 2 . c lstl•'I IbJ LKEKt. UZ43bu FokTKAN H t:XTt NOEU UAlt -ld * iVlV/L0.3I.4-i ISN OJ47 rtsUm=u.0 CLN04202 ISN 0. 443 Sr1=U * U I:LN0426+r I SN 03 49 UU 'td G 1=1, N:+ 60404= Gc. ISN 0.1.3't, S4(!)=32111 /*um I 6cNcv2cu { __–""Shcll iN Mott ::U'M g tK5r KG– MQLt^ 1/KO 'M1X(UKr ljt_JV4r4,-'1G IbN 0351 brNL4212 ISN 0.»1 I1 1 I bkNc-"Z14 ISN uj59 UIHLU I.1141,mw II tst[rC'tlib ISN u j 24 WKilr-1 0 14tIG) Ir1AJUfiilrJlr . = lr3J : SNYJ{11^521IIsUIttLV beNU4111t INN to 3-,; 47u FOAM_ A IDAt iZtIM. f ,txr3.A^,2P3t32U*31► 6tNU4*220 ISN 0-456 -+8tu LUAl I INtut b1=Niv"211 L-----ti W60 sN juuLtJ /Kb Kt; ALTANJ MIAI UKt btNO&o-224 ISN 335 1 htÛ ;O-".>LM*KbAb' l K 6ENU4.i2b L------i hLe i Pir.SS ucnttA lY, tai /Lu m 6tN:;-r1L6 -NI ISiv 6-1.]o K hb AS * IKV bM I ucNubc;.Ci ,, - u t n► +142 31 _ IJN G—^ t^ y Z:ihI v V = 4. .t:/JM b frtvi,•eL3:► ISN Gib" 6tN4+r2;:o 14N U:ol -r5. FuniYiE31 tl.fiJ//12hrlahlt [wP^rrAIUhGE =,/'F':^li..,rJl. r^f^1,1CLa et% 6Eiv:.»i::u hi^x,lîncNl+^kLt• Y = ,.^^,zru1 ^•3y^7^r^Jt'1J^ÎULca/Kt;! UrN^^/^r l ch, t^rî% itc^Juh:t = ,sX,LF' Utc.s r3lt, [ Cla/M * / 6t14 4146 ..1cX,7^tt..ktu^1T!' =,^x,c+'t.t[.3,ix^ It'tK1a/M+*^S/ ^±-1VC4L+^^. Vi,-Arl.ZhPUtAN MUL w1 = , Lt'U14.9,^Xs ytttCUlKbMULt`//! ^sEN4 •rL4o L b f=iv G reL 4ti C-----uN KtIuKNs, CA LLING PRUW(AM MUSI S IUKL MULE NUMCEE2a S211)v 6kN04Ly4 L ----- ex.c SUK c, TcMPcKATUKr, tNTHALPY ANo utN's[ TY At A,PPhUPAlA1' c INLri 6kN ftZ.^4 L-----if4Lt f 4,KIU NUut U&NU4Z54 L btNo42 5b ISIV U^^1 Kc fUKN •taENl.4t531 IaN U.; b. E1%U cat NrJwZt^G *OPT IUNS 114 tt- FtLI *'NAmtIMAINJ NLsUNJIMILt L.INLCUUNIt!)?1 SIZL(mAX) AU I UU -b L CHUNt I *OPTIONS IN rFFrL ) *SL:UALL CbLUIL Nu LtSi NuUtCK UbJcLl NUMAP NuFuKMAT NuGUSTMT NOUL-t- NUAL.L' NUANSI= TtkM 1=L *S TA Ti ST1CS v :;L1UKLE tAATeMtNlS = 3b2, PR(16KAM SILT = i0b20, SUBPk06KAM NAMt = CReKO *STAIIsTIc:a*- NU UlA biNUSIlLS brr^lr.hhTcu ***T** ENU OF LUMPI LA i lUN 4444+v -110hK LYILa OF LtJKt NOF USrU

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h i . LEVEL 2.c iSE.Yt 7a) LALL US IJ60 PUKTkAN H tXTtNDW UAfk 78015► Sr/ 10.18.40 Y y N fl42 n WDUK V'= it (-t.* a4 * 1,K+.io*6)j I* lK +2.*w11 V I A+Qi 1*TmI GENU47b2 t ISN UU21 ZG CLM INut GkN0dr7b t L 6tN04786 ISN ti'utS IF ILtk.UiL1 uv Tu 3LU btMt)41bb L _ 61:(46,49L IbN 0L Khbm- vA4-r u" s lnF + ININV bt:iV'1i4%4iL ISN UO31 eKmuV= xnbmvt%m1kv tstN0475r*+ ISN W1 32 C Rin!+w= knlJ ,*-f 2 tstN;,479 L• * * 4 W + * * 4 + 4 * * * s f * s * *. * * * 4* + L:HaNTtrt I } + {• * +btNi:.FSCt! L # * * f a + * * * * * s * s s * * * LhAPTLk 1 * * V * * * stskNV4bf,2 1: 6rNi)4b G4 L *'&--N-6i LUCAL K V A C 1 i l)h*4* GEN044bC•a L b,LUt)^L Rj l t t ,,uA t IuNS F-UK mYul.►sGAKbUl% 1•'YkLLY,`,i.,,... 6CNU4bt.'b L 6LU6hL RAlt tXPFtitJ , Itih uut IL CUCLMrN L+ eaASL L,tNv4tl4 L t,XfIY + IA/-J U1 x LU + 4V/4 1 H[ btNL4t 1t t N U-+b 1.r ISN UG.as 6U et, LIUI bt(46.41a Is.4 :ii3!> lr ;T FL .L1. : r, i, .1 VJ IL: i C 6t:N04bIt ISN Li p r uv lLo L J = ! vNk7LLb btN ^J4LlGG ISEV t^.3u 1=AL)i ipJ1 1: Z+ 35N uu3^ ^t=luU^ btN[.klich INN uu +r y M =4WL0 6LNU4821b IJN O1 ;%i EV=1Ur+c btNG•rL+1b ISN 0,041- X L=AL ( ILL 9 1) WEN 146.;W ISN G(J4 .a Yeti =AL t ILnvl ) {atNil.832 ISN G(+44 TKl=TAL'iljj*TKiNV 6LNG4834 1 ISN uu+*:) TM2=TKi-bXlJ1*lLi.dLD * PPLNl 6EN04836 ISN G, U46 I F 1 G AIN t 1 M21.6) . blG 1 . 6U t U 100 bi;NG4#s 3d I SN G,L-rt3 K 1=LfLxe 1-10121 6EN04840 L btN(3tirliy2 G-----N'RLVlSlGh FOR L oNfACT IN'mtX GtN04844 1 SN ^t74 y FK i.=X1 tJ 1 *kl 6EN048d*6 ISW G,c,a . 0 kI= t l+.U00941K -U.51*K I* 1.RnUP4toZtKI US UKTtKrl0P*S2 II GEN64848 i I5Fv 0051 fMl=k1*u.5 btN046to0 ISN Jîi52 AlI,I1 =Al1911+7MI 6EN04652 1SN 0, Q 53 R 19K J = ^ I 9 K I+ki GtNG4854 ISM 004 ti;null =A ttC^ L l + k1 a► XL^1'. ^ 6i:N;i4tt^t ISN AIK.KI =AtV,wr I IMI*AL bENU4t35b ISN Ûô A ( M: I) =A try , I )— I m i 4 AL btNGgbb0 ISN (rGa! A I m KI = A;Mv1-Ki*Al-n btNU46b2 0 ,...0 I,4,N Uu;td A i N Il= g (N,II -, K.l*YH* U.25 btNU4bb4 G) ® ISN 4)U5v AtNPK1 =AtNvKI-IML*Yh 6EN048b6 L------'Hl/+îY^r^1=r► 1At^lY^lvl = G 6LLAUSt: NU ktVtKSt ecAL T IUN ASSUMED 16tNG486t! F ISN o uou RN=Ri *- i e 5 16tNo4b?U ISN U(,oI A; 1:NbM)=At 19NZM!-kk btNt)4872 1!>N F;,Lb2 AteL, NSMI=x;eitNSr^l1-KN*AL*G.^ bCN04b7,4 C a ISEv OUO3 AlM,NJM) -AjM,jN .),M1+R"* AL 6t:N04810 14N 400-e btNt487L+ INN UUc► 5 tstNu4u6L? ISN 0000 btmulc Cu ^L ISN UUo! AIM*1Vti)-A(MtNNI +kI*xL t7t mo-tbb-t ISN 0-L-0V btNtodlh66 1564 GOb `1 it I . NU1.La,Kb) UU I Ik 0 bL-14040bb 1 SEY Ol u1 1 Fit =K1+l IK1*1.G / K 4VI -1 5I l. ktVu-.liSG LEVtL 2.2 I bLV I 7bJ C ALL US/ 300 FUNIKA N ti titltNUtu UAIL 70 9 199/1 0o-ibe40 ISN OU72 AIIpNWJ=AII.N.W1*Ki 6kN04bW ISN OC73 AlttîvfJJ=AIJI.IVW1+fti *xG*f^. h ISN UU 14 AlmoNW=:.11•f t,,01- KI -X t. I SN UAL 1 :5 btNUtibye i^N 0 0 16 J GL GW INUr GEN*1*900 ISN Jvil 1 iU Luli'I lituc btNU- 4Gl L . btNl -',vlu4► a I Sty G::7 8 to tNo-r tUb L b ttYt:45s Ufi ** 6LN049IU ^+^ fir* ^* ** +aF +* *^ ^^ ^^ Y:A ** ** LHAN^ Crt L ;r* :^* ii LsîYl?•r^11^ L • GtNU4 y 1+ L btNQ -y I t,► L * 4, *KtALT1bN KAItL**+ btNU4N !b L Lti,UV6LAIC t-UKA KL, ANO kcVcKht KAltz K1 ANu RZ to t114 .,-r9c u L Inlic^. IYrts lst- Kt:Ht. 11l3lvJ 4 IrCNU-► Y^k L I^ i U U K 1 ... A L+ U L "lluui% 2 ... ,10 + M ----1 R r. * + M 1-. tN4. -fi Z 1 L Pli» i. F. 3 ... i+ + G + M --- -. A t + M btNt'•*y3L a 4 btrJvtiy -1t IS%N 0C7y 1=IUt 11011 L,,tNi;'+V A 4 ISN r.= iU11,JJ btN044 _3c ISN Ot,b; M=iul 3 0 1 J br-NLo 419 3 s ISN Gb^2 fl - W 14 t J J taEN649dfQ I Slv G,Gb -1 L btNG4'i44 ,Q ISN 0'u o-t ti 1=0. G bE N0494tt be NO,t9 ,+ti I S"i 0t,ts o TM1=G... bt NG45 9G ISN uud7 rm2=o.0 bkNu"9a[► ISN QOdd RN=U. G bI:f4049 !;4 ISN G-U.8y i K I =0 . 6 k N049 56 1SN 06 9-0 Ir,i=I AC k 4 I v i ttINV btNU-t51 bG ISN O't, y 1 IM2=fKI-bA(iI t,tNU&r5► 62 I514 ()u92 lt- I ICvHIJJ . Nt.t.• . J IMe IMk-Wttv1UJ*ILN btNLh9b4 1 SN u i 9-* It lUAc.l.l 'IMCJ.b1.o1bJ tit] lU GL> bkN4i4V bb ISN 0:,4a► K 1==Ut A-W 1-'f M 2 ) b t NG"y bfs L ----- r'r UV 1;.108 hUK LOO I AL I 1I4 or X bkN04y 7J ISN i1vy7 k 1- rcl+xi 1.11 bk(1fGky 7c 1'>N U09b !t- 1MUut-1J dluluvzolvkGL bLNGh974 I SN 0 599 20u K L = KJ.*s2 c I 1 4 kn.:b w 4. b 4i. 4 K 1 btNO44 7b I SN J 100 KN =kl+[. t, ISN Uiul 1t- ILhKttif K 'i x- K l v 11tlit 0+tn1-2.01 ULNO49UU IS+v 1: 103 uu IU 40:;p L btNC4984 I a 1 U lik 1U1 K.L =R l *vHSM * i-%hUP+SL(1J Gt C404b bCD ISN U 1 U^ rtiv=K1 btNU-%V tb 1JN 0LjC, I r 1 r_+KU) f, 1 =.K1^ IrcN l ,1l+i f< ^- .UJ btNVyy'i[y I 5,v O 1 U6 bU i u iuD tat wl"yy2 L b t !1 j"v4 94t 1 s GlG't LUG lZl-itl+Krl:,M F 1A1 4 KtiZ%W ,'è I I!>N G11G k.N-KI4,L L I'NtL&fVyr ISw 04,1.1 . -- Ir tLfrht,l h1=k. lYlfrNl -it+lr.i-^.E,1 L- t N a ^kG t,t: R,

LEVEL 2 * 2 ISEPI 1D1 LALL US/ -"#u6 VuR IKAN n tATtNOtO UATt 78.IV9/10.3tt.40 i t1 Nu 5o u2 ISN 0113 207 TM1=,Ei1 4,:kNG?1 04 L bkNODOC► O L-°^-_-^.kL1. U•L.+ i e h: vch^t hA fc LUNZA r-xum rNU KaT- cuNt;T ANV rPlul L tOK-%T brNtiaJ lfl L-----WhttiikVtK TtMP la IMAM 156E K bt:Nu!)U1Z 1. bkNU9G 14 1514 ii 114 It 1 FKoGT. AL—bwQ . 0) bU iU 22u LzklYti?t}lb C ta.kNtiS{i 1ti i ISN Olio h1Fi=M0 i ! 1 -MCi t i71 6EN050 20 ISPA 0117 S =Ji! l! 1--5t: i M^1 6LN(i?0 22 e ISN oils it tF0i't -21 tLN6tu24 '- t>tNUD020 ISN Oily 1u rrn =nrt*hCi lK 1-!tU # Iv b b1LNt;?[i 2b ISN ULG1i SS = :,1 •ryJ latl-^t. lw) t^tivt,ûsii I ^. i:,:•1 Jiî GAX =ax(J1* .^, utiYlSU L 151 Ji^2 Fn< _ F tti *nh btfvuSU ^^+ I^tV u^ t3 F lr^ =-car"f l d J ukWt.^L 3ta. ISN uit4 UL iU .4L L,cNi:)0--% t UtNV?() ^ Ci LSN X1.:7, t ti rti =rltt-rrulNi btNC!U42► l,lv u110 S =SS-^t, 1 f! 1 6tN1:504-* L -4-:,Uio.J U-. IS r-L" Ur tiAS WNbl 4.(.b2 L-b M:4-*6 -AFM /KbMUL-U,tb K. 6tNUDU46 ISN 0127 tsxx = L1x+tJ 1 * SS-2.ûG3l^ •r bkAlu?U+:B I 5jv U l is is I nc= FK:+hn sil:NO ?o 50 ISN O1tY TN2=Ttw(J)*I.0 VkN05452 IStY U13v ub i W isliu G:tNC15054 1bN 0131 21t Htv-tiN+nU 1K btNU:10bu ISjv n.,2 SS =aS+,AIK) (xkNG5O60 ISN U 13 tixx-tsxi .f 1+j5*2. ? UCi3Lis l^t1vU5Gb2 15N U134 TitZ= TK 1+hN btNLi5Grb*e 1W4 U1.;n5 TN2 = 7t1V#d ) - 1.0 bkNi!?U6b I SW a 1. rb bU lU C3G bF:NiJSObFt ^ c; GtNOy#I ÌU 1514 0131 GGk3 axx=bX,! GkNa5072 ISN 01411 f NZ=F At. 1. i J i'^'LKINV btNQ50 14 1JiY J13`! TW1= IUal ij) VtNt39a ^b L bENG9ti 7t3 0 IS14 01 4 ^s t^ ! Ms = 1 Ki-t^XX I^tNJ508{i QA 0 f ISN Olrt I!^ # INL.ht.U.! t'M^-IML- IN2ÎLri btNCt3atS2 ^^ ISN 0144 1F- 1UAb!A TMz1.VF . uttj w K2?0 bl:NC?O b4 ISN 0145 K2 =UExNl-- fiK21 - vtN050ub L----- MuLllr LY "U MU4-P O +lLMS KAYt: LUN SlANI M UtNFAI.I INDEX bt:NODUbb Z 1 SN U l-tb K.: =K2A, A2 t 1 btNG^GNO L bkN050y2 '^ ^ ISN U147 Lf ;MUUt-.21 6EN0509% ~~ 10 L btN050yc I sN U 1-+5 14G 111 =KZ +J2iMI KMS^J+521+11) - btNUaaytf► IS N 011*9 KF+1-KN -n^^?.l, bl-Nl+71(1ti ^ A 1 b G 1 56 IV tLNKU1 rcF=rt!-tic l #N[ + fKC-L . C}^ t,tNtlSii?2 ISN C1t11L L 1. t I+i ti ? 1 On Z 41 ltl=k2îilt,M^SlI .Ml^lit, S+or}5211{ 1 btNC^+10b 1514 U1^>4 Kiv=tyly -e.G+^.O bttvti^ll(.

.M ^. 7..,..... ,..-.w ... ^-...... ,..:.+... .:..: ... n:S ^ .^..-. .. - • - ryf yy- .•-+r,T!IKa:9'irq'i!W, •^'".^_ „?'ri/.^f, .. r ,.^-.. -. ^ _.,. .,, — ...... o...... -.., .. a .°ice.' _

LEVEL 2.2 lSLel 7b) t~ AL(. U.4 bbl) FUKIAAN H tXTLNUtU UATL 78*1V9/10.&8o40 ISN UL59 11- ILNKG1 Ft1=Hi-K ,^ !)ti2+1K1- GENU511c - 1SN 61DI t:U iu 25u VtN0s11-4 L bkN.Ub116 ISN G138 ^Lti1 K2=K2*e-ht . ;rKMur4SclM/ 14N J1 a y 1"N=Ki11—r.L bENODI cL INN J1b.0 IF &L tVKG) i.1 =Kt-k[' l^N^ +IIL^—t.tl) btNo!)l Z[ l,ti•JUbl[ti 1J4 U102 fig l = fM1- K 2 btNG5l zb L bf•NUb12b 4I:040D13O L *4-iK1f.Ktllt.4-zi^^ 1stNCYaL 32 G ULKIVAIIVt KNU Fut% Ll iuN M AIKJA ruk 'K1rnE1IL Sut_UIIUN GENv5I^4 L btlliîylô ISr1 t31o.:s A1 1f1)=Ativi) +'KL I:t+Vt:°5L jtt ibol [11b-r AiMv1)= A1Ms1)"Ki bI-NL 514G I JN Uib: A 1 11 M)•_A11IM ) —t%,. btllt(.r1!4^ 'N. ISN 6100 ti^rs , M)=:^tM,M)+Kt btNt;5l+.4 I Sf4 0101 mJ ;z&:I11 N :M1—P, btWo 44b 1JN 0 o AIMIN!iM/= NIMINSMI+hN (at No51+4:t Is m U wy ;a{1^lYldl =.a l1*^, w1 *KT btNt: 51 rL I J1Y oi l ,, A(MtNAi I =Flei F's Q1 U 040:4 I%N J171 AIAIN I= k I1 911f, )-U-1 1 6CNu51^4 ISN U172 AI-siwNA1=AiM wkA)*IM1 GtN^ti15 b ISN 0173 lr tMUi,t.cL .5) Lxu TL 2oU vtNG.15t L • VtNaSi a1? 1Sil 017 A i N I=A (N, i ) -KI . _ VtNObtb2 ISN U47b AlN , M)=AMwM)+K2 6ENU51b4 IS1v Ui77 A{1 N z--AlisWI -Kt 1 k:NG51 ab iSN 0170 A 4 M N) =AIM 1Y)+K2 6EN05108 1SN U17 A I N N)= y A ( N9N ► +k2 6tNG51 70 ISN U1 $•U A(Nsoi" m ) =AIN NSM)+KN bJ:NG3172 ISN 0181 A ) NfNWj mf,(N*N4J - KI u,ENU:4174 Isw t4b2 AlNt NA) =AINI1YA.I +I M L VtN0a1.7b 1SN old-) Lr (Mu:ut.tV.L) tal] IU 270 6t:N0517e V GI=Na51 bG . I'SN b1 82 Lbi3 GUNTINUE u:N05182 iSN Uiub Aln,1) - AIKvi)+K1 G tNt-15184 ISN 016 7 Al1*K)=At1rK)+K1 6040bltb ISN OIbb A(.KtK )=A(Kp1i)*KL GLNO!5I b8 ISN UIU9 A1M vK1=AlMgK) - K1 btN051yo IbN [ AVJ AIKtM)=AIK*M) -KZ GENU5191 laN 019 1 Air%vNSMI-I+!•KINbMJ-RN GLNUD194 ISN Ul y2 A4NvNW)=A1tSv1Y1))+K1 • btNu51y6 ISN GIV i A1h:i4'h) =At r%I N A 1-TMl btNt}9i58 ISN 0194 lr lMU'IJ L * C 1..:1) bl3 1U 210 GcNO5z00 L -^^N^^zoz 1 ISN 0196 AlNvK)=AINs&)-KL bEnlCrat 44 ISN 0191 AIK114S=AIK111) --Ke bkNub20o L 6tNU-',^20L ISN OL96 21 U GUNI I14ut 6tNG521G L artNC:b211 I JN GiV y H UM=O.0 btNL"Dz 14 3 ISN Uzu4 ur) zau 1=1•N:, 16LNt3 92 AO ISN U20i ^X1=S,cli) 6fcNU521b ISN 0 0e— All : ll=dilsl ) + ^fyV {SZ! vtNu^t2C^ ,mot . LEVEL 1.2 (SEPT 7:, j LALL US3 3bG FUKTRAN H L x TEmutU UAlk 111 . 19WIG. :3tt.40 ISN 0103 A119NAl = AIiINAI+rMV*iS1(1I-b21! 6bWb222 i ISN 0204 AiNSM,I)=S21 btNGtit24 ISN 02135 AINbM * NA1=A(NSM,1Â1-S21 brIV1 .^t26 ISN 0113th A(mw , IJ=nul11wS^:1 btNr ►^2'lts I SN Utu I rlsuM = ":WM*A (1Yd, I J lttNC^2 4 ISN 0t:08 e.86 1:usv f 'LN u1: bENU5^3[ L 6L14 Ott 2 34 ISN OZL't AIJY.'A i wNSIO =-sM btNG.0)13b L-----A fNIM ipNWI ANI, A(NLwNSM) ARt tVUAL I: U L t KU. GtNUroljE ISN 0; lLU AiNbM v N AI =A t NSM * NA1+SM bt:Wt! 2 40 1Siv Gill A4WwipOwJ =LeSLM*wliKV 6kUD2N2 1SN 0412 a1 Nr,1 ,Nr;1=NiN-{,}-rISUM 6tNii:,1+-= L bLNU! 2 -t ISN :J 13 I r1k 1=Nu btNU 92 4b ISN 0414 b1. Tu ItU G ttN::3 c:, L L b tNts^1^ LhR #^ *^ +iF 4F4 4^* +-M 4 4 GH-Af' Ye ^3 * •^'^ bkNie^G9ti - ^J K '] r ^M T TAT ^"7'4 +^k T'r'+ T T A T ` - LtiAf T tK J TT! to t: c 4 N(lt,"L, rt 1 {TtÛILi I^ 1uII+ '* ta^1ltG .ctit) L :jtn1VAliV= ..iglu t- uN:, I 1i-N Im4,, T1•:0, f-Ue. _ e-ulLIt r i'Um Jt:LUTiL'N btNi;92bL 1. 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