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Numerical simulation of a semi-indirect evaporative cooler
Energy and Buildings 41 (2009) 1205–1214
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Numerical simulation of a semi-indirect evaporative cooler R. Herrero Martı´n * Departamento de Ingenierı´a Te´rmica y de Fluidos, Universidad Polite´cnica de Cartagena, C/Dr. Fleming, s/n (Campus Muralla), 30202 Cartagena, Murcia, Spain
A R T I C L E I N F O
A B S T R A C T
Article history: Received 2 September 2008 Received in revised form 21 June 2009 Accepted 26 June 2009
This paper presents the experimental study and numerical simulation of a semi-indirect evaporative cooler (SIEC), which acts as an energy recovery device in air conditioning systems. The numerical simulation was conducted by applying the CFD software FLUENT implementing a UDF to model evaporation/condensation. The numerical model was validated by comparing the simulation results with experimental data. Experimental data and numerical results agree for the lower relative humidity series but not for higher relative humidity values. ß 2009 Elsevier B.V. All rights reserved.
Keywords: Energy recovery Porous evaporative cooling Numerical simulation
1. Introduction Heat and mass transfer phenomena are present in a wide range of applications, such as in air conditioning, humidifiers, cooling towers and evaporative coolers as well as in the fields of liquid dehumidification and seawater distillation. With ideal evaporative cooling processes, the air can be cooled under these conditions getting saturated while passing over an appropriate wetted surface. If there is no heat transfer from surroundings, the process is adiabatic, i.e., air loses a certain amount of sensible heat but gains an equal amount of latent heat from water vapour. Nevertheless, in most cases, the thermal process does not behave in such an ideal way. To account for the complicated thermal process that takes place in an evaporative cooler, a comprehensive mathematical model has to be formulated. Mathematical modelling of heat and mass transfer processes in evaporative fluid coolers has been the subject of numerous works. Among them, the followings studies should be mentioned. In the early 1960s, Baker and Shryock [1] analyzed the crossflow cooling tower using the finite difference method. The model of Parker and Treybal [2] was the first complete computational model which took into account the changes of the temperature of the water spraying the tube surface. It was assumed that the amount of water evaporated into air could be neglected and that, in the range of temperatures considered, the enthalpy of the saturated air was a linear function of temperature. The dependencies for heat and mass transfer coefficients developed on the basis of their experiments were also given. Mizushina et al. [3] presented two methods of heat calculations for coolers: one simplified, in which
* Tel.: +34 968 32 59 85; fax: +34 968 32 59 99. E-mail address: [email protected]. 0378-7788/$ – see front matter ß 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.enbuild.2009.06.008
constant temperature of the water spraying the tubes was assumed and another, which took into account the variation of that temperature in a heat exchanger. In a later paper by these authors [4], empirical equations for heat and mass transfer coefficients were given. Finned exchangers were also studied by Kreid et al. [5]. They presented an approximate method of calculation based on mean logarithmic enthalpy difference. Maclaine-Cross and Banks [6] proposed a theory to correlate heat transfer coefficients of wet and dry surfaces. Vilser [7] described a mathematical model for nonadiabatic process of water evaporation into air and presented the experimental results for heat and mass transfer on finned tubes sprayed with water. Kettleborough and Hsieh [8] analyzed the performance of a counter flow indirect evaporative cooler using the theory of enthalpy potential, which had good agreement with the experimental results. Webb [9] unified the methods of approach to heat calculations of three types of evaporative heat exchangers: cooling towers, evaporative fluid coolers and evaporative condensers. In their work, Webb and Villacres [10] presented computational algorithms for computer calculations of the three types of exchangers aforementioned. Perez-Blanco and Bird [11] considered an idealized case of counter-current evaporative exchanger which consisted of a vertical tube with sprayed inner surface. Erens and Dreyer [12,13] modified the methods of Bourillot [14], Poppe and Ro¨gener [15] used for calculations of cooling towers to the case of evaporative fluid coolers with counter-current and cross-flow of agents. In a later work [16] they presented the experimental results of the studies on coefficient of heat and mass transfer at cross-flow of air and water. Several researchers have analyzed the heat and mass transfer at the entrance region for falling film [18–21] and Emaes et al. [22] discussed and presented the summary on the coefficient of water evaporation. Another remarkable evaporative cooling study, with
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Nomenclature A b C C2 cp D DAB Ef Es f g 0 h fg hfg h¯ L h¯ m Ja k keff kf ks L m˙ m Nu NL Pr q00conv q00e p Red ReD.max Shf Sc ¯ D Sh w T
surface area width (m) Zhukauskas constant inertial resistance factor heat capacity (J/kg K) tube diameter binary diffusion coefficient (m2/s) total fluid energy total solid medium energy friction factor gravity constant (m/s2) modified latent heat of vaporization (kJ/kg) latent heat of vaporization (kJ/kg) average convection coefficient (W/m2 K) average mass transfer convection coefficient (m/s) Jakob number thermal conductivity (W/m K) effective thermal conductivity of the medium fluid phase thermal conductivity (including the turbulent contribution, kt) solid medium thermal conductivity pipe length (m) condensate mass flow (kg/s) Zhukauskas constant Nusselt number number of rows Prandtl number convection heat transfer (W) evaporative heat transfer (W) Reynolds number (condensation transition criterion) Reynolds number based on the maximum fluid velocity fluid enthalpy source term Schmidt number Sherwood number specific humidity (kg water/kg dry air) temperature (K)
Greek letters a permeability r density (kg/m3) Drlm log-mean density difference (kg/m3) DTlm log-mean temperature difference (K) g porosity of the medium m viscosity (Ns/m2) Subscripts o outlet i inlet noteworthy references is the one carried out by Yan and Lin [17]. More recently Yan [23] extended this study developing a detailed numerical analysis where the characteristics of the evaporative cooling of liquid film in turbulent mixed convection channel flows were studied in depth. Recently, He et al. [24] considered a vertical tube with liquid water film cooling. The gas flow was considered to be turbulent and the liquid film to be laminar. Feddaoui et al. [25]
investigated numerically the co-current turbulent mixed convection heat and mass transfer in a falling film of water inside a vertical heated tube and recently, [26] developed an analysis for studying the evaporative cooling of liquid film falling inside a vertical insulated tube in a turbulent gas stream. This paper presents the experimental study and numerical simulation of a semi-indirect evaporative cooler (SIEC), which acts as an energy recovery device in air conditioning systems. The numerical model was developed to simulate the thermal behaviour of the semi-indirect evaporative cooler. The simulation results were verified by the experimental data. 2. Design and description of the semi-indirect evaporative cooler The semi-indirect evaporative cooler (SIEC) has two independent airflow supplies, one used for cooling, together with a second, the return airflow, in direct contact with water to favour heat and mass transfer. Water is forced against the return airflow and is constantly circulating (Fig. 1). The cooling effect of the impulsed air would thus be the addition of two processes: the heat exchanges between the two airflows (supply and return) plus the heat exchange process, through evaporation, between the air supply and the external wall. The semi-indirect evaporative cooler works with the following mechanisms: Heat and mass transfer in the return airflow. Spread of mass due to porosity and heat transport through the solid wall. Evaporation or condensation as well as heat and mass exchange in the airflow supply. All of these features are presented together, thus combining heat and mass transfer, increasing the cooling effect of the air to be conditioned and achieving optimisation of the thermal process [27]. Depending on the permeability of the wall of the solid porous cooler which separates the two airflows, there is greater or lower liquid diffusion (water) towards the airflow supply from the external pores, in all cases. The partial pressure of the water vapour in the air supply is the controlling factor in this mass transport process. In Fig. 2, a photograph of the device and its arrangement over the water tank is shown, and in Tables 1 and 2 and Fig. 3 the geometric dimensions and the staggered configuration of the ceramic exchanger are also presented. 3. Experimental facility The equipment used to carry out the experiments was the following (Fig. 4): Supply system: it consists of a fan with a potentiometer to keep the airflows under control. Air handling unit (AHU): this equipment allows us to simulate the conditions of the air supplied (temperature and humidity). Air distribution system: all the measuring instruments are inserted here. Water distribution system: a water pump conveys water from the tank to the pressure spray system with downward directed nozzles. A semi-indirect evaporative cooler. The conditioned room: the dimensions are 2 m 2 m 2.5 m, which contains a heat pump inside to guarantee when needed that the space is properly conditioned. Monitoring and data-acquisition system: a computer controls and stores all the results from the measuring instruments.
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Fig. 1. The semi-indirect ceramic evaporative cooler.
Fig. 2. SIEC device.
From the AHU the air enters the SIEC. This main air stream is called the primary airflow and when this air stream is conditioned in the SIEC it enters the room. Thus, the air expelled from the room goes through the SIEC in a cross-flow (recovery configuration), going up the SIEC until it leaves from the upper part (secondary airflow). The measurement sensors are shown in Fig. 5:
T: temperature measurement sensor. Type: Technoterm 60, accuracy: 0.1 8C. HR: relative humidity measurement sensor. Type: Honeywell HIH-3610, accuracy: 2% RH (0–100% RH). DP: differential pressure transducer. Type: DWYER 603-2, accuracy: (70 8F) 2% scale range.
Table 1 Geometric dimensions. Internal diameter (di) 3
15 10
m
External diameter (de) 3
25 10
m
Thickness (d) 3
5 10
m
Section T (ST) 3
30 10
m
Section L (SL) 3
25 10
m
Section D (SD) 3
29.2 10
m
Pipe length
Area (Ao)
0.6 m
2.3 m2
R.H. Martı´n / Energy and Buildings 41 (2009) 1205–1214
1208 Table 2 Geometric configuration. Arrangement
Number of columns
Number of rows
Number of pipes
Material
Staggered
7
7
49
Ceramic
(proportional to the temperature difference), as could be predicted from the characteristic definition. Also, when humidity rises, the sensible heat recovered decreases, this fact can be explained due to the existence of evaporative cooling on the pipes’ outer surfaces, in the primary air stream. Best results are then expected for the lowest relative humidity levels and the highest temperature differences. 3.3. Latent heat analysis
Fig. 3. Schema of the staggered tube bank.
3.1. Experimental results The columns of Table 3 give the following data for each case; in columns 2–4 and 7–10 for the primary air stream: specific humidity at the inlet (w1 ), dry temperature at the inlet (T1), wet bulb temperature at the inlet (T1h), specific humidity at the outlet (w2 ) and dry temperature at the outlet (T2) are given, and also, in columns 5 and 6 for the return airflow: dry temperature at the inlet (T3) and wet bulb temperature at the inlet (T3h) are shown. In order to explain the SIEC behaviour, the sensible heat recovered, the latent heat recovered and the total heat recovered was determined from the experimental data (see Table 4). The corresponding average uncertainty values for the characteristics analyzed are 5.4%, 5.5% and 7.8%, respectively [28,29]. 3.2. Sensible heat analysis When the temperature difference between the outdoor and the return air stream rises, the sensible heat recovered is higher
Evaporation is defined by the vapour pressure difference between the pipes’ outer surfaces and the primary air stream. Consequently, when the temperature rises, the latent heat exchanged tends to fall (for the same relative humidity values) due to the fact that the vapour pressure rises with the temperature. When the humidity level is low, evaporation is promoted from the pipes outer surfaces, and the conditioned air stream is humidified. A humidity increment leads to condensation in the primary airflow, decreasing its humidity content (dehumidification process, negative values of latent heat). Air with low relative humidity and high temperature has a large evaporative capacity, while for the same temperatures, high humidity levels result in high specific humidity values, which create good conditions for the appearance of condensation on the pipes (negative values of latent heat). The same effect can also be explained for low temperature values but the effects provoked in the humidity gradients are lower and thus the latent heat exchange obtained is less. 3.4. Total heat analysis Initial characterization tests show how, for low relative humidity contents and high temperatures of the air supply, the main effect is evaporative from the surface of the ceramic pipes, while for high temperatures and relative humidity of the air supply, dehumidification takes place and thus condensation appears on the exterior surface of the pipes and the latent and sensible heat recovered are the latent and sensible heat recovered are added (being negative values). However, the evaporative effect takes priority over sensible heat recovered. This is a very important fact in comparison with indirect evaporative cooling systems where only sensible heat recovery is involved. Thus, one possible use of this recovery system can be in climates with high temperatures and humidity, such as tropical environ-
Fig. 4. The test facility.
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Fig. 5. Schema of the experimental installation with the measurement sensors.
Table 3 Experimental results. Case
Data
Experimental Results
w1 (g/kg) RH <30 %
T1 (8C)
T1h (8C)
T3 (8C)
T3h (8C)
w2 (g/kg)
T2 (8C)
1 2 3 4 5
3.94 5.14 5.46 6.15 6.51
24.5 28.3 31.9 36.6 37.7
12.3 14.9 16.5 18.7 19.4
20.6 21.3 21.3 21.4 21.4
15.0 15.9 15.3 15.0 15.3
6.99 8.15 8.01 8.72 8.94
17.3 19.2 20.0 21.4 21.4
30% < RH < 60%
6 7 8 9 10
9.7 13.13 16.33 14.42 14.33
25.5 28.1 31.5 36.1 39.1
17.9 21.3 24.4 24.4 25.1
21.3 21.2 21.3 21.5 21.6
14.3 14.0 15.5 14.3 16.3
6.58 6.76 8.71 8.52 11.02
18.4 19.4 20.9 22.8 23.9
RH > 60%
11 12 13 14 15
19.61 18.2 17.49 23.57 22.53
26.5 29.4 32.6 38.5 40.8
25.1 25.0 25.4 30.0 30.0
21.5 21.6 21.7 21.5 21.8
16.9 17.1 17.4 16.6 16.5
10.42 11.42 12.57 15.63 14.95
21.9 23.3 24.4 29.1 28.8
ments where the system could reduce the humidity of the primary air supply, by using the cooling power of the secondary air. As Wang [41] mentioned, the performance factor (PF) is the parameter that properly characterize the effectiveness of indirect evaporative coolers. This characteristic is defined by the following expression:
Table 4 Experimental results characterization. Case
Sensible heat (W)
Latent heat (W)
Total heat (W)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
1008.91 1262.73 1665.29 2134.88 2299.92 1017.39 1289.50 1562.20 1954.45 2207.34 713.37 919.07 1216.06 1427.48 1800.61
1067.93 1053.92 892.86 899.86 850.84 1092.44 2230.39 2668.07 2065.83 1158.96 3217.79 2373.95 1722.69 2780.11 2654.06
59.02 208.81 772.43 1235.02 1449.08 2109.83 3519.89 4230.27 4020.28 3366.30 3931.16 3293.01 2938.75 4207.59 4454.67
Expanded uncertainty (k = 2)
5.44%
5.52%
7.75%
PF ¼
m˙ 1 ðT 1 T 2 Þ m˙ 2 ðT 1 T 3h Þ
(1)
where m˙ 1 and m˙ 2 are the mass flow rates in the primary and secondary airflows, respectively. The average PF value obtained (see Table 5) is over 60% which represents an adequate behaviour of the SIEC device [41].
4. SIEC CFD modelling In this work, the general purpose CFD software FLUENT was used. FLUENT is one of the most widely employed commercial codes for simulating engineering fluid flow due to its accuracy, robustness and convenience. In FLUENT, the conservation equa-
R.H. Martı´n / Energy and Buildings 41 (2009) 1205–1214
1210 Table 5 Performance factor values. Case
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Mean value
PF
0.76
0.73
0.71
0.7
0.73
0.63
0.62
0.66
0.61
0.67
0.48
0.49
0.54
0.43
0.49
0.62
tions of mass, momentum and energy are solved using the finite volume method. In general, the computational methods described in the literature differ in their approach to the method of the determination of heat flux from cooled fluid into air. They also use various equations for the determination of heat and mass transfer coefficients. Qureshi and Zubair [30] summarized the major assumptions that are used to derive the basic modelling equations to model evaporative coolers and condensers: The system is in steady state. The apparatus and the cooling water re-circulating circuit are insulated from the surroundings. Radiation heat transfer is ignored. Viscous heat dissipation and other secondary effects are also negligible [31]. Negligible water loss due to drift. The heat and mass transfer coefficients are constant within the tube bundle. Complete surface wetting of the tube bundle. The distribution of air and water is uniform at the inlets and this uniformity is maintained. The film temperature at the air–water interface is equal to the bulk film temperature. The re-circulating water temperature at the inlet and outlet is the same. The water film on the tubes is considered to be very thin, i.e., the air–water interface area is approximately equal to the outer surface area of the dry tubes.
The first step of the CFD simulation was the mesh generation; the model was created and meshed by using Gambit software. In order to accelerate the mesh generation process a TRANSCRIPT program was written. The mesh chosen was a non-uniform structured hexahedral mesh [32,33]. The computational domain is divided into three different zones (which correspond to the physical flows): the external one (linked to the primary flow) and two internal zones associated to the liquid film annular flow and the one linked to the secondary flow (return flow). This latter area is not meshed, due to the fact that the evaporative cooling process under study takes place in the interface that separates the liquid film and the return air, establishing a boundary condition at this interface temperature (if steady-state conditions are to be maintained, the latent energy lost by the liquid because of evaporation must be replenished by energy transfer to the liquid from its surroundings, neglecting radiation effects, this transfer may be due to the convection of sensible energy from the air) [34]. Moreover, by the imposition of this boundary condition and also because the problem to solve is the thermal process in the primary air stream, the inner return flow is not considered beyond the boundary condition aforementioned. The second step was to complete the establishment of the boundary conditions and material properties. Mass flow boundary condition has to be defined at the inlets (the volumetric primary and secondary flow rate is a constant value of 140 m3/h). The outflow condition is imposed at the outlet surface. Finally, the exterior walls were modelled as adiabatic. The outer flow, which actually is moist air, is assumed to be dry air. This is justified in terms of the low mass fraction that the vapour content represents.
The external flow is also considered to be incompressible. The solid porous material has a density of 2200 kg/m3 and a porosity of 25%. 4.1. Mathematical formulation For steady, incompressible, constant property flow, the following forms of the momentum, energy and species conservation equations taking into account the effects of turbulence are well known [35]. But some consideration should be made for the case studied [33]. 4.1.1. Momentum equations for porous media in FLUENT Porous media are modelled by the addition of a momentum source term to the standard fluid flow equations. The source term is composed of two parts, a viscous loss term (Darcy, the first term on the right-hand side of Eq. (2)), and an inertial loss term (the second term on the right-hand side of Eq. (2)): 0 Si ¼ @
1 3 3 X X 1 Di j mn j þ C i j rn j jn j jA 2 j¼1 j¼1
(2)
where Si is the source term for the ith (x, y, or z) momentum equation, and D and C are prescribed matrices. This momentum sink contributes to the pressure gradient in the porous cell, creating a pressure drop that is proportional to the fluid velocity (or velocity squared) in the cell. To recover the case of simple homogeneous porous media: m 1 Si ¼ ni þ C 2 rni jni j 2 a
(3)
where a is the permeability and C2 is the inertial resistance factor, simply specify D and C as diagonal matrices with 1/a and C2, respectively, on the diagonals (and zero for the other elements). 4.1.2. Treatment of the energy equations in porous media FLUENT solves the standard energy transport equation (Eq. (4)) in porous media regions with modifications to the conduction flux and the transient terms only. In the porous media, the conduction flux uses an effective conductivity and the transient terms includes the thermal inertia of the solid region on the medium:
@ ðgr f E f þ ð1 g Þrs Es Þ þ rð~ nðr f E f þ pÞÞ @t " # ¼ r ke f f rT
X
hi J¯i þ ðt¯ e f f ~ nÞ þ Shf
(4)
i
where Ef is the total fluid energy, Es the total solid medium energy, g the porosity of the medium, keff the effective thermal conductivity of the medium and Shf is the fluid enthalpy source term. 4.1.3. Effective conductivity in the porous medium The effective thermal conductivity in the porous medium, keff, is computed by FLUENT as the average volume of the fluid conductivity and the solid conductivity: ke f f ¼ g k f þ ð1 g Þks
(5)
R.H. Martı´n / Energy and Buildings 41 (2009) 1205–1214
where g is the porosity of the medium, kf the fluid phase thermal conductivity (including the turbulent contribution, kt) and ks is the solid medium thermal conductivity. When this simple volume averaging is not desirable, perhaps due to the effects of the medium geometry, the effective conductivity can be computed via a user-defined function. In all cases, however, the effective conductivity is treated as an isotropic property of the medium. The porous media model incorporates an empirically determined flow resistance in a region of the model defined as ‘‘porous’’. In essence, the porous media model is nothing more than an added momentum sinks in the governing momentum equations. As such, the following modelling assumptions and limitations should be recognized: since the volume blockage that is physically present is not represented in the model, by default FLUENT uses and reports a superficial velocity inside the porous medium, based on the volumetric flow rate, to ensure continuity of the velocity vectors across the porous medium interface, and also the effect of the porous medium on the turbulence field is only approximated. 4.2. Physical modelling Some parameters have to be previously calculated for FLUENT simulation, such as the convection calculation, or the evaporative cooling process involved, because FLUENT does not simulate the evaporation automatically but there is an option of implementing a user-defined function (UDF) to model evaporation/condensation [33]. All the calculations carried out and the corresponding expressions used are addressed below. 4.2.1. Evaporation in the external flow The expressions used to compute the convective mass transfer for the external flow are summarized in Fig. 6. Taking into account the heat and mass transfer analogy, the correlation used for convective mass transfer was the one proposed by Zhukauskas [36] (see Fig. 6, Eq. (4)), applying the corresponding constant for the staggered configuration studied (C = 0.363 and m = 0.6) and the correction factor for NL < 20 (C2 = 0.95). The data for FLUENT is a heat density in terms of qevap/volume. This is the energy source to be used in the user-defined function (UDF) built. Since the evaporation process takes place in the proximity of the porous pipes, this is the area to consider in the volume calculations. Thus, the volume used is limited to the surrounding area of the pipes.
1211
Fig. 7. Expressions used for modelling the evaporative cooling process in the internal flow.
4.2.2. Evaporative cooling in the Internal Flow The evaporative cooling process is modelled by assuming that steady-state conditions are to be maintained, thus the latent energy lost by the liquid (the water film) by means of evaporation must be replenished by energy transfer to the liquid from its surroundings. Neglecting radiation effects, this transfer may be due to convection of sensible energy from the gas (the return airflow). Applying conservation of energy to a control surface around the liquid, there is a balance between convection heat transfer from the gas and the evaporative heat loss from the liquid (see Fig. 7, Eq. (1)). With regard to the internal flow calculations, for turbulent flow in circular tubes, the correlation of Ginielinski [37] was used. Ginielinski modified the correlation attributed to Petukhov et al. [38] to obtain agreement with data for smaller Reynolds numbers (see Fig. 7, Eq. (9)). 4.2.3. Condensation in the external flow When condensation occurred, the total heat transfer to the surface was obtained by using Eq. (2) in Fig. 8, and the total heat transfer to the surface was obtained by using the previous equation with the following form of Newton’s law expressed by Eq. (1) in Fig. 8. In Eq. (3) (recommended by Roshenow) latent heat is modified in terms of the Jakob number. Finally, laminar flow conditions are verified (Eq. (5)). 4.2.4. Energy source considerations (UDF) There is an option of implementing a user-defined function (UDF) to model evaporation/condensation considering an energy source term. This function is written in C language and is
Fig. 6. Expressions used for calculating qevap/volume for the external flow under evaporation conditions.
Fig. 8. Expressions used for calculating qevap/volume for the external flow under condensation conditions.
R.H. Martı´n / Energy and Buildings 41 (2009) 1205–1214
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associated to the external flow volume, in a zone near the pipes. With regard to the energy source term, only the energy effect is considered, neglecting the mass transfer and the variation of momentum [33]. The tubes of the bank, the porous pipes, are considered to exchange only sensible heat through the outer surface in direct contact with the primary airflow. The modelling of the evaporative cooling process in the external flow, is done under the assumption that the heat required to sustain the evaporation phenomenon comes from the external flow (moist air). This means considering a function that subtracts energy from the external flow, which, as a result, loses sensible heat. In order to achieve this, a UDF is built, which is basically a C program linked to the rest of the program. To build this program it was taken into account that the heat given by the external flow to the liquid fraction in the porous media is the same as the vaporization heat linked to the mass of liquid vaporized. These calculations were carried out using the corresponding correlations for staggered banks of tubes. Afterwards, the heat associated to the mass evaporation was estimated and finally this heat was subtracted from external flow. To model the condensation effect a constant source term was associated to the porous volume.
Fig. 9. Comparison between FLUENT and experimental data (HR < 30%).
where Rm ’ denotes the maximum residual value of w variable after m iterations, w applied for p, ui, and for T. Tests were also conducted to verify the grid independency of the results. Simulations were performed with decreasing size grids, until the results were consistent. The variable used in this comparison was the mean outlet temperature.
4.3. Numerical model The solution algorithm selected was the segregated solver. Using this approach, the governing equations are solved sequentially. When using segregated solver in FLUENT a number of pressure interpolation schemes are available. For most cases, the standard scheme is acceptable, but some types of models may benefit from one of the other schemes such as the employed PRESTO scheme which is recommended for flows involving porous media [33]. The most widely used and validated turbulence model, the k–e model, was selected [39]. The model performs particularly well in confined flows, this includes a wide range of flows with industrial engineering applications. A summary of the performance assessment for the standard k–e model is given by Versteeg and Malalasekera [40]. The numerical computation is considered converged when the residual summed over all the computational nodes at nth iteration, Rn’ , satisfies the following criterion: Rn’ Rm ’
105
Fig. 10. Comparison between FLUENT and experimental data (30% < HR < 60%).
(6)
Table 6 Comparison between FLUENT and experimental results. Case
FLUENT Results w2 (g/kg)
RH < 30%
Experimental Results T2 (8C)
w2 (g/kg)
T2 (8C)
1 2 3 4 5
5.37 6.53 6.85 7.44 7.85
16.6 18.5 19.4 20.9 21.5
6.99 8.15 8.01 8.72 8.94
17.3 19.2 20.0 21.4 21.4
30% < RH < 60%
6 7 8 9 10
10 11.03 12.78 11.82 13.05
17.7 19.1 21.5 22.1 24.1
6.58 6.76 8.71 8.52 11.02
18.4 19.4 20.9 22.8 23.9
RH > 60%
11 12 13 14 15
13.68 13.96 14.38 15.81 15.49
21.1 22.0 23.1 25.3 25.9
10.42 11.42 12.57 15.63 14.95
21.9 23.3 24.4 29.1 28.8
Fig. 11. Comparison between FLUENT and experimental data (HR > 60%).
Fig. 12. Total heat recovered: comparison between FLUENT and experimental data.
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Table 7 Total heat recovered: error obtained between FLUENT and experimental value. Case
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Mean value
Error (%)
27.06
21.19
12.37
14.89
16.45
14.85
16.96
16.77
17.54
18.23
16.51
16.51
17.71
18.72
19.13
17.66
5. CFD results and discussion A comparison between data and FLUENT simulation was performed (see Table 6). The columns of Table 6 give the following data for each case; in columns 2–4 and 7–10 for the primary air stream: specific humidity at the inlet (w1 ), dry temperature at the inlet (T1), wet bulb temperature at the inlet (T1h), specific humidity at the outlet (w2 ) and dry temperature at the outlet (T2) are given, and also, in columns 5 and 6 for the return airflow: dry temperature at the inlet (T3) and wet bulb temperature at the inlet (T3h) are shown. In Figs. 9–11 a comparative between inlet temperatures and the temperature increments for the primary air stream are plotted. Furthermore, in Fig. 12 a comparison between numerical and experimental results in terms of total heat recovered is provided. This comparison yields to average error values of 18.4, 16.9 and 17.7% for the corresponding three RH series, respectively, as calculated in Table 7. It is observed that the numerical results are higher compared to the experimental ones. The average error between experimental and numerical data in terms of total heat recovered is 17.66%, which, in spite of the fact that it is above 15%, is an adequate value. The complexity of the underlying physics should be taken into account, as well as the assumptions made to reduce the complexity to a manageable level whilst preserving the salient issues. The heat transfer coefficient associated with a tube is determined by its position in the bank. The coefficient for a tube in the first row is approximately equal to that for a single tube in cross-flow, whereas larger heat transfer coefficients are associated with tubes of the inner rows. The tubes of the first few rows act as a turbulence grid, which increases the heat transfer coefficient for tubes in the following rows. In most configurations, however, heat transfer conditions stabilize, such that little change occurs in the convection coefficient for a tube beyond the fourth or fifth row. As Incropera and Dewitt [34] also mentioned the average heat transfer coefficient for the entire tube bundle is the value to determine. The average heat transfer coefficient calculated by FLUENT was 79.88 W/m2 K; the experimental and the theoretical ones were 68.67 and 67.92 W/m2 K, respectively. The discrepancies between the numerical and the experimental results are satisfactory. The numerical simulation yields to slightly higher values of total heat power. The error computed is of the same order as that obtained for the heat transfer coefficient.This allows stating the adequacy of FLUENT for the prediction of the heat transfer characteristics in evaporative cooling devices. Moreover, the methodology proposed has been satisfactorily validated. Besides, the numerical simulation arises as a complementary tool for the design and analysis of this kind of heat exchangers. 6. Conclusions The characterization of the SIEC system in terms of heat recovered was carried out. Sensible, latent and total heat recovered was evaluated and the associated performance factor values were also calculated. The average PF value obtained, over 60%, represents an adequate behaviour of the SIEC device. For low relative humidity content and high temperatures of the air supply, the main effect is evaporative from the surface of the ceramic pipes. For high temperatures and relative humidity of
the air supply, dehumidification takes place and thus condensation appears on the exterior surface of the pipes and the latent and sensible heat recovered are added (being negative values). However, the mass transfer phenomenon takes priority over sensible heat recovered. A possible use of this recovery system can be in climates with high temperatures and humidity, such as tropical environments where the system could reduce the humidity of the primary air supply, by using the cooling power of the secondary air. A CFD model with a commercial program FLUENT was developed to simulate the behaviour of a porous semi-indirect evaporative cooler implementing a user-defined function (UDF) to model evaporation/condensation. The numerical model was validated by comparing the simulation results with experimental data. The comparison between temperature increments and the data (measured and modelled) agree for the lower relative humidity level (evaporation modelling). There are important deviations for the RH > 60% series, where condensation appears. The assumption of considering the outer flow which is moist air as dry air has to be modified to improve condensation modelling by including the properties of the air– water vapour mixture at each step of numerical calculation.
Acknowledgements The author wish to thank Dr. Rey and Dr. Velasco for their suggestions in the frame of the research project: ‘‘Waste Energy Recovery using a combined system: SIECHP’’. References [1] D.R. Baker, H.A. Shryock, A comprehensive approach to the analysis of cooling tower performance, ASME Journal of Heat Transfer 83 (3) (1961) 339–350. [2] R.O. Parker, R.E. Treybal, The heat mass transfer characteristics of evaporative coolers, AIChE Chemical Engineering Progress Symposium Series 57 (3) (1961) 138–149. [3] T. Mizushina, R. Ito, H. Miyashita, Experimental study of an evaporative cooler, International Chemical Engineering 7 (4) (1967) 727–732. [4] T. Mizushina, R. Ito, H. Miyashita, Characteristics and methods of thermal design of evaporative coolers, International Chemical Engineering 8 (3) (1968) 532– 538. [5] D.K. Kreid, B.M. Johnson, D.W. Faletti, Approximate analysis of heat transfer from the surface of a wet finned heat exchanger, ASME paper no. 78-HT-26, 1978. [6] I.L. Maclaine-Cross, P.J. Banks, A general theory of wet surface heat exchangers and its application to regenerative evaporative cooling, ASME Journal of Heat Transfer 103 (1981) 579–585. [7] L. Vilser, Wa¨rme-und Stoffaustausch an wasserberieselten Rippenrohren, Dissertation, University Stuttgart, 1982. [8] C.F. Kettleborough, C.S. Hsieh, The thermal performance of the wet surface plastic plate heat exchanger used as an indirect evaporative cooler, ASME Journal of Heat Transfer 105 (1983) 366–373. [9] R.L. Webb, A unified theoretical treatment of thermal analysis of cooling towers, evaporative condensers and fluid coolers, ASHRAE Transactions, Part B 2B (90) (1984) 398–415. [10] R.L. Webb, A. Villacres, Algorithms for performance simulation of cooling towers, evaporative condensers and fluid coolers, ASHRAE Transactions, Part B 2B (90) (1984) 416–458. [11] H. Perez-Blanco, W.A. Bird, Study of heat and mass transfer in a vertical-tube evaporative cooler, Journal of Heat Transfer-Transactions of the ASME 106 (1) (1984) 210–215. [12] J. Erens, A.A. Dreyer, An improved procedure for calculating the performance of evaporative closed circuit coolers, AIChE Symposium Series 84 (263) (1988) 140– 145. [13] J. Erens, A.A. Dreyer, A general approach for the rating of evaporative closed circuit coolers, N and O Journal 5 (1) (1989) 1–10. [14] C. Bourillot, TEFERI numerical model for calculating the performance of an evaporative cooling tower, EPRI Report CS-3212-SR, California, 1983. [15] M. Poppe, H. Ro¨gener, Berechnung von Ru¨ckku¨hlwerken, VDI-Wa¨rmeatlas, VDIVerlag, Du¨sseldorf, 1984.
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[16] A.A. Dreyer, P.J. Erens, Heat and mass transfer coefficients and pressure drop correlations for a crossflow evaporative cooler, in: Proceedings of the 9th International Heat Transfer Conference, Jerusalem, (1990), pp. 233–238, 19EN-20. [17] W.M. Yan, T.F. Lin, Evaporative cooling of liquid film through interfacial heat and mass transfer in a vertical channel. II. Numerical study, International Journal of Heat Mass Transfer 34 (4–5) (1991) 1113–1124. [18] G. Grossman, Heat and mass transfer in film absorption in the presence of nonabsorbable gases, International Journal of Heat Mass Transfer 40 (15) (1997) 3595–3606. [19] R. Yang, B.D. Wood, A numerical modelling of an absorption process on a liquid falling film, Solar Energy 40 (3) (1992) 195–198. [20] T.A. Ameel, H.M. Habib, B.D. Wood, Effect of non-absorbable gas on interface heat and mass transfer for the entrance region of a falling film absorber, ASME Journal of Solar Energy Engineering 118 (1996) 45–49. [21] C. Wei, G.C. Vliet, Effect of inert gas on heat and mass transfer in a vertical channel with falling film, ASME Journal of Solar Energy Engineering 119 (1997) 24–30. [22] I.W. Emaes, N.J. Marr, H. Sabir, The evaporation coefficient of water: a review, International Journal of Heat Mass Transfer 40 (1997) 2963–2973. [23] W.-M. Yan, Evaporative cooling of liquid film in turbulent mixed convective channel flows, International Journal of Heat Mass Transfer 41 (1998) 3719–3729. [24] S. He, P. An, J. Li, J.D. Jackson, Combined heat and mass transfer in a uniformly heated vertical tube with water film cooling, International Journal of Heat Fluid Flow 19 (1998) 401–417. [25] M. Feddaoui, A. Mir, E. Belahmidi, Co-current turbulent mixed convection heat and mass transfer in falling film of water inside a vertical heated tube, International Journal of Heat Mass Transfer 46 (2003) 3497–3509. [26] M. Feddaoui, H. Meftah, A. Mir, The numerical computation of the evaporative cooling of falling water film in turbulent mixed convection inside a vertical tube,
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Energy and Buildings journal homepage: www.elsevier.com/locate/enbuild
Numerical simulation of a semi-indirect evaporative cooler R. Herrero Martı´n * Departamento de Ingenierı´a Te´rmica y de Fluidos, Universidad Polite´cnica de Cartagena, C/Dr. Fleming, s/n (Campus Muralla), 30202 Cartagena, Murcia, Spain
A R T I C L E I N F O
A B S T R A C T
Article history: Received 2 September 2008 Received in revised form 21 June 2009 Accepted 26 June 2009
This paper presents the experimental study and numerical simulation of a semi-indirect evaporative cooler (SIEC), which acts as an energy recovery device in air conditioning systems. The numerical simulation was conducted by applying the CFD software FLUENT implementing a UDF to model evaporation/condensation. The numerical model was validated by comparing the simulation results with experimental data. Experimental data and numerical results agree for the lower relative humidity series but not for higher relative humidity values. ß 2009 Elsevier B.V. All rights reserved.
Keywords: Energy recovery Porous evaporative cooling Numerical simulation
1. Introduction Heat and mass transfer phenomena are present in a wide range of applications, such as in air conditioning, humidifiers, cooling towers and evaporative coolers as well as in the fields of liquid dehumidification and seawater distillation. With ideal evaporative cooling processes, the air can be cooled under these conditions getting saturated while passing over an appropriate wetted surface. If there is no heat transfer from surroundings, the process is adiabatic, i.e., air loses a certain amount of sensible heat but gains an equal amount of latent heat from water vapour. Nevertheless, in most cases, the thermal process does not behave in such an ideal way. To account for the complicated thermal process that takes place in an evaporative cooler, a comprehensive mathematical model has to be formulated. Mathematical modelling of heat and mass transfer processes in evaporative fluid coolers has been the subject of numerous works. Among them, the followings studies should be mentioned. In the early 1960s, Baker and Shryock [1] analyzed the crossflow cooling tower using the finite difference method. The model of Parker and Treybal [2] was the first complete computational model which took into account the changes of the temperature of the water spraying the tube surface. It was assumed that the amount of water evaporated into air could be neglected and that, in the range of temperatures considered, the enthalpy of the saturated air was a linear function of temperature. The dependencies for heat and mass transfer coefficients developed on the basis of their experiments were also given. Mizushina et al. [3] presented two methods of heat calculations for coolers: one simplified, in which
* Tel.: +34 968 32 59 85; fax: +34 968 32 59 99. E-mail address: [email protected]. 0378-7788/$ – see front matter ß 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.enbuild.2009.06.008
constant temperature of the water spraying the tubes was assumed and another, which took into account the variation of that temperature in a heat exchanger. In a later paper by these authors [4], empirical equations for heat and mass transfer coefficients were given. Finned exchangers were also studied by Kreid et al. [5]. They presented an approximate method of calculation based on mean logarithmic enthalpy difference. Maclaine-Cross and Banks [6] proposed a theory to correlate heat transfer coefficients of wet and dry surfaces. Vilser [7] described a mathematical model for nonadiabatic process of water evaporation into air and presented the experimental results for heat and mass transfer on finned tubes sprayed with water. Kettleborough and Hsieh [8] analyzed the performance of a counter flow indirect evaporative cooler using the theory of enthalpy potential, which had good agreement with the experimental results. Webb [9] unified the methods of approach to heat calculations of three types of evaporative heat exchangers: cooling towers, evaporative fluid coolers and evaporative condensers. In their work, Webb and Villacres [10] presented computational algorithms for computer calculations of the three types of exchangers aforementioned. Perez-Blanco and Bird [11] considered an idealized case of counter-current evaporative exchanger which consisted of a vertical tube with sprayed inner surface. Erens and Dreyer [12,13] modified the methods of Bourillot [14], Poppe and Ro¨gener [15] used for calculations of cooling towers to the case of evaporative fluid coolers with counter-current and cross-flow of agents. In a later work [16] they presented the experimental results of the studies on coefficient of heat and mass transfer at cross-flow of air and water. Several researchers have analyzed the heat and mass transfer at the entrance region for falling film [18–21] and Emaes et al. [22] discussed and presented the summary on the coefficient of water evaporation. Another remarkable evaporative cooling study, with
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Nomenclature A b C C2 cp D DAB Ef Es f g 0 h fg hfg h¯ L h¯ m Ja k keff kf ks L m˙ m Nu NL Pr q00conv q00e p Red ReD.max Shf Sc ¯ D Sh w T
surface area width (m) Zhukauskas constant inertial resistance factor heat capacity (J/kg K) tube diameter binary diffusion coefficient (m2/s) total fluid energy total solid medium energy friction factor gravity constant (m/s2) modified latent heat of vaporization (kJ/kg) latent heat of vaporization (kJ/kg) average convection coefficient (W/m2 K) average mass transfer convection coefficient (m/s) Jakob number thermal conductivity (W/m K) effective thermal conductivity of the medium fluid phase thermal conductivity (including the turbulent contribution, kt) solid medium thermal conductivity pipe length (m) condensate mass flow (kg/s) Zhukauskas constant Nusselt number number of rows Prandtl number convection heat transfer (W) evaporative heat transfer (W) Reynolds number (condensation transition criterion) Reynolds number based on the maximum fluid velocity fluid enthalpy source term Schmidt number Sherwood number specific humidity (kg water/kg dry air) temperature (K)
Greek letters a permeability r density (kg/m3) Drlm log-mean density difference (kg/m3) DTlm log-mean temperature difference (K) g porosity of the medium m viscosity (Ns/m2) Subscripts o outlet i inlet noteworthy references is the one carried out by Yan and Lin [17]. More recently Yan [23] extended this study developing a detailed numerical analysis where the characteristics of the evaporative cooling of liquid film in turbulent mixed convection channel flows were studied in depth. Recently, He et al. [24] considered a vertical tube with liquid water film cooling. The gas flow was considered to be turbulent and the liquid film to be laminar. Feddaoui et al. [25]
investigated numerically the co-current turbulent mixed convection heat and mass transfer in a falling film of water inside a vertical heated tube and recently, [26] developed an analysis for studying the evaporative cooling of liquid film falling inside a vertical insulated tube in a turbulent gas stream. This paper presents the experimental study and numerical simulation of a semi-indirect evaporative cooler (SIEC), which acts as an energy recovery device in air conditioning systems. The numerical model was developed to simulate the thermal behaviour of the semi-indirect evaporative cooler. The simulation results were verified by the experimental data. 2. Design and description of the semi-indirect evaporative cooler The semi-indirect evaporative cooler (SIEC) has two independent airflow supplies, one used for cooling, together with a second, the return airflow, in direct contact with water to favour heat and mass transfer. Water is forced against the return airflow and is constantly circulating (Fig. 1). The cooling effect of the impulsed air would thus be the addition of two processes: the heat exchanges between the two airflows (supply and return) plus the heat exchange process, through evaporation, between the air supply and the external wall. The semi-indirect evaporative cooler works with the following mechanisms: Heat and mass transfer in the return airflow. Spread of mass due to porosity and heat transport through the solid wall. Evaporation or condensation as well as heat and mass exchange in the airflow supply. All of these features are presented together, thus combining heat and mass transfer, increasing the cooling effect of the air to be conditioned and achieving optimisation of the thermal process [27]. Depending on the permeability of the wall of the solid porous cooler which separates the two airflows, there is greater or lower liquid diffusion (water) towards the airflow supply from the external pores, in all cases. The partial pressure of the water vapour in the air supply is the controlling factor in this mass transport process. In Fig. 2, a photograph of the device and its arrangement over the water tank is shown, and in Tables 1 and 2 and Fig. 3 the geometric dimensions and the staggered configuration of the ceramic exchanger are also presented. 3. Experimental facility The equipment used to carry out the experiments was the following (Fig. 4): Supply system: it consists of a fan with a potentiometer to keep the airflows under control. Air handling unit (AHU): this equipment allows us to simulate the conditions of the air supplied (temperature and humidity). Air distribution system: all the measuring instruments are inserted here. Water distribution system: a water pump conveys water from the tank to the pressure spray system with downward directed nozzles. A semi-indirect evaporative cooler. The conditioned room: the dimensions are 2 m 2 m 2.5 m, which contains a heat pump inside to guarantee when needed that the space is properly conditioned. Monitoring and data-acquisition system: a computer controls and stores all the results from the measuring instruments.
R.H. Martı´n / Energy and Buildings 41 (2009) 1205–1214
1207
Fig. 1. The semi-indirect ceramic evaporative cooler.
Fig. 2. SIEC device.
From the AHU the air enters the SIEC. This main air stream is called the primary airflow and when this air stream is conditioned in the SIEC it enters the room. Thus, the air expelled from the room goes through the SIEC in a cross-flow (recovery configuration), going up the SIEC until it leaves from the upper part (secondary airflow). The measurement sensors are shown in Fig. 5:
T: temperature measurement sensor. Type: Technoterm 60, accuracy: 0.1 8C. HR: relative humidity measurement sensor. Type: Honeywell HIH-3610, accuracy: 2% RH (0–100% RH). DP: differential pressure transducer. Type: DWYER 603-2, accuracy: (70 8F) 2% scale range.
Table 1 Geometric dimensions. Internal diameter (di) 3
15 10
m
External diameter (de) 3
25 10
m
Thickness (d) 3
5 10
m
Section T (ST) 3
30 10
m
Section L (SL) 3
25 10
m
Section D (SD) 3
29.2 10
m
Pipe length
Area (Ao)
0.6 m
2.3 m2
R.H. Martı´n / Energy and Buildings 41 (2009) 1205–1214
1208 Table 2 Geometric configuration. Arrangement
Number of columns
Number of rows
Number of pipes
Material
Staggered
7
7
49
Ceramic
(proportional to the temperature difference), as could be predicted from the characteristic definition. Also, when humidity rises, the sensible heat recovered decreases, this fact can be explained due to the existence of evaporative cooling on the pipes’ outer surfaces, in the primary air stream. Best results are then expected for the lowest relative humidity levels and the highest temperature differences. 3.3. Latent heat analysis
Fig. 3. Schema of the staggered tube bank.
3.1. Experimental results The columns of Table 3 give the following data for each case; in columns 2–4 and 7–10 for the primary air stream: specific humidity at the inlet (w1 ), dry temperature at the inlet (T1), wet bulb temperature at the inlet (T1h), specific humidity at the outlet (w2 ) and dry temperature at the outlet (T2) are given, and also, in columns 5 and 6 for the return airflow: dry temperature at the inlet (T3) and wet bulb temperature at the inlet (T3h) are shown. In order to explain the SIEC behaviour, the sensible heat recovered, the latent heat recovered and the total heat recovered was determined from the experimental data (see Table 4). The corresponding average uncertainty values for the characteristics analyzed are 5.4%, 5.5% and 7.8%, respectively [28,29]. 3.2. Sensible heat analysis When the temperature difference between the outdoor and the return air stream rises, the sensible heat recovered is higher
Evaporation is defined by the vapour pressure difference between the pipes’ outer surfaces and the primary air stream. Consequently, when the temperature rises, the latent heat exchanged tends to fall (for the same relative humidity values) due to the fact that the vapour pressure rises with the temperature. When the humidity level is low, evaporation is promoted from the pipes outer surfaces, and the conditioned air stream is humidified. A humidity increment leads to condensation in the primary airflow, decreasing its humidity content (dehumidification process, negative values of latent heat). Air with low relative humidity and high temperature has a large evaporative capacity, while for the same temperatures, high humidity levels result in high specific humidity values, which create good conditions for the appearance of condensation on the pipes (negative values of latent heat). The same effect can also be explained for low temperature values but the effects provoked in the humidity gradients are lower and thus the latent heat exchange obtained is less. 3.4. Total heat analysis Initial characterization tests show how, for low relative humidity contents and high temperatures of the air supply, the main effect is evaporative from the surface of the ceramic pipes, while for high temperatures and relative humidity of the air supply, dehumidification takes place and thus condensation appears on the exterior surface of the pipes and the latent and sensible heat recovered are the latent and sensible heat recovered are added (being negative values). However, the evaporative effect takes priority over sensible heat recovered. This is a very important fact in comparison with indirect evaporative cooling systems where only sensible heat recovery is involved. Thus, one possible use of this recovery system can be in climates with high temperatures and humidity, such as tropical environ-
Fig. 4. The test facility.
R.H. Martı´n / Energy and Buildings 41 (2009) 1205–1214
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Fig. 5. Schema of the experimental installation with the measurement sensors.
Table 3 Experimental results. Case
Data
Experimental Results
w1 (g/kg) RH <30 %
T1 (8C)
T1h (8C)
T3 (8C)
T3h (8C)
w2 (g/kg)
T2 (8C)
1 2 3 4 5
3.94 5.14 5.46 6.15 6.51
24.5 28.3 31.9 36.6 37.7
12.3 14.9 16.5 18.7 19.4
20.6 21.3 21.3 21.4 21.4
15.0 15.9 15.3 15.0 15.3
6.99 8.15 8.01 8.72 8.94
17.3 19.2 20.0 21.4 21.4
30% < RH < 60%
6 7 8 9 10
9.7 13.13 16.33 14.42 14.33
25.5 28.1 31.5 36.1 39.1
17.9 21.3 24.4 24.4 25.1
21.3 21.2 21.3 21.5 21.6
14.3 14.0 15.5 14.3 16.3
6.58 6.76 8.71 8.52 11.02
18.4 19.4 20.9 22.8 23.9
RH > 60%
11 12 13 14 15
19.61 18.2 17.49 23.57 22.53
26.5 29.4 32.6 38.5 40.8
25.1 25.0 25.4 30.0 30.0
21.5 21.6 21.7 21.5 21.8
16.9 17.1 17.4 16.6 16.5
10.42 11.42 12.57 15.63 14.95
21.9 23.3 24.4 29.1 28.8
ments where the system could reduce the humidity of the primary air supply, by using the cooling power of the secondary air. As Wang [41] mentioned, the performance factor (PF) is the parameter that properly characterize the effectiveness of indirect evaporative coolers. This characteristic is defined by the following expression:
Table 4 Experimental results characterization. Case
Sensible heat (W)
Latent heat (W)
Total heat (W)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
1008.91 1262.73 1665.29 2134.88 2299.92 1017.39 1289.50 1562.20 1954.45 2207.34 713.37 919.07 1216.06 1427.48 1800.61
1067.93 1053.92 892.86 899.86 850.84 1092.44 2230.39 2668.07 2065.83 1158.96 3217.79 2373.95 1722.69 2780.11 2654.06
59.02 208.81 772.43 1235.02 1449.08 2109.83 3519.89 4230.27 4020.28 3366.30 3931.16 3293.01 2938.75 4207.59 4454.67
Expanded uncertainty (k = 2)
5.44%
5.52%
7.75%
PF ¼
m˙ 1 ðT 1 T 2 Þ m˙ 2 ðT 1 T 3h Þ
(1)
where m˙ 1 and m˙ 2 are the mass flow rates in the primary and secondary airflows, respectively. The average PF value obtained (see Table 5) is over 60% which represents an adequate behaviour of the SIEC device [41].
4. SIEC CFD modelling In this work, the general purpose CFD software FLUENT was used. FLUENT is one of the most widely employed commercial codes for simulating engineering fluid flow due to its accuracy, robustness and convenience. In FLUENT, the conservation equa-
R.H. Martı´n / Energy and Buildings 41 (2009) 1205–1214
1210 Table 5 Performance factor values. Case
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Mean value
PF
0.76
0.73
0.71
0.7
0.73
0.63
0.62
0.66
0.61
0.67
0.48
0.49
0.54
0.43
0.49
0.62
tions of mass, momentum and energy are solved using the finite volume method. In general, the computational methods described in the literature differ in their approach to the method of the determination of heat flux from cooled fluid into air. They also use various equations for the determination of heat and mass transfer coefficients. Qureshi and Zubair [30] summarized the major assumptions that are used to derive the basic modelling equations to model evaporative coolers and condensers: The system is in steady state. The apparatus and the cooling water re-circulating circuit are insulated from the surroundings. Radiation heat transfer is ignored. Viscous heat dissipation and other secondary effects are also negligible [31]. Negligible water loss due to drift. The heat and mass transfer coefficients are constant within the tube bundle. Complete surface wetting of the tube bundle. The distribution of air and water is uniform at the inlets and this uniformity is maintained. The film temperature at the air–water interface is equal to the bulk film temperature. The re-circulating water temperature at the inlet and outlet is the same. The water film on the tubes is considered to be very thin, i.e., the air–water interface area is approximately equal to the outer surface area of the dry tubes.
The first step of the CFD simulation was the mesh generation; the model was created and meshed by using Gambit software. In order to accelerate the mesh generation process a TRANSCRIPT program was written. The mesh chosen was a non-uniform structured hexahedral mesh [32,33]. The computational domain is divided into three different zones (which correspond to the physical flows): the external one (linked to the primary flow) and two internal zones associated to the liquid film annular flow and the one linked to the secondary flow (return flow). This latter area is not meshed, due to the fact that the evaporative cooling process under study takes place in the interface that separates the liquid film and the return air, establishing a boundary condition at this interface temperature (if steady-state conditions are to be maintained, the latent energy lost by the liquid because of evaporation must be replenished by energy transfer to the liquid from its surroundings, neglecting radiation effects, this transfer may be due to the convection of sensible energy from the air) [34]. Moreover, by the imposition of this boundary condition and also because the problem to solve is the thermal process in the primary air stream, the inner return flow is not considered beyond the boundary condition aforementioned. The second step was to complete the establishment of the boundary conditions and material properties. Mass flow boundary condition has to be defined at the inlets (the volumetric primary and secondary flow rate is a constant value of 140 m3/h). The outflow condition is imposed at the outlet surface. Finally, the exterior walls were modelled as adiabatic. The outer flow, which actually is moist air, is assumed to be dry air. This is justified in terms of the low mass fraction that the vapour content represents.
The external flow is also considered to be incompressible. The solid porous material has a density of 2200 kg/m3 and a porosity of 25%. 4.1. Mathematical formulation For steady, incompressible, constant property flow, the following forms of the momentum, energy and species conservation equations taking into account the effects of turbulence are well known [35]. But some consideration should be made for the case studied [33]. 4.1.1. Momentum equations for porous media in FLUENT Porous media are modelled by the addition of a momentum source term to the standard fluid flow equations. The source term is composed of two parts, a viscous loss term (Darcy, the first term on the right-hand side of Eq. (2)), and an inertial loss term (the second term on the right-hand side of Eq. (2)): 0 Si ¼ @
1 3 3 X X 1 Di j mn j þ C i j rn j jn j jA 2 j¼1 j¼1
(2)
where Si is the source term for the ith (x, y, or z) momentum equation, and D and C are prescribed matrices. This momentum sink contributes to the pressure gradient in the porous cell, creating a pressure drop that is proportional to the fluid velocity (or velocity squared) in the cell. To recover the case of simple homogeneous porous media: m 1 Si ¼ ni þ C 2 rni jni j 2 a
(3)
where a is the permeability and C2 is the inertial resistance factor, simply specify D and C as diagonal matrices with 1/a and C2, respectively, on the diagonals (and zero for the other elements). 4.1.2. Treatment of the energy equations in porous media FLUENT solves the standard energy transport equation (Eq. (4)) in porous media regions with modifications to the conduction flux and the transient terms only. In the porous media, the conduction flux uses an effective conductivity and the transient terms includes the thermal inertia of the solid region on the medium:
@ ðgr f E f þ ð1 g Þrs Es Þ þ rð~ nðr f E f þ pÞÞ @t " # ¼ r ke f f rT
X
hi J¯i þ ðt¯ e f f ~ nÞ þ Shf
(4)
i
where Ef is the total fluid energy, Es the total solid medium energy, g the porosity of the medium, keff the effective thermal conductivity of the medium and Shf is the fluid enthalpy source term. 4.1.3. Effective conductivity in the porous medium The effective thermal conductivity in the porous medium, keff, is computed by FLUENT as the average volume of the fluid conductivity and the solid conductivity: ke f f ¼ g k f þ ð1 g Þks
(5)
R.H. Martı´n / Energy and Buildings 41 (2009) 1205–1214
where g is the porosity of the medium, kf the fluid phase thermal conductivity (including the turbulent contribution, kt) and ks is the solid medium thermal conductivity. When this simple volume averaging is not desirable, perhaps due to the effects of the medium geometry, the effective conductivity can be computed via a user-defined function. In all cases, however, the effective conductivity is treated as an isotropic property of the medium. The porous media model incorporates an empirically determined flow resistance in a region of the model defined as ‘‘porous’’. In essence, the porous media model is nothing more than an added momentum sinks in the governing momentum equations. As such, the following modelling assumptions and limitations should be recognized: since the volume blockage that is physically present is not represented in the model, by default FLUENT uses and reports a superficial velocity inside the porous medium, based on the volumetric flow rate, to ensure continuity of the velocity vectors across the porous medium interface, and also the effect of the porous medium on the turbulence field is only approximated. 4.2. Physical modelling Some parameters have to be previously calculated for FLUENT simulation, such as the convection calculation, or the evaporative cooling process involved, because FLUENT does not simulate the evaporation automatically but there is an option of implementing a user-defined function (UDF) to model evaporation/condensation [33]. All the calculations carried out and the corresponding expressions used are addressed below. 4.2.1. Evaporation in the external flow The expressions used to compute the convective mass transfer for the external flow are summarized in Fig. 6. Taking into account the heat and mass transfer analogy, the correlation used for convective mass transfer was the one proposed by Zhukauskas [36] (see Fig. 6, Eq. (4)), applying the corresponding constant for the staggered configuration studied (C = 0.363 and m = 0.6) and the correction factor for NL < 20 (C2 = 0.95). The data for FLUENT is a heat density in terms of qevap/volume. This is the energy source to be used in the user-defined function (UDF) built. Since the evaporation process takes place in the proximity of the porous pipes, this is the area to consider in the volume calculations. Thus, the volume used is limited to the surrounding area of the pipes.
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Fig. 7. Expressions used for modelling the evaporative cooling process in the internal flow.
4.2.2. Evaporative cooling in the Internal Flow The evaporative cooling process is modelled by assuming that steady-state conditions are to be maintained, thus the latent energy lost by the liquid (the water film) by means of evaporation must be replenished by energy transfer to the liquid from its surroundings. Neglecting radiation effects, this transfer may be due to convection of sensible energy from the gas (the return airflow). Applying conservation of energy to a control surface around the liquid, there is a balance between convection heat transfer from the gas and the evaporative heat loss from the liquid (see Fig. 7, Eq. (1)). With regard to the internal flow calculations, for turbulent flow in circular tubes, the correlation of Ginielinski [37] was used. Ginielinski modified the correlation attributed to Petukhov et al. [38] to obtain agreement with data for smaller Reynolds numbers (see Fig. 7, Eq. (9)). 4.2.3. Condensation in the external flow When condensation occurred, the total heat transfer to the surface was obtained by using Eq. (2) in Fig. 8, and the total heat transfer to the surface was obtained by using the previous equation with the following form of Newton’s law expressed by Eq. (1) in Fig. 8. In Eq. (3) (recommended by Roshenow) latent heat is modified in terms of the Jakob number. Finally, laminar flow conditions are verified (Eq. (5)). 4.2.4. Energy source considerations (UDF) There is an option of implementing a user-defined function (UDF) to model evaporation/condensation considering an energy source term. This function is written in C language and is
Fig. 6. Expressions used for calculating qevap/volume for the external flow under evaporation conditions.
Fig. 8. Expressions used for calculating qevap/volume for the external flow under condensation conditions.
R.H. Martı´n / Energy and Buildings 41 (2009) 1205–1214
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associated to the external flow volume, in a zone near the pipes. With regard to the energy source term, only the energy effect is considered, neglecting the mass transfer and the variation of momentum [33]. The tubes of the bank, the porous pipes, are considered to exchange only sensible heat through the outer surface in direct contact with the primary airflow. The modelling of the evaporative cooling process in the external flow, is done under the assumption that the heat required to sustain the evaporation phenomenon comes from the external flow (moist air). This means considering a function that subtracts energy from the external flow, which, as a result, loses sensible heat. In order to achieve this, a UDF is built, which is basically a C program linked to the rest of the program. To build this program it was taken into account that the heat given by the external flow to the liquid fraction in the porous media is the same as the vaporization heat linked to the mass of liquid vaporized. These calculations were carried out using the corresponding correlations for staggered banks of tubes. Afterwards, the heat associated to the mass evaporation was estimated and finally this heat was subtracted from external flow. To model the condensation effect a constant source term was associated to the porous volume.
Fig. 9. Comparison between FLUENT and experimental data (HR < 30%).
where Rm ’ denotes the maximum residual value of w variable after m iterations, w applied for p, ui, and for T. Tests were also conducted to verify the grid independency of the results. Simulations were performed with decreasing size grids, until the results were consistent. The variable used in this comparison was the mean outlet temperature.
4.3. Numerical model The solution algorithm selected was the segregated solver. Using this approach, the governing equations are solved sequentially. When using segregated solver in FLUENT a number of pressure interpolation schemes are available. For most cases, the standard scheme is acceptable, but some types of models may benefit from one of the other schemes such as the employed PRESTO scheme which is recommended for flows involving porous media [33]. The most widely used and validated turbulence model, the k–e model, was selected [39]. The model performs particularly well in confined flows, this includes a wide range of flows with industrial engineering applications. A summary of the performance assessment for the standard k–e model is given by Versteeg and Malalasekera [40]. The numerical computation is considered converged when the residual summed over all the computational nodes at nth iteration, Rn’ , satisfies the following criterion: Rn’ Rm ’
105
Fig. 10. Comparison between FLUENT and experimental data (30% < HR < 60%).
(6)
Table 6 Comparison between FLUENT and experimental results. Case
FLUENT Results w2 (g/kg)
RH < 30%
Experimental Results T2 (8C)
w2 (g/kg)
T2 (8C)
1 2 3 4 5
5.37 6.53 6.85 7.44 7.85
16.6 18.5 19.4 20.9 21.5
6.99 8.15 8.01 8.72 8.94
17.3 19.2 20.0 21.4 21.4
30% < RH < 60%
6 7 8 9 10
10 11.03 12.78 11.82 13.05
17.7 19.1 21.5 22.1 24.1
6.58 6.76 8.71 8.52 11.02
18.4 19.4 20.9 22.8 23.9
RH > 60%
11 12 13 14 15
13.68 13.96 14.38 15.81 15.49
21.1 22.0 23.1 25.3 25.9
10.42 11.42 12.57 15.63 14.95
21.9 23.3 24.4 29.1 28.8
Fig. 11. Comparison between FLUENT and experimental data (HR > 60%).
Fig. 12. Total heat recovered: comparison between FLUENT and experimental data.
R.H. Martı´n / Energy and Buildings 41 (2009) 1205–1214
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Table 7 Total heat recovered: error obtained between FLUENT and experimental value. Case
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Mean value
Error (%)
27.06
21.19
12.37
14.89
16.45
14.85
16.96
16.77
17.54
18.23
16.51
16.51
17.71
18.72
19.13
17.66
5. CFD results and discussion A comparison between data and FLUENT simulation was performed (see Table 6). The columns of Table 6 give the following data for each case; in columns 2–4 and 7–10 for the primary air stream: specific humidity at the inlet (w1 ), dry temperature at the inlet (T1), wet bulb temperature at the inlet (T1h), specific humidity at the outlet (w2 ) and dry temperature at the outlet (T2) are given, and also, in columns 5 and 6 for the return airflow: dry temperature at the inlet (T3) and wet bulb temperature at the inlet (T3h) are shown. In Figs. 9–11 a comparative between inlet temperatures and the temperature increments for the primary air stream are plotted. Furthermore, in Fig. 12 a comparison between numerical and experimental results in terms of total heat recovered is provided. This comparison yields to average error values of 18.4, 16.9 and 17.7% for the corresponding three RH series, respectively, as calculated in Table 7. It is observed that the numerical results are higher compared to the experimental ones. The average error between experimental and numerical data in terms of total heat recovered is 17.66%, which, in spite of the fact that it is above 15%, is an adequate value. The complexity of the underlying physics should be taken into account, as well as the assumptions made to reduce the complexity to a manageable level whilst preserving the salient issues. The heat transfer coefficient associated with a tube is determined by its position in the bank. The coefficient for a tube in the first row is approximately equal to that for a single tube in cross-flow, whereas larger heat transfer coefficients are associated with tubes of the inner rows. The tubes of the first few rows act as a turbulence grid, which increases the heat transfer coefficient for tubes in the following rows. In most configurations, however, heat transfer conditions stabilize, such that little change occurs in the convection coefficient for a tube beyond the fourth or fifth row. As Incropera and Dewitt [34] also mentioned the average heat transfer coefficient for the entire tube bundle is the value to determine. The average heat transfer coefficient calculated by FLUENT was 79.88 W/m2 K; the experimental and the theoretical ones were 68.67 and 67.92 W/m2 K, respectively. The discrepancies between the numerical and the experimental results are satisfactory. The numerical simulation yields to slightly higher values of total heat power. The error computed is of the same order as that obtained for the heat transfer coefficient.This allows stating the adequacy of FLUENT for the prediction of the heat transfer characteristics in evaporative cooling devices. Moreover, the methodology proposed has been satisfactorily validated. Besides, the numerical simulation arises as a complementary tool for the design and analysis of this kind of heat exchangers. 6. Conclusions The characterization of the SIEC system in terms of heat recovered was carried out. Sensible, latent and total heat recovered was evaluated and the associated performance factor values were also calculated. The average PF value obtained, over 60%, represents an adequate behaviour of the SIEC device. For low relative humidity content and high temperatures of the air supply, the main effect is evaporative from the surface of the ceramic pipes. For high temperatures and relative humidity of
the air supply, dehumidification takes place and thus condensation appears on the exterior surface of the pipes and the latent and sensible heat recovered are added (being negative values). However, the mass transfer phenomenon takes priority over sensible heat recovered. A possible use of this recovery system can be in climates with high temperatures and humidity, such as tropical environments where the system could reduce the humidity of the primary air supply, by using the cooling power of the secondary air. A CFD model with a commercial program FLUENT was developed to simulate the behaviour of a porous semi-indirect evaporative cooler implementing a user-defined function (UDF) to model evaporation/condensation. The numerical model was validated by comparing the simulation results with experimental data. The comparison between temperature increments and the data (measured and modelled) agree for the lower relative humidity level (evaporation modelling). There are important deviations for the RH > 60% series, where condensation appears. The assumption of considering the outer flow which is moist air as dry air has to be modified to improve condensation modelling by including the properties of the air– water vapour mixture at each step of numerical calculation.
Acknowledgements The author wish to thank Dr. Rey and Dr. Velasco for their suggestions in the frame of the research project: ‘‘Waste Energy Recovery using a combined system: SIECHP’’. References [1] D.R. Baker, H.A. Shryock, A comprehensive approach to the analysis of cooling tower performance, ASME Journal of Heat Transfer 83 (3) (1961) 339–350. [2] R.O. Parker, R.E. Treybal, The heat mass transfer characteristics of evaporative coolers, AIChE Chemical Engineering Progress Symposium Series 57 (3) (1961) 138–149. [3] T. Mizushina, R. Ito, H. Miyashita, Experimental study of an evaporative cooler, International Chemical Engineering 7 (4) (1967) 727–732. [4] T. Mizushina, R. Ito, H. Miyashita, Characteristics and methods of thermal design of evaporative coolers, International Chemical Engineering 8 (3) (1968) 532– 538. [5] D.K. Kreid, B.M. Johnson, D.W. Faletti, Approximate analysis of heat transfer from the surface of a wet finned heat exchanger, ASME paper no. 78-HT-26, 1978. [6] I.L. Maclaine-Cross, P.J. Banks, A general theory of wet surface heat exchangers and its application to regenerative evaporative cooling, ASME Journal of Heat Transfer 103 (1981) 579–585. [7] L. Vilser, Wa¨rme-und Stoffaustausch an wasserberieselten Rippenrohren, Dissertation, University Stuttgart, 1982. [8] C.F. Kettleborough, C.S. Hsieh, The thermal performance of the wet surface plastic plate heat exchanger used as an indirect evaporative cooler, ASME Journal of Heat Transfer 105 (1983) 366–373. [9] R.L. Webb, A unified theoretical treatment of thermal analysis of cooling towers, evaporative condensers and fluid coolers, ASHRAE Transactions, Part B 2B (90) (1984) 398–415. [10] R.L. Webb, A. Villacres, Algorithms for performance simulation of cooling towers, evaporative condensers and fluid coolers, ASHRAE Transactions, Part B 2B (90) (1984) 416–458. [11] H. Perez-Blanco, W.A. Bird, Study of heat and mass transfer in a vertical-tube evaporative cooler, Journal of Heat Transfer-Transactions of the ASME 106 (1) (1984) 210–215. [12] J. Erens, A.A. Dreyer, An improved procedure for calculating the performance of evaporative closed circuit coolers, AIChE Symposium Series 84 (263) (1988) 140– 145. [13] J. Erens, A.A. Dreyer, A general approach for the rating of evaporative closed circuit coolers, N and O Journal 5 (1) (1989) 1–10. [14] C. Bourillot, TEFERI numerical model for calculating the performance of an evaporative cooling tower, EPRI Report CS-3212-SR, California, 1983. [15] M. Poppe, H. Ro¨gener, Berechnung von Ru¨ckku¨hlwerken, VDI-Wa¨rmeatlas, VDIVerlag, Du¨sseldorf, 1984.
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