Low Reynolds Number Research Articles

Numerical investigation of heat transfer characteristics of hydrogen flow in a randomly packed bed

In this study, two randomly packed beds with small tube-to-particle diameter (D/d) ratios of D/d = 4 (PB-4) and D/d = 5 (PB-5) are constructed using the discrete element method (DEM). The pore-scale heat transfer characteristics of hydrogen flow at low pore Reynolds numbers (Rep < 100) are investigated using a DEM-CFD simulation approach, with the temperature-dependent thermo-properties of hydrogen being considered. Distinct local channeling flow patterns are revealed by detailed analyses of the flow fields in PB-4 and PB-5. The overall friction factors for both beds are found to agree well with empirical correlations. Notably, a faster spatial temperature increase is exhibited by PB-5, with a larger D/d ratio, as evidenced by a shorter axial distance for fully-heated hydrogen flow compared to PB-4. For the pore-scale heat transfer in the packed beds, the radial temperature profiles are compared at various heights of the packed beds depending on the radial porosity oscillation, in which the wall effect should be especially considered in the near-wall region. Furthermore, the axial pore-scale Nusselt number (Nup,axial) exhibits an inverse fluctuation with the axial porosity oscillation. Finally, the global Nusselt numbers (Nu) in the packed beds are analyzed under different operating conditions, which are in good agreement with empirical correlations.

Centerline shock reflection for supersonic internal flows in the non-Rankine-Hugoniot zone: Overexpanded supersonic microjets

The viscous and rarefaction effects on centerline shock reflection occurring in an overexpanded axisymmetric microjet have been investigated numerically by means of a fully coupled pressure-based shock capturing scheme. Due to the low free-stream Reynolds number, the Navier–Stokes equations were coupled with slip velocity and temperature jump boundary conditions to account for rarefied gas effects in the Knudsen layer. It has been found that pronounced viscosity levels can cause a transition from a three-shock to a two-shock configuration, which is impermissible by inviscid theory. This is the first observation of such phenomena in the case of over-expanded jets. Analysis of the von Neumann and detachment criteria indicates that the transition from Mach reflection to regular reflection is analogous to the dual-solution domain transition for planar shocks. In addition, prediction of the longitudinal curvature of the incident shock has been conducted from a mathematical standpoint.

Flexible non-Brownian filament in intensified shear flow

The behavior of a three-dimensional, non-Brownian flexible filament in a low Reynolds number shear flow was investigated through theoretical and numerical analyses. In the phase plane with Reynolds number Re∈[0.03,8] and flow intensity Z∈[800,35 000], four primary motion modes of the filament were identified: rigid, C-buckling, U-turn, and S-turn. By employing the principle of symmetry, a theoretical model was developed to explain the S-turn mode, and we discovered that the critical flow strength for the transition from U-turn to S-turn was approximately Zc=4900. Our numerical simulations confirmed this transition value. In a system devoid of thermal fluctuations, it was observed that the mode transitions of microscale filament precisely corresponded to the abrupt scale rate changes in the non-Newtonian behavior of the macroscopic solution. Although the polymer stress under different modes has distinct underlying causes, they can all be predicted by the generalized Hooke's law.

Rotational dynamics of a disk in a thin film of weakly nematic fluid subject to linear friction

Dynamics at low Reynolds numbers experiences recent revival in the fields of biophysics and active matter. While in bulk isotropic fluids it is exhaustively studied, this is less so in anisotropic fluids and in confined situations. Here, we combine the latter two by studying the rotation of a disk-like inclusion in a uniaxially anisotropic, globally oriented, incompressible two-dimensional fluid film. In terms of a perturbative expansion in parameters that quantify anisotropies in viscosity and in additional linear friction with a supporting substrate or other type of confinement, we derive analytical expressions for the resulting hydrodynamic flow and pressure fields as well as for the resistance and mobility coefficients of the rotating disk. It turns out that, in contrast to translational motion, the solutions remain well-behaved also in the absence of the additional linear friction. Comparison with results from finite-element simulations shows very good agreement with those from our analytical calculations. Besides applications to describe technological systems, for instance, in the area of microfluidics and thin cells of aligned nematic liquid crystals, our solutions are important for quantitative theoretical approaches to fluid membranes and thin films in general featuring a preferred direction.

Aerodynamic shape optimization at low Reynolds number using multi-level hierarchical Kriging models

Aerodynamic shape optimization at low Reynolds number using multi-level hierarchical Kriging models

Toward sustainable energy resource: Integrated concentrated photovoltaic and membrane distillation systems for fresh water and electricity production

This study introduces and evaluates a novel Concentrated Photovoltaic (CPV)-assisted Direct Contact Membrane Distillation (DCMD) system, examining its efficiency and energy output under varying operational conditions. A Computational Fluid Dynamics (CFD) model, validated with experimental data, assesses the system's performance at different concentration ratios ranging from 1x to 10x and 25x to 100x, flow patterns (counterflow and parallel flow) at different Reynolds numbers (30–1200). This study investigates the seasonal performance of the CPV-DCMD system, providing valuable insights into its reliability and sustainability throughout the year. Results show increased mass flux and electric power with higher concentration ratios, especially at lower Reynolds numbers. In the counter-flow arrangement, the mass flux increases notably under specific conditions, while seasonal analysis reveals peak flux during summer and autumn afternoons. Electric power output follows a consistent trend across seasons, with high output observed during noon hours. The study demonstrates the system's energy efficiency, with notable energy gain compared to consumption across diverse operational conditions. Overall, the findings provide insights into optimizing the performance of CPV-assisted DCMD systems for sustainable energy generation and water desalination applications.

Multiple stable postures of a falling object in fluids

We present evidence revealing that an object with specific properties can exhibit multiple stable falling postures at low Reynolds numbers. By scrutinizing the force equilibrium relationship of a fixed object at various attack angles and Reynolds numbers, we introduce a methodology that can obtain the stable falling postures of the object. This method saves computational resources and more intuitively presents the results in the full parameter domain. Our findings are substantiated by free-fall tests conducted through both physical experiments and numerical simulations, which validate the existence of multiple stable solutions in accordance with the interpolation results obtained with fixed objects. Additionally, we quantify the abundance and distribution patterns of stable falling postures for a diverse range of representative shapes. This discovery highlights the existence of multiple stable solutions that are universally present across objects of different shapes. The implications of this research extend to the design, stability control and trajectory prediction of all free and controlled flights in both air and water.

Heat transfer enhancement and pressure drop performance of Al2O3 nanofluid in a laminar flow tube with deep dimples under constant heat flux: An experimental approach

This study examines the heat transfer enhancement and pressure drop of Al2O3 nanofluid in deep dimpled tubes in both longitudinal and circumferential directions. It explores mechanisms that improve the thermal performance of this novel tube geometry. Experiments were conducted using plain and deep dimpled tubes under laminar flow with Reynolds numbers from 500 to 2250, a constant heat flux of 10,000 W/m2, and nanofluid concentrations from 0.1 wt% to 1 wt%. The findings indicate that local velocity enhancement, vortex generation, and flow rotation and mixing are the three main mechanisms that improve the thermal performance of deep dimpled tubes. The results demonstrate that a deep dimpled tube with 1 wt% nanofluid can increase the convective heat transfer coefficient by up to 3.42 times compared to a smooth tube at Re = 2250. At this Reynolds number, the Nusselt number reaches a maximum of 41.80, and the friction factor ratio increases by only 1.82. Additionally, circumferential analysis reveals how dimple-induced vortices enhance heat transfer. The results also indicate that the tube geometry modification changes the flow regime zones, allowing turbulent flow at lower Reynolds numbers near Re = 2000, as identified by Nusselt number and friction factor plots. The deep dimpled tube has a low improvement penalty, with the highest friction factor of 0.38 at Re = 500 and high thermal enhancement, resulting in a performance evaluation criterion (PEC) of up to 2.80 in the studied region. However, the deep dimpled tube is unsuitable for Reynolds numbers below 1000. For higher velocities, replacing simple tubes with deep dimpled tubes in traditional heat exchangers is highly recommended.

Performance Estimation of Fixed-Wing UAV Propulsion Systems

The evaluation of propulsion systems used in UAVs is of paramount importance to enhance the flight endurance, increase the flight control performance, and minimize the power consumption. This evaluation, however, is typically performed experimentally after the preliminary hardware design of the UAV is completed, which tends to be expensive and time-consuming. In this paper, a comprehensive theoretical UAV propulsion system assessment is proposed to assess both static and dynamic performance characteristics via an integrated simulation model. The approach encompasses the electromechanical dynamics of both the motor and its controller. The proposed analytical model estimates the propeller and motor combination performance with the overarching goal of enhancing the overall efficiency of the aircraft propulsion system before expensive costs are incurred. The model embraces an advanced blade element momentum theory underpinned by the development of a novel mechanism to predict the propeller performance under low Reynolds number conditions. The propeller model utilizes XFOIL and various factors, including post-stall effects, 3D correction, Reynolds number fluctuations, and tip loss corrections to predict the corresponding aerodynamic loads. Computational fluid dynamics are used to corroborate the dynamic formulations followed by extensive experimental tests to validate the proposed estimation methodology.

Mathematical analysis of isothermal study of reverse roll coating using Micropolar fluid

This article demonstrates a mathematical model and theoretical analysis of the Micropolar fluid in the reverse roll coating process. It is important because micropolar fluids account for the microstructure and microrotation of particles within the fluid. These characteristics are significant for accurately describing the behavior of complex fluids such as polymer solutions, biological fluids, and colloidal suspensions. First, we modeled the flow equations using basic laws of fluid dynamics. The flow equations are made modified using low Reynolds number theory. The simplified equations are solved analytically. The exact expression for velocity and pressure gradient are obtained, while pressure is calculated numerically using Simpson Rule. Graphical depictions are carried out to comprehend the impact of the newly emerged physical constraints. The influence of micropolar and microrotation parameters on the velocity, pressure and pressure gradient are elaborated with the help of different graphs.

Exploring multiple phases and first-order phase transitions in Kármán Vortex Street

Kármán Vortex Street, a fascinating phenomenon of fluid dynamics, has intrigued the scientific community for a long time. Many researchers have dedicated their efforts to unraveling the essence of this intriguing flow pattern. Here, we apply the lattice Boltzmann method with curved boundary conditions to simulate flows around a circular cylinder and study the emergence of Kármán Vortex Street using the eigen microstate approach, which can identify phase transition and its order-parameter. At low Reynolds number, there is only one dominant eigen microstate W1 of laminar flow. At Rec1 = 53.6, there is a phase transition with the emergence of an eigen microstate pair W2,3 of pressure and velocity fields. Further at Rec2. = 56, there is another phase transition with the emergence of two eigen microstate pairs W4,5 and W6,7. Using the renormalization group theory of eigen microstate, both phase transitions are determined to be first-order. The two-dimensional energy spectrum of eigen microstate for W1, W2,3 after Rec1, W4–7 after Rec2 exhibit −5/3 power-law behavior of Kolnogorov’s K41 theory. These results reveal the complexity and provide an analysis of the Kármán Vortex Street from the perspective of phase transitions.

Fabrication of Patterned Magnetic Particles in Microchannels and Their Application in Micromixers.

Due to the extremely low Reynolds number, the mixing of substances in laminar flow within microfluidic channels primarily relies on slow intermolecular diffusion, whereas various rapid reaction and detection requirements in lab-on-a-chip applications often necessitate the efficient mixing of fluids within short distances. This paper presents a magnetic pillar-shaped particle fabrication device capable of producing particles with planar shapes, which are then utilized to achieve the rapid mixing of multiple fluids within microchannels. During the particle fabrication process, a degassed PDMS chip provides self-priming capabilities, drawing in a UV-curable adhesive-containing magnetic powder and distributing it into distinct microwell structures. Subsequently, an external magnetic field is applied, and the chip is exposed to UV light, enabling the mass production of particles with specific magnetic properties through photo-curing. Without the need for external pumping, this chip-based device can fabricate hundreds of magnetic particles in less than 10 min. In contrast to most particle fabrication methods, the degassed PDMS approach enables self-priming and precise dispensing, allowing for precise control over particle shape and size. The fabricated dual-layer magnetic particles, featuring fan-shaped blades and disk-like structures, are placed within micromixing channels. By manipulating the magnetic field, the particles are driven into motion, altering the flow patterns to achieve fluid mixing. Under conditions where the Reynolds number in the chip ranges from 0.1 to 0.9, the mixing index for substances in aqueous solutions exceeds 0.9. In addition, experimental analyses of mixing efficiency for fluids with different viscosities, including 25 wt% and 50 wt% glycerol, reveal mixing indices exceeding 0.85, demonstrating the broad applicability of micromixers based on the rapid rotation of magnetic particles.

Investigation of a novel active flow control technology on the chronology of the dynamic stall of oscillating airfoils at low Reynolds number

Investigation of a novel active flow control technology on the chronology of the dynamic stall of oscillating airfoils at low Reynolds number

Analyzing heat transfer and entropy generation in catheterized, stenosed arteries

A frequent cardiovascular condition that reduces blood flow is arterial stenosis. Tangent stress pressure, produced by a stenotic blood artery, diminishes the arterial side and results in an aneurysm. We explored the dynamics of entropy generation in blood stream via arteries observing mild overlapping stenosis, using a Prandtl fluid and focusing on the eccentric placement of catheters to enhance patient comfort. The governing equations assume conditions of mild stenosis and low Reynolds number, and applied the homotopy perturbation method. Several critical physical aspects are characterized, including velocity, temperature, impedance, entropy generation, wall shear stress, the Bejan number, and flow streamlines. The results show that a rise in the catheter radius tends to elevate impedance levels, whereas an increase in eccentricity, amplitude ratio, and inner cylinder speed leads to a decrease. These behaviors may serve to optimize catheter placement to minimize patient discomfort during medical interventions.

Entropy generation in newtonian vs non-newtonian nanofluid flow under vibration

Numerical investigation into the effects of vibration on heat transfer and entropy generation in Newtonian and Non-Newtonian nanofluid flows through pipes reveals enhanced heat transfer via intensified fluid agitation and improved particle dispersion. Thermal entropy generation analysis shows reduced irreversibility in vibrated flow, indicating improved flow mixing. Vibration enhances heat transfer by intensifying fluid agitation and promoting particle dispersion near the wall, resulting in a significantly more uniform temperature distribution along the pipe, approximately 100 times more than steady-state flow. This study underscores vibration’s potential to optimize heat transfer and reduce entropy generation in nanofluid systems, emphasizing velocity and rheological impacts. Comparison of vibrated flow to steady-state flow for Newtonian and non-Newtonian fluids reveals significant improvements under vibration, particularly at lower Reynolds numbers where non-Newtonian fluids exhibit pronounced effects. Future research directions include exploring thermal radiation’s impact on entropy generation, analyzing different nanofluid compositions, and investigating varied boundary conditions and geometries to advance understanding in this field. This study provides valuable insights into the complex interplay among vibration, fluid dynamics, and heat transfer in nanofluid flows. Its findings have practical implications for optimizing thermal management systems in diverse engineering applications.

Novel Close-Clearance Impeller Structure for Solid–Liquid Mixing at Low Reynolds Numbers Based on the Paravisc Impeller

Novel Close-Clearance Impeller Structure for Solid–Liquid Mixing at Low Reynolds Numbers Based on the Paravisc Impeller

Physics-Informed Neural Networks for Prediction of a Flow-Induced Vibration Cylinder

Abstract Flow-induced vibration (FIV) is a common phenomenon in ocean engineering for subsea structures with circular-shaped cross sections. A large amount of computational resources or experimental efforts are required to predict or measure the complicated motions and flow field surrounding a circular cylinder undergoing vortex-induced vibration (VIV). Physics-informed neural networks (PINNs) are powerful deep learning techniques for solving governing partial differential equations (PDEs) of dynamic systems as an alternative to complex numerical methods. In the present study, a framework is built employing PINNs for solving the Navier–Stokes equations to predict flows past an FIV cylinder using sparsely distributed spatiotemporal data inside the domain. The training process involves minimizing the supervised loss of flow data at these sparse points and the residuals of the governing PDEs. For the training of the PINN model, a moving frame around an FIV cylinder is used to collect the training flow data from two-dimensional direct numerical simulation results at a low Reynolds number. The structural displacements of the cylinder are also implemented in the residuals of the equations of the developed PINN. The performance of the PINN is evaluated by comparing the predicted contours of the surrounding flow velocities with the training data. The hydrodynamic forces prediction is achieved using the PINN-obtained flow field predictions combined with the force partitioning method.

Influence of bioinspired morphing on the flow field characteristics of UAV wings at low Reynolds number

The aerodynamic performance of unmanned aerial vehicles (UAV) can be improved by optimizing the surface flow characteristics over a wide range of angle of attack (AoA) through novel mechanisms. Recently, the bioinspired camber morphing concept has received greater attention because of the proven ability of nature species towards the retention of aerodynamic performance under different environmental conditions. In particular, birds like Eagles ( Accipitriformes) increase their wing camber in the course of flight to achieve maximum climbing altitude with good manoeuvring capability. The biomimetic designs such as the corrugated bone structure of Eel fish ( Anguilliformes) helps to achieve the wing camber morphing with optimal aerodynamic load distributions. The present work is focused on the bioinspired variable camber morphing (VCM) strategy to enhance the flow control behaviour and aerodynamic forces for a specific UAV wing configuration at various AoA. Here, NACA 4412 airfoil is used as a baseline wing configuration and the camber morphing mechanisms which are derived through Eel fish and Eagle are analysed. The model with Eagle wing morphing (EWM) mechanism is considered as a primary case of VCM and Eel fish’s corrugated structure is taken as a secondary case of VCM model. The coefficient of lift ( C L ), coefficient of drag ( C D), coefficient of pressure ( C p) and endurance factor are estimated for both morphed and baseline wing configurations through high fidelity numerical simulations. Interestingly, it is observed that the EWM wing configuration has excellent surface flow control characteristics than the CSM wing configuration and the results are presented with a detailed discussion.

Optimizing heat transfer with electro-osmotic ciliated propulsion in a non-uniform canals with Cu-blood characteristics considering thermal casson nano fluid

Electroosmosis peristaltic flows find promising applications in electro-fluid thrusters in space propulsion, polymer injection systems, ion exchange membrane designs, microbe fuel cells, biochip fabrication and fossil fuel energy process. In light of this, the current work aims to investigate blood based electroosmotic peristaltic flow in a ciliated, non-uniform propagation channel when copper nanoparticles are present. For that purpose, mathematical modeling is done in two dimensional frame and then governing partial differential equations are simplified and converted in ordinary differential equations using dimensionless quantities and long wave length and low Reynolds number approximations. In result we got coupled nonlinear boundary value problem that is solved numerically using three-stage Lobatto IIIa formula known as bvp4c invoking shooting technique. Peristaltic ciliated waves are thought to pass along the channel wall. The properties of both fluid phase and particle phase flow are modeled and investigated. Plotting against various parameters, streamline contours, temperature contours, concentration and temperature profiles, and pressure rise graphs are examined in-depth from a physical perspective. The obtained results revealed that concentration profile α upsurges for rising values of Casson fluid parameter β, nanoparticle volume fraction ϕ and flow rate Q while it drops with an increase in particulate volumetric fraction C, Eckert number Ec, Soret number Sr, Schmidt number Sc and viscosity constant. A decrease in temperature is also caused by an increase in the volumetric percentage of nanoparticles. In the pumping portion, there is a decrease in pressure rise; however, this decrease changes to an increase in the increased pumping zone.

Unified framework for laser-induced transient bubble dynamics within microchannels

Oscillatory flow in confined spaces is central to understanding physiological flows and rational design of synthetic periodic-actuation based micromachines. Using theory and experiments on oscillating flows generated through a laser-induced cavitation bubble, we associate the dynamic bubble size (fluid velocity) and bubble lifetime to the laser energy supplied—a control parameter in experiments. Employing different channel cross-section shapes, sizes and lengths, we demonstrate the characteristic scales for velocity, time and energy to depend solely on the channel geometry. Contrary to the generally assumed absence of instability in low Reynolds number flows (<1000\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$<1000$$\\end{document}), we report a momentary flow distortion that originates due to the boundary layer separation near channel walls during flow deceleration. The emergence of distorted laminar states is characterized using two stages. First the conditions for the onset of instabilities is analyzed using the Reynolds number and Womersley number for oscillating flows. Second the growth and the ability of an instability to prevail is analyzed using the convective time scale of the flow. Our findings inform rational design of microsystems leveraging pulsatile flows via cavitation-powered microactuation.