Equilibrium composition data for combustible stoichiometric mixtures of hydrogen-oxygen (water)

EQ.UILIBRIUM COMPOSITION DATA

FOR COMBUSTIBLE STOICHIOMETRIC MIXTURES OF HYDROGEN-OXYGEN (WATER)

April, 1976

Lo

l

SEP. 1975

by

Randy A. Roig

•

EQUILIBRIUM COMPOSITION DATA

FOR COMBUSTIBLE STOJ;CHIOMErRIC MIXTURES OF HYDROGEN-OXYGEN (WATER)

Submitted: April, 1976

April, 1976

by

Randy A. Roig

UTIAS Teelmical Note No. 201 CN ISSN 0082-5263

Acknowledgements

The encouragement and discussions with Prof. I. I. Glass are very much appreciated. The financial assistance from the National Research Council of Canada and the U.S. Air Force Office of Scientific Research, Air Force Systems Command, U.S.A.F., under Grant No. AF-AFOSR-72-2274, is acknowledged

wi th thanks. .

The author appreciates the assistance given by Dr. R. W. Nicholls, Physics Department, York University, in obtaining a copy of the Horton and Menard cOl~uter program.

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---Abstract

Equilibrium properties qf combustible stoichiometrie mixtures of hydrogen-oxygen (water) have been computed for a range of pressures and

temperatures consistent with a gas-driven implosion • Dissociation, ionization, and lowering of the ionization potential have been taken into account for

computation of the chemical equilibrium conditions. The program is based on

the shock equilibrium program of Horton and Menard (1969). To this program

were added corrections due to van der Waal's forces and lowering of the ionization potential. The la.tter effect was especially important at high electron number densities. The results should provide insight into spectro-scopie data obtained from gas-dri ven implosions •

TABLE OF CONTENTS

Page

Acknow1edgeJllents ii

Abstract iii

Tab1e of' Contents iv

Notation v

1. INTRODUCTION 1

2. THE COMPUTATIONAL METHOD 1

3. RESULTS 1

4.

C ONC LUS IONS 2

REFERENCES 3

P RHOO RHO MOL

wr

Z DBLAM

GAM

HMO/RTO SMO/R Notation pressure (dynes/ cm2)

density of air at STP (gm/litre) density of test gas (gm/litre) molecular weight (gm)

compressibility Debye length in cm

expansion parameter of ionization potential dimensionless enthalpy per unit mass

dimensionless entrapy

J"

.;',1

1 • INTRODUCTION

One requirement for a detailed spectroscopic study of a gas-driven

implosion is an accurate calculation of the equilibrium properties of the imploded gas. From this calculation, one can relate measured line intensities to total pressures, determine the best way to measure temperatures, and estimate the

sensitivities required for the experimental apparatus.

Previous calculations within this regime (Benoit, 1966), did not consider such effects as ionization, lowering of the ionization potential, and van der Waal forces. It was eipected that these effects would become important at temperat'llIes greater than 5000 K and at densi ties larger than 10 gm/litre. Corrections to reaction constants were found to be up to

700/0

at the highe st

temperatures and

2CP/o

at the highest densities considered in this calculation. This report has applied these corrections for an initial mixture of pure :820 in the temperature range 4000 K

<

T

<

6800 K, and density range

10 < RHO/RHOO < 100. The results are avaIlable numerically and the trends are shown gr aphi caIly •

2. THE COMPUTATIONAL MmHOD

The basic program of Horton and Menard (1969) was used for the chemical equilibrium calculations. The interested reader is referred to that publication and to Horton (1970) for details of the calculational methode It involves a numerical iterative technique for minimizing the Gibbs free energy.

To correct for higher densities, the method described by Hilsenrath and Klein (1965) was'utilized for providing second virial coefficient corrections~

The coefficients provide up to a

2CP/o

correction to reaction constants at the upper limit of the den!i ty range. Again, the interested reader rnay refer to the original paper for details of the calculation.

The theory of lowering the ionization potential has been a topic of extensive discussion since the early 1950's. A review of the subject through 1964 is given in Drawn and Felenbok (1965). We have adopted the expressions given in Rouse (1969). That is, below the critical density:

e2

m

0:: = GAM

*

kT DBLAM

where, DBLAM is the Debye length and GAM isthe ionization expansion parameter. The expansion has been carried out to three terms in GAM, ignoring terms ef order lCfl/ç in the worst case.

3.

RESULTS

The numerical results rnay.be obtained from UTIAS (see Appendix 1). The available tabulation is by temperature with a range of parametric densities. The outputs include concentrations of individual species, dimensionless enthalpy, dimensionless entropy, pressure , the compressibili ty factor, the Debye length , and the ionization expansion parameter.

As expected, the results deviate considerably from those of Benoi t

(1966)

at high temperatures and pressures. Even at lower values, the agreement is only

3-5%.

These deviations can be explained by the use of more accurate techniques for the calculation of reaction constants and the inclusion of more molecular and ionic species.

Figure

1

shows, for constant temperature

(5400

K), what changes in mole fraction occur when the density is increased. As might be expected; the mole fraction of the polyatomic species increase while that of the ionic species

(both negative and positive) tend to decrease or remain constant. This trend will reverse at higher densities (typically RHO/RHOO

= 200-300)

where pressure dissociation becomes important (Vardya,

1964).

Figures 2 and

3

show, for constant density (RHO/RHOO =

50),

what changes in mole fraction occur as the temperature is increased. The dominating features are the product1on of negative and positive ioris and the dissociation of H20. It is expec"ted that all neutral molec\llar species will begin to decline in mole fraction at about T =

7200

K, and the mole fraction of all neutral

species will have begun to de cline by

7800

K. In this example, the lowering of the ionization potential has changed the typical ionic reaction constant by

10%

at

5000

K and

40%

at

6600

K.

4 .

CONC LUS IONS

Accurate calculations were performed for the equilibrium proper ties of combustible stoichiometric mixtures of hydrogen and oxygen (water) at

moderately high densi ty and temperature • The computed concentrations should be accurate to ±

5%

at the highest densities (RHO/RHOO =

100)

and temperatures

(6800

K) considered, and ±

1%

for the lower values. These results may help to provide a better understanding of spectroscopic data obtained from gas-driven implosions.

1. Benoi t, A. 2. Drawn, H. W. Fe1enbok, P. 3. Hi1senrath, J. IG.ein, M. 4. Hort on , T. E. 5. Hort on , T. E. Menard, W. E. 6. Rouse, C. A. 7. Vardya, M. S. REFERENCES

(1966) "Thermodynamic and Co~osi tion Data for Constant-Volume Combustion of stoichiometrie Mixtures of Hydrogen-Oxygen Di1uted with Helium

or Hydrogen", UTIAS Tech. Note No. 104.

(1965) Data for Plasmas in LTE, Gauthier-Vil1ars (Paris), 503 p.

(1965) "Tables of Thermodynamie Properties of Air in Chemical Equilibrium Inc1uding Second Viria1 Corrections from 1500K to 15000K", AEDC_°.Report

No. TR-65-58.

(1970) "The Computation of Partition Functions and Thermochemistry Data for Atomie, Ionic, Diatomic, and Po1yatomic Species", JPL Teeh. Report 32-1425. (1969) "A Program for Computing Shock-Tube

Gas-dynamic Properties ", JPL Tech. RepE>rt 32-1350.

(1965) "Pressure Dissociation and Molecular Hydrogen", Mon. Not. Roy. Ast. Soc. 129, 345-50.

10.0 02 (-7) 8.0

ç

OH- (-6) 6.0 03(-5) H20 4.0 02(-1) 10- 1 30 OH+(-6) 2.0 OH H2 0-(-6) Z Q ~ _0+(-7) u

«

Cl:: U-lO LLI ...J 0 8 _{O~ (-7)} :E H 6 H-(-7) 4 10- 2 ₀ 3 H+(-7) 2 H;(-6) E- (-5)

I~~~~~~~--~--~--~~-=~~~~~~~---~

_o

_{10 20 30 40 50 60 70 80 90 100} RHO / RHOO

FIG. 1 CHANGES IN MOLE FRACTION AS A FUNCTION OF DENSITY FOR CONSTANT

10 10-6 4 10-7 4 2 10 z _10-8 0 ~ u

ei

4 U-w 2 ...J 0 ~

FIG. 2 CHANGES IN MOLE FRACTION AS A FUNCTION OF TEMPERATuRE FOR A CONSTANT DENSITY (RHO/RHOO = 50)

03 O

2

OH OH+ 0- E- H-02

10-1 10-2 z 10-3 0 i= ü ct 0:: u.. LLJ ...J 0 ~ 10- 4 10 8 4

OH

2 _~H2

~~O

02 6 4 ₀₂ 4 2 10 8 4 2 10 8 I~ ________ ~ ________ ~ ________ ~~ ________ ~ ________ -L ____ ~ 4 5 6 T (103K)

FIG. 3 CHANGES IN MOLE FRACTION AS A FUNCTION OF TEMPERATURE FOR A

APPENDIX 1

Due to the large expense of printing, it was decided not to reproduce the tables • A copy of the tables will be maintained at the UTIAS library, running approximately 555 pages. Xerox copies may be obtained at cost by writing the librarian at the Institute.