Low Reynolds Number Flow Research Articles

Pore-scale simulation on flow and heat transfer characteristics in packed beds with internal heat sources at low Reynolds numbers

Packed beds with internal heat sources are widely used in various engineering applications. But the effects of the internal heat source on the flow and heat transfer in the packed beds received less attention. In this study, the flow and heat transfer characteristics in packed beds with internal heat sources were studied at low Reynolds numbers to assist the design of the solid breeding blanket in the fusion reactors. Through the pore-scale simulations, the local behaviors (including flow velocity, temperature and fluid properties) and macroscopic flow and heat transfer characteristics were analyzed. It was found that with the internal heat sources, the fluid properties vary significantly form the packing inlet to outlet (e.g. the density decreases by 34% and the viscosity increases by 31% in the most). Due to the variations of the fluid density and viscosity, the conventional Ergun and Blake-Kozeny-Macdonald equation do not predict the pressure drop in the packed bed well. Then a modified model by introducing a modified coefficient considering the variable properties is proposed to predict the pressure drop of the packed bed with internal heat sources. The average deviation between the modified pressure drop model and the pore-scale simulation results is only 1.5%. Then a modified heat transfer model was proposed to predict the heat transfer characteristics of the packed bed with internal heat sources at low Reynolds number flow (Re <1.8). The deviations of the predictions by the modified model are within ±30% from the simulation values.

Thermal boundary layer depletion in minichannels by electrohydrodynamic conduction pumping

The article presents a numerical analysis of two-dimensional laminar flow and heat transfer in a minichannel with flat plate electrode pairs periodically flushed to the bottom wall. The two-way coupled governing equations of flow, heat transfer, electric potential and charge conservation are solved using the opensource finite-volume framework of OpenFOAM. Two cases of the minichannel at completely horizontal (case A) and 90° bent (case B) configurations are considered. The inlet laminar flow with Reynolds number varying from 10 to 1000 has been taken into account. The applied electric potential is varied in three steps 0, 0.5 and 1 kV. Electrohydrodynamic (EHD) conduction pumping due to the residual conductivity of the working fluid and the electric-field enhanced dissociation of free charges generate vortices in the proximity of electrodes. The flow and thermal performance of the minichannel in the presence of EHD conduction induced vortices are quantified in terms of pressure drop, Nusselt number and a performance factor (which is a combined function of pressure drop and Nusselt number). The vortices generated by EHD conduction pumping phenomenon deplete the thermal boundary layer, aid mixing and enhance the heat transfer. The mean and local Nusselt numbers are notably increased with only a minimal raise in pressure drop. In both the configurations of the minichannel, the performance factor is greater than 1 for the entire parameter space considered in this study. However, the thermal boundary layer depletion and heat transfer enhancement is prominent at low Reynolds number flows. The maximum drop in performance factor from case A to case B is only 18.5%. Results of this study indicate that EHD conduction pumping is a potential technique to enhance heat transfer in minichannels with minimum additional power consumption.

Influence on the magnetic field on the scale formation in a microfluidic channel under a low Reynolds number flow

This study presents an external magnetic array to rapidly investigate the calcium carbonate formation in a microfluidic channel. The system comprises a copper coil capillary serving as the heat exchanger, a high-precision thermostatic water tank, a magnetic drive pump, and an external magnetic array. Various factors were considered during the experiment, including different concentrations (3 mM and 10 mM) of the test solution, magnetic treatment efficiency (magnet length 4.0 cm and 14.0 cm, treatment time 24 h and 72 h), and temperatures ranging from 25 ℃ to 50 ℃. The concentration of calcium ions, electrical conductivity, and pH value were measured to monitor subtle changes during water treatment. Additionally, particle size distribution and morphology of calcium carbonate were analyzed using SEM and XRD under various magnetic treatments. The experimental results revealed that (1) applying a magnetic field to the solution in a microfluidic channel under low Reynolds number flow led to a decrease in the particle size of calcium carbonate, (2) aragonite did not form in the microfluidic channel, and (3) the physicochemical properties of the solution remained unaltered by the magnetic treatment. Consequently, the reduction in particle size can prevent blockage in microchannels, providing an alternative solution to mitigate scaling issues in micro-heat exchangers.

Effects of annulation on low Reynolds number flows over an orthocone

This study numerically examines the influences of transverse annulation around a cone surface on the characteristics of a flow over an orthocone. This work is inspired by Spyroceras, a fossilized genus of nautiloid cephalopods from the Paleozoic era, whose method of locomotion is understudied. As a baseline case, a flow over a smooth orthoconic model with a blunt cone end is investigated numerically at Reynolds numbers from 500 to 1500. As Reynolds increases, two different shedding mechanisms—hairpin-vortex wake and spiral-vortex wake—are captured. We notice that an introduction of annulation over the cone surface changes the critical Reynolds number for the transition of the shedding mechanism. The dominant shedding frequency increases with the Reynolds number for the smooth and annulated cone flows. Moreover, the annulation reduces the dominant frequency for the same Reynolds number and increases the time-averaged drag coefficient. Modal decompositions—Proper Orthogonal Decomposition (POD) and Spectral Proper Orthogonal Decomposition (SPOD)—are used to capture the coherent structures and their oscillating frequencies. We have captured modes corresponding to the hairpin-vortex wake and spiral-vortex wake shedding mechanisms. Comparing the leading POD modes for the smooth and the annulated cone flows, we find that the annulation can reduce the twisting effects of the coherent structures in the wake. Additionally, we find that the SPOD analysis can identify modes presenting both hairpin-vortex wake and spiral-vortex wake in one flow condition as leading modes, while the POD leading modes only reveal one shedding mechanism in each flow.

Self-learning swimming of a three-disk microrobot in a viscous and stochastic environment using reinforcement learning

Artificial Intelligence (AI) is a novel and fascinating tool in the control of robots. In this study, using a reinforcement learning approach, we have trained an artificial three-disk microrobot in order to learn how to swim at low Reynolds number flow (Re≪1) like the behavior of young microorganisms. Here, as the first contribution, we introduced a discrete model of a novel microswimmer. As the second contribution, we demonstrated that, using the proposed intelligent method, the microswimmer will be able to not only escape the physical constraints of swimming in a viscous medium, but also find the best sequence of actuation to reach the target point in a stochastic environment. The proposed reinforcement learning strategy can be applied to any other type of self-propelled microswimmers consisting of disks and actuators, which swim with continuous state space in a perturbed environment. In the end, we investigated the effect of learning hyperparameters on the performance of the swimmer’s training, and showed that, in the current agent and environment, the optimal values for the discount factor γ and learning rate α are 0.7 and 0.001 respectively which should be properly set for other types of mechanisms and environments.

Vibration for enhancement of electrochemical analysis of biomolecules in a droplet on the rough surface of a disposable working electrode

Although electrochemical detection of microliters-level solutions is attractive for analysis of low-amount biological samples, its performance could be weakened by limited mass transfer due to low Reynolds number and laminar flow. Herein we designed a 3D-printed electroanalytical device to apply vibration for improvement of mass transfer during electrochemical detection. In our approach, the droplet-size sample solution containing Indole-3-acetic acid (IAA, as a model) was directly applied on the effective surface of a disposable working electrode. We demonstrated that vibration could enhance electrochemical responses of IAA more on the rough surface than on the smooth surface of the working electrodes. After optimization, the sensitivity for electrochemical detection of a 20-μL droplet under vibration with the voltage of 7 V increased more than 100% compared with the static condition. The enhanced electrochemical responses brought by vibration could be achieved reproducibly, which could be ascribed to improved mass transfer. Our strategy could be practically applied for differentiation of IAA in different tissues of Marchantia polymorpha with enhanced responses. This study suggested that vibration might become a simple and effective method to improve mass transfer in analysis of microliter-volume solutions, which might be extended for more biochemical assays.

Heat transfer and rheological performance of a phase change dispersion during crystallisation

A phase change dispersion consists of a phase change material dispersed within a continuous fluid, generally water. The phase change material changes from liquid to solid or vice versa whilst releasing or absorbing heat at a nearly constant temperature. Due to the phase change of the dispersed phase, phase change dispersions can be classified as high potential heat transfer fluids that can transport and store heat isothermally. Despite the promise of phase change dispersions the physical mechanisms governing their fundamental heat transfer and rheological behaviour is poorly documented, especially during the crystallisation process. Therefore, this paper reports experimental results on the heat transfer and rheological behaviour of a 16 wt% paraffin-in-water dispersion during crystallisation. Additionally, thermophysical properties and emulsion stability properties are documented. The Nusselt numbers of the phase change dispersion during cooling in low Reynolds number flow conditions were determined to be higher than water at all investigated Reynolds numbers. Furthermore, the observation of a temperature-dependent flow-regime transition at a Reynolds number much below the classical transition for Newtonian fluids was observed and a discussion on the physical mechanisms generating this phenomenon is presented. Additionally, rheological analysis showed that the phase change dispersion is a non-Newtonian fluid, with shear-thinning behaviour, and dynamic viscosities higher than water. As a result an experimental Reynolds number was calculated to account for the variations of the dynamic viscosity with shear-rate and temperature. Figure of merit analysis was also performed, taking into consideration the Nusselt numbers and friction factors of the developed phase change dispersion and water where it was found that at Reynolds numbers above 650 it was more favourable to use the investigated phase change dispersion than water.

A computational study of trailing edge noise suppression with embedded structural compliance.

A unique concept for suppression of trailing edge noise scattering from a splitter plate in a low Reynolds number flow is proposed. The key idea of the concept is the adoption of a structural compliance system embedded with a finite number of elastic panels. Specific compliance system designs are devised for promotion of panel structural resonance that effectively absorbs broadband flow/acoustic fluctuation energy responsible for noise scattering. The concept is examined using high-fidelity direct aeroacoustic simulation together with spatiotemporal aeroacoustic-structural interaction analysis. The concept is confirmed feasible and outperforms many similar trailing edge noise reduction approaches reported in the literature.

150USRT Class R-513A Refrigerant Two-Stage Centrifugal Compressor Design Point and Separation Point Flow Field Simulation Analysis

This study used computational fluid dynamics for low greenhouse effect refrigerant (R-513A) simulation analysis in the two-stage 150 USRT class oil-free centrifugal refrigerant compressor using integrated part load value (IPLV) and internal flow field. The compressor rotor speed and mass flow rate for the IPLV working conditions with various loads were planned using Stage 1 and Stage 2 simulations, respectively. The performance and flow field numerical simulation analyses for the two-stage centrifugal compressor is discussed. This study used Ansys-CFX software for numerical simulation analysis and the conservation form of a 3D steady-state Navier–Stokes equation set with the finite volume discretization method for computation. The computing mode produced better computing efficiency and flexible mesh setting using the k-omega (k-ω) model, which has better computational performance in the near wall boundary layer and low Reynolds number flow field (used as the turbulence model) for simulation. The R-513A refrigerant property setting was calculated using the Soave–Redlich–Kwong gas equation. This study discusses the shaft work, pressure ratio, and isentropic efficiency and also describes the main research findings with the meridional pressure, isentropic efficiency contour maps, and flow field velocity vector diagrams. According to the numerical simulation results, in Stage 1 and Stage 2 simulations, the isentropic efficiency produced the highest numerical results in the 75% load case, which are 88.19% and 89.06%, respectively. The isentropic efficiency decreased to 75.93% and 82.26%, respectively, in the 25% load case. The flow field velocity vector diagram shows that in the 25% load case, there was back-flow field distribution near the impeller shroud. The compressor performance was also analyzed.

The Hindered Settling Velocity of Particles of Any Shape in Low Reynolds Number Flow

This article takes insights from a previously derived mathematical framework for the free settling velocity of particles of any shape to model analytical constructs to solve the hindered settling velocity of hard particles of any shape. Because the geometry of the physical environment and continuity can be strictly enforced in the construct model, the relative velocity of the fluid front pumped upward by the settling particles can be found, thus allowing for calculation by subtracting the front velocity from the calculated velocity.

Uncertainty quantification study of the aerodynamic performance of high-altitude propellers

Performance evaluations for propellers operating at high altitudes are subject to increased uncertainty due to scarce experimental or flight data and difficulties in modeling low Reynolds number flows. For this reason, the Polynomial Chaos Expansion (PCE) method is used in this paper to assess the performance uncertainty of propellers operating at high altitudes. Aleatoric (i.e. linked to the geometry or operating conditions) and epistemic (i.e. linked to the mathematical model describing the flow) uncertainty variables are included in this study to estimate the total uncertainty related to performance predictions made by two physical models, namely 3D RANS with the use of γ−Reθ transition model and Blade Element Momentum Theory (BEMT). In order to validate the proposed method, multipoint uncertainty quantification (UQ) studies are performed for two benchmark propeller geometries under various operating conditions for which experimental data are available. The UQ method is further illustrated on a propeller operating at high altitude. The efficacy of UQ with Computational Fluid Dynamics (CFD) and BEMT is compared and the most influential uncertain variables are found using Sobol's total order indices. As a result of the CFD-based uncertainty quantification studies, two major uncertain variables are identified, providing a direction for more computationally affordable UQ studies.

A Method for Generating Streamwise Velocity Disturbance in Low-Speed Wind Tunnel

A method of wind tunnel testing is proposed for generating streamwise velocity disturbance in low Reynolds number flows. When a model moves along the free stream at a constant speed, the effective turbulence intensity for the translating model can be adjusted through the change in the relative velocity between the free stream and the model. The feasibility of the proposed method is experimentally verified in a wind tunnel with a linear motion mechanism installed in the test section. The experiment shows that the effective turbulence intensity for the translating model increases when the model moves along the free stream. Agreement in the lift coefficients between the tests with and without using the linear-motion mechanism confirms the feasibility of the proposed method. The experimental range available in turbulence intensity can be extended using the model streamwise translation. Moreover, a stepwise gust can be generated while the turbulence intensity remains almost constant when the model moves against the free stream.

Identifying location of flow excitation on rotating disks in low Reynolds number flow using gain/phase relationships between vibration modes

Identifying location of flow excitation on rotating disks in low Reynolds number flow using gain/phase relationships between vibration modes

An IFDM analysis of low Reynolds number flow generated in a complex wavy curved passage formed by artificial beating cilia

Mother nature utilizes an assembly of beating cilia to transport liquid in various circumstances. The arrays of these hair-like cellular appendages also aid in propelling microorganisms like spermatozoa and paramecium. In our implicit finite difference analysis, we present a pumping performance of a curved channel comprising mucus flow induced via active cilium. The non-Newtonian mucus is modelled as Carreau fluid model. The undulating cilia attached with curved walls are assumed to be complex wavy. The tips of these cilia form a complex wavy peristaltic curved passage with porous medium effects. Well-known continuity and momentum equations (in curvilinear coordinates) are utilized to model the flow problem. Cilia-driven flow is creeping which is based on low Reynolds number assumption. Moreover, long wavelength assumption is also employed in this analysis. The reduced fourth-order BVP is solved via implicit finite difference method (IFDM). The computed results are plotted by using MATLAB (2021a). The mucus velocity is plotted at three different cross-sections and flow rates. Moreover, velocity of mucus, pressure gradient, pressure rise, and level curves are also expounded for various rheological, porous and cilia-based parameters. A special case of straight passage is also presented in the graphical result section.

Mixing enhancement of passive type T-mixer through shape optimization

This study looked at optimizing the geometrical shape of a simple T-mixer using Bernstein polynomials-based shape optimization technique to improve the mixing of the T-mixer. Passive micromixers of planar geometry are preferred in a wide range of applications such as lab-on-chips and chemical processing applications, due to their ease of fabrication and low processing costs. Studies conducted on T-mixers have revealed that the performance of T-mixers at low Re (&lt;30) is dismal. At low Reynolds number flows, the mixing is completely dominated by diffusion because of laminar flow conditions. In the present work, an attempt to improve the mixing performance of the T-mixer was made and a nearly three-fold improvement in performance was reported. The adjoint-based shape optimization technique was employed to optimize the wall profile without losing the advantage of the ease of fabrication. The T-mixer boundaries were represented parametrically using Bernstein polynomials that could take any shape within a constrained plane. Different shapes can be generated for different polynomial orders. A limit on the minimum channel thickness (60 microns) was imposed, while the inlet and outlet boundary lengths were fixed. For this particular geometry, the 12th-order polynomial exhibits an optimized shape for maximum mixing performance. The optimized shape of the T-mixer also shows significant improvement in mixing compared to a conventional T-mixer with a reduced channel thickness of 60 microns.

The effect of scalable PDMS gas-entrapping microstructures on the dynamics of a single cavitation bubble

The effect of gas-entrapping polydimethylsiloxane (PDMS) microstructures on the dynamics of cavitation bubbles laser-induced next to the PDMS surface is investigated and compared against the cavitation dynamics next to a flat smooth boundary. Local pressure gradients produced by a cavitation bubble cause the air pockets entrapped in the PDMS microstructures to expand and oscillate, leading to a repulsion of the cavitation bubble. The microstructures were fabricated as boxed crevices via a simple and scalable laser ablation technique on cast acrylic, allowing for testing of variable structure sizes and reusable molds. The bubble dynamics were observed using high speed photography and the surrounding flows were visualized and quantified using particle tracking velocimetry. Smaller entrapped air pockets showed an enhanced ability to withstand deactivation at three stand-off distances and over 50 subsequent cavitation events. This investigation provides insight into the potential to direct the collapse of a cavitation bubble away from a surface to mitigate erosion or to enhance microfluidic mixing in low Reynolds number flows.

Contribution of spanwise and cross-span vortices to the lift generation of low-aspect-ratio wings: Insights from force partitioning

This study reports on the vortex-induced lift production mechanisms in low Reynolds number flows over low aspect-ratio rectangular wings. We use a rigorous force partitioning method which allows for the estimation of the pressure-induced aerodynamic loads due to distinct flow features or vortex structures in the flow around the wing. The specific focus of this work is on distinguishing the effect of spanwise and cross-span oriented vortex structures on pressure-induced lift production. We quantify the lift induced on the wing by these different vortices, and also estimate their influence within different regions of the flow-field around the wing and in the wake. By varying the aspect-ratio and angle-of-attack of the wing, we show that for most cases, the spanwise oriented vorticity contributes less to the total lift than cross-span oriented vortices. Furthermore, the spanwise vorticity in the near wake is capable of producing net negative lift on the wing and this is explained by separating and quantifying the influence of vortex cores and regions of strain in the wake. The results demonstrate the utility of the force partitioning method for dissecting the flow physics of vortex dominated flows.

Experimental investigation of the laminar boundary layer vortex-shedding noise by an airfoil within a closed-vein wind tunnel

This study concerns the experimental characterization of trailing edge noise, the understanding of which is crucial for mitigating acoustic pollution across major industries. An aeroacoustic experiment is carried out using a closed-vein wind tunnel to investigate the laminar boundary layer vortex-shedding (LBL-VS) noise of a symmetric NACA0021 airfoil in low Reynolds number flows (Re ≤ 163,500). Steady aerodynamic and acoustic measurements are performed, with numerous conditions covered (flow velocity from 10 m/s to 24.5 m/s, airfoil incidence from −10° to 10°). The aerodynamic results reveal that, in the pre-stall regime, the airfoil’ suction side exhibits both a laminar separation bubble (LSB) and a trailing edge detached flow – which both make LBL-VS noise likely to occur. The acoustic results reveal that, when at low speed and moderate incidence, the airfoil emits one to two tones, which can be both attributed to LBL-VS noise. In particular, their respective frequency is seen to scale as the 0.8th power of the flow velocity, whereas varying linearly with the incidence. At higher speeds, these two tones vanish to the profit of other, more intense tonal emissions, whose frequency does not scale with the velocity nor the incidence. These tones are attributed to resonance effects coming from a retroaction of the reverberant environment onto the LBL-VS noise emission, which then locks-on to some of the duct resonant frequencies via an acoustic feedback loop. Revealing indirectly the presence of the pre-existing LBL-VS noise, these resonant tones emerge only when the flow velocity and incidence obey specific conditions, namely a roughly linear relationship.

Frozen propagation of Reynolds force vector from high-fidelity data into Reynolds-averaged simulations of secondary flows

Successful propagation of information from high-fidelity sources (i.e., direct numerical simulations and large-eddy simulations) into Reynolds-averaged Navier–Stokes (RANS) equations plays an important role in the emerging field of data-driven RANS modeling. Small errors carried in high-fidelity data can propagate amplified errors into the mean flow field, and higher Reynolds numbers worsen the error propagation. In this study, we compare a series of propagation methods for two cases of Prandtl's secondary flows of the second kind: square-duct flow at a low Reynolds number and roughness-induced secondary flow at a very high Reynolds number. We show that frozen treatments result in less error propagation than the implicit treatment of Reynolds stress tensor (RST), and for cases with very high Reynolds numbers, explicit and implicit treatments are not recommended. Inspired by the obtained results, we introduce the frozen treatment to the propagation of the Reynolds force vector (RFV), which leads to less error propagation. Specifically, for both cases at low and high Reynolds numbers, the propagation of RFV results in one order of magnitude lower error compared to the RST propagation. In the frozen treatment method, three different eddy-viscosity models are used to evaluate the effect of turbulent diffusion on error propagation. We show that, regardless of the baseline model, the frozen treatment of RFV results in less error propagation. We combined one extra correction term for turbulent kinetic energy with the frozen treatment of RFV, which makes our propagation technique capable of reproducing both velocity and turbulent kinetic energy fields similar to high-fidelity data.

Analysis of Heat Transfer and Flow Characteristics of a Helically Coiled Tube with Twisted Elliptical in a Low Reynolds Number Flow

In this paper, the heat transfer and flow characteristics of a helically coiled tube with twisted elliptical in a low Reynolds number (Re = 500–3000) flow were investigated numerically. The working fluid flowed in a laminar regime. Numerical results were compared with empirical correlations in the existing literature, demonstrating the accuracy of the analysis in this study. Firstly, we investigated the effects of geometric parameters and Reynolds number on the heat transfer and flow characteristics. The results showed that lower twist pitch length and semi-major axis length could induce sufficient fluid mixing and a larger temperature gradient near the tube wall, enhancing the heat exchange and producing larger friction resistance. Overall, the heat transfer performances were improved by about 1.04–1.21 times and 1.02–1.23 times for different semi-major axis lengths and different twist pitch lengths, respectively, compared to the smooth helical coil. Secondly, by changing the working fluid, it was found that the Nu when oil was chosen as the working fluid was all 6–6.8 times higher than that of water. Moreover, the effect of using Al2O3 nanofluids with a concentration of 0.10 wt.%, 0.25 wt.% and 0.50 wt.% was discussed. It can be seen that the heat transfer capacity of nanofluids increased by approximately 2–18% compared to the reference model with water as the working fluid, and the nanofluid solution with higher concentration has better heat transfer performance. Finally, Nu and f correlations are given to predict the heat transfer and pressure drop in practical applications.