Experimental study on transient heat transfer characteristics of intermittent spray cooling

ABSTRACT

Experiments were performed to investigate the transient cooling characteristics of intermittent spray cooling (ISC) in single-phase and nucleate-boiling regimes. The consumption of residual liquid in the non-injection period was confirmed via observations of the dynamic behavior through visualization experiments. The time variation of the surface heat transfer is relatively small in the single-phase regime and minimal in the initial nucleate-boiling regime. Further, ISC was considered as a process where the transient mass flow rate was specified by the characteristic time. This idea was successfully evaluated in the prediction of the critical heat flux in cryogen spray cooling.

Abbreviations: CHF: critical heat flux; CSC: cryogen spray cooling; DC: duty cycle; ISC: intermittent spray cooling; SFSM: sequential function specification method

KEYWORDS:

• Intermittent spray cooling
• transient spray cooling
• electronics cooling
• critical heat flux

Nomenclature

$\overline{d_{32}}$	=	Sauter mean diameter averaged over spray impact area, $\mu \mathrm{m}$
f	=	frequency, Hz
h	=	heat transfer coefficient, W/(cm2⋅K)
Hfg	=	latent heat of vaporization, J/g
k	=	thermal conductivity, W/(m·K)
L	=	heater length, m
P	=	pressure, MPa
r	=	number of future time steps
q	=	surface heat flux, W/cm2
qmax	=	critical heat flux, W/cm2
$q_{\mathrm{m}\mathrm{a}\mathrm{x}}^{\prime }$	=	modified critical heat flux, $q_{\mathrm{m}\mathrm{a}\mathrm{x}}^{\prime }$=$q_{\mathrm{m}\mathrm{a}\mathrm{x}}/\left({\rho }_{\mathrm{g}}{H}_{\mathrm{f}\mathrm{g}}\overline{Q^{\prime \prime }}\right)$
$Q_{\mathrm{m}}$	=	spray flow rate, ml/min
$\overline{Q^{\prime \prime }}$	=	volumetric flow rate averaged over spray impact area, m3s−1/m2
t	=	time, s
$t^{+}$	=	dimensionless time
T	=	temperature, °C
$\mathrm{\Delta }{t}_{\mathrm{i}\mathrm{n}\mathrm{j}}$	=	injection time, ms
$\mathrm{\Delta }\overline{t_{\mathrm{i}\mathrm{n}\mathrm{j}}}$	=	non-injection time, ms
$x$	=	distance coordinate, m
$x^{+}$	=	dimensionless distance coordinate

Dimensionless groups

$St$	=	Strouhal number $St=\overline{d_{32}}/\left(\tau \overline{Q^{\prime \prime }}\right)$
$Ja$	=	Jacob number $Ja=C_{\mathrm{p},\mathrm{l}}\left(T_{\mathrm{w}}-T_{\mathrm{f}}\right)/H_{\mathrm{f}\mathrm{g}}$
$Re$	=	Reynolds number $Re={\rho }_{\mathrm{f}}\overline{d_{32}}\overline{Q^{\prime \prime }}/{\mu }_{\mathrm{f}}$
$We$	=	Weber number $We={\rho }_{\mathrm{f}}\overline{d_{32}}{\overline{Q^{\prime \prime }}}^2/\sigma$

Greek symbols

$\rho$	=	density, kg/m3
$\mu$	=	viscosity, Pa⋅s
$\sigma$	=	surface tension, N/m
$\phi$	=	unit impulse response
$\tau$	=	characteristic time
${\lambda }_{\mathrm{n}}$	=	the characteristic value

Superscript

ˆ

=

estimated (computed) quantity

Subscript

0	=	at x=0 or t=0
0+	=	near the surface
f	=	liquid
L	=	at x=L
i	=	spatial index
j	=	time index
w	=	wall
s	=	surface
sub	=	Subcooling

Acknowledgments

This work was supported by the National Natural Science Foundation of China under grant NO. 51876020, the Joint Fund of Equipment Development Department Pre-research Project and the Ministry of Education under grant No. 6141A02022505.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [51876020];the Joint Fund of Equipment Development Department Pre-research Project and the Ministry of Education [6141A02022505];