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].

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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].

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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