ML19309E152
| ML19309E152 | |
| Person / Time | |
|---|---|
| Site: | Kewaunee, Prairie Island  |
| Issue date: | 02/29/1980 |
| From: | WESTERN NUCLEAR, INC., WESTINGHOUSE ELECTRIC COMPANY, DIV OF CBS CORP. |
| To: | |
| Shared Package | |
| ML111651196 | List: |
| References | |
| NUDOCS 8004180475 | |
| Download: ML19309E152 (100) | |
Text
{{#Wiki_filter:.- . WESTINGHOUSE CLASS 3 0 . STRUCTURAL ANALYSIS OF REACTOR COOLANT SYSTEM FOR POSTULATED LOSS-0F-COOLANT-ACCIDENT PRAIRIE ISLAND /KEWAUNEE. NUCLEAR POWER PLANT PRELIMINARY ISSUE FEBRUARY 1980 l i WESTINGHOUSE ELECTRIC CORPORATION Nuclear Energy Systems P. O. Box 355 ' Pittsburgh, Pennsylvania 15230 t ON o AN SO
SECTION 1
1.0 INTRODUCTION
The prairie. Island 1 and 2 and Kewaunee Nuclear Power Plants have been evaluated for . postulated pipe ruptures at the reactor vessel inlet and outlet nozzles and the reactor coolant pump discharge nozzle. This report summarizes the analysis assump-tions, methods used, and evaluatio.1 results. The pipe rupture analysis consisted of (1) calculating hydraulic forcing functions for the reactor vessel and coolant loops, (2) determining reactor cavity pressure, (3) finding the reactor vessel response for the postulated ruptures, (4) evaluating the broken and unbroken reactor coolant loops and supports, and (5) evaluating the reactor vessel internals and fuel. Each of these analyses are discussed in detail in the following sections. f 9 0 1-1 1 1
SECTION 2 l 2.1 HYDRAULIC FORCING FUNCTIONS This section describes the analysis of the applied hydraulic forces on the reactor coolant loop (RCL) and reactor pressure vessel (RPV) internals. Hydraulic loads were developed for the broken and unbroken legs for the reactor vessel inlet break case. This break was assumed to be limited to 150 square inches with a 10 millisecond break opening time. . 2.2 CALCULATION OF RCL HYDRAULIC FORCING FUNCTIONS Following a LOCA, there is a rapid decay in the primary coolant system pressure, which results in several hydraulic loading phenomena occurring in the RCL piping, and in the reactor pressure vessel region. Initially, a decompression wave originates at the location of the postulated pipe break due to the assumed instantaneous severance of the pressure boundary. This depressurization wave propagates at the local speed of sound through-out the coolant piping, pump, steam generator, and vessel region. The transien: fluid pressure and mass flow behavior in the reactor coolant system (RCS) imposes hydraulic blowdown forces of large magnitude and short duration on the coolant loop piping and primary equipment. The calculation of these loop and vessel forces is performed in two steps. The first step is to determine the transient pressures, mass velocities, and densities in the coolant loops and vessel as a function of time. This is accomplished by utilizina the MULTIFLEX computer program [8] . In the second step, the THRUST code ** , using these time-history values, calculates the hydraulic forcing functions at specified locations along the coolant loop piping; likewise, the LATFORC ** and FORCE-2 ** codes calculate lateral and vertical forces, respectively, at specified locations on the reactor vessel internals. The following sections briefly describe these computer codes. Additional detail about these programs can be found in the referenced WCAP reports. 2-1 i
. a .
s 2.3 MULTIFLEX CODE The MULTIFLEX computer program is an engineering design tool that can be employed to evaluate the transient response of a PWR primary coolant system followina a postulated LOCA. The thermal-hydraulic portion of the MULTIFLEX code is based on the one-dimensional homogeneous flow model which is expressed as a set of mass, momentum, and energy conservation equations. These equations are quasi-linear, first-order, partial differential equations which are solved by the method of characteristics. The employed numerical method utilizes an explicit time scheme along the respective characteristics. Consequently, time steps for stable numerical integration are restricted by sonic propagation (Courant-Friedrich-Levy Criterion) [12] 2.3.1 MULTIFLEX MODELS In order to make the computer program applicable to a complex thermal-hydraulic-mechanical system, a large number of hydraulic legs (regarded as pipes of arbitrary length and flow area) are required. The reactor pressure vessel region and the external coolant. loops were represented by an equivalent piping network (EPN) composed of approximately two hundred legs. Equivalent networks were developed using the standard techniques and nodalization rules outlined in Reference [3]. As an example, Figures 2.3-1 through 2.3-5 illustrate a typical EPN representation of the entire primary system for a two-loop-thermal shield plant. Also included is a schematic of the primary reactor coolant system. 'The broken external loop, containing a cold leg rupture, is shown in Figure 2.3-1. The equivalent piping for the unbroken external loop is given in Figure 2.3-2. 2-2
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The downcomer annulus region in the reactor pressure vessel consists of two concentric annuli in the region of the themal shield, and one annulus above and below the shield. For a two-loop plant a vertical plane of syninetry can be drawn, containing the axis of the broken loop's inlet nozzle and the reactor vessel's : vertical axis. Therefore, only one half of the downcomer annulus is modelled, and the volume in this region is adjusted to represent the entire downcomer volume. Figure 2.3-4 shows the EPN representation of the reactor vessel internals region. The fluid volume within the core barrel is described by a series of flowpaths. 2.4 THRUST CODE Utilizing MULTIFLEX-conputed fluid pressures, mass velocities, and densities, together with geometric plant layout information (relative elevations, anoles, etc.), the THRUST program detemines the time-dependent loads exerted by the fluid on the coolant loop piping. Figure 2.4-1 illustrates the standard locations of the force nodes, and the nodal numbering system used in the THRUST calculation. The force nodes are located in the loop piping where' there is a change in either flow area or flow direction. Note that Reference ** provides a description of the STHRUST computer program. The two codes, THRUST and STHRUST, compute loop blowdown forces in an identical manner, the only differences being that THRUST is used in conjunction with MULTIFLEX, while STHRUST is employed with the SATAN computer code ** .. The MULTIFLEX-THRUST calculation is the current Westinghouse licea:;ing design tool, and was therefore utilized in the Prairie Island and Kewaunee analyses.
, In evaluating the RCL hydraulic forcing functions, the THRUST code represents the primary RCS with the same two loop model that is used in the MULTIFLEX blowdown calculation; i.e., with a broken and intact loop. A total of twenty-six nodes are selected along the two loop geometric piping model of the RCS (see Figure 2.4-1) for computation of resultant vector forces and their components in the global coordinate system. There may be one or two blowdown control volumes associated with each force node, depending on the location of the force node in the system.
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WNERE M 15 THE MUWBER OF THE NODAL PolNT SHOWN A50VE h Figure 2.4-1: RCL Model Showing Hydraulic Force Locations l I 2-9 l-
{ for force nodes 2, 3, 6, 7,_11,12,15,16,19, 20, 24, and 25, a single aperture (flow area) is assigned. For force nodes, 1, 4, 5, 8, 9, 10, 13, 14, 17, 18, 21, 22, 23, and 26, two' apertures are assigned. The blowdown force at each aperture ; is calculated by the following equation: , F = [(P - Pa ) + o 144] *A (144) where: F = force (1bf) P = system pressure (psia) P, = external pressure (psia) 2 l G = massvelocity(ibgft-sec) 2 p = fluid density (1bgft ) g c
= gravitational constant (32.17 ft-lb/lbf-sec2 )
A = aperture area (ft2 ) The force components determined at each aperture were vectorally sunned to obtain the total force at the node. This total force was in turned resolved into three components (x, y, and z) in the global coordinate system. After proper coordinate transformation, these forces were applied to the reactor coolant loop dynamic structural models as , external loadings, as described in Section 4 i r 2.5 LATFORC CODE Utilizing MULTIFLEX-computed fluid pressures, together with geometric reactor pressure vessel information (component radii and axial lengths), the LATFORC e d 9 P 2-10
L program determines the horizontal forces on the vessel wall, core barrel, , and thermal shield (if applicable). The LATFORC code represents the , vessel region with a model t' is consistent with the model used in the MULTIFLEX blowdown calculat 'n . The downcomer annulus is subdivided into cylindrical segments, formed by Jividing this region into circumferential and axial zones. Figure 2.5-1 illustrates the distribution of the horizontal force coi.., .sunts acting on the vessel wall and core barrel. This figure corresponds to an earlier MULTIFLEX calculation. In the current design model, the barrel is represented by a ten mass points beam structure model; thus, there are ten horizontal force components. Also, if applicable, there are four horizontal force components acting on the thermal shield. Note that in the adapted choice, the X-axis coincides with the axis of the broken loop's RPV inlet nozzle, and the positive direction is directed away from this nozzle, , Figure 2.5-2 shows the calculation of the horizontal force on a cylindrical segment. The X-component of the hydraulic force acting on a segment, i, equals the X-projected segment area times the mean fluid pressure acting over the segment: ,
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, o Since these hydraulic forces are being projected onto the X and Y axes, they may be algebraically added. Therefore, at each corresponding axial elevation,[, the X-component' hydraulic forces are added to give a resultant X-direction load, and likewise, the Y-component forces are sumraed to field a resultant Y-direction load. As noted earlier, in the current design model, resultant X- and Y-component hydraulic forces are 4 computed at ten different elevations on the vessel wall and core barrel.
The total hydraulic force on the reactor vessel wall is equal to the instantaneous fluid pressures in the downcomer annulus integrated over the entire wetted surface of the vessel wall: p vessel wall dA total Af 10 E IE fi j) total "1-1 J 10 F{otal1-1 E j (IFj) 4 The inrsr term in the double summation denotes the icece subtotal form-ing part of all circumferential segments located at elevatioa h These subtotals are also recorded on magnetic tape to provide a detailed distr h. tion of the horizontal force c s ponent3 along the reactor vessel height, as required for the structural analysis, if "a" denotes the ratio of the core barrel outer surface ciameter to the reactor vessel's inner surface diameter, then the horizontal force acting on the core support barrel in the positive X and Y direction,- at elevationK,'becomesasfollows: F barrel,i - -aj E F* 3, barrel,i - -a4 IF{,3 F 2 ,
-o. . The above relationships are only valid at the axial elevations where the same pressure can be utilized for both the vessel and core barrel force calculation; for instance, these equations do not apply in the region of the thermal shield. Note that whenever a reactor vessel inlet or outlet nozzle coincides (totally or pertially) with the projected segment area, the nozzle flow . area times the local pressure is subtracted from the integrated force: (F9,3) corrected - Fg,3 - Pgg,,j,Anozzle cosd j The results obtained from the MULTIFLEX/LATFORC analysis of the herizon-tal forces are stored on magnetic tape, usually for the initial 500 msec of the accident transient. These forcing functions are part of the required input for the structural analysis to determine the resultant mechanical loads on the primary equipment and loop supports, vessel internals, and fuel grids. 2.6 FORCE-2 Code . The FORCE-2 program calculates the hydraulic forces which the fluid exerts on the vessel internals in the vertical direction, by utilizing a detailed geometric description of the vessel components and the tran-sient pressures, mass velocities, and densities computed by the MULTI-FLEX code. The analytical basis for the derivation of the mathematical equations employed in the FORCE-2 code is the Conservation of Linear Momentum (one-dimensional). Note that the computed vertical forces do not include body forces on the vessel internals, such as deadweight and buoyancy. As part of developing the FORCE-2 input data and model, each reactor vessel component for which force calculations are required is designated as an element, and assigned a specific element number. If in the MULTI-FLEX code's hydraulic model, the flow region associated with an glement in FORCE-2 is divided into more than one flow path, then the element in FORCE-2 is subdivided into a corresponding number of divisions and assigned a division number. 2-15
When evaluating the vertical forces on the RPV internals, the following types of transient forces are considered - 4
- a. Pressure differential acting across the element:
F p
-AP*A eff where AP is the computed pressure difference across the element, snd A is the effective area of the element upon which the above ff pressure differential acts. ,
- b. Flow stagnation on, and unrecoverable orifice losses across the element:
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where C is a coefficient which accounts for flow stagnation, I unrecoverable orifice losses, etc., u is the local fluid velocity through the orifice, flow passage, etc. associated witn tnat specific element, and 3 o is the corresponding fluid density.
- c. Friction losses along the element:
cA shear p f,], 89c 2-16
where A shear is the total surface area of the element along which the shear forces act, and fu2is the average product of the friction factor and the square of the local fluid velocity alongside the. element. The above three types of forces are summed together, depending upon what types of forces are significant, to give the total force on each elemen t. For instance, where friction can be considered negligib't (e.g., across core plates and fuel assembly grids) the total fore would only consider F p and F3 ; where friction is important (e.g., al(.ig thermal shield and fuel rods) the total force,would consider Fp and F. f Individual forces on elements are further combined, depending upon what particular vessel component is being considered, to yield the resultant vertical force on that component. In the current design model, vertical hydraulic forces are determined at sixteen standard locations within the vessel region:
- 1. Friction forcs on thermal shield
- 2. Pressure force on top surface of thermal shield
- 3. Pressure force on bottom surface of thermal shield
- 4. Friction force on core barrel
- 5. Pressure force on top surface of core barrel flange
- 6. Pressure force on bottom edge of core barrel
- 7. Pressure force on bottom surface of' core barrel flange
- 8. Force on lower support plate
- 9. Force on lower core plate
'2-17
- 10. Force on lower end plate of fuel assembly; i.
- 11. Force os. fuel grids and thimbles f
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- 12. Forcelon upper end plate of fuel assembly 1
- 13. Force on fuel rod
- 14. Force on upper core plate i 15. Force on upper support plate I 16. Force on reactor vessel shell 1
- As before, the results obtained from the MULTIFLEX/FCRCE-2 analysis of
! the vertical forces are stored on magnetic tape, usually for the initial 500 msec of the transient. These forcing functions serve as input for the structural evaluation of the primary equipment and loop supports, vessel internals, and fuel grids. I i i r 9 4 2 >
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SECTION 3 3.1 REACTOR CAVITY PRESSURIZATION LOADS Reactor cavity forces arise from the steam and water which are released into the reactor cavity through the annulus around the broken pipe. These forces occur only for postulated breaks at the RPV nozzle safe end locations. The reactor cavity is pressurized asymmetrically, with higher pressure on the side adjacent to the break. The horizontal differences in pressure across the reactor cavity result in horizontal forces on the reactor vessel. Vertical forces on the reactor vessel arise from similar variations in pressure on the upper and lower head and the tapered parts of the reactor vessel. Reactor cavity loads were calculated for a 150 square inch guillotine break openina at the cold leg nozzle safe end. The reactor cavity loads applied to the reactor vessel model are shown in Figures 3.2-7, 3.2-8, and 3.2-9. The vertical, horizontal, and moment loads applied at the intersection of the vessel vertical and broken nozzle centerline are in the coordinate system shown in Ficure 3.2-10. Reactor vessel and reactor coolant system analyses for the assuned 150 square inch break size resulted in an actual break size much less than 150 square inches. Consequently, the reactor cavity pressure analysis was redona for a 115 square inch break area to obtain more realistic pressures for the biological shield wall evaluation (not included in this report). 3 . 2' METHOD OF DETERMINING THE REACTOR CAVITY LOADS The TMD computer codh with an unaugmented homogeneous critical flow correlation and
'the isentropic compressible subsonic flow correlation was used to calculate pressure transients in the reactor cavity region.
3-1
O O Modelling techn'iques used to define the reactor cavity are censistent with current analysis methods. Nodalization sensitivity studies were performed before the analysis was begun. All changes in area in the immediate vic nity of the broken loop nozzle
, were modelled. Consequently, any further nodalization in this region may introduce fictitious boundaries between elements.
All insulation was assumed in place and uncrushed durina the entire transient exceat l for the insulation on the broken loop nozzle. This insulation was assumed to crush to zero thickness. This assumption maximizes the flow area toward the reactor vessel and is therefore conservative. The inspection plugs are in place during the entire transient. The loss coefficient (k) values were determined by changes in flow area and by turns the flow makes in traveling from the centroid of the upstream node to the centroid of the downstream node. Tne k and f factors for each path were determined using methods from FLOW OF FLUIDS THROUGH VALVES, FITTINGS AND PIPES _ by the Crane Company and CHEMICAL ENGINEERING by J. M. Coulson and J. F. Richardson. Tables 3.1 and 3.2 provide the volumes and flow path data for the elements and their connections. *** ] [ presented in Table 3.3.
*** The mass and energy release rates for the break are The data for converting Dressures into forces is presented in Table 3.4.
Figures 3.2-1, 3.2-2, and 3.2-3, illustrate the general configuration of the reactor vessel annulus nodalization. Figure 3.2-4 shows the flow path connections for the
- 78. element model. In the model, the lower containment is divided into two loop compartments (46, 47). The upper containment is represented by compartment 38. The break occurs in element 40, immediately surrounding the nozzle. The corresponding broken loop pipe annulus is represented by elements 48 and 49. The lower reactor cavity is modeled by element 39 and the majority of the remainder of the elements.
as shown in Figure 3.2-1 model the reactor vessal-. annulus. Compartments 2 and 3
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Table 3.5 shows the peak pressures and time of peak pressures for all the elements for'the 115 square inch break case. This table also conservatively estimates the peak differential pressures acting across the primary shield wall. This table
- demonstrates that the pressure gradient is steep near the break location and is '
very gradual farther away from the break. This indicates that the model must be very detailed close to the break location, but that less detail is required with increasing distance. Figures 3.2-5, and 3.2-6 present the pressure time-histories for the break element (#40) and the reactor vessel annulus element (#1) that experiences the largest pressure following break.
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. 1 4
1 i i ! j '! i ! i j t r Figure 1 i 3.2-9: Oyerturning Moment Cavity Presgure load On
. Reactor Vessel' for RVIN 150 IN Break (MZ) i-3-37..
W ' -, . + t
13844 Y Generator l i Crossover Leg Hot Leg i LOOPB ; Reactor Y Coolant Pump
+ Upward *"% Cold Leg -
- X Cold Leg g
% \_
/" Reactor
\ Coolant
\ Pump ,
i
'I 2 '
LOOP A
?
Hot Leg Crossover Leg XY Z Coordinate system for break postulated to occur in cold leg Steam I Generator FIGURE 3.2-10: COORDINATE SYSTEM FOR POSTULATED f PIPE RUPTURES 3-38
SECTION 4 4.1 REACTOR PRESSURE VESSEL The reactor vessel motion for postulated breaks at the vessel nozzles was determined
~
with a non-linear dynamic model of the reactor vessel and internals. A finite element representation usino the WECAN computer code is used to solve the transient response for postulated LOCA excitations. The model schematic is shown in Figure 4.1-1 to 4.1-3. The model is three-dimensional representing the six geometric degrees of freedom. Elements inrut to the model include beams, pipes,
- spring-gap (concentric and linear), lumped mass, mass matrices, and stiffness l
matrices. The model is best described as three sub-models: 3 concentric structural models connected by spring-gap elements and mass and stiffness matrices. Ficure 4.1-2 depicts the pipe representation of the core barrel which concentrically surrounds the internals Figure 4.1-3 and is concentrically enclosed by the. vessel shell model Figure 4.1-1. The elemental properties.of the pipe seaments are consistent with the actual physical properties of the core barrel, and lumped masses are included for miscellaneous variations from the -ideal pipe such as the core barrel flange. 4-1
. _ _ = .- . . =_. -. . . - . -. ~ .
I' 4 4 15867 3 i i, 1 i F k 1 l 4 J 1
?
2 ; i i t l [ t d t + i ' - FIGURE 4.1-1: RPV SHELL SUBMODEL Y ! 4-2 i.
- - , ..w- -
r.w.- - -er ,-+% - e -rwm , --v. w t-s+-
. .. s 15867 2 i
i- ). 1 - i [ I i P t i: i I - i, i :
+
i 4 n-1 4' I 4 .i 1 i N s i I
~ FIGO,- 4.'l -2 : CORE BARREL SUBMODEL-
'4-3 e
15867 1 FIGURE 4.1-3: INTERNALS SURMODEL 4-4
The outermost portion of the structural model, shown in Fiaure 4.1-1, depicts the vessel shell and vessel support mechanism. Pipe elements model the vessel shell with lumped inertias' for the effect of the reactor vessel flange, and the upper ! and lower domes. The stiffness of the vessel support mechanism and shield wall restraints (shoe, box, and concrete) is included by vertical spring-gap elements and linear horizontal springs. Thus, the potential for vertical lift-off of the supports and the geometrical configuration of the reactor vessel support mechanism is included in a three-dimensional manner. A stiffness matrix was developed from detailed models of the remainder of the primary coolant system for each of the plants and included between Node 3 and ground. These three concentric sub-models are coupled together by stiffness matrices and spring-gap elements at structural interface locations. . O i i e 1 4 m f 4 4-5
?
The reactor vessel models were analyzed for the effect of LOCA at the reactor inlet nozzle. LOCA excitation results from the releas'e of the pressurized primary system's coolant and from the disturbance of the mechanical equilibrium in the piping which is present prior to the rupture. The release of coolant leads to depressurization waves traveling internal to the primary coolant system and, for ruptures postulated at the RPV safe ends, pressurization occurs rapidly in the cavity surroundina the vessel as described in a separate section. Thus, the loads induced on the RPV and internals for LOCA may be characterized as: (1) reactor coolant loop mechanical loads (for ; i guillotine ruptures), (2) reactor internals hydraulic loads and (3) RPV cavity ; pressurization loads. These loads were summed in a time-history manner, applied to ' the reactor structural model described above, and a non-linear, transient dynamic analysis performed. Resultant vessel motions were used to determine loads on reactor vessel supports, and to provide input motion to loop and component support evaluations (see Section 5.3). o e e 4 4-6
~
f r
SECTION 5 5.1 POSTULATED BREAKS
^
The breaks considered for the reactor coolant system analysis were limited area, guillotine ruptures at the reactor vessel inlet, reactor vessel outlet, and reactor coolant pump discharge nozzles. The reactor vessel nozzle breaks were assumed to be limited to 150 square inches area by pipe restraints to be installed in the plants. The pump discharge break area has previously been calculated to be less than 150 square inches in analyses performed and summarized in Reference *. .; Once the vessel nozzle pipe rupture analyses werr completed, the actual break areas were calculated and shown to be lower t'in the assumed break areas. A break opening time of 10 milliseconds was used in the development of the hydraulic , forcing functions. ' 5.2 SYSTEM LOADINGS 5.2.1 STEADY STATE LOADS Weight To determine the. loading due to system deadweight, a 1.0G load downward is applied to the piping system. The piping was assigned a distributed mass or weight as a
- function of its properties. This method provides a distributed loading as a ,
function of both the weight of the pipe and the contained fluid. The dry weight of the primary equipnent components, which is a deadweight leading on the respective supports, does not consistute a load on the coolant piping since' the primary equipment components are set on their_ respective supports prior to installation and welding of the connecting piping. y 5-1 e a i
Thermal The free vertical growth of the reactor vessel nozzle centerline during heat-up is considered in the thermal analysis to account for the equipment nozzle displacement as an external movement to the piping. The growth was assumed to be 0.15 inches based on previous analyses performed for current day plants. The modulus of elasticity (E), the' coefficient of thermal expansion at the operating metal temperature (a), the external movements transmitted to the piping as described above, and the temperature increase above ambient (AT), define the re_ quired input data to perform the flexibility analysis for thennal expansion. Pressure and Momentum The s .ady-state hydrauMc forces which result from normal operating internal pressure and flow romentum conditions are treated as externally applied loads to the system model. The loads applied are the initial forces (prior to the break) calculated by the Multiflex/ Thrust analysis described in Section 2. 5.2.2 TRANSIENT LOADS Loss-of-coolant-blowdown loads are developed in the reactor vessel, broken and unbroken loops as a result of transient flow and pressure fluctuations following a postulated pipe break in one of the reactor coolant loops. These time-varying externally applied forces were calculated by the MULTIFLEX/ THRUST hydraulic analysis described in detail in Section 2. External cavity pressure loads are developed around the reactor vessel; the detailed analysis of the cavity pressure is described in Section 3.
- 5. 3 ' ANALYTICAL METHODS AND MODELS 5.3.1 RCL PIPING AND EQUIPMENT This section describes the development of the structural analytical model required to represent the mass and stiffnessLof the reactor coolant system for the_ dynamic' loss-of-coolant accident' event, and the analytical methods employed to generate the system response due to the applied loads.
5-2
. , Tc
An integrated reactor coolant loop / support system model is the basic system model , used to compute loadings, displacements, and stresses on components, component supports and piping. This lumped parameter system model includes the stiffness and mass contributions of the reactor coolant loop piping, steam generator, and coolant pump and the stiffness of supports which constrain the system. It is used to obtain both the steady state and dynamic response of the entire reactor coolant system and, subsequently, the internal member forces and piping stresses. Detailed models of the primary equipment supports were developed separately, Section 5.3.2, and either linear, or piecewise linear (with gaps) representations . of their stiffness characteristics were incorporated in the system model. Although the reactor vessel is not modelled with the loop, its effect upon the loop is included by extending the hot and cold legs to the RPV centerline with weightless rigid links such that RPV centerline displacements can be imposed on L the loop. r The reactor coolant loop piping and primary equipment models were developed for ; analysis on the approved Westinghouse piping analysis computer program, HEST 0YN * . ; The systera layout geometry was defined in three dimensional space by locating ' discrete node points along neutral axes of th'e components. Appropriate cros~s-sectional properties then described the interconnecting stiffness properties of the elements. The elements consist of three-dimensional elastic pipes and elbows. Structural system models of the steam generator and reactor coolant pump were developed from detailed multimass component models employed by the Westinghouse manufacturing divisions. The various equipment and piping supports were represented by stiffness matrices and springs with gaps to define the restraint characteristics of the supports. Figure 5.3-1 shows an isometric line diagram-of a typical mathematical model used for RCL' LOCA analysis. The mass of the piping was discretely lumped as shown in Figure 5.3-1. The effect of the equipment motion on the reactor coolant loop and supports was obtained by similarly including the mass and stiffness characteristics of the equipment in the system model. 5-3
Steam Generator l M v S.G. Upper m Support Reactor . Vessel L / Reactor v d Leg [ hj Coolant Pum M Hot A le9
.G. Lower Support o
( Crossover Leg Figure 5.3-1: Reactor Coolant System Model. O
l' The steam generator was represented by four discrete masses as shown in Figure 5.3-1. The lower nass is located at the intersection of the centerlines of the inlet and outlet nozzles. The second mass is located at the upper support elevation. The third mass is located at the midpoint of the upper shell. The fourth mass is at the top of the S.G. This four-mass model was obtained from " the reduction of a more detailed multimass model of the steam generator by preserving the following properties: The total mass: EMj=MT The first moment of mass center of gravity IMXj$-MX T The second moment of mass about a given axis (radius of gyration) IMXjj 2 2
=,1 J=
M)Xj M 9
= Individual lumped masses ,
M = Total component mass T X =M 9 Distances from the reference point
$3 X =M Distance from the reference point T
The reactor coolant pump was represented by two discrete masses as shown in Figure 5.3-1. The lower mass is located at the intersection of the centerlines of the pump suction and discharge nozzles. The top mass is located at the center of gravity of the motor. 5-5
Static analyses were performed to obtain the initial steady state condition of the system for the ~ LOCA event. The resulting loads, described in Section 5.2, consist of the plant normal steady state hydraulic forces, the piping and coolant weight, and the effects of thermal expansion. The reactor pressure vessel was represented as a fixed boundary in the static system analyses due to its large relative mass and support stiffness characteristics,- and layout symmetry considerations. The reactor vessel vertical thennal growth was also applied to the model at the vessel
~
centerline in establishing the initial deflected state. The steam generator and pump upper and lower lateral supports are designed to be inactive during plant heatup, cooldown, and normal plant operating conditions to prevent binding due to thermal expansion. However, these restraints become active during the rapid motions of the reactor coolant loop components that occur from the dynamic loadings of LOCA. They were thus excluded from the static models, and included as stiffness matrices or piecewise linear springs with gaps in the dynamic models. The static solutions for deadweight, thermal, and generai pressure loading conditions
- WESTDYN is the production are obtained by using the WESTDYN computer program .
code used by Westinghouse in all current piping analyses. The entire dynamic problem is solved by the application of three computer codes; WESTDYN, FIXFM, and WESDYN2 * . A flow diagram representing the algorithm for the solution to the time-history analysis is shown in Figure 5.3-2. Natural frequencies and normal modes are determined by the WESTDYN computer program by using models which were previously described modified to include mass and to represent the structural discontinuity at the postulated rupture location. The component lateral supports having non-linear characteristics were represented by single acting compression springs in the dynamic analysis. 5-6
e e' t e REACTOR COOLANT EQU I PMEN T LOCA FORCING SUPPORT FUNCTIONS LOOP STRUCTilRE 1r if f SUPPORT STRUCTURE 0 00lL SilFFMESS MATRICES FOR STATIC AND OYNAMIC BEHAVIOR if DEFINE INITIAL FORCES AND MOMENTS If 0F THE SYSTEM 1r 1f N ATURAL FREQUENCIES ' AND NORMAL MODES I DYNAMIC DISPLACEMENT RESPONSE AT MASS P0lNTS
- ~
if , COMPUTE TIME-HISTORY SUPPORT - ' LO ADS MEMBER FORCES STRESSES AND DISPLACEMENTS II 1f i f l PIPING STRESS EVALUATION l l SUPPORT MEMBER EVALUATION l Figure 5.3-2: Time History Dynamic Solution for DBA Loading 5-7
The time-history solution was performed using program FIXFM * . The input to this program consists of the following: (1) the natural frequencies and normal modes determined by WESTDYN for the broken loop model (2) the non-linear support elements (3) the time varying internal hydraulic forces (Section 5.2.2) (4) the internal energy release forces in the system at the postulated break location due to'the steady state hydraulic forces, thermal forces and weight forces calculated by the static analysis (Section 5.2.1) (5) the time-history reactor vessel displacements (Section 4) The postulated break is assumed to occur at steady-state normal operating conditions. The energy released by the pipe severance is accounted for by negatively applying the steady-state forces at the break as a step function loading. Four percent of critical damping is employed in the system for the time-history solution, and is based upon prior testing of similar components and supporting mechanisms. This has been approved for current production analyses, and is documented in Reference * . From the dynamic analyses, time-history displacements are generated for all dynamic degrees-of-freedom by FIXFM. The time-history displacement response is that used as a boundary condition to compute support loads. The displacements are additionally used as inpur to WESDYN2 to determine the internal member deflections and forces at each of the pipi.ng elements. 5.3.2 RCL SUP.0RTS This section discusses in detail the steam generator and pump supports and the manner in which they were modelled for ' stiffness calculations and stress evaluations. 5-8
. o The reactor vessel is supported on six vertical H-columns embedded in the biological shield concrete. An air-cooled support box is fastened at the top of each column to provide a suitable temperature gradient between the hot reactor vessel nozzle and the biological shield concrete. Machined support faces on the bottom of each reactor vessel nozzle and support lug rest on shoes bolted to the air cooled support boxes. This support arrangement allows radial thermal expansion of the reactor vessel, but restrains lateral motion. A bracing system embedded in concrete is used to provide lateral restraint to the support boxes. Figure 5.3-3 illustrates this support. Each individual support was modelled as a single acting vertical spring, and a double - acting horizontal spring. The lower supports for the steam generator, shown in Figure 5.3-4, consist of: (1) four vertical pin-ended columns t,olted to the bottom of the steam generator support pads; and (2) lateral support girders and pedestals that bear against horizontal bumper blocks bolted to the side of the generator support pads. The model for the columns is shown in Figure 5.3-5. The lateral supports were modelled as single acting springs. The upper lateral steam generator support consists of a ring girder around the generator shell connected to four hydraulic snubbers on the reactor vessel side and supported by struts on other sides. Loads are transferred from the equipment to the ring girder by means of a number of bumper blocks between the girder and generator shell. The plane-frame model of this structure is shown in Figure 5.3-6. The reactor coolant pump supports, shown in Figure 5.3-7, consist of three pin-ended structural steel columns and three lateral tie bars. A large diameter bolt connects each column and tie rod to a pump support pad. The ou er ends ' of two tie rods have slotted pin holes such that one receives only tension load and the other receives only compression load. The third tie rod receives both . tension and compression. The tie rods were modelled as single or double acting springs as appropriate. The pump columns were similarly incl"td in the reactor coolant loop model as individual spring elements having dif & rent tension and compression stiffness. 5-9
.. s The static and dynamic structural analyses assume both linear and non-linear behavior for the support members. The complexity of the support systems to be analyzed requires the use of a separate computer model and program for obtaining stiffness matrices to be used in the RCL system model. This is accomplished on the program STRUDL **.
Mathematical models were developed for the steam generator columns and upper supports. The models are dual-purpose because they are used (1) to represent quantitatively (in terms of stiffness matrices) the elastic restraints which.the supports impose upon the reactor coolant system, and (2) to evaluate the individual support member stresses due to the forces imposed upon the supports by the reactor coolant system. Stiffness analyses of the model were performed by applying unit displacements and rotations along each coordinate axis of the model at the equipment vertical centerline and support intersection. Results of the analyses include loads at the joint at which the displacements are applied (which were used to form the stiffness matrices) and six force components at the ends of each member in the structure. The member forces, known as influence coefficients, were later used to evaluate the support structure from the actual displacement response of the system. The specific support structures were represented as three-dimensional frame-type models using beam elements. Structure geometry, joint connectivity, and member properties were obtained from the support structural drawings for the plant. Appropriate joint and member releases were included to accurately represent the directional behavior of the support system. Rigid links extending from a point on the equipment vertical axis to points where the loads transfer from the equipment to the support were included in the model. The outer ends of these spoke members were appropriately released to depict actual load transfer. The following member and joint notations are used for the support structure model figures presented in this section:
- Numbers in circles define support structure members, e.g. , @ is member 12 '
- Numbers of each end of nembers are joint labels, e.g.,12 is joint node 12
- Directions of global co)rdinate axes are as indicated.
5-10 ,
CONTINUOUS STEEL BAND t RING EMBEDDED IN TE y _ PLATE
' 'N .
7 l- , y ) MS .. , . L---{ x f g" ,___ _ _________
\ , m m -- - - - . m ,. w h 4! J 3 ! E~._'2! '_~.'_~_'_'_1 _ ?
s
~s' A 'l l #,l
~. , \ \
l '- l '- l , j ll SHIELD CONCRETE
, 3 ' I$ ll , f
.e .
K ., A !A i- - N ( l TAINLESS STEEL REACTOR CAVITY l LINER PLATE . STRUCTURAL TEE xl < -rf VENTILATED SUPPORT HORIZONTAL TIE BRACING PADS (AIR SUPPLY AND WELDED TO BAND RING i DISCHARGE DUCT SYSTEM I NOT SHOWN) COLUMN CAP PLATE -{- AND BRACING GUSSET 8 N
^ fTi !T*
\ -* - , , T- mu~ ---
% /
N - e.
$$55$55?$$$e.
=
L m/ ,.....
.,e i ,. .
EMBEDDED STRUCTURAL J \ 'l */*
- STEEL COLUMh! \l /
CONCRETE EMBEDMENT - y t/
/(NOT SHOWN) f v
l U I EMBEDDED COLUMN BASE PLATE AND
- ANCHOR BOLTS m
D**D 3 eo o 2 N l Figure 5.3-3: Reactor Vessel Supports l S-11 1 \ ~. . - _ . . . . .. l I l
, 'e
-]
s ) 1 CABLE RESTRAINTS 1 1 i N
<H STEAM GENERATOR j
COMPARTMENT
,f
.',\ f
/
l::.
/ -
i HYDRAULIC SUPPRESSORS UPPER l.ATERAL RING SUPPORT GIRDER
.-,;xgk .
.....:: w .
SUMPER BLOCK d SUMPER PEDESTAL
/ . .
y"r Par (. i i STRUCTURAL LOWER LATERAL i / STEEL COLUMNS SUPPORTGlRDER l l i l , l l
! dl '
, & q >
4 'm o m. g - oo o 3 . _a FIGURE 5.3-41 STEAM GENERATOR SUPPORTS 5-12
HOT LEG c. 5/ h \
/ 6
/ \
I 5 6 \
)
Z<!
\ 8 I g 7 /
/
8\ / PLAN N N % ,/ 7 Yg i YA i B 8
>X !
8 D6 i n a n I d) C0 ELEVATION ug Wi 3g g2 Flct'RE 5.3-5: STEAM GENERATOR VERTICAL SUPPORT MODEL 5-13 W
- O
_ _ _ _ __ m . ___ __ _
.o .* ,
e { NOT LE6 n is 27 as.9 2s F
; L d L 28 29 26 27 j 22 to '
32 Ui' 23 t Ta ts N I 59 57 , 36 55 60 56 es 3 3
. gg M
" 35 54 ,, l
,y 53 39 g ,)
-- D*
- I ff >
a er 5e 3,
,6 5, ..
5 3, , s2 si (a ,, So gg 43 47 45 y g 46 8 n s2 en
~ ~en 12 10 9 .
la 1 s 33 1 r r 13 k i3I o Z FIGURE 5.3 6: STEAM GENERATOR UPPER LATERAL SUPPORT MODEL - 5-14 i
GO - jv;
$h ,
@uCt J 3 I
ve nn ne san O 0
-J,{d,y
,/
wan sten FIGURE 5.3-7: REACTOR COOLANT PUMP SUPPORTS 5-15
Three pipe. thrust blocks attached to the internal concrete structure are included in the RCL support system. These are located on the crossover leg pipe; one at each end of the horizontal run and the third on the steam generator side vertical run. These supports were considered as a single acting linear springs having stiffness values computed for a steel structure supported by the concrete. Hot leg and cold leg primary shield wall restraints were also incorporated in the reactor coolant model. A load deflection curved for the horizontal cold leg restraint was developed with the aid of an elastic-plastic finite element model of the reactor coolant pipe and restraint. This model was constructed using the WECAN ** computer Droaram. The remainion two blocks of the cold lea restraint and the hot leg restraint were modelled as single acting linear springs (the loads on these restraint portions are much smaller than the cold leg horizontal load and do not result in significant pipe plasticity. The hot gaos between the pipe and the restraints v.ere included in the model. 5.4 EVALUATION CRITERIA 5.4.1 PIPING The basic system criteria for postulated LOCA loadings is to ensure that the severity of the accident will not be increased in order that the system can be brouaht to a safe shutdown condition. portions of the reactor coolant loopp must retain their physical integrity so attached safety systems are allowed to perform their functions. The general criteria to be applied is that the rupture of a reactor coolant pipe shall not violate the integrity of the unbroken legs of the broken loop and the unbroken loop. Gross rup'ture of the piping system is prevented by satisfying general and local membrane stress criteria. This is accomplished by limiting the primary stress intensity resulting from design pressure, weight, and applied LOCA loads to a value of H* [ 5-16
I i
*** 5 i
W P t 5.4.2 SUPPORTS The function of the primary equipment supports for a postulated LOCA is to maintain the supported piping and equipment within acceptable stress limits. This was evaluated by generally requiring support stress to not exceed the member yield stress. In particular,~the following criteria were observed. 5-17
(1) For single acting members, axial loads were limited to the yield load for tension, and ninety percent of the critical buckling load for compression. Average shear stresses were maintained below Fy/G, where Fy is the yield stress. (2) Stresses in bolts and pins were limited to yield for tension and compression, and Fy//T for shear. (3) For frame-type structural members which received combined axial, bending, shear, and torsion loads, Subsection NF and Appendix F [3] rules for linear-type supports were followed, except that member ;ompressive loads were limited to ninety percent of the critical buckling load. Subsection
'iF references Appendix XVII for linear type support design stress equations, while Appendix F specifies a stress increase factor that is applied to the allowable stresses in the design equations.
This critieria meets or exceeds the FSAR criteria, which states that the permanent deflection of the supports must be limited to maintain the supported equipment within its faulted condition stress limits. Where su;:: ort elements were considered as sir.gle acting members in the system analyses, the peak member loads occurring throughout the LOCA transient were obtair.ed from the analysis (WEST 0YN-FIXFM computer code results) and were compared directly with the member allowable loads. This situation is typical for reactor coolant pump tie rods, pipe restraints, and equipment latera' restraint bumpers. The steam generator columns and steam generator upper support structure were evaluated using the computer program WESAN ++ . Input for the WESAN program includes time-history LOCA loads or displacements acting on the support structure obtained from the RCL analysis, support structure member properties, and force influence coefficients at each end of each member (determined from the support stiffness analysis). l 5-18
8 L The following Appendix XVII aress, interaction, and dimensional ratio equations with the Appendix F stress increase factors were solved for each member by the WESAN program ** . ;
# Combined bending and compression load interaction equation f
UmIb UI
# + m b*
g . g . L1 f* +
, F (Fac) I b (Fac) 1-F Fy - Y b*
. *z, i
# Combined bending and tension stress equation i
I I f, + b y + b, i (Fac) (0.6) (Fy) (Fac I iib} y Ifac} ifb} z r
# Shear stress equation l
HCg r f = + < y a (0.40)(F).(Fac) y i I # Dimensional ratio equation : l t iA 1B where f = actual axial stress, P/A, where P is the axial load a on the member and A is the member cross-section area. . F = allowable compressive stress if member is subjected a to compression loads only. F is a function of the ; member slenderness ratio, effective buckling, and ; material properties. F a
= 0.9 [1 - (K3I)j ] F 2C Y c i for the faulted condition.
5-19
C, = coefficient defined in the code. , f b
= actual bending stress, M/S, where M is the bending
, moment at end of member and S is the member section modulus.
- p. , 12n2(Fac)(E) 23 (Ktb /rb)
E = modulus of elasticity. i K = effective length. , i l t = member length, t a r = radius of gyration. F = allowable bending stress if member is subjected to bending b alone. Fs is a function of cross-section dimensions and shape, member length 'and lateral . support conditions, and material properties. F = minimum member yield strength. y l . [ V = member shear force. l 5-20
A 3
= member cross-section shear area.
M = torsion moment in member. t C = effective distance to point of maximum stress. J = torsion constant. ! b ,t , = width and thickness of member cross-section dtg elements. A,8 = limiting ratios deperaing upon member cross-section configuration and material properties. In addition, member critical buckling (PCR) loads were calculated to be p , j, *(Kf/r)2 x FA CR Y 2C c 2 where 2 2n E ' C c F y Compressive axial member loads were compared with 0.9 times this value. 5-21
The Appendix F stress increase factor (Fac) is calculated as the lesser of: Y or 0.7p_ Su ; where t t Fy = material yield strength Su = material tensile strength Fi = allowable tensile stress The ASTM minimum tabulated yield and tensile strenaths were used in the reactor coolant system analyses. The pump column loads were obtained directly from the reactor coolant system analyses, and were substituted into this interaction equations for evaluations. In some instances, the pump tie rods were allowed to yield. The resultino load redistribution was accounted for in the coolant loop system analyses. B 9 4 1
. !5-22 m- __
( o . 5.4 EVALUATION RESULTS This section presents the results of the reactor coolant system, reactor vessel internals, and fuel evaluation for the reactor vessel inlet and outlet nozzle breaks. 5.4.1 Piping Table 5.4.1 shows the piping stress intensities in the broken and unbroken loops for the reactor vessel inlet and outlet break cases. The allowable stresses are also specified. ~ 5.4.2 Supports Table 5.4.2 presents the calculated percent of allowable stress for steam generator and reactor coolant pump supports. Results are given for all of the break cases considered. Table 5.4.3 shows the maximum horizontal and vertical reactor vessel support loads for the vessel nozzle breaks, and the corresponding allowable loads. The primary shield wall pipe restraint loads are defined in Table 5.4.4. The shield wall restraints will be evaluated by others. 5-23 .
m*b4 49 w 6 -Ah-e &.4,e s m 4 e 4 -&-h a h-4J44-+ 4 -.- & -M---. A-'- L
- 3-m% J 4.n I & K '
g e t
~
'I.. a f-I~ F. . i l . .ah f f i 5
, ' TABLE 5.4.1 !
j - . i RCL PIPING STRESS SUMARY FOR 150 IN} BREAKS ! 2 1 - - i, a i s f 6 3 4
}
6 1 & 3
. t i >
i,- .
- f. *** - .
-r 4
1 . p i
'f' 1
[ r
- -l*
1
}
i t
?
i s
! A s
t r 4 i 4 1 4 f 1 ! ,i k p t g-. d l l -I, f i t h
'..t f -- I i
- ~
.e t
e-5-24' : r -
.y J
w< f
,,. . c. . --.-. - -., , ., . ....,, .. . ....., ,..,- - - . . . - . - , . . -. . ._ _ . . -..--.... .- - . .. ..a- - -- .. . -.
j .i i TABLE 5,4.2 ; SG, RCP SUPPORT STRESS
SUMMARY
FOR RPV N0ZZLE 150 IN2 BREAKS !
. (Stresses Expressed As Percent of Allowable)
~
'l R e t i l i 2 I t 6'
- e 3
i : i l l l 5 , l
4 8 TABLE 5,4.3 RPVSUPPORTLOADSANDgTRESSESFOR RPV N0ZZLE 150 IN BREAKS 5-26
e } TABLE 5.4.4 PRIMARY SHIELD WALL PIPE R LOADS FOR RPV N0ZZLE 150INgSTRAINT BREAKS 4 5-27
. a REFERENCES
- 1) ***
i
- 2) " Ice Condenser Containment Pressure Transient Analysis Methods", 4 -v a ;
WCAP-8078 March 1973, (Non-Proprietary).
- 3) ASME Boiler and Pressure Vessel Code, Section III, Division I, Nuclear power Plant Components,1977.
- 4) A**
- 5) 4 **
- 6) A**
- 7) +**
- 8) MULTIFLEX, A Fortran-IV Computer Program for Analyzina Thermal-Hydraulic Structure System Dynamics, Takeuchi, K., et. al. , *** t WCAP-8709 (Non-Proprietary), September 1977.
- 9) <,a
- 10) +
- ar
- 11) e**
- 12) Richtmyer, R.D., and K. W. Morton, " Difference Methods for Initial-Value i Problems", Interscience Publishers, New York (1967).
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