The structure of near-wall re-entrant flow and its influence on cloud cavitation instability
The so-called 're-entrant jet' is fundamental to periodic cloud shedding in partial cavitation. However, the exact physical mechanism governing this phenomenon remains ambiguous. The complicated topology of the re-entrant flow renders whole-field, detailed measurement of the re-entrant flow cumbersome. Hence, most studies in the past have derived a physical understanding of this phenomenon from qualitative analyses of the re-entrant jet. Thus, quantitative studies are scarce in the literature. In this work, we present a methodology to experimentally measure the re-entrant flow below the vapour cavity in an axisymmetric venturi. The axisymmetry of the flow geometry is exploited to image tracer particles in the near-wall re-entrant flow. The main objective of employing tomographic imaging and subsequent velocimetry is to resolve the thickness and the velocity of the re-entrant flow. Additionally, phase-averaging conditioned on cavity length sheds light on the temporal evolution of re-entrant flow in a shedding cycle. The measured re-entrant film is as thick as mm for a maximum cavity length of , where is the venturi throat diameter. However, the re-entrant film thickness at higher cavitation number is measured to be about 0.5 mm. Further, the re-entrant flow is seen to attain a maximum velocity up to half the throat velocity as the vapour cavity grows in time and the re-entrant flow thickens. We observe that a complex spatio-temporal evolution of re-entrant flow is involved in the cavity detachment and periodic cloud shedding. Finally, we apply the demonstrated methodology to study the evolution of the near-wall liquid flow, below the vapour cavity in different cavity shedding flow regimes. The role of two main mechanisms responsible for cloud shedding, i.e. (i) the adverse-pressure gradient driven re-entrant jet, and (ii) the bubbly shock wave emanating from the cloud collapse are quantitatively assessed. We observe that the thickness of the re-entrant liquid film with respect to the cavity thickness can influence the cavity shedding behaviour. Further, we show that both the mechanisms could be operating at a given flow condition, with one of them dominating to dictate the cloud shedding behaviour.
Editorial: Topical Collection 'complex interactions with droplets'
Shock loss measurements in non-ideal supersonic flows of organic vapors
This paper presents the first ever direct measurements of total pressure losses across shocks in supersonic flows of organic vapors in non-ideal conditions, so in the thermodynamic region close to the liquid-vapor saturation curve and the critical point where the ideal gas law is not applicable. Experiments were carried out with fluid siloxane MM (hexamethyldisiloxane, C H OSi ), commonly employed in medium-/high-temperature organic Rankine cycles (ORCs), in the (TROVA), a blowdown wind tunnel at the Laboratory of Compressible fluid dynamics for Renewable Energy Applications (CREA lab) of Politecnico di Milano. A total pressure probe was inserted in superheated MM vapor flow at Mach number with total conditions in the range and at varying levels of non-ideality, with a compressibility factor evaluated at total conditions between . These operating conditions are representative of the first-stage stator of ORC turbines. Measured shock losses were compared with those calculated from pre-shock quantities by solving conservation equations across a normal shock, with differences always below attesting a satisfactory reliability of the implemented experimental procedure. An in-depth analysis was then carried out, highlighting the direct effects of non-ideality on shock intensity. Even at the mildly non-ideal conditions with considered here, non-ideality was responsible for a significantly stronger shock compared to the ideal gas limit at same pre-shock Mach number, with differences as large as .
Pollutant dispersion by tall buildings: laboratory experiments and Large-Eddy Simulation
Pollutant dispersion by a tall-building cluster within a low-rise neighbourhood of Beijing is investigated using both full-scale Large-Eddy Simulation and water flume experiments at 1:2400 model-to-full scale with Particle Image Velocimetry and Planar Laser-Induced Fluorescence. The Large-Eddy Simulation and flume results of this realistic test case agree remarkably well despite differences in the inflow conditions and scale. Tall buildings have strong influence on the local flow and the development of the rooftop shear layer which dominates vertical momentum and scalar fluxes. Additional measurements using tall-buildings-only models at both 1:2400 and 1:4800 scales indicates the rooftop shear layer is insensitive to the scale. The relatively thicker incoming boundary layer affects the Reynolds stresses, the relative size of the pollutant source affects the concentration statistics and the relative laser-sheet thickness affects the spatially averaged results of the measured flow field. Low-rise buildings around the tall building cluster cause minor but non-negligible offsets in the peak magnitude and vertical location, and have a similar influence on the velocity and concentration statistics as the scale choice. These observations are generally applicable to pollutant dispersion of realistic tall building clusters in cities. The consistency between simulations and water tunnel experiments indicates the suitability of both methodologies.
Direct velocity measurements in high-temperature non-ideal vapor flows
Direct velocity measurements in a non-ideal expanding flow of a high temperature organic vapor were performed for the first time using the laser Doppler velocimetry technique. To this purpose, a novel seeding system for insemination of high-temperature vapors was specifically conceived, designed, and implemented. Comparisons with indirectly measured velocity, namely inferred from pressure and temperature measurements, are also provided. Nozzle flows of hexamethyldisiloxane (MM, C H OSi ) at temperature up to and pressure up to 10 bar were taken as representative of non-ideal compressible-fluid flows. The relative high temperature, high pressure and the need of avoiding contamination pose strong constraints on the choice of both seeding system design and tracer particle, which is solid. A liquid suspension of tracer particles in hexamethyldisiloxane is injected through an atomizing nozzle in a high-temperature settling chamber ahead of the test section. The spray droplets evaporate, while the particles are entrained in the flow to be traced. Three different test cases are presented: a subsonic compressible nozzle flow with a large uniform region at Mach number 0.7, a high velocity gradient supersonic flow at Mach number 1.4 and a near-zero velocity gradient flow at Mach number 1.7. Temperature, pressure and direct velocity measurements are performed to characterize the flow. Measured velocity is compared with both computational fluid dynamics (CFD) calculations and velocity computed from pressure and temperature measurements. In both cases, the thermodynamic model applied was a state-of-the-art Helmoltz energy equation of state. A maximum velocity deviation of 6.6% was found for both CFD simulations and computed velocity.
The influence of water turbulence on surface deformations and the gas transfer rate across an air-water interface
We present experimental results of a study on oxygen transfer rates in a water channel facility with varying turbulence inflow conditions set by an active grid. We compare the change in gas transfer rate with different turbulence characteristics of the flow set by four different water channel and grid configurations. It was found that the change in gas transfer rate correlates best with the turbulence intensity in the vertical direction. The most turbulent cases increased the gas transfer rate by 30% compared to the low turbulence reference case. Between the two most turbulent cases studied here, the streamwise turbulence and largest length scales in the flow change, while the gas transfer rate is relatively unchanged. In contrast, for the two less turbulent cases where the magnitude of the fluctuations normal to the free surface are also smaller, the gas transfer rate is significantly reduced. Since the air-water interface plays an important role in the gas transfer process, special attention is given to the free-surface deformations. Despite taking measures to minimise it, the active grid also leaves a direct imprint on the free surface, and the majority of the waves on the surface originate from the grid itself. Surface deformations were, however, ruled out as a main driver for the increase in gas transfer because the increase in surface area is < 0.25%, which is two orders of magnitude smaller than the measured change in the gas transfer rate.
Interaction of a droplet spray with a turbulent plane air jet impacting a wall: Application to the confinement of atmospheres contaminated with particles by air curtain
Experiments are carried out to study the interaction of a spray of spherical micronic oil droplets with a turbulent plane air jet impacting a wall. The context is the separation of a contaminated atmosphere with passive particles from a clean atmosphere by using a dynamical air curtain. A spinning disk is used to produce the spray of oil droplets close to the air jet. The diameter of the produced droplets varies between 0.3 and m. The jet and particulate Reynolds numbers and the jet and Kolmogorov-Stokes numbers are, respectively, equal to Re , , and . The ratio of the jet height to nozzle width is . The flow properties in the experiments are measured by particle image velocimetry and are in good agreement with large eddy simulation results. The droplet/particle passing rate (PPR) through the air jet is measured by an optical particle counter. The PPR decreases with the increase in the droplet diameter for the studied droplet size range. Whatever the droplet size is, the PPR increases with time due to the presence of two large vortices on each side of the air jet that bring the droplets back to the jet. The accuracy and repeatability of the measurements are verified. The present results can be used to validate Eulerian/Lagrangian numerical simulations on the interaction of micronic droplets with a turbulent air jet.
Ultrasonic particle volume fraction profiling: an evaluation of empirical approaches
We discuss empirical techniques to extract quantitative particle volume fraction profiles in particle-laden flows using an ultrasound transducer. A key step involves probing several uniform suspensions with varying bulk volume fractions from which two key volume fraction dependent calibration parameters are identified: the peak backscatter amplitude (acoustic energy backscattered by the initial layer of the suspension) and the amplitude attenuation rate (rate at which the acoustic energy decays with depth owing to scattering losses). These properties can then be used to reconstruct spatially varying particle volume fraction profiles. Such an empirical approach allows circumventing detailed theoretical models which characterize the interaction between ultrasound and suspensions, which are not universally applicable. We assess the reconstruction techniques via synthetic volume fraction profiles and a known particle-laden suspension immobilized in a gel. While qualitative trends can be easily picked up, the following factors compromise the quantitative accuracy: (1) initial reconstruction errors made in the near-wall regions can propagate and grow along the reconstruction direction, (2) multiple scattering can create artefacts which may affect the reconstruction, and (3) the accuracy of the reconstruction is very sensitive to the goodness of the calibration. Despite these issues, application of the technique to particle-laden pipe flows shows the presence of a core with reduced particle volume fractions in laminar flows, whose prominence reduces as the flow becomes turbulent. This observation is associated with inertia-induced radial migration of particles away from the pipe axis and is observed in flows with bulk volume fractions as high as 0.08. Even transitional flows with low levels of intermittency are not devoid of this depleted core. In conclusion, ultrasonic particle volume fraction profiling can play a key complementary role to ultrasound-based velocimetry in studying the internal features of particle-laden flows.
Superposition of AC-DBD plasma actuator outputs for three-dimensional disturbance production in shear flows
This investigation explores the utility of Alternating Current, Dielectric Barrier Discharge (AC-DBD) plasma actuators for producing three-dimensional disturbances of a desired spanwise wavelength via superposition. The technique utilizes two pairs of exposed and covered electrodes on a single dielectric layer arranged in streamwise succession. Two-dimensional forcing is achieved through operation of the upstream, spanwise uniform electrode pair, while three-dimensional forcing at a prescribed spanwise wavelength is attained by operating both electrode pairs simultaneously, with the downstream actuator spanwise modulating the upstream, two-dimensional output. The ability to produce disturbances of different spanwise wavelengths but with equal streamwise wavelength, frequency and total momentum is established through a combined characterization effort that considers quiescent and in-flow conditions. A demonstration of the technique in an exemplary wall-bounded shear flow, a laminar separation bubble, is provided, revealing spanwise wavelength dependent disturbance growth in the flow that could be exploited for performance gains in future flow control endeavours.
Interferometric laser imaging for respiratory droplets sizing
Due to its importance in airborne disease transmission, especially because of the COVID-19 pandemic, much attention has recently been devoted by the scientific community to the analysis of dispersion of particle-laden air clouds ejected by humans during different respiratory activities. In spite of that, a lack of knowledge is still present particularly with regard to the velocity of the emitted particles, which could differ considerably from that of the air phase. The velocity of the particles is also expected to vary with their size. In this work, simultaneous measurements of size and velocity of particles emitted by humans while speaking have been performed by means of Interferometric Laser Imaging Droplet Sizing (ILIDS). This technique allowed us to detect emitted particles with size down to 2 µm as well as to quantify all three components of the velocity vector and the particle concentration. The outcomes of this work may be used as boundary conditions for numerical simulations of infected respiratory cloud transmission.
Hybrid algorithm for the detection of turbulent flame fronts
This paper presents a hybrid and unsupervised approach to flame front detection for low signal-to-noise planar laser-induced fluorescence (PLIF) images. The algorithm combines segmentation and edge detection techniques to achieve low-cost and accurate flame front detection in the presence of noise and variability in the flame structure. The method first uses an adaptive contrast enhancement scheme to improve the quality of the image prior to segmentation. The general shape of the flame front is then highlighted using segmentation, while the edge detection method is used to refine the results and highlight the flame front more accurately. The performance of the algorithm is tested on a dataset of high-speed PLIF images and is shown to achieve high accuracy in finely wrinkled turbulent hydrogen-enriched flames with order of magnitude improvements in computation speed. This new algorithm has potential applications in the experimental study of turbulent flames subject to intense wrinkling and low signal-to-noise ratios.
Jetting bubbles observed by x-ray holography at a free-electron laser: internal structure and the effect of non-axisymmetric boundary conditions
In this work, we study the jetting dynamics of individual cavitation bubbles using x-ray holographic imaging and high-speed optical shadowgraphy. The bubbles are induced by a focused infrared laser pulse in water near the surface of a flat, circular glass plate, and later probed with ultrashort x-ray pulses produced by an x-ray free-electron laser (XFEL). The holographic imaging can reveal essential information of the bubble interior that would otherwise not be accessible in the optical regime due to obscuration or diffraction. The influence of asymmetric boundary conditions on the jet's characteristics is analysed for cases where the axial symmetry is perturbed and curved liquid filaments can form inside the cavity. The x-ray images demonstrate that when oblique jets impact the rigid boundary, they produce a non-axisymmetric splash which grows from a moving stagnation point. Additionally, the images reveal the formation of complex gas/liquid structures inside the jetting bubbles that are invisible to standard optical microscopy. The experimental results are analysed with the assistance of full three-dimensional numerical simulations of the Navier-Stokes equations in their compressible formulation, which allow a deeper understanding of the distinctive features observed in the x-ray holographic images. In particular, the effects of varying the dimensionless stand-off distances measured from the initial bubble location to the surface of the solid plate and also to its nearest edge are addressed using both experiments and simulations. A relation between the jet tilting angle and the dimensionless bubble position asymmetry is derived. The present study provides new insights into bubble jetting and demonstrates the potential of x-ray holography for future investigations in this field.
Cavitation in blunt impact traumatic brain injury
Traumatic brain injury (TBI) poses a major public health challenge. No proven therapies for the condition exist so protective equipment that prevents or mitigates these injuries plays a critical role in minimizing the societal burden of this condition. Our ability to optimize protective equipment depends on our capacity to relate the mechanics of head impact events to morbidity and mortality. This capacity, in turn, depends on correctly identifying the mechanisms of injury. For several decades, a controversial theory of TBI biomechanics has attributed important classes of injury to cavitation inside the cranial vault during blunt impact. This theory explains counter-intuitive clinical observations, including the coup-contre-coup pattern of injury. However, it is also difficult to validate experimentally in living subjects. Also, blunt impact TBI is a broad term that covers a range of different head impact events, some of which may be better described by cavitation theory than others. This review surveys what has been learned about cavitation through mathematical modeling, physical modeling, and experimentation with living tissues and places it in context with competing theories of blunt injury biomechanics and recent research activity in the field in an attempt to understand what the theory has to offer the next generation of innovators in TBI biomechanics.
Large volume scanning laser induced fluorescence measurement of a bluff-body stabilised flame in an annular combustor
This study outlines a variant of three-dimensional OH planar laser-induced fluorescence and its application in characterising a single bluff body stabilised flame inside a 12 burner annular combustor. In this variant of the method a relatively large volume was scanned slowly in order to calculate the full three-dimensional Flame Surface Density (FSD) distribution. The method used a combination of two scanning directions to overcome bias errors associated with laser sheet positions close to the flame edges. The source of this bias error was confirmed numerically through a complimentary synthetic PLIF study, which was also used to refine the experimental setup. The bias error resulted in a reduction of FSD magnitude, although the method was still capable of capturing the flame structure. This was demonstrated by comparing the reconstructions from the two independent scan directions. Combining the data from both directions overcame the bias, and allowed flame asymmetry due to the confinement to be assessed. The FSD was used to determine the heat release rate of the flame with varying local azimuthal angle for different downstream regions. This highlighted the highly asymmetric structure, produced by the asymmetric confinement.
Assessment and application of wavelet-based optical flow velocimetry (wOFV) to wall-bounded turbulent flows
The performance of a wavelet-based optical flow velocimetry (wOFV) algorithm in extracting high accuracy and high-resolution velocity fields from tracer particle images in wall-bounded turbulent flows is assessed. wOFV is first evaluated using synthetic particle images generated from a channel flow DNS of a turbulent boundary layer. The sensitivity of wOFV to the regularization parameter ( ) is quantified and results are compared to cross-correlation-based PIV. Results on synthetic particle images indicated different sensitivity to under-regularization or over-regularization depending on which region of the boundary layer is being analyzed. Nonetheless, tests on synthetic data revealed that wOFV can modestly outperform PIV in vector accuracy across a broad range. wOFV showed clear advantages over PIV in resolving the viscous sublayer and obtaining highly accurate estimates of the wall shear stress and thus normalizing boundary layer variables. wOFV was also applied to experimental data of a developing turbulent boundary layer. Overall, wOFV revealed good agreement with both PIV and a combined PIV + PTV method. However, wOFV was able to successfully resolve the wall shear stress and correctly normalize the boundary layer streamwise velocity to wall units where PIV and PIV + PTV showed larger deviations. Analysis of the turbulent velocity fluctuations revealed spurious results for PIV in close proximity to the wall, leading to significantly exaggerated and non-physical turbulence intensity in the viscous sublayer region. PIV + PTV showed only a minor improvement in this aspect. wOFV did not exhibit this same effect, revealing that it is more accurate in capturing small-scale turbulent motion in the vicinity of boundaries. The enhanced vector resolution of wOFV enabled improved estimation of instantaneous derivative quantities and intricate flow structure both closer to the wall and more accurately than the other velocimetry methods. These aspects show that, within a reasonable range that can be verified using physical principles, wOFV can provide improvements in diagnostics capability in resolving turbulent motion occurring in the vicinity of physical boundaries.
An experimental/numerical investigation of non-reacting turbulent flow in a piloted premixed Bunsen burner
In this paper, an experimental study of the non-reacting turbulent flow field characteristics of a piloted premixed Bunsen burner designed for operational at elevated pressure conditions is presented. The generated turbulent flow fields were experimentally investigated at atmospheric and elevated pressure by means of high-speed particle image velocimetry (PIV). The in-nozzle flow through the burner was computed using large-eddy simulation (LES), and the turbulent flow field predicted at the burner exit was compared against the experimental results. The findings show that the burner yields a reasonably homogeneous, nearly isotropic turbulence at the nozzle exit with highly reproducible boundary conditions that can be well predicted by numerical simulations. Similar levels of turbulence intensities and turbulent length scales were obtained at varied pressures and bulk velocities with turbulent Reynolds numbers up to 5300. This work demonstrates the burner's potential for the study of premixed flames subject to intermediate and extreme turbulence at the elevated pressure conditions found in gas turbine combustors.
In situ measurements of void fractions and bubble size distributions in bubble curtains
We report the development of a novel measurement system designed to measure bubble properties in bubble curtains (i.e. planar bubble plumes) in situ alongside acoustical measurements. Our approach is based on electrical, contact-based needle sensors in combination with an optical system. The latter is used for calibration and validation purposes. Correcting for the insensitive distance of the needle tips yields very good agreement between the two approaches in terms of the local void fraction and bubble size distributions. Finally, the system is employed to study bubble plumes evolving from three different hose types. All hoses display consistent self-similar behaviour with spreading rates increasing with increasing gas flow. The spreading is further found to be significantly higher when the bubble plumes originated from a porous hose compared to the two other hose types featuring either discrete holes or nozzle elements.
A conveyor belt experimental setup to study the internal dynamics of granular avalanches
This paper shows how a conveyor belt setup can be used to study the dynamics of stationary granular flows. To visualise the flow within the granular bulk and, in particular, determine its composition and the velocity field, we used the refractive index matching (RIM) technique combined with particle tracking velocimetry and coarse-graining algorithms. Implementing RIM posed varied technical, design and construction difficulties. To test the experimental setup and go beyond a mere proof of concept, we carried out granular flow experiments involving monodisperse and bidisperse borosilicate glass beads. These flows resulted in stationary avalanches with distinct regions whose structures were classified as: (i) a convective-bulged front, (ii) a compact-layered tail and, between them, (iii) a breaking size-segregation wave structure. We found that the bulk strain rate, represented by its tensor invariants, varied significantly between the identified flow structures, and their values supported the observed avalanche characteristics. The flow velocity fields' interpolated profiles adjusted well to a Bagnold-like profile, although a considerable basal velocity slip was measured. We calculated a segregation flux using recent developments in particle-size segregation theory. Along with vertical velocity changes and high expansion rates, segregation fluxes were markedly higher at the avalanche's leading edge, suggesting a connection between flow rheology and grain segregation. The experimental conveyor belt's results showed the potential for further theoretical developments in rheology and segregation-coupled models.
Quantifying Brownian motion in the presence of simple shear flow with particle diffusometry
Particle diffusometry, a technology derived from particle image velocimetry, quantifies the Brownian motion of particles suspended in a quiescent solution by computing the diffusion coefficient. Particle diffusometry has been used for pathogen detection by measuring the change in solution viscosity due to amplified DNA from a specific gene target. However, particle diffusometry fails to calculate accurate measurements at elevated temperatures and fluid flow. Therefore, these two current limitations hinder the potential application where particle diffusometry can further be used. In this work, we expanded the usability of particle diffusometry to be applied to fluid samples with simple shear flow and at various temperatures. A range of diffusion coefficient videos is created to simulate the Brownian motion of particles under flow and temperature conditions. Our updated particle diffusometry analysis forms a correction equation under three different polynomial degrees of shear flow with varying flow rates and temperatures between 25 and 65 °C. An experiment in a channel with a rectangular cross section using a syringe pump to generate a constant flow is done to analyze the modified algorithm. In simulation analysis, the modified algorithm successfully computes the diffusion coefficients with 10% error for an average flow rate of up to 8 on all three flow types. Complementary experiments confirm the simulation results.
An experimental approach to analyze aerosol and splatter formations due to a dental procedure
Throughout 2020 and beyond, the entire world has observed a continuous increase in the infectious spread of the novel coronavirus (SARS-CoV-2) otherwise known as COVID-19. The high transmission of this airborne virus has raised countless concerns regarding safety measures employed in the working conditions for medical professionals. Specifically, those who perform treatment procedures on patients which intrinsically create mists of fine airborne droplets, i.e., perfect vectors for this and other viruses to spread. The present study focuses on understanding the splatter produced due to a common dentistry technique to remove plaque buildup on teeth. This technique uses a high-speed dentistry instrument, e.g., a Cavitron ultrasonic scaler, to scrape along the surface of a patient's teeth. This detailed understanding of the velocity and the trajectory of the droplets generated by the splatter will aid in the development of hygiene mechanisms to guarantee the safety of those performing these procedures and people in clinics or hospitals. Optical flow tracking velocimetry (OFTV) method was employed to obtain droplet velocity and trajectory in a two-dimensional plane. Multiple data collection planes were taken in different orientations around a model of adult mandibular teeth. This technique provided pseudo-three-dimensional velocity information for the droplets within the splatter developed from this high-speed dental instrument. These results indicated that within the three-dimensional splatter produced there were high velocities (1-2 m/s) observed directly below the intersection point between the front teeth and the scaler. The splatter formed a cone-shape structure that propagated 10-15 mm away from the location of the scaler tip. From the droplet trajectories, it was observed that high velocity isolated droplets propagate away from the bulk of the splatter. It is these droplets which are concerning for health safety to those performing the medical procedures. Using a shadowgraphy technique, we further characterize the individual droplets' size and their individual velocity. We then compare these results to previously published distributions. The obtained data can be used as a first step to further examine flow and transport of droplets in clinics/dental offices.
Heterodyne background-oriented schlieren for the measurement of thermoacoustic oscillations in flames
In aircraft engines, thermoacoustic oscillations in the combustion chamber contribute significantly to noise emissions, which, like all other emissions, must be drastically reduced. Thermoacoustic oscillations are not only a concern, they can also be beneficial in hydrogen combustion. This work demonstrates that thermoacoustic density oscillations with amplitudes at least an order of magnitude smaller than those resulting from density gradients in a turbulent flame can be detected using laser interferometric vibrometry. This improvement was made possible by heterodyning a carrier fringe system in background-oriented schlieren (BOS) recordings, which were subsequently analyzed using techniques commonly used for holographic interferometry. In comparison with other BOS evaluation techniques, the filtering of the individual frames in the Fourier domain offers a more efficient computational approach, as it allows for phase averaging of a high number of single recordings to reduce noise from turbulence. To address fringe pattern distortions and cross talk in the Fourier domain, which both have been observed by other authors, we propose background subtraction methods and an optimized background pattern. Additionally, the procedure provides a visualization tool for marking the high turbulence regions of heat release by the variations in fringe amplitude. Finally, the line-of-sight data are reconstructed using the inverse Abel transform, with the data calibrated by laser interferometric techniques, resulting in local values for density oscillations.