A Sub-Miniature Laser-Doppler Velocimeter for High Speed Flow

14th Int Symp on Applications of Laser Techniques to Fluid Mechanics Lisbon, Portugal, 07-10 July, 2008

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A Sub-Miniature Laser-Doppler Velocimeter for High Speed Flow

Measurements

K. Todd Lowe1 and Roger L. Simpson

2

1: Applied University Research, Inc., Blacksburg, Virginia, USA, [email protected]

2: Cowling Professor, Department of Aerospace and Ocean Engineering, Virginia Tech, Blacksburg, Virginia, USA, [email protected]

Abstract A new laser-Doppler velocimeter (LDV) for high speed flow measurements (three-dimensional flows with speeds greater than 610 m/s) is being developed based in-part upon an existing low speed instrument capable of high resolution, near surface velocity vector measurements. The key technology for the instrument is a sub-miniature laser-Doppler velocimeter (SMLDV); a similar low-speed version of which has been used effectively in past work to obtain novel measurements from within a small model in a low speed wind tunnel (Byun and Simpson 2006). The instrument is based upon the LDV technique but with enhancements that allow ultra-miniaturization, operation through curved access windows, remote operation, robust performance even with low signal-to-noise ratios as may be encountered in some high speed flows, and particle acceleration measurements. To this end, the SMLDV is an extended LDV concept that may be deployed inside models with nearly arbitrary surface curvature to obtain high resolution three-component velocity and acceleration statistics profiles throughout the boundary layer of the model. The current paper is divided into two parts. In the first part, the robust design and operating capabilities of the SMLDV for in-model measurements at high speeds are discussed. In the second part, an important potential application for the SMLDV utilizing the capability to measure turbulent flow accelerations is highlighted including aspects of signal processing and application-oriented descriptions of acceleration-related flow physics.

1. Introduction For proper design and modification of high speed (i.e., Mach numbers approaching or

greater than one) flight systems, flow modeling based upon observed physics for high Reynolds number three-dimensional (3-D) turbulent flows at those Mach numbers is essential. Unfortunately, nearly all of the existing higher Reynolds number turbulence structural measurements have been done for nominally 2-D flows, and they show mean flow behavior similar to lower Reynolds number flows. However, the structure of 3-D turbulent boundary layer (3DTBL) flows is dramatically different from 2-D flows, and there are many differences in the turbulence structure even over the momentum-thickness Reynolds number range 7000 < Reθ < 23000 for which detailed measurements have been reported for the well-known wing/body junction 3DTBL test flow (Simpson 2001, 2005; Ölçmen et al., 2001). For instance, the highest Reθ 3-D turbulence structure research that has been done in the world to this date at Reθ = 23000 shows that 3 or more length scales are very important to the flow behavior, which is much different from 2-D flows (Ölçmen et al. 2001). Important results crucial to improving the understanding of high Reynolds number 3DTBLs greatly motivate the development of advanced measurement technologies capable of providing 3-D turbulence information.

Numerous authors have discussed the clear need for continued experimental research in high speed flows (Gaitonde et al. 2004; Dolling, 2001a; Miles et al., 2001). For example, Gaitonde et al. stress the importance of obtaining experimental turbulence structural measurements in 3-D flows to overcome the deficiencies of Reynolds-averaged Navier-Stokes (RANS) and Reynolds stress transport (RST) modeling commonly used in designing flight systems. To make realizable impacts, data for non-equilibrium and 3-D flows involving shock/boundary layer interactions are severely needed (Dolling, 2001b), including but not limited to flow field measurements of mean


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velocities, all Reynolds stresses, velocity triple product correlations, and turbulent velocity spectra from experiments. The sub-miniature laser-Doppler velocimeter (SMLDV) described herein is capable of obtaining these velocity statistics in high speed flows of practical and fundamental interest—a feat which has not occurred in the past.

While numerous techniques exist for the measurement of velocities in turbulent flows, the LDV technique sets the standard for low statistical uncertainties achievable for single-point measurements since it requires no calibration, is a zeroth-order direct measurement, is directionally sensitive, and is non-intrusive to the flow (Durst et al. 1981, Albrecht et al. 2003). Planar measurement techniques such as particle image velocimetry (PIV) and Doppler global velocimetry are not suited for detailed low-uncertainty measurements in arbitrary flow conditions and typically suffer poor performance near flow boundaries (Adrian 2005; Samimy and Wernet 2000), although some improvements for the near wall region have been achieved in low Reynolds number flows (Theunissen et al. 2008). The LDV technique stands as the most-viable current option to accomplish low uncertainty, spatially resolved velocity measurements over the large dynamic ranges encountered in high speed, high Reynolds number turbulent boundary layer flows.

The state-of-the-art in sub-miniature 3-D LDV designs has been set by the development of the credit-card-sized probe arrangement shown in figure 1 (Byun et al. 2004; Byun 2005). This probe was successfully employed for measurements in a highly-complex three-dimensional, weakly-separating turbulent flow over a contoured surface (Byun and Simpson 2006). Those measurements have been used extensively by the computational research community for improving prediction methods in separating flows (Menon et al. 2004; Wang et al. 2004; Davidson and Dahlström 2004; Tessicini et al. 2007). The success of the operation of the credit-card-sized probe and the worth of the data that arose from its use makes the technology an excellent candidate for extension to supersonic flows where a distinct lack of such detailed data exists.

2. The SMLDV Instrument Description Most previous LDV work in supersonic flows was done prior to the advent of fiber-optic

beam-handling designs, improved high signal-to-noise ratio (SNR) photomultiplier technologies, high sampling rate analog-to-digital boards, inexpensive high performance PCs with large amounts of data storage, and user-friendly and versatile software. Of the works consulted, commercial LDV systems with large fringe spacings were most-often used and all of the measurements were one-or two-velocity component and utilized large measurement volumes on the order 1mm long (e.g., Bowersox 1996; Bur et al. 1998; Kerhervé et al. 2004). The SMLDV extensively improves upon the capabilities from the previous high speed experimental research by making use of extremely low noise electronics and photomultipliers; high sampling rate data acquisition; and integrated optical probe arrangements with off-axis light receiving that greatly limits the spatial extent of the measurement volume. In addition, signal recognition and processing techniques are developed that enable processing for low signal-to-noise ratio signals, even in the presence of wall flare (Lowe 2006).

The SMLDV instrument is comprised of a fiber optic probe, a photonics hardware system (PHS), and a PC for data acquisition and post-processing, as depicted schematically in figure 2. A primary goal of the SMLDV development is the capability of very near wall measurements in difficult-to-access flows, requiring extra attention to the details of miniaturization while providing a solution for optical access through nearly arbitrarily contoured surfaces. The fiber optic, miniaturized probe is externally similar in shape and dimension to the one in the photograph in figure 1 with a proprietary internally-integrated optics design. The probe may be positioned with micron precision using a servo-controlled three-axis miniature traverse system that is specified to satisfy the spatial constraints imposed by mounting the probe within models under test. The laser source for the SMLDV is a single Nd:YVO4 CW laser operating at 532 nm, operated remotely from the fiber optic probe within the PHS. The PHS consists of the light generation and detection


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photonics that condition and couple laser light into the five single-mode fiber optic cables leading to the SMLDV probe and convert the scattered light signal collected at the probe and coupled into a multimode fiber optic cable into a conditioned electronic RF signal that may be digitized by the data acquisition computer. To accommodate customer requirements for remote access, the three primary units—the probe, PHS, and data PC—may be operated up to 30m apart with power, data and fiber optic cable bundles less than 10mm in diameter allowing for simple routing of the cabling within facility constraints. The data acquisition and processing PC is controlled by the ‘AUR Suite’ custom software package. This user-friendly suite is completely user-configurable, making use of a modular software architecture, and, in addition to enabling the end-user to implement their own processing modules, includes the proven signal processing and post-processing algorithms described by Lowe (2006) that perform robustly and efficiently for most flow situations.

Fig. 1 Photograph of the subminiature fiber optic laser-Doppler velocimeter for in-model measurements of three-component velocity vectors in three-dimensional low speed flows. The ruler in the background is in inches. Photograph courtesy Byun (2005).

Fig. 2 Schematic depiction of the SMLDV system components.

2.1 Optical access The technique of LDV measurements via model-embedded miniature fiber optic probes

has been used with great success in low speed flows (Chesnakas and Simpson 1996, 1997; Byun and Simpson 2006). The problem of optical access through contoured models such as those tested in the above works was solved through the use of 0.508mm thick optical quality polycarbonate windows that were formed to the model surface. The refraction through such a window is nearly negligible; so the optical integrity of the system is preserved even for large and changing curvature.


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In the case of the SMLDV, high speed flows with much greater dynamic pressures than those encountered in previous work are of interest so that greater constraints are imposed on the structural integrity of the windows. The window for the SMLDV design measures 80mm by 30mm to allow the full traversable range of the fiber optic probe normal to the model surface (a distance of 30mm). The static analysis of a clamped rectangular plate subjected to a uniform pressure difference has been formulated in solutions such as the Ritz Method(e.g., see pg. 292 of Shames and Dym 1985):

( ) ( )222222

42240

747

/383.0),( byax

bbaa

Dqyxw −−

++= (1)

where w(x,y) is the deflection of the plate at the locus of locations, (x,y), in the plane of the un-deformed plate, the uniform loading per unit area is q0, a is the half-length of the plate, b is the half-

width of the plate, and [ ])1(12/ 23 ν−= EhD where E is Young’s modulus, h is the plate thickness,

and ν is the Poisson ratio. It is assumed for design purposes that the worst case loading is a pressure difference of 100% of the flow dynamic pressure. An example study may consider a facility with a dynamic pressure of 192kPa, i.e., a high speed flow case. In this example, the center of the 0.508mm thick window deflects by 600microns, while stresses are kept well below the yield stresses of polycarbonate material. For additional integrity of the model shape, it may be desired to use a thicker window, up to 1.016mm thick, requiring additional consideration of the potential effects of refraction. To predict the impact of refraction on the SMLDV system utilizing windows up to 1.016mm thick, the ZEMAX software package was used to model the optical system. The results indicate that the effective focal point of the imaging system when transmitting through the 1.016mm thick, double convex window changes by less than 30% of the measurement volume length over the entire traversable range of the probe volume. The ZEMAX software was also used to compute the physical optics propagation of two of the probe laser beams to determine the influence of the window on the interference within the measurement volume. The post-processing technique is depicted schematically in figure 3, wherein the intensity distribution of the overlapping coherent laser beams obtained from the model in ZEMAX is first averaged along the fringes to obtain a burst-like one-dimensional function and then Fourier transformed to obtain the spatial frequency of the fringes. This calculation was conducted for three heights of the measurement volume relative to the window, as the ZEMAX model screenshots in figure 4 depict. The results for the fringe spacing within the measurement volume, plotted in figure 5, reveals no change from height to height for the range of probe positions examined, although a very small variation of the fringe spacing was detected which is negligible over the length of the measurement volume viewed by the receiving optics (i.e., a 100 diameter cone).

Fig. 3 Diagram of the process for determining the fringe spacing of a measurement volume cross section. The intensity cross section of the measurement volume (upper left) is averaged along the length of the fringes (upper right) and is finally Fourier transformed to obtain the distribution of intensity fluctuation power as a function of fringe spacing.

Fringe space, microns


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Fig. 4 Screenshot of the ZEMAX model for three measurement locations through a double convex window, each screenshot varying in the normal-to-wall measurement distance, where axial variations of the fringe spacing were

computed. (a) mmy 1.14−=δ ; (b) mmy 6.10−=δ ; (c) 0≡yδ . Note that some details of the optics modeled

prior to the transmitting lens have been omitted.

Fig. 5 Fringe spacing variation along the measurement volume beam bisector relative to the measurement volume center obtained from a simulation of the SMLDV measurement volume as computed with ZEMAX. Symbols correspond to the three measurement locations of figure 4.

2.2 SMLDV laser probe details

While various custom probe designs are possible using the current design methodology, the proof-of-concept version of the SMLDV has been designed to perform within wind tunnel models of the scale of 1 to 2m in length at flow speeds greater than 610m/s. Very low uncertainties in velocity components were sought in order to provide the capability for measurements of high frequency velocity spectral data as well as flow acceleration measurements. A balance was sought between a measurement volume diameter with high spatial resolution and one with sufficient numbers of fringes and robust preservation of optical coincidence. The compromise was made with a measurement volume of 100 microns diameter as mentioned above. The five laser beams which cross to form three nominally orthogonal fringe sets define a quasi-spherical measurement volume and the matched scattered light receiving optics collect light only from the crossed volume of the laser beams—i.e., off-axis receiving optics are employed in the integrated probe package. The fringe spacing of nominally 2.3 microns provides approximately 44 fringes within the measurement volume and results in statistical RMS velocity uncertainties of 0.23% of the particle speed. This uncertainty has been computed assuming that the majority of the uncertainty arises from noise-


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limited signal processing such that fdU δδ ±= where d is the fringe spacing and fδ is the RMS

uncertainty in the Doppler frequency estimate obtained from the data of Shinpaugh et al. (1992). 2.3 Velocity directional sensitivity

The SMLDV operates using a single wavelength of laser light. This is possible by the technique of frequency division multiplexing in which signals from multiple measurement volumes are distinguished by their relationship in the frequency domain to their unique carrier frequencies. In this way, several Doppler signals may be simultaneously acquired on a single data channel and subsequently distinguished from one-another in the frequency domain. If one assumes that no a

priori knowledge of the flow velocity behavior is known, the only logic available in separating the signals from one-another and matching them unambiguously with the correct measurement volume is to require that for any velocity vector possible, the signals retain the same relative order in the frequency domain. For instance, if there are three signals that give the relationship f1<f2<f3 in some nominal, known operating configuration, this same set of inequalities must hold for any other configuration where unambiguous operation is expected (barring the introduction of additional logic that may be available to sort the signals).

Fig. 6 Thumbprint plot of the regions in the transverse (W) and normal-to-wall (V) velocities over which unambiguous velocity vectors may be measured. The labels on the individual curves indicate the stream-wise velocity for that curve. Valid velocity vectors may be determined within the interior of the curves plotted.

It was sought to determine the measurement ranges possible for sampling rates and carrier

frequencies (Bragg frequencies) that are realistic to the SMLDV. The results for a particular signal configuration are plotted in figure 6 wherein boundaries on the range of transverse (W) and normal-to-wall (V) velocities for which unambiguous three-component velocity vectors are possible are plotted for several values of stream-wise velocity. Note that the zones of unambiguous velocity measurements lie within the boundaries of the curves in this figure. Of particular interest here is, for the case of nominally-zero stream-wise velocity, the transverse and normal-to-wall velocities can achieve full-scale ranges of ±1500 ft/s independent of one another. The ranges possible are even greater at larger values of stream-wise velocity; and even for backflow, the ranges of valid secondary velocities are substantial.


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3. Acceleration sensing with the SMLDV An important added value to the SMLDV is the ability to obtain turbulent flow acceleration measurements with no modification to the hardware. With conventional LDV techniques, the signal processing step ends when the particle velocity has been estimated by determination of the Doppler frequency. By introducing an additional step to estimate the signal chirp, dtdf /≡γ , the SMLDV technique is extended to allow for Lagrangian particle acceleration

estimates. Since the LDV is a zeroth-order instrument, a Taylor expansion of the velocity gives:

) ( ) ( )[ ]{ }dttOttfdtftU ttDoppler

2

000 0)()( −+−+== =γ (2)

where U is the measured particle velocity component and Dopplerf is the measured Doppler

frequency . Obtaining the time derivative of equation (2) yields the acceleration, 0A , of the

particle,

) ( )[ ]2

00 0ttOdA tt −+= =γ (3)

In addition to implementing custom advanced signal processing techniques, considerations are made for the non-uniform behavior of the fringe patterns that affect the acceleration measurement. Calibration schemes have been devised in known flows to assess the variation of the fringe patterns so that reduced-bias acceleration measurements are possible.

3.1. Acceleration signal processing Many techniques have been considered for obtaining the burst chirp needed for flow

acceleration measurements. Some of these include finite difference of short-time Fourier transforms (Lehmann et al. 2002; Lowe and Simpson 2006), time-frequency analysis by quadrature demodulation (Bayer et al. 2008), and many model-based parametric techniques which optimize the model parameters to best fit the signal (Nobach et al. 2006; Lehmann et al. 2002). Of these techniques, the Fourier transform-related techniques have been shown to be robust for low SNR signals (Shinpaugh et al. 1992) and will be considered further here as techniques for determining the Doppler frequency and chirp.

In the SMLDV signal processing, the discrete chirp Fourier transform (DCFT; e.g., Jenet and Prince 2000), a method for examining signals with quadratic phase evolutions, is employed to obtain the Doppler frequency and chirp. The DCFT is directly analogous to the discrete Fourier transform, but with an additional phase term for the chirp rate,

∑−

=

−+

−−

=1

0

2/2

2/2

),)](([N

k

N

Nkl

N

Nkmi

kesmltsCFππ

(4)

where l is the frequency spectral line number and m is the chirp spectral line number, and N is the number of samples in the signal. Just as the discrete Fourier transform is limited in its frequency

range by the Nyquist criterion, the chirp rate range is limited by a similar parameter, ( ) 2

max 4/1 sf=γ ,

where fs is the sampling rate. Another observation for the technique is the relationship for the chirp

line width, ( ) ( )22/ fNf s δδγ == , which scales the chirp rate uncertainties as the frequency

spectral line width analogously scales the frequency uncertainties (Lowe 2006; Bayer et al. 2008). As noted by Lowe and Simpson (2006) and explained further by Bayer et al. (2008), the random uncertainties and bias of the acceleration technique scale with the square of the particle velocity.

To benchmark the performance of the Fourier transform related techniques for obtaining Doppler chirps, the finite difference of frequency (reader is referred to Lehmann et al. 2002 for a description) and DCFT algorithms were both applied to signal simulations of chirped Doppler bursts with added Gaussian noise. The signal parameters for the simulation were the same as the


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ones used by Lehmann et al. (2002), namely N=256; f0/ fs = 0.04; γ / fs2 = 0.00015; and the

reference phase, 0φ =1.2rad. It was sought to examine the impact of zero-padding (with N zeros),

spectral interpolation function, center-time frequency estimation scheme and chirp estimation scheme used. For each noise level the signal was processed 5000 times, each time with an independently realized Gaussian noise time series.

To generalize the signal variance estimates, Shinpaugh et al. (1992) illustrated the usefulness of the proper normalization for the variance and a more pertinent definition of the signal-to-noise ratio (SNR). It was shown that the Cramer-Rao lower bound (CRLB, i.e., the lower bound for the variance of an unbiased estimator applied to a signal with noise) for the constant frequency burst will collapse for all signal parameters when the frequency and chirp variance is normalized using the spectral line width of the Fourier transformed signal, Tf /1=δ where T is the duration of

the sampling period, and the SNR is modified by multiplying with the number of signal samples, N. The expression for the SNR used by Shinpaugh et al. is

( )2

2

1

n

signalNSNRNSNR

σ

σ== or in decibel form: )

=

2

2

101 log10n

signal

dBNSNR

σ

σ (5)

where 2signalσ is the mean-square of the model signal and Nn /2σ is one-half the noise variance per

spectral line in the spectral vicinity of the signal. The SNR1 formulation is particularly meaningful because the noise metric is representative of the narrowband noise that directly affects signal parameter estimation. It is only the narrowband noise that degrades spectral estimates because broadband noise may be filtered before processing.

The RMS error in the estimation of center-time frequency computed in the simulation is plotted in figure 7 for a variety of processing schemes. Note that in the cases in which zero-padding was employed, the spectral line width was still calculated based upon the sampling period of the actual signal before zero-padding. There are a few interesting features from the simulations that deserve mention. First, the onset of the zone of non-biased estimation of the center-time frequency occurs at dBSNR 201 ≈ when the Fourier transform is applied to the entire burst. However, for the

cases in which the burst is separated into parts (as done with the finite difference of Doppler frequency described by Lehmann et al.) in order to compute the parameters, the break occurs at

dBSNR 241 ≈ . As noted previously by Lehmann et al., the use of the entire burst in the spectral

calculation is the superior technique—particularly when chirps are on the order of one chirp line width in magnitude (Lowe 2006). It is also concluded that three point Gaussian spectral interpolation out-performs three point centroid interpolation (see Shinpaugh et al., for example, for definitions of these interpolations), while zero-padding is only beneficial when SNR1>30dB.

In the case of chirp estimation, the DCFT technique far out-performs the finite difference technique, as clearly exhibited in the chirp estimator RMS variation with SNR1 in figure 8. The failure of the finite difference technique to approach the CRLB is attributed to the loss of amplitude information when the envelope of the signal is removed to avoid biases (Lehmann et al. 2002). As in the frequency estimation, the method of dividing the burst into two parts pushes the minimum useable SNR1 value up by about 5dB. In contrast to the finite difference of frequency technique, the convergence of the DCFT method occurs at very nearly the same value of SNR1 as the entire-burst discrete Fourier transform method, in the range of 18-20dB. For the practical range of SNR1 below 35dB common for backscatter LDV systems, the DCFT algorithm closely approaches the CRLB, to within about 20%. Two methods of chirp domain interpolation, three point centroid and three point parabolic, were considered for the DCFT to determine which may be better suited for the application. Virtually no differences may be seen between the two techniques when no zero padding is employed; however, the centroid interpolation slightly out-performs the others when it is zero-padded. For practical implementation, either interpolation scheme is viable with no zero-padding


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due to the very small pay-off it achieves.

Fig. 7 RMS error in midpoint frequency calculations for signal simulations of a chirped burst with noise. Gaussian, Gaussian frequency interpolation; Centroid, Centroid frequency interpolation; whole, entire burst used for computing single DFT; average, burst broken into two parts to form two power spectral densities and frequency result determined by average; ZP, N zeros padded.

3.2. Roles of acceleration statistics in turbulence

The SMLDV capability to obtain turbulent acceleration measurements is a powerful tool for future studies in turbulence. Interest continues to grow in the fluid mechanics research community in the push to better understand and measure Lagrangian turbulent flow physics (Xu et al. 2007). Well beyond the fundamental knowledge that may be gleaned from studies in isotropic turbulence, acceleration statistics produce meaningful physical measurements of interest to turbulence modelers and designers. These measurements include valuable Reynolds stress transport data, direct measurements of near wall Reynolds shear stress gradients and quantification of particle/shock interactions.

As discussed by Lowe and Simpson (2006), the single point fluctuating

velocity/acceleration correlation, ijji auau + is the balance of the pressure and viscous

contributions to Reynolds stress transport. Such a measurement offers a single point method of computing transport contributions without the need for measuring velocity gradients of turbulence structural terms via finite difference. Prior research to obtain velocity/acceleration correlation measurements has proven successful and the results compare favorably with lower Reynolds number DNS results and transport measurements obtained from multipoint structural measurements (Lowe and Simpson 2006; Lowe 2006).

, dB


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Fig. 8 RMS error of estimated Doppler frequency chirp (γ ) as a function of normalized signal-to-noise ratio, SNR1 for

finite difference methods (FD) and DCFT methods. CRLB: Cramer-Rao lower bound, ZP: 2-times zero-padding, Parabolic: Parabolic interpolation of chirp power distribution, Centroid: centroid interpolation of chirp power distribution.

The measured mean accelerations directly give information on the normal-to-wall mean gradients of the Reynolds shear stresses—a potentially power application for the SMLDV. Consider the Reynolds-averaged total derivatives of the flow velocities or the stream-wise acceleration Ax and span-wise acceleration Ay parallel to the wall:

z

x

Az

w

y

vw

x

uw

z

WW

y

WV

x

WU

Dt

DW

Az

uw

y

uv

x

u

z

UW

y

UV

x

UU

Dt

DU

=∂

∂+

∂

∂+

∂

∂+

∂

∂+

∂

∂+

∂

∂=

=∂

∂+

∂

∂+

∂

∂+

∂

∂+

∂

∂+

∂

∂=

2

2

(6)

Considering the magnitude of the terms in these relationships (Rotta 1962), one is able to see that near the wall where the mean normal-to-wall velocity vanishes, the total derivatives may be reduced to

y

vwuvAA

Dt

WDUzx

∂

∂≈=

,,

, (7)

Since these gradients must be computed for proper evaluation of the near-wall momentum in RANS simulations, they offer an important bit of information for the near-wall region. Particularly when measuring high Reynolds number flows with correspondingly small absolute spatial scales, the direct measurement of gradients is very valuable.

The particle acceleration measurements also give information about the local unsteadiness of shock waves and allow correction of size-dependent particle lag effects in the vicinity of shocks. The low frequency modes of the acceleration signal may be used to determine to behavior of shock waves in the vicinity of the SMLDV measurement volume by examining how short-time mean accelerations change. In the very near-field of the shock, large particle accelerations are encountered and drop rapidly with distance from the shock. The information about how the shock is fluctuating is useful, as noted by Gaitonde et al. (2004), in validating LES and unsteady RANS models as well as determining proper modeling by examining the behavior of the turbulence accompanying the unsteadiness. In the case of semi-steady waves, the particle acceleration


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measurements may be used to gage size-dependent particle lag so that measurements may be corrected for this anomaly.

4. Conclusions A new instrument for high Reynolds number, high speed flow measurements very near the

surface of test models is being developed. The technology leverages several recent advancements in photonics and data acquisition components that enable a robust and powerful instrument. A key feature of the SMLDV described is the capability to operate from within the bodies of models within wind tunnels by making use of a highly miniaturized design and through the use of thin polycarbonate windows. The aspects of employing such windows have been considered from the angles of structural robustness and optical integrity necessary for successful measurements. The analysis and computational modeling indicates that the window methodology will transition from the proven low speed applications to the more demanding high speed flows for which the SMLDV is being developed. In the second part of the paper, the specific attributes of the acceleration measurement capabilities of the SMLDV have been considered in light of the potential for obtaining novel information in high speed, high Reynolds number turbulent boundary layers. It was demonstrated that the signal chirp processing scheme used by the SMLDV, making use of the discrete Chirp Fourier transform approaches the Cramer-Rao lower bound within 20% for signal-to-noise ratios expected. Thanks to many recent advances described, the SMLDV offers an exciting new possibility for high resolution three-component turbulent flow measurements in difficult to measure flows which have received little detailed study.

Acknowledgements: This work has been supported in part by the US Air Force Arnold Engineering Development Center’s Small Business Innovation Research program under contract FA-9101-07-M-0014. Additional support was provided for work conducted at the Department of Aerospace and Ocean Engineering at Virginia Tech by AFOSR grant F49620-03-1-0057 under program manager Dr. T. Beutner and by NSF grant CTS-0233653 under program manager Dr. M. Plesniak. The authors are grateful to these sponsors for the opportunity to perform this work.

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A Sub-Miniature Laser-Doppler Velocimeter for High Speed Flow

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