Recent Advances in Fluid Mechanics, Heat & Mass Transfer and Biology
Discussion of the Problem on Designing the Global Database for Different
Kinds of Quenchants
NIKOLAI KOBASKO
IQ Technologies Inc, Akron, USA and Intensive Technologies Ltd, Kyiv, Ukraine
[email protected]
Abstract: To make computer simulation for heat treating industry possible, engineers need a database for cooling
capacity of different kinds of quenchants. Unfortunately, there is no such database available for engineers and
computer programmers yet. As a rule, investigators use standard Inconel 600 probe or silver probe with one
thermocouple at the core to measure cooling capacity of quenchants. It is shown that Inconel 600 probe can
provide average effective heat transfer coefficients. Silver probes can be used to measure the heat transfer
coefficients during full film boiling and to measure critical heat flux densities. It is shown that critical heat flux
densities must be measured to predict heat transfer modes during quenching and optimize the process of cooling.
It is stated that heat transfer coefficients should be calculated on the basis of solving inverse problem based on
testing real steel parts with thermocouples near the surface. The possibility of use the first kind of boundary
condition in the paper is widely discussed. Such approach simplifies significantly calculations and can be
combined with the third kind of boundary condition.
Key – Words: - Quenchants, Cooling capacity, Initial and critical heat flux densities, Shock and nucleate boiling,
Global database, Designing.
boiling point,
immediately.
1 Introduction
During quenching of steel parts four heat transfer
modes can be observed,
which have been
investigated by Prof. Tensi and other scientists [1,
2]. The first mode is characterized by moving film
blanket along the surface of steel part. Film and
nucleate boiling, and also convection can act
simultaneously on the surface (see Fig. 1). The
second mode is characterized by simultaneous
transition from film boiling to nucleate boiling and
then to convection. The third mode is characterized
by existing the local film boiling on the surface of
steel parts. The fourth mode differs from mentioned
above modes by periodical appearing and
disappearing of film boiling (see Fig. 2). The first
mode was investigated by many authors [1, 2, 4, 5].
In this paper the second mode is considered and
widely discussed. During quenching of steel parts
the process of the second mode can be developed by
two scenarios (see Fig. 3). When hot steel part is
immersed into cold liquid, the convection takes
place initially because there are no bubbles yet.
When liquid in the boundary layer is heated to
ISBN: 978-960-474-268-4
then
boiling
process
starts
Fig. 1 The first type of heat transfer during
quenching in water at 60oC [1].
Fig. 2 Periodical changes of heat flux density
during quenching of a cylindrical probe in some
polymer water solutions [3].
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Recent Advances in Fluid Mechanics, Heat & Mass Transfer and Biology
Fig. 4 Typical stages of cooling, shown as the
logarithm of temperature difference against time: 1,
when full film boiling is eliminated; 2, when full
film boiling exists.
Fig. 3 Two possible boiling processes that may
occur during quenching, depending on critical heat
flux densities.
Unfortunately, it is impossible to investigate shock
boiling and measure real heat transfer coefficients by
use standard probe since shock boiling is extremely
short and standard probe doesn’t provide surface
temperature during quenching which is needed to
calculate heat transfer coefficients. However,
standard probe allows to measure average effective
heat transfer coefficients. The authors [7, 8]
developed a method for measuring average heat
transfer coefficients and made thousands of
experiments to measure duration of nucleate boiling
process on the basis of noise control system [6].
Some results of experiments are provided in Table 1.
As one can see from Table 1, the average
generalized Biot number BiV is almost the same
against the size of samples. For example, when
diameter of probe changes from 6 mm to 40 mm,
average generalized Biot number remains equal to
average value 1.05. Duration of nucleate boiling
process depends significantly on diameter of probe.
The transition temperature Ttr also depends on size
of the probe. It should be noted that during
developed transient nucleate boiling process surface
temperature
changes
insignificantly,
i.e.
Tsf = TS + ∆ξ ≈ const . Here Tsf is the surface
Due to very high initial heat flux density, the
thousands of tiny vapor nucleus appear which
oscillate at a high frequency and make noise which
can be measured by noise control system [6]. This is
so called shock boiling which follows after
“convection” (see Fig. 3). When at the end of shock
boiling the heat flux density is less than the first
critical heat flux, film boiling is absent and tiny
vapor nucleus grow and start to produce vapor
babbles which departure with frequency 67 – 76 Hz
when cooling by water or water salt solutions. In the
first scenario the film boiling is absent. In this case
initial heat flux density is less than the first critical
heat flux density. The second scenario consideres the
passway when the initial heat flux density is higher
as compared with the first critical heat flux. The
transient full film boiling appears first and then
nucleate boiling switches by film boiling which in
due time passes to convection (Fig. 3). During
nucleate boiling process the surface temperature of
steel parts mantains at the level of boiling point.
Many theoretical investigations and many
experimental data consider the process of quenching
like a heat transfer problem with the third kind of
boundary condition. For instance, Grossmann factor
H is used in heat treating industry [1, 2, 7]. The
standard cylindrical probe 12.5 mm in diameter was
developed and instrumented with one thermocouple
at the core to measure cooling rate when quenching
it in different quenchants (standarsd ASTM D6200).
ISBN: 978-960-474-268-4
temperature during transient nucleate boiling
process; TS is the saturation temperature (the boiling
point of liquid); ∆ξ is average overheat of liquid in
a boundary layer which causes the boiling process.
The average overheat can be measured as
∆ξ =
ϑI + ϑII
2
(see Table 2). It means that in many
cases the boundary condition of the first kind can be
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Recent Advances in Fluid Mechanics, Heat & Mass Transfer and Biology
used instead of nonlinear third kind of boundary
condition.
transfer coefficient during nucleate boiling can be
Table 1
Generalized Biot number (BiV,),
Kondratjev number (Kn), and temperature transition
from boiling to convection versus size of cylindrical
probes.
where ∆T is overheat; 3< m< 10/3.
evaluated by equation [8, 9, 10]: α nb = C∆T
m −1
Ttr ,o C
Dia, mm
6
20
30
40
BiV
1.07
1.1
1.15
1.2
Kn
0.56
0.565
0.58
0.59
150
180
210
220
Table 2 Overheat of the boundary layer at the
beginning of developed nucleate boiling ( ϑI ) , at the
end of boiling ( ϑII ), and duration of nucleate boiling
Fig. 5 Liscic-Nanmac steel probes: (a) first version
of probe [1]; (b) accurate thermocouple furnishings;
(c) second version of probe [2].
process ( τ nb ) versus diameter of cylindrical probe.
Diameter of ϑI , oC
cylinder,
mm
6
14.3
20
9.96
30
8.82
40
8.1
ϑII , oC
τ nb , s
3.66
3.66
3.66
3.66
1.40
11.9
24.0
39
Liscic – Nanmac probe can be used to design global
database. However, the problem remains opened
since it is not enough clear how to transfer data
received by Liscic – Nanmac probe to the very big
steel parts like rollers, rotors or discs of turbines.
This problem is discussed below.
In contrast to standard probe, Liscic – Nanmac
probe (see Fig.5) allows to investigate accurately
boiling processes and measure heat flux densities,
heat transfer coefficients versus surface temperature
or time. As is well known, real heat transfer
coefficient during transient nucleate boiling process
changes significantly with changing of boundary
layer overheat and doesn’t depend on size of probe
and thermal properties when overheat is fixed [9,
10]. In Table 1 average effective heat transfer
coefficients are
provided
which
simplify
calculations. Here effective heat transfer coefficients
are considered because heat treating industry deals
with the effective heat transfer coefficients, and
rarely real heat transfer coefficients are used. To be
on one page, one must analyze both real heat transfer
coefficients (HTC) and effective HTC. The real heat
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2 Mathematical model for transient
nucleate boiling process investigation
For understanding processes of cooling connected
with steel quenching let us firstly consider cooling
of classical bodies like plate, cylinder and sphere.
The differential equation of heat conductivity at
symmetric statement of the problem for solids has
the form
 ∂ 2T (r ,τ ) j − 1 ∂T (r , τ ) 
∂T (r , τ )

(1)
= a
+
2
∂τ
r
∂r 
 ∂r
( τ > 0; 0 < r < R j = 1,2,3 for a plate, cylinder
and sphere correspondingly) with the boundary
conditions (2), initial conditions (3) and condition
of symmetry (4):
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Recent Advances in Fluid Mechanics, Heat & Mass Transfer and Biology
 ∂T β m

+
(T − TS ) m  = 0

λ
 ∂r
r =R
;
T (r ,0) = T0 ;
∂T (0, τ )
=0.
∂r
Table 3 Kondratjev form coefficients K =
(3)
bodies of a simple configuration (results of
analytical calculations)
(4)
Shape of steel
part
An approximate analytical solution for mathematical
model (1) – (4), in the case of regular thermal
condition, was received by authors in 1979 [11]
which is very simple and can be written as:
τ − τ ir =
ϑ
2mR 2
ln Ι .
( j + 1)( j + 5) a ϑ
This solution is true for nucleate boiling process
when within the interval ϑI - - ϑII
surface
temperature maintains at the level of boiling point
and changes very slowly with the time (see Table 2).
For example, during quenching of cylinder (40 mm
in diameter ) surface temperature changes from
108.1oC to 103.7oC during 39 seconds. In many
cases engineers and scientists, who work in heat
treating industry, consider the process of quenching
as the process which should be governed by heat
conductivity Eq (1) and third kind of boundary
condition (6):
2.467
Cylinder of
radius R
R2
5.784
Square prism
with equal
sides of L
2R 2
5.783
4.935
π2
4R 2
3π 2
7.403
R2
9.87
π2
According to the universal correlation Kn = ψBiV ,
generalized Biot number also remains the same with
the size changes of the samples [12], i.e.
B iV = idem .
(9)
For a cylinder, when j = 2, Kondratjev number Kn
(7)
is equal Kn =
Here K is Kondratjev form factor [12] which for
different shapes of steel parts is provided in Table 3.
By equating (5) and (7) and taking into account
Table 3, one can receive
2
b
π2
Sphere
(6)
K
ϑ
ln Ι .
aKn ϑ
R2
, m2
b
4R2
Cube
Consume that it can be done, then, according to the
regular thermal condition theory [12], it is another
equation true:
τ − τ ir =
K=
Slab
(5)
 ∂T α

 ∂r + λ (T − Tm )  = 0 .

r =R
R2
for
b
(2)
3,
21
= 0.545; for a sphere, when j =
2mb
Kondratjev
number
Kn
is
equal
16
Kn =
= 0.487 . Taking into account universal
mb
correlation [12]
2
R
2mR
=
abKn ( j + 1)( j + 5)a
Kn =
or
(Bi
V
Kn =
( j + 1)( j + 5)
= idem .
2mb
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BiV
2
)
+ 1.437BiV + 1
0.5
, one can evaluate
generalized effective Biot numbers for cylinder, and
sphere which are equal correspondently 1.05 and
(8)
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Recent Advances in Fluid Mechanics, Heat & Mass Transfer and Biology
0.84. Calculations coincide
well
experiments presented in Table 1.
with
the
3 Inverse problem in quenching and
boiling processes investigation
To understand the transient nucleate boiling process
more deeply, let’s consider accurate experiments of
French [13] which are presented in Table 4 below.
Fig. 6 Depiction of how thermocouples were
arranged and accurately flattened to the wall of
spheres and polished by French [13].
Fig. 7 Heat flux density vs. time during immersion
of heated spherical steel samples (875oC) into 5%
water solution of NaOH at 20 oC: a) - 6.35mm; b) 12.7 mm; c) - 25.4 mm.
Table 4 Cooling time in seconds of spherical steel
probes cooled from 875oC in 5% NaOH water
solution at 20oC (moving at 0.914 m/s), according to
French [13].
Dia, mm
6.35
12.7
25.4
63.5
120
180
500oC
0.043
0.058
0.055
0.065
0.09
0.10
150oC
0.69
0.60
0.82
0.59
0.95
1.15
As we can see from Table 4, surface temperature of
samples drops from 875oC to 150oC for less than 1
second and this time is almost the same for different
diameters. More information and more experimental
data are provided in publications of French [13].
Using these experimental data and our software
IQLab [14], the initial heat flux densities, HTC , and
Kn were calculated which are presented in Fig. 7,
Fig. 8, Fig. 9, and Fig. 10.
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Fig. 8 Heat flux density vs. time during immersion
of heated spherical steel samples ( 875oC) into 5%
water solution of NaOH at 20 oC: a) – 63.5mm; b) 120 mm; c) - 180 mm.
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Recent Advances in Fluid Mechanics, Heat & Mass Transfer and Biology
Table 5 Coefficients Ω depending on properties of
quenchants at 20 oC [15]
As one can see from Fig. 10 , the average
Kondratjev
number
Kn
is
equal
to
0.15 + 0.95
= 0.55 . In this case generalized
2
Quenchant
Ω
Kn =
Water, 20oC
4.17
30-50% CaCl2
4.78
5 – 12% NaOH
3.6
Biot number BiV is equal to 1.05 that agrees well
with Table 1. Also author [7] reported that average
Kn, during quenching of cylindrical specimens in
12% NaOH water solutions, was 1.1 when their
temperature was 20oC .
6 – 8% NaNO3
3.76
5 Duration of transient nucleate
boiling process and its characteristics
Note: Initial temperature is fixed at 850oC
The transient nucleate boiling and self – regulated
thermal processes were investigated since 1968 and
their results were published in [7]. Duration of self –
regulated thermal process differs insignificantly
from the time of transient nucleate boiling (within
0.5 – 1 second). The notion of self- regulated
thermal process was proposed in 1968 [7] and it
means that wall temperature of steel part is kept at
the level of saturation point varying insignificantly.
The real heat transfer coefficients during nucleate
boiling process are very high and can reach 200 –
250 kW/m2K (see Fig. 9). The effective Kondratjev
number Kn is linear function of Fourier number
during transient nucleate boiling process (Fig. 10).
The equation for determining the duration of
transient nucleate boiling (self-regulated thermal
process) was firstly received by generalization of
experimental data and then derived from the
analytical equation and has the form [15]:
Fig. 9 Shock and nucleate boiling heat transfer
coefficients versus time for a sphere of 38.1 mm in
diameter quenched from 875oC in a 5 % aqueous
NaOH solution at 20oC [15].
τ nb = Ω k F kW
D2
,
a
(9)
where value Ω depends on initial temperature of a
steel part and condition of cooling. For initial
temperatures 850oC it can be within 3.6 – 4.17 (see
Table 5) [15]. As known, before quenching in
liquid media, steel parts are heated to high
temperature 800oC – 900oC. Coefficient k F depends
Fig. 10 Kondratjev number Kn versus Fourier
number Fo suitable for cylinders 20, 30, and 40 mm
quenched in 5% water alkaline solution [15].
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on configuration of steel part. For plate- shaped form
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Recent Advances in Fluid Mechanics, Heat & Mass Transfer and Biology
From the above considerations follow that
there is no universal correlation between heat
transfer coefficient and surface temperature of the
tested sample. At least three curves can exist
depending on value of the critical heat flux density.
For instance, in some cases during quenching film
boiling can prevail. During intensive quenching film
boiling is completely eliminated. And also pure
convection can prevail [8]. And also three modes
can exist simultaneously on the surface.
k F = 0.1013; for cylinder – shaped form k F =
0.0432; for spherical – shaped form k F = 0.0253;
kW is dimensionless coefficient which depends on
liquid flow velocity. For motionless liquid kW = 1.
For high flow velocity of liquid which prevents
nucleate boiling kW = 0. That is why for different
condition we have 0 ≤ kW ≤ 1. D is thickness of the
component: diameter of cylinder, sphere or thickness
of the plate; a is thermal diffusivity of a material.
Using the average results of experiments from Table
6 Discussion
0
1 (BiV = 0.92, Kn = 0.516, and Ttr = 190 C ) and
Cooling capacity of quenchants should be
characterized by many parameters which includes
critical heat flux densities, initial heat flux densities,
heat transfer coefficients, and boiling temperature of
vaporizable liquids [16, 17]. To predict what kind of
heat transfer mode will appear during immersion of
steel parts into liquid, initial heat flux densities
should be compared with the first critical heat flux
which is one of the most important parameter of the
quenchant (see Table 6).
generalized equation (10) , we obtain Eq (11):

2 BiV
T −T  K ,
+ ln 0 m 
T − Tm  aKn
 2.095 + 3.867 BiV
τ =

(10)
2
 850 − 20  D

 190 − 20  a ,
τ nb = 0.0432 ×1.94 0.33 + ln

τ nb = 3.72k F kW
D2
,
a
(11)
Table 6 The first critical heat flux density for
water and water salts and alkaline solutions at 20oC
[8]
Quenchant at 20oC
Critical heat flux
densities,
qcr1 (MW/m2)
12 % NaCl water
13
solution
5 % NaOH water
15
solution
12 % NaOH water
15 - 16
solution
Water
6.9 – 7.0
Investigations show that during quenching of steel
samples in 5-12% alkaline and salt water solutions
film boiling is absent; and surface temperature drops
very rapidly almost to boiling temperature and then
maintains at the level of boiling point. The equation
(9) is proposed for calculating duration of transient
nucleate boiling process suitable for the second type
of heat transfer mode. When convection increases
significantly, duration of nucleate boiling process
where kF = 0.0432; Ω = 3.72 .

 850 − 20 
Ω = 1.94 × 0.33 + ln
 = 3.72 ,
 190 − 20 

1
D2
= 1.94 .
K=
,
Kn
23.132
0
K = k F D 2 = 0.0432D 2 ; Ttr = 190 C .
The average transition temperature from nucleate
boiling to convection (Ttr) is taken from Table 1.
As we can see, Eq (11) is similar to Eq (9).
This equation was received early analytically by
author [15] which is widely used at intensive
quenching technologies designing and recipes
development. Note that BiV = 0.92 when Kn =
0.516.
That
is
why
for
cylinders
2 BiV
.
For
our
particular
case
kW = 1 .
= 0.33
2.095 + 3.867 BiV
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Recent Advances in Fluid Mechanics, Heat & Mass Transfer and Biology
calculations. There is a great interest to solve inverse
problem for hyperbolic heat conductivity equation
and use it for shock boiling investigation. The new
methods of solving of such inverse problem are
discussed in literature [18 – 21]. Unfortunately, there
is no appropriate DATABASE for cooling capacity
of quenchants to be widely used by engineers and
metallurgists which could accelerate solving
environment problem because optimizing the
process of quenching in many cases leads to
switching of oils with plain water or neutral water
salt solutions.
decreases and in some cases convection can prevail.
In this case just existing dimensionless equation can
be used to calculate heat transfer coefficients during
convection. If transient nucleate boiling prevails,
the first kind of boundary condition can be used,
taking into account that temperature maintains at the
boiling point. The full film boiling, and local film
boiling should be eliminated because full film
boiling doesn’t provide suitable hardness and high
compressive residual stresses at the surface of steel
parts. The local film boiling causes the high
distortion of steel parts during quenching. That is
why the critical heat flux densities should be
measured and included into global database to serve
engineers and metallurgists in heat treating
technologies development. Especially important are
investigations connected with the initial period of
cooling where shock boiling takes place. Shock
boiling can increase the first critical heat flux density
due to creation of thousands of tiny bubbles which
remove very quickly heat from the steel part surface.
Fig. 7 supports this point of view because during
quenching of small spherical probes in 5% alkaline
water solution film boiling is absent in spite of high
initial heat flux which is equal to 23.5 MW/m2 (see
Fig. 7). It means that the first critical heat flux
density during shock boiling should be at least 25
MW/m2. Table 6 provides critical heat flux densities
received by conventional method of measurement.
Summary
1. Cooling capacity of quenchants should
include critical and initial heat flux
densities, heat transfer coefficients, and
boiling temperature of vaporizable liquids.
2. There is a big difference between real heat
transfer coefficient and effective heat
transfer coefficient which should be taken
into account during computer simulation.
3. When initial heat flux density exceeds the
first critical heat flux, full film boiling starts.
When initial heat flux is less than qcr1, film
boiling is absent. In this case surface
temperature of steel parts drops rapidly
almost to saturation temperature and a rather
long time maintains at the level of boiling
point of liquid.
4. A correlation for evaluating duration of
transient nucleate boiling process is
analyzed and explained from different points
of view.
5. If film boiling is absent, the first kind of
boundary condition can be used instead of
third kind of boundary condition using
proposed correlation.
6. For intensive quenching processes, when
convection prevails, existing dimensionless
correlations can be used for evaluation HTC.
7. Developed approach significantly simplifies
computer simulations.
With increase the size of probes the initial heat flux
decreases and becomes less than the first
conventional critical heat flux density (see Fig. 8 and
Table 6). This comparison shows that it is easy to
eliminate film boiling when quenching large steel
parts. It should be noted that real heat transfer
coefficients are evaluated as a ratio q/(Tsf – Ts) and
effective heat transfer coefficients as q/(Tsf – Tm).
Since Tsf – Tm >> Tsf – Ts , real heat transfer
coefficients have a very high value (see Fig. 9). As
one can see, there is a big difference between real
heat transfer coefficient and effective heat transfer
coefficient which should be taken into account
during generalization results of experiments and
ISBN: 978-960-474-268-4
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Recent Advances in Fluid Mechanics, Heat & Mass Transfer and Biology
[12] Kondratjev, G. M., Regulyarnyi Teplovoy
Rezhim (Regular thermal mode), Gostekhizdat,
Moscow, 1954.
[13] H.J.French, The Quenching of Steels,
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