Radiative heat transfer analysis of 37-pin fuel bundle of Indian pressurized heavy water reactor under heat-up condition: experimental, numerical and analytical study

ABSTRACT

Radiative heat transfer between the different components of the nuclear reactor channel (fuel pins, pressure tube (PT) and calandria tube (CT)) is the predominant mechanism of heat transfer in a channel when coolant flow is ceased. In this paper, the thermal behavior of the channel of Indian PHWR that has thirty-seven fuel elements is analyzed for a postulated accident such as loss of coolant accident (LOCA) coupled with the failure of the emergency core cooling system. (ECCS). The analysis has been performed using experimental, numerical and analytical techniques. The experiment is performed under the pseudo-steady-state condition, and the temperature profiles for the different parts of a simulated channel are obtained. The numerical analysis of the above problem is carried out using the ANSYS® Fluent 19.0. The code calculation is compared with the exact solution which is obtained using the radiosity network method. There is a reasonably good agreement between these three types of analysis. The results from these analyzes show that the temperature gradient (along the radial direction) is developed in the fuel bundle simulator (FBS) from the center fuel element to the outer ring fuel element. Also, an insignificant circumferential temperature gradient is observed in the FBS, PT and CT.

KEYWORDS:

• Radiation heat transfer
• radiosity
• 37-fuel pins
• PHWR
• LOCA

Nomenclature

Ac	=	cross-sectional area (m2)
As	=	surface area (m2)
$c_j$	=	quadrature weights corresponding to the direction $\vec{s}$
cp	=	specific heat (J kg−1 K−1)
D	=	diameter (m)
fy	=	body force along the y-direction (N)
$F_{i,j}$	=	view factor between two radiating surfaces i and j
$\vec{F}$	=	view factor matrix
g	=	acceleration due to gravity (m s−2)
$G$	=	intensity of incident radiation (W m−2 sr−1)
h	=	convective heat transfer coefficient (W m−2 K−1)
$I$	=	radiation intensity (W m−2 sr−1), or cuurent (amp)
$\vec{I}$	=	identity matrix
J	=	radiosity (W m−2)
K	=	thermal conductivity (W m−1 K−1)
$\overrightarrow{n}$	=	outward unit vector normal to the surface
Nu	=	Nusselt number
P	=	pressure (Pa)
Pr	=	Prandtl number
q	=	heat flux (w m−2)
Q	=	heat transfer (W)
$Q_v$	=	volumetric heat source (W m−3)
$\vec{r}$	=	position vector
Ra	=	Rayleigh number
$\vec{s}$	=	direction vector
$\vec{s}$	=	scattering direction vector
T	=	absolute temperature (K)
${\vec{T}}^4$	=	vector containing the fourth power of the temperature of the radiating surfaces
u,v,w	=	velocity component along x-,y- and z-direction
V	=	Voltage (V)
x, y, z	=	coordinates

Greek symbols

$\beta$	=	coefficient of thermal expansion (K-1), or extinction coefficient (m-1)
$ϵ$	=	emissivity
$\overrightarrow{ϵ}$	=	diagonal emissivities
$\kappa$	=	absorption coefficient (m-1)
$\rho$	=	density (kg m-3)
$\sigma$	=	Stefan-Boltzmann constant = W m-2 K-4
${\sigma }_s$	=	scattering coefficient (m-1)
$\upsilon$	=	kinematic viscosity (m2 s-1)
$\varphi$	=	scattering phase function
$\omega$	=	scattering albedo
$\mathrm{\Omega }$	=	solid angle (sr)

Superscript

in	=	incoming intensity
out	=	Outgoing intensity

Subscript

a,b	=	radiating surfaces
B	=	black body
cu	=	copper
cu	=	copper
f	=	fluid
fbs	=	fuel bundle simulator
l	=	discrete direction
loss	=	axial heat loss
pt	=	pressure tube
ref	=	reference
s	=	solid
un	=	unaccountable
wall	=	wall-related quantities
water	=	water (moderator)

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.