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Research Papers: Techniques and Procedures

The Focusing Laser Differential Interferometer, an Instrument for Localized Turbulence Measurements in Refractive Flows

[+] Author and Article Information
Gary S. Settles

Distinguished Professor Emeritus
Fellow ASME
Mechanical and Nuclear
Engineering Department,
Penn State University,
Reber Building,
University Park, PA 16802
e-mail: gss2@psu.edu

Matthew R. Fulghum

Mechanical and Nuclear
Engineering Department,
Penn State University,
Reber Building,
University Park, PA 16802
e-mail: mfulghum@gmail.com

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received December 30, 2015; final manuscript received May 27, 2016; published online July 21, 2016. Assoc. Editor: Francine Battaglia.

J. Fluids Eng 138(10), 101402 (Jul 21, 2016) (10 pages) Paper No: FE-15-1962; doi: 10.1115/1.4033960 History: Received December 30, 2015; Revised May 27, 2016

The theory, design, and use of a focusing laser differential interferometer (FLDI) instrument are described. The FLDI is a relatively simple, nonimaging, common-path polarization interferometer for measuring refractive signals generated by turbulence, as well as small-amplitude acoustics and boundary-layer instabilities. It has in principle a unique ability to look through wind-tunnel windows, ignore sidewall boundary-layers and vibration, and concentrate only on the refractive signal near a pair of sharp beam foci in the core flow. The instrument's low cost and ease of implementation make it a promising alternative to traditional hot-wire anemometry (HWA) and particle-based methods for turbulence characterization. A matrix equation is written for the overall optical behavior of the FLDI, and transfer functions are developed to account for spatial filtering, f/number of the field lenses, various turbulence profiles, etc. Benchtop experiments using a turbulent sonic airjet demonstrate the focusing ability of the FLDI, its frequency response, and unwanted signal rejection. The instrument is also used to optically interrogate the flow in the Penn State Supersonic Wind Tunnel and in USAF AEDC Hypervelocity Tunnel 9, where it made preliminary measurements of freestream disturbance levels and power spectra. A central feature of the FLDI used here is the replacement of traditional fixed Wollaston birefringent prisms with variable Sanderson prisms for separation and recombination of the helium–neon laser beams, and for the accurate setting of micrometer-range beam separation distances required for successful turbulence measurements. The instrument also features phase compensation of the output, where perpendicularly polarized light signals are separately sensed by the twin photodetectors. This provides a unique ability to measure the coherence of turbulent spectra and thus to reject low-coherence noise.

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References

Figures

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Fig. 3

Diagram of FLDI polarization states from input to output

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Fig. 2

Calibration of laser-beam separation Δx versus Sanderson prism deflection X by the weak meniscus lens method

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Fig. 1

Layout of the FLDI instrument

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Fig. 4

Transfer function magnitude versus wavenumber for Monte Carlo simulation of FLDI response to random turbulence with no mean flow and Δx = 100 μm

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Fig. 5

Diagram of airjet with Gaussian velocity profile used as a probe of FLDI response

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Fig. 6

Transfer function magnitude versus wavenumber for a Gaussian airjet offset from the FLDI focus

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Fig. 11

Comparison of density-based turbulence intensity in the present airjet at M = 1.3 with that of Panda and Seasholtz [25] at M = 1.4

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Fig. 7

Diagram of FLDI focus centered in a wind-tunnel test section with uniform freestream turbulence and turbulent boundary layers on both sidewalls

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Fig. 8

Simulated FLDI spectra of the wind tunnel flow shown in Fig. 7 with different levels of boundary-layer turbulence TuBL/Tu

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Fig. 9

Turbulent spectra of the D = 1 mm round airjet with P0 = 138 kPa and various values of Δx after deconvolution of thebeam-separation spatial filtering effect. Ordinate units are rad2/Hz.

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Fig. 10

Normalized FLDI RMS profiles of the turbulent sonic airjet at 7 x/D locations downstream of its nozzle exit

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Fig. 12

Comparison of centerline turbulence intensity distribution in the P0 = 207 kPa, D = 1 mm sonic airjet measured by FLDI and by HWA. ρ′ and u’ are density and velocity fluctuations, ρCL and UCL are the mean centerline density and velocity, and ρ is the density of the surrounding atmosphere.

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Fig. 13

Comparison of the P0 = 207 kPa, D = 1 mm sonic airjet spectra measured by FLDI and HWA at x/D = 30. Ordinate units are rad2/Hz for FLDI and V2/Hz for HWA. Spectra are shifted vertically for clarity.

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Fig. 14

Freestream turbulence power spectrum of M = 3 airflow on the centerline of the Penn State Supersonic Wind Tunnel. Ordinate units are rad2/Hz.

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Fig. 15

Freestream turbulence power spectrum of M = 10 airflow on the centerline of AEDC hypervelocity tunnel 9. Ordinate units are rad2/Hz.

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