Synthesis and in vitro antibacterial activity of 7-(3-Amino-6,7-dihydro-2- methyl-2H-pyrazolo[4,3-c] pyridin-5(4H)-yl)fluoroquinolone derivatives

Article abstract of DOI:10.3390/molecules16032626

A series of novel 7-(3-amino-6,7-dihydro-2-methyl-2H-pyrazolo[4,3-c] pyridin- 5(4H)-yl)fluoroquinolone derivatives were designed, synthesized and characterized by 1H-NMR, MS and HRMS. These fluoroquinolones were evaluated for their in vitro antibacterial

Full text of DOI:10.3390/molecules16032626

Journal of Energy and Power Engineering 8 (2014) 1964-1973
D
DAVID PUBLISHING
Calculation of Steady SF6 Gas Flow through a 420 kV
Circuit Breaker Nozzle and Electric Field Distribution
Dejan Bešlija1, 2, Sead Delić1, 2, Kyong-Hoe Kim 1, 3, Mirsad Kapetanović1, 2 and Almir Ahmethodžić1
1. Faculty of Electrical Engineering, University of Sarajevo, Sarajevo 71000, Bosnia and Herzegovina
2. EnergoBos ILJIN d. o. o., Sarajevo 71000, Bosnia and Herzegovina
3. ILJIN Electric Co. Ltd., Seoul 121-716, Republic of Korea
Received: July 17, 2014 / Accepted: September 01, 2014 / Published: November 30, 2014.
Abstract: Special interest in current interruptions is dedicated to the processes close to the current zero instant, the so-called interaction
region, which determines the circuit breakers’ performance. The quantities of interest in this region are the distribution of temperature,
density and pressure, velocity and gas mass flow along the electric arc axis, as well as the distribution of electric stress between contacts.
Calculation of steady SF6 gas flow through the nozzle of a 420 kV circuit breaker at the current zero instant, for different arcing
durations, was carried out using a commercial CFD (computational fluid dynamics) simulation tool. The calculation results were used
to get insight into improvement possibilities of the SF6 gas flow model used in the software for computer simulation of HV
(high-voltage) circuit breakers. Electric field calculation results were performed for the same 420 kV circuit breaker, in order to
estimate the breakdown voltage at the current zero instant.
Key words: HV SF6 circuit breaker, nozzle, gas flow regime, shock wave, breakdown voltage.
1. Introduction
interaction interval is the time from the start of
significant change in arc voltage, prior to current zero,
A serious approach to design of switching devices
to the moment when the current, including the post-arc
requires a basic knowledge of physical processes
current, if any, ceases to flow. During the interaction
related to the electric arc, arc establishing and
interval, the short circuit current stress changes into
characteristics. The question of electric arc instability
high voltage stress, and the circuit breaker behavior
is crucial, not only for switching devices, but also for
significantly influences the current and the voltages in
many other devices where it is used as the key
the circuit. This interaction between the circuit and the
phenomena, e.g., arc furnaces, arc welding, etc.. In
circuit breaker during the interaction interval is of
these cases, maintaining of arc stability is important,
extreme importance to the interrupting process and
while for switching devices, this is not the case. For
determines its breaking performance. The distribution
switching devices, quite opposite conditions are
of following variables in the interaction region is of
desirable, i.e., unstable arc burning [1].
high importance: SF6 gas pressure and density, gas
For AC (alternating current) switching, special
velocity along the electric arc axis, as well as electric
interest is devoted to processes that happen at and
stress in the contact gap [2].
around the moment when the current passes through its
A proper design of circuit breaker components is of
zero. This time interval, about 100 μs before and after
high importance for its breaking capability and the
current zero, is called the interaction interval. The
dielectric recovery of the contact gap (more intensive
evacuation of hot gases), since the gas flow is highly
Corresponding author: Dejan Bešlija, Ph.D. student,
research field: development of HV circuit breakers. E-mail:
dejan.beslija@gmail.com.
dependent on the nozzle downstream shape. Interaction

Calculation of Steady SF6 Gas Flow through a 420 kV Circuit Breaker
Nozzle and Electric Field Distribution
1965
of the gas flow and the electric field creates critical
ꢌꢇꢈ
ꢆ ꢋ ꢃ ꢇꢈ · ꢄ ꢇꢈꢎ ꢊ
ꢌꢍ
ꢅ
ꢉ
regions characterized by low gas density and high
electric field strength. The probability of dielectric
breakdown in these regions is very high. Therefore, for
the given distribution of electric stresses in the contact
gap, it is desirable to preserve the highest possible gas
flow density. Since the local properties of gas flow
determine its dielectric strength, it is very important to
understand the dynamic flow behavior of gas through
HV (high-voltage) SF6 circuit breaker nozzles. CFD
(computational fluid dynamics) offers big advantages
regarding this matter, i.e., simulation and visualization
of flow processes in HV circuit breakers. CFD analyses
can save a large number of expensive testing shifts in
HV power laboratories and significantly accelerate the
prototype design process, which is directly related with
the reduction of development expenses. Since the
design methodology of HV circuit breakers is based
primarily on experience and previous test results, it is
necessary to invest great effort into developing such
computer simulation tools, with the final goal to
improve the performance of such apparatus.
ꢓ
ꢔ
ꢅ
ꢉ
ꢅ
ꢉ
ꢏꢄꢐ ꢃ ꢄ ꢑꢒꢄ · ꢇꢈ ꢃ ꢄ ꢄ · ꢇꢈ
(2)
(3)
(4)
ꢕ
ꢌ
ꢖꢆꢗꢘꢙꢚꢛ ꢃ ꢖꢆꢇꢈꢗꢘꢙꢚꢛ ꢊ
ꢌꢍ
ꢀꢀꢘꢂ ꢃꢝꢞ ꢃ ꢟ ꢃ ꢠꢡ
ꢅ
ꢉ
ꢃ
ꢄ · ꢜꢒ · ꢄꢙꢚ
ꢌꢆꢢ
ꢌꢍ
ꢅ
ꢉ
ꢃ ꢄ · ꢆꢢꢇꢈ ꢊ
ꢄ · ꢣꢥꢓꢤ ꢄꢢꢧ ꢃ ꢑꢂꢟ ꢏ ꢆꢨ
ꢦ
ꢌꢆꢨ
ꢅ
ꢉ
ꢃ ꢄ · ꢆꢨꢇꢈ ꢊ
ꢌꢍ
ꢄ · ꢣꢥꢓꢤ ꢄꢨꢧ ꢃ ꢗꢪꢫꢑꢂ ꢫ ꢟ ꢏ ꢗꢬꢫꢆ ꢫ
ꢭ
(5)
(6)
ꢞ
ꢞ
ꢩ
Wherein,
ꢭ
ꢡ
ꢙꢚ ꢊ ꢙ ꢏ ꢬꢮ
ꢯ
ꢭ
ꢑꢒ ꢊ ꢑꢰ ꢃ ꢑꢂ ꢊ ꢑꢰ ꢃ ꢗꢓꢆ ꢫ
(7)
(8)
ꢞ
ꢜꢒ ꢊ ꢜꢰ ꢃ ꢜꢂ ꢊ ꢜꢰ ꢃ ꢓꢥꢤ ꢗꢘ
ꢩ
2. Mathematical Model of Compressible
Viscous Fluid Flow
where, t is time, ꢇꢈ, ꢇ are the velocity vector and its
magnitude, ρ is gas density, p is static gas pressure, T0
is total (stagnation) temperature, T is static temperature,
Cp is specific heat capacity at constant pressure, μe is
effective dynamic viscosity, μt is turbulent dynamic
viscosity, μl is laminar dynamic viscosity, λe is
effective thermal conductivity, λt is turbulent thermal
conductivity, λl is laminar thermal conductivity, Ek is
the kinetic energy term, θ is the viscous dissipation
term, Wv is the viscous work term, k is turbulent kinetic
energy, ε is the turbulent kinetic energy dissipation rate,
σk is the turbulent Prandtl number for turbulent kinetic
energy, σε is the turbulent Prandtl number for
dissipation of turbulent kinetic energy, σt is the energy
Prandtl number, while Cμ, C1ε, C2ε are the standard k-ε
turbulence model coefficients. The model of SF6 gas
must completely reproduce the behavior of real SF6 gas
and have a sufficient temperature range of applicability.
Due to the compressible nature of SF6 gas, the type
of flow occurring during a HV circuit breaker opening
operation is compressible. Having this in mind, the
used mathematical model must take into account all
possible compressibility effects. On the other hand,
high flow velocities through HV circuit breaker
nozzles dictate high Reynolds numbers. Therefore,
viscous effects and turbulent flow behavior must also
be taken into consideration. Accordingly, the flow type
inside the analyzed HV circuit breaker is chosen to be
compressible, viscous and turbulent, and includes
equations for conservation of mass (continuity
equation), momentum (Navier-Stokes equation),
energy, turbulent kinetic energy and its dissipation,
given in Eqs. (1)-(8), respectively [3]:
ꢀꢁ
ꢅ
ꢉ
ꢃ ꢄ · ꢆꢇꢈ ꢊ 0
(1)
ꢀꢂ

1966
Calculation of Steady SF6 Gas Flow through a 420 kV Circuit Breaker
Nozzle and Electric Field Distribution
 specific heat at constant volume Cv at the inlet
and outlet (s);
In this range, it is necessary to provide lowest possible
deviation of all gas parameters from their real values,
and have appropriately modeled all required EOS
(equations of state), needed to complete the gas flow
model. They determine the following relationships:
 speed of sound c at the inlet and outlet (s).
This is illustrated on the example of a simple
one-sided exhaust nozzle (see Fig. 1).
The values of all aforementioned variables, which
represent boundary conditions for steady flow CFD
calculations, relate to the current zero instant, where
the electric arc finally extinguishes. Variables of state
of gas (pressure, temperature, specific density) are
considered to be averaged values of those parameters.
According to this assumption, variables of state of gas
are describing the state of gas in the entire chamber
volume. This will be of importance for defining of
nozzle geometry, in the sense of prolonging the
calculation domain to the surrounding circuit breaker
chambers, especially for the thermal chamber, since
the pressure rise in this chamber is the main cause for
gas flow through the nozzle.
ꢅ
ꢉ
ꢆ ꢊ ꢱ ꢐ, ꢙ
(9)
(10)
(11)
(12)
ꢅ
ꢉ
ꢉ
ꢉ
ꢑꢰ ꢊ ꢱ ꢐ, ꢙ
ꢅ
ꢜꢰ ꢊ ꢱ ꢐ, ꢙ
ꢅ
ꢗꢘ ꢊ ꢱ ꢐ, ꢙ
It is important to mention that the same SF6 model [4]
was used in all performed calculations (including CFD).
Since the complete history of the interrupting process is
responsible for arc behavior, the computer simulation
must take into consideration the interrupting process
from its very beginning.
A SF6 circuit breaker is generally of cylindrical
shape and with an existing axial symmetry, which
allows a 2D flow simulation and can significantly
reduce the necessary CPU (central processing unit)
time duration. Also, for high pressure and temperature
acting inside the circuit breaker, it is reasonable to
assume local chemical, as well as local thermal
equilibrium [5]. All performed calculation examples
take into account the aforementioned, considering that
the entire process up to the current zero is calculated
Input data in this form is not compatible with the
input required for CFD boundary conditions.
Therefore, it is necessary to adapt them, in order to
meet the required input. Given below is a set of
equations used for this purpose. This set is applied for
every boundary of the calculation domain.
Eqs. (13) and (14) are used for establishing the total
temperature T0 and total pressure p0 of the nozzle inlet
boundary:
using
a high-voltage circuit breaker computer
simulation tool [6].
ꢲ
ꢊ 1 ꢃ ꢴꢵꢪ ꢶꢬ
(13)
Data obtained from this application represent input
data for further calculations in a commercial CFD
simulation tool. Amongst them are the following
variables:
ꢳ
ꢲ
ꢬ
ꢷ
ꢊ ꢣ1 ꢃ ꢴꢵꢪ ꢶꢬꢧꢷꢸꢹ
(14)
ꢘ
ꢳ
ꢘ
ꢬ
where, κ is the isentropic expansion factor (ratio of the
 position of arcing contacts inside the nozzle at
current zero dz (depending on arc duration ta, contact
penetration dpen and their travel h);
 static pressure P, temperature T and density ρ at
the inlet and outlet (s);
 total SF6 gas mass flow at the inlet Ginlet
;
 individual gas mass flow at the outlet (s) Goutlet
;
 specific heat at constant pressure Cp at the inlet
Fig. 1 One-Sided exhaust nozzle and necessary data
obtained from the HV circuit breaker simulation tool [6].
and outlet (s);

Calculation of Steady SF6 Gas Flow through a 420 kV Circuit Breaker
Nozzle and Electric Field Distribution
1967
specific heat capacity at constant pressure Cp to
specific heat at constant volume Cv) and M is the
Mach number (ratio of fluid speed v and speed of
sound c):
3. Steady SF6 Gas Flow through a 420 kV
Circuit Breaker Nozzle
Test duty L75, according to IEC (International
Electrotechnical Commission), for three different
arcing times, 10, 15 and 20 ms (milliseconds), was
analyzed in this paper. Thus, three CFD calculations of
steady SF6 gas flow through the analyzed 420 kV 63
kA circuit breaker were performed. The required
geometry input and boundary conditions (see Table 1A
in Appendix) for the current zero instant were obtained
using the HV CB simulation tool. Results of these
calculations are presented in Figs. 2 and 3. Depicted in
these figures are the distribution of static pressure and
the Mach number, and the distribution of density and
gas velocity along the analyzed 420 kV circuit breaker
nozzle for different arcing times, respectively. The
drop of pressure in the downstream of the main and
auxiliary nozzle indicates the appearance of a shock
wave and a supersonic flow region in these locations.
The drop of pressure in the downstream of the main
and auxiliary nozzle indicates the appearance of a
shock wave and a supersonic flow region in these
locations. This fact confirms also the distribution of
Mach number in the nozzle downstreams. Nevertheless,
the pressure ratios are not sufficient to expand the
supersonic flow regions around the arcing contacts,
associated with highly increased electric stresses. It can
also be noticed that both auxiliary and main nozzles are
chocked. The Mach number in both nozzles is equal to
one, which means that the pressure ratios in both flow
directions are sufficient in this case to cause their
choking. The limitation of gas mass flow is due to the
above described phenomenon. Therefore, gas mass
flow limitation is defined by the minimal cross-sectional
flow area and the established state of gas in this flow
region. Most often, this happens inside the nozzle
throat of the circuit breaker. If the pressure ratio is
greater, the supersonic region expands even more into
the nozzle downstream, i.e., the shock wave front
dislocates further to the nozzle outlet. This applies to
both main and auxiliary nozzles. For the minimal
ꢮ
ꢯ
ꢺ ꢊ
(15)
(16)
(17)
ꢮ
ꢻ
ꢡ
ꢼ
ꢶ ꢊ
ꢇ ꢊ ꢽ · ꢁꢪ
·
ꢪ
ꢾ
wherein, G is gas mass flow and A is the considered
cross-sectional area. Eqs. (13)-(17) describe the
variation of static pressure and temperature depending
on flow velocity change (Mach number) with the
assumption of an isentropic process. For a specific
value of this ratio, for SF6 gas, Eq. (13) predicts
nozzle flow choking (M = 1, sonic flow) in the
minimal cross-section, e.g., nozzle throat. In the
cross-sectional area after the minimal, the gas can
additionally accelerate, thus, establish supersonic flow
conditions, characterized by a drop in pressure and gas
density, which is most often the case in circuit breaker
nozzles. If the supersonic flow is imposed to a
pressure increase on the inlet boundary, a shock wave
occurs, alongside with a sudden pressure drop. After
the shock wave front, a subsonic region forms, where
again, a gas density and pressure rise can be observed.
Further on, for determining of laminar dynamic
viscosity, the Reynolds number Re and the turbulence
intensity I [7], i.e., defining turbulence parameters at
the boundaries, Eqs. (18)-(20) are used respectively:
ꢑꢰ ꢊ 1.533 · 10ꢵꢿ ꢃ 4.8 · 10ꢵꣀ · ꢙ ꢏ 300
(18)
ꢅ
ꢉ
ꢁꣃ
ꢡ
꣄
ꣁꣂ ꢊ
(19)
ꢓ
ꣅ
ꢹ
꣇
꣆ ꢊ 0.16 · ꣁꣂꣃꢵ
(20)
꣄
Eqs. (19) and (20) introduce the so-called hydraulic
diameter DH of the circuit breaker nozzle inlet and
outlet. This diameter for a cylindrical boundary is
identical to its diameter, while for a coaxial cylindrical
boundary with its inner and outer diameter, equals
their difference [8].

1968
Calculation of Steady SF6 Gas Flow through a 420 kV Circuit Breaker
Nozzle and Electric Field Distribution
Fig. 2 Distribution of static pressure and Mach number
along the 420 kV circuit breaker nozzle for different arcing
durations.
Fig. 3 Distribution of density and gas velocity along the 420
kV circuit breaker nozzle for different arcing durations.

Calculation of Steady SF6 Gas Flow through a 420 kV Circuit Breaker
Nozzle and Electric Field Distribution
1969
arcing time of 10 ms, the main nozzle outlet pressure is
the lowest of all analyzed, so that the shock wave front
in this case is the farthest from the main nozzle throat.
Since the main nozzle outlet pressure rises for longer
arcing durations, the shock wave front retrieves ever
more towards the main nozzle throat. Consequently,
the supersonic region gets narrower. The pressure ratio
in case of the auxiliary nozzle is largest for maximum,
then medium and shortest arc duration, respectively
(see Table 1A in Appendix). Table 2A (in Appendix)
gives an overview of gas mass flow values calculated
in CFD and the HV CB simulation tool. CFD
calculations predict a lower value of gas mass flow at
the current zero instant. This can be explained by Eq.
(17) written in the following form:
flow. This assumption additionally increases the gas
mass flow.
On the other hand, by comparing the values of gas
mass flow in Table 2A (in Appendix), it is important to
notice that the mutual difference between ratios of gas
mass which flows through the main and auxiliary
nozzle compared to the total gas mass flow, for all arc
durations, is less than 5%, and that only the values of
gas mass flow show deviation due to previously
discussed reasons. All gas mass flow reducing
phenomena cannot be taken into account in the HV CB
simulation tool.
The occurrence of shock waves is happening in the
nozzle downstream, which is of high importance
because it is very likely to coincide with high
electrically stressed regions around the arcing contact
tip. This coincidence of shock wave related gas density
drop and high values of electric field strength is an
undesirable phenomenon that should be avoided as
much as possible.
ꢽ ꢊ ꢇ · ꢆ · ꣈
(21)
Gas mass flow, according to Eq. (21), is defined by
gas density and velocity, as well as the nozzle throat
cross-sectional area. Since nozzle throats of both main
and auxiliary nozzles of the analyzed 420 kV circuit
breaker are choked at the current zero instant, the Mach
number appearing in both throats is equal to one and
sonic flow regime, i.e., gas speed equals the speed of
sound of SF6 gas. The calculated value of speed of
sound in both used applications is the same; since they
used the same SF6 gas model under the assumption of a
isentropic process (speed of sound dominantly depends
on gas temperature, which is approximately the same in
both applications). Due to the use of a viscous flow
model in the performed CFD calculations, the effective
cross-sectional area is reduced due to friction on the
nozzle walls and the characteristic near-wall velocity
profile is obtained. This phenomenon is one of the
reasons for lower values of gas mass flow in CFD
compared to the ones obtained using the HV CB
simulation tool. The second reason is lower gas density
in the nozzle throat compared to the thermal chamber.
Namely, in the HV CB simulation tool, it is assumed
that state of gas in the nozzle throat equals the one in
the thermal chamber, thus, not taking into account the
reduction of gas density in the nozzle throat due to gas
The previous short analysis of some calculation
results shows that CFD analyses represent a powerful
tool for designing of HV circuit breaker nozzles and
greatly helps in understanding of complex processes
that happen inside SF6 gas filled HV circuit breakers.
4. Electric Stresses of a 420 kV Circuit
Breaker
Estimation of breakdown withstand voltage in
high-voltage circuit breakers is a very challenging and
demanding engineering problem. The breakdown
withstand voltage Up is estimated based on a criterion
of dielectric strength of SF6 gas, which is determined
by the local gas flow field and the electric field
distribution.
꣉ꢘ ꢊ C · ꣊꣋ꢁ꣍
(22)
꣌
꣎꣏꣐
꣌
where, ꢝ is the local electric field strength when a unit
voltage is applied. Constant C contains information
about influences from surface roughness, area and
voltage frequency on breakdown voltage. Measurements

1970
Calculation of Steady SF6 Gas Flow through a 420 kV Circuit Breaker
Nozzle and Electric Field Distribution
from cold dielectric experiments determine the
contents of C. For a reliable estimation of breakdown
withstand voltage, it is required to know the local
density distribution (see Fig. 3), as well as the electric
field distribution for the given nozzle geometry (see
Fig.4). Fig. 5 depicts the chosen profile along which
the breakdown voltage estimation will be performed.
Results of this calculation are given in Fig. 6. The
upper part of Fig. 6 shows the calculated electric field
distribution, while the lower part depicts gas density
along the same profile. The ratio of gas density and
electric field strength in Eq. (22) multiplied by
constant C, where C = 0.225 (MVm)2/kg is represented
in Fig. 7.
The profile to be analyzed was not chosen randomly.
It was selected to take into consideration high electric
field strength around the arcing contacts, as well as the
shock wave region in the nozzle downstream. The
upper part of Fig. 6 indicates that the electric field
strength peaks around the arcing contacts, while the
lower part
Fig. 5 Chosen profile for breakdown voltage estimation.
Fig. 4 Electric field strength vectors along the calculation
domain boundary at minimum arcing duration inside the
analyzed 420 kV circuit breaker.
Fig. 6 Distribution of local electric field and gas density
along the chosen estimation profile.

Calculation of Steady SF6 Gas Flow through a 420 kV Circuit Breaker
Nozzle and Electric Field Distribution
1971
7,000
6,000
5,000
4,000
3,000
2,000
1,000
0
Fig. 7 Ratio of gas density and electric field strength along the chosen estimation profile.
of the same figure shows a pronounced gas density
drop in the nozzle downstream where a shock wave
occurs. Based on Eq. (22) and these two curves, the
breakdown voltage along the chosen profile can be
estimated (see Fig. 7). In the initial part of the
breakdown voltage estimation curve along the chosen
profile, it can be observed that the ratio of gas density
and the local electric field strength dominantly follows
the electric field strength curve, since gas density in
this part of the nozzle is relatively constant. The local
minimum of this ratio in this part of the chosen profile
is located next to the arcing contact, due to the highest
electric field strength at this place.
electric field strength increases again, since this part of
the chosen profile lies in the vicinity of the second
arcing contact. Due to this increase, the ratio of gas
density and electric field strength is decreasing. Thus, a
considerable decrease of the analyzed ratio, whose
minimum value defines the breakdown voltage, can be
expected in regions with high electric field strengths
(vicinity of arcing contacts) or in low-density regions
(supersonic shock wave flow regions). For the
analyzed case and chosen profile, the minimal ratio is
located in the supersonic region.
6. Conclusions
As distance from the arcing contact increases, the
electric field strength decreases, so that the gas density
and electric field strength ratio decreases. In the second
part of the breakdown voltage curve along the chosen
profile, the dominant influence on this ratio has gas
density. This part of the profile passes through the
supersonic region, which is characterized by high
speeds and low gas densities. It can be noticed that the
minimum value of the ratio of gas density and electric
field strength is obtained in this region, which,
according to Eq. (22), determines the breakdown
withstand voltage. In the third part of the analyzed
curve, there is an increase of gas density, while the
This paper demonstrates a method for combining two
computer applications using a system of Eqs. (13)-(20),
which are used for adapting of certain output variables
from one software, in this case, a fast and simple HV
CB simulation tool, to the required input for more
complex analyses in a CFD tool.
The model of SF6 gas in calculations must accurately
reproduce the behavior of real SF6 gas, have a
sufficiently wide temperature range of applicability in
which lowest possible deviation of gas parameters
from real values must be provided and have properly
modeled all important characteristics. In this paper,
such a model of real SF6 gas was implemented. This

1972
Calculation of Steady SF6 Gas Flow through a 420 kV Circuit Breaker
Nozzle and Electric Field Distribution
model has a wide temperature range, which is very
important for modeling of processes inside
high-voltage circuit breakers, where gas temperatures
can occur much over 1,000 K, due to large currents to
be interrupted, and also modeled transport coefficients
of thermal conductivity and SF6 gas viscosity. They
entail all viscous flow effects, such as flow separation,
recirculation phenomena, backflow, near-wall effects,
as well as turbulent behavior of gas, etc..
significant drop in gas density at this region.
Finally, it can be said that the analyses performed
throughout this work represent the basis for further
research in the direction of dielectric stresses of the
circuit breakers contact gap, state of gas along the
circuit breaker nozzle, as well as some simulation
software improvements.
References
[1] Kapetanovic, M. 2011. High Voltage Circuit Breakers.
Sarajevo: Elektrotehnicki fakultet.
Steady flow calculations through a real-world 420
kV circuit breaker nozzle for different arcing durations
confirm turbulent, viscous and compressible behavior
of SF6 gas, typical for convergent-divergent nozzles, as
used in HV circuit breakers.
[2] Zildzo, H., Gacanovic, R., and Matoruga, H. 2011.
“Electro-Gas Model Breaking of Capacitive Currents
within High Voltage SF6 Circuit Breaker.” In
Proceedings of 2011 XXIII International Symposium on
Information,
Communication
and
Automation
The analysis conducted in this paper can give
guidelines for improvement possibilities of the HV
CB simulation tool which is reflected in the limitation
of the evidently increased gas mass flow by
calculating the state of gas in the nozzle throat in
every time step, as well as the implementation of
viscous SF6 gas behavior that would also introduce
gas mass flow limitation effects. Another challenging
task would be improvement of this simulation tool by
introducing a proper shock wave and supersonic flow
model.
Technologies, 1-7.
[3] Delic, S., Beslija, D., Muratovic, M., Kim, M. H.,
Kapetanovic, M., and Zildzo, H. 2014. “New Approach to
Breakdown Voltage Estimation after Interruption of
Capacitive Currents.” Presented at 2014 IEEE
International Power Modulator and High Voltage
Conference, Santa Fe, New Mexico, USA.
[4] Blagojevic, N. 1989. “Proracun Sastava Produkata
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i Realnih Gasova.” Sarajevo:
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Design and Optimation for UHV SF6 Circuit Breakers.
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Calculations of this type may further on be used as
the basis for additional analyses regarding processes in
HV circuit breakers. This possibility is demonstrated in
this paper in the form of a breakdown voltage
estimation analysis that can be used for small
capacitive current switching duties or heavy current
interruption duties after current zero [3]. Results of the
performed estimation show that a substantial decrease
of the ratio of gas density and the electric field strength
in the nozzle downstream can be expected, due to a
[6] Ahmethodzic, A., Gajic, Z., and Kapetanovic, M. 2011.
“Computer Simulation of High Voltage SF6 Circuit
Breakers: Approach to Modeling and Application Results.”
IEEE Transactions on Dielectrics and Electrical
Insulation 18 (4): 1314-22.
[7] Steinbruck, H. 2014. “Institute of Fluid Mechanics and
Heat
http://cdlab2.fluid.tuwien.ac.at/.
[8] Computational Fluid Dynamics Online. 2014. Accessed
July 16, 2014.
http://www.cfd-online.com/Wiki/Hydraulic_diameter.
Transfer.”
Accessed
July
16,
2014.

Calculation of Steady SF6 Gas Flow through a 420 kV Circuit Breaker
Nozzle and Electric Field Distribution
1973
Appendix
Table 1A Overview of output variables for the analyzed 420 kV circuit breaker for chosen arcing times and test duty.
Output variables from HV CB simulation
Arc duration (ms)
Analyzed 420 kV, 63 kA CB nozzle (L75 47.25 kA)
10
15
20
Contact travel = Contact distance + Contact penetration (mm)
Nozzle inlet hydraulic diameter (mm)
Main nozzle outlet hydraulic diameter (mm)
Auxiliary nozzle outlet hydraulic diameter (mm)
Nozzle inlet area (m2)
252.412 + 92
100.088
35.0558
32.7538
0.0204304
0.00319121
0.00084239
2,155,782
802.366
0.0254
342.811 + 92
100.088
67.8348
32.7538
0.0204304
0.00402898
0.00084239
2,534,408
991.919
0.022694
1,022.265
964.848
249.08
409.431 + 92
100.088
67.8348
32.7538
0.0204304
0.00402898
0.00084239
2,647,433
1,241.45
0.027277
1,046.984
989.912
Main nozzle outlet area (m2)
Auxiliary nozzle outlet area (m2)
Static pressure at nozzle inlet (Pa)
Static temperature at nozzle inlet (K)
Specific gas density at nozzle inlet (m3/kg)
994.877
936.731
222.723
10.49
Specific heat capacity at constant volume at nozzle inlet (J/kg·K)
Specific heat capacity at constant pressure at nozzle inlet (J/kg·K)
Speed of sound at nozzle inlet (m/s)
279.024
Gas mass flow at nozzle inlet (kg/s)
11.201
10.572
Static pressure at main nozzle outlet (Pa)
599,374.75
322.374
0.028894
731.796
654.882
135.806
9.085
861,570.5
464.194
0.030071
861.434
799.862
165.554
9.719
1,018,623.2
544.431
Static temperature at main nozzle outlet (K)
Specific gas density at main nozzle outlet (m3/kg)
0.030129
908.939
Specific heat capacity at constant volume at main nozzle outlet (J/kg·K)
Specific heat capacity at constant pressure at main nozzle outlet (J/kg·K)
Speed of sound at main nozzle outlet (m/s)
849.438
180.452
Gas mass flow at main nozzle outlet (kg/s)
9.191
Static pressure at auxiliary nozzle outlet (Pa)
609,167
801.704
0.075124
992.874
935.842
220.67
609,038.75
463.792
0.042748
857.358
798.142
166.205
1.482
608,226.81
544.154
Static temperature at auxiliary nozzle outlet (K)
Specific gas density at auxiliary nozzle outlet (m3/kg)
0.050617
905.996
Specific heat capacity at constant volume at auxiliary nozzle outlet (J/kg·K)
Specific heat capacity at constant pressure at auxiliary nozzle outlet (J/kg·K)
Speed of sound at auxiliary nozzle outlet (m/s)
848.152
180.915
Gas mass flow at auxiliary nozzle outlet (kg/s)
1.405
1.381
Table 2A Calculated gas mass flow on the domain boundaries for the analyzed 420 kV circuit breaker at current zero.
Used simulation tool
HV CB simulation
15 20
10.49 11.2 10.57 6.12
9.19 5.32
1.381 0.76
0.87 0.87
0.131 0.13
CFD
15
Arcing duration (ms)
10
10
20
Gas mass flow at nozzle inlet (kg/s)
6.45
5.61
0.84
0.87
0.13
6.16
5.37
0.796
0.871
0.129
Gas mass flow at main nozzle outlet (kg/s)
Gas mass flow at auxiliary nozzle outlet (kg/s)
Ratio of gas mass flow at main nozzle outlet and nozzle inlet
Ratio of gas mass flow at auxiliary nozzle outlet and nozzle inlet
9.09
1.41
0.87
9.72
1.48
0.87
0.134 0.13