Abstract. Modelling the water transport along the soil–plant–atmosphere continuum is fundamental to estimating and predicting transpiration fluxes. A Finite-difference Ecosystem-scale Tree Crown Hydrodynamics model (FETCH3) for the water fluxes across the soil–plant–atmosphere continuum is presented here. The model combines the water transport pathways into one vertical dimension, and assumes that the water flow through the soil, roots, and above-ground xylem can be approximated as flow in porous media. This results in a system of three partial differential equations, resembling the Richardson–Richards equation, describing the transport of water through the plant system and with additional terms representing sinks and sources for the transfer of water from the soil to the roots and from the leaves to the atmosphere. The numerical scheme, developed in Python 3, was tested against exact analytical solutions for steady state and transient conditions using simplified but realistic model parameterizations. The model was also used to simulate a previously published case study, where observed transpiration rates were available, to evaluate model performance. With the same model setup as the published case study, FETCH3 results were in agreement with observations. Through a rigorous coupling of soil, root xylem, and stem xylem, FETCH3 can account for variable water capacitance, while conserving mass and the continuity of the water potential between these three layers. FETCH3 provides a ready-to-use open access numerical model for the simulation of water fluxes across the soil–plant–atmosphere continuum.
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Theoretical Modeling of Levitated Clusters of Water Droplets Stabilized by Infrared Irradiation
Abstract This paper shows how clusters of radiation-stabilized water droplets levitated in an upward flow of air and water vapor above a heated water surface can be modeled using Spalding's self-similarity theory of heat and mass transfer and Stefan flow. The model describes equilibrium droplet states, including stability conditions, as well as nonequilibrium (quasi-steady) transient evolution. Equilibrium states are shown to exist when Stefan-flow supersaturation, which has a quadratic-like variation with height above the water surface, and radiation-stabilized equilibrium supersaturation, which is nearly constant with height, are equal. The latter can be predicted by a fundamentally derived function of absorbed radiant flux (linear), droplet radius (linear if opaque), continuum thermal conductivity, and thermodynamic properties. In fact, all of the experimentally observed droplet behavior can be predicted using simple analytical results based on quasi-steady droplet energy and continuum transport. Unsteady droplet energy, Knudsen-layer transport, numerical solutions, and curve-fitting of numerical computations, as used previously in modeling this behavior, are not necessary. An interesting reversal of the usual effect of mass transfer on droplet drag in low-Re flow when levitated droplets are irradiated asymmetrically by significant infrared radiation is also postulated, which relates to the relative importance of normal (pressure) and tangential (shear stress) drag. This theory of radiation-augmented droplet evaporation, condensation, and relative motion in a moving gas has application to conditions in clouds, wherein droplets can experience either net radiative heating or cooling and fluctuating updrafts or downdrafts.
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- Award ID(s):
- 2152233
- NSF-PAR ID:
- 10395124
- Date Published:
- Journal Name:
- Journal of Heat Transfer
- Volume:
- 144
- Issue:
- 4
- ISSN:
- 0022-1481
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1115/1.4053415
