The enhanced dew-point evaporative cooling with a macro-roughened structure

Dew-point evaporative cooling (DPEC) is renowned for its great cooling effectiveness and energy savings. However, to improve its cooling performance by optimizing the cooler ’ s common design parameters (e


Introduction
Air conditioning, the ability to control indoor or local thermal environment, is a great achievement of human civilization.With the rapid economic growth and social development in the past century, modern air conditioning has been an essential infrastructure in many buildings.Today, almost 90% of the air conditioning market are dominated by mechanical vapor compression systems (MVCs), which are energy-intensive and could account for 50% of the total energy consumption in buildings [1].The chemical refrigerants used in MVCs, commonly hydrochlorofluorocarbons (HCFCs) and hydrofluorocarbons (HFCs), have strong greenhouse effects equivalent to tens to thousands of carbon dioxide [2].As net-zero carbon emission has become an emergent mission to ensure our sustainable future, it is imminent to seek for an energy-saving and environmentally friendly cooling technology.Among all potential cooling technologies [3][4][5][6], dew-point evaporative cooling (DPEC) has witnessed a burgeon due to its outstanding sensible cooling effectiveness and coefficient of performance (COP) at a low cost, allowing the air to be cooled towards its dew-point (DP) temperature [7].
The remarkable advantages of DPEC have encouraged researchers to perform detailed investigations of its performance and feasibility.Hsu et al. [8] studied three different configurations of indirect evaporative cooling (IEC).It was reported that sub-wet bulb cooling could be achieved through a closed-loop configuration with a wet-bulb (WB) effectiveness of 1.3.Riangvilaikul and Kumar [9] constructed a counter-flow dew-point evaporative cooler and conducted numerical simulations based on energy and mass balance equations.The cooler performed well under different conditions, with DP effectiveness varying between 0.58 and 0.84.Hasan et al. [10] proposed an improved ε-NTU analytical approach for IEC.The results indicated that the modified model was in good agreement with numerical models and experiments with an error of 7.4%.Anisimov et al. [11,12] and Pandelidis et al. [13] explored the performance of the Maisotsenko cycle (M-cycle) exchanger by developing a modified ε-NTU model for different cooler configurations.They evaluated the performance of the M-cycle exchanger under various conditions and applications, i.e., air conditioning and cooling tower.Lin et al. [14,15] investigated the counter-flow DPEC via the first and second law of thermodynamics and computational fluid dynamics (CFD).The evaporative characteristics and governing dimensionless groups were analyzed.The transient and steady-state sensible cooling performance in battery thermal management was also discussed [16].Sadighi et al. [17] proposed an analytical model for a multi-stage DPEC by assuming a varying surface temperature distribution of the water film.The key parameters and performance were analyzed by considering real working conditions caused by air passing through perforations.Comino et al. [18] optimized the performance of DPEC for different applications using a NTU model.The optimized COP values were 50.26, 44.19, and 37.14 for office, restaurant, and auditorium, with corresponding working-supply air ratios of 0.45, 0.45-0.8and 0.45-0.8,respectively.Gao et al. [19] studied a tube-type DPEC.The evaporation and cooling characteristics of the tube channels were analogously modeled to the plate channels.The results indicated that the cooling effect of the tube channels was improved by 1.6-3.0• C. Li et al. [20] investigated the effect of non-uniform water film on cooler performance.The characteristics of wettability and the influence of parameters on the Marangoni number were studied, and a favorable wetting rate of 96.2% was suggested.Zhu et al. [21] simulated the effect of surface water distribution in the vertical wet channels of DPEC via a 3D CFD model.If the unwet area is close to the inlet or outlet of the wet channel, the cooling effect will be significantly weakened.To date, numerous comprehensive investigations have been proposed to analyze DPEC and optimize its geometric and operating parameters for favorable cooling performance.However, current research efforts have confined their focus on the operation of DPEC at a low or moderate air velocity, i.e., 0.5-3.0m/s with a regular laminar flow pattern, while little has been explored beyond, e.g., at air velocities of 4.0-5.5 m/s.In many applications like cooling tower [22] and gas turbine [23], a large supply air flow with complex patterns is essential to ensure their proper operations.This imposes a great challenge in DPEC to maintain the cooling performance [24], which could deteriorate rapidly under increased air velocity.One alternative solution is to increase the discharge outlet area without altering the air velocity, but this could lead to an enormous volume and entail prohibitive cost.Some research in gas turbines has shown that macro-roughened structures can effectively enhance convective heat transfer at high airflow velocity.Xie et al. [25] studied heat transfer on the one-side wall with various ribs.They suggested that the use of alternating large-small ribs could reduce friction loss and improve heat transfer at Reynolds number (Re)>20000.Liu et al. [26]  transfer by 4-8% compared with transverse ribs while slightly reducing the pressure drop.In addition to rib-roughness in the square channels, heat transfer of other macro-roughened structures has been investigated.Webb et al. [27] studied the heat transfer in tubes with repeated rings, and established the analytical correlations for turbulent convective heat transfer.The correlations are effective in 0.01<e/D<0.04,10<p/e<40, and 0.71<Pr<37.6, where e is the rings' height, D is the tubes' diameter, p is the rings' pitch, and Pr is the Prandtl number.Zheng et al. [28] studied capsule-protrusions tubes.The flow and heat characteristics of the two types of arrangement were compared.The results showed that the V-type tubes were more effective, with a higher thermal performance of 27-41%.Hu et al. [29] compared three configurations of corrugate pipes for heat transfer.The performance of helically corrugated pipes was the best, with a thermal performance factor (TPF) of 1.09.Although macro-roughened structures are likely to increase pressure drops compared to micro-roughened structures (e.g., Cu nano-porous layer [30]), they exhibit high heat transfer enhancement and TPF while micro-roughened structures show weak enhancement of heat transfer [31].Therefore, employing macro-roughened structures in DPEC seems to be a promising approach to extend its working range and enhance its cooling performance.Following this idea, Kabeel et al. [32] investigated a baffle cooler's overall performance using an NTU model.They compared the DP effectiveness of five different channel configurations with the smooth channels, and the baffle channels demonstrated a superior cooling effect.Liu et al. [33] studied corrugated channels through a CFD model.The product air temperature and DP effectiveness of corrugated channels showed a 10% higher efficiency than that of the flat channels.Pacak et al. [34] studied a complex cooler with multiple fins along the flow direction.A NTU model was used to simulate the flow field and COP.It was reported that variations in channel height of 1-3 mm led to a 0.12 change in DP effectiveness.Zhou et al. [35] investigated inclined membrane DPEC using a numerical model based on energy and mass balance equations.They analyzed the effects of the inclination angle and channel structure on temperature reduction and DP effectiveness.A 45 • rotational sinusoidal corrugated configuration with an inclination angle of 15 • /75 • was recommended to effectively improve the cooling performance.However, the focus of these studies was limited to introducing macro-roughened structures to enhance the apparent cooling effect, while the governing heat and mass transfer mechanisms have been barely investigated.Particularly, a comprehensive mathematical model which can fully capture and elucidate the key heat and mass transfer processes has yet to be developed.
To fill in the research gap, this study aims to establish an in-depth physical model and analyze the fundamentals of heat and mass transfer in DPECs with macro-roughened structures.A novel dew-point evaporative cooler prototype with rib-roughened dry channels is constructed and its cooling performance is evaluated under various test conditions, particularly at high air flow rate.Meanwhile, a 2D CFD model is developed for the cooler considering continuity, momentum, energy, and species equations, as well as turbulent closures.Upon validation with the test results, the model is used to investigate the turbulent heat and mass transfer in the macro-roughened channels.The temperature, humidity, and velocity distributions in the cooler are evaluated, and the governing dimensionless variables of convective heat and mass transfer are quantitatively analyzed and compared with those of normal flat channels.Additionally, the key-parameters that impact the apparent cooling effect are investigated under a wide range of operating conditions.The findings of this study are expected to guide the design and optimization of the enhanced DPEC through macroroughened structures.

Description of the rib-roughened channels and the enhanced cooler
The enhanced DPEC with rib-roughened channels is shown in Fig. 1 (a).Similar to the flat ones, the rib-roughened cooler adopts a counterflow configuration.The supply air enters the dry channels and is gradually cooled by the working air in the adjacent wet channels towards its inlet dew-point temperature.As can be seen in Fig. 1(a), repeated ribs are staggered and spaced on the upper and lower sides of the dry channels.This design can lead to potential local turbulence when the supply air passes through.In contrast, the flat surface of the normal channels usually provides a steady airflow, as shown in Fig. 1(b).
According to this design, a cooler prototype is fabricated for experimental investigation, as shown in Fig. 2. The enhanced cooler consists of seven pairs of stacked dry-wet channels in Fig. 2(a) with the size of 0.6 m × 0.15 m × 0.09 m (L × W × H).Since metal thin-walled sheets with a thickness of less than 1 mm are difficult to machine into rib-roughened surfaces, acrylic sheets with a thickness of 0.4 mm are selected and reassembled with ribs, as shown in Fig. 2(b).The size of the ribs on them is 1 mm × 0.15 m × 1 mm (b × W × e).The enhanced cooler is placed on an acrylic base, as shown in Fig. 2(c).By adhering the natural-fiber wick material to the rib-roughened plates, water at the ambient temperature is absorbed from a water tank into the wet channels of the enhanced cooler to form uniform water films and ensure complete wetting of the surfaces.

Test process and facilities
To measure the performance of the enhanced cooler, a testing system was constructed, as shown in Fig. 2(c).Resistance Temperature Detectors (RTDs) were used to obtain the dry-bulb (DB) temperature and a relative humidity (RH) meter was used to measure the humidity of the supply air.The RTDs were calibrated by placing the RTDs and a reference RTD which has been calibrated by the manufacturer in the thermal chamber and measuring the deviation under a temperature range of 15-50 • C. Hot-wire sensors were used to obtain the air velocity, and differential pressure sensors were used to measure the pressure drop between the inlet and outlet of the dry channels.The RH meter, velocity sensors, and pressure sensors were calibrated by the manufacturers.The specifications of the sensors are provided in Table 1.RTD temperature sensors were connected to a data logger to collect data, while the air velocity, pressure drop, and humidity signals were wirelessly transmitted to the computer.
Before each test, distillated water was filled into the water tank and rested for 5 minutes to ensure completely wetted surfaces and uniformly distributed water films.A thermal chamber was employed to regulate the temperature and humidity of the supply air for tests.Two axial air blowers (HR-AE series, HonGuan Electronics), which can provide a sufficient pressure of 550 Pa at an air speed of 3 m/s, were installed at the dry channel inlet and wet channel outlet, respectively, to control the working air flow from the supply air.The test conditions of this study are shown in Table 2, and the test results will be presented in Section 4.1.

Uncertainty analysis
After the tests, the experimental uncertainty needs to be examined to verify the validity of the tests.Based on the accuracy of the sensor shown in Table 1, the uncertainty of the measured parameters can be obtained.For an objective parameter (Y), its uncertainty can be calculated by: where Y is the objective parameter with a given function of measured parameters X n ; ΔX 1 , ΔX 2 , …, ΔX n are the uncertainties of the measured parameters.The uncertainties of the objective parameters will be presented in Section 4.1.

Descriptions of the 2D CFD model
Previous studies on macro-roughened DPEC primarily adopted lumped parameter methods to calculate the thermodynamic performance, and empirical correlations were used to analyze the convective heat and mass transfer at the channel surfaces [32][33][34].However, these approaches could ignore the detailed flow field and its significant impact on the heat and mass transfer in complex structures, which would increase the error in the predicting the cooling performance.Therefore, this study proposed a 2D CFD model to capture the interaction between the flow field and heat/mass transfer.A pair of dry-wet channels on the central plane is selected as the model and computational domain, as shown in Fig. 3.The following assumptions need to be stated are made before proceeding with the modeling: (1) The airflows are incompressible, steady, and turbulent, and the thermophysical properties of air are constant.(2) The effects of gravity and viscous dissipation are ignored.
(3) The channels are thermally insulated from the surrounding environment.(4) The wet channel surfaces are entirely covered by uniform water films.( 5) The exemplary rib-roughened channels and cooler are designed with a sufficient width-to-height ratio (W/H) of 37.5, thus the components in the z-direction are neglected.( 6) The water film in direct contact with the air flow is at a saturated state.

Governing equations and boundary conditions
The proposed 2D computational domain can be divided into dry channel, rib plate, water film, and wet channel.In view of the repeated ribs, a pair of dry and wet channels can be divided into same generic units, as shown in Fig. 4. The following Eqs.( 2)-( 8) are the governing equations within the turbulent supply and working air and Eqs. ( 9)-( 10) are the governing equations within the rib-roughened plate and water film.The governing equations consider turbulent momentum, energy, and mass conservations, which are based on Reynolds-average Navier-Stokes (RANS) equations.
(1) Supply air Continuity: Momentum: Energy: where u di is the time-averaged component in x-or y-direction of the supply air velocity vector u d , i, j represent x, y coordinates in the form of the Einstein notation [36], ρ a is the density of air, P d is the pressure of supply air, μ a is the kinetic viscosity, ρ a u ′ di u ′ dj is the Reynolds-stress tensor of supply air, T d is the time-averaged thermodynamic temperature of supply air, λ a is the thermal conductivity of air, c p,a is the constant-pressure specific heat of air, and u ′ dj T ′ d is the turbulent heat flux of supply air.
(2) Working air Continuity: Momentum: Energy: Species: where λ f is the thermal conductivity of the water film, and T f is the timeaveraged water film temperature.
To ensure the governing equations are well posed, it is necessary to The Reynolds-stress is modeled by the eddy-viscosity closures, which are routinely used in engineering design [37].Based on Boussinesq's assumption [38], the 2D Reynolds-stress can be represented by: where μ t is the eddy viscosity, δ ij is the Kronecker-δ symbol [36], and 1 2 ) is the mean strain rate sensor, which can be abbreviated by S ij , k is the turbulent kinetic energy.Similarly, turbulent heat flux is modeled by Fourier's law, which gives a linear relationship between the heat flux and time-averaged temperature gradient: where Pr t is the turbulent Prandtl number and is assigned the value of 0.85 [38] in this study.
Furthermore, for most fluids, the ratio of Pr t /Sc t is normally set to 1 [38], where Sc t is turbulent Schmidt number.This ratio represents the analogy between turbulent heat flux and turbulent humidity flux, thus the turbulent humidity flux can be represented by: Various eddy-viscosity models have been developed to solve μ t , among which the k-ε model has excellent robustness, but weak prediction accuracy of near-wall flow especially with a reverse pressure gradient.In contrast, the k-ω model is competent to capture near-wall regions, especially the separation flow.In the DPEC channels, local separation flow is expected near the rib walls, the mechanisms of which are of key interest.Therefore, a low Reynolds number model, namely, shear stress transport (SST) model is selected.This model combines the advantages of the outer free-flow k-ε model and the near-wall flow k-ω model to capture separate flow behaviors near walls in detail and is also able to accurately calculate turbulent heat and mass transfer.
Here, k is the turbulent kinetic energy, ω is the specific turbulence dissipation rate, P is the production of turbulence kinetic energy, μ t is the turbulent viscosity need to solve, and coefficient β * 0 = 0.09.P and μ t can be expressed as: where S is the characteristic magnitude of the mean velocity gradients, S ij is the mean strain rate sensor, and coefficient a 1 = 0.31.Meanwhile, there is a blending function ϕ = f v1 ϕ 1 + (1 − f v1 )ϕ 2 for ϕ = β, γ, σ k , σ ω between k-ε and k-ω model, and f v1 and f v2 are interpolation function and limiter, respectively. ) where CD kω is the cross-diffusion: and the constants within blending functions ϕ 1 and ϕ 2 are listed in Table 3: The 2D CFD laminar model for DPEC has been proposed by the authors in [14,19].To solve the governing equations and additive turbulent closures, the boundary conditions that contain the heat transfer between supply air and rib-roughened plate, as well as the evaporative heat and mass transfer at the interface between the water film and the working air, are given in Fig. 5.

Parameter evaluation
In addition to analyzing the locally enhanced convection mechanisms, comparing the average heat and mass transfer parameters of macro-roughened channels with normal flat channels is important.One essential parameter related to convective heat and mass transfer is Reynolds number (Re), which is defined as: where u d,in is the air velocity of the inlet supply air, and D h is the hydraulic diameter.
The dimensionless numbers governing the strength of convective heat and mass transfer are the Nusselt number (Nu) and Sherwood number (Sh), derived from the non-dimensionalization of heat and mass transfer coefficients.The heat and mass transfer coefficients can be calculated by Newton's law of cooling, which relates the temperature difference between the bulk fluid and the surface to their heat and mass fluxes (calculated from interfacial heat conduction and mass diffusion): Arranging the Eqs.( 22)-( 24), the local convective heat and mass coefficients are expressed as: The dimensionless Nusselt and Sherwood numbers governing Eqs. ( 28)- (30) in DPEC are defined as: The average convective heat and mass transfer along the channels can be obtained by integrating the local Nusselt and Sherwood numbers: where The overall friction property of the channel is represented by Darcy friction coefficient f, while the local friction characteristic is represented by Fanning friction factor C f [39].
where To manifest the overall thermal performance of DPEC, the thermal performance factor (TPF) [40] is used to compare the relative strength of thermal enhancement and power consumption under different applied conditions: where the subscript "flat" is the condition of the flat channels with a smooth plate.TPF > 1 indicates the overall thermal performance of a rib-roughened channel is superior to that of a flat channel, namely, a more effective heat transfer is achieved than its energy consumption.Besides, dew-point effectiveness (ε dp ) represents the degree of cooling for supply air towards its DP temperature, expressed as: where t d,in and t d,out are the measured inlet and outlet temperature of supply air, and t dp,in is the calculated DP temperature of t d,in .

Numerical method and grid independence study
The model geometry is constructed in the COMSOL Multiphysics software platform.The partial differential governing equations with defined boundary conditions are numerically solved by the finite element method (FEM).The geometry of computational domain in Section 3.1 is divided into finite quadrilateral grid elements, and the nonlinear partial differential equations are discretized into polynomial equations.The flow, temperature, and moist-air fields are solved simultaneously.If the relative tolerance iterations are less than 10 − 6 , it is considered to satisfy the convergence standard [41].
An example of the non-uniform quadrilateral grid of a generic unit (Fig. 4) located in the middle of the channel (0.374 m<x<0.4m) is shown in Fig. 6(a).The grid is intentionally refined in near-wall regions of both the dry and wet channels, especially at the upstream and downstream of rib-roughness to adapt to the steep change of convection characteristics within the boundary layer.The grid becomes sparse in the y-direction near the upper and lower boundaries, as symmetric condition is defined at the centerline of the channels.For a fair comparison, the mesh of the flat channels at the same location is shown in Fig. 6(b).The mesh is built in the same environment based on [19], besides their difference in governing physics.
Four types of grids (from 97750, 190740, 308210 to 450160) are designed to test the grid independence, with a proportional increase in the mesh number of x-and y-direction (Fig. 6 (a)).The performance of the cooler with different grid numbers is evaluated under the same and plotted in Fig. 7.As mesh number increases, the product air temperature and dry-channel pressure drop approach 22.7 • C and 55.7 Pa, respectively.The average dimensionless numbers (Nu d , Nu w , Sh w ) for heat and mass transfer are close to 15.00, 9.00, and 8.35, respectively.When the mesh number exceeds 308210, the maximum variation in product air temperature, dry channel pressure drops, and Nu d are all less than 5%.Therefore, to balance computational accuracy and costs, the mesh number of 308210 is employed.The dimension of the first cell at the air interface in the dry channel is 0.020 mm, while the wet channel is 0.025 mm (satisfies y + ≈ 1, where y + is the dimensionless wall distance [27]).The dimensions ratio of the outermost layer to the first layer is 10, so the fine grid is sufficient to solve the viscous sublayer.
Additionally, to estimate the error of the mathematical model with measured experimental data for validating the model, the relative error between numerical simulation and experiment for evaluation parameters is defined as: where Er is the absolute relative error, Y n,exp is the test result of a specific parameter, and Y n,sim is the simulation result of the parameter.

Test results and model validation
Under various operating conditions, the cooler exhibits temperature reduction and DP effectiveness in the ranges of 9-14 • C and 0.53-0.86,respectively, demonstrating excellent cooling performance.As the supply air temperature and humidity increase in Fig. 8(a) and (b), the product air temperature rises from 21.6 • C to 24.3 • C and from 21.9 • C to 28.9 • C, respectively.Meanwhile, the DP effectiveness decreases by 0.17 with the rise in supply air temperature and increases by 0.13 with the increment in supply air humidity.Among the conditions, the working to supply air ratio has the most significant impact, as it determines the amount of air used for evaporative cooling, resulting in a DP effectiveness variation of 0.33 in Fig. 8(d).Notably, when the supply air velocity is elevated from moderate (2 m/s) to high (4 m/s) levels, as shown in Fig. 8(c), the deterioration of cooling effect is mitigated, with only a slight change of 2.1 • C in product air temperature and 0.12 in DP effectiveness.This is attributed to the enhanced overall convective heat and mass transfer due to the roughened channel surfaces, indicating that the cooler still exhibits satisfactory cooling effect even under high airflow conditions while keeping constant volume.
Furthermore, the test results agree well with the predictions of the CFD model.When variations occur in the supply air temperature and humidity, the model provides predictions with a marginal discrepancy of ±5.0-7.0%.Similarly, when the working-to-supply air ratio changes, the maximum discrepancy in model predictions falls within the range of ±3.0-4.0%.Even when the supply air velocity varies, affecting the level of internal turbulence in the channels, the model still offers predictions within ±8.0% discrepancies.Considering all the test results, the CFD model effectively simulates the final product air temperature within a maximum absolute relative error of ±8.0% in Fig. 8(e).It should be noted that the CFD laminar model for the flat DPEC in this study has been validated under a wide range of temperature, humidity, air velocity, and working-to-supply air ratio conditions, with a maximum discrepancy between model predictions and experiments of ±5% [42].
Therefore, the proposed 2D CFD model is reliable for subsequent analysis of the heat and mass transfer mechanisms in the enhanced cooler.

Temperature, humidity, and velocity distributions
Before discussing the underlying heat and mass transfer mechanism, it is necessary to understand the thermodynamic performance of the enhanced DPEC through its multiple physical fields.The nominal values of simulation parameters shown in Table 4 are employed on the computational domain as presented in Section 3.1, and the temperature, humidity, and velocity distributions of the channels are obtained.It should be noted that, except the temperature of the water film surface, other distributions are calculated based on bulk-averaged values.
The temperature variation is shown in Fig. 9(a).As the supply air flows into the dry channel, sensible heat is transferred from the hot air to the plate wall, leading to a decrease in air temperature.As the working air enters the wet channel, the temperature of the working air near the channel inlet is higher than that of the water film, and heat is transferred from working air to the water film.In the rib-roughened channels, a significantly steeper temperature decrease is observed along the dry channel, leading to faster air cooling and a lower working-air inlet temperature.Additionally, the smaller temperature difference between the supply air and the working air indicates more efficient sensible heat transfer.The region where temperatures of the working air and the water film are equal occurs earlier in the rib-roughened channel (x=0.53 m) compared to the flat channel (x=0.5 m), also indicating a faster cooling effect.The water film temperature in the rib-roughened channels increases along the flow direction while exhibiting fluctuations.This is mainly due to the non-uniform convective heat transfer of the supply air caused by rib-roughness, leading to variations in the heat and mass transfer at the water film surface.
The variation in air humidity in the wet channel is shown in Fig. 9(b).At the wet channel inlet, a significant humidity difference between the working air and the water film surface stimulates water evaporation, increasing the humidity of the working air.After the working air approaches saturation, the increasing temperature of the water film sustains the evaporation process.For the rib-roughened channel, the fluctuating humidity increase is also attributed to the non-uniform heat transfer, which perturbs the water film temperature and its saturation humidity.Meanwhile, it exhibits a greater increase in working air humidity, and the saturation point (x=0.38 m) occurs earlier than in the flat channel (x=0.34 m), promoting more efficient latent heat transfer and faster evaporation rate.
The most distinctive characteristic of the rib-roughened channel is the pronounced non-uniformity in the velocity of the supplied air, which is directly related to local turbulence, as shown in Fig. 9(c).In the flat channel, a fully developed laminar flow leads to a stable velocity distribution, indicating an invariant bulk-averaged velocity.However, for the rib-roughened channel, the development of the boundary layer is abrupted by ribs, and the sudden expansion of the channel height at the vertical wall leads to a reduction in the x-direction component of the air velocity.The velocity recovers after passing the expansion and accelerates before meeting the next rib.The temperature characteristic suggests that the variation of bulk velocity may result in an enhanced sensible heat transfer.Key mechanisms and relevant parameters will be discussed in the next section.

Enhanced heat and mass transfer mechanism 4.3.1. Flow field characteristics
The flow field under the conditions listed in Table 4 is further investigated.The contours of the supply air velocity u in flat and ribroughened channels are plotted in Fig. 10(a) and (b), respectively.For the flat channel with a smooth plate, the boundary layer is fully developed.At the fully developed region, a large velocity increment is found from the surface to center of the channel, i.e., from 0 to above 3 m/s, as depicted in Fig. 10(a).The bulk flow (air flow velocity greater than 2.5 m/s) occupies nearly 70% of the channel space, which is unfavorable for heat transfer.While in the rib-roughened channels, as shown in Fig. 10 (b), protrusions on the surface continuously disrupt the boundary layer, creating turbulence in the air flows.As the air passes over, some air separates from the bulk flow and forms detached vortices v1 and v2 near the wall of the ribs.
A detached vortex is essential for local turbulence.The roughness creates a sudden contraction and expansion of the flow, as shown in Fig. 10(b).For v2, the sudden expansion results in a decrease in air velocity.Under the influence of the adverse pressure gradient (∂P/∂x) and viscosity, the x-component velocity gradient along the y axis (∂u x / ∂y) at the top corner of rib leeward (SP2) abruptly drops to 0, as shown in Fig. 10(c).This leads to a flow separation between the bulk flow and leeward air and generates a separated region.The air in the separated region flows in the adverse direction to the bulk flow under the influence of adverse pressure gradient and forms v2.The decelerating bulk flow downstream represents the increasing adverse pressure gradient, which infers the acceleration of the adverse flow.Then the adverse pressure gradient decreases to zero (∂P/∂x=0) and the adverse flow velocity in v2 decreases.Eventually, at the reattachment point (AP2), the adverse flow merges with the bulk flow (∂u x /∂y=0).For v1, there is a significant flow resistance as it is hindered by the windward wall, the x-component of the air velocity near this wall decreases to 0 (u x =0), as shown in Fig. 10  (c).Meanwhile, under the suppression from the coming flow and windward wall, the air separates at the top of wall SP1 and flows in the adverse direction, forming a tiny corner vortex.The adverse flow decreases due to the air viscosity and merges with the bulk flow at the reattachment point AP1.At the lower curve edge of v2, the two opposite air streams form a free shear layer which is extended downstream.The adverse pressure gradient effect increases first and then decreases, along with the influence of viscosity, leading the curve edge (u x =0) to approach AP2 with a gentle and then a steep slope.Therefore, from the exemplary analysis, the region in the dry channel between every two roughness of any kinds (not just staggered ribs) can be divided into three types: types 1 and 3 mainly exhibit the flow state of detached vortices, while type 2 refers to the reattachment and developing boundary layer region.
At the local turbulence, the transfer of turbulent energy caused by fluctuation is represented by turbulent kinetic energy (TKE).
where u ′ i represents the velocity fluctuations.It also serves as a measure of turbulence intensity, and its distribution in the rib-roughened channel is shown in Fig. 10(d).TKE is lower within the detached vortices and the wet channel because their x-component velocity gradient on the y direction is small.It is worth noting that in shear layer regions, TKE remains at relatively high values, and it keeps increasing in the free shear layer outside v2 and reaches the maximum downstream of the shear layer.This is because the steep x-component velocity gradient evolves from adverse (∂u x /∂y<0) to forward (∂u x /∂y>0) direction in the shear layer, stimulates turbulent vortices and fluctuations, and generates large turbulence intensity, which accumulates as the shear layer develops.After the layer merges with the bulk flow, the higher TKE dissipates along with the bulk flow and gradually approaches the bulk flow's TKE level.
In DPEC with macro-roughened structures, the key element contributing to local turbulence is the detached vortex, which is generated by the adverse pressure gradient and hinders the development of the boundary layer.The shear layer formed between the vortex and the bulk flow signifies stronger disturbances.The mixing of these disturbances produces a significant amount of TKE, which is transferred downstream through the merging of the shear layer with the bulk flow, resulting in a stronger mixing effect for the supply air.

Heat transfer, mass transfer, and friction
In principle, the heat and mass transfer and fluid flow are governed by the Nusselt number, Sherwood number, and friction factor.In this section, the local distributions of these dimensionless numbers in the dry and wet channels are studied, as shown in Fig. 11(a)-(d).It is worth noting that the heat transfer and flow field on the upper and lower plates of the dry channel are similar, thus the upper plate and the water film in contact are selected for in-depth discussion.Moreover, the behaviors of the flat channel are simulated and used to highlight the distinctions of the rib-roughened channel.
Due to the small temperature and humidity differences between the channel surfaces and the flows at the inlet and outlet of the channels (isothermal or constant-humidity boundary condition), the Nusselt number and Sherwood number approach infinity at both ends.In the fully developed region, the heat and mass transfer performance of the flat channel becomes stable, whereas the rib-roughened channel shows significant and regular fluctuations.
The local Nusselt number in the dry channel is shown in Fig. 11(a)    Later, the channel widens, and the convective heat transfer is weakened due to the developing boundary layer, leading to the reduction of Nu d before the next v1.Therefore, the adverse flow in the detached vortex keeps the increasing trend of Nu d , although the values near the rib corner are smaller than that of a flat channel.It should be noted that the accumulation of trapped air in the corner leads to an unfavorable heat conduction effect.Hence, the design of macro-roughness is suggested to avoid the air trap.
The non-uniform heat flow absorbed by the water film from the adjacent dry channel eventually transfers to the working air through convection.Therefore, there is a similar trend in Nu w in Fig. 11(b).But due to the slight temperature difference between working air and water film, the curve of Nu w is smoother.For the flat channel and ribroughened channel, infinite values occur at positions 0.1 m and 0.067 m away from the inlet of the wet channel, respectively.This is attributed to the circumstance where the water film and working air temperature are equal.The early occurrence of this isothermal point is favorable, as it suggests the fast cooling of the working air to below the water film temperature.In the enhanced channel, multiple isothermal points lead to huge fluctuations in Nu w within the regions between them.The latent heat transfer in DPEC is determined by the water evaporation rate.When the water film temperature varies, the saturated water vapor density follows and yields a perturbation in the convective mass transfer rate.This process eventually resulting in the fluctuations of Sh w similar to Nu w , as can be observed in Fig. 11(c).In Fig. 11(b) and (c), the enhanced channel also improves the sensible and latent heat transfer in the wet channel.Nu w and Sh w increase from 8-9 for the flat channel to a maximum value of 10, the location of which is near the region of maximum Nu d in the adjacent dry channel.The improvement of the average Nusselt and Sherwood number will be discussed in the next section.
Numerous local turbulent regions, namely vortices and shear layers also significantly increase the frictional losses, as depicted in Fig. 11(d).Based on the Eq. ( 35), the friction factor relates to the skin shear stress, which is determined by the x-component velocity gradient at the channel surface.The trapped air in the corner on the leeward results in a friction coefficient of close to 0. The adverse flow in v2 accelerates first and then decelerates, leading to an initial increase and a following decrease in the x-component velocity gradient on the y direction, and the friction factor varies accordingly.After merging with the bulk flow at AP2, the channel contraction results in flow acceleration and an increase in the friction coefficient.Subsequently, the channel expansion leads to flow deceleration and a decrease in the friction coefficient.Under the influence of the adverse flow in v1, the friction factor changes again.At the windward surface of the ribs, the air impact leads to a steep decrease in u x , and the friction factor increases significantly.Therefore, the design of macro-roughened surfaces should minimize air impacts on the windward surface, which would increase the friction factor.

Average characteristics
Upon understanding the local heat and mass transfer mechanism, enhancement in the average performance of DPEC through the ribroughened structure is investigated.According to Eq. ( 31)- (33), the average heat and mass transfer intensities along the dry and wet channels are determined by Nu d , Nu w , and Sh w .Also, the effectiveness of heat transfer enhancement is measured by TPF according to Eq. (36).
As discussed, when the supply air velocity increases, the intensity of adverse flow and the air velocity behind the reattachment point rises, leading to an enhancement of convective heat transfer, which is consistent with the trend shown in Fig. 12(a).Nu d after the enhancement is 1.5-4 times higher than that of a flat channel, indicating that the local turbulence can significantly improve heat transfer in the dry channel, and the effect is more pronounced under high-velocity conditions.
The comparison of heat and mass transfer in the wet channel is shown in Fig. 12(b) and (c).Through the ribs in the dry channel, more sensible heat can be transferred to the working air, resulting in a corresponding increase in Nu w .Concurrently, the large sensible heat transmitted by the dry channel increases the temperature of the water film and contributes to an increased difference between the saturated water vapor density near the water film and the water vapor density in the working air.This driving force eventually improves the evaporation flux, hence a higher Sh w is obtained.
The proposed rib-roughened channel's TPF increases with higher supply air velocity, from 1.02 at 2 m/s to a maximum of 1.82, as shown in Fig. 12(d).Within the simulation range, it indicates that increasing system energy consumption in exchange for more efficient heat transfer enhancement is worthwhile.However, if the supply air velocity is below 1.5 m/s, TPF is below unity.This is because the low flow rate is no longer sufficient to support effective local turbulence, but the presence of macro-roughened structures increases friction.Therefore, it is suggested that the air velocity be kept above a threshold.

Enhanced thermodynamic performance
To investigate the potential of the enhanced DPEC through macroroughened structures, numerical investigations are conducted using the simulation conditions in Table 5.Four important operating parameters commonly considered in evaporative cooling are selected: supply air temperature, supply air humidity, supply air velocity, and working to supply air ratio.
When the supply air temperature and humidity change, as shown in Fig. 13(a) and (b), the rib-roughened channel demonstrates an improvement in cooling performance compared to the flat channel under the moderate velocity condition of 2.5 m/s.Increasing the supply air temperature and humidity promotes the thermodynamic performance of the rib-roughened channel.Specifically, when the supply air humidity is 0.026 kg/kg, the rib-roughened channels achieve a higher DP effectiveness of above 0.8.
With an increase in the supply air velocity, the rib-roughened channels show significant advantages, as illustrated in Fig. 13(c).Notably, the deterioration in cooling effect is mitigated.Under highvelocity conditions exceeding 3.5 m/s, the DP effectiveness improves by over 0.15, and the cooling effect enhances by over 2.0 • C. Remarkably, at a supply air velocity of 5.5 m/s, the rib-roughened channel maintains a product air temperature below 25.0 • C, corresponding to a DP effectiveness of 0.6.These results indicate that the enhanced DPEC with macro-roughened structure is suitable for high airflow applications without altering the equipment volume, while maintaining an excellent cooling effect.
As the working to supply air ratio increases, the rib-roughened channel can achieve a DP effectiveness above 0.8 at a ratio of 0.5, whereas the flat channel requires a ratio of 0.8 to achieve the same effectiveness.This reveals that the macro-roughened structure can achieve excellent cooling performance with a considerably lower working air ratio.

Conclusions
The fundamental fluid flow, heat transfer, and mass transfer in the macro-roughened structure are crucial for understanding its potential contribution and application in DPEC.A rib-roughened dew-point evaporative cooler with square transverse macro-ribs staggered in the dry channels was designed, fabricated, and investigated in this study.A CFD model was developed to analyze the governing parameters of its distinctive convection process.The cooling performance of the cooler was evaluated under a wide range of applied conditions, and the complex velocity, temperature and humidity fields in the cooler channels were numerically simulated.The key findings of this study are as follows: Besides, the proposed CFD model can be applied to optimizing the rib structures via multi-objective optimization of the cooler's thermodynamic performance.A faster cooler model can be trained for this purpose using CFD simulations as the training and validation datasets and advanced techniques like neural networks.Additionally, the CFD model

Table 5
Operating conditions in numerical investigations.

Fig. 4 .
Fig. 4. Model geometry of a generic unit of the channels

Fig. 5 .
Fig. 5. Boundary conditions of: (a) supply air; (b) rib-roughened plate; (c) water film; (d) working air; the local convective water vapor flux, h c and h m are the local heat and mass transfer coefficients, respectively, y s is the y value at the convective surface, T s and ρ v,s are the time-averaged temperature and water vapor density at the convection surface y s , and T d and ρ v,b are the time-averaged bulk temperature and bulk water vapor density, respectively.It should be noted that, for the rib-roughened structure, the local bulk-averaged temperature of dry channel T d,b is calculated by ∫ Hd − Hd u d T d dy/ ∫ Hd − Hd u d dy , and T d,b for Nu d at the vertical surface section of a rib is substituted by that in adjacent horizontal surface section.
d = P d,in − P d,out , P d,in and P d,out are pressure measured at the inlet and outlet of the dry channels, u d,b is the bulk-averaged velocity of supply air, is calculated by ∫ Hd − Hd u d dy/2H d , and τ s is the skin shear stress.

Fig. 6 .
Fig. 6.Scheme of grid-distribution of: (a) the rib-roughened channels and (b) the flat channels.

Fig. 8 .
Fig. 8. Test results and model validation of product air temperature under different conditions: (a) supply air temperature; (b) supply air humidity; (c) supply air velocity; (d) working to supply air ratio; (e) comprehensive relative error.

Fig. 10 .
Fig. 10.Flow patterns of channels: (a) and (b) velocity contour and streamlines of the flat channels and the rib-roughened channels; (c) velocity vectors of the ribroughened channels; (d) TKE distribution of the rib-roughened channels.

Fig. 11 .
Fig. 11.Local distributions of governing dimensionless numbers on upper rib plate and flat plate: (a) Nu d , (b) Nu w , (c) Sh w , (d) C f .

( 1 )
Detached vortices are the main factors contributing to the enhanced heat transfer in the dry channel with rib-roughened surfaces.The sudden change in the channel height leads to the formation of detached vortices.The adverse flow within the vortex enhances the surface convection and thus increases the local Nusselt number.Additionally, the significant TKE generated by the shear layer indicates intensive energy mixing in the dry channel.(2) The enhancement of convective heat and mass transfer increases with the degree of turbulence.As the air velocity increases, the average Nusselt number in the dry and wet channels and the average Sherwood number in the wet channel are increased by 1.5-4 times, 1-1.13 times, and 1-1.14 times from those of the flat channels, respectively, leading to an excellent TPF of 1.82 at 5.5 m/s.However, if the air velocity is below 1.5 m/s, the local turbulence effect is marginal, resulting in an ineffective enhancement, with TPF<1.(3) The enhanced performance with square rib-roughened structures demonstrates superior cooling and DP effectiveness to a normal flat DPEC under various operating conditions, with temperature reduction and DP effectiveness improvements of 0.6-3.0• C and 4-18%, respectively.Under high air velocities, the enhanced DPEC significantly mitigates the deterioration of the cooling effect.

9 Fig. 13 .
Fig. 13.Effect of conditions on product air temperature and dew-point effectiveness: (a) supply air temperature; (b) supply air humidity; (c) supply air velocity; (d) working to supply air ratio.
studied three configurations of perforated ribs on one wall.Perforated ribs could improve overall heat K.Wu et al.

Table 1
Specifications of sensors.

Table 2
Test conditions of the cooler prototype.

Table 3
Constants for blending functions.

Table 4
Simulation conditions.