Mixing length Research Papers

A Computational Study of Turbulent Structure Formation

2024

Direct Numerical Simulation of channel flow was utilized to study the evolution of various vortex configurations presented as flow initial conditions. Simulations of longitudinally, laterally and cross-flow oriented vortices suggested... more

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Investigation of Transition to Turbulence in Natural Convection

by hossein Vasheghani Farahani

2024

Based on the book "Convection Heat Transfer" by Adrian Bejan, this study examines the transition time of flow from laminar to turbulent in natural convection near turbulent walls. The presented analysis investigates the hydrodynamic... more

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Thermally Driven Mass Flows in the Convection Zone of the Sun

by Geert Dijkhuis

2024, Ph.D. Thesis, Stanford University, California, USA

In this dissertation a formulation of the fluid dynamics of convective regions is developed which leads to an analytic description of the solar rotation, the Evershed flow and the supergranulation. The starting point of the present... more

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A Computational Study of Turbulent Structure Formation

by Anthony Linn

2023

Direct Numerical Simulation of channel flow was utilized to study the evolution of various vortex configurations presented as flow initial conditions. Simulations of longitudinally, laterally and cross-flow oriented vortices suggested... more

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Dynamics of liquid–liquid flows in horizontal pipes using simultaneous two–line planar laser–induced fluorescence and particle velocimetry

by Christos N Markides

2023, International Journal of Multiphase Flow

Experimental investigations are reported of stratified and stratified-wavy oil-water flows in horizontal pipes, based on the development and application of a novel simultaneous two-line (two-colour) technique combining planar... more

Experimental investigations are reported of stratified and stratified-wavy oil-water flows in horizontal pipes, based on the development and application of a novel simultaneous two-line (two-colour) technique combining planar laser-induced fluorescence with particle image/tracking velocimetry. This approach allows the study of fluid combinations with properties similar to those encountered in industrial field-applications in terms of density, viscosity, and interfacial tension, even though their refractive indices are not matched, and represents the first attempt to obtain detailed, spatiotemporally-resolved, full 2-D planar-field phase and velocity information in such flows. The flow conditions studied span mixture velocities in the range 0.3-0.6 m/s and low water-cuts up to 20%, corresponding to in situ (local) Reynolds numbers of 1750-3350 in the oil phase and 2860-11,650 in the water phase, and covering the laminar/transitional and transitional/turbulent flow regimes for the oil and water phases, respectively. Detailed, spatiotemporally-resolved in situ phase and velocity data in a vertical plane aligned with the pipe centreline and extending across the entire height of the channel through both phases are analysed to provide statistical information on the interface heights, mean axial and radial (vertical) velocity components, (rms) velocity fluctuations, Reynolds stresses, and mixing lengths. The mean liquid-liquid interface height is mainly determined by the flow water cut and is relatively insensitive (up to 20% the highest water cut) to changes in the mixture velocity, although as the mixture velocity increases the interfacial profile transitions gradually from being relatively flat to containing higher amplitude waves. The mean velocity profiles show characteristics of both laminar and turbulent flow, and interesting interactions between the two co-flowing phases. In general, mean axial velocity profiles in the water phase collapse to some extent for a given water cut when normalised by the mixture velocity; conversely, profiles in the oil phase do not. Strong vertical velocity components can modify the shape of the axial velocity profiles. The axial turbulence intensity in the bulk of the water layer amounts to about 10% of the peak mean axial velocity in the studied flow conditions. In the oil phase, the axial turbulence intensity increases from low values to about 10% at the higher Reynolds numbers, perhaps due to transition from laminar to turbulent flow. The turbulence intensity showed peaks in regions of high shear, i.e., close to the pipe wall, and at the liquid-liquid interface. The development of the mixing length in the water phase, and also above the liquid-liquid interface in the oil phase, agrees reasonably well with predicted variations described by the von Karman constant. Finally, evidence of secondary flow structures both above and below the interface exists in the vertical velocity profiles, which is of interest to explore further.

Fig. 1. Schematic of the TOWER flow facility (FT: turbine flowmeter, TT: tempera- ture transducer, DPT differential pressure transducer, PT: pressure transducer).

Fig. 2. TOWER inlet section design, where D and H denote the internal diameter and the clearance height of the splitter plate above the bottom of the pipe; here H/D=0.31.

Fig. 3. Optical diagnostic technique schematics: (a) laser sheet arrangement at the measurement section, and (b) high-speed camera arrangement. (For interpretation of the references to colour in this figure, the reader is referred to the web version of this article.)

Fig. 5. Example of the water phase velocity vector field obtained from: (a) PIV and (b) PTV, for conditions: Um =0.3 m/s, WC=20%, and a 1-kHz image acquisition frequency.

Fig. 7. (a) Time-averaged water layer height (interface level) relative to the bottom of the pipe, (hw), and (b) interface height fluctuation or rms normalised by the pipe diameter, D, as a function of water cut, WC, for different mixture velocities, Um.

Fig. 8. Temporal evolution of the interface and probability histograms for WC=20% and mixture velocities of: (a) Um =0.4m/s, (b) Um =0.5 m/s, and (c) Um =0.6 m/:

Fig. 9. Interface temporal evolution PSD for different mixture velocities, Um, and WC =20%.

Fig. 11. Normalised mean: (a) axial velocity profiles, and (b) vertical velocity profiles, at different water cuts for Um, =0.3m/s (Reo =1750, Rew =2860 for WC=5%; Regi = 1810, Rew =4140 for WC=10%; Regi = 1850, Rew =5820 for WC=20%). The in situ interface positions for all flows can be found in Fig. 7, and these generally match the velocity gradient discontinuities at y/D ~ 0.08-0.09, 0.16-0.17, 0.26-0.30 for WC=5, 10, 20%, respectively.

Fig. 12. Normalised mean axial (a) and (b) and vertical (c) and (d) velocity profiles, at different WC with U, =0.4m/s (a) and (c), and different Un with WC= 10% (b) a (d).

Fig. 14. Axial turbulence intensity at different Re, or Um, and a WC of: (a) and (c) 10%, and (b) and (d) 20%, normalised by the peak mean velocity, Umax, (a), (b) and loc. mean axial velocity, (u) (c), (d).

Fig. 15. Vertical turbulence intensity at different Re, or Um, and a WC of: (a) 10%, and (b) 20%.

Fig. 16. Reynolds stress (u’v’) normalised by the square of the corresponding mixture velocity, Um, at different Re, or Um, and a WC of: (a) 10%, and (b) 20%

Fig. 17. (a-c) Comparison of the Reynolds stress, (u’v’), and viscous shear-stress, T,;, = — {40 (u)/dy, normalised by the square of the mixture velocity, Um, at different Re, or Um, and WC= 20%.

Fig. 18. (a) Axial, and (b) vertical normal stresses normalised by the square of the mixture velocity, Um, at different Re, or Um, and WC= 20%

Fig. 19. Mixing length profiles for different Re, or Um, at WC=10%, and predictions based on the von Karman constant (k=0.41) shown as the black solid lines ‘1’, ‘2’ anc 37.

‘ig. 20. Mixing length profiles for different Re, or Um, at WC=20%, and predictions based on the von Karman constant (k=0.41) shown as the black solid lines ‘1’, ‘2’ anc 3".

Fig. 21. Velocity field normalisation based on the mean water-layer or interface height, (hw).

Physical properties of the test liquids. Table 1

Inlet mixture velocities, water cuts and corresponding in situ Reynolds number: (see text for all definitions) for the experimental condition envelope investigated ir this work.

Coefficients for the mixing length prediction approach. Table 3 sponding predictions based on the von Karman constant (k=0.41), which are shown as straight solid lines labelled ‘1’, ‘2’ and ‘3’. Mix- ing length predictions have the form Im =nk(y-yo) where coeffi- cients n and yo are given in Table 3, and are functions of the mean interface height, (hw). The mean interface height for the flow con- ditions in Figs. 19 and 20 is located between y/D=0.16-0.17 for WC= 10% and y/D=0.26-0.30 for WC= 20%, depending on the flow condition (see Fig. 7).

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Impact of mesoscale meteorological processes on anomalous radar propagation conditions over the northern Adriatic area

by Mladen Viher

2023, Journal of Geophysical Research: Atmospheres

The impact of mesoscale structures on the occurrence of anomalous propagation (AP) conditions for radio waves, including ducts, superrefractive, and subrefractive conditions, was studied. The chosen meteorological situations are the bora... more

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Characterization of micromixing in a Continuous Oscillatory Baffled Reactor

by Martine POUX

2023

Micromixing is the limiting step in the progress of fast reactions and fast crystallization processes. Micromixing performance of a Nitech© glass COBR has been characterized using the competing parallel iodide-iodate test reactions.... more

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A Tesla Valve as a Micromixer for Fe3O4 Nanoparticles

by Theodoros Karakasidis

2023, Processes

A large number of microfluidic applications are based on effective mixing. In the application of water purification, the contaminated water needs to be effectively mixed with a solution that is loaded with nanoparticles. In this work, the... more

Figure 5. Streamlines into the micromixer for velocity ratios equal to (a) Vp/Ve = 20, (b) Vp/Vc = 10, and (c) Vp/V¢- = 1.

Figure 4. Mixing efficiency for Vp /V-=10 and Vp /V. = 20 under inlet rates equal to 500, 1000, and 3000 nanoparticles per second.

Figure 1. Micromixer geometry and nanoparticles, contaminated water inlets, and outlet flow directions. Bn a , — = The inlet and the outlet of the micromixer was a squared cross-section with rien and width of W = H = 10-4 m. The angle of 8 = 30° and the length ratio of Ly /L2 = were selected from an existing Tesla structure [21]. In addition, properties of Fe3O4 were numerically embedded in the simulations. The values of these properties found from the literature correspond to a density equal to 5180 kg/m? [28], Poisson’s ratio equal to 0.31, and Young’s modulus of 200 x 10? Pa [29]. Determination of the selection of nanoparticle diameters was based on Chang and Chen [30]. Successful removal of heavy metal ions was achieved within 1 min for monodisperse Fe304 magnetic nanoparticles having a mean diameter size of 13.5 nm. In addition, an even lower time (30 s) of adsorption equilibrium was achieved [31], which is encouraging for the mixing length of the microfluidic devices. The two water streams enter the micromixer from different inlets, are mixed, and the leave the domain from the common outlet, as shown in Figure 1.

4 ae ol The OpenFoam platform is used for the calculation of the flow field and correction method. Upon finding the flow field, pressure, and velocity, particles is evaluated by the Lagrangian method. The equations are evolved in time by Euler’s time marching method. An unstructured computational grid composed of 96,88 (tetrahedra) cells was used here, as shown in Figure 2, which is adequa Reynolds number of the flow. However, the selectivity of the mesh based on the importance of geometric and operating parameters was assessed to obtain a significant number of the uncoupled equations of particle motion [33,34]. The simulation process reads as follow: initially, the fluid flow is found using the incompressible Navier-Stokes equations and the pressure he motion of e for the low computational predictions in a reasonable time without compromising the validity of the results [19]. In the current project, the mixing efficiency was evaluated. The mixing efficiency (n) is alculated as follows [35]:

Figure 3. Distribution of nanoparticles (diameter = 13.5 nm) in the micromixer for a rate equal to 1000 nanoparticles per second under (a) Vp/Ve = 20, (b) Vp/Ve = 10, and (c) Vp/Ve = 1.

Figure 6. Streamlines into the micromixer for the velocity ratio equal Vp /V_ = 20 for the longest inlet. Further simulations with a diameter increase in nanoparticles were performed for nanoparticles having a diameter set to 27 nm, which is double that of the above simulations. The difference in mixing efficiency between different diameters of nanoparticles for various inlet conditions is presented in Figure 7. The mixing difference is imperceptible, as shown below. For lower inlet rates, the difference is slightly lower. Moreover, for higher inlet velocity ratios, the difference is minimized.

Table 1. Characteristics and mixing efficiency of different Tesla-type micromixers.

Table 2. Comparison of the present results against experimental and simulation results from Ref. [27]. Investigation was carried out of nanofluid flow through a microchannel subjected to various effects [11]. The slow water flow in the micromixer duct was expected to be laminar and steady-state. The selection among the different Tesla mixing units was made with the criterion that the specific geometry has been studied less compared to those in Table 1.

Table 3. Parameters during the simulations. Simulations were divided into two main parts, which were the evaluation of the velocity and pressure field, and the particle distribution into the micromixer. Initially, from the variance in the fluids, a cross-section of the microchannel parallel to the flow direction [37] was evaluated for Vp/V¢ = 20, Vp/Vc = 10, and Vp/V¢- = 1. Under higher velocity ratios, the velocity field decreases inside the duct, which arises from the comparison of the selected velocity ratios. This decrease is not proportional to the increase in the velocity ratio. The rate of nanoparticles remained constant for the entire simulations. Part of the present results are visualized in Figure 3. From simulation results shown in Figure 3a-—c, the inlet rate was equal to 1000 Fe3O4 nanoparticles per second in the upper half inlet of the micromixer. Hence, the only difference between 3a, 3b, and 3c is the inlet velocity ratio. Under Vp/V¢- = 20 (3a) and Vp/V- = 10 (3b), the distribution is satisfied, as observed from the beginning of the micromixer. In the first loop (upper part of the micromixer), the distribution of the nanoparticles is uniform, whereas in the second loop (lower part of the micromixer), the distribution is not satisfied. Near the common outlet, a very satisfying distribution is observed. It should be noted that, in the present simulations, only two Tesla valves were used in series compared to previous works, as shown in Table 1. However, under Vp/V¢ = 1 (3c), no mixing was observed inside the whole length of the micromixer. Moreover, the results were almost identical when the inlet rates of Fe3O4 nanoparticles (diameter = 13.5 nm) were either 1000/s or 3000/s for both velocity ratios.

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Simulations of Tesla Valve Micromixer for Water Purification with Fe3O4 Nanoparticles

by Theodoros Karakasidis

2023, EWaS5

This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY

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Rapid mixing in micromixers using magnetic field

by Alireza Zabihihesari

2018

In this paper, the rapid mixing of deionized water and Fe 3 O 4 ferrofluid in a Y-shaped microchannel using a permanent magnet is studied both numerically and experimentally. The microchannel has a rectangular cross section with 500 m in... more

Fig. 1. Components of the experimental setup. above-mentioned studies did not investigate the effects of magnet field’s strength, flow rate and nanoparticles mass fraction on the mixing length. Furthermore, the effect of nanoparticles mass frac- tion on the mixing efficiency was not studied. All of these effects are examined and discussed in this paper. The process, assumed to be two-dimensional and steady state, is simulated by COMSOL numer- ical software. In the numerical simulation, the Maxwell equations are solved to obtain the magnetic potential. Then, the magnetic force can be calculated. Obtaining the magnetic force, the fluid flow equations including continuity and the Navier-Stokes equa- tions along with an equation for transport-diffusion are solved. The effects of magnetic field’s strength, mass fraction of nanoparticles, and volume flow rate of mixing fluids on the mixing efficiency and mixing length are investigated to predict the micromixer perfor- mance under various conditions.

Fig. 2. a) A top view of the Y-shaped micro-mixer, b) A schematic view of the investigated domain. the body forces (here, magnetic forces) exerted on the fluid per unit volume(N/m?). Other body forces including buoyancy and interac- tion forces between particles are negligible since the nanoparticle content of the fluid is not significant. density and viscosity of the mixture are obtained from the following relations [8].

Fig. 4. Comparison of the numerical and experimental mixing efficiency along the mixing channel. Fig. 3. Time evolution of the mixing process for a flow rate of 60 cc/min in the mixing channel and a nanoparticle mass fraction of 0.05. a) A magnetic field of 3000G was applied and capturing photographs were started at t=0. b) The mixing fluids passed the channel and capturing photographs were started at t=0 without the magnet.

Fig. 5. Concentration distribution for a length of 8mm at the end of microchannel for different magnetic field’s strengths.

Fig. 7. The effect of magnetic field’s strength on the mixing length. Fig. 6. The effect of magnetic field’s strength on the mixing efficiency along the microchannel.

Fig. 9. The effect of flow rate on the mixing efficiency along the microchannel. Fig. 8. Concentration distribution for a length of 8mm at the end of microchannel for several flow rates.

Fig. 10. The effect of flow rate on the mixing length.

Fig. 12. The effect of nanoparticle mass fraction on the mixing efficiency along the microchannel. Fig. 11. Concentration distribution for a length of 8 mm at the end of microchannel for various mass fraction of nanoparticles.

Fig. 13. The effect of nanoparticles mass fraction on the mixing length.

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