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: ggrazzini@ing.unifi.it ABSTRACT A comparison is made between an ice-urry 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-urry 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-urry 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-urry, 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-urry 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-urry inlet temperature, different ice fraction and different ice-urry 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: S m& T = c p ln T out in 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 =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 1200 mm Width 420 mm Height 70 mm Tube Material Copper Fin Material Aluminium Inside pipe diameter (D i ) 11,3 mm Pipe number 20 Pipe thickness 0.35 mm Number of fins 171 Fin thickness 0.23 mm Rank Type In-line Rank Number 10 Table2:Values of ice-urry and R404a used to make the comparison Antifreeze Methanol Ice fraction (X s ) 0.2-0.15-0.10 Ice-urry (Tout-Tin) 0.5-1- 1.5 2 C αe 43 (W/m 2 K) Warm fluid Tin [ C] 0-2 -5 R404a Tin [ C] -11-13 -16 Ice-urry Tin [ C] -10.4-12.4-15.4 As showed in equation (1) is possible to claim that the ice-urry entropy variation is given by two terms, where the first one is a function of the temperature ( S t ), and the second one is a function of pressure losses ( S p ): S t S p T = mc & * out p ln (2) Tin β = m& p (3) ρ Where c p * is evaluated as /( m& (T o -T in )).The ice-urry pressure losses ( p) can be calculated using the same relation for a liquid solution (Grazzini, 1999, Cavallini, 2000), while the ice-urry characteristic parameters, as density (ρ ), dynamic viscosity (µ ) etc., are calculated using Melinder equations (1997). Figure 1 shows the dependence of the ice-urr's pressure losses from ice concentration and from temperature difference between inlet and outlet.
DP [Pa] 1 600 1 400 1 200 1 000 800 600 400 200 0 iceu20% iceu15% iceu10% 0 0.5 1 1.5 2 2.5 DT [ C] Figure 1 Ice-urry pressure losses versus inlet-outlet temperature difference Evaluating the flow rate as: m& = (4) r X + cp( Tout Tin) then equation (1) becomes: S = * Tout β cp ln p T + in ρ r X + cp out in ( T T ) (5) From equation (5) is possible to say that, with ice-urry having fixed inlet ice fraction and constant exchanged thermal power, an increase in the inlet-outlet temperature difference lead to a decrease of S/ (fig. 2 ). While, under the same condition, a reduction of the ice-urry inlet temperature lead to an increase of S/ (fig. 3). The heat transfer coefficient of ice-urry can be calculated by the correlation given by Christensen and Kauffeld (1997): Nu fl 0,192(30 i) / 30 0,339(Re/1000) ( 1+ 0,103X 2,003 Re X ) = Nu, X > 5% (6) Nu fl s Nu =, X < 5% (7) s Using thermal conductivity of ice-urry λ, the heat transfer coefficient is: Nu λ α = (8) Di
3.804E-03 3.802E-03 3.800E-03 DS/ [K -1 ] 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/ versus ice-urry inlet-outlet difference temperature, with fixed inlet ice fraction X = 0,20 DS/ [K -1 ] 0.00389 0.00388 0.00387 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/ versus ice-urry inlet temperature, with fixed inlet ice fraction X = 0,20 The λ, considering the ice-urry 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 λ is obtained by Jeffrey equation (Jeffrey, 1973): 2 2 λ = λl (1+ 3ϕ sβ + 3ϕ s β γ ) (9) with: β 3β α+ 2 γ = 1+ + ; 4 16 2α + 3 α 1 β = ; α + 2 λg α = (10) λ l
2. COMPARISON BETWEEN ICE-SLURRY AND R404a The comparison is made using ice-urry solution with different inlet ice fraction, (X s l = 0,20 X s l = 0,15, X s l = 0,10) and different inlet-outlet temperature difference ( T=0,5, T=1, T=1,5, T=2 ). The classical equations: ( ( T T ) + r X ) = m& cp out in s (11) 1 = UA 1 1 + hi πndi L heπn( Di + s)l (12) ( Tg ) ( ) = = in Tout Tgout T UA T in log UAln ( ) ( ) (13) Tgin Tout Tgout Tin are used to evaluate the ice-urry 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/ is calculated. Figure 4 and 5 shows the values of entropy ratio ( S/) R404a /( S/). (DS/)R404a/(DS/) 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 2 2.5 DT [ C] Figure 4 - ( S/) R404a /( S/) versus T for ice-urry 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-urry solution can work with higher inlet temperature then R404a (Table 2). When the entropy ratio is greater then one ice-urry solution is preferable to the R404a. Ice-urry 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/)R404a/((DS/) 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/) R404a /( S/) versus Xs for ice-urry 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-urry 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-urry gives more stability to the plant. NOMENCLATURE A heat exchanger surface(m 2 ) c p specific heat (J kg -1 K -1 ) D pipe diameter (m) L pipe length (m) m& mass flow rate (kg/s) p pressure (Pa) heat power (W) r heat of fusion (J kg -1 ) Re Reynolds number fl fluid S entropy (J K -1 ) T temperature (K) U global heat transfer coeff. (W K -1 m -2 ) V specific volume (m 3 kg -1 ) X mass fractions ice Greek symbols α heat transfer coeff. (WK -1 m -2 ) β volumetric expansion coeff.(k -1 ) λ heat conductivity (WK -1 m -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 ice-urry
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-urry, 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.