Low Reynolds Number Region Research Articles

A Review of Flapping Mechanisms for Avian-Inspired Flapping-Wing Air Vehicles

This study focuses on the flapping mechanisms found in recently developed biometric flapping-wing air vehicles (FWAVs). FWAVs mimic the flight characteristics of flying animals, providing advantages such as maneuverability, inconspicuousness, and excellent flight efficiency in the low Reynolds number region. The flapping mechanism is a critical part of determining the aerodynamic performance of an FWAV since it is directly related to the wing motion. In this study, the flight characteristics of birds and bats are introduced, the incorporation of these flight characteristics into the development of FWAVs is elucidated, and the utilization of these flight characteristics in the development of FWAVs is explained. Next, the classification and analysis of flapping mechanisms are conducted based on wing motion and the strategy for improving aerodynamic performance. Lastly, the current research gap is elucidated, and potential future directions for further research are proposed. This review can serve as a guide during the early development stage of FWAVs.

The influence of material on the power performance of Savonius turbines in wind and water applications

Savonius turbines are practical for rivers with low speeds due to their simple design and good self-starting capabilities. Despite these advantages, real implementation is still limited due to their low power efficiency. However, the experimental studies are scarce as they mainly focus on power performance, neglecting the impact of materials exposed to the wind or water medium. Therefore, the current study aims to address this gap by investigating the influence of materials on the power performance of Savonius turbines in wind and water, particularly the effect of their mass moment of inertia (I). Aluminum (ALU) and Polylactic Acid (PLA) were selected as the materials for the turbines as they are the typical materials frequently used to fabricate the turbines. They were tested experimentally in a wind tunnel and a water flume with Reynolds numbers ranging from 52, 000 to 83, 600. The findings discovered that although the turbine materials have the exact mass moments of inertia, they perform differently in water and wind. The turbines exhibit higher power coefficient with increasing mass moment of inertia in the wind at low Reynolds numbers (Re < 70,000), which is most likely due to reduced bearing friction that is more pronounced in the low Reynolds number region. The power coefficient was more likely to be affected in the wind than in water due to the effect of water buoyancy force, which reduces the influence of the increased mass moment of inertia. The results also revealed that the ALU and PLA with the same overall mass moment of inertia had maximum power coefficients of 11% and 18% in wind and water, respectively. There is no significant difference in terms of self-starting speed due to the variation in the moment of inertia. The Reynolds number and the turbine starting angle appeared to have a greater effect on self-starting capabilities than the moment of inertia. The findings of this study help to establish the types of materials that are optimal for enhancing the turbine performance in wind or water applications and could potentially save a lot of costs in generating power.

Onset of instability with collapse observed in relatively high density and medium beta regions of LHD

Edge MHD instabilities with pressure collapse are found in relatively high beta and low magnetic Reynolds number regions with a magnetic axis torus outward-shifted configuration of the large helical device (LHD), and characteristics and onset conditions of the instability are investigated. The instability has a radial structure with an odd parity around the resonant surface, which is different from that of the interchange instability typically observed in the LHD. The onset condition dependence on the magnetic axis location shows that the onset beta increases as the magnetic axis location moves more torus inwardly, and the instability appears only in limited configurations where the magnetic axis is located between 3.65 and 3.775 m. In such configurations, the resonant surface location is close to an index of the plasma boundary. This fact suggests that the distance between the resonant surface location and the plasma boundary plays an important role in the onset, and a possibility that the instability is driven by an external mode.

Analysis of heat transfer characteristics and entransy evaluation of high viscosity fluid in a novel twisted tube

• A novel twisted tube is to improve the secondary flow distribution inside the tube. • Heat transfer performance and entransy evaluation are investigated numerically. • The novel twisted tube reduces the entransy dissipation compared with the plain tube. • Effects of geometry parameters and Reynolds number are analyzed comprehensively. The non-uniformity of the secondary flow distribution in the twisted oval tube has impeded its further improvement of the heat transfer performance. A novel twisted tube (NTT) improves the distribution of the secondary flow and enlarges the effect of the secondary flow on the main flow, intensifying the radial mixing and equalizing the temperature distribution of the fluid, which strengthens the convective heat delivery in the near wall region and the core zone comprehensively. Heat transfer characteristics and entransy evaluation of water and engine oil in the NTT are investigated in the low Reynolds number ( Re ) region. The heat delivery performance of the NTT improves with the reduction of the distance ratio ( DR ) and the twist pitch ratio ( PR ), and also raises with the increase of Re . The friction factor of the NTT increases with the reduction of DR and PR , and decreases with the rise of Re . Compared with the twisted oval tube, the NTT could elevate the Nusselt number and enlarge the friction factor by 1.49–1.56 times and 1.32–1.41 times, respectively. Compared with the plain tube, the NTT could improve the Nusselt number and increase the friction factor by 2.42–2.76 times and 1.48–1.56 times, respectively. The equivalent thermal resistance of the NTT decreases with the reduction of DR and PR and reduces with the increase of Re . The Case 4 with the minimum DR and the smallest PR shows the supreme heat transfer performance and the lowest equivalent thermal resistance. The NTT could reduce the entransy dissipation remarkably, compared with the plain tube, the NTT could decrease the equivalent thermal resistance by up to 58% for water under the condition of constant wall temperature and could reduce the equivalent thermal resistance by as much as 53% for engine oil under the condition of given heat flux on the tube wall.

Weighted Moving Square-Based Solver for Unsteady Incompressible Laminar Flow Simulations

For computational fluid dynamics simulations, grid systems are generally used in the Eulerian frame for both structured and unstructured grids and solvers designed for the chosen grid systems. In contrast to the grid-based method, in which the connection information with neighboring grids must be maintained, gridless methods do not require an underlying connectivity in the form of control volumes or elements. Hence, gridless methods are feasible and robust for the problems with moving boundary and/or complicated boundary shapes. In this study, a Eulerian gridless solver is proposed, and its application for simulating two-dimensional unsteady viscous flows in low Reynolds number regions is investigated. The solver utilizes the weighted moving square method to obtain the spatial derivatives of the governing equations and solve the pressure Poisson equation iteratively. Simple remedies to satisfy the boundary conditions in the finite difference method are applied. The fractional step method with the second-order Adams–Bashforth method is used for time integration. Some benchmark problems were solved using the developed solver, and the results were compared with those of other experimental and computational methods. Good agreement with the results of other methods confirmed the validity of the proposed solver.

Multi-objective optimization of micro-fin helical coil tubes based on the prediction of artificial neural networks and entropy generation theory

The heat transfer, flow resistance and entropy generation characteristics of micro-fin helical coil tubes (MFHCTs) are investigated numerically. MFHCT with different fin numbers (2≤N≤6), coil pitches (150mm≤P≤450mm), coil diameters (600mm≤D≤1200mm) and Reynolds numbers (10945≤Re≤30845) are examined. The effects of these geometric parameters on the Nusselt number (Nu), friction factor (f) and improved entropy generation number (Ns′) are discussed. The performance of MFHCT is then compared to that of a smooth helical coil tube (SHCT). The results show that MFCHT always performs better than SHCT, especially in the lower Reynolds number region. Moreover, artificial neural networks (ANNs) are established to predict Nu, f and Ns′, which are trained by simulation data. This model fits the simulation results better than the multiple linear regression, and the maximum error is no greater than 8%. With the prediction of the network, the micro-fin helical coil tubes are optimized by the entropy minimization method and NSGA-III algorithm. Through optimization, the distribution of design variables is examined. The results demonstrate that a higher Reynolds number and a larger coil diameter and coil pitch lead to a better performance. Additionally, the optimal Pareto points can be utilized to guide the design and operation conditions of micro-fin helical coil tubes.

Effect of periodic metamaterial structures with different arrangement patterns on the effectiveness of hydroelastic energy harvesters: Computational investigation

This study introduces the concept of periodic metamaterials to determine an optimal arrangement for performance enhancement of flow-induced vibration energy harvesters. Three two-dimensional metamaterial structures including four-interference, six-interference, and eight-interference cylindrical structures are computationally explored and discussed. The displacement of the cylinder is calculated by a user-defined function based on the fourth-order Runge-Kutta algorithm. The computational simulation is set under a low Reynolds number region (64 ≤ Re ≤ 388), and the increase of Reynolds number is controlled by the reduced velocity (2 ≤ U* ≤ 12). It is found that the output harvested power of the three metamaterial structures is more significant than the single-cylinder system. The four-interference cylindrical structure shows both maximum output power of 2.4 μW when U* = 5, and good suppression when 10 ≤ U* ≤ 12. Besides, the six-interference cylindrical structure shows a trend of “advance” and the eight-interference cylindrical structure displays “beating” when U* = 9 and 10. In the comparison scheme of reducing the radius, the dimensionless amplitude of the metamaterial scheme is still larger than that of the single-cylinder scheme, however, the property of expanding “lock-in” has not been found. This study shows the possible advantages and disadvantages of considering metamaterial structures to enhance the effectiveness of flow-induced vibration energy harvesters.

Numerical Study of Thermal-Hydraulic Performance of a New Spiral Z-Type PCHE for Supercritical CO2 Brayton Cycle

Printed circuit heat exchangers (PCHEs) have the characteristics of high temperature and high pressure resistance, as well as compact structure, so they are widely used in the supercritical carbon dioxide (S-CO2) Brayton cycle. In order to fully study the heat transfer process of the Z-type PCHE, a numerical model of traditional Z-type PCHE was established and the accuracy of the model was verified. On this basis, a new type of spiral PCHE (S-ZPCHE) is proposed in this paper. The segmental design method was used to compare the pressure changes under 5 different spiral angles, and it was found that increasing the spiral angle θ of the spiral structure will reduce the pressure drop of the fluid. The effects of different spiral angles on the thermal-hydraulic performance of S-ZPCHE were compared. The results show that the pressure loss of fluid is greatly reduced, while the heat transfer performance is slightly reduced, and it was concluded that the spiral angle of 20° is optimal. The local fluid flow states of the original structure and the optimal structure were compared to analyze the reason for the pressure drop reduction effect of the optimal structure. Finally, the performance of the optimal structure was analyzed under variable working conditions. The results show that the effect of reducing pressure loss of the new S-ZPCHE is more obvious in the low Reynolds number region.

Molecular viscosity and diffusivity effects in transitional and shock-driven mixing flows.

This paper investigates the importance of molecular viscosity and diffusivity for the prediction of transitional and shock-driven mixing flows featuring high and low Reynolds and Mach number regions. Two representative problems are computed with implicit large-eddy simulations using the inviscid Euler equations (EE) and viscous Navier-Stokes equations (NSE): the Taylor-Green vortex at Reynolds number Re=3000 and initial Mach number Ma=0.28, and an air-SF_{6}-air gas curtain subjected to two shock waves at Ma=1.2. The primary focus is on differences between NSE and EE predictions due to viscous effects. The outcome of the paper illustrates the advantages of utilizing NSE. In contrast to the EE, where the effective viscosity decreases upon grid refinement, NSE predictions can be assessed for simulations of flows with transition to turbulence at prescribed constant Re. The NSE can achieve better agreement between solutions and reference data, and the results converge upon grid refinement. On the other hand, the EE predictions do not converge with grid refinement, and can only exhibit similarities with the NSE results at coarse grid resolutions. We also investigate the effect of viscous effects on the dynamics of the coherent and turbulent fields, as well as on the mechanisms contributing to the production and diffusion of vorticity. The results show that nominally inviscid calculations can exhibit significantly varying flow dynamics driven by changing effective resolution-dependent Reynolds number, and highlight the role of viscous processes affecting the vorticity field. These tendencies become more pronounced upon grid refinement. The discussion of the results concludes with the assessment of the computational cost of inviscid and viscous computations.

Aerodynamic Characteristics of a Corrugated Wing at Low Reynolds Number Region

Aerodynamic Characteristics of a Corrugated Wing at Low Reynolds Number Region

Drift-flux correlation for upward gas-liquid two-phase flow in vertical rod bundle flow channel

This paper has reviewed 17 available drift-flux correlations and collected 959 existing void fraction experimental data for air-water and steam-water two-phase flows in the vertical rod bundle flow channels. The performances of these drift-flux correlations have been evaluated with the collected experimental data. The evaluations conclude that the recently-developed drift-flux correlation of Schlegel and Hibiki gives the best predictions, and the drift-flux correlations of Clark et al. and Ye et al. can provide reasonable predictions for the collected experimental data. However, these drift-flux correlation series of Clark et al., Ye et al. and Schlegel and Hibiki are found to have the following three shortcomings. (1) Their distribution parameter correlation has ignored the flow regime and bubble behavior effects due to the different combinations of the non-dimensional superficial gas and liquid velocities at the same non-dimensional mixture volumetric flux under the high non-dimensional mixture volumetric flux conditions. (2) Their distribution parameter correlation has used the non-dimensional superficial gas and liquid velocities which cannot effectively reflect the pressure effect on the distribution parameter. (3) Their drift velocity correlation has ignored the drift velocity difference due to the flow regime transitions and has used the bubbly flow drift velocity correlation for all flow regimes, including the cap-bubbly, churn and annular flows. In view of these shortcomings, the present drift-flux correlation development adopts the segmented drift velocity correlations considering the features of bubbly, cap-bubbly, churn and annular flows in vertical rod bundle flow channel. The analysis for the experimental data of the asymptotic distribution parameter has shown that the asymptotic distribution parameter depends on the gas-phase Reynolds number with a feature that it linearly increases with gas-phase Reynolds number in the low gas-phase Reynolds number region, peaks at a critical gas-phase Reynolds number and exponentially decreases in the high gas-phase Reynolds number region under a certain liquid-phase Reynolds number flow conditions. This phenomenon is found to be caused by the formation and breakup processes of large-cap bubbles and their resultant intensive secondary flows corresponding to the flow regime transitions in the vertical rod bundle flow channel. So, a new distribution parameter correlation has been developed based on the gas- and liquid-phase Reynolds numbers reflecting the ratio of each phase inertial force to viscous force for the two-phase flows in vertical rod bundle flow channel. The newly-developed drift-flux correlation has been checked against various experimental data of air-water and steam-water two-phase flows in the rod bundle flow channel and a good agreement has been reached.

Mechanism of temperature-difference-induced spiral flow in microchannel and investigation of mixing performance of a non-invasive micromixer

Liquid mixing is important in Micro-TAS, but the mixing is difficult in microscale because the flow is difficult to disturb in low Reynolds number region. There are few methods to mix the microscale fluid in a non-contact manner and high mixing efficiency. In the case of the contact mixing method, the system tends to be complicated and large. This paper proposes a novel non-contact micromixer that uses two Peltier modules and generates a temperature difference inside a microchannel to generate a spiral flow. Our previous study has experimentally found that the temperature difference creates the spiral flow. In this study, the mechanism of the spiral flow was clarified by numerical calculation and the mixing efficiency was verified. As the result, the spiral flow was found to be generated by natural convection. The effect of natural convection on the channel volume was relatively large in the submillimeter scale, and it was found that the temperature difference could be used most effectively for mixing. When a temperature difference of 1.18 °C/mm was applied to a rectangular channel with a width and depth of 4 mm, and inflow velocity was 50 μm/s, the distance to complete the mixing was 3.56 mm. In low Reynolds number and high Peclet number environment of Re = 0.2, Pe = 4120, natural convection was utilized in the sub-milli scale channel and mixing was achieved at the short distance. By using a metal channel, the temperature difference generated inside the channel could be increased. We have developed an efficient micro mixer that can simplify the channel shape and reduce its size by controlling only the temperature from the outside of the chip.

The effects of different jet velocities and axial misalignment on the liquid sheet of two colliding jets

This experimental study investigated the patterns and characteristics of the liquid sheet formed by two axial misaligned colliding jets and two colliding jets with different velocities. The tests were limited to the low Reynolds number region, 100<Re<400, of two Newtonian colliding jets (a glycerol-water mixture). This range of Reynolds number includes the triple-chain, double-chain, closed-rim, and open-rim regimes. In the case of misaligned collision, it was found that an open-rim pattern, called trigonous liquid sheet, was formed for a specific measured degree of skewness in the triple-chain, double-chain, and closed-rim regimes. In the case of colliding with different velocities, two effects were observed, including the rotation of the liquid sheet in the direction of the jets axis and the deformation of the liquid sheet. A cancer-like instability, similar to what has been observed in two identical viscoelastic colliding jets, was also captured in the central region of the liquid sheet in the case of different velocities. This instability confirmed the sheet-driven mechanism of the fishbone pattern formation. In addition, the quantitative measurement of the geometrical characteristics of the liquid sheet and the droplets size distribution of the fishbone pattern were comprehensively discussed for different Reynolds numbers, skewness factors, and velocity ratios in the cases of two misaligned jets and different velocities of the two jets.

Numerical Analysis of Corrugated Wings at Low Reynolds Number Region

Numerical Analysis of Corrugated Wings at Low Reynolds Number Region

Fluid flow through male rotor housing clearances of dry running screw machines using dimensionless numbers

The efficiency of positive displacement machines is strongly influenced by clearance flows. The prediction of the mass flow rate is a challenging task since it depends on thermodynamic and operating boundary conditions as well as the shape of the clearance path. When simulating positive displacement machines using chamber models, clearance flow is commonly estimated by using simplified approaches, such as equations for isentropic nozzle flow combined with a flow coefficient. Knowledge of these flow coefficients is important for an accurate simulation of the machine. For this reason one of the goals of the European Union funded project “MOTOR” (Multi-ObjecTive design Optimization of fluid eneRgy machines) is the determination of the flow coefficient for different clearance shapes. This paper deals with the simulation of the two-dimensional fluid flow in the housing clearance of twin-screw machines using the finite volume method for air as ideal gas. Dimensionless numbers are varied to show their individual influence on the mass flow. Results are compared with experimental data from reports in the literature and show good accordance. The primary factors affecting the results are Reynolds number and the moving boundary in the low Reynolds number region.

Effect of the Reynolds Number on the Performance of a NACA0012 Wing with Leading Edge Protuberance at Low Reynolds Numbers

A study on the improvement of the NACA0012 wing performance in the low Reynolds number (Re) region of 10,000 ≤ Re ≤ 60,000 using a leading edge protuberance (LEP) was conducted. In this study, we focused on the effects of varying Re on the effectivity of the LEP. Wind tunnel tests and numerical simulations were performed to measure the wing performance and to visualize the flow structures around the airfoil. In the higher angle of attack region of α > 10∘, LEP causes the lift to increase independently of Re. Furthermore, in the lower angle of attack region, i.e., α ≤ 10∘, with Re ≤ 20,000, the lift coefficient also increases when using the LEP. The separation control is caused by the streamwise vortices generated by LEP which provides the momentum from the freestream flow into the separation region near the valley section, and the mechanism was basically the same at all Reynolds numbers and angle of attacks used in this study.

Flow-induced rotation of circular cylinder in Poiseuille flow of power-law fluids

The Poiseuille flow of power-law fluid over a free rotating cylinder eccentrically situated in a two-dimensional channel is numerically investigated via a BGK lattice Boltzmann method. Effects of power-law index, eccentricity ratio and Reynolds number on flow patterns and rotational behavior of the pinned cylinder are systematically explored within wide ranges of Reynolds numbers (1 ≤ Re ≤ 100), eccentricity ratios (0 ≤ λ ≤ 11/12) and power-law indexes (0.6 ≤ n ≤ 1.4). Results show that the ‘anomalous’ rotation (clockwise rotation) of the pinned cylinder is mainly induced by flow inertia. The mean rotating velocity generally decreases with an increase in Reynolds number except in low Reynolds number region and it also increases with power-law index because viscosity progressively becomes essential. Such effect of power-law index on the mean rotating velocity is greater at moderate local Reynolds number and intermediate eccentricity ratio. A physical argument is created to characterize the combined effect of Reynolds number and power-law index. In the vicinity of channel wall or near the centerline, the pinned cylinder tends to rotate in a normal way. The ‘anomalous’ rotation is inclined to appear at intermediate eccentricity ratio. Moreover, the critical Reynolds numbers beyond which the pinned cylinder changes the rotating direction are evaluated at various combinations of eccentricity ratio and power-law index. In addition, the instantaneous rotating velocity of the pinned cylinder is more stable at a lower Reynolds number, higher power-law index, considerably higher eccentricity ratio or quite near the channel centerline.

Analysis of the effect of the size of three-dimensional micro-geometric structures on physical adhesion phenomena using microprint technique.

Thrombus formation on biomaterial surfaces with microstructures is complex and not fully understood. We have studied the micro-secondary flow around microstructures that causes components of blood to adhere physically in a low Reynolds number region. The purpose of this study was to investigate the effect of micro-column size on the adhesion phenomena and show a quantitative relationship between the micro-secondary flow and physical adhesion phenomena, considering microstructures of various sizes. The flow simulation and quantitative assessment of adhesion rates around micro-columns was conducted using four sizes of micro-columns. This study also calculated the vectors of micro-secondary flow and average shear rate around a micro-column using a computational fluid dynamics analysis. The simulation showed the micro-secondary flow toward the bottom surface at upstream side and low shear rate distribution generated around a micro-column. Furthermore, physical adhesion tests were conducted using microbeads and a perfusion circuit to examine the size effect of the micro-columns on the physical adhesion. The results showed that the average adhesion rate around the micro-column increases with the associated size increase of the micro-column. Our results indicate that quantification of micro-secondary flow on a material surface with microstructures of several sizes and shapes (such as in a rough surface) is important for the evaluation of the adhesion phenomenon even though the surface roughness value on the material surface is small.

A study of film thickness and hydrodynamic entrance length in liquid laminar film flow along a vertical tube

The liquid film thickness and hydrodynamic entrance length in a vertical tube was studied experimentally and numerically. Measurements using distilled water, 30 wt % MEA and 40 wt % sugar solutions were carried out to investigate the effects of liquid flow rate on the formation of the liquid film. The experimental results validate the new Navier‐Stokes based equation in cylindrical coordinates (Eq. 16) and the volume of fluid (VOF) model giving a competitively high prediction of the liquid film thickness especially in the low Reynolds number region. In addition, a new empirical model and an improved minimal surface model have been first proposed for calculation of the hydrodynamic entrance length, with a relatively reasonable average absolute relative deviation (AARD) of 3.03% and 6.83%, respectively. Furthermore, the effects of the hydrodynamic entry length on the gas–liquid interfacial area calculated by the improved minimal surface model were comprehensively studied, and can be ignored if the ratio of the liquid film length (y) and the hydrodynamic entrance length (λE) is lower than 10. However, it should be noted that the hydrodynamic entrance length cannot be ignored in packed columns in which the liquid flow is very complex due to the packings with different structures and materials. © 2018 American Institute of Chemical EngineersAIChE J, 64: 2078–2088, 2018

Combined boundary singularity method and finite volume method with application to viscous deformation of polymer film in synthesis of sub-micron fibers

For sub-micron fiber production involving interaction of melted polymer with flow, the inner sub-domain has the Reynolds number smaller then unity while the outer domain has the Reynolds number exceeding unity. The flow in the inner sub-domain is described by the Stokes equations while the outer flow is described by either the Navier-Stokes equations or Reynolds equations. A combined boundary singularity method (BSM) for the solution of the Stokes equation and finite volume method (FVM) for the solution of the Reynolds equations is developed and applied to the viscous deformation of 2-D tracks by air impinging into polymer film. The proposed FVM-BSM predicts viscous deformation of perturbed surface for the manufacturing process of sub-micron fibers.Sole use of FVM would require highly refined grid and re-meshing of gas flow domain. The FVM-BSM facilitates the advantage of BSM to mesh only the boundary of BSM sub-domain. The advantage of FVM also enables the solving of the Navier-Stokes equations for an arbitrary Reynolds number. In frame of the proposed coupled FVM-BSM approach, the velocity vector field at the boundaries of the low-Reynolds number region in the vicinity of the stagnation point, where deformation occurs, was computed by FVM. This method is used to obtain the deformation of melted pitch for the range of jet impingement angles.