Formulation And Validation Of A Water Air Intercooler

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02 Nov 2017

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Eindhoven University of Technology, Netherlands

Copyright c 2013 Society of Automotive Engineers, Inc.

ABSTRACT

At the TU/e (Eindhoven University of Technology) a

Volvo T5 turbocharged engine set-up is built for research

purposes in the field of alternative fuels and

waste energy recovery. Originally, this Volvo engine

is equipped with an air-air intercooler. Due

to the absence of wind in the engine cell, a waterair

intercooler is used instead, which origins from a

Mercedes-Benz SL55 AMG. For research purposes,

it is desirable to be able to tune the intake air temperature

by means of a control system. This is e.g. interesting

for engine knock studies. As the cooling capacity

is decisive for the intake air temperature of the

combustion engine, the principle objective of this research

is to analyze the cooling capacity of the waterair

intercooler. The ultimate goal is to specify the lowest

intake air temperature at each rotational speed.

This theoretical analysis is based on heat transfer theory

from two different perspectives: the energy content

of the water- and air flow and the heat transfer

rate within the intercooler based on its geometry and

material properties. This analysis is fulfilled by means

of a physical model using the software package MATLAB.

The main result of this analysis is that the intake

air can be reduced with 22.9 K to an intake air temperature

of 310.5 K. From the performed sensitivity analysis

it can be concluded that the results of the initial

model are stable. Nevertheless, due to the assumption

of adiabatic heat transfer, this does not guarantee

the overall reliability of the solution. Hitherto, this

theoretical analysis is limited to one rotational speed,

namely 6000 rpm.

INTRODUCTION

Since many years, intercoolers are used to cool down

compressed air before entering the intake manifold.

In most cases, air is compressed by means of a compressor

which is part of the turbocharger. Due to

irreversible operation of the compressor, air will not

only be compressed but some mechanical power is

converted into heat. This induces a temperature increase

of the air. An increased intake air temperature

increases the tendency for knock and deteriorates the

volumetric efficiency [1]. By cooling the intake air

through the intercooler, also the density is further increased.

The efficiency for an intercooler is defined as the ratio

of the actual heat transfer rate to the maximum possible

(potential) heat transfer rate. [2]

...

METHODOLOGY

The research goal of this paper is to determine the

cooling capacity of the Mercedes-Benz SL55 AMG

water-air intercooler (Figure 1) and to analyze the influence

of different parameters on the intercooler outgoing

air temperature.

A physical model has been made using formulae

and correlations related to the specific intercooler

type. Using equation balances, the outgoing air temperature

can be calculated when input values are

given. Accordingly, a sensitivity analysis has been

1

Figure 1: Render of the Mercedes-Benz SL55 AMG

water-air intercooler

performed to validate the reliability and robustness of

the model.

INTERCOOLER CLASSIFICATION

An intercooler can be interpret as a heat exchanger.

Heat exchangers are usually classified by flow arrangement

and construction type. For modeling purposes,

it is important to distinct the different types of

heat exchangers for applying the right formulae and

correlations [3, 4, 5].

Figure 2: Intercooler classification by flow arrangement

In Figure 2 and 3 the intercooler is classified by flow

arrangement and construction respectively. From this

classification it is concluded that the heat transfer theory

applied must be applicable for a (recuperative indirect)

plate-fin-tube multi pass cross flow heat exchanger

(i.e. intercooler).

THEORY & ANALYSIS

The analysis starts with a theoretical approach. In

Figure 4 below a schematic overview of the intercooler

with associated in- and outgoing flows is displayed

Figure 3: Intercooler classification by construction

T1 = Tin,air T2 = Tout,air

T3 = Tin,water T4 = Tout,water

Figure 4: Schematic overview intercooler and flows

In this heat exchanging process the heat is transferred

from the air flow to the water flow. Assumptions made

for this theoretical analysis are:

_ The heat exchange process is only between the

hot gas and cold fluid. This means there is no

heat loss to the surroundings, i.e. adiabatic heat

transfer process. The red line in Figure 4 indicates

the boundary of the heat exchange process.

_ Potential and kinetic energy changes are negligible.

The heat transfer rate q that occurs in the intercooler

can be described by its overall heat transfer coefficient

and the heat exchanging surface.

q = U _ A _ _Tlm (1)

In this relation U describes the overall heat transfer

coefficient, A the cooling surface, and _Tlm the logarithmic

mean temperature difference. Both factors,

2

U and A depend on the intercooler geometry and the

flow through the intercooler, while _Tlm exists as a

boundary condition. The analysis for the total heat

transfer rate q is divided in two parts. First the term

U _ A will be analyzed. Subsequently, the quantity

_Tlm will be regarded and finally, the fluid flows and

conservation of energy will be treated.

OVERALL HEAT TRANSFER COEFFICIENT

The product of U and A is used to describe the overall

thermal resistance.

Rtot =

X

Rt =

1

UA

(2)

For the specific heat exchanging process of the intercooler

this relation can be written as

1

UA

=

1

(_0hA)water

+ Rw +

1

(_0hA)air

(3)

in which the first term of the right hand side represents

the inverse of the convective heat transfer coefficient

between the intercooler and water flow and the

last term of the right hand side the inverse of the convective

heat transfer coefficient between the air flow

and the intercooler. Both terms are derived from the

relation for convective heat transfer for fin-equipped

applications.

q = _0 _ h _ A _ (Tb ô€€€ T1) (4)

In this relation Tb and T1 represent the base temperature

and the surroundings temperature respectively.

The quantity _0 is known as the overall surface efficiency,

which will be explained later on.

The middle term of the right hand side from Equation

3 represents the conductive heat transfer coefficient

of the wall that separates the air and the water flow

(the tube). All three terms can be regarded as a thermal

resistance for their specific mechanism of heat

transfer. The different mechanisms of heat transfer

are displayed in a schematic overview of a random

finned-pipe configuration.

In the lower right part of Figure 5 the convection from

the hot air to the outer tube wall is illustrated, in the

upper part the conduction from outer to inner tube

wall, and in the lower left part the convection from the

inner wall to the cooling water.

Figure 5: Schematic overview heat exchange for

finned tube configuration

During normal heat exchanger operation, surfaces

are often subject to pollution or fouling. Sources for

fouling can be reactions between the fluid and the

heat-exchanging wall material. Most common form is

rust formation. Also fluid impurities contribute to fouling

[2]. Fouling leads to a film on the surface which

can greatly increase the resistance to heat transfer

between the fluids. To include fouling in the model, an

additional thermal resistance is introduced in Equation

3, called the fouling factor Rf . This leads to

1

UA

=

1

(_0hA)water

+

R"

f;water

(_0A)water

+ Rw+ (5)

R"

f;air

(_0A)air

+

1

(_0hA)air

wherein the thermal conduction resistance term Rw

(for circular tubes) is defined as

Rw = Rt;cond =

ln (r2=r1)

2_Lk

(6)

in which r2 is the outer radius, r1 the inner radius, L

the length, and k the thermal conductivity of the tube.

As stated earlier, the quantity _0 in Equation 5 is the

overall efficiency of a finned surface. It is defined as

_0 = 1 ô€€€

Af

A

_ (1 ô€€€ _f ) (7)

where Af =A is the ratio between the fin surface and

3

total surface. The fin efficiency for rectangular fins is

defined as

_0 =

tanh (mL)

mL

(8)

where m = (2h=kt)1=2. In Equation 8 t is the fin thickness,

k the thermal conductivity of the fins, and h the

convection heat transfer coefficient from the flowing

air to the fins. The convection heat transfer coefficient

is now the only uncertain parameter in Equation 5.

To determine the value of this parameter the Sieder-

Tate and Dittus-B ¨ olter correlations must be used [6].

Both correlations calculate the Nusselt number. By

means of the Nusselt number the corresponding convection

heat transfer coefficient can be determined.

The above mentioned correlations must be applied to

a laminar and turbulent flow respectively. A laminar

flow is characterized by a Reynolds number smaller

than 2300 (Re < 2300) and a turbulent flow by a

Reynolds number larger than 10000 (Re > 10000).

After several manipulations and substitutions, which

can be read over in the Appendix, the correlations for

the convection heat transfer coefficient for both laminar

and turbulent case end up in

hlaminar =

(

k _ 1:86 _

_

De _ ReDe _ Pr

L

_1

3

)

=De

(9)

hturbulent =

n

k _ 0:023 _ Re

4

5D

e

_ Prn

o

=De:

From the Equations 2 up to 9 the factor U _ A can be

determined. In the following subsection, the logarithmic

mean temperature will be regarded.

LOGARITHMIC MEAN TEMPERATURE DIFFERENCE

The logarithmic mean temperature difference can be

expressed as

_Tlm = F _

_T1 ô€€€ _T2

ln (_T1=_T2)

(10)

= F _

T1 ô€€€ T3 ô€€€ T2 + T4

ln ([T1 ô€€€ T3] = [T2 ô€€€ T4])

More details about the derivation of Equation 10 can

be found in [2]. The correction factor in Equation 10

is the result of the fact that the initial correlation of

_Tlm (without correction factor) is derived from a parallel

flow arrangement. For a cross flow or other than

parallel configuration, the correction factor should be

used [6]. The correction factor can be determined

graphically from a correction factor chart. The factor

is dependent on temperatures of the in- and out flows

of the intercooler.

CONSERVATION OF ENERGY

For the prediction of the performance of a heat exchanger,

it is necessary to relate the total heat transfer

rate to quantities such as the overall heat transfer

coefficient, the inlet and outlet fluid temperatures, and

the total surface area for heat transfer. Partly this is

satisfied with equations above. However, those were

only applied to the equipment itself, not to the fluid

flows. The required relations can be obtained by applying

an overall energy balance to the hot and cold

fluids [2]. For the air and water flow this leads to

qair = m_ air (i1 ô€€€ i2) (11)

qwater = m_ water (i4 ô€€€ i3) :

In Equation 11, i denotes the specific enthalpy of the

fluid.

The specific enthalpy is the multiplication of the specific

heat capacity and temperature, which leads to

qair = m_ air (cp;1 _ T1 ô€€€ cp;2 _ T2) (12)

qwater = m_ water (cp;4 _ T4 ô€€€ cp;3 _ T3) :

According to the conservation of energy, the retained

heat of the ingoing air and water flow should be equal

to the retained heat of the outgoing air and water flow.

This means that

qin = qout (13)

m_ air _ cp;1 _ T1 + m_ water _ cp;3 _ T3 =

m_ air _ cp;2 _ T1 + m_ water _ cp;4 _ T4

m_ air _ (cp;1 _ T1 ô€€€ cp;2 _ T2) =

m_ water _ (cp;4 _ T4 ô€€€ cp;3 _ T3)

The difference in heat (i.e. energy) content, for each

4

of the fluids (air and water), between ingoing and outgoing

flow described in Equation 13 should equal the

heat transferred in the intercooler described in Equation

1.

qtransferred = _qair = _qwater (14)

U _ A _ _Tlm = m_ air _ (cp;1 _ T1 ô€€€ cp;2 _ T2)

With Equation 13 and 14 the heat transfer problem

can be solved for the outgoing temperatures T2 and

T4. The Equations were solved using the software

package MATLAB. However, many parameters required

to calculate U _ A are temperature dependent.

Therefore, fluid property data from the NIST (National

Institute of Standards and Technology) database was

used to implement the temperature dependence [7].

The intercooler ingoing air temperature is the compressor

outgoing air temperature and can be calculated

using the relation from the book of Hiereth [8].

The increase in temperature in the compressor depends

on the pressure ratio selected and on the compressor

efficiency which was estimated 0.7.

T1 = Tamb

(

1 +

1

_C

"_

pamb + pover

pamb

_(_ô€€€1)=_

ô€€€ 1

#)

(15)

In Equation 15, _C is the compressor efficiency, _ the

heat capacity ratio, and pover the over pressure with

respect to the ambient pressure pamb.

The heat capacity ratio is also dependent on temperature,

however its value ranges from 1.4035 to 1.3983

using the NIST database. Due to this insignificant

change its value is fixed at 1.4. Some other important

input parameters are listed in Table 1.

Table 1: Model input parameters

Value Unit

Cylinder volume 2.5x10ô€€€3 [m3]

Compressor efficiency 0.7 [-]

Maximum over pressure 0.38 [bar]

Heat capacity ratio 1.4 [-]

Ingoing water temperature 285 [K]

Mass flow water 0.7 [kg/s]

In the following section, the model results will be presented

and discussed.

RESULTS & DISCUSSION

First, model results will be presented using the input

parameters listed in Table 1. Accordingly, some of

these parameters will be varied to analyze the effect

on the outgoing air temperature and cooling capacity.

Finally, a sensitivity analysis will be performed on the

geometrical intercooler quantities.

MODEL RESULTS

The model results with above mentioned input parameters

are listed in Table 2.

Table 2: Model input parameters

Value Unit

T1= Tin;air 333.3 [K]

T2= Tout;air 310.5 [K]

T4= Tout;water 286.7 [K]

_Tair -22.9 [K]

_Twater +1.7 [K]

U _ A 156.5 [W/K]

q 4.58x103 [W]

It is obvious that the air temperature decrease of -22.9

K is obtained with a water temperature increase of

only +1.7 K. This has among other things to due with

the much higher heat capacity from water compared

to air. Furthermore, the maximum cooling capacity

from the intercooler reaches up to nearly 5 kW.

Compressor efficiency The compressor efficiency

is uncertain for the specific system to be

investigated. In literature it can be found that on

average this value is between 60 and 75 %. For this

reason the examined domain is set on the average

domain _ 10 %. This means between 50 and 85 %.

The results for the outgoing air temperature and the

associated _Tair are presented in Figure 6 and 7.

In Figure 6 it is obvious that the outgoing air temperature

decreases with increasing compressor efficiency.

This is not due to an increased _Tair over the

intercooler, as this quantity decreases for increasing

compressor efficiency (Figure 7). The reason can be

found in Figure 8. From this Figure it is obvious that

the outgoing air temperature of the compressor (ingoing

air temperature of the intercooler) decreases for

increasing compressor efficiency. This means that a

lower compressor efficiency results in a larger temperature

difference between the water and air flow

which results in a larger heat flux and thus cooling

capacity (Figure 9) .

5

0.5 0.55 0.6 0.65 0.7 0.75 0.8

308

310

312

314

316

318

Air Temperature Out Intercooler [K]

Compressor Efficiency [−]

Figure 6: Air temperature out intercooler as function

of compressor efficiency

0.5 0.55 0.6 0.65 0.7 0.75 0.8

−30

−28

−26

−24

−22

−20

Delta T Air Intercooler [K]

Compressor Efficiency [−]

Figure 7: Delta T air intercooler as function of compressor

efficiency

These two contradictory effects, however, do not compensate

each other. The net effect results in a lower

outgoing air temperature for a higher compressor efficiency.

Therefore, a higher compressor efficiency has

a positive effect on the intake air temperature of the

engine.

Ingoing temperature cooling water The ingoing

temperature of the cooling water ranges from 277 up

to 293 K depending on the season. In Figure 10 the

result of the variation in this temperature is presented.

From this result it can be concluded that an increase

in the water ingoing temperature results in a proportional

higher outgoing air temperature. In other words,

they are linear related. Due to the decrease of temperature

difference between the water and air flow the

cooling capacity becomes smaller too [Add Figure

0.5 0.55 0.6 0.65 0.7 0.75 0.8

330

335

340

345

Air Temperature In Intercooler [K]

Compressor Efficiency [−]

Figure 8: Air temperature in intercooler as function of

compressor efficiency

0.5 0.55 0.6 0.65 0.7 0.75 0.8

1.2

1.3

1.4

1.5

1.6

1.7

1.8

x 104

Cooling Capacity [W]

Compressor Efficiency [−]

Figure 9: Cooling capacity as function of compressor

efficiency [VERIFY FIGURE!!!]

appendix].

Mass flow water The water mass flow is freely adjustable

in the engine set-up. However, the maximum

value of the water mass flow is unknown. This is dependent

on the head and the pressure drop of the integrated

cooling system. However, with the model the

variation of different quantities can be analyzed for a

varying water mass flow.

Looking at Figure 11, the most interesting phenomenon

in this analysis is the non linearity of the

trend lines. It can be seen that the _Tair tends to approach

an asymptote (for _Twater the same holds). In

other words from a certain mass flow (approximately

0.9 kg/s) the air temperature does not decrease significant

anymore regardless an increase of the water

6

280 285 290

308

309

310

311

312

313

Air Temperature Out Intercooler [K]

Water Temperature In Intercooler [K]

Figure 10: Air temperature out intercooler as function

of water temperature in

0.2 0.4 0.6 0.8 1 1.2

−24

−22

−20

−18

−16

−14

−12

Delta T Air Intercooler [K]

Mass Flow Water [kg/s]

Figure 11: Delta T air intercooler as function of mass

flow water

mass flow. The reason for this phenomenon is the increase

of the heat transfer convection coefficient for

an increasing mass flow of water.

As can be seen in Figure 12 this increase is linear.

However, the fifth factor of U _ A is inversely proportional

with h. This causes the _Tair to tend to an

asymptote. In Figure 13 and 14 this is plotted for both

the first factor of U _ A as for U _ A total (Equation 5).

SENSITIVITY ANALYSIS

To validate the reliability and robustness of the model

for the intercooler outgoing air temperature (i.e. intake

air temperature engine), the values for the geometrical

quantities of the intercooler (Table 3) are varied

with _10, _20, and _40 %. In this analysis only one

value is changed at a time, while all other parameters

0.2 0.4 0.6 0.8 1 1.2

0.5

1

1.5

2

2.5

x 104

Convection Heat Transfer Coefficient [W/m2K]

Mass Flow Water [kg/s]

Figure 12: Convection heat transfer coefficient as

function of mass flow water

0.2 0.4 0.6 0.8 1 1.2

0.5

1

1.5

2

x 10−3

1st factor U A [W/K]

Mass Flow Water [kg/s]

Figure 13: 1st factor U _ A as function of mass flow

water

0.2 0.4 0.6 0.8 1 1.2

125

130

135

140

145

150

155

160 U



A

[

W/K]

Mass Flow Water [kg/s]

Figure 14: U _ A as function of mass flow water

7

are kept fixed to the value of the initial model treated in

the first part of this section. In this way the sensitivity

of a specific quantity can be analyzed. An important

note is that some quantities are dependent on each

other (e.g. Aw is dependent on Lp and r1). Furthermore,

in reality a situation can occur that two changes

compensate each other due to opposite effects on the

outgoing air temperature. For this reason Aa and Aw

are considered separately from the other quantities in

Table 3.

Table 3: Model input parameters

Geometrical quantity Unit

t Fin thickness [m]

r1 Inner radius tube [m]

r2 Outer radius tube [m]

La Length air channel [m]

Lp Length water channel [m]

Lf Length fins [m]

Aa Air contact surface [m2]

Aw Water contact surface [m2]

Considering the results in Figure 15 from the above

described analysis it can be concluded that the initial

solution is rather stable.

t r1 r2 L_a L_p L_f A_a A_w

305

310

315

320

Changed Quantities

Air Temperature Out Intercooler [K]

+10%

+20%

+40%

−10%

−20%

−40%

Figure 15: Results sensitivity analysis on outgoing air

temperature intercooler

The absolute differences that occur in the outgoing air

temperature are maximum 1.5 K for a relative geometric

change of 10 %. This 1.5 K temperature change

holds for Aa. As said before, Aa and Aw are composed

of the quantities listed previously. This means

that theoretically a 10 % deviation for Aa and Aw is

harder to induce than for the other geometric quantities.

This means that a temperature difference of 1.5

K is not plausible.

It must be taken into account that a combination of deviations

is much more likely to occur than only value

at a time. It is also possible that a combination of

deviations for the assumed values leads to a larger

increase or decrease of the outgoing air temperature.

This leads to infinite many possibilities to analyze.

However, although not analyzed, larger deviations

than a few degrees should not be expected for

_10 %.

The results for _20 and _40 % show more or less

a similar trend than for _10 %. The quantities show

the same relative changes in output for different input

values. The most sensitive quantity is Aa, the total

contact surface of the air. The least sensitive quantity

is the outer radius r2. It hardly affects the outgoing air

temperature, even not for _40 %.

For _20 % the largest decrease in outgoing air temperature

is 2.6 K, the temperature increase amounts

3.3 K. For _40 % values of 4.6 and 7.9 K hold for

the maximum temperature decrease and increase respectively.

These maximum values occur for relative

changes for the most sensitive quantity Aa.

In Figure 16 the same results are presented for the

additional _T. It is the temperature difference between

the initial outgoing air temperature (310.5 K,

Table 2) and the acquired outgoing air temperature

following from the sensitivity analysis.

t r1 r2 L_a L_p L_f A_a A_w

−6

−4

−2

0

2

4

6

8

Changed Quantities

Delta T Air Intercooler [K]

plus 10%

plus 20%

plus 40%

minus 10%

minus 20%

minus 40%

Figure 16: Results sensitivity analysis on Delta T air

intercooler

It can be be concluded that the sensitivity analysis is

suitable to use for analyzing the effect of varying the

value of a single quantity on the outgoing air temperature.

However, in reality several quantities can change

simultaneously. This can amplify or cancel out the net

effect on the outgoing air temperature. This means

that in practise the outgoing air temperature can ex-

8

ceed the upper or lower values presented in Figure 16

and that this analysis can not be interpret as an error

analysis.

CONCLUSIONS

_ It is determined that the considered intercooler

can be classified as a (recuperative indirect)

plate-fin-tube multi pass cross-flow heat exchanger.

This classification is important because

it justifies the used formulae and correlations.

_ From the initial model parameters it can be concluded

that the cooling capacity is about 4.6 kW

and that the air temperature can be decreased

with 22.9 K to an outgoing air temperature of

310.5 K. However, the uncertainties concerning

the compressor efficiency (0.5 to 0.85), ingoing

water temperature (278 to 293 K), and water

mass flow (0.1 to 1.2 kg/s) result in outgoing air

temperatures of 318 to 307 K, 307 to 314 K, and

323 to 309 K respectively.

_ From the sensitivity analysis on the geometrical

quantities it can be concluded that the contact

surface on the air side is most sensitive, namely

_1.5 K for _10 %, -2.6 K and +3.3 K for _20

%, and -4.6 K and +7.9 K for _40 %. The least

certain geometrical quantity is the length of the

water tube inside the intercooler. The sensitivity

analysis shows that the outgoing air temperature

is rather insensitive to this quantity, only -1.3 K

and +2.2 K for a deviation of _40 %. In general,

it can be concluded that the solution is rather stable.

_ The assumption for adiabatic heat transfer is expected

to lead to a significant, non negligible error

in the estimation of the actual heat transfer or

cooling capacity. To improve the model accuracy,

heat transfer (i.e. radiation and convection) to the

surroundings should be incorporated.

_ In this analysis, the cooling capacity was determined

for one rotational speed. In further investigation

the full rotational speed domain should be

considered.

_ In future research, an experimental analysis

could be carried out to compare, validate and further

improve the model.

REFERENCES

[1] J.B. Heywood. Internal Combustion Engine Fundamentals.

McGraw-Hill, 1988.

[2] F.P. Incropera, D.P. de Witt, T.L. Bergman, and

A.S. Lavine. Introduction to Heat Transfer, 5th edition.

John Wiley & Sons Inc: Hoboken, 2007.

[3] G. Walker. Industrial Heat Exchangers - A Basic

Guide. Hemisphere Publishing Corporation, 1982.

[4] W.M. Rohsenow and J.P. Hartnett. Handbook of

Heat Transfer. New York: McGraw-Hill Book Company,

1973.

[5] E.A.D. Saunders. Heat Exchangers - Selection,

Design and Construction. Longman Scientific and

Technical, 1988.

[6] B.P.M. van Esch and H.P. van Kemenade. Proces

technische constructies. Eindhoven University of

Technology, 2010.

[7] S.R. Turns. Thermodynamics - Concepts and

Applications, 6th edition. Cambridge University

Press: New York, 2006.

[8] H. Hiereth and P. Prenninger. Charging the internal

combustion engine. SpringWienNewYork:

New York, 2003.

CONTACT INFORMATION

Dr. ir. M.D. Boot (Director PI)

Progression Industry

Eindhoven, Den Dolech 2

[email protected]

Ir. R. Dijkstra (Employee R&E)

University of Technology

Eindhoven, Den Dolech 2

[email protected]

T.H. Kingma BSc (Student)

University of Technology

Eindhoven, Den Dolech 2

[email protected]

ACKNOWLEDGEMENTS

The authors would like to express their gratitude towards...

DEFINITIONS/ABBREVIATIONS

NIST National Institute of Standards

and Technology

Re Reynolds number

Nu Nusselt number

9

Pr Prandtl number

De Deborah number



rev

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