energies

Article Performance Analysis of an Updraft Tower System for Dry Cooling in Large-Scale Power Plants

Haotian Liu ID , Justin Weibel and Eckhard Groll *

Ray W. Herrick Laboratories, School of , Purdue University, West Lafayette, IN 47906, USA; [email protected] (H.L.); [email protected] (J.W.) * Correspondence: [email protected]; Tel.: +1-765-494-7429

Academic Editor: George Tsatsaronis Received: 13 October 2017; Accepted: 7 November 2017; Published: 9 November 2017

Abstract: An updraft tower cooling system is assessed for elimination of use associated with power plant rejection. Heat rejected from the power plant condenser is used to warm the air at the base of an updraft tower; buoyancy-driven air flows through a recuperative inside the tower. The secondary loop, which couples the power plant condenser to a at the tower base, can be configured either as a constant- pump cycle or a vapor compression cycle. The novel use of a can elevate the air in the tower base to increases the turbine power recovery and decrease the power plant condensing temperature. The system feasibility is evaluated by comparing the net power needed to operate the system versus alternative dry cooling schemes. A thermodynamic model coupling all system components is developed for parametric studies and system performance evaluation. The model predicts that constant-pressure pump cycle consumes less power than using a compressor; the extra compression power required for temperature lift is much larger than the gain in turbine power output. The updraft tower system with a pumped secondary loop can allow dry cooling with less power plant efficiency penalty compared to air-cooled condensers.

Keywords: power plant dry cooling; updraft tower; air-cooled condenser; vapor compression; thermodynamic feasibility analysis

1. Introduction Utility scale power plants must reject a huge amount of heat based on the second law of . The heat is not useful for power production, and must be rejected to the ambient at the lowest possible temperature to maximize the power plant efficiency. Typically, for each megawatt of generated, one to two megawatts of heat must be rejected [1]. The most common method of rejecting heat from the condenser of the power plant uses cooling towers. towers are widely used in industry and provide reliable long-term operation. The return water temperature from the to the condenser can be well controlled by the cooling tower water temperature. However, processing heat rejection using cooling towers consumes a large amount of water. The United States Geological Survey (USGS) data shows that water usage in thermoelectric power generation was 45% of the total national water use in 2010 [2]. In water-stressed arid regions, there is not enough water available to simultaneously satisfy the needs of power production and other critical functions. In areas with physical access to water sources, cooling towers are co-located with rivers or lakes. Nevertheless, heat rejected to the environment may cause temperature increases that negatively affect the local ecological system. From an energy perspective, the cooling towers do not recover or utilize any of the that is rejected. As a consequence of these disadvantages, government agencies have changed policy to limit open-loop water cooling for power plants [3–5].

Energies 2017, 10, 1812; doi:10.3390/en10111812 www.mdpi.com/journal/energies Energies 2017, 10, 1812 2 of 23

Thus, there is a significant need for alternatives to existing water cooling approaches that reduce or eliminate the water consumption associated with power plant heat rejection. Several different methods for power plant heat rejection have been investigated in recent decades that utilize the waste heat stream, such as a water canal system [6], a spray pond system [7], or rejecting the heat to an algae pond to produce biofuel [8,9]. However, water canal systems or spray pond systems still consume significant amounts of water when rejecting heat to the environment. In order to solve the water consumption problem, this paper concentrates on alternative dry cooling methods, a topic of recent significant technological interest due to regional water shortages [10]. One dry cooling method that is becoming increasingly adopted in newly constructed utility scale power plants is the use of air-cooled condensers (ACC) [11]. There are two general types of dry cooling systems using air-cooled condensers: direct and indirect. Indirect dry cooling systems use secondary water loops; the from the power plant is condensed by water in the secondary loop, which is then cooled within the air-cooled condenser. In the direct system, the power plant steam is ducted directly to the air cooled condenser with either mechanical draft or natural draft. Air-cooled condensers with a mechanical draft system are used in most of the dry cooling power plants [11]. In mechanically-driven direct air-cooled condensers, the power plant exhaust steam exiting the passes through a system of air-cooled heat exchangers, typically finned-tube heat exchangers arranged in an A-frame configuration [12]. The exhaust steam condenses on the inner tubes walls, flows downward to a condensate receiver tank by gravity, and then is pumped back to the . On the floor of the condenser, large mechanically-driven axial flow fans force the cooling air through the condenser. The power consumption associated with using air-cooled condensers can be classified in two categories: the mechanical power consumption required to drive the air through the heat exchanger and the penalty in power generation efficiency compared to cooling tower heat rejection due to the higher condensing temperature. Based on a report from the California Energy Commission [13], the fan power consumption is usually 1 to 1.5% of the total power output. The reported efficiency penalty on the power generation ranges from 5% on normal days to 20% on hot and windy days; wind reduces the ACC rates due to reduced fan performance or recirculation of the hot air [14]. The condensing temperature and the power generation efficiency penalty is strongly influenced by the environmental temperature, and hence is affected by the location. In the studied case, the location of the power plant had an average temperature 13.8 ◦C. A solar-driven updraft tower concept was originally proposed over 100 years ago and only later studied for generation purposes [15,16]. A solar updraft tower comprises a tall tower with a large solar collection area surrounding the base of the tower, and gas turbines at the inlet. Air is heated by the sun in the collector. Air at the top of the tower is cooler due to the height above sea level. The temperature and difference between the heated air and the ambient air at the top of the tower establishes the driving buoyancy force to draw air into the tower without any mechanical draft. is thereby converted to kinetic energy that can be extracted by the gas turbines. A 50 kW experimental plant was built in Manzanares (Spain) in 1981 and operated for two years [17]; the operating principle, construction details, and preliminary test results were described and analyzed [18]. This plant had a tower height of 194.6 m and a vertical axis single- turbine configuration with four blades. The experiment showed that the updraft tower would operate in real-world conditions and the performance agreed with model predictions [19]. A number of different theoretical modeling efforts have followed this first experimental demonstration to analyze various parameters’ influence on solar updraft tower system performance. Padki and Sherif developed a simple analytical model for a constant-diameter tower by using a momentum balance and assuming the Boussinesq approximation was valid to calculate the air velocity and kinetic energy at the outlet; the power output was assumed equivalent to the kinetic energy. Bernardes et al. studied the power output using a model that balanced the pressure potential and theoretical maximum volume flow rate at the tower inlet under a no-load condition to obtain the pressure drop and the volume flow rate at the updraft tower inlet; the same method was adopted by Koonsrisuk Energies 2017, 10, 1812 3 of 23 and Chitsomboon and Zhou et al. [20–22]. Pastohr et al. calculated the temperature and flow field in the solar updraft tower numerically [23]. The simulation results were validated against experimental data and showed a good agreement. Fluri and von Backström compared different modeling approaches and layouts for solar updraft turbines, and confirmed the assumptions of previous researchers that the turbine efficiency of a solar updraft tower is approximately 80% [24,25]. Nizetic and Klari evaluated the influence of turbine pressure drop on the updraft tower; the turbine pressure drop factors were in the range of 0.8 to 0.9 [26]. While solar updraft towers use solar energy to heat air at the tower base, an updraft tower could also operate in an analogous manner using power plant waste heat as the energy source. Namely, the solar updraft tower collector is replaced by a heat exchanger at the tower base. A secondary loop is needed to couple the waste heat source to the heat exchanger at the tower base to heat the air. A constant-pressure pump secondary loop with a condenser (i.e., tower base air heater) and an (i.e., power plant steam condenser) can be used as the secondary loop that transfers the heat from power plant steam to atmospheric air. The condenser surface area is distributed around the tower base and rejects heat to the buoyant-driven airflow. The updraft tower system with a constant-pressure pump cycle is one possible design. This technology is known as the natural draft dry cooling tower and has been analyzed in the literature and applied in large power plants. Zhao et al. developed a 3D numerical model to assess the cooling performance of a natural draft system with vertical and validated the model against published data [27]. Zou et al. combined the solar updraft tower concept with a natural draft cooling tower and analyzed this solar-enhanced natural draft cooling scheme [27,28]; they concluded that a solar updraft tower coupled to a power plant can significantly increase the updraft tower turbine power output, but requires a larger heat transfer area to reject the power plant condensing heat. In this paper, an innovative indirect dry cooling method is analyzed that uses an updraft tower, combined with a secondary loop with vapor compression cycle, to reject the power plant condenser heat and increase the energy recovered from the turbine. The system cooling efficiency and performance is benchmarked against air-cooled condensers to evaluate the thermodynamic feasibility. A traditional natural draft cooling system couples the updraft tower to the power plant using a constant-pressure pump cycle; this requires a larger heat transfer area to reject the condensing heat. In order to increase the heat rejection rate to the ambient air, the secondary fluid temperature can be increased at the tower base using a modified system with a conventional vapor compression cycle as the secondary loop. In this context, the constant-pressure pump cycle can be considered a special case of the vapor compression cycle by eliminating the compressor (pressure ratio equal to one) and using a liquid pump instead of the expansion valve. Results and design insights gained through study of the vapor compression secondary loop system can generally be applied to the traditional constant pressure pump system. In this paper, a quantitative, model-based analysis is used to evaluate the system performance and compare with traditional methods of power plant cooling. This paper includes a detailed thermodynamic feasibility analysis of the components and system performances of an updraft tower dry cooling system. State-point thermodynamic models are developed for the power plant, updraft tower, and secondary loop, and are coupled together to analyze the system performance. The simulation model is built in Engineering Equation Solver (EES), which has libraries for properties and can solve coupled systems of equations [29]. The analysis considers two secondary loop systems, a constant-pressure pump secondary loop as well as a vapor compression secondary loop. Parametric studies of the vapor compression secondary loop system are first carried out to determine the influence of the tower height, tower diameter, secondary loop condenser depth, and secondary loop evaporator heat transfer area on turbine power output and the required compressor work. A realistic updraft tower system design is formulated based on the results of these parametric studies. For this design, the constant-pressure pump secondary loop system performance is evaluated and compared to the vapor compression secondary loop system. Lastly, the penalty in power generation efficiency using a dry cooling updraft tower system is compared to a power plant using air-cooled condensers. Energies 2017, 10, 1812 4 of 23

Energies 2017, 10, 1812 4 of 23 2. System Description and Modeling Approach Energies2. System 2017, Description10, 1812 and Modeling Approach 4 of 23 The updraftThe updraft tower tower dry cooling dry cooling system system comprises comprise threes majorthree major subsystems: subsystems: the power the power plant, secondaryplant, loop,2. andsecondary System updraft Description loop, tower. and Figure updraftand Modeling1 presents tower. ApproachFigure a schematic 1 presen illustrationts a schematic of the illustrati dry coolingon of system the dry with cooling a power plantsystem connectedThe with updraft toa power an tower updraft plant dry connected towercooling using system to an a updraft vaporcomprise tower compressions three using major a vaporsecondary subsystems: compression loop. the The secondary power secondary plant, loop. loop transferssecondaryThe waste secondary heatloop, loop from and transfers theupdraft power wastetower. plant heat Figure steam from 1 condenser thepresen powerts a toplant schematic the steam heat exchanger condenserillustration atto of thethe the updraftheat dry exchanger cooling tower base. This heatsystemat the will withupdraft increase a power tower the plant base. air temperatureconnected This heat to will an at the updraftincrease base tower and,the air dueusing temperature to a thevapor density compression at the difference, base secondary and, drive due airflowloop.to the up throughThedensity thesecondary tower.difference, loop The drivetransfers kinetic airflow energywaste up heat through of thisfrom air the stream powertower. canplantThe thenkinetic steam be energycondenser converted of this to to theair electric heatstream exchanger powercan then using turbinesatbe the insideconverted updraft the towertotower electric core.base. power TheThis driving heatusing will turbines buoyancy increase inside forcethe airthe eliminates temperaturetower core. the atThe need the driving forbase mechanical and, buoyancy due to fans force the found eliminates the need for mechanical fans found in conventional dry cooling using air-cooled in conventionaldensity difference, dry cooling drive usingairflowair-cooled up through condensers. the tower. TheThe kinetic power energy generated of this by air the stream turbines can then can assist becondensers. converted Theto electric power generatedpower using by theturbines turbines inside can theassist tower in compression core. The driving of the refrigerantbuoyancy forcein the in compression of the refrigerant in the secondary loop. Detailed descriptions of the component models eliminatessecondary theloop. need Detailed for descriptionsmechanical offans the found compon inent conventional models developed dry cooling to predict using the behaviorair-cooled of developed to predict the behavior of this dry cooling system are introduced in this section. The coupled condensers.this dry cooling The systempower generatedare introduced by the in turbinesthis section. can The assist coupled in compression thermodynamic of the refrigerantmodels are insolved the thermodynamicsecondaryusing Engineering loop. models Detailed Equa are solvedtiondescriptions Solver using (EES). of Engineering the component Equation models Solverdeveloped (EES). to predict the behavior of this dry cooling system are introduced in this section. The coupled thermodynamic models are solved using Engineering Equation Solver (EES).

FigureFigure 1. Schematic 1. Schematic illustration illustration of of an an updraft updraft tower tower systemsystem with with a avapor vapor compression compression secondary secondary loop loop

for dryfor cooling dry cooling in large-scale in large-scale power power plants. plants. Figure 1. Schematic illustration of an updraft tower system with a vapor compression secondary loop 2.1. forPower dry Plantcooling Model in large-scale power plants. 2.1. Power Plant Model A simplified power plant model was developed based on realistic power plant components and 2.1.Aoperating simplified Power Plant conditions. power Model plantA block model diagram was describing developed the based key components on realistic of power the power plant plant components is shown and operatingFigureA conditions. simplified 2. The power power A block plant plant diagram modelis a three-pressure-s was describing developed thetage ba keysed -fired on components realistic Rankine power of thecycleplant power componentswith plantreheat is andand shown Figureoperatingregeneration.2. The power conditions. The plant primary A is block a three-pressure-stage steam diagram line fromdescribing the coal-firedboiler the key passes components Rankine through cycle aof high-pressure the with power reheat plant and(HP) is regeneration. turbine.shown The primaryFigurePart of 2. steamtheThe HP power line turbine from plant outlet the is boiler asteam three-pressure-s passes is reheat throughedtage in the acoal-fired high-pressure boiler andRankine passes (HP) cycle through turbine. with reheata Part two-stage ofand the HP turbineregeneration.intermediate outlet steam Thepressure is primary reheated (IP) steamturbin in the linee and boiler from two and the five-stage boiler passes passes low through pressure through a two-stage (LP) a high-pressure turbines. intermediate The (HP) other turbine. pressure portion (IP) of the HP turbine outlet steam floes to the feed-water heater that preheat the return water. turbinePart and of twothe HP five-stage turbine low outlet pressure steam (LP)is reheat turbines.ed in The the otherboiler portion and passes of the through HP turbine a two-stage outlet steam intermediateFurthermore, pressure portions (IP) of steamturbin aree and extracted two five-stage at the IP low turbine pressure and (LP)the LP turbines. turbines The to preheatother portion return floes to the feed-water heater that preheat the return water. Furthermore, portions of steam are extracted ofwater the inHP additional turbine outletfeed-water steam heaters. floes toThe the steam feed-water exiting theheater LP turbinesthat preheat flows intothe returnthe condenser. water. at the IP turbine and the LP turbines to preheat return water in additional feed-water heaters. The steam Furthermore,There are eight portions feed-water of steam heaters are extractedto preheat at the the re IPturn turbine water and from the the LP condenser.turbines to Fivepreheat feed-water return exitingwaterheaters the in LP areadditional turbines located flows feed-waterupstream into of theheaters. the condenser. condensa The steamte There pump exiting are and eight the three LP feed-water downstreamturbines flows heaters of intothe topump. the preheat condenser. the return waterThere from are the eight condenser. feed-water Five heaters feed-water to preheat heaters the re areturn located water upstreamfrom the condenser. of the condensate Five feed-water pump and threeheaters downstream are located of the upstream pump. of the and three downstream of the pump.

Figure 2. Schematic diagram of power plant model.

Figure 2. Schematic diagram of power plant model. Figure 2. Schematic diagram of power plant model.

Energies 2017, 10, 1812 5 of 23

A simplified model is built to predict the condensing heat transfer rate of the power plant for given operating conditions, and to subsequently couple the model with the secondary loop model in the system model. Pressure drop in the piping is neglected. The pressure and temperature are assumed to be known inputs based on baseline power plant operation with a water cooling tower. The outlet state of the condenser (and hence feed-water heaters) are saturated water. The power plant model is built as the system of equations formed from balancing energy and mass for each component. For the , the of the inlet and outlet steam are known for both heating and reheating processes. For the turbines, the power output is calculated based on the inlet properties, the outlet pressure, and a known isentropic efficiency: Energies 2017, 10, 1812 5 of 23 hin − hout ηs,turb = where hout,s = h(P = Pout,s = sin) (1) A simplified model ish builtin − toh outpredict,s the condensing heat transfer rate of the power plant for given operating conditions, and to subsequently. . couple the model with the secondary loop model in the system model. Pressure drop Win =them pipingout(h inis −neglected.hout) The condensation pressure and (2) temperature are assumed to be known inputs based on baseline power plant operation with a water For thecooling feed-water tower. heaters,The outlet itstate is assumedof the condenser that (a thend hence heater feed-water temperature heaters) isare the saturated saturated water. temperature at the given pressure;The power plant to model model theis built regeneration as the system cycleof equations performance formed from and balancing preheat energy of the andcondensing mass flow, it is also assumedfor each that component. all heaters For the have boilers, a constant the enthalpies terminal of the inlet temperature and outlet steam difference are known (TTD) for both that is used to heating and reheating processes. For the turbines, the power output is calculated based on the inlet calculate theproperties, outlet temperature the outlet pressure, of the an heater:d a known isentropic efficiency:

, = , where , =(=, =) (1) T,out = Theater − TTD (3) = ( − ) (2) Because the pressure drop in the heater is neglected, the inlet and outlet of the heaters have the same pressure. TheFor the water feed-water temperature heaters, it isis assumed assumed that constant the heater acrosstemperature the is pumps, the saturated and temperature the constant at the given pressure; to model the regeneration cycle performance and preheat of the condensing across any valves.flow, it Allis also other assumed component that all heaters models have a are constant modeled terminal using temperature energy difference and mass (TTD) balances. that is Given the input operatingused conditions,to calculate the the outlet power temperature plant of model the heater: solves for the steam mass flow rate and condensing heat transfer rate. = − TTD (3) Because the pressure drop in the heater is neglected, the inlet and outlet of the heaters have the 2.2. Secondarysame Loop pressure. Model The water temperature is assumed constant across the pumps, and the enthalpy constant across any valves. All other component models are modeled using energy and mass The secondarybalances. Given loop the can input be operating configured conditions, either the as power a constant-pressure plant model solves for pump the steam cycle mass withflow condenser, evaporator,rate and and pump condensing (Figure heat transfer3a) or rate. a vapor compression cycle with condenser, evaporator, expansion device, and compressor (Figure3b). The heat exchanger types and key geometric parameters 2.2. Secondary Loop Model of the secondary loop evaporator and condenser are shown in Figure3c,d respectively. The geometric The secondary loop can be configured either as a constant-pressure pump cycle with condenser, parameters areevaporator, selected and for pump a given (Figure existing 3a) or a vapor 702 compre MWssion power cycle plant, with condenser, the detailed evaporator, operating expansion conditions are given in Sectiondevice, 4.1 and. A compressor staggered-tube (Figure plate3b). The fin heat heat exch exchangeranger types is and selected key geometric as the parameters secondary of loopthe condenser for its low pressuresecondary drop loop andevaporator wide usageand condenser in air toare refrigerant shown in Figure heat transfer.3c,d respectively. The geometric The refrigerantparameters inside are selected the evaporatorfor a given existing of the 702 secondaryMW power plant, loop the must detailed condense operating conditions the power are plant steam. given in Section 4.1. A staggered-tube plate fin heat exchanger is selected as the secondary loop The exhaustedcondenser steam for mass its low flow pressure rate drop is generallyand wide usage very in air large to refrigerant for a power heat transfer. plant, which requires a large refrigerant massThe flow refrigerant rate in inside the secondary the evaporator loop. of the A second plateary heat loop exchanger must condense is the selected power plant as the steam. secondary loop evaporator forThe the exhausted current steam study mass due flow torate the is generally compact very design large for and a power efficient plant, heat which exchange; requires a large a large number refrigerant mass flow rate in the secondary loop. A plate heat exchanger is selected as the secondary of plates (orloop heat evaporator exchangers) for the can current be combinedstudy due to inthe parallelcompact design to accommodate and efficient heat the exchange; large massa large flow rates at reasonable flownumber velocities. of plates (or The heat number exchangers) of heat can be exchanger combined in plates parallel isto aaccommodate variable parameter the large mass that flow is modified as necessary torates maintain at reasonable the desired flow velocities. operating The number conditions. of heat exchanger The component plates is a variable sizes summarized parameter that is in Table1 are modified as necessary to maintain the desired operating conditions. The component sizes summarized chosen basedin on Table a guide 1 are chosen book based for heaton a gui exchangerde book for designheat exchanger [30]. design [30].

Figure 3. Cont.

Energies 2017, 10, 1812 6 of 23

Energies 2017, 10, 1812 6 of 23

Figure 3. (a) Schematic diagram of the constant pressure pump secondary loop model; (b) schematic Figure 3. (adiagram) Schematic of the vapor diagram compression of the secondary constant loop pressure model; keypump geometric secondary parameters of loop the (c model;) chevron (b) schematic diagram ofplate the vaporevaporator compression and (d) plate fin secondary condenser are loop also model; shown. key geometric parameters of the (c) chevron plate evaporator and (d) plate fin condenser are also shown. Table 1. Secondary loop evaporator and condenser key geometric parameters.

Parameter Value Evaporator plate length (mm) 320 Table 1. SecondaryEvaporator loop evaporator plate width and (mm) condenser key 110 geometric parameters. Evaporator channel spacing (mm) 3.5 EvaporatorParameter port diameter (mm) 10 Value Evaporator chevron angle (deg) 30 EvaporatorCondenser plate tube length diameter (mm) (mm) 25.4 320 EvaporatorCondenser plate fin widthspace (mm) (mm) 10 110 EvaporatorCondenser channel tube distance spacing (mm) (mm) 50.8 3.5 EvaporatorCondenser port fin diameter thickness (mm) 0.4046 10 EvaporatorCondenser chevron fin efficiency angle (deg) 0.8 30 Condenser tube diameter (mm) 25.4 The plate heat exchangerCondenser was modeled fin space for (mm) parallel flow operation. The 10 water-side inlet condition is determined by the powerCondenser plant operating tube distance conditions (mm); the refrigerant-side 50.8 conditions are set by the secondary loop evaporatingCondenser temperature. fin thickness The secondary (mm) loop model 0.4046 assumes that the refrigerant enters the evaporator asCondenser saturated finliquid efficiency and exits as saturated vapor. 0.8Hence, heat transfer occurs between the fluid streams exclusively in the two-phase region; the thermophysical properties and heat transfer coefficient are functions of quality. To evaluate the model, the heat exchange surface The platearea is heat discretized exchanger into stream-wise was modeled segments, for so parallel that the quality flow change operation. in each Thesegment water-side is small and inlet condition is determinedcan be by assumed the power constant. plant The properties operating and conditions; heat transfer coefficient the refrigerant-side can then be determined. conditions Given are set by the the inlet properties of both fluids, as well as the water-side mass flow rate, the outlet states for both secondary loopfluids evaporatingcan be calculated temperature. segment by segment. The secondary The total loopheat transfer model rate assumes can bethat calculated the refrigerant by enters the evaporatorsumming as saturated the segment-by-segment liquid and heat exits transfer as saturated rate. The plate vapor. overall Hence,heat transfer heat coefficient transfer in the occurs between the fluid streamsith segment exclusively is calculated in as: the two-phase region; the thermophysical properties and heat transfer coefficient are functions of quality. To evaluate the model,1 the heat exchange surface area is discretized into = (4) 1 + + + 1 stream-wise segments, so that the quality change, in each segment, is small and can be assumed constant. The propertieswhere and heatis the transferfouling resistance coefficient and can thenis the beconduction determined. resistance Given for the the plate. inlet The properties heat of both fluids, as welltransfer as the rate water-side through each mass plate for flow different rate, segments the outlet can statesbe determined for both as: fluids can be calculated segment by segment. The total heat transfer rate can = be( calculated, −,) by summing the segment-by-segment(5) heat transfer rate. TheThe plate outlet overallof the water/refrigeran heat transfert sides coefficient then can be in determined: the ith segment is calculated as:

, −,= (6) 1 U = , −= (7) (4) i 1 1 /αcold,i + R f l + Rcon + /αhot,i The correlation for the water-side two-phase heat transfer coefficient is [31]: where R f l is the fouling resistance and Rcon is the conduction resistance for the plate. The heat transfer rate through each plate for different segments can be determined as:

. Qi = Ui Ai(Thot,i − Tcold,i) (5)

The outlet of the water/refrigerant sides then can be determined:

. . mhot(hhot,i − hhot,i+1) = Qi (6)

. . mcold(hcold,i+1 − hcold) = Qi (7) The correlation for the water-side two-phase heat transfer coefficient is [31]: Energies 2017, 10, 1812 7 of 23

! −0.0848 kl Reg −0.0597 0.0973 Reg α = 98.7 Bo Xtt , < 9.0 (8) Dhyd Rel Rel

! −0.576 kl Reg −0.275 0.660 Reg α = 234.9 Bo Xtt , > 9.0 (9) Dhyd Rel Rel

 0.875 0.875 0.125 Reg x µl 1 − x ρg µl = , Xtt = (10) Rel 1 − x µg x ρl µg The refrigerant-side two-phase heat transfer coefficient is [32]:

 0.315   1.101 G2D  ρ −0.224 α = 982 kl β hyd g Bo0.320 Dhyd βmax ρmσ ρl (11) Bd < 4

  0.248 xGD 0.135 GD 0.351 ρ −0.223 α = 18.495 kl β hyd hyd g Bd0.235Bo0.198 Dhyd βmax µg µl ρl (12) Bd ≥ 4

 2 ρl − ρg gDhyd Bd = , β = 70◦ (13) σ max For the constant-pressure pump secondary loop, the pump is used to overcome the pressure drop in the piping and heat exchangers. Assuming an adiabatic process, the enthalpy of the pump inlet and outlet is known based on the temperature and pressure. The power input can then be calculated by:

. .  W pump = mre f h3,p − h5,p (14)

For the vapor compression secondary loop, the compressor located downstream of the evaporator compresses the refrigerant vapor to a higher pressure. The required compression work is calculated using the isentropic compressor efficiency and the refrigerant compressor inlet properties from the outlet of the secondary loop evaporator. Based on the given isentropic efficiency, the outlet enthalpy is solved:

h5,s − h4 ηcomp = (15) h5 − h4

Given the outlet pressure, the compressor outlet state can be calculated and the compressor work given by: . . Wcomp = mre f (h5 − h4) (16) The condenser of the secondary loop, at the circumference of the tower base, the ambient air drawn into the tower. A staggered-tube, plate fin heat exchanger was selected for this study due to the low air-side pressure drop characteristics. While the outer diameter of the annular condenser footprint will increase slightly with the condenser depth (DHX), the cross-sectional air flow area is assumed constant (based on the inner diameter for the footprint) for simplicity of calculating the heat transfer area. The refrigerant-side pressure drop is assumed to be dominated by the frictional pressure drop in the tubes. The pressure drop is calculated using the two-phase correlation method of Friedel [33], as detailed in AppendixA. The refrigerant-side heat transfer coefficient is calculated by the Chato correlation [34]: 3 gρl(ρl − ρv)kl h f g αre f = 0.555[ ] (17) µl(Tsat − Ts)D The air-side pressure drop is determined by an expression given by Kays and London [35]: Energies 2017, 10, 1812 8 of 23

2   Gmax v1  2 v2 As (v1 + v2) ∆PHX = [ 1 + σ − 1 + f ] (18) 2 v1 A f f 2v1 where Gmax = ρVmax is the maximum mass flux. The air-side heat transfer coefficient is calculated using a correlationEnergies 2017, 10, given 1812 by Kays and London [35]: 8 of 23

−0.418 0.011 k DhydReD ( + ) Δ = [(1+) −1+ ] αair = [Gmaxcp,air 2 ] (18) (19) 2D 2 hyd k2Pr 3 where = is the maximum mass flux. The air-side heat transfer coefficient is calculated Theusingε-NTU a correlation method wasgiven used by Kays to calculate and London the heat[35]: transfer rate. The overall UA, NTU, and condenser effectiveness can be calculated: . 0.011 Re = [ 1 ] UA = , (19) (20) 1 1 + A ηf inhD Atubes α s The ε-NTU method was used to calculate the heat transfer rate. The overall UA, NTU, and UA condenser effectiveness can be calculated:NTU = . (21) mair1cp,air UA = 1 −NTU1 (20) εcond = 1 − e + (22) ℎ The heat transfer rate from the refrigerant side toUA the air side is given by: NTU = (21) , . .   = ε − Qcond εcondm=1−aircp,air T f ,i Ti (22) (23) The heat transfer rate from the refrigerant side to the air side is given by: Given the refrigerant inlet properties and the condenser geometry, the model must be coupled =ε ( −) with the updraft tower model presented in the next section, , to solve the air mass flow rate(23) and outlet properties forGiven both the the refrigerant refrigerant inlet andproperties air side. and the condenser geometry, the model must be coupled Thewith expansion the updraft device tower model located presented after in the the condensernext section to reduced solve the theair mass pressure flow rate and and controlsoutlet the properties for both the refrigerant and air side. low-pressure-side mass flow rate. The expansion device model used assumes constant enthalpy. The expansion device located after the condenser reduced the pressure and controls the low- The expansionpressure-sidedevice mass outlet flow rate. state The pointexpansion is devi determinedce model used by assumes the low-side constant pressureenthalpy. The and inlet refrigerantexpansion enthalpy. device outlet state point is determined by the low-side pressure and inlet refrigerant enthalpy. 2.3. Updraft Tower Model 2.3. Updraft Tower Model The updraft tower has three main parts: a base, a tall chimney, and recuperative turbines (Figure4). The secondaryThe loop updraft condenser tower has is three installed main parts: around a base, the a circumference tall chimney, and of recupe the towerrative base. turbines The (Figure recuperative 4). The secondary loop condenser is installed around the circumference of the tower base. The turbines are located in the cross section of the chimney inlet. For each state point, two independent recuperative turbines are located in the cross section of the chimney inlet. For each state point, two variablesindependent are usedto variables determine are used the to properties. determine the properties.

Figure 4. Schematic diagram and key geometric parameters of the updraft tower. Figure 4. Schematic diagram and key geometric parameters of the updraft tower. The tower base inlet (state point 7) is ambient air that is drawn across the refrigerant-to-air heat Theexchanger tower base located inlet in the (state tower point base 7)and is exits ambient at stat aire point that 8. isUsing drawn the air-side across pressure the refrigerant-to-air drop and the heat predicted condenser heat transfer rate determined by the secondary loop condenser model presented exchanger located in the tower base and exits at state point 8. Using the air-side pressure drop and the in Section 2.2, the air pressure and enthalpy in the tower base can be respectively calculated as: predicted condenser heat transfer rate determined by the secondary loop condenser model presented in Section 2.2, the air pressure and enthalpy in the= tower−Δ base can be respectively calculated(24) as:

Energies 2017, 10, 1812 9 of 23

P8 = P7 − ∆PHX (24) . . Qcond = mair(h8 − h7) (25) The hot air inside the tower base flows through the turbine assuming an isentropic process and a constant head loss Hturb: P9 = P8 − ρ8gHturb (26)

s9 = s8 (27) . . Wturb = mair(h8 − h9) (28) The turbine outlet air (state point 9) rises to the tower outlet (state point 10); inside the tower, Bernoulli’s equation is used to describe the flow considering the gravitational head and frictional head:

. 2 . 2  ρ + ρ   m   1 1  m H − = 9 10 + air − + air ( + tower + ) P9 P10 gHtower 2 2 f K gρ10 (29) 2 A ρ10 ρ9 2gA ρ10 Dtower where K = 1 and f is Darcy friction coefficient calculated using the Colebrook relation [36]. The outlet state of the tower (state point 10) is determined by the tower height above sea level. According to Munson et al. [37], the temperature and pressure can be calculated as:

Ta = Tamb − βH (30)

g H βR P10 = Pamb[1 − β ] (31) Tamb where β = 0.0065 K m−1 is the laps rate, g is gravitational acceleration, and R = 287 J kg−1 K−1 is the gas constant. Note that Ta is the air temperature outside the tower, not necessarily the temperature of the tower outlet (state point 10), which should be higher. For T10, as reported by previous research [21,22], the temperature change across the chimney can assumed to be small, and thus:

T10 = T9 (32)

Since the pressure and temperature vary over a relatively small range, the air is assumed to behave as an ideal gas; the air enthalpy is a function of temperature while density and entropy are also . functions of pressure. The unknown system variables (P8, T8, P9, T9, P10, T10, ∆PHX and mair), can be determined by solving the system of Equations (11), (27), (33)–(36), (38) and (40). The updraft tower model can then be used to predict the turbine power output.

3. System-Level Model The objective of this model is to allow for a parametric analysis of the updraft tower system performance for a fixed power plant model. All component models are coupled together to solve for the system-level behavior. The secondary loop condenser is coupled with the updraft tower; the secondary loop evaporator is coupled with the power plant. The refrigerant mass flow rate through the condenser and evaporator must match in the closed secondary loop. A schematic diagram of the coupled model, with key input and output variables, is shown in Figure5. In the air flow path, the inlet temperature and pressure are fixed at the ambient conditions. The power plant condensing temperature and steam mass flow rate are determined by the fixed power plant operating data. These parameters are the external inputs to the system. Other system variables must be specified as the operating conditions (e.g., refrigerant type, secondary loop condensing and evaporating temperature) or selected geometries (e.g., tower height and diameter, secondary loop condenser size). The state point variables are unknown and need to be solved by the coupled system model. Energies 2017, 10, 1812 10 of 23 Energies 2017, 10, 1812 10 of 23

Figure 5. Coupled system model schematic drawing and key input and output variables. Figure 5. Coupled system model schematic drawing and key input and output variables. The following process is used to solve the coupled system model for the complete set of Theoperating following conditions: process is used to solve the coupled system model for the complete set of operating1. conditions:The water-side conditions determined by the power plant model, the evaporator heat exchanger area, and refrigerant evaporating temperature are used to predict the refrigerant mass flow rate. 1. The2. water-sideThe ambient conditions conditions, determined tower size, by and the conden powersing plant temperature model, the are evaporatorused in the heatcoupled exchanger area, andcondenser refrigerant and tower evaporating model to predict temperature the refrigerant are used mass to flow predict rate. the refrigerant mass flow rate. 2. The3. ambientThe predicted conditions, refrigerant tower mass size,flow rates and in condensing steps 1 and 2 must temperature match. If they are do used not match, in the the coupled condenseroperating and towercondition model (tower to size predict and condensing the refrigerant temperature) mass flow are adjusted rate. and the refrigerant mass flow rate is recalculated until it matches step 1. 3. The4. predictedThe pump/compression refrigerant mass work flow is predicted rates in using steps the 1 pump/compressor and 2 must match. model. If they do not match, the operating5. The conditionair mass flow (tower rate and size turbin ande power condensing output are temperature) calculated. are adjusted and the refrigerant mass flow rate is recalculated until it matches step 1. 4. The4. pump/compressionResults and Discussion work is predicted using the pump/compressor model. 5. The4.1. air Power mass Plant flow Operation rate and turbine power output are calculated. The power plant model is based on a real power plant system. Full-load operation data from this 4. Results and Discussion system are used to solve the condensing heat transfer rate and steam mass flow rate. The power plant pressure ratio, turbine work output, and steam condensing temperature are given as input variables. 4.1. Power Plant Operation The input parameters of the power plant are shown in Table 2. The model outputs for these inputs Theare power shown plant in Table model 3. is based on a real power plant system. Full-load operation data from this system are used to solve the condensing heat transfer rate and steam mass flow rate. The power plant Table 2. Power plant model key input parameters. pressure ratio, turbine work output, and steam condensing temperature are given as input variables. Parameter Value The input parameters of the power plant are shown in Table2. The model outputs for these inputs are Higher pressure (bar) 173.7 shown in Table3. Intermediate pressure (bar) 54.6 Low pressure (bar) 37.1 Table 2. PowerHP plantturbine model efficiency key input parameters. 0.9 IP and LP turbine efficiency 0.8 ParameterTTD Value5.5 Boiler heat input (MW) 1442 HigherSteam condensing pressure (bar) temperature (°C) 42.6 173.7 Intermediate pressure (bar) 54.6 LowTable pressure 3. Power (bar) plant simulation results. 37.1 HP turbine efficiency 0.9 Parameter Value IP and LP turbine efficiency 0.8 Work output (MW) 702 TTD 5.5 Steam mass flow rate (kg s−1) 357.8 Boiler heat input (MW) 1442 Condensing heat (MW)◦ 842 Steam condensing temperatureEfficiency ( C)0.49 42.6

Table 3. Power plant simulation results.

Parameter Value Work output (MW) 702 Steam mass flow rate (kg s−1) 357.8 Condensing heat (MW) 842 Efficiency 0.49 Energies 2017, 10, 1812 11 of 23

4.2. Updraft Tower System Parametric Studies A single secondary loop refrigerant type is selected in order to conduct parametric analyses of system performance. Considering the practical concerns of safety, heat transfer performance, and wide usage in the power production industry, water was selected as the secondary loop refrigerant. It has to be noted that for regions that experience temperature below freezing, water by itself would not be a suitable secondary refrigerant. However, in such regions, water could be mixed with to provide suitable freeze protection or a conventional HFC refrigerant could be selected. Different parametric studies have been completed to explore how the plate heat exchanger area, the tower size (height and diameter), and the secondary loop condenser size and temperature influence the system performance. A set of baseline system parameters and operating conditions for the tower and secondary loop that are used for the parametric studies is given in Table4. The baseline operating condition in Table4 will be explained in detail in Section 4.3. All of the parametric studies are carried out using the vapor compression secondary loop, which is more general and allows broader parametric variations compared to the simplified constant-pressure pump secondary loop. The compressor and turbine isentropic efficiency are set constant to 0.85 [38]. The ambient temperature is set as 25 ◦C, and the ambient pressure at 1 atm.

Table 4. Baseline operating conditions of the secondary loop and key parameters for the parametric studies.

Parameter Value Condensing temperature (◦C) 45.5 Evaporating temperature (◦C) 40 Tower height (m) 350 Tower diameter (m) 180 Condenser height (m) 50 Condenser depth (m) 23.7 Refrigerant type Water (R-718)

4.2.1. Secondary Loop Evaporating Temperature The secondary loop evaporating temperature set point determines the required plate heat exchanger heat transfer area (i.e., number of plates). A parametric study is conducted by varying this evaporating temperature and observing the change in the required heat transfer area and compression work (results shown in Figure6). All other variables are fixed at the baseline conditions shown in Table4. The compression work will decrease significantly as the evaporating temperature increases. For the constant power plant steam-side inlet temperature, a higher secondary loop evaporating temperature will increase the evaporating pressure accordingly. Hence, the pressure ratio across the compressor will decrease, which lowers the compression work (for a fixed secondary loop condensing pressure). However, the required evaporator heat transfer area increases significantly as the evaporating temperature increases. As the temperature difference in the plate heat exchanger decreases, more heat exchange area is required to condense heat at the same rate. Furthermore, plates are added to the heat exchanger in order to increase the heat transfer area, which will decrease the mass flow rate in each channel and lower the heat transfer coefficient, leading to the nonlinear trend observed in Figure6. The turbine power output of the updraft tower system is 4.0 MW and is constant with varying secondary loop evaporating temperature because the secondary loop condenser and updraft tower operate at fixed conditions. Hence, the secondary loop evaporating temperature presents a tradeoff between increasing the system efficiency and reducing the required heat exchanger area. Energies 2017, 10, 1812 12 of 23 Energies 2017, 10, 1812 12 of 23 Energies 2017, 10, 1812 12 of 23

Figure 6. Secondary loop evaporator heat transfer area and compression work change with secondary FigureFigure 6.6. Secondary loop evaporator heat transfer area and compression workwork changechange withwith secondarysecondary loop evaporating temperature. looploop evaporatingevaporating temperature.temperature. 4.2.2. Updraft Tower Height and Diameter 4.2.2.4.2.2. UpdraftUpdraft TowerTower HeightHeight andand DiameterDiameter The updraft tower operation, in tandem with the secondary loop condenser design, determines TheThe updraftupdraft tower tower operation, operation, in in tandem tandem with with the the secondary secondary loop loop condenser condenser design, design, determines determines the the recuperated power and compression work of the system. Parametric studies varying the tower recuperatedthe recuperated power power and compressionand compression work work of the of system. the system. Parametric Parametric studies studies varying varying the tower the heighttower height and tower diameter were carried out separately for a fixed secondary loop evaporating andheight tower and diameter tower diameter were carried were out carried separately out sepa for arately fixed secondaryfor a fixed loop secondary evaporating loop temperatureevaporating temperature and power plant operating conditions. Figure 7 shows the air mass flow rate and andtemperature power plant and operatingpower plant conditions. operating Figure conditions.7 shows Figure the air 7 mass shows flow the rate air and mass refrigerant flow rate mass and refrigerant mass flow rate as a function of the updraft tower height. A taller tower yields a larger flowrefrigerant rate as mass a function flow rate of as the a updraftfunction tower of the height.updraft Atower taller height. tower A yields taller atower larger yields temperature a larger temperature differential from the bottom to top of the tower. This increases the buoyancy-driven air differentialtemperature from differential the bottom from to topthe ofbottom the tower. to top This of the increases tower. theThis buoyancy-driven increases the buoyancy-driven air mass flow rate. air mass flow rate. However, for the fixed secondary loop condenser design, the higher air-side mass However,mass flow for rate. the However,fixed secondary for the loop fixed condenser secondar design,y loop thecondenser higher air-side design, mass the flowhigher rate air-side necessitates mass flow rate necessitates a lower condensing temperature for the refrigerant mass flow rate to match the aflow lower rate condensing necessitates temperature a lower condensing for the refrigerant temperature mass for the flow refrigerant rate to match mass the flow evaporator rate to match side the of evaporator side of secondary loop. secondaryevaporator loop. side of secondary loop.

Figure 7. Air and refrigerant mass flow rate change with tower height. FigureFigure 7.7. AirAir andand refrigerantrefrigerant massmass flowflow raterate changechange withwith towertower height.height. Figure 8a shows the variation of the condensing temperature as a function of tower height. A Figure 8a shows the variation of the condensing temperature as a function of tower height. A givenFigure secondary8a shows loop thecondensing variation temperature of the condensing then determines temperature the ascompressor a function work of tower and height.turbine given secondary loop condensing temperature then determines the compressor work and turbine Apower given outputsecondary (Figure loop 8b). condensing The reduced temperature condensing then temperature determines offered the compressor by a taller tower work andreduces turbine the power output (Figure 8b). The reduced condensing temperature offered by a taller tower reduces the powercompressor output ratio, (Figure and8 therebyb). The reducedcompression condensing work, si temperaturegnificantly. offeredThe turbine by a tallerpower tower output reduces increases the compressor ratio, and thereby compression work, significantly. The turbine power output increases withcompressor the tower ratio, height and due thereby to the compression increased driving work, significantly. buoyancy force. The Note turbine that power this increased output increases driving with the tower height due to the increased driving buoyancy force. Note that this increased driving withbuoyancy the tower force, height due to due the toreduced the increased temperature driving at buoyancythe top of the force. taller Note tower, that dominates this increased the drivingturbine buoyancy force, due to the reduced temperature at the top of the taller tower, dominates the turbine powerbuoyancy output force, behavior due to thecompared reduced with temperature the decrease at the of topthe ofair the inlet taller temperature tower, dominates due to the the lowered turbine power output behavior compared with the decrease of the air inlet temperature due to the lowered powercondensing output temperature. behavior compared with the decrease of the air inlet temperature due to the lowered condensingcondensing temperature.temperature.

Energies 2017, 10, 1812 13 of 23 Energies 2017, 10, 1812 13 of 23 Energies 2017, 10, 1812 13 of 23

FigureFigure 8. 8.( a()a) Condensing Condensing temperature;temperature; ( (bb)) as as well well as as compression compression work work and and turbine turbine power power output, output, Figure 8. (a) Condensing temperature; (b) as well as compression work and turbine power output, changechange with with tower tower height. height. change with tower height. Figure 9 similarly shows the system performance, but for varying updraft tower diameter. The Figure9 similarly shows the system performance, but for varying updraft tower diameter. effectsFigure of increasing 9 similarly the showstower diameterthe system are performanc analogouse, to but increasing for varying the towerupdraft height. tower Increasing diameter. theThe The effects of increasing the tower diameter are analogous to increasing the tower height. towereffects diameter of increasing reduces the towerthe condensing diameter are temperature analogous toand increasing compression the tower work; height. the turbine Increasing power the Increasing the tower diameter reduces the condensing temperature and compression work; the turbine outputtower willdiameter increase reduces due to the the condensing increasing conden temperatureser area and available compression for increasing work; towerthe turbine diameter. power poweroutput output will increase will increase due to due the to increasing the increasing conden condenserser area available area available for increasing for increasing tower tower diameter. diameter.

Figure 9. Compression work and turbine power output change with tower diameter. FigureFigure 9. 9.Compression Compression work work andand turbineturbine power output output change change with with tower tower diameter. diameter. 4.2.3. Secondary Loop Condenser Depth 4.2.3.4.2.3. Secondary Secondary Loop Loop Condenser Condenser Depth Depth The baseline secondary loop condenser height is selected to prevent significant flow constriction intoThe theThe baseline tower, baseline such secondary secondary that air loop loop flow condenser condenser can be assu heightheightmed is uniform se selectedlected acrossto to prevent prevent the significanttower significant base flow inlet. flow constriction constrictionA larger intosecondaryinto the the tower, tower, loop such condensersuch that that air flow depthair flow can presents be can assumed be a assutradeoff uniformmed betweenuniform across larger across the tower heat the baseexchangetower inlet. base surface A inlet. larger areaA secondary larger and loopincreasedsecondary condenser air-side loop depth condenser pressure presents depthdrop; a tradeoff presentsthe higher betweena tradeoff inlet temperature larger between heat larger exchangeand heatincreased exchange surface pressure area surface and drop area increased will and air-sideoppositelyincreased pressure air-sideaffect drop; the pressure air the mass higher drop; flow inlet therate temperature higherthrough inle thetand temperaturetower. increased Thus, and pressurefor aincreased specific drop workingpressure will oppositely condition, drop will affect thethereoppositely air massis an optimized flow affect rate the through depthair mass to the beflow identified tower. rate Thus,through via fora parametric the a specific tower. study workingThus, offor the condition,a specificcondenser thereworking size. is an condition, optimized depththere toFigure is be an identified optimized10 shows viathe depth refrigerant a parametric to be identified mass study flow via of rate thea parametric an condenserd turbine study power size. of output the condenser with varying size. condenser Figure 10 shows the refrigerant mass flow rate and turbine power output with varying condenser depth.Figure The horizontal10 shows dotted the refrigerant line shows the mass refriger flowant rate mass and flow turbine rate required power to match output the with mass varyingflow depth. The horizontal dotted line shows the refrigerant mass flow rate required to match the mass flow condenserrate of the depth. evaporator.The horizontal There are dottedtwo possible line shows condenser the refrigerantdepths for the mass specific flow tower rate required size and toother match rate of the evaporator. There are two possible condenser depths for the specific tower size and other thebaseline mass flowparameters. rate of The the evaporator.smaller condenser There depth are two opti possibleon yields condenser a much higher depths power for output the specific than the tower baseline parameters. The smaller condenser depth option yields a much higher power output than the sizelarger and depth. other The baseline smaller parameters. depth condenser The smaller should condenser always be depthchosen optionfrom a yieldspower aoutput much perspective, higher power larger depth. The smaller depth condenser should always be chosen from a power output perspective, outputand also than saves the largerspace depth.and material. The smaller This result depth can condenser be explained should by alwaysthe change be chosen of air mass from flow a power rate and output towerand also inlet saves air temperaturespace and material. in Figure This 11. result With can an bein creasingexplained condenser by the change depth, of theair massheat transferflow rate area and perspective,tower inlet and air alsotemperature saves space in Figure andmaterial. 11. With Thisan in resultcreasing can condenser be explained depth, by the the heat change transfer of air area mass flowbecomes rate and larger tower and inletthe operating air temperature condensing in Figure temperature 11. With is fixed. an increasing The ambientcondenser air passing depth, through the heat thebecomes condenser larger will and take the operatingup more heatcondensing and this temp willerature increase is fixed.the tower The ambientinlet (condenser air passing outlet) through air transfer area becomes larger and the operating condensing temperature is fixed. The ambient air passing temperaturethe condenser as willwell takeas the up temperature more heat anddifference this w illacross increase the towerthe tower height, inlet which (condenser will increase outlet) the air through the condenser will take up more heat and this will increase the tower inlet (condenser outlet) drivingtemperature buoyancy as well force as inside the temperature the tower. Conversely, difference acrossthe larger the air-sidetower height,pressure which drop will increaseincrease thethe air temperature as well as the temperature difference across the tower height, which will increase the flowdriving resistance. buoyancy The force air-side inside pressure the tower. drop Conversely, is dominant, the and larger causes air-side the airpressure mass flow drop rate will through increase the the driving buoyancy force inside the tower. Conversely, the larger air-side pressure drop will increase the towerflow resistance.(and power The output) air-side to decreasepressure withindrop is increasing dominant, condenser and causes depth. the air mass flow rate through the flowtower resistance. (and power The output) air-side to pressure decrease drop within is dominant,increasing condenserand causes depth.the air mass flow rate through the tower (and power output) to decrease within increasing condenser depth.

Energies 2017, 10, 1812 14 of 23 EnergiesEnergies 2017 2017, 10,, 10 1812, 1812 14 14of 23of 23 Energies 2017, 10, 1812 14 of 23

Figure 10. Refrigerant mass flow rate and work output change with condenser depth. Figure 10. Refrigerant mass flow flow rate and work output change with condenser depth. Figure 10. Refrigerant mass flow rate and work output change with condenser depth.

Figure 11. Air mass flow rate and condenser outlet air temperature change with condenser depth. Figure 11. Air mass flow flow rate and condenser outlet airair temperature change with condenser depth. 4.2.4.Figure Power 11. Plant Air mass Condensing flow rate Temperature and condenser outlet air temperature change with condenser depth. 4.2.4. Power Plant Condensing Temperature 4.2.4.4.2.4. PowerPowerThe power PlantPlant CondensingCondensingplant model TemperaturewasTemperature fixed at constant operating conditions for the results shown in SectionsThe power 4.2.1–4.2.3. plant However, model was from fixed the updraft at constant tower operating system perspective, conditions a higherfor the steam results condensing shown in TheThe powerpower plant model was was fixed fixed at at constant constant operating operating conditions conditions for for the the results results shown shown in Sectionstemperature 4.2.1–4.2.3. would However, decrease from the secondary the updraft loop tower compressor system perspective, pressure ratio a higher and compressor steam condensing work. inSectionsConversely, Sections 4.2.1–4.2.3. 4.2.1 a higher–4.2.3 However, However,power fromplant fromthe condensing updraft the updraft to temperaturewer system tower perspective,will system reduce perspective, thea higher power steam aplant higher condensing thermal steam temperature would decrease the secondary loop compressor pressure ratio and compressor work. condensingtemperatureefficiency. Thetemperaturewould reduction decrease in would power the secondary decrease generation theloop as a secondary fucompressornction of the loop pressure condensing compressor ratio temperature, and pressure compressor calculated ratio work. and Conversely, a higher power plant condensing temperature will reduce the power plant thermal compressorConversely,using the work.power a higher plantConversely, power model, plant is a shown higher condensing in powerFigure temperature 12. plant condensing will reduce temperature the power will plant reduce thermal the efficiency. The reduction in power generation as a function of the condensing temperature, calculated powerefficiency. plant Thethermal reduction efficiency. in powerThe generation reduction as in a power function generation of the condensing as a function temperature, of the condensing calculated using the power plant model, is shown in Figure 12. temperature,using the power calculated plant model, using theis shown power in plant Figure model, 12. is shown in Figure 12.

Figure 12. Relative reduction in power plant output with increasing condensing temperature from a baseline temperature of 42.2 °C.

Figure 12. Relative reduction in power plant output with increasing condensing temperature from a FigureFigureThe 12.tradeoff12. RelativeRelative between reductionreduction the in indecreased powerpower plantplant required outputoutput compressor withwith increasingincreasing power condensingcondensing versus the temperaturetemperature power generation fromfrom aa baseline temperature of 42.2 °C. reductionbaselinebaseline for temperaturetemperature an increasing ofof 42.242.2 power◦ °C.C. plant condensing temperature is analyzed for the baseline updraft tower system, as defined by Table 4. The net power for cooling compared with the water-cooled The tradeoff between the decreased required compressor power versus the power generation powerThe planttradeoff at abetween condensing the temperaturedecreased required of 42.2 °C compressor under normal power operation, versus canthe bepower calculated generation by reductionThe tradeoff for an increasing between thepower decreased plant condensing required compressor temperature power is analyzed versus for the the power baseline generation updraft reduction for an increasing power plant condensing temperature is analyzed for the baseline updraft reductiontower system, for an as increasing defined by power Table plant 4. The condensing net power temperature for cooling is compared analyzed forwith the the baseline water-cooled updraft tower system, as defined by Table 4. The net power for cooling compared with the water-cooled power plant at a condensing temperature of 42.2 °C under normal operation, can be calculated by power plant at a condensing temperature of 42.2 °C under normal operation, can be calculated by

Energies 2017, 10, 1812 15 of 23

towerEnergies system,2017, 10, 1812 as defined by Table4. The net power for cooling compared with the water-cooled15 of 23 power plant at a condensing temperature of 42.2 ◦C under normal operation, can be calculated by combiningcombining thethe powerpower reductionreduction duedue toto anyany changechange inin power plantplant efficiencyefficiency (negative),(negative), compressioncompression workwork (negative),(negative), andand updraftupdraft towertower powerpower outputoutput (positive).(positive). TheThe resultsresults areare shownshown inin FigureFigure 13 13..

FigureFigure 13.13. CompressorCompressor power,power, powerpower reduction,reduction, turbineturbine powerpower outputoutput andand netnet powerpower forfor coolingcooling toto water-cooledwater-cooled baselinebaseline withwith varyingvarying powerpower plantplant condensingcondensing temperature.temperature.

TheThe updraftupdraft towertower powerpower outputoutput staysstays constantconstant becausebecause thethe updraftupdraft towertower sizesize andand operatingoperating conditionsconditions areare fixed.fixed. TheThe compressorcompressor powerpower decreasesdecreases asas thethe powerpower plantplant condensingcondensing temperaturetemperature increasesincreases duedue toto thethe lowerlower pressurepressure ratioratio needed.needed. TheThe net total power produced increases even though thethe powerpower plantplant condensingcondensing temperaturetemperature isis increasing.increasing. This indicates thatthat thethe compressorcompressor powerpower requiredrequired toto operateoperate thethe vaporvapor compressioncompression secondarysecondary looploop atat thethe normalnormal powerpower plantplant condensingcondensing temperaturetemperature isis dominantdominant comparedcompared toto thethe powerpower plantplant efficiencyefficiency penalty.penalty. Similarly,Similarly, decreasingdecreasing thethe powerpower plantplant condensingcondensing temperaturetemperature willwill decreasedecrease thethe netnet totaltotal powerpower producedproduced becausebecause thethe extraextra compressioncompression power required would be much larger th thanan the increase in power plant plant outputoutput power. power. Ultimately,Ultimately, thethe casecase withoutwithout anyany compressioncompression workwork andand thethe highesthighest powerpower plantplant condensingcondensing temperaturetemperature providesprovides thethe leastleast powerpower penaltypenalty forfor drydry coolingcooling comparedcompared toto waterwater cooling.cooling. SectionSection 4.44.4 willwill furtherfurther explore explore this this extreme extreme case case in whichin which there there is no is compression no compression work (constant-pressurework (constant-pressure pump secondarypump secondary loop) and loop) the powerand the plant power condensing plant temperaturecondensing istemperature allowed to increaseis allowed accordingly. to increase accordingly. 4.3. Baseline Design Performance 4.3. Baseline Design Performance Based on the results of the parametric studies presented in Section 4.2, the reasoning for the chosen baselineBased design on the parameters results of forthe the parametric updraft towerstudies dry presented cooling systemin Section with 4.2, the the vapor reasoning compression for the secondarychosen baseline loop, shown design in Tableparameters4, can befor understood the updraft for thetower given dry power cooling plant system heat rejection with the load vapor and workingcompression conditions. secondary The loop, secondary shown loop in Table evaporating 4, can be temperature understood was for selectedthe given by power considering plant heat the tradeoffrejection between load and increased working requiredconditions. heat The transfer secondary area and loop reduced evaporating compression temperature work was as presented selected by in Figureconsidering6. There the is tradeoff a diminishing between return increased in reducing required the heat compression transfer area work and as thereduced heat transfercompression area increaseswork as presented rapidly above in Figure an evaporating 6. There is temperature a diminishing of 40 return◦C. For in example,reducing the the heat compression transfer area work must as bethe tripled heat transfer to increase area increases the evaporating rapidly temperatureabove an evaporating to 41 ◦C totemperature achieve amarginal of 40 °C. For reduction example, in thethe compressorheat transfer work. area Itmust is likely be tripled that the to cost increase of the evaporating a larger heat temperature exchanger would to 41 not °C outweighto achieve the a performancemarginal reduction benefit forin anthe evaporating compressor temperature work. It is of likely ~40 ◦ C,that corresponding the cost of tobuilding a heat transfer a larger area heat of ~620,000exchanger m 2would(~170,000 not platesoutweigh in the the selected performance heat exchanger). benefit for an evaporating temperature of ~40 °C, correspondingThe tower to height a heat (350 transfer m) and area diameter of ~620,000 (180 m m)2 (~170,000 were chosen plates to inbe the as selected large as heat possible exchanger). based on extensionThe tower of height practical (350 construction m) and diameter limits. (180 For m) example, were chosen the tallest to be cooling as large tower as possible in the based world on is theextension202 m tallof practical cooling towerconstruction (142 m limits. diameter) For exam of theple, Kalisindh the tallest Thermal cooling Power tower Station in the world in Jhalawar, is the India202 m [ 39tall]. cooling Using the tower selected (142 towerm diameter) height of and the diameter, Kalisindh the Thermal secondary Power loop Station condensing in Jhalawar, temperature India is[39]. 45.5 Using◦C to the match selected the refrigeranttower height mass and flowdiameter rate,in the the secondary secondary loop loop condensing evaporator. temperature A required is compression45.5 °C to match work ofthe 18.1 refrigerant MW is calculated mass flow using rate the in compressor the secondary model. loop evaporator. A required compression work of 18.1 MW is calculated using the compressor model. Lastly, the secondary loop condenser depth must be optimized for maximum turbine power output. The secondary loop condenser height is first fixed as 50 m considering the flow area of the condenser inlet and the size of existing large air condensers. The condenser depth of 23.7 m

Energies 2017, 10, 1812 16 of 23

Lastly, the secondary loop condenser depth must be optimized for maximum turbine power output. The secondary loop condenser height is first fixed as 50 m considering the flow area of the condenser inlet and the size of existing large air condensers. The condenser depth of 23.7 m maximizes the work output while ensuring that the refrigerant mass flow rate in the secondary loop is balanced on the condenser and evaporatorEnergies sides. 2017, For 10, 1812 the baseline design, the turbine power output is 4.0 MW. 16 of 23 The performance of the system is assessed based on the required net power input, calculated as the requiredmaximizes compressor the work input output power while minus ensuring the that turbine the refrigerant output power mass flow recovered. rate in the In secondary the baseline loop design, is balanced on the condenser and evaporator sides. For the baseline design, the turbine power output the required net power input is 14.1 MW (compressor input power of 18.1 MW and turbine output power is 4.0 MW. of 4.0 MW) toThe condense performance the steamof the system of a 700 is assessed MW power based plant. on the required net power input, calculated as the required compressor input power minus the turbine output power recovered. In the baseline 4.4. Constantdesign, Pressure the required Pump net Secondary power input Loop is 14.1 MW (compressor input power of 18.1 MW and turbine output power of 4.0 MW) to condense the steam of a 700 MW power plant. In the previous parametric studies (Section 4.2), the influence of system components geometry and operating4.4. conditions Constant Pressure have been Pump studied Secondary for Loop a realistic benchmark design of an updraft tower dry cooling system with a vapor compression secondary loop; the system was designed to maintain the same power In the previous parametric studies (Section 4.2), the influence of system components geometry plant condensingand operating temperature conditions ashave the been original studied water-cooled for a realistic powerbenchmark plant. design However, of an updraft Section tower 4.2.4 dry revealed that allowingcooling the system power with plant a vapor condensing compression temperature secondary to loop; increase, the system so as was to reducedesigned the to compressionmaintain the work, yielded asame net benefitpower comparedplant condensing to operating temperature the updraft as the toweroriginal system water-cooled at the same power condensing plant. However, temperature as the water-cooledSection 4.2.4 revealed power plant.that allowing In this the section, power theplant compressor condensing temperature of the secondary to increase, loop so is as effectively to replacedreduce with a the pump compression and, assuming work, yielded no pressure a net benefit drop compared in the connection to operating piping, the updraft the secondary tower system loop was at the same condensing temperature as the water-cooled power plant. In this section, the compressor evaluated as a constant-pressure pump loop; the refrigerant evaporates in the power plant condenser at of the secondary loop is effectively replaced with a pump and, assuming no pressure drop in the the sameconnection temperature piping, as it the condenses secondary in theloop updraft was eval toweruated condenser.as a constant-pressure pump loop; the In comparisonrefrigerant evaporates to the vapor in the compression power plant condenser cycle, the at updraft the same tower temperature secondary as it condenses loop condenser in the has a lower refrigerantupdraft tower inlet condenser. temperature when using a constant pressure pump cycle. The tower height itself must be adjustedIn comparison in order to to the match vapor the compression refrigerant cycle, mass the flowupdraft rates tower with secondary the secondary loop condenser loop evaporator. has a lower refrigerant inlet temperature when using a constant pressure pump cycle. The tower height For any given tower height, this sets the power plant condenser temperature. The relationship of tower itself must be adjusted in order to match the refrigerant mass flow rates with the secondary loop height andevaporator. the power For plant any given condensing tower height, temperature this sets is the shown power in plant Figure condenser 14a. The temperature. net power forThe cooling ◦ comparedrelationship with the of water-cooled tower height and power the power plant atplant a condensing condensing temperature temperature is shown of 42.2 in FigureC under 14a. normal operationThe can net bepower calculated for cooling by compared combining with thethe water-cooled power deduction power plant due at to a condensing any change temperature in power plant efficiencyof (negative),and 42.2 °C under normal updraft operation tower powercan be calc outputulated (positive). by combining The the result power is shown deduction in Figuredue to any14. With a constantchange pressure in power pump plant secondary efficiency loop, (negative),and an intractably updraft tall tower tower power (820 output m) is(positive). required The to result maintain is the shown in Figure 14. With a constant pressure pump secondary loop, an intractably tall tower (820 m) power plant condensing temperature at the water-cooled operational temperature where there is no is required to maintain the power plant condensing temperature at the water-cooled operational efficiencytemperature loss; however, where atthere this is condition, no efficiency there loss; ishoweve a netr, increase at this condition, in power there plant is a output. net increaseAs the in tower height decreasespower plant and output. power plantAs the condensing tower height temperature decreases and increases, power theplant net condensing power for temperature cooling decreases due to aincreases, reduced turbinethe net power power for output cooling anddecreases significant due to a power reduced plant turbine efficiency power output penalty. andThere significant is a critical tower heightpower of plant 590 efficiency m for which penalty. the There constant is a pressurecritical tower pump height secondary of 590 m loop for which system the that constant yields zero net changepressure in total pump power secondary output. loop At system the tower that yields height zero of net 350 change m, the in constanttotal power pressure output. At pump the tower secondary height of 350 m, the constant pressure pump secondary loop provided a net change in total power − loop providedoutput of a net−3.7 changeMW, consistent in total with power the result output for ofthe vapor3.7 MW, compression consistent secondary with the loop result without for any the vapor compressioncompression secondary work loop in Figure without 13. any compression work in Figure 13.

Figure 14. (a) Required tower height to maintain a power plant condensing temperature at varying Figure 14. (a) Required tower height to maintain a power plant condensing temperature at temperature; (b) net power for cooling. varying temperature; (b) net power for cooling.

Energies 2017, 10, 1812 17 of 23 Energies 2017, 10, 1812 17 of 23

4.5. Dry Cooling Performance Comparison In this section, the constant-pressure pump secondary loop and vapor compression secondary loop areare compared compared to to an air-cooledan air-cooled condenser condenser for dry for cooling. dry cooling. As described As described in Section in1, Sectionthe traditional 1, the powertraditional plant power cooling plant method cooling is method a water-cooled is a water-cooled cooling tower. cooling All tower. of the All dry of coolingthe dry systems’cooling performancessystems’ performances are benchmarked are benchm againstarked the against water-cooled the water-cooled cooling tower cooling by calculating tower by calculating the net change the netin total change power in total when power using when each using different each drydifferent cooling dry system cooling to system reject theto reject same the amount same amount of heat asof heatthe cooling as the tower.cooling For tower. the water-cooled For the water-cool cooling tower,ed cooling the power tower, plant the condensingpower plant temperature condensing is temperaturefixed at 42.2 ◦isC, fixed which at is42.2 the °C, original which operating is the orig conditioninal operating for the condition power plant. for the The power only powerplant. thatThe onlyneeds power to be that considered needs to when be considered using a water-cooled when using a cooling water-cooled tower iscooling the water tower pump is the power, water whichpump power,is relatively which small; is relatively for this givensmall; 702 for MWthis powergiven 702 plant, MW the power water pumpplant, the power water is typicallypump power ~2 MW. is typicallyFor the air-cooled ~2 MW. For condenser, the air-cooled a 5% reduction condenser, in totala 5% power reduction output in total of the power power output plant isof assumed the power to plantreject is the assumed heat from to reject the power the heat plant from [13 the]. For power the calculationplant [13]. For of constant-pressurethe calculation of constant-pressure pump secondary pumploop and secondary vapor compression loop and vapor secondary compression loop, second varyingary tower loop, heights varying are tower considered; heights are all ofconsidered; the other parametersall of the other including parameters tower including diameter, tower heat diamet exchangerer, heat area, exchanger and heat area, exchanger and heat depth exchanger are otherwise depth arefixed otherwise at the values fixed shownat the values in Table shown4. At eachin Table specific 4. At tower each specific height, tower the corresponding height, the corresponding power plant powercondensing plant temperaturecondensing temperature will be different will be for differen the twot for different the two secondary different loopsecondary cycles, loop as discussedcycles, as discussedin Section 4.2in Section; the constant-pressure 4.2; the constant-pressure pump secondary pump loopsecondary needs loop a higher needs power a higher plant power condensing plant condensingtemperature. temperature. The power reductionThe power and reduction turbine and output turbine can thenoutput be calculated.can then be A calculated. 2 K temperature A 2 K temperaturedifference is assumeddifference in is the assumed secondary in the loop secondary heat exchanger. loop heat exchanger. Figure 1515 shows shows the the change change in total in totalpower power for the for vapor the compression vapor compression secondary secondary loop, constant- loop, pressureconstant-pressure pump secondary pump secondaryloop, and loop,air-cooled and condenser air-cooled system condenser compared system to comparedthe water-cooled to the water-cooledcooling tower coolingcase as towera function case of as tower a function height. of towerThe water-cooled height. The cooling water-cooled tower and cooling air-cooled tower condenserand air-cooled results condenser appear resultsas horizontal appear lines as horizontal because linesthe tower because height the toweris not heightapplicable. is not The applicable. change Thein total change powerin becomes total power less negative becomes as less the negativetower height as the increases tower for height the updraft increases tower for system. the updraft The constanttower system. pressure The pump constant secondary pressure loop pump has a secondary much smaller loop reduction has a much in the smaller total power reduction compared in the tototal the power vapor comparedcompression to secondary the vapor loop. compression At the same secondary tower loop.height, Ateven the though same towerthe constant- height, pressureeven though pumpthe secondary constant-pressure loop requires pump a higher secondary power loop plant requires condensing a higher temperature power plant that condensing decreases thetemperature that decreases of power the thermalgeneration, efficiency it takes of more power power generation, to use a itcompressor takes more to power increase to usethe refrigeranta compressor loop to condensing increase the temperature refrigerant loopto reject condensing the sametemperature amount of heat. to reject The theconstant-pressure same amount pumpof heat. secondaryThe constant-pressure loop universally pump has secondary better perf loopormance universally than the has vapor better compression performance secondary than the loop. The performance difference between these two secondary loop types will eventually become vapor compression secondary loop. The performance difference between these two secondary loop zero, because, if the tower becomes high enough, a pump loop can condense all the heat from power types will eventually become zero, because, if the tower becomes high enough, a pump loop can plant and no pressure ratio is needed. The constant pressure pump secondary loop has a better condense all the heat from power plant and no pressure ratio is needed. The constant pressure pump efficiency for the given tower design. secondary loop has a better efficiency for the given tower design.

Figure 15. 15. ChangeChange in total in total power power of constant- of constant- pressure pressure pump pumploop, vapor loop, compression vapor compression loop, and loop, air- cooledand air-cooled condenser condenser compared compared against againsta water-cooled a water-cooled cooling coolingtower. tower.

Energies 2017, 10, 1812 18 of 23

The performance comparison with an air-cooled condenser shows that with a tower height over 220 m, the vapor compression secondary loop works better than an air-cooled condenser, while still providing dry cooling capability. The constant pressure pump secondary loop has a higher performance than an air-cooled condenser for all tower heights shown. Even compared to the traditional water-cooled cooling tower, the pumped loop can produce a net power benefit if a tower higher than approximately 480 m is constructed, due to the heat recovery by the updraft tower turbine. This is consistent with the result of the constant-pressure pump secondary loop shown in Figure 14; note that Figure 14 shows the net power consumed by the cooling system, which is offset from Figure 15 by 2 MW due to the power required by the water-cooled cooling tower. When rejecting same amount of heat from the power plant, the constant-pressure pump secondary loop has a better energy performance than the vapor compression secondary loop. While the tower height of 480 m is very tall compared with a water cooling tower, the primary motivation of this updraft tower system is to eliminate the water usage; the air-cooled condenser system is the appropriate dry cooling benchmark. Compared to the air-cooled condenser, the constant-pressure pump secondary loop updraft tower system can achieve better energy performance for reasonable tower heights and achieve the same performance with ~225 m height. This first-order analysis of the updraft tower system suggests that this system is competitive from an energy consumption perspective.

4.6. Practical Considerations In this research, the simulation model analyzes the system performance and feasibility from a thermodynamic perspective. However, there are multiple other constraints that would need to be considered to construct and operate an updraft tower system. Several of these challenges, and potential solutions, are discussed in the following section.

4.6.1. Updraft Tower While the system performance always increases with the updraft tower size, the maximum size will be limited due to the practical construction constraints, especially the height. The constant pump pressure loop needs a tower height of at least 225 m to provide improved performance comparable to the air-cooled condenser benchmark. A multi-tower system could be used with several smaller updraft towers in parallel, yielding a very large effective tower diameter. The smaller height towers could be easier to build while providing a similar performance to a single tall tower with smaller diameter. Condensing the same amount of heat using smaller tower will decrease the turbine power output slightly because of the decreasing height. However, the reduced tower height helps to overcome challenges in design, construction, and cost of the updraft tower system. As an example, if three smaller updraft towers with heights of 110 m each were used to condense the same amount of heat, the multi-tower system results in the approximately same power output with less than 0.5 MW decrease as compared to the original optimized design using a single 225 m-tall tower. Special design considerations would be needed for the turbine in the updraft tower. Considering the system proposed in this paper has a tower diameter of 180 m, one turbine with a single rotor is not feasible. Multiple turbines as well as the number and arrangement of blades should be considered with a design and layout to maximize power output and minimize the pressure head loss [40].

4.6.2. Secondary Loop Refrigerant If the updraft tower system were to be used in large-scale power plant with hundreds of megawatts of condensing heat, a very large amount of refrigerant (and mass flow rate) would be required. Different types of refrigerant can be used in the system such as R134a, R290, or R600a. The performance of different would most likely not vary significantly except for the required refrigerant mass flow rate. The turbine power outputs would be similar because the condensing of the secondary loop as well as the tower and condenser geometries remain similar. However, the required Energies 2017, 10, 1812 19 of 23 mass flow rates will be quite different because the secondary loop must handle the same heat rejection from the power plant steam for all of the refrigerants. The enthalpy of evaporation determines the refrigerant mass flow rate in each case. Handling and selection of the refrigerant should mainly consider safety, potential ecological impacts, and affordability. Among all considered refrigerants, water has the smallest mass flow rate with very low price and safe properties, which makes water an attractive refrigerant for this application. However, the low pressure operation of water could be a problem. The operating are far lower than the ambient pressure, which needs special consideration in design and maintenance. Another potential challenge is that the freezing point of water is high, and would require certain precautions to avoid freezing problem in cold climates. One possible solution is to use a water-ammonia mixture. Ammonia has a much lower freezing temperature, and as a secondary potential benefit, the mixture will have a temperature glide when going through two-phase heat transfer region. This can be advantageous for the condenser operation because the air side will also have a temperature glide that can be aligned with the refrigerant side. In order to realize the benefits of such a temperature glide, and solve the freezing problem, the mass fraction of ammonia needs to be carefully evaluated.

5. Conclusions An updraft tower dry cooling system for large-scale power plant is evaluated. The updraft tower system can condense steam from the power plant without using mechanical fans or consuming water. The performance of the system is evaluated based on the net power needed to drive the system (i.e., difference between the recuperative turbine power output and required work to drive the pump or compressor), which depends on the refrigerant type, component sizing, and operating conditions. The system can work with a vapor compression secondary loop or a constant pressure pump secondary loop. Parametric studies are performed to illustrate the influence of different key parameters using a model-based analysis. For the vapor compression secondary loop: higher tower height and larger condenser inner diameter increase the turbine power output and decrease the compression work; the secondary loop condenser placed at the base of the tower has an optimized depth to maximize turbine power output; increasing the power plant condensing temperature reduces the power plant efficiency but requires a smaller pressure ratio across the compressor; the compression work is dominant compared to the power plant efficiency reduction. From evaluation of the constant pressure pump secondary loop, it was found that replacing the compressor with a pump will require a higher power plant condensing temperature to reject the same amount of heat, which will reduce the power plant output, but also eliminates the compression work. Our results show that the compression work is dominant compared to the power plant efficiency reduction; the compression work required by the vapor compression secondary loop is not compensated by the additional power generated in return. Using the same tower diameter, the constant pressure pump secondary loop has a better energy efficiency than the vapor compression secondary loop. Compared to alternative dry cooling with an air-cooled condenser, an updraft tower system with constant pressure pump secondary loop has better performance. For a 702 MW full-load operation power plant, using a secondary constant pressure pump loop, an updraft tower system with a tower 225 m in height and 180 m in diameter has half of the power generation penalty compared to the air-cooled condenser. Therefore, when using a secondary constant pressure pump loop, the tower size can be further reduced based on the allowable performance penalty. Increasing the tower height to 480 m with the same system yields the same power generation efficiency as a water-cooled cooling tower system, but eliminates water consumption entirely. This research only analyzes the system feasibility from an energy efficiency perspective; further economic analysis is required to further understand the cost-feasibility compared to the capital investment and payback period of alternative dry cooling technologies. Energies 2017, 10, 1812 20 of 23

Acknowledgments: Special thanks to Duke Energy for their financial support of this work and to Neil Kern for his technical oversight and mentorship of the project. Author Contributions: Haotian Liu built the simulation model. Eckhard Groll, Justin Weibel and Haotian Liu analyzed the data and wrote the paper. Conflicts of Interest: The authors declare no conflict of interest.

Nomenclature

A area, m2 2 Aff free flow area of finned passages in heat exchanger, m 00 Bo Boiling number (q /Gh f g ) −1 −1 cp specific heat, kJ kg K D diameter, m De depth, m f friction factor Fr Froude number (µ/pgl) g gravitational constant, m s−2 G mass flux, kg m−2 s−1 3 2 Gr Grashof number (gβ(Ts − T∞)L /υ ) k thermal conductivity, W m−1 K−1 K minor loss coefficient H height, m Hturb turbine head loss, m h specific enthalpy, kJ kg−1 −1 h f g heat of vaporization, kJ kg L length, m . m mass flow rate, kg s−1 Nu Nusselt number (hL/k) NTU Number of Transfer Units p pump P pressure, kPa Pr Prandtl Number (cpµ/k) Q heat, kJ . Q heat rate, kW q00 heat flux, kW m−2 R gas constant, kg−1 K−1 Re Reynolds number (ρυL/µ) 2 −1 Rth thermal resistance, K m W T temperature, ◦C U velocity, m s−1 U overall heat transfer coefficient, W m−2 K−1 t time, s TTD terminal temperature difference, ◦C v specific volume, m3 kg−1 . W mechanical power, W We Weber Number (ρν2l/σ) Greek α heat transfer coefficient, W m−2 K−1 χ vapor quality β laps rate, K m−1 η efficiency ε effectiveness Energies 2017, 10, 1812 21 of 23

µ dynamic , kg m s−1 ρ density, kg m−3 σ surface tension, N m−1 φ relative Φ f ric friction multiplier Subscripts amb ambient bo boiler cold cold fluid cond condenser evap evaporator fin heat exchanger fin g gas hot hot fluid heater feed water heater HX heat exchanger HP high-pressure turbine hyd hydraulic l liquid LP low-pressure turbine i index number in inlet IP intermediate-pressure turbine max maximum out outlet p pump pp power plant pump secondary loop pump re f refrigerant s isentropic sat saturation sur surroundings sur f surface tt turbulent-turbulent turb turbine v vapor water water

Appendix A The friction pressure drop is calculated by the multiplier:

2 ∆Pf ric = ∆PlΦ f ric (A1) where ∆Pl is the liquid pressure drop, calculated by:

L 2 1 ∆Pl = 4 fl( /di )Gl ( /2ρl ) (A2) and fl and fv are the vapor phase and liquid phase friction coefficient, which are determined by:

0.079 0.079 = = fl 0.025 , fv 0.025 (A3) Rel Rev

The friction multiplier is calculated by:

3.24FH 2 = E + Φ f ric 0.045 0.035 (A4) Frl Wel Energies 2017, 10, 1812 22 of 23 where G2 0.045 = l Frl 2 (A5) gdiρH ρ f E = (1 − χ)2 + χ2 l v (A6) ρv fl

F = χ0.78(1 − χ)0.224 (A7)

 ρ 0.91 µ 0.19 µ 0.7 H = l v 1 − v (A8) ρv µl µl 2 Gl Wel = (A9) σρH −  χ 1 − χ  1 ρH = + (A10) ρv ρl

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