Direct interferometric measurement of streaming birefringence

The two refractive indices in the flow of a colloidal birefringent liquid are measured separately by means of a Mach-Zehnder interferometer. For a quantitative evaluation of the resulting interferograms it is not necessary to linearize the respective equations relating the refractive index distribution to the deformation velocity in the flow. Therefore it becomes possible to perform velocity measurements in the non-Newtonian flow range. An additional measurement of the mean flow rate enables one to determine the velocity field without the need of a calibration of the observed interference fringes.     

Effects of renal artery stenosis on realistic model of abdominal aorta and renal arteries incorporating fluid-structure interaction and pulsatile non-Newtonian blood flow

The effects of the renal artery stenosis(RAS) on the blood flow and vesselwalls are investigated.The pulsatile blood flow through an anatomically realistic model ofthe abdominal aorta and renal arteries reconstructed from CT-scan images is simulated,which incorporates the fluid-structure interaction(FSI).In addition to the investigationof the RAS effects on the wall shear stress and the displacement of the vessel wall,it isdetermined that the RAS leads to decrease in the renal mass flow.This may cause theactivation of the renin-angiotension system and results in severe hypertension.     

Experimental study of the induced flow birefringence of a suspension of rigid particles at the transition from Couette flow to Taylor vortex flow

The flow birefringence induced in solutions of rigid particles is studied experimentally in the region of the axisymmetrical Taylor vortex flow which arises once the velocity gradient G in the annular gap of a conventional Couette cell reaches a critical value G _c .The measurements are performed for several values of G > G _c and for 10 radial observation points in the annular gap. Solutions of two types of rigid particles are investigated: the first is a suspension of flattened clay particles like bentonite, while the second contains rod-like particles of tobacco mosaic virus (TMV). The variations of the birefringence intensity n and of the extinction angle measured in the domain of the axisymmetrical flow show a different behavior according to the shape of the particle in solution. This fact is confirmed theoretically with a good agreement for the measurements performed with solutions of flat particles.     

Characteristic relations of flow birefringence

The general problems of the flow-induced birefringence in liquids have been presented and discussed in Part 1 of this paper, in which some particular responses of an aqueous solution of NGS 1828 were presented, namely, the pertinent mechanical responses and the birefringence responses in transmitted radiation. This paper presents the optical responses of NGS 1828 observed in the scattered radiation. It is shown that the scattered-light techniques can become a powerful and indispensable tool of flow-birefringence techniques, if the actual patterns of light scattering are taken into account. Proof is given that the light scattering and the related birefringence cannot be described by Rayleigh's mathematical model of scattering (Part 1, Ref. 51). The optical effects of the modulation of the primary beam and the scattered beam, called scattered primary isochromatics and scattered secondary isochromatics, are described in terms of the parameters of the system. A practical example is presented. Samples of typical recordings of light-intensity modulation by typical flow patterns are given in the form of scattered primary and secondary isochromatics and integrated isochromatics. One type of intensity modulation enables the determination of shear-strain rate at an interior point in the flow field. Using the determined shear-strain rates at the interior points, a velocity profile along the axis of symmetry of a rectangular-conduit flow was obtained. The results so obtained were satisfactory when compared with the results of direct volumetric measurement. The other type of intensity modulation reveals the nonuniform distribution of birefringence along the path of the transmitted light in the rectangular-conduit flow. The results presented in Part 1 of this paper, are complementary to the results presented below.     

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.     

Three dimensional flow at the junction between a turbine blade and end-wall

A visualization of the flow on the suction side and end-wall of a passage between two neighboring turbine blades is compared with mass (heat) transfer measurements on the same surfaces. Besides the horseshoe and passage vortices, there are several smaller vortices formed near the junction of blade and end-wall whose origins are discussed. The vortices detach from the end-wall and move up the blade's span. These vortices, sometimes in counter rotating pairs, are responsible for substantial local variations of heat transfer.

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Drei-dimensionale Strömung an der Naht zwischen Turbinenschaufel und Endwand

Zusammenfassung Der Durchfluß auf der Saugseite und an der Endwand eines Kanals zwischen zwei benachbarten Turbinenschaufeln wird sichtbar gemacht und mit gemessenen Massen-(Wärme)strömen der selben Oberflächen verglichen. Neben den hufförmigen Wirbeln und Durchflußwirbeln werden mehrere kleinere Wirbel in der Nähe der Verbindungsstelle von Schaufel und Endwand gebildet und die Ursache ihrer Entstehung wird diskutiert. Die Wirbel lösen sich von der Endwand ab und bewegen sich über die Spannweite der Schaufel. Diese Wirbel, manchmal als gegenläufige rotierende Paare, sind für die wesentlichen lokalen Variationen des Wärmeflusses verantwortlich.

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Nomenclature AT Attachment line between counter-rotating vortices - C Chord length of the test blade, c.f. Fig. 1 b;C=16.91 cm in the present study - DE Detachment line between pairs of counter-rotating vortices - DL Flow dividing line-line along which surface flow divides into neighboring blade passages - Re ₁ Reynolds number based on cascade inlet velocity and blade chord length,U ₁ C/ - S _s Suction side curvilinear distance from the stagnation line of the test blade (see Fig. 1 b). Note thatS _s /C=1.355 at the trailing edge of the blades in the present study - U ₁ inlet velocity to the cascade - V _h the horseshoe vortex - V _Lc the leading edge corner vortex - V _p the passage vortex - V _ph pressure side leg of the horseshoe vortex - V _pLc pressure side leg of the leading edge corner vortex - V _s1 leading edge stagnation region vortex 1 - V _s2 leading edge stagnation region vortex 2 - V _sc1 suction side corner vortex 1 - V _sc1s portion ofV _sc1 which climbs up the blade suction surface - V _sc2 suction side corner vortex 2 - V _sc3 suction side corner vortex 3 - V _sh suction side leg of the horseshoe vortex - V _sLc suction side leg of the leading edge corner vortex - kinematic viscosity Dedicated to Prof. Dr.-Ing. F. Mayinger's 60th birthday     

An experimental study of a turbulent wing-body junction and wake flow

Extensive measurements were conducted in an incompressible turbulent flow around the wing-body junction formed by a 3∶2 semi-elliptic nose/NACA 0020 tail section and a flat plate. Mean and fluctuating velocity measurements were performed adjacent to the wing and up to 11.56 chord lengths downstream. The appendage far wake region was subjected to an adverse pressure gradient. The authors' results show that the characteristic horseshoe vortex flow structure is elliptically shaped, with ? (W)/?Y forming the primary component of the streamwise vorticity. The streamwise development of the flow distortions and vorticity distributions is highly dependent on the geometry-induced pressure gradients and resulting flow skewing directions. The primary goal of this research was to determine the effects of the approach boundary layer characteristics on the junction flow. To accomplish this goal, the authors' results were compared to several other junction flow data sets obtained using the same body shape. The trailing vortex leg flow structure was found to scale on T. A parameter known as the momentum deficit factor (MDF = (Re _T)² (θ/T)) was found to correlate the observed trends in mean flow distortion magnitudes and vorticity distribution. Changes in δ/T were seen to affect the distribution of u′, with lower ratios producing well defined local turbulence maxima. Increased thinning of the boundary layer near the appendage was also observed for small values of δ/T.     

Two dimensional flow quantitative visualization by the hybrid method of flow birefringence and boundary integration

Flow birefringent method and its data processing was reviewed and a new hybrid method of flow birefringence and boundary integration was introduced. The basic equations and boundary conditions suitable to the hybrid method were derived, and a comparison of the hybrid and other classical methods was given. Finally as an example, the flow in a step converging tube was analyzed by the given method. The project supported by National Natural Science Foundation of China (NSFC)     

An improved method for the measurement of strong flow birefringence

An improved procedure is proposed to solve the problem of measuring strong birefringence on flowing samples which have a retardation larger than /2 The procedure can be applied to devices which are based on the modulation of the polarization vector with a high-speed rotating half-wave plate. It uses two optical configurations which have different responses to the retardation. By combining the information obtained from the two configurations, one can easily and accurately determine the actual retardation of the sample, irrespective of the quadrant in which the measured retardation is located, provided the sample is isotropic. This technique can also overcome the problem of large errors occurring in the vicinity of = (2m+1)/2 due to the limited sensitivity around these values of . The use of the technique is illustrated with measurements on an isotropic solution of poly(benzyl glutamate) in m-cresol, which is strongly birefringent during shear flow.     

Effect of concentration and polydispersity on flow birefringence of polystyrene

Summary Normal stresses were estimated from viscosity and flow birefringence measurements on solutions and melts of substantially two samples of polystyrene. A large range of concentration and temperatures was covered.The interpretation of results was tried along lines originally handled for dilute solutions only. In meeting the requirements of this method, a well-known reduction scheme with respect to concentration (and temperature) was rediscussed and applied. For the sample with a narrow molecular weight distribution this procedure was very satisfactory. For the polydisperse sample, however, the reduction with respect to concentration was only partly successful.For this latter sample it could be shown that results on very dilute solutions corresponded with those on the bulk polymer. This is in favour of the current concept for molten bulk polymers and, in particular, of the interpretation given to polydispersity effects. Deviations at intermediate concentrations are qualitatively interpreted in terms of an inhomogeneous dispersion of solvent between high and low molecular weight species.

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Zusammenfassung Für die Abschätzung von Normalspannungen, wie sie an strömenden Lösungen und Schmelzen auftreten, wurden Daten von Viskosität und Strömungsdoppelbrechung herangezogen, die in der Hauptsache an zwei Polystyrolproben gemessen wurden. Hierfür wurde ein großer Bereich von Konzentrationen und Temperaturen bestrichen.Für die Interpretation wurden Gedankengänge herangezogen, die ursprünglich nur für verdünnte Lösungen entwickelt wurden. Deshalb war die Verwendung eines Reduktionsschemas in bezug auf Konzentration (und Temperatur) angezeigt. Für die Probe mit einer schmalen Molekulargewichtsverteilung wurden hiermit sehr befriedigende Resultate erzielt. Für die polydisperse Probe war die Reduktion in bezug auf die Konzentration jedoch nur zum Teil erfolgreich.Dieser Erfolg besteht darin, daß die an sehr verdünnten Lösungen erhaltenen Ergebnisse zu den an der reinen Schmelze erhaltenen passen. Dies liefert eine Stütze für die herrschenden Auffassungen über Polymerschmelzen und insbesondere über die Interpretation von Polydispersitätseffekten. Bei mittleren Konzentrationen gefundene Abweichungen wurden als Folge einer inhomogenen Verteilung des Lösungsmittels zwischen hoch- und niedermolekularen Anteilen betrachtet.

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Paper read at the Annual Meeting of the German Rheologists, Bad Ems, May 18–19, 1967.     

Experimental study of aortic flow in the ascending aorta via Particle Tracking Velocimetry

A three-dimensional, pulsatile flow in a realistic phantom of a human ascending aorta with compliant walls is investigated in vitro. Three-Dimensional Particle Tracking Velocimetry (3D-PTV), an image-based, non-intrusive measuring method is used to analyze the aortic flow. The flow velocities and the turbulent fluctuations are determined. The velocity profile at the inlet of the ascending aorta is relatively flat with a skewed profile toward the inner aortic wall in the early systole. In the diastolic phase, a bidirectional flow is observed with a pronounced retrograde flow developing along the inner aortic wall, whereas the antegrade flow migrates toward the outer wall of the aorta. The spatial and temporal evolution of the vorticity field shows that the vortices begin developing along the inner wall during the deceleration phase and attenuate in the diastolic phase. The change in the cross-sectional area is more distinct distal to the inlet cross section. The mean kinetic energy is maximal in the peak systole, whereas the turbulent kinetic energy increases in the deceleration phase and reaches a maximum in the beginning of the diastolic phase. Finally, in a Lagrangian analysis, the temporal evolution of particle dispersion was studied. It shows that the dispersion is higher in the deceleration phase and in the beginning of the diastole, whereas in systole, it is smaller but non-negligible.     

The split of vertical annular flow at a large diameter T junction

Measurements and observations have been made of the split of gas—liquid flow at a T junction where the main pipe was vertical and the side arm horizontal. All three pipes connecting to the junction were of 0.125 m dia. The gas and liquid flow rates were chosen to ensure annular flow in the inlet pipe. The resulting data have been compared with existing models.     

Periodical streaming potential and electro-viscous effects in microchannel flow

This paper presents an analytical solution to periodical streaming potential, flow-induced electric field and velocity of periodical pressure-driven flows in twodimensional uniform microchannel based on the Poisson-Boltzmann equations for electric double layer and Navier-Stokes equation for liquid flow. Dimensional analysis indicates that electric-viscous force depends on three factors： （1） Electric-viscous number representing a ratio between maximum of electric-viscous force and pressure gradient in a steady state, （2） profile function describing the distribution profile of electro-viscous force in channel section, and （3） coupling coefficient reflecting behavior of arnplitude damping and phase offset of electro-viscous force. Analytical results indicate that flow-induced electric field and flow velocity depend on frequency Reynolds number （Re = wh^2/v）. Flow-induced electric field varies very slowly with Re when Re 〈 1, and rapidly decreases when Re 〉 1. Electro-viscous effect on flow-induced electric field and flow velocity are very significant when the rate of the channel width to the thickness of electric double layer is small.     

Periodical streaming potential and electro-viscous effects in microchannel flow

This paper presents an analytical solution to periodical streaming potential,flow-induced electric field and velocity of periodical pressure-driven flows in twodimensional uniform microchannel based on the Poisson.Boltzmann equations for electric double layer and Navier-Stokes equation for liquid flow.Dimensional analysis indicates that electric-Viscous force depends on three factors:(1)Electric-viscous number representing a ratio between maximum of electric-viscous force and pressure gradient in a steady state,(2)profile function describing the distribution profile of electro-viscous forcein channel section,and(3)coupling coefficient reflecting behavior of amplitude damping and phase Offset of electro-viscous force.Analytical results indicate that flow-induced electric field and flow velocity depend on frequency Reynolds number(Re=wh2/v).Flow-induced electric field varies very slowly with Re when Re＜1.and rapidly decreases when Re＞1.Electro-viscous effect on flow-induced electric field and flow velocity are very significant when the rate of the channel width to the thickness of electric double layer is small.     

Utilizing phase retard integration method of flow birefringence to analyse the flow with symmetric plane

The formulas which are suitable to birefringent medium with symmetric plane are derived by means of phase retard integration. We have adopted this concept to the axisymmetric problems and deduced some useful formulas for these cases. As a practical application, the strain rate analysis of flow in a diverging or a converging vessel is illustrated at the end of this paper. The project supported by National Natural Science foundation of China