One-Dimensional Steady-State Thermal Model of CNTP Reactor

Abstract

A more advanced form of nuclear propulsion known as centrifugal nuclear thermal propulsion (CNTP) promises increased propellant temperatures that could lead to a high specific impulse in the range of 1500 to 1800 s with hydrogen. This design has the potential of opening opportunities to perform missions to destinations much farther than currently possible. However, the CNTP concept poses many engineering challenges due to the nuclear fuel operating at high temperature in a liquid phase. A one-dimensional, steady-state thermal model of the liquid uranium fuel has been constructed to understand the limitations of this concept and the potential design considerations. Three related basic designs are considered, and key design parameters are varied in order to predict the temperature levels and void fractions across the liquid uranium pool.

Keywords:

• Nuclear thermal propulsion
• advanced propulsion
• hydrogen

Nomenclature

A =	=	coefficient matrix for system of temperature equations (W/K)
Atot =	=	total surface area in contact with propellant in cell (m2)
a =	=	equivalent bubble radius (m)
C =	=	solution vector for matrix equation (W)
$c_p$ =	=	constant-pressure specific heat (J/kg∙K)
d =	=	diameter (m)
$\mathrm{E}\mathrm{o}$ $\equiv$	=	$\frac{g\left({\rho }_l-{\rho }_g\right){d_B}^2}{\sigma },$ Eötvös number
${\dot{E}}_{gen}$ =	=	heat generated in a computational cell (W)
g =	=	gravitational or centrifugal acceleration (m/s2)
h =	=	heat transfer coefficient (W/m2∙K)
k =	=	thermal conductivity (W/m∙K)
L =	=	length of CFE (m)
M =	=	total number of computational cells, Morton number
$\dot{m}$ =	=	mass flow rate through a CFE (kg/s)
N =	=	total number of computational cells in liquid annulus
Nu =	=	Nusselt number
Pe =	=	Peclet number
Pr =	=	Prandtl number
p =	=	pressure (Pa)
p0 =	=	pressure in central core of CFE (Pa)
${\dot{Q}}_{condin}$ =	=	heat conducted into computational cells (W)
$\mathrm{R}{\mathrm{e}}_B$ =	=	Reynolds number for a bubble
r =	=	radial location of a computational cell node (m)
rB =	=	radius of curvature of a spherical cap bubble (m)
T =	=	temperature (K)
u =	=	propellant radial velocity (m/s)
V =	=	volume (m3)
X =	=	void fraction
z =	=	pressure integration term (N/m3)

Greek

Δr =	=	radial thickness of a computational cell (m)
Δθ =	=	angle subtending differential elements of a CFE (rad)
κ =	=	viscosity ratio
μ =	=	dynamic viscosity (Pa∙s)
ν =	=	kinematic viscosity (m2/s)
ρ =	=	density (kg/m3)
σ =	=	surface tension (N/m)
ω =	=	angular velocity of CFE (rad/s)

Subscript

0 =	=	thermodynamic conditions in core of CFE referenced
B =	=	bubbles referenced
g =	=	propellant referenced
i =	=	alternative computational cell index
l =	=	uranium liquid referenced
m =	=	computational cell index
upstream =	=	reference to cell in “upstream” propellant direction, usually the $m+1$ cell

Acknowledgments

We thank Dale Thomas of the Industrial and Systems Engineering Department of the University of Alabama in Huntsville for his role as director of the CNTP program at our university. We also thank William Walters of the Ken and Mary Alice Lindquist Department of Nuclear Engineering of The Pennsylvania State University for supplying the fission power distributions.

Disclosure Statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the Space Technology Mission Directorate of the National Aeronautics and Space Administration through the Space Nuclear Propulsion project.