An aerodynamic characterization facility for micro air vehicle research

Abstract

The Aerodynamic Characterization Facility is a unique facility located at the University of Florida’s Research and Engineering Education Facility designed with the intent to study complex low Reynolds number, unsteady aerodynamic phenomena. This facility includes an open jet, open return wind tunnel specifically designed to operate in the low Reynolds number regime where current research efforts are being tasked for Micro Air Vehicle flight platforms. Specifically, the wind tunnel operates with freestream velocities ranging from nominally 0 to 22 m/s with 0.1 m/s resolution provided by a variable frequency drive utilized to control the tunnel. The test section entrance is 1.07 m² with a length of 4.6 m. Flow uniformity investigations at free stream velocities of 2 and 4 m/s demonstrate a uniform flow core throughout the test section of at least 50% of the 1.14 m² contraction exit. Hot wire anemometry investigations present turbulence intensities less than 0.22% for free stream velocities greater than 1 m/s. The facility is also equipped with a dynamic motion rig and active turbulence generator. The dynamic motion rig is utilized to investigate unsteady aerodynamics over dynamic kinematic motions similar to what one might find in small birds and insects. The active turbulence generator provides a means to introduce atmospheric-like turbulence into the wind tunnel to understand the coupling between turbulence and unsteady flow phenomena associated with bird and insect flight.

Keywords

Low Reynolds number atmospheric turbulence micro air vehicle wind tunnel

Introduction

In recent years, there has been a push to develop Micro Air Vehicles (MAVs) that employ the flight characteristics of low Reynolds number natural fliers such as birds, bats, and insects.^1,2 These natural fliers have been shown to utilize unsteady flow phenomena to increase their agility and efficiency. Therefore, current research topics are focused on understanding the unsteady flow physics associated with flexible structures integrated on static and moving wing configurations.³ However, lack of facilities exists that utilize air as the working medium and can operate in the realm of chord based Reynolds numbers (Re_c) existing in the flight regime of small natural fliers (∼10⁴).

One of the consequences of low Reynolds number flow is the introduction of added mass effects which relate the local acceleration of the flow to a force vector. The consequence of added mass effects on the aerodynamics of flexible wings between various working fluid mediums is of current interest in the research community. Currently, multiple facilities utilize water as their fluid medium. These facilities are capable of measuring the flow field and aerodynamics of low Reynolds number, unsteady vortex structures. However, a relationship does not currently exist relating these aerodynamic forces to those utilizing air as the working medium.⁴ This provides the need to have a facility that can perform similar measurements in a more flight realistic environment. Additionally, this facility will provide a needed role in understanding the flow physics associated with low Reynolds number flight as well as providing a controlled testing environment for new flight vehicles before they are utilized in an open environment.

To this end, a new wind tunnel facility located at the University of Florida’s Research and Engineering Education Facility (UF-REEF) was built in a joint effort with the Air Force Research Laboratory (AFRL). Much of the design criteria for this facility was discussed in a paper by Babinsky et al.⁵ along with some trade studies on different facility designs.

Facility description

The Aerodynamic Characterization Facility (ACF) provides a unique facility to investigate the effects of unsteady fluid phenomena, particularly at low velocities, as they pertain to MAVs. The ACF consists of a low-speed wind tunnel designed to operate with relatively low turbulence intensity and uniform flow over its entire operating range of free stream velocities ( $U_{\infty})$ . The control of the tunnel’s speed is also sensitive at low speeds for a velocity resolution on the order of 0.1 m/s. The ACF is equipped with a dynamic motion rig (DMR) to traverse a wing through various plunge and pitching kinematic motions. The ACF also has a capability to introduce atmospheric turbulence conditions into the flow through the use of an Active Turbulence Grid (ATG). The following sections will describe each of the following systems.

Wind tunnel

The wind tunnel is of Eiffel type design which corresponds to the fan being on the downstream side of the test section which pulls air through the tunnel. The flow enters the wind tunnel through a 3.45 m² bell mouth collector. This can be seen in Figure 1. The flow proceeds through a screen pack to reduce any large coherent structures existing within the system air. The flow first enters a 1.27 cm, hexagonal cell, aluminum honeycomb which is sandwiched between two high porosity stainless steel, wire mesh screens with mesh densities of 9.45 wires/cm. Four wire mesh screens with densities 9.45, 12.6, 18.1, and 22 wires/cm are placed downstream at equal distance of 8.6 cm. After exiting the final mesh screen, the flow enters a settling chamber approximately 1.37 m length which allows for small scale fluidic structures generated by the flow conditioning to decay.

Figure 1.

ACF wind tunnel flow entrance section.

The flow is accelerated through the use of an 8:1 contraction section designed using the tools discussed by Mathew et al.⁶ This method fits two eighth-order polynomials such that the slope at a user-defined intermediate location is equivalent for each polynomial. This algorithm utilizes a series of geometric constraints including the length of the nozzle, one half of the nozzle exit height, a normalized matching point, and the contraction ratio of the inlet. The result is continuous inlet profile with a zero slope at start and end of the profile. The curve utilized for the ACF inlet is shown in Figure 2.

Figure 2.

ACF contraction section curve from Mathew et al. algorithm.

The flow exits the contraction section and proceeds into the test section portion of the wind tunnel. The test section is comprised of an open test section 3.35 m high, 3.66 m wide, and 4.57 m long in the streamwise direction. This results in a test section volume just less than 56.6 m³. This design allows for experimental equipment to be placed around the flow core throughout the test section. The uniform flow core enters the test section in the form of a 1.07 m² column of air and proceeds to exit through the diffuser.

Figure 3 presents the aft end of the wind tunnel with the flow leaving the test section and ultimately exiting into the surrounding room. The diffuser collects the flow core from the test section utilizing a bellmouth entrance with an inner dimension of 1.16 m². The square cross section of flow is transitioned into a 1.52 m circular cross section of flow through the length of the diffuser so as to provide a net area increase. The area increase was designed to avoid unfavorable pressure gradients and ensuing flow separation over the entire velocity regime of interest. The diffuser also gives some pressure recovery to the flow and allows for higher maximum velocity operation. The fan was designed to provide 23.6 m³/s flow rate accounting for all head losses, and it was tested in the complete system to provide up to 27.6 m³/s which corresponds to a mean 24.2 m/s velocity. Realistic tests with all instrumentation in the facility put the top speed at approximately 22 m/s.

Figure 3.

ACF wind tunnel diffuser/fan section.

The fan section is connected to the end of the diffuser with a flexible coupling to isolate any motor vibrations from the rest of the tunnel. The axial fan driving the flow is a Howden Buffalo 60-26-1200AP unit driven by a 37.3 kW, Totally Enclosed Air Over (TEAO), constant speed, 1185 r/min, AC induction motor. This motor is controlled from a Toshiba-VF-AS1 inverter, or variable frequency drive (VFD). The flow finally proceeds through an inline flow silencer providing at least 10 dB attenuation of the main fan beat frequencies over the operating range. The flow leaves the silencer ultimately entering the surrounding room.

Dynamic motion rig

The DMR provides a capability to investigate the development of unsteady fluid phenomena over wings driven through various kinematic motions. Specifically, the DMR is designed to perform pitch, plunge, and coordinated pitch–plunge maneuvers. These maneuvers are performed using two Parker Ironless linear positioners (Model: T4DB53-6NPB1-B73-1BA) capable of 767 mm of travel. Figure 4(a) presents the DMR located in the test section of the wind tunnel. Both motors are mounted vertically on a support structure built out of 8020 extruded aluminum. Each motor is equipped with a 5 µm resolution linear encoder along with limit and homing sensors for consistent positioning. Power is applied to the motors through Parker AR-08AE drivers which provide 750 W of continuous shaft power. This results in a continuous force of approximately 663 N (∼150 lbs). The maximum velocity attainable by each linear motor is 7 m/s. A Galil DMC-2030 controller is used to communicate the desired linear kinematic motions. The controller also provides a means to trigger external measurement devices from motor location information.

Figure 4.

Dynamics motion rig (a) configuration in test section and (b) sting linkage mechanism.

The sting mechanism converts the two linear motions to a pitching motion by pivoting the sting about the upstream linear motor position. Figure 4(b) presents the degrees of freedom associated with the sting mechanism. Each degree of freedom is indicated by a blue arrow. The upstream linear motor is connected to the sting mechanism with a rotational degree of freedom. The downstream linear motor is connected by rotational and transvers degrees of freedom. Pitch angles of approximately ± 60° are achievable.

Active turbulence grid

The ACF is equipped with an active turbulence grid (ATG) designed similar to that by Makita⁷ with a few modifications leveraging on lessons learned.^8–16 This increases the capabilities of the ACF to enable gust and turbulence research. This type of ATG consists of two orthogonal grids of 7 × 7 rotating vanes with an axial spacing, M, of 13.3 cm which can be seen in Figure 5. Each vane consists of a shaft with attached winglets which are driven to rotate by a computer controlled motor. The vanes are separated by isolators to prevent vibrations from causing impacts similar to Poorte and Bishuviel.¹⁵ The ATG is located at the exit of the contraction upstream of the test section, and the action of the spinning vanes causes the air flowing through the device to become highly turbulent.

Figure 5.

Active turbulence grid.

The ATG is controlled via a National Instruments PXI-6533 high speed, digital I/O card similar to Larssen and Devenport.⁸ The forcing protocol for each vane is a randomized process where duration and rotational rate are randomly selected from a uniform distribution. After specified rate and time delay have been randomly selected, the motors accelerate to spin at a particular constant rate in one direction for the selected time period and then ramp through a full stop to the reverse rate and hold that for the same time period previously selected. After the second time period has elapsed, the motors ramp to the next randomly selected rate, time period and direction, and they then follow the same behavior. This method causes a randomization in rotational rate and direction, and asynchronous operation of all the motors. This also has an added benefit of adding zero net vorticity to the flow over two time periods. This method avoids frequency spikes that occur in synchronous operation shown by Makita, and more recently by Roadman and Mohseni^7,19,20 and generates a smooth frequency distribution with desired, adjustable turbulence statistics.⁸ Motion profiles are stated as a mean and variance of rotational rate, Ω ± ω, and a fixed mean and variance in time, T ± t = 1.5 ± 1 s.

Baseline flow quality

The ACF was built for the purpose of producing clean flow at Re_c of approximately O[10₄]. Characterization experiments are performed to ascertain the effectiveness of achieving the desired criteria. Flow uniformity experiments are conducted at a nominal Re_c of 2 × 10⁴ and 4 × 10⁴ which corresponds to mean velocities of 2.0 and 4.0 m/s. Turbulence intensity measurements are acquired to determine the minimal turbulence intensity associated at these Reynolds numbers. The following sections discuss these studies.

Flow uniformity

Flow uniformity studies were conducted at freestream velocities of 2 m/s and 4 m/s with a total pressure rake equipped with 32 ports equally space 2.54 cm from one another. Figure 6 displays the total pressure rake and its mounting. The coordinate system is aligned such that X is the streamwise direction, Y is spanwise, and Z is vertical. Velocity measurements are obtained through manually positioning the rake through 21 vertical locations and two spanwise locations. This results in a uniform grid spacing of 5.08 cm over the entire cross section of the flow core. Differential pressure readings are acquired with a Heise differential pressure transducer with a full scale resolution of 249 Pa. The quoted accuracy of this transducer is 0.07% of full scale. A Scannivalve pressure switch is utilized to switch between each pressure port on the rake. The static pressure of the air in the test section was measured with a GE Druck DPI 142 Barometric Indicator with a range between 0.75 and 1.15 Bar and a resolution of 0.01% full scale. The temperature inside the test section was measured with an Omega P-M-1/10 RTD sensor. This RTD is accurate to within ± 0.04℃ at a reference temperature of 20℃. These devices result in a measurement error of 1.8% and 0.48% at a mean velocity of approximately 2 m/s and 4 m/s, respectively. Each measurement was averaged over 120 samples which were acquired at a rate of 2 Hz.

Figure 6.

Flow uniformity pressure rake setup.

Figure 7 presents contour plots of the normalized mean flow fields of 2 m/s at four streamwise locations. All measured velocities are normalized by the freestream velocity. It can be seen that the flow possesses a uniform core that covers at least 50% of the cross-sectional area even at the furthest streamwise location equal to 62.5% of the length of the test section. There appear to be small asymmetries, but in general the flow evolves in a symmetric fashion. At 4 m/s shown in Figure 8, the small asymmetries appear to be reduced. For both cases, the region of uniform flow at the center was within 1.5% of the centerline velocity; this demonstrates a clean flow clear of any disturbances.

Figure 7.

Normalized streamwise mean velocity profiles for a freestream velocity of 2 m/s at streamwise locations: (a) 0.0%, (b) 0.5%, (c) 40%, and (d) 62.5%.

Figure 8.

Contour plots of normalized streamwise mean velocity profiles for a freestream velocity of 4 m/s at streamwise locations (a) 0.0% and (b) 40%.

Further assessment of the flow quality is obtained through plots of the normalized velocity at the vertical and horizontal centerlines for each spanwise location at 2 m/s. Figure 9 shows that no significant velocity gradients are present in the vertical or horizontal directions. Also apparent in these plots is maintenance of flow core uniformity to within 1.5% at such a small freestream velocity.

Figure 9.

Normalized streamwise velocity profiles of the (a) vertical and (b) horizontal centerline for various streamwise locations with a uniform core of 2 m/s.

The unsteadiness of the flow has yet to be realized due to the low frequency response of the static-pitot measurements. Therefore, a single component, constant temperature hot wire anemometer (CTA) system will be utilized to measure the spectral content of the flow. An Auspex Corp. hot wire with a sensing element diameter of 5 microns and a length of approximately 1 mm was used in these experiments. A Dantec 55M10 bridge was connected to the sensing element. The analog output of the bridge was acquired with a National Instruments 4472 card with a sigma-delta analog-to-digital converter with 24 bit resolution. These experiments will consist of acquiring measurements at the center of the entrance of the test section. The resulting data sets included 256 independent ensembles acquired at a rate of 2048 Hz for 4096 samples. This results in a spectral bin width of 0.5 Hz.

Calibration of the hot wire probe was accomplished by placing a pitot-static probe in close proximity to the hot wire and collecting data for a series of freestream velocities extended over the full range of velocities for evaluation. For each of the freestream velocities, the mean velocity and voltage are utilized to fit a fourth-order polynominal curve.⁹ The calibration curve fit resulted in error of the mean velocities to be less than 1% for all velocities greater than 1 m/s. To calculate turbulence intensity in a wind tunnel, it is common practice to high pass filter the fluctuations. This insures that fluctuations associated with scales larger than the facility are not taken into account. This is accomplished by calculating a minimal, physically realized frequency based on the time it would take a disturbance to propagate across the entire test section length (L) at the mean centerline velocity (U), resulting in a frequency cutoff value defined by

f_{c} = \frac{U_{\infty}}{L}

(1)

After filtering out these scales, the values are listed in the last column of Table 1 and are all less than 0.25% for freestream velocities greater than 1 m/s. The turbulence frequency shows increase at freestream velocities between approximately 8 m/s and 13 m/s. To understand this development, the spectra of the hot-wire signal will be utilized.

Table 1.

Turbulence intensity as a function of mean velocity.

U, Mean velocity (m/s)	Turbulence intensity <u’_filtered/U_∞>
0.42	1.16%
1.13	0.08%
1.85	0.06%
2.58	0.07%
3.68	0.08%
7.78	0.11%
9.67	0.15%
11.56	0.21%
13.58	0.16%
15.37	0.10%
17.24	0.07%
19.00	0.05%

The power spectral density of the hot-wire signal is investigated to determine the magnitude of each frequency on the overall turbulence intensity. Figure 10 presents the power spectral density of the hot wire signal with respect to the frequency and non-dimensional Strouhal number. The Strouhal number is defined by

St = \frac{fc}{U_{\infty}}

(2)

where f is the frequency, c is the chord, and

U_{\infty}

is the freestream velocity. In Figure 10(a), no significant spikes in the power spectral density are present at the baseline case of 0.0 m/s, as this value represents the noise floor measurement of the system. As the free stream velocity is increased, a spike at the lower frequencies between 1 and 10 Hz develops and increases in magnitude as the corresponding velocity is increased. The frequencies of 15 and 30 Hz are also indicative of large power spectral density spikes which become more significant at the larger mean velocities.

Figure 10.

Power spectral density: (a) function of frequency and (b) function of Strouhal number.

Figure 10(b) presents the power spectral density as a function of the Strouhal number. The high power spectral densities associated with 15 and 30 Hz do not collapse onto one another; therefore, it is reasoned that these spikes are more indicative of noise introduced into the hotwire signal. In contrast, the lower frequency spikes collapse into a Strouhal number range of 0.3–0.5. This Strouhal number range corresponds to what is generally expected for a jet column mode.¹⁰

The jet column modes are further investigated utilizing a Kulite LQ-125-5SG pressure transducer placed on the bell mouth of the wind tunnel diffuser and a hot wire located in the center of the entrance to the test section. The Kulite and hot wire signals are sampled simultaneously using a National Instruments 4472 card. The ordinary coherence between the signals present a significant spike at lower frequency values in Figure 11. High values of the ordinary coherence function are indicative of the hotwire and pressure signals measuring the same physical phenomenon. Therefore, it is concluded that power spectral density spikes associated with frequencies between 1 and 10 Hz are indeed a result of the jet column modes.

Figure 11.

Coherence between hotwire and pressure signals.

Atmospheric turbulent environment

The ATG gives a unique ability to generate freestream turbulence with different statistics by varying the programmed run mode; however, this complicates characterization. Fifteen different run modes were investigated with a single-point hot wire measurement performed at five downstream locations and four freestream velocities. A two-point, hot wire measurement was then performed to determine how the incoming integral length scale compared to cross-stream length scales. Lastly, the turbulence flow uniformity was assessed by measuring the turbulence profiles at multiple points in the flow field.

Single point measurements

A single point CTA X-wire investigation was used to determine the dependence of turbulence statistics on ATG run mode, wind tunnel speed and downstream location. The X-wire was an Auspex AHWX-100 probe with 5 µm wires approximately 1 mm long, and this was connected to two Dantec 55M10 bridges. The probe was calibrated according to Sytsma and Ukeiley.¹¹ The tunnel speed was changed through throttle settings of 14.5, 28.5, 43.5 and 58%. Running higher speeds with the ATG was neglected due to a potentially dangerous scenario where the vanes vibrate and impact each other. Five downstream locations of $X / M$ are selected to be 5, 10, 12.5, 15 and 20. These downstream distances were chosen because models would typically be mounted between $X / M$ of 10 to 12. The ATG run modes consist of 15 experiments to better understand how run mode affects statistics. Each experiment was specified by mean and variance rotational rate pairs. The following modes are tested: Ω ± ω = 2 ± 1, 3 ± 1.5, 4 ± 2, 5 ± 2.5, 4 ± 1, 5 ± 1.25, 6 ± 1.5, 0 ± 3, 0 ± 4, 0 ± 5, 0 ± 6, 0 ± 8, 2.5 ± 0, 5 ± 0 and 8 ± 0. Each test is completed with the probe oriented horizontally as well as vertically to obtain data for all three components of the velocity vector.

The data were sampled at 50 kHz for 20 s in eight ensembles. This yielded reasonably small 95% confidence intervals on mean velocity. The mean fresstream velocity (

U_{\infty})

is calculated according to Zhang’s method⁹ for autocorrelated data to within a 95% confidence interval. The three components of velocity allowed for directional turbulence intensities,

{TI}_{X}, {TI}_{Y}

and

{TI}_{Z}

, to be calculated. The incoming autocorrelation length scale (

L_{XX})

was calculated the same as Mydlarski and Warhaft.^12–14 Anisotropy ratios

I_{XY, XZ, YZ} = \frac{{TI}_{X}}{{TI}_{Y}}, \frac{{TI}_{X}}{{TI}_{Z}}, \frac{{TI}_{Y}}{{TI}_{Z}}

(3)

indicate the level of anisotropy in the flow. A sample of the results of these tests at

X / M

= 12.5 and the highest velocity setting at around 10 m/s are included in Table 2.

Table 2.

Calculated turbulence statistics at downstream location at $X / M$ = 12.5 and 58% throttle setting.

Ω ± ω	U_∞ ± 95% CI	${TI}_{X}$	${TI}_{Y}$	${TI}_{Z}$	L_XX	I_XY	I_XZ	I_YZ
Hz	m/s	%	%	%	m
2 ± 1.0	11.49 ± 0.35	20.2	19.3	18.7	0.504	1.05	1.08	1.03
3 ± 1.5	11.48 ± 0.28	18.8	18.6	18.1	0.439	1.01	1.04	1.03
4 ± 2.0	11.31 ± 0.25	18.4	17.8	17.6	0.413	1.03	1.05	1.01
5 ± 2.5	10.96 ± 0.25	18.4	17.5	17.2	0.469	1.05	1.07	1.02
4 ± 1.0	11.25 ± 0.24	18.4	17.5	17.7	0.400	1.05	1.04	0.99
5 ± 1.25	10.96 ± 0.23	18.0	17.0	17.0	0.442	1.06	1.05	1.00
6 ± 1.5	10.42 ± 0.34	18.6	16.7	17.2	0.701	1.11	1.08	0.98
0 ± 3.0	11.15 ± 0.40	21.8	19.4	18.7	0.608	1.12	1.16	1.04
0 ± 4.0	11.20 ± 0.36	20.6	19.5	18.5	0.549	1.06	1.12	1.05
0 ± 5.0	11.20 ± 0.32	19.9	19.1	18.3	0.507	1.04	1.08	1.04
0 ± 6.0	11.12 ± 0.34	20.2	18.9	18.1	0.584	1.07	1.12	1.04
0 ± 8.0	10.96 ± 0.32	19.3	18	17.5	0.614	1.07	1.11	1.03
2.5 ± 0	11.45 ± 0.30	18.9	19.6	18.4	0.427	0.97	1.03	1.06
5 ± 0.0	10.93 ± 0.24	18.1	17.1	17.2	0.479	1.06	1.05	0.99
8 ± 0.0	9.56 ± 0.42	19.3	16.4	16.7	0.86	1.18	1.16	0.98

The results show interesting trends. The turbulence intensity decays rapidly from $X / M$ = 5 to $X / M$ = 10 after which the decay is much slower. This means that upstream of $X / M$ = 10, the turbulence is in active development, whilst downstream it is approximately well developed. This is consistent with findings by other authors.^7–18 Part of the decay process involves the transition from a strong anisotropy at $X / M$ = 5 to isotropy nearing unity downstream. The $I_{YZ}$ parameter trends greatly towards unity indicating that the cross-stream directions are nearly isotropic downstream of the development region.

Two-point measurements

The single-point hot wire measurements allow for a quantitative assessment of how variables such as downstream location, wind tunnel throttle and resulting velocity, horizontal Y and vertical Z location, and ATG run mode affected the turbulent statistics. In particular, the assumptions of homogeneity and Taylor’s hypothesis¹⁵ allow for the calculation of the incoming integral length scale, $L_{XX}$ . The high turbulence intensities indicate that Taylor’s hypothesis is to some extent invalid, hence the length scales should be measured in another way less prone to error. In order to determine the integral length scales in the other two orthogonal directions without the assumption of Taylor’s hypothesis, multi-point CTA measurements are taken and the integral of the spatial cross-correlation coefficient is used to find length scale.

The procedure is to start the ATG motion profile that had been selected and then simultaneously gather data from two calibrated X-wire CTA probes. One probe was held fixed at the tunnel centerline while the other was moved by a known distance in either the Y or Z directions. The measurement planes of both probes were equivalent and co-linear with the axis of measurement. One probe was connected to the two independent Dantec 55M10 bridges while the other probe was connected to two Dantec 54T30 MiniCTA bridges. The Dantec 54T30 MiniCTA bridges have a stated maximum frequency resolution of 10 kHz. The velocity measurements were acquired at a sampling frequency of 20 kHz for 20 s. Eight ensembles were acquired in total at each location. This was completed at multiple locations in the YZ plane with a 1 cm spacing.

The spatial cross-correlation coefficient (CC) is calculated at each displacement by taking the inner product of the Y or Z velocity component measured from probe 1 and 2, and dividing it by the L² norm of each signal as shown by

{CC}_{Y} = \frac{v_{1} v_{2}}{v_{1} v_{2}}

(4)

and

{CC}_{Z} = \frac{w_{1} w_{2}}{w_{1} w_{2}}

(5)

The advantage of this method is that Taylor’s hypothesis is not a required assumption, which is probably more realistic in light of the large turbulence intensities involved. The cross-correlation coefficients are then numerically integrated using trapezoidal rule over distance to yield the integral length scales

L_{{YY}_{CC}} = \frac{1}{2} \sum_{i = 2}^{N} (Y_{i} - Y_{i - 1}) ({CC}_{Y_{i}} - {CC}_{Y_{i - 1}})

(6)

and

L_{{ZZ}_{CC}} = \frac{1}{2} \sum_{i = 2}^{N} (z_{i} - z_{i - 1}) ({CC}_{z_{i}} - {CC}_{z_{i - 1}})

(7)

which may then be compared against the temporal autocorrelation-derived length scale

L_{XX}

The Y displacements were able to be traversed much further than the Z due to the presence of the tunnel ceiling. The probe was traversed upwards to avoid interference with the supporting material. The measured cross-correlation coefficients compared to the temporal autocorrelation coefficients, presented in Figure 12, indicate the level of anisotropy in length scale. The autocorrelation length scale was determined by integrating to the same limits as the Y traverse, while the Z length scale was only integrated to its maximum traverse length. An interesting result is that the Y and Z cross-correlation coefficients fall neatly on top of each other indicating that similar to the single-point statistics, the Y and Z directions have a great deal of isotropy. However, an unanticipated effect is that the Ω ± ω = 2.5 ± 0 run mode showed a great deal of XY and XZ anisotropy in length scales at all speeds, even though the anisotropy ratio is near unity. Conversely, the Ω ± ω = 0 ± 3 and 0 ± 8 run modes appear to have little XY and XZ anisotropy in length scales at higher speeds despite the fact that their anisotropy ratios are far from unity.

Figure 12.

Auto and cross-correlation coefficients plotted against length at 58% throttle setting and $X / M = 12.5$ for (a) Ω ± ω = 2.5 ± 0 and (b) Ω ± ω = 0 ± 3.

Turbulent flow uniformity

Single-point X-wire CTA measurements traversed across the $X / M = 12.5$ plane in Y and Z directions indicate the dependence of turbulence statistics across the measurement plane. This investigation highlights the uniformity of the turbulent flow field, particularly in the region where a wind tunnel model would be placed. A baseline case was also investigated for comparison purposes. Models to be tested are expected to range from 15 cm in span to 60 cm in span, and the chord may vary from 15 to 30 cm, with angles of attack less than 30°. The traverse survey was performed to accommodate any future models by moving the single X-wire ± 25 cm in the vertical Z direction and ± 37.5 cm in the Y direction. Figure 13 shows the traversed area overlaid on test section size with a notional maximum model size.

Figure 13.

Diagram of traversed area (red) with measurement location (red squares) compared to test section size (black), largest expected model (blue) and core averaging region (green).

The data were sampled using the Dantec 54T30 bridges at 20 kHz and using the same parameters and periods used to gather the single point statistics, and the X-wire was oriented to measure the velocity components in the X–Z plane. Contour plots of important statistical properties are shown in Figure 14. The contour data are presented as a percent variation from a mean of an averaged core region which is comprised of the innermost nine points, where the dummy variable θ is replaced by flow statistics such as mean velocity, turbulence intensity, etc. The survey indicated a general uniformity in the freestream velocity and other statistics within the core region and extending outward for all cases. The baseline case agreed with the pitot rake data presented earlier in Figure 8. The turbulent flows exhibited similar uniformities across the region of interest, although the shear layer was evident in the Y direction. The Z shear layer indicated an up-down non-uniformity that is attributed to the asymmetric shape of the test section enclosure. The statistics indicate that any model inside of Y = 30 cm and Z = 12 cm should be away from most of the effects of the shear layer and be within an essentially uniform flow. Although not strictly homogeneous, the turbulent flow field as measured has shown itself to be acceptably uniform for the purposes of this research.

Figure 14.

Survey results for $U_{\infty}$ = 9.48 m/s and X/M = 12.5 for Ω ± ω = 2.5 ± 0. Data are presented as a percentage variation from the mean of the core region, θ_%. Plotted are mean velocity (a), incoming turbulence intensity (b), anisotropy ratio I_XZ (c), and integral length (d).

Summary

In this paper, the Aerodynamic Characterization Facility was introduced as a unique facility with flow characteristics that are well suited for investigating low Reynolds number flow phenomena. The low speed wind tunnel is capable of velocities from 0.5 to 22 m/s, and the dynamic motion rig is used to position models in the test section and move them rapidly. Passive and active turbulence grids are available to simulate varying degrees of atmospheric turbulence up to 30% turbulence intensity, while baseline flows at the test section exit can exhibit less than 0.2% turbulence intensity. The baseline tunnel was characterized for flow uniformity and exhibited a nearly flat velocity profile and predictable shear layer growth downstream, and turbulence intensity and spectra were evaluated. The flow behind the ATG was similarly characterized and was shown to possess similarly uniform velocity and turbulent statics flow in a core region, although shear layer growth is more rapid.

Footnotes

Acknowledgement

The authors would like acknowledge a large number of individuals associated with the facility, specifically Prof. Roberto Albertani, Mr Judson Babcock, Prof. Louis Cattafesta, Mr Parvez Khambatta, and Ms Pam Prather.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors at the University of Florida would like to acknowledge partial support for the development and characterization of the facility from both AFOSR, under the Research Institute for Autonomous and Precision Guided Systems and AFRL-RW along with the Florida Center for Advanced Aero Propulsion (FCAAP).

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