City Research Online

Abstract

Liquid flow penetrating into porous media, such as rocks, metal foam, soil, and drug delivery, are often simulated as a single phase or multiphase continuum using Darcy’s law. Darcy’s law considered being the most used model of many approaches for simulating the flow through porous media, where the Darcy model assumes a simple proportional relationship between the instantaneous discharge rate through a porous medium, the viscosity of the fluid, and the pressure drop over a given distance. The law was formulated based on the results of experiments on the flow of water through beds of sand. It also forms the scientific basis of fluid permeability used in the earth sciences, particularly in hydrogeology. The underlying assumption with the Darcy method is that the microscopic concept of the liquid flow in any porous material will involve the use of the microscopic velocities associated with the actual paths of the liquid. However, in practice, it is challenging to measure the real microscopic velocities and for this reason, the average value of the real velocities is accepted. By averaging the steady-state Stokes equation this leads to Darcys law, which was introduced as an empirical relationship to describe flow in sand filters, as discovered by Darcy in 1856 and this served as a starting point for numerous practical applications and as a constant challenge for theoreticians. While the original conditions studied by Darcy are found in many practical situations, its extensions to more general cases that are especially designed for theoretical analysis are widely used to represent situations in which experiments are difficult to perform. While this form of Darcy’s law is used with great frequency, it is difficult to get experimental verification of the obvious terms representation of Darcy’s law. For example, the Darcy velocity, which is defined as a volume-average of the flow field, does not represent the real velocity inside the porous media, but rather, the volume of fluid flowing per unit area of the porous medium, including both solids and voids. Also, the pressure gradient does not represent the microscopic pore-level quantity, but rather, is defined over a representative elementary volume medium. To explore Darcy assumptions and to understand the controlling pore-scale mechanisms, a numerical framework has been developed that involves using a reconstructed real porous medium to present a detailed numerical domain for multiphase flow simulations. For the numerical multiphase flow methodology the Volume-of-Fluid (VoF) method combined with additional sharpening, smoothing and filtering algorithms is used as a basis for interface capturing. These algorithms help in the minimisation of the parasitic currents presented in flow simulations. The framework is implemented within a finite volume code (OpenFOAM) using a limited Multidimensional Universal Limiter with Explicit Solution (MULES) implicit formulation. This framework allows for more substantial time steps at low capillary numbers to be utilised compared to the standard solver. In addition, a novel adaptive interface compression scheme is introduced. This allows for dynamic estimation of the compressive velocity only at the areas of interest and thus, has the advantage of avoiding the use of a priori defined compression coefficient parameters. The adaptive method increases the numerical accuracy and reduces the sensitivity of the methodology to tuning parameters. The accuracy and stability of the proposed model are verified against different benchmark test cases. Moreover, the numerical results are compared against analytical solutions as well as available experimental data and this reveals improved predictions relative to the standard VoF solver. This thesis is focused on two different applications that involve porous media: first, flow and transport inside a porous structure, where the presented simulations results show the importance of liquid front invasion. Also, the salience of phase wettability on the residual phase using different wetting dynamic conditions is demonstrated. The results for simulations relating the pore-scale physics, thereby obtaining permeability values are presented. The overall results provide a detailed pore-scale analysis of multiphase flow, serving as a foundation for large-scale modelling and flow prediction. The second application is droplet impact on porous structures and the penetration physics on porous media. The work is focused on droplet spreading and absorption during the early stages of impact. Using the developed framework, the droplet penetrating the porous media is also studied. In addition, simulations of the penetration of different sizes of droplets with different fluid properties in the pore network with different porosities are performed to characterise the effect of the Re and We numbers on the penetration behaviour. The capability to estimate the key features of the flow dynamics has been investigated. For example, in order to relate the microscopic effects to the macroscopic ones, it is important to focus on the maximum spreading, while considering the influence of liquid properties, and wetting behaviour with relation to porous media properties such as porosity. Some conclusions regarding the relation between porosity and porous wall wetting conditions have been drawn using the developed numerical framework for studying the liquid spreading onto porous media. Also, in the thesis, the influence of the porous structure wetting behaviour, the morphology of porous surfaces and the effects of porosity on droplet penetration and spreading are presented. Using the proposed developed solver, a direct relation between penetration volume and the imposed dynamic contact angle was found. This would appear to contradict the expected behaviour in vertical liquid penetration that is obtained using the macroscopic multiphase Darcy’s law. The goals of this research have been achieved by deploying the complex flow physics using the two described applications and by showing the importance of the developed framework in relation to a wide range of applications. This provides evidence for the effectiveness of studying multiphase flows at the microscale level uisng interface tracking methods.

Publication Type:	Thesis (Doctoral)
Subjects:	T Technology > TJ Mechanical engineering and machinery
Departments:	School of Science & Technology > School of Science & Technology Doctoral Theses School of Science & Technology > Engineering

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