Session A22: Porous Media Flows: Convection and Heat Transfer

Transfer learning enhanced physics-informed neural networks for forward and inverse transport problems in heterogeneous domains

The study of coupled fluid flow and heat transfer processes in heterogeneous domains such as porous media is computationally expensive and often the exact parameters of the system (e.g., the permeability distribution) are not known. Physics-informed neural networks (PINN) provide a hybrid data-driven and physics-based solution to these problems. However, they are computationally not efficient for forward problems. Additionally, in inverse problems, PINN sometimes converges to unrealistic patterns due to the non-uniqueness of the solution. In this presentation, we propose two different approaches using transfer learning to overcome these issues. First, a multi-fidelity approach that combines fast low-fidelity computational fluid dynamics (CFD) solution strategies with transfer learning and PINN is presented for forward problems. Second, we propose an approach where an ensemble of parallel neural networks, each initialized with a meaningful pattern of the unknown parameter, is used to guide PINN to enhance the predictions made in inverse problems. Several forward and inverse problems such as heterogeneous porous media transport are presented to demonstrate the efficiency of the proposed approaches.   

Experimental assessment of mixing layer scaling laws in Rayleigh-Taylor instability

We assess experimentally the scaling laws that characterize the mixing region produced by the Rayleigh-Taylor instability in a confined porous medium. We aim at verifying the existence of a superlinear scaling for the growth of the mixing region, as was observed in recent two-dimensional simulations. The configuration consists of a Hele-Shaw cell and a heavy fluid layer overlying a lighter fluid layer, initially separated by a horizontal, flat interface. When perturbations of the concentration field occur, convective mixing is produced: Perturbations grow and evolve into large finger-like convective structures that control the transition from the initial diffusion-dominated phase to the subsequent convection-dominated phase. As the flow evolves, diffusion acts to reduce local concentration gradients across the interface of the fingers. We employ an optical method to obtain high-resolution measurements of the density fields and we perform experiments for values of the Rayleigh-Darcy number sufficiently large to exhibit all the flow phases, which we characterize via the mixing length, i.e., the extension of the mixing region. We confirm that the growth of the mixing length during the convection-dominated phase follows the superlinear scaling predicted by previous simulations.   

Hydrodynamic and thermal characteristics of metal foam filled compact heat exchanger in cryogenic conditions

Thermal performance of metal foam heat exchanger in cryogenic environments was examined through experiment and computational fluid dynamics (CFD) simulation. A plate type heat exchanger with metal foam was designed and manufactured. The metal foam was 20-pore-per-inch nickel metal foam and brazed to stainless steel channel plates. Nitrogen gas in cryogenic conditions was supplied to both hot and cold-side channels with a counter-flow configuration. The data obtained through the experiment were compared with those of CFD simulations and previous correlations obtained at room temperature conditions. Pressure drop correlation models at room temperature conditions agreed well with the experimental results in cryogenic conditions. Among the pressure drop models, the Dietrich model showed the best agreement. CFD predicts the heat transfer well within 10% discrepancy from the experiment. However, the heat transfer in cryogenic conditions is 15 to 20% higher than that of the previous correlations obtained at room temperature conditions. This can be explained that the hydraulic performance is not being affected by the temperature difference, while the heat transfer of the metal foam filled channel has higher Nusselt number due to lower heat conductivity of gas at a cryogenic environment.   

Double Diffusive Instability in a Thin Vertical Channel

In highly confined environments, single constituent Rayleigh-Taylor instabilities are suppressed. In this talk we will demonstrate that double-diffusive instabilities persist in highly confined environments while, in the absence of differential diffusion, instabilities such as the single constituent Rayleigh-Taylor instabilities cannot form.

We will present direct numerical simulations of double-diffusive instabilities in the finger regime with domain widths of 1-4mm. Using these results, we will show that double-diffusive instabilities demonstrate complex time-dependent evolution down to lateral extents of 1.25mm. This implies that differential diffusion may be significant in driving localized mixing within porous media with large pore spaces. We will discuss the energetics, horizontal asymmetry and buoyancy flux due to the instability and utilize these results to characterize the instability within domain-dependent regimes. Further, we will demonstrate that instabilities associated with wider domains are well-characterized by a time-dependent Grashof number which quantifies the ratio of diffusive effects to buoyancy forces.

Time permitting, we will discuss the impact of side wall topography on the double diffusive instabilities.   

Impact of viscous dissipation on the conjugate heat transfer between the walls of a porous microchannel

In this work, we study numerically the viscous dissipation that occurs when a Newtonian fluid circulates through a porous microchannel that operates as a heat sink, in which a constant heat flux is applied from the outer walls of the porous microchannel into the fluid. The temperature fields of both the porous medium and the wall are unknown, for instance, there are two well-known asymptotic limits in order to obtain the solution for this problem: the thermally thick wall limit and the the thermally thinwall limit, where the longitudinal effects of heat conduction in the microchannel wall are considerably more important than the ones occurring in the transverse direction. Therefore, in this study, we analyze the competition between these effects and viscous dissipation, as well as the influence that both have on the temperature profiles of the fluid and the wall. The results show that for a Brinkman number (Br) equal to …0.1, a notable temperature increase occurs in the system, which offers interesting results that have not been reported in the literature yet, because there is a higher temperature in the center of the microchannel than in the vicinity of the wall; that is, the fluid temperature is higher at the center of the microchannel than in the heated walls.   

Convection slip flow in a microchannel filled with homogeneous and heterogeneous porous medium

In this paper, we have studied the rarefied gaseous flow through a micro-tube filled with homogeneous and heterogeneous porous medium. An analytical investigation is performed to model the flow and heat transfer using Brinkman momentum along with the energy equation. Velocity slip and temperature jump conditions are utilized to account for effect of the rarefied gaseous flow at the wall of the micro-tube. A uniform heat flux boundary condition is applied at the wall of the microtube. A rigorous explicit expression for velocity, temperature, and Nusselt number are obtained. Effect of porous media shape parameter and Knudsen number on velocity, temperature and Nusselt number are analysed and compared for both homogeneous and heterogeneous cases. Results show that an increase in the velocity slip coefficient leads to an increase in Nusselt number, since an increase in the slip at the wall leads to an increased velocity, which results in higher convective heat transfer. Moreover, increasing the temperature jump coefficient reduces the Nusselt number because higher slip causes a smaller temperature gradient at the wall, which reduces the heat transfer. Results also show enhanced heat transfer characteristics for heterogeneous porous medium, as compared to homogenous porous medium.

    

Resonance, Rayleigh Flows and Thermal Choking: Compressible Coolant States in Porous Electromagnetic Heat Exchangers

Electromagnetic (EM) Heat Exchangers (HX) are systems which convert EM energy into heat or mechanical work. One potential design consists of a porous lossy ceramic material heated by EM waves with a compressible gas coolant. EM heating of ceramics is nonlinear, since the loss factor is temperature dependent.  Designing such EM HXs requires an understanding of the coupling between temperature, the electric field, and gas dynamics at the pore scale. To mimic this microscale phenomena, a single channel with a high-speed gas coolant in perfect thermal contact with a thin solid ceramic layer is considered, with an applied plane-wave electric field propagating normal to the channel walls. From a thin-domain asymptotic analysis, the conservation laws reduce to a Rayleigh flow in the gas coupled with averaged thermal energy conservation equations at leading order. The kinetic energy of the gas increases about 12 times the inlet value when thermal runaway occurs in the ceramic region, and themal choking is possible when the coolant reaches the sonic state. Local maximum efficiencies occur on a discrete set of ceramic thicknesses which correspond to Fabry-Bragg resonances of the electric field.

    

Energy partitioning of thermally driven flows confined in Hele-Shaw systems

Thermally driven flows in strongly confined environments, such as permeable media, are ubiquitous in nature, and they contribute to the heat transfer across the Earth's lithosphere and fluid mixing process within aquifers. The Hele-Shaw system is an ideal laboratory analogue to investigate geometrically constrained convective flows. However, in these environments, the energy pathways have not been characterized experimentally. In this work, we study the energy pathways of thermal convection in Hele-Shaw systems by laboratory experiments. Transparent fluid layers built for the laboratory experiments allow elucidating kinetic and potential energies of the whole domain by particle image velocimetry and background oriented schlieren method. The experimental results are then compared with theoretical and numerical results that characterize the energy partitioning as a function of the controlling parameters, the Rayleigh-Darcy number, the Prandtl, and the anisotropic ratio of the Hele-Shaw cell. We will discuss the flow features, energy partitioning, and mixing efficiency of thermal convection in Hele-Shaw systems.   

Energetics and mixing in Rayleigh-Benárd-Darcy convection in Hele-Shaw cells

Thermally driven flows in fractures play a fundamental role in enhancing the heat transfer and fluid mixing across the Earth’s lithosphere. Yet little is known about the energy pathways in such confined environments. Building on the quasi-two dimensional (Q2D) Hele-Shaw model able to characterize flows in permeable media, we introduce and analyse expressions for energy transfer rates—energetics—of geometrically controlled Rayleigh-Bénard-Darcy convection in Hele-Shaw cells considering the Boussinesq limit. Based on the conceptual framework, we investigate theoretically the mechanical energy partition and we derive the efficiencies that allow characterising the transformation of the injected energy into motion and irreversible mixing. The analytical expressions for the energy partitioning are supported by direct numerical simulations of the governing equations. Finally, we discuss the relationship between the global Nusselt number and the Rayleigh number of the system, and we show how strength of the thermal forcing may lead the system to transition from a Darcy-like medium to a three-dimensional environment.