A Novel Method for Predicting Power Transient CHF via the Heterogeneous Spontaneous Nucleation Trigger Mechanism

Abstract

Using the Laplace transform for solving a two-region (cladding/liquid) conduction problem with an exponentially increasing heat flux boundary condition, an analytic temperature profile has been found. The rate of the temperature increase in the second region (liquid) is used to determine energy deposition in the thermal boundary layer of the liquid. Energy deposition rates are then compared to the latent heat capacity of the growing thermal boundary layer to create a condition for predicting transient critical heat flux (CHF) via the heterogeneous spontaneous nucleation (HSN) trigger mechanism. These analytic predictions are then compared to existing data for exponential power ramp transients with periods ranging from 5 ms up to 10 s. Comparison with experimental data show that the trends of the expected HSN-triggered CHF are in good agreement with the magnitude being controlled by the determination of the maximum boundary layer energy. This work presents the first known attempts to derive a mechanistic CHF prediction model for HSN. Though further work is necessary to develop the HSN model (and is being pursued in parallel to this research), this work will allow for a quantitative prediction of HSN-triggered CHF. Further developments of the HSN model will inform the boundary layer energy threshold that triggers CHF.

Keywords:

• Transient critical heat flux
• heterogeneous spontaneous nucleation

Nomenclature

$A$	=	= heater area
$\mathrm{B}{\mathrm{i}}^{\ast }$	=	= modified Biot number, $k_2/k_1$
$c$	=	= specific heat capacity
$E_i$	=	= energy into the liquid domain
$e_L$	=	= specific latent heat absorbed in superheated boundary layer
$E_o$	=	= energy out of the superheated boundary Layer
$E_s$	=	= sensible heat absorbed in superheated boundary layer
$\mathrm{F}\mathrm{o}$	=	= Fourier number, $\alpha \tau /L^2$
$H$	=	= heat capacity per Area
$h_{lv}$	=	= latent heat of vaporization
$k$	=	= thermal conductivity
$L$	=	= length
$m_{\delta }$	=	= mass in the superheated boundary layer
$P$	=	= pressure
$q^{\prime \prime }$	=	= heat flux
$s$	=	= Laplace transform variable
$T$	=	= temperature
$t$	=	= time
$t^{\ast }$	=	= nondimensional time, $t/\tau$
$x$	=	= linear distance into domain
$x^{\ast }$	=	= nondimensional length, $x/L$

Greek

$\alpha$	=	= thermal diffusivity
${\delta }_{sat}$	=	= superheated boundary layer thickness
$\mathrm{\Delta }{T}_{sub}$	=	= subcooling
$\mathrm{\Delta }{T}_{\tau }$	=	= temperature difference from the initial state to a time of one period
$\rho$	=	= density
${\theta }^{\ast }$	=	= nondimensional temperature, $\left(T-T_{\mathrm{\infty }}\right)/\mathrm{\Delta }{T}_{\tau }$
$\tau$	=	= exponential period

Subscripts

0	=	= initial
$\mathrm{\infty }$	=	= evaluated at the bulk
l	=	= liquid
v	=	= vapor
sat	=	= evaluated at saturation
P	=	= evaluated at constant pressure
i	=	= initial
1	=	= region 1 (typically cladding)
2	=	= region 2 (typically fluid)