A Study to Investigate the Viscosity Effect on Micro-Confined Fluids Flow in Tight Formations Considering Fluid–Solid Interaction

Understanding different fluids flow behavior confined in microscales has tremendous significance in the development of tight oil reservoirs. In this article, a novel semiempirical model for different confined fluid flow based on the concept of boundary layer thickness, caused by the fluid–solid interaction, is proposed. Micro-tube experiments are carried out to verify the novel model. After the validation, the viscosity effect on the flow rate and Poiseuille number considering the fluid–solid interaction is investigated. Furthermore, the novel model is incorporated into unstructured networks with anisotropy to study the viscosity effect on pore-scale flow in tight formations under the conditions of different displacement pressure gradients, different aspect ratios (ratio of the pore radius to the connecting throat radius), and different coordination numbers. Results show that the viscosity effect on the flow rate and Poiseuille number after considering the fluid–solid interaction induces a great deviation from that in conventional fluid flow. The absolute permeability is not only a parameter related to pore structures but also depends on fluid viscosity. The study provides an effective model for modeling different confined fluid flow in microscales and lays a good foundation for studying fluid flow in tight formations.

Fully-developed laminar flow in trapezoidal ducts with rounded corners: a numerical solution and case study

Purpose This paper aims to numerically solve fully developed laminar flow in trapezoidal ducts with rounded corners which result following forming processes. Design/methodology/approach A two-dimensional model for a trapezoidal duct with rounded corners is developed and conservation of momentum equation is solved. The flow is assumed to be steady, fully developed, laminar, isothermal and incompressible. The key flow characteristics including the Poiseuille number and the incremental pressure drop have been computed and tabulated for a wide range of: sidewall angle (θ); the ratio of the height of the duct to its smaller base (α); and the ratio of the fillet radius of the duct to its smaller base (β). Findings The results show that Poiseuille number decreases, and all the other dimensionless numbers increase with increasing the radii of the fillets of the duct; these effects were found to amplify with decreasing duct heights or increasing sidewall angles. The maximum axial velocity was shown to increase with increasing the radii of the fillets of the duct. For normally used ducts in hydrogen fuel cells, the impact of rounded corners cannot be overlooked for very low channel heights or very high sidewall angles. Practical implications The data generated in this study are highly valuable for engineers interested in estimating pressure drops in rounded trapezoidal ducts; these ducts have been increasingly used in hydrogen fuel cells where flow channels are stamped on thin metallic sheets. Originality/value Fully developed laminar flow in trapezoidal ducts with four rounded corners has been solved for the first time, allowing for more accurate estimation of pressure drop.

Entropy generation and Poiseuille number link in developing isothermal laminar micro-flow

It is well-known that Poiseuille number (Po, hitherto viewed mainly as a Fluid Mechanics parameter) decreases along a hydrodynamically developing flow, from infinity at inlet to a fixed value downstream. This study reveals that the dimensionless entropy generation rate per unit length due to fluid friction (Sgen,fr) varies exactly the same way; hence, Po and Sgen,fr are jointly studied for their dependence. Laminar hydrodynamic development of isothermal flow of incompressible fluid (water) in a circular micro-tube (diameter, D) is examined. Results are obtained for a given flow velocity for different D and then numerical experiments are conducted for different flow velocities for the same D-values. Striking similarity in trends of Po and Sgen,fr show a unique linear relation between them for the hydrodynamically developing region. It is theoretically shown that Po is a direct measure of entropy generation due to fluid friction, which explains its numerically obtained linear relation with Sgen,fr. It is found that in hydrodynamically developing region, both Po and Sgen,fr decrease with decreasing D, which is the identified micro-effect.

Pressure Losses at Moderate Reynolds Numbers in Diamond-Shaped Cylinders Arrays: Application to Microregenerators

Cylinders with an elliptical, oblong, lenticular, sinus, or diamond transveral shape are very interesting geometries for the design of compact heat exchangers. This work investigates the role of the porosity and of the apex angle of diamond-shaped cylinders networks on the pressure losses, at moderate Reynolds numbers, inside microheat regenerators. The design of the geometry under test has been chosen so that the cross section of the flow remains almost constant along the path of the flow between cylinders. Experiments have been performed at 1 ⩽ Re ⩽ 30 and a porosity range 0.40<ε<0.90 for an apex angle of α=33deg. Numerical simulations have been conducted using the same Reynolds and porosity ranges but varying the apex angle 33deg ⩽ α ⩽ 90deg. Experimental measurements and dimensional analysis have shown that the friction factor can be affected by the porosity. Two-dimensional numerical simulations confirmed that the friction factor increases with the porosity but also with the apex angle. An analysis at the scale of a channel flanked by adjacent cylinders has provided an original correlation able to describe easily the evolution of the Poiseuille number and the collective effects on the drag coefficient as a function of α and ε. Such a diamond-shaped design is found to induce much lower Poiseuille numbers than those expected from conventional stacked spheres, woven wires, and circular cylinders arrays. The findings of this study can help for better understanding the optimization of low pressure drop regenerators and how to reduce associated hydraulic power.

Laminar fluid flow in concentric annular ducts of non-conventional cross-section applying GBI method

Fluid flow in concentric or eccentric annular ducts have been studied for decades due to large application in medical sciences and engineering areas. This paper aims to study fully developed fluid flow in straight ducts of concentric annular geometries (circular with circular core, elliptical with circular core, elliptical with elliptical core, and circular with elliptical core) using the Galerkin-based Integral method (GBI method). The choice of method was due to the fact that in the literature it is not applied in ducts of cross-sections of the annular shape with variations between circular and elliptical. Results of different hydrodynamics parameters such as velocity distribution, Hagenbach factor, Poiseuille number, and hydrodynamic entrance length, are presented and analyzed. In different cases, the predicted hydrodynamic parameters are compared with results reported in the literature and a good concordance was obtained.

Gas Flow in Microchannels and Nanochannels With Variable Cross Section for All Knudsen and All Mach Number Values

The analytical solution for steady viscous pressure-driven compressible isothermal gas flow through micro- and nanochannels with variable cross section for all Knudsen and all Mach number values is presented in this paper. The continuum one-dimensional governing equations are solved using the friction factor that is established in a special way to provide solutions for mass flow rate, pressure, and velocity distribution through the microchannels and nanochannels in the entire rarefaction regime. The friction factor, defined by the general boundary condition and generalized diffusion coefficient proposed by Beskok and Karniadakis (1999, “A Model for Flows in Channels, Pipes, and Ducts at Micro and Nano Scales,” J. Microscale Thermophys. Eng., 3, pp. 43–77), spreads the solution application to all rarefaction regimes from continuum to free molecular flow. The correlation between the product of friction factor and Reynolds number (Poiseuille number) and Knudsen number is established explicitly in the paper. Moreover, the obtained solution includes the inertia effect, which allows the application of the solution to both subsonic and supersonic gas flows, which was not shown earlier. The presented solution confirms the existence of the Knudsen minimum in the diverging, converging, and microchannels and nanochannels with constant cross section. The proposed solution is verified by comparison with experimental, analytical, and numerical results available in literature.

A NOVEL FRACTAL SOLUTION FOR LAMINAR FLOW RESISTANCE IN ROUGHENED CYLINDRICAL MICROCHANNELS

In this work, a novel fractal model for the laminar flow in roughened cylindrical microchannels is proposed. The average height of rough elements is derived using the fractal theory. The effects of relative roughness on the friction factor and the Poiseuille number are discussed. It is found that the Darcy friction factor and the Poiseuille number increase with the increase in the relative roughness in the cylindrical microchannel. Besides, it is observed that the Darcy friction factor decreases with the increase in the Reynolds number. Each parameter of the proposed model has a clear physical meaning. The present model can properly reveal some mechanisms that affect the laminar flow in roughened cylindrical microchannels. The present model improves the understanding of the physical mechanisms of fluid flows through roughened cylindrical microchannels. Our model predictions are compared with the existing experimental data, and good agreement can be found.

Experimental Study on Liquid Flow and Heat Transfer in Rough Microchannels

Although roughness is negligible for laminar flow through tubes in classic fluid mechanics, the surface roughness may play an important role in microscale fluid flow due to the large ratio of surface area to volume. To further verify the influence of rough surfaces on microscale liquid flow and heat transfer, a performance test system of heat transfer and liquid flow was designed and built, and a series of experimental examinations are conducted, in which the microchannel material is stainless steel and the working medium is methanol. The results indicate that the surface roughness plays a significant role in the process of laminar flow and heat transfer in microchannels. In microchannels with roughness characteristics, the Poiseuille number of liquid laminar flow relies not only on the cross section shape of the rough microchannels but also on the Reynolds number of liquid flow. The Poiseuille number of liquid laminar flow in rough microchannels increases with increasing Reynolds number. In addition, the Nusselt number of liquid laminar heat transfer is related not only to the cross section shape of a rough microchannel but also to the Reynolds number of liquid flow, and the Nusselt number increases with increasing Reynolds number.