Before reading this article, I sincerely invite you to click "Follow", which is convenient for you to discuss and share, but also brings you a different sense of participation, thank you for your support~
Wen | Yanzi looks at the world
Editor|Yanzi sees the world
preface
Flapping wing dynamics have important implications in many research fields, such as bio-excitation systems and aeroelasticity of aircraft.
The main objective is to improve propulsion characteristics by adding a pitch leading edge to the conventional NACA0012 airfoil in the lower Reynolds number range. This problem is solved numerically in the case of Reynolds number 104 under various beating conditions.
How does leading edge pitch amplitude affect propulsion power and efficiency? What is the root cause of increased thrust?
methodology
The proposed geometry is first experimentally studied, which consists of a brief investigation focused on flow visualization. The experiment was carried out on the equipment of the AEROG-UBI wind velocity measurement laboratory using an open loop, open section and a 0.3×0.2 m outlet section of the blower wind tunnel with a fan.
Flow velocity is measured in the center of the outlet section using a two-component laser Doppler velocimetry that has previously been used in the wind velocity measurement laboratory, and the horizontal and vertical average speeds are determined by the two-speed channel Dantec BSA F60 processor. Adjust the average speed by opening the gate knife located upstream.
The wing is adjusted to 2 cm from the exit, with 20 cm chords and 40 degrees cm span. A wingspan larger than the outlet section is chosen to mitigate the wingtip effect (wingtip vortex) and eliminate the possibility that the image acquisition system will capture it. The wing model is supported by a structure connected to a propulsion motor, which itself is fixed to the ground.
The linear actuator has a stroke rate of 0.2 m, 0.0012 m ahead of 0.0012 m, and a maximum operating speed of 0.8 m/s−1. The device has previously been used and verified when studying the effects of unequal rising and falling speeds in dive airfoils26].The pitch movement of the leading edge is done by the PKE543AC-PS50 stepper motor, which is also produced by Dongfang Electric Co., Ltd.
It is fixed on a wingtip, has a basic step angle of 0.0144°, a gear ratio of 50:1, and controls the dive and pitch movements using the ARD-CD and RKSD503-CD controllers, respectively. These two controllers are connected to a laptop equipped with MEXE02 support software using the CC05IF-USB data setup software communication cable.
The wing was designed with CATIA V5 R20 software and its production was done with additive manufacturing. The wing was produced using the original Prusa i3 MK3S+ 3D printer and PLA filament.
On the other wingtip, a camera is installed to capture the flow field, the camera is the GoPro HERO10, which provides a wide view close to the airfoil phenomenon in a Lagrangian perspective. Video recording was shot at a resolution of 2704 × 1520 pixels at 240 frames per second, and the video was lightly processed on MATLAB to enhance the flow characteristics.
Image processing is used to collect instructions such as resizing, grayscale conversion, pixel value adjustment, and sharpening. By using a machine that thermally evaporates the water-glycerin mixture, which condenses into small particles, this flow is marked with smoke. Smoke enters the wing passage through a pipe.
Downstream of this tube, a flow straightener is placed to eliminate any vertical velocity component generated by smoke insertion. In the outlet section, an array of light-emitting diodes is used to illuminate the smoke particles.
After experimental studies, a numerical study ® of the NACA0012-IK30 airfoil fluent 2022 R1 using Ansys, a similar numerical method has been used and validated in previous studies when studying the oscillating airfoil, assuming that the flow around the flapping airfoil is laminar to turbulent flow.
The turbulence model used is the (intermittent) transition model, which is the −transition model [29].The latter cannot be used because it is a Galilean variant, which means that it cannot be applied to surfaces moving relative to the coordinate system of the calculated velocity field. The Fluent solver implementation transition model can only be used in combination with other turbulence models, and SST− The model was chosen for this study.
The control equations are solved using a pressure-based coupling algorithm that links momentum-based and pressure-based continuity equations.
The gradient is evaluated by the method based on the least squares element, and the pressure interpolation scheme has second-order accuracy. The momentum, turbulent flow energy, specific dissipation rate, and intermittent convection terms are second-order welcoming style discrete, while the diffusion terms are central differential and second-order precision. Transient discretization is done using a first-order implicit method.
The calculation area consists of four parts: NACA0012-IK30 airfoil, inlet, outlet and interior, which are numerically solved due to the relative movement between the front and rear - IK30 presents several challenges regarding the mesh design process. This is solved by using an overlapping grid configuration where two component grids and a background grid are designed.
The background grid includes unstructured outer and inner areas with triangular elements, where a structured grid with rectangular elements is used. The air intakes and outlets are located away from the airfoil and are about 20 chords. The movement of the component mesh is done using user-defined functions (UDFs).
Motion parameters, such as frequency, diving, and pitch amplitude, are determined based on dimensionless parameters that dominate the problem. These are the Reynolds number, =/ reduced frequency, =2/dimensionless amplitude, h=/ and dimensionless velocity, h, where is fluid density, is dynamic viscosity, c is the aerochord length when the leading edge is undeflected, and A is the magnitude of the plunge.
The parameters used to evaluate the propulsion performance of the proposed airfoil are average propulsion power, average required power and propulsion efficiency. In its coefficient form, the propulsion power is given by the following equation
Its value is the same as the thrust coefficient. 1 and 2 are the thrust in the front and rear, respectively. The required power factor is
Where 1 and 2 are front and rear lift, respectively, and 1 is the leading edge pitch moment calculated at the fulcrum. The term ( 7 ) does not exist in equation 2 because pitch is not prescribed for the rear. The Fluent solver provides all these coefficients based on air density, wind speed, U and wing area, S, for the case of 2D, equal to chord length. The propulsion efficiency is calculated by the following equation
These two values were obtained during the last simulation, when negligible transients were found.
Grid and time step independence studies were carried out on numerical methods, in which the number of elements increased by a factor of 2 and the time step size decreased by a factor of 1/2 for the three meshes.
All grid elements close to the wall are designed with + being approximately 1. The conditions used for the study were =1.0×104, =1.0, h=0.50, and =5°. The propulsion coefficient plots dimensionless time/in Figure 4, where T is the period of motion. N represents the number of grid elements, and the final grid (2) has about two hundred thousand elements.
No significant differences were found, suggesting that the independence of grid and time steps has been achieved. In addition, this method was compared with numerical data from the plummeting NACA0012 [30] and experimental data from Heathcote et al. [31].
The average propulsion coefficient and the required power coefficient are used to verify the reliability of computational hydrodynamic results at low Reynolds numbers. The calculations are performed at =2.0×104, h=0.175 and a Strauhar number, between 0.1 and 0.4. The Strauhar number is related to dimensionless velocity.
Propulsion performance
The propulsion capability of NACA0012-IK30 has two dimensionless input amplitudes at Reynolds number 104, h=0.25 and 0.50 and three dimensionless velocities, h=0.25, 0.50 and 1.00. For each case, five leading edge pitch amplitudes (0°, 5°, 10°, 15°, and 20°) were considered.
First, propulsion performance is evaluated using three basic parameters commonly used in flapping wings: average propulsion power, average required power, and propulsion efficiency, and the average propulsion power coefficient is plotted relative to the pitch amplitude of the leading edge.
Increasing the pitch amplitude within a certain amplitude is beneficial, and then begins to decrease, except for h=1.00, which does not reach the maximum. The results also show that the slower beat state does not benefit from the dynamic leading edge and does not show good propulsion, very close to the state where drag is generated.
Although the behavior of these two dimensionless amplitudes is very similar, h=0.50 is a much more significant improvement in terms of quantity. When it comes to average propulsion power, an improvement of up to 177.4% relative to a dive only gains the leading edge. In addition, the results show that the higher the dimensionless speed, the higher the leading edge pitch amplitude needs to be for optimal propulsion power.
Except for cases where dimensionless amplitudes are low and dimensionless velocities are highest, the effect of dynamic activation of the leading edge is generally beneficial but rather small. In this particular case, the required power decreases linearly, increasing as shown below, with a decrease of 13.0% compared to the leading edge that only slopes forward.
Combining the two propulsion coefficients, the resulting propulsion efficiency is shown in Figure 8. The graph shows that when the front edge is deflected, the dimensionless amplitude is greatly improved, with an increase of 229.8%. Overall, medium dimensionless velocities are more efficient for propulsion, although it is unclear whether h=1.00 provides better efficiency at larger pitch amplitudes, as larger values are not considered.
Based on these results, it is clear that the addition of the pitch leading edge provides a significant advantage to the propulsion characteristics of the conventional NACA0012 dive airfoil. These improvements are inevitably related to the flow field changes caused by the dynamic leading edge. Again... Figures 9 and 10 analyze the influence of leading edge pitch amplitude on flow characteristics under all the previously proposed conditions.
The representation of the numerical field uses the total pressure contour to observe the flow separation, as the separated flow regions show lower values due to the associated losses. Snapshots are given at the end of the oscillation period (/=1.0) because they provide a representation of what happened throughout the period.
All conditions show some separation of airflow, as the airfoil oscillates at dimensionless velocities exceeding its static stall angle (about 12°).Only in the case of the dive leading edge, the maximum effective angle of attack is between 14° and 45° (unknown node type: trans unknown node type: trans=unknown node type: trans(h)), which can be reduced by ≈ 6° when the front edge inclination is 20°.
However, even if two dimensionless amplitudes have the same effective angle of attack profile, the phenomena around the airfoil are different. When the airfoil oscillates with a large dimensionless amplitude, the flow feature increases proportionally, and when the front edge is not deflected, the leading edge vortex occupies the entire upper surface of the airfoil.
For both amplitudes, the presence of leading edge vortices becomes more pronounced as the dimensionless velocity increases and moves upstream. This is to be expected, as the effective angle of attack triggering separation is reached faster and, therefore, LEV (leading edge vortex) formation begins earlier.
In a dive airfoil, leading edge vortices only serve as thrust enhancement features when located upstream of the maximum thickness position, as described in the High Man 32] as thrust boosters for dive airfoils. The NACA0012-IK30 airfoil follows the same principle, although it should not be considered a conventional subduction airfoil.
Looking at the effect of the pitch amplitude of the leading edge, we see that it plays a crucial role in controlling the lever size. The size and growth process of the leading edge vortex is explained.
When there is no leading edge deflection, LEV takes on its maximum size, and as the pitch amplitude increases to 20°, the size of the vortex decreases to about 50% for both dimensionless amplitudes. This decrease is due to a decrease in the inverse pressure gradient due to a decrease in the effective angle of attack of the leading edge section.
Instead, we are looking for a way to take advantage of its presence. This is contrary to the separation of air currents that occur at higher Reynolds numbers, which is completely undesirable, meaning that understanding LEV dynamics (its position, strength, and residence time on airfoil) is critical to optimal use of NACA0012-IK30 as a thrust enhancement mechanism.
In addition, determining the evolution of propulsion coefficients over time is critical to understanding the sources of propulsive improvements and, more specifically, the time frame in which they occur. The figure below focuses on conditions that show good propulsion characteristics and are clearly dependent on the pitch amplitude of the leading edge.
The deflection leading edge increases the propulsion power for most of the oscillation periods when the airfoil has its maximum effective angle of attack (/= 0.25 and /=0.75).
This coincides with the moment when the leading edge has the maximum angle of attack, increasing the frontal area of the airfoil, which leads to an increase in thrust. This will be illustrated below by the distribution of pressure around the airfoil.
In the studied range, a higher pitch amplitude results in a higher propulsion power value, although the upper pitch amplitude and h=0.50 scenario is expected because excessive deflection does not provide practical benefits. This upper limit is not observed, simply because of the relative importance between the dive and pitch terms of the effective angle of attack.
The trans front can provide a limit of 6° when the pitch amplitude is set to 20°. Therefore, increasing h gives the effective angle of attack caused by the dive motion more dominant. This is why, at higher dimensionless speeds, we need high pitch amplitudes to achieve higher propulsion power values.
conclusion
An improved NACA0012 airfoil was proposed and successfully tested. In the case of Reynolds numbers, numerical research was carried out104 using the (intermittent) transition model under different swinging conditions of turbulence, supplementing the numerical calculation with experimental flow display data.
A parametric study of the proposed movable front was carried out, with special attention to the enhancement potential of its propulsion capability. The pitch leading edge is very fond of the average propulsion power, mainly because of the h≥0.5.
At the lowest dimensionless velocity, the airfoil approaches the drag generation zone and there is no real benefit to the dynamic leading edge. In addition, higher beat speeds require greater pitch amplitude to maximize propulsion. The mechanism also reduces power consumption, but the improvement is not as significant as the propulsion power.
The numerically obtained flow field is used to correlate the propulsion power with the flow characteristics. The results show that the improvement of propulsion performance can be obtained by exploiting the presence of leading edge vortices, rather than eliminating them.
Over time, an in-depth analysis of the propulsion coefficient showed that the overall improvement in propulsion or required power occurred roughly where the leading edge of the airfoil was deflected greatest. This is reinforced by the pressure coefficient distribution, indicating that the increase in propulsion power is mainly due to an increase in the frontal area rather than a change in the pressure distribution.
Bibliography:
Design and aerodynamic analysis of flapping mechanism of two-stage flapping wing aircraft; Zeng Zhiqiang; Crown Group; Li Xinyue Mechanical Transmission 2022
Numerical simulation study on energy harvesting and dynamic characteristics of parallel flapping wing WANG Yulu; Han Ying; Karen Guo, Journal of Xi'an Technological University, 2022
Research on flapping wing aircraft control system based on sliding mode adaptive control HE Ying, Beijing Jiaotong University, 2022