ML12335A576
| ML12335A576 | |
| Person / Time | |
|---|---|
| Site: | Indian Point  |
| Issue date: | 12/22/2011 |
| From: | Combustion Engineering |
| To: | Atomic Safety and Licensing Board Panel |
| SECY RAS | |
| References | |
| RAS 21634, 50-247-LR, 50-286-LR, ASLBP 07-858-03-LR-BD01 | |
| Download: ML12335A576 (169) | |
Text
{{#Wiki_filter:United States Nuclear Regulatory Commission Official Hearing Exhibit 5,9% In the Matter of: Entergy Nuclear Operations, Inc. 6XEPLWWHG 'HFHPEHU (Indian Point Nuclear Generating Units 2 and 3) ASLBP #: 07-858-03-LR-BD01 Docket #: 05000247 l 05000286 Exhibit #: RIV00052B-00-BD01 Identified: 10/15/2012 Admitted: 10/15/2012 Withdrawn: Rejected: Stricken: Other: E-~~~~~___ BY'~~~LL CHECK DA E'--...:f...::Z.!.f:E:eL_I!IIY~A:: IPEC00069733
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6:;rF.l'l.-y'.;;;-.;r.Y /69.17;' I 15i<'.1Z- I ,-' J j ~ --yr1 Y1. R!!"AC'TtIR PUINT M.",..v r _~':I¥.,v§*7Ilf7i 1 ~>'S OF' /1,:-- ,)'- -~~;-CI'*I/..! )/ ,;;;;.el?, H Y/.-r!). '. y:;.;//? 3/25 r~;/'" /0(i19/.} .'*',i':£;lU.... 5 5 f1:i;nt.e -- It' ~ S..,., SHIN t2.~ t);:- ..If:A,;.JA 't!5 / - ;#fir N* 1/ Fe.!)/-) ;:;6. A!-41:J:I') f' \ 2:53,18 -3.24- >" Ilf.2b f'Oo 0.000?5 OF l}',c:-/ 111.60 -3.2"01- fa fuz !4N) &> (-;714-Ii? 7b -324 [IS 9$,5'0 ISOI) {/.o7tr;" /H".3(' 0 S 776.5> 33<10 !.."". t(/s t f!.24 0 ~ 4a.bZ SO; ao" tJ. ctJt!(J,? /1'1-.08 /.~tJ.l2. 1'0 '- 16.90 00 (7 IPEC00069868 "'U m A-367 () a a a(J) NOMENCLATIJRE <D ex> ~- Poisson's ratio - taken to be 0.3 (J) <D E - Elastic modulus (lbs/in 2 ) ~ - Coefficient of thermal expansion (in/in/oF) P - Pressure (lbs/in 2) W - Resultant axial force at any transverse c section (lbs) T Temperature (oF or as specified) V _ Axial component of unit edge force (lbs/in) H Radial component (perpendicular to unit edge force (lbs/in) M - Unit bending moment (in-lbs/in) .!l ( J - Components of deflection normal to the A-l:I.A.U:; radial deflection; (positive outward) where results from the action of redundant forces results from all other causes(in) ,l4 d" Components of rotation(positive if radial deflections of successive adjacent points t d the positive X direction are increasing) results from the action of redundant forces *
- results from all other causes (radians)
X m Axis of revolution RIV000052B R A radial distance measured normal to the revolution (in) t .. Shell thickness as mea,sured normal to the mim-surface (in) or = Normal stress; the subscripts x, and r te meridional, circumferential, and radial (or ateral) Submitted: December 22, 2011 stresses, respectively (lbs/in2)
- c= Strain - Elongation per unit length (in/in)
RIV000052B Submitted: December 22, 2011 IPEC00069870 RIV000052B Submitted: December 22, 2011 B-1 APPENDIX B
- THEfu"fAL ANALYSIS TABLE OF CONTENTS Page B.l.O INTRODUCTION .................................................................. B-2 B.2.0 NOMENCLATURE ............................................................................ B-2 B. 3. 0 GENERAL SOLUTIONS ********************************.* B- 3 B. 3.1 Transient and Steady :;tate - One. Two or Three Dimensional *** '............... ********* B-3 B.3.2 Transient - One Dimensional ................................. B-5 B.3.3 Transient - One Dimensional ................................ B-7 B.3.4 Transient - One Dimen sional ................................. B-8 B.3.5 , steady state - One Dimensional - Heat Generation **************************.******* B-10 B.3.6 Thermal Moment *********** "~""",, ********* B-12 B.3.7 Material Properties & Film Coefficients B-12 B.4.0 APPLICATION OF GENERAL MI--'"I'HOD.'3 OF SOLUTION AND RESULTS AT SPECIFIC LOCATIONS *********.***.******** 8-14 B.4.1 Head ,and Vessel Flanges..................... B-14 B.4.2 Inlet Nozzle................................ B-16 B.4.3 OUtlet Nozzle ******************* 0........... 8-17 B.4.4 Closure Head ................................. 8-19 B.4,.5 Vessel 'dall ........................ " .................................... . B-19 B.4.6 Bottom Head .................................................................. 8-19 B.4.7 Vessel Supports............................. B-20
- B. 5.0 B.
6.0 REFERENCES
DETAILED RESULTS ................................. '" .................. . B-21 8-22, IPEC00069871
RIV000052B Submitted: December 22, 2011 B-2 B.
1.0 INTRODUCTION
This appendix presents a summary of the thermal analysis of the Indian Point, Plant #2 Pressurized water Reactor Vessel. The assumptions made, method of analysis and results of the 1,n:'ot.,tlgations are presented. Temperature distrtbutions obtained from two-dimensional heat flow analyses .are pre-sented on cross sections of the components considered. R~su.lts of the one-dimensional heat flow analyses are pr**..-,ted in the form of graphs. The times f,Jr which dis-tI';1btitlons are presented were selected to present the
'tbtlil effects of the transients.
B.2.0 NbMENCLATURE a - Actual thickness of clad material, ft A' - Cross section area, ft2 b - Dimension, ft Cj - Thermal capacitance of node j, BTU/'F cp - Specific heat, BTU/lb-oF c - Actual thickness of base metal, ft d .- Equivalent thickness of clad material, ft E - Modulus of elasticity, psi g - Acceleration of gravity, ft/sec 2 h - Heat transfer coefficient, BTUjhr-ft 2 - O p k - Thermal conductivity, BTUjhr-ft-OF L - Length along a heat flow path, ft m - Slope of temperature vs time curve, OF/hI' NFo - Fourier modulus, dimensionless p - Slope of temperature vs time curve at x=o, QFjhr q - Rate of heat flow, BTU/hr qj - Heat generation of the node j, BTU/hI' qlll - Rate of heat generation per unit volume; BTU/hr-ft 3 qo "' - Rate of heat generation per unit volume at,the surface, BTU/hr-ft 3 I' - Dimension, ft R Thermal resistance, hr~oF/BTU T - Temperature, OF To - Uniform initial temperature, OF T1 -Temperature at x=b, OF t.T - Temperature difference, OF
,u - Slope of temperature vs time curve at x~b, °F/Hr V - Volume, ft 3 x' - Dimension, ft ex ., Thermal diffuslvity, ft2jhr ex' - Coefficient of thermal expansion, ft/ft-OF IPEC00069872
RIV000052B Submitted: December 22, 2011 B-3
- Linear absorption coefficient for heat gen ion, l/ft
- Emissivity for radiation, ft 2 /hr e - T-To, Temperature change, of IJ. - Absolute viscosity, lb/ft-hr v - Poisson's ratio, dimensionless x
= b ' distance ratio, dimensionless
- Density, Ib/ft 3
- Thermal stress, psi
- Time, hr
- Time difference, hr u-r b2 ' temperature ratio, dimensionless
- Natural convection property function, lIftS 0 B.3.0 GENERAL SOLUTIONS Various procedures were used to determine the the tion presented in this appendix. The following describe the techniques used and the conditions unde would be applicable.
B.3.I Transient and steady state temperature distri
- determined by use of a finite difference me grammed for solution on a digital computer.
A code has been written which makes use of heat balance equations derived by Hellman, general etler, and Babrov (1). Through the use of this code tem-perature distributions can be obtained in bo es having irregular geometries and composed of differen materials. The object being investigated is divided into of blocks or nodes. The thermal capaCitance node and the thermal resistance between nodes lated using the physical properties of the ma The thermal capacitance of node j is: The thermal resistance between homogeneous j and 1 is: IPEC00069873
RIV000052B Submitted: December 22, 2011 B-4 where jLl is the length of the heat flow path between nodes j and i, jAi is the area normal to jLi and Common to both nodes. k is the thermal conductivity of the material. Tne thermal resistance between non-homogeneous nodes J and 1 in series Is: The thermal resistance for a fIlm is: The equation for the change in temperature of a parti-cular node in the time 6~ is: 6T = 6T Cj [q(conducted) + q(generated)] The rate at which heat is conducted into the node is: q n Z 1=1 where i represents each bordering node and jRi is the thermal resistance between the i node and the node under consideration. Thus, the equation for the change in temperature of a particular node becomes: The temperature of each node is calcuJated at succes-sive time intervals through the use of the finite difference equation: IPEC00069874
RIV000052B Submitted: December 22, 2011 B-5 where ~T is obtained from the previous equati nand evaluated.at time ~. For a steady state problem, the term in brac ts must be equal to zero; hence, n L: ~ Tj + qj 1=1 j 1 n 1 L: i=l l i This expression is equivalent to performing a heat balance about node j. B.3.2 Transient solution for a finite slab in which one boundary has a linear temperature* change, whi the other boundary is insulated. Initially the s ab is isothermal.
---r
)(=0 X= b Assumptions:
- 1. One-dimensional heat flow.
- 2. Thermal properties of the material do not with temperature and may be evaluated at the a temperature over the range covered.
- 3. Infinite heat transfer coefficient at x=o, Mathematical statement of the problem:
for 0< x O Boundary conditions: T = To at, = 0 for 0< x "+;::'4 L Fo 0 2 1f oa 0 e
- (n+~)
( 21f2 NF
~)4 0
j Fo n= n+2" Th13 solution only considers slabs of one material. To include'clad on the base metal, an equivalent thickness must be added to be base metal thickness. The equation for the equivalent thickness of clad is:
+ a2a
____2 + 2k 2 ac d = -c + Jc 2 al ~ IPEC00069876
RIV000052B Submitted: December 22, 2011 B-7 where, d equivalent thickness of clad C actual thickness of base mate a actual thickness of clad mater a1 and k1 diffusivity and conductivity a2 and k2 diffusivity and conductivity metal The slab thickness "b" now becomes (d+c) The final graph of temperature vs distance be plot-ted using (d+c) as the total length. The t in the section d<x<<d+c) are correct for the However, the temperature distribution from d must be "foreshortened" and replotted from temperature at x=a is the temperature x=d. B.3.3 Transient solution for a finite slab with un initial temperature in which one boundary a linear temperature change while the other boundary s kept at zero temperature . x'" b Assumptions:
- 1. One-dimensional heat flow.
- 2. Thermal properties of the material do vary with temperature and can be evaluated at the verage temperature over the range covered.
- 3. Infinite heat transfer coefficient at Mathematical statement of the problem:
o for 0< x <h and ,,>0 IPEC00069877
RIV000052B Submitted: December 22, 2011 13-8 Boundary conditions: T To at ,=0 for 0< x 0 The solution is: where,
-n 2 /f2 N e 1 00 Fo NFo
+~
/f3 Z e sin rJ/f~ j n=l n3 j
b 1 T mean b J (T + q::m:r )dx o B.3.4 Transient solution for a finite slab with non-uniform ~ initial temperature which undergoes a linear temperature change on each surface. x X= b Assumptions:
- 1. One-dimensional heat flow
- 2. Thermal properties of the material do not vary with temperature and can be evaluated at the average temperature over the range covered.
- 3. Infinite heat transfer coefficient at x=o.
- 4. u=O forcing the surface at x=b tu remain at T1.
Mathematical statement of the problem: o for 0< x <b and ,)0
~
IPEC00069878
RIV000052B Submitted: December 22, 2011 B-9 Boundary conditions: T f(x) at '!"=O for 0< x O, but u=O so T = T1 at x=b The solution is: 00 T g Z e sin sin mrx x .*.. b n"'l b
+ ~ b Je o
- I f f{x)
T To + ~ (T1-T o ) the solution become J sin mr~ IPEC00069879
RIV000052B Submitted: December 22, 2011 B-lO The equation for the mean temperature is: 1 b T mean b J T dx o B.3.5 Nonlinear gradient at steady state resulting from heat generation due to gamma ray capture in a two material finite slab with one surface at a fixed temperature and the other surface perfectly insulated.
!os cs Assumptions:
- 1. One-dimensional heat flow.
- 2. Thermal properties of the materials do not vary with temperature and can be evaluated at the mean tem-perature of the body in quest-ion.
- 3. No contact resistance at the junction of the two materials.
- 4. Heat generation of the form q "' = qo '" e-l3 x .
Mathematical statement of the problem: d2Tss A
-k ss dx 2
= qo "' e - ....x for 0 < x < a~
d2Tcs f3
-k - = qo II' cs dx e- x for a~ < x < a2 Boundary conditions:
Tss = To at x=o dT cs
-k dx at cs ---- x.=a~
IPEC00069880
RIV000052B Submitted: December 22, 2011 B-11 Taa = Tca at x=al. The solution is: Tss qo "' ~1~ e -~x 2
- - xe -l3a ] + To I3k ss Tcs qo "'
/3kcs
[a.e -~ae e -l3 l.
+ -
a e -t3x
- xe
-/3a2 Tangential thermal stresses at x=a~ and x=a2 due to this temperature distribution in a thin walled ends free to expand axially but restrained f bending are:
0, (~~ )(~::.~) {e -~a, [~- ~e(a,l_a,j]
+ e-~'e ~e(a!-ad -aed}
Ea' ~ { e -t'>al. -t'>a21. U- 1 1 02 = (r:v)(k cs !3) 132(a2-al.) - e 13""""'a-2---a-l.....,-I+ ~+ where: Ol. Tangential thermal stress at x=al. 02 Tangential thermal stress at x=a2 E Modulus of elasticity v = Poisson.t s ratio a' Linear coefficient of thermal expans IPEC00069881
RIV000052B Submitted: December 22, 2011 B-12 B.3.6 Thermal moment: A term used in the structural analysis generally at locations of discontinuity where cuts are taken. The moment is due to a radial temperature gradient and is defined mathematically as: b Ea' f T (R-r)d(R-r)
~ = I-v a
The equation for the mean temperature at a cut through a cylinderical section is: Trdr where. a Dimension to inside surface b Dimension to outside surface r Dimension (a<r<b) R Mean radius a' Coefficient of thermal expansion v Poisson's ratio B.3.7 Material Properties and Film Coefficients: Properties of materials used in this appendix are pre-sented below. All were evaluated at 325°F. Stainless Steel Carbon Steel k 9.8 Btu/hr-ft-OF k 26.2 Btu/hr-ft-OF P 495 Ib/ft 3 P 490 Ib/ft 3 cp .127 Btu/lb-oF cp .12 Btu/lb-oF Air water k .0204 Btu/hr-ft-OF k .40 Btu/hr-ft-OF 1{1 = 3.0 X 10 5 1{1 = 4.7 x lOs The following equations were used to calculate the heat transfer coefficients us~d in the analysis of the head and vessel flanges. IPEC00069882
RIV000052B Submitted: December 22, 2011 B-13 convection film coefficient in a vertically losed gap: heX 0.071 ~X3p2gt3 6.T cpf.L J~ k = 1. ,,2 (k) (L/X)9 ,... Convection film coefficient in a horlzonta+ losed gap: b x e k = 0.075 he = 0.0751<
- Convection film off the top of a heated plate heL k = 0.14 fL3p,:g2t311T L ,. . (cPkf.L)]~
1. h = 0.14k[ 6.T]3 c The convection film coefficient on the bot the same plate is assumed to be half that e top side. The equation for the radiation coefficient ss the
.air gaps and off the top and bottom of the eling plate is as follows:
IPEC00069883
RIV000052B Submitted: December 22, 2011 B-14 B.4.0 APPLICATION OF GENERAL SOLUTIONS AND RESULTS AT SPECIFIC LOCATIONS B.4.1 Head and Vessel Flanges: A representative section of the vessel flange - head flange region was divided into a series of nodes as in Figure B-1 on Page B-23. Por calculating node volumes and heat transfer areas, a cylindrical sector with an angle equal to half the angle between two studs was taken. This model con-siders two dimensional heat flow (axial and radial) except in the head flange where the studs pass through. In this area, a third dimension is considered as heat is transferred between the stud and flange. Assumptions:
- a. Two-dimensional heat flow.
- b. Heat generation negligible.
- c. Thermal properties do not vary with temperature.
- d. Natural convection is assumed in the gap between the core barrel and vessel flange.
- e. All other surfaces in contact with primary coolant f.
g. are assumed to have an infinite heat transfer co-efficient. OUtSide surfaces of flanges, vessel and head are perfectly inSUlated. Natural convection and radiation is assumed in the annulus between the stud and head flange and in the gap between the head and vessel flanges.
- h. The refueling plate transfers heat to the sur-roundings by both radiation and convection.
The head and vessel flanges were analyzed for the fol-lowing thermal conditions USing the method described in B.3.l.
- a. Heatup Transient: Inside surfaces are heated from IOOoF to 547°F at a linear rate of lOOoF/hr while the ambient condition remains at 120o P.
~
I I IPEC00069884
RIV000052B Submitted: December 22, 2011 B-15
- b. Steady State: Inside surfaces are held onstant at 547°F and the ambient at 120oF .
C. cooldown Transient: The inside surfaces from 547°F to 1000F at a linear while the ambient is held at condition for this transient condition described in b. Results: Nodal layouts of the flanges showing tempe dis-tributions at times during heatup and cooldo tran-sients plus steady state are presented in Fi B-1 thru B- 9. Figure B- 39 is a sketch of the f gion showing the locations of discontinuity ef'fects of' radial gradients were considered. locations, the radial gradients were plotted these gradients values were obtained for the temperature at the cut and the thermal momen radial gradients are shown in Figures B-40 and the thermal moments resulting from these are tabulated on Page B-IOO.
- Axial gradients in the flanges were also plo the temperature distributions at times duri cooldown and at steady state. These gradien sented in Figures B-78 thru B-83.
For the Plant Hydrostatic Test (2500 psia), surfaces are heated from 1000F to 400°F at while the plant is being pressurized. Du depressurization, the inside surfaces are to 100 0 F at lOOoF/hr. These heatup and coo wn tran-sients are at the same rate but over a sho range than the normal heatup and cooldown. The , it would be conservative to use the results rmal heat-up and cooldown for the hydrostatic test other operating transients applied to this faster rates than heatup and cooldown, but temperature change is much shorter. There!' conservative to consider the mean tempera body did not change from the initial conditi the temperature of the inside surface foIl fluid transient. Differences between the ture and the inside surface temperature at these transients are tabulated on Page B-121 IPEC00069885
"'U m B-16 () a a B.4.2 Inlet Nozzle: A cross section of the nozzle was di-a(J) <D vided into a series of nodes as in Figure B-10 on Page B-32. This model, consisting of a cylindrical
~
ex> ex> sector with an angle of one radian, was used to per-(J) form a two-dimensional thermal analysis using the technique described in B.3.1 and the following assumptions.
- a. Two~dimensional heat flow.
- b. Heat generation negligible.
- c. Thermal properties do not vary with temperature.
- d. All surfaces in contact with the primary coolant are assumed to have an infinite heat transfer coefficient.
- e. Outside surfaces are perfectly insulated.
Results: Temp-erature distributions were obtained for times dur-ing a lOOoF/hr heatup from lOOoF to ~47°F. These dis-tributions are shown on nodal layouts in Figures B-10 thru B-13. Figure B- 50 shows the locations of dis-continuity where the effects of radial gradients were considered. At these locations, the radial gradients were plotted, and from these gnadients values were obtained for the mean temperature at the cut and the
~
thermal moment. The radial gradient plots are found in Figures B- 51 thru B- 55 and the thermal moments are tabulated on Page B,-101. Gradients in the axial direction were also plotted for the nozzle at times during the heatuptransient. These plots are found in Figures B-84 and B-85. Temperature distributions were not obtained for the cool-RIV000052B down transient. Since cooldown is over the same range and at the same rate as heatup, cooldown gradients would simpiy be mirror images of those for the heatup transient. Also, the values for thermal moments which were obtained for heatup, with signs reversed, can be used for cor-responding times during cooldown. The results of normal heatup and cooldown were used for the hydrostatic test transients as described for the Submitted: December 22, 2011 flanges in B.4.1. , At steady state, the nozzle will be isothermal at the inlet coolant temperature since there is no heat sink.
~
I I I
RIV000052B Submitted: December 22, 2011 B-17 The operating transients for the inlet noz investigated in the same manner as for the analysis in Section B.4.1. The results are on Page B-122. B.4.3 outlet Nozzle: A representative section of outlet nozzle was divided into a series rif nodes as Figure B-l4 on page B-36. This model, conSisting a cylindrical sector with an angle of one rad was used to perform a thermal analysis using the method described in B.3.l. Assumptions:
- a. Two-dimensional heat flow.
- b. Heat generation negligible.
- c. Thermal properties do not vary ',""U';l"ctture.
- d. All surf'ace s in contact with the p coolant are assumed to have an inf'inite heat sfer coefficient.
- e. Outside surfaces perfectly Temperature distributions in the outlet noz ob-tained for the following transient and stead condi tion s .
- a. Heatup: Inside surf'aces are heated f'rom 547°F at a linear rate of 100o F/hr. Bo and outlet fluids follow the same
- b. 100% Power Steady state: The coolant in the nozzle is held constant at 613°F while coolant contacting the vessel shell adjacent to is held at 555°F.
- c. Operat1ng TranSients: Temperatu~e dist tions were obtained for operating transients inclu g plant loading and unloading, step reduction 100% to 50% load, reactor trip from full power, ss of flow, one pump and loss of load. Fluid transi S for these cases are found in the Equipment cification.
Results: Nodal layouts of the outlet nozzle showing t erature distributions for times during heatup, plant ading, at 100% power steady state and during plant loading are presented in Figures B-14 thru B-26. gure B- 56 IPEC00069887
RIV000052B Submitted: December 22, 2011 B-18 is a sketch o£ the nozzle showing the locations of discontinuity where effects of radial gradients were considered. At these locations, radial gradients were plotted for.the conditions above. From these gra-dients, values were obtained for the mean temperature at the cut and the thermal moment. The radial gradient plots are found in Figures B- 57 thru B-7l and the resulting thermal moments are tabulated on Pages B-I02 andB-103. Axial gradients were also plotted for the nozzle at times during heatup, plant loading at 100% power steady state and during plant unloading. They are
£ound in Figures B-86 thru B-91.
As in the inlet nozzle analYSis, the cooldown transient was not completely analyzed. The gradients are mirror images of those for heatup and the thermal moments, with reversed signs, can be used for corresponding times during cooldown. At zero power steady state, both inlet and outlet fluids are at 547°F. With the outer surface of the nozzle in-sulated. there is no heat sink. Therefore, at this steady state the nozzle will be isothermal at S47 0 F. The results of heatup and cooldown were also used for the plant hydrostatic test tranSients as described for the£lange analysis in B.4.1. Temperature distributions for operating transients in-cluding step reduction from 100% to 50% load, reactor trip from full power, loss of flow, one pump and loss of load are presented in Figures B- 27 thru B- 38. These transients have faster rates than heatup, plant loading and plant unloading, and their effects are only seen a short distance from the surface. In view of this, it was conservative to consider the inside surface fol-lows the fluid temperature and calculate the 6T between the mean temperature and inside surface temperature. These temperature differences are tabulated on Pages B- 123 and B- 124. For the step load tranSients of +/- 10% of full power and steam break from hot zero power where both inlet and outlet fluids follow the same tranSient, the inside surface temperature was assumed to follow the fluid temperature while the mean temperature of the Dozzle did IPEC00069888
RIV000052B Submitted: December 22, 2011 B-19 not change from the initial condition. Dif erences between the mean and surface temperatures a tabulated on Pages B-123 and B-124. B.4.4 Closure Head: The vessel closure head was determine the mean temperature of the head of the lOOoF/hr heatup and cooldown transie lOOoF and 547°F and at the end of the hydro transients during which the vessel is haate between lOOoF and 4000 F at lOOoF/hr. Results of the one-dimensional analytical s described in Section B.3.2 showed the mean emperature of the head to be 51S o F at the end of heatu anJ 129°F at the end of cooldown. At the end of the heatup and cooldown transients, the mean temperatu the heed is 3S4°F and 116°F, respectively. B.4.5 Vessel Wall: The procedure described 1n used to perform the one-dimensional analysis of wall in the nozzle region and in the lower for the heatup and hydro heatup transients.
- Temperature distributions for the two wall presented in the form of graphs, for times and hydro heatup are on pages 8-94 thru 8-9 these curves, the mean temperature and ins side surface temperatures were obtained for ctions, r1ng heatup Using and out-investigated. Differences between the and the temperatures of the inside are tabulated on Page B-I04.
The procedure in B.3.5 was used in determin the maxi-mum allowable rate of gamma heating in the er section of the vessel wall. This rate was c culated by substitut1ng 2 3m for 01 in the equation fo thermal s'tress at x=a1 and solving for qo I I I . IH th = 0.4 io- 1 and 2 3m = 53,400 p'si, the maximum value determined to be 164,000 Btu/ft 3 -hr. B.4.6 Bottom Head: The method in B.3.2 was also u termine the mean, inside surface and outside surface temperatures in the bottom head at times dur ng the heatup and hydro heatup transients. Diffe between the mean temperature and the temperatures of inside
- and outside surfaces during these transients are pre-sented on Page B-105.
IPEC00069889
RIV000052B Submitted: December 22, 2011 B-20 B.4.7 Vessel Supports: The vessel i.S supported off the noz-zles. Four nozzles, two inlet and two outlet, are used in the support arrangement. These nozzles have inte-gral pads built up on the bottom sides and rest on support shoes. The support shoes are attached to a ring girder which rests on a concrete foundation. Although both inlet and outlet nozzles are used for supports, the geometry of the inlet nozzle presents the more severe case and was used for both nozzles in the analySis. The following transients and steady state conditions were investigated. For all conditions, the back surface is held at lOOoF. This temperature represents the tempera-ture at the bottom of the support shoe and is assumed to be equal to the ambient temperature.
- a. Plant Heatup - Inside surface is heated from .100oF to 547°F at a linear rate of lOOoF/hr.
- b. Hydro Heatup - Inside surface is heated from 100°F to 400°F at a linear rate of 100°F/Hr.
- c. Steady State - at steady state, the temperature dis-tribution through the nozzle wall and pad is assumed to be linear between the fluid temperature inside the nozzle and 100°F at the bottom of the support shoe.
Inside temperatures for the steady states investi-gated are:
- l. Hydro Steady state - 400 0 F (inlet and outlet nozzles).
- 2. Zero Power Steady State - 5470 F (inlet and out-let nozzles).
.3. 100% Power Steady State - 5550 F (inlet nozzle only) .
- 4. 100% Power Steady State _ 613 0 (outlet nozzle only) .
- d. Plant Cooldown - Inside surface 1s cooled from 547°F to lOOoF at a linear rate of lOOoF/hr. The initial condition for this transient is the zero power steady state distribution.
- e. Hydro Cooldown - This transient starts from the hydro steady state. The inside surface is cooled Crom 400°F to 100°F at 100°F/hr. The distribution at the end of hydro cooldown is assumed to be the same as that for the end of plant cooldown IPEC00069890
RIV000052B Submitted: December 22, 2011 B-21 The procedure 1n B.3.3 was used to perform e one-dimensional thermal analysis for plant and hydro heatup. The plant cooldown transient was yzed using the one-dimensional analytical solution de in B.3.4. Temperature distributions thru the nozzle at the end of plant heatuPI hydro heatup cooldown are presented in Figure B-76. Di for hydro, zero power and 100% power stea presented in Figure B-77. From these dist temperatures of the inside and outside su mean temperature were obtained, The ~T b temperature and the temperatures of the in side surfaces was calculated. These result sented on Page B-106. B.
5.0 REFERENCES
- 1. Hellman, Habetler, and BabrOV 1 "Use of Numeric in Transient Solution of Two Dimensional Heat Problems with Natural and Forced Convection",
actions, 1956.
- 2. McAdams, W. H., Heat Transmission, Third Edit , McGraVl-Hill Book Co" New York, 1954.
- 3. Anthony, M. L., "Temperature Distributions a Linear Temperature Rise at One Surface", Dis-cussion on Heat Transfer, 1951.
- 4. Mac Robert, T. M., Spherical Harmonics, 2nd Ed 1948.
- 5. Westinghouse Equipment Specification No, 6762
- 6. Westinghouse P.A.R. No. 27.
- 7. Westinghouse Drawing No. E.D. Sk. 328832-F.
- 8. CE Drawing No. E-232-o42.
- 9. CE Drawing No. E-232-0~5.
- 10. CE Drawing No. E-232-o46.
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