Critical exergy analysis of counterflow reversibly used cooling towers Jiasheng Wu 1, Guoqiang Zhang 1,*, Quan Zhang 1, Jin Zhou 1 1 College of Civil Engineering, Hunan University, Changsha, China * Corresponding email: gqzhang@188.com SUMMARY Reversibly used cooling towers (RUCT) are used to extract heat from atmospheric to water. In this study, exergy analysis is used to investigate the exergy and exergy destruction of air and water flowing through the counterflow RUCT. Exergy analysis then has been carried out for investigating the RUCT performance with various inlet conditions. The results indicated that the exergy destruction in the RUCT is increased by decreasing the the water inlet temperature, whereas increased by increasing the air inlet wet bulb temperature, and also increased by increasing water to air flow rate ratio. Investigation of the calculated results can be used to further understand details of the energy and exergy transfer processes in counterflow RUCTs. KEYWORDS Counterflow; Reversibly used; Cooling tower; Exergy analysis; Dead state 1 INTRODUCTION The wet cooling tower is one of the most important evaporative heat exchangers, playing a role in air-conditioning systems. The theoretical analysis of cooling tower has a long history, which has led to an excessively large number of publications (Haidavalloo, et al., 2010; Heidarinead, et al., 2009; Ibrahim, et al., 1995; Khan, et al., 2003; Klimanek and Bialecki, 2009; Shi, 1990). However, the wet cooling tower may be also reversibly used, as a part of a heat pump system for heating, to extract low grade energy from ambient air (Tan, K. and Deng, S., 2002). Therefore, a year-round hot water supply in buildings can be made possible without requiring any other backup electric heating equipment. Under winter operating conditions, although the COP was lower than that under summer operating conditions, the system is more economical than electric water heating. Another advantage of this system is that only a single system is required to supply hot water and chilled water. This heat pump system coupled with RUCT is most suitable to buildings in tropical or subtropical areas. Traditional methods of RUCT analysis are based on the first law of thermodynamics. These methods used an energy balance on system to determine heat and mass transfer between the water and ambient air (Tan and Deng, 2002, 2003; Wu, et al., 2011; Zhang, et al.). In general, energy balances provide no information on the quality or grades and no information about internal losses. By contrast, the second law of thermodynamics introduces the useful concept of exergy in the analysis of thermal systems. Exergy analysis is a measure of the quality or grade of energy and it can be destroyed in the RUCT. Muangnoi, et al., 2007 presented a method for the prediction cooling tower performance by employing an exergy analysis and validated by the experiment data reported. It can be noted from the results that the choice of the ambient conditions affects the results of exergy analysis quite strongly. In addition, it reveals that exergy destruction is high at
the bottom and reducing at the top of the tower. Qureshi and Zubair, 2007 summarized an exergetic analysis for the wet cooling towers performance. The analysis of exergy efficiency varies for inlet water temperature and air inlet wet bulb temperature. It also noted that an increase in the air inlet wet bulb temperature consistently increase the exergy efficiency. Muangnoi, et al., 2008 analysed the variation in exergy change of water and air under various inlet air conditions, also with corresponding exergy destruction and exergy efficiency when the condition of water side is fixed. Wang and Li, 2011 found that the exergy transfer processes inside the counterflow wet cooling towers have different types depending on the states of the bulk air, water and the environment. The results show that less than 25% exergy input is effectively transferred to the cool exergy of outlet water. The exergy parameters are very sensitive to the thermal efficiency when it is very close to 1.0 at lower water to air ratios. So far, there are still a small number of researchers who study and investigate the energy utilization of counterflow RUCT, especially via exergy analysis. Currently, little is known about the applicability of exergy analysis for RUCT investigation. As an extension of previous studies and in order to develop the exergy analysis methods, the main obective of this study is to examine the exergy transfer characteristics of a counterflow RUCT based on mathematical modelling and simulation results. 2 MATHEMATICAL MODEL FOR RUCT The assumptions and simplifications of RUCT applied to derive the basic modelling equations are summarized in Zhang, et al. m m h ( - ) A (1) i1, i, i, i, i, w w m a s h ( - ) A (2) i1, i, m i, i, i, a a a s mda T ( c c ) m T c m ( - ) T h ( T - T ) A i, i, i1, i, i, i, i, i, i1, da v a da a v da a a w c a w a i1, ( cda cva ) mda (3) T i, i, i, i, i1, i, i1, i, hc ( Ta - Tw ) A rw ( mw - mw ) w Tw i, cwmw (4) where m w is mass flow rate of water, ω a is humidity ratio of saturated moist air, ω s is humidity ratio of saturated moist air at water temperature, T a is air temperature, T w is water temperature, h m is mass transfer coefficient, h c is heat transfer coefficient, A is heat and mass transfer area, c da is specific heat of dry air, c v is specific heat of water vapor, m da is mass flow rate of dry air, m w is mass flow rate of water, r w is latent heat of condensation of water at water temperature. Equations (1)-(4) are iteratively solved from top to bottom of the counterflow RUCT. The proposed heat and mass transfer model of RUCT was validated with the experimental data reported by Tan and Deng (2002). Furthermore, the comparison between the results by the proposed model and by Tan showed very good agreement in the validation computations.
3 EERGY CALCULATION In the counterflow RUCT, air and water are the only two kinds of working fluids revealed in operation. Therefore, it is necessary to write the exergy equations for both air and water for applying in the analysis. Considering no pressure change throughout the RUCT, the exergy of moist air a can be finally written as (Muangnoi, et al., 2007, 2008) T a a G cp, a 0.001dcp, v Ta -T0 -T0 ln T 0 Rg, a 0.001d 0 R g, v d T0 Rg, a 0.001dR g, v ln 0.001d 0 Rg, v ln Rg, a 0.001dR g, v d0 (5) where G is dry air mass flow rate, d is humidity ratio, 0 is restricted dead state, R g,v =0.461 kj kg - 1 K -1 The exergy of water can be expressed as (Wang and Li, 2011) - - ln / ln / - 2501-2.32 1- / w L cp, v Tw T0 cp, vt0 Tw T0 T0 Rg, v Pv, s Pv,0 tw T0 T w (6) where L is water mass flow rate, P v,s is saturation vapor pressure of water, P v,0 is vapor pressure of environment, c p,a =1.004 kj kg -1 K -1, c p,v =1.872 kj kg -1 K -1, R g,a =0.287 kj kg -1 K -1, and R g,v =0.461 kj kg -1 K -1, 0 is restricted dead state. For the purpose of this study, we define the exergy destruction of the RUCT considering the condensation water, which is given by,,,,, (7) D a i w i a o w o w con where a, i w, i is considered as total exergy entering, and a, o w, o w, con is the total exergy leaving.. The exergy efficiency of the counterflow RUCT can be written as 1 D a, i w, i (8) Exergy is defined as the maximum work that can be withdrawn from the system when it is allowed to reach the dead state. In this paper, the dead state is set at the ambient pressure and temperature.
3 RESULTS AND DISCUSSION For the counterflow RUCT, the air inlet wet-bulb temperature and water inlet temperature were found to be the two most important input parameters (Wu, et al., 2011; Zhang, et al.). Therefore, variation in exergy efficiency is studied with respect to these two parameters. Figure 1 (a) shows the effect of the air inlet wet bulb temperature on exergy destruction at different water-air flow rate ratios. Figure 1 (b) illustrates effect of air inlet wet bulb temperature on exergy efficiency at different water-air flow rate ratios. These plots are generated based on the following input data: P atm =101.325 kpa; T w,i =7 o C; T a,i =20 o C; m a =8 kg s -1. As shown in Figure 1 (a), when the air inlet wet bulb temperature is 14 ºC and m w /m a =0.5, the exergy destruction of the RUCT is 1.229 kw. With the increase of 6 ºC in the air inlet wet bulb temperature (20 ºC), the exergy destruction of the RUCT increases to 2.351 kw. However, for m w /m a =1.5, when the air inlet wet bulb temperature is 14 ºC, the exergy destruction of the RUCT is 1.731 kw, then with the increase of 6 ºC in the air inlet wet bulb temperature (20 ºC), the exergy destruction of the RUCT increases to 3.513 kw. For different mass flow ratios, it is noted that the exergy destruction increases with the increasing inlet wet bulb temperature. From Figure 1 (a) and (b), it is obvious that the exergy efficiency decreases as the exergy destruction increases for the increasing inlet wet bulb temperature. As inlet wet bulb temperature increases, the outlet water temperature also rises and the exergy of the outlet water stream increases. On the other hand, the exergy of the incoming water is constant. The exergy destroyed increases due to the continuously decreasing value of temperature different between dry bulb and wet bulb. These factors combine so that the exergy efficiency decreases and can be attributed to the decreasing value of temperature different between dry bulb and wet bulb, as the volume of the tower is kept constant. Figure 1. a) Effect of air inlet wet bulb temperature on exergy destruction at different water-air flow rate ratios; b) Effect of air inlet wet bulb temperature on exergy efficiency at different waterair flow rate ratios. The exergy destruction and exergy efficiency of the counterflow RUCT versus water-air flow rate ratios at different water inlet temperature is shown in Figure 2 (a) and (b) respectively. These plots are generated based on the following data: P atm =101.325 kpa; T a,i =20 o C; T wb,i =18 o C; m a =8 kg s -1.
In this case, it demonstrates that when the water-air flow rate ratio is 0.5, the exergy destruction of the RUCT is 3.667 kw at a water inlet temperature of 3 o C, and the exergy destruction is 0.670 kw for a water inlet temperature of 12 o C at the same water-air flow rate ratio. In conclusion, the exergy destruction continues to decrease at higher water inlet temperatures. In Figure 2 (b), it is noted that exergy efficiency increases as the exergy destruction described in Figure 2 (a) increases for the increasing water inlet temperature. The exergy of the outlet air stream continuously increases as it gets farther from the dead state humidity ratio. On the other hand, exergy of the inlet air stream is constant. Also, the quantity of condensed water increases due to the increasing difference of the inlet water and wet-bulb temperatures. The exergy of the outlet water stream decreases as its temperature approaches the dead state. However, the exergy of the incoming water stream constantly decreases due to higher inlet water temperatures used. The increase in the exergy destruction is due to the continually increasing difference between the inlet and outlet water temperatures. These factors cause the exergy efficiency to increase. Figure 2. a) Effect of water-air flow rate ratio on exergy destruction at different air inlet wet bulb temperature; b) Effect of water-air flow rate ratio on exergy efficiency at different air inlet wet bulb temperature. 5 CONCLUSIONS In this study, exergetic analysis is conducted on counterflow RUCTs. To achieve this obective, the exergy destruction of the RUCT in terms of different operational conditions is investigated. 1. For different input variables investigated, it is shown that the exergy efficiencies are often increasing or decreasing monotonically. 2. It is shown that the exergy destruction in the RUCT is increased by decreasing the water inlet temperature, whereas increased by inceeasing the air inlet wet bulb temperature. 3. It is also shown that the exergy destruction in the RUCT is increased by increasing water to air flow rate ratio. Investigation of the calculated results can be used to further understand details of exergy in RUCTs.
ACKNOWLEDGEMENT The research reported herein has been carried out with the help of the National Natural Science Foundation of China (Nos.51108165 and 51178170). These supports are gratefully acknowledged. 6 REFERENCES Haidavalloo, E., Shakeri R., and Mehrabian M.A. 2010. Thermal performance of cross flow cooling towers in variable wet bulb temperature. Energy Conversion and Management, 51 (6), 1298-1303. Heidarinead, G., Karami M., and Delfani S. 2009. Numerical simulation of counter-flow wetcooling towers. International Journal of Refrigeration, 32 (5), 996-1002. Ibrahim, G.A., Nabhan M.B.W., and Anabtawi M.Z. 1995. An investigation into a falling film type cooling tower. International Journal of Refrigeration, 18 (8), 557-564. Khan, J.-U.-R., Yaqub M., and Zubair S.M. 2003. Performance characteristics of counter flow wet cooling towers. Energy Conversion and Management, 44 (13), 2073-2091. Klimanek, A., and Bialecki R.A. 2009. Solution of heat and mass transfer in counterflow wetcooling tower fills. International Communications in Heat and Mass Transfer, 36 (6), 547-553. Muangnoi, T., Asvapoositkul W., and Wongwises S. 2007. An exergy analysis on the performance of a counterflow wet cooling tower. Applied Thermal Engineering, 27 (5 6), 910-917. Muangnoi, T., Asvapoositkul W., and Wongwises S. 2008. Effects of inlet relative humidity and inlet temperature on the performance of counterflow wet cooling tower based on exergy analysis. Energy Conversion and Management, 49 (10), 2795-2800. Qureshi, B.A., and Zubair S.M. 2007. Second-law-based performance evaluation of cooling towers and evaporative heat exchangers. International Journal of Thermal Sciences, 46 (2), 188-198. Shi, Y.J. 1990. Operation and Experiment of Cooling Tower. Water Consevancy and Electric Power Press, Beiing. Tan, K., and Deng S. 2002. A method for evaluating the heat and mass transfer characteristics in a reversibly used water cooling tower (RUWCT) for heat recovery. International Journal of Refrigeration, 25 (5), 552-561. Tan, K., and Deng S. 2003. A numerical analysis of heat and mass transfer inside a reversibly used water cooling tower. Building and Environment, 38 (1), 91-97. Wang, L., and Li N. 2011. Exergy transfer and parametric study of counter flow wet cooling towers. Applied Thermal Engineering, 31 (5), 954-960. Wu, J., Zhang G., Zhang Q., Zhou J., and Wang Y. 2011. Artificial neural network analysis of the performance characteristics of a reversibly used cooling tower under cross flow conditions for heat pump heating system in winter. Energy and Buildings, 43 (7), 1685-1693. Zhang, Q., Wu J., Zhang G., Zhou J., Guo Y., and Shen W. 2012. Calculations on performance characteristics of counterflow reversibly used cooling towers. International Journal of Refrigeration, 35(2), 424-433.