aiaa-2002-2861 makita turbulence generator

32nd AIAA Fluid Dynamics Conference and

Exhibit 24-26 June 2002

St. Louis, Missouri

AIAA-2002-2861 The Generation of High Reynolds Number Homogeneous Turbulence

Jon Vegard Larssen and William J. Devenport Department of Aerospace and Ocean Engineering, Virginia Polytechnic Institute and State University, Blacksburg VA 24061

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American Institute of Aeronautics and Astronautics 1

AIAA-2002-2861

THE GENERATION OF HIGH REYNOLDS NUMBER HOMOGENEOUS TURBULENCE Jon Vegard Larssen† and William J. Devenport*

Aerospace and Ocean Engineering Department

Virginia Polytechnic Institute and State University Blacksburg, VA 24061

ABSTRACT

An active turbulence generating grid, based on the rotating-vane design of Makita (1991) has been developed for the Virginia Tech Stability Wind Tunnel. At 2.13-m square, the grid is the largest of this type ever developed. To improve the isotropy of the turbulence generated, the grid was placed in the wind tunnel contraction. Measurements made 37.3 mesh sizes downstream of the grid show a closely uniform mean flow and homogeneous isotropic turbulence to within one integral scale from the wall. By varying the flow speed and parameters controlling the random motion of the vanes (rotation rate, time between direction reversals and the limits of the random variations in these parameters) a wide variety of turbulence characteristics were produced, with Taylor Reynolds numbers from 108 to 1250 and integral scales from 6.8 to almost 60cm. The extreme cases represent some of the highest Reynolds number and largest scale homogeneous turbulent flows ever generated in a wind tunnel. The dependence of turbulence quantities upon grid and flow parameters is investigated.

LIST OF SYMBOLS E11 One-dimensional spectral energy density k Turbulent Kinetic Energy L Characteristic Macroscale l Integral Length Scale (m) Reλ Taylor Reynolds Number T Cruise time in vane maneuver, page 3 (s) t Max. deviation in cruise time (s) u Local rms velocity fluctuation in x direction Uref Reference Streamwise Mean Velocity U Local Streamwise Mean Velocity v Local rms velocity fluctuation in y direction w Local rms velocity fluctuation in z direction x Streamwise coordinate (origin in grid plane) y Transverse coordinate (positive upwards) z Transverse coordinate (oriented to complete a right-handed system) α Grid acceleration rate (rev/s2) ε Dissipation rate (m2/s3)

λ Taylor Microscale (m) κ Wavenumber (m-1) η Kolmogorov scale (m) ν Kinematic Viscosity (m2/s) Ω Average rotation rate (rev/s) ω Max deviation of rotation rate (rev/s)

INTRODUCTION This paper describes the design and development of an active grid system to generate large-scale high-Reynolds number homogeneous turbulence, and the study of that turbulence as a function of grid and flow parameters. The present design is based upon the rotating vane grid of Makita (1991), which was developed as a means for generating large scale turbulence in small wind tunnels. Similar grids have since been constructed by Mydlarski and Warhaft (1996, 1998) and Kang et al. (2002). Makita’s original grid design consists of a rectangular array of diamond-shaped vanes attached to 8 horizontal and 8 vertical rows of rotating bars. The rotation of each bar is controlled using a separate stepper motor. The stepper motors operate independently and change direction randomly. Makita (1991) and Mydlarski and Warhaft (1996, 1998) built active grids using this design for 3 fairly small wind tunnels with square cross sections 0.46, 0.71, and 0.91-m on edge. Kang et al. (2002) built their grid for a rectangular section tunnel 0.91×1.22m. By varying the flow speed and grid operation these investigators were able to generate a number of large-scale turbulent flows, summarized in table 1. Mydlarski and Warhaft found the turbulence generated in this way to be closely homogeneous, to decay in the same manner as conventional grid turbulence, and to have spectral and statistical properties closely consistent with the fundamental expectations of homogeneous turbulence theory. They also found that, despite the small size of the wind tunnels, the turbulence had very large integral scales, quite high intensity and thus big Taylor Reynolds numbers. Indeed they were able to generate turbulence with integral scales of over 40cm and Taylor Reynolds numbers of over 730, in a closely homogeneous field. Kang et al. (2002) generated turbulence of similar scale and Reynolds number (750) using their grid. These are some of the highest Reynolds number homogeneous turbulent flows ever generated in wind tunnels. Mydlarski and Warhaft (1998) were thus

†Graduate student, student member AIAA *Professor, senior member AIAA

Copyright © 2002 by J. Larssen and W. Devenport. Published by American Institute of Aeronautics and Astronautics, Inc. with permission.


able to examine some of the high Reynolds number asymptotic behavior of the turbulence. Kang et al. studied the high Reynolds-number performance of large eddy simulations. Not all of the properties of the turbulence produced by this type of grid are attractive for the present study. Makita (1991) and Mydlarski and Warhaft (1996, 1998) and Kang et al. (2002) all report that the turbulence is anisotropic with streamwise turbulence intensities being about 20% greater than cross-stream intensities. Kang et al. (2002) found this anisotropy to occur primarily at scales of the order of the test section size, and found the turbulence to be isotropic in the inertial subrange, and at higher wavenumbers. In the present study an active grid has been developed for the Virginia Tech Stability wind tunnel. This facility is significantly larger than those used in previous studies, with a square test section 1.8m on edge. The larger test section provides greater room for homogeneous flow and thus, at least in principle, larger turbulent scales. The active grid was sited in the contraction to reduce the turbulence anisotropy. Measurements were made at a range of streamwise positions and conditions in an attempt to determine and document the effects of the important parameters governing the turbulence.

APPARATUS AND INSTRUMENTATION

Stability Wind Tunnel The Virginia Tech Stability Wind Tunnel

(figure 1) is a closed-loop wind tunnel with an air-exchange tower which allows for temperature stabilization. The 24' long constant 6' by 6' test section is configured with removable steel panels on three sides while the side facing the control room features Plexiglas panels. The fan, measuring 14' in diameter, consists of 8 custom made constant pitch blades, and is powered by a 600 hp Westinghouse Model No. 28767 motor generator which rotates at a maximum speed of 900 rpm.

Upstream of the contraction there are seven stainless steel anti-turbulence grids to improve the flow quality in the test section. Turbulence intensity levels for the empty tunnel have been measured by Choi and Simpson (1987) to be extremely low: less than 0.05% for flow speeds up to 38.1 m/s. It should be noted, however, that since this study took place the original fan blades have been replaced, which should result in further improvement of the flow quality.

The top speed of this facility is some 80 m/s, however, with the significant blockage introduced by the Active Turbulence Grid, the flow speed never exceeded 20 m/s. The nominal testing speeds included 8, 12, 16, and, for a few conditions, 20 m/s.

Existing wind tunnel instrumentation was used to monitor the reference flow parameters. This included

a Validyne DB-99 Digital Barometer (resolution: 0.01”Hg), an Omega Thermistor type 44004 (accuracy: ±0.2°C), and a Pitot-Static Tube connected to a Setra 239 Pressure Transducer (accuracy: ±0.14%). The Active Turbulence Grid The basic concept design for the Active Turbulence Grid (ATG) is shown in figure 2. Based on the results of Makita (1991) and Mydlarski & Warhaft (1996, 1998) a configuration consisting of 10 horizontal and 10 vertical vanes was chosen in order to attempt to keep the turbulence intensities and integral lengthscales from becoming too large, and at the same time retain the homogeneity of the flow. A 10 by 10 rod configuration yielded 180 (20x9) full agitator vanes and 40 (20x2) rotating half vanes which were placed at the end of each rod so as to simulate an infinitely extending grid, when accounting for images in the test section wall. The heart of the ATG is the stepper motors which are mounted outside the Stability tunnel underneath a weather cover. Aluminum brackets which can hold ten motors were fitted to the roof and the starboard outside wall of the tunnel. Aluminum couplings which fit onto the motor shafts protrude into the tunnel section and allow for mounting of the grid. On the non-motor side of the test section (floor and port side) there are two ½” thick brackets with 10 ball bearings mounted into the wall to accommodate the end bearings which slide and mount into the rods. In order to align the grid-mounting hardware both inside and outside the tunnel a RoboSquare 3-coordinate laser level was used to ensure full grid alignment.

A bi-planar design was adopted in which all the vertical rods were placed in the same streamwise plane with the horizontal placed 2.5" upstream of the vertical rods. This configuration reduces the drag on the grid, yet eliminates the danger of the agitator vanes ever hitting each other even in the event of a malfunctioning coupling/bearing. Also, to keep the moment of inertia symmetric for each rod, all agitator vanes were alternately positioned on opposite sides of the rod. To reduce vibration and friction during operation some 20 vinyl couplings with lubricated sleeve bearings were placed in strategic positions throughout the grid joining the horizontal and vertical rods.

Based on initial tests and calculations it was decided to build the grid using thin-walled aluminum rods with Luan plywood vanes to reduce the inertial load. To further reduce the load, twelve ¾" holes were drilled in each of the 180 full vanes. All holes were then covered with self-adhesive plastic sheet. Prototype tests also showed that the original endvanes left too big of a gap between the wall and the edge of the grid which yielded a smaller region of uniform flow. This was remedied by custom fitting each rod with extended half-vanes.


Following Compte-Bellot and Corrsin (1966) the ATG was placed in the contraction of the Virginia Tech Stability Tunnel where the local cross section is approximately 7' on edge and the cross-sectional area is about 36% larger than the test section. This location was chosen based on Rapid Distortion Theory calculations (Batchelor and Proudman, 1954) which suggested that a 36% contraction would be just enough to cancel the 20% anisotropy of the turbulence observed in previous active grid studies.. The streamwise location of the grid was 2.75 m upstream of the test section entrance. Along with the 24' long test section this gives a maximum overall developing length of 10.0m. With a grid spacing, M, measuring 8.25" this gives a maximum x/M location of about 48.

The stepper motors driving the ATG are 20 Applied Motion Products (AMP) HT34-348. Wired in bipolar parallel this configuration can supply up to 2140 oz-in of torque. These 200-steps/rotation motors can operate on up to 6A per phase. Each motor is separately controlled in half-stepping mode by an Intelligent Motion System (IMS) IB 106 stepper motor driver located inside the control room. The drivers are powered in pairs by ten IMS IP806 80V (nominal) unregulated linear power supplies. The IB 106 outputs an adjustable current from 1 to 6A to the motors through twisted shielded 16 gauge wire. In order to avoid excessive heating of the motors/drivers the current was set at 4.5A. To provide additional cooling a fan is placed at the entrance of the weather cover duct and a regular table fan is required to provide convective cooling of the drivers. The stepper motor drivers are controlled through two coupled National Instruments (NI) PCI-6534 digital 32 channel I/O cards with 32Mb RAM and Direct Memory Access transfer from the computer’s motherboard memory. At a rate of 140 kHz the cards can output the required pulses much faster than the inertia of the motors will allow for, and hence the speed of the grid is limited by the friction/load attached to the motors as well by the internal windings in the motors. Under ideal conditions the motors under no load can be have been tested in a uni-directional mode to get up to speeds of around 40Hz (i.e. 40 revolutions per second) without any load, while the ATG itself has been taken up to 20Hz in test modes. However, for continuous reliable operation over a long period of time the top average speed has been limited to 10Hz. The low-end limit of smooth operation is about 1Hz. With the current computer control program programmed in house, it is possible to operate the ATG to operate in synchronous mode as well as randomly with full control of the range of speeds, cruise times as well as the linear acceleration/deceleration. While synchronous operation, with its phase delay capability, has a lot of potential for generating periodic

disturbances into the flow, it is a poor generator of turbulence. Therefore the random mode was used for all tests presented in this paper. The random motion is defined as follows. A single vane is accelerated from rest at a constant rate α to an angular velocity Ω. The vane then remains at this speed for a ‘cruise’ time T after which it decelerates at the same constant rate to zero. The vane then immediately reaccelerates in the reverse direction and performs a qualitatively identical maneuver. The cruise time and rotation rate are varied randomly between successive maneuvers according to a top-hat probability density functions with maximum deviations of t and ω respectively. The motion of each vane is independent of, and uncorrelated with all the others. The ATG can also be used as a static grid by aligning all the agitator vanes with the flow. At high flowspeeds (Uref>15m/s) it is necessary to lock the rods in place, as even the slightest misalignment can cause the entire grid to close causing maximum blockage in the tunnel. Hot-wire anemometry Two different single-wire hot wire probes were used to obtain streamwise velocity measurements. A TSI 1210T1.5 probe, with a 1.7-mm long 5-µm diameter sensor wire was utilized for the majority of the tests. At certain points the results were checked by using a custom built Auspex single-wire probe with a 0.5-mm long, 2.5-µm diameter sensor. The single wires were operated using a Dantec 55M01 anemometer unit and the system optimized to give a flat frequency response to 12.5kHz (TSI probe) and 33kHz (Auspex probe). These frequency response functions were measured and accounted for in data processing, effectively extending the flat response to the Nyquist frequency of the data acquisition. Output voltages from the anemometer bridge were recorded by Dell Latitude using a Hewlett Packard HPE1432A 16-bit A/D converter through an IEEE 1394 interface. Hot-wire signals were buffered by four ×10 buck-and-gain amplifiers containing calibrated RC-filters to limit their frequency response to 50 kHz (included in the probe response correction described above). The A/D converter also sampled voltage outputs from the wind tunnel digital thermometer and Pitot-static pressure transducer was utilized. 100 records, with a record length of 218 samples were obtained at a sampling rate of 51,200 Hz. This resulted in a good resolution of frequencies in the low end of the spectrum, while simultaneously allowing for further averaging of the energy contained in the higher wavenumbers during post-processing.

Three-component velocity measurements were made downstream of the ATG using the computerized hot-wire system described in detail by Wittmer et al.


(1997). A miniature four-sensor hot-wire probe manufactured by Auspex Corporation (type AVOP-4-100) was used. This probe consists of two orthogonal X-wire arrays with each sensor inclined at a nominal 45o angle to the probe axis. The 5µm sensors are close to 0.8-mm in length. The total measurement volume is approximately 0.5 mm3. Each of the four hot wire sensors was operated separately using a Dantec 56C17/56C01 constant temperature anemometer unit. The anemometer bridges were optimized to give a matched frequency response greater than 25 kHz. Anemometer output voltages were recorded using the same amplifier/converter/computer system employed with the single-wire probes. For measurements of turbulence spectra the same sampling scheme was used. For profiles of mean velocity and turbulence stresses (to examine homogeneity and isotropy) typically 150 records each of 1600 samples were recorded at a sampling rate of 1600Hz.

Probes were calibrated for velocity before and after each sequence of measurements by placing them in the uniform jet of a TSI calibrator and using King's law to correlate the wire output voltages with the cooling velocities. For the 3-component probe, velocity components were determined from the cooling velocities by means of a direct angle calibration, described in detail by Wittmer et al. (1997). To generate this calibration the probe was pitched and yawed over all likely flow angles in the calibrator jet. Comparing the known pitch and yaw angles with the probe outputs gives the true relationship between the cooling velocities and the flow angle. Hot-wire signals were corrected for ambient temperature drift using the method of Bearman (1971). Other Equipment A Dwyer Pitot-static probe was mounted on a computer-controlled traverse gear described above for uniformity studies. The same traverse gear was used to measure velocity profiles using the 4-sensor probe. The traverse gear has a blockage of about 10%. However, probes were mounted 36” upstream of the traverse by means of a streamlined sting support. For all other measurements probes were mounted at the center of the tunnel on an airfoil-section strut with a blockage of less than 0.4%. Two wires were used to tie the strut to the walls of the tunnel in order to counteract the effects of unsteady lift and vibrations from gusts. The wires had to be weighted to avoid a standing resonant wave forming in the wire between the wall and the strut.

RESULTS AND DISCUSSION

The ATG was tested and velocity spectra were obtained using single hot-wire probes at x/M=37.3. Four additional streamwise stations at x/M=21.3, 29.3, 41.0, and 47.5 were added for a few baseline cases for

purposes of examining streamwise decay. Velocity spectra were measured using the two single hot-wire probes with different wire-lengths, for dissipation estimation purposes. Uniformity studies were performed first with a traversing pitot-static probe at x/M=37.3 and then checked with a four-sensor hot-wire at x/M=37.3 to establish the level of homogeneity and isotropy. The nominal flowspeeds tested were 8, 10, 12, 16, and 20 m/s. Mean grid rotation rates were set at 2, 4, 6, 8, and 10 Hz (rev/s). Grid vane acceleration rate and maximum deviations in rotation rate and cruise time were also varied to examine the effects of these parameters. Table 1 shows the conditions and locations of all measurements together with some basic results. Results from previous studies are included for comparison purposes. The coordinate system used is as follows: the origin is at the center of the tunnel section with its origin placed in the plane of the grid. The x-coordinate is measured positive downstream, y is positive vertically upwards and z completes the right-handed system. The values for the turbulence intensity, u/U, were found by integrating the one-dimensional energy spectra based on the hot-wire data. Turbulence kinetic energy was then estimated based on equation 1.

223 uk = 1)

By computing the second moment of the spectra, assuming local isotropy and invoking Taylor’s hypothesis equation 2 was used to obtain an estimate for dissipation rate:

∫∞

=0

111121 )(15 κκυκε dE 2)

This integration must be done with care as minor contamination of the spectrum by high-frequency noise can result in a large overestimate. From the cumulative sum of the integrand, it was found in all cases that the integral reached an asymptotic value at high frequency before noise became a factor. This asymptotic value was taken as the dissipation. Comparison between results from the two single hot-wire probes with different wire lengths was used to verify the validity of the dissipation estimate. In the four cases (11, 12, 24, 25, refer to table 1) where both probes were used, the 1.7-mm and 0.5−mm probes gave values of dissipation within 9%, after accounting for the measured dynamic response of the anemometer and data acquisition systems. Dissipation was also calculated based on equation 3 for a few cases where several streamwise measurements had been obtained. This method gave values typically 20% larger than equation 2 for the downstream measurement locations, the discrepancy increasing with distance upstream. In our opinion estimates based on the decay of turbulence kinetic


energy are less reliable because of their greater dependence on the low frequency end of the turbulence spectrum, which shows the greatest departure from the standard homogeneous isotropic form. The dissipation estimates used here were therefore all obtained using equation 2. This is consistent with Mydlarski and Warhaft (1996, 1998).

DtDk

=ε 3)

The characteristic macroscale L (Pope, 2001) can be defined as:

ε/23

kL = 4) The ratio of the integral lengthscale l to the macroscale approaches an asymptotic value of 0.43 as the Taylor Reynolds Number increases. A slightly higher factor of 0.45 was used for calculations of the integral scale in the present flow, such that l=0.45L. The Taylor Reynolds number, Kolmogorov scale and Taylor microscale were calculated from equations 6 and 7.

ευυ

2

Re kkLL == 5)

43

Re−= LLη

6)

31

32

10 Lηλ = 7) The range of the turbulence properties produced with the present grid (see table 1) deserves some comment. The turbulence intensity varies from 5.5 to 12% depending on location and other parameters. (The highest levels were measured closest to the grid for the highest flow speeds and lowest grid rotation rates.) This seems roughly consistent with levels measured by Mydlarski and Warhaft (1996,1998) and Kang et al. (2002). Perhaps more remarkable are the integral scales and Taylor Reynolds numbers, which reach 0.57m and 1250 respectively in case 26, and 0.59m and 1081 in case 8. The very large integral scales in this case (and thus the extreme Taylor Reynolds numbers), are roughly twice the values reported by Mydlarski and Warhaft (1998) and Kang et al. (2002), who had test section widths about half the present size, and four times those reported by Mydlarski and Warhaft (1996) who had a test section one quarter the size (see table 1). Note that the grid cell sizes M for these studies are not in this proportion (Kang et al. used a grid cell size 1.6 times that of Mydlarski and Warhaft (1998).) It thus appears that the maximum turbulence scale produced by this type of active grid scales approximately on the test section size and not the grid cell size. A possibly simplistic interpretation of this result is that the largest integral scale may simply reflect the largest scale of turbulence that can be contained

within the test section. However, this doesn’t explain how such scales are generated. We suspect that scales on the order of the wind tunnel size are generated because, although they are in random motion, each vane row rotates together, across the entire width or height of the section. Thus the largest lengthscale will always be the tunnel size. Homogeneity and Isotropy The uniformity of the mean flow was mapped out by traversing a Pitot-static probe in each direction from the center of the cross section at x/M=37.3 for cases 5, 7, 10 and 12 (see table 1). U/Uref as a function of z-coordinate (at y=0) can be seen in figure 3. The measurements extend out to 3 inches from each wall. Overall the flow looks uniform with the exception of the boundary-layers close to the wall. There is a very slight jet-effect centered around z=±25. This, we suspect, is caused by the air escaping through the gaps between the grid and the wall. The problem is a little more pronounced at on the negative z side where the grid does not have a bearing strip and thus there is less flow blockage. This test was also repeated with the four-sensor hot wire, which confirmed the Pitot results. The homogeneity and isotropy of the test section was mapped out at x/M=37.3 for cases 11 and 12 by traversing a four sensor hot wire in the test section. The 3 component velocity fluctuations as a function of z-coordinate (y=0) for case 11 (Ω=4Hz and a U=12.4 m/s can be seen in figure 4. A few conclusions can immediately be drawn: The turbulent flow field is closely homogenous and isotropic within 15" of the centerline. Closer to the wind tunnel walls w-component fluctuations fall off. Profiles in y show a similar fall off in v-component fluctuations. This fall-off is an inevitable result of the large integral scale in the flow (of 0.394m) and the imposition of the non-penetration condition on the wind tunnel walls. Based on the model of Hunt and Graham (1978) this fall off should occur over a distance equivalent to one integral scale from the wall – consistent with what is seen here. The fact that the ATG was placed in the contraction seems to have alleviated some of the problems with anisotropy experienced in earlier studies, confirming that Compte-Bellot and Corsin’s (1966) method is effective with this type of grid. Anisotropy ratios u/v, w/u, for the inner 30" region in each direction lie between 1.02 and 1.05 for the measured cases (see table 1). Spectra Figures 5 through 8 show a representative sets of power spectra measured at x/M=37.3 for different grid rotation rates. Spectra are plotted in dimensional form as E11(κ1) vs. κ1 where E11 is the one-dimensional energy spectrum (in m3/s2) and κ1 is the wavenumber in


m-1, with the exception of figure 8 which has been normalized using the Kolmogorov scaling. Note that a wavelength equal to the tunnel width has a wavenumber of 3.5 m-1. All spectra show a clear inertial subrange of constant slope. Close examination of the spectra reveals a slight increase in slope towards -5/3 with increase in Taylor Reynolds number (table 1), at least in qualitative agreement with Mydlarski and Warhaft (1998). The extent of the inertial subrange increases with Reynolds number and, in the highest Reynolds number case shown in these figures (case 8) it extends over 2.2 decades. The greatest departure from the smooth spectral shape expected for homogeneous turbulence occurs at the lowest wavenumbers, where the corresponding frequency is comparable to the grid rotation rate, and the implied lengthscales are largest compared to the 1.8m tunnel width. The influence of the grid on the spectrum is most apparent in case 8 (figure 5), at wavenumbers around 1. The spectral signature of the grid reduces both with reduction in flow speed and increase in rotation rate, suggesting that it is controlled primarily by the non-dimensional parameter U/(ΩM). Turbulence Properties Vs Non-Dimensional Parameters There are five major non-dimensional parameters one can define that could control the properties of the grid turbulence; the normalized distance from the grid, the grid Reynolds number, the vane Rossby number, the average number of vane revolutions in each maneuver and, the normalized maximum deviations in cruise time and rotation rate. Symbolically these are

ΩΩ

Ωω

υ,,,,,

TtT

MUMU

Mx

8)

Not included in the above non-dimensional parameters is the acceleration rate a. Some limited study of the effects of acceleration rate was made, but in most cases this rate was kept constant at 20 rev/s2. As far as practicable, the test matrix listed in table 1 was designed to reveal the independent effects of these parameters. Most parameter variations were made relative to the baseline case for which,

4.2,107.1,3.37 5 =Ω

⋅==MUMU

Mx

υ

9)

5.0,13.25 =Ω

==Ωω

TtT 10)

Dissipation Figure 9 shows the relation between dissipation rate vs MU/ν. As expected there is a strong relationship between Reynolds Number and dissipation rate. Plotting the same data as a function of U/MΩ shows no significant dependency on this parameter.

Integral Lengthscale Integral length scales appear to be a weak function of MU/ν and a strong function of U/MΩ which can be seen from figures 10 and 11. Figure 12 displays Integral Length Scale vs. TΩ for deviations from the baseline case. Several datapoints representing slightly different grid conditions have been added to display the effects of varying acceleration and the remaining non-dimensional parameters. Integral length scale is unaffected by a change in TΩ for the baseline condition, however as t/T is decreased the integral lengthscale starts decreasing as TΩ increases. There are not enough points present to see the general shape of this trend, but the falloff of the integral length is definite. When manipulating ω/Ω it can be seen that the integral lengthscale decreases linearly with ω/Ω. Since data is only present for one value of TΩ it can not be stated whether this is the case everywhere, or if this is simply a characteristic at TΩ=25.13. It can also be seen that if the acceleration is lowered below 10 rev/s2 then the integral length goes up substantially. Turbulence Intensity u/U does not appear to be a consistent function of MU/ν although, as can be seen from figure 13, the variation of turbulence intensity with this parameter does appear bounded from below. On the other hand, there is a definite increasing relationship between turbulence intensity and U/MΩ (figure 14) Figure 15 displays Turbulence Intensity Vs TΩ for deviation from the base condition from 9) and 10) in the same way as figure 12 does for the Integral scale. u/U first increases, reaching a maximum around TΩ for the base condition, and then falls off again. When t/T is lowered the maximum value seems to decrease and the curve is shifted to the right. There are however not enough datapoints present to fully this trend. Manipulating ω/Ω does not seem to induce a clear pattern. Although it is possible that the Turbulence Intensity reaches a maximum around ω/Ω=0.2 and that it falls off on either side of this for a constant value of TΩ. can be seen that the Integral length scale decreases linearly with ω/Ω. Since data is only present for one value of TΩ it can not be stated whether this is the case everywhere, or if this is simply a characteristic at TΩ=25.13. Decreasing the acceleration gives an increase in Turbulence Intensity, with the step increase being kept constant by successively halving the acceleration. Taylor Reynolds Number and the Kolmogorov Scale. Figure 16 displays Reλ as a function of MU/ν. Obviously, the overall trend is very similar to that observed for the integral length scale, but the figure


has nevertheless been included for quick reference. The effect of MU/ν and U/MΩ on the Kolmogorov lengthscale is shown in figures 17 and 18 respectively. While the dependency of U/MΩ is relatively weak, there is a remarkably good correlation for the Kolmogorov lengthscale when plotted against MU/ν.

CONCLUSIONS An active turbulence generating grid, based on the rotating-vane design of Makita (1991) has been developed for the Virginia Tech Stability Wind Tunnel. At 2.13-m square, the grid is the largest of this type ever developed. To improve the isotropy of the turbulence generated, the grid was placed in the wind tunnel contraction. Measurements made 37.3 mesh sizes (M) downstream of the grid show a closely uniform mean flow and homogeneous isotropic turbulence to within one integral scale from the wall. Turbulence spectra measured at the tunnel centerline over a range of conditions and locations have a typical homogeneous turbulence form, except in a few cases at the very lowest wavenumbers where lengthscales are of the order of the tunnel size and frequencies are comparable to the rotation rates of the vanes. By varying the flow speed and parameters controlling the random motion of the vanes (rotation rate, time between direction reversals and the limits of the random variations in these parameters) a wide variety of turbulence characteristics were produced, with Taylor Reynolds numbers from 108 to 1250 and integral scales from 6.8 to almost 60cm. The extreme cases represent some of the highest Reynolds number and largest scale homogeneous turbulent flows ever generated in a wind tunnel. Comparing with earlier studies it appears that the largest lengthscale that can be produced by this type of grid scales with the size of the wind tunnel, not the grid cell size. The dependence of turbulence quantities upon grid and flow parameters is investigated. Integral scale is found to increase with the ratio of flow speed to mean grid rotation rate U/(MΩ). Grid Reynolds number UM/ν primarily controls the dissipation rate (and thus Kolmogorov microscale) and the Taylor Reynolds number.

ACKNOWLEDGEMENTS The authors would like to thank the Office of Naval Research, in particular Drs. L Patrick Purtell and Ronald Joslin, for their support under grant N00014-01-1-0406. We also express our gratitude to Prof. Stewart Glegg for his comments, discussion and ideas and to Derek Geiger, Drew Vaughan, Jean-Baptiste Vaylet, Chittiappa Muthanna Kolera, Bruce Stanger, Mike Vaught, Bancroft Henderson, and Nicolas Spitz in developing and running the grid. The extensive

cooperation of the Virginia Tech Stability Wind Tunnel, under the directorship of Prof. Roger L. Simpson, is also gratefully acknowledged.

REFERENCES 1. Batchelor G K and Proudman, 1954, "The effect or

rapid distortion on a fluid in turbulent motion", Quarterly Journal of Mechanics and Applied Mathematics, vol. 7, part 1, pp. 83-103.

2. Bearman, P W, 1971, "Corrections for the Effect of Ambient Temperature Drift on Hot-Wire Measurements in Incompressible Flow," DISA Information, no. 11, pp. 25-30.

3. Choi, K and R. L. Simpson, 1987: “Some Mean Velocity, Turbulence, and Unsteadiness Characteristics of the VPI & SU Stability Wind Tunnel”, AOE Dept., Virginia Tech, Blacksburg VA.

4. Hunt J C R and Graham J M R, 1978, "Free-stream turbulence near plane boundaries", Journal of Fluid Mechanics, vol. 84, part 2, pp. 209-235

5. Kang H S, Chester S and Meneveau C, 2002, “Decaying turbulence in an active-grid-generated flow and comparisons with large-eddy simulation”, Submitted to Journal of Fluid Mechanics.

6. Makita H, 1991, "Realization of a large-scale turbulence field in a small wind tunnel", Fluid Dynamics Research, vol. 8, pp. 53-64.

7. Mydlarski L and Warhaft Z, 1996, "On the onset of high-Reynolds-number grid-generated wind tunnel turbulence", Journal of Fluid Mechanics, vol. 320, pp. 331-368.

8. Mydlarski L and Warhaft Z, 1998, "Passive scalar statistics in high Peclet number grid turbulence", Journal of Fluid Mechanics, vol 358, pp. 135-175.

9. Pope, S.B, 2002, “Turbulent Flows”, 2000, Cambridge University Press, Cambridge.

10. Wittmer, K. S., Devenport, W. J. and Zsoldos, J. S., 1998, “A four-sensor hot-wire probe system for three-component velocity measurement”, Experiments in Fluids, Vol. 24, No. 5-6, pp. 416. See also Vol. 27, No. 4, pp. U1-U1, September 1999.

American Institute of Aeronautics and Astronautics

Table 1. Comparison of present and previous studies of active grid generated turbulence

Study Vanes Ω±ω (Hz) T±t (s) α (Hz/s) x/M U (m/s) u'/U (%) l (m) Reλ Tunnel size (m) u/v u/wMakita (1991) 8x8 2 50 5 16.4 0.197 387 0.91×0.91 1.22M&W (1996) 8x8 1 or 2 68 13.3 10.4 0.170 469 0.71×0.71M&W (1996) 8x8 2 68 7.1 7.4 0.119 262 0.46×0.46 1.21M&W (1996) 8x8 2 68 10.4 8.6 0.143 377 0.46×0.46M&W (1996) 8x8 2 68 14.3 9.5 0.148 473 0.46×0.46M&W (1998) 8x8 1 or 2 62 3.3 9.1 0.300 306 0.91×0.91M&W (1998) 8x8 1 or 2 68 11.4 8.9 0.160 407 0.91×0.91M&W (1998) 8x8 1 or 2 62 7 10.9 0.430 582 0.91×0.91M&W (1998) 8x8 1 or 2 31 6.9 17.4 0.400 731 0.91×0.91

Kang et al. (2002) 5x7 5.3±1.8 20 11.9 16.0 0.270 755 0.91×1.22 1.188Kang et al. (2002) 5x7 5.3±1.8 30 11.2 12.9 0.303 696 0.91×1.22 1.171Kang et al. (2002) 5x7 5.3±1.8 40 11 10.8 0.323 654 0.91×1.22 1.167Kang et al. (2002) 5x7 5.3±1.8 48 11.1 9.5 0.334 624 0.91×1.22 1.162Present, case 1 10x10 0 (static) 20 37.3 7.8 2.1 0.084 108 1.82×1.82Present, case 2 10x10 0 (static) 20 37.3 13.0 2.0 0.068 141 1.82×1.82Present, case 3 10x10 0 (static) 20 37.3 15.5 2.0 0.068 155 1.82×1.82Present, case 4 10x10 0 (static) 20 37.3 20.5 1.9 0.065 171 1.82×1.82Present, case 5 10x10 2±1 2±1 20 37.3 8.0 7.2 0.382 518 1.82×1.82Present, case 6 10x10 2±1 2±1 20 37.3 12.4 8.0 0.501 784 1.82×1.82Present, case 7 10x10 2±1 2±1 20 37.3 15.0 8.0 0.549 900 1.82×1.82Present, case 8 10x10 2±1 2±1 20 37.3 19.9 8.3 0.587 1081 1.82×1.82Present, case 9 10x10 4±2 1±1/2 20 37.3 8.3 6.2 0.343 472 1.82×1.82Present, case 10 10x10 4±2 1±1/2 20 37.3 10.9 6.8 0.366 582 1.82×1.82Present, case 11 10x10 4±2 1±1/2 20 37.3 12.4 7.0 0.394 653 1.82×1.82 1.02 1.05Present, case 12 10x10 4±2 1±1/2 20 37.3 15.4 7.5 0.458 815 1.82×1.82 1.04 1.03Present, case 13 10x10 6±3 2/3±1/3 20 37.3 8.1 5.8 0.282 403 1.82×1.82Present, case 14 10x10 6±3 2/3±1/3 20 37.3 12.2 6.6 0.347 587 1.82×1.82Present, case 15 10x10 8±4 1/2±1/4 20 37.3 8.3 5.9 0.315 434 1.82×1.82Present, case 16 10x10 8±4 1/2±1/4 20 37.3 10.7 6.2 0.352 541 1.82×1.82Present, case 17 10x10 10±2 1/2±1/4 20 37.3 8.2 5.6 0.329 439 1.82×1.82Present, case 18 10x10 4±2 1±1/2 20 47.5 12.4 6.3 0.377 591 1.82×1.82Present, case 19 10x10 4±2 1±1/2 20 47.5 15.3 6.7 0.407 700 1.82×1.82Present, case 20 10x10 4±2 1±1/2 20 41 12.2 6.8 0.385 625 1.82×1.82Present, case 21 10x10 4±2 1±1/2 20 41 15.5 7.1 0.442 766 1.82×1.82Present, case 22 10x10 4±2 1±1/2 20 29.3 12.4 8.1 0.414 722 1.82×1.82Present, case 23 10x10 4±2 1±1/2 20 29.3 15.2 8.7 0.382 764 1.82×1.82Present, case 24 10x10 4±2 1±1/2 20 21.3 12.5 9.8 0.352 714 1.82×1.82Present, case 25 10x10 4±2 1±1/2 20 21.3 15.6 10.4 0.405 874 1.82×1.82Present, case 26 10x10 2±1 2±1 20 21.3 20.2 11.9 0.574 1250 1.82×1.82Present, case 27 10x10 4±2 3±1/2 20 37.3 12.33 6.83 0.382 642.7 1.82×1.82Present, case 28 10x10 4±2 1 20 37.3 12.27 7.04 0.411 677.8 1.82×1.82Present, case 29 10x10 4 1±1/2 20 37.3 12.41 7.10 0.322 583.7 1.82×1.82Present, case 30 10x10 4±2 1±1/2 10 37.3 12.62 7.29 0.393 660.6 1.82×1.82Present, case 31 10x10 4±2 0 20 37.3 12.64 8.04 0.504 774.6 1.82×1.82Present, case 32 10x10 4±1 1±1/2 20 37.3 12.36 7.26 0.366 620.5 1.82×1.82Present, case 33 10x10 4±2 1±1/2 5 37.3 12.51 7.62 0.439 700.7 1.82×1.82Present, case 34 10x10 4±2 3±3/2 20 37.3 12.60 7.09 0.383 635.5 1.82×1.82Present, case 35 10x10 4±2 2±1 20 37.3 12.48 7.20 0.39 645 1.82×1.82Present, case 36 10x10 4±2 2 20 37.3 12.51 6.97 0.374 623.2 1.82×1.82Present, case 37 10x10 4±3 2±1/2 20 37.3 12.48 7.10 0.413 662.5 1.82×1.82Present, case 38 10x10 8±4 3/2±1/4 20 37.3 8.01 5.20 0.254 360.5 1.82×1.82Present, case 39 10x10 8±4 0 20 37.3 8.46 6.50 0.359 495.6 1.82×1.82


Placement of Active Grid

Figure 1: Schematic of the Virginia Tech Stability Wind Tunnel, showing the location of the Active Turbulence Grid

Figure 2a: Concept design of the Active Turbulence Grid

Figure 2b: Actual Active Turbulence Grid mounted in the contraction of the Virginia Tech Stability Tunnel

Perforated Luan vanes

Bearing strips

7ft


0.00

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1.00

-35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35

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z (inches)

Q4Hz12(both)i.nh

uvw

Figure 3: Uniformity measured with the Pitot-static probe as a function of z (y=0) at x/M=37.3 for cases 5, 7 10 and 12

R.m

.s. v

eloc

ity(m

/s)

z (in)

Figure 4: Sample homogeneity and isotropy data. Velocity fluctuations plotted as functions of z (y=0) at x/M=37.3, case 11

Figure 5: Energy spectra for cases 5 through 8 Figure 6: Energy spectra for cases 9 through 12

571012


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7

0 50000 100000 150000 200000 250000 300000

UM/ν

Dis

sipa

tion ,

ε (

m2 /s

3 )

Figure 7: Energy spectra for cases 13 through 16 Figure 8: Normalized energy spectra for cases 12, 19, 21, 23, and 25

Figure 9: Dissipation rate vs. UM/ν for all cases at x/M=37.3

0

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0 50000 100000 150000 200000 250000 300000 350000

UM/ν

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gral

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le (m

)

Figure 10: Integral lengthscale vs. UM/ν for all cases at x/M=37.3

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U/MΩ

Inte

gral

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le (m

)

Figure 11: Integral lengthscale vs. U/MΩ for all cases at x/M=37.3

Figure 12: Integral lengthscale vs. TΩ for variations from the baseline case x/M=37.3

ω/Ω: 0.25

t/T: 0t/T: 1/8

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default

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UM/nu

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0 50000 100000 150000 200000 250000 300000 350000

UM/ν

Re λ

Figure 13: Turbulence intensity vs. UM/ν for all cases at x/M=37.3

Figure 14: Turbulence intensity vs. U/MΩ for all cases at x/M=37.3

Figure 15: Turbulence intensity vs. TΩ for variations from the baseline case at x/M=37.3

Figure 16: Taylor Reynolds number vs. UM/ν for all cases at x/M=37.3

Figure 17: Kolmogorov microscale vs. UM/ν for all cases at x/M=37.3 except static grid

Figure 18: Kolmogorov scale vs. U/MΩ for all cases at x/M=37.3 except static grid.

0.00000

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0 50000 100000 150000 200000 250000 300000

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acc: 5 Hz/sacc: 10 Hz/st/T: 0/0baseline

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6.60%

6.80%

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0 10 20 30 40 50 60 70 80

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Static grid

Static grid

aiaa-2002-2861 makita turbulence generator

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