Eddy genesis and transformation of Stokes flow in a double-lid-driven cavity. Part 2: deep cavities

This paper extends an earlier work [1] on the development of eddies in rectangular cavities driven by two moving lids. The streamfunction describing Stokes flow in such cavities is expressed as a series of Papkovich-Faddle eigenfunctions. The focus here is deep cavities, i.e. those with large height-to-width aspect ratios, where multiple eddies arise. The aspect ratio of the fully developed eddies is found computationally to be 1.38 > 0.05, which is in close agreement with that obtained from Moffatt's [2] analysis of the decay of a disturbance between infinite stationary parallel plates. Extended control space diagrams for both negative and positive lid speed ratios are presented, and show that the pattern of bifurcation curves seen previously in the single-eddy cavity is repeated at higher aspect ratios, but with a shift in the speed ratio. Several special speed ratios are also identified for which the flow in one or more eddies becomes locally symmetric, resulting in locally symmetric bifurcation curves. By superposing two semi-infinite cavities and using the constant velocity damping factor found by Moffatt, a simple model of a finite multiple-eddy cavity is constructed and used to explain both the repetition of bifurcation patterns and the local symmetries. The speed ratios producing partial symmetry in the cavity are shown to be integer powers of Moffatt's velocity damping factor

Simulation of the spreading of a gas-propelled micro-droplet upon impact on a dry surface using a lattice-Boltzmann approach

Spray cooling is one of the most promising methods of cooling high heat flux electronics. Depending on the type of the nozzle, spray cooling can be categorized as single phase or two phase. In the latter, which is known to be more effective, a secondary gas is used to further pressurize the liquid and form smaller droplets at higher velocities. The gas is also assumed to assist the spreading phase by imposing normal and tangential forces on the droplet free surface which adds to the complicated hydrodynamics of the droplet impact. Moreover, the order of magnitude of droplet size in spray cooling is 10¯⁶m thereby introducing a low Weber and Reynolds numbers impact regime which heretofore has not been well understood. A 3D lattice Boltzmann method was implemented to simulate the impact of a single micro-droplet on a dry surface in both ambient air and under a stagnation gas flow. Two cases were closely compared and correlations were proposed for the instantaneous spreading diameter. Contrary to recent findings at higher impact We and Re, it was found that stagnation flow only significantly affects the spreading phase for Ca*⩾0.35 but has little influence on the receding physics

Substrate Wettability Influences Internal Jet Formation and Mixing during Droplet Coalescence

The internal dynamics during the axisymmetric coalescence of an initially static free droplet and a sessile droplet of the same fluid are studied using both laboratory experiments and numerical simulations. A high-speed camera captured internal flows from the side, visualized by adding a dye to the free droplet. The numerical simulations employ the volume of fluid method, with the Kistler dynamic contact angle model to capture substrate wettability, quantitatively validated against the image-processed experiments. It is shown that an internal jet can be formed when capillary waves reflected from the contact line create a small tip with high curvature on top of the coalesced droplet that propels fluid toward the substrate. Jet formation is found to depend on the substrate wettability, which influences capillary wave reflection; the importance of the advancing contact angle subordinated to that of the receding contact angle. It is systematically shown via regime maps that jet formation is enhanced by increasing the receding contact angle and by decreasing the droplet viscosity. Jets are seen at volume ratios very different from those accepted for free droplets, showing that a substrate with appropriate wettability can improve the efficiency of fluid mixing

Mixing and internal dynamics of droplets impacting and coalescing on a solid surface.

The coalescence and mixing of a sessile and an impacting liquid droplet on a solid surface are studied experimentally and numerically in terms of lateral separation and droplet speed. Two droplet generators are used to produce differently colored droplets. Two high-speed imaging systems are used to investigate the impact and coalescence of the droplets in color from a side view with a simultaneous gray-scale view from below. Millimeter-sized droplets were used with dynamical conditions, based on the Reynolds and Weber numbers, relevant to microfluidics and commercial inkjet printing. Experimental measurements of advancing and receding static contact angles are used to calibrate a contact angle hysteresis model within a lattice Boltzmann framework, which is shown to capture the observed dynamics qualitatively and the final droplet configuration quantitatively. Our results show that no detectable mixing occurs during impact and coalescence of similar-sized droplets, but when the sessile droplet is sufficiently larger than the impacting droplet vortex ring generation can be observed. Finally we show how a gradient of wettability on the substrate can potentially enhance mixing.This work was supported by the Engineering and Physical Sciences Research Council (Grant No. EP/H018913/, Innovation in industrial inkjet technology) and the KACST-Cambridge Research Centre.This is the accepted version of the original article published in Physical Review E and available online here: http://link.aps.org/doi/10.1103/PhysRevE.88.023023

The mutual interaction between tribochemistry and lubrication: Interfacial mechanics of tribofilm

A new mechanism for the action of antiwear tribofilms is proposed. The antiwear action of ZDDP additive is believed to be mainly due to the formation of tribofilms that reduce wear by chemical action. In this study, a mixed lubrication model is developed and tribofilm growth integrated into this model to simulate the effects of tribofilms on lubrication. The dynamic evolution of the contacting surfaces due to plastic deformation, wear and tribofilm growth continuously change the lubrication characteristics inside the contact. It is observed that the growth of tribofilm roughens the contact and increase contact severity. It was found that this roughness increase also helps to entrain more lubricant, resulting in thicker lubricant films. Therefore, the plot of the evolution of film thickness ratio (hcentral(t)/Rq(t)) shows that the lubrication regime is improved by the presence of tribofilm. Therefore, not only the chemical presence but the physical presence of the tribofilm on the surfaces also helps to improve contact performance by retaining more lubricant and improving the lubrication regime

Exponential mixing by orthogonal non-monotonic shears

Non-monotonic velocity profiles are an inherent feature of mixing flows obeying non-slip boundary conditions. There are, however, few known models of laminar mixing which incorporate this feature and have proven mixing properties. Here we present such a model, alternating between two non-monotonic shear flows which act in orthogonal (i.e. perpendicular) directions. Each shear is defined by an independent variable, giving a two-dimensional parameter space within which we prove the mixing property over open subsets. Within these mixing windows, we use results from the billiards literature to establish exponential mixing rates. Outside of these windows, we find large parameter regions where elliptic islands persist, leading to poor mixing. Finally, we comment on the challenges of extending these mixing windows and the potential for a non-exponential mixing rate at particular parameter values

Benefits of spanwise gaps in cylindrical vortex generators for conjugate heat transfer enhancement in micro-channels

Cylindrical vortex generators placed transversely over the span of a micro-channel can enhance heat transfer performance, but adding full-span vortex generators incurs a substantial pressure drop penalty. This paper examines the benefits of introducing various gaps along the length of the vortex generators, both for reducing pressure drop and improving the thermal conductance of the system. Three particular configurations are considered with varied dimensions: symmetrical gaps at each end of the vortex generator, i.e. adjacent to the channel side walls; a single central gap; and a combination of a central and end gaps. The performance is investigated numerically via 3D finite element analysis for Reynolds number in the range 300–2300 and under conditions of a uniform heat flux input relevant to microelectronics cooling. Results demonstrate that having end gaps alone substantially improves heat transfer while reducing the pressure drop. As well as generating longitudinal vortices which draw heat from the adjacent channel side walls, hot fluid passing through the gaps is swept directly upwards and inwards into the bulk flow, where it remains as it flows to the outlet. A thermal-hydraulic performance evaluation index is improved from 0.7 for full-span vortex generators to 1.0 with end gaps present. The central and central-plus-end gap geometries are less effective overall, but do offer localised improvements in heat transfer

Assessment of vortex generator shapes and pin fin perforations for enhancing water-based heat sink performance

In this study, two models have been analysed numerically to examine the impact of the geometry and the working fluid under laminar flow on heat and flow characteristics. The first model is a perforated pinned heat sink (PPHS) and the second is a new design of a uniform micro-channel having different shapes of vortex generators (VGs) positioned at intervals along the base of the channel. The VG shapes are circular, triangular and rectangular, and are compared to each other based on constant volume. Models with Reynolds number in the range of 50 to 2300 are subjected to a uniform heat flux relevant to microelectronics air and water cooling. Validations against previous micro-channel studies were conducted using the COMSOL Multiphysics® software package and found to be in good agreement. The results show that there is no significant enhancement in heat transfer using water in PPFHS. However, the VGs described here are shown to offer significant potential in combatting the challenges of heat transfer in the technological drive toward lower weight/smaller volume electrical and electronic devices. It is also found that the circular VGs offer the best heat performance among the proposed shapes

A practical evaluation of the performance of Al2O3-water, TiO2-water and CuO-water nanofluids for convective cooling

The convective heat transfer, pressure drop and required pumping power for the turbulent flow of Al2O3-water, TiO2-water and CuO-water nanofluids in a heated, horizontal tube with a constant heat flux are investigated experimentally. Results show that presenting nanofluid performance by the popular approach of plotting Nusselt number versus Reynolds number is misleading and can create the impression that nanofluids enhance heat transfer efficiency. This approach is shown to be problematic since both Nusselt number and Reynolds number are functions of nanofluid concentration. When results are presented in terms of actual heat transfer coefficient or tube temperature versus flow rate or pressure drop, adding nanoparticles to the water is shown to degrade heat transfer for all the nanofluids and under all conditions considered. Replacing water with nanofluid at the same flow rate reduces the convective heat transfer rate by reducing the operating Reynolds number of the system. Achieving a target temperature under a given heat load is shown to require significantly higher flow rates and pumping power when using nanofluids compared to water, and hence none of the nanofluids are found to offer any practical benefits

Understanding the Mechanism of Load-Carrying Capacity between Parallel Rough Surfaces through a Deterministic Mixed Lubrication Model

Experimental results have confirmed that parallel rough surfaces can be separated by a full fluid film. However, such a lift-off effect is not expected by the traditional Reynolds theory. This paper proposes a deterministic mixed lubrication model to understand the mechanism of the lift-off effect. The proposed model considered the interaction between asperities and the micro-elastohydrodynamic lubrication (micro-EHL) at asperities within parallel rough surfaces for the first time. The proposed model is verified by predicting the measured Stribeck curve taken from literature and experiments conducted in this work. The simulation results highlight that the micro-EHL effect at the asperity scale is critical in building load-carrying capacity between parallel rough surfaces. Finally, the drawbacks of the proposed model are addressed and the directions of future research are pointed out