Process engineering experimental determination of heat and mass transfer coefficients in thermoformed PVC evaporative media

Technical Summary: Process Engineering Experimental Determination of Heat and Mass Transfer Coefficients in Thermoformed PVC Evaporative Media

Problem Statement
Direct evaporative cooling (DEC) is a widely accepted technology due to its energy efficiency and use of water as a working fluid. However, the engineering design of DEC systems is hindered by several critical gaps identified in existing literature. A primary issue is the widespread assumption that heat and mass transfer rates in evaporative cooling proceed at equal rates, implying a Lewis factor ($N_{Le}$) of unity. Previous studies have shown significant discrepancies between this assumption and experimental results, with Lewis factors varying between 0.6 and 1.3 depending on humidity and flow conditions. Furthermore, there is a lack of reliable, exact correlations for assessing heat and mass transfer coefficients specifically for thermoformed PVC media, and a scarcity of simplified yet precise mathematical equations relating these coefficients to air linear velocity. This paper addresses the need to bridge these gaps by experimentally determining these coefficients and developing a dependable design methodology.

Methodology
The study employed an experimental setup consisting of a direct evaporative cooler unit equipped with four suction fans and two test sections capable of accommodating up to 40 cm thick blocks of thermoformed PVC evaporative media. Three types of film fill media (Onda 12, 19, and 27) with specific surface areas of 248, 152, and 120 $m^2/m^3$ respectively, were utilized.

The experimental campaign covered a wide range of operating parameters:

• Air Volumetric Flow Rates: 4,000 to 16,000 $Nm^3/h$ (corresponding to frontal air velocities of 0.79–3.16 $kg/m^2\cdot s$).
• Water Sprinkling Rates: 2.39–9.58 $kg/m^2\cdot s$.
• Thermal Conditions: Inlet dry-bulb temperatures ranging from 35°C to 43°C and wet-bulb temperatures from 17°C to 25.5°C.

Measurements were conducted using E-type thermocouples for dry- and wet-bulb temperatures, a hot-wire anemometer for air velocity, and a thermohygrometer for humidity. Data were recorded automatically every minute. The experimental data were analyzed using mathematical modeling based on simultaneous heat and mass balance equations. The study utilized statistical regression to correlate experimental data with theoretical models, specifically examining the relationship between the Nusselt ($Nu$) and Sherwood ($Sh$) numbers.

Key Contributions and Results
The research yielded several specific technical findings and contributions:

1. Disproportionate Transfer Rates: Experimental data confirmed that heat and mass transfer rates are not equal ($N_{Le} \neq 1$). The study demonstrated that both heat and mass transfer coefficients are directly proportional to frontal air velocity and pad module specific surface area, but inversely proportional to pad module thickness.
2. New Dimensionless Number ($N_{Sb}$): To explain the deviation from unity in the Lewis factor, the author introduced a new thermal fluid dynamic dimensionless number, the Shaaban's number ($N_{Sb}$), defined as the ratio of the Nusselt number to the Sherwood number ($N_{Sb} = Nu/Sh$). This number relates convective heat and mass transfer rates to their conductive (diffusional) counterparts.
3. Empirical Correlations: The study derived exact mathematical expressions for heat ($h_{ch}$) and mass ($k_{cdm}$) transfer coefficients as functions of air frontal velocity ($V_{ma}$), following the relationship $Coefficient \propto V_{ma}^{0.8}$.
4. Design Equations: A universal relationship between cooler efficiency ($\varepsilon$) and the Number of Transfer Units (NTU) was established. The paper provides both logarithmic and 6th-order polynomial equations to predict efficiency based on NTU, offering a more reliable basis for sizing DEC units than previous methods.
5. Parameter Sensitivity:
   • Pad Thickness: Increasing thickness improves efficiency, though gains become impractical beyond 0.4 m.
   • Air Velocity: Lower frontal air velocities result in higher cooling efficiencies and greater temperature drops.
   • Temperatures: Higher inlet dry- and wet-bulb temperatures generally lead to higher transfer coefficients, though the effect on overall efficiency varies with velocity.

Significance and Claims
The paper claims to provide a "dependable engineering methodology" for the design of direct evaporative coolers. By moving away from the assumption that the Lewis factor equals unity, the proposed correlations and the introduction of the Shaaban's number ($N_{Sb}$) offer a more accurate representation of the physical processes occurring at the air-water interface.

The author asserts that utilizing these derived equations allows for the precise sizing of DEC units, considering both volumetric air flow rates and the specific surface area of the media. The study concludes that implementing these optimized designs in large-scale applications, such as a "green DEC-farm" with a capacity of 1075 Rt, can significantly reduce energy consumption and CO2 emissions (estimated at 22,800 metric tons annually from coal plants and 9,500 from natural gas plants), thereby contributing to the mitigation of global warming. The work emphasizes that the developed correlations are experimentally verified and provide a solid foundation for process engineering in evaporative cooling.