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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
