Pressure Drop Correlation Improvement for the Near-Wall Region of Pebble-Bed Reactors

Abstract

Packed beds play an important role in many engineering fields, with their applications in nuclear energy being driven by the development of next-generation reactors utilizing pebble fuel. The random nature of a packed pebble bed creates a flow field that is complex and difficult to predict. Porous media models are an attractive option for modeling pebble-bed reactors (PBRs), as they provide intermediate fidelity results and are computationally efficient. Porous media models, however, rely on the use of correlations to estimate the effect of complicated flow features on the pressure drop and heat transfer in the system. Existing correlations were developed to predict the average behavior of the bed, but they are inaccurate in the near-wall region where the presence of the wall affects the pebble packing.

This work aims to investigate the accuracy of a porous media model using the Kerntechnischer Ausschuss (KTA) correlation, the most common pressure drop correlation for PBRs compared to the high-fidelity large eddy simulation (LES). A bed of 1568 pebbles is investigated at Reynolds numbers from 625 to 10 000. The bed is divided into five concentric subdomains to compare the average velocity, friction losses, and form losses between the porous media and LES codes. The comparison between the LES simulation and the KTA correlation revealed that the KTA correlation largely underpredicts the form losses in the near-wall region, leading to an overprediction of the velocity near the wall by nearly 30%. An investigation of the form losses across the range of Reynolds numbers in the LES results provided additional insight into how the KTA correlation may be improved to better predict these spatial effects in a pebble bed. These data suggest that the form coefficient near the wall must be increased by 48% while decreasing the form coefficient of the inner bulk region of the bed by 15%. The implementation of these improvements to the KTA correlation in a porous media model produced a radial velocity profile that saw significantly improved agreement with the LES results.

Keywords:

• Pebble-bed reactor
• pressure loss
• large eddy simulation
• porous media
• wall-channel effect

Acronyms

CFD :	=	computational fluid dynamics
DEM :	=	discrete element method
GPU :	=	graphics processing unit
HTGR :	=	high-temperature gas-cooled reactor
KTA :	=	Kerntechnischer Ausschuss
LES :	=	large eddy simulation
MOOSE :	=	Multiphysics Object-Oriented Simulation Environment
PBR :	=	pebble-bed reactor

Nomenclature

$C_{form}$ =	=	Forccheimer form factor
$D_h$ =	=	hydraulic diameter
$D_{peb}$ =	=	pebble diameter
$f$ =	=	Darcy friction factor
$g$ =	=	gravitational acceleration constant
P =	=	pressure
$Re$ =	=	Reynolds number ($\frac{\rho v_s{D}_{peb}}{\mu }$)
$R{e}_m$ =	=	modified Reynolds number ($\frac{\mathrm{R}\mathrm{e}}{1-\text{isin}})$
t =	=	time

Greek

ϵ =	=	porosity
$v_i$ =	=	interstitial velocity
$v_s$ =	=	superficial velocity
ρ =	=	density
${\tau }_w$ =	=	wall-shear stress

Disclosure Statement

No potential conflict of interest was reported by the authors.