Section: New Results

Numerical models and simulations applied to heat transfer

Small scale modeling of porous media

Participants : Édouard Canot, Salwa Mansour.

Grants: ECOS Sud Chili (ARPHYMAT project) 9.3.2

Software: GLiMuH 6.2

Publications: [13]

Conferences: [20]

Abstract: This study is devoted to the heat transfer between two spherical grains separated by a small gap; dry air is located around the grains and a liquid water meniscus is supposed to be present between them. This problem can be seen as a micro-scale cell of an assembly of solid grains, for which we are looking for the effective thermal conductivity. For a fixed contact angle and according to the volume of the liquid meniscus, two different shapes are possible for the meniscus, giving a “contacting” state (when the liquid makes a true bridge between the two spheres) and a “non-contacting” one (when the liquid is split in two different drops, separated by a thin air layer); the transition between these two states occurs at different times when increasing or decreasing the liquid volume, thus leading to a hysteresis behavior when computing the thermal flux across the domain. We consider also another process where humidity varies, for example during an evaporation or condensation process; in this situation, the shape of the menisci changes a lot, because some liquid bridges may break, and this can strongly affect the effective thermal conductivity. Then, the reorganization of the liquid menisci is predicted, especially their surface area variation; it is an important parameter for a global model of the evaporation phenomenon in wet porous media.

Inverse problem for determining the thermo-physical properties of a porous media

Participants : Édouard Canot, Salwa Mansour.

Grants: HYDRINV 9.3.3

Software: TPIP ( 6.7 )

Publications: [15] , [27]

Conferences: [22]

Abstract: This study concerns the inverse problem which consists of the estimation of thermophysical properties of the soil knowing the temperature at few selected points of the domain. In order to solve this inverse problem, we used the least square criterion where we try to minimize the error function between real measures and simulated ones. The coupled system composed of the energy equation together with the three sensitivity boundary initial problems resulting from differentiating the basic energy equation with respect to the soil properties must be solved. To overcome the stiffness of our problem (due to the use of Apparent Heat Capacity method), the high nonlinearity of the coupled system and the problem of large residuals we used the Damped Gauss Newton and Levenberg-Marquardt methods. To take into account uncertainties of the position of the sensors, some constraints have been added to the least square problem. Results are good when the number of sensors is sufficiently large.

Evaporation/Condensation in a wet granular medium: the EWGM model

Participants : Édouard Canot, Salwa Mansour.

Grants: ECOS Sud Chili (ARPHYMAT project) 9.3.2

Software: HeMaTis ( 6.4 )

Publications: [26] , [25]

Abstract: The physical model of the HeMaTiS code ( 6.4 ) has been completed by a new variant dedicated to the unsaturated case. The pendular regime concerns the special case where a very few quantity of liquid water is contained in a granular medium. The new model involves seven variables and can be considered as a two-phase two-component one; it contains both air and water, this latter component being liquid or gas. Generally, the diffusive transport of humidity in soils is extremely slow, we numerically show that humidity is convected quickly when the medium is subjected to a strong temperature gradient. The key feature of the thermal process is the simultaneous evaporation and condensation of water near a discontinuity of the liquid layout.