ML19312C748
| ML19312C748 | |
| Person / Time | |
|---|---|
| Site: | Oconee  |
| Issue date: | 08/19/1969 |
| From: | Ross D US ATOMIC ENERGY COMMISSION (AEC) |
| To: | Long C US ATOMIC ENERGY COMMISSION (AEC) |
| References | |
| NUDOCS 7912190959 | |
| Download: ML19312C748 (16) | |
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UNITED STATES s
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August 19, 1969 Charles G. Long, Chief, Reactor Projects Branch :'o. 3, Division of Reactor Licensing MIXI;iG COEFFICIE::T3 AS RELATED TO TIIE B&W DESIG'I PRESENTED I:I TIIE OCO::EE POL (DOCKET :'0S. 50-269, 50-270 and 50-287) r A brief literature review on rai::ing has been performed acd is enclosed, in preparation for the thernal-hydraulic.ceting trith Duke, now antici-parer for Septenber 24, 1969.
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D. F. Ross, Reactor Project Branch !o. 3 Di'Jicion of Reactor Licensing Enclosura:
Revicu cc:
Docket filca (3)
A. Schwancer R. DeYoung M. Rosen R. Boyd B. Crimes D. Ross (3)
RP3-3 Reading 4
1 i
- 7 912190 /f7 C
BRIEF REVIEW 0F MIXING COEFFICIENT LITEPATURE 4
Several references on mi::ing coefficients were reviewed as part of the Oconee POL review. A list of references is attached.
Su== aries of each were prepared and follow below.
Reference 1, WCAP-1645 Two models were developed to describe flow redistribution caused by bulk boiling in an open lattice core.
Flow redistributes due to vol'. ne e:< pan-sion and increased pressure drop.
One of the two models was called the semi-open channel model.
Terms are shown in the sketch below:
M2' M2' #M2 N2' M2' CM2 i
A,1 6W c
2C4 AZ
+
s 4
l i
M1' 0:11 ' M1
- 1, P31, pgy Other Channels I
i Channel Channel l
M U
K i
I Terms include:
A, flow area
.g;, lateral flow area 4
D, hydraulic dicmeter H, enthalpy P, pressure AZ, elevation p, density V, a:cial velocity Vg, lateral velocity e
a
=
e e
2 The analysis used the term " channel" but this is not necessarily the same as one coolant channel in a fuel assembly. Within each channel properties are assumed conytant.
The density is assumed to vary with temperature but not pressure.
Flow mixing between channels is neglected.
Three basic equa-tions were written (for Channel N).
Continuity Out the top
.In the bottom = In from M - Out to K 2E.
N2b1N2 Ni^N N1 v
NKk'K NK
!Ci E b >A' ~ P P
~#
Energy Inlet enthalpy + heat transferred + cnthalpy from M = outlet enthalpy +
cathalpy to K 9.E.
Nlb!N1"N1+9fhZD4aZ + -
v -
v 'l
'v H
M;'2+#Eb'K E gg H
2Ci Ci e
Moret.tum (A:cial)
('iV) 4-momentum from M = outlet force + outlet (MV) +
Inlet force + inlet e
from bottom to top outlet momentum to K + elevation term + frictica loss RE N1bl N1 Pgh; +
'N1 +
MNkCIMN M
N2b1N2 V
O P
g3
=P
/
8 8
g3 g.
+
C C
C 7VNK UK<tJK)
N f
a3 IV
+ 0.1Z + D I
A.
- V ~
9 p
g a
3 W
c e
c s.
3 A momentum equation was also written for the transverse dir' ction.
e Approximations were made for small AZ-values.
A correlation for lateral flow resistance 6 based on. APD tests was presented,(for presence of strong axial flow):
2 V #
A K/K
=C 2g AP
=
c NL, where K is the overall lateral resistance coefficient K, is the conventional pressure coefficient between the tuo channels.
V is the axial velocity A
C a constant AP a era p ssure difference.
NK A transverse momentum equation is:
2
-0., V,,t.
=K gg gg C
where K;g incorporates the common friction terms.
7 If the latter two equations are combined:
9 9
K,C V "#
- 7 A
NK ap NK 2g AP,JL.
2g c
c or, putting in proper subscripts:
2 2^
2
-MK' N1
- E:11 NK Ng)2 (AP
=
(2g )9
~
and taking square root:
/C K, Ng 37 g7 0
V AP V
=
NK 2g NK c
L e
o
~
4 d
is known from geometrical configuration and C is known from
=,NK the original correlation.
4 Similar equations may be written for each channel.
A sample problem was run for the Saxton core.
Four channels were assumed.
A AZ of 0.37 f t was used -(core is 2.96 f t tall, for a total of 8 steps).
The output was a graph of density vs core height and radius.
Reference 2 - UCAP-3704 The THINC code was described.
The output of the code is density, velocity, and pressure-in a semiopen or closed channel core. The effects of boiling are included.
Spatial heat generation is an input.
Inlet density, pressure,.
and velocity is assumed to be knovn.
Outlet pressure is assumed t'o be uniform.
The code iterates the inlet velocity distribution, holds total mass flow rate constant, with the constraint of equal outlet pressure.
The same equations developed in Reference 1 were used.
Where' ruo-phase flow is involved, weighted steam-water velocities were used.
A given chsnnel may
' be coupled to as many as four adjacent channels. ' Variation of the friction pressure drop constant with void fraction is provided.
A sampic problem for the Saxton core was run.
The core was represented by four concentric regions.
As in Reference 1 the output is density vs r&z.
. Reference 3 - UCAP-2211' A second code, THINC-II was described for use in evaluating hot cell factors within; an assembly. As before, THINC-I is used for determining hot channel enthalpy. rise,in the core.
Both codes account for flow redistribution and mixing.
?
i 1.
5 The coupling of the two codes permits the calculation of the hot asscebly factor, with flow mi:cing between assemblies (THIUC-I). Then the hot cell factor is comppted (THIiC-II) for the hot assembly. A new term has been added to account for ficw exchange as opposed to cross ficw.
The sketch belcw identifies terms:
Hn2 ' Vn2' pn2' Pn2 Hm2' Vm2 ' pm2' Pm2 f
__ 3e i
l-1 1
l A
U A
AZ n
an m
r
t 1
i i
H Hn1' Vnl' onl' Pnl ml' Vml' pml' Pml i
Q heat input to channel m in interval AZ
=
g W
= cross flow, n to a 1
H, o, V, mean., values vs AZ w' = ficw c:cchange rate / unit length j
4 K
pressure loss coefficient for channel m, in interval AZ
=
l The three equations are:
Mass p
A Val +W
=p A V ml m mn m2 m m2 i
L
6 Energy p
A V Hm1 + Q
+W II + w'
-H' AZ = p A V H
ml m ml mz
. mn
.n
,n m,
m2 m m2 m2 Momentum V
'o A V V
o A V Vml, Wmn n "2
"2 "2 +
ml m mi p.
=P A +
mi m g
g m2 n ge A __
_2 p V
- K
+ 5 AZ E mz 2g m
g Mixing and cross-flow was discussed. The two types of mixing are cross-flou and diffusion mixing.
The amount of flou exchange by diffusion is proportional to density and diffu,1vity:
w ' = 1; p c c = cddy diffusivity, ft /sec c= Yb, V the axial velocity; b = rod spacing K = proportionality constant A cross-flow resistance correlation was pre ent.ed.
The THI::C-I code uses these equations written with the variaoles being Ao, AV, AP.
Within an assembly the effect of local cross-flow on exit pressure distribution is small.
Consequently for THINC-II the static pressure was constrained to be the same at each elevation.
A sample calculation was run on the Yankee Core III. THINC-I was used for nineteen as semblies in one quadrant.
THINC-II was used for one quarter of a hot assembly.
9 S
r 7
L_
t
7 Reference 4 - WCAP-3735 Mixing coefficients for fuel assemblies were determined. Tests vere a
conducted in a low pressure water loop at Reynolds numbers of 15,000 to 46,000.
The mixing induced by spring-finger grids was much larger than that for bare rods. A correlation of the Peclet number uith the Reynolds number was obtained.
The use of staggered spacer grids can be useful in reducing the enthalpy rise of a peripheral channel.
An overall mixing coefficient, c, was defined as the combination of c 'D diffusivity, and cFR, f wr s r au n,
is report could not separate c into its two terms.
Reference 5 - CVMA-227 A computer code was used to determine the flow and enthalpy distribution within the CVTR hot tube.
The terms used uere:
A'
= lateral convecting area for tuo adjacent channels per axial foot.
U,2 = channel flow rate, lb/hr 1
11, 2 = 1 cal enthalpy, Btu /lb 7
Q'
= heat input per unit length, Btu /hr-ft
= tt rbulent intensity, /(' /V, a
r V,
= axial velocity
)
l V
= radial component of V, A
= channel' area cs
~
Z
= axial ' distance i
8 An energy balance is:
dH aA'W y
y i
U "9
+
1 dZ 1
A
("2~"l}
cs For the two channels:
dH dH W
y+
2 "E'+9' 1 dZ 2 dZ l
2 dH, if the first equation is differentiated with respect to Z, and if is dZ clininated by the second equation, then 2
d H dH
+#
"X 2
dZ dZ a A' W[
where c=
1 + g2 cs aA' il'+Q
y X"
A W
cs 2
The solution is H = lig+-
(f
- 91) (c'Z-1) +XZ 1
-4 p
1 A sample calculation uns run for the case uhere the heat output in Channel 2 was twice that of Channel 1.
Flow was equal; a = 0.05; Z = 5 feet.
The enthalpy rise was reduced from 49.6 to 38'.8 Btu /lb for the hot channel with a = 0.05.
The a-factor accounts for cross-ficw but not thermal diffusion.
s.
l l
i
9 Author's Note:
I used these gechniques,for a B&Il design, as follows:
~
A
= 1.235 x 10 ft es
-2 2
A ' = 12 in. x 0.138 in. x 4 = 6.44 in.
= 4.46 x 10 ft jgt a
= 0.03 W
- 2790 lb/hr 1
f W /W = 0.946 y 3 U
= 2950 lb/hr j 2
Q ' = 40,000 Btu /hr-ft y
Q ' = 35,000 Btu /hr-ft 2
oA '/A
= 1.~08 3
4
= 2.1 X = 27.5
-1 t
= 0.476 Q'
y X/) = 13.1
= 14.3 1,
'l Z
= 8 ft (@ MDNBR)
-iZ e
% 0 9
L
J 10 AH
=$~
(f g ) (-1) + x2 y
1 4
4H = 0.476 (13. '. - 14. 3) (-1) + 8 (27. 5) y 4H = 10 Bru/lb y
Q1 for a = 0 (no mixing) AH
= 114 Btu /lb
=
y g
1 Decrease in enthalpy rise is 8%
Reference 6 - UCAP-7015 (Revision 1)
This report presents many of the factors discussed in Reference 3 (UCAP-2211).
THINC-I is used for the region-wide core analysis, treating one fuel assembly, or a group of assemblics, as one channel. Within a channel properties are considered uniform.
Each channel is divided into axial increments.
Properties vary axially only.
Adjacent channels are semi-open. Coverning equatiens are conservation of mass, energy, and momentum. Two types of interaction between adjacent channels are considered.
The thermal diffusion heat exchange rate, TC, is determined by TC = v' aZ AH where w' = flou exchange per unit length AZ = height of. increment AH = enthalpy diffusion of adjacent channel w' is determined from a mixing coefficient c, by:
c = w'/o.
The term c is in turn relate'd to the thermal diffusion coefficient a, by:
a = c/Va where V = axial velocity a = characteristic dimension.
l L
l e
11 In this case a = lateral area / unit length.
Thus v' = pc = pava and TC = pava (Z AH At a given point in the core matrix, V, p, a, and AH are functions of location.
AZ is initially fixed, and a'is known by experiment.
~
- ross-Note that use of a does not imply that there is cross flow.
This is merely\\,t enthalpy exchange due to thernal mixing.
However it can be shoun that a = pa where V is the transverse velocity, V is the axial velocity.
t a
c w'
1
'w ' '
Proof:
a = V,a Va V
, a, p
V e
t = f7 hence a = 91 but V a
E6W calls a the intensity of turbulence.
Westinghouse calls it the thermal diffusion coefficient.
Cross-flou, as opposed to mixing,results from static pressure differences.
The correlation for flow rate vc pressure drop is:
2 pV AP
=K lbf L
i 28c The constant K is a function of the open-ing geometry and of the ratio of g
lateral velocity to axial velocity (V /V ).
For large V /V ratios,,K a g y g
approaches an asymptotic value denoted K,.
O e
6
+
e
13 2g AP 2
c g
and V
=
g 1
s 2
K yV K
g y
(K ) = 2g so
,- - 1 1.
1 0
c 1
9 Y[
K Y
Z or
-1
=
K, 2g AP g 2
YV g and K
=K 1 + 2g E
a?
=
c tj he:1cc U=a aZ 0 *'2g SP 2 l
i o K, 2g APg + yVy
)
c 2g SP C
L W=a aZp 2
2 c
4g AP c
L 4,
2 P K.
(2g aPg + yVl) c W = 2g a aZ AP
/
o C C L
K, (2g APg + yV7)
W = 2g a aZ AP c c 1
/K 2
a- (2g aPL + yv1)
O c
6
14 How the cross-flow is a function of the local pressure gradient, the axial flow rate, and the cross-ficw geometry.
The transverse velocity term has disappeared.
Also in WCAP-7015 are correlations for local boilin'g voids, and two-phase pressure drop.
In practice,. parameters are assumed to be known at.the bottom of the control volume. W is found.
Q is calculated and (TC) is found.
Outlet enthalpy is found, giving o.
Velocity is found from continuity.
From momentua, outlet pressure is found.
This procedure is marched up the core.
A constraint is uniform core outlet pressure.
The subchannel analysis, THINC-II is also described.
Hot assembly flow and enthalpy are obtained from THINC-I.
Flow properties vary in a channel only with z.
It is assumed that static pressure across the flow channel is equal.
1.. the momantum equation the cross flow term disappears.
There is cross-flow, but it is not ascribable to AP values.
An isolatcd hot assembly analysis may be run.
For n channels there will be n equations for momentum and n equations for energy, plus one for:
the sum of the cross-flows = 0.
There will be one AP per axial step, n A0-values and n AV-values for a total of 2n + 1 unknowns.
As opposed to the isolated hot assembly, flow interchange may be assumed.
For THINC-II purposes exchange may be assumed to occur at the inlet of each aZ-step.
An experimental verification was obtained by use of a nonuniformly heated rod bundle.
A 5 x 5 ' rod bundle was used.
The results showed less than 6%
variation in enthalpy gains.
15 Reference 7 - Duke POL Chapter 3, pag'e 3-52 and 3-53, centain some information cn E&W's mixing calculations.
The hot assembly (IIA) has less flow than the average because of increased pressure drop due to higher enthalpy and quality.
A direct calculation is made of the hot assembly flow.
The minimum IIA flow rate is 89% of the average at 114% overpower. Mixing coefficients within a hot assembly were calculated by a mixing code. Mixing coefficients were deter-mined from r.ultirod mixing tests. Mixed enthalpy rise are shown on Figures 3-41 and 3-42 of the FSAR. A minimum intensity of turbulence a = 0.02 was assumed.
A parametric analysis of a uns performed, ranging from 0.01 to 0.05 (Figure 3-29).
Under isothermal conditions it was assumed that the hot acaembly, HA, receives 95% of the average, due to inlet plenum effects.
Figure 3-41 uses nominal values of water gaps and HA flow rate and presents nominal flux peaking and c::it enthalpies.
Figure 3-42 presents similar results for minimum water gap and IIA flow rate.
In each case a = 0.n2.
O b
e
16 REFERENCES l.
WCAP-1645! " Flow Redistribution in an Open Lattice Core," L. S. Tong, et al, October 1960.
2.
WCAP-3704, "THINC - A Thermal Hydrodynamic Interaction Code for a Semi-Open or Closed Channel Core," W. Zernik, et al, February 1962.
3.
UCAP-2211, " Hot Channel Factors for Flow Distribution and MAxing in Core Thermal Design," L. S. Tong, et al, February 1963.
4.
WCAP-3735, " Coolant Mixing in Open Lattica Reactor Cores," R. A. Dean, August 1963.
5.
CVNA-227, "CVTR Thermal-Hydraulic Design for 65 Mw Gross Fission Pover" R. O. Sandberg and A. A. Bishcp, February 1965.
6.
WCAP-7015, "Subchannel Thermal Analysis of Rod Bundle Core," H. Chelemer, et al, June 1967, Revision 1 January 1969.
7.
Oconee 1, 2, and 3 FSAR, Chapter 3, June 1969.
6 6
b
.