Prediction of the nuclear fuel rod abrasion

Transcription

1 Applied and Computational Mechanics 7 (1) 5 5 Prediction of the nuclear fuel rod abrasion V. Zeman a,,z.hlaváč a a Faculty of Applied Sciences, University of West Bohemia, Univerzitní, 6 14 Plzeň, Czech Republic Received September 1; received in revised form December 1 Abstract The paper is focused on calculation of the friction forces wor in the contact of nuclear fuel rods with fuel assembly spacer grid cells. This friction wor is deciding factor for the prediction of the fuel rod coating abrasion. The fuel rod abrasion is caused by fuel assembly vibrations ecited by pressure pulsations of the cooling liquid generated by main circulation pumps. A prediction of fuel rod coating abrasion maes use of eperimentally investigated dependence of the abrasion on the friction force wor in laboratory conditions. The presented original analyticalnumerical method is applied for nuclear fuel rod inside of the Russian TVSA-T fuel assembly in the WWER 1/ type reactor core in NPP Temelín. c 1 University of West Bohemia. All rights reserved. Keywords: vibrations, nuclear fuel assembly, pressure pulsations, dynamic load, fuel rod abrasion 1. Introduction An assessment of nuclear fuel assemblies (FA) behaviour at standard operating conditions of the nuclear reactors belongs to important safety and reliability audits. A significant part of FA assessment plays abrasion of fuel rods coating [1]. The goal of this paper, in direct consequence of FA modelling in [7] and FA dynamic response ecited by pressure pulsations presented in [5], is an introduction of the newly developed method for prediction of fuel rod abrasion caused by their fleural vibration. Elastic properties of the spacer grids between inner FA components are in the FA computational model epressed by alternate linear spring g centrally placed between fuel rods, guide thimbles and centre tube (see Fig. 1) on several vertical spacings g =1,...,G[5, 7]. A real contact between inner fuel rods and spacer grids is realized by three cells i = 1,, (see Fig. ). Elastic properties of each cell can be epressed by three springs with identical stiffnesses. The contact forces (in the picture F u,i ) between fuel rods (FR) and cells are deciding factor for the prediction of the FR abrasion. The undermentioned method is focused on prediction of the FR abrasion caused by fleural FR vibrations in-spacer grids. FR vibrations are caused by spatial motion of the FA support plates in reactor core ecited by pressure pulsations generated by main circulation pumps in the coolant loops of the reactor primary circuit []. Solution is based on nowledge of the spacer grid cell stiffnesses calculated by FEM in ŠKODA JS [] and eperimentally investigated dependence of the FR abrasion on the friction force wor in the contact line between FR laboratory sample and pressure plate [4]. Corresponding author. Tel.: , zemanv@me.zcu.cz. 5

2 V. Zeman et al. / Applied and Computational Mechanics 7 (1) 5 5 y y v v v 1 g F (F,F y) g u + 1 v 1 y F (F, F y) u + 1 u 1 g g y u u g g w + 1 u 1 y Fu, F u, y u F u, 1 u y w + 1 w w Fig. 1. The alternate couplings between fuel rods Fig.. The real couplings between fuel rods by means of cells. Shortly to computational and mathematical model of the nuclear fuel assembly The FA basic structure is formed from large number of parallel identical fuel rods, some guide thimbles and centre tube. These FA components are lined by transverse spacer grids to each other and with seleton construction (Fig. ). The spacer grids are placed on several horizontal level spacings between support plates in reactor core (RC) as it is shown in the scheme of the reactor WWER 1 in the Fig. 4. Fig.. Scheme of the fuel assembly Fig. 4. Scheme of the reactor 6

3 V. Zeman et al. / Applied and Computational Mechanics 7 (1) 5 5 Number of segments S=6,number of lines h=1,number of fuel rods= s= AP GR s=1 fuel rods guide thimbles centre tube AP AP 1.5 y s= s=6.5 AP 4 AP 6.1 s=4 s=5.15 AP Fig. 5. The FA cross-section In order to model the fuel assembly, the system is divided into subsystems identical rod segments (S), centre tube (CT) and load-bearing seleton (LS) fied in bottom part in lower piece (Fig. ). Because of the cyclic and central symmetric pacage of fuel rods and guide thimbles with respect to centre tube (Fig. 5), the FA decomposition to the identical rod segment s =1,...,S (on the Fig. 5 for S =6) shall be applied. Each rod segment is composed of R fuel rods with fied bottom ends in lower piece (LP) and guide thimbles (GT) fully restrained in lower and head pieces (HP). The fuel rods and guide thimbles are lined by transverse spacer grids of three types (SG 1 SG ) inside the segments. Elastic properties of the spacer grids in the FA computational model are epressed by linear springs placed on several level spacings g =1,...,G(see Fig. 1). The fuel rods are embedded into spacer grid cells with small initial radial tension which should not be negative during core operation. The mathematical model of the rod segment s isolated from adjacent segments (without linages between segments) was derived in the special coordinate system [7] q s =[q T 1,s,...,qT r,s,...,qt R,s ]T, (1) where q r,s is vector of nodal point displacements of one rod r (fuel rod or guide thimble) on the level of all spacer grids g in the form q r,s =[...,ξ (s) r,g,η(s) r,g,ϑ(s) r,g,ψ(s) r,g,...]t, r =1,...,R; g =1,...,G. () Lateral displacements ξ r,g (s), η r,g (s) of the rod centres are mutually perpendicular whereas displacements ξ r,g (s) are radial with respect to vertical central ais of FA. Displacements ϑ (s) r,g, ψ r,g (s) are bending angles of rod cross-section around lateral aes (see Fig. 6). The fully restrained centre tube (see Fig. and Fig. 5) is discretized into G nodal points on the level of spacer grids g =1,...,Gby means of G +1prismatic beam finite elements in the coordinate system q CT =[..., g,y g,ϑ g,ψ g,...] T, g =1,...,G, () where lateral displacements g, y g are oriented into aes, y (Fig. 5). 7

4 V. Zeman et al. / Applied and Computational Mechanics 7 (1) 5 5 y s η (s) v,g (s) ψ v,g r v v γ q ξ (s) v, g υ (s) v, g η(s) u, g (s) ψ u, g g (s) ξ u, g βq r u u (s) υ u, g α u α v s Fig. 6. The spring between two rods replacing the stiffness of spacer grid g The load-bearing seleton (further only seleton) is created of S (on the Fig. 5 for S =6) angle pieces (AP) coupled by divided grid rim (GR) at all levels of spacer grids. Each angle piece with fied bottom ends in lower piece is discretized into nodal points in cross-section centre of gravity on the level of spacer grids g =1,...,G. The mathematical model of the seleton without couplings with spacer grids is derived in the coordinate system q LS =[q T AP 1,...,q T AP s,...,q T AP S ] T, (4) where q APs is vector of nodal points displacements for particular angle piece s on the level of all grid rim g in the form q APs =[...,ξ (s) AP,g,η(s) AP,g,ϕ(s) AP,g,ϑ(s) AP,g,ψ(s) AP,g,...]T, g =1,...,G. (5) Lateral displacements ξ (s) AP,g,η(s) AP,g of cross-section centre of gravity on the level of spacer grid g are mutually perpendicular whereas displacement ξ (s) AP,g is radial. Displacements ϕ(s) AP,g, ϑ(s) are torsional and bending angles of angle piece cross-section around vertical and lateral ψ (s) AP,g aes (detailed to [7]). The subsystems of FA are lined by spacer grids of different types for g =1, g =,..., G 1 and g = G. Mathematical models of segments are identical in consequence of radial and orthogonal fuel rods and guide thimbles displacements. Therefore, the conservative model of the fuel assembly in configuration space of dimension n =4GRS +4G +5GS can be written as AP,g, q =[q T 1,...,q T s,...,q T S, q T CT, q T LS] T (6) M q +(K + K S,S + K S,CT + K S,LS )q =. (7) The symmetrical mass M and stiffness K matrices correspond to a fictive fuel assembly divided into mutually uncoupled subsystems. Therefore, these matrices are bloc diagonal M =diag[m S,...,M S, M CT, M LS ], K =diag[k S,...,K S, K CT, K LS ], (8) 8

5 V. Zeman et al. / Applied and Computational Mechanics 7 (1) 5 5 Fig. 7. Spatial motion of the FA support plates where segment stiffness matri KS includes couplings between all fuel rods and guide thimbles inside the segment. The coupling symmetrical stiffness matrices K SS, K S,CT and K S,LS epress interaction between appropriate subsystems mared by subscripts. The stiffness matri of all couplings between subsystems K C = K S,S + K S,CT + K S,LS (9) has, for the heagonal type FA (S =6), bloc structure K 1,1 K1, S K1,6 S K 1,CT K 1,LS K,1 S K, K, S K,CT K,LS K, S K, K,4 S K,CT K,LS K C = K4, S K 4,4 K4,5 S K 4,CT K 4,LS K5,4 S K 5,5 K5,6 S K 5,CT K 5,LS, (1) K6,1 S K6,5 S K 6,6 K 6,CT K 6,LS K CT,1 K CT, K CT, K CT,4 K CT,5 K CT,6 K CT,CT K LS,1 K LS, K LS, K LS,4 K LS,5 K LS,6 K LS,LS where subscripts separated by comma denote lined FA subsystems. Each fuel assembly (see Fig. ) is fied by means of lower tailpiece (LP) into mounting plate in core barrel bottom and by means of head piece (HP) into lower supporting plate of the bloc of protection tubes. These support plates with pieces can be considered in transverse direction as rigid bodies. Let use consider the spatial motion of the support plates described in coordinate systems X,y X,z X (X = L, U) with origins in plate gravity centres L, U by displacement vectors (see Fig. 7) q X =[ X,y X,z X,ϕ,X,ϕ y,x,ϕ z,x ] T,X= L, U. (11) The lateral ξ (s) r,x, η(s) r,x and bending ϑ(s) r,x, ψ(s) r,x displacements in the end-nodes of the fuel rod or guide thimbles r in segment s (in Fig. 7 illustrated for s =1) coupled with plates can 9

6 V. Zeman et al. / Applied and Computational Mechanics 7 (1) 5 5 be epressed by the displacements of the lower (X = L) and upper (X = U) plates (detailed to [5]). The vectors of generalised coordinates of the fully restrained subsystems (rod segments and centre tube) loosed in inematically ecited nodes can be partitioned in the form q s =[(q (s) L )T, (q (s) F )T, (q (s) U )T ] T,s=1,...,6,CT (1) and the seleton s = LS fied in bottom ends only has the form q LS =[(q (LS) L ) T, (q (LS) F ) T ] T. (1) The displacements of free system nodes (uncoupled with support plates) are integrated in vectors q (s) F R ns. The vibration of the FR ecited by pressure pulsations generated by main circulation pumps are described by corresponding components ξ r,g (s), η r,g (s), ϑ (s) r,g, ψ r,g (s) of the generalised coordinate vectors q (s) F. Their calculation was presented in [5].. The contact forces between fuel rods and spacer grid cells Consider the inner fuel rod u that is surrounded with si fuel rods u +1, v, v 1, u 1, w, w +1(see Fig. ) that are uniformly arranged. Their maring correspond to the one applied in the global fuel assembly model. A real contact between fuel rod u and the spacer grid on every one level is realized by three cells i =1,,. Elasticproperties of one cell can be epressed by three springs with identical stiffnesses. Let the fuel rod u be loaded by eternal static force F (F,F y ) and the centres surrounded fuel rods are fied. The static displacements i,y i (i =1,, ) of the cell centres and u,y u of the FR u centre in the directions of coordinate aes, y, due to their fleibility, satisfy the relations F u,1 = ( u 1 ), ( ) F u, =.5 y.5 u + y u, (14) ( ) F u, =.5 + y.5 u y u, where F u,i are contact forces between fuel rod u and cells. From the static equilibrium conditions of each cell we obtain static displacements of their centres 1 = u; y 1 =, ( = 1 ).5 u y u ( = 1 ).5 u + y u ; y = (.5 1 u + ; y = 1 ) (.5 u + y u, (15) ) 4 y u.

7 V. Zeman et al. / Applied and Computational Mechanics 7 (1) 5 5 The deformation energy of all three cells is ( E p = 1 ( u 1 ) ) ( ) y y 1 + ( ) ( ) y u.5 u +.5 y y + (16) ) ) ( y.5 u y u + (.5 + y. By elimination of the displacements i,y i in term (16) according to (15) we get E p = 1.5( u + y u ). (17) The deformation energy of si alternate springs, which represent the elastic properties of couplings between fuel rod u and si surrounding fuel rods in the global fuel assembly model, is ( ) E p = 1 ) g u +.5y u + yu ( + u +.5y u + ( ) ( ) + u.5y u + yu + u.5y u (18) and after modification E p = 1 g( u + y u). (19) An equality of the right hand sides of the epressions (17) and (19) leads to g g =.5 b,where b is the cell stiffness defined by = 1 6 or b = F u,1. () u The dynamic contact forces F u,1,f u, and F u, (see Fig. 8) between fuel rod u of segment s and cells at the level spacer grid g (indees g and s is father let-out) in the course of fuel assembly vibration can be epressed by means of cell centres displacements i,y i (i =1,, ) and lateral displacements ξ u,η u,...,ξ w+1,η w+1 of si fuel rods surrounding the chosen FR. Fuel rod lateral displacements are generalised displacements of the fuel assembly global mathematical model presented in [5, 7]. These dynamic contact forces acting between spacer grid cell 1 and fuel rods u, u +1and w +1can be epressed as [ ( F u,1 = 1 + ξ u C(α u )+η u C α u + π )], [ F u+1,1 = y 1 + ξ u+1 C (α u+1 + ) ( π + η u+1 C α u ) ] 6 π, (1) [ F w+1,1 =.5 1 y 1 ξ w+1 C (α w ) π η w+1 C 41 ( α w π ) ].

8 V. Zeman et al. / Applied and Computational Mechanics 7 (1) 5 5 η v ξ v v η v 1 ξ v 1 F v 1 v 1, y η u β u, v F v, F u, u ξ u F u, 1 η u + 1 F u + 1, 1 y ξ u + 1 u + 1 η u 1 u 1 ξ u 1 F u 1, y F u, η w + 1 F w + 1,1 ξ w + 1 w + 1 F w, η w ξ w y s w α u s Fig. 8. The contact forces between the fuel rods and the spacer grid cells The function cosine is shortly mared C with argument in bracet which describes fuel rod angle position in the local coordinate system s,y s of the segment s. The epressions for centre cell lateral displacements follow from the static equilibrium of the considered cell F u,1 = F u+1,1 = F w+1,1. These displacements can be written as 1 = 1 [ ξ u C(α u )+η u C (α u + 1 ) π ξ u+1 C (α u+1 + ) π η u+1 C (α u ) π + ξ w+1 C (α w ) π + η w+1 C (α w )] π, y 1 = 1 [ ξ u+1 C (α u+1 + ) π η u+1 C (α u ) π () ξ w+1 C (α w ) π η w+1 C (α w )] π. In a similar way we derive centre cell lateral displacements of other cells and = 1 [ ξ v 1 C(α v 1 )+η v 1 C (α v ) π + ξ u C (α u + 1 ) π + η u C (α u + 56 ) π + ξ v C (α v 1 ) π + η v C (α v + 16 )] π, () y = 1 [ξ v C (α v 1 ) π + η v C (α v + 16 ) π ξ u C (α u + 1 ) π η u C (α u + 56 )] π, 4

9 V. Zeman et al. / Applied and Computational Mechanics 7 (1) 5 5 = 1 [ ξ u 1 C(α u 1 )+η u 1 C (α u ) π ξ u C (α u + ) π η u C (α u + 76 ) π + ξ w C (α w + 1 ) π + η w C (α w + 56 )] π, (4) y = 1 [ ξ u C (α u + ) π η u C (α u + 76 ) π ξ w C (α w + 1 ) π η w C (α w + 56 )] π. The total contact forces between fuel rod u in the segment s =1,...,6 and the spacer grid cells at the level g =1,...,G(indees s and g are let-out) are determined by the sum of the static contact force F st after fuel rods installation into the load-bearing seleton with spacer grids and the dynamic contact forces caused by vibration N u,i (t) =[F st + F u,i (t)]h(f st + F u,i (t)), i=1,,. (5) H is Heaviside function (for F st + F u,i (t) <, when contact is interrupted, H =). The dynamic contact forces of the fuel rod u with cells are epressed in the form (see Fig. 8) [ F u,1 = 1 + ξ u C(α u )+η u C (α u + 1 )] π, [ F u, =.5 y ξ u C (α u + 1 ) ( π η u C α u + 5 ) ] 6 π, (6) [ F u, =.5 + y + ξ u C (α u + ) ( π + η u C α u + 7 ) ] 6 π, where is the stiffness of the one substitute spring of the cell. Substituting the epressions (), (), (4) of the centre cell lateral displacements into force equations (6), we obtain dynamic contact forces occuring in Eq. (5). The fuel rod u angle position in each segment after its installation is determined by polar coordinate α u (see Fig. 6). 4. The power and the wor of the friction forces in the contact of fuel rods coating with the spacer grid cell The slip speeds between the transfer vibrating spacer grid on the level g and the fuel rod u in segment s due to the fuel rod bending inside of the spacer grid cell in contact points C i, i =1,, (see Fig. 9) are [ ( ) ( ) ] 1 1 c u,1 = r sin π β u,v ϑ u cos π β u,v ψ u, [ ( ) ( ) ] 7 7 c u, = r sin 6 π β u,v ϑ u cos 6 π β u,v ψ u, (7) [ ( ) ( ) ] c u, = r sin 6 π β u,v ϑ u cos 6 π β u,v ψ u, 4

10 V. Zeman et al. / Applied and Computational Mechanics 7 (1) π β u, v 6 C 7 6 π β u, v υ u ψ u ηu ξ u β u, v π β u, v r C 1 C y s α u s Fig. 9. The contact point positions of the fuel rod u with the spacer grid cells where r is outside diameter of the fuel rod coating. Bending angular velocities of the fuel rod cross-sections are epressed by corresponding components of the vector q (s) F (t) obtained by the derivative with respect to time of the generalised coordinate vector q (s) F of the fuel assembly free node displacements defined in (1). The power of the friction forces in the contact points C j of the fuel rod u coating in segment s and the spacer grid cells on the level g is P u,i (t) =f N u,i (t)c u,i (t), i =1,,, (8) where f is computational friction coefficient. The criterion of the fuel rod coating abrasion can be epressed by the wor of the friction forces during the period T [s] of the first harmonic component of pressure pulsations W u,i = T P u,i (t) dt. (9) On the basis of eperimental investigated friction coefficient f(t ) and mass loss μ [gj 1 ] in grams [4] of the fuel rod coating caused by the wor of the friction force W =1[J] we can calculate the fuel rod coating abrasion in the contact line segment during the operational period t p [s] 5. Application Δm i = μw u,i f(t ) f tp T [g], i =1,,. () The presented methodology was applied for steady polyharmonic dynamic response of the Russian TVSA-T fuel assembly in the WWER 1/ type reactor core in NPP Temelín. Mathematical model of the WWER 1/ type reactor ecited by pressure pulsations was derived in [6] by the decomposition method presented in [8]. The linearized model has the standard form M q(t)+b q(t)+kq(t) =f(t), (1) where the vector of generalised coordinates of dimension 17 is specified in [6]. 44

11 V. Zeman et al. / Applied and Computational Mechanics 7 (1) 5 5 The reactor is a large multi-body system which includes no special dampers. The first approimation of the damping consists in assuming that the system is lightly damped and that the damping matri B satisfies the general condition of proportional damping in the form V T BV =diag[d ν Ω ν ],wherev =[v ν ] is modal matri of the reactor conservative model. Its eigenfrequencies are noted Ω ν and eigenvectors v ν satisfying the norm v T ν Mv ν =1, ν =1,...,17. The dimensionless damping factors D ν were considered, on the basis of eperience in modelling of nuclear reactor vibrations, equal.5 with the eception of the damping factors corresponding to eigenmodes, where the reactor core dominantly vibrates. In consequence of an influence of coolant these factors were considered larger, concretely D ν =.8. After an estimation of all damping factors the damping matri in the mathematical model (1) is calculated as B =(V 1 ) T diag [D ν Ω ν ]V 1. The ecitation vector f(t) can be written as a real part of the comple ecitation vector [ ] f(t) =Re f () j e iω jt, j =1,,, 4, () j j where f () j is vector of comple amplitudes of -th harmonic component of the hydrodynamic force generated by one j-th main circulation pump. The fluctuation of the main circulation pump angular speeds ω j = π n j, n j 997., [rpm] is based on the measurement at the first and second NPP Temelín blocs [6]. The steady-state dynamic response of the reactor is given by the particular solution { [ q(t) =Re (ωj ) M +iω j B + K ] } 1 f () j e iω jt. () The generalised coordinates in dependence on time can be written in the form q i (t) = ( ) q () i,j cos ω jt q () i,j sin ω jt, (4) j where real (with one strip) and imaginary (with two strips) components of comple vector q () j = [ (ω j ) M +iω j B + K ] 1 f () j (5) are introduced. Subscript i =1,...,17 is assigned to the generalised coordinate, subscript j =1,,, 4 to the operating main circulation pumps and subscript to the harmonic component of pressure pulsations. The components of the vectors q () j, corresponding to displacements of the lower fuel assembly supporting plate in the lower part of core barrel (CB) depicted in Fig. 4 and the upper fuel assembly supporting plate (SP) in the bloc of protection tubes (BPT), are transformed into displacement vector q X defined in (11) and net into lateral and bending displacements in the end-nodes of the subsystem components [5]. As an illustration, etreme values of the total contact forces F u,i, vertical slip displacements y u,i and speeds c u,i of the fuel rod coating in contact points C i,powerp (s) u,i and wor W (s) u,i of 45

12 V. Zeman et al. / Applied and Computational Mechanics 7 (1) s= AP GR s=1 fuel rods guide thimbles centre tube chosen fuel rods AP AP y s= s= AP 4 AP 6.1 s=4 s=5.15 AP Fig. 1. The fuel assembly cross-section with chosen rods Table 1. Etreme values at contact points of the fuel rod u in segment s =with spacer grid cells on the level g =1 Quantity units mar Etreme values u =9 u =11 u =8 u =1 u =46 FR contact forces vs. N F u, cells F u, F u, FR slip displacements μm y u, vs. cells y u, y u, FR slip speeds PP vs. mm/s c u, cells c u, c u, Friction power in con- mw P u, tact points P u, P u, Friction wor in contact μj W u, points W u, W u, the friction forces for chosen fuel rods u =9, 11, 8, 1, 46 (see Fig. 1) in segment s =on the level of spacer grid g =1are demonstrated in Table 1. The time behaviour of these quantities for spacer grid cells surrounding the fuel rod u =46, with the eception of wor, in time interval t ; 1 [s] are shown in Figs This time interval of the numerical simulation includes the long period 6 [s] of the beating vibrations Δ n caused by slightly different main circulation pumps revolutions Δ n [rpm]. 46

13 V. Zeman et al. / Applied and Computational Mechanics 7 (1) 5 5 N 1 [N] N [N] N [N] t [s] Fig. 11. The contact forces between fuel rod u =46in segment s =and spacer grid cells on the level g = z 1 [m] z [m] z [m] t [s] Fig. 1. The vertical slip displacements between fuel rod u =46in segment s =and spacer grid cells on the level g =1 47

14 V. Zeman et al. / Applied and Computational Mechanics 7 (1) c 1 [m/s] c [m/s] c [m/s] t [s] Fig. 1. The vertical slip speeds between fuel rod u =46in segment s =and spacer grid cells on the level g =1 P 1 [W] P [W] P [W] t [s] t [s] Fig. 14. The power of the friction forces between fuel rod u =46in segment s =and spacer grid cells on the level g =1 48

15 6. Conclusion V. Zeman et al. / Applied and Computational Mechanics 7 (1) 5 5 The described method enables to investigate the fleural inematically ecited vibrations of all fuel assembly components. The vibrations are caused by spatial motion of the two horizontal supporting plates in the reactor core transformed into displacements of the inematically ecited nodes of the fuel assembly components fuel rods, guide thimbles, centre tube and seleton angle pieces. The special coordinate system of radial and orthogonal lateral and fleural angular displacements around these directions of the fuel rods and guide thimbles enables to separate the heagonal type FA into si identical revolved rod segments characterized in global fuel assembly mathematical model by identical mass, damping and stiffness matrices. These identical subsystems are lined each other and with centre tube and seleton by spacer grids on the several level. The elastic properties of the spacer grid on the different horizontal levels g are epressed in the fuel assembly global model by alternate springs with stiffnesses g calculated on the basis of their identical deformation energy with cells. All fuel assembly components are modelled as one dimensional continuum of beam type with nodal points in the gravity centres of their cross-sections on the level of the spacer grids. The developed methodology was used for steady-state vibration analysis of the Russian type nuclear fuel assembly caused by motion of the support plates, ecited by pressure pulsations generated by main circulation pumps in the coolant loops of the primary circuit. The developed software in MATLAB is conceived in such a way that enables to choose an arbitrary configuration of operating pumps whose rotational frequencies are slightly different in the eperimentally determined frequency interval f 16.65; Hz. This phenomenon results in beat vibrations, which amplify dynamic normal and friction forces in the contact of the fuel rod coating and spacer grid cells. The software enables an identification of the maimal dynamic loaded spacer grid cell and calculation of the maimal normal contact forces between fuel rod coating and surrounding spacer grid cells for the arbitrary fuel rod on the arbitrary spacer grid levels. Subsequently we can calculate the friction force wor in the contact lines of the chosen fuel rod with cells during defined time period. In this way the abrasion of fuel rod coating can be estimated. Acnowledgements This wor was supported by the European Regional Development Fund (ERDF), project NTIS, European Centre of Ecellence, CZ.1.5/1.1./.9 within the research project Fuel cycle of NPP of the NRI Řež plc. References [1] Fuel Assembly Mechanical Test Report, volume I a II, TEM-MC-4.RP (Rev ), Property of JSC TVEL, NRI Řež, 11. [] Jení, J., Mechanical model for cell stiffness determination of the TVSA-T fuel assembly. Research report Ae /Do, Šoda JS, a. s., 1 (in Czech). [] Pečína, L., Stulí, P., The Eperimental Verification of the Reactor WWER 1/ Dynamic Response Caused by Pressure Pulsations Generated by Main Circulation Pumps. In: Proceedings of Colloquium Dynamics of Machines 8, ed. L. Peše, Institute of Thermomechanics AS CR, Prague (8), pp

16 V. Zeman et al. / Applied and Computational Mechanics 7 (1) 5 5 [4] Svoboda, J., Šmíd, Z., Kláštera, P., Study of the influence of selected factors on the abrasion of components made of ZR material. Research report Z-1497/1, Institute of Thermomechanics, Academy of Sciences of the Czech Republic v.v.i, Pilsen, 1 (in Czech). [5] Zeman, V., Hlaváč, Z., Dynamic response of nuclear fuel assembly ecited by pressure pulsations. Applied and Computational Mechanics 6() (1) 19. [6] Zeman, V., Hlaváč, Z., Dynamic response of VVER 1 type reactor ecited by pressure pulsations. Engineering Mechanics 15(6) (8) [7] Zeman, V., Hlaváč, Z., Modelling and modal properties of the nuclear fuel assembly. Applied and Computational Mechanics 5() (11) [8] Zeman, V., Hlaváč, Z., Modelling of WWER 1 type reactor vibration by means of decomposition method. In: Engineering Mechanics 6, Boo of etended abstracts, ed. J. Náprste and C. Fischer, Institute of Theoretical and Applied Mechanics AS CR, Prague (6), pp (full tet on CD-ROM) (in Czech). 5