Page 317 - Fundamentals of Magnetic Thermonuclear Reactor Design

Blanket Chapter | 10 297

acting as a neutron multiplier. The calculations were made for a 1D cylindrical
model with a central axis coinciding with the reactor axis (Fig. 10.1). The BZ,
radiation shield and frame dimensions were varied to achieve minimal radial
lengths. A theoretical TBR was 1.05–1.1 (1.3–1.4 in the 1D model), and the
toroidal field coils were radiation shielded with materials, such as tungsten car-
bide (80%) and lithium or a Na–K alloy as coolants.
The following relations may be convenient for thermal hydraulic and MHD
calculations:

l For the calculation of the FW temperature and the magnitude of the liquid
metal temperature rise

T fw = T + q ( ′ ⋅ t fw λ fw + q fw t ⋅ 2 fw 2λ fw );
int
fw
q ) (
∆ T = T lm out − T lm in = q ( ′ + q fw t ⋅ fw + q ⋅ t + ′ bw ⋅ l ρ CUt ) ;
ch
p
ch
lm
,
,
fw
lm
T − T = q ( ′ + q fw ⋅ t ) ⋅ t 2 fw ( λ ⋅ Nu . ) Tfw=Tint+(q′fw⋅tfw/λfw+qfw
int
fw
lm
lm
fw
⋅tfw2/2λfw);∆Tlm=Tlm,out−
l For the calculation of the pressure gradient caused by MHD forces in a liquid Tlm,in=(q′fw+qfw⋅tfw+qlm⋅t
metal flowing in a rectangular cross-section channel in a magnetic field, if ch+q′bw)⋅l/ρCpUtch;Tint−T-
l the channel has uninsulated walls: lm=q′fw+qfw⋅tfw⋅2tfw/λlm⋅Nu.
2
dpdx = k p σUB , dp/dx=kpσUB ,
2
σ
where k p = c ( + ab c1 3 + ), =c σ t σa (for walls of the same thickness) kp=c/1+a/3b+c
σ
w
a
/
c
=
t
w
ww
 σ ⋅a 1 σ ⋅a  −1
⋅
k p = 1 + σ w t + ⋅ 3 β σ w ⋅t   (for walls of different thickness); kp=1+σ⋅aσw⊥tw⊥+13⋅β⋅σ⋅aσw″⋅tw″−1


′′
⊥
⊥ w
l the channel has insulated walls: w ′′
−
1
−
=
1
1 2
( ⋅
dp dx ξρ U 2 2 = Ha Re 1 0.852 ( Ha β) − Ha ) ⋅ ρ U 2 ≈
−
2
L
/
L 2
≈ HaU ρν ( L at ) Ha 1.
2
2
dp/dx=ξρU /2L=2Ha/Re⋅1−0.852/
Ha1/2β−Ha−1−1⋅ρU /2L⊥⊥HaUρ
2
In these relations, T , T and T are the temperatures of the FW, the wall/ ν/L at Ha≫1.
2
fw
int
lm
'
'
liquid metal interface and the liquid metal, respectively; q and q are the qfw’
fw
bw
heat fluxes to the first and the back walls of the channel; q and q are the
lm
fw
radiation-induced volume heat release rates in the FW and the liquid metal; λ
fw
and λ are the thermal conductivities of the FW material and the liquid metal; qbw'
lm
t and t are the radial lengths of the FW material and the liquid metal chan-
fw
ch
nel; Nu = αL/λ is the Nusselt number; U is the average velocity of the liquid
metal flow; l and L are the channel’s poloidal length and characteristic size;
Ha = BL(σ/ρν) is the Hartmann number; Re = UL/ν is the Reynolds number;
σ, ρ and ν are the liquid metal’s electrical conductivity, density and kinematic
viscosity, respectively; α is the heat transfer coefficient; b and a are the channel