Open-jet facility for bio-inspired micro-air-vehicle flight experiment at low speed and high turbulence intensity

Abstract

Bio-inspired micro-air-vehicles (MAVs) usually operate in the atmospheric boundary layer at a low Reynolds number and complex wind conditions including large-scale turbulence, strong shear, and gusts. We develop an open jet facility (OJF) to meet the requirements of MAV flight experiments at very low speed and high turbulence intensity. Powered by a stage-driven fan, the OJF is capable of generating wind speeds covering 0.1 – 16.8 m/s, with a velocity ratio of 100:1. The contraction section of the OJF is designed using an adjoint-driven optimization method, resulting in a contraction ratio of 3:1 and a length-to-diameter ratio of 0.75. A modularized design of the jet nozzle can produce laminar or high-turbulence wind conditions. Flow field calibration results demonstrate that the OJF is capable of producing a high-quality baseline flow with steady airspeed as low as 0.1 m/s, uniform region around 80% of the cross-sectional test area, and turbulence intensity around 0.5%. Equipped with an optimized active grid (AG), the OJF can reproduce controllable, fully-developed turbulent wind conditions with the turbulence intensity up to 24%, energy spectrum satisfying the five-thirds power law, and the uniform region close to 70% of the cross-sectional area of the test section. The turbulence intensity, integral length scale, Kolmogorov length scale, and mean energy dissipation rate of the generated flow can be adjusted by varying the area of the triangular through-hole in the wings of the AG.

1 Introduction

In recent years, micro-air-vehicles (MAVs) employed the flight characteristics of natural flyers, such as birds, bats, and insects at low Reynolds numbers $Re = 10^{2} -10^{4}$, with growing interests for their small size, low weight, and good stealthiness [1,2,3]. With excellent agility and flight performance, small natural flyers can navigate in densely cluttered environments and fly under unsteady wind conditions with strong turbulence, wind shear, and gusts [4,5,6,7]. Most challenging issues of bio-inspired vehicles and natural flyers include the unsteady flow phenomenon and aerodynamic performance of complex flapping wing motions in low-Re and highly unsteady wind environments [1, 8, 9].

Previous studies of experimental diagnostics, computational fluid dynamics (CFD), and theoretical modeling showed that the flyers employ several unsteady aerodynamic mechanisms, including clap and fling [10], delayed stall [11], added-mass effect [12, 13], and paddling [14,15,16,17,18,19], to gain enough lift to counteract their weight, or thrust to exceed the drag. However, these mechanisms are far from being fully understood due to their complex flight parameters and challenging flight control strategies in highly unsteady flows with turbulence and gusts. Since these problems are still hard to be fully solved by state-of-the-art CFD techniques, it is necessary to obtain sufficient experiment data of the unsteady aerodynamics in a wind tunnel generating low-Re and highly unsteady flow conditions.

A wind tunnel is a pipe-like facility generating controllable airflow extensively used in the laboratories [20, 21], but there is a lack of specially designed wind tunnels for insects and bio-inspired MAV flight experiments at a wide range of $Re = 10^{2}- 10^{4}$. Such a wind tunnel requires the ability to generate a controllable flow with the airspeed range covering the flight speed of typical insects (e.g., mosquito: $1.6- 2.4$ km/h [22], honeybee: 27 km/h [23], and dragonfly: 54 km/h [24]), and create the unsteady flow environment with large-scale turbulence, wind shear, and gusts [4,5,6,7, 25]. The design and construction of the wind tunnel also prefers a sizeable test area, low cost, and ease of use.

A general-purpose low-speed wind tunnel usually generates a uniform flow with a low turbulence intensity, an airspeed of $5- 100$ m/s, and a maximum-to-minimum velocity ratio ≈ 10. Several studies obtained the flow with an ultra-low airspeed less than 1 m/s in the wind tunnel. Plate and Cermak [26] used a variable pitch propeller driven by a stabilized DC motor with $230- 1450$ rpm to control the airspeed of $1-30$ m/s, but this sophisticated technique is costly for the implementation and maintenance of the wind tunnel. Other methods for lowering the airspeed include using the auxiliary exhaust duct, valves, and low-speed driven motors. Terao et al. [27] used shut valves to control the flow rate of a suction-type wind tunnel, achieving an operating airspeed of $0.045- 1.4$ m/s. Sun and Zhu [28] designed an open-jet wind tunnel using micro-regulating exhaust holes after the power section, achieving an airspeed of $1- 13$ m/s. Leith et al. [29] designed a wind tunnel driven by a micro-stepping motor, generating a working airspeed of $0.03 - 3$ m/s. Pezzotti et al. [30] built a suction-type wind tunnel powered by a blower, generating a low-speed range of $0.2- 1.25$ m/s for anemometer calibration. These approaches are suitable for mini wind tunnels for anemometer calibration but hard to be extended to large ones for MAV flight experiments.

Generating highly unsteady wind conditions is challenging in the laboratory. Early methods employed grids and stakes in the wind tunnel to generate turbulent flows [31,32,33,34]. Later, active systems were used, e.g., the jet grid/array [35, 36], active grid (AG) [37], multiple controlled fans [38,39,40,41,42,43]. In particular, the “Makita-style” AG showed advantages in terms of high turbulence intensity, real-time adjustable parameters, and easy integration to the existing wind tunnel. It is multifunctional to produce various unsteady flows [44,45,46,47,48,49]. Some wind tunnels [50,51,52] integrated the Makita-style AG in the open-jet test section to conduct flight experiments of flying animals and MAVs at $Re = 10^4 - 10^5$.

The experimental models placed in the open-jet region at the AG downstream lead to conflicting requirements. When the turbulent jet fully develops further downstream, the open jet flow diffuses with a diminishing uniform region. Therefore, it is critical to properly install and optimize the AG in the open-jet test section to produce a sizeable uniform test area (more than $70\%$ of test section’s cross-sectional width/height) with controllable turbulence intensity ($10\%- 20\%$).

The present study designs and constructs a blower-type open-jet facility (OJF) for bio-inspired MAV flight experiments at low speed and high turbulence intensity. It is also featured by the low construction cost, small footprint area, and good extensibility. The OJF design is described in Section 2. The OJF consists of a stage-driven fan, an optimized flow conditioning section, and a modular, interchangeable nozzle with the AG. It can generate steady laminar jet flows or controllable, fully developed turbulent jet flows. The flow quality of a sub-scale prototype wind tunnel is assessed in Section 3. Conclusions are drawn in Section 4.

2 Design of the open-jet facility

As sketched in Fig. 1, the OJF consists of three parts – the power section, the flow conditioning section, and the modularized jet flow generation system. An airflow is first driven by an axial fan. Then the flow conditioning section re-laminarizes the flow. Finally, the modularized system can generate different wind conditions, including laminar and turbulent jets.

Fig. 1

Schematic of the OJF

2.1 Drive system

A powerful, high-precision drive system is essential for generating an air flow at a wide range of $Re = 10^{2}- 10^{4}$ in the test section of a wind tunnel. As shown in Fig. 2a, it consists of an eight-blade fan, a nine-vane anti-twisting deflector, a faring cone, a 315 W brushless DC electric motor, and a step motor. The design methods for the fan and stator can be found in Refs. [53, 54]. The DC motor, with its rotor and stator embedded in the fan and deflector, respectively, powers the fan running at speed from 1000 to 3000 rpm. To obtain a lower, stable speed from 10 to 1000 rpm, a 57-step motor (around 60 W) with a long axis links the rotor through shaft coupling. Additionally, a streamline faring cone improves airflow performance at fan downstream. As marked by “power section” in Fig. 1, the drive system, housed in a 315 mm diameter, 815 mm long circular duct, generates an axial airflow.

Fig. 2

a Schematic of the drive system. b Steadiness of the fan speed

Figure 2b demonstrates the steadiness of the fan rotating at various speeds, measured with a Testo 470 handheld tachometer. The horizontal axis shows the number of sample points at one-minute intervals, and the vertical axis shows the speed of rotation. The stage-driven scheme successfully drives the fan operating at a wide speed range from 19.1 to 3000 rpm with a relative standard deviation (RSD) less than 0.2%, and its cost is much lower than that of large servo motors or DC motors. Moreover, it is straightforward to scale up the power section to larger wind tunnel sizes.

2.2 Flow conditioning

In Fig. 3, from left to right, the flow conditioning section includes a diffuser, a variable-density damping screen, a honeycomb, and homogeneous damping screens to straighten and laminarize the flow. The diffuser, with a divergence angle of $6.73^{\circ }$, converts kinetic energy into pressure energy. A variable-density damping screen is installed downstream to pre-rectify the velocity deficit in the central region of the axial fan wake, as shown in Fig. 3b. The variable-density damping screen is made of three circular mesh layers with different mesh counts welded together – the outer mesh (outer diameter 400 mm, inner diameter 250 mm, 24 mesh counts, and wire diameter around 0.2 mm), middle mesh (outer diameter 250 mm, inner diameter 100 mm, 18 mesh counts, and wire diameter around 0.25 mm), and inner mesh (diameter 100 mm, 10 mesh counts, wire diameter around 0.35 mm). A honeycomb (hexagonal cell of width 3.2 mm, wall thickness 0.1 mm, and length-to-diameter ratio of 10) and four homogeneity damping screens (with nominal apertures of $2 \times 2$ mm² and open areas of 72%) are employed to straighten the flow and suppress turbulence.

Fig. 3

a Schematic of the flow conditioning section (all dimensions in mm). b Variable-density damping screen. c Flow conditioning section of the sub-scale prototype OJF

At the last screen downstream, a contraction is applied to accelerate the flow and improve the flow quality, i.e., the uniformity and steadiness, at the test section. Many factors should be considered in contraction design, including the contraction ratio, length, wall shape, and manufacturing method, and they determine the flow quality, size of the test section, and cost. Typical design methods include potential flow theory, CFD, and simulation-driven optimization methods [55,56,57,58]. These methods typically adopted a uniform velocity inlet boundary, combined with contraction ratios of 6 to 10:1 and length of $0.75 -2 D_i$ to improve the flow quality in the test section, where $D_i$ denotes the contraction inlet diameter. The present OJF for MAV flight experiments in an atmospheric boundary layer aims to reproduce unsteady wind conditions in a relatively sizeable experimental area, so we adopted a very small contraction ratio of 3:1, and used an adjoint-driven method [59, 60] to optimize the contraction shape.

The CFD and adjoint simulations were conducted using ANSYS Fluent 19.0. As shown in Fig. 4a, the computational domain is an axisymmetric plane for the contraction. It consists of an inlet, a leading portion with the length of 0.075D, a contraction section, a straight nozzle with the length of 0.5D, and an outlet. Here, $D=230$ mm was set for the diameter of the contraction exit. A measured airspeed profile at the fan speed 1700 rpm (blue solid line in Fig. 4c) was set as the inlet boundary condition, with a turbulence intensity of 2%. The pressure outlet boundary condition was applied, and the non-slip boundary conditions were applied for walls of the leading portion, contraction, and straight nozzle. The flow was solved in a steady state with spatially resolved boundary layers at $y^{+} < 1$, where $y^{+}$ denotes the wall unit [61].

Fig. 4

a Schematic for the optimization of the contraction wall shape in the x–y symmetry plane, with the control volume (grey dashed line) and 11 control points (dots) in x- and y-directions. b Velocity contours of the initial (upper) and optimized (lower) contractions in the symmetry plane, where $U_{o,\mathrm {out}}$ is the axial velocity at the outlet center ($(x/D,y/D,z/D)=(0.5,0,0)$) of the initial contraction. c Axial velocity profiles at the outlet ($x/D = 0.5$). The velocity profiles at the outlet of the initial contraction and the optimized contraction are labeled as $U_{\text {out,Initial}}$ and $U_{\text {out,Optimized}}$, respectively. The measured velocity profile at the inlet of the contraction is labeled as $U_{\text {in,Measured}}$. The flow uniformity in region $S=\{(x/D,z/D) = (0.5,0), y/D \in [0, 0.4]\}$ is represented by $\mu _{\text {out,Initial}}$ for the initial contraction and $\mu _{\text {out,Optimized}}$ for the optimized contraction

The optimization aims to minimize the variance of the time-averaged axial velocity and the magnitude of the time-averaged radial velocity. Thus, the adjoint observable is defined as

$$\begin{aligned} J = \frac{\sum \nolimits _f {A_f} {\left( {{U_f} - \overline{U}_f} \right) }^2 }{\sum \nolimits _f {A_f} {U_{o,\text{in}}^2} } + \beta \frac{\sum \nolimits _f {A_f} {|{{V_f} } |} }{\sum \nolimits _f {A_f} U_{o,\text{in}}}, \end{aligned}$$

(1)

where the subscript f denotes the cell facet, $A_f$ is the facet area, ${U}_{f}$ is the locally time-averaged axial velocity on the facet f, ${V}_{f}$ is the locally time-averaged radial velocity on f, $\overline{U}_f$ is the averaged $U_f$ over the region $(x/D,y/D) \in [0.25,0.5] \times [0,0.475]$, $U_{o,\text{in}}$ is the axial velocity at the inlet center, and $\beta =10$ is a weight.

In Fig. 4a, the shape to be optimized is enclosed by the dash-dotted lines, with 11 control points in both x- and y-directions. The black dashed line represents the contraction shape designed by matching 3rd- and 5th-order curves [55, 62], and the red solid line represents the optimized shape calculated with the adjoint solver. Figure 4b shows velocity contours in the contraction before and after optimization, where the velocity is calculated by the 2D Reynolds-averaged Navier–Stokes simulation with the SST $k-\omega$ model and axisymmetric swirl correction [63].

Figure 4c displays the axial velocity profiles at the outlet resulting from the initial contractions and the optimized contractions. The flow uniformity of the velocity profile over a region S is defined by

$$\begin{aligned} \mu = \frac{U-\overline{U}}{\overline{U}}, \end{aligned}$$

(2)

where U denotes the time-averaged axial velocity, and $\overline{U}$ denotes the averaged U over the region S. The results demonstrate that the optimized contraction produces a more uniformly distributed velocity within a cross-sectional plane $S=\{(x/D,z/D) = (0.5,0), y/D \in [0, 0.4]\}$.

Although the turbulence intensity and non-uniformity under the current 3:1 contraction ratio may be slightly higher than those under larger contraction ratios of 6 to 10:1 (with turbulence intensity less than 0.2% and non-uniformity less than 0.5%) in typical aeronautical wind tunnels, it fulfills the requirements for flight experiments involving MAVs operating within the atmospheric boundary layer. Furthermore, with equivalent footprint areas and construction costs, the effective cross-sectional area of the test section with the current 3:1 contraction ratio is one to two times larger than that of conventional designs with contraction ratios of 6 to 10:1.

2.3 Jet generation

The modularized jet generation section can be tested in two configurations. First, the baseline laminar-jet (LJ) configuration generates a uniform flow with low turbulence intensity. Here, $Tu=\sqrt{\sum \nolimits _{i=1}^{N}u^2/N}/U$ is calculated over N samples of measured instantaneous streamwise velocity u.

In the implementation, a straight round nozzle with the diameter 1D and length 0.5D is connected to the contraction outlet with the diameter to improve flow uniformity [64].

Second, the turbulent-jet (TJ) configuration consisting of an AG and an extension nozzle is equipped at the outlet of the straight nozzle. This configuration produces a turbulent flow for testing insect/MAV flight in an atmospheric boundary layer. The grid consists of 10 rows and 10 columns of agitator wings, which are actuated independently by 20-step motors. In order to generate turbulent jets with controllable Tu, an improved AG consisting of agitator wings is used. Each wing has an isosceles right-triangular hole. By varying the hole size characterized by the porosity ratio $R_p$ (defined in Fig. 5c), the blockage is adjusted to vary Tu and integral length scale L. An extension nozzle with the diameter 1D and length 1D connected to the contraction exit is installed at the AG downstream to ensure that the jet reaches the fully-developed turbulent state in the test section.

Fig. 5

a Schematic of the jet-flow generation section. b AG. c Schematic of rods and agitator wings in the AG, with $M=20$ mm, $d=5$ mm, and $g=0.7$ mm

3 Assessment of flow quality

To assess the flow quality of the OJF in the LJ/TJ configuration, several experiments were conducted to evaluate the flow steadiness, uniformity, and turbulence intensity. Experimental setups are sketched in Fig. 6. A TSI IFA-300 constant temperature hot-wire anemometry (HWA) system, incorporating a single hot-film probe (model 1210-20), was used to acquire the airspeed and turbulence intensity. The probe was calibrated by the TSI model 1128B calibrator, with a relative calibration error less than 2%. An automatic XY positioning stage controlled the movement of the hot film probe to the measurement points. In the experiment, the room temperature was kept at 26 ± 0.5 °C. A Testo 622 thermo hygrometer and barometer measured the ambient absolute pressure and air temperature. In addition, measurement uncertainties, associated with bias and random errors, are estimated based on the method in Refs. [65,66,67] and plotted as error bars in some figures for results.

Fig. 6

a Measurement planes (dashed lines) in the LJ configuration. b Location of measurement points (blue stars) and the diameter of jet exit (green line). c Airspeed measurement using the hot film probe. d Measurement planes (dashed lines) in the TJ configuration

3.1 Baseline laminar flow

The OJF is first assembled into a baseline LJ configuration, which is used to generate high-quality laminar flow for MAV flight experiments at $Re = 10^{2}- 10^{4}$. Here, we utilized the HWA to assess the airspeed stability, uniformity, and the Tu-distribution of LJ. The HWA is an effective technique for capturing unsteady velocities, making it particularly suitable for quantifying turbulence intensity in wind tunnel test sections [68]. In the LJ configuration, the correlation of the fan speed and time-averaged velocity U at (x/D, y/D, z/D) = (0.1, 0, 0) is shown in Fig. 7, along with Tu.

Fig. 7

Left vertical axis: the dependence between the rotational speeds of the fan and the time-averaged axial velocity. Right vertical axis: the relation between the turbulence intensity and the time-averaged axial velocity (U)

The correlation is in excellent agreement with the linear fit, with a slope of $0.0056 \pm 4.403 \times 10^{-5}$, an intercept of $-0.284 \pm 0.0278$, and the coefficient of determination $R^2=0.999$ at 95% confidence.

The OJF can reach a minimum airspeed of 0.1 m/s and a maximum of 16.8 m/s. In general, it shows that $Tu<0.5\%$ for $U > 1$ m/s and $Tu<1\%$ for $U\in [0.2,1]$ m/s. At very low $U<0.2$ m/s, Tu is slightly higher, around 1% to 3%.

The flow steadiness over the operating airspeed range is shown in Fig. 8. Airspeeds of eight set points were recorded at (x/D, y/D, z/D) = (0.1, 0, 0) within a sampling period of 420 s at 10 kHz. The generated flow is generally steady within a deviation of $u'/U = \pm 0.02$, where $u'$ is the fluctuating axial velocity.

Fig. 8

Left: instantaneous axial velocity at (x/D, y/D, z/D) = (0.1, 0, 0) over the operating airspeed range. Right: closed-up view for comparing the instantaneous axial velocity and the time-averaged one (solid black line with its value shown on the right vertical axis), where the dashed horizontal lines denote $u'/U = \pm 0.02$. For clarity, the data are downsampled by every 100 points when plotting the profiles

The flow uniformity is assessed from the distribution of U along the radial y-direction (defined in Fig. 6c) at different $U_c$. Here, $U_c$ denotes the time-averaged axial velocity at $(x/D,y/D,z/D)=(0.1,0,0)$. Unless stated otherwise, the hot film acquisition frequency is fixed at 10 kHz for 52 s.

Figure 9 plots $U/U_c$ and Tu at $x/D=0.1$ for $U_c=0.21$, 1.04, 4.53, and 13.77 m/s. All of these plots display a flat-topped profile of U. The flow uniformity, with $|\mu |< 1\%$ in the cross-sectional plane $S=\{(x/D,z/D)=(0.1,0), y/D \in [-0.4, 0.4]\}$ indicates that the homogeneous core region occupies no less than $80\%D$. Moreover, Tu remains generally uniform in the core region, with $Tu<0.5\%$ for $U_c>1$ m/s and $Tu\approx 1\%$ for $U_c<1$ m/s, consistent with Fig. 7. The uniformity of the flow field along the z-direction is also excellent (not shown). Considering the axisymmetric design of the OJF, we only used the measurements along the y-direction.

Fig. 9

Normalized time-averaged axial velocity (circles) and turbulence intensity (asterisks) along the radial direction at $x/D=0.1$ for a $U_c=0.21$ m/s, b $U_c=1.04$ m/s, c $U_c=4.53$ m/s, and d $U_c=13.77$ m/s. The distribution of measurement points near the shear layer of the jet is refined. The flow uniformity (diamonds) in the cross-sectional region $S=\{(x/D,z/D)=(0.1,0), y/D \in [-0.4, 0.4]\}$ is plotted, with the reference (dashed) lines for $\mu = \pm 1\%$. Error bars denote measurement uncertainties for velocity and turbulence intensity within the core region with $|\mu |< 1\%$

3.2 Turbulent jet flow

The flow quality for a turbulent jet flow is assessed in the TJ configuration of the OJF. A classical Makita-style AG consisting of agitator wings with $R_p=1$ is added into the LJ configuration, followed by a 1D extension tube to generate a fully developed turbulent flow with a large statistically homogeneous region before the jet diffuses.

The AG was driven in the “double random” mode [69], which can avoid resonance spikes in the energy spectrum at low wavenumbers [46, 70,71,72]. The grid wings rotate at an angular velocity $\Omega \pm \Delta \Omega = 3.5 \pm 2$ rps (revolution per second), and the duration $T \pm \Delta T = 0.8 \pm 0.7$ s.

The distributions of U and Tu along the y-direction, as well as the temporal power spectral density E(f) in terms of the frequency f are shown in Fig. 10, where E(f) is measured at the center of the measurement plane over a time period of 52 s. The dimensionless velocity profile of $U/U_n$ was measured on four y–z measurement planes at $x/D =1.1$, 1.5, 2, and 2.5 after the AG along the y-direction, where $U_n$ denotes the time-averaged axial velocity measured at $(x/D, y/D, z/D) = (0.1, 0, 0)$ without the AG installed. Note that in the TJ configuration the extension tube length is included in the x coordinate, e.g., $x/D=1.1$ represents the sum of 1D for the extension tube and 0.1D for the streamwise distance from the measurement point in the free jet.

Fig. 10

a,c,e,g Normalized time-averaged axial velocity (circles) and turbulence intensity (asterisks) along the radial direction. b,d,f,h Temporal power spectral density at the nozzle exit downstream with different x. With the AG ($R_p=1$), $U_n$ is a,b 1.04 m/s, c,d 4.53 m/s, e,f 9.15 m/s, and g,h 13.77 m/s. Error bars are added to a few points (within the core region with $|\mu |< 2\%$) to show the typical uncertainty of velocity and turbulence intensity

With the AG installed, the actual jet velocity U is lower than $U_n$ due to the blockage of AG. In Fig. 10, the dimensionless velocity profile of $U/U_n$ along the y-direction exhibits a flat-topped shape. The core region at the downstream AG is generally homogeneous. The flow uniformity $\mu$ over $S=\{(x/D,z/D)=(0.1,0), y/D \in [-0.35, 0.35]\}$ remains $|\mu |< 2\%$. This indicates that the homogeneous core region occupies about $70\%D$. As a result of the jet spreading, the homogeneous zone of the jet diminishes downstream, and the spreading rate grows with decreasing U [73]. There are slight bumps on the outer side of the jet near the exit, perhaps due to the small gap between the AG and the extension tube.

In Fig. 10, Tu grows with $U_n$, up to about 24% at $U_n=13.77$ m/s in $x/D = 1.1$, and peaks on the outer sides of the jet. Along the axial direction from $x/D=1.1$ to $x/D=2.5$, U remains nearly unchanged, while $T_u$ decreases. The width of the central homogeneous zone of Tu grows with $U_n$ and decays with x. The energy spectrum in the inertial range shows the -5/3 power law and broadens with $U_n$ [70, 74], indicating that the generated turbulent flow is fully developed. The core region with $|\mu |< 2\%$ exhibits similar well-developed energy spectra. Note that no special processing was applied to mitigate industrial frequency interference in the measurements, so the presence of 50 Hz power frequency interference and its harmonics as high frequency peaks were observed in E(f) in Fig. 10, especially at low $U_n$.

We demonstrate that the present modular OJF operated in the TJ configuration is capable of generating a fully developed turbulent flow in the test area and meanwhile maintaining a wide homogeneous region of 0.7D. This design meets the demanding requirements of achieving a large, homogeneous, fully developed turbulent field in the OJF test section.

3.3 Controllable turbulence intensity and integral length scale

Generating a turbulent field with controllable turbulence intensity and integral length scale is of importance in designing the wind tunnel and AG. The integral length scale L in the atmospheric boundary layer spans a wide range from centimeters to tens of meters, which has an impact on the flying speed, steadiness, and maneuverability of insects/MAVs [75]. We demonstrate that an improved AG consisting of wings with triangular holes (see Fig. 5c) is able to generate a turbulent flow with controllable Tu and L, where the porosity of AG wings is adjusted by varying the hole area.

The effect of $R_p$ of the AG on the distribution of $U/U_n$, Tu, and L at $(x,y)=(1.5D,0)$ along z is shown in Fig. 11. Here, the longitudinal integral length scale L is computed based on the integration of the auto-covariance of u [76] with the method in [77]. In Fig. 11a, c, e, g, $U/U_n$ decays while $T_u$ grows with increasing $R_p$, indicating the important role of $R_p$ in tuning Tu. Additionally, $U/U_n$ decreases with increasing $U_n$, i.e., a higher flow velocity results in a greater relative deficit with the same $R_p$. The overall uniformity of the velocity profile is maintained in the homogeneous region with $W_T/D \approx 0.7$.

Fig. 11

Distribution of a, c, e, g $U/U_n$ and Tu and b, d, f, g normalized integral length scale along the y direction at $(x/D, z/D) = (1.5, 0)$ with different $R_p$ at $U_n$ of a, b 1.04 m/s, c, d 4.53 m/s, e, f 9.15 m/s, and g, h 13.77 m/s. Error bars are added to a few points (within the core region with $|\mu |< 2\%$) to show the typical uncertainty of velocity, turbulence intensity, and integral length scale

Figure 11b, d, f, h plots the distribution of the normalized integral length scale ${L\Omega }/{U}$ along z at different x. The flat-topped profile of ${L\Omega }/{U}$, similar to the velocity distribution, has a homogeneous region with the width 0.8D. The collapse of ${L\Omega }/{U}$ along z with different $R_p$ demonstrates their self-similarity, except at low speed $U_n = 1.04$ m/s, because the blockage change caused by the AG movement and the disturbance caused by wing rotation can influence the AG-generated turbulence.

The effect of $R_p$ on the turbulence statistics at $(x/D, y/D, z/D) = (1.5, 0, 0)$ or $x/M=17.25$ at the AG downstream is shown in Table 1. The statistics, including the Kolmogorov length scale $\eta =(\nu ^{3}/\epsilon ) ^{1/4}$, the Taylor microscale $\lambda = \sigma _u \sqrt{15 \nu /\epsilon }$, the Taylor microscale Reynolds number $Re_{\lambda }=\sigma _u \lambda / \nu$, the mean dissipation rate of turbulent kinetic energy $\epsilon = 15\nu \left\langle {{{\left( \partial u'/\partial t\right) }^2}} \right\rangle /U^2$, are estimated under the assumptions of statistically local homogeneity and isotropy, along with the Taylor frozen hypothesis. Here, $\langle \cdot \rangle$ denotes the time average over 52 s.

Table 1 Effect of $R_p$ on turbulence statistics measured at $(x/D, y/D, z/D) = (1.5, 0, 0)$

The results indicate that the normalized turbulence statistics, including Tu, L, $\eta$, $Re_{\lambda }$, and $\epsilon$, can be adjusted by varying $R_p$ at fixed $U_n$. Namely, the generated turbulence of the OJF is controllable. In general, for fixed AG motion parameters $\Omega \pm \Delta \Omega$ and $T \pm \Delta T$, Tu grows with $U_n$ and $R_p$. The value of Tu for $R_p$ = 1 is almost doubled from that for $R_p$ = 0.5; L/M increases with $U_n$ and decreases with $R_p$ at high velocities 4.53, 9.15, and 13.77 m/s; $Re_{\lambda }$ increases nonlinearly with $R_p$ and $U_n$, reaching a maximum near 1500 at 13.77 m/s; $\eta /M$ decreases with increasing $R_p$ at 4.53, 9.15, and 13.77 m/s; $\epsilon M/{U}^3$ decreases with $U_n$ and increases with $R_p$, which shows the capability of controlling scale separation in turbulence by adjusting both $U_n$ and $R_p$. Note that the present AG size is generally smaller than those reported in the literature [44]. The minimum value of $R_p$ here is 0.5, due to challenges in manufacturing grid wings with small $R_p$. Decreasing $R_p$ could further reduce Tu.

Figure 12 plots the relation between $R_p$ and Tu at $x/D=1.5$ and $x/D=2$ for different $U_n$. In general, Tu increases linearly with $R_p$, and the increment of Tu diminishes along the flow direction. Moreover, Tu increases with $U_n$.

Fig. 12

The relation between $R_p$ and Tu under different $U_n$ at a $x/D=1.5$ and b $x/D=2$

The above results demonstrate that the TJ configuration is able to achieve controllable turbulent flow within the test area. The flow with a good uniformity $|\mu |< 2\%$ in the core region occupies about $70\%D$. It is possible to achieve continuously adjustable turbulence in real time by further optimizing the control strategy of $R_p$.

4 Conclusions

We design the OJF operating at very low speed and high turbulence intensity for bio-inspired MAV/insect flight experiments. The OJF can be also used for anemometer calibration, e.g., hot wire/film probes, vane anemometers, and multi-hole pressure probes in low-speed and highly unsteady wind environments.

The key techniques/concepts in designing the OJF are summarized below. First, a stage-driven motor is designed to power the fan of the OJF, enabling it to generate wind speeds covering a typical range of airspeeds for MAV flight experiments. The minimum speed is as low as 0.1 m/s, and the speed ratio is up to 100:1.

Second, the optimized flow conditioning section integrates a variable-density screen to pre-rectify the wake deficit of the axial fan wake flow, along with a 3:1 contraction optimized through an adjoint-driven method based on the inlet velocity. This configuration enables the OJF to generate high-quality flows across a large test section area, which is up to two to three times larger than conventional designs with a contraction ratio ranging from 6:1 to 10:1.

Third, the modularized design of the jet generation nozzles has two configurations. The baseline LJ configuration produces high-quality laminar flow. The TJ configuration, featured by an AG consisting of improved wings with triangular holes, can generate controllable turbulent wind conditions.

Flow field calibration results show that the OJF in the LJ configuration can generate a high-quality baseline flow with a steady wind speed of $0.1- 16.8$ m/s and low turbulence intensity $Tu\approx 0.5\%$ in a uniform region covering above $80\% D$. In the TJ configuration, the OJF can generate a fully developed turbulent jet flow with Tu up to 24% in a statistically homogeneous region close to $70\% D$.

In the future work, the OJF can reproduce wind shear and gusts in MAV flight experiments, and elucidate flow mechanisms of AG-generated turbulence. Multiple OJFs can form a large array with a larger cross-sectional area such as $3 \times 3$ m² for MAV swarm applications.

Appendix A: Aerodynamic load of the NACA0012 airfoil at low speed and high turbulence intensity

In-flight disturbances, such as turbulence, induce additional loads that can impact the aerodynamic efficiency and stability of MAVs. To demonstrate the capability of the present OJF at low speed and high turbulence intensity, we illustrate the influence of turbulence intensity on the aerodynamic load of the NACA0012 airfoil at low Re.

The airfoil with chord length $C=0.06$ m and span $B=0.1188$ m has an aspect ratio close to 2. It is manufactured using photosensitive resin and 3D printing, and its surface is polished to achieve a smooth finish. The inlet velocity is 10.2 m/s, corresponding to $Re \approx 3.9 \times 10^4$. Four typical flow conditions, $Tu=0.5\%$ (no AG), $Tu=2.4\%$ (AG in passive mode with agitator wings aligned with the mean flow), $Tu=8.9\%$, and $Tu=19.5\%$ (AG with wings of $R_p=0.5$ and 1, respectively, with $\Omega \pm \omega =3.5 \pm 2$ rps, $T \pm \Delta T=0.8 \pm 0.7$ s), are adopted. These turbulence intensities were measured at $x/D=0.5$ from the OJF outlet. Then the airfoil was installed, and the airfoil 1/4 aerodynamic center is also located at $x/D=0.5$.

As sketched in Fig. 13a, the airfoil is linked to a three-component force balance (LMC3501A-10N, Nissho) via a steel rod at its 1/4 aerodynamic center. Thus, the lift $F_L$ and drag $F_D$ can be measured at the frequency 5 kHz. Here, we denote time-averaged lift as $F_L$, time-averaged drag as $F_D$, and instantaneous lift and drag as $F_l$ and $F_d$, respectively, and their corresponding coefficients as $C_L=2F_L/(\rho U^2 C B)$, $C_D=2F_D/(\rho U^2 C B)$, $C_l=2F_l/(\rho U^2 C B)$, and $C_d=2F_d/(\rho U^2 C B)$. The force balance connecting to a turntable enables aerodynamic measurements from $-5^{\circ }$ to $25^{\circ }$ with the interval of $1^{\circ }$ and accuracy of $0.025^{\circ }$. To maintain two-dimensionality, endplates on both sides of the airfoil are positioned approximately 1 mm from the model tip and securely affixed to the OJF outlet. Corrections [78] were applied to the aerodynamic forces and angle of attack $\alpha$. The uncertainty for $C_L$ and $C_D$ is estimated using the method outlined in Ref. [79] and plotted in Fig. 13 as error bars.

Fig. 13

a Schematic for the OJF and the measurement of the aerodynamic load of the NACA0012 airfoil. b Lift and drag coefficients versus the angle of attack at $Re \approx 3.9 \times 10^4$ and various turbulence intensities, along with the theoretical result and the experimental results in Ref. [80]. c Fluctuations of the total aerodynamic force coefficient versus the angle of attack at $Re \approx 3.9 \times 10^4$ and various turbulence intensities

Figure 13b plots the profile of $C_L=2F_L/(\rho U^2 C B)$ versus $\alpha$ with various Tu. At $Tu=0.5\%$, the profile of $C_L$ shows a dip around $0^{\circ }$. Then, up to $\alpha \approx 4^{\circ }$, $C_L$ grows steeper than the theoretical estimation $2 \pi \alpha$. Finally, the growth slows down, reaching stall near $\alpha =10^{\circ }$. This result generally agrees with that in Ref. [80] for $Re=3 \times 10^4 - 4 \times 10^4$ at $Tu=0.1\%$, except for slight discrepancies perhaps due to inflow turbulence and blockage corrections.

The turbulence intensity has an impact on $C_L$. As Tu increases, the negative lift near $0^{\circ }$ disappears. For $\alpha =3^{\circ }-10^{\circ }$, the overall growth of $C_L$ (versus $\alpha$) is enhanced with Tu from $0.5\%$ to $8.9\%$, whereas it is mitigated with $Tu=19.5\%$. The stall angle and the maximum $C_L$ grow with Tu. In addition, $C_D=2F_D/(\rho U^2 C B)$ at different Tu are similar before stall for small $\alpha$, whereas $C_D$ increases with Tu for $\alpha >10^\circ$ due to post-stall changes in pressure drag.

Figure 13c plots the standard deviation $\sigma _{C_t}$ of the coefficient $C_t = 2\sqrt{F_l^2+F_d^2}/(\rho U^2 C B)$ of the total force. The overall load fluctuation increases with Tu, e.g., $\sigma _{C_t}$ at $Tu=19.5\%$ is about eight times of that at $Tu=0.5\%$. Moreover, $\sigma _{C_t}$ has minor variations before stall and rises after stall, and the largest growth of $\sigma _{C_t}$ occurs at $Tu=19.5\%$.

These observations indicate that Tu has an impact on airfoil fatigue loads. Therefore, the present OJF operating at a range of Tu can facilitate understanding the influence of Tu on airfoil loads and developing control methods for MAVs in atmospheric turbulence.