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416 2nd PALENC Conference and 28th AIVC Conference on Building Low Energy Cooling and Advanced Ventilation Technologies in the 21st Century, September 2007, Crete island, Greece

Modelling of Indirect Evaporative Air Coolers Gh. HeidarinejadBuilding and Housing Research Centre (BHRC), Iran

M. BozorgmehrUniversity of Tarbiat Modares, Iran

tion of temperature. The resulting decoupled equations describing the wet and the dry passages of the cooler were solved by defining a new independent variable: wet bulb depression which is the difference between dry bulb and wet bulb temperatures. This model could be used to predict the cooler performance by analogy to dry surface heat exchangers. Hsu et al. (1989) investigated three basic types of wet sur-face heat exchangers. They found that cooling effective-ness of each configuration increases with increasing dry channel NTU (Number of Transfer Units) and reaches maximum values asymptotically at some large values of NTU. They assumed that the non-circulating water is lo-cally replenished and its local temperature was calculated from the mass and energy balance equations. They took into account the effect of longitudinal plate conduction. Their results showed that it has almost no effect on the co-current and counter-current configurations and its degrad-ing effect on efficiency of cross flow is accelerated when the dry-passage length to that of the wet passage is large.Pescod (1979) proposed a simple design method for indi-rect evaporative cooler using parallel plastic plates with small protrusions. Although the thermal conductivity of plastic is very low, the heat transfer resistance across a thin plastic plate would be less than of the thermal resistance between the air and plate in dry side. Predictions of the efficiencies of Pescod’s wet surface plate heat exchang-er were found to be higher than the experimental data. Thus incomplete wetting of plate surfaces was suspected. Kettleborough and Hsieh (1983) described a counterflow indirect evaporative cooler with configuration of upward flow of the primary air and downward flows of second-ary air and water. Numerical analysis was utilized to study the thermal performance of the unit. By applying wetting factor better agreement between calculated and measured performance data qualitatively was achieved. Erens and Dreyer (1993) reviewed three different models describing evaporative indirect cooler: (1) Poppe model- considering a variable Lewis factor, spray water evapora-tion rate and modeling over saturation in the secondary air; (2) Merkel model- can be derived from Poppe model by assuming a Lewis factor of unity and negligible effect of spray water evaporation and assuming that the sec-

ABSTRACT

In this paper, indirect evaporative cooling in an air cooler has been modeled. This model has been obtained from the governing equations of heat and mass transfer in pri-mary and secondary air and water flows. Factors affect-ing on evaporative cooling performance such as mass flow rates, geometry and flow configuration has been investigated. Results show that cooling efficiency con-siderably depends on mass flow rates ratios of primary and secondary air flows and spacing between plates of wet and dry passages. The performance of this cooling system for typical conditions of some Iranian cities has been investigated. Using a first stage indirect evaporative cooling prior to conventional direct evaporative cooling systems in most regions of Iran will provide cooling comfort conditions as a low energy consumer alternative.

1. INTRODUCTION

Evaporative air conditioning is an environmentally friendly and energy efficient method for cooling build-ings. Two main different methods are used, the direct and the indirect one. In the direct method air passes through a wetted media in an adiabatic saturation proc-ess. In the indirect method, two distinct air flows pass through a wet surface heat exchanger, primary flow in the dry channels and secondary flow in the wet chan-nels. In this case without adding water to the primary air, it is cooled and secondary air carries away the heat energy from it as water evaporates in wet channels, so the indirect stage sensibly cools the primary air. Second-ary air could be supplied from outdoor or room exhaust which is so-called recovery. Also it may be extracted from primary air outlet which is referred to regenerative and in this case secondary air passes two times through the heat exchanger. Heat and mass transfer occur simul-taneously in an indirect evaporative heat exchanger. Maclaine-cross and Banks (1983) analyzed the evapo-rative heat transfer in an indirect cooler. They suggested a simplified analysis model assuming that water film is stationary and continuously replenished with water at the same temperature and saturation line is a linear func-

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ondary air never becomes over saturated; (3) Simplified model- assuming that the water temperature is constant through out the cooler. They applied these models to a cross flow indirect cooler and simplified model was rec-ommended for small units and for initial design purpose. Chengqin and Hongxing (2006) developed an analytical model for the indirect evaporative cooling with parallel/counter flow configurations. Similar to any other analyti-cal model, humidity ratio of air in equilibrium with water surface was assumed to be a linear function of the surface temperature. Effects of spray water evaporation, spray water temperature variation along the heat exchanger, non unity surface wetability and Lewis factor were considered in the model. Results of analytical solutions were found to be in good agreement with those of numerical integrations.Review of the previous researches show that there are two main approaches to model indirect evaporative cooler: 1-Numerical integration; 2-Analytical model. Analytical models are limited to co-current and counter-current configurations with some simplifications and linear assumption for the satu-ration curve. In this paper using a numerical integration approach, three different configurations i.e. parallel, counter and cross flow are analyzed to determine the configuration that optimizes the performance.

2. MODELLING

2.1 Physical description of indirect coolerIndirect evaporative cooler consists of a series of paral-lel plates in which one is open for primary air flow and the other one is open for water and secondary air flows. Circulation water is sprayed onto the top of the heat ex-changer and flows downward along wall surfaces of wet channels. Primary air flows in the alternative channels. A typical indirect cooler with counter flow configura-tion can be shown schematically in Figure 1.

Figure 1: Typical indirect evaporative cooler with counter flow configuration.

As can be seen from Figure 1 each repeated section of the cooler consists of a half of dry channel, plate wall and a half of wet channel. Figure 2 shows this section and a differential element.

Figure 2: (a) Model section and its adjacent section, (b) Differen-tial element. Sp: Dry channel spacing, Sa: Wet channel spacing.

The following assumptions here are considered:− There is no diffusion in the flow direction; − Cooler is insulated from the surrounding; − Specific heats are constant;− Heat and mass transfer coefficients are constant and Lewis factor is unity;− Plate wall, bulk water and air/water interface have the same temperature;− Spray water is circulated.

2.2 Governing equations of heat and mass transferFor a differential element as shown in Figure 2b, by ap-plying principles of mass and energy conservation, a set of differential equations can be obtained as follows.

2.2.1 Energy balance Energy balance equation for the primary air

(1)

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418 2nd PALENC Conference and 28th AIVC Conference on Building Low Energy Cooling and Advanced Ventilation Technologies in the 21st Century, September 2007, Crete island, Greece

where:q: Rate of heat transfer (W)

: Mass flow rate (kg/ s)cp: Specific heat at constant pressure (J/kg K)t: Temperature (ºC)

: Overall heat transfer coefficient (W/m2 K)A: Area (m2)Subscripts p and w stand for primary air and spray water respectively. Energy balance equation for the secondary air

(2)where:i: Enthalpy of moist air (J/kg dry air)K: Mass transfer coefficient (kg/m2 s)Subscripts asw and a stand for saturated air at water temperature and secondary air, respectively. This equation is a result of the assumption of Lewis number being unity (Hassan, 2005). Another approach considers the effect of variable Lewis number. Erens and Dreyer (1993) implemented the two methods on a cross flow wet liquid cooler. Their calculation showed insignificant differences between the results by these two methods.Energy balance equation for the three streams flowing inside the elementWith the assumption of constant water flow rate, energy balance equation for the streams flowing inside the ele-ment shown in Figure 2b is:

(3)Spray water temperature varies inside the heat exchang-er. Because of water circulation, the inlet spray water temperature will equal the outlet spray water temperature .

(4)

2.2.2 Mass balance The mass balance for the element gives the rate of spray water evaporation (kg/s)

(5)where:w: Humidity ratio of air (kg water/ kg dry air)Equations (1)-(5) govern heat and mass transfer in an indirect evaporative cooler.

2.3 Numerical integration procedureEquations (1)-(3) form a set of coupled ordinary dif-ferential equations which can be solved simultaneously, using a multi step numerical integration procedure.

Equation (4) sets the condition for inlet and outlet wa-ter temperature and this temperature has to be found iteratively. Equation (5) can be solved separately after once solution of the set of equations (1)-(3) has been found, because water temperature is necessary to solve this equation. The solution procedure depends on the configuration of the cooler. Three main configurations could be considered which are parallel, counter and cross flow. These configurations are shown schemati-cally in Figure 3. The main purpose of this paper is to study the cooling performance of these configurations.For parallel flow the integration starts from the top with known conditions of primary and secondary air flows and a guessed inlet water temperature. Integration for each element proceeds from top to the bottom. At the bottom obtained value for the outlet water temperature is compared with guessed inlet value and is corrected until both inlet and outlet water temperatures would be the same. For the counter flow, because of scattered inlet conditions at the top and bottom of the heat exchanger, another iteration to find the outlet enthalpy of second-ary air is added. Each time at the bottom, calculated en-thalpy at the inlet and inlet enthalpy of the secondary air are compared until they would be equal. For cross flow configuration, because primary air and secondary air flow in perpendicular direction, the heat exchanger is divided into a series of two-dimensional elements. In-tegration starts from the upmost element in the inlet of primary air and proceeds downward.

Figure 3: Three flow configurations, (a) parallel, (b) counter, (c) cross. P: primary air, W: spray water, S: Secondary air. Inlet,

Outlet

3. RESULTS AND DISCUSSION

Results for typical temperature profiles in various con-figurations of indirect cooler have been shown in Figure 4. The size of cooler is assumed 1×1×1 m3. For the sake of comparison between different configurations, values for mass transfer coefficient and overall heat transfer coefficient has been considered equal. Outdoor air tem-

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perature is assumed 25ºC and has a relative humidity of 50%. Results show that counter configuration has the highest cooling efficiency. In cross configuration, aver-aged temperature of primary air in outlet is close to that in counter configuration.

Figure 4: Profiles of primary air temperature in various configu-rations along the flow direction.

In some simplified methods, water temperature is considered constant throughout the cooler because of its circulation. Figure 5 shows the water temperature profiles along the water flow direction for various con-figurations. As it can be seen only for parallel flow it is expected to be constant and for counter and cross configuration it somehow varies in opposite manner. It should be noted that temperatures for cross configura-tion are averaged in each section because they shape a two dimensional distribution. Ratio of mass flow rates of primary and secondary air is a design parameter and its effect on cooling performance just for cross configu-ration is illustrated in Figure 6.

Figure 5: Profiles of water temperature in various configurations along the flow direction.

Figure 6: Effect of ratio of primary to secondary air mass flow rate on temperature for cross configuration. (mass flow rate of secondary air, ms=2.0 kg/s)

It can be seen from Figure 6, higher cooling efficiency is obtained as mass flow rate ratio decreases. For evap-orative air conditioning, cooling capacity is defined which is determined from supply air temperature and mass flow rate. However lower primary air temperature is obtainable as mass flow rate ratio is decreased, but an optimum value for this ratio can be found from view-point of cooling capacity.Minimum spacing between channels should be con-sidered while minimizing the total pressure drop (dry and wet passages). Figure 7 shows the effect of channel width on primary air temperature. In a fixed cooler vol-ume, decreasing spacing between plates means increas-ing number of channels and therefore more area for heat and mass transfer. The efficiency of an evaporative cooler is defined as follows:

(6)where:

: Dry bulb temperature of primary air inlet Dry bulb temperature of primary air inlet: Dry bulb temperature of primary air outletDry bulb temperature of primary air outlet: Wet bulb temperature of secondary air inletWet bulb temperature of secondary air inlet

From Figure 4 it can be seen that for cross configuration a cooling efficiency of 80% is predicted which agrees with expected values for modern plate type indirect evaporative cooler (Watt, 1997). Pescod (1979) meas-ured temperature cooling efficiency between 69 and 82 percent, while Maclaine-cross (1983) calculated 78 to 98 percent as possible in a theoretical model based upon cross-flow cooling tower theory. Excess water flow down the wet passages seemed to be the reason of difference between measured and calculated efficien-cies, because mathematical model assumed stationary water layer which for finite water mass flow rate is not true. In the present work water is not stationary and it is

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circulated. For perfect surface wetting, circulation wa-ter mass flow should be several times of that evaporate. However excess water flow deteriorates cooling effi-ciency and should be kept as minimum as possible.

Figure 7: Effect of channel width on primary air tem-perature profile for cross configuration.

4. COMFORT PERFORMANCE

Iran has a wide variety of climatic conditions. In most hot and dry regions direct evaporative cooler is a com-mon cooling system providing comfort for residential buildings. In regions or conditions with high wet-bulb temperature that the direct systems do not provide com-fort conditions, vapour-compression cooling systems are used. If a first indirect stage is added to a second di-rect stage, a two stage indirect/direct cooler is obtained which could provide comfort conditions for a number of cities. Commonly 65% indirect stage efficiency (per-formance factor) and 85% direct stage efficiency is reached. Table 1 illustrates 2.5% design conditions in four major cities of Iran.

Figure 8: shows that room air comfort condition is achieved with indirect/direct cooling systems for major cities of Iran. For each city the process consists of indirect stage cooling, direct stage cooling and room air conditioning.

5. CONCLUSIONS

Main results of modelling indirect cooler for three main configurations are as follows.− Counter configuration has the highest cooling effi-ciency.− Increasing ratio of primary to secondary air mass flow and heat exchanger plates spacing decreases cooling ef-ficiency.− Using a pre cooling indirect stage prior to a direct stage provides comfort conditions in major cities of Iran as a clean and energy efficient alternative for conven-tional systems.

REFERENCES

Chengqin, R., Hongxing, Y. (2006). An analytical model for the heat and mass transfer processes in indirect evaporative cooling with par-allel/counter flow configurations. Heat Mass Transfer 49 617-627. Erens, P. J., Dreyer, A. A. (1993). Modeling of indirect evapora-tive air cooler. Heat Mass Transfer 36 17-26.Hasan, A. A. (2005). Performance analysis of heat transfer proc-esses from wet and dry surfaces: cooling towers and heat exchang-ers. Doctoral dissertation. Helsinki University of technology.Hsu, S. T., Lavan, Z., Worek, W.M. (1989). Optimization of wet surface heat exchangers. Energy 14 757-770.Kettleborough, C. F., Hsieh, C. S. (1983). The thermal perform-ance of the wet surface plastic plate heat exchanger used as an in-direct evaporative cooler. ASME J. Heat Transfer 105 366-373.Maclaine-cross, I. L., Banks, P. J. (1983). A general theory of wet surface heat exchangers and its application to regenerative cool-ing. ASME J. Heat Transfer 103 579-585.Pescod, D. (1979). A heat exchanger for energy saving in an air conditioning plant. Trans. ASHRAE 85 238-251.Watt, J. R., Brown, W. K. (1997). Evaporative air conditioning handbook. Lilburn: Fairmont Press.

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