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Numerical simulation of water spray for pre-cooling of inlet air in natural draft dry cooling towers
Applied Thermal Engineering 61 (2013) 416e424
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Numerical simulation of water spray for pre-cooling of inlet air in natural draft dry cooling towers Abdullah Alkhedhair*, Hal Gurgenci, Ingo Jahn, Zhiqiang Guan, Suoying He Queensland Geothermal Energy Centre of Excellence, School of Mechanical and Mining Engineering, The University of Queensland, Brisbane 4072, Australia
h i g h l i g h t s Numerical investigation of inlet air cooling by water spray in NDDCTs was performed. Strong links identified between droplet size, air velocity, evaporation and trajectory. Pre-cooling of up to 8.1 C predicted. The maximum evaporation was achieved with the smallest droplet size.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 26 April 2013 Accepted 7 August 2013 Available online 24 August 2013
This paper presents a numerical investigation of inlet air pre-cooling with water sprays to enhance the performance in Natural Draft Dry Cooling Towers (NDDCT). A 3-D numerical model of a test channel was generated and the evaporation from a single spray nozzle was analyzed. The droplet evaporation and the resulting cooling of air were predicted for a range of inlet air conditions and spray characteristics. The results showed that up to 81% evaporation can be achieved for water droplets of 20 mm at a velocity of 1 m/s and that, droplet transport and evaporation strongly depend on droplet size and air velocity. Ó 2013 Elsevier Ltd. All rights reserved.
Keywords: Natural draft Spray cooling Pre-cooling Numerical modelling Complete evaporation
1. Introduction This paper presents results of a study on the effect of droplet size and air velocity on the droplet transport, the droplet evaporation, and the cooling performance of inlet air spraying to enhance the performance of natural draft dry cooling towers (NDDCTs). This knowledge is crucial for designing spray cooling systems for NDDCTs in hot and dry ambient conditions. Deployment of dry cooling technologies rather than wet cooling technologies has become a necessity for many power plants despite the lower performance (particularly during high ambient temperate periods), owing to water consumption restrictions, environmental regulations and flexibility of plant site selection. For geothermal plants, perhaps, dry cooling is the only option as they are located in arid areas. Although dry cooling systems offer advantages of water conservation and environmental protection, the cooling * Corresponding author. Tel.: þ61 411217779. E-mail addresses: [email protected], (A. Alkhedhair).
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performance is low relative to wet cooling as it relies mainly on convective heat transfer to dissipate heat rather than evaporation. This is worst during high ambient temperature periods, where dry cooling systems experience a significant reduction in power generation [1]. The impact on the plant revenue is even higher since these periods represent peak power demand for most locations. Dry cooling tower performance can be enhanced during these periods, by spraying water into the inlet air in order to reduce the cooling air temperature. Reducing the cooling media temperature, leads to an increase in overall cycle efficiency, thus allowing some of the performance reduction to be recovered. However, this requires careful consideration of water spray generation to avoid issues related to incomplete evaporation of droplets. Although a considerable amount of literature has been published on droplet transport and evaporation in air, no study exists on analyzing spray cooling under conditions typical of NDDCTs. Many efforts have been made over the past decades to improve the performance of dry cooling systems in order to make them more efficient compared to wet cooling. A number of studies have found that hybrid cooling technologies have the potential to
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Nomenclature a CD Cpa Cpw D Df Dv90 E F FD FG hc hD hfg hi0 J i0 k _a m _w m md Nu Pr P q_ conv q_ lat
Acceleration of droplet (m/s2) Drag coefficient Specific heat of air (J/kg K) Specific heat of water (J/kg K) droplet diameter (mm) Diffusion coefficient (m2/s) 90% of water volume made up of droplets of this size and smaller (mm) Internal energy (J/kg) Forces acting on droplet (N) Drag force (N) Gravity force (N) Heat transfer coefficient (W/m2K) Mass transfer coefficient (m/s) Latent heat of water vaporization (J/kg) 0 Sensible enthalpy of species i (J/kg) 0 Diffusing flux of species i (Kg/m2s) Thermal conductivity of air (W/m K) Air flow rate (kg/s) Water flow rate (kg/s) Droplet mass (kg) Nusselt number Prandtl number Pressure (Pa) Convective heat transfer (J/s) Latent heat transfer rate (J/s)
alleviate this problem while avoiding issues related to wet cooling, particularly in terms of water utilization [2,3]. Several hybrid cooling approaches have been developed to offset the disadvantages related to the use of dry cooling during high temperature periods [4]. One of the patterns of hybrid cooling to boost the performance during hottest hours is the use of evaporative cooling by introducing a small amount of water for a limited time to cool the entering air. There are two methods that carry out this concept which can be classified: deluge cooling and evaporative pre-cooling (spray cooling and wetted-media cooling) [5]. Regarding to deluge cooling, due to the direct contact of water with heat exchanger bundles, corrosion and fouling become crucial issues. This requires using treated water and regular cleaning or utilizing condenser tubes with galvanic corrosion protection which prevents use of fins. Wetted-media cooling also is an efficient way to cool inlet air. However, significant pressure drop is created which reduce air mass-flow rate causing a decline in heat rejection rate [6]. Over the past decades, spray cooling has become more popular due to its simplicity, low capital cost, and ease of operation and maintenance [7]. Furthermore, air stream motion is not affected by the presence of droplets. Thus, pressure drop due to spray existence is insignificant and can be neglected [8]. Inlet air spray cooling has many applications such as gas turbine fogging and refrigerative cooling. It has been used extensively in gas turbine systems. More than 1000 gas turbine stations are equipped with inlet air spray cooling [9]. Applications found in power plants employing dry cooling towers include one of the largest coal fired station in Australia with 750 MW power output [10], a waste wood plant in USA with 25 MW capacity, and a geothermal plant in USA [3]. Inlet air cooling by spray can provide 100% saturation efficiency depending on the design conditions [11]. In this method, the inlet air is cooled by evaporation. Spray nozzles are used to distribute water into the inlet air and to provide a large watereair contact
RH ReD Sc Sd Se Sm Smo Sh T Va Vd Vr vi vj Yj
417
Relative humidity (%) Droplet Reynolds number Schmidt number Droplet surface area (m2) Source term of energy (W/m3) Source term of mass (Kg/m3s) Source term of momentum (Kg/m2s2) Sherwood number Temperature ( C) Air velocity (m/s) Droplet velocity (m/s) Droplet relative velocity (m/s) Air velocity components (m/s) Mass fraction of species j
Greek symbols Density (kg/m3) Mean strain tensor (1/s) Dynamic viscosity of air (kg/m s) Viscous dissipation (W/m3)
r dij m F
Subscripts a air d droplet t time int dropleteair interface i,j Cartesian coordinate directions
surface by producing small droplets through atomization as can be seen in Fig. 1. Although spray cooling has found successful applications in process coolers and gas turbine fogging, the large scale applications in power industry have been limited. Several issues limit the application and the main one is the incomplete evaporation of water droplets before reaching the heat exchanger bundles. This can cause corrosion, scaling and fouling [12]. Special spray nozzles may be required to achieve full evaporation requirement. High pressure nozzles provide small water droplets but at a higher cost. Droplet size is a critical parameter of spray characteristics. The knowledge of the optimum droplet size is crucial for designing spray cooling systems. According to Wells [13], droplet size distribution in the sprays is a major parameter that impacts droplet movement and evaporation efficiency during its interaction with air. Over the past decades, droplet size effect on evaporation distance has been the subject of many studies, experimentally and numerically. Complete evaporation of droplets was first considered in an experiment carried out by Wachtell [14]. The study aimed to
Water Tank
Water
Air
Cooling Tower
Fig. 1. A schematic diagram of inlet air cooling by spray.
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investigate the effect of spray cooling on heat exchanger performance by injecting water droplets into the intake air stream. The study showed that droplets of 20 mm diameter or smaller would evaporate completely. He concluded that droplet size and wet-bulb depression are two principal parameters that control the evaporation rate. However, the findings of Wachtell [14] experiment are not supported by the subsequent research. Effectiveness of using water spray to cool the inlet air of an air cooled heat exchanger was investigated experimentally [15]. In the experiment, various droplet diameters ranging from 16 to 28 mm were injected from a distance of 2.7 m below the heat exchanger. The average air velocities were 1.3 m/s and 3 m/s for low and high fan speeds, respectively. His study showed that droplets of 16e28 mm in diameter did not evaporate completely and reached the heat exchanger pipes. This was argued due to dissimilarity on the operating conditions where a small change of one parameter would have a significant difference on the distance required for complete evaporation. Furthermore, Branfield [16] performed an experiment and found that even droplets of 10 mm diameter and smaller reached the heat exchanger surface. The relation between droplet size and evaporation distance was also studied numerically and experimentally in relation to gas turbine fogging. Most of these studies were not concentrating on complete evaporation. For example, in gas turbine applications, droplet sizes of 5e15 mm are permitted to enter the compressor, where droplets provide additional cooling [17]. Nevertheless, as small droplet size is often used in gas turbine to achieve high evaporation efficiency, complete evaporation was achieved in a number of studies. Numerical investigations were carried out by Chaker [18] and Wang [19] for residences time of 1 and 0.8 s, respectively. It was found by Chaker [18] that for sprays with Dv90 ¼ 18.5 mm, all injected water evaporated, whereas 14% nonevaporated water was existed when Dv90 ¼ 46.2 mm. Likewise, Wang [19] illustrated that for a spray with Dv90 ¼ 40 mm, 0.8 s residence time is not enough for full evaporation. The study of droplet behaviour during its movement through air has implications into several applications besides previous applications, including dust control, pesticide spray, irrigation industry, fire fighting, disease transmitting, spray drying, painting and coating process [20]. However, each application has a different purpose where complete evaporation was included tacitly in some of them. Moreover, complete evaporation in some applications was a matter that needs to be avoided, e.g. in pesticide spray [21]. This brief literature review showed the differences reported on the required distance for full evaporation of droplets plumes. The difference can be explained by that each study had different test conditions affecting droplets behaviour substantially. Applications of spray cooling in gas turbine fogging and air conditioning generally have different operating conditions to those for natural draft cooling towers. In present work, the droplet transport, the droplet evaporation, and the resulting cooling of the air were investigated numerically for a range of inlet air conditions and a number of spray nozzle characteristics. Thus, for typical inlet air conditions, the droplet size requirements to achieve full evaporation were investigated. The impacts of droplet size and air velocity on droplet evaporation and air cooling performance were characterized. The calculations were carried out in a geometry equivalent to an experimental rig that will be used to study droplets behaviour for future validation.
equations with the standard ke3 model were used to model turbulence effects. The standard ke3 model was selected as it is the simplest and offers reasonable accuracy at low computational cost. It has proven to be applicable for a study related to spray injection into air [22]. Turbulent dispersion of droplets was taken into account by implementing a stochastic droplet tracking method with 20 tries for each parcel. For spray modelling purposes, the most common method in use is the EulerianeLagrangian approach [23]. In this approach, the continuous phase (air) is described utilizing the Eulerian framework while the dispersed phase (droplet) is solved using the Lagrangian framework. The air was modelled as a steady, incompressible and turbulent flow and droplets as steady flow. A staggered grid solution method was used with the SIMPLE algorithm for the pressure and velocity coupling. The spatial discretization scheme utilized was the first order upwind, except for the pressure where the standard scheme was employed. For momentum and mass fraction of H2O, the second order scheme was employed. Slightly more accurate results could be obtained by using second order scheme. However, first order schemes are reliable and robust in steady state solution, especially at simple flow using hexahedral meshes as in the present study. 2.2. Governing equations 2.2.1. Continuous phase (air) To achieve a significant amount of cooling, a significant amount of droplets are injected in air. The influence of droplets on the air flow needs to be taken into account and can be done by introducing source terms of mass, energy and momentum into the air phase governing equations. The air flow field was described by the Reynolds-time averaged NaviereStokes conservation equations combined with the standard ke3 model developed by Launder [24] to account for the turbulence effects. The governing equations of the air flow are [25]:
vðrvi Þ ¼ Sm vxj
(1)
" ! !# v r vi vj vvj v vvi vvj 2 ! vP m ¼rg þ þ mdij þ Smo vxj vxj 3 vxj vxi vxj vxj (2) vE vv v rvi ¼ p i þ vxj vxj vxj
rvi
vYj vJi0 ;i ¼ þ Sm vxj vxj
n X i0
! hi0 Ji0
v þ vxj
vT Ka vxj
! þ F þ Se
(3)
(4)
The parameters Sm, Smo, Se are the source terms of droplet mass, momentum and energy, respectively. These source terms are computed from the Lagrangian framework by an alternate process through volume averaging method and then incorporated into the Eulerian air equations. Thus, for every computational cell, the volume averaged source terms are computed by collecting the influence of the droplets that cross the cell [26]. A more comprehensive discussion can be found in Ref. [27].
2. Numerical approach 2.1. Numerical method Simulations were performed using the finite volume CFD software, Fluent (version 14.0). The time-averaged NaviereStokes
2.2.2. Discrete phase (water droplets) In spray cooling, water injected into the air is quickly disintegrated on exit from the nozzle into droplets that follow their own trajectories. The motion of any particular droplet through the air depends on the droplet-to-air interaction mechanism which is
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affected by simultaneous heat, mass, and momentum transfers between the droplet and the surrounding air. Momentum transfer determines the droplet motion, mass transfer results in droplet size change, and heat transfer causes a change in the droplet temperature [28]. Since there are too many droplets to be tracked individually, the droplets were tracked in terms of parcels of droplets. The computations were done for only one droplet in each parcel and the other droplets in the parcel were expected to behave in the same manner. 2.2.2.1. Droplet heat and mass transfer. Air cooling by water spray utilizing direct evaporation involves the conversion of sensible heat of air into latent heat. Whenever a droplet is in contact with unsaturated air, simultaneous heat and mass transfer occurs at its surface. There is convective and radiative heat transfer, and latent heat transfer caused by mass transfer. The contribution of radiation to the energy conservation is negligible [29]. An extensive discussion can be found in Ref. [30]. The heat and mass transfer between air and droplets takes place at the interface of the droplets and the surrounding air. Whenever a water droplet is in contact with an air stream, a film of saturated air-vapour is formed on the droplet surface as shown in Fig. 2. Heat transfer takes place if a temperature difference exists between the liquid temperature at the surface and the air dry-bulb temperature. Additionally, mass transfer takes place if a vapour concentration gradient exists between the vapour layer and the ambient air. The rate of energy absorbed by each droplet can be expressed as:
_ w Cpw DTd ¼ hc $Sd $ðTa Td Þ þ m
dmd h dt fg
(5)
where, hc is the convection heat transfer coefficient, which was obtained by the empirical correlation of [31]:
Nu ¼
hc D 0:33 ¼ 2 þ 0:6$R0:5 eD $Pr ka
(6)
dmd =dt is the mass flux transferred to the air by evaporation and governed by the variance between the vapour densities at droplet surface and air:
droplet individually within the air flow by integrating the motion equations governed by Newton’s second law and including the influence of the relevant forces from the air. There is a multitude of forces acting on the droplets including drag, gravity, buoyancy forces, and forces due to pressure gradient, Basset effect, and thermophoresis [19,32]. However, by using the assumption that all droplets are isolated and have spherical shapes, adjustment in speed or direction of a droplet in air are brought mainly by drag and gravity. Previous studies demonstrated that other forces have a negligible effect in flow conditions similar to ours. Normally, only gravity and drag forces are considered in the analysis of spray cooling applications [21,33]. Under this assumption, the motion equation of a single droplet can be written as:
! d m Vd dt
! ! ¼ FD þ Fg
(9)
! ! FD is the drag force and Fg is the gravitational force. The drag force acting on a spherical drop can be expressed in terms of drag coefficient as:
! 1 FD ¼ CD rAD Vr2 2
(10)
where Vr is the relative velocity of droplet with respect to air and CD is the drag coefficient. An empirical correlation for an isolated solid spherical droplet known by Ref. [34] which is valid for Reynolds numbers up to 800 was utilized. This correlation is:
CD ¼
24 1 þ 0:15 R0:687 eD ReD
(11)
where ReD is the droplet Reynolds number based on the droplet velocity relative to the air and the droplet diameter. Droplets moving in turbulent flows are affected by turbulence which imposes the need to calculate the instantaneous air velocity. As in the time-averaged NaviereStokes equations approach the local instantaneous turbulence quantities are not provided, stochastic particle tracking model velocity was employed. 2.3. Computational geometry
dmd ¼ Sd hD rs;int rva dt
(7)
where, hD is the mass transfer coefficient and (rs,int rva) is the water vapour mass density difference between the air and the saturated airevapour layer. The mass transfer coefficient was obtained by the empirical correlation of Ranz and Marshall [31]:
Sh ¼
419
hD D 0:33 ¼ 2 þ 0:6$R0:5 eD $Sc Df
(8)
2.2.2.2. Droplet trajectory. Droplet trajectories were described by the Lagrangian framework. This formulation tracks each discrete
Droplet
Saturated air-vapor film Fig. 2. Droplet heat and mass transfer mechanism.
To study water spray transport and evaporation in air, the domain for the computational investigation was based on a wind tunnel set-up (an approximation to the inlet flow in a NDDCT). As droplets discharged from a spray nozzles travel in three dimensions, a 3-D numerical model was developed with channel size of 10 m long, 1 1 m2 cross section. One spray nozzle with a hollow cone spray was simulated. It was located 0.5 m from the inlet and 0.7 m above the floor. The inlet air flow was of uniform velocity representing the action of the flow conditioners in the test tunnel being simulated. The nozzle was set-up to inject in the co-flow direction and had a spray cone angle of 120 . Fig. 3 shows the 3D computational domain. The full domain extends over the full channel to be able to represent actual non-symmetric droplet distributions and to correctly capture turbulent dispersion. The computational grid was a uniform mesh made from hexahedral elements. Several uniform grids were constructed to examine grid dependency. Cell edge lengths in the range 30e9 mm were investigated. The grid was refined near the nozzle (injection area) to allow more accurate capturing where exchange of momentum and mass between air and droplets is largest. A grid independence test has found the total mass of water evaporated and the mean air temperature along the duct to converge with the grid size in whole domain as 15 mm and in the injection region as
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Fig. 3. Geometry model utilized in this study and boundary conditions.
1.87 mm, resulting in a total of 4,710,259 cells. The resulting grid is shown in Fig. 4. Typically, more than 2000 iterations were required to obtain a converged result. According to Collin [35], residuals are not a good indicator for convergence in two phase flows with EulerianeLagrangian couplings as fluctuation in the residuals are induced by source terms of the discrete flow which disturb the residuals. Therefore, iteration convergence was also judged by monitoring sensitive quantities such as droplet concentration on selected planes and positions. Converged solutions required 32 h of CPU time on a 2.4 GHz Intel(R) Xeon (R) 8 processors machine. 2.4. Model verification using single droplet evaporation There is a lack of validation cases for spray plumes containing droplets having diameters less than 50 mm. Thus no validation data exists for the code when predicting evaporation of multiple droplets. However empirical models are available for single droplet injection. Ranz and Marshall [31] studied the evaporation of a single water droplet suspended in still dry air experimentally. Ranz and Marshall correlation is implemented in Fluent. Hence, to verify the internal consistency of our model, the injection of single droplets was simulated. For matching starting and ambient conditions, the results for 20 mm and 50 mm droplets as well as the corresponding empirical predictions are shown in Fig. 5. The results showed that the numerical model scarcely overestimates the evaporation rate of the empirical model. The CFD model correctly captured the evaporation rate of the single droplet, thereby verifying our modelling approach.
Fig. 4. Grid structure of the computational model.
Fig. 5. Comparison of the droplet diameter reduction between the present numerical simulation and Ranz and Marshall Model (1952).
2.5. Boundary conditions and operating parameters The boundary conditions and operating parameters of the simulation domain which is representative of typical conditions of natural draft cooling towers are outlined: 2.5.1. Continuous phase (air) The continuous phase was assigned as an ideal air mixture contains water vapour, oxygen and nitrogen, with different compositions depending on the mixture humidity and assuming that the dry air part composed of 77% of nitrogen and 23% of oxygen by mass. Uniform humid air flows of 1, 2, 3 m/s were prescribed at the inlet. Temperature and relative humidity values for the inlet humid air considered in this study were Ta ¼ 40 C and RH ¼ 40%. The inlet turbulence intensity was assigned as 1% for all cases. The exit flow pressure was atmospheric pressure. All the computational domain side walls were prescribed as adiabatic walls with no-slip velocity boundary condition. The standard wall function was used in the near wall regions. 2.5.2. Discrete phase (water droplets) Different uniform droplet size distributions with a hollow cone spray pattern were applied. Droplets were represented by a specified number of parcels in which each parcel contains a number of particles with the same characteristics (size, velocity, temperature, etc.). A numerical sensitivity test illustrated that 400 parcels were adequate to describe the spray accurately. Droplets were injected at a uniform temperature equal to the room temperature (27 C). It was assumed that droplets have spherical shape and temperature gradient within the droplets was negligible due to the small size of droplets used [36]. The droplet medium was pure water. The wall boundary condition for droplets impacting walls was assigned as “escape” which means that droplets are terminated and excluded from further calculation once impacting the walls. In an industrial application, the injected amount would rely mainly on the coverage area by individual nozzles if injection uniformity is essential. Depending on the cross-sectional area covered, the required flow rate per nozzle can be assigned to obtain full saturation of air (theoretically) assuming adiabatic cooling. However, preliminary CFD modelling showed that inlet air conditions and spray characteristics affect the coverage area. Nevertheless, at the operating conditions used in this study, it has been found that approximately half of the 1 m2 cross section is covered at the outlet. The amount of injected water for one nozzle was
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421
Table 1 Inlet boundary conditions for the continuous and discrete phases. Continuous phase (air)
Discrete phase (water)
Velocity: 1,2,3 m/s Temperature: 40 C Relative humidity: 40%
Droplet size: 20, 35, 50 mm Temperature: 27 C Flow rate: for full saturation (3.25, 6.65, 9.85 g/s for 1, 2, 3 m/s, respectively)
therefore calculated as the amount that, if fully evaporated, would achieve full saturation for an air stream flowing through an area of 0.5 m2. 3. Results and discussion In the following section, the distribution of the water droplets inside the duct and the resulting air cooling due to water evaporation obtained from the CFD model for a number of spray nozzle characteristics under a hot and dry ambient condition are discussed in detail. The operating conditions selected in this investigation are typical of NDDCTs. The operational conditions are presented in Table 1. 3.1. Inlet air cooling The air temperature and the equivalent mass fraction of water vapour profiles at various distances across the duct obtained for various droplet sizes (20, 35, 50 mm) and air velocities (1, 2, 3 m/s) are discussed. The temperature and mass fraction of water vapour distributions contours are illustrated in Figs. 6 and 7, coloured by their local temperature and water vapour contents. Air enters the duct at a temperature of 40 C and relative humidity of 40% for all cases. It can be noted that due to droplets evaporation, a significant cooling effect resulted and a drop of temperature from 40 C to 28 C (wet-bulb temperature) was attained in regions where droplets were travelling. Non-uniform temperature distributions existed in the longitudinal and transversal directions of the duct. From Figs. 6 and 7, it can be seen that there were large difference in the temperature and mass fraction of water vapour. While maximum cooling was achieved in the centre of the spray plume where droplets were highly concentrated, lower cooling levels were achieved at the outside of the plume. This was a consequence of droplets trajectories. Small droplets move in a small coverage area due to their inertia. One of the issues that emerges from Figs. 6 and 7 is nozzle placement. Due to this circumstance, non-uniform cooling existed in the duct where a large portion of the duct (w50% by area) was not affected
Fig. 7. Mass fraction of water vapour (kg/kg) profile at various distances across the duct (20 mm and 2 m/s).
by spray injection. Comparison between the areas weighted average temperature values across the duct for the whole cross section of the duct and for only the spray plume cone area is plotted in Fig. 8. It was apparent that more nozzles were required to cover the full duct area. There was a significant difference in the average temperature between the two illustrations. The average temperature was approximately 35.3 C considering the whole cross section while cooling to about 32 C was achieved if we consider only the spray plume cone area. This puts emphasis that an effective application must be designed ensuring an appropriate nozzle arrangement in order to reach an efficient uniform cooling. 3.2. Droplet trajectory and evaporation The calculated droplet trajectories demonstrated why the air was cooled most in the lower half-region of the duct. The droplet trajectories obtained from the numerical model for 20 mm droplet size spray at 2 m/s air velocity are shown in Fig. 9 coloured by residence time. From these figure, it is evident that droplets were airborne in the duct until reaching the outlet or impacting the bottom of the duct depending on the droplet size injected. Furthermore, due to small droplet sizes tested in which droplets have low momentum compared to the air momentum, droplets followed the air flow direction very rapidly in a short distance. This resulted in droplets dispersed in a narrow spray shape which affect the evaporation rate and uniformity in the air cooling process. It can be noticed that droplets travelled slowly to the bottom wall due to gravitational effect. The predicted normalized mass fraction change of water droplets along the duct for different droplet sizes and air velocities are
Spray plume cone area
Air average temperature
40
Full
38 36 34 32 30 28 0
2
4
6
8
10
Duct Length (m)
Fig. 6. Air temperature ( C) profile at various distances across the duct (20 mm and 2 m/s).
Fig. 8. The weighted average temperature ( C) along the duct for the whole duct and the spray plume cone area.
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Normalized Water mass fraction (%) Fig. 9. Registered droplets trajectories across the duct (20 mm and 2 m/s).
80
60
40
20
0 0
3.3.1. Effect of droplet size Droplet size is a key parameter of spray characteristic and affects the spray cooling significantly. The effect of droplet size was investigated by testing three droplet sizes (20, 35, 50 mm) at three air velocities (1, 2, 3 m/s) under the same ambient condition. Therefore, at each velocity, the air and water mass-flow rate were the same for any given droplet size. Fig. 10 shows the predicted normalized mass fraction change of water droplets along the duct for different droplet sizes. The mass fraction evaporated, the mass fraction in droplet form reaching the duct outlet, and the mass fraction hitting the walls are plotted as a function of position along the duct. The minimum evaporation was 51% of the injected water for 35 mm and 3 m/s air velocity. The smaller the droplet diameter was, more evaporation and consequently more air cooling were observed. For instance, at 1 m/s air velocity, total mass evaporated for 20 mm droplets was approximately 81% while it was 57% for 50 mm droplets. Although the overall evaporation fractions were lower because of the lower residence time, the tendency of smaller droplets to evaporate faster was also recognized at 2 m/s air velocity. Smaller droplets evaporate faster because they provide more surface area per unit volume than larger droplets and evaporation only occurs at the water/air interface. Evaporation rate per unit volume of droplets in gaseous media is related to the square of the droplet diameter and increases rapidly when droplet diameter is decreased [37].
4
6
8
10
(a) 2 m/s
100
Normalized Water mass fraction (%)
3.3. Effect of air and droplet variables on droplet evaporation and transport
2
Duct length (m)
20 µm 35 µm 50 µm
80
60
40
20
0 0
2
4
6
8
10
Duct length (m)
(b) 3 m/s
100
Normalized Water mass fraction (%)
presented in Table 2. Interestingly, data from this table shows that although droplet sizes in this study were very small along with sufficient residence time, there was no complete evaporation in any case. The maximum evaporation was about 81% for droplet size of 20 mm and air velocity of 1 m/s as can be seen in Table 2.
20 µm 35 µm 50 µm
1 m/s
100
20 µm 35 µm 50 µm
80
60
40
20
0 0
Table 2 Predicted normalized mass fraction change of water droplets along the duct. Droplet size 20 mm
35 mm
50 mm
1 2 3 1 2 3 1 2 3
m/s m/s m/s m/s m/s m/s m/s m/s m/s
% of water evaporated
% of water at outlet
% of water impacted walls
80.7 70.0 53.0 71.4 63.1 51.0 57.1 57.1 52.9
5.3 25.4 47.0 3.3 22.1 48.3 0.3 10.1 43.0
13.9 4.6 0.0 25.3 14.8 0.8 42.6 32.8 4.0
2
4
6
8
10
Duct length (m)
(c) Fig. 10. Plots of predicted normalized mass fraction change of water droplets along the duct for different droplet sizes (a) Va ¼ 1 m/s, (b) Va ¼ 2 m/s, (c) Va ¼ 3 m/s. (Solid Square) represents mass fraction reaching the outlet, (solid circle) represents mass evaporated, and (solid triangle) represents mass hitting walls.
In contrast to the results of 1 and 2 m/s air velocity, the total mass fraction evaporated at 3 m/s air velocity was independent of droplet size, as can be seen in Fig. 10(c). Assuming each droplet behaves independently, smaller droplets are more efficient than
A. Alkhedhair et al. / Applied Thermal Engineering 61 (2013) 416e424
Normalized Water mass fraction (%)
larger droplets in air spray cooling. However, owing to the fact that larger droplets have a higher inertia to drag ratio, they tend to penetrate the flow deeper. Thus large droplets produce a larger plume. This outcome is more pronounced the higher the speeds. At 3 m/s, the effect of droplet size on evaporation is balanced by the effect of penetration on evaporation. This conclusion is in agreement with Tissot [38] findings which had higher evaporation at larger droplet diameter under the same operational condition.
1 m/s 2 m/s 3 m/s
20 µm
100
80
60
40
20
0 0
2
4
6
8
10
Duct length (m)
(a)
Normalized Water mass fraction (%)
1 m/s 2 m/s 3 m/s
35 µm
100
80
60
40
20
0 0
2
4
6
8
10
Duct length (m)
(b) 50 µm
100
Normalized Water mass fraction (%)
423
1 m/s 2 m/s 3 m/s
80
60
40
20
3.3.2. Effect of air velocity Air velocity had a large influence on droplet trajectory and evaporation efficiency. The effect of air velocity was investigated comparing three air velocities (1, 2, 3 m/s) for three droplet sizes under the same ambient condition. Fig. 11 shows the predicted normalized mass fraction change of water droplets along the duct for different air velocities. The mass fraction evaporated, the mass fraction in droplet form reaching the duct outlet, and the mass fraction hitting the walls are plotted as a function of position along the duct. We can see from this figure that air velocity had a significant influence. For instance, for 20 mm droplet size spray, total mass evaporated at 1 m/s air velocity was about 81% while it was 53% for 3 m/s. The reason for this is because droplet velocity was the same as the air velocity along the duct except for a short time at the beginning. Thus, lower air velocity means longer travelling (residence) time, therefore, better evaporative cooling efficiency. However, due to gravitational effect, falling rate per unit length will be higher for lower velocities which make droplets fall out quicker than higher velocities. Hence, there is a clear trade-off between droplet size and air velocity. In addition, it can be seen from Fig. 11 that for 20 mm droplet size spray, more evaporation was experienced when the velocity was lowered where the residence time increased. Moreover, this trend was observed for 35 mm droplet size spray with less significant influence. In contrast, the predicted evaporation efficiencies of 50 mm droplet size sprays at the air velocities (1, 2, 3 m/s) were nearly the same. In fact, results of 50 mm droplets at air velocity of 1 and 2 m/s were not consistent as a large portion of the water hits the ground and then terminated from the calculation. This is because larger droplets has greater falling rate compared to small droplets which causes droplets reach the ground faster. The data in Figs. 10 and 11, particularly at the lower air speeds, show that the rate of evaporation reduced with distance along the duct. A similar trend was also observed for the temperature data (Fig. 6). This was due to the fact that inside the region where droplets were present, the humidity has increased to 100%. This is a combined effect of evaporation and localized temperature reduction. Based on Fig. 10, it can be concluded that for 1 m/s, no significant further evaporation took place after 7 m, for all the investigated droplet sizes. This was most pronounced for 20 mm diameter droplets. In contrast at 3 m/s air velocity, the rate of evaporation has not yet levelled-off at 10 m, suggesting that longer ducts would enhance evaporation. 4. Conclusions The main conclusions from this study are as follows:
0 0
2
4
6
8
10
Duct length (m)
(c) Fig. 11. Plots of predicted normalized mass fraction change of water droplets along the duct for different air velocities (a) Dp ¼ 20 mm, (b) Dp ¼ 35 mm, (c) Dp ¼ 50 mm. (Solid Square) represents mass fraction reaching the outlet, (solid circle) represents mass evaporated, and (solid triangle) represents mass hitting walls.
(1) In the range of droplet sizes and air velocities studied, a significant cooling performance achieved. In the droplet saturated region an average temperature reduction of 8.1 C was achieved, while across the duct average reduction of 4.8 C was achieved. (2) Correct nozzle arrangement is essential to ensure effective cooling. Non-uniform temperature distribution existed and the air was cooled mostly in the lower half-region.
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(3) Air velocity played a significant role in droplet transport and evaporation. At high air speeds, large droplets performed as well as small droplets. While at low air speeds, small droplets performed 25% superior than large droplets. (4) Due to the compromise effect of momentum exchange and evaporation rate, there is a trade-off between droplet size and air velocity and resulting plum dispersion. This must be considered to identify optimum droplet size. This effect explains the similar performance of small and large droplets mentioned in (3). Acknowledgements This work was financially supported by the Saudi Arabian Government and the Queensland Geothermal Energy Centre of Excellence. References [1] A.E. Conradie, D.G. Kröger, Performance evaluation of dry-cooling systems for power plant applications, Appl. Therm. Eng. 16 (1996) 219e232. [2] R.B. Boulay, M.J. Cerha, M. Massoudi, Dry and hybrid condenser cooling design to maximize operating income, in: ASME Conference Proceedings, 2005, pp. 167e175. [3] J.S. Maulbetsch, Comparison of Alternate Cooling Technologies for California Power Plants: Economic, Environmental and Other Tradeoffs, EPRI, California Energy Commission (PIER), 2002. [4] A. Ashwood, D. Bharathan, Hybrid Cooling Systems for Low-temperature Geothermal Power Production, NREL, National Laboratory of the U.S, 2011. [5] J. Maulbetsch, M. DiFilippo, Spray Enhancement of Air Cooled Condensers, EPRI, California Energy Commission (PIER), 2003. [6] S. He, H. Gurgenci, Z. Guan, A.M. Alkhedhair, Pre-cooling with Munters media to improve the performance of natural draft dry cooling towers, Appl. Therm. Eng. 53 (2013) 67e77. [7] M.A. Chaker, Key parameters for the performance of impaction-pin nozzles used in inlet fogging of gas turbine engines, J. Eng. Gas Turbines Power 129 (2007) 473e477. [8] S. Molis, P. Levine, Combustion Turbine Spray Cooler Guide, EPRI, EPRIGEN, 1999. [9] R.K. Bhargava, C.B. Meher-Homji, M.A. Chaker, M. Bianchi, F. Melino, A. Peretto, S. Ingistov, Gas turbine fogging technology: a state-of-the-art reviewepart i: inlet evaporative foggingeanalytical and experimental aspects, J. Eng. Gas Turbines Power 129 (2007) 443e453. [10] A. Bletchly, Evaluation of Ambient Condition Correction Curves for Power Station Capacity, CQUniversity, Faculty of Science, Rockhampton, Queensland, 2010. [11] A.M. Al-Amiri, M.M. Zamzam, M.A. Chaker, C.B. Meher-Homji, Application of inlet fogging for power augmentation of mechanical drive turbines in the oil and gas sector, in: ASME Conference Proceedings, 2006, pp. 847e855. [12] B.D. Esterhuyse, D.G. Kröger, The effect of ionisation of spray in cooling air on the wetting characteristics of finned tube heat exchanger, Appl. Therm. Eng. 25 (2005) 3129e3137. [13] W. Wells, On air-borne infection. study II. droplets and droplet nuclei, Am. J. Trop. Med. Hyg. 20 (1934) 611e618. [14] G.P. Wachtell, Atomized Water Injection to Improve Dry Cooling Tower Performance, National Technical Information Service, 1974.
[15] A.M. Rubin, Demonstration of Adiabatic Cooling to Improve the Performance of Air-cooled Heat Exchangers, Energy Research Administration, Franklin Institute Research Laboratories, 1975. [16] G. Branfield, Precooling of Fin-tube Heat Exchanger Inlet Air Using Ultra Fine Water Spray. Vol. Unpublished B.Ing thesis, in: Stated by (The Effect of Ionisation of Spray in Cooling Air on the Wetting Characteristics of Finned Tube Heat Exchanger), University of Stellenbosch, 2003. [17] S. Sanaye, M. Tahani, Analysis of gas turbine operating parameters with inlet fogging and wet compression processes, Appl. Therm. Eng. 30 (2010) 234e244. [18] M. Chaker, C.B. Meher-Homji, Gas turbine power augmentation: parametric study relating to fog droplet size and its influence on evaporative efficiency, J. Eng. Gas Turbines Power 133 (2011) 1e10. [19] T. Wang, X. Li, V. Pinninti, Simulation of mist transport for gas turbine inlet air cooling, in: ASME Conference Proceedings, 2004, pp. 389e398. [20] S.S. Kachhwaha, P.L. Dhar, S.R. Kale, Experimental studies and numerical simulation of evaporative cooling of air with a water spraydI. Horizontal parallel flow, Int. J. Heat Mass Transf. 41 (1998) 447e464. [21] D.L. Reichard, H. Zhu, R.D. Fox, R.D. Brazee, Computer simulation of variables that influence spray drift, Trans. ASAE 35 (5) (1992b) 1402e1407. [22] X. Li, T. Wang, Effects of various modeling schemes on mist film cooling simulation, J. Heat Transf. 129 (2007) 472e482. [23] J.J. Nijdam, B. Guo, D.F. Fletcher, T.A.G. Langrish, Lagrangian and Eulerian models for simulating turbulent dispersion and coalescence of droplets within a spray, Appl. Math. Modell. 30 (2006) 1196e1211. [24] B.E. Launder, D.B. Spalding, The numerical computation of turbulent flows, Comput. Meth. Appl. Mech. Eng. 3 (1974) 269e289. [25] Fluent, Ansys Fluent Theory Guide, 14.0 ed., ANSYS, Inc., 2011. [26] X. Jiang, G.A. Siamas, K. Jagus, T.G. Karayiannis, Physical modelling and advanced simulations of gaseliquid two-phase jet flows in atomization and sprays, Prog. Energy Combust. Sci. 36 (2010) 131e167. [27] A. Berlemont, M.S. Grancher, G. Gouesbet, Heat and mass transfer coupling between vaporizing droplets and turbulence using a Lagrangian approach, Int. J. Heat Mass Transf. 38 (1995) 3023e3034. [28] J. Smolík, L. Dumbová, J. Schwarz, M. Kulmala, Evaporation of ventilated water droplet: connection between heat and mass transfer, J. Aerosol Sci. 32 (2001) 739e748. [29] S.J. Palaszewski, L.M. Jiji, S. Weinbaum, A three-dimensional airevapordroplet local interaction model for spray units, J. Heat Transf. 103 (1981) 514e521. [30] M. Chaker, C.B. Meher-Homji, T. Mee III, Inlet fogging of gas turbine enginespart a: fog droplet thermodynamics, heat transfer and practical considerations, in: Proceedings of ASME Turbo Expo 2002, 2002. [31] W.E. Ranz, W.R. Marshall, Evaporation from drops, Chem. Eng. Prog. 48 (1952) 141e146. [32] A. William, Fluid Dynamics and Transport of Droplets and Sprays, second ed., Cambridge University Press, New York, 2010. [33] H.K. Jiusheng Li, Simulating water-drop movement from noncircular sprinkler nozzles, J. Irrig. Drain. Eng. 121 (1995) 7. [34] L. Schiller, A.Z. Naumann, Uber die grundlegenden berechnungen bei der schwerkraftaufbereitung, Ver. Deut. Ing. 77 (1933) 318e320. [35] A. Collin, P. Boulet, G. Parent, D. Lacroix, Numerical simulation of a water spraydRadiation attenuation related to spray dynamics, Int. J. Therm. Sci. 46 (2007) 856e868. [36] H. Barrow, C.W. Pope, Droplet evaporation with reference to the effectiveness of water-mist cooling, Appl. Energy 84 (2007) 404e412. [37] A.L. Thompson, J.R. Gilley, J.M. Norman, A sprinkler water droplet evaporation and plant canopy model: ii model application, Trans. ASAE 36 (1993) 743e750. [38] J. Tissot, P. Boulet, F. Trinquet, L. Fournaison, H. Macchi-Tejeda, Air cooling by evaporating droplets in the upward flow of a condenser, Int. J. Therm. Sci. 50 (2011) 2122e2131.
Contents lists available at ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Numerical simulation of water spray for pre-cooling of inlet air in natural draft dry cooling towers Abdullah Alkhedhair*, Hal Gurgenci, Ingo Jahn, Zhiqiang Guan, Suoying He Queensland Geothermal Energy Centre of Excellence, School of Mechanical and Mining Engineering, The University of Queensland, Brisbane 4072, Australia
h i g h l i g h t s Numerical investigation of inlet air cooling by water spray in NDDCTs was performed. Strong links identified between droplet size, air velocity, evaporation and trajectory. Pre-cooling of up to 8.1 C predicted. The maximum evaporation was achieved with the smallest droplet size.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 26 April 2013 Accepted 7 August 2013 Available online 24 August 2013
This paper presents a numerical investigation of inlet air pre-cooling with water sprays to enhance the performance in Natural Draft Dry Cooling Towers (NDDCT). A 3-D numerical model of a test channel was generated and the evaporation from a single spray nozzle was analyzed. The droplet evaporation and the resulting cooling of air were predicted for a range of inlet air conditions and spray characteristics. The results showed that up to 81% evaporation can be achieved for water droplets of 20 mm at a velocity of 1 m/s and that, droplet transport and evaporation strongly depend on droplet size and air velocity. Ó 2013 Elsevier Ltd. All rights reserved.
Keywords: Natural draft Spray cooling Pre-cooling Numerical modelling Complete evaporation
1. Introduction This paper presents results of a study on the effect of droplet size and air velocity on the droplet transport, the droplet evaporation, and the cooling performance of inlet air spraying to enhance the performance of natural draft dry cooling towers (NDDCTs). This knowledge is crucial for designing spray cooling systems for NDDCTs in hot and dry ambient conditions. Deployment of dry cooling technologies rather than wet cooling technologies has become a necessity for many power plants despite the lower performance (particularly during high ambient temperate periods), owing to water consumption restrictions, environmental regulations and flexibility of plant site selection. For geothermal plants, perhaps, dry cooling is the only option as they are located in arid areas. Although dry cooling systems offer advantages of water conservation and environmental protection, the cooling * Corresponding author. Tel.: þ61 411217779. E-mail addresses: [email protected], (A. Alkhedhair).
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performance is low relative to wet cooling as it relies mainly on convective heat transfer to dissipate heat rather than evaporation. This is worst during high ambient temperature periods, where dry cooling systems experience a significant reduction in power generation [1]. The impact on the plant revenue is even higher since these periods represent peak power demand for most locations. Dry cooling tower performance can be enhanced during these periods, by spraying water into the inlet air in order to reduce the cooling air temperature. Reducing the cooling media temperature, leads to an increase in overall cycle efficiency, thus allowing some of the performance reduction to be recovered. However, this requires careful consideration of water spray generation to avoid issues related to incomplete evaporation of droplets. Although a considerable amount of literature has been published on droplet transport and evaporation in air, no study exists on analyzing spray cooling under conditions typical of NDDCTs. Many efforts have been made over the past decades to improve the performance of dry cooling systems in order to make them more efficient compared to wet cooling. A number of studies have found that hybrid cooling technologies have the potential to
A. Alkhedhair et al. / Applied Thermal Engineering 61 (2013) 416e424
Nomenclature a CD Cpa Cpw D Df Dv90 E F FD FG hc hD hfg hi0 J i0 k _a m _w m md Nu Pr P q_ conv q_ lat
Acceleration of droplet (m/s2) Drag coefficient Specific heat of air (J/kg K) Specific heat of water (J/kg K) droplet diameter (mm) Diffusion coefficient (m2/s) 90% of water volume made up of droplets of this size and smaller (mm) Internal energy (J/kg) Forces acting on droplet (N) Drag force (N) Gravity force (N) Heat transfer coefficient (W/m2K) Mass transfer coefficient (m/s) Latent heat of water vaporization (J/kg) 0 Sensible enthalpy of species i (J/kg) 0 Diffusing flux of species i (Kg/m2s) Thermal conductivity of air (W/m K) Air flow rate (kg/s) Water flow rate (kg/s) Droplet mass (kg) Nusselt number Prandtl number Pressure (Pa) Convective heat transfer (J/s) Latent heat transfer rate (J/s)
alleviate this problem while avoiding issues related to wet cooling, particularly in terms of water utilization [2,3]. Several hybrid cooling approaches have been developed to offset the disadvantages related to the use of dry cooling during high temperature periods [4]. One of the patterns of hybrid cooling to boost the performance during hottest hours is the use of evaporative cooling by introducing a small amount of water for a limited time to cool the entering air. There are two methods that carry out this concept which can be classified: deluge cooling and evaporative pre-cooling (spray cooling and wetted-media cooling) [5]. Regarding to deluge cooling, due to the direct contact of water with heat exchanger bundles, corrosion and fouling become crucial issues. This requires using treated water and regular cleaning or utilizing condenser tubes with galvanic corrosion protection which prevents use of fins. Wetted-media cooling also is an efficient way to cool inlet air. However, significant pressure drop is created which reduce air mass-flow rate causing a decline in heat rejection rate [6]. Over the past decades, spray cooling has become more popular due to its simplicity, low capital cost, and ease of operation and maintenance [7]. Furthermore, air stream motion is not affected by the presence of droplets. Thus, pressure drop due to spray existence is insignificant and can be neglected [8]. Inlet air spray cooling has many applications such as gas turbine fogging and refrigerative cooling. It has been used extensively in gas turbine systems. More than 1000 gas turbine stations are equipped with inlet air spray cooling [9]. Applications found in power plants employing dry cooling towers include one of the largest coal fired station in Australia with 750 MW power output [10], a waste wood plant in USA with 25 MW capacity, and a geothermal plant in USA [3]. Inlet air cooling by spray can provide 100% saturation efficiency depending on the design conditions [11]. In this method, the inlet air is cooled by evaporation. Spray nozzles are used to distribute water into the inlet air and to provide a large watereair contact
RH ReD Sc Sd Se Sm Smo Sh T Va Vd Vr vi vj Yj
417
Relative humidity (%) Droplet Reynolds number Schmidt number Droplet surface area (m2) Source term of energy (W/m3) Source term of mass (Kg/m3s) Source term of momentum (Kg/m2s2) Sherwood number Temperature ( C) Air velocity (m/s) Droplet velocity (m/s) Droplet relative velocity (m/s) Air velocity components (m/s) Mass fraction of species j
Greek symbols Density (kg/m3) Mean strain tensor (1/s) Dynamic viscosity of air (kg/m s) Viscous dissipation (W/m3)
r dij m F
Subscripts a air d droplet t time int dropleteair interface i,j Cartesian coordinate directions
surface by producing small droplets through atomization as can be seen in Fig. 1. Although spray cooling has found successful applications in process coolers and gas turbine fogging, the large scale applications in power industry have been limited. Several issues limit the application and the main one is the incomplete evaporation of water droplets before reaching the heat exchanger bundles. This can cause corrosion, scaling and fouling [12]. Special spray nozzles may be required to achieve full evaporation requirement. High pressure nozzles provide small water droplets but at a higher cost. Droplet size is a critical parameter of spray characteristics. The knowledge of the optimum droplet size is crucial for designing spray cooling systems. According to Wells [13], droplet size distribution in the sprays is a major parameter that impacts droplet movement and evaporation efficiency during its interaction with air. Over the past decades, droplet size effect on evaporation distance has been the subject of many studies, experimentally and numerically. Complete evaporation of droplets was first considered in an experiment carried out by Wachtell [14]. The study aimed to
Water Tank
Water
Air
Cooling Tower
Fig. 1. A schematic diagram of inlet air cooling by spray.
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investigate the effect of spray cooling on heat exchanger performance by injecting water droplets into the intake air stream. The study showed that droplets of 20 mm diameter or smaller would evaporate completely. He concluded that droplet size and wet-bulb depression are two principal parameters that control the evaporation rate. However, the findings of Wachtell [14] experiment are not supported by the subsequent research. Effectiveness of using water spray to cool the inlet air of an air cooled heat exchanger was investigated experimentally [15]. In the experiment, various droplet diameters ranging from 16 to 28 mm were injected from a distance of 2.7 m below the heat exchanger. The average air velocities were 1.3 m/s and 3 m/s for low and high fan speeds, respectively. His study showed that droplets of 16e28 mm in diameter did not evaporate completely and reached the heat exchanger pipes. This was argued due to dissimilarity on the operating conditions where a small change of one parameter would have a significant difference on the distance required for complete evaporation. Furthermore, Branfield [16] performed an experiment and found that even droplets of 10 mm diameter and smaller reached the heat exchanger surface. The relation between droplet size and evaporation distance was also studied numerically and experimentally in relation to gas turbine fogging. Most of these studies were not concentrating on complete evaporation. For example, in gas turbine applications, droplet sizes of 5e15 mm are permitted to enter the compressor, where droplets provide additional cooling [17]. Nevertheless, as small droplet size is often used in gas turbine to achieve high evaporation efficiency, complete evaporation was achieved in a number of studies. Numerical investigations were carried out by Chaker [18] and Wang [19] for residences time of 1 and 0.8 s, respectively. It was found by Chaker [18] that for sprays with Dv90 ¼ 18.5 mm, all injected water evaporated, whereas 14% nonevaporated water was existed when Dv90 ¼ 46.2 mm. Likewise, Wang [19] illustrated that for a spray with Dv90 ¼ 40 mm, 0.8 s residence time is not enough for full evaporation. The study of droplet behaviour during its movement through air has implications into several applications besides previous applications, including dust control, pesticide spray, irrigation industry, fire fighting, disease transmitting, spray drying, painting and coating process [20]. However, each application has a different purpose where complete evaporation was included tacitly in some of them. Moreover, complete evaporation in some applications was a matter that needs to be avoided, e.g. in pesticide spray [21]. This brief literature review showed the differences reported on the required distance for full evaporation of droplets plumes. The difference can be explained by that each study had different test conditions affecting droplets behaviour substantially. Applications of spray cooling in gas turbine fogging and air conditioning generally have different operating conditions to those for natural draft cooling towers. In present work, the droplet transport, the droplet evaporation, and the resulting cooling of the air were investigated numerically for a range of inlet air conditions and a number of spray nozzle characteristics. Thus, for typical inlet air conditions, the droplet size requirements to achieve full evaporation were investigated. The impacts of droplet size and air velocity on droplet evaporation and air cooling performance were characterized. The calculations were carried out in a geometry equivalent to an experimental rig that will be used to study droplets behaviour for future validation.
equations with the standard ke3 model were used to model turbulence effects. The standard ke3 model was selected as it is the simplest and offers reasonable accuracy at low computational cost. It has proven to be applicable for a study related to spray injection into air [22]. Turbulent dispersion of droplets was taken into account by implementing a stochastic droplet tracking method with 20 tries for each parcel. For spray modelling purposes, the most common method in use is the EulerianeLagrangian approach [23]. In this approach, the continuous phase (air) is described utilizing the Eulerian framework while the dispersed phase (droplet) is solved using the Lagrangian framework. The air was modelled as a steady, incompressible and turbulent flow and droplets as steady flow. A staggered grid solution method was used with the SIMPLE algorithm for the pressure and velocity coupling. The spatial discretization scheme utilized was the first order upwind, except for the pressure where the standard scheme was employed. For momentum and mass fraction of H2O, the second order scheme was employed. Slightly more accurate results could be obtained by using second order scheme. However, first order schemes are reliable and robust in steady state solution, especially at simple flow using hexahedral meshes as in the present study. 2.2. Governing equations 2.2.1. Continuous phase (air) To achieve a significant amount of cooling, a significant amount of droplets are injected in air. The influence of droplets on the air flow needs to be taken into account and can be done by introducing source terms of mass, energy and momentum into the air phase governing equations. The air flow field was described by the Reynolds-time averaged NaviereStokes conservation equations combined with the standard ke3 model developed by Launder [24] to account for the turbulence effects. The governing equations of the air flow are [25]:
vðrvi Þ ¼ Sm vxj
(1)
" ! !# v r vi vj vvj v vvi vvj 2 ! vP m ¼rg þ þ mdij þ Smo vxj vxj 3 vxj vxi vxj vxj (2) vE vv v rvi ¼ p i þ vxj vxj vxj
rvi
vYj vJi0 ;i ¼ þ Sm vxj vxj
n X i0
! hi0 Ji0
v þ vxj
vT Ka vxj
! þ F þ Se
(3)
(4)
The parameters Sm, Smo, Se are the source terms of droplet mass, momentum and energy, respectively. These source terms are computed from the Lagrangian framework by an alternate process through volume averaging method and then incorporated into the Eulerian air equations. Thus, for every computational cell, the volume averaged source terms are computed by collecting the influence of the droplets that cross the cell [26]. A more comprehensive discussion can be found in Ref. [27].
2. Numerical approach 2.1. Numerical method Simulations were performed using the finite volume CFD software, Fluent (version 14.0). The time-averaged NaviereStokes
2.2.2. Discrete phase (water droplets) In spray cooling, water injected into the air is quickly disintegrated on exit from the nozzle into droplets that follow their own trajectories. The motion of any particular droplet through the air depends on the droplet-to-air interaction mechanism which is
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affected by simultaneous heat, mass, and momentum transfers between the droplet and the surrounding air. Momentum transfer determines the droplet motion, mass transfer results in droplet size change, and heat transfer causes a change in the droplet temperature [28]. Since there are too many droplets to be tracked individually, the droplets were tracked in terms of parcels of droplets. The computations were done for only one droplet in each parcel and the other droplets in the parcel were expected to behave in the same manner. 2.2.2.1. Droplet heat and mass transfer. Air cooling by water spray utilizing direct evaporation involves the conversion of sensible heat of air into latent heat. Whenever a droplet is in contact with unsaturated air, simultaneous heat and mass transfer occurs at its surface. There is convective and radiative heat transfer, and latent heat transfer caused by mass transfer. The contribution of radiation to the energy conservation is negligible [29]. An extensive discussion can be found in Ref. [30]. The heat and mass transfer between air and droplets takes place at the interface of the droplets and the surrounding air. Whenever a water droplet is in contact with an air stream, a film of saturated air-vapour is formed on the droplet surface as shown in Fig. 2. Heat transfer takes place if a temperature difference exists between the liquid temperature at the surface and the air dry-bulb temperature. Additionally, mass transfer takes place if a vapour concentration gradient exists between the vapour layer and the ambient air. The rate of energy absorbed by each droplet can be expressed as:
_ w Cpw DTd ¼ hc $Sd $ðTa Td Þ þ m
dmd h dt fg
(5)
where, hc is the convection heat transfer coefficient, which was obtained by the empirical correlation of [31]:
Nu ¼
hc D 0:33 ¼ 2 þ 0:6$R0:5 eD $Pr ka
(6)
dmd =dt is the mass flux transferred to the air by evaporation and governed by the variance between the vapour densities at droplet surface and air:
droplet individually within the air flow by integrating the motion equations governed by Newton’s second law and including the influence of the relevant forces from the air. There is a multitude of forces acting on the droplets including drag, gravity, buoyancy forces, and forces due to pressure gradient, Basset effect, and thermophoresis [19,32]. However, by using the assumption that all droplets are isolated and have spherical shapes, adjustment in speed or direction of a droplet in air are brought mainly by drag and gravity. Previous studies demonstrated that other forces have a negligible effect in flow conditions similar to ours. Normally, only gravity and drag forces are considered in the analysis of spray cooling applications [21,33]. Under this assumption, the motion equation of a single droplet can be written as:
! d m Vd dt
! ! ¼ FD þ Fg
(9)
! ! FD is the drag force and Fg is the gravitational force. The drag force acting on a spherical drop can be expressed in terms of drag coefficient as:
! 1 FD ¼ CD rAD Vr2 2
(10)
where Vr is the relative velocity of droplet with respect to air and CD is the drag coefficient. An empirical correlation for an isolated solid spherical droplet known by Ref. [34] which is valid for Reynolds numbers up to 800 was utilized. This correlation is:
CD ¼
24 1 þ 0:15 R0:687 eD ReD
(11)
where ReD is the droplet Reynolds number based on the droplet velocity relative to the air and the droplet diameter. Droplets moving in turbulent flows are affected by turbulence which imposes the need to calculate the instantaneous air velocity. As in the time-averaged NaviereStokes equations approach the local instantaneous turbulence quantities are not provided, stochastic particle tracking model velocity was employed. 2.3. Computational geometry
dmd ¼ Sd hD rs;int rva dt
(7)
where, hD is the mass transfer coefficient and (rs,int rva) is the water vapour mass density difference between the air and the saturated airevapour layer. The mass transfer coefficient was obtained by the empirical correlation of Ranz and Marshall [31]:
Sh ¼
419
hD D 0:33 ¼ 2 þ 0:6$R0:5 eD $Sc Df
(8)
2.2.2.2. Droplet trajectory. Droplet trajectories were described by the Lagrangian framework. This formulation tracks each discrete
Droplet
Saturated air-vapor film Fig. 2. Droplet heat and mass transfer mechanism.
To study water spray transport and evaporation in air, the domain for the computational investigation was based on a wind tunnel set-up (an approximation to the inlet flow in a NDDCT). As droplets discharged from a spray nozzles travel in three dimensions, a 3-D numerical model was developed with channel size of 10 m long, 1 1 m2 cross section. One spray nozzle with a hollow cone spray was simulated. It was located 0.5 m from the inlet and 0.7 m above the floor. The inlet air flow was of uniform velocity representing the action of the flow conditioners in the test tunnel being simulated. The nozzle was set-up to inject in the co-flow direction and had a spray cone angle of 120 . Fig. 3 shows the 3D computational domain. The full domain extends over the full channel to be able to represent actual non-symmetric droplet distributions and to correctly capture turbulent dispersion. The computational grid was a uniform mesh made from hexahedral elements. Several uniform grids were constructed to examine grid dependency. Cell edge lengths in the range 30e9 mm were investigated. The grid was refined near the nozzle (injection area) to allow more accurate capturing where exchange of momentum and mass between air and droplets is largest. A grid independence test has found the total mass of water evaporated and the mean air temperature along the duct to converge with the grid size in whole domain as 15 mm and in the injection region as
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Fig. 3. Geometry model utilized in this study and boundary conditions.
1.87 mm, resulting in a total of 4,710,259 cells. The resulting grid is shown in Fig. 4. Typically, more than 2000 iterations were required to obtain a converged result. According to Collin [35], residuals are not a good indicator for convergence in two phase flows with EulerianeLagrangian couplings as fluctuation in the residuals are induced by source terms of the discrete flow which disturb the residuals. Therefore, iteration convergence was also judged by monitoring sensitive quantities such as droplet concentration on selected planes and positions. Converged solutions required 32 h of CPU time on a 2.4 GHz Intel(R) Xeon (R) 8 processors machine. 2.4. Model verification using single droplet evaporation There is a lack of validation cases for spray plumes containing droplets having diameters less than 50 mm. Thus no validation data exists for the code when predicting evaporation of multiple droplets. However empirical models are available for single droplet injection. Ranz and Marshall [31] studied the evaporation of a single water droplet suspended in still dry air experimentally. Ranz and Marshall correlation is implemented in Fluent. Hence, to verify the internal consistency of our model, the injection of single droplets was simulated. For matching starting and ambient conditions, the results for 20 mm and 50 mm droplets as well as the corresponding empirical predictions are shown in Fig. 5. The results showed that the numerical model scarcely overestimates the evaporation rate of the empirical model. The CFD model correctly captured the evaporation rate of the single droplet, thereby verifying our modelling approach.
Fig. 4. Grid structure of the computational model.
Fig. 5. Comparison of the droplet diameter reduction between the present numerical simulation and Ranz and Marshall Model (1952).
2.5. Boundary conditions and operating parameters The boundary conditions and operating parameters of the simulation domain which is representative of typical conditions of natural draft cooling towers are outlined: 2.5.1. Continuous phase (air) The continuous phase was assigned as an ideal air mixture contains water vapour, oxygen and nitrogen, with different compositions depending on the mixture humidity and assuming that the dry air part composed of 77% of nitrogen and 23% of oxygen by mass. Uniform humid air flows of 1, 2, 3 m/s were prescribed at the inlet. Temperature and relative humidity values for the inlet humid air considered in this study were Ta ¼ 40 C and RH ¼ 40%. The inlet turbulence intensity was assigned as 1% for all cases. The exit flow pressure was atmospheric pressure. All the computational domain side walls were prescribed as adiabatic walls with no-slip velocity boundary condition. The standard wall function was used in the near wall regions. 2.5.2. Discrete phase (water droplets) Different uniform droplet size distributions with a hollow cone spray pattern were applied. Droplets were represented by a specified number of parcels in which each parcel contains a number of particles with the same characteristics (size, velocity, temperature, etc.). A numerical sensitivity test illustrated that 400 parcels were adequate to describe the spray accurately. Droplets were injected at a uniform temperature equal to the room temperature (27 C). It was assumed that droplets have spherical shape and temperature gradient within the droplets was negligible due to the small size of droplets used [36]. The droplet medium was pure water. The wall boundary condition for droplets impacting walls was assigned as “escape” which means that droplets are terminated and excluded from further calculation once impacting the walls. In an industrial application, the injected amount would rely mainly on the coverage area by individual nozzles if injection uniformity is essential. Depending on the cross-sectional area covered, the required flow rate per nozzle can be assigned to obtain full saturation of air (theoretically) assuming adiabatic cooling. However, preliminary CFD modelling showed that inlet air conditions and spray characteristics affect the coverage area. Nevertheless, at the operating conditions used in this study, it has been found that approximately half of the 1 m2 cross section is covered at the outlet. The amount of injected water for one nozzle was
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421
Table 1 Inlet boundary conditions for the continuous and discrete phases. Continuous phase (air)
Discrete phase (water)
Velocity: 1,2,3 m/s Temperature: 40 C Relative humidity: 40%
Droplet size: 20, 35, 50 mm Temperature: 27 C Flow rate: for full saturation (3.25, 6.65, 9.85 g/s for 1, 2, 3 m/s, respectively)
therefore calculated as the amount that, if fully evaporated, would achieve full saturation for an air stream flowing through an area of 0.5 m2. 3. Results and discussion In the following section, the distribution of the water droplets inside the duct and the resulting air cooling due to water evaporation obtained from the CFD model for a number of spray nozzle characteristics under a hot and dry ambient condition are discussed in detail. The operating conditions selected in this investigation are typical of NDDCTs. The operational conditions are presented in Table 1. 3.1. Inlet air cooling The air temperature and the equivalent mass fraction of water vapour profiles at various distances across the duct obtained for various droplet sizes (20, 35, 50 mm) and air velocities (1, 2, 3 m/s) are discussed. The temperature and mass fraction of water vapour distributions contours are illustrated in Figs. 6 and 7, coloured by their local temperature and water vapour contents. Air enters the duct at a temperature of 40 C and relative humidity of 40% for all cases. It can be noted that due to droplets evaporation, a significant cooling effect resulted and a drop of temperature from 40 C to 28 C (wet-bulb temperature) was attained in regions where droplets were travelling. Non-uniform temperature distributions existed in the longitudinal and transversal directions of the duct. From Figs. 6 and 7, it can be seen that there were large difference in the temperature and mass fraction of water vapour. While maximum cooling was achieved in the centre of the spray plume where droplets were highly concentrated, lower cooling levels were achieved at the outside of the plume. This was a consequence of droplets trajectories. Small droplets move in a small coverage area due to their inertia. One of the issues that emerges from Figs. 6 and 7 is nozzle placement. Due to this circumstance, non-uniform cooling existed in the duct where a large portion of the duct (w50% by area) was not affected
Fig. 7. Mass fraction of water vapour (kg/kg) profile at various distances across the duct (20 mm and 2 m/s).
by spray injection. Comparison between the areas weighted average temperature values across the duct for the whole cross section of the duct and for only the spray plume cone area is plotted in Fig. 8. It was apparent that more nozzles were required to cover the full duct area. There was a significant difference in the average temperature between the two illustrations. The average temperature was approximately 35.3 C considering the whole cross section while cooling to about 32 C was achieved if we consider only the spray plume cone area. This puts emphasis that an effective application must be designed ensuring an appropriate nozzle arrangement in order to reach an efficient uniform cooling. 3.2. Droplet trajectory and evaporation The calculated droplet trajectories demonstrated why the air was cooled most in the lower half-region of the duct. The droplet trajectories obtained from the numerical model for 20 mm droplet size spray at 2 m/s air velocity are shown in Fig. 9 coloured by residence time. From these figure, it is evident that droplets were airborne in the duct until reaching the outlet or impacting the bottom of the duct depending on the droplet size injected. Furthermore, due to small droplet sizes tested in which droplets have low momentum compared to the air momentum, droplets followed the air flow direction very rapidly in a short distance. This resulted in droplets dispersed in a narrow spray shape which affect the evaporation rate and uniformity in the air cooling process. It can be noticed that droplets travelled slowly to the bottom wall due to gravitational effect. The predicted normalized mass fraction change of water droplets along the duct for different droplet sizes and air velocities are
Spray plume cone area
Air average temperature
40
Full
38 36 34 32 30 28 0
2
4
6
8
10
Duct Length (m)
Fig. 6. Air temperature ( C) profile at various distances across the duct (20 mm and 2 m/s).
Fig. 8. The weighted average temperature ( C) along the duct for the whole duct and the spray plume cone area.
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Normalized Water mass fraction (%) Fig. 9. Registered droplets trajectories across the duct (20 mm and 2 m/s).
80
60
40
20
0 0
3.3.1. Effect of droplet size Droplet size is a key parameter of spray characteristic and affects the spray cooling significantly. The effect of droplet size was investigated by testing three droplet sizes (20, 35, 50 mm) at three air velocities (1, 2, 3 m/s) under the same ambient condition. Therefore, at each velocity, the air and water mass-flow rate were the same for any given droplet size. Fig. 10 shows the predicted normalized mass fraction change of water droplets along the duct for different droplet sizes. The mass fraction evaporated, the mass fraction in droplet form reaching the duct outlet, and the mass fraction hitting the walls are plotted as a function of position along the duct. The minimum evaporation was 51% of the injected water for 35 mm and 3 m/s air velocity. The smaller the droplet diameter was, more evaporation and consequently more air cooling were observed. For instance, at 1 m/s air velocity, total mass evaporated for 20 mm droplets was approximately 81% while it was 57% for 50 mm droplets. Although the overall evaporation fractions were lower because of the lower residence time, the tendency of smaller droplets to evaporate faster was also recognized at 2 m/s air velocity. Smaller droplets evaporate faster because they provide more surface area per unit volume than larger droplets and evaporation only occurs at the water/air interface. Evaporation rate per unit volume of droplets in gaseous media is related to the square of the droplet diameter and increases rapidly when droplet diameter is decreased [37].
4
6
8
10
(a) 2 m/s
100
Normalized Water mass fraction (%)
3.3. Effect of air and droplet variables on droplet evaporation and transport
2
Duct length (m)
20 µm 35 µm 50 µm
80
60
40
20
0 0
2
4
6
8
10
Duct length (m)
(b) 3 m/s
100
Normalized Water mass fraction (%)
presented in Table 2. Interestingly, data from this table shows that although droplet sizes in this study were very small along with sufficient residence time, there was no complete evaporation in any case. The maximum evaporation was about 81% for droplet size of 20 mm and air velocity of 1 m/s as can be seen in Table 2.
20 µm 35 µm 50 µm
1 m/s
100
20 µm 35 µm 50 µm
80
60
40
20
0 0
Table 2 Predicted normalized mass fraction change of water droplets along the duct. Droplet size 20 mm
35 mm
50 mm
1 2 3 1 2 3 1 2 3
m/s m/s m/s m/s m/s m/s m/s m/s m/s
% of water evaporated
% of water at outlet
% of water impacted walls
80.7 70.0 53.0 71.4 63.1 51.0 57.1 57.1 52.9
5.3 25.4 47.0 3.3 22.1 48.3 0.3 10.1 43.0
13.9 4.6 0.0 25.3 14.8 0.8 42.6 32.8 4.0
2
4
6
8
10
Duct length (m)
(c) Fig. 10. Plots of predicted normalized mass fraction change of water droplets along the duct for different droplet sizes (a) Va ¼ 1 m/s, (b) Va ¼ 2 m/s, (c) Va ¼ 3 m/s. (Solid Square) represents mass fraction reaching the outlet, (solid circle) represents mass evaporated, and (solid triangle) represents mass hitting walls.
In contrast to the results of 1 and 2 m/s air velocity, the total mass fraction evaporated at 3 m/s air velocity was independent of droplet size, as can be seen in Fig. 10(c). Assuming each droplet behaves independently, smaller droplets are more efficient than
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Normalized Water mass fraction (%)
larger droplets in air spray cooling. However, owing to the fact that larger droplets have a higher inertia to drag ratio, they tend to penetrate the flow deeper. Thus large droplets produce a larger plume. This outcome is more pronounced the higher the speeds. At 3 m/s, the effect of droplet size on evaporation is balanced by the effect of penetration on evaporation. This conclusion is in agreement with Tissot [38] findings which had higher evaporation at larger droplet diameter under the same operational condition.
1 m/s 2 m/s 3 m/s
20 µm
100
80
60
40
20
0 0
2
4
6
8
10
Duct length (m)
(a)
Normalized Water mass fraction (%)
1 m/s 2 m/s 3 m/s
35 µm
100
80
60
40
20
0 0
2
4
6
8
10
Duct length (m)
(b) 50 µm
100
Normalized Water mass fraction (%)
423
1 m/s 2 m/s 3 m/s
80
60
40
20
3.3.2. Effect of air velocity Air velocity had a large influence on droplet trajectory and evaporation efficiency. The effect of air velocity was investigated comparing three air velocities (1, 2, 3 m/s) for three droplet sizes under the same ambient condition. Fig. 11 shows the predicted normalized mass fraction change of water droplets along the duct for different air velocities. The mass fraction evaporated, the mass fraction in droplet form reaching the duct outlet, and the mass fraction hitting the walls are plotted as a function of position along the duct. We can see from this figure that air velocity had a significant influence. For instance, for 20 mm droplet size spray, total mass evaporated at 1 m/s air velocity was about 81% while it was 53% for 3 m/s. The reason for this is because droplet velocity was the same as the air velocity along the duct except for a short time at the beginning. Thus, lower air velocity means longer travelling (residence) time, therefore, better evaporative cooling efficiency. However, due to gravitational effect, falling rate per unit length will be higher for lower velocities which make droplets fall out quicker than higher velocities. Hence, there is a clear trade-off between droplet size and air velocity. In addition, it can be seen from Fig. 11 that for 20 mm droplet size spray, more evaporation was experienced when the velocity was lowered where the residence time increased. Moreover, this trend was observed for 35 mm droplet size spray with less significant influence. In contrast, the predicted evaporation efficiencies of 50 mm droplet size sprays at the air velocities (1, 2, 3 m/s) were nearly the same. In fact, results of 50 mm droplets at air velocity of 1 and 2 m/s were not consistent as a large portion of the water hits the ground and then terminated from the calculation. This is because larger droplets has greater falling rate compared to small droplets which causes droplets reach the ground faster. The data in Figs. 10 and 11, particularly at the lower air speeds, show that the rate of evaporation reduced with distance along the duct. A similar trend was also observed for the temperature data (Fig. 6). This was due to the fact that inside the region where droplets were present, the humidity has increased to 100%. This is a combined effect of evaporation and localized temperature reduction. Based on Fig. 10, it can be concluded that for 1 m/s, no significant further evaporation took place after 7 m, for all the investigated droplet sizes. This was most pronounced for 20 mm diameter droplets. In contrast at 3 m/s air velocity, the rate of evaporation has not yet levelled-off at 10 m, suggesting that longer ducts would enhance evaporation. 4. Conclusions The main conclusions from this study are as follows:
0 0
2
4
6
8
10
Duct length (m)
(c) Fig. 11. Plots of predicted normalized mass fraction change of water droplets along the duct for different air velocities (a) Dp ¼ 20 mm, (b) Dp ¼ 35 mm, (c) Dp ¼ 50 mm. (Solid Square) represents mass fraction reaching the outlet, (solid circle) represents mass evaporated, and (solid triangle) represents mass hitting walls.
(1) In the range of droplet sizes and air velocities studied, a significant cooling performance achieved. In the droplet saturated region an average temperature reduction of 8.1 C was achieved, while across the duct average reduction of 4.8 C was achieved. (2) Correct nozzle arrangement is essential to ensure effective cooling. Non-uniform temperature distribution existed and the air was cooled mostly in the lower half-region.
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(3) Air velocity played a significant role in droplet transport and evaporation. At high air speeds, large droplets performed as well as small droplets. While at low air speeds, small droplets performed 25% superior than large droplets. (4) Due to the compromise effect of momentum exchange and evaporation rate, there is a trade-off between droplet size and air velocity and resulting plum dispersion. This must be considered to identify optimum droplet size. This effect explains the similar performance of small and large droplets mentioned in (3). Acknowledgements This work was financially supported by the Saudi Arabian Government and the Queensland Geothermal Energy Centre of Excellence. References [1] A.E. Conradie, D.G. Kröger, Performance evaluation of dry-cooling systems for power plant applications, Appl. Therm. Eng. 16 (1996) 219e232. [2] R.B. Boulay, M.J. Cerha, M. Massoudi, Dry and hybrid condenser cooling design to maximize operating income, in: ASME Conference Proceedings, 2005, pp. 167e175. [3] J.S. Maulbetsch, Comparison of Alternate Cooling Technologies for California Power Plants: Economic, Environmental and Other Tradeoffs, EPRI, California Energy Commission (PIER), 2002. [4] A. Ashwood, D. Bharathan, Hybrid Cooling Systems for Low-temperature Geothermal Power Production, NREL, National Laboratory of the U.S, 2011. [5] J. Maulbetsch, M. DiFilippo, Spray Enhancement of Air Cooled Condensers, EPRI, California Energy Commission (PIER), 2003. [6] S. He, H. Gurgenci, Z. Guan, A.M. Alkhedhair, Pre-cooling with Munters media to improve the performance of natural draft dry cooling towers, Appl. Therm. Eng. 53 (2013) 67e77. [7] M.A. Chaker, Key parameters for the performance of impaction-pin nozzles used in inlet fogging of gas turbine engines, J. Eng. Gas Turbines Power 129 (2007) 473e477. [8] S. Molis, P. Levine, Combustion Turbine Spray Cooler Guide, EPRI, EPRIGEN, 1999. [9] R.K. Bhargava, C.B. Meher-Homji, M.A. Chaker, M. Bianchi, F. Melino, A. Peretto, S. Ingistov, Gas turbine fogging technology: a state-of-the-art reviewepart i: inlet evaporative foggingeanalytical and experimental aspects, J. Eng. Gas Turbines Power 129 (2007) 443e453. [10] A. Bletchly, Evaluation of Ambient Condition Correction Curves for Power Station Capacity, CQUniversity, Faculty of Science, Rockhampton, Queensland, 2010. [11] A.M. Al-Amiri, M.M. Zamzam, M.A. Chaker, C.B. Meher-Homji, Application of inlet fogging for power augmentation of mechanical drive turbines in the oil and gas sector, in: ASME Conference Proceedings, 2006, pp. 847e855. [12] B.D. Esterhuyse, D.G. Kröger, The effect of ionisation of spray in cooling air on the wetting characteristics of finned tube heat exchanger, Appl. Therm. Eng. 25 (2005) 3129e3137. [13] W. Wells, On air-borne infection. study II. droplets and droplet nuclei, Am. J. Trop. Med. Hyg. 20 (1934) 611e618. [14] G.P. Wachtell, Atomized Water Injection to Improve Dry Cooling Tower Performance, National Technical Information Service, 1974.
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