Low Reynolds Number Research Articles

Life at low Reynolds number isn’t such a drag

Life at low Reynolds number isn’t such a drag

Aerodynamic Optimization and Flow Mechanism for a Compressor Cascade at Low Reynolds Number

Aerodynamic Optimization and Flow Mechanism for a Compressor Cascade at Low Reynolds Number

WAKE – SEPARATION BUBBLE INTERACTION OVER AN EXPERIMENTALLY SIMULATED AXIAL COMPRESSOR BLADE UNDER LOW REYNOLDS NUMBER FLOW

Abstract For the most part, the flow over an axial compressor blade is subjected to adverse pressure gradients. Under low Reynolds number conditions, the flow could separate off the blade surface especially on the suction side, where it first accelerates to a peak velocity and then decelerates towards the blade exit. The ‘separation bubble’ thus formed could trigger laminar to turbulent flow transition on reattachment downstream of the point of separation. Since blade profile losses depend on the transition location, the modification of the separation bubble due to any upstream generated disturbances is of great interest. In this paper the interaction between periodically incoming wakes and the separation bubble that exists on the blade surface is investigated. Results are presented from wind tunnel experiments conducted over a flat plate that is imposed with a surface pressure profile similar to that over a highly loaded compressor blade. The wakes are introduced using a bar passing mechanism that produces representative unsteady parameters. The spatio-temporal development of the flow along the mid-span region is described with the help of particle-image-velocimetry based flow mapping at a relatively low Reynolds number of 210,000. Several interesting observations were made, but the most important one is the existence of a slow-moving thickened boundary layer feature that convects immediately behind the wake. While the calmed region that forms behind this feature can suppress the bubble, the thickened boundary layer itself is seen to have high unsteadiness and contributes to a large momentum deficit.

Experimental Aerodynamics of a NACA 4424 Airfoil at Low Reynolds Number Flow

This paper presents wind tunnel data on the aerodynamic characteristics of a NACA4424 airfoil operating under low Reynolds number flow conditions (∼ Re = 2 × 105). The study investigates the lift, drag, and stall behavior of the airfoil, which are critical for applications in engineering such as small unmanned aerial vehicles (UAVs) and micro air vehicles (MAVs). Experimental data were collected through wind tunnel testing across various angles of attack at a fixed Reynolds number.To provide further insight, the experimental results are complemented by XFOIL simulations, which illustrate the impact of low Reynolds number conditions on aerodynamic performance. These findings enhance the understanding of airfoil behavior in low Reynolds number regimes and support the design and optimization of efficient airfoil profiles for small-scale aerial systems.

Peristaltic pumping of viscoelastic fluid in a diverging channel: effects of magnetic field and surface roughness

Purpose Surface properties (smooth or roughness) play a critical role in controlling the wettability, surface area and other physical and chemical properties like fluid flow behaviour over the rough and smooth surfaces. It is reported that rough surfaces are offering more significant insights as compared to smooth surfaces. The purpose of this study is to examine the effects of surface roughness in the diverging channel on physiological fluid flows. Design/methodology/approach A mathematical formulation based on the conservation of mass and momentum equations is developed to derive exact solutions for the physical quantities under the assumption of low Reynolds numbers and long wavelengths, which are appropriate for biological transport scenarios. Findings The results reveal that an increase in surface roughness reduces axial velocity and volumetric flow rate while increasing pressure distribution and turbulence in skin friction. Research limitations/implications These findings offer valuable insights for biological flow analysis, highlighting the effects of surface roughness, non-uniformity of the channel and magnetic fields. Practical implications These findings are very much applicable for designing the pumping devices for transportation of the fluids in non-uniform channels. Originality/value This study examines the impact of surface roughness on the peristaltic pumping of viscoelastic (Jeffrey) fluids in diverging channels with transverse magnetic fields.

Computational Fluid Dynamics Analysis of Self-Sustained Laminar Flow Oscillations in Singular Grooved Ducts

Research Background: Modeling oscillatory flow in singular grooved ducts within the laminar regime provides insight into fluid mechanics that could enhance applications such as heat transfer in nuclear reactors. Previous research has identified pulsations in grooved channels under turbulent conditions with high Reynolds numbers, contributing to enhanced heat exchange efficiency. These pulsations are influenced by the axial flow in and out of the main channel from a continuous groove. Contribution of This Study: This study extends the understanding of flow oscillations to simpler geometries and lower Reynolds numbers, specifically within a laminar flow regime capped at a Reynolds number of 2,000. By simplifying the duct geometry to a rectangular main channel with a singular continuous groove, the research employs computational fluid dynamics tools, primarily OpenFOAM, facilitated by Compute Canada's clusters. It investigates the fluid flow characteristics—strength, frequency, velocity gradient, and oscillation behaviours—associated with the geometry of the gaps and channels. This approach helps in pinpointing the dependency of flow characteristics on specific geometric configurations, potentially laying groundwork for optimizing designs in practical applications.

CFD modelling of micro turbomachinery blade: integrating surface roughness with novel reverse-engineering strategies

Abstract This paper presents the results of reverse-engineering (RE) strategies, surface roughness and computational fluid dynamics (CFD) modelling for a Wren100 micro gas turbine (MGT). Utilising silicone moulds and resin tooling, precise blade geometry capture was achieved for 3D reconstruction allowing for discrete and parametric geometric models to be created. Using these geometries, CFD simulations employing both Reynolds-averaged Navier–Stokes (RANS) and large eddy simulation (LES) models, alongside experimental wind tunnel cascade tests, were used to evaluate these reverse engineering strategies. The results show that while the parametric model captures overall MGT performance with fewer parameters, the discrete model provides enhanced accuracy, highlighting its suitability for detailed aerodynamic analyses. Contrary to initial expectations, surface roughness exhibited a noticeable impact on performance despite the lower Reynolds numbers (40,000), as demonstrated by the CFD model and wind tunnel experiments. The results indicate that surface roughness can reduce laminar separation bubbles on the blade leading edge, delay the onset of transition, and mitigate secondary flow losses. Overall, this study contributes to knowledge advancement in turbine blade reverse engineering and aerodynamics by detailing the impact of surface roughness on performance.

Transition Boundary from Laminar to Turbulent Flow of Microencapsulated Phase Change Material Slurry-Experimental Results.

An ice slurry or an emulsion of a phase change material (PCM) is a multiphase working fluid from the so-called Latent Functional Thermal Fluid (LFTF) group. LFTF is a fluid that uses, in addition to specific heat, the specific enthalpy of the phase change of its components to transfer heat. Another fluid type has joined the LFTF group: a slurry of encapsulated phase change material (PCM). Technological progress has made it possible for the phase change material to be enclosed in a capsule of the size of the order of micrometers (microencapsulated PCM-mPCM) or nanometers (nanoencapsulated PCM-nPCM). This paper describes a method for determining the Reynolds number (Re) at which the nature of the flow of the mPCM slurry inside a straight pipe changes. In addition, the study results of the effect of the concentration of mPCM in the slurry and the state of the PCM inside the microcapsule on the value of the critical Reynolds number (Recr) are presented. The aqueous slurry of mPCM with a concentration from 4.30% to 17.20% wt. flowed through a channel with an internal diameter of d = 4 mm with a flow rate of up to 110 kg/h (Re = 11,250). The main peak melting temperature of the microencapsulated paraffin wax used in the experiments was around 24 °C. The slurry temperature during the tests was maintained at a constant level. It was 7 °C, 24 °C and 44 °C (the PCM in the microcapsule was, respectively, a solid, underwent a phase change and was a liquid). The experimental studies clearly show that the concentration of microcapsules in the slurry and the state of the PCM in the microcapsule affect the critical Reynolds number. The higher the concentration of microcapsules in the slurry, the more difficult it was to maintain laminar fluid flow inside the channel. Furthermore, the laminar flow of the slurry terminated at a lower critical Reynolds number when the PCM in the microcapsule was solid. Caution is advised when choosing the relationship to calculate the flow resistance or heat transfer coefficients, because assuming that the flow motion changes at Re = 2300, as in the case of pure liquids, may be an incorrect assumption.

Numerical treatments for peristaltic transport of Johnson‐Segalman nanofluid through a vertical divergence irregular channel in the presence of inclined magnetic field and double‐diffusive

AbstractThis paper presents a computational study for the peristaltic pumping within vertical irregular divergence channels filled with magnetic Johnson—Segalman nanofluid. Various configurations of the outer boundaries are considered, namely, square wave, multi‐sinusoidal wave, trapezoidal wave, and triangular wave. An inclined magnetic field together with nanoparticles and mass concentrations is considered. Influences of the Dufour and Soret numbers are examined, and the cases of low Reynolds number and long wavelength are applied. All the computations are obtained numerically using Mathematica symbolical software (ND‐Solve), and the obtained results are presented in terms of the axial velocity , heat transfer rate , nanoparticle fraction profile , concentration profile , temperature profile , extra stress tensor , pressure gradient , pressure rise , and stream function . The major outcomes revealed that the square wave shape gives higher pressure gradients near the inlet and outlet parts while the multi‐sinusoidal wave gives periodic behaviors of . Also, the maximizing in thermophoresis parameter is better to obtain a higher rate of heat transfer while the increase in thermo‐diffusion and diffusion thermo effects causes a reduction in the rate of heat transfer. The discipline of biological and medical engineering, particularly for nanofluid peristaltic pumps, can benefit from the practical uses of such a model, which can be used to simulate the small vessel transport of particles in hemodynamics.

A comparative numerical evaluation of solar air heater performance having W-contoured, taper-contoured and reverse taper-contoured turbulators

The use of different turbulators in solar air heaters can significantly impact their thermal and hydraulic performance. This study compares solar air heaters equipped with W-contoured, taper-contoured, and reverse taper-contoured turbulators. It examines heat transfer coefficients, pressure drops, velocity contours, turbulent kinetic energy contours, and thermal perfor-mance factors for these systems under varying operating conditions. The air Reynolds number ranges from 4000 to 18 000, while design parameters such as relative roughness height and relative pitch ratio remain constant for accurate comparison. The simulations were conducted with a uniform heat flux of 1200 W/m2. The W-shaped contour roughness achieved the greatest heat transfer coefficient, surpassing both the tapered and reverse tapered configurations. In terms of friction factor, the tapered contour on the absorber plate led, followed by the reverse tapered and W-shaped contours. Overall, the W-shaped contour delivered the best performance. At lower Reynolds numbers, the reverse tapered contour outperformed the tapered contour, whereas at higher Reynolds numbers, the tapered contour showed superior performance compared to the reverse tapered contour.

Impact of Permeable Lining of the Wall on the Peristaltic Flow of Rabinowitsch Fluid in a Vertical Channel

Rabinowitsch fluid model is a well-established model for studying the non-Newtonian nature of the fluid This study is carried out to analyze the Rabinowitsch fluid through flexible and symmetric vertical channel with suction and injection under peristaltic motion. Considering long wavelength and low Reynolds number assumptions,. The present work is the mathematical investigation of permeable lining of the wall on the peristaltic flow of Rabinowitsch fluid in vertical channel with suction and injection . Pressure rise and the variation of various influencing parameters of the flow are studied graphically Keywords: peristalsis,vertical channel, Rabinowitsch fluid ,porous thickness of wall, permeable wall,

Numerical analysis of full-scale multi-path shell-and-tube heat exchangers with corrugated tubes

Shell-and-tube heat exchangers (STHx) are extensively implemented in modern energy sectors due to their robustness and cost-effectiveness. Advancements in compact, high-performance STHx designs are critical for optimizing energy transfer and reducing overall energy consumption. The main drawback of STHx is their low compactness. This paper presents a detailed numerical study of retrofitted STHx with enhanced features aimed at improving the compactness and thermal efficiency. This study employs a high-resolution finite element method to model a series of multi-path STHx with plain and corrugated tube bundles. The study shows that even small-sized STHx models require a large number of grid points—10 million for plain tubes and 50 million for corrugated tubes. Retrofitting with PIC tubes increased heat transfer by 12 % to 28 %, albeit with higher pressure drops. Significant pressure losses were observed at the header and distributor, accounting for 35.8 % of total pressure loss in PIC configurations and 69.2 % in plain-tube cases. PIC tubes also promoted more uniform mass flux distribution and enhanced heat transfer via in-tube secondary flows, particularly at lower Reynolds numbers. These findings highlight the merit of high-resolution modeling in heat exchanger analysis and demonstrate the effectiveness of corrugated tubes in enhancing STHx performance.

Enhancing darrieus wind turbine performance through varied plain flap configurations for the solar and wind tree

Plain flaps (PFs) significantly increase camber, enhancing lift and aerodynamic performance when deployed. In Darrieus Vertical Axis Wind Turbines (VAWTs), which perform efficiently in low-speed, turbulent wind conditions, structural modifications like PFs can improve efficiency. This study explores plain flaps with 10-20-degree deflections at different chord lengths to enhance the NACA 2412 aerofoil’s performance. Using Unsteady Reynolds-Averaged Navier-Stokes (URANS) equations and the Shear Stress Transport (SST) k-ω turbulence model, simulations were conducted across high (Re ≈ 2.71 × 105), medium (Re ≈ 1.35 × 105), and low (Re ≈ 5.4 × 104) Reynolds numbers (Re). The 0.7–10 and 0.8–10 configurations significantly improved torque and Cp. At a Tip Speed Ratio (TSR) of 2.5, the 0.8–10 configuration increased the Cp by 19.51% over the flapless NACA 2412 without PF. The 0.7–10 configuration achieved the highest Cp across all TSRs, while a three-blade setup improved Cp by 43% compared to four- and five-blade configurations. The modified blades demonstrated consistent torque gains across all Re, proving the effectiveness of blade shape modifications in enhancing VAWT efficiency, particularly under fluctuating wind conditions, indicating the potential of PF-modified blades in improving small-scale wind turbine performance in varied urban environments.

Application of the Immersed Boundary Method in the Study of Two Tandem Cylinders

The study of fluid flow around various surfaces is crucial in several applications of mechanical engineering, especially in cylindrical geometries of circular section, common in structures such as bridges, wind turbines, cooling systems, and power towers. In this work, we solve the two-dimensional mass conservation and Navier-Stokes equations in the x and y variables, ignoring gravitational effects, applying the Fourier pseudo-spectral method coupled with the immersed boundary method. We define a domain with two cylindrical boundaries of diameter equal to 0.0016m and a low Reynolds number. The obtained results are promising, approaching existing literature reviews.

Multi-objective optimization of unconventional airfoils at low Reynolds numbers

The widespread exploration of drones has generated increasing interest in Micro Aerial Vehicles (MAVs). Furthermore, an application that has gained notoriety is the use of aerial vehicles for exploration on Mars. Thus, the quest for efficient aerodynamic profiles for these applications has been intensified. These types of applications operate in a Reynolds number range from 10^4 to 10^5, which is significantly smaller than those commonly found in conventional low Reynolds regimes, such as when commercial drones are adopted. The main objective here is to identify more efficient shapes for airfoils, optimizing them through a multi-objective process aiming to maximize the lift coefficient and minimize the drag coefficient. To achieve this goal, two models of unconventional airfoils were optimized using the Generalized Differential Evolution 3 (GDE3) algorithm. The acquisition of aerodynamic coefficients, essential for evaluating the performance of the evolutionary algorithm, was carried out through simulations using Computational Fluid Dynamics (CFD). The method applied to describe the aerodynamic behavior of the structures proved to be consistent with experimental data. We used two base structures: a cubic Bézier-profile plate and a planar model with two inflections. Employing the aircraft's range or autonomy as decision criteria, it was observed that the cubic Bézier-profile plate presented superior results. Analyzing the graphs of the aerodynamic coefficients in relation to the angle of attack, the considerable increase in the stall point and lift provided by this model is notable. Such improvements, however, were accompanied by a slight disadvantage in the drag coefficient for small or negative angles of attack. It was also found that the evolutionary algorithm resulted in aerodynamic profiles with interesting characteristics for these applications when compared to existing models in the literature. In conclusion, the proposed cubic Bézier-profile plate model proved to be an interesting alternative for applications with a significantly small Reynolds number.

Wind loads on square lattice towers with tubular members based on wind tunnel test and numerical simulation

The square lattice tower with tubular members (SLTTM) is widely used in civil engineering. Wind load is the primary factor affecting the stability of these structures. This paper presents the wind loads of the SLTTM at different Reynolds numbers (Re) through wind tunnel testing and large eddy simulation (LES). A series of wind tunnel tests with four segment models were first conducted to discuss the effects of wind direction, turbulence intensity, and solidity ratio on the aerodynamic force under low and subcritical Reynolds numbers. The LES method was subsequently employed to determine the aerodynamic force coefficient at Re = 191–1.34 × 106 in both the smooth and uniform turbulent wind fields. The results from wind tunnel tests indicate that the mean and fluctuating drag coefficients at low Reynolds numbers are somewhat different from those at subcritical Reynolds numbers. The solidity ratio and wind direction exert a notable influence on the mean drag coefficient, whereas their impact on the fluctuating drag coefficient is relatively minimal. As the turbulence intensity increases, both the mean and fluctuating drag coefficients exhibit a notable rise. The results of the LES at Re = 191–1.34 × 106 show that an increase in turbulence intensity can markedly elevate the fluctuating drag coefficient. However, the effect on the mean drag coefficient is found to depend on the Reynolds number range. The Reynolds number effect on the mean and fluctuating drag coefficients of the SLTTM may be primarily attributed to the members without and with a shielding effect, respectively.

Review on internal flow mechanism and control methods of axial flow compressor at low Reynolds number

Review on internal flow mechanism and control methods of axial flow compressor at low Reynolds number

Rotationary feedback control of the cylinder wake flow using a linear dynamic model

This study presents an active feedback control of the Kármán vortex shedding flow past a circular cylinder at low Reynolds numbers. The cylinder's rotational motion functions as the control actuator, while the transverse velocities of points along the wake axis serve as the feedback signals. First, using the autoregressive with exogenous input method, a linear reduced-order model (ROM) for the unstable flow is developed to capture the input–output behavior between the cylinder's rotational displacement and the feedback signals. This model is then utilized for controller design using the proportional and linear quadratic regulator (LQR) control methods, respectively, with their effectiveness analyzed and validated through high-fidelity numerical simulations. The results show that both methods can effectively suppress the unstable vortex shedding flow, while proportional control exhibits strong sensitivity to monitoring point locations and time delays. The ROM-based model can accurately predict the stability characteristics of the control system, providing valuable guidance for selecting optimal feedback signals. Moreover, we show that by appropriately adjusting the phase angle between the control input and feedback signals via time delays, the performance of proportional control can be significantly enhanced. Lastly, based on the ROM, an output-feedback suboptimal control law is designed using the LQR method. This suboptimal feedback control transforms unstable fluid modes into stable ones, resulting in complete suppression of the unsteady vortex shedding. It is further revealed that the inherent mechanism of suboptimal flow control is to construct an optimal phase shift through the linear superposition of multiple feedback signals. Overall, model-based analysis results agree well with those obtained from direct numerical simulations, confirming the validity of the proposed ROM-based feedback control procedure.

Reynolds-averaged Navier–Stokes assisted direct numerical simulation of low Reynolds number flow over airfoils

The simulation of insect flight, like that of dragonflies operating at low Reynolds numbers, has numerical challenges due to the complex morphological structure. The corrugated airfoils trap vortices, and in these recirculation zones, turbulence models may be inadequate to resolve the near-wall flow features well. Hence, accurately capturing the laminar–turbulence transition and identifying the point of separation and reattachment requires resorting to direct numerical simulations (DNS) over a large domain, that is computationally expensive. We propose conducting DNS over a truncated subdomain constrained by Reynolds-averaged Navier–Stokes (RANS) solution to reduce the computational domain size and costs. A precomputed RANS simulation over a large domain is used to prescribe a velocity boundary condition (BC) at the truncated domain of the DNS; a convective BC is imposed as outflow. We validate the proposed RANS-assisted DNS (DNSR) by simulating subdomains of varying sizes and comparing the mean and fluctuating velocity fields, and aerodynamic characteristics with the DNS with free-slip BC. This technique reduces domain size and computational cost significantly (by at least half). A criterion for the ideal subdomain size is determined by satisfying the condition at the location where the non-dimensional mixing length is approximately 60. We validated our criterion by simulating flow over the NACA (National Advisory Committee for Aeronautics) 0012 airfoil at angles of attack α≤12°, corroborating with established literature. Finally, we study a three-dimensional corrugated airfoil with our approach, to capture the transition from two- to three-dimensional structures in the wake as the angle of attack increases.

Hidden field discovery of turbulent flow over porous media using physics-informed neural networks

This study utilizes physics-informed neural networks (PINNs) to analyze turbulent flow passing over fluid-saturated porous media. The fluid dynamics in this configuration encompass complex features, including leakage, channeling, and pulsation at the pore-scale, which pose challenges for detailed flow characterization using conventional modeling and experimental approaches. Our PINN model integrates (i) implementation of domain decomposition in regions exhibiting abrupt flow changes, (ii) parameterization of the Reynolds number in the PINN model, and (iii) Reynolds Averaged Navier–Stokes (RANS) k−ε turbulence model within the PINN framework. The domain decomposition method, distinguishing between non-porous and porous regions, enables turbulent flow reconstruction with a reduced training dataset dependency. Furthermore, Reynolds number parameterization in the PINN model facilitates the inference of hidden first and second-order statistics flow fields. The developed PINN approach tackles both the reconstruction of turbulent flow fields (forward problem) and the prediction of hidden turbulent flow fields (inverse problem). For training the PINN algorithm, computational fluid dynamics (CFD) data based on the RANS approach are deployed. The findings indicate that the parameterized domain-decomposed PINN model can accurately predict flow fields while requiring fewer internal training datasets. For the forward problem, when compared to the CFD results, the relative L2 norm errors in PINN predictions for streamwise velocity and turbulent kinetic energy are 5.44% and 18.90%, respectively. For the inverse problem, the predicted velocity magnitudes at the hidden low and high Reynolds numbers in the shear layer region show absolute relative differences of 8.55% and 4.39% compared to the CFD results, respectively.