A Modified Beavers and Joseph Condition for Gravity-Driven Flow over Porous Layers

Gravity-driven flow through an inclined channel over a semi-infinite porous layer is considered in order to obtain a modification to the usual Beavers and Joseph slip condition that is suitable for this type of flow. Expressions for the velocity, shear stress, volumetric flow rates, and pressure distribution across the channel are obtained together with an expression for the interfacial velocity. In the absence of values for the slip parameter when the flow is over a Forchheimer porous layer, this work provides a relationship between the slip parameters of the Darcy and Forchheimer layers. Expressions for the interfacial velocities in both cases are obtained. This original work is intended to provide baseline analysis and a benchmark with which more sophisticated types of flow, over porous layers in an inclined domain can be compared.

Advances and Challenges in Purging Pipeline Sections: Field Measurements vs. 1D Purging Model

Effective purging of air out of a pipeline section before commissioning by direct displacement with natural gas has been safely practiced for decades with the recognition that flammable interfacial mixing zone between the driving gas (behind) and the air (ahead) is inevitable. In cases when the purge velocity is below a threshold dictated by the gravity current velocity (defined in AGA Purging Principles and Practices, 2001), natural gas being lighter than air can in fact ride over air being the heavier gas and short circuit the flow path to the vent at the other end of the pipe section, thus trapping behind pockets of air that could potentially introduce risk of internal explosion with subsequent damage to the pipe section and pose a safety issue to field personnel. Therefore, maintaining the purge velocity above this threshold by a good margin has been a common practice in the purging procedure to-date. In fact, maintaining the purge velocity above the threshold can be controlled by the injection press or flow, where tools and dynamic purging models have been successfully developed and proven to be useful. However, AGA recommends that the drive purge gas pressure be limited to 689 kPag (100 psig) in the inlet purge line to the pipe section to avoid the risk of detonation. In some cases when the inlet purge line is relatively small compared to the main pipe section, this limit on the purge pressure would result in gas/air interfacial velocity much lower than the threshold velocity, hence stratification will occur. This paper provides insight into the possibility of increasing the purge pressure above AGA limit to avoid stratification, while conforming to the safety aspects related to detonation. A purge model is developed to overcome the shortcoming in AGA purge software that limits the purge pressure to maximum of 689 kPag (100 psig). Field trial was conducted to validate the model which demonstrated, as a proof of concept, a successful purge procedure with purge pressure = 5517 kPag (800 psig) in NPS 1.5 purge line to purge nitrogen out of NPS 42, 5.8 km section of a pipeline.

A four-field three-phase flow model with both miscible and immiscible components

A three-phase flow model with hybrid miscibility constraints is proposed: three immiscible phases are considered (liquid, solid and gas) but the gaseous phase is composed with two miscible components (steam water and non-condensable gas). The modelling approach is based on the building of an entropy inequality for the system of partial dfferential equations: once an interfacial velocity is given by the user, the model is uniquely defined, up to some relaxation time scales, and source terms complying with the second principle of thermodynamics can then be provided. The convective part of the system is hyperbolic when fulfilling a non-resonance condition and classical properties are studied (Riemann invariants, symmetrization). A key property is that the system possesses uniquely defined jump conditions. Last, preservation of thermodynamically admissible states and pressure relaxation are investigated.

Ferrofluid Thin Films for Airfoil Lift Generation

In this work, consideration is given to a novel concept for airfoil lift generation and flow control. In this concept, the goal is attained by preventing the growth of the boundary layer from the elimination of the zero slip condition between the surface and the air stream. The concept would simulate all effects of a moving wall leading in the appearance of slip velocity in the gas-fluid interface including the injection of momentum into the boundary layer, with one exception: there is no moving wall but instead a ferrofluid thin film attached at the wall by a magnetic field which permit to attain much more higher velocities at the interface which is not allowable if mobil surface wall are used. Utilizing a simplified physical model for the profile velocity of the ferrofluid film and from ferrohydrodynamic stability considerations an analytical expression for the interfacial velocity was derived. Finally, from the available experimental data on moving walls the expected lift and attack angle enhancement was found. Additional R\&D is required in order to explore the possibilities in the use of ferrofluid thin films.

Lattice-Boltzmann simulation of free nematic-isotropic interfaces

We use a hybrid method of lattice Boltzmann and finite differences to simulate flat and curved interfaces between the nematic and isotropic phases of a liquid crystal described by the Landau-de Gennes theory. For the flat in¬terface, we measure the interfacial velocity at different temperatures around the coexistence. We show that the interface is completely static at the coexistence temperature and that the profile width is in line with the theoretical predictions. The interface is stable in a range of temperatures around coexistence and dis¬appears when one of the two phases becomes mechanically unstable. We stabi¬lize circular nematic domains by a shift in temperature, related to the Laplace pressure, and estimate the spurious velocities of these lattice Boltzmann simu¬lations.

Closure conditions for a one temperature non-equilibrium multi-component model of baer-nunziato type

A class of non-equilibrium models for compressible multi-component uids is investigated. These models are subject to the choice of interfacial pressures and interfacial velocity as well as relaxation terms for velocity, pressure and chemical potentials. Sufficient conditions are derived for these quantities that ensure meaningful physical properties such as a non-negative entropy production and thermodynamical stability as well as mathematical properties such as hyperbolicity. For the relaxation of chemical potentials a three-component model gas-water-vapor is considered.