ORIG. RUSSIAN: SOME PROBLEMS OF HEAT TRANSFER IN LIQUID-COOLED REACTORS

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP88-00904R000100100027-1
• Release Decision: RIPPUB
• Original Classification: U
• Document Page Count: 23
• Document Creation Date: December 22, 2016
• Document Release Date: August 12, 2009
• Sequence Number: 27
• Publication Date: May 1, 1964
• Content Type: STUDY

 Approved For Release 2009/08/17: CIA-RDP88-00904R000100100027-1
Third United Nations
International Conference
on the Peaceful Uses
of Atomic Energy
Confidential until official release during Conference
A/CONF. 28/P/326
USSR
May 1964
Original: RUSSIAN .
SOME PROBLEMS OF [HEAT"I'LiANSFER IWL.IQUII)-COOLED REACTORS
V . S.Osmachkin
1. INTRODUCTION
The modern nuclear paver reactors are highly forced. Large heat fluxes and specific power,
rigid limitations on the coolant and fuel elements temperatures demand knowledge of temlxera-
ture distribution in the core with a high reliability.
The main problem in thermal reactor design is to prove reliably that the impermissible
coolant and fuel element temperatures will not be realized at any reactor operational regimes.
Specific features of heat transfer problems in modern reactor technology are defined with
core arrangement, which for the most of power liquid cooled reactors is a set of assemblies
of canned cylindrical fuel elements. The knowledge of the flow pattern and heat transfer rate
is necessary for determination of the temperature distribution in such a complicated geometry.
In compact cores it needs to account for the effect of the axial heat flux variations on the
heat transfer coefficient. These problems are considered in the paper.
2. TRANSPORT PROCF,SSI?S IN 'I'URfUJLENI' FLOW
The motion of fluids in nuclear reactors is turbulent. Theoretical study of the processes
occurring in turbulent flows is very complicated.-Due to irregularity of turbulent motions it is
desirable to applicate statistical methods. However, the realization of such an approach in
all details is very difficult. Therefore,in practice semi-empirical phenomenological theories
are used. The object of these theories is to find some relations between mean and fluctuating
parts of the motion. On Prandtl's mixing-length theory the velocity pulsations in a flat channel
can be presented as
ul,lyaU,
y
where ly - is a characteristic distance passed by the pulsations.
Let us derive a more exact formulation of Prandtl's hypothesis. Introducing the suitable
Green functions, we can write the equations of motion for the turbulent fluctuations
aui a ul aUi
t + Uk axi +4-
(9 axk =
I 02 Uz
P a + " ' + X (uilu - ui u1) (1)
ax a k k
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That Green's function is determined by the following equation
avo
+(UV) Vo - vAVo =- a(r - r )a (t -tl)
(2)
with the corresponding boundary conditions.
The function Vo describes the velocity distribution in liquid flow under an instantaneous
local disturbance.
Then equations (1) can be written as
1
u1(~ , t) = f Vo (r, r 1, t, tl) [ p a xi
Such a form of Eq
uk aU; (ui ul - ui uk)] do 1dtl (3)
axk ax}i
(1) permits an iteration method to be applied. To obtain the first approxima-
Lion formulas we may neglect in Eq. (3) all nonlinear terms and the pressure pulsations.
Then
t
ui (r, t) = f ukl di Vo (r
axk
T 1, t, t1) dF 1 dtl
(4)
Provided the width of the region, where the probability Vo is not zero, is small compared with
that one, where significant change of the mean velocity occurs, Eq. (4) can be simplified.
Expanding the mean velocity gradient into a Taylor series near the point c and limiting to two
series terms, we obtain the approximate formulae for the velocity fluctuations
ul (r, t) aui juk (r 1, tl)V0(r,r it, tl)dr ldtl + a2111 jir -r l eu l(r 1, tl)Vo(?, rl,t,tl)drldtl
axk axk axe k
(5)
In the turbulent core near the flow symmetry axis the first mean velocity derivatives are small.
Therefore the velocity pulsational components are determined by the second items in Eq.(5), i.e.
are dependent upon Lite second mean velocity derivatives. Conversely, far from the flow sym-
metry axis the first items of the equation are large. In this region
ul (r,t) l full (r 1, ti) Vo (-r -r 1,t,tl)d-Jr 1dt1 lk
a x aUt (6)
k axk
Note, that the quantity
1(k' t) = juk (i-tl) Vo (T 1, t, tl) dr l dtl
has the length dimension and represents the width of the region which is a velocity pulsation
"supplier".
To improve Green's function we must take into account the turbulent diffusion of the
velocity fluctuations. Using these relations and determining the pulsational diffusion coefficient
by means of the equality
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ui Ul - J uk
l) _
aul
axk
we may introduc the new Green function by means of the equation
aV
-8 (r -rl)8(t-t1)
Then the second approximation velocity pulsation formulae are
a Ui
u. 1 (r , t) =
1 f a ?
xk
(7)
(8)
uk (r 1, tl) V (7,71, t, t1)dr 1 dt1 (9)
As above, the velosity fluctuations in the region not far from the wall equal
uk (r , t) aUi f ul (r 1, t1) V (7, 71,t,t1) dr 1dt' (10)
k
Using this expression the turbulent stress tensor components can be calculated
u~ u i = lim 1
ax k 1 _f ul (r ,t)dt fuk(7 t') V (r,71, t, t1) dr 1 dt1 (11)
v
Since Green's function is dependent on the difference r = t - t 1 only, relation (11) can be
written in the more convenient form
1
U. U. 1im a k ~rdr L fu~(7,t)dt fu 1(r 1,t-r)V(7,r1,r)d71=
1 ] ax d 2v -v k
aUi
axk f drf u~(r,t)uk(7 l,t - r) V (7, c 1, r)d71 =
aUioo T aUi
ax f Kj k(r , r) dr = vjk- ax k
k
Lagrange coordinate system the function v(-r, r) approximately equals v r e-kr, where
k = - \ T L /
, a is constant, e is a characteristic dimension of the region.
e2
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(12)
The factor?v~k ( e) _ f Kok (r , r) dr is the component of the eddy diffusivity tensor. In the
0
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 Then for homogeneous isotropic turbulence may be written as the eddy diffusivity of
momentum
?`l' f u1(t)u1(t - r)e-krdr
(13)
This expression correlates with Taylor's determination of the turbulent diffusion coefficient
[1, 2].
Similarly using the equations for the temperature fluctuations
aT1 +Uk aT1 - +uk aT =a d2 T1 + a (ujT1 -ukT1)
at aXk axk ax axk
(14)
and introducing temperature Green's function by means of the equation
(3 to +(UV)Wo -aAWo=-S(1 -ri)6(t - ti) (15)
we can obtain the integral equations for the temperature fluctuations in the following form
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T1(r,t)=fW ( r , r 1,t,t1) [uI aT C1 - (u1T1 - ul TI)dr ldtl (16)
o k d xk axk k k
In the first approximation
Ti (r t) = j uk a T % (r 1, t, ti) dr ldti (17)
k
or with the same assumptions, which have been used in deriving of formula (5)
T1(r,t)= ~T fuk(F 1,t1)W0(r , r i,t,ti)dr ldtl +
+a2T fIF - r 11eu1(r 1,t1)Wo(F, r 1,t,tl)de 1dt1 k axkaxe
In the region not far from the wall
T1 (= ,t)= a k f u (r,l t1) ( r - , ,F1,t,t1)dr idtl=a kk .lk(r,t) (18)
where I k (F , t) is an analog of the mixing-length for the temperature pulsations. Just as in
equality (7) it can be approximately accounted for the turbulent diffusion of the temperature
pulsations by means of introducing the turbulent diffusion coefficient
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'j' u