Characteristic relations of flow birefringence

This is the first of two closely related papers on the flow-birefringence response to the velocity vector field of a particular liquid representing a certain class of birefringent bodies.^* The flowing material under study was the aqueous solution of the compound known under the name NGS 1828 and commonly known as “milling yellow” or “acid yellow”. This solution appears to exhibit all three major mechanisms of birefringence. The physical parameters characterizing this material depend strongly on temperature, concentration and age and, therefore, it can be considered as representing a typical class of liquids used in flow-model experiments. The paper presents the experimental evidence that the flow birefringence cannot be explained and described by the simple mathematical model of birefringence in solid continuum which relates the changes of the components of dielectric tensor to the components of stress and strain tensors, or their derivatives, and which neglects the influence of the spectral frequency (wavelength of radiation). Results are presented for transmission birefringence (and for scattered-light birefringence in the second paper) in the visible and the infrared bands of radiation. It is shown that:

- the amount of birefringence depends strongly and non-monotonically on wavelength of radiation;

- the linear range of optical response to shear-strain rate depends on wavelengths of radiation;

- the directions of optic axes strongly depend both on the shear-strain rate and on the wavelength of radiation, even in the linear range of mechanical response.

It is further shown that there exists a relation between the absorption bands, the maximum transmittance, the dispersion of birefringence, the spectral dependence of optic-axes direction, and the linear range of optical response. Within the maximum transmittance band and the linear range of mechanical response the linear range of birefringence is maximum and the dispersion of birefringence is minimum with respect to the shear-strain rate; the corresponding dispersion of optic axis is also minimum. Samples of typical recordings are given in the visible and the infrared radiation for typical flow patterns. One of the practical conclusions is that to optimize the flow-birefringence studies of engineering problems it is advisable to choose the radiation in the near-infrared range. The evidence presented shows that the common trend in engineering research toward simplification of the model of the flow-birefringence response is not necessary.     

Study of basic patterns of light scattering in aqueous solution of milling yellow

Basic characteristics of light scattering in an aqueous solution of milling yellow are presented in a form of relations between the scattered radiant power, states of polarization of primary radiation and scattered radiation, observation angle and azimuthal angle.It is found that the state of polarization of the scattered light in milling-yellow solution can be utilized as a foundation of reliable photoelastic scattered-light techniques for flow analysis. However, Rayleight's model of scattering is nnt directly applicable.Paper contains data on major parameters of light scattering, knowledge of which is necessary to correctly design flowbirefringence experiments. In particular, these data can be used to develop a set of conditions and constraints for designing of particular scattered-light flow-birefringence experiments, and of corresponding transfer functions.     

Suitability of the photoelastic implementation of polymers with material birefringence

Scattered photoelastic techniques would gain considerable momentum through better understanding of the nature and response of the available photoelastic materials. The influence of the prevailing birefringent effect in the state of load-free polymers on the radiated scattered light energy is investigated. Six different photoelastic materials are considered. The impact of material birefringences on the quality of reading the fringe orders of the scattered radiation in a stressed photoelastic medium is explored. Spectral dependence of the modulation of light vectors in acrylic materials (Plexiglas) is illustrated. The advantage of this characteristic as a convenient means of compensation in scattered photoelasticity is pointed out. Acrylic sheets, a relatively cheap transparent polymer, seem to be suitable for scattered photoelastic analysis. The moiré technique might find application in determining fringe orders in a material such as Homalite-100. Replacing the primary beam by a primary sheet saves the cost and effort consumed in the scanning process. Paper was presented at the 1988 SEM Spring Conference on Experimental Mechanics held in Portland, OR on June 5–10.     

A scattered-light method in photoelasticity

The birefringence and, thereby, the stresses in a photoelastic model are investigated utilizing the light scattered from a beam of light propagating through the model. The retardance from the entry point of the beam into the model to a certain point along the beam is expressed in terms of the intensity of the scattered light. The retardance for a short distance along the light path within the model is determined as a function of the total retardances from the entry point of the model to the two end points of the distance investigated. The effects of retarders and polarizers on the state of polarization of the light beam are treated by Mueller calculus. It is not necessary to make other assumptions than those made in the usual stress-freezing and slicing method.     

Imaging of an underexpanded nozzle flow by UV laser Rayleigh scattering

 Rayleigh scattering of ultra-violet laser light is applied as a diagnostic tool to record gas density distributions in a supersonic nozzle flow. The output beam of a pulsed ArF excimer laser (λ=193.4 nm) is focussed into a thin light sheet radially intersecting a dry air flow emanating from a circular nozzle. An intensified CCD camera is used to record the Rayleigh scattered light in a direction perpendicular to the light sheet. Since the Rayleigh scattering intensity is directly proportional to the local gas density, this results in two-dimensional gas density distribution maps of radial slices through the flow. Images of the flow density are presented for stagnation pressures between 0.2 and 0.7 MPa (0.1 MPa ≡1 bar), showing the transition from subsonic to supersonic flow and, at higher pressures, the formation of a Mach disk. Density maps can be recorded with single laser pulses, effectively freezing the flow structure on a 20 ns time scale. The diamond pattern, characteristic for underexpanded supersonic nozzle flows, is quantitatively monitored, with the experimental results being in reasonable agreement with predictions from a simplified theoretical model. Received: 25 September 1996/Accepted: 19 May 1997     

Displacement measurements in the interior of 3-D bodies using scattered-light speckle patterns

Two new techniques making use of the scattered-light speckle pattern have been developed which yield the displacements on an arbitrary interior plane of a 3-D body. When a sheet of coherent light passes through a transparent 3-D body, a small fraction is scattered. This scattered light produces a speckle pattern in an imaging system. By recording two superimposed images of this speckle pattern, one before and one after body deformation, the displacements on the interior illuminated plane can be found. The technique of scattered-light photography uses a single illuminating beam and is sensitive to displacements greater than one speckle diameter, approximately 3 μm. Scattered-light speckle interferometry uses two illuminating beams and is sensitive to displacements greater than one half the wavelength of light being used, approximately 0.2 μm. With both techniques, the double-exposed speckle photograph is optically processed to yield displacement information. With both techniques, the maximum displacement measurable is limited by correlation requirements between the two speckle patterns. Experimental results are presented demonstrating the two new techniques.     

Birefringence measurements on polymer melts in an axisymmetric flow cell

 The stress-optical rule relates birefringence to stress. Consequently, measurement of flow birefringence provides a non-intrusive technique of measuring stresses in complex flows. In this investigation we explore the use of an axisymmetric geometry to create a uniaxial elongational flow in polymer melts. In axisymmetric flows both birefringence and orientation angle change continuously along the path of the propagating light. The cumulative influence of the material's optical properties along the light's integrated path makes determination of local birefringence in the melt impossible. One can nevertheless use birefringence measurements to compare with predictions from computer simulations as a means of evaluating the constitutive equations for the stress. More specifically, in this investigation we compare the light intensity transmitted through the experimental set-up vs entry position, with the theoretically calculated transmitted intensity distribution as a means of comparing experiment and simulation. The main complication in our experiments is the use of a flow cell that necessarily consists of materials of different refractive indices. This introduces refraction and reflection effects that must be modeled before experimental results can be correctly interpreted. We describe how these effects are taken into account and test the accuracy of predictions against experiments. In addition, the high temperatures required to investigate polymer melts mean that a further complication is introduced by thermal stresses present in the flow cell glass. We describe how these thermal-stresses are also incorporated in the simulations. Finally, we present some preliminary results and evaluate the success of the overall method. Received: 2 April 2001 Accepted: 27 August 2001     

Dynamic measurement of temperature, velocity, and density in hot jets using Rayleigh scattering

A molecular Rayleigh scattering technique is utilized to measure gas temperature, velocity, and density in unseeded gas flows at sampling rates up to 10 kHz, providing fluctuation information up to 5 kHz based on the Nyquist theorem. A high-power continuous-wave laser beam is focused at a point in an air flow field and Rayleigh scattered light is collected and fiber-optically transmitted to a Fabry–Perot interferometer for spectral analysis. Photomultiplier tubes operated in the photon counting mode allow high-frequency sampling of the total signal level and the circular interference pattern to provide dynamic density, temperature, and velocity measurements. Mean and root mean square velocity, temperature, and density, as well as power spectral density calculations, are presented for measurements in a hydrogen-combustor heated jet facility with a 50.8-mm diameter nozzle at NASA John H. Glenn Research Center at Lewis Field. The Rayleigh measurements are compared with particle image velocimetry data and computational fluid dynamics predictions. This technique is aimed at aeronautics research related to identifying noise sources in free jets, as well as applications in supersonic and hypersonic flows where measurement of flow properties, including mass flux, is required in the presence of shocks and ionization occurrence.     

Time-resolved spectral-line-filtered velocimetry

Measurements were obtained with a velocimeter that simultaneously illuminates the particulate in a flow with argon and He–Ne lasers and the scattered light is passed through a carefully controlled iodine filter. The iodine cell absorbs the argon emission at a rate proportional to the velocity of the scattering particle, while the absorption of scattered He–Ne light is independent of velocity. A tunable acousto-optic filter is used to multiplex the argon and He–Ne signals collected from a single photodetector. The problem of detector alignment in conventional Doppler global velocimetry is thus avoided. Experimental results on a scattering disk and an axisymmetric jet are presented and compared with laser Doppler anemometry measurements. Received: 7 March 2000/Accepted: 5 January 2001     

Scattered light streaming birefringence in colloidal solutions

Summary The light scattered from particles or molecules in a fluid flow is often used to perform local measurements in a three-dimensional flow field. The scattered light technique has been adopted by McAfee and Pih to the field of streaming birefringence. Their empirical relationship between the observed optical pattern and the state of the flow is extended here to describe more general flow situations. The new set of equations which includes all possible shear and dilatation terms is tested with a number of experiments in the flow of a colloidal solution. The range of validity of these equations is restricted to low-Reynolds number flows.With 14 figures     

Heterodyne Doppler global velocimetry

Doppler Global Velocimetry (DGV) is an imaging flow measurement technique which allows the measurement of the velocity distribution in a plane. In DGV the frequency shift of scattered light from moving particles within the flow is used to determine the local flow velocity. Heterodyne Doppler Global Velocimetry (HDGV) is a new approach which combines the imaging and geometrical characteristics of DGV with the measurement principles of reference beam laser Doppler anemometry. The frequency shifted scattered light from the flow tracers is heterodyned with a reference beam from the same light source. Due to interference the result of this superposition is a harmonic intensity modulated signal. This signal is detected using a smart pixel detector array to obtain the velocity distribution. Two different experiments are presented. The first experiment compares the measured velocity distribution of a rotating disk with its actual velocity. The second experiment demonstrates the capability of the technique to measure a real flow.     

3D stress local nondestructive analysis in the middle plane of a plate

The Isodyne technique based on the scattered light scanning from a thin laser beam can be used to obtain the information inside the loaded object in the room temperature nondestructively, so it is a very powerful technique in 3D stress analysis. The problems are how to interpret the information and how to get sufficient information from the few interference fringe. Birefringence phase shift technique can distinguish the fringe orders automatically and enrich the information in 256 gray levels between maxim and minim light intensity. In the paper the Isodyne birefringence phase shift method with an oblique incidence and equilibrium equation is presented, by which the 3D stresses in the middle plane of a plate with U shape notch are separated successfully. The project supported by the National Natural Science Foundation of China under the Grant No. 1380345     

Three-dimensional nonlinear vibrations of composite beams — III. Chordwise excitations

Three nonlinear integro-differential equations of motion derived in Part I are used to investigate the forced nonlinear vibration of a symmetrically laminated graphite-epoxy composite beam. The analysis focuses on the case of primary resonance of the first in-plane flexural (chordwise) mode when its frequency is approximately twice the frequency of the first out-of-plane flexural-torsional (flapwise-torsional) mode. A combination of the fundamental-matrix method and the method of multiple scales is used to derive four first-order ordinary-differential equations describing the modulation of the amplitudes and phases of the interacting modes with damping, nonlinearity, and resonances. The eigenvalues of the Jacobian matrix of the modulation equations are used to determine the stability of their constant solutions, and Floquet theory is used to determine the stability and bifurcations of their limit-cycle solutions. Hopf bifurcations, symmetry-breaking bifurcations, period-multiplying sequences, and chaotic motions of the modulation equations are studied. The results show that the motion can be nonplanar although the input force is planar. Nonplanar responses may be periodic, periodically modulated, or chaotically modulated motions.     

A neoteric interferometer for use in holographic photoelasticity

A shortcoming of the conventional holographic interferometer used in photoelasticity is that, for the double-exposure cases, the resulting fringe patterns are a complex combination of conventional isochromatic and isopachic fringes. This paper describes a holographic interferometer that may be used to obtain separate but simultaneous isochromatic- and isopachic-fringe patterns for photoelastic models in states of plane stress. The method requires a model with a partially reflecting front surface. Isopachics, which are proportional to the thickness change, are recorded using holographic interferometry from the transmitted light. The isochromatics are obtained from the transmitted light by conventional means. General equations relating the surface displacement of the specimen to the observed fringe patterns are developed, and examples of static and dynamic loadings are shown.     

Determination of the parameters of particles suspended in two-phase media by means of penetrating radiation

Determination of the concentration, size, and internal structure of microscopic particles suspended in two-phase media by means of contactless methods constitutes an important technological problem. If the particle sizes are on the order of the wavelength of light, methods based on light scattering by particles are widely used for this purpose. The most direct method consists in observing the optical signal scattered by an individual particle [1]. There are also several methods where the total signal from a large number of particles is recorded, but, in this case, multiple rescattering of light on particles must be negligible [2, 3]. At the same time, the complex relationship between the scattering amplitude and the refraction index, the shape of particles, etc., as well as the increasing background of multiply scattered light with greater thickness of the scattering layer, restrict the scope of application of such methods and make other measurement methods desirable, e.g., in the case of instrument calibration. Our aim is to point out the advisability of investigating two-phase media by means of penetrating radiation, which has been used successfully for radiation flaw detection [4] and for inspecting the composition and density of matter [5], We shall mention the most important advantages of the proposed method. First, the interaction between individual particles and nonrefracted radiation is described by simple expressions, which makes the interpretation of results much easier. Second, in using the most informative scheme whereby scattering media are investigated by transillumination, the background of multiply scattered radiation with a low information content (or, to borrow a term from radiation protection physics, the build-up factor [6]) increases with an increase in the scattering layer thickness much more slowly than it does for light. This makes it possible to use radiation methods for investigating optically dense two-phase media. We shall consider below the possibility of determining the distribution function of particle sizes by measuring the radiation attenuation as a function of the linear coefficient of attenuation inside the particles.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 11–14, May–June, 1979.     

Development of a double-beam rheo-optical analyzer for full tensor measurement of optical anisotropy in complex fluid flow

The design and testing of the Double-Beam Rheo-Optical Analyzers, DB-ROA is described. The DB-ROA contains the two optically modulated laser beams that are transmitted through a sheared sample in different angles. The full components of the stress tensor can be evaluated simultaneously by a single measurement of the birefringence and orientation angle of each beam. The mechanical properties are also measured simultaneously with the optical properties. This system can be applied to both steady and transient shear flows. Three types of DB-ROAs are designed. They are distinguished by the optical modulation system, that is (1) a single modulator system, (2) a synchronization of two modulators, and (3) a two individual modulator system. The performance tests were carried out and its validity was demonstrated by comparison between the optical and the mechanical measurements of the first normal stress difference. The signal-to-noise ratio was strongly affected by the choice of the oblique angle of the second beam. The design features for the different optical modulation systems are discussed.     

Towards RGB photoelasticity: Full-field automated photoelasticity in white light

In this paper a new full-field method for the automatic analysis of isochromatic fringes in white light is presented. The method, named RGB photoelasticity, eliminates the typical drawbacks of the classical approach to photoelasticity in white light which requires a subjective analysis of colors and an experienced analyst to acquire and interpret the results. The proposed method makes it possible to determine retardations uniquely in the range of 0–3 fringe orders. For this purpose the isochromatics are acquired by means of a color video camera and the colors are decomposed in the three primary colors (red, green and blue) and compared to those stored in a calibration array in the system. Furthermore, the influence of various spurious effects on the accuracy of the proposed method is experimentally evaluated.     

Some experimental results on the development of Couette flow for non-Newtonian fluids

This paper reports some experimental results on the time development of a Couette flow following the start-up of shear flow using the technique of two-color flow birefringence. Measurements obtained on collagen solutions are consistent with two theoretical studies which predict that for some viscoelastic liquids, momentum is transferred from the moving Couette cell boundary to the interior of the fluid through a velocity wave propagating and reflecting between the cell boundaries. This non-Newtonian phenomenon, exhibited as an oscillatory response in the measured birefringence and orientation angle, is observed at shear rates above a critical value when the response time of the polymer solution approaches the flow development time in the Couette flow cell.     

Photoviscoelastic analysis of thermal stress in a quenched epoxy beam

This paper reports on a procedure for photoviscoelastic analysis where the axes of principal stress, principal strain and polarization of light coincide in the presence of a large temperature change. More specially, the transient-thermal stress and strain due to stress in an epoxy beam subjected to quenching from both the upper and lower surfaces, are determined using the time-temperature-equivalent law for stress, strain and birefringence. The transient-thermal stress and strain in the beam were determined experimentally using hereditary integrations from the measurement of the transient temperature and birefringence due to the quenching of the beam. The transient thermal stress and strain were also calculated theoretically using the linear-viscoelastic theory. The experimentally determined thermal stress agrees closely with the theoretical results. The experimentally determined strain agrees qualitatively with the theoretical values. Thus, it is concluded that the photoviscoelastic technique is useful in analyzing the proposed problem.Paper was presented at 1982 SESA/JSME Spring Meeting held in Maui and Oahu, HI on May 23–28, 1982.     

Transmission photoelasticity of centrally loaded generally and specially orthotropic beams

Transmission photoelastic patterns for generally and specially orthotropic beams and an isotropic beam are presented. Theoretical isochromatic and isoclinic results for these beams, calculated from classical elasticity stress equations and stress-optic laws, are also presented and compared with experiment. The agreement between the theory and experiment is excellent. For the orthotropic beams, a stressoptic law which accounts for the effects of residual birefringence was used. The residual birefringence observed for the composite used in this study is greater than one fringe order and results from a matrix residual tension which is about one fourth of the resin's ultimate tensile strength. Finally, the influence of such a large residual birefringence on beam and calibration photoelastic data is discussed in detail. Paper was presented at the 1986 SEM Spring Conference on Experimental Mechanics, held in New Orleans, LA on June 8–13.