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INTRODUCTION

Conventional design of several types of heat exchangers is

well standardized and established. The procedures are mostly

available in handbooks of heat transfer [1-7]. However, these

design procedures might deviate if specific constructional

features or thermal conditions of the media deviate from the

established norms and standards. The overall heat transfer

coefficient is the essential parameter in the evaluation of area

requirement separating both the hot and cold media. These

values in turn determine the number of transfer units. The

thermal resistances on the hot and cold surfaces depend on the

thermo-physical properties of the thermally interacting hot and

cold media. In the heat exchanger under consideration, the

thermo-physical property variations of the engine oil are found

to be dependent on the bulk temperature of oil. In contrast, the

properties of coolant air strongly vary with the altitude of the

flight unlike in the case of a stationery heat exchanger on the

test bed. Thus, special considerations in the design are to be

taken care to accomplish targeted performance and

effectiveness at different air velocities and altitudes of the

plane. The present study is related to a specific heat exchanger

employed in unmanned aircraft of VRDE. The task is the one

related to the reengineering technology of an already working

model of a heat exchanger shown in Plate 1.

For a cross flow heat exchanger with both streams unmixed,

the effectiveness, can be predicted from the following

available empirical equation (1) available in the literature [4]

22.0

78.0

1)(

1)exp(

exp1 NTUC

NTUC

(1)

where the Number of Transfer Units is defined as,

NTU=

min

C

UA (2)

max

min

C

C

C (3)

Cmin is the minimum of cchh mCmC :

& Cmax is maximum of

cchh mCmC :

In the conventional design of cross flow heat exchangers

available in the hand books the surface area ‘A’ for both hot

and cold fluids is more or less the same. In a previous attempt

[9], the authors investigated the case of a stationery radiator

and the effectiveness parameters are obtained as functions of

system variables. It is found that by varying the fin

effectiveness ratio, the predictions from the model agree

reasonably with the results from Equation 1of the hand book .

However, the present study is mainly devoted to the case of an

unmixed heat exchanger for cooling the engine oil flowing at

high values ranging from 90 – 140 0C at different altitudes of

the flight of an aero-engine.

Description of the oil cooled heat exchangers

The heat exchanger to be analyzed is an air cooled compact

heat exchanger of cross flow type with triangular plate fins on

air side ducts sandwiched between narrow rectangular

passages of hot engine oil. The ambient air is made to flow at

right angles to flow of the engine oil as can be seen from Fig.

1. The dimensions of the heat exchanger under study are as

follows:

Particulars of hot fluid channels

Number of engine oil channels=10

Equivalent diameter of rectangular channel mmD

P

Ah

h

h7.4

4

Length of the channel from header to header=180mm

3.387.4/180

h

h

D

L

Total surface area of the engine oil ducts=0.15 m2

ANALYSIS OF ENGINE OIL COOLER OF AN UNMANNED AERO-ENGINE AT

VARIOUS ALTITUDES

P.K.Sarma1*, D.Radha Krishna2, C.P.Ramanarayanan2, V.DharmaRao3, V.Srinivas1

1GITAM University, Visakhapatnam, INDIA

2Vehicle Research & Development Establishment, Ahmednagar, INDIA,

3GVP College of Engineering, Visakhapatnam-530048, INDIA

*Corresponding author, Email: sarmapk@yahoo.com

ABSTRACT

The present analysis is essentially a theoretical approach to establish the performance characteristics of engine oil cross

flow heat exchanger with cold air as the unmixed coolant at different altitudes of the flight. The present configuration of the

heat exchanger is a specific case being used by Vehicle Research Development Establishment (VRDE). The study takes

into account the thermo- physical property variation of engine oil with respect to temperature in the oil ducts. The

predictions from theoretical considerations are compared with the conventional empirical equations available in heat

transfer handbooks. It is observed that the theoretical results related to effectiveness of heat exchanger deviate markedly

from results of computational procedures found in the heat transfer data books. Further, the present analytical approach is

rendered into a dimensionless correlation .The outlet temperature estimates from the analytical study for the engine oil

and cold air at different altitudes agree very satisfactorily with the corresponding values from the proposed correlation

equation.

Key words: Mixed cross flow heat exchanger, property variation, altitude effects on effectiveness

45

Cross section of tube

(for flow of hot fluid)

Height of tube = 2.5 mm

Width of tube = 40 mm

Length of tube = 180 mm

Fin triangle formed by two fins on tube surface

(for flow of cold fluid)

Height of triangle) = 8.5 mm

Base of triangle) = 3 mm

Thickness of fin = 0.5 mm

Side of triangle = 8.63 mm

Number of tubes = 10 Number of fins in a row = 72

Number of fin rows = 12

Dimensions of Tube and Fin triangle

Particulars of air ducts

Total number of air ducts in all rows=780

Equivalent diameter of triangular duct mmD

P

Ac

c

c2

4

Length of the duct=40mm

04.19

c

c

D

LTotal surface area of the oil ducts=0.68m2

Properties of Engine oil

The properties of SAE 20W 40 oil are taken from the available

data books and subjected to regression analysis. The

regression analysis gives correlations for various properties as

a function of temperature for the varying temperature between

the limits 90 to 140 oC.

Density,

=899.75-0.595[T] [kg/m3]

k=0.1473-1.18e-4[T] + 1.309e-7*(T2) [w/m k]

Cp=1798.03+4.076[(T] +1.309e-3*[T2] [j/kg k]

=0.6022-0.01755[T] +1.993e-4[(T2]-1.0198e-6[T3] +1.96e-

9[T4] [kg/m-s]

Table 1. Property variation of Engine oil

T

0C

[kg/m3]

k

[w/m k]

Cp

[j/kg

k]

(m2/s]

[kg/m-

s]

40 876 0.1422 1964 2.41E-

04

0.2111

60 864 0.1407 2047 8.30E-

05

0.0717

80 852 0.1384 2131 3.70E-

05

0.0315

100 840 0.1372 2219 2.00E-

05

0.0168

120 828 0.1349 2307 1.20E-

05

9.94E-

03

140 816 0.1338 2395 8.00E-

06

6.53E-

03

160 805 0.1314 2483 5.00E-

06

4.03E-

03

Properties of air with altitude:

Source of information:

Density, Specific heat, thermal conductivity and viscosity

shown in table 1. are taken from the website named

“www.aerospaceweb.org”

Table 2. Property variation of air at different altitudes

X = Height / 10000

Density (kg/cu.m) = 1.224 – 0.3494 X + 0.03164 X2

Viscosity (kg/m-s) = 10-5 (1.789 – 0.0954 X – 0.00173 X2

Kinetic Temperature (oC) = 14.99 – 19.8 X + 0.008 X2

Pressure (milli bar) = 1.011 – 0.3502 X + 0.03814 X2

Thermal conductivity (W/m-K) = 10-2 (2.533 – 0.1557 X –

0.001474 X2)

Height

ft

Density

kg/m3

Viscosity

kg/m-s

X105

Kinetic

Temp

oC

Thermal

Conductivity

X102

0 1.225 1.7894 15 2.5326

500 1.207 1.7846 14 2.5248

1000 1.189 1.7798 13 2.5170

2000 1.154 1.7702 11 2.5014

5000 1.055 1.7412 5.1 2.4544

10000 0.904

1.6922 -4.8 2.3754

15000 0.771

1.6424

-14.7

2.2957

20000 0.653 1.5917 -24.6 2.2153

25000 0.549 1.5401 -34.47 2.1341

30000 0.459

1.4876

-44.35

2.0522

View of the En

g

ine Oil Heat Exchan

g

er

Dimensions of Tube and Fin triang

le in the oil

46

Cp = 1007 J/kg-K

k = 0.0263 W/m-K

FORMULATION

The following assumptions are made in the formulation of the

problem

1. The wall of the tubes dissipates heat to the triangular

fin geometry under constant wall temperature

conditions.

2. The mean operating temperature of the air ducts will

be slightly at different temperature dependent on fin

efficiency f

of the walls. However, f

in the

analysis is taken as unity.

3. The thermo physical properties of hot fluid i.e. engine

oil are dependent on local bulk temperature .

For the temperature range 60-160 0C the following

relationships hold good for the data of engine oil

taken from [5]

Density=899.75-0.595[T] [kg/m3]

k=0.1473-1.18e-4[T] + 1.309e-7*(T2) [w/m K]

Cp=1798.03+4.076[(T] +1.309e-3*[T2] [j/kg K]

=0.6022-0.01755[T] +1.993e-4[(T2]-1.0198e-6[T3]

+1.96e-9[T4] [kg/m-s]

These relationships are employed in the thermal

modeling of the cross flow unmixed heat exchanger.

The local heat transfer for the hot fluid channel can

be estimated from the relations:

Nuh=1.9656 Gzh

0.333: NuC=1.9656 GzC

0.333 where Gzh

and GzC are estimated as local magnitudes.

4. The flow of the hot and cold fluid correspond to

laminar regime i.e. Rec and Reh <2300.Hence, the

analysis is confined to these practical ranges of

Reynolds number of the heat exchanger under

consideration.

With in the framework of these assumptions, the

enthalpy variation of the medium in the hot channel

can be written by the energy equation as follows:

Hot Fluid

The variation of mean bulk temperature Th of hot fluid at

any location in the hot fluid channel

12

4

hhh

hh

h

hh

hh

Wh

h

TTTwhere

L

z

d

)Z(Gz

)Z(Nu

dz

Cm

Dh

)TT(

dT

(4)

Where

333.0

PrRe86.1)(

h

h

hhh L

D

zNu

Further,

3/2

)(Pr)(Re86.14

)(

)(

h

h

hh L

D

zzx

ZGz ZNu (5)

The term

h

h

hh L

D

zz )(Pr)(Re can be expressed as a

function of

h

h

hh L

D

zz )0(Pr)0(Re

with a factor of

multiplication

)/(

)()0(

)0()(

1hh

p

pTT

zkzC

zkzC

(6)

For engine oil with the aid of data from [5], the

multiplication factor can be expressed as follows

hh

hh

h

hTxTx TxTx

T

T

72

1

7

1

2

110767.210548.11495.0

10767.210548.11495.0

332.45.1787

332.45.1787

(7)

Thus, for constant wall temperature condition equation (4)

becomes highly non-linear and it can be expressed as

follows:

Wh

h

TT dT 4x1.86

h

L

z

d

3/2

1

(8)

where

h

h

hh L

D

zz )0(Pr)0(Re

1

(9)

Cold Fluid (air)

The heat transfer on the cold fluid side can be estimated

from equation

NuC=1.9656 GzC

0.333 (10)

ccccc

c

cc

cc

wfc

CL

z

d

LD

Nu

dz

Cm Dh

TT dT

/PrRe

4

(11)

where

333.0

PrRe86.1

c

c

ccc L

D

Nu

Thus equation (10) can be simplified as follows

wfc

CTT dT

=4x1.86

c

L

z

d

3/2

2

(12)

Where

cccc LD /PrRe

2

(13)

f

is the fin efficiency corresponding to the triangular

ducts through which coolant air is force drafted

Besides, the energy balance between the hot and cold

media should satisfy the condition

hhCC

hhhhcccc mNGmNGwhere

TTCGTTCG

21

211

:

)()(

(14)

Thus, the formulation is complete in respect of evaluation

of the outlet temperatures of hot and cold fluids for given

inlet Reh and Rec

Numerical Method of Evaluation

The following iterative procedure is employed step wise:

1. Qh , Vc , Th(I=1), TC(I=1),Lh/Dh, Lc/Dc and f

are

prescribed

2. Equations (8) and (11) are written in finite

difference form respectively as follows

Whhh TITIITIT )()(86.14)()1( 3/2

1

(15)

WfCCc TITITIT )(86.14)()1( 3/2

2

(16)

Where 1<I<J and J=11 is prescribed and

1

1

J

Th(1) and TC(1) are the hot and cold media at inlet of

heat exchanger.

For an assumed value TW, wall temperature approximately

)1()1(6.0 ch TT

T

h(I=J) and TC(I=J) are determined

from equation (15)and (16)

3. With these computed values the energy balance i.e

equation (14) is verified with error criteria defined as

47

Error= %100

)()1((

)1()((

1

JITITG ITJITG

hhh

CCc (17)

If ERROR< 0.1%, the mean wall temperature TW for

prescribed, f

,Qh, Vc is assumed to converge and

the salient output is printed for the inputs Gh,Gc

,Th(1),TC(I=J) .

4. If convergence is not achieved, a linear interpolation

technique is employed till convergence is obtained

for the prescribed accuracy by following steps 1 to 3.

RESULTS AND DISCUSSION

For the flying ranges of altitudes of aero engine between

0 to 30000ft, the thermo physical properties of air are

evaluated at temperatures from the information

available in the www.aerospaceweb.org / The properties

are rendered into correlations which are subsequently

employed in the programs. Besides the properties of

engine oil are also assessed for the ranges of temperatures

from 60 to 140oC.

Thus following the computational procedure outlined the

heat exchanger effectiveness and other relevant

characteristics are shown plotted in figures 2-11. In

the Figures 2, 3 and 4 the coolant air velocity is altered at

three typical altitudes of 7000ft, 10750ft and 22500ft. The

respective inlet temperatures of coolant respectively at

these altitudes will be -0.1 0C, -6.3 0C and -29.50C. The

effectiveness of the heat exchanger is found to be

profoundly influenced by the altitude of the flight as

evident from figures (5), (6),(7). On the same plots the

effectiveness variations as per the computations from the

heat transfer hand books are also indicated. Evidently, the

deviation between present theoretical study and the

empirical equations of the data book is found to be quite

substantial for identical system parameters. Hence for

design considerations a dimensionless correlation

applicable to the present configuration of the aero heat

exchanger is carried out.

Computer runs are accomplished for wide ranges of Reh,

Rec within laminar ranges for flow conditions of the

media and the data are further subjected to regression

analysis to obtain a correlation as follows.

5643.0

1

0187.0241.0

19.0 ReRe..61.1

hC

UTN (18)

1

is to be computed from equation(1)

The correlation (see plot Fig8) satisfies the analytical

value from the runs with an average deviation of 0.586%

and a standard deviation of 0.724%

The predictions from the correlation (18) agree well with

the theoretical values as evident from figure-9, 10 &

11.The continuous solid line in the plots are from the

theory and the solid symbols are computations from the

correlation[18)

Conclusions

Thus the following conclusions can be arrived from the

analysis.

1. The effectiveness of the heat exchanger will be

affected by the altitude of the flight. It is seen that the

effectiveness increases with the altitude.

2. It is observed that the thermo physical properties vary

with the altitude and hence the effectiveness of the

heat exchanger in turn is also found to be a function

of Reh, Rec, NTU, Cmin/Cmax.

3. The effectiveness of the heat exchanger can be

calculated from equation (18 ) for the particular heat

exchanger.

REFERENCES

1. Kays, W. M., and A. L. London, 1998, Compact Heat

Exchangers, reprint, 3d ed., Krieger, publishing

house.

2. W.M. Rohsnow., J.P. Hartnett. and Y.I. Cho., Hand

book of heat transfer, 3rd Edition, McGraw hill

publications.

3. “Heat exchangers design hand book” edited by Ernst

U. Schlunder, published by Taylor and Francis,

1983.

4. Shah, R. K., and D. P. Sekulic, 2003, Fundamentals

of Heat Exchanger Design, Wiley, Hoboken, N.J.

5. C.P.Kothandaraman and S.Subramanyan ’Heat and

Mass Transfer Data Book’, New Age International

Publishers, New Delhi

6. Webb, R. L., 1994, Principles of Enhanced Heat

Transfer, Wiley, New York.

7. R.K. Shah, A.L. London, in: Laminar Flow Forced

Convection in Ducts, Academic Press Inc., New

York, 1978, pp. 253–260.

8. F.P. Incropera, D.P. Dewitt, in: Introduction to Heat

Transfer, third ed., Wiley, New York, 1996, p. 416,

Chapter 8.

9. P.K.Sarma, D.Radha Krishna,V.Srinivas,V.Dharma

Rao,C.P.Ramnarayananan,

‘An analytical approachto solve a cross flow heat

exchanger for unmixed hot and cold media’ Heat and

Technology ,Vol29.n.1.2011 Italy

Figures

200 400 600 800 1000 1200 1400 1600 1800 2000 2200

0

20

40

60

80

100

120

140 TH1=1300C

TH11

TW WALL TEMPERATURE VARIATION

TC11

TC1=0.10C[ Temp. of cold air ]

ReC

Height of Flight=7000 ft

ReH=80

Fig2. Variation of hot and cold fluid temperatures at height of 7000 ft

Temperature

DACHE1

48

ReC

200 400 600 800 1000 1200 1400 1600 1800 2000 2200

Temperature

-20

0

20

40

60

80

100

120

140

TW Wall temperature

TH1 Hot Fluid temperature at inlet

TH11,Hot fluid temperature at the o utlet

TC1,Cold fluid temperature of air a t the inlet

TC11 Cold fluid temperature at the outlet

Height of the air craft in flight =10,750ft

DACHE2

Fig3: Variation of Hot and cold fluid temperatures at a height 10,750 ft

ReH=80

ReC

200 400 600 800 1000 1200 1400 1600 1800 2000 2200

Temperature

-40

-20

0

20

40

60

80

100

120

140

TW Wall temperature

TH1 Hot Fluid temperature at inlet

TH11,Hot fluid temperature at the outlet

TC1,Cold fluid temperature of air at the inlet

TC11 Cold fluid temperature at the outlet

Height of flight the air craft =22,500ft

DACHE3

Fig4: Variation of Hot and cold temperatures at a height 22,500 ft

REH=80

1e+4 2e+4 3e+4 4e+4

E,Effectiveness of heat exchanger

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Predictions from Equation [ 1 ]

Predictions from Presnt theory

ReC= 500

ReH=100

H,Height of the flight from the ground in feet

TH1=1300C

DACHE4

Fig5: Comparison of Present analysis with Equation from Hand book

1e+4 2e+4 3e+4 4e+4

E,Effectiveness of heat exchanger

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Predictions from Equation [ 1 ]

Predictions from Presnt theory

ReC= 1000

ReH=200

H,Height of the flight from the ground in fee t

TH1=1300C

DACHE5

Fig6: Comparison of Present analysis with Equation from Hand book

1e+4 2e+4 3e+4 4e+4

E,Effectiveness of heat exchanger

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Predictions from Equation [ 1 ]

Predictions from Presnt theory

ReC= 1000

ReH=500

H,Height of the flight from the ground in feet

TH1=1300C

DACHE6

Fig7: Comparison of Present analysis with Equation from Hand b ook

49

Correlation

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

theory

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Fig 8 Validation of the correlation

DACHE7

=1.61 [N.T.U]0.19ReC-0.241ReH-0.0187 10.5642

Average deviation=0.586%

Standars deviation=0.724%

Temperature of engine oil

104

Temperature ,0C

-100

-50

0

50

100

150

Height of flight from mean sea level in feet

temperature of cold air at inlet

Temp. of engine oil at the exit

Temp. of air at the exit

Temp. variation of the wall between hot & cold media

SOLID SYMBOLS - PREDICTIONS FROM CORRELATION EQUATION

SOLID LINE PREDICTIONS FROM THEORY

Fig9 Variation of salient temperatures with height of flight

ReH=100

ReC=2000 DACHE8

Temperature of engine oil

104

Temperature ,0C

-100

-50

0

50

100

150

Height of flight from mean sea level in feet

temperature of cold air at inlet

Temp. of engine oil at the exit

Temp. of air at the exit

Temp. variation of the wall between hot & cold media

SOLID SYMBOLS - PREDICTIONS FROM CORRELATION EQUATION

SOLID LINE PREDICTIONS FROM THEORY

Fig 10 Variation of salient temperatures with height of flight

ReH=500

ReC=2000

DACHE9

Temperature of engine oil

104

Temperature ,0C

-100

-50

0

50

100

150

Height of flight from mean sea level in feet

temperature of cold air at inlet

Temp. of engine oil at the exit

Temp. of air at the exit

Temp. variation of the wall between hot & cold media

SOLID SYMBOLS - PREDICTIONS FROM CORRELATION EQUATION

SOLID LINE PREDICTIONS FROM THEORY

Fig 11 Variation of salient temperatures with height of flight

ReH=300

ReC=1500 DACHE10

ACKNOWLLEDGEMENTS

The team of investigators gratefully acknowledges the

assistance received from VRDE (DRDO) Ahmednagar. The

authors specially thank the President, GITAM University Dr.

M.V.V.S. Murthi and the Vice chancellor GITAM University

Prof. G .Subrahmanyam for their support to R&D activities in

GITAM University

Nomenclature

A Area, m2

c specific heat, kJ/kg K

C Cmin/Cma x Ratio

D Hydraulic Diameter, m

G Total Mass flow rate, kg/s

Gz Greatz Number, Re.Pr.(L/D)

h Heat transfer coefficient , W/m2 K

k thermal conductivity, W/m K

L length, m

MC, MH Mass flow rate of cold and fluid respectively

in each channel, kg/s

N1 Number of cold channels

N2 Number of hot channels

NTU Number of Transfer Units, [UA/Cmin]

Nu Nusselt Number, [hD/k]

P Perimeter, m

Pr Prandtl Number

Q Volume flow rate, LPM

Re Reynolds Number

t Thickness of the fin, m

T Temperature,

0C

W Width of the fin, m

N1 Number of triangular ducts

Z Distance along the length, m

Roman letters

Effectiveness

Efficiency

Subscripts

1 inlet

2 outlet

C cold fluid.

f Fin

h hot fluid

w wall

50