Computer aided tools in gas circuit breaker design

IEEE Transactions on Power Delivery, Vol. 5, No. 1, January 1990

Computer Aided Tools in Gas Circuit Breaker Design

M.Reggio, J-Y.TrCpanier and R.Camarero Ecole Polytechnique de Montrkal

R. Jeanjean Cegelec Industrie Inc.

Abstract

A software tool that allows the numerical investigation of the gas flow in circuit breaker chambers, has been devised. A zonal grid methodology, with a corresponding finite volume flow solver for the Euler equations, has been implemented for the treatment of the intricate geometries of the interrupter. Computational examples to illustrate the validity of the method are presented. Experimental tests were done on full-size breakers, and the results analyzed using the proposed computational approach.

Keywords: ler equations, finite volume, zonal discretization.

design tool, circuit breaker, numerical simulation, Eu-

Introduction

The interruption action in high-power networks is carried out by circuit breakers devices. When these operate, electrodes separate giving raise to an electric arc. At this point, the main task consist of the arc extinction and to avoiding its restriking. In order to accomplish this, the current technology employs a gas blast directed to the arc path.

The extinction and reignition phenomena are strongly affected by the gas flow which is intimately related to the geometry of the interrupting chamber. This will govern the coupling between the arc and the flow that substantially contribute to the design of an effective circuit breaker. To improve the interrupter’s capacity and reliability, it is of interest to gain insight into the flow field, and its associated phenomena, such as for example shock wave location, reverse flow regions, etc.

In this work we present a computational approach to obtain this type of information that hopefully will lead to a more efficient interrupter. The paper is organized as follows: First, the physical model for the flow is presented, followed by a description of the equations to be solved. A short description of the numerical scheme is given, and finally two examples are discussed. The first illustrates the validation of the approach, and the second shows an application of the method in a realistic situation.

Modelling and Numerical Approach

Over the last few years considerable effort in the research and development of analysis and design aids for engineering purposes, has been carried out. In this respect, important inroads have been made in computational fluid dynamics allowing numerical simulations which gives a complementary understanding of the physics of a fluid flow problem.

89 SM 763-4 PWRD A paper recommended and approved by the IEEE Switchgear Committee of t h e I E E E Power Engineering Society f o r presenta t ion a t the IEEE/PES 1989 Summer Meeting, Long Beach, Cal i forn ia , J u l y 9 - 14, 1989. made a v a i l a b l e f o r p r i n t i n g June 7, 1989.

Manuscript submitted January 31, 1989;

163

Following this approach, some CFD tools have been adopted to carry out numerical investigations of the fluid flow in the circuit breaker chamber. The realisation of such simulations requires that the complexity of the geometric and physical aspects be adequately adressed by the numerical tools.

From the geometric point of view, the numerical approach should be able to solve the conservation equations on complex geometries, as for example the configuration illustrated in Fig.l(Ref.1). In this type of puffer breaker, the piston and electrode move, and the computer code should treat this problem of moving boundaries. With this kind of transient simulation, the clogging effect and the pressure rise in the puffer cylinder, could be predicted.

Fig.1 - Diagram of a puffer breaker in closed position and during opening. (From Ref.[l]).

From the physics point of view, a correct treatment of the electric arc, even within the LTE framework, would require the solution of the Maxwell equations inside the breaker’s chamber. Energy and momentum source terms would then be added to the governing equations of the flow, introducing a coupling between these and Maxwell’s equations. Also one has to take into account the radiation phenomenon. [2,3]

In order to simplify the task, approximate methods are currently employed. A common investigation is represented by the study the arc itself on the basis of 1-D or quasi 1-D models. Among the variety of works we distinguish those of Refs.[4,5,6]

In the present study we rather propose to tackle the problems associated with the geometry. In this respect, a numerical methodology for a flow field simulation, without the presence of a burning arc, but in complex 2-D and/or axisymmetrical configurations is presented. At this stage the boundaries of the calculation domain(i.e. the piston and the electrodes) %are supposed static, and the physical characteristics of the sF6 have been simplified to those of an ideal gas, inviscid and non-conducting. The model used to represent the flow of such fluid is based on the Euler equations.

The geometric treatment of the interrupter chamber, being a multi- branched passage, has required the development and application of advanced techniques concerning the domain discretisation as well the data structure.

0885-8977/90/0100-0163$01.~ O 1989 IEEE

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164

Governing Equations

The flows to be considered are governed by the conservation of mass, momentum and energy. For unsteady two-dimensional or axisymmetric flows, these can be written for curvilinear coordinates (, t) as:

aq aE aF at a t arl -+-+-+H=O

The flux vectors in Eq. (1) are defined as:

r p i r p~ 1

In the above relations p is the density, u,v are the velocities in the z- and y-directions, p is the pressure, and e the total energy. The terms &, (u ,qz ,qu and J represent the metrics and the Jaco- bian respectively. The curvilinear velocity components U, V and the Cartesian velocity components U, v are related by:

U = u g + v & #

v = urlz+vrly (2)

Finally 6 is a geometric index that denotes an axisymmetric (6 = 1) two-dimensional (6 = 0) configuration. In the axisymmetric case y is equivalent to the radius r.

Numerical Scheme

The solution method for the system(1) is based on the Ni scheme[7] which is a variation of the Lax-Wendroff method. The scheme can be obtained by first approximating the temporal derivative of the primary variables using the following Taylor series expansion:

(3) At2

q(t + At) - q(t) = qtAt + q t t y + B(AtS)

Using Eq. ( l ) , the time derivatives appearing in this relation can be expressed in terms of space derivatives as:

where: aE aF

A = - a n d B = - aq aq (4)

Substituting into Eq. (3), yields for the variable increment in time, the following expression:

According to Ni, the finite volume approximation of this equation can be carried out on a nine-node computational cell of volume V = 4ACAr) (Fig.%), resulting from the assembly of the four basic sub-cells A, B,C and D of volume V = A(Av. In doing so, one can obtain the following expression for the correction to the conservation variables:

1

1

1

1

6qp = 4 [ A s + At(AE* + AF*)]A

+ 4 [AS + At(AE* - AF')],

+ 4 [ A s + At(-AE* - AF")],

(6) + - 4 [Aq + At(-AE' + AF*)lD

where the superscript star is used to denote fluxes across the faces. Finally the dependent variable q is updated by:

q"+l = q" + 6q

Aqc

P

Fig.2 - Nine-node computational cell and basic sub-cells.

Domain Discretization

The numerical solution of the finite-volume approximations of the flow governing equations requires some discretization of the domain. A valuable discretization tool currently employed in grid generation, is the body-fitted technique[8,9]. By means of this method a curvilinear grid is numerically generated via the solution of an appropriate system of partial differential equations. In its basic form, this automatic procedure yields a curvilinear mesh on a single region bounded by two pairs of opposite curves.

For the present application represented by the multi-branched channel of an interrupter (Fig.l), the single grid system is no longer suitable. In such a case, a better approach is to segment the physical field, that is the region between electrodes and nozzle, into several sub- domains, each of them bounded by four curves and logically treated as rectangles. Then within each of these subregions, a grid is generated. Finally, the entire coordinate system is formed by assembling the different sub-systems at the common boundaries. This methodology is referred aa a zonal approach or grid patching technique. Details concerning the application of the current zonal methodology together with the adopted flow solver can be found in Ref[lO].

165

Computed Results

In order to illustate the application of the proposed methodology, two kind of studies were carried out. The first with the purpose of validating the numerical scheme with the subdivision technique. The second to show a real-world situation, where the present tool was used in the design of a circuit breaker.

Partial Duo-flow Breaker

The geometry chosen for this test consists of a breaker-like shape named by Reflll] as Model One. The details of the geometric characteristics can be found in that work.

The nozzle, which represents a partial duo-flow breaker, was divided into four elementary zones (Fig.3), and calculations were made for subsonic, subsonic-supersonic with a shock, and fully supersonic operation modes. Fig.3a shows the computed results represented by iso-mach lines for a fully subsonic flow, using for both branches a pressure ratio of 0.92. Fig.3b illustrates an enlarged view of the velocity field near the stagnation region. The knowledge of this position is very important for the analysis of the breaker, because it consti- tutes a place where the convective heat transfer becomes zero. Fig. 3c depicts the calculated and experimental values of the pressure at the nozzle wall. The concordance of the numerical results with the measurements of Reqll] is quite satisfactory.

On Fig.& the computed isomach contours are displayed for an operating condition of Pdt/Ptotd of 0.73. Fig.4b illustrates the computed nozzle wall pressure together with the experimental data. The numerical simulation correctly predicts the intensity of the shock and the pressure recovery ala0 compares well with the measurements

Finally a case with a pressure ratio of Pefit/Ptotal of 0.20. leading to supersonic exit conditions in both branches was studied. Fig.5a shows the computed iso-ma& distribution. In Fig 5b, the pressure at the nozzle wall is shown and compared with the experimental results. The agreement is also very good.

Fig.3b - Zoom of the velocity field near the stagnation point.

PRESSURE DISTRIBUTION I

t I 0.0 d.5 i.0 1.5 2.0 2.5 J.O s.5

FOSliION

Fig.3 - Subdivision of the geometry of Ref. [ll] into 4 elementary zones.

Fig.3~ - Pressure distribution on the nozzle wall. P&t/Ptotd,= 0.92.

Fig.3a - h m a c h contours for Pdt/Ptotdr = 0.92. Isolines A to H, Fig.4a - Isomach contours for Pefit/Pt,td, = 0.73. Isolines A to M, Mach 0.0 to 0.7, A Mach = 0.1. Mach 0.0 to 1.8, A Mach = 0.15.

166

8

PRESSURE DISTRIBUTION e

Fig.4b - Pressure distribution on the nozzle wall. Pdt/Pt,td, = 0.73.

Fig.5a - Isomach contours for Peit/Ptotd, = 0.20 Isolines A to 0, Mach 0.0 to 2.1, A Mach = 0.15.

PRESSURE 0 ISTR 1 BUT I ON

, 1 I 1 1

POSI 'I I ON .o d.5 i .0 1.1 2.0 2.5 LO 3.5

Fig.5b - Pressure distribution on the nozzle wall. P&t/Ptotd,= 0.20.

Industrial Circuit Breaker

This study shows how the interaction between numerical and experimental approaches can lead to a better design of an interrupter, by understanding the fluid phenomenon taking place during a breaking process.

During the development phase of a puffer-type circuit breaker, the performance of two different nozzle shapes were compared for a terminal fault test. The tests were conducted according the standard IC56, and the synthetic method for current injection was applied.

The parameters of the circuit were;

I,, = 40 LA V, = 370 kVpe& Recovery voltage

RRRV = 2.7 k V / p Rate of Rise Recovery Voltage

The nozzle shapes are shown in Fig. 6, these will be referred as nozzle A and B respectively.

Figs. 7a and 7b show the current and the recovery voltage for the nozzle A after long arcing time. From these figures it is clear that the breaking is succesfull. Figs. 8a and 8b show the same parameters for the test using nozzle B. In this case it can be appreciated that the arc restrikes around 360 kV. The tests were repeated several times giving the same results.

At this point and in order to gain insight into the reason of such difference, the simulation of the flow in both chambers was under- taken.

The domain of calculation was divided in 13 zones for each nozzle. The zonal discretization of nozzle A is depicted in Fig.9. The numerical investigation was carried out applying a pressure ratio

Fig.lOa illustrates the computed mach number isolines for the nozzle A. These indicate a smooth expansion of the flow into the down- stream part of the nozzle, up to a region near the electrode where a bow shock appears. The velocity field in front of the electrode (Fig.lOb) is regular, which suggests that the gases in front of the electrode are well evacuated.

On the other hand, the calculated mach contours for the nozzle B (Fig.lla), show the presence of an oblique shock in the divergent part. The interaction of this shock with the electrode causes a reverse flow and a recirculating flow region, as shown in the velocity plot(Fig.llb). This type of field probably precludes the ejection of the hot gases left by the arc, thus lowering the dielectric strength.

As a consequence of these analyses, it was concluded that the sudden change in the shape of nomle B introduces an inadequate perturbation of the flow field, and this model was dropped out.

PexitlPtotal = 0.1.

Fig.6 - Nozzle A and nozzle B shapes.

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................ ................ ................ ............... .............. e.,*e x i o ~ . s UOLW

! i e.)se : i :. i 0 . ,e* ................ 1 ............. -..i ................ !* ............... i- .............

................ ................ i ................ i ............... i- ........... ('1 e.iSo

................ ................ ................ ............... ......... ... ............ ............... ............

s.25p i i i i...

e.208 i .._ i. i

................ ................ ................................ ............ i

................ ............ ................ ........ ............ e.1e~ i i i

*.e50 i.... i i j

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- 0 . m 0.00 @ . I D 0.2D @.)e *.a@ @.Sa 0.6* 0.7D 0.80 0.90 I.*@ x 1DE-3 + D.1 03SZ ¶CCMIDES

Fig.7 a) Experimental arc current diagram for nozzle A. b) Experimental recovery voltage plot for nozzle A.

RCR-Jn ee.os6

(.10, ................................. i ............ . i .............. .i ............... i ................ i ................ I............ .... 8.,e8x IeE+6 W L T S

................ ............... ............

............... ............................. a.zoe L i

*.,a, .i

- D . ~ w ................ i ................ i ................ i ................ i. -8.L08 ..... ...........i... ............. ; ................ : ................ i. -8.3.1 ................ i ................ i ................ 1 ............... .!.

e.eee

1 - e . w - e.eo e.30 e.60 8.30 1.28 1.50 i .80 L I D e.40 e.7r 3 . m

X 18E-3 t D.149119 SLCOIIDES

Fig.8 a) Experimental arc current diagram for nozzle B. b) Experimental recovery voltage plot for nozzle B.

Fig.9 - Zonal discretization of nozzle A.

168

Fig.lOa - Isomach contours for the nozzle A. PedtlPtotd,= 0.1. Isolines A to P , Mach 0.0 to 3.0, A Mach = 0.2.

. - - .- --=--- - - - - - - -.I..-

- - - - - - + '.---- - - - - - -pi-I'-:1 ---... ----, - - - - _ - - - - - - _ _ - - - - - - - - - - - - _ _ - - - - - -

' - - _ - - - - -. _---.

- - - - - - - - - - - - - - - - - - - - - - - - - -

. - -_ - - - . - - - - - - - - - - -

Fig.lOb - Computed velocity field near the electrode for the nozzle A.

Fig.lla - Isomach contours for the nozzle B. Pdt /Ptotd,= 0.1. hlinea A to P , Mach 0.0 to 3.0, A Mach = 0.2.

Fig.llb - Computed velocity field near the electrode for the nozzle B.

Conclusions

A numerical scheme for the solution of the Euler equations in axisymmetric arbitrary shapes, has been applied to the computation of the flow field within circuit breaker devices. The results of the simulations has led to a plausible explanation of certains phenomenons observed during terminal fault tests. Classical CFD tools, together with a modern zonal methodology have been employed to treat the geometric complexities of the interrupting chamber.

The present approach can correctly predict important aspects such as the shock position or the location of the stagnation point on the axis. The computation of the bow shock in front of the electrode in Fig.lOa, was obtained on the basis of the axisymmetric formulation. It is not possible to capture this type of discontinuity using a quasi-1D model. On the other hand, the kinetic energy level plays a key role in the efficiency of the breaking process. It is critical where the cooling is the slowest, and it is probably there where the dielectric breakdown takes his origin. The correct prediction of the flow properties at sta- tions of low kinetic energy is thus essential. This only can be properly achieved via 2-D or axisymmetric formulations.

169

Biographies

References

1. Maller, V.N. and Naidu, M.S.,Advances in high voltage insula- lation and arc interruption in SFg and vacuum, Pergamon Press, 1981.

2. Liebermann, R.W. and Lowke, J.J., “Radiation emission coefficients for sulfur hexafluoride arc plasmas”, J. Quant. Spectros. Radiat. Transfer, Vol. 16, pp.253-264, 1976.

3. Zollweg, R.J., “Radiation emission coefficients for modeling finite high-pressure thermal plasmas”, IEEE Trans., Vol. PS-14, pp.300-305, 1980.

4. Cowley, M.D., ‘Integral method of arc analysis”, J . Phys. D, Vol. 7, NO. 5, 1974, pp.1118-1145.

5. Swanson, B.M. and Roidt, R.M., “Some numerical solutions of the boundary layer equations for an sF6 arc”, Proc. IEEE, Vol. 59, 1971, pp.493-501.

6. Mitchell, R.R., “Analysis of electric arcs in gas-blast circuit breakers”, Ph.D. thesis, Canergie-Mellon University, 1985.

7. Ni Ron-Ho., “A Multiple-Grid Scheme for Solving the Euler Equations” AIAA Paper 81-1025, 1981.

8. Thompson, J.F. and Warsi Z.U., “Boundary-Fitted Coordinate Systems for Numerical Solution of Partial Differential Equations A-Review” , Journal of Computational Physics, Vol47, pp.1-108, 1982.

9. Camarero et al., “Introduction to Grid Generation Systems in Turbomachinery” , VKI Lecture Series 2, Numerical Techniques for Viscious Calculation in Turbomachinery, 1986.

10. Reggio, M., Trepanier, J-Y., and Camarero, R. “A composite Grid Approach for the Euler Equations” 1nt.Jour. for Num. Methods in Fluids, submitted.

11. Whang, Ho-Chang “Experimental and Theoretical Results for Low Current D.C. Arc in Nozzle Flows and Calculation of Cold Flow Field and Correlation with Experimental Data for Asym- metrical Flow Circuit Breaker Nozzles”, Ph.D. Thesis Rensse- laer Polytechnic Institute, 1986.

Marcelo Reggio was born was born in 1946 in Chili. In 1983 he received his Ph.D. in mechanical engineering at Ecole Polytechnique de Montrkal.

Presently, he is a research fellow in the Applied Mathematics De- partment at Ecole Polytechnique de Montrkal. His current research concerns the development of numerical schemes in the area of CFD.

Jean- Yves Tripanier WBS born in 1959 in Canada and received his B.Sc. in Physics at University of Sherbrooke in 1982.

He is currently engaged in a Ph.D. program in the Applied Math- ematics Department at Ecole Polytechnique de Montrkal. The object of his thesis is the study of arc-flow interaction in circuit breaker devices.

Ricardo Camarero was born in 1943 in Spain and educated in Canada at McGill University. He received his Ph.D. in mechanical engineering in 1972.

His present position is professor in the Applied Mathematics De- partment at Ecole Polytechnique de Montrkal. The research interest concern the development of computer codes for CFD applications.

Robert Jeanjean was born in 1945 a t Givors, France. He obtained his Ph.D. at University of Lyon in 1972.

In 1978, he became head of the circuit breaker research group at Alsthom-Villeurbanne. Since 1985, he is head of the circuit breaker R&D group at Cegelec.

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Computer aided tools in gas circuit breaker design