Fin efficiency of the newly developed Compartmented Coil of a Single Coil Twin Fan System

Transcription

1 Fin eiciency o the newly developed Compartmented Coil o a Single Coil Twin Fan System ABSTRACT In predicting the perormance o any cooling coil, HVAC designers ace multiold challenges in designing the system to deliver the desired conditions in an energy eicient manne under many stringent constraints, leading to the need or an optimized solution. Perormance o innovative coils and air-conditioning systems could be predicted using the concept o in eiciency, which is a representative index o the actual coil perormance. The calculation o in eiciency or dierent in geometries started as early as 1945 with Gardner s work and yet a number o modiications to the same are being proposed to the method even until very recent times. The newly developed compartmented coil o the Single Coil Twin Fan (SCTF) system diers rom the conventional cooling coils in that the outdoor and the re-circulated air streams remain distinct and do not mix through the coil by lowing through two separate compartments albeit connected by the same chilled water tubes. The in eiciency o the newly developed compartmented coil is thus envisaged to be quite dierent and this paper proposes two methods to obtain the values o the same. The simpliied method used in this paper adopts McQuiston s ormulation o in eiciency with some modiications and the second method proposes an elaborate numerical model considering the unique eatures o the compartmented coil. INTRODUCTION Finned tube cooling coils are used extensively in the ield o heat exchangers, especially or cooling and dehumidiying requirements as the eectiveness o the total heat exchanger is enhanced through the additional area available or heat transer. The perormance o a inned surace is determined mainly using the knowledge o the in eiciency, the average heat transer coeicient o the inned region and the riction actor. The ratio o the average temperature dierence over the extended surace to that over the basic surace is commonly called the in eiciency (Gardner, 1945). The in eiciency calculation shall depend mainly on the in geometry and whether there is latent heat transer contribution. Fins o given size, shape and material possess dierent in eiciencies and the eiciency o any in will vary with its thermal conductivity and the mode o heat transer with respect to its environment. Apart, the temperatures o the luid and the heat transer coeicients involved are additional constraints. The prediction and analysis o in eiciency and perormance involves constraints or assumptions that are employed to deine and limit the problem as well as the solution. The conventional method o calculating in eiciency employs a set o assumptions proposed by Murray (1938) and Gardner (1945). These assumptions are reerred to as the Murray-Gardner assumptions (Krauss, 001). The elimination o these assumptions, either individually or in combination has been the sel-imposed task o the researchers. As these assumptions are removed, the mathematical models used or analysis come closer to the real-world situation (Kraus, 001). This paper is an attempt to study in detail how the concept o calculating in eiciency has changed over time and also to explore the method o calculating the same or the newly developed compartmented cooling coil (Sekhar et. al., 004) o the SCTF system. CONCEPT OF FIN EFFICIENCY The ratio o the average temperature dierence over the extended surace to that over the basic surace is commonly called the in eiciency (Gardner, 1945). It was Parsons and Harper in 19, who irst derived an equation or the eiciency o straight ins o constant thickness on air plane engine radiators (Krauss, 001). Attempts to present equations or temperature gradient and eectiveness o annular ins o constant thickness with a symmetrical temperature distribution around the base o the in were made (Murray, 1938), ollowing which a stepwise procedure or calculating the temperature gradient and in eiciency or ins with varying thickness was given by Hausen in 1940 (Krauss, 001). Straight ins o constant thickness, annular ins o constant thickness and annular ins o constant cross-sectional area and their respective in eiciencies were C.R.Uma Maheswaran is Research Scholar and S.C.Sekhar is Associate Proessor, Department o Building, National University o Singapore, Singapore

2 discussed in 1944 (Carrier and Anderson, 1944). Following these initial attempts, it was Gardner in 1945, who gave a comprehensive orm to the concept o eiciency practically covering any orm o extended surace whose thickness varies as some power o the distance measured along the axis normal to the basic surace. Later, attempts were made to determine an equation or in eiciency covering both annular and rectangular ins o both tapered and constant cross section (Rich, 1966). This was achieved by deining a dimensionless thermal resistance and developing expressions or its maximum limiting value. This was ollowed by the widely accepted practice o modelling in eiciency as in ARI 410 7, which was merely an adaptation o the work o Ware and Hacha in 1960 (McQuiston, 1975). However, McQuiston identiied the importance o considering moist air properties along with surace temperature, which was then the only criterion or in eiciency. His model clearly showed that mass transer decreases in eiciency and this was signiicant or highly moist air with a low evaporator temperature. This was indeed the irst attempt to model wet in eiciency. However, a comprehensive modelling o the same was yet to be developed. Elmahdy and Biggs (1979) proposed an overall model or in eiciency o a wet surace using the temperature and speciic humidity dierences as the driving orces or heat and mass transer. The model predicted by them was also to be used to optimize the cooling and dehumidiying coil design or speciic operating conditions. Material composition o ins was explored urther and eiciency o such ins composed o two materials was considered taking into account the eect o thickness o the in (Lalot, et. al., 1999). The assumption o negligible in thickness was overcome in this attempt and it was proven that a higher thermal conductivity coating increases the eiciency o the ins and this was especially important to large height and very thin ins. Recent attempts on in eiciency or plate-in-tube heat exchangers came rom Liang et. al. (000) wherein they have investigated the wet surace in eiciency o such a heat exchanger. Their modelling was both one and two dimensional and they concluded that one dimensional model which considers local mass transer eect was good enough in accuracy in comparison with the two dimensional model which considered the complex in geometry and the variation o moist air properties over the in. The paper presents that, or a partially wet in, the in eiciency decreases rapidly with the increase in air inlet relative humidity. It also adds that or a completely wet in, the eect o air inlet Relative Humidity (RH) on in eiciency is relatively very small. CALCULATION OF FIN EFFICIENCY McQuiston method o calculating in eiciency is widely extended in practice to the plate-in-tube heat exchanger. However, it has been shown that the method over predicts the in eiciency or a partially wet in and under predicts the in eiciency or a totally wet in at a high air relative humidity (Liang et. al., 000). The McQuiston method is also not representative o the variation o in eiciency with local variation o heat transer coeicient on the in, temperature based thermal conductivity o the in, eect o mass transer and the other basic Murray Gardner assumptions. The ollowing section illustrates the ormulation o in eiciency under dierent time periods: The in eiciency as proposed by McQuiston (1975) is given by η = tanh( Ml) m ( Ml) (1) where M hp Ci = 1 + ka C g p 1/ This expression considers both heat and mass transer eects in a in. It was shown that condensing moisture reduces in eiciency especially as the relative humidity becomes large. Harper and Brown proposed an extension to the in height or the purpose o dissipating the heat which normally would pass through the in edge. Applying Harper Brown approximation on in height would result in a corrected in height l c, which is given by 3

3 h l c l + km =, where 1/ h m = () kδ The eect o a variable heat transer coeicient is discussed by many researchers. Han and Lekowitz (1960) assumed linear as well as parabolic variation o the coeicient which is a unction o the height o the in given by, γ x h o = ( γ + 1)h (3) b γ is a constant determining the dependence o the variable coeicient. When γ =0, h o is a constant, when γ =1, h o varies linearly and a parabolic variation is observed when γ is set between 1 and. The eect o temperature dependent thermal conductivity in materials has been studied by Aziz and Enamul-Huq (1975). The temperature dependence o the thermal conductivity is o the orm, [ + ( T )] k = k 1 β (4) a T a where k a = thermal conductivity o the in material at the given temperature, β is the ratio o tip radius to the base radius o the in, T a is the temperature o the in base. Combining the three equations (), (3) and (4) into equation (1) will give a modiied equation or in eiciency which can then orm the basis o calculating the in eiciencies o the newly developed compartmented cooling coil. The combined equation is given as where M = h tanh M l + km η =, (5) h M l + km x ( γ + 1) h b k T [ 1+ β ( T )] a γ P Ci 1 + C A g p 1/ However, equation 6 does not hold good in the case o a compartmented cooling coil where the rate o heat transer is not uniorm across the dierent tube rows. Hence, such direct ormulations will not be representative o the actual heat transer occurring across the compartmented coil. A complex numerical model becomes necessary in order to achieve the in eiciency and in turn the actual heat transer across the two compartments. CONCEPT OF COMPARTMENTED COIL A compartmented coil is a single undivided coil section located in an intermediate point between the upstream and downstream sections o the AHU (Figure 1). A thermally insulated metal barrier is provided or separation o the two dierent air streams in the cooling coil. The coolant low through the common coil is such that both the resh and the return air streams encounter each pass o the coolant eed (Sekhar et. al., 004). However, the circuiting o the tubes o the coil is such that as much o a counter low arrangement as possible is achieved. This implies that each pass o the coolant eed will irst interact with the outside air stream (6) 4

4 ollowed by the return air stream. This is to ensure that the humid outside air aces the coldest coolant surace or good dehumidiying perormance (Uma Maheswaran et. al., 003). The compartmented coil is an integral part o a recently developed air-conditioning and air distribution system or the tropics, called the Single Coil Twin Fan (SCTF) system, that is energy eicient and also signiicantly enhances indoor air quality (Sekhar et. al., 004). FIN EFFICIENCY OF COMPARTMENTED COIL In capturing the limitations to the deinition o the term in eiciency, it was shown that even or a single in with heat dissipation rom the tip, the coeicient o heat transer at the tip need not coincide with that o the in ace (Krauss, 001). This clearly elucidates that violation o the underlying Murray Gardner assumptions result in high values o deviations to the concept o in eiciency even or a conventional cooling coil. A variation o around 10% has been shown in actual real time solutions, when one such violation o the underlying assumptions had been attempted (Mokheimer, 00). From the recent works, it is clearly shown that the calculation o in eiciency is debated even or conventional cooling coils. The use o in eiciency in calculations o heat transer in inned tubes helps avoid complex analytical expressions and makes the calculations simpler and more convenient (Zukauskas and Ulinskas, 1988). The calculation o in eiciencies or the compartmented coil is dierent rom that o conventional coil in the ollowing aspects: The impact o continuous coolant low and dierent air streams on the heat transer across the tube banks is likely to aect the resulting in eiciency. Numerous investigations showed that the heat transer rom the irst row o the tubes in a bank amounts to 60% o heat transer rom the third row, ater which it begins to stabilize (Zukauskas and Ulinskas, 1988). Similar generalization is necessary in the case o a compartmented coil as there are two dierent air streams and the driving potential in the two compartments are dierent. Fin eiciency is dependent on the height o the in, shape, material and the heat transer coeicient on the surace (Zukauskas and Ulinskas, 1988). The variation o heat transer coeicient across the in surace or the compartmented coil due to the diering heat transer rates across the tube bank is to be addressed in the calculation. However, conventional methods o accounting or variable heat transer coeicient are with an assumed distribution o the values (Krauss, 001). Two phase low situation (partial condensation) can exist on the in surace during cooling and dehumidiying o the Fresh Air and Return Air streams on the in surace. This implies that there would be two dierent in eiciencies computed across the two compartments and the method used or calculating the same is to account or this variation. From current literature, it is anticipated that the resh air compartment o the coil is likely to be a ully wet one and the re-circulated compartment o the coil is anticipated to be either ully dry or partially wet depending on the on coil conditions. It has been shown that under high humidity conditions, the wet surace in eiciency can be as much as 35% below the dry surace in eiciency (Hong and Webb, 1996). Hence, to obtain required o coil conditions, it is necessary to include the impact o condensation on calculating the compartment in eiciencies or the coil. A SIMPLIFIED MODEL FOR THE COMPARTMENTED COIL The method expressed in equation (5) and (6) can be used to calculate the in eiciencies o the compartmented coil with two modiications. The value o C is calculated as an average o the inlet and the outlet conditions. It has been shown that there is up to 5 6% dierence between the values o C inlet and C outlet (McQuiston, 1975). However, this holds good only or conventional cooling coils. In a compartmented coil, the tube wall temperature and the air conditions need to be measured at each tube row so as to get a more thorough understanding as to the value o C obtained. This is possible through empirical measurements that give us the temperature and RH conditions at the dierent tube rows. From such empirical measurements, a generalized variation can 5

5 be proposed and this could be used as a basis to use the simpliied model to calculate the dierent compartment in eiciencies. Similarly the temperature at the in base T b is to be measured at each o the tube rows, as the rate o temperature drop cannot be applied uniormly over the entire coil section. This could also be generalized rom empirical studies proposed on the coil and using this as an input, a localized distribution o the in base temperature speciic to the compartment can be considered in the simpliied model. However, it is seen that the proposed model also assumes a distribution o the heat transer coeicient and is approximated over or the entire low area. This inherent incapability is to be eliminated i a more precise and accurate prediction o in eiciency is anticipated or optimization purposes. This simpliied model can be used as a starting point with some approximations through empirical results to obtain or to predict the compartment in eiciencies o the newly developed coil. However, to obtain precise and accurate values o in eiciencies, a more complex numerical model is deemed essential in the case o the compartmented coil. NUMERICAL MODEL FOR THE COMPARTMENTED COIL A numerical model or the compartmented coil aims to eliminate the conventional approximations in calculation o in eiciency. These approximations arise in the orm o the underlying Murray Gardner assumptions and elimination o such assumptions is possible only when a more characteristic unction is obtained as the basis o calculating the in eiciency. Calculation o in eiciency using the conventional Gardner s equation (dry ins) or McQuiston s equation (wet ins) has been constantly debated by many researchers and several attempts have been made to violate one or more o the assumptions through empirical methods. Violation o Murray Gardner assumptions in conventional coils have shown variations in the range o - 49% in the values o the computed in eiciency (Mokheimer, 00) and it is envisaged that similar observations are inevitable with the compartmented coil. Hence, a complete model based on the in surace temperature distribution measurement is proposed as this would be able to account or both bulk and localised variations across the two dierent compartments in the new coil. A two dimensional numerical model is deemed necessary to obtain the distribution o the in surace temperature. k x x φ + k x y y φ + Aφ + B = 0 y (7) Using temperature o the in surace as the parameter Φ, the two dimensional model attempts to calculate the temperature variation along the in. T T k x + k y + AT + B = 0 (8) x x y y k x x T x + k y y T y + m (1 + β. C) T + m (1 + β. C) T = 0 (9) a α i sen where m g Wa W =, β = andc = k L c T T δ e p a s,. This model will then take every node into consideration or heat and mass transer coeicients and the resultant in surace temperature distribution can be used to obtain the in surace eiciency at each o these nodes. However, this model will be applicable only when the in base temperature is available as a boundary condition. The in base temperature can be ound by using an independent water side model. Due to the complexity in terms o varying heat transer rates along the water side a three dimensional model on the water side will be more representative o the values o the in base temperature obtained at each o the nodes (Uma Maheswaran et. al., 003). The solution to the above model is obtained by dividing the entire in surace into 6

6 smaller triangular elements. The tubes are considered as nodes and the obtained in base temperatures rom the water side model are used as inputs to the two dimensional model. The model will account or the variations in obtaining the perormance o a compartmented cooling coil in the ollowing aspects: The model starts rom the water side and with ew empirical measurements it is possible to obtain the in base temperature representing the temperature variation along the water side. The idea o maintaining the air streams separate through the coil is to maximize the driving potential o each o the two air streams (Sekhar et. al., 004). The air side modeling starts rom the irst tube row where the obtained in base temperature is representative o the inlet water condition and goes on to the subsequent tube rows. As each o the tubes is used as nodes, the in base temperature is obtained as an input to the model at every node in the orm o the boundary condition. However, i the variation around the tubes in terms o temperature is large, the model can use iner mesh points at the tube areas to capture such small variations and their impact on the overall perormance o the coil. This would also enable the visualization o the temperature and velocity proiles o both the air streams using available CFD codes. Violations like varying heat transer coeicient, temperature based thermal conductivity and correction or in height mentioned above are inherently present in the model as the parameter considered or measurement is undamental and is obtained rom both bulk and localised heat transer eects. CONCLUSION The models proposed in this paper are an initial attempt to conceptualise the compartment in eiciencies o the newly developed cooling coil. However, empirical results are necessary or validation and urther reinement o the models and experiments are being planned with dierent conigurations o the compartmented coil to obtain validation o the proposed models. The inherent limitations in the calculation o in eiciency or conventional cooling coils is discussed and attributed to the underlying Murray-Gardner assumptions. The simpliied model is an attempt to violate some o the assumptions that are known to cause signiicant deviations rom real values. A comprehensive numerical solution or the calculation o compartment in eiciencies is proposed by considering a undamental and locally varying parameter which could be more representative o the actual heat and mass transer phenomenon that takes place in both the coil compartments. It is envisaged that the numerical model would result in solutions that are more precise and close to real time values. LIST OF NOMENCLATURE A cross-sectional area o the in, m C Constant (or mass transer) C p Speciic heat capacity o air, J/kg.K h modiied heat transer coeicient, W/m.K h 0 average heat transer coeicient, W/m.K i g latent heat o vaporization o water, KJ/kg k thermal conductivity o the in material, W/m.K k a temperature dependent thermal conductivity, W/m.K l Fin height, m L e Lewis Number M Fin Perormance Parameter, m -1 P circumerence o the in, m T a Ambient Temperature, o C T Fin base temperature, o C W a Speciic Humidity o the ambient air, kg(water)/kg(air) W s, Speciic Humidity o the in at saturation, kg(water)/kg(air) x distance measured rom the base o the in, m Φ Fin surace temperature parameter, o C Coeicient in Variable Heat Transer Coeicient, dimensionless γ 7

7 η δ β Fin Eiciency Fin Thickness, m Optimizing Parameter, dimensionless α sen Sensible heat transer coeicient (kw/m.c) A, B Constant Parameters used to deine the two dimensional ield problem (subscript) Fin REFERENCES Aziz, A., and Enamel Huq, S.M, Perturbation solution or convective ins with variable thermal conductivity. Journal o Heat transer, 97, 300. Carrier, W.H. and Anderson, S.W., The Resistance to Heat low through inned tubing, Heating, Piping and Air-conditioning, 16(5), 304. Elmahdy, A.H. and Biggs, R.C, Finned Tube Heat Exchanger: Correlation o Dry Surace Heat Transer Data, ASHRAE Transactions, 85, 117. Gardner, K.A., Eiciency o Extended suraces, ASME Transactions, 67. Han, L.S. and Lekowitz, S.G., Constant cross section in eiciencies or non-uniorm surace heat transer coeicients, ASME Pap., New York. Hong, K.T. and Webb, R.L, Calculation o Fin eiciency or wet and dry ins, HVAC & R Research, (1). Kraus, A.D., Aziz, A., and Welty, J, 001. Extended Surace Heat Transer. John Wiley & Sons Inc., New York. Lalot, S., Tournier, C., and Jenson, M, Fin eiciency o annular ins made o two materials. Int. J. o Heat and Mass Transer. 4, Liang, S.Y., Liu, M., Wong, T.N., and Nathan, G.K, 000. Comparison o one-dimensional and twodimensional models or wet-surace in eiciency o a plate-in-tube heat exchanger. Applied thermal engineering. 0, McQuiston, F.C., Fin eiciency with combined heat and mass transer, ASHRAE Transactions, 81(1), 350. Mokheimer, E.M.A., 00. Perormance o annular ins with dierent proiles subject to variable heat transer coeicient, International Journal o Heat and Mass transer, Vol.45, Murray, W.M, Heat Transer through an annular disk or in o Uniorm thickness, ASME Transactions, J. App. Mechanics, 60, 78. Rich, D.G, The eiciency and thermal resistance o annular and rectangular ins. Proceedings o the Third International Heat Transer Conerence, Chicago..Vol. III, 81. Sekhar, S.C., Uma Maheswaran, C.R., Tham, K.W, and Cheong K.W, 004. (To appear). Development o energy eicient single coil twin an air-conditioning system with zonal ventilation control, ASHRAE Transactions. 8

8 Uma Maheswaran, C.R., Sekhar, S.C., and Tham, K.W, 003. Considerations in the ormulation o a mathematical model or a newly developed compartmented cooling coil. In Proceedings o HB003 7 th International Conerence, Vol., pp Zukauskas,A., and Ulinskas, R, Heat Transer in tube banks in cross low, Hemisphere Publishing Corporation, USA. outdoor air section o tube and plate in heat exchanger Upstream outdoor air low Two circuits o coolant recirculated air section o tube and plate in heat exchanger Upstream recirculated air low Downstream outdoor air low Downstream recirculated air low Figure 1 : A compartmented cooling coil 9