Focused Laser Differential Interferometry Research Articles

Imaging focused laser differential interferometry.

Focused laser differential interferometry (FLDI) is an important diagnostic for measuring density fluctuations in high-speed flows. Currently, however, high dynamic range FLDI is limited to photodiode measurements. In order to spatially resolve multiple locations within complex flows, we present a novel, to the best of our knowledge, refractive-optic imaging FLDI concept that not only produces two-dimensional images without scanning but also reduces the measurement noise floor of those images. To demonstrate this concept, a 33 × 33 grid of FLDI points is first generated using a microlens array. Then, the beams are split and recombined using two polarized Mach-Zehnder interferometers to maximize flexibility in beam separation and optimize signal sensitivity. Next, the FLDI points are collected slightly out of focus on a high-speed camera in order to increase the number of pixels n per FLDI point, thereby reducing noise floor by n. Finally, an under-expanded jet with a characteristic screech at 14.1 kHz is tested with the imaging FLDI setup, showing clear barrel and reflected shock features as well as spatially varying turbulence densities. Overall, this unique concept enables the creation of reduced-noise-floor, two-dimensional FLDI datasets for the study of supersonic and hypersonic flows.

Time-resolved wave packet development in highly cooled hypersonic boundary layers

Boundary-layer disturbances are analysed on a $5^{\circ }$ half-angle blunted cone in Mach 5, high-enthalpy flow ( $h_0 = 9\ {\rm MJ}\ {\rm kg}^{-1}$ ) with a low wall-to-edge temperature ratio, $T_w/T_e = 0.18$ . Schlieren and focused laser differential interferometry (FLDI) are utilized to assess the structures and frequency content associated with disturbances. Wave packets are identified from bursts of modal content on time-resolved spectrograms. Bandpass filtering, proper orthogonal decomposition (POD) and space–time POD are then applied to the schlieren data. Bandpass filtering suggests the presence of wave packet dispersion and elongation indicative of slow-acoustic-wave synchronization. Modal reconstruction techniques indicate the radiation of content outside the boundary layer and distinct orientation changes within disturbances, potentially the first experimental evidence of the supersonic-mode instability in such a flow field. Cross-bicoherence computations are carried out for discrete time segments of data from both schlieren and FLDI data. They demonstrate that the most dominant nonlinear interactions are the fundamental–first-harmonic and the fundamental–low-frequency interactions.

Experimental Verification of a Modified Cylindrical Focused Laser Differential Interferometer

A modification to cylindrical focused laser differential interferometry (CFLDI) that, without beam intersection, can achieve smaller stand-off distances from flat geometries than conventional FLDI is presented. The modified system uses a cylindrical lens pair to expand and collimate the beam in a single direction, parallel to the model surface, forming a long, flat, elliptical profile. Subsequently, a spherical lens focuses the beam. Mach 7.3 hypersonic flow, produced by the T4 Stalker Reflected Shock Tunnel, was used for an experimental comparison between the responses of the modified CFLDI and a similar FLDI system in the freestream and just above the boundary-layer edge. Good agreement between the modified CFLDI and FLDI among all measured frequencies was observed when probing near the boundary-layer edge. The comparison in the freestream had good agreement up to 1500 kHz, and higher frequencies saw the modified CFLDI response attenuated at a shallower angle than the FLDI. A combination of different system parameters and base noise levels between the experiments is believed to account for this difference. The modified CFLDI system was used to probe inside the boundary layer, achieving a y/δ of approximately 0.4, where broadband turbulence is detected.

Multi-depth focused laser differential interferometer based on chromatic aberration.

A modified version of focused laser differential interferometry (FLDI) is demonstrated with adjacent beam pairs distributed along the optical axis. This feature is accomplished using two different wavelengths of light in the interferometer and accounting for the chromatic aberration of the lenses in the optical setup. It is demonstrated that ray trace calculations can be modified to predict the focal points of each of the two different colored beams, and experiments using a tube jet and a laser-induced blast wave show the instrument still has the expected features of an FLDI as well as continued capability for velocimetry. This modification is in effort to allow FLDI to be used for the analysis of three-dimensional flows, especially if combined with other multi-point variations and targeting high-frequency flow content.

Wall-Normal Focused Laser Differential Interferometry

A new approach for measuring boundary-layer disturbances with focused laser differential interferometry (FLDI) for planar models is presented. By integrating a glass window into a flat plate, the optical axis was aligned normal to the model surface, and the focal plane was set inside the boundary layer. By determining the extent of the sensitive volume along the optical axis and calculating the analytical transfer function of the setup, the implications of the FLDI properties on the measured data are analyzed. Measurements performed on a flat plate at Mach 6 are used to demonstrate the effects of the laminar–turbulent transition on the spectral distribution of the power density and to explicitly verify the detectability of the expected second-mode instabilities. Advantages and disadvantages of the proposed setup compared to the conventional one are discussed.

Linear and 2D arrays for Focused Laser Differential Interferometry using a high-speed camera

Since the introduction of linear array focused laser differential interferometry (LA-FLDI), its use has rapidly proliferated as it extends the capabilities of FLDI to multiple measurement positions, greatly increasing the amount of data that can be simultaneously collected. To collect and store the signal data from LA-FLDI, arrays of photodiodes have primarily been utilized in recent literature, and, while photodiodes have the distinct advantage of reaching sampling rates on the order of 100＋ MHz, custom setups for photodiode arrays can be cumbersome to build and align as the number of points in the FLDI beam array increases and nonlinear array designs begin to be considered. As an alternative to photodiode arrays, high-speed cameras are promising, but their usage for LA-FLDI has been quite limited thus far. Compared to photodiodes, modern high-speed cameras are both expensive and possess lower sampling rates, but they are easy to align and provide expanded ability to measure larger arrays of FLDI points. The camera sensor needs only to be placed perpendicular to the array path, and, if appropriately sized, the entire array can be captured without individually aligning the beams. In this work, a high-speed camera is used to record measurements of spectral content, in a Mach 1 free jet flow obtained via imaging FLDI with 5 × 5, 3 × 3, 1 × 5, 1 × 10, and 1 × 12 arrays created using a combination of a 5 × 5 diffractive optical element and post-process sampling of individual pixels to form what we have named “virtual arrays”. For the sake of comparison and proof of similar applicability, the signal from the center point of the 5 × 5 grid is also measured using a high frequency bandwidth photodiode. The experiments show similar capability between the photodiode and camera results when measuring dominant frequencies in the spectral content, even when sampling individual pixels within FLDI points. Possibly due to the significantly smaller size of the pixels, the magnitudes of the individual pixel spectra are often less than that of the photodiode. However, the camera results imply the potential for arrays of arbitrary sizes and shapes, which are only limited by camera sensor size, to be imaged and yield informative estimates of spectral content. Furthermore, sampling individual camera pixels appears to provide significantly enhanced spatial resolution. For FLDI applications involving lower frequency ranges, say 0–2 MHz, current high-speed cameras may provide a suitable if not advantageous alternative to photodiode arrays.

Colinear focused laser differential interferometry and self-aligned focusing schlieren.

A colinear focused laser differential interferometer (FLDI) and self-aligned focusing schlieren (SAFS) system has been assembled and tested in the laboratory, using a turbulent jet of compressed air issuing from a small needle nozzle to provide a high frequency density object. Measurements verified that the coupling of the SAFS system onto the optical axis of the FLDI system had negligible influence on the FLDI system's data, including tests that assessed the influence of the inclusion of dichroic mirrors, dichroic mirror reflection angle, dichroic mirror positioning relative to the Wollaston prisms of the FLDI system, and SAFS light propagation direction. A qualitative comparison of the focusing ability of the two systems was made, and FLDI power spectral density estimates and SAFS spectral proper orthogonal decomposition were used for quantitative comparisons of the acoustic frequency of the jet, with good agreement between the two. The success of the system integration and resulting jet testing demonstrates the utility of this colinear, simultaneous FLDI/SAFS measurement system.

Recovering density disturbance spectra from FLDI. Part 1.

Focused laser differential interferometry (FLDI) measures the phase shift corresponding to localized fluctuations in the refractive index of a medium. The sensitivity, bandwidth, and spatial filtering properties of FLDI make it particularly suited to applications in high-speed gas flows. Such applications often require the quantitative measurement of density fluctuations, which are related to changes in the refractive index. In a two-part paper, a method is presented for the recovery of a spectral representation of density disturbances from the measured time-dependent phase shift for a particular class of flows able to be modeled using sinusoidal plane waves. The approach is based on the ray-tracing model of FLDI due to Schmidt and Shepherd [Appl. Opt.54, 8459 (2015)APOPAI0003-693510.1364/AO.54.008459]. In this first part, the analytical results for FLDI response to single- and multiple-frequency plane waves are derived and validated against a numerical implementation of the instrument. A spectral inversion method is then developed and validated, including consideration for the frequency-shifting effects of any underlying convective flows. In the second part [Appl. Opt.62, 3054 (2023)APOPAI0003-693510.1364/AO.480354], results from the present model are compared with previous exact solutions temporally averaged over a wave cycle and with an approximate method.

Focused laser differential interferometry post-processing methodology for flowfields with circular symmetry

An analytic methodology is presented to reconstruct the pressure waveform of flowfields with circular symmetry from the phase shift detected with Focused Laser Differential Interferometry (FLDI). A weak blast wave generated by an electric spark in ambient air is investigated with the proposed approach. Values of separation distance between the differentiating foci of the FLDI Δx of 76, 120, 175, and 252 μm are employed to probe the flowfield at locations between 3 and 50 mm from the spark source. In a subset of these distances, reference measurements of peak pressure obtained with a surface pressure sensor indicate good agreement with the reconstructed data when small separation distances are used. Further analysis of FLDI reconstructed data is conducted using theoretical correlations for N-waves in terms of the distribution of pressure peak amplitude and compression phase as the wave front propagates. Agreement with theory is verified for all differentiation separation distances except the largest, for which peak pressure comparison shows a 10% loss of measured vs predicted value. A computational FLDI is employed to scrutinize the simplifying hypotheses supporting the waveform reconstruction approach. The direct comparison between experimental and computational FLDI output reveals additional discrepancies for intermediate Δx values but very good agreement for the smallest Δx. The proposed methodology is thus verified to be reasonable, upon appropriate minimization of the FLDI differentiation distance. A parametric analysis using computational FLDI indicates the adequate value of FLDI Δx to be 20% or less of the flowfield characteristic length in terms of density gradient.

Recent progress in high-speed laser diagnostics for hypersonic flows [Invited].

The recent progress in high-speed (≥100k H z) laser diagnostics for hypersonic flows is reviewed. Owing to the ultrahigh flow speed, a laser frequency of 100 kHz or higher is required for hypersonic diagnostics. Here, two main laser diagnostic techniques are discussed: focused laser differential interferometry (FLDI) and pulse-burst laser-based diagnostics. Single- and multiple-point FLDI measurements have been widely applied to hypersonic flows for flow velocity and density fluctuation measurements. The progress of pulse-burst laser-based hypersonic diagnostics, including flow velocity measurements and 2D flow visualization, is also discussed.

Quantitative focused laser differential interferometry with hypersonic turbulent boundary layers.

The effect of turbulent wind-tunnel-wall boundary layers on density change measurements obtained with focused laser differential interferometry (FLDI) was studied using a detailed direct numerical simulation (DNS) of the wall from the Boeing/AFOSR Mach-6 Quiet Tunnel run in its noisy configuration. The DNS was probed with an FLDI model that is capable of reading in three-dimensional time-varying density fields and computing the FLDI response. Simulated FLDI measurements smooth the boundary-layer root-mean-square (RMS) profile relative to true values obtained by directly extracting the data from the DNS. The peak of the density change RMS measured by the FLDI falls within 20% of the true density change RMS. A relationship between local spatial density change and temporal density fluctuations was determined and successfully used to estimate density fluctuations from the FLDI measurements. FLDI measurements of the freestream fluctuations are found to be dominated by the off-axis tunnel-wall boundary layers for lower frequencies despite spatial suppression provided by the technique. However, low-amplitude (0.05%-5% of the mean density) target signals placed along the tunnel centerline were successfully measured over the noise of the boundary layers (which have RMS values of about 12% of the mean). Overall, FLDI was shown to be a useful technique for making quantitative turbulence measurements and to measure finite-width sinusoidal signals through turbulent boundary layers, but may not provide enough off-focus suppression to provide accurate freestream noise measurements, particularly at lower frequencies.

Megahertz-Rate Imaging of Hypersonic Boundary-Layer Instabilities in a Mach 10 Shock Tunnel

The transition of the boundary-layer state from laminar to turbulent on a 7° sharp cone in Mach 10 flow is measured using several high-speed optical diagnostics capable of time-resolved measurements of the second-mode instability with high spatial resolution. Specifically, megahertz-rate nitric oxide planar laser-induced fluorescence (NO PLIF) imaging is done at 1 MHz to provide a non-path-integrated visualization of second-mode associated structures in the transitioning boundary layer. A recent variation of focused laser differential interferometry (FLDI), namely, linear array FLDI (LA-FLDI), is also applied for multipoint measurements of frequency content in the transitioning boundary layer. From each data set, the frequency of the most unstable second-mode instability is obtained along with the phase velocity of the second-mode waves. Measurements show good agreement relative to each other and also with surface pressure sensors and high-speed schlieren imaging. Furthermore, the 1 MHz NO PLIF imaging demonstrated here shows great potential for visualization of transitional and turbulent boundary layers when path-integrated diagnostics cannot be used.

Measurement of Wall-Cooling Effects on Hypersonic Boundary-Layer Transition Using Focused Laser Differential Interferometry

The boundary layer on a sharp-tip, partially flared, actively cooled cone with discrete roughness elements has been studied in a quiet Mach 6 wind tunnel using linear array–focused laser differential interferometry (LA-FLDI). The conditions were varied by sweeping the unit Reynolds number of the flow from to and the wall temperature was set to one of two conditions by setting the coolant setpoint temperature to 293.2 or 253.2 K. The spectral content showed the presence of the second-mode instability, which is the dominant instability, and two of its harmonics across the Reynolds number sweep. A novel analysis of FLDI data is presented where turbulent wave packet amplitudes have been analyzed and show how the cooler wall condition transitions to turbulence sooner and it is supported by observations in the spectra. This analysis may also be of benefit for defining a transition location or region from FLDI data in general. The turbulent wave packet analysis results were compared with an intermittency analysis and showed consistency.

Experimental study on surface arc plasma actuation-based hypersonic boundary layer transition flow control

Effective control of hypersonic transition is essential. In order to avoid affecting the structural profile of the aircraft, as well as reducing power consumption and electromagnetic interference, a low-frequency surface arc plasma disturbance experiment to promote hypersonic transition was carried out in the Φ0.25 m double-throat Ludwieg tube wind tunnel at Huazhong University of Science and Technology. Contacting printed circuit board sensors and non-contact focused laser differential interferometry testing technology were used in combination. Experimental results showed that the low-frequency surface arc plasma actuation had obvious stimulation effects on the second-mode unstable wave and could promote boundary layer transition by changing the spectral characteristics of the second-mode unstable wave. At the same time, the plasma actuation could promote energy exchange between the second-mode unstable wave and other unstable waves. Finally, the corresponding control mechanism is discussed.

Interpreting single-point and two-point focused laser differential interferometry in a turbulent jet

Interpreting single-point and two-point focused laser differential interferometry in a turbulent jet

Supersonic Freestream Density Fluctuations from Focused Laser Differential Interferometry and Pitot-Probe Measurements

Focused laser differential interferometry (FLDI) is used to make freestream density fluctuation measurements in the von Kármán Gas Dynamics Facility (VKF) Wind Tunnel D at Arnold Engineering Development Complex. A comparison is made between pitot-probe and FLDI measurements after converting both to freestream pressure fluctuation spectra. A modification of Stainback and Wagner’s theory, incorporating recent numerical results from Chaudhry et al., is used to interpret the pitot data, while a new inversion algorithm is applied to the FLDI data. These methods of interpretation make the assumption that the tunnel freestream disturbance environment is dominated by the acoustic Kovásznay mode, in line with the theoretical and experimental evidence. Close agreement is found between the two sets of spectra, showing that accurate quantitative data can be obtained with FLDI, and the instrument can be used to extend spectra beyond the pitot bandwidth.

Focused Laser Differential Interferometric Investigation of Turbulent Jet Spectra

In this work, a model of focused laser differential interferometry (FLDI) is derived by incorporating the local intensity of each beam in an FLDI beam pair. We rederive some known transfer functions to reduce FLDI data. Additional transfer functions are also derived, intended to model increasingly complex disturbance fields, namely, isotropic turbulence. The new transfer functions account for disturbances not only in the streamwise direction but also in the two spanwise directions. Additionally, it is shown that strategically selecting the integration limits for the idealized FLDI in the denominator of the transfer functions () can simplify the FLDI data-reduction procedure. This is done for disturbance fields in a finite boundary (e.g., a wind tunnel of scale ), by removing the need to characterize the FLDI probe-volume length scale. Finally, results are presented from experiments performed with a turbulent jet probed by an FLDI that indicate that increasing the complexity of the transfer function has merit with some qualifications.

Instability evolution in the hypersonic boundary layer over a wavy wall

The effects of a wavy wall on the stability of a hypersonic boundary layer on a flared cone are investigated by detailed experimental measurements and direct numerical simulations. The non-contact optical measurement method of focused laser differential interferometry is used to measure the disturbance development within the wavy region. The measurement results show that the second mode for the wavy wall is suppressed significantly compared with the smooth wall, and that multiple disturbances at low frequencies appear within the wavy region. Numerical corroboration against experimental measurements reveals good quantitative agreement. It is found that the disturbances at $f=360$  kHz on the wavy wall are suppressed appreciably, which are very significant on the smooth wall. And the disturbances at $f=140$  kHz and $f=260$  kHz develop within the wavy region, and increase considerably. Also, the disturbances achieve a significant increase over the first half of a wavy trough and become more stable over the second half of a wavy trough. The physical mechanism is found to be due to the change in wall geometry and is attributed to the spatially modulated mean flow. The disturbance growth rate is closely related to the level of the mean-flow distortion.

Transitional flow structures in heated hypersonic boundary layers

Transition in a Mach 6 flared cone boundary layer over a heated wall has been investigated in the Mach 6 wind tunnel at Peking University using visualization, focused laser differential interferometry, infrared imaging, particle image velocimetry (PIV), and direct numerical simulation (DNS). The model's wall-temperature ratio η=Tw/T0 (where Tw and T0 are, respectively, the wall temperature and oncoming stream stagnation temperature) can be controlled to vary from 0.66 to 1.77. An ultrafast illumination image system has been used for Rayleigh-scattering visualization and PIV to experimentally capture the dynamics of the transition. Lagrangian flow structures are revealed by both the DNS results and the time-resolved PIV data. The effect of wall temperature on the transition is investigated, and it is found that increasing η initially delays but then promotes the transition to turbulence, with the reversal point being near η≈1. The turbulence onset mechanism over the heated wall for η=1.50, where first-mode-induced oblique breakdown dominates, is then investigated, and it is shown that lifting-up three-dimensional (3D) waves appear around the critical layer owing to the nonlinear development of the oblique first mode. Consequently, a downward sweep motion occurs to compensate for the lifting low-speed fluid, with the formation of a warped wave front. High-shear layers are created around the 3D Lagrangian waves and strengthened to cause the formation of a Λ-vortex. In general, this lifting-up 3D wavepacket has been confirmed to play a determining role in hypersonic turbulence production over a heated wall, which is similar to the findings in incompressible boundary layers.

Experimental Measurements of Hypersonic Instabilities over Ogive-Cylinders at Mach 6

Hypersonic boundary-layer instability disturbance and transition experiments were performed in the Air Force Research Laboratory Mach-6 Ludwieg Tube on a 1-m-long ogive-cylinder model with interchangeable nose-tip geometries of varying ogive radii and nose bluntnesses. Boundary-layer disturbances were measured via focused laser differential interferometry, surface-mounted pressure sensors, and high-speed schlieren videography at unit Reynolds numbers ranging from to . Three primary disturbance structures were observed that were dependent on ogive radius and nose bluntness. Each disturbance structure exhibits unique characteristics that are closely tied to the leading-edge geometry of the model. The addition of nose bluntness is shown to have an overall delay in transition onset, and a possible blunt nose transition reversal is observed as bluntness is further increased. It is also shown that the effects of the ogive radius in addition to nose bluntness alter the flow instability disturbance and transition behaviors and are likely tied to a modification of the entropy layer structure. A novel curvature-based Reynolds number is proposed that successfully correlates the effects of multiple leading-edge radii of curvature to dominant downstream boundary-layer disturbances and transition onset locations.