Fluid Flow in Composite Regions Past a Solid Sphere

A steady, 2-D, incompressible, viscous fluid flow past a stationary solid sphere of radius 'a' has been considered. The flow of fluid occurs in 3 regions, namely fluid, porous and fluid regions. The governing equations for fluid flow in the clear and porous regions are Stokes and Brinkman equations, respectively. These governing equations are written in terms of stream function in the spherical coordinate system and solved using the similarity transformation method. The variation in flow patterns by means of streamlines has been analyzed for the obtained exact solution. The nature of the streamlines and the corresponding tangential and normal velocity profiles are observed graphically for the different values of porous parameter 'σ'. From the obtained results, it is noticed that an increase in porous parameters suppresses the fluid flow in the porous region due to less permeability; as a result, the fluid moves away from the solid sphere. It also decreases the velocity of the fluid in the porous region due to the suppression of the fluid as 'σ' increases. Hence the parabolic velocity profile is noticed near the solid sphere.

Parabolic velocity profile causes shape-selective drift of inertial ellipsoids

Understanding particle drift in suspension flows is of the highest importance in numerous engineering applications where particles need to be separated and filtered out from the suspending fluid. Commonly known drift mechanisms such as the Magnus force, Saffman force and Segré–Silberberg effect all arise only due to inertia of the fluid, with similar effects on all non-spherical particle shapes. In this work, we present a new shape-selective lateral drift mechanism, arising from particle inertia rather than fluid inertia, for ellipsoidal particles in a parabolic velocity profile. We show that the new drift is caused by an intermittent tumbling rotational motion in the local shear flow together with translational inertia of the particle, while rotational inertia is negligible. We find that the drift is maximal when particle inertial forces are of approximately the same order of magnitude as viscous forces, and that both extremely light and extremely heavy particles have negligible drift. Furthermore, since tumbling motion is not a stable rotational state for inertial oblate spheroids (nor for spheres), this new drift only applies to prolate spheroids or tri-axial ellipsoids. Finally, the drift is compared with the effect of gravity acting in the directions parallel and normal to the flow. The new drift mechanism is stronger than gravitational effects as long as gravity is less than a critical value. The critical gravity is highest (i.e. the new drift mechanism dominates over gravitationally induced drift mechanisms) when gravity acts parallel to the flow and the particles are small.

Flow Induced by a Two Stage Electrohydrodynamic Gas Pump in a Square Channel

In this study, fluid flow induced by a two stage electrohydrodynamic (EHD) gas pump in a square channel has been evaluated by experimental measurement and numerical simulations. This study is implemented for a two stage EHD gas pump with three emitting electrode configurations: 8, 24, and 56 respectively to seek the relation between the number of stages and emitting electrodes. The EHD pump is evaluated for a wide range of operating voltages starting from 20 kV up to 28 kV for further improvement in its performance over a single stage. To achieve the maximum enhancement, the emitting electrodes of the EHD gas pump are flush mounted on the channel walls so that the corona wind produced directly disturbs the boundary layer thickness and improves the heat transfer. This is leading to a higher velocity near the channel walls and resulting in an inverted parabolic velocity profile at the center of the channel, which is opposite to the fully developed velocity profile of a forced flow. Velocities are measured at three cross-sections along the tube length and then integrated to obtain the volume flow rate. The results show that EHD technique has a great potential for many engineering applications.

FPGA-Based Architecture for Sensing Power Consumption on Parabolic and Trapezoidal Motion Profiles

The objective of this work is to design and implement a scalable Field-Programmable Gate Array (FPGA)-based motion control system for DC servo motors using a parabolic velocity profile for industrial applications. The implementation in this device allows the obtaining of a fast, flexible and low-cost system. The system is divided into control, communication and closed-loop coupling. The work also addresses a comparative analysis of the most used profiles, the trapezoidal and parabolic. The comparison is made considering the energy consumption of both profiles. As a consequence of the comparison made, the velocity profile can be selected to reduce production costs by saving energy and reducing wear on machinery. The discrete models of the velocity profiles are obtained through numerical methods that permit the control blocks to be implemented in an FPGA. To reduce maintenance costs and energy consumption in servo mechanisms, the derivation of the acceleration or jerk of the motor is shown. A Graphic User Interface (GUI) is presented, which allows monitoring the position, velocity and angular acceleration of the motor shaft. In addition, the developed interface supports modification of parameters of the final position and maximum velocity in the motor. The delivered current is compared, evaluating its decrease using a parabolic velocity profile. Finally, the experimental results are illustrated.

Numerical simulation of bubble deformation in various velocity profiles across a conduit

<p>Tube pumice is characterized by aligned highly elongated bubbles and is a common product of explosive silicic eruptions. The relative abundance of tube pumice and non-tube pumice in the stratigraphy has been interpreted as resulting from temporal and spatial variations in a conduit flow. Therefore, understanding the formation mechanism of tube pumice is valuable, but still debated. Most previous studies interpret tube pumice forming from simple shear deformation, assuming a parabolic velocity profile across a conduit. However, simple shear cannot explain the observation that tube pumice is rare in plinian falls but frequent in ignimbrites (interpreted to have wider vents).</p><p>In this study, we combine a bubble deformation model with a quasi-two-dimensional steady conduit flow model. A bubble is deformed by the velocity gradient while moving within the conduit flow. The conduit flow model is calculated for the 1.8 ka Taupo plinian eruption, which produced a high proportion of tube pumice in the ignimbrite phase. In this abstract, we explain results from two rheological models showing distinct velocity profiles. In the Newtonian isothermal fluid, the velocity profile across the conduit becomes parabolic. In a fluid that allows viscous heating, the temperature near the conduit wall rises up sharply, leading to a strong reduction in viscosity, and the velocity profile changes from a parabolic shape to a plug-like shape. The parabolic velocity profile produces highly elongated bubbles mainly by simple shear, while the plug-like velocity profile is dominated by pure shear and accumulates less strain to elongate bubbles. The bubble shape at the fragmentation surface depends significantly on the velocity profile and its change along the conduit.</p><p>We also conduct a quantitative and statistical bubble shape analysis of pumice erupted at Taupo volcano. It shows that the plinian pumices have a single peak in the bubble shape distribution, while the ignimbrite pumices have a broad distribution and contain highly elongated bubbles. The comparison of the distribution of pumice textures with the simulation results suggests that the velocity profile of the plinian phase is close to a plug-like shape. We also calculate bubble deformation for the Taupo ignimbrite eruption, using the viscous-heating model. We model a　wider conduit for the ignimbrite phase which leads to lower shear rate around the conduit walls and a higher proportion of the conduit experiencing parabolic flow compared to the plinian phase. This increased proportion of parabolic velocity profile in the conduit can explain a large number of tube pumice in the Taupo ignimbrite.</p>

Flow behavior in weakly permeable micro-tube with varying viscosity near the wall

Weakly permeable micro-tubes are employed in many applications involving heat and/or mass transfer. During these processes, either solute concentration builds up (mass transfer) or steep change in temperature (heat transfer) takes place near the permeable wall causing a change in the viscosity of the fluid. Results of the present work suggest that such change in viscosity leads to a considerable alteration in the flow behavior, and the commonly assumed parabolic velocity profile no longer exists. To solve the problem numerically, the equation of motion was simplified to represent permeation of incompressible, Newtonian fluid with changing viscosity through a micro-tube. Even after considerable simplification, the accuracy of the results was the same as that obtained by previously reported results for some specific cases using rigorous formulation. The algorithm developed in the present work is found to be numerically robust and simple so that it can be easily integrated with other simulations.

A Numercial Investigation of the Skin Friction Coefficient and Nusselt Number in a Laminar Wall Jet That Evolves From a Parabolic Velocity Profile to its Self-Similar Behavior

A finite volume numerical approach is used to study the steady, laminar, plane wall jet that evolves from a parabolic velocity profile with uniform temperature to its self-similar behavior downstream of the jet exit. A variety of Reynolds numbers ranging between 50 and 250 is considered in this numerical investigation. The working fluids are air and water with constant physical properties corresponding to Prandtl number of 0.712 and 7 at ambient conditions. In these types of flows, a developing region over which the flow converges to its self-similar behavior is observed in the vicinity of the jet exit. The location of the dimensionless virtual origin, which is of main importance in determining the flow field in the self-similar region, is carefully studied and correlated as a function of Reynolds number. The local skin friction coefficient is observed to converge to the analytical self-similar solution at downstream locations. Given that an analytical solution for the thermal behavior of this problem doesn’t exist in either the developing or self-similar regions, the thermal solution of this problem is studied for isothermal and uniform heat flux boundary conditions at the wall. The idea of a dimensionless thermal virtual origin is introduced and correlated as a function of Reynolds number. The Nusselt number dependence on Prandtl number, Reynolds number and the downstream location are obtained for both thermal boundary conditions at the wall.