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2 Geothermal Resources Council Transactions, Vol. 24, September , 2000 Development of a Porous Fin Air-Cooled Condenser Charles Kutscher and Keith Gawlik National Renewable Energy Laboratory Cole Boulevard Golden, CO ABSTRACT Many binary-cycle geothermal plants are air-cooled. For these plants, the air-cooled condenser arrays contribute significantly to the installed plant cost and the operating parasitics. While conventional finned tube condensers may be adequate for typical fossil-fuel power plants, geothermal plants, which operate at lower temperatures, can benefit significantly from improved condenser designs that allow the condenser temperature to more closely approach the ambient air temperature. This paper discussed innovative porous finned tube designs in which the cooling air passes through, rather than along the fins. These designs improve the heat transfer coefficient by reducing the average thermal boundary layer thickness and also increase the total heat transfer area. Results of analytical and experimental work are discussed. Tests of a small prototype indicated a 30% increase in heat transfer when operated at the same fan power. Analytical predictions show that even greater performance enhancement is possible and that it should be possible to achieve a 40% reduction in the total life-cycle condenser cost as measured in cents per Watt of heat transferred. Introduction Air-cooled condensers (ACCs) are commonly used in binary-cycle geothermal power plants in arid regions and in situations where water vapor plumes are undesirable. NREL is engaged in a research program to develop better performing air-cooled condensers that can lower the delivered electric energy cost of geothermal power plants. Analysis indicates that net power increases by approximately 1 % for every one degree F drop in condenser temperature. Thus improved condenser heat transfer that can allow the condensate temperature to more closely approach the ambient air temperature can have a very favorable impact on overall plant performance. The cost of the condensers and the parasitic load of the fans are also significant. A reduction of ACC capital cost by 50% can result in a cost of electricity (COE) reduction of about 1 $/kwh. A reduction of ACC fan power by 50% could lead to a COE reduction of about 0.5 $/kwh. Current finned tube condenser designs have considerable room for improvement. The NREL research effort has focused on innovative fin geometries that increase the ratio of heat transfer to fan power. To accomplish this, we increase the overall heat transfer coefficient by reducing the average boundary layer thickness, and we also increase the effective heat transfer area. Computer models have been developed and one prototype was built and tested. A patent application has been filed. Description of New Concepts Air-cooled condensers and other heat exchangers that involve the use of air on one side are limited in performance by the heat transfer on the air side. This is because air is a poor heat transfer fluid, owing to its low thermal conductivity and density. In order to compensate for this, such heat exchangers typically employ extended surfaces on the air side to increase the total area for air-side heat transfer. Air-cooled condensers used in geothermal power plants typically use tubes with circular fins packed together at perhaps ten fins per inch. A schematic of a single tube is shown in Figure 1. While the fins improve the situation, these condensers are still significantly limited in performance by the thermal resistance on the air side. Various means have been used to improve the heat transfer. These often circular tins \ tu... TIT TI Air Flow Figure 1. Conventional finned tube. 485

3 involve the generation of vorticity or turbulence to bring cooler air to the fin surface. While these techniques can increase heat transfer, they often result in an unacceptably large increase in pressure drop, and hence fan power, as well. The resistance to heat transfer on a surface is proportional to the thickness of the thermal boundary layer on that surface, because the boundary layer acts as an insulating layer of air. NREL research has focused on the development of innovative geometries that reduce the average thermal boundary layer thickness. Such a reduction in thermal boundary layer thickness will result in a proportional reduction in momentum boundary layer thickness and an associated increase in frictional pressure drop. However, total pressure drop is the sum of frictional pressure drop and form pressure drop (the latter being essentially independent of thermal boundary layer thickness), so it is possible to develop geometries for which the ratio of heat transfer to total pressure drop is increased. In conventional finned tube condensers, as the air passes between the fins and flows parallel to them, the thermal boundary layer thickens along the fins, resulting in increasing heat transfer resistance. Also, the tube itself tends to block flow over the portions of the fins downstream of the tube, reducing heat transfer in the wake region. NREL designs currently under development use porous fins in which the air flow is forced through the fins, instead of along the fins. We refer to these as transpired designs. These designs can use various types of thermally conductive porous material. One design we have considered involves a pleated array of plain perforated metal fins as shown in Figure 2. In this design, the condensate tube passes through the fins, much like a conventional design. However, the fins are connected in such a way that all (or a major portion of) the air flow is forced through the fins. rectangular perforated Air Flow Figure 2. Simple pleated tube-through-fin design. Another design is shown in Figure 3. Here, each condensate tube lies in the plane of a thicker porous fin. The fin might be a thicker metal plate containing holes. Or it might be built up from smaller strips of metal running parallel to the tube and containing grooves that provide passages for the upward flow or air E - I T -! k u b e air flow Figure 3. Simple tube-in-fin design. \perforated fin In either design, the flow through the holes or passages reduces the thermal boundary layer thickness on the front (upstream face) of the fin. This is because the air impinges on the surface and accelerates toward the holes. (Acceleration thins a boundary layer.) Also, because there are many holes, there is not sufficient travel distance along the fin for the boundary layer to thicken. (The front surface can also be viewed as undergoing boundary layer suction, which thins the overall boundary layer.) Even more importantly, the boundary layer is very thin inside the holes. Each hole acts like the entrance region of a pipe, where the boundary layer is very thin, because it has not yet had a chance to develop. Because we use fins of high porosity, the heat transfer area inside the holes is very significant and can be several times greater than the front surface area. (Heat transfer on the back of each fin is poor, but this is more than compensated for by the large amount of heat transfer on the front surface and in the holes.) Although perforated fin designs have been used before, virtually all of these have used the holes simply to disrupt the parallel flow and have not taken advantage of transpired flow. The geometry selected for the fins, together with the pressure drop across the fins, ensures fairly uniform flow through the entire fin surface. Thus this design also overcomes the wake problem associated with conventional finned tubes. The ratio of heat transfer to pressure drop is maximized by properly adjusting a number of available degrees of freedom: fin thickness, passage diameter, porosity, and fin face velocity (controlled by adjusting fin spacing, or the average space between fins arranged in a pleated, sawtooth-type configuration). Consideration must also be given to the fin efficiency, to ensure that sufficient heat can be transferred from the tube to the outer reaches of the fins. This constraint places an upper limit on the fin porosity. Using the most applicable heat transfer and pressure drop correlations available, we developed a spreadsheet model to optimize performance. However, the geometries being employed fall outside the range of correlations available in the literature and required extrapolation. Small-scale samples were built and tested to provide refinements. 486

4 Modeling Work where Re is Reynolds number based on the minimum free flow area air speed and the tube diameter; Pr is the Prandtl number; S, fin spacing [in]; h, fin height [in]; b, fin thickness [in]; AP, pressure drop [in water column]; G, mass velocity based on minimum free flow area [lbm/ft2h); d, tube diameter [in]; p, air density [lbm/ft3]; P,, tube pitch tranverse to approach air flow [in]; P1, tube pitch in the flow direction [in:]; T, tube temperature [OF]; M, air molecular weight [lbm]; and N, number of tube rows. For the tube-through-fin design, we used a Nusselt number heat transfer correlation and a correlation for pressure drop across a fin from Kutscher (1992): Nuporous = 2.748(P / D)"*208 Re, AP,,oro,s = 0.5pV (3' Re, where Nuporous is defined in terms of hole diameter and a heat transfer coefficient based on log mean temperature difference; P is hole pitch; D, hole diameter; Re,,, Reynolds number based on hole diameter and the speed of the air approaching the fin; APpomUs, pressure drop through the fin [Pal; p, air density [kg/ ms]; V, approach air speed [m/s]; and 6, fin porosity. It was necessary to extrapolate these correlations, because they were developed for transpired plates of lower porosity and lower face velocity, but no better correlations could be found. To model pressure drop in the channels between fins, we used a correlation developed for pleated air filters by Chen (1993). Heat conduction through the fins was modeled using normal fin efficiency relationships but with the thermal conductivity decreased in proportion to the void fraction caused by the holes. Details of the analysis can be found in Kutscher and Gawlik (1999). Because correlations directly applicable to the new geometries were not available in the literature, we also developed computational fluid dynamic models using FLUENT. FLU- ENT analysis of the pleated fin design revealed that the flow through the fins would be non-uniform with more of the flow entering a fin at its downstream end. We found that by making the fins in a parabolic shape, we could cause the flow to be quite uniform. FLUENT analysis also revealed the advantages of going to larger fin thicknesses, and reinforced the attractiveness of a tube in the plane of a thick fin. Experimental Work An Excel spreadsheet model was prepared for both the con- A small sample test rig was built to study the performance ventional finned tubes and the advanced transpired fin designs. of 8 cm by 8 cm (3 in by 3 in) pleated fin sections. This in- For the conventional finned tubes, correlations for Nusselt volved a simple transient heat transfer test in which the sample number and pressure drop were obtained from Ganapathy was heated and then allowed to cool by blowing room air through (1978): it. The overall heat transfer coefficient was determined from the rate of change of the temperature of the sample as it cooled. Nu = 0.134Re0.681 Pr1'3(S/h)o-200(S/ b) Pressure drop across each sample was also measured as a function of flow rate. AP = l. 5 8 ~ 1 0 ~ ~ G ' ~ ~ ~ ~ ((T d + ~ 460)/ ~ ~ M)N " ~ ~ ~ ~ ' ~ P Designers, ~ ~ ~ of ' pleated ~ P ~ air ~ filters ~ ~ ' have ~ long known that as the number of pleats increases, the pressure drop decreases because the velocity across each pleat decreases with the increasing filter area. However, eventually the channels become so small that channel pressure drop becomes significant. The sum of pressure drop across the pleats and in the channels reaches a minimum for a particular material at a particular pleat density, typically on the order of ten pleats per inch. Tests of our pleated fins with a number of different fin spacings revealed that total pressure drop was a minimum at only about 80 to 120 findm (2 to 3 firdin). We believe this is because the pressure drop across the fins is so low that channel pressure drop quickly becomes the dominant term. Of course, total heat transfer increases as the number of fins per inch increases. To test larger prototypes of advanced finned tube designs, we designed a heat exchanger test facility. The equipment consists of a 2.4 m3/s (5000 ftvmin) capacity wind tunnel, air duct and vacuum blower, and data acquisition equipment and instrumentation consisting of temperature and pressure transducers. The finned heat exchanger tubes are heated by electric resistance heaters. The electrical heat input is controlled by two Variacs. The wind tunnel is an open-circuit, blow-through design that provides wind speeds of up to 10 nl/s (2000 ftlimin) over the finned tubes located at the tunnel outlet. Room air is drawn into a belt-driven centrifugal fan with a 2 kw (3 hp) motor whose speed is controlled by a variable frequency AC drive. The air passes through a plywood diffuser and then into a flow-conditioning box which contains a honeycomb and a series of screens. The air then passes over the finned, heated tubes. The tubes are instrumented with thermocouples. Pressure drop across the tubes and temperature rise of the air passing through the bundle are measured and recorded with an HP data acquisition system. A 30 cm by 61 cm (1 ft by 2 ft) prototype of a pleated tubethrough-fin design was built. This consisted of six tubes with perforated fins. Each rectangular, perforated fin was bent such that the ends of every other adjacent fin would touch to force the air to pass through the fins. The prototype had a fin density of 276 fins/m (7 fins/in) and contained staggered holes of 1.2 mm (0.047 in) diameter with 28% porosity. Each fin was 0.8 mm (0.03 1) inches thick. (Although model predictions have indicated that higher porosities are desired, for the first prototype we chose material that was readily available off the shelf.) Electric heaters were installed inside the tubes to provide a controllable and measurable heat source. The prototype was mounted at the exit of an open-circuit, low-speed wind tunnel 487

5 that provided overall face velocities up to 4 m/s (790 ft/min). To allow a direct comparison with conventional technology, a conventional test unit was also constructed using finned tubes with fins spaced at 394 fins/m (10 firdin). For both the conventional and the prototype units, we measured heat input and air temperature rise over a range of air velocities. Figure 4 shows heat transfer and pressure drop results for the conventional design. At 3.5 m/s (689 ft/min), the overall UA (product of overall heat transfer coefficient and heat transfer area) per unit volume of heat exchanger is about 12,000 W"/C-m3 (644 BTU/h"F-fts) The fan power is about 5 kw/m3 (0.2 hp/ft3) Figure 5 shows the same results for the prototype design. Note that there is a large increase in the amount of heat transfer per unit volume (18,000 W/"C-m3 at 3.5 m/s (966 BTU/h F-ft3 at 689 fdmin}). The fan power has increased as well (to 8 kw/m3 (0.3 hp/ft3}), but to get such a high rate of heat transfer with the conventional design would require much higher flow rates and much higher fan power. To allow a meaningful comparison, we can reduce the air velocity for the prototype until its fan power matches that of the conventional unit. Fan power goes as the cube of velocity and heat transfer goes as velocity raised to a power less than one, so lowering the velocity or air for the prototype will reduce fan power much more rapidly than it reduces heat transfer. If we lower the face velocity on the prototype unit until the fan power is the same as for the conventional unit, the prototype delivers 30% more heat transfer than the conventional unit. This early prototype used a porosity of only about 28%, which we now know from our computer modeling is much lower than optimum. So we believe we can increase the ratio of heat transfer to fan power in optimum designs by 50% or more. The advantage of the prototype can best be seen when costs are taken into account. Figure 6 shows cost results for the conventional 394 findm (10 findin) finned tube design, the prototype (labeled as 7 findin), and another perforated fin design in which the tubes lie in the plane of thick fins. (The latter is not an experimental result, but was generated using FLU- ENT.) In this plot, the y-axis is the capital cost per unit Watt of heat duty, and the x-axis is the total present value of fan power cost (over a 20-year plant life) per unit of heat duty. Thus at >1\. r 0.2 e Ip om 0.1 constant cost line 0.0 I I I power $/W finned tube 7 finsfin. -tube in fin Figure 6. Capital and fan power costs per unit of heat duty for the conventional design and two advanced transpired fin designs vo Figure 4. UA per unit volume and fan power per unit volume as a function of air velocity for the conventional design. 14,000 12, ,000-8, , ,000-2, VO volume *Fan power per unit volume Figure 5. UA per unit volume and fan power per unit volume as a function of air velocity for the prototype design. any point on the plot, the total cost is the sum of the x-coordinate (fan power cost) and the y-coordinate (capital cost of the equipment). The straight dotted lines are lines of constant total cost (Le., the sum of x and y). Each curve was generated from a range of air velocities. The optimum velocity would be that for which the curve reaches the minimum total cost line. Note that the two advanced concepts show significantly lower total costs over the entire range. The minimum total costs (capital plus parasitic) are as follows: $0.20/W ($O.O59/(BTU/ h)) for the conventional design, $0.15/W ($0.044/(BTU/h)) for the transpired 276 fins/m (7 findin), tube-through-fin design, and $0.12/W ($0.035/(BTU/h)) for the transpired tube-in-fin design. These costs do not include any added material or construction costs associated with the new designs, because they will depend on the construction methods chosen. However, the results are conservative from a performance standpoint, because we believe there is considerable room for improvement of the advanced designs, as we develop better correlations for the many degrees of freedom. Interestingly, this analysis showed that the minimum-cost air velocity for all designs is about 1.5 m/s (295 fdmin). A typical design velocity for air-cooled condensers is 3.5 m/s (689 ftlmin). While this may be appropriate for many applications, our analysis suggests that this may be too high for a binary-cycle geothermal power plant, resulting in excessive fan power costs. 488

6 Future Work We are conducting additional FLUENT simulations to develop correlations that we can use in our spreadsheet model to develop improved designs. We will then build and test a second prototype. Once we have determined the best design, we will plan to conduct a field test at an operating binary-cycle plant that will allow a side-by-side test with a conventional unit. We are also seeking to collaborate with an industrial manufacturer to develop a cost-effective manufacturing technique for the best design. References Chen, D., D. Pui, B. Lui, Numerical Study and Optimization of Pleated Gas Filters, Proceedings-Insrirure of Envimnmentul Sciences, 1993, p Ganapathy, V. Design of Air-Cooled Exchangers: Process Design Criteria, Chemical Engineering, March 27, 1978, p Kutscher, C., Heat Exchange Effectiveness and Pressure Drop for Air Flow through Perforated Plates With and Without Crosswind, Journal ofheur Trunsfer, May 1994, Vol. 116, p Kutscher, C. and K. Gawlik, Air-Cooled Condenser Development: FY 1999 Progress Report, Sept. 30,