Direct evaporative cooling

The case of direct evaporative cooling is selected to demonstrate: that the present formulation accurately captures the mass and energy exchange in the porous region; that the trends of cooling and heating are correct with appropriate thresholds for moisture addition/removal; and that the activity at the interfaces between all fluid-porous interfaces is reasonable. The domain considered consists of a wet porous material

inserted into a channel, as shown in Fig. 2.2. The domain contains two fluid/porous interfaces, one where air-vapour flows from fluid to porous regions, and one where air- vapour flows from porous to fluid regions. The (three-dimensional) domain is discretized using structured hexahedral control volumes. After grid-convergence testing, the final grid consists of 21 control volumes in the y-direction. In the x-direction, each fluid region contains 20 control volumes and the porous region contains 40 control volumes, for a total grid size of 1680 (1 control volume in z-direction since 3D effects are not considered). The properties of air and water vapour at 27°C, and the porous material used in the simulations are presented in Tab. 2.1. Because of the small ratio of thermal conductivities between the solid and fluid-constituents, thermal dispersion is ignored in the porous region.

Figure 2.2: Domain geometry for direct evaporative cooling validation case. A fully developed velocity profile is imposed at the inlet (x=0), using the expression

𝑢 =6𝑈𝑦 𝐻 [1 −

𝑦

𝐻] , 𝑣 = 0

where, 𝑈 is the average axial velocity in the channel, set to yield a Reynolds number

𝑅𝑒_𝐻= 1000. The flow enters the domain at 25°C, with relative humidity of 30%. The inlet pressure is extrapolated from the interior of the domain. At the outlet, a zero- derivative condition is imposed for both 𝑢 and 𝑣 velocity components, for temperature T

and for moisture mass fraction Y. The outlet pressure is set to atmospheric pressure, 101.3 [kPa]. No-slip, hydrodynamic conditions are imposed at the walls, combined with extrapolation of pressure from the domain interior. The walls are also considered adiabatic and impermeable to moisture.

Table 2.1: Fluid and porous media properties. Air [28] 𝑐_𝑝 [J/(kg.K)] 1005 𝑅 [J/(kg.K)] 287 Water vapour [28] 𝑐_𝑝 [J/(kg.K)] 1872 ℎ_𝑓𝑔 [J/kg] 2500 × 103 𝑅 [J/(kg.K)] 461.5 Fluid mixture [34-37] 𝐷_𝑓 [m2_{/s] 2.600 × 10}-5 𝐷𝑒𝑓𝑓,𝑓 [m2/s] 1.522 × 10-5 𝑘_𝑓 [W/(m.K)] 0.0258 𝑘𝑒𝑓𝑓,𝑓 [W/(m.K)] 0.0237 µ_𝑓 [N.s/m2_{] 1.830 × 10}-5 Domain 𝐻 [m] 0.02 Porous material [1, 34, 35] 𝐴_𝑓𝑠 [m-1_{] 917.7} 𝑐𝑝𝑠 [J/(kg.K)] 1590 𝑐_𝐸 0.244 𝐾 [m2_{] 4.00 × 10}-6 𝑘_{𝑒𝑓𝑓,𝑠} [W/(m.K)] 0.087 𝑙𝑑 [m] 0.55 × 10-3 𝜌𝑠 [kg/m3] 350 𝜀 0.7

For advection schemes in fluid and porous regions, Peclet-weighted upwinding and central differencing schemes are utilized. The results show less than 0.1% change when central differencing scheme is selected instead of upwinding scheme due to the unidirectional flow field. The solution procedure advances in time taking a single iteration per time-step towards its steady-state. The solution is said to be converged when the maximum normalized residual of all the transport equations decreases below 10-9. The residual convergence of the transport equations is presented in Fig. 2.3, which

shows the reduction of the maximum residual values with the number of carried out iterations. The residuals of the fluid energy equation and vapour transport equation are normalized by the average domain values of 𝑇𝑓 and 𝑌𝑓, respectively. The criterion of

convergence was also checked by increasing and decreasing it one order of magnitude, and the results showed further variation of less than 0.8%, indicating that a criterion of 10-9 was sufficient. A time-step size of 0.02s was selected for the current simulations, based on the inlet flow velocity and duct size. Variation of the time-step size from 0.2 to 0.002s showed no significant change in terms of computational time nor convergence behavior.

Figure 2.3: Reduction of the maximum residuals of the transport equations for the direct evaporative cooling case.

Three simulations were carried out for direct evaporative cooling. In case 1, the interfacial heat transfer between the solid and fluid-constituent of porous media is neglected. In cases 2 and 3, the solid-constituent is kept at a temperature of 10°C and 40°C, respectively. The results of specific and relative humidity and the variation temperature for all the three cases are presented in Figs. 2.4, 2.5, and 2.6, respectively.

For case 1, it can be observed from Fig. 2.4 that the specific humidity starts to increase as the flow enters the porous zone, which indicates the addition of moisture to the air. This moisture addition results in an increase in relative humidity and decrease in temperature as observed from Figs. 2.5 and 2.6, respectively. The decrease in fluid temperature due to moisture addition indicates the occurrence of evaporative cooling. Moreover, as soon as the relative humidity reaches 100% no further moisture addition occurs, resulting in constant relative humidity and temperature for the remainder of the region. Case 1 mimics an adiabatic saturation process, which means that the air flow is expected to achieve the wet bulb temperature. The outlet fluid temperature, relative and specific humidities obtained from the simulation are 14.1 °C, 100%, and 10.03 gmwater/kgair, respectively. Compared to a psychrometric chart (for standard barometric pressure), the predicted outlet fluid temperature is approximately 1.5% lower than the charted value of 14.3 °C, while the specific humidity is predicted to be 1.4% higher than the charted value of 9.88 gmwater/kgair. These errors are considered small, and can attributed mainly to the correlation used to compute the saturation pressure of water, which has an error of approximately 0.5%, and to numerical and discretization errors.

Figure 2.4: Centerline specific humidity along the domain length for the direct evaporative cooling case.

Figure 2.5: Centerline relative humidity along the domain length for the direct evaporative cooling case.

Figure 2.6: Centerline fluid temperature along the domain length for the direct evaporative cooling case.

For case 2, in the porous region close to the upstream interface, moisture addition takes place, but then appears to overshoot the 100% relative humidity threshold. This apparent overshoot is due to sensible cooling of the air, which results in a reduction of moisture capacity. To maintain its 100% relative humidity threshold, the moist air begins to reject moisture as it flows through the remainder of the porous domain, although the threshold is never reached due to the continuous reduction in temperature of the air; see Fig. 2.4. It is clear from the trends shown in Figs. 2.4-2.6 that if the porous region was longer, steady-state values of air temperature and 100% relative humidity would be reached. Case 3 considers sensible heating of the air, which produces the opposite effect to that shown in Case 2. In this case, moisture addition occurs throughout the porous region due to the sensible heating and continuously increasing moisture capacity of the air. The slight drop in temperature that occurs close to the upstream interface of the porous region can be explained by the fact that initially the relative humidity of the air is very low, which results in very high moisture transfer rates which lowers the air temperature despite the sensible heating. Once the relative humidity of the air increases, less moisture addition occurs, which results in the sensible heating of the air dominating the evaporative cooling effect. Once again, the trends in Figs. 2.4-2.6 indicate that if the porous region were longer, the air would eventually become saturated at the elevated temperature of the solid

The specific humidity plots illustrate the capability of air to absorb or shed moisture with or without sensible heat transfer, which shows the robustness of the formulation to capture the natural phenomena. Moreover, the relative humidity plots show the excellent coupling of energy and vapour mass fraction, which again shows the efficacy of the developed formulation. The results also illustrate that heat and mass are transferred smoothly across the fluid/porous interfaces without over/under-shoots or wiggles, indicating the robustness of the implemented interface conditions even at a reasonably high Reynolds number (Re= 1000).