The Process of Semi – Axles Quenching is Analysed as a Conjugate Heat

Transfer Problem

P.KRUKOVSKYI1, N.KOBASKO

2, A.POLUBINSKIY

1

1. Engineering Thermal Physics Institute

Zhelyabova 2a, 03113, Kyiv, kruk@i.kiev.ua

2. Intensive Technologies Ltd.

Blwr Wernadskoho 63, off.71, 03142, Kyiv

UKRAINE

nikobasko@yahoo.com , www.itl.kiev.ua

Abstract:- In the paper process of quenching semi-axles in the water flow is considering. The two approaches are

analysed. The traditional approach for the parts thermal state analysis under quenching is based on the Newton’s

sort boundary condition between the solid wall of the parts and fluid surrounding it. In the second approach the

problem solves as a conjugate heat transfer problems (Navie-Stocks equations full set solving) with CFD

(Computation Fluid Dynamics) computer technology, when it is do not need to know the heat transfer coefficients

at the surface of the part. Both approaches and results of calculations were compared and in this way it was shown

that generalized correlation can be used for cooling time calculation. Results of calculations coinside very well. It

means that generalized equation is suitable for express method of calculations.As an example the process of

quenching of semi-axle is considered.

Key- Words: - Quenching, Heat transfer, Conjugate problem, Semi- axles, New technology..

1 Itroduction The simulation of cooling process and stress-strain

state during quenching of semi axles is conventionally

connected with the use of Newton boundary

conditions for heat transfer between the solid surface

and fluid flowing around it. It is very important to

solve this task on the basis of conjugate heat transfer

problems, i.e. solving the full Navier-Stokes and

application of CFD (Computation Fluid Dynamics)

computer technologies, where it is not necessary to

know heat transfer coefficients at the surface of the

part. It is important to compare both approaches to see

how far both calculations differ from each ather. In

our paper CFD analysis was used to calculate cooling

time during quenching of semi-axles which was

compared with the time of quenching calculated by

well known generalized correlation [1]. Such

calculations are needed when applying new method of

quenchind in the practice [2,3]. We continue

discussion the new results of calculations [4]. As a

result we came to conclusion that generalized

correlation can be used as an express or simplified

method of calculation. Results of calculations on the

basis of both approaches are available below. The

tipical quench chamber with automatic control system

for quenching semi- axles in the water flow is shown

on the Fig 1.

Fig. 1, Detailed scheme of quench chamber with

automatic control:

1 half-axles; 2 quench chamber; 3 pressurized water

flow; 4 mechanical drive for half-axles; 5 sensor for

analyzing the process of nucleate and film boiling; 6

sensor for analyzing the portion of transformed

structures by changing the ferromagnetic state; 7

electronic device (amplifier and microprocessor); 8

amplifier

2 Generalized Equations Generalized equation received by author [1] can be

used for cooling time calculation and time of

achieving maximal residul stresses at the surface of

steel parts to be quenched:

Proceedings of the 4th WSEAS Int. Conf. on HEAT TRANSFER, THERMAL ENGINEERING and ENVIRONMENT, Elounda, Greece, August 21-23, 2006 (pp217-220)

Fo Knk Bi

Biv

v

v

=+

+

2095 3867. .lnθ (1)

Kna

K

TT

TT

Bi

Bikt

C

C

v

v

−−

++

= 0ln867.3095.2

. (2)

For deeper understanding of the criterion dependences

(1,2), consider concrete example.

Truck half-axles of 42-mm diameter, made of steel

40G are cooled in a water flow at 20ºC from 860ºC in

a special chamber with a folding cover (Fig. 1). The

inner diameter of the quench chamber is 80 mm. It is

just necessary to calculate the convection heat transfer

coefficient convα.

In the generalized form the equation of similarity for

calculating the heat transfer during convection is as

follows [6, 7]:

esfmuN ε⋅⋅= 25.043.08.0 )PrPr(PrRe021.0 (3)

In our case when quenching long semi-axles 25.0

Pr

Pr

sf

m = 1; eε =1 , and heat transfer coefficients

during convection can be avaluated from the Table 1

as a function of ,12 ddd −=∆ water flow and

water temperature.

Table 1, Convection heat transfer coefficient in a ring

tube ,12 ddd −=∆ W / (m2⋅Κ)

20оС 40

оС W,

m/s 0.02 0.04 0.06 0.02 0.04

0,5 2863 2837 2893 3470 3438

1 4385 4940 5036 6041 5986

2 8680 8601 8769 10519 10422

3 12006 11897 12129 14549 14416

4 15113 14975 15267 18314 18147

5 18067 17902 18251 21893 21693

6 20904 20713 21117 25331 25100

7 23648 23432 23889 28656 28394

8 26314 26074 26582 31886 31595

9 28914 28650 29208 35037 34717

10 31456 31169 31777 38118 37770

Note: d1 is diameter of axle, d2 is inner diameter of

tube.

Table 2, First critical heat flux density versus water

temperature and water flow rate with respect to the

surface to be quenched, MW/m2.

W,

m/s 20

оC 30

оC 40

оC 60

оC

5 7.94 7.18 6.43 4.91

6 9.32 8.44 7.57 5.83

7 10.57 9.59 8.62 6.66

8 11.7 10.63 9.56 7.42

9 12.76 11.6 10.44 8.13

10 13.74 12.51 11.27 8.79

15 17.97 16.39 14.81 11.65

20 21.4 19.56 17.71 14.00

With the increase in water flow, the first critical heat

flux density increases too ( Table 2).

3 Critical Heat Flux Density Critical heat flux density qcr1 for water flow can be

evaluated from the equation (4) [1, 5-9]:

( ) uh

uh

cr WWq ϑ)1(1.0175.08.2 35.05.0

1 −+−= (4)

where W is water speed rate = 8 m/s,

MSuh TT −=ϑ is underheating temperature; Ts is

boiling temperature; Tm Some results of calculations are presented in Table 2.

During intensive quenching film boiling should be

absent. It means that initial heat flux density should be less then the first critical heat flux qcr1 .

Results are fair for ring channels with the width of the

clearance exceeding 1.2 mm.

It is apparent from the tables that with increase of

speed of movement of water the first critical heat flux

density and convection heat transfer coefficient

increase.

4 CFD – Analysis of the Problem and

Comparison The results of calculations based on both approaches

are compared in Table 3. The water was moving from

the left to the wright side of the chamber (see Fig. 1

and Fig. 2 ). The edge of the semi-axles is cooled

faster as compared with the another points of semi-

axles surface. The temperature at the core of the semi-

axles vs. time is shown in Fig. 3. The forehead of the

axle is cooled faster than inverse side of axle, Fig. 3.

Proceedings of the 4th WSEAS Int. Conf. on HEAT TRANSFER, THERMAL ENGINEERING and ENVIRONMENT, Elounda, Greece, August 21-23, 2006 (pp217-220)

There is difference between heat flux densities on

both sides the axle ( see Tables 4 and 5).

Fig. 2, Temperature field distribution at the begining

of cooling in the cylinder and in the fluid at 1 s.

The main task of the presentation is to campare results

of calculations achieved on the basis of CFD –

analyses and Newton’s sort of boundary conditions

through checking equations (1) and (3). It has been

shown that difference between two methods of

calculationa is about 5% (see Table 6). It means that

equation (1) can be used when designing new

equipment for intensive quenching technologies. For

example, equation (1) is used for calculating speed of

conveyors. In this case speed of conveyor is

calculated as W = L/t, where L is length of conveyor

which is moving in a quenchant.

Thus, there is opportunity to use generalized equation

(1) at designing of a governing Software.

Температура серцевины образца для разных расстояний от

лобовой поверхности

0

100

200

300

400

500

600

700

800

900

0 10 20 30 40

Время, сек

Температура, С

0 м

0.3 м

0.6 м

Fig. 3, Temperature vs. time in differents points of

axle

Table 6, Comparison of cooling time calculation

from 860oC to 500,400,300

oC based on CFD-Analysis

and Newton’s boundary condition approaches.

T, oC

t, sec

Eq.

(2)

t, sec

CFD-

Analysis

Error

%

Av.

error

%

500 14.6 14 4.3 -

400 18 17.7 1.7 4.5

300 23.7 22 7.7 -

5 Discussion

The CFD – analysis alows to calculate initial heat flux

densities during immersion of steel parts into

quenchant. By comparison initial heat flux density

with the first critical heat flux density one can predict

of heat transfer modes. If initial heat flux density is

less than the first critical heat flux then full film

boiling will be absent. If initial heat flux density is

higher than the first critical heat flux density then will

be observed full film boiling. When both heat fluxes

are equal then transition boiling could be observed.

This information also is very important for engineers

and designers. For example, at water flow velocity of

8 m/s the initial heat flux density is equal to 11.5

MW/m2 which is less as compared with the first

critical heat flux density which for our case is equal

11.7 MW/m2. Thus, during quenching of semi – axles

film boiling is absent if water flow velocity is within 8

– 10 m/s. The fullfilled calculations and achieved

results coinside very well with the experimental data.

There is no sence to exide flow velocity of 10 m/s

since it will be connected with the cost increasing and

more complicated equipment.

Table 4, Initial heat flux density at the edges of the

semi-axle at time 0.1 sec.

Heat flux density, kW/m2

Value Forehead

surface

Opposite

surface

Maximum,

Minimum 11496 7810.8

Average 10220.4 8917.54

Proceedings of the 4th WSEAS Int. Conf. on HEAT TRANSFER, THERMAL ENGINEERING and ENVIRONMENT, Elounda, Greece, August 21-23, 2006 (pp217-220)

Table 5 Initial heat flux density along the length of

the axle ( at the moment of time 0.1 sec).

Heat flux density, kW/m2 Distance along the

specimen, m Side surface

0 (Edge) 11496.1

0.1 10142.9

0.2 10108.1

0.3 10066.2

0.4 9944.63

0.5 9766.21

0.6 9776.84

6 Summary 1. The process of semi-axles quenching was

analysed on the basis of CFD- analysis and

Newton’s approach (the third boundary

condition). It has been established that there is

a good agreement between both approaches

when during process of quenching convection

prevails or is the main mode.

2. The CFD – Analysis gives more accurate

results concerning the smoothness of cooling

around of steel parts beeing quenched.

3. The CFD – Analysis can predict time and

place where film boiling begins firstly or is

absent entire all surface.

References: [1] N.I.Kobasko, Steel quenching in liquid media

under pressure, Kyiv, Naukova Dumka, 1980,

206p.

[2] N.I.Kobasko, Ukraine Patent #56189

[3] N.I.Kobasko, US Patent # 6,364,974B1

[4] P.Krukovskyi, N. Kobasko, A.Polubinskiy, CFD

– Analysis of a Part Under Quenching as a Heat

Transfer Conjugate Problem, IASME

TRANSACTIONS, Issue 9, Vol. 2, Nov. 2005, pp.

1723 – 1728.

[5] M.A.Mikheev, I.M.Mikheeva, Basics of Heat

transfer (in Russian: Osnovy teploperedachi),

Moscow, Energy, 1977, 344p

[6] V.P.Isachenko, V.A.Osipova, A.S.Sukomel, Heat

Transfer (in Russian: Teploperedacha),

Moscow, Energoizdat, 1981, 417p.

[7] F.Maringer, Thermo - and Fluiddynamic

Principles of Heat Transfer During Cooling. In a

Handbook “Theory and Technology of

Quenching”, B. Liščić, H.M. Tensi, W. Luty

(Eds.), Berlin, Springer-Verlag, 1992, p 41-72.

[8] M.A.Mikheev, Basics of Heat Transfer (in

Russian: Osnovy teploperedachi), Moscow -

Leningrad, Gosenergoizdat, 1949, 396p; 1956,

392p.

[9] М.А.Mikheev, in a Book: Heat Transfer and

Thermal Modeling, Moscow, (in Russian:

Teploperedacha i teplovoe modelirovanie),

Izdatelstvo AN USSR, 1959, p 122-137.

Proceedings of the 4th WSEAS Int. Conf. on HEAT TRANSFER, THERMAL ENGINEERING and ENVIRONMENT, Elounda, Greece, August 21-23, 2006 (pp217-220)