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Advances in Engineering Software 40 (2009) 193–201

Contents lists available at ScienceDirect

Advances in Engineering Software

journal homepage: www.elsevier .com/locate /advengsoft

Flow analysis in valve with moving grids through CFD techniques

C. Srikanth a,1, C. Bhasker b,*,2

a Department of Mechanical Engineering, Vasavi College of Engineering, Ibrahimbag, Hyderabad 500031, Indiab BHEL, Corp R&D Division, Hyderabad 500093, India

a r t i c l e i n f o

Article history:Received 8 February 2007Received in revised form 7 January 2008Accepted 4 April 2008Available online 3 June 2008

Keywords:Puffer chamberMoving elementFixed electrodesMulti-block single volume gridCompressible flowMoving gridsCFXCCLFlow simulationElectro-fluid dynamics

0965-9978/$ - see front matter � 2008 Elsevier Ltd. Adoi:10.1016/j.advengsoft.2008.04.003

* Corresponding author. Address: 402 Residency ApHyderabad 500 093, India. Tel.: +91 040 27641584; c

E-mail addresses: [email protected] (C. SrikaBhasker).

URL: http://www.geocities.com/bskr2k (C. Bhaske1 BE(final year) project work. Presently working as Pr

Technology Solutions India Private Limited, Madhapur2 Member, AIAA/USA, Life Member, EDAF/India.

a b s t r a c t

The compressible air flow in a typical puffer chamber with moving contact between fixed electrodes hasbeen studied using computational fluid dynamics techniques. Moving grid methods in CFD process notonly plays a pivotal role in understanding the flow behavior in time domain but also helps for fixingthe internals at optimal locations. A typical laboratory puffer chamber geometry has been extracted fromthe published literature and generated multi-block structured grid using Altair’s HyperMesh software.Flow simulation in axi-symmetry duct comprises fixed electrodes, moving contact and exit duct has beencarried out with ANSYS-CFX software. It has been observed that, due to steps and curvature in the geom-etry, flow takes different turns from inlet and velocity distribution between fixed electrodes indicatesvortex flow with turbulent eddies. CFD simulation with valve element mesh motion indicates that pres-sure history is significantly affected by the velocity of moving contact in the puffer chamber. The resultsobtained for a typical puffer chamber with the mesh motion are qualitative in nature and forms the soundbasis for future design studies of electro-fluid dynamics of circuit breakers.

� 2008 Elsevier Ltd. All rights reserved.

1. Introduction

Substations with circuit breakers in electrical power-stations[1] are very critical and protect the auxiliary components due tofault currents. SF6 gas-insulated substations (GIS) are preferredfor several voltage ratings to protect power plant componentsdue to internal breakdowns (see Fig. 1). In such a substation, thevarious equipments like circuit breakers, bus-bars, isolators, loadbreak switches, current transformers, voltage transformers earth-ing switches, etc. are housed in metal enclosed modules filled withSF6 gas as shown in Fig. 2. Due to high dielectric strength of SF6 gasthan air, the clearances required are smaller. Hence, the overall sizeof each equipment and the complete substation is reduced to about10% of conventional air-insulated substations.

Transportation of SF6 gas in circuit breaker shown in Fig. 3 issubjected to moving and stationary components. Although, the

ll rights reserved.

artments, Ashoknagar Bridge,ell: 9849252948.nth), [email protected] (C.

r).ogrammer Trainee. Cognizant

, Hyderabad-500081, India.

reliability of gas-insulated system is high, any internal breakdownthat occur invariably causes extensive damage and an outage ofseveral days duration is needed to effect the repair and it has beenreported [2] that the consequential losses are high.

Because of the flow structure peculiar to blast waves and nozzlejet flows, low-density portions inevitably yields in high pressuregases such as SF6, especially, when it is subjected to multiple mov-ing and fixed objects. Immediately after the current interruption, ahigh voltage of alternating current is imposed to the breaker andthere arises a possibility that regeneration of arc might affect itsperformance. The transient electric arc is described by the Na-vier–Stokes equations, Maxwell equations and radiation transportequations. Besides the numerical solution of these partial differen-tial equations, an exact knowledge of the material properties likegas density, thermal capacity, viscosity, thermal and electric con-ductivity are required. Even with the present available computerpower, the research for understanding electro-fluid dynamics ofquenching the arc is limited success.

The arc in conventional gas-blast circuit breakers is merely apassive element to be quenched by a transonic gas flow of suffi-cient pressure. The latter is generated mechanically by rather sim-ple means, but uneconomically from the modern point of view. Thearc in a self-blast circuit breaker is an active element controllingthe breaker action in a complicated manner all the time from con-tact separation to extinction at one of the subsequent current-

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194 C. Srikanth, C. Bhasker / Advances in Engineering Software 40 (2009) 193–201

zeros. In order to understand flowing fluid behavior for arc extinc-tion with moving contacts, simulation through computational fluid

Fig. 2. Circuit breakers and it

Fig. 3. Cross-sectional vie

Fig. 1. Electrical substat

dynamics – CFD plays significant role [3] in design of circuitbreakers.

s internals in substation.

w of circuit breaker.

ion in power plant.


C. Srikanth, C. Bhasker / Advances in Engineering Software 40 (2009) 193–201 195

2. Problem description

The geometrical and physical modeling involved in circuitbreakers are complex and requires multi-disciplinary approachesto account electro-fluid dynamics. When the working fluid is SF6,accurate description of flow properties are highly essential. Thefluid medium present in the circuit breaker is compressible forwhich thermodynamic properties are very sensitive and any inac-curate input values for viscosity, thermal conductivity, specificheat, etc., will not yield meaningful results. In order to gain insights,the present paper examines typical puffer breaker based on labora-tory setup using air as flow medium detailed [4] for prediction ofseveral field variables as a function of valve movement. In reality,the geometry is circular nature with multiple moving and station-ary objects and simulation process is difficult in generation ofgeometry, grid and convergence of fluid flow equations, To under-stand flow effects with the movement of valve element in streamwise direction, the typical geometry of puffer chamber is consid-ered and shown in the Fig. 4. The model considered in this paperis of axi-symmetric puffer breaker, wherein gas flow enters fromthe duct joining to fixed electrode and leaves through exit duct at-tached rightside fixed electrode along with moving object. When,the currents are interrupted, the valve element begins to move fromleft to right. Then, the fluid in the puffer chamber is compressed be-cause of reducing volume between the walls of fixed electrodes.

3. Computational grid

One of the essential pre-requisite is to generate quality compu-tational grid for the geometry, which takes three-fourths of thetime of any CFD project. Several commercial grid generators likeICEM, Gridgen, Gridpro, HyperMesh are used to generate the tetra-hedral/polyhedral, structured multi-block hexagonal grids and canbe exported to CFD solvers along with boundary regions. AltairHyperMesh is the best choice for generation of quality structuredgrids and its usage in CFD solver through user friendly.

Advanced functionality within HyperMesh allows users to effi-ciently mesh high fidelity models. This functionality includes userdefined quality criteria and controls, morphing technology to up-date existing meshes to new design proposals, and automaticmid-surface generation for complex designs with varying wallthicknesses. Automated tetra-meshing and hexa-meshing mini-mizes meshing time, while batch meshing enables large scalemeshing of parts with no model clean up and minimal user input.HyperMesh presents users with a sophisticated suite of easy-to-use tools to build and edit models. For 2D and 3D model creation,users have access to a variety of mesh generation panels besidesHyperMesh’s powerful automeshing module.

inlet

exit

Moving element

Fixed electrode

Fig. 4. Geometry of puffer breaker.

The surface automeshing module in HyperMesh is a robust toolfor mesh generation that provides users the ability to interactivelyadjust a variety of mesh parameters for each surface or surfaceedge. These parameters include element density, element biasing,mesh algorithm and more. Element generation can be automati-cally optimized for a set of quality criteria. HyperMesh can alsoquickly automesh a closed volume with high-quality first or secondorder tetrahedral elements.

The geometry of puffer chamber has been extracted from thepublished literature and created plan view of the model with thenumber of 2D blocks. The geometry has been extruded for arbitrarythickness to obtain the three dimensional volume. Using 3D solidmesh options, volume planes with uniform grid points has been se-lected to generate the three dimensional computational mesh.After repeating this process for all other volumes and removal ofduplicate elements at mating surface three dimensional grid forconsidered geometry comprises 57,096 nodes and 51,250 elementshas been imported to flow solver.

The computational grid for the puffer chamber with the valveopening and closed states are shown in the Fig. 5a and b. In thesegrids, legend red3 color surface indicates the moving contact. Thegreen color surface area represents inlet to puffer chamber. The or-ange color surface describes the exit location. The blue color surfaceon front and back shows wall surface between fixed electrodes andmoving contact. The rest of the colored surfaces are treated as de-fault domain.

4. Mathematical formulation for moving grid

The governing equations for prediction of compressible Navier–Stokes equations are detailed in [5–11]. The standard formulationof the conservation of the variable for a volume V with movingboundaries is

o

ot

ZUdV

� �þZ

Uðuj � vjÞdAj ð1Þ

where uj, vj is the velocity of the moving boundary element dAj. Astraightforward first order time discretisation of the equation is asfollows:

ðUnþ1Vnþ1 �UnVnÞDt

þX½Uipðuj � vjÞ�nþ1

ip DAnþ1j;ip ð2Þ

With the definition

U ¼ 1V

ZUdV ð3Þ

The goal is to formulate the equations in a way that they can be dis-cretised consistently with a standard finite volume formulation. Theconservation equation can be re-written as

o

ot

ZUdV

� �þZ

UðuÞj dAj �ZðU�UÞvj dAj �

ZUvj dAj ¼ 0 ð4Þ

The variations U is constant when integrated over the surface of thecontrol volume. This meansZ

Uvj ¼ UZ

vj dAj ¼ UV ð5Þ

It may be noted that due to elimination of time derivative, change inthe time derivative and volume change from the surface extensionare balanced analytically. The conservation equation therefore bere-written as

3 For interpretation of color in Fig. 5, the reader is referred to the web version ofthis article.


Fig. 5. (a) Computational grid in valve open condition. (b) Computational grid in valve closed condition.


UV þZ

Uðuj � vjÞdAj þZ

Uvj dAj ¼ 0 ð6Þ

The Eq. (6) is exact, as only trivial manipulations and average con-cepts have been introduced in the derivation. The conservation withmoving mesh option can therefore be written as the standard equa-tion plus a term due to the mesh movement. The surface integralincluding grid velocities are discretised asZðU�UÞvj dAj ¼

X½ðU�UÞvj�ipDAj;ip ð7Þ

DAj,ip is the volume swept by the integration point face. The vol-ume change from the time derivative and the volume change fromthe surface integral is implemented consistently through CELscript. Further details concerned to computational algorithm andimplementation in software are outlined in [12–15].

4.1. CFD solver

CFD solver used in this paper to compute Navier–Stokes equa-tions are based on finite volume technique. As a finite volumemethod, it satisfies global conservation by enforcing local conser-vation over control volumes that are constructed around eachmesh vertex or node. Advection fluxes are evaluated using ahigh-resolution scheme that essentially, second order accurateand bounded. For transient flows, an implicit second order accuratetime differencing scheme is used. This technology is available in asingle solver that covers all supported physical models.

In the applications of puffer circuit breakers, accurate resultsare realizable by simply repositioning existing mesh points. Inthe ANSYS-CFX product, this is accomplished in two ways; by spec-ifying the motion of points on particular mesh regions or by explic-itly specifying the positions of all points in the mesh. If the motionof particular two and three dimensional mesh regions are known,they can be specified as displacements relative to the initial meshor as absolute locations (which may be relative to the previousmesh). This motion may depend upon space, time or any othersolution variable that is accessible through the CFX ExpressionLanguage (CEL) or FORTRAN-based user-CEL calls.

ANSYS-CFX software then solves a displacement diffusion equa-tion to determine the mesh displacements throughout the remain-ing volume of the mesh. Contrary to point-iterative spring-analogy-based methods, this approach takes advantage of the com-putational efficiency of the ANSYS-CFX multigrid solver and auto-matically preserves features of the mesh, such as inflatedboundary layers. The ability to vary the mesh stiffness (that is,the diffusivity for the mesh displacement equation) provides addi-

tional control over the resulting mesh distribution. Locally increas-ing mesh stiffness, for example, is a particularly useful approach toavoid mesh folding in regions of large deformation. The ability tospecify the positions of all points in the mesh is offered throughjunction box routine calls to user FORTRAN code. In applicationsthat involve extreme deformations, a topologically valid mesh can-not be maintained by mesh repositioning only. In these cases, localor global re-meshing is required and the existing solution can beinterpolated to the updated mesh using tools provided with theANSYS-CFX product.

5. Boundary conditions

After importing the grid in Ansys pre-processor, simulation typehas been selected as unsteady with the initial and final time stepvalues, based on which moving contact displacement is subjectedfrom open to closed position in puffer chamber.

The other important step is to create the domain with theassignment of fluid type and its properties – compressible fluid,i.e., ideal air, thermally treated as total energy, turbulence is ac-counted through high Reynolds number k–e with standard wallfunctions. Air flow with specified component velocities are enter-ing the inlet chamber and after taking different turns leave throughexit location, where atmosphere pressure is prescribed. The refer-ence pressure of fluid is defined in the simulation as 101,325 Pa.Connected surfaces of moving element under mesh motion is de-fined as unspecified in the wall boundary conditions. In a separatewall boundary condition, the displacement of moving element isprescribed in stream wise direction. The inputs for wall boundaryconditions of moving wall are specified in Table 1 through CEL.

5.1. Convergence

Segregated solvers employ a solution strategy, where themomentum equations are first solved, using a guessed pressure,and an equation for a pressure correction is obtained. Because ofthe guess-and-correct nature of the linear system, a large numberof iterations are typically required in addition to the need for judi-ciously selecting relaxation parameters for the variables. ANSYS-CFX uses a coupled solver, which solves the fluid flow equations(for u, v, w, p) as a single system. This solution approach uses a fullyimplicit discretisation of the equations at any given time step. Forsteady state problems the time step behaves like an accelerationparameter, to guide the approximate solutions in a physically basedmanner to a steady state solution. This reduces the number of iter-ations required for convergence to a steady state, or to calculate


Table 1CEL script for moving grid in CFD simulation

CEL: BOUNDARY: sqrEXPRESSIONS: Boundary Type = WALL

tStep = .1 [s] Location = MW1pvel = 40. [m s-1] BOUNDARY CONDITIONS:

dsqr = pvel*tStep HEAT TRANSFER:dsqr1 = ave(Total MeshDisplacement x)@ sqr

Option = Adiabatic

dsqrn = dsqr1+dsqr ENDtTotal = 2.1 [s] MESH MOTION:

END Displacement X Component = dsqrnDisplacement Y Component = 0 [m]Displacement Z Component = 0 [m]Option = Specified DisplacementEND


the solution for each time step in a time dependent analysis. At anystage of a calculation, each equation will not be satisfied exactly,and the residual of an equation identifies by how much the left-hand-side of the equation differs from the right-hand-side at anypoint in space. If the solution is exact then the residuals are zero.Exact means that each of the relevant finite volume equationsare satisfied precisely. However, since these equations only modelthe physics approximately, this does not mean that the solutionexactly matches, what happens in reality. If a solution is converg-ing, residuals should decrease with successive time steps. Mathe-matically, convergence rate in simple form can be defined by

Convergence rate ¼ Rn

Rn�1ð8Þ

where Rn is the normalised log residual at time step n, and Rn�1 isthe normalised log residual at time step n � 1. It should be possibleto obtain a value of 0.95 or smaller for most situations. The time

Fig. 6. Residuals behavior in t

step iteration is controlled by the physical time step (global) or localtime step factor (local) setting to advance the solution in time for asteady state simulation.

A first indication of the convergence of the solution to steadystate is the reduction in the residuals. Experience shows, however,that different types of flows require different levels of residualreduction. For example, it is found regularly that swirling flowscan exhibit significant changes even if the residuals are reducedby more than 5–6 orders of magnitude. Other flows are well con-verged with a reduction of only 3–4 orders. In addition to the resid-ual reduction, it is therefore required to monitor the solutionduring convergence and to plot the pre-defined target quantitiesof the simulation as a function of the residual (or the iterationnumber). A visual observation of the solution at different levelsof convergence are recommended.

When fluid-domain involves movement of internal objects,transient flow simulations are highly dependent on grid qualityand skew angles between mesh points. The mesh quality check isto enforce positive control volumes in the grid. This check is per-formed at the beginning of every global iteration step and the tech-nique works well for wide range of applications with reasonabledeformations/time step sizes. If the grid quality is below a certainlevel, i.e., skew angle becomes very small, the associated meshpoints becomes highly distorted and solver fails. However, thistechnique will have the limitations, if the computational mesh in-volves multi-domain and solver inevitably fails due to lack ofremeshing algorithm due to distortion of mesh points.

Full transient file has been created using the upwind discretisa-tion scheme with second order backward Euler algorithm. Thevalve movement will take about 21 times from its initial state toreach closed position based on the inputs of moving contact veloc-ity, tStep, tTotal and mesh motion of object in specified direction.For each valve displacement, flow, turbulence and energy equa-

ransient flow simulation.



tions iterates in several time steps till the residuals are reaches tothe order 1e�04. As the valve element moves to next incrementaldistance towards closure state, with the results available at previ-ous step, flow equations are reiterated for the stretched grid points.This will continue, till the valve movement is reached to almostclosed position (see Fig. 6).

The residual history for flow turbulence and energy equations areshown in Fig. 7 wherein each peak corresponds one global time step.Within each global time step, flow, turbulence, energy equationsmarches on all grid points through couple solver in 10 local timesteps till the root mean square residual values reaches to the order1e�04. As global time increases, valve element moves towardsclosed state, computational mesh automatically adjusts to the chan-ged geometry and checks grid skew for linear solver. The residual er-rors within inner time step iterations, which uses previouslycalculated field variables, rapidly drops in fewer iterations. Depend-ing upon tTotal and moving body velocity as a product of tStep, con-verged simulation results are stored in transient file folder.

5.2. Judging convergence

In many cases, global quantities will stabilize within 20 to 30time steps, but convergence will not be achieved until approxi-

Fig. 7. (a) t = 0.3 s. (b) t = 1.0 s. (c) t = 2.1 s.

mately 100 time steps are completed. For most applications, con-vergence should be achieved (or well on its way) within 200time steps. If the problems with convergence are encountered, itis required to find the source of the problem rather than takingthe results as they are.

There are many factors that may lead to poor convergence,including poor mesh quality, improper boundary condition selec-tion and time step selection to name a few. When there problemswith convergence, it is required to determine whether the problemis local or global. Compare the (root mean square) RMS and (max-imum) MAX residuals of the equations having difficulty. If the MAXresidual is more than one order of magnitude larger than your RMSresidual, it usually indicates that the problem is concentrated to alocal region. If it is a locally high residual, identifying the locationof the MAX residual will help in diagnosing the problem. Typicallythe location of the MAX residual of the momentum equations is themost useful to identify. When the linear solver fails, it can mean

Fig. 8. (a) t = 0.3 s. (b) t = 1.0 s. (c) t = 2.1 s.


Fig. 9. (a) t = 0.3 s. (b) t = 0.6 s. (c) t = 0.8 s. (d) t = 1.0 s. (e) t = 2.0 s. (f) t = 2.1 s.


that non-physical boundary conditions have been applied, or thatthe initial values were inappropriately set.

In simulations that involve mesh deformations of internal ob-jects in the domain, extra care is required to ensure that mass,momentum and energy are conserved. This is generally not possi-ble, when points are dynamically added and removed from themesh. ANSYS-CFX software employs an advanced mesh movementor mesh morphing model to reduce the need for remeshing and,hence, increase the accuracy of the prediction. There are situationsthat mesh movement in ANSYS-CFX solver fails during mesh morp-hing due to distortion of grid.

6. Results and discussion

After convergence, ANSYS-CFX writes .gtm, .def, .cfx and .outfiles in the working directory. In case of transient flow simulation,a separate directory generates, in which grid files are stored foreach global time. The field variables such as velocity vectors, machnumber, velocity magnitude, pressure are available for all grid

points in the computational domain for visualisation and interpre-tation through contour plots, velocity vectors and streamlines.

The velocity vectors from inlet to exit location of puffer cham-ber at the mid plane of puffer chamber are shown in Fig. 7a–c.When the valve is fully open, the flow from inlet to the exit exhib-its high velocity in the region of fixed electrodes. As valve is 50%open, the air flow distribution tend form swirl motion with consid-erable velocity magnitudes between fixed electrode region. Indica-tions of flow recirculation between fixed electrodes and at certainplaces in exit duct becomes stronger, when the moving contact isreaching closed position. The Mach number distribution at corre-sponding times in the middle plane of computational domain is de-scribed in Fig. 8a–c. It is observed from these plots, that the flow issubsonic and highest Mach number indicates at exit location whenvalve is in opening condition. As valve element moves towardsclosed state, highest Mach number shifts to the fixed electrodes re-gion where velocity magnitude highest. The variation of Machnumber is found to increase with the displacement of moving con-tact in the puffer chamber.


Fig. 10. (a) t = 0.3 s. (b) t = 0.6 s. (c) t = 0.8 s. (d) t = 1.0 s. (e) t = 1.0 s. (f) t = 1.0 s.


To substantiate velocity vectors and Mach number pattern inthe puffer chamber, velocity pattern is detailed for different timesin Fig. 9a–f. Due to steps and curvature in puffer chamber geome-try, the velocity distribution exhibits irregular, increases betweenfixed electrodes and drops rapidly in the exit duct. The behaviorof flow pattern indicates the swirl flow with turbulent eddies notonly in the area of fixed electrodes but also occurs in the exit duct.It is also noticed that due to displacement of moving contact, areabetween fixed electrodes is compressed and volume is reduced.Highest velocity which is taking place at this region increases withthe volume reduction in fixed electrodes due to displacement ofmoving contact in the puffer chamber.

Static pressure distribution for the corresponding times at themiddle plane of computational domain of puffer chamber is shownin Fig. 10a–f. High pressure in puffer chamber in the neighborhoodof moving contact increases with the displacement of valve to-wards closed position. Pressure contours in the puffer chamberplane are highly fluctuating and forms the low pressure zone be-tween fixed electrodes. This low pressure expands over volume be-tween fixed electrodes becomes smaller incrementally. The flowparametric database generated for typical puffer chamber with

moving contact through CFD provides several insights for under-standing to quench the arcs due to fault currents.

7. Conclusions

Compressible air flow simulation in a typical puffer type cham-ber comprises fixed electrodes, moving contact, inlet and exit loca-tions are carried out using CFD techniques. The velocity vectors inthe middle plane of puffer chamber indicates swirl flow with tur-bulent eddies over the displacement of moving contact towardsclosed position. Indications of swirl flow between fixed electrodesand at exit duct becomes stronger with the displacement of mov-ing contact. Static pressure contours in the middle plane of pufferchamber are highly fluctuating and forms the low pressure regionbetween fixed electrodes, which however increases with the valvemovement towards closed state. The variations in pressure historyare significantly affected by the velocity of moving contact in thepuffer chamber. The CFD study carried out for prediction of severalflow characteristics provides valuable insights for quenching thearcs in circuit breakers.



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Author's Personal Copy - · PDF fileauthor’s benefit and for the benefit of the author’s institution, ... Multi-block single volume grid ... various equipments like circuit breakers,