Nonequilibrium hydrogen flow in a cylindrical channel

In Honor of
Mikhail Ivanov
70th Birthday
Nonequilibrium hydrogen flow
in a cylindrical channel:
dissociation and expansion into
vacuum
Alexey Rebrov, Ivan Yudin
Kutateladze Institute of Thermophysics, 1
Ave. Lavrentiev, 630090, Novosibirsk,
Russia
2015
Subtitle of presentation:
”High temperature hydrogen activation by
diamond gas jet deposition”
The scope of topics
•Key experiments
•Rarefied gas in cylindrical channels
(review)
•Heterogeneous physical chemical
processes
•Direct statistical simulation of flows
with heterogeneous reactions
•Data on dissociation degree and
characteristics of flows in cylindrical
channels
•Conclusion
H. Koschmieder, V. Raible, and H. Kleinpoppen, Resonance structure in
the exitation cross section by electron impact of the 2s state in atomic
hydrogen, Phys. Rev. N3, 8, (1973)
Studies of rarefied flows in cylindrical channels
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Constants of interactions of
hydrogen molecule and atom
interaction with clean
tungsten surface in the range
of temperature 2000-2500K
dissociation degree Н2/W [20];
energy distribution on on internal step of
freedom by recombination [22] ;
sorption coefficients of Н2 и Н/W [21];
accommodation coefficients of Н и Н2/W with
scattering indicatrix [19];
recombination degree of Н/W;
internal energy exitation Н2/W;
[19] Межфазовая граница газ-твёрдое тело. Мир, Москва, (1970).
[20] Joe N. Smith, Jr., and Wade L. Fite J. Chem. Phys. 37, 898 (1962).
[21] K.O.E. Henriksson, K. Vortler, S. Dreissigacker, K. Nordlund, J.
Keinonen, Surf.Sci. 600, 3167 (2006).
[22] M. Rutigliano and M. Cacciatore, AIP Conf. Proc. 1333 464-468
(2011).
The lack of data on specular-diffuse reflection,
probabilities of atom recombination and exited
molecule dissociation generates a need to find
unknown constants by the trial-and-error method,
comparing the calculated and experimental values.
The probability of recombination of atoms after
sorption in the range of temperatures 2000-2500K is
determined equal to 0.3 [23], also as the result of
molecular dynamics analysis. But in this paper there is
no comment what is going on with rest 70% of atoms,
which have prevented the recombination after first
collisions with partners. We suppose the full
recombination of atoms after sticking. The important
result of calculation [22] is the distribution of internal
energy on degrees of freedom of strongly excited
molecules. The translational energy fraction is close to
sum of vibrational and rotational one. Such molecules
are to dissociate by collisions with higher probability
than unexcited ones. But there is no knowledge about
such processes. Preliminary calculations shew, that
dissociation degree correlates with experimental one
only at very high probability of dissociation of excited
molecules. For subsequent analysis this value was taken
equal to 1.
Direct statistical simulation of
flows with heterogeneous
reactions
Fig.2. The scheme of modelling area. L=20; 50
and100mm.
In wide use Bird algorithm [19] was adopted to analysis of
flows in capillaries and behind them up to the detector,
registering current in the mass-spectrometer. The calculated
field had 1.25105 cells; 5106 H and H2 particles in total were
used. The VSS model of molecules (soft spheres with a variable
cross section) was used for translational relaxation calculation.
Calculations were performed for conditions of experiments H.
Koschmieder, V. Raible, and H. Kleinpoppen, Resonance
structure in the exitation cross section by electron impact of
the 2s state in atomic hydrogen, Phys. Rev. N3, 8,
(1973)H+H2.The capillary diameter is 3mm, length is 100mm,
surface temperature is 2400K. The boundary conditions at the
entrance correspond to evaporation of molecules from the
circle with flux 61017 molecules per second in the point of
detector set. The dissociation degree of exited hydrogen
molecules
was
found
equal
to
1.
Results of calculations
Using the found constants,
analysis of flows with physical–
chemical reactions on surfaces
were performed for capillaries
with the diameter 3mm at the
temperature 2400K, different
length (20, 50 and 100mm) and
different fluxes (3, 30 and
300sccm). Flow regimes were
enclosed from free-molecular to
continuum ones.
Figure 3. Dissociation degree
K d = nVx H /{(nVx H + 2nVx (H2)} in different
channels with flow rate 3 sccm at temperature 2400 K.
High dissociation degree is obliged to catalytic
reactions on surfaces. The equilibrium Kd is much
lower. The decreasing of Kd behind capillary is
explained by atomic hydrogen scattering. The star on
the line L=100mm points experimental value by
Kosschmieder at all.
Figure 4. Dissociation degree in different channels with
flow rate 300 sccm.
Gas phase reaction are frozen for conditions of
calculations. The decay of radial diffusion decreases the
average dissociation degree. Near capillary exit one can
see crevasses at low flow rate (Fig.3), and splashes at
high flow rate (Fig.4). Our explanation: at low pressure
(Fig.3) atomic hydrogen leaves freely trans-sonic zone,
but at high pressure the knob of molecular hydrogen is
formated due to strong baro-diffusion, and hinders the
atomic hydrogen flight off. Any way these intriguing
nonequilibrium effects worth of attention.
Figure 5. Average fluxes of H and H2 and dissociation
degree in the channel with length 20mm.
Figure 6, Average fluxes of H and H2 and dissociation
degree in the channel with length 100mm.
Figure 7. Velocities of H and H2 along the axis for
flow rates 300, 30 and 3 sccm. Behind the capillary
the higher velocity for higher flow rate.
V=V(H)–V(H2)
Figure 8. Slip velocity V=VH–VH2 along the channel
with length 100mm at flow rates 3, 30 and 300sccm
Figure 9. The pressures at the entrance of capillary;
capillary length is 50mm, temperature changing in the
range 2000-2500K, hydrogen flow rate equal to 30sccm.
.
Conclusion
The value of presented study is the original
analysis of hydrogen flow in channels with
heterogeneous physical-chemical reactions, the
possibility to evaluate, calculate and predict
unknown constants of heterogeneous reactions
by experimental data on dissociation degree.
Authors are not familiar with investigations of
dissociating gas behavior by free molecular and
transition flows in channels. The presented
research allows formulate the problem of studies
the heterogeneous reactions not only for flows in
tungsten channels. In the result of precise
measurements of fragments flux behind heatresistant capillaries from refractory metals or
ceramics at low pressure and direct statistical
simulation of gas mixture flows one can
determine collisional constants for simple
molecules. Such approach is much more
preferential than expensive and sophisticated
molecular beam method.
Acknowledgements This work was supported by RFBR grants 14-08-01949, 14-08-31399
and 14-08-00534.