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Evaporation from Wavy Porous Surfaces into Turbulent Airflows

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Abstract

The relief and roughness of natural surfaces interacting with airflows and with radiation affect rates and distributions of heat and vapor fluxes into the atmosphere. The study quantifies interactions of regular sinusoidal wavy porous surfaces (with different geometrical characteristics) affecting heat and vapor transport into prescribed turbulent airflows. A model for turbulent eddies interacting with an undulating evaporating surface with mean boundary layer that varies across sinusoidal wavy surfaces was developed and experimentally evaluated in a wind tunnel. The surface of a \(1\,\hbox {m}^{2}\) shallow (0.3 m deep) sand-filled basin was imprinted with regular sinusoidal ridges and troughs; water content and temperature sensors were embedded in the sand, and the instrumented basin was placed on a balance in the wind tunnel. Detailed thermal signatures of the evaporating surface for different wind speeds and surface patterns were obtained using high-resolution infrared thermography. The evaporative mass loss measurements and observed thermal patterns were in good agreement with model predictions for turbulent exchange over various wavy sand surface geometries. Results suggest that evaporative fluxes can be either enhanced or suppressed (relative to a flat surface) due to complex interplay between local boundary layer thickness and internal limitations to water flow to the evaporating surface. For a practical range of air velocities (0.5–4.0 m/s), and for sinusoidal configurations studied (amplitudes of 50–100 mm), the evaporative mass loss (relative to the flat surface) was reduced by up to 60 % for low surface aspect ratio and high wind velocity, and enhanced by up to 80 % for high aspect ratio and low wind velocity. The study offers a framework for interpreting and upscaling evaporative fluxes from rough terrestrial surfaces. Ongoing work considers shortwave radiation and geometrical interactions for a more complete account of surface energy balance and fluxes from natural rough surfaces.

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Abbreviations

\(A_\mathrm{b}\) :

Surface area of wavy building block \((\hbox {m}^{2})\)

\(C_\mathrm{a}\) :

Vapor concentration in air \((\hbox {kg/m}^{3})\)

\(C_\mathrm{s}\) :

Saturated vapor concentration \((\hbox {kg/m}^{3})\)

\(c_{1}\) :

Coefficient in Eq. (1) (–)

\(c_{2}\) :

Coefficient in Eq. (4) (–)

\(c_{3}\) :

Coefficient in Eq. (4) (–)

\(c_{4}\) :

Coefficient in Eq. (8) (–)

\(c_{p}\) :

Air-specific heat capacity (J/kg K)

D :

Water vapor diffusion coefficient in air \((\hbox {m}^{2}/\hbox {s})\)

E :

Evaporation flux \((\hbox {kg/m}^{2}\,\hbox {s})\)

\(E^\mathrm{o}\) :

Potential evaporation flux \((\hbox {kg/m}^{2}\,\hbox {s})\)

e :

Total evaporation rate (kg/s)

\(e_\mathrm{b}\) :

Evaporation rate from wavy building block (kg/s)

\(g_\mathrm{h}\) :

Aerodynamic conductance (m/s)

H :

Drying front depth (m)

\(H_\mathrm{C}\) :

Evaporative characteristic length (m)

\(H_\mathrm{G}\) :

Gravity characteristic length (m)

\(H_\mathrm{wt}\) :

Water table depth measured from ridges (m)

\(K_\mathrm{a}\) :

Air thermal conductivity (W/mK)

\(K_\mathrm{eff}\) :

Effective hydraulic conductivity (m/s)

\(K_\mathrm{s}\) :

Saturated hydraulic conductivity (m/s)

\(\ell \) :

Length of evaporating system (m)

\(M_\mathrm{w}\) :

Molar mass of water (kg/mol)

m :

Largest integer smaller than \(\alpha \) (–)

\(N_\mathrm{b}\) :

Number of wavy building blocks (–)

n :

Pore size distribution index (–)

\(P_\mathrm{sat}\) :

Saturated vapor pressure (Pa)

\(R_\mathrm{BL}\) :

Boundary layer resistance (s/m)

\(R_\mathrm{sv}\) :

Capillary–viscous resistance (s/m)

\(\hbox {Re}_\mathrm{K}\) :

Permeability Reynold number (–)

RH:

Relative humidity (–)

\(\mathfrak {R}\) :

Universal gas constant (J/mol K)

r :

Mean pore radius (m)

s :

Length of wavy building block (m)

\(T_\mathrm{a}\) :

Air temperature (K)

\(T_\mathrm{s}\) :

Surface temperature (K)

t :

Eddy residence time (s)

\(U_\mathrm{a}\) :

Air velocity (m/s)

w :

Width of wavy building block and evaporating system (m)

x :

Distance along x-axis (m)

\(x_\mathrm{r}\) :

Reattachment point (m)

\(x_\mathrm{s}\) :

Separation point (m)

\(Z_\mathrm{T}\) :

Height of trough above water table (m)

\(\alpha \) :

Shape parameter of eddy residence time distribution (–)

\(\alpha _\mathrm{s}\) :

\(\alpha \) over separation zone (–)

\(\chi \) :

Surface wetness-dependent coefficient of \(K_\mathrm{eff}\) (–)

\(\delta \) :

Viscous sublayer thickness (m)

\(\gamma \) :

Amplitude of wavy building block (m)

\(\lambda \) :

Wavelength of wavy building block (m)

v :

Air kinematic viscosity \((\hbox {m}^{2}/\hbox {s})\)

\(\Theta _\mathrm{surf}\) :

Effective surface water saturation (–)

\(\theta _\mathrm{r}\) :

Residual water content (–)

\(\theta _\mathrm{s}\) :

Saturated water content (–)

\(\theta _\mathrm{surf}\) :

Surface water content (–)

\(\rho \) :

Water density \((\hbox {kg/m}^{3})\)

\(\rho _\mathrm{a}\) :

Air density \((\hbox {kg/m}^{3})\)

\(\tau \) :

Tortuosity (–)

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Acknowledgments

The authors thank three reviewers for their insightful comments that helped improve the manuscript. The funding by the Swiss National Science Foundation of the project “Evaporation from terrestrial surfaces—linking pore scale phenomena with landscape processes” (200021-113442) and the financial support of the German Research Foundation DFG of the project “Multi-Scale Interfaces in Unsaturated Soil” (MUSIS; FOR 1083) are gratefully acknowledged. Technical assistance of Daniel Breitenstein and Hans Wunderli (ETH Zurich) is greatly appreciated.

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  1. Soil and Terrestrial Environmental Physics, Department of Environmental Systems Science, ETH Zurich, Universitätstrasse 16, 8092, Zürich, Switzerland

    Erfan Haghighi & Dani Or

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Haghighi, E., Or, D. Evaporation from Wavy Porous Surfaces into Turbulent Airflows. Transp Porous Med 110, 225–250 (2015). https://doi.org/10.1007/s11242-015-0512-y

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