Evaluation of the shadowgraph method for the convective flow in a side-heated cavity

The shadowgraph method is used to visualize the convective flow in a water-filled square cavity, which is differentially heated and cooled from the opposing vertical sidewalls. Since in this system a quantitative recovery of the temperature field from the observed shadowgraph images is not possible, we apply a somewhat reverse procedure. The numerical solution of the cavity flow yields the field of the refractive index. By numerically integrating the path of light through this field, artificial shadowgraph images are constructed. This makes a comparison of the numerical and the experimental temperature fields possible and also leads to a clearer interpretation of the shadowgraph images and a better understanding of the way in which certain features are generated. The procedure is not restricted to the cavity flow, but can be applied whenever the field of the refractive index is available.     

Optical measurement uncertainties due to refractive index mismatch for flow in porous media

Application of optical techniques such as PIV, PTV, and LDA for velocity field estimation in porous media requires matching of refractive indices of the liquid phase to that of the solid matrix, including the channel walls. The methods most commonly employed to match the refractive indices have been to maximize the transmitted intensity through the bed or to rely on direct refractometer measurements of the indices of the two phases. Mismatch of refractive indices leads to error in estimation of particle position, ε _PD, due to refraction at solid–liquid interfaces. Analytical ray tracing applied to a model of solid beads placed randomly along the optical path is used to estimate ε _PD. The model, after validating against experimental results, is used to generate expression for ε _PD as a function of refractive index mismatch for a range of bead diameters, bed widths, bed porosity, and optical magnification. The estimate of ε _PD, which is found to be unbiased, is connected to errors in PIV measurement using the central limit theorem. Mismatch in refractive indices can also lead to reduction in particle density, N _s, detected light flux, J, and degrade the particle image. The model, verified through experiments, is used to predict the reduction in N _s and J, where it is found that particle defocusing caused by spherical beads in refractive index mismatched porous bed is the primary contributor to reductions of N _s and J. In addition, the magnitude of ε _PD is determined for the use of fluorescent dye emission for particle detection due to wavelength-dependent index of refraction.     

An investigation of matched index of refraction technique and its application in optical measurements of fluid flow

Optical distortions caused by non-uniformities of the refractive index within the measurement volume is a major impediment for all laser diagnostic imaging techniques applied in experimental fluid dynamic studies. Matching the refractive indices of the working fluid and the test section walls and interfaces provides an effective solution to this problem. The experimental set-ups designed to be used along with laser imaging techniques are typically constructed of transparent solid materials. In this investigation, different types of aqueous salt solutions and various organic fluids are studied for refractive index matching with acrylic and fused quartz, which are commonly used in construction of the test sections. One aqueous CaCl₂·2H₂O solution (63 % by weight) and two organic fluids, Dibutyl Phthalate and P-Cymene, are suggested for refractive index matching with fused quartz and acrylic, respectively. Moreover, the temperature dependence of the refractive indices of these fluids is investigated, and the Thermooptic Constant is calculated for each fluid. Finally, the fluid viscosity for different shear rates is measured as a function of temperature and is applied to characterize the physical behavior of the proposed fluids.     

Refractive index matching in large-scale stratified experiments

The measurement of dilution in jets and plumes by planar laser-induced fluorescence in large-scale stratified environments with refractive index matching is discussed. The density and refractive index of various salt (NaCl) and ethanol solutions were measured to high precision, and it is shown that linear stratifications with density differences at least up to 20 σ _t with acceptably small refractive index variations can be achieved at reasonable cost. Equations are presented to facilitate the design of experiments with arbitrary density differences. The presence of ethanol significantly increases the laser attenuation, however. The rate of attenuation was measured for various solute concentrations and equations presented to predict the attenuation for arbitrary salt and ethanol concentrations. The rapid attenuation due to ethanol may limit the maximum density differences attainable with long laser traverse distances. Examples are given of discharges into linearly stratified fluids including a jet in a stationary environment, and a buoyant jet in a cross flow. Received: 9 April 1999/Accepted: 8 November 2000     

Monte Carlo simulation of radiative transfer in a refractive layered medium

In this work, we adapted the Monte Carlo method to simulate radiative transfer in a two-layer scattering slab with continuously varying refractive index in each of the two layers and a jump of refractive index at the interface between the two layers. The hemispherical reflectance (R _h ) and transmittance (T _h ) of the slab are obtained by tracing photon bundles propagating along curved trajectories. There is a very satisfying correspondence between the present results and those obtained by numerical solution of integral radiative transfer equation for the special cases with constant refractive index in each of the layers. The magnitude of numerical uncertainty decreases with the increase of bundles. The results show that the R _h decreases with the increase of the positive gradient of the refractive index considered. For the cases with constant total thickness, the R _h and the T _h increase with the increase of the ratio of upper-layer thickness to lower-layer thickness.     

Application of rainbow schlieren deflectometry for concentration measurements in an axisymmetric helium jet

 The rainbow schlieren deflectometry technique was used to measure oxygen concentrations in a laminar, isothermal helium jet discharged vertically into ambient air. The concentration distributions were inferred from the color schlieren image by taking into consideration the sampling interval and noise in measurements, especially near the jet center. Excellent quantitative agreement was reached between measurements from schlieren and a continuous sampling probe. This work demonstrates the capability of the schlieren technique for providing accurate, spatially-resolved, nonintrusive, full-field of view measurements of species concentration in an isothermal binary system. Because the basic quantity measured is the refractive index, the present schlieren technique can be extended for quantitative measurements of other scalar flow properties related to the refractive index. Received: 21 April 1997 / Accepted: 14 November 1997     

A simple model for the refractive index of sodium iodide aqueous solutions

A model for predicting the refractive index of sodium iodide (NaI) aqueous solution n _NaI as a function of temperature T, NaI concentration c and wavelength λ was determined for moderate parameter variations. The equation accurately predicted the salt concentration required to match n _NaI to the refractive index of Pyrex n _P. Received: 30 July 1998/Accepted: 14 December 1998     

Refractive index matching methods for liquid flow investigations

A difficulty common to most optical diagnostic techniques that are applied to fluid dynamics studies is the refraction of light passing through model and/or test section walls. The method of choice to eliminate refraction problems in liquid flows is to match refractive index. This paper presents techniques for refractive index matching including, (i) arrangement of test section and model, (ii) choice of solid and liquid materials, and (iii) methods for tuning the match. In addition, a new application of refractive index matching to liquid-liquid droplet studies is presented.The author would like to thank Rick James and Jon Martinez for their assistance in conducting the matching experiments and Professor Mickey Gunter for his comments on refractometry. We are grateful to the United States Department of Energy for financial support of the droplet work under Grant DE-FG07-86ER13572     

Radiation equilibrium temperature field in a gradient index medium with specular surfaces

The radiation equilibrium temperature field in a gradient index semitransparent absorbing-emitting gray medium is analyzed. The medium is bounded by two semitransparent specular surfaces and possesses a refractive index varying spatially or dependent on temperature. By discretizing the medium into many sublayers and adopting a linear refractive index approximation for each sublayer, the curved ray tracing technique is developed to solve the radiation transfer in medium. The temperature field at radiation equilibrium is obtained based on the energy conservation. The influences of refractive index distribution and optical thickness on the temperature field as well as the coupled effect of temperature and refractive index are examined. The results display the significant influences of gradient index on radiation transfer and the temperature distribution.     

Measurement of 3D pore-scale flow in index-matched porous media

We present the experimental analysis of fluid flow at the pore-scale of a transparent porous medium with matched refractive indices of the solid and liquid phases. The planar laser-induced fluorescence (PLIF) technique described is the first to simultaneously visualize the 3D pore-scale flow of two immiscible liquid phases in porous media. Through the application of a highly precise index matching method and the employment of up-to-date CCD imaging hardware, the system features a high spatial resolution and sampling rate. The method was used to study the dispersion of a tracer dye in single-phase flow and the displacement of oil by water in an imbibition process.     

The determination of the refractive index of a photoelastic specimen by immersion technique

Conventional methods for determining the refractive index demand specimens of optical quality, the preparation of which is often very difficult. An indirect determination by matching the refractive indices of specimen and immersion liquid is a practical alternative for photoelastic specimen of nonoptical quality. An experimental arrangement used for this technique and observations made while matching the refractive indices of three different specimens are presented.     

On the mixing of photoelastic immersion fluids

It is shown that an equation can be used to determine the exact quantities of components to yield a specified refractive index for an immersion fluid. The results obtained from this equation are compared with values obtained experimentally for two different immersion fluids, IMF 163 and Hallowax. The paper also discusses the kinds of errors that are introduced when a mismatch in refractive index occurs between model material and immersion fluid. Graphs are presented which show the effect of temperature on the refractive index, the degree of refraction of the light beam when the refractive indices are different between immersion fluid and birefringent model, and effect of the angle of incidence.     

Experimental study of flow structures in a large range downstream the spacer grid in a 5 × 5 rod bundle using TR-PIV

In this paper, the time-resolved particle image velocimetry (TR-PIV) and match index refractive (MIR) techniques were used to study the flow field in a large range (0 – 22 D_h) downstream a spacer grid (SG) in a 5 × 5 rod bundle channel at different Reynolds number. The sodium chloride solution (1%) is used as the working fluid to reduce the refractive index error of fluorinated ethylene propylene (FEP) and water. The proper orthogonal decomposition (POD) background removal technique was used to minimize the FEP reflection. These methods greatly reduced the interference of background noise and improved the accuracy of cross-correlation calculation. For TR-PIV velocity fields downstream of the mixing vanes, time-averaged, statistical, spectral, and cross-correlation analysis were performed for the instantaneous full-field experimental data. The transport characteristics of coherent structures in different subchannels of rod bundles are calculated and discussed. The results show that the SG caused a relatively large transverse velocity and reduces the axial velocity. With the increase of the Reynolds number, the SG promotes the generation of transverse flow and has a great resistance to the axial flow. There is relatively large turbulence intensity downstream of the SG due to the mixing effect. The attenuation of transverse turbulence intensity component is slower than the axial component. Moreover, spectrum analysis shows that cross-arranged mixing vanes will generate periodic vortices but single mixing vane will not. These periodic vortices gradually propagate downstream along the inner subchannel and dissipate in the gap subchannel due to the effect of viscosity. The cross-correlation analysis shows that the mixing effect of the SG will reduce the scale of the coherent structure, and increase the convection velocity. The results of current research are helpful for understanding the strong anisotropic turbulence in the rod bundle channel with SG. Finally, the experimental results can be utilized to benchmark the applicability of turbulence models under different Reynolds number and the performance of partially averaged Naiver–Stokes or multiple RANS algorithms downstream of the SG.     

Oblique wave propagation in a compressible general magnetoplasma

Summary The refractive index equation has been derived for arbitrarily directed oblique waves in compressible general magnetoplasma with arbitrarily directed magneto-static field. The q factor obeys a general sixth order algebraic equation. Booker's quartic equation and Seshadri's result are found as particular cases and other particular cases have been discussed. The general result is checked by using tensor analysis methods and transformation of coordinates.Any views expressed in this paper are those of the author. They should not be interpreted as reflecting the views of The RAND Corporation or the official opinion or policy of any of its governmental or private research sponsors.Consultant to The RAND Corporation, Santa Monica, California; affiliated with the Electrical Engineering Department, University of Kansas, Lawrence, Kansas, U.S.A.     

微悬臂梁生化传感系统的性能分析

在基于光杠杆原理检测微悬臂梁变形的生化传感实验系统中,液体折射率的变化会导致PSD上光斑的位移,从而影响系统的检测信号。本文从理论上分析了在不同检测光束的入射角度、微梁的放置角度等参数条件下,液体折射率的变化对系统检测信号的影响。结果表明：在传统的光路下,液体折射率改变10-3引起的光斑位移与一般的生化反应引起的位移相当,即液体折射率的改变严重影响系统的检测信号。通过理论分析还发现在适合的参数配置下,可以忽略折射率变化对系统检测信号的影响。同时,参数的改变不影响系统的检测灵敏度。理论分析的结果得到了实验验证。     

Recent high-resolution resonant refractivity studies of a sodium-seeded flame

A new experimental technique, namely, the combination of a Fabry-Perot etalon with a Mach Zehnder interferometer (MZI) makes it possible to deduce the index of refraction resonant dispersion curve near the center of an atomic line from the superimposed fringe system. A tunable pulsed dye laser as light source and a sodium seeded flame as test flow enabled us to verify the very large enhancement of sensitivity for refractive flow-visualization methods such as shadowgraph, schlieren and interferometry. The specific refractivity is a direct measure of the sensitivity, and that quantity increases from a non-resonant value of 4 × 10^?3 m'/kg to a peak value of 189 m3/kg at the half-power points of the sodium D₂-line.     

Extended glare point velocimetry and sizing for bubbly flows

A novel measuring technique for bubbly flows, named glare point velocimetry and sizing (GPVS), was developed in order to measure both bubble size and velocity with high accuracy in a 2D plane. This is accomplished by observing glare points in-focus under an observation angle of 96°. When a second laser-sheet is added, even higher accuracies are obtained and the relative refractive index of the bubble can be measured. It also allows non-spherical bubbles to be rejected and arbitrary angles to be used (e.g. 90°). The accuracy of the size and refractive index measurements was found to be within 1.3%.     

Flow visualization in a scanning electron microscope scale

This paper describes a method of visualizing the two-dimensional flow around small bodies by means of a scanning electron microscope (SEM). The advantages, compared to light microscopic methods, are, for example, a greater distance between objective lens and object, a higher depth of focus and the possibility of observing smaller details. The disadvantages are the restriction to certain fluids and the expensive equipment. The described method may be important for the investigation of stationary objects as well as that of unsteady flow. In the near future we shall try to visualize three dimensional flow in a scanning electron microscope scale.     

Error estimation of laser-Doppler anemometry measurements in fluids with spatial inhomogeneities of the refractive index

We report a combined experimental and theoretical investigation of the influence of spatial non-uniformities of the refractive index on the accuracy of laser Doppler anemometry (LDA) measurements in transparent fluids. One LDA beam is guided through heated air of a thermal boundary layer near a heated vertical flat plate. It is found that the hot air is deflecting the beam because of a modification of the refractive index n in the fluid. This deflection causes three effects: (1) spatial displacement of beam intersection, (2) waist mismatch in the measurement volume and (3) variation in interference fringe distance. With the help of a rotating disk calibration system the resulting displacement of the LDA measurement volume and the Doppler frequency variation is systematically studied at different temperatures. Using a simple model of beam propagation under the influence of well-defined temperature inhomogeneities, the displacement of measurement volume and change in Doppler frequency are calculated and are found to be in agreement with the experimental observations. The results provide a rational framework for an assessment of the accuracy of LDA data in arbitrary transparent fluids with non-uniform refractive index.