Low Reynolds Number Research Articles

A Novel Arrangement of Multiple Cylinders of Different Structural Conditions Dictating Wind Energy Harvesting at Very Low Reynolds Number

A Novel Arrangement of Multiple Cylinders of Different Structural Conditions Dictating Wind Energy Harvesting at Very Low Reynolds Number

An experimental investigation on the flow control of the partially stepped NACA0012 airfoil at low Reynolds numbers

An experimental study of flow control around a NACA0012 airfoil modified with fully and partially step geometry was conducted at Reynolds numbers of 6 × 104 and 1.2 × 105. Partially step geometries, the location of the step on the airfoil, and Reynolds number are varied to show their effect on aerodynamic performance and flow structures on the airfoil. Experimental results show that fully and partially step geometries are effective for flow control around the airfoil and aerodynamic performance enhancement. The maximum increase in lift coefficient is approximately 46%, and the stall angle is shifted about 1° by the SM4 model at Re of 6x104 while the step geometry is on the pressure side. For a Reynolds number of 1.2 × 105, the highest increase in the lift-to-drag ratio of the airfoil is observed about 17.1 at an angle of attack of 6° by the SM2 model when step geometry is placed on the pressure side of the airfoil. In the event of partially or fully stepped at the pressure side of the model, step flow structures, including the reattachment line, recirculation zone, and corner eddy, are obtained. However, even though the step geometry is at the suction surface of the model, the formation of a laminar to turbulent transition is observed. The overall results suggest that the partially stepped geometry length, Reynolds number, and step location side on the airfoil have an important role in flow control to improve aerodynamic performance for various angles of attack.

Asymptotic predictions on the velocity gradient statistics in low-Reynolds-number random flows: onset of skewness, intermittency and alignments

Stirring a fluid through a Gaussian forcing at a vanishingly small Reynolds number produces a Gaussian random field, while flows at higher Reynolds numbers exhibit non-Gaussianity, cascades, anomalous scaling and preferential alignments. Recent works (Yakhot & Donzis, Phys. Rev. Lett., vol. 119, 2017, 044501; Khurshid et al., Phys. Rev. E, vol. 107, 2023, 045102) investigated the onset of these turbulent hallmarks in low-Reynolds-number flows by focusing on the scaling of the velocity gradients and velocity increments. They showed that the onset of power-law scalings in the velocity gradient statistics occurs at low Reynolds numbers, with the scaling exponents being surprisingly similar to those in the inertial range of fully developed turbulence. In this work we address the onset of turbulent signatures in low-Reynolds-number flows from the viewpoint of the velocity gradient dynamics, giving insights into its rich statistical geometry. We combine a perturbation theory of the full Navier–Stokes equations with velocity gradient modelling. This procedure results in a stochastic model for the velocity gradient in which the model coefficients follow directly from the Navier–Stokes equations and statistical homogeneity constraints. The Fokker–Planck equation associated with our stochastic model admits an analytic solution that shows the onset of turbulent hallmarks at low Reynolds numbers: skewness, intermittency and preferential alignments arise in the velocity gradient statistics through a smooth transition as the Reynolds number increases. The model predictions are in excellent agreement with direct numerical simulations of low-Reynolds-number flows.

Experimental study on single-phase heat transfer performance of internal helically finned tubes covering low Reynolds number in turbulent flow

ABSTRACT This paper experimentally investigated the heat transfer performance of two internal helically finned tubes covering low Reynolds number in turbulent flow. A water-ethylene glycol mixture flowed inside and R134a boiled outside. The numbers of fin, the helix angles, and the ratios of fin height to diameter for the two test tubes were 38 and 60, 60° and 45°, and 0.0534 and 0.0222, respectively. The experimental Reynolds number was lower to 5400, covering the critical Reynolds number Re cr for turbulent flow. The data was divided into good and poor linearity regions by the modified Wilson plot method, which was much suitable for this case than that the data was treated as one region. The j factors showed ascending trend for Re below Re cr and descending trend for Re above Re cr. Enhancement factors of friction factor or j factor of the test tubes increased with increasing Reynolds number and eventually approached at the maximum for the Reynolds number above Re cr. The test tubes exhibited maximum efficiency indexes of 2.1 and 1.88, indicating superior overall performance compared to the majority of existing tubes. By utilizing the experimental data, a correlation was established basing on the critical Reynolds number, resulting in over 96% of the predicted errors falling within the range of ± 8%. This study has the potential to provide valuable insights for industrial implementation and the advancement of general correlation development.

The Role of Turbulence Transport in Mechanical Energy Budgets

Abstract In this article, we study the role of turbulence transport on loss prediction using high fidelity scale-resolving simulations. For this purpose, we use eight high-fidelity simulation datasets and compute flux of entropy and stagnation pressure transport equation budgets for all the cases. We find that under certain unsteady inflow conditions, the stagnation pressure coefficient is not a reliable loss metric even at low Mach number conditions. This is due to the turbulence transport terms. The impact of these terms, typically assumed to be negligible, made stagnation pressure loss coefficient underpredict loss from 0% to over 40% when compared to entropy loss coefficient for cases considered here. This effect was most pronounced for the cases with highly unsteady inflow conditions and at low Reynolds numbers.

Quasi-steady aerodynamic modeling and dynamic stability of mosquito-inspired flapping wing pico aerial vehicle

Recent exploration in insect-inspired robotics has generated considerable interest. Among insects navigating at low Reynolds numbers, mosquitoes exhibit distinct flight characteristics, including higher wingbeat frequencies, reduced stroke amplitudes, and slender wings. This leads to unique aerodynamic traits such as trailing edge vortices via wake capture, diminished reliance on leading vortices, and rotational drag. This paper shows the energetic analysis of a mosquito-inspired flapping-wing Pico aerial vehicle during hovering, contributing insights to its future design and fabrication. The investigation relies on kinematic and quasi-steady aerodynamic modeling of a symmetric flapping-wing model with a wingspan of approximately 26 mm, considering translational, rotational, and wake capture force components. The control strategy adapts existing bird flapping wing approaches to accommodate insect wing kinematics and aerodynamic features. Flight controller design is grounded in understanding the impact of kinematics on wing forces. Additionally, a thorough analysis of the dynamic stability of the mosquito-inspired PAV model is conducted, revealing favorable controller response and maneuverability at a small scale. The modified model, incorporating rigid body dynamics and non-averaged aerodynamics, exhibits weak stability without a controller or sufficient power density. However, the controller effectively stabilizes the PAV model, addressing attitude and maneuverability. These preliminary findings offer valuable insights for the mechanical design, aerodynamics, and fabrication of RoboMos, an insect-inspired flapping wing pico aerial vehicle developed at UPM Malaysia.

Experimental and numerical assessment and performance optimization of a novel T-arrow microfluidic device to mix two fluids with different thermophysical properties

Micromixers are critical parts of integrated microfluidic systems and their performance improvement has been a crucial problem for many investigators. Since the mixing enhancement in passive micromixers is hindered by the low-Reynolds number regime, multiple inlets have been recommended to create chaotic advection and improve the mixing quality. In this paper, a novel T-arrow micromixer is introduced to augment the mixing index (MI) of two liquids with different thermophysical properties. Numerical and experimental investigations are carried out by changing the distance between the inlets (a), the angle of the arrow-shaped inlet (α), the velocity ratio (VR), and the width-to-height aspect ratio (AR). Five optimization algorithms are also utilized to optimize the micromixer performance to achieve the most appropriate geometrical characteristics. It is found that MI is enhanced significantly by adding a Y-type inlet compared to a T-shaped mixer. The results demonstrate that while MI declines with a, there are optimal values for α, VR, and AR. Besides, parallel optimization of MI and pressure drop recommends two optimal micromixers with mixing energy cost (MEC) of 2841 Pa and 3370 Pa.

DEM-CFD Simulation Analysis of Heat Transfer Characteristics for Hydrogen Flow in Randomly Packed Beds

DEM-CFD Simulation Analysis of Heat Transfer Characteristics for Hydrogen Flow in Randomly Packed Beds

The effect of high values of relative surface roughness on heat transfer and pressure drop characteristics in the laminar, transitional, quasi-turbulent and turbulent flow regimes

AbstractThis study investigated the effect of large values of relative surface roughness on the heat transfer and pressure drop characteristics using simultaneously measured heat transfer and pressure drop data. Experiments were conducted using a horizontal circular tube with a base inner diameter of 5 mm and length of 4 m. One smooth and two rough tubes, with relative roughnesses of 0.04 and 0.11, were tested at different constant heat fluxes between Reynolds numbers of 100 and 8 500. Water was used as the test fluid and the Prandtl number varied between 3 and 7. Contrary to the trend in the Moody Chart, a significant increase in laminar friction factors with increasing surface roughness was observed. Both the friction factors and Nusselt numbers as functions of Reynolds number showed a clear upward and leftward shift with increasing surface roughness across the different flow regimes. Furthermore, the boundaries between the flow regimes were the same for the pressure drop and heat transfer results. The width of the transitional flow regime was narrower for rough tubes and had a differing trend. The quasi-turbulent and turbulent flow regimes occurred at lower Reynolds numbers for increasing roughness. When investigating the relationship between heat transfer and pressure drop, it was found that an increase in surface roughness favoured heat transfer in the quasi-turbulent flow regime. This is useful for rough tubes as the quasi-turbulent flow regime onsets early with regards to the Reynolds number in tubes with large roughnesses.

Effect of Tip Gap Size on the Tip Flow Structure and Turbulence Generation in a Low Reynolds Number Compressor Cascade

Abstract Efficient and compact axial compressors are currently undergoing rapid development for use in microcooling systems and small-scale vehicles. Limited experimental work concentrates on the inner flow field of the compressors working at such low Reynolds numbers (Re∼104). This study examines the vortical structures and the resulting turbulence production in the transitional flow over a C4 compressor blade at a Reynolds number Re of 24,000, with a specific focus on the impact of tip clearance. The particle image velocimetry measurements reveal the tip flow structures in detail, including the tip leakage vortex (TLV) and its induced complex vortical structures. The tip secondary flow at the low Reynolds number can be divided as the tip leakage flow (TLF)/vortex and transitional boundary layer both at the end walls and the blade surfaces. The TLV propagates at the highest spanwise positions and farthest pitchwise positions at the middle tip gap size (τ/C = 3%) for the three tip gap sizes investigated. The tip flow fluctuations decrease from τ/C = 5% to τ/C = 3% and then increase from τ/C = 3% to τ/C = 1%. The spatial distribution, streamwise evolution, and individual Reynolds normal stress components contributing to the turbulent kinetic energy (TKE) are discussed. The primary contributors to the turbulence generation are examined to elucidate the flow mechanism leading to the distinct anisotropic turbulence structure in the tip region with various tip gap sizes.

Effects of Leading-Edge Blowing Control and Reduced Frequency on Airfoil Aerodynamic Performances

Abstract Airfoil leading-edge fluid-blowing control is computationally studied to improve aerodynamic efficiency. The fluid injection momentum coefficient Cμ (the ratio of injection to incoming square velocities times the slot's width to airfoil's half chord length) varies from 0.5% to 5.4%. Both static and dynamic conditions are investigated for a NACA0018 airfoil at low speed and Reynolds number of 250 k based on the airfoil's chord length. The airfoil is dynamically pitched at a reduced frequency (the pitching tangential speed to the freestream speed ratio), varying between 0.0078 and 0.2. Reynolds-averaged Navier–Stokes (RANS) and unsteady RANS (URANS) is used in the simulations as based on the Transition SST and Spalart–Allmaras models, generally achieving good agreement with experimental results in lift and drag coefficients and in the pressure coefficient distributions along the airfoil. It is found that oscillating the airfoil can delay stall, as expected, in dynamic stall (DS). Leading-edge blowing control can also significantly delay stall both in static and dynamic conditions as long as sufficient momentum is applied to the control. On the other hand, for a small Cμ such as 0.5%, the leading-edge control worsens the performance and hastens the appearance of stall in both static and dynamic conditions. The airfoil's oscillation reduces the differences between pitch-up and pitch-down aerodynamic performances. Detailed analysis of vorticity, pressure, velocity, and streamline contours is given to provide plausible explanations and insight to the flow.

Computational study on effect of free-stream turbulence on bio-inspired corrugated airfoil at different sections at low Reynolds number

Computational study on effect of free-stream turbulence on bio-inspired corrugated airfoil at different sections at low Reynolds number

Ciliary propulsion through non-uniform flows

The classical paper by Lighthill (Commun. Pure Appl. Maths, vol. 109, 1952, p. 118) on the propulsion of ciliated microorganisms has become the reference against which many modern studies on swimming in low Reynolds number are compared. However, Lighthill's study was limited to propulsion in a uniform flow, whereas several biologically relevant microorganisms experience non-uniform flows. Here we propose a benchmark for ciliary propulsion in paraboloidal flows. We first consider the axisymmetric problem, with the microorganisms on the centreline of the background flow, and derive exact analytical solutions for the flow field. Our results reveal flow features, swimming characteristics and performance metrics markedly different from those generated in a uniform flow. In particular, the background paraboloidal flow introduces a Stokes quadrupole singularity at the leading-order flow field, generating vortices. Moreover, we determine the necessary conditions on the strength of the background flow for optimal power dissipation and swimming efficiency. We then consider the more general case of a microorganism off the centreline of the background flow. In this case, the squirmer experiences a paraboloidal, linear shear and uniform flows due to its position relative to the flow's centreline. Our findings show that while the linear shear flow does not affect the translational and rotational velocities of the squirmer, it does influence the velocity field and, therefore, the power dissipation.

Low-Frequency Intensity Modulation of High-Frequency Rotor Noise

Acoustic spectra of rotor noise yield frequency distributions of energy within pressure time series. However, they are unable to reveal phase relations between different frequency components while these play a role in the fundamental understanding of low-frequency intensity modulation of higher-frequency rotor noise. A methodology to quantify interfrequency modulation is applied to a comprehensive acoustic dataset of a fixed-pitch benchmark rotor, operating at a low Reynolds number and at advance ratios ranging from J=0 to 0.61. Our findings strengthen earlier observations in case of a hovering rotor, in which the modulation of the high-frequency noise is strongest around an elevation angle of θ=−20° (below the rotor plane). For the nonzero advance ratios, modulation becomes dominant in the sector −45°≲θ≲0° and is most pronounced at the highest advance ratio tested (J=0.61). Intensity modulation of high-frequency noise is primarily the consequence of a far-field observer experiencing a cyclic sweep through the noise directivity pattern of relatively directive trailing-edge noise. This noise component becomes more intense with increasing J and is associated with broadband features of the partially separated flow over the rotor blades.

Harnessing Flagella Dynamics for Enhanced Robot Locomotion at Low Reynolds Number

Harnessing Flagella Dynamics for Enhanced Robot Locomotion at Low Reynolds Number

Virtual leading-edge aero-shaping of an airfoil using a dielectric barrier discharge plasma actuator

Recently, it has been demonstrated that dielectric barrier discharge plasma actuators, which can be capable of generating a quasi-steady wall jet under the effect of a sinusoidal power supply, are well suitable for controlling the flow around the airfoil at a low Reynolds number. To uncover the controlling mechanism of plasma actuators, flow separation control over an SC (2)-0714 supercritical airfoil using an asymmetrical plasma actuator arranged at the leading edge of the airfoil, is studied at Reynolds number of 7.8 × 104. The stall angle of attack is delayed from 9° to 13°, and the maximum lift coefficient is increased by about 27%. In addition to the momentum injection to the boundary layer, which is one of the control mechanisms and can be achieved by the induced spanwise vortex of the plasma actuator, the closed recirculation region, which is similar to superimposing a hump on the leading edge of the airfoil, is another control mechanism, leading to an increase in the effective camber of the airfoil. The localized recirculation zone, which is created by the plasma actuator and modifies the leading-edge aero-shaping and results in the enhancement of the lift coefficient, is first observed, and this effect of the plasma actuator is called the virtual leading-edge aero-shaping.

Experimental study on the retention of aerosol particles through concrete cracks under high Reynolds number flow

In the event of severe accidents in pressurized water reactor (PWR) nuclear power plants, the potential leakage of radioactive aerosols through containment cracks poses a considerable radioactive hazard to the public. Understanding aerosol transport and retention in cracks helps reduce the conservatism and uncertainty of radioactive hazard assessment. Concrete cracks are recognized as a pivotal pathway for the leakage of radioactive aerosols, and several researchers have undertaken experimental investigations concerning the aerosol transport and retention in concrete cracks. However, the majority of these studies have rather low gas flow Reynolds numbers. In this work, an experimental setup is built to study aerosol transport and retention in concrete cracks under high Reynolds number flow. The TiO2 aerosol with a mass median diameter of 1μm and two concrete crack specimens are used in experiments. The results of gas flow experiments indicate that the Reynolds number is capable of reaching 10547. Combining the flow experimental data and Suzuki’s formula, the equivalent heights of these two crack specimens are approximated as 303.67μm and 231.48μm. The experimental results indicate a notably high retention rate of aerosols, exceeding 0.8. Furthermore, under high Reynolds number flow, the retention rate varies over a relatively narrow range, with the larger the equivalent height of the crack resulting in a lower retention rate. The experimental results match well with the mechanistic analysis based on inertial deposition theory, demonstrating the rationality of the inertial deposition theory.

Research on thermal stratification of surge line in the marine reactor based on fluid-solid thermal coupling model

Due to the requirements of ship movement, the power of the marine reactor is constantly changing, and the expansion and contraction of the primary coolant make the fluid flow in and out through the surge line. This paper establishes a fluid-solid thermal coupling model for the thermal stratification of a Marine reactor surge line. The low Reynolds number eddy viscosity model and the curvature modification of the bending pipe are used in this model. Qiao experiment is provided to verify the model's applicability to the thermal stratification analysis. The typical working conditions of the Marine reactor are analyzed, and the results show that: the temperature difference between the top and bottom of the pipe changes constantly with the fluctuation of the fluid, the maximum temperature difference in the horizontal section is 59.6K, and the maximum temperature difference in the vertical area is 23.9K. The maximum stress fluctuation of the horizontal section is 36MPa, while that of the vertical section is 5MPa. In the non-destructive testing, many small pits were found in the horizontal section of the pipeline, while no obvious damage was found on the surface of the vertical section, which is consistent with the results of our numerical analysis.

On the orientation dependence of the pressure and frictional drag experienced by spheroids in creeping flow

The present work deals with the creeping flow past a single oblate or prolate spheroid. On the basis of the investigations by Aoi [J. Phys. Soc. Jpn. 10, 119 (1955)] on the contributions of pressure and frictional drag to the total drag experienced by spheroids when the fluid streams with a speed parallel to the axis of symmetry, we find that the pressure contribution corresponds to half of the dimensionless shape factor γ0 provided by Happel and Brenner, Low Reynolds Number Hydrodynamics (Prentice-Hall Inc. Englewood Cliffs, NJ, 1965). Accordingly, we conjecture the validity of this finding when the fluid streams with a speed perpendicular to the axis of symmetry. Therefore, the formulations of dimensionless shape factors α0/2 and β0/2 are confronted with the numerical results at particle Reynolds number of 0.1. Furthermore, the formulations of the pressure and the frictional drag are deduced and extended to any orientation relative to the flow direction. These results give physical insight into the total drag experienced by spheroids in creeping flow and can be helpful for the validation of simulations of the flow past an obstacle.

A Comprehensive Dataset of the Aerodynamic and Geometric Coefficients of Airfoils in the Public Domain

This study presents an extensive collection of data on the aerodynamic behavior at a low Reynolds number and geometric coefficients for 2900 airfoils obtained through the class shape transformation (CST) method. By employing a verified OpenFOAM-based CFD simulation framework, lift and drag coefficients were determined at a Reynolds number of 105. Considering the limited availability of data on low Reynolds number airfoils, this dataset is invaluable for a wide range of applications, including unmanned aerial vehicles (UAVs) and wind turbines. Additionally, the study offers a method for automating CFD simulations that could be applied to obtain aerodynamic coefficients at higher Reynolds numbers. The breadth of this dataset also supports the enhancement and creation of machine learning (ML) models, further advancing research into the aerodynamics of airfoils and lifting surfaces.