Function Of Channel Aspect Ratio Research Articles

Re-examining log law velocity profile in smooth open channel flows

A comprehensive investigation of velocity distribution is presented, and the log law is re-examined using experimental data from a smooth uniform open channel flow. It is widely reported that the coefficients of the log law in channel flows deviate from those obtained from circular pipe flows by Nikuradse (Laws of flow in rough pipes, 1933), but the mechanism is not clear and no theoretical formulae are available to express these deviations. A Laser Doppler Velocimetry system was used to measure velocity profiles at the centre of the channel. The data obtained support previous conclusions that the additive constant B of the log law in channel flows can no longer be considered to be 5.5. Interestingly, the experimental data also support Tracy and Lester’s discovery that the shear velocities on both sides of the log law are different. Better agreement can be achieved if the global shear velocity (U*1) is used to normalize the measured velocity, and the local shear velocity (U*2) is used to normalize the distance from the wall. Other researchers’ data in the literature also validates this new relationship. Based on this new relationship, a theoretical value of B is obtained, which agrees well with the observed B, thus a new form of log law for channel flow is suggested. The new relationship developed was verified with present experimental and past literature data suggesting its universality irrespective of wide or narrow open channels, or subcritical or super critical flow conditions. By using the developed relationship the large scatter associated with the additive constant B associated with the log law has been explained. It is found that the additive constant B in the log law is a function of channel aspect ratio. The developed relationship for B is validated from a wide range of data from the literature to confirm its universality.

Hydrodynamic focusing and interdistance control of particle-laden flow for microflow cytometry

Single-file focusing and minimum interdistance of micron-size objects in a sample is a prerequisite for accurate flow cytometry measurements. Here, we report analytical models for predicting the focused width of a sample stream b as a function of channel aspect ratio α, sheath-to-sample flow rate ratio f and viscosity ratio λ in both 2D and 3D focusing. We present another analytical model to predict spacing between an adjacent pair of objects in a focused sample stream as a function of sample concentration C, mobility ϕ of the objects in the prefocused and postfocused regions and flow rate ratio f in both 2D and 3D flow focusing. Numerical simulations are performed using Ansys Fluent VOF model to predict the width of sample stream in 2D and 3D hydrodynamic focusing for different sample-to-sheath viscosity ratios, aspect ratios and flow rate ratios. Experiments are performed on both planar and three-dimensional devices fabricated in PDMS to demonstrate focusing of sample stream and spacing of polystyrene beads in the unfocused and focused stream at different sample concentrations C. The predictions of the analytical model and simulations are compared with experimental data, and a good match is found (within 12 %). Further, mobility of objects is experimentally studied in 2D and 3D focusing, and the spread of the mobility data is used as tool for the demonstration of particle focusing in flow cytometer applications.

Numerical Investigation of Heat Transfer in Rectangular Microchannels Under H2 Boundary Condition During Developing and Fully Developed Laminar Flow

Study of fluid flow characteristics at microscale is gaining importance with shrinking device sizes. Better understanding of fluid flow and heat transfer in microchannels will have important implications in electronic chip cooling, heat exchangers, MEMS, and microfluidic devices. Due to short lengths employed in microchannels, entrance header effects can be significant and need to be investigated. In this work, three dimensional model of microchannels, with aspect ratios (α = a/b) ranging from 0.1 to 10, are numerically simulated using CFD software tool fluent. Heat transfer effects in the entrance region of microchannel are presented by plotting average Nusselt number as a function of nondimensional axial length x*. The numerical simulations with both circumferential and axial uniform heat flux (H2) boundary conditions are validated for existing data set for four wall heat flux case. Large numerical data sets are generated in this work for rectangular cross-sectional microchannels with heating on three walls, two opposing walls, one wall, and two adjacent walls under H2 boundary condition. This information can provide better understanding and insight into the transport processes in the microchannels. Although the results are seen as relevant in microscale applications, they are applicable to any sized channels. Based on the numerical results obtained for the whole range, generalized correlations for Nusselt numbers as a function of channel aspect ratio are presented for all the cases. The predicted correlations for Nusselt numbers can be very useful resource for the design and optimization of microchannel heat sinks and other microfluidic devices.

Optimisation of a microfluidic analysis chamber for the placement of microelectrodes

The behaviour of droplets entering a microfluidic chamber designed to house microelectrode detectors for real time analysis of clinical microdialysate is described. We have designed an analysis chamber to collect the droplets produced by multiphase flows of oil and artificial cerebral spinal fluid. The coalescence chamber creates a constant aqueous environment ideal for the placement of microelectrodes avoiding the contamination of the microelectrode surface by oil. A stream of alternating light and dark coloured droplets were filmed as they passed through the chamber using a high speed camera. Image analysis of these videos shows the colour change evolution at each point along the chamber length. The flow in the chamber was simulated using the general solution for Poiseuille flow in a rectangular chamber. It is shown that on the centre line the velocity profile is very close to parabolic, and an expression is presented for the ratio between this centre line velocity and the mean flow velocity as a function of channel aspect ratio. If this aspect ratio of width/height is 2, the ratio of flow velocities closely matches that of Poiseuille flow in a circular tube, with implications for connections between microfluidic channels and connection tubing. The droplets are well mixed as the surface tension at the interface with the oil dominates the viscous forces. However once the droplet coalesces with the solution held in the chamber, the no-slip condition at the walls allows Poiseuille flow to take over. The meniscus at the back of the droplet continues to mix the droplet and acts as a piston until the meniscus stops moving. We have found that the no-slip conditions at the walls of the chamber, create a banding effect which records the history of previous drops. The optimal position for sensors is to be placed at the plane of droplet coalescence ideally at the centre of the channel, where there is an abrupt concentration change leading to a response time ≪16 ms, the compressed frame rate of the video. Further away from this point the response time and sensitivity decrease due to convective dispersion.

Heat transfer in trapezoidal microchannels of various aspect ratios

Heat transfer in the thermal entrance region of trapezoidal microchannels is investigated for hydrodynamically fully developed, single-phase, laminar flow with no-slip conditions. Three-dimensional numerical simulations were performed using a finite-volume approach for trapezoidal channels with a wide range of aspect ratios. The sidewall angles of 54.7° and 45° are chosen to correspond to etch-resistant planes in the crystal structure of silicon. Local and average Nusselt numbers are reported as a function of dimensionless length and aspect ratio. The effect of Prandtl number upon the thermal entrance condition is explored. The fully developed friction factors are computed and correlated as a function of channel aspect ratio. Correlations are also developed for the local and average Nusselt numbers in the thermal entrance region as a function of a dimensionless axial length variable.

Confinement effects on nucleate boiling and critical heat flux in buoyancy-driven microchannels

Pool boiling and CHF experiments were performed for vertical, rectangular parallel-plate channels immersed in the dielectric liquid FC-72 at atmospheric pressure to elucidate the effects of geometrical confinement in immersion cooled electronics applications. Heat transfer enhancement in the low flux region of the nucleate boiling curve was observed for channel spacings near and below expected bubble departure diameters, but was widely different for two different heater materials. Relative degradation of CHF with decreasing channel spacing was found to be a strong function of channel aspect ratio and independent of surface material and finish.

Quasi-static liquid–air drainage in narrow channels with variations in the gap

This paper studies the shape of an air bubble quasi-statically flowing in the longitudinal direction of narrow channels. Two bottom topographies are treated, i.e., linear and quadratic variations of the gap along the transverse direction. This work analyses the main characteristics of the gas–liquid interface with respect to the wedge aspect ratio. From the convergence of asymptotic, numerical and experimental analyses, we found simple dependences for the finger width and total curvature as a function of channel aspect ratio. These results provide simple and general expressions for the pressure drop needed to overcome capillary forces and push the air finger inside the channel.

FLOW DEVELOPMENT OF CO-FLOWING STREAMS IN RECTANGULAR MICRO-CHANNELS

The diffusion and flow development characteristics of two co-flowing, laminar streams in a high aspect ratio rectangular micro-channel have been examined. A long, thin splitter plate initially separates the two streams such that fully developed flow in each of the two channels is established prior to merging. The co-flowing micro-channel has an aspect ratio of 16 with a width of 1006 μm and a height of 63 μm. Micro-Particle Image Velocimetry (μPIV) was utilized to observe the interaction between the streams for a range of flow rate ratios ranging from one to nine, for Reynolds numbers of one and ten. For flow rate ratios greater than one, a cross-stream pressure gradient exists immediately downstream of the splitter plate, which results in a strong lateral flow of the faster moving fluid into the slower moving fluid. Despite this rapid expansion, the fluids in the two streams do not mix. The two streams eventually recover a fully developed velocity profile across the entire channel. A model is presented to predict this development length based on the pressure imbalance between the two streams. The model is expressed in terms of the flow rate ratio between the streams, which is shown to be a function of channel aspect ratio. An asymptotic condition for the development length is found for high flow rate ratios and high aspect ratio channels. It is shown that existing entrance length relationships greatly underpredict this development length.

The flow properties of fluidized solids

Because of the bubbling nature of gas-fluidized beds and the degree of particle—particle interaction occurring within them, it is to be expected that they will exhibit a wide range of flow properties. The general inferences of viscometric studies are outlined and work on the open channel flow behaviour discussed in relation to apparent non-Newtonian flow properties. The study of fluidized bed flow is made more difficult because of its anisotropic nature and the varying degree of influence presented by the distributor and vertical walls on the flow properties. The velocity profile in open channel flow is a function of channel aspect ratio and it can readily be predicted from a power law model for the case where the influence of the distributor is similar to that at the vertical walls.