Coating Flow Near Channel Exit. A Theoretical Perspective

The planar flow of a steady moving-wall free-surface jet is examined theoretically for moderate inertia and surface tension. The method of matched asymptotic expansion and singular perturbation is used to explore the rich dynamics near the stress singularity. A thin-film approach is also proposed to capture the flow further downstream where the flow becomes of the boundary-layer type. We exploit the similarity character of the flow to circumvent the presence of the singularity. The study is of close relevance to slot and blade coating. The jet is found to always contract near the channel exit, but presents a mild expansion further downstream for a thick coating film. We predict that separation occurs upstream of the exit for slot coating, essentially for any coating thickness near the moving substrate, and for a thin film near the die. For capillary number of order one, the jet profile is not affected by surface tension but the normal stress along the free surface exhibits a maximum that strengthens with surface tension. In contrast to existing numerical findings, we predict the existence of upstream influence as indicated by the nonlinear pressure dependence on upstream distance and the pressure undershoot (overshoot) in blade (slot) coating at the exit.

Wintertime Easterly and Southeasterly Airflow in the ‘Alenuihāhā Channel, Hawaii

During the wintertime, easterly (E) to southeasterly (SE) flow in the Hawaiian coastal waters is frequent. These wind regimes alter the location and magnitude of channel and tip jet accelerations and the orientation and horizontal extent of the wake zones from east-northeast (ENE) trade wind conditions. The differences are the result of changes in orographic blocking by the Big Island and Maui, with respect to the prevailing wind. During an E wind event, the fastest winds over the ‘Alenuihāhā Channel (>9 m s−1) occur in the channel exit with sinking of the inversion, which rises again downstream. Although the upstream wind speed is similar to typical summer ENE trade winds (7–8 m s−1), the maximum channel wind speed is 3–4 m s−1 slower in the exit. The SE flow is characterized by maximum (~6 m s−1) northeasterly (NE) channel winds along Maui’s south shore and at the channel exit. These winds are the result of orographic blocking on the eastern end of Maui as the northwestern tail of a tip jet off the northeastern coast of the Big Island impinges on Mount Haleakalā. Channel wind speeds are modulated by the speed and direction of this tip jet, which itself varies diurnally and throughout the approach of a midlatitude cold front. Removal of the Big Island shows how the tip jet speed and orientation modulate the pressure gradients and winds in the ‘Alenuihāhā Channel. Removal of the Maui County terrain reveals the impact of orographic blocking on the occurrence of channel winds off Maui’s south shore.

Effects of the magnetic field gradient on the wall power deposition of Hall thrusters

The effect of the magnetic field gradient in the discharge channel of a Hall thruster on the ionization of the neutral gas and power deposition on the wall is studied through adopting the 2D-3V particle-in-cell (PIC) and Monte Carlo collisions (MCC) model. The research shows that by gradually increasing the magnetic field gradient while keeping the maximum magnetic intensity at the channel exit and the anode position unchanged, the ionization region moves towards the channel exit and then a second ionization region appears near the anode region. Meanwhile, power deposition on the walls decreases initially and then increases. To avoid power deposition on the walls produced by electrons and ions which are ionized in the second ionization region, the anode position is moved towards the channel exit as the magnetic field gradient is increased; when the anode position remains at the zero magnetic field position, power deposition on the walls decreases, which can effectively reduce the temperature and thermal load of the discharge channel.

The dynamics of confined extensional flows

I present a theoretical and experimental study of floating viscous fluid films introduced into a channel of finite length, motivated by the flow of glacial ice shelves. The dynamics are characterized by a mixture of viscous extensional stresses, transverse shear stresses and a driving buoyancy force. A theory based on a width-integrated model is developed and investigated using analytical, asymptotic and numerical methods. With fluid introduced at a constant rate, the flow is found to approach a steady state with two possible asymptotic forms depending on the length of the channel. For channel lengths less than half the width, the flow is similar to a purely extensional one-dimensional flow, characterized by concave surface profiles and being insensitive to the position of the channel exit (or calving front). Greater lengths result in a more complex asymptotic structure in which the flow adjusts over a short distance towards a prevailing flow of universal dimensionless form. In complete contrast to the extensional regime, the prevailing flow is controlled by the position of the channel exit. Data from a new laboratory experiment involving particle velocimetry of a floating fluid film compares well with the predicted along-channel velocity. Motivated by glaciological application, the analysis is generalized to power-law rheologies and the results used to classify the flow regimes of a selection of ice shelves. The prediction for the frontal speed is in good agreement with geophysical data, indicating that the universal profile predicted by the theory is common in nature.

Slipping free jet flow near channel exit at moderate Reynolds number for large slip length

The flow of a slipping fluid jet is examined theoretically as it emerges from a channel at moderate Reynolds number. The ratio of the slip length to the channel width $S$ is assumed to be of order one, one order of magnitude larger than the perturbation parameter ${\it\varepsilon}=Re^{-1/2}$, $Re$ being the Reynolds number. Poiseuille flow conditions are assumed to prevail far upstream from the exit. The problem is solved using the method of matched asymptotic expansions. A similarity solution is obtained in the inner layer of the free surface, with the outer layer extending to the jet centreline. The inner-layer thickness grows like $\sqrt{x/Re\,S}$. A slipping jet is found to contract like $x/Re$ very near and far from the channel exit, but does not have a definite behaviour in between compared to $(x/Re)^{1/3}$ for an adhering jet, $x$ being the distance from the channel exit. Eventually, the jet reaches uniform conditions far downstream. As in the case of entry flow, there is a rapid departure in flow behaviour for a slipping jet from the $S=0$ limit. This rapid change is notably observed in the drop of boundary-layer thickness, increase in exit and relaxation lengths as well as in jet width with slip length. Finally, the connections with microchannel and hydrophobic flows are highlighted.

A CFD technique to investigate the chocked flow and heat transfer characteristic in a micro-channel heat sink

In this research, a Computational Fluid Dynamics (CFD) technique was used to investigate the effect of choking on the flow and heat transfer characteristics of a typical micro-channel heat sink. Numerical simulations have been carried out using Spalart–Allmaras model. Comparison of the numerical results for the heat transfer rate, mass flow rate and Stanton number with the experimental data were conducted. Relatively good agreement was achieved with maximum relative error 16%, and 8% for heat transfer and mass flow rate, respectively. Also, average relative error 9.2% was obtained for the Stanton number in comparison with the experimental values. Although, the results show that the majority of heat was transferred in the entrance region of the channel, but the heat transfer in micro-channels can also be affected by choking at channel exit. Moreover, the results clearly show that, the location where the flow is choked (at the vicinity of the channel exit) is especially important in determining the heat transfer phenomena. It was found that Spalart–Allmaras model is capable to capture the main features of the choked flow. Also, the effects of choking on the main characteristics of the flow was presented and discussed.

Kühlkanalaustrittsbedingungen beim Bohren*/Cooling Channel Exit Conditions in Drilling

Auf Basis von CFD (Computational Fluid Dynamics)-Simulationen wurden VHM (Vollhartmetall)-Wendelbohrer mit unterschiedlichen Kühlkanalaustrittspositionen hergestellt. Mithilfe von Mantelthermoelementen lässt sich die Temperatur während des Bohrens ermitteln und mit der Simulation abgleichen. Die Temperaturen wurden mit dem Verschleiß der Werkzeuge in Relation gesetzt. Davon ausgehend erfolgten Untersuchungen, um die Einflüsse von Kühlkanalaustrittsposition und KSS (Kühlschmierstoff)-Volumenstrom auf den Werkzeugverschleiß zu ermitteln.   Based on CFD simulations, cemented carbide twist drills with different cooling channel exit positions were manufactured. These were equipped with thermo couples to measure the temperature during drilling and to correlate it with the simulation. The temperatures were related to the wear of the tools. Based on this, the influences of cooling channel exit position and cooling liquid volume flow rate on tool wear were investigated.

Manufacturing Influences on Pressure Losses of Channel Fed Holes

Variations from manufacturing can influence the overall pressure drop and subsequent flow rates through supply holes in such applications as film-cooling, transpiration cooling, and impingement cooling that are supplied by microchannels, pipe-flow systems, or secondary air systems. The inability to accurately predict flow rates has profound effects on engine operations. The objective of this study was to investigate the influence of several relevant manufacturing features that might occur for a cooling supply hole being fed by a range of channel configurations. The manufacturing variances included the ratio of the hole diameter to the channel width, the number of channel feeds (segments), the effect of hole overlap with respect to the channel sidewalls, and the channel Reynolds number. The results showed that the friction factors for the typically long channels in this study were independent of the tested inlet and exit hole configurations. The results also showed that the nondimensional pressure loss coefficients for the flow passing through the channel inlet holes and through the channel exit holes were found to be independent of the channel flow Reynolds number over the tested range. The geometric scaling ratio of the hole cross-sectional area to the channel cross-sectional area collapsed the pressure loss coefficients the best for both one and two flow segments for both the channel inlet and channel exit hole.