ASTM - Intensive Quenching Systems - Engineering and Design 2010 - N I Kobasko, M A Aronov, J A Powell, G E Totten

CHAPTER 2 n TRANSIENT NUCLEATE BOILING AND SELF-REGULATED THERMAL PROCESSES 27
where:
R cr is a critical size of a bubble which is capable to grow and
function;
r is surface tension (N/m);
T S is a saturation (boiling) temperature (K);
r * is latent heat of evaporation (J/kg);
r 00 is vapor density (kg / m 3 ); and
DT ¼ T Sf – T m is wall overheat.
Active nucleating centers are the basic carriers that
remove heat from a surface and transfer it to a cooler bath,
as explained by Dhir [2, p. 372]: After initiation, a bubble
continues to grow (in a saturated liquid) until forces cause
it to detach from the surface. After departure, cooler liquid
from the bulk fills the space vacated by the bubble, and the
thermal layer is re-formed. When the required superheat is
attained, a new bubble starts to form at the same nucleation
site. Bubble dynamics include the processes of growth,
bubble departure, and bubble release frequency, which
includes time for reformation of the thermal layer (induction
period). The bubble acts like a pump, removing hot liquid
from the surface and replacing it with cooler liquid.
This mechanism is the essential factor causing the high
intensity of heat transfer during boiling, and the bath temperature
essentially has no effect [1,2]. Therefore, it is necessary
for the heat flux density during boiling to relate to a
difference of T Sf – T S ,butnottoT Sf – T m , which can lead
to large errors since
T Sf T S << T Sf T m :
These calculations were conducted at the saturation
temperature of a liquid. However, it is important to determine
the effect of underheat on the inner characteristics of
the boiling process. Underheat is defined as a difference in
temperatures between the saturation temperature and the
bath temperature (bulk temperature):
DT uh ¼ T S T m : ð6Þ
The effect of underheat on the maximum diameter
d max of bubbles and their departure frequency f, and also
on the average vapor bubble growth rate W 00 during boiling
of underheated water at normal pressure, is shown in
Fig. 5.
From Fig. 5, when underheating increases, the bubble
departure diameter decreases and the release frequency
increases. The average growth rate of vapor bubbles also
increases. All of these facts are probably also true for partial
nucleate boiling. Shock boiling and developed nucleate boiling
close to transition boiling have, as yet, not been exhaustively
studied.
When pressure increases, the bubble departure diameter,
bubble release frequency, and average vapor bubble
growth rate decrease (see Fig. 6).
These characteristics will be used for the computation
of temperature fields during steel quenching.
Tolubinsky obtained the following generalized equation
for the calculation of a heat transfer coefficient during nucleate
boiling:
Nu ¼ 75K 0:7 Pr 0:2 ;
where: qffiffiffiffiffiffiffiffiffiffiffiffiffi
Nu ¼ a r
k gðr 0 r 00 Þ
is the Nusselt criterion (number);
a
Pr ¼ v a
is the Prandtl number;
ð7Þ
Fig. 5—The effect of underheat upon the maximal diameter
d max (1), bubble release frequency f (2), and average vapor bubble
growth rate W 00 (3) at boiling of underheated water (P ¼ 0.1
MPa) [1].
is the heat transfer coefficient during nucleate boiling
(W/m 2 K);
k is the heat conductivity of the liquid (W/mK);
r is the surface tension (N/m);
g is gravitational acceleration (m/s 2 );
r 0 is liquid density (kg/m 3 );
r 00 is vapor density (kg/m 3 );
q is heat flux density (W/m 2 );
r * is latent heat of evaporation (J/kg);
W 00 is vapor bubble growth rate (m/s);
m is kinematic viscosity (m 2 /s); and
a is thermal diffusivity of liquid (m 2 /s).
In the expanded form, Eq 7 can be rewritten as follows:
a
k
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
r
q 0:7
a
0:2:
gðr 0 r 00 ¼ 75
Þ r r 00 w 00 v
Fig. 6—The effect of pressure upon bubble parameters at boiling
of underheated water (DT uh ¼ 20K): solid dots indicate bubble
departure frequency; open dots show bubble departure diameter;
lower graph plots vapor bubble growth [1].
ð8Þ