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Neutron & Parallel Flow Channel Coupling Effects on T-7 Flux Trap Reactor
	ML19340A520
Person / Time
Site:	Dresden
Issue date:	08/15/1960
From:	Case J, Imhoff D; GENERAL ELECTRIC CO.
To:	; NRC
References
	CON-AT(04-3)189-PA-5, CON-AT(4-3)189-PA-5 GEAP-3508, NUDOCS 8008070705
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._/_d i -~7 ,pern24) / % W f- /l.g, ? P% -~x a.ag Q'1,~, NEUTRON RID PARALLEL FLOW CZANNEL CCUPLING EFFECTS CN THE T-7 FLUX TRAP ICACTOR by J. M. Case August 15, 1960 Prepared under ' D/ AEC CCNTRACT AT(04-3)1d9. FA #5 b ,j g9 $e p ' Ij 'f ; _ _ '- 'L .2_ oo o .a h ELECTRIC GENERAL ' ATOMIC POWER EQUIPMENT DEPARTMENT SAN JOSE, CALIFORNIA ~. . :' UI'!, - - ..~ - - -.......N,, Ila,i [Z[,_ "u0m ca,-QLAIO.H DOCE f 800s0 70 7M-g

GEAP 3508 AEC Research and Development Report NEUTRON AND PARALLEL FLOW CHANNEL COUPLING EFFECTS ON THE T-7 FLUX TRAP REACIVR. by J. M. Case August 15, 1960 Approvcd by: bb D. H. Imhoff,' & nager Engineering D;velopment Prepared under AEC CONTRACT AT(o4-3)189, PA #5

LEGAL NOTICE 2his report was prepared as an account of Govemment sponsored work. Neither the thited States, nor the Co==is-sion, nor any person acting on behalf of the Co==ission: A. Makes any varranty or representation, expressed or i= plied, with respect, to the accuracy, completeness, or usefulness of the infor=ation contained in this report, or that the use of any infor=ation, apparatus, method, or pro-cess disclosed in this report =ay not infringe privately owned rights; or B. Assumes any liabilities with respect to the use of, or for damages resulting from the use of any informa-tion, apparatus, method, or process disclosed in this report. As used in the above, " person acting on behalf of the Corcission" includes any e=ployee or contractor of the Co=- mission, or employee of such contractor, to the extent that such e=ployee or contractor of the Cc==1ssion, or e=ployee of such centractor prepares, disseminates, or provides access to, any infomation pursuant to his e=ploymet or contract with the Co==1ssion, or his e= ploy =ent with such contractor.

\\ 4 SIRetARY ~ An analytical model and analogue computer circuit is developed for the study of both neutron and parallel flow channel coupling in a large natural circulation boiling water reactor. te effect of neutron coupling by itself is to cause the reactor power and inlet water velocity of a remote region to behave in a manner similar to the disturbed region. Ihat is to say, if power is increased in one portion' of the reactor, neutron coupling tends to increase power in the other regions a2-Be effect of hydraulic cour11ng by itself, however, is opposite i to the efrect of neutron coupling. It causes, for example, the power in the remote reactor areas to decrease when the power in the disturbed region is i increased. He analytical model developed here makes possible a means for the quantitative evaluation of ccmbined neutron and hydraulic coupling effects. his quantitative evaluation includes a clear detemination of the predominating coupling influence. me analogue computer circuit can be easily adapted to any reactor configuration by simply calculating the necessary computer coefficients from physics, thermodynamics, and fluid dynamics design data. 4 Applied to the T-7 flux trap design conditiens, the analytical. model indicates that the reactor core is influenced more by the effect of hydraulic coupling than by the effect of neutron coupling. Trarisient analogue predictions of the flux tiap reactor responses to asy=:mtrical 10% step pressure disturbances were obtained for two values of reactivity in voids: $1 50 and $3 00. he a - asymmetrical 10% step pressure disturbance is equivalent to a large ship's j =otion sloshing effect. S e folleving is a table of these analogue predictions: ) _ Peak Transient Respense Final Equilibrium Value oK in voids aK in volds aK in voids AK in voids Regien $1 50 $3 00 $1,.50 $3 00 Variation of 1 +55% +50% +55% +5 5 % inlet water velocity 2 -5 5 % -5 0 % -5 5 % -3 5 % Variation of 1 +90% +15 0 % +55% + 6.0 % i power 2 -9 0 % -15 0 % -5 5 % -6.0 % \\ It is concluded th ' the asy==etrical flow disturbances introacced to the reactor core by slosuing are s=all in comparisen to the ay==etr. cal flow disturbances induced by pitching ship's motion which have been i.etemined elsewhere to be of the order of magnitude of i 256 i

INTRODRUCTION 2e T-7 flux trap core appears to be of sufficient size to allow some flexibility in the neutron flux distribution. 'Ihis situation of flux flexibility is closely related to the behavior of coupled parallel flow channels because unequal and s zying flow conditions will be the principal driving force in radial power fluctu-ations. It was the objective of this investigation to develop an analytical model which cmzid be used to study the effects of neutron and hydraulic coupling subject to the lateral variations in core flow caused by ship's motion. To this end an analytical r.::lel vr 3 developed which e= ployed considerations for both large reactor neutma ;oupling and coupled parallel flow channels. The flow portion of this model has its origin in the principles which were developed for the steady-state digital computer code HERCULES Rese principles have since been broadened to include the transient behavior of two-phase flow and the resulting analytical flov model has produced predictions which correspend well with experi-mental data ( }. It was only necessary then, for the purpose of this study, to extend the existing transient two-phase flow model to include considerations for the hydraulic coupling itich is present in a parallel flow channel configuration. 2e coupled reactor portion of the analytical =odel used here was based upon the large rsactor neutron coupling theory (3),

1) Seckjord, E. S. and Harker, W. H., "he Steady-State Calculation of Vertical Two-Phase Flow", GEAP 3261.

2) quinn,

. P. and Case, J. M., " Natural Circulation Icop Performance at 1000 psia Uhder Periodic Accelerations", GEAP 3397, Rev.1

3) Beckjord, E. S. and Harker, W. H., "'Ihe Dynamics of Large Ibiling Water Reactors",

j GEAP 3074. i

= DEVELOPMENT OF THE DUAL CHANNEL - TWIN REACTOR ANALYTICAL ICDEL A schematic diagram of the analytical model which was conceived for this study of large reactor neutron coupling and coupled parallel flow channels is presented in Figure 1. Be diagram includes two coupled nodes; extension to n nodes is trivial. He reactor core is divided into two separate regions; each coupled to the other by virtue of leakage neutron flux. H e pnysical significance of this croas-coupling arrangement can be visualiced in the folicving manner: the effect of cross-coupling is for each region to supply neutrons to the other and if the coupling vere teminated suddenly in a condition of steady-state, each region vould become sub-critical. Flow channel 1 (the conduit heated by reactor 1) 8 and flow channel 2 (the conduit heated by reactor 2) are supplied with feedvater from a single downcomer. The effect of this common leg in each of the two flow i paths is to provide an interaction of pressu:e contributions which manifests i itself as a hydraulic coupling arrangement. Hat is to say, any flow disturbance i which is induced in the downco=er by one of the flow channels is felt by the o ther channel; the degree of which depends upon the relative ma6nitude of the down-comer pressure contribution. A logic block diagram which is equivalent to the physical arrangement shown in Figure 1 is illustrated in Figure 2. Although the logic scheme is, for the most part, straight forward and self-explanatory, the author feels it necessary to call the reader's attention to three points: 1) the input excitation to the system enters each of the flow and themodynamic models in the fom of a pressure disturbance. He construction of the system pemits this excitation to be applied in either a symmetrical or asymmetrical manner. Previous studies point out t; hat both types of perturbations can be introduced by ship's motion. One effect of -_

I Schematic Diagram of the Dual Flow Channel 'lVin Reactor Analytical !bdel e Steam y ._s_.__. s_ 2 - m -4 s.s_'m 8 0 s Atter l h 8 i I l ( i p5 a l i t-i Saturated Steam i e N (G, P, h, u) i 3 g s e I i ~ l 4 a a Reactor 1 Reactor 2 a t e Saturated thter 8 ,' Wg^ (w, P y, h, (1-u)) l a y ny g,$ m

2 Nl Es a

I Y ,P ,A 4* --+- Q1 2 'd - 0 I d Single Phase Feedwater y i (v, P,h A y fy, ff) ^ i V1 g V2 V 1 'i ln Dovacomer hath Tength 7 (Lp) FIGURE 1

Iogic Block Diagram of the Dual Flow Channel - Twin Beactor Analytical mdel Input. Excitation (Presrure distitrbnn< r-)1 r'v1 gk 1 = A 11 (F & T)1 ~+ HC1 + -+- f11 12 v e O1 7 i P22 I + +- --+- Y.2 g PK E If a g (F & T)2 -+ HC2 Input Excitation (Prescure disturbance)2 K Void coefficient of reactivity F&T Flow and themodynamics y with time constants BK Beactor kinetics IIC Ilydrar.lic coupling (from pressure i consiierations) II Fuel element thennal time constants P Neutron coupling coefficients FIGUBE 2

roll is similar to the effect of pitch in that it causes a sy=etrical disturbance in pressure. A second effect of roll, however, is to cause sloshing within the reactor vessel which in tum introduces an asy==etrical pressure variation. It is the effect of asy=cetrical disturbaneca which are studied in this report.

2) he flow and themodyna=ics model of each channel is influenced by pressure considerations from itself and from the other flow channel.

3) he reactor kinetics model of each node is affected by both its own neutron flux density and that of the other node.

He following sections describe each component portion of the dual flow channel - twin reactor walytical model. Flov and termodynamics hbdel te transient two-phase flov =odel used in this study is based upon an analysis which was developed for the description of a single node natural circulation loop b) with point heat input Bis analysis can be described by a system of six (6) equations which are established upon the physical concept cf momentum interchange and not upon steam void versus quality correlations, en assumed ratios or differ-ences between steam velocity and water velocity. Five of these s1x equations are applied directly to a description of the flow behavior in the two-phase region of the loop and the re=aining equation relates the pressure contribution of the downcomer to that of the two-phase region. After incorporating a provisier f.- the effect of variable boiling length upon piessure variation, the equations becone:

4) BeclQord, E.S., "Be Stability of Two-Phase Flow Icops", GEAP 3493 X + Gw/'f") {I-X + h] =

0 (1) A (s-w) + w = v(1 + s - w) t fo-1)1' (2) H+ t,a, {0* E)["$ ))+ f(!-d){Gw

tl,i,]+(I-A)f +(1-^))$= 0 (3) 5 + g. _)( *fko + ku +(Lu - La) ct.

L o +Lw - L i, Q_ 2L Ln+Lg Ln tLa de (1 -U) W = V(l + +) ~ T (5) knrLe x ul0.rt)WW% (6a) p: u(X,2)dx = Ln tle Ln t LB .Latim 0 w US where: x : gy %

lug- $)

Equation (6b) is a fair approximation for the calculation of average steam void in the two-phase flow retgion: deft, C2 W)(6 W) y_ (G W) clA (R W) (G W) p i et z * <xv Ls) (ta rie) et;e cln e t s) ".his approxi=ntion is considered satisfactory for the purposes of this study. However, more accurate detez ::1 nations are available if additional accuracy is required. Equation (4) above is a fom of Eulers equation written for the single phase fluid in the downcomer. It is seen upon examination of this relationship that the pressure variation in the two-phase flow region is equated +4 the difference between the elevation head (gravity influence) and the sum of the pressure losses due to friction and acceleration in the downconer. It is there-fore this equation that, if rewritten for both parallel flow channels with an accoccodation for a co==on downcomer, vill provide the hydraulic coupling needed for this investigation. Se acco==cdation referred to above entails just the l

4 mere separation of pressure contributions due to the single phase vnter in the downcomer and that in the flow channel (See Figure 1). Perfoming the foregoing manipulation we get for channel 1: vo Ko Q & + (Lxi ~ l e r) Q. D y', A LMo

S s 2

LMo + A RI B (7) Lo d vo (Lur - Les d Yo _ g _[LMo } dr f Lgl (LM/t'LBJ dL 1 4 Since a new variable (V ) has been introduced into the analysis, it is necessary D to write an additional equation which relates the water velocity in the downcomer to the single phase water velocities in each of the parallel flow channels. Assuming sy=netrical conditions and a downcomer area equal to the sum of the channel areas, the continuity equation for the coupled system is: Vo = 12. + MIL (8) a. 2 Se assumptiens implied in equation (8), as used in this analysis, are good. The pressure loss coefficients were scaled to acco=modate the assu=ed area relationship and it can be shown that flow area has no effect upon the single p'2ase acceleration te=s of the analysis. Equations (1), (2), (3), (5), (6), and (7) describe the transient two-phase flow behavior of cch channel in a parallel flow channel model. 'Ihese six equations written for each channel and equation (8) constitute a thirteen equation de-scription of transient two-phase flow in symmetrical parallel flow channels. Icop dynamics can be investigated for small disturbances, by the linear 1:ation and nomal1:ation of the foregoing equations. Linearit.ation - the variables are expanded in a hylor series about a steady-state solution and second order tems and cross products are ignored. Nomalization - the incremental variation ir =ach parameter is divided by its steady-state value which reduces the incremental ch..ge to a fractional variation of steady-state conditions. Perfomance of the %bove mentioned operations upon the foregoing transient equations yields: Gas (1-x + )(S, - W.) 2 ~y_4 x (9) ~ ~ O 'l) To "(lo) A (V. (i * * - AG) _)y (S*-M) A:o.] ~ ",, A.,,_ W$ F l S*- Wo) ^'o (s.~ Wo) Ao i tbt'.#=-{3* g* + (I-/t )Wo g fWo2().n +Lg) +g, +.3 h,2 A'a Me + d% Wo 2 OctleU_) Lu& Vo 2 h!*^*) Wo.] To (La ele)*W,(I A.)l _ s^ 2Vw, - g ) 4. wo (,_ s)y# y* (2) o 4 3 2 W*fi.x)g gi-W.'- %^f _ 6.n +1e) % ?;y* ~ L a & Vo s g A"" 7l(Intia)*Wo(!*A) L CI-d'.') y, g, 4 Ma w* We ,_[(La e Aa) (/ - 4.) C/-e rad dV,*_ fL, (Ls, VLa,31,% 'sYou (Ls, tia,) ']g,*_*_) Yoi(Asi-Led.)) tvd Ko, 3 de L Vor C Ln, - L as) ] L% CLui-L a O.J [eYMa 1. ark *hYlln YLuk+ka g,[kni+(Lw-1ai)m 4 (12y r (4-z )(An, + Leo) (Lui -La0 l' er ' h %,*,"'* + '"f N," [(Ln,dn,)ar ske,] mgf x i, g, { (Lai-led (Ln, + lad j (Lur-lad %i.]dt yr= 0-u.) y_ V, Ci+a) yy r' T* /de u, W. /1, M (13) d*h _ f(2Wo)(6 Wo) t_ f fa Wo ]ds "_l (in + z aa) J4, f'(2W,)(Gwo) '] (14) dz' L C in + 1eo) J L Cin +1es).l dx l L

i M' Vo + Voz V+ ~ + 0 [ g y,o g y,, 2 (15) dV*, Va a dVe

clVo Vor dx 2 Vo o de avoo dx (16)

1) subscript (o) der '.es the steady state value of the Miere:

J parameter

2) superscript (*) denotes the variation of the parameter about the average: expressed in fraction of average value.

The steady-state solutions are found by settin6 the time derivatives in equations (1), (2), (3), (5), (6), (7), and (8) equal to zero and solving tha nsulting system of equations si=ultaneously. 21e steady-state solutions and des 16n conditions for the T-7 flux trap core configuration at rated power are presented in Table I. Table I -8 76 Tsec2 II

II gy o2 V

= see oD 01 02 K = 1*1 D K

K

'37 gt E2 1.67 K K m m 3 96 M L = D a h

1*5 M L

Lg % = 1 52 M %1 %2= 94 M =, J 1

hble I (Cont'd.) 9 8 $sec2 8ol

42

= l 4 G,<2 35 ti G G,y G.as2 23 8 Ff a

a

I M y

2 T2 Te .067 Wsec 0 20.6 A =.ols 2 .0254 X1

X o1 o2 1.84 #sec W

= W (So - W )y (S - V )2 .86 Wsec = = o g g U

.268 ot

A,,

= U

da2.

o2 Substitution of the above values into Equations (9) through (16) yields for channel 1: I, * - 2 (5-93," (17) (s-n)? - - Af - 8. 00 w, " + x 0 7 K * + r yo 7; * (18) fl' = - 0.5329, + 0.216 s,* 1-o.srK* + o.oir y r, o.oggy, r-o,ggy g!(19) ff= -2.32 5'- O.32G Yo*+ 0.l2r7; *- 0. Syg g% 2,r9yf-o,ggf"' (20) l4 " = + 2. 73 >H * - 3.1/ Vi ! - c.134 ?l1 (21) t flf = 4.53 XI.5/44*- MC3 f-Mrsx/.siA.,+ zggy 1 -u-s 1 .i

Vo = d,5 K

r 0.5 V (23) 2 dD-s o,g
0,5 (24)

Equations (20,), (23), and (24) can be combined to eliminate the downcomer parameters:

~2.32 5O./63 Va#- 0.517V+ 0.12rY+2.57g *-c.4skV-O&f (25) 1 Equations (17), (18), (19), (21), (22), and (25) comprise the parallel flow channel analogue equations which were used in this study.

Void Coefficients of Peactivity Reactivity (A K) was generated in the conventional fashion from voids existent in the flow channel adjacent to the reactor core. Rese voids (n) differ from the driving head voids (/t) in that they only represent a segment of the two-phase flow region. 'Ihe average void in the reactor core can be expressed as a function of transit time across the core. 'Ihe resulting equation has the sa=e fom as equation (6b): d R,. (a wMs d u, _ s w; da, a m)(aw,) 72-(asy gg2 5 81 J. GI $C J.B t me nor=alized fom of this equation after substitution of the appropriate steady-state values becomes: 4'E'* //. 7 X 3. 9 No*- //* 7g,iT' * - //. 7X 3, 7 /d, r (27) d = 2 $3 00 reactivity in voids was assumed for those portions of the analysis which studied the separate effects of neutron and hydraulic coupling. 4

he inrge value was purposely used in order to illustrate more clearly the effects of coupling. Le combined effects of neutron and hydraulic coupling vere studied with two values of reactivity in volds ($3 00 and $150). It was hoped that by providing the above spread in reactivity a more realistic evaluation of the T-7 flux trap design conditions could be obtained. (A, k* ~ 3 A Ny OR ~ lo Ybkr W Reactor Kinetics and Coupling The reactor kinetics model used here was a linearized form of the conventional kinctics sicalation(E). 97, # / = N (29) b Kg sf?; + 4 'S t ).4 2e above relationship differs from the conventional non-linear fom in that it makes no account for the combined 1Afluence of flux density and 4K upon reactor p over. mis is a consequence of linearization. Se reactor coupling which was described in conjunction with Figure 2, however, was based upon the effect of neutron flux density. It was necessary then, in order to make the linearized reactor kinetics =odel co=patible with the aforementioned coupling scheme, to accc=plish a chan6e in the excitation variables. Mis was achieved by defining the reactivity in coupled fom: '72 I Ak ; + Akg, S(%+(,ff, (30) i 'nhere:4 Kil = reactivity in channel 1 voids which is contributed 'A reac+or 1 power. 4K 21 reactivity in channel 2 voids which is contributed to reactor 1 power..

c An 80% - 20% neutron coupling was assumed for this investigation, i.e., 80% of the power in either reactor at rated power is due to its own flux density and 20% of its power is attributed to the leakage neutmn flux from the other reactor. Se properties of the delayed neutrens were taken from Design Engineering Data and are presented in Table II. 1 Table II Delay Group hban Life t'j; DecayConstantMi Fraction (see ) (sec-1) 1 80 39 .0124 .033 2 32 78 .0306 .219 3 8 97 .112 .196 4 3 32 302 395 5 .880 1.14 .115 6 332 3 02 .0h2 O:.0064 *.0002 5 x 10-5 l = 3ee i T: L/(3 = .0078 sec Fuel Element Re mal Time Constants he fuel element thermal time constants were taken from design engineering data (I) and are presented below in equatio.'1 form: Q'+ _ l[~/ + 8.G4(S) 0.7G O. l3 0.o77 -f + + + d. 032 g/ (31) / + l.6 3(s) l + 0.357 (s)

5) Jones, A.B., " Transient Analysis of Nuclear Power Plants", Design Engineering Data Book, APED, thy 13, 1959

6) Hand, M.A. and Pflasterer, G.R., " Interim Report of Effect of Gravity Variations on T-7 Reactor", APED, November 17, 1959

6) Pflasterer,.

G.R., "Teminal Report on Ship's Motion Studies in Nuclear Syste=s Unit", APED, June 30, 1960. _.

'Ihe Combined Dual Flow Channel - Brin Reactor Analytical ?bdel Re combined dual flow channel - twin reactor analytical model was developed by combining, for each nude, the componen; models described in tin preceding pages. An analogue circuit diagram of the resulting combined model is presented in Figure 3 METHOD OF ANALYSIS It is necessary, in order to give full appreciation to the analysis used here, to understand the physical significance of coupling arrangements and the input exci-tation used in the analegue computer circuit. It can be seen from Figure 3 that the driving excitation which was e= ployed in the analogue analysis was in the form of a gravity or pressure contributing disturbance (g*) applied to each of the flov enarmels. Eis gravity disturbance, when applied in opposite sign to the two parallel '.ov charmels, provided a driving force analogous to sloshing caused by ship's motion. 'lhe construction of the circuit, however, made it possible to excite the system with any combination of the two gravity disturbsnees. Re autron coupling in the analogue circuit was provided by a parallel network of two potentioneters, each of which had a numerical setting equivalent to the two neutron coupling coefficients (f'). 21s coupling arrangement afforded a convenient scheme for supplying to the circuit a variety of neut:on coupling combinations. "le hydraulic coupling arrange =ent of the ci:cuit was supplied by an interchange of downco=er pressure contributing elements; acceleration and friction. Se degree cf coupling caused by acceleration is controlled by the ratio of downcomer length to two-phase flow length (see equation 7). He value of this ratio is essentially fixed. Se degree of coupling caused by friction is controlled by the relative magnitudes of the pressure losses realized a h Noort carnnr1 no. 1 e. .e.x,.<4,1, PEKTIVITY N:CCL M(, 1. 7 - s *, I ow? l I -I l I fM (/',) l / l ,j04 j + AA ] h (50 V KME) l gp(Q s "4 -

o

) i ro r2se Cxavsn j I b uo. 2

/f '.

I gil m,' ("!O"'H'C l **'? - V, ' o { l / ~- .a. "Ih I i l (g,'; .01 .I t Y, i, i +. i i ---,y 12) I l IT -u, r_ ! ' sj f4 N-e- / \\ l -ui I To ArncitR Nc. 2 p., n (ururrrcit rn pues) l li1. i vow crecrivity 40. 2 o ( m-rn,w ccvoum mm , st$ If .m.........--. 'S1_ _ C//M Y14 NA i d T (nem mcimir m.1 l hTVERCN ClotP!IN(~~ ) p , t,dl: +t1), l ro mer:n n 1 (Hwrwycetparer,).~l m ouem,r _ pe:c

u. a
g

._ 973,... -w. i ) (r,,) no L/ ,c.,L N.,, i L~' g8 f(70 V XCE){ fn) I f ~ b t p wo. 2 +"1 i

K n'

i+ .v; i I, N evi (""" G"*') 11 7 ~ .s -M$s%** no g I in, o l/ I I 8 r -/ -a. a 1 29L v' .' 'H .n, I FIGU:'? 3 l in the downcomer and the single-phase region of the heated channel. This relation-ship, unlike that of acceleration, is not fixed or of well defined magnitude. Friction pressure losses could vary a great deal in either region with a slight change in the gec=etry of the flow paths. It was for the above reason that an accommodation was cade in the circuit to permit varying the degree of friction coupling. (Potslitand26withhydrauliccouplingcoefficientsoff). The analysis presented here is a fundamental study of the effects of neutron and hydraulic coupling. There was not sufficient time to investigate the transient respcase of the analogue circuit to oscillatory excitation. Sherefore, this analysis does not contain a description of the expected frequency responses, phase relationships, etc., of the system. It does contain, however, a study of the circulis transient response to step excitation which in turn provides basic information about the effects of coupling. Tne value of the excitations (6*) used in this analysis was a ten percent dis;urbance from steady-state nor=al power conditions. This was a realistic value because it is expected that the effect of ship's motion vill induce disturbances of ttis order of magnitude. The parameters which vere recorded as representative of the analytical codel's behavior were: (1) the nor=alized variation of reactor power for each node (n*) and (2) the normalized variation of inlet water velocity to each parallel flow channel (v*). The following is the schedule of analysis which was used to study the effects of neutron and hydraulic coupling: 1) All coupling, both neutron and hydraulic, was removed from the model and transient responses recorded..

~ 4 2) We effect of neutron coupling was isolated by removing the hydraulic coupling. Analogue ntna vore made with 60% - 20,; neutron coupling (rated) and with 50$ - 50% neutron coupling. 3) The effect of hydraulic coupling f.as isolated by removing the neutron i coupling. Analogue runs were made with " rated" hydraulic coupling dictated by the design condition solutions and with a frictional hydraulic coupling of three times the " rated" condition. 4) The effect of combined hydraulic and neutron coupling was recorded by providing both coupling arrangements in the circuit simultaneously. l Inalogue runs were made with " rated" hydraulic and neutron coupling' and with " rated" neutron and three times " rated" hydraulic coupling. It was believed that the ef:.ect of coupling could best be seen by exciting only one node and observing the relative behavior of the other. However, a I tnie simulation of the sloshing effect is, as mentioned previously, an appli-cation of opposite sign excitation to the two parallel flow channels. ] It vac for the above two reasons that all of the analogue runs in this analysic vere performed with the following excitation combinations: 1) y +10% and g2* =

O g*

d

2) st*

+10% and g2* -10% = 1'racco of these analogue runs are presented in Figures 4 through 19 -.-

l j DISCUSSION OF RESULTS 'Ihe traces of the analogue co=puter solutions which appear in this report present results which are concurrent with expected trends. Se following is a discussion of the observations which were =ade concerning each of the points in the analysis schedule. 'Ihe transient response of the dual flow channel - twin reactor analvtical model with no coupling. Traces of the analogue solutions for this =odel configuration appear in Figures k and 5 It is observed from these solutions that: (a) the effect of a gravity increase in flow channel 1 causes a rise in the channel's inlet water velocity, a subsequent collapse in voids, and a ensuing rise in reactor power. (b) Be final or equilibrium value of v* is greater than the peak t:snsient value of this parameter. 2his response can be explained by the fact that the reactor is operating en the positive-slope side of natural circulation loop character-istic curve, i.e., heat energy is added to the fluid by an increase in reactor j power through a fuel ele =ent time delay and the net result is a further increase in inlet water velocity. (c) The performance of either node has no effect upon the other. 'Ihe effect of neutron coupling on the dual flow channel - tvi. reactor analytical codel. Traces of the analogue solutions for this model configuration appear in Figures 6 through 9 It is observed from these solutions that: (a) Neutron coupling causes a positive effect, i.e., an increase in v

causes a subsequent increase in n1*, and the effect of neutron coupling is to cause a corresponding increase v2* and n **

2 9 his can be explained as follows: he effect of a gravity increase in channel 1 causes an increase in the channel's inlet water velocity, which in turn causes a collapse in voids and a subsequent rise in reactor 1 power. Since the reactors are coupled, reactor 2 also increases in power and the resulting effect of heating causes an increase in channel 2 inlet water velocity. (b) he trsnsient effect of increased heating in a flow channel is felt as an initial " backfire" in inlet water velocity. his can be explained by the fact that the increased steam 4g rate causes an initial " push" in both directions of the flow channel which results in a preliminary deceleration in inlet water velocity. (c) he effect of increased neutron coupling is to cause a decrease in the equilibrius values of both n* and v*. This can be explained by recognizing that neutron coupling tends to distribute reactor power change a=ong the two reactors, thus decreasing the amplitudes of n* in both nodes and reducing the influence of increased heating on inlet water velocity. The effect of hydraulic couplint on the dual flow channel - twin reactor analytical =cdel. Traces of the analogue solutiens for this model configuration are presented in Figures 10 through 13 It is observed from these solutions that: (a) Hydraulic coupling causes a negative effect. i.e., an increase in vi* causes a subsequent increase in n *, and the effect of hydraulic coupling is to cauce a decrease in v

and n *. His can be explained as follows: he effect of a gravity increase 2

in channei 1 causes an increase in the channel's inlet water velocity, which, as explained before, results in an increase in reactor 1 power. H e increase in inlet water velocity 1, however, also produces an increased pressure loss in the co==on flow path of the downcomer which in turn reduces the driving head of channel 2, thus causing a decrease in inlet water velocity 2 and reactor 2 power. (b) he effect of increased hydraulic cc pling is to cause an increase in the equilibrium values 4 "'r+ +

} of n* and v*. His can be explained by recognizing the fact that hydraulic coupling tends to drive the change of inlet water velocity in opposite directions which also causes an increased spread in reactor powers. Bis behavior has a tendency to a=plify the influence of increased heating on inlet water velocity. Se effect of combined hydraulic and neutron coupling on the dual flow channel - twin reactor analytical =odel. Traces of the analogue solutions for this model configuration appear in Figures 14 through 17 It is observed from these solutions that: (a) he coupled system, at rated design conditions, is under a predominate influence of hydraulic coupling. (b) Hydraulic coupling is in co=plete control of the system when the friction contribution to hydraulic coupling is raised to three times the rated design conditions. Figures 18 and 19 illustrate the influence of reactivity in voids upon the response o f the system. In these two computer runs the gain between voids and reactivity was reduced to one half its original value (AK in voids : $150) and a solution was co=puted for the same conditions as Figure 14 and 15 It is observed by comparison of the solutions that the effect of increased reactivity in voids is to increase the severity of the system response to a given excitation. It is believed that the value of $3 00 is considerably greater than realistic. mere-f ore, it is suggested that the reader bear in mind, while exnMning Figures 4 through 17, that the response are likely to be overdramatic. CCNCLUSICNS Me effect of neutron coupling by itself is to cause the reactor power and water velocity of a remote region to behave in a manner similar to the disturbed region. Mat is to say, if reactor power is increased in one portion of the reactor, the effect of neutmn coupling is to cause the power to increase in the other regions also. Me effect of hydraulic coupling by itself, however, is opposite from the effect of neutron coupling. It causes, for excgle, the power of remote reactor areas to decrease when the power of the disturbed region increases. Rese trends in the individual effects of neutmn and hydraulic coupling have been observed and studied before. Se analytical model which was developed here, however, makes possible a means for the quantitative evaluation of combined neutron and parallel flow channel ecupling effects in a natural circulation type reactor. Bis quanti-tatise evaluation includes a clear detemination of the predominating coupling lufluence. He analytical mode). can be adapted to any reactor configuration by merely calculating the necensry analogue coefficients from physics, themodynamics, and fluid dynamics design data. De model does, therefore, have a wide range of utility from further analytical investigations to future reactor testing schemes. Applied to the 'i-7 flux trap design conditions, the analytical model indicates that the reactor core is influenced more by the effect of hydraulic couplir4 than by the effect of neutron coupling. It is concluded that the asymmetrical flow disturbances intmduced to the reactor core by sloshing are small in comparison l to the symmetrical flow disturbances induced by pitching ship's motion which have been determined elsewhere to be of the order of =agnitude of + 25%. l -

e ACKNOWLEDGEMENTS i 'Ihe author wishes to extend sincere appreciation to E. S. Beckjord for his guidance and suggestions, and to G. R. Pflasterer and A. D. Meek for their assistance in the operation of the analogue computer equipment. f i 1 i-4 m 4 k i I i i n

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ML19340A520

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