Analytical Modelling of Laminar Developing Flow Between Hydrophobic Surfaces with Different Slip-Velocities

Theoretical analysis of the entrance hydrodynamics of microchannels is an important design aspect in connection with the development of microfluidic devices. In this paper, pressure-driven fluid flow in the entrance region of two infinite hydrophobic parallel plates with dissimilar slip-velocities is analytically modelled. The linearized momentum equation is solved by applying the Navier-slip model at the boundaries to achieve the most generalized two-dimensional form. The velocity profile is obtained by combining the developed and developing velocities, which is estimated by invoking the separation of variable method. It is observed that the velocity profile is asymmetric and the shear-free region can be shifted from the geometrical central line by altering the wall hydrophobicity. Moreover, the zero shear zone is transferred more towards the surface having high hydrophobicity. The expression for wall shear stress is obtained analytically using Newton's law of viscosity. Moreover, the boundary layer growth from the upper and lower walls are found to be entirely different and they merge at the entrance length and is noticed to be off-setted from the geometric centre-line. The effect of slip-length on the entrance length is analysed and an empirical correlation is deduced.

Numerical analysis of a 3-D printed porous trailing edge for broadband noise reduction

Lattice Boltzmann simulations were carried out to investigate the noise mitigation mechanisms of a 3-D printed porous trailing-edge insert, elucidating the link between noise reduction and material permeability. The porous insert is based on a unit cell resembling a lattice of diamond atoms. It replaces the last 20 % chord of a NACA 0018 at zero angle-of-attack. A partially blocked insert is considered by adding a solid partition between 84 % and 96 % of the aerofoil chord. The regular porous insert achieves a substantial noise reduction at low frequencies, although a slight noise increase is found at high frequencies. The partially blocked porous insert exhibits a lower noise reduction level, but the noise emission at mid-to-high frequency is slightly affected. The segment of the porous insert near the tip plays a dominant role in promoting noise mitigation, whereas the solid-porous junction contributes, in addition to the rough surface, towards the high-frequency excess noise. The current study demonstrates the existence of an entrance length associated with the porous material geometry, which is linked to the pressure release process that is responsible for promoting noise mitigation. This process is characterised by the aerodynamic interaction between pressure fluctuations across the porous medium, which is found at locations where the porous insert thickness is less than twice the entrance length. Present results also suggest that the noise attenuation level is related to both the chordwise extent of the porous insert and the streamwise turbulent length scale. The porous inserts also cause a slight drag increase compared to their solid counterpart.

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.

Mass transfer in 3D printed electrolyzers: The importance of inlet effects

This paper investigates the effect of inlet shape, entrance length and turbulence promoters on mass transfer by using 3D printed electrolyzers. Our results show that the inlet design can promote turbulence and lead to an earlier transition to turbulent flow. The Reynolds number at which the transition occurs can be predicted by the ratio of the cross-sectional area of the inlet to the cross-sectional area of the electrolyzer channel. A longer entrance length results in more laminar behavior and a later transition to turbulent flow. With an entrance length of 550mm, the inlet design did no longer affect the mass transfer performance significantly. The addition of gyroid type turbulence promoters resulted in a factor 2 to 4 increase in mass transfer depending on inlet design, entrance length and the type of promoter. From one configuration to another, there was a minimal variation in pressure drop (<16 mbar).

Entrance length effects on the flow features of rectangular liquid jets

An experimental study was carried out to investigate the effects of entrance length on the main characteristics of rectangular liquid jets discharged into the stagnant atmosphere. Six rectangular nozzles, all with the same aspect ratio of 3 but with different entrance length ratios ranging from 3.3 to 60 were constructed. The physics of the fluid flows was visualized by the aid of backlight shadowgraph technique and high speed photography. Flow visualizations revealed that in the mid-range of Weber numbers, the perturbations induced over the liquid surface remarkably depended on the entrance length ratio. Moreover, the characteristics of the axis-switching instability of rectangular liquid jets were measured. It was found that axis-switching wavelength was independent of the entrance length, while the amplitude of axis-switching was directly influenced. For entrance length ratios smaller than 10, the amplitude was increased with increase of entrance length, whereas for entrance length ratios higher than 10, this trend was reversed. Measurements of breakup length also showed that the transition of flow regimes was not perceptibly affected by the entrance length.

Entrance length of oscillatory flows in parallel plate microchannels

This paper presents the numerical investigation of the purely oscillatory laminar flows of incompressible Newtonian fluids, in the entrance region of parallel plate microchannels. Development of the axial velocity profiles and the required entrance length were studied in the low Reynolds number regime (20[Formula: see text] 200) and for the low dimensionless oscillation frequency or the Stokes number (1.08 [Formula: see text] 2.80), which is applicable particularly for microchannel flows. To obtain more realistic and applicable results, the time-dependent parabolic entry conditions were considered for all simulations. The results show that for ([Formula: see text]1.53), the entrance length can be estimated by the steady-state results for corresponding inlet velocity profiles, while for the (1.53 [Formula: see text] 2.80), the deviation from the steady-state condition occurs for the entrance length. Further, according to the obtained numerical data, in this work, a useful correlation is proposed to predict the entrance length for the studied ranges of the purely oscillatory flows through the parallel plate microchannels.

Thermally Developing Laminar Liquid Flow and Heat Transfer in Microtubes at Slip Regime

Heat transfer enhancement is usually accompanied by an increase in pressure drop. With the implementation of the various drag reduction methods, the researches and applications of DR methods in heat transfer enhancement have attracted more and more attention. The research on drag reduction by introducing superhydrophobic surface shows that the slip regime plays an important role in drag reduction. This study numerically investigated thermally developing laminar liquid flow and heat transfer in microtubes at slip regime, with a hydraulic diameter of 200 μm, a constant heat flux of 105 W/m2, a Re of 100 and a slip length ls ranging from 2 μm to 20 μm. The dimensionless thermal entrance length increases with the increased slip length. The results show that microtube with slip boundary has the larger local Nusselt number and a longer thermal entrance length compared with available experimental data of non-slip boundary. Local and average Nusselt numbers are obtained, and start high and rapidly decrease with the increased dimensionless axial distance. Meanwhile, Nusselt number increases with the increased slip length. The correlations of the dimensionless thermal entrance length and local Nusselt number have mean absolute relative deviation of no more than 0.12% and 1.53% respectively, which can be used to optimize microchannel heat sinks.

Numerical Investigation to Derive Correlations for Hydrodynamic Entrance Length in Very Low Reynolds Number Regime in Rectangular Microchannels

A three-dimensional laminar flow model was used for 37 Reynolds numbers (0.1, 0.2…1, 2…10, 20…100, and 200…1000) through six rectangular microchannels (aspect ratios: 1, 0.75, 0.5, 0.25, 0.2, and 0.125) to develop correlations for hydrodynamic entrance length. The majority of the Reynolds numbers are in the low regime (Re &lt; 100) to fulfill the need to determine the hydrodynamic entrance length for microchannels. Examination of the fully developed flow condition was considered using the velocity or fRe criteria. Numerical results from the present simulations were validated by comparing the fRe results. Two new correlations were developed from a vast amount of numerical data (222 simulations). The velocity criterion correlations predict entrance length with a mean error of 4.67% and maximum error of 10.28%. The fRe criterion generated better correlations and were developed as a function of aspect ratio to predict entrance length with a mean error less than 2% and maximum error of 5.75% for 0.1 ≤ Re ≤ 1000 and 0 ≤ α ≤ ∞.