How to chose cooling fluid in finned tubes heat exchanger
G.Grazzini, A.Gagliardi
Dipartimento di Energetica, Via Santa Marta, 3
50139 Firenze, Italy. e-mail: [email protected]
ABSTRACT
A comparison is made between an ice-slurry solution with different inlet ice mass fractions and an
R404a refrigerant utilised in an evaporator with constant heat power and fixed geometry. The
comparison is obtained using a parameter that represents the ratio between the total real entropy
variation and the exchanged heat. This parameter, introduced by Grazzini and Ferraro (2000),
shows that ice-slurry solution is better than a R404a as refrigerant fluid, when considering the
particular heat exchanger.
The used heat exchanger is a finned tube heat exchanger with an in-line tube bank. The results point
out that by the same heat power the ice-slurry entropy variation is lower than that given by R404a.
INTRODUCTION
The necessity to find an alternative to the common refrigerant fluids has led to study different kinds
of secondary refrigerant fluids. In particular two phase refrigerant fluid known as ice-slurry,
composed by water, an additive and small ice crystals.
The presence of ice crystals in the solution allows more cooling energy to be transported per unit of
mass than an usual refrigerant fluid, and that lead to some advantages as to have lower flow rate,
lower pumping power, and smaller piping diameters.
In this work, utilising a finned tube heat exchanger with an in-line tube bank, fixed geometry and
constant heat power, a comparison is made between an ice-slurry solution with different inlet ice
mass fractions and different inlet temperatures, and R404a refrigerant. The parameter, introduced
by Grazzini (Grazzini and Ferraro, 2000) that represents the ratio between the total entropy
variation and the exchanged heat, is used. The results show how total entropy production is
influenced from different ice-slurry inlet temperature, different ice fraction and different ice-slurry
inlet-outlet temperature difference.
1. PARAMETER EVALUATION OF AN ICE-SLURRY
Considering only one stream of a heat exchanger, the parameter, introduced by Grazzini and Ferraro
(2000), is:
T
∆S m& 
=  c p ln out
Q Q
 Tin
 β ⋅ ∆P 

 +

ρ


(1)
where β and ρ are assumed constant along the considered length.
For the particular in line bank finned tube heat exchanger utilised to make the comparison the
geometric and the physical values are reported in table 1 and 2. A constant thermal power Q=1 kW
and a constant inlet-outlet temperature difference of 10°C is assumed on the refrigerated air side.
Under these conditions the external heat transfer coefficient remain constant.
Table1: Geometric specification of heat exchanger
Length
Width
Height
Tube Material
Fin Material
Inside pipe diameter (Di)
Pipe number
Pipe thickness
Number of fins
Fin thickness
Rank Type
Rank Number
1200 mm
420 mm
70 mm
Copper
Aluminium
11,3 mm
20
0.35 mm
171
0.23 mm
In-line
10
Table2:Values of ice-slurry and R404a used to make the comparison
Antifreeze
Ice fraction (Xs)
Ice-slurry (Tout-Tin)
αe
Warm fluid Tin [°C]
R404a Tin [°C]
Ice-slurry Tin [°C]
Methanol
0.2 - 0.15 - 0.10
0.5 - 1- 1.5 – 2 °C
43 (W/m2K)
0
-2
-11
-13
-10.4
-12.4
-5
-16
-15.4
As showed in equation (1) is possible to claim that the ice-slurry entropy variation is given by two
terms, where the first one is a function of the temperature (∆St), and the second one is a function of
pressure losses (∆Sp):
T
∆St = m& c p* ln out
 Tin
∆S p = m&
β
∆p
ρ



(2)
(3)
Where cp* is evaluated as Q/( m& (To-Tin)).The ice-slurry pressure losses (∆p) can be calculated using
the same relation for a liquid solution (Grazzini, 1999, Cavallini, 2000), while the ice-slurry
characteristic parameters, as density (ρsl), dynamic viscosity (µsl) etc., are calculated using Melinder
equations (1997). Figure 1 shows the dependence of the ice-slurr's pressure losses from ice
concentration and from temperature difference between inlet and outlet.
1 600
iceslu20%
1 400
iceslu15%
DP [Pa]
1 200
iceslu10%
1 000
800
600
400
200
0
0
0.5
1
1.5
2
2.5
DT [°C]
Figure 1 – Ice-slurry pressure losses versus inlet-outlet temperature difference
Evaluating the flow rate as:
m& =
Q
r∆X sl + c p (Tout − Tin )
(4)
then equation (1) becomes:
T  β
c p* ln out  + ∆p
∆S
 Tin  ρ
=
Q
r∆X sl + c p (Tout − Tin )
(5)
From equation (5) is possible to say that, with ice-slurry having fixed inlet ice fraction and constant
exchanged thermal power, an increase in the inlet-outlet temperature difference lead to a decrease
of ∆S/Q (fig. 2 ). While, under the same condition, a reduction of the ice-slurry inlet temperature
lead to an increase of ∆S/Q (fig. 3).
The heat transfer coefficient of ice-slurry can be calculated by the correlation given by Christensen
and Kauffeld (1997):
(
Nu sl = Nu fl 1 + 0,103 X s − 2,003 Re sl
−0 ,192 ( 30−i ) / 30
Xs
0 , 339 (Re sl / 1000 )
Nusl = Nu fl
), X
> 5%
(6)
, X sl < 5%
(7)
sl
Using thermal conductivity of ice-slurry λsl , the heat transfer coefficient is:
α sl =
Nusl λsl
Di
(8)
3.804E-03
3.802E-03
-1
DS/Q [K ]
3.800E-03
3.798E-03
3.796E-03
3.794E-03
3.792E-03
3.790E-03
0
0.5
1
1.5
2
2.5
DT [°C]
Figure 2 - ∆S/Q versus ice-slurry inlet-outlet difference temperature, with fixed inlet ice fraction
Xsl = 0,20
0.00389
0.00388
0.00387
-1
DS/Q [K ]
0.00386
0.00385
0.00384
0.00383
0.00382
0.00381
0.0038
0.00379
-16
-15
-14
-13
-12
-11
-10
Tin [°C]
Figure 3 - DS/Q versus ice-slurry inlet temperature, with fixed inlet ice fraction Xsl = 0,20
The λsl , considering the ice-slurry a combination of a pure solid phase, the ice, and a liquid phase,
is normally correlated to the ice fraction and thermal conductivity of both phases.
Thermal conductivity λsl is obtained by Jeffrey equation (Jeffrey, 1973):
λ sl = λl (1 + 3ϕ s β + 3ϕ s 2 β 2γ )
(9)
with:
γ = 1+
β
4
+
3β  α + 2 

 ;
16  2α + 3 
β=
α −1
;
α +2
α=
λg
λl
(10)
2. COMPARISON BETWEEN ICE-SLURRY AND R404a
The comparison is made using ice-slurry solution with different inlet ice fraction, (Xs l= 0,20
Xs l= 0,15, Xs l= 0,10) and different inlet-outlet temperature difference ( ∆T=0,5, ∆T=1, ∆T=1,5,
∆T=2 ).
The classical equations:
(
Q = m& c p (Tout − Tin ) + r∆X s
)
(11)
1
1
1
=
+
UA hiπnDi L heπn(Di + s )L
(12)


 (Tg − Tsl ) − (Tg − Tsl ) 
out
out
in 
Q = UA∆Tlog = UA ln  in
(Tgin − Tslout )




(Tg out − Tslin )


(13)
(DS/Q)R404a/(DS/Q)sl
are used to evaluate the ice-slurry temperatures and the global heat transfer coefficient is calculated
neglecting the thermal resistance of pipe wall.
Once known the inlet and outlet temperatures for both fluid, using equation (4) the parameter ∆S/Q
is calculated. Figure 4 and 5 shows the values of entropy ratio (∆S/Q)R404a/(∆S/Q)sl.
1.21
1.209
1.208
1.207
1.206
1.205
1.204
1.203
1.202
1.201
Tin=-10.4
Tin=-1.24
Tin=-15.4
0
0.5
1
1.5
DT [°C]
2
2.5
Figure 4 - (∆S/Q)R404a/(∆S/Q)sl versus ∆T for ice-slurry with ice fraction Xs=0.2 and different inlet
temperatures
From table 2 and figures 4 and 5 it is possible to point out some considerations. To obtain warm
fluid the required temperatures, an ice-slurry solution can work with higher inlet temperature then
R404a (Table 2). When the entropy ratio is greater then one ice-slurry solution is preferable to the
R404a. Ice-slurry solution can exchange the same thermal power with different ice mass fraction
and inlet-outlet temperature differences as figures 4 and 5 show. In particular an increase of entropy
ratio is obtained increasing inlet temperature, with constant inlet-outlet temperature difference or,
with constant inlet-outlet temperatures difference, increasing inlet temperature. Lower contribution
gives the increase of ice fraction, figure 5, in comparison with increase of inlet temperature.
(DS/Q)R404a/((DS/Q)sl
1.2065
1.206
1.2055
1.205
1.2045
1.204
1.2035
1.203
1.2025
1.202
1.2015
Tin=-10.4
Tin=-12.4
Tin=-14.4
0
5
10
15
20
25
Xs%
Figure 5 - (∆S/Q)R404a/(∆S/Q)sl versus Xs for ice-slurry solution with ∆T=0.5 inlet-outlet
temperature difference
The proposed entropy production parameter gives a simple criteria to chose between different fluids
when a fixed geometry heat exchanger is used and permits to verify how the use of ice-slurry is
better than R404a although the ice mass fraction change. This characteristic permits to assert that,
when a cooling plant is considered, the changing in ice mass fraction doesn’t influence, in a certain
range of values, the operating condition. In other words the ice-slurry gives more stability to the
plant.
NOMENCLATURE
A
cp
D
L
m&
p
Q
r
Re
S
T
U
V
X
heat exchanger surface(m2)
specific heat (J kg-1K-1)
pipe diameter (m)
pipe length (m)
mass flow rate (kg/s)
pressure (Pa)
heat power (W)
heat of fusion (J kg-1)
Reynolds number fl fluid
entropy (J K-1)
temperature (K)
global heat transfer coeff. (W K-1m-2)
specific volume (m3 kg-1)
mass fractions ice
Greek symbols
α
heat transfer coeff. (WK-1m-2)
β
volumetric expansion coeff.(K-1)
λ
heat conductivity (WK-1m-1)
ϕ
volumetric ice fraction
ρ
density (kgm-3)
Subscripts
c
cold
e
external
fl
fluid
g
gas
h
hot
i
internal
in
inlet
out
outlet
s
ice
sl
ice-slurry
REFERENCES
[1] Grazzini, G., Ferraro, P., 2000, A thermodynamic parameter to choose secondary coolant fluid,
2° Workshop on Ice Slurries, Paris , pp.20-27.
[2] Grazzini, G., Ferraro, P., 1999, Il calcolo delle perdite di carico di un fluido secondario,
Sottozero, n. 4 , pp. 76-80.
[3] Cavallini, A., Fornasieri, E., 2000, L’impiego del ghiaccio fluido (sospensione acqua-ghiaccio)
nella refrigerazione, Proc.41° Conn.Ann.AICARR, Milano, pp.475-508.
[4] Christensen, K.G.; Kauffel, M., 1997, Heat transfer measurements with ice-slurry, Heat transfer
issues in natural refrig., College Park, USA, IIF/IIR, pp.161-175.
[5] Jeffrey D. J., 1973, Conduction through a random suspension of spheres, Proc. Royal Soc.
London, A335, pp.355-367.