AIAA Technical Conference LDV Design paper

Three-component LDV Probe for AFRL-TGF for SWBLI Studies Chaize DeSioi, Kevin Millerii, Philip Schinetskyi, Narendra Chagantii, Brian T. Brooker i, and Semih M. Olcmeniii The University of Alabama, Tuscaloosa, Alabama 35487 and Jon A. Tinappleiv U.S Air Force Research Laboratory, Wright-Patterson Air Force Base, OH 45433, USA

Design and development of a three-simultaneous velocity component, miniature, three-color, fiberoptic laser-Doppler velocimetry (LDV) probe for use in Trisonic Gas Dynamics Facility at Air Force Research Laboratories is described. The probe is designed to be used in shock-wave boundary-layer interaction (SWBLI) studies. LDV probe was specifically designed to fit into an existing generic supersonic inlet model developed by AFRL. The probe incorporates four separate traversing mechanisms to access hard to reach measurement locations in the flow. This paper describes the details of the probe and gives the results of the exploratory measurements made in a subsonic turbulent boundary layer to demonstrate the probe’s capabilities. Measurements made in a two dimensional turbulent boundary layer were compared to existing DNS solutions with success. Nomenclature

v p

= velocity component perpendicular to fringes

fp fr fb fsh λb

= = = = =

frequency of the light scattered from particle particle frequency received by a stationary detector laser light frequency shift frequency laser wavelength

I. Introduction

O

ne of the most popular techniques used in measuring turbulent flow fields is the Laser Doppler Velocimetry (LDV). Identification of flow features of the shockwave/boundary layer interaction (SWBLI) is an ongoing research and is the motivation behind the design of the three component LDV probe. In the SWBLI studies the objective is to measure the flow mean velocity, shear stress and higher order correlations to aid understanding the physics of shock/boundary layer interaction flow field. Measurement of such quantities require non-intrusive laserbased velocity measurement techniques to be employed. There are many such techniques that exist in the literature, such as the particle-image velocimetry, Doppler-global velocimetry. While these techniques have advantages and disadvantages one to another the LDV technique proves to be the best technique to use in flows where the access to the flow is rather limited, such as in the case of the SWBLI inlet model. Figure 1 shows the generic inlet model developed by AFRL for inlet flow studies. It was desired that a probe was built to make measurements in such a model that would fit into an existing chamber geometry that was previously used in flow control studies. A generic LDV system is composed of on-table optics, the probe and the data acquisition and reduction unit. While the on-table optics is responsible forming the laser beams required and transmitting them to the probe, the probe is used to focus the laser beams to form the measurement probe volume, collect the scattered light from the particles, and transmit the light to the data acquisition and reduction unit. The data acquisition and reduction unit is composed of photomultipliers, electronic amplifiers, electronic and optical filters, a frequency-domain processor, and a PC, and it is the unit used to deduce the velocity information.

i

Graduate Student, AEM Department, University of Alabama Mechanical Engineer, Lockheed Martin, Manassas, Virginia iii Associate Professor, AEM Department, The University of Alabama, AIAA Associate Fellow iv Senior Aerospace Engineer, U.S Air Force Research Laboratory, Ohio ii

1 American Institute of Aeronautics and Astronautics

Figure 1. The SWBLI model built by AFRL. Picture also shows the trapezoidal plenum cavity where the LDV probe will be located. In this paper, basic working principle of the LDV technique is summarized first. This is followed by the section describing the stages of the development of the probe and final probe specifications. The data obtained in a turbulent boundary layer in a subsonic tunnel using the probe is compared to existing DNS solutions, next.

II. Working principle of the LDV Technique It is well known that once a laser beam with a known frequency is scattered from an object, the observed frequency of the scattered light changes according to the position of the observer due to the Doppler Effect (Figure 2). The frequency of the observed light is given with the following equation:

f r  fb  Where, c: speed of light,

v p   e pr  eb 

b

v p particle velocity, f b frequency of the laser light scattered from particle, f r

frequency of light observed by a stationary detector, 𝜆𝑏 wavelength of the laser light,

eb unit vector along the

incident beam direction, e pr unit vector in the direction of the observer from the particle.

Figure 2. Schematic Drawing to demonstrate the Doppler Effect 2 American Institute of Aeronautics and Astronautics

Once two separate incident beams are scattered from the same particle then the dependency of the observed frequency on the orientation of the observer drops out of the equations. In the dual beam LDV technique two laser beams are used to determine particle velocity following the flow. Once two mutually coherent laser beams intersect with each other, they interfere constructively and destructively to form fringes (Figure 3). The overlapping region is called as the probe volume.

Figure 3. Intersecting beams and vector relations (Albrecth et. al, 2002). Once a particle passes over the fringes it scatters light with a frequency that is directly related to the particle velocity and the fringe spacing. The particle passage frequency is determined by analyzing the scattered light using instruments such as frequency domain processors. The relation between the particle passage frequency and the particle velocity is given as follows:

fD 

2 sin 

b

2 v cos   p

2 sin 

b

2v

p

(v p   v p cos  )

The angle,  is the angle between the two laser beams, and the v p is the particle velocity as shown in Figure 3. Fringe spacing is calculated using: fringe spacing =

𝜆𝑏 𝛩 2 sin ( 2 )

The range of the Doppler frequency is generally between a few kilohertz to about 150 Megahertz, which is very small in comparison to the 1014 Hz frequency of the laser light, requiring the use of specialized techniques and electronic equipment, such as frequency analyzers, counters, and photon correlators, for detection of this frequency. The dual-beam method as described requires frequency shifting of one of the beams to determine the direction of the flow. Frequency shifting is usually accomplished by acousto-optic modulators, and results in moving fringes. Once a particle moves in the same direction of the fringes, the frequency of the collected light is then equal to the difference between the Doppler and shift frequencies. When the particle moves against the fringes, the collected light frequency becomes the sum of the Doppler and the shift frequency.

f r  f sh  where

   v p  (e1  e2 )

b

 f sh 

2 sin 

b

2 v  f  f p sh D

f sh is the shift frequency.


III.Design and assembly of probe The unique LDV probe manufactured was specifically designed to fit in the inlet model that is currently being used at Aerospace Systems Directorate for SWBLI studies. The probe is accompanied by on table optics, and data acquisition and reduction electronics. The LDV system uses an optical table, on table optical equipment such as an 8 Watt Coherent laser, a frequency domain processor (TSI-FSA-4000) and electronic equipment for data collection and processing required for the operation of the LDV probe. The following sections describe each component in the LDV system. III.A. LDV Probe-summary: The probe is a three-simultaneous-velocity component, three-color, fiber-optic probe using 514.5 nm, green, 488 nm, blue, and 476.5 nm violet laser beams. These colors contain most of the powers that emerge from an Argon-Ion laser. In general, three-component velocity measurements require three separate probe volumes, each formed by crossing two laser beams. The probe volumes separately formed are then overlapped to measure the three velocity components at the same point in space. The probe is designed to measure three-velocity components simultaneously with a resolution of ~150 microns and to fit into the suction plenum chamber of inlet model that has been used in previous flow control demonstrations at AFRL. The suction plenum chamber has a flexible pipe extending outside the tunnel. The flexible pipe will act as the access route for the fiber-optic cables to transmit the laser beams and also to transmit the light collected from the measurement probe volume back to the data acquisition and reduction unit. Flexible pipe will also be used as access for the traversing mechanism power and control cables. The miniature probe is held using four traversing mechanisms which are capable of traversing the probe back and forth, up and down, sideways, and also allow tilting the probe up to 45 degrees. Traversing mechanisms were used to maximize the measurement domain. III.B. Probe Design The probe works based on the Doppler principle. Once two coherent laser beams are focused by a lens to a point they intersect to form a measurement probe volume. Particles in air passing through the measurement probe volume scatter light that can be used to determine the velocity component in a direction perpendicular to the bisector of two beams that form the measurement probe volume. By using three separate probe heads, it is possible to measure all the three components of the velocity of the particles. Figure 4 shows the two probe heads and four beams forming two overlapping measurement probe volumes. In the current design the included angle between the bisectors of the beam pairs was chosen as 60 to enable designing a probe that can fit into the space available. The design had to include provisions for the laser beams passing through a 0.25 inch thick insert glass to take into to account the refraction effects displacing the beams. Insert glass that will be integrated to the inlet model will allow the beams to reach the flow field inside the model. Given that the probe had to measure at least one inch above a glass insert, the height of the actual measurement volume above the probe had to be at least an inch and a quarter to account for the thickness of the glass, and the refraction that is caused by light travelling in different mediums. All the parts of the probe were manufactured using steel to make sure that thin and small structures did not bend easily and that the surfaces would not mar when set screws are used to hold them in place. Previous Figure 4. Two probe heads and the laser beams experience with building such probes has shown that the forming two measurement probe volumes. Black probe parts require realignment multiple times prior to arrows show the velocity component measurement the final alignment is achieved. directions. The scattered light is collected by the receiving optics unit. The receiving optics holder is built using steel to keep the probe sturdy. (Figure 5). Extraneous material was shaved off to reduce the weight. When designing the receiver aspect of the probe it was necessary to keep in mind that the overall size of this probe had to remain small. 4 American Institute of Aeronautics and Astronautics

Figure 5. Probe design with receiver and path for fiber optic cables.

Figure 6. X direction traverse traverseand anditsits Figure 9. X -– Direction motor highlighted in blue motor highlighted in blue

The next design challenge was holding the receiver and probe heads together. Each probe head was equipped with its own independent manual traversing capabilities for adjustment. This was required to ensure that all the beams could be placed on top of another. These traversing mechanisms were also needed to be as sturdy as possible, since any vibration in these

mechanisms would cause the probe volumes generated by each of the probe heads not to overlap at all times. The final design included a series of rods and bars that were held in place with tightening screws. Probe heads held by the manual traversing mechanisms were then attached to the receiving unit with bars. As a last stage in the design an additional probe head that could measure the third component was added. As opposed to the first two probe heads, being attached to the receiver, the third probe head is attached to one of the probe heads, so that it was not intrusive and could be added on without disturbing the current configuration. The bisector of the beams is oriented at about 47 with respect to the centerline of the receiving optics. Also, if it was determined that if the third component was not needed for a certain measurement, it need not be used, with no effect to the other two components. Just like the other two probe heads, the third component head was equipped with its own adjustment traversing system in all three degrees of freedom. In an effort to simplify the probe, the number of moveable parts was reduced. The transmitting optics connections were also consolidated to a minimum. The main benefit of this was that it left less room for binding. The transmitting optics geometry was also modified in order to make the path easier for the fiber optic cables (Figure 5). III.C. Traversing mechanisms

It was a necessary requirement that the probe could be traversed remotely. This required a fully motorized traversing system design to move the probe about the chamber with four degrees of freedom. For traversing in x-direction (along the direction of the chamber/test section), a Linear DC-Servomotor made by Micromo (Model number: LM1247, together with MCLM3006S Figure 7. SolidWorks Model of LPM-2 Motor Cradle controller) was used as it could provide the rigidity and traversing length required. Figure 6 shows the x-direction traverse rods and the motor highlighted in blue. For the lateral traversing, an initial design manufactured using a Squiggle motor (Newscale Tech) was not successful and modifications were made to accept a new motor. The lateral traverse was accomplished with a Discovery Tech International, LPM-2 motor, together with a homemade controller employing Arduino kit. Figure 7 shows this motor cradle and Figure 8 shows a close up of the cradle supporting the LPM-2 motor in the assembled probe. 5 American Institute of Aeronautics and Astronautics

For the vertical traversing a Non-Captive Linear Actuator (Haydon-Kerk-21F4U2.5, together with PCM4806XK stepper motor drive) was used. This motor has a small motor base with a threaded rod running through it, providing the height that is required by the design constraints. Figure 9 shows the y-component traversing mechanism with its motion rods and its motor enclosing highlighted in blue. Another level of traversing capability was the stepper motor which was needed to actuate the rotary stage to tilt the probe along the base centerline. The rotary motor used was Micromo-AM1524 (part#:AM1524V0065). The rotary worm gear purchased from Charles Supper Company (360º Micro-Rotation Stage - Catalog #2330, Figure 10) was used to convert the rotational action of the motor to a rotation along the longitudinal axis. The mount for the rotary motor was designed to obtain Figure 8. Close-up of LPM-2 Motor Cradle in Motor smooth alignment between the motor and stage. Assembly Several roller bearings were used to assist the longitudinal and lateral motion motors. The bearings were housed in fixtures used to attach the motors, and the rods were inserted through the bearings. The use of bearings was needed to eliminate the binding of the motion. Binding that was observed at earlier design stages is due to the use of single motors located only on one side of the axial and lateral traverses. Usage of bearings improved the operation of the traversing mechanisms and eased the force needed from the motors (Figure 11). `

Figure 9. Y-direction traversing rods and its Figure 12. Z-direction traversing rods and motor enclosure highlighted in blue its motor enclosure highlighted in blue

Figure 12 shows the distances the measurement volume can be translated with the traversing mechanisms. Figure 13 shows the drawing of the probe in the plenum chamber. Figure 10. The rotary configuration highlighted in Programs are written for the traversing systems to blue. correctly read the position of the probe. Additional arms have been added to the unit that holds the probe heads, allowing the probe to be in desired place more securely. Figure 14 shows the three dimensional drawing on the left while the picture on the right shows the actual manufactured model with the optical fibers attached to the probe. Figure 15 shows the images of the traversing mechanisms and the probe.


Figure 11. Bearings highlighted in blue. Motion in the x, y, and z translation benefit from the addition of these bearings.

Figure 12. Measurement probe volume location dimensions that can be reached in the flow.

Figure 13. Probe and the traversing mechanisms placed in the plenum chamber. The region shown in red denotes the measurement locations.


Figure 14. Three-component LDV SolidWorks drawing (left); actual manufactured probe on the optical table during alignment (right).

Figure 15. a) Traversing mechanisms, b) the probe on the traversing mechanism inside the chamber, c) the probe and traversing mechanism during alignment.

III.D. Probe Volume dimensions: Table 1 lists the lenses used with collimation, focusing, and receiving optics. The probe volume dimensions for each color pair is given in Table 2. The combined measurement volume is the overlapping region of the measurement probe volumes formed by the separate color beam pairs. The receiving optics fiber used had a 50μm diameter. With the use of the two back to back achromatic lenses the receiving optics fiber sees a 90μm diameter section of the flow. As the receiving optics collects the light from a 90 micron window this results in a probe resolution of approximately 156 micron size perpendicular to the wall. The bisector of the blue or the green beams makes an angle about 30 to the perpendicular to the wall. The 156 micron is calculated as the distance perpendicular to the wall required for blue or the green beams to pass through the 90 micron collection window.


Table 1. Lenses used in the design Lens type Diameter(mm) Achromatic Doublet Achromatic Doublet Achromatic Doublet Achromatic Doublet Plano-Convex

18

Focal length(mm) 40

18

22.5

9

45

15

70.2

2

1.5

Plano-Convex

2

2

usage

focus collimated light onto the fiber terminator in receiver focus beam pairs in transmitting optics for blue and green beams focus beam pairs in transmitting optics for purple beams collimate the light emerging from fiber terminator for blue and green beams collimate the light emerging from fiber terminator for purple beams

collimate collected scattered light in receiver

Table 2 Probe volume specifications Fringe Focused spacing beam (micron) diameter (micron)

Length of the probe volume (mm)

Green Blue Purple

1.9379 2.0585 1.9938

6.9558 7.3885 7.1563

71.719 68.016 66.414

Length visible by collection optics (micron) 156 156 156

Included angle between beams (degree) 4.239 3.785 3.8157

Rayleigh range (mm), 2

𝑧𝑅 =

d 𝜋( 2m )

λ

7.85 7.44 7.27

III.E. On-table Optics: On table equipment includes a Coherent-Innova-8W laser, two dispersion prisms used back to back to separate the single laser beam emerging from the laser to different colors. The colors used in the current system were 514.5 nm (green), 488 nm (blue), and 476.5 nm (purple). The beams were next guided using mirrors to the Bragg cells. Bragg cells were used to split a single laser beam into two beams and shift the frequency of one of the beams by a prescribed frequency to eventually determine the measured velocity direction. The beams were next reflected by mirrors to the laser-to-fiber couplers. The use of Bragg-cell-shifts more than twice the expected Doppler frequency minimizes the angular bias, which is an effect caused by limitations for LDV processors to measure all speeds at all angles (Edwards 1987). Laser-to-fiber couplers were used to couple the laser beams into fiber-optic cables to carry the beams to the LDV probe. A schematic drawing of the on-table optical equipment is shown in Figure 19. It is imperative that the laser used is equipped with an etalon, an optical device residing in the laser that reduces the longitudinal modes of the laser beam. Use of etalon ensures working with limited longitudinal modes only, which in turn ensures that the fringes that form in the measurement probe volume will not jitter due to the frequency variations that occur in the laser beams. In the current system a hand-picked etalon was used. The etalon operated simultaneously at all the previously mentioned wavelengths. III.F. Data acquisition and reduction units: The scattered light collected by the LDV probe is transferred to the data acquisition and reduction units. The light collected was first passed through a color separator unit (TSI Colorbar) to separate the signal into signals for different colors. Each color signal was then directed to photomultiplier tubes (Ludlum Measurements, model no:9124SB). Photomultiplier (PM) tubes convert the light signal to an electrical signal. The electrical signal is then processed to extract the Doppler frequency of the signal to determine the velocity of the particle passing through the measurement probe volume. The data acquisition and reduction units consist of several passive amplifiers, passive filters, radio frequency (RF) generators, electrical signal splitters and combiners, a frequency domain processor and a PC. A schematic drawing of the data acquisition and reduction unit train used in the current system is shown in Figure 16.The electrical signal generated by the photomultiplier tube is first amplified since the signal level is usually very low. This signal is next combined with a signal generated by an RF generator and then fed to the frequency domain processor. Combining the electrical signal from the PM tube with the RF signal is required to subtract the frequency 9 American Institute of Aeronautics and Astronautics

shift imposed on the laser beams by the Bragg cells. This process is required for correct determination of the Doppler frequency by the frequency domain processor. Frequency domain processor is the key element that calculates the Doppler frequency of the signal by employing a fast-Fourier-transformation (FFT) on the signal and then determining the peak frequency of the resulting spectrum. The device also generates key information required for further processing the data to determine the correct mean velocity or shear stress values. Key information includes arrival time and transit time, which denote when particles arrive to the measurement probe volume from the beginning of the data acquisition, and the duration they spend in the measurement probe volume. The frequency domain processor that was used in the project was FSA-4000 (Frequency and size analyzer – 4000) by TSI Inc.

RF

RF

RF filter

PC FSA

MIX

dispersion prism s

LASER AMP M M

BC PM M BC light bar

M

0 Mhz 50 Mhz

M: m irror LTFC: laser-to-fiber c oupler BC: Bragg c ell RF: radio frequency generator MIX: mixer AMP: am plifier PM: photo-m ultiplier tube

M

LTFC

BC

M

LTFC

probe transmitting fibers

receiving fiber

Figure 16. On-table optical equipment. M: mirror, PR: polarization rotator, BSC: beam-splitter cube, BC: Bragg cell, LTFC: laser-to-fiber coupler, PM: photo-multiplier tube.

IV. Experimental Verification The probe developed was tested in the subsonic wind tunnel at the University of Alabama to measure a twodimensional turbulent boundary layer forming on the wall of the tunnel. This section details the specifications of the wind tunnel, data reduction algorithms, data acquired and the uncertainties in the measured quantities. IV.A. University of Alabama Subsonic Wind tunnel: •

Preliminary results were obtained in the UA Subsonic wind tunnel. The subsonic wind tunnel at UA is powered with a 75 Hp DC motor running a centrifugal fan. The fan speed could be adjusted to achieve a 10 American Institute of Aeronautics and Astronautics

0.1 m/s accuracy in the velocity setting in the test section. The tunnel is equipped with two flow straighteners and 5 screens to reduce the swirl and turbulence of the flow. The flow passes through a 4:1 area contraction ratio nozzle before it enters the 30” x 30” test section. The tunnel has a maximum speed of 25 m/s. The tunnel also has an interchangeable 9:1 contraction ratio nozzle that is designed to work with a 16 ft long test section that can be used especially in boundary layer measurements. For that nozzle the highest achievable velocity is 50 m/s. Current experiments were made at 15 m/s free-stream velocity setting in the 30” x 30” test section tunnel. Figure 17 shows the pictures of the wind tunnel and the probe attached

Figure 17. Pictures of the University of Alabama Subsonic Wind Tunnel, and the probe during measurements. on to the floor of the tunnel. Reynolds number based on momentum thickness, 𝑅𝜃 , calculated was 1800. IV.B. Measurement Details: Measurement location and seeding: Measurements were made at a free-stream velocity of 15 m/s, and about 47 cm downstream of the entrance to the tunnel test section. The seeding used during the experiments was di-octyl phthalate with a nominal diameter of 0.7 microns. The seeding was introduced from the ports at the beginning of the contraction section. The smoke generated by a TSI-six-jet atomizer was fed to a plenum chamber residing under the tunnel. Hoses attached to the plenum chamber were fed into the ports and the hoses were made flush with the internal wall of the contraction section. The seeding material travels following the wall of the contraction section before entering the test section. It is believed that the injection of the smoke minimally disturbs the flow quantities. The smoke travels of about 2.5 m prior to entering the test section along the curved surface of the contraction section. Finding the wall: The measurements were made on a 5 mm thick anti-reflective coated insert glass. The glass was used to minimize the effect of the reflections in the measurements especially very near the wall. The wall location was determined by observing the data rate on the computer. Once the probe volume intersects the wall the reflections from the wall result in a coherent data signal that can result in very high data rates. This is due to the presence of a non-moving object being present at the measurement probe volume. The measurement probe location was retreated into the glass insert using the vertical traverse first, and then the probe was traversed up until a very high data rate was achieved. Once the wall location was determined the probe volume was traversed up by approximately 150 11 American Institute of Aeronautics and Astronautics

microns to bring the probe volume to the first measurement location. The accuracy in finding the zero wall location was determined after obtaining several velocity profiles and comparing them again the DNS data and the law-of-thewall profiles. Data indicates that the wall could be accurately determined within ±50 microns. Traversing capability: The traverse used for the purpose allowed moving the measurement probe location by 25 micron increments. This resolution was satisfactory for the measurements at hand. The maximum traversing distance is limited with the design of the probe and the measurements probe location could be traversed as high as 1 inch within the current experiments. Effect of angular orientation: The probe was also designed such that the probe head could be rotated along the longitudinal axis so the angular orientation of all the six beams emerging into the flow could be modified. The probe could be held in position with the rotary motor while the Y traverse could be used to traverse the probe. This would allow measuring the velocity at different lateral locations without moving the probe. This feature of the design allows accessing measurement locations where traversing using the lateral traverse is not possible. During the experiments the probe was tilted by 20 degrees such that the blue and the green beams that are nominally on the same plane would emerge on a plane rotated along the X axis by 20 degrees. The angular alignment quickly alters the beam paths traversed with the purple beams (3rd component) and modify the location where the purple beams cross. This effect very quickly eliminates the option of making threedimensional velocity measurements in tilted configurations. Another issue observed was that higher angular settings reduce the data rate such that measurements cannot be accomplished even for two component measurements, requiring probe realignment. The angular orientation of the blue and the green beams and the receiving optics change due to the angular setting. It appears that the receiving optics no longer sees the measurement probe volume requiring new beam crossing alignments at this new angle. However two -velocity-component measurements can be made while the probe is tilted up to 20 degree orientation. Three-dimensional measurements at selected angular orientations can be made once the probe beams are aligned to cross while they pass through the optical glass at desired angles. IV.C. Data reduction algorithms: The probe measures the time-dependent velocity components U1, U2 and U3 simultaneously (during the experiments a 5 µsec coincidence window was used) and the time dependent U, V, and W velocity components in in tunnel coordinates were calculated using the cosine angles given in Table 3. Tunnel coordinates are defined such that the X axis is in the main flow direction, Y axis is perpendicular to the wall, and the Z axis completes a righthanded coordinate system. 𝑼𝟏 = 𝒈𝟏 𝑼 + 𝒈𝟐 𝑽 + 𝒈𝟑 𝑾 𝑼𝟐 = 𝒑𝟏 𝑼 + 𝒑𝟐 𝑽 + 𝒑𝟑 𝑾 𝑼𝟑 = 𝒃𝟏 𝑼 + 𝒃𝟐 𝑽 + 𝒃𝟑 𝑾 Table 3 Cosine angles for the positive measurement direction unit vectors. X Y Green 𝑔1 =0.8776 𝑔2 =-0.47932 Blue 𝑏1 =-0.86445 𝑏2 =-0.48109 Purple 𝑝1 =0.26219 𝑝2 =0.19713

Z 𝑔3 =-0.0084915 𝑏3 =0.14584 𝑝3 =0.94467

The mean velocities, normal stresses and the Reynolds stresses were calculated using the particle residence time as the weighting factor to eliminate the bias due to particle-rate/velocity correlation that may exist during the measurements (Albrecht et al 2003, Edwards, 1987). Residence time is the time the particle spends in the probe volume and it is determined by the frequency domain processors for each valid signal. It is also named as the “gate pulse” (section 6.2 in Albrecht et al, 2003). Prior to the residence time averaging, velocity data were first used to calculate the standard deviation,  of the data. Next the data outside the ±3 were discarded. During the boundary layer measurements 15,000 to 30,000 samples were obtained at each measurement location, while the TSI frequency-domain processors were set to 2-20 MHz filter range. Data rates varied between a couple hundred near 12 American Institute of Aeronautics and Astronautics

the wall to several hundred away from the wall. Data acquisition period was about 3 minutes per point near the wall and more than a minute at locations away from the wall. The equations used are:

U mean  (U i t i ) /  t i , 2 u 2  ( (U i2  U mean )t i ) /  t i

uv  ( (U iVi  U meanVmean )t i ) /  t i where, “t” denotes the residence time for each validated data and the subscript “i” denotes the instantaneous values. The other mean velocity, normal stress and shear stresses were calculated using the appropriate instantaneous and mean velocity components. IV.D. Experimental data: Figures 18-22 show the data obtained in comparison to the DNS calculations of Schlatter et al. (2009). The experimental data show a fairly well match to that of the DNS results. The differences between the results are attributed to the experimental uncertainty in the velocity measurements, and the uncertainty in the friction velocity calculations.

Figure 18. U mean velocity profiles in comparison to the DNS data (Schlatter, 2009).


Figure 19. Axial normal stress profiles in comparison to the DNS data (Schlatter, 2009).

Figure 20. Wall-normal stress profiles in comparison to the DNS data (Schlatter, 2009).


Figure 21. Spanwise normal stress profiles in comparison to the DNS data (Schlatter, 2009).

Figure 22. Reynolds shear stress profiles in comparison to the DNS data (Schlatter, 2009).

IV.E. Uncertainty analysis: Measurement uncertainty was calculated using two separate data sets taken under the same conditions and using Chauvenet’s criterion (Holman, 2012). Chauvenet’s criterion specifies that a reading may be rejected if the probability of repeating the particular deviation from the mean is less than 1/2𝑚 where m is the number of readings. For two readings, the standard deviation is given by: 15 American Institute of Aeronautics and Astronautics

𝑑max = 1.15 𝜎 where 𝑑𝑚𝑎𝑥 is half the difference between two measurements at the same location, 𝜎 is the standard deviation, and 1.15 is the constant from Chauvenet’s criterion. Table 4 gives the uncertainties (±2𝜎) in the measured quantities. Table 4. Uncertainties in measured quantities in 21:1 odds. 𝒖𝝉 = 𝟎. 𝟔𝟒𝟑 𝒎/𝒔 ± 0.226 𝑈/𝑢𝜏 ± 0.038 𝑉/𝑢𝜏 ± 0.046 𝑊/𝑢𝜏 ̅̅̅2 /𝑢𝜏2 ± 0.220 𝑢 ̅̅̅ ± 0.145 𝑣 2 /𝑢𝜏2 2 2 ̅̅̅̅ ± 0.096 𝑤 /𝑢𝜏 2 ± 0.180 ̅̅̅̅/𝑢𝜏 𝑢𝑣 ± 0.063 ̅̅̅̅/𝑢𝜏2 𝑢𝑤 ± 0.037 ̅̅̅̅/𝑢𝜏2 𝑣𝑤 Fringe distortion uncertainty: It is well known that, if the beams forming the probe volume do not overlap at their beam waists, the fringe spacing in the probe volume becomes non-uniform leading to biased estimates of mean velocity and higher moments (Albrecht et al, 2003, Ch. 7). Fringe spacing uniformity in the probe volume was ensured by making sure that the collimated beams forming the probe volume were parallel before the focusing lens, and then observing the crossing using a microscope objective at a far distant wall. For the current design the d 𝜋( 2m )

2

Rayleigh length, the distance over which the beam diameter becomes, d= √2 dm , was calculated as, 𝑧𝑅 = = λ 7.85, 7.44, 7.27 mm, for green, blue, and purple beams respectively, which is considerably larger than the longitudinal length of the probe volume (l m = 1.9379, 2.0585, and1.9938mm, for green, blue and purple colors respectively) as shown in Table 2. A conservative estimation made using the discussions by Albrecht et al. (2003, Chapter 7.2.4), shows that if the beams cross at a full probe volume length distance away from their waists, the error in the measured √𝑢2 /𝑈𝑗 would be ~ 0.1%. Transit time broadening: The finite transit time broadening is due to the fact that a signal generated by a particle only lasts as long as the particle is in the probe volume, and presence of several particles entering and exiting the probe volume affects the observed signal. This results in increase in the measured fluctuation velocity, and depends solely on the number of fringes in the measurement volume. An estimate of the transit time broadening for the ∆𝑢′

1

current experiments was made using = = 0.0125 (Durst, et al., 1981, p. 207) where N (N ≈ 9 in the 𝑈 2√2 𝜋𝑁 present measurements) is the number of fringes. Number of samples and particle number density: Considering that the time scale of a turbulent boundary layer could be described as 𝜏 = 𝛿/𝑈 the time scale ranged between 𝜏 ≈ 6ms – 1.1 ms. Data acquired allowed ample amount of statistically independent number of samples (N=data acquisition duration/ 2𝜏) for estimation of the mean and the fluctuating velocity components (Albrecht et al., 2003, Section 10.3). In addition, given that a typical inter𝜏 arrival time of the data was in the range, ∆𝑡𝑝 =0.2 to 20 ms, the data density, (𝑁𝐷 = ), varied 𝑁𝐷 ≈ 0.05 𝑡𝑜 30, ∆𝑡𝑝

indicating that the transit time weighting, as used in the current data reduction, is required to achieve low estimator errors (Albrecht et al., 2003, Section 11.1). Instrument broadening: FSA-4000 employs multiple 8-bit digitizers to continuously and simultaneously sample the incoming signal at three different rates and a 16-bit digital output. This results in a frequency resolution of 0.0015%, minimizing instrument broadening (Lai et al., 2013). The accuracy of a measured single frequency by the FSA-4000 is 0.5% of the measured frequency, while the repeatability of a set velocity determined with a large number of samples is within 0.05% (Lai et al., 2013). Gradient broadening: The gradient broadening in the signal occurs due to the presence of mean velocity gradients in the measurement volume. This is a large uncertainty source once the longitudinal length of the probe volume is fairly large. In the present probe the portion of the longitudinal length seen is dictated by the receiving optics and is limited to lo=~156 μm. An estimate of the gradient broadening effect on the fluctuating velocity was 16 American Institute of Aeronautics and Astronautics

calculated near the wall especially where the mean velocity gradients are the highest, using,

∆𝑢′ 𝑈𝑗

=

𝑙𝑜 /2 𝑑𝑈 𝑈𝑗

( ) (Durst et 𝑑𝑦

al., 1981, p.210). The values calculated for the ̅̅̅̅̅ 𝑢2 /𝑢𝜏2 result in as large as 5% variations near the wall below y+< 25 but the overall effect does not result in overlapping the experimental and computational profile. The velocity gradient broadening in the mean velocity for the same flow was calculated using

∆𝑈 𝑈𝑗

=

(𝑙𝑚 /2)2 𝑑 2 𝑈 2𝑈𝑗

(

𝑑𝑥 2

), with minimal

effect on the presented data. Thus the results were not corrected.

V. Future work: Utilization of the Probe at University of Alabama Supersonic Wind Tunnel In rectangular supersonic inlets, the interaction of the oblique shock waves with the side wall boundary layers generate complex three dimensional separation zones and cause unsteadiness in the flow as well as increase drag (Eagle et al., 2011). Above mentioned LDV system along with the three component LDV probe will be used in the study of the flow in 3” x 3” supersonic wind tunnel at The University of Alabama. V.A. Wind tunnel The picture of the wind tunnel is shown in Figure 23. Figure 23 shows the assembly of pressure regulator, settling chamber, nozzle, test section with wedge and finally the diffuser. The wind tunnel receives dry compressed air from a compressed air storage tank. The storage with a volume of 28m3 and with a maximum allowable design pressure of 1.38 MPa is used for this purpose. Two, Ingersoll – Rand compressors of model SSR – HXP50SE with a capacity of 170 CFM supplies the compressed air to the storage tank. The compressors are operated at 1.275 MPa, while each compressors is powered with a 3 phase, 60 Hz, 50 HP motor. For the purpose of drying the air, an automatic air-cooled Ingersoll – Rand dryer, model TZ300HP-EMS-3V-LDP is used. The desiccant used in the dryers is activated alumina with dew point of -73° C (-100° F).

Figure 23. A picture of the University of Alabama, 3” x 3” cross section supersonic wind tunnel. Wind tunnel’s operating pressure is regulated by a 76.2 mm LESLIE pressure regulator. The stagnation chamber contains a flow straightener, damping screen and a pitot probe. The flow straightener is made up of 101.6 mm long 12.7 mm in diameter steel tubes. The air inside the flow straightener first goes through a perforated cone and then passes through the steel tubes and finally through a damping screen and enters the nozzle. In the experiments, an aluminum nozzle manufactured in house is used to obtain a Mach 3 flow in the test section. The nozzle is of 25.4 cm in length with throat area of 1.65 x 7.62 cm2. The test section dimensions are 7.62 x 7.62 x 30.5 cm3. The side walls of the test section contain 2.54 cm (or 1.905cm) thick, 7.62 cm diameter optical glass to have optical access into the flow to visualize both the boundary layer and SWBLI flow field. An isosceles triangle prism with 12° side angles bolted to the ceiling of the test section generates the desired oblique shock. Dimensions of the wedge are 11.95 x 17 American Institute of Aeronautics and Astronautics

7.62 cm2 and 1.27cm thick at the center. The wedge is placed at a location such that the interaction region can be visualized through the glass windows. A variable area supersonic diffuser of dimensions 63.5 cm long with an inlet area of 7.62 cm x 7.62 cm and the outlet area of 12.7 cm x 7.62 cm is used downstream of the test section to recover pressure to reduce the total pressure required to run the tunnel. The walls of the diffuser includes a hinged plate, which could be adjusted to work with the different Mach numbers in the test section.

Figure 24 New design for the bottom floor with adjustable plates. Figure 25 Side view of the test section with new bottom floor with equal sized adjustable plates. Bottom floor for the test section is modified such that the LDV probe can be attached to the tunnel to capture the SWBLI data. Figure 24 shows the new design for the bottom floor. The bottom floor contains adjustable plates with support lips such that the glass pane insert of dimensions 3.81cm x 7.62cm x 0.635cm can be placed. The position of glass pane can be adjusted using the adjustable plates, such that data can be acquired throughout the SWBLI region. Figure 25 shows the side view of the test section with new bottom floor with equal sized adjustable plates such that the glass insert is at the center.

VI. Conclusions Development of a three-velocity component, three color, fiber-optic laser-Doppler-velocimetry probe has been discussed. The miniature probe was designed to fit into a chamber that is an integral part of a generic inlet model. The probe includes four traversing mechanisms for boundary layer measurements at desired locations with a 156 micron resolution. The probe developed was tested in a subsonic tunnel to demonstrate its capabilities. The comparison of the data to that of the direct numerical simulation results show that the probe works as designed and it can accurately measure boundary layer profiles.

Acknowledgments The authors would like to acknowledge the United States Air Force for their review and clearance of this research. This paper is cleared for public Release, Unlimited Distribution, 88ABW-2015-2867, Wright Patterson Air Force Base.

References Albrecth, H.E., Borys, M., Damaschke, N., Tropea, C., 2002, Laser Doppler and Phase Doppler Measurements Techniques. Springer. Byun, G., Ölҫmen, S.M., Simpson, R.L., 2004. A Miniature Laser-Dopler Velocimeter for Simultaneous ThreeVelocity-Component Measurements. Measurement Science and Technology, Vol. 15, 2075-2082. Durst, F., Melling, A., Whitelaw, J.H., 1981, Principles and Practice of Laser-Doppler Anemometry, Academic Press. Eagle, W.E., Driscoll, J.F., and Benek, J.A., 2011,“Experimental Investigation of Corner Flows in Rectangular Supersonic Inlets with 3D Shock-Boundary Layer Effects”, AIAA-2011-857, 49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, Orlando, Florida. Edwards R V (ed) 1987 Report of the Special Panel on Statistical Particle Bias Problems in Laser Anemometry J. Fluid Eng.109 89–93. Esirgemez, E., Olcmen, M.S., 2005, “Spark-Plug LDV Probe for In-Cylinder Flow Analysis of Production IC Engines”, Measurement Science and Technology, 16, 2038-2047. 18 American Institute of Aeronautics and Astronautics

Lai W, Shakal J, Troolin D, 2013, “Accuracy, Resolution, and Repeatability of Powersight PDPA and LDV Systems,” TSI Technical Note P/N 5001520 (A4), TSI Incorporated, Shoreview, MN, USA. Schlatter, P., Örlü, R., Li, Q., Brethouwer, G., Fransson, J. H. M., Johansson, A. V., Alfredsson, P. H., and Henningson, D. S., 2009, “Turbulent boundary layers up to Re_ =2500 studied through simulation and experiment”, Phys. Fluids 21 (051702), 1–4. Schlatter, P., Örlü, R., 2010-a, “Assessment of direct numerical simulation data, of turbulent boundary layers ”, J. Fluid Mech. (2010), vol. 659, pp. 116–126. Schlatter, P., Li, Q., Brethouwer, G., Johansson, A.V., and Henningson, D.S., 2010-b, “Simulations of Spatially Evolving Turbulent Boundary Layers up to Reθ = 4300”, International Journal of Heat and Fluid Flow, Volume 31, Issue 3, June 2010, Pages 251–261
