A design of experimental apparatus for studying coupled heat and moisture transfer in soils at high-temperature conditions

ABSTRACT

The objective of this paper is to present a design of an experimental apparatus for studying coupled heat and moisture transport phenomena in soils at high temperatures up to 90°C and to present some preliminary testing results from the apparatus for understanding the extent of its measurement uncertainties. A soil cell was designed and constructed for enclosing a vertical soil column for experimental studies of one-dimensional heat and moisture transfer in the soil column. The design of the experimental apparatus was realized based on the worst condition of achieving one-dimensional heat flow within a soil cell filled with dry soil. The soil cell, which is of cylindrical shape and contains five thermo-time domain reflectometry (T-TDR) probes, was sandwiched between a hot plate on the top and a cold plate at the bottom for studying coupled heat and moisture transfer in soils. The existence of one-dimensional heat flow from the top to the bottom of the soil column can be indicated by two conditions. In an ideal steady-state condition, first, the amounts of inflow and outflow rates of heat transfer at the top and bottom of the soil column should be the same, and secondly, the heat flux distribution at any cross-section of the soil column should be uniform. In the present design, these conditions were met within ±5% of their variations, as a design criterion. With respect to the design criterion, the general integrity and reliability of the design models were numerically assessed using COMSOL, based on realistic geometries and boundary conditions. Once the apparatus was built, a preliminary test of the apparatus was performed to check the existence of one-dimensional heat flow through the soil column in the soil cell.

KEYWORDS:

• Experimental design
• moisture transport phenomena
• moisture content
• heat pulse
• T-TDR probe
• coupled heat and moisture transfer
• soil cell

Nomenclature

$c$ Specific heat (J/kg·K)

$C$ Volumetric heat capacity (J/m³·K)

$d$ Distance from the heat-pulse emitter (m)

$D_a$ Soil thermal diffusivity (m²/s)

$k$ Thermal conductivity (W/m·K)

$L$ Length of heat-pulse emitter (m)

$\dot{m}$ Mass flow rate (kg/s)

$n$ Number of variables

$q$ Heat flux (W/m²)

$q^{\prime }$ Heat-pulse heating strength per unit length (W/m)

$Q$ Total heat transfer (J/s)

$R_c$ Thermal contact resistance (K/W)

$S_r$ Degree of saturation (m³ of water/m³ of pore space)

$t$ Time (s) or student’s t multiplier

$t_m$ Time in which $\mathrm{\Delta }T$ reaches to its maximum (s)

t_o Duration of heat pulse (s)

T Temperature (K or °C)

$V$ Voltage difference (V)

$x$ Vertical distance from top (m)

Greek

$\alpha$ Sensitivity of HFM (μV/W·m⁻²)

$\eta$ Soil porosity (m³ of pore space/m³ of soil)

$\theta$ Volumetric water content (m³/m³)

$\rho$ Density (kg/m³)

$K$ Dielectric constant (dimensionless)

$\mathrm{\Delta }T$ Temperature difference (K)

$\mathrm{\Delta }{T}_m$ Maximum temperature difference (K)

Subscript

ave Average

bot Bottom

dry Dry soil

eff Effective

LTD Linear temperature profile

m Mean or maximum

ss Stainless steel 304

top Top

w Water

xx coordinate

Acknowledgments

Financial support through a Discovery Grant provided by the Natural Sciences and Engineering Research Council of Canada (NSERC) is gratefully acknowledged. Authors would also like to sincerely thank Professor Tusheng Ren of China Agricultural University, Beijing, China for his priceless information about the T-TDR probes, guidance, and recommendations throughout this research.

Notes

¹ https://www.dlsc.ca/about.htm.

Additional information

Funding

This work was supported by the Natural Sciences and Engineering Research Council of Canada [Discovery Grant].