Critical Heat Flux Densities and Grossmann Factor as Characteristics of
Cooling Capacity of Quenchants
N.I.KOBASKO1, M.A. ARONOV
1, MASAHIRO KOBESSHO
2, MAYU HASEGAWA
2,
KATSUMI ICHITANI2, V.V.DOBRYVECHIR
3
1IQ Technologies, Inc., Akron, USA
2Idemitsu Kosan Co., Ltd., Ichihara, Chiba, JAPAN
3Intensive Technologies Ltd, Kyiv, UKRAINE
Abstract:- In the paper, it is shown that critical heat flux densities and Grossmann factor H, along with the cooling
curves analysis, could be very important characteristics of different types of quenchants. On the basis of critical
heat flux densities, it is possible to predict heat transfer modes taking place during quenching. When the initial
heat flux density (qin) is less than the first critical heat flux density (qcr1), a film boiling mode of heat transfer is
absent. When qin is greater than qcr1, the full film boiling could occur. When qin = qcr1 the local film boiling is
observed. The paper underlines that the Grossmann factor H can correctly characterize a quenchant when the film
boiling is absent, or when both the film boiling and the nucleate boiling are absent and direct convection takes
place during quenching. Calculating methods and software are proposed for evaluating of the critical heat flux
densities and Grossmann factor H. Examples of calculations are provided.
Key – Words:- Critical heat flux density, Grossmann factor, Quenchant, Software, Calculation, Cooling
capacity.
1. Introduction
A classical cooling curve during quenching of steel
parts represents three stages of cooling: a film
boiling, nucleate boiling and convection. It is still
questionable whether film boiling can be absent
when quenching parts having a temperature of 800-
1000oC in cold water or water solutions. At the first
glance, one thinks that the film boiling stage during
such condition must exist. However, in many cases
film boiling is absent due to the following reasons:
• Prior to boiling, the cold liquid should be heated
to the saturation temperature. During this period
of time, the temperature of the steel part surface
decreases almost to the saturation temperature
due to a very high value of the specific heat of
water and aqueous salt solutions [1].
• When quenching in water and aqueous salt
solutions, a double electrical layer is established
between the part surface and the quenchant,
which eliminates film boiling [1].
• Recent studies show that initial heat flux density
from the part surface to the quenchant at the
very beginning of immersion is a finite value
that is often less than the first critical heat flux
density [1, 2].
• Computational fluid dynamics (CFD) modeling
has shown that during quenching in an agitated
water, the temperature of the boundary layer
remains below the saturation temperature [2].
• It has been discovered that the shock boiling
increases the critical heat flux density and the
part surface superheat [1].
Recent Advances in Fluid Mechanics, Heat & Mass Transfer and Biology
ISBN: 978-1-61804-065-7 94
• Acoustical analyses have provided evidence that
the film boiling is absent [3].
These all factors show that film boiling can be
absent in many cases. When film boiling is absent
the cooling curve and cooling rate look like it is
shown in Fig. 1 below (see curve 1).
Fig. 1 Cooling rate vs. surface temperature: 1, film
boiling is absent; 2, cooling rates of a silver
spherical probe of 20-mm diameter after immersion
in still water at different temperatures when film
boiling exists [1].
2. Procedures for the evaluation of
the critical heat flux density and
Grossmann factor H
A procedure for the evaluation of the critical heat
flux density and Grossmann factor H is as follows.
To evaluate critical heat flux densities, the full film
boiling mode of heat transfer must exist and a
transition from the film boiling to nucleate boiling
must be clearly seen (see Fig. 1 curves 2). For
example, for water of 40oC the transition from film
boiling to nucleate boiling occurs at the temperature
of 325oC when the cooling rate is 118
oC/s.
Knowing these data, it is possible to evaluate the
first and second critical heat flux densities using the
following equations [1, 4]:
vS
V
aqcr
λ=2
(1)
2.01
2 ≈cr
cr
q
q (2)
Where 1crq is the first critical heat flux density
(W/m2); 2crq is the second critical heat flux density
(W/m2); λ is heat conductivity (W/m K); a is
thermal diffusivity (m2/s); V is a volume of the
probe (m3); S is a surface of the probe (m
2); v is an
average cooling rate of the probe (oC/s). The ratio
V/S for a spherical probe is R/3, where R is a radius
of the sphere. The heat conductivity and thermal
diffusivity of the material should be taken at the
transition temperature from film boiling to nucleate
boiling. In our case, it is 325oC. The thermal
properties of silver and Inconel 600 are provided in
Table 1 and Table 2.
Table 1 Thermal conductivity of silver, AISI 304
steel and Inconel 600 in W/m K vs. temperature
(oC)
Temperature 100 200 400 600 800
Silver 410 372 365 353 340
AISI 304 13.1 17.6 21 23.6 25.2
Inconel 600 13 16 19.7 23.7 28
Table 2 Thermal diffusivity of silver, AISI 304
steel and Inconel 600 in m2/s vs. temperature (
oC).
Temperature 100oC 200 400 600 800
oC
Silver, 410−× 1.7 1.6 1.52 1.39 1.25
Steel 304, 610−×
4.55 4.63 4.95 5.65 6.19
Inconel 600, 610−×
3.7 4.1 4.8 5.4 5.8
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Having thermal properties of silver, it is very easy to
determine critical heat flux densities by using silver
probes. As an example, let’s consider a spherical
probe of 20mm diameter. Some experimental data
are presented in Fig. 1. Let’s calculate critical heat
flux densities for the water at 20oC. As one can see
from Fig. 1, the cooling rate of the spherical silver
probe is 161 oC/s when cooling in water at 20
oC.
For these conditions, the transition from film boiling
to nucleate boiling occurs at 400oC. The thermal
properties of silver at this temperature are as
follows: mK
W365=λ and
s
ma
241052.1 −×= and their
ratio is 8.315,401,2=a
λ . For the spherical probe of
20mm diameter, the ratio V/S is
.003333.03
01.0
3m
R
S
V===
According to the obtained data and Eq. (1), the
critical heat flux density 2crq is equal to
.3.577,288,1161003333.08.315,401,222
m
Wqcr =××=
According to Eq. (2), .44.6
2.0 2
21
m
MWqq crcr ==
Similar calculations can be conducted for the water
at the temperature of 40oC where cooling rate is 115
oC/s and
mK
W371=λ ;
s
ma
24106.1 −×= ;
.485,248,2=a
λ
Following the same procedure as described above,
we obtain: 22 888.0
m
MWqcr = and
21 44.4m
MWqcr = .
Let’s compare obtained results with the data which
can be derived from the equations of Tolubinsky and
Kutateladze [5, 6]. Some results of the comparison
are shown in Table 3.
Table 3 Comparison of 1crq [MW/m2] obtained by
author’s method and equations of Tolubinsky and
Kutateladze [5, 6]
Underheat,
oC
20 40 60 80 100
Tolubinsky 2.40 3.57 4.72 5.90 7.06
Kutateladze 2.25 3.33 4.3 5.5 6.6
Authors - - 4.44 6.4 -
In practice, it is necessary to quantify quenching
conditions. A parameter used by heat treaters for
this purpose is the Grossmann quench severity factor
H. The H value is determined from hardness
measurements of a series of cylinders quenched in
oil or water like those shown in Fig. 2 and Fig. 3. In
the chart shown in Fig. 2, the Du/D values on the y-
axis represent a ratio of the diameter of the center
portion that remains unhardened (Du) to the full
diameter (D) for several of the bars of the cylinder
series. Measured values of Du/D can be plotted
against the D values on a transparent paper with the
same coordinates. Some results of such an approach
are provided in Table 3 [7].
Fig. 2 Chart for estimating Grossmann H values
from a cylinder series [7].
Fig. 3 Hardenability depending on cylinder size
[7].
Recent Advances in Fluid Mechanics, Heat & Mass Transfer and Biology
ISBN: 978-1-61804-065-7 96
From the Grossmann method consideration, it
follows that D
Duis a function of a temperature
gradient in the cylindrical specimen during its
quenching, which is characterized by the Grossmann
factor H. On the other hand, the temperature gradient
in the cylindrical specimen is a function of the
generalized Biot number BiV [8, 9]:
( )1437.1
12 ++
=−
−
VVmV
msf
BiBiTT
TT (3)
It means that the ratio D
Du is a function of the
generalized Biot number BiV. Taking this
consideration into account, the authors [10] came to
the conclusion that the generalized Biot number BiV
and Grossmann factor H are the same value.
Let’s assume that this conclusion is true. Then
equation (4) can be used for calculating the HTC
(see Table 4) [10]:
D
Hλα
783.5= (4)
For Grossmann factor H = 0.25:
Km
W2
590,1020.0
25.022783.5=
××=α
For Grossmann factor H = 0.30:
Km
W
m
mK
W
2908,1
020.0
3.022783.5
=
××
=α
These results of calculations are in very good
agreement with the results of solving an inverse heat
conduction problem and of the Kondratjev method
of calculation shown in Fig. 4.
During quenching of cylindrical probes of 20 mm
diameter in water (H=0.9), the heat transfer
coefficient (HTC) is equal:
Km
W
m
mK
W
2724,5
020.0
9.022783.5
=
××
=α
This value of HTC agrees well with the data
presented in Fig. 6 (see curve 1).
According to Grossmann, during quenching of
cylindrical probes of 20 mm diameter in brine
solutions, the HTC is equal:
Km
W
m
mK
W
2720,12
020.0
222783.5
=
××
=α
These results correlate well with the results
presented in Table 3.
According to Grossmann, for a violent agitation, the
HTC can be:
Km
W
m
mK
W
2800,31
020.0
522783.5
=
××
=α
This value of HTC can be achieved in high
velocity quench systems during quenching of steel
parts in water flow of about 7 – 8 m/s [1].
Table 4 Original Grossmann’s factor H
depending on type of quenching and severity of
agitation [7]
Agitation
Oil Water Brine
None 0.25–0.3 0.9 – 1.0 2.0
Mild 0.30–0.35 1.0–1.1 2.0–2.2
Moderate 0.35–0.4 1.2–1.3 —
Good 0.4–0.5 1.4–1.5 —
Strong 0.5–0.8 1.6–2 —
Violent 0.8–1.1 4.0 5.0
Developed method of calculations allows engineers
to use Grossmann factors H to develop recipes for
conventional and intensive quenching processes and
can be also used during designing of quenching
systems. For getting more detail information on
quenching processes, conducting of accurate
experiments are needed where temperature is
measured on the part surface or near the surface . By
solving an inverse heat conduction problem, it is
possible to evaluate a real HTC. The obtained
values of HTC can be used for calculations of
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ISBN: 978-1-61804-065-7 97
temperature fields and residual stresses to optimize
quenching processes.
Fig. 4 HTC vs. surface temperature for oil MZM-16
at 61oC: 1 is HTC as a function of the surface
temperature received by solving an inverse problem;
2 is an average effective HTC received by
Kondratjev method [1].
Fig. 4 Windows for software IQ Manager.
The Grossmann factor H can be calculated using a
theory of regular conditions since the generalized
Biot number in the regular area can be calculated
from the following equations [1, 8, and 9]:
( )mTTK
aKnv −= (5)
( ) 5.021437.1 ++
=
VV
V
BiBi
BiKn (6)
Table 5 Universal correlation VBiKn ψ= of
regular condition theory.
VBi ψ Kn VBi ψ Kn
0.00 1 0 1.8 0.38 0.69
0.10 0.93 0.093 2.00 0.36 0.71
0.20 0.87 0.174 3.00 0.26 0.79
0.30 0.81 0.24 4.00 0.21 0.84
0.40 0.76 0.304 5.00 0.17 0.87
0.60 0.69 0.385 6.00 0.15 0.89
0.80 0.60 0.48 7.00 0.13 0.90
1.00 0.54 0.54 8.00 0.11 0.915
1.2 0.49 0.59 10.0 0.093 0.93
1.4 0.45 0.63 50.0 0.019 0.986
1.6 0.41 0.66 100 0.0099 0.993
On the basis of the theory of the regular thermal
condition, a software IQ Manager was developed by
Intensive Technologies Ltd. of Kyiv, Ukraine to
calculate the critical heat flux densities and
Grossman factor H. The notion in this software is
that there is no need to evaluate a point of the
transition temperature from film boiling to nucleate
boiling and a maximum cooling rate during
quenching. The Grossmann factor evaluation
approach is very effective for intensive quenching
Recent Advances in Fluid Mechanics, Heat & Mass Transfer and Biology
ISBN: 978-1-61804-065-7 98
when a “direct convection” method of cooling is
applied [1, 11, 12]. During a nucleate boiling
process, the Grossmann factor H takes into account
an effective HTC, which is an average value. The
average HTC can be used for calculations of the
cooling rate, cooling time at the core temperature of
steel parts [1, 2]. The Grossmann factor H is
calculated using data from the experiment at the
point (a) and point (b) as shown in Fig. 1 (see curve
1). The main goal of the joint project initiated by IQ
Technologies, Idemitsu Kasan Co., Ltd. and
Intensive Technologies, Ltd is developing special
additives to different kinds of quenchants to
eliminate local film boiling and full film boiling
during quenching. Critical heat flux densities should
be included into a global database for different types
of quenchants [3, 13, 14].
3. Summary
1 Methods for calculation of the critical heat flux
densities and Grossmann factor H are proposed and
software IQ Manager is designed to simplify
significantly calculations during testing of
quenchants.
2 The aim of joint investigations is developing
special additives for different types of quenchants to
eliminate full film boiling and local film boiling,
which are major reasons for excessive distortion of
steel parts and low material mechanical properties
after quenching.
References:
[1] Kobasko, N.I., Aronov, M.A., Powell, J.A., and
Totten, G.E., Intensive Quenching Systems:
Engineering and Design, ASTM International,
West Conshohocken, 2010, 252 pages.
[2] Krukovskyi, P.G., Kobasko, N.I., and
Yurchenko, D., Generalized equation for cooling
time evaluation and its verification by CFD
analysis , Journal of ASTM International, Vol.
6, No 5,2009.
[3] Kobasko, N.I., Discussion of the problem on
Designing the Global Database for Different
Kinds of Quenchants, In a book: Recent
Advances in Fluid Mechanics, Heat & Mass
Transfer and Biology, Zemlliak, A., Mastorakis,
N. (Eds.), WSEAS Press, Athens, 2011, pp. 117
– 125.
[4] Kobasko, N.I., Aronov, M.A., Powell, J.A.,
Ferguson, B.L., Dobryvechir, V.V., Critical heat
flux densities and their impact on distortion of
steel parts during quenching, In a book: New
Aspects of Fluid Mechanics, Heat Transfer and
Environment, WSEAS Press, Athens, 2010, pp.
338 – 344
[5] Tolubinsky, V. I., Teploobmen pri kipenii (Heat
transfer at boiling), Naukova Dumka, Kyiv,
1980.
[6] Kutateladze, S. S., Fundamentals of Heat
Transfer, Academic Press, New York, 1963.
[7] Lyman, T.Ed., Metals Handbook: 1948 Edition,
Americal Society for Metals, Cleveland, OH,
1948.
[8] Kondratjev, G.M., Regular Thermal Mode,
Gostekhizdat, Moscow, 1954.
[9] Kondratjev, G.M., Thermal Measurements,
Mashgiz, Moscow, 1957.
[10] Aronov, M.A., Kobasko, N.I., Powell, J.A.,
and Hernadez – Morales, J.B., Correlation
between Grossmann H-Factor and Generalized
Biot Number BiV, Proceedings of the 5th
WSEAS International Conference on Heat and
Mass Transfer (HTM’08), Acapulco, Mexico,
January 25 – 27, 2008, pp. 122 – 126.
[11] Kobasko, N.I., US Patent # 6,364,974B1
[12] Kobasko, N.I., Intensive Steel Quenching
Methods, In a Handbook: Theory and
Technology of Quenching, B.Liscic, H.M.Tensi,
and W.Luty (Eds.), Berlin, Springer – Verlag,
1992, p 367 – 389
[13] Liščić, B., Filetin, T., Global Database of
Cooling Intensities of Liquid Quenchants,
Proceedings of the European Conference on
Heat Treatment 2011, “Quality in Heat
Treatment”, Wels, Austria, 2011, pp. 40 – 49.
[14] Kobasko Nikolai I., Intensive Steel Quenching
Methods, In a book: Quenching Theory and
Technology, Second Edition, Liščić Bozidar,
Tensi Hans M., Canale Lauralice C.F., Totten
George E. (Eds.), CRC Press, Boca Raton,
London, New York, 2010, pp. 509 –568.
Recent Advances in Fluid Mechanics, Heat & Mass Transfer and Biology
ISBN: 978-1-61804-065-7 99