Mixing Enhancement in a Chaotic Micromixer Using Pulsating Flow

2014 ◽  
Author(s):  
Mohammad Karami ◽  
Mojtaba Jarrahi ◽  
Ebrahim Shirani ◽  
Hassan Peerhossaini
Keyword(s):  
Reynolds Number ◽  
Lyapunov Exponent ◽  
Steady Flow ◽  
Concentration Distribution ◽  
Pulsating Flow ◽  
Chaotic Advection ◽  
Mixing Enhancement ◽  
Mean Flow ◽  
Number Range ◽  
Velocity Amplitude

This study determines the simultaneous effects of spatial disturbance and flow pulsation on micromixing by using three different metrics: concentration distribution, Lyapunov exponent and axial vorticity. Numerical simulations are performed for both steady and pulsating flows through a microchannel made up of C-curved repeating units. Moreover, a straight microchannel is analyzed to compare the effects of chaotic advection and molecular diffusion, the main mechanisms of transverse mixing in the chaotic and straight mixer respectively. Simulations are carried out in the steady flow for the Reynolds number range 1≤Re≤50 and in the pulsating flow for velocity amplitude ratios 1≤β≤2.5, and the ratio of the peak oscillatory velocity component to the mean flow velocity, Strouhal numbers 0.1≤St≤0.5. It was found that chaotic advection improves mixing without significant increase in pressure drop. The analysis of concentration distribution implied that full mixing occurs after Reynolds number 50 in the steady flow. When the flow is pulsatile, small and moderate values of the Strouhal number (0.1≤St≤0.3) and high values of velocity amplitude ratio (β ≥ 2) are favorable conditions for mixing enhancement. Moreover, mixing has an oscillating trend along the microchannel due to the coexistence of regular and chaotic zones in the fluid. These results correlate closely with those obtained using two other metrics, analysis of the Lyapunov exponent and axial vorticity.

Mixing by Time-Dependent Orbits in Spatiotemporal Chaotic Advection

2014 ◽  
Vol 137 (1) ◽  
Author(s):  
Mohammad Karami ◽  
Ebrahim Shirani ◽  
Mojtaba Jarrahi ◽  
Hassan Peerhossaini
Keyword(s):  
Secondary Flow ◽  
Lyapunov Exponents ◽  
Amplitude Ratio ◽  
Flow Patterns ◽  
Chaotic Advection ◽  
Mixing Enhancement ◽  
Flow Pulsation ◽  
Mean Flow ◽  
Homoclinic Connections ◽  
Vorticity Vector

The simultaneous effects of flow pulsation and geometrical perturbation on laminar mixing in curved ducts have been numerically studied by three different metrics: analysis of the secondary flow patterns, Lyapunov exponents and vorticity vector analysis. The mixer that creates the flow pulsation and geometrical perturbations in these simulations is a twisted duct consisting of three bends; the angle between the curvature planes of successive bends is 90 deg. Both steady and pulsating flows are considered. In the steady case, analysis of secondary flow patterns showed that homoclinic connections appear and become prominent at large Reynolds numbers. In the pulsatile flow, homoclinic and heteroclinic connections appear by increasing β, the ratio of the peak oscillatory velocity component of the mean flow velocity. Moreover, sharp variations in the secondary flow structure are observed over an oscillation cycle for high values of β. These variations are reduced and the homoclinic connections disappear at high Womersley numbers. We show that small and moderate values of the Womersley number (6 ≤ α ≤ 10) and high values of velocity amplitude ratio (β ≥ 2) provide a better mixing than that in the steady flow. These results correlate closely with those obtained using two other metrics, analysis of the Lyapunov exponents and vorticity vector. It is shown that the increase in the Lyapunov exponents, and thus mixing enhancement, is due to the formation of homoclinic and heteroclinic connections.

Measurement of Steady-Flow Instability and Turbulence Levels in Dacron Vascular Grafts

1992 ◽  
Vol 114 (4) ◽  
pp. 521-526 ◽  
Author(s):  
D. G. Shombert
Keyword(s):  
Reynolds Number ◽  
Pressure Drop ◽  
Steady Flow ◽  
Flow Instability ◽  
Dynamic Properties ◽  
Fluid Dynamic ◽  
Vascular Grafts ◽  
Turbulent Regime ◽  
Number Range ◽  
Measured Transition

Fluid dynamic properties of Dacron vascular grafts were studied under controlled steady-flow conditions over a Reynolds number range of 800 to 4500. Knitted and woven grafts having nominal diameters of 6 mm and 10 mm were studied. Thermal anemometry was used to measure centerline velocity at the downstream end of the graft; pressure drop across the graft was also measured. Transition from laminar flow to turbulent flow was observed, and turbulence intensity and turbulent stresses (Reynolds normal stresses) were measured in the turbulent regime. Knitted grafts were found to have greater pressure drop than the woven grafts, and one sample was found to have a critical Reynolds number (Rc) of less than one-half the value of Rc for a smooth-walled tube.

scholarly journals Effects of Channel Wall Twisting on the Mixing in a T-Shaped Micro-Channel

2019 ◽  
Author(s):  
Dong Jin Kang
Keyword(s):  
Reynolds Number ◽  
Cross Section ◽  
Channel Wall ◽  
Numerical Study ◽  
Twist Angle ◽  
Mixing Enhancement ◽  
Micro Channel ◽  
Number Range ◽  
Mixing Performance ◽  
Two Fluids

A new design scheme is proposed for twisting the walls of a microchannel, and its performance is demonstrated numerically. The numerical study was carried out for a T-shaped microchannel with twist angles in the range of 0 to 34π. The Reynolds number range was 0.15 to 6. The T-shaped microchannel consists of two inlet branches and an outlet branch. The mixing performance was analyzed in terms of the degree of mixing and relative mixing cost. All numerical results show that the twisting scheme is an effective way to enhance the mixing in a T-shaped microchannel. The mixing enhancement is realized by the swirling of two fluids in the cross section and is more prominent as the Reynolds number decreases. The twist angle was optimized to maximize the DOM, which increases with the length of the outlet branch. The twist angle was also optimized in terms of the relative mixing. The two optimum twisting angles are generally not coincident. The optimum twist angle shows a dependence on the length of the outlet branch but it is not affected much by the Reynolds number.

Axially homogeneous, zero mean flow buoyancy-driven turbulence in a vertical pipe

2009 ◽  
Vol 621 ◽  
pp. 69-102 ◽  
Author(s):  
MURALI R. CHOLEMARI ◽  
JAYWANT H. ARAKERI
Keyword(s):  
Reynolds Number ◽  
Rayleigh Number ◽  
Turbulent Flow ◽  
Density Gradient ◽  
Schmidt Number ◽  
Shear Stresses ◽  
Mean Flow ◽  
Vertical Pipe ◽  
Velocity Correlation ◽  
Number Range

We report an experimental study of a new type of turbulent flow that is driven purely by buoyancy. The flow is due to an unstable density difference, created using brine and water, across the ends of a long (length/diameter=9) vertical pipe. The Schmidt number Sc is 670, and the Rayleigh number (Ra) based on the density gradient and diameter is about 108. Under these conditions the convection is turbulent, and the time-averaged velocity at any point is ‘zero’. The Reynolds number based on the Taylor microscale, Reλ, is about 65. The pipe is long enough for there to be an axially homogeneous region, with a linear density gradient, about 6–7 diameters long in the midlength of the pipe. In the absence of a mean flow and, therefore, mean shear, turbulence is sustained just by buoyancy. The flow can be thus considered to be an axially homogeneous turbulent natural convection driven by a constant (unstable) density gradient. We characterize the flow using flow visualization and particle image velocimetry (PIV). Measurements show that the mean velocities and the Reynolds shear stresses are zero across the cross-section; the root mean squared (r.m.s.) of the vertical velocity is larger than those of the lateral velocities (by about one and half times at the pipe axis). We identify some features of the turbulent flow using velocity correlation maps and the probability density functions of velocities and velocity differences. The flow away from the wall, affected mainly by buoyancy, consists of vertically moving fluid masses continually colliding and interacting, while the flow near the wall appears similar to that in wall-bound shear-free turbulence. The turbulence is anisotropic, with the anisotropy increasing to large values as the wall is approached. A mixing length model with the diameter of the pipe as the length scale predicts well the scalings for velocity fluctuations and the flux. This model implies that the Nusselt number would scale as Ra1/2Sc1/2, and the Reynolds number would scale as Ra1/2Sc−1/2. The velocity and the flux measurements appear to be consistent with the Ra1/2 scaling, although it must be pointed out that the Rayleigh number range was less than 10. The Schmidt number was not varied to check the Sc scaling. The fluxes and the Reynolds numbers obtained in the present configuration are much higher compared to what would be obtained in Rayleigh–Bénard (R–B) convection for similar density differences.

scholarly journals Effects of Channel Wall Twisting on the Mixing in a T-Shaped Micro-Channel

Micromachines ◽  
2019 ◽  
Vol 11 (1) ◽  
pp. 26 ◽  
Author(s):  
Dong Jin Kang
Keyword(s):  
Reynolds Number ◽  
Cross Section ◽  
Channel Wall ◽  
Numerical Study ◽  
Twist Angle ◽  
Mixing Enhancement ◽  
Micro Channel ◽  
Number Range ◽  
Mixing Performance ◽  
Two Fluids

A new design scheme is proposed for twisting the walls of a microchannel, and its performance is demonstrated numerically. The numerical study was carried out for a T-shaped microchannel with twist angles in the range of 0 to 34π. The Reynolds number range was 0.15 to 6. The T-shaped microchannel consists of two inlet branches and an outlet branch. The mixing performance was analyzed in terms of the degree of mixing and relative mixing cost. All numerical results show that the twisting scheme is an effective way to enhance the mixing in a T-shaped microchannel. The mixing enhancement is realized by the swirling of two fluids in the cross section and is more prominent as the Reynolds number decreases. The twist angle was optimized to maximize the degree of mixing (DOM), which increases with the length of the outlet branch. The twist angle was also optimized in terms of the relative mixing cost (MC). The two optimum twisting angles are generally not coincident. The optimum twist angle shows a dependence on the length of the outlet branch but it is not affected much by the Reynolds number.

Steady flows in rectangular cavities

1967 ◽  
Vol 28 (4) ◽  
pp. 643-655 ◽  
Author(s):  
Frank Pan ◽  
Andreas Acrivos
Keyword(s):  
Reynolds Number ◽  
Steady Flow ◽  
Creeping Flow ◽  
Large Reynolds Number ◽  
Steady Flows ◽  
Viscous Effects ◽  
Number Range ◽  
Infinite Depth ◽  
Aspect Ratios ◽  
High Reynolds

This paper deals with the steady flow in a rectangular cavity where the motion is driven by the uniform translation of the top wall. Creeping flow solutions for cavities having aspect ratios from ¼ to 5 were obtained numerically by a relaxation technique and were shown to compare favourably with Dean & Montagnon's (1949) similarity solution, as extended by Moffatt (1964), in the region near the bottom corners of a square cavity as well as throughout the major portion of a cavity with aspect ratio equal to 5. In addition, for a Reynolds number range from 20 to 4000, flow patterns were determined experimentally by means of a photographic technique for finite cavities, as well as for cavities of effectively infinite depth. These experimental results suggest that, within finite cavities, the high Reynolds number steady flow should consist essentially of a single inviscid core of uniform vorticity with viscous effects being confined to thin shear layers near the boundaries, while, for cavities of infinite depth, the viscous and inertia forces should remain of comparable magnitude throughout the whole domain even in the limit of very large Reynolds number R.

Chaotic Heat Transfer in a Laminar Pulsating Flow With Constant Wall Temperature

2014 ◽  
Author(s):  
Mohammad Karami ◽  
Mojtaba Jarrahi ◽  
Zahra Habibi ◽  
Ebrahim Shirani ◽  
Hassan Peerhossaini
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Heat Transfer Enhancement ◽  
Secondary Flow ◽  
Wall Temperature ◽  
Pulsating Flow ◽  
Mean Flow ◽  
Transfer Enhancement ◽  
Constant Wall Temperature ◽  
Homoclinic Connections

The correlation between heat transfer enhancement and secondary flow structures in laminar flows through a chaotic heat exchanger is discussed. The geometry consists of three bends; the angle between curvature planes of successive bends is 90°. Numerical simulations are performed for both steady and pulsating flows when the walls are subjected to a constant temperature. The temperature profiles and secondary flow patterns at the exit of bends are compared in order to characterize the flow. Simulations are carried out for the Reynolds numbers range 300≤Re≤800, velocity amplitude ratios (the ratio of the peak oscillatory velocity component to the mean flow velocity) 1≤β≤2.5, and wall temperatures 310 ≤ Tw(K) ≤ 360. The results show that in the steady flow, heat transfer enhancement occurs with increasing Reynolds number and wall temperature. However, heating homogenization becomes almost independent of Reynolds number when homoclinic connections exist in the flow. Moreover, at high values of wall temperature, heat transfer enhancement is greater than mixing improvement due to the presence of homoclinic connections. In the pulsating flow, Nusselt number improves with β, and β≥2 is a sufficient condition for heat transfer enhancement. The formation and development of homoclinic connections are correlated with the heating homogenization.

Flow Pulsation and Geometry Effects on Mixing of Two Miscible Fluids in Microchannels

2014 ◽  
Vol 136 (12) ◽  
Author(s):  
Houssein Ammar ◽  
Ahmed Ould el Moctar ◽  
Bertrand Garnier ◽  
Hassan Peerhossaini
Keyword(s):  
Reynolds Number ◽  
Residence Time ◽  
Pure Water ◽  
Mixing Efficiency ◽  
Mixing Enhancement ◽  
Flow Pulsation ◽  
Mean Flow ◽  
Mixing Index ◽  
Two Fluids ◽  
Passive Mixing

Many microfluidic applications involve chemical reactions. Most often, the flow is predominantly laminar, and without active or passive mixing enhancement the reaction time can be extremely long compared to the residence time. In this work we demonstrate the merits of the combination of flow pulsation and geometrical characteristics in enhancing mixing efficiency in microchannels. Mixing was studied by introducing a mixing index based on the gray level observed in a heterogeneous flow of pure water and water colored by rhodamine B. The effects of the injection geometry at the microchannel inlet and the use of pulsed flows with average Reynolds numbers between 0.8 and 2 were studied experimentally and numerically. It appeared that the mixing index increases with the nondimensional residence time (τ), which is inversely proportional to the Reynolds number. In addition, we show that the mixing efficiency depends strongly on the geometry of the intersection between the two fluids. Better mixing was achieved with sharp corners (arrowhead and T intersections) in all cases investigated. In pulsed flow, the mixing efficiency is shown to depend strongly on the ratio (β) between the peak amplitude and the mean flow rate. Optimal conditions for mixing in the microchannels are summarized as a function of Reynolds number Re, the ratio β, and the geometries.

scholarly journals Numerical analysis of mixed convection in pulsating flow for a horizontal channel with a cavity heated from below

2016 ◽  
Vol 20 (1) ◽  
pp. 35-44 ◽  
Author(s):  
Fatih Selimefendigil
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Mixed Convection ◽  
Richardson Number ◽  
Amplitude Ratio ◽  
Pulsating Flow ◽  
Pulsation Frequency ◽  
Transfer Enhancement ◽  
Velocity Amplitude

In this study, a channel with a cavity heated from below is numerically investigated for the mixed convection case in pulsating flow for a range of Richardson numbers (Ri=0.1, 1, 10, 100) at Reynolds number of 50 in the laminar flow regime. At the inlet of the channel, pulsating velocity is imposed for Strouhal numbers between 0.1 to 1 and velocity amplitude ratio between 0.3 to 0.9. The effect of the pulsation frequency, amplitude and Richardson number on the heat transfer enhancement is numerically analyzed. The results are presented in terms of streamlines, isotherm plots and averaged Nusselt number plots. FFT plots for the Nusselt number response to single sinusoidal velocity forcing at the inlet and nonlinearity in the response is also provided.

Numerical solutions for steady flow past a circular cylinder at Reynolds numbers up to 100

1970 ◽  
Vol 42 (3) ◽  
pp. 471-489 ◽  
Author(s):  
S. C. R. Dennis ◽  
Gau-Zu Chang
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Steady Flow ◽  
Numerical Solutions ◽  
Equations Of Motion ◽  
Reynolds Numbers ◽  
Reliable Data ◽  
Time Dependent ◽  
Cylinder Surface ◽  
Number Range

Finite-difference solutions of the equations of motion for steady incompressible flow around a circular cylinder have been obtained for a range of Reynolds numbers from R = 5 to R = 100. The object is to extend the Reynolds number range for reliable data on the steady flow, particularly with regard to the growth of the wake. The wake length is found to increase approximately linearly with R over the whole range from the value, just below R = 7, at which it first appears. Calculated values of the drag coefficient, the angle of separation, and the pressure and vorticity distributions over the cylinder surface are presented. The development of these properties with Reynolds number is consistent, but it does not seem possible to predict with any certainty their tendency as R → ∞. The first attempt to obtain the present results was made by integrating the time-dependent equations, but the approach to steady flow was so slow at higher Reynolds numbers that the method was abandoned.

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