Toward Improved Correlations for Mixed Convection in the Downcomer of Molten Salt Reactors

Abstract

Developing heat transfer correlations for buoyancy-driven flows and mixed convection is challenging, especially if the fluid’s Prandtl (Pr) number is not close to 1. For advanced nuclear reactor (Generation IV) designs, the downcomer plays a crucial role in normal operation and loss-of-power scenarios. The fluid-flow behavior in the downcomer can involve forced, mixed, or natural convection. Characterizing the heat transfer for these changing regimes is a serious challenge, especially in the heat transfer deterioration region. In this paper, the downcomer is simplified to heated parallel plates. The high–Pr number fluid FLiBe (a mixture of lithium fluoride and beryllium fluoride) is considered for all simulations. Direct numerical simulations using the graphics processing unit–based spectral element code NekRS are performed for a wide range of the Richardson number, from 0 to 400, at two different FLiBe Pr numbers (12 and 24). This results in an unprecedented 74 cases in total. Each case’s Nusselt number is calculated to evaluate existing heat transfer correlations.

Moreover, we propose several new modifications for cases without satisfactory choice. As a result, several novel mixed-convection heat transfer correlations have been built for high–Pr number fluids. The correlations are expressed as a function of the buoyancy number, covering several mixed-convection regimes. The Pr number effect on the Nusselt number behavior is also analyzed in detail. We also propose a novel method to evaluate the heat transfer deterioration region. Modified Reynolds-Gnielinski forced-convection correlations are defined for the laminarization region, and a free-convection correlation is used for the natural-convection-dominated region. These correlations can describe well the trend in the heat transfer–deficient region.

Keywords:

• Direct numerical simulation
• FLiBe
• NekRS
• Nusselt number, correlation

Acronyms

BC:	=	boundary condition
Bo:	=	buoyancy number
CFL:	=	Courant-Friedrichs-Lewy condition
DNS:	=	direct numerical simulation
DOF:	=	degree of freedom
GPU:	=	graphics processing unit
Gr:	=	Grashof number
HT:	=	heat transfer
KP-FHR:	=	Kairos Power fluoride salt–cooled high-temperature reactor
LES:	=	large eddy simulation
MSR:	=	molten salt reactor
Nu:	=	Nusselt number
OCCA:	=	Open Concurrent Compute Abstraction
Pe:	=	Peclet number
Pr:	=	Prandtl number
PN:	=	polynomial order
Ra:	=	Rayleigh number
RANS:	=	Reynolds-averaged Navier-Stokes
Re:	=	Reynolds number
Ri:	=	Richardson number
rms:	=	root mean square
SEM:	=	spectral element method
St:	=	Strouhal number
THF:	=	turbulence heat flux
TKE:	=	turbulent kinetic energy

Nomenclature

cp0	=	= inlet FLiBe heat capacity
Dh	=	= hydraulic diameter ($D_h=2L_y=2\mathit{\delta }$)
f	=	= dimensional heat flux
f*	=	= nondimensional heat flux
k0	=	= inlet FLiBe conductivity
LZ2	=	= heated length
P*	=	= nondimensional pressure
T	=	= temperature of working fluid (FLiBe)
T*	=	= nondimensional temperature
T0	=	= inlet FLiBe temperature
t*	=	= nondimensional time
U	=	= inlet FLiBe velocity
Greek	=
ΔT	=	= temperature difference between inlet and outlet of the bed
µo	=	= inlet FLiBe dynamic viscosity
ρ0	=	= inlet FLiBe density
ρ*	=	= nondimensional density

Disclosure Statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was funded by a U.S. Department of Energy Integrated Research Project entitled, “Center of Excellence for Thermal-Fluids Applications in Nuclear Energy: Establishing the knowledgebase for thermal-hydraulic multiscale simulation to accelerate the deployment of advanced reactors—IRP-NEAMS-1.1: Thermal-Fluids Applications in Nuclear Energy.” Computational resources were provided by the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory.