Photoviscoelastic behavior and residual thermal birefringence in optical-grade polycarbonates

The stress-optical coefficient functions of two optical-grade polycarbonates (PCs) have been obtained by simultaneous measurements of the relaxation modulus and strain-optical coefficient functions. Nonlinear behavior of the relaxation modulus and strain-optical coefficient was observed at small strains at room temperature. Comparison of these functions in the linear region with those of a commercial grade PC was made. These functions have been incorporated to linear viscoelastic and photoviscoelastic constitutive equations to calculate residual thermal birefringence in freely quenched PC plates. The numerical results have been compared with the measurements indicating a fair agreement between them.     

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)     

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     

Two-color rotary modulated flow birefringence

A method is described that solves the problem of determining the correct birefringence and orientation angle of samples having multiple orders of retardation. The approach simultaneously uses two wavelengths of light combined with modulation of the polarization vector using a high-speed rotating half waveplate. The simultaneous application of two wavelengths is possible with the use of an achromatic waveplate. The technique is demonstrated by performing start-up Couette flow experiments on a concentrated polystyrene solution that produced multiple orders in retardation.     

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.     

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.     

Simultaneous measurement of transient stress and flow birefringence in one-sided compression (biaxial extension) of a polymer melt

Summary Investigation of time dependent behaviour of a polystyrene melt is carried out with the aid of a new apparatus for biaxial extension. Use is made of the method of two impinging fluid streams guided by lubricated trumpet shaped metal walls. The flow birefringence is measured in the plane of symmetry and, at the same time, the force is measured which tends to separate the trumpets. The linear stress-optical relation turns out to be valid in this new flow geometry. An accurate value for the stress-optical coefficient can be determined from the relaxation experiments. The stress build-up as calculated from the optical measurements, is compared with the pertinent result of the theory of linear viscoelasticity. For the desired interconversion of dynamic moduli use is made of the approximation by Schwarzl and Struik. The steady state measurements are checked by the results of the non-linear model of Acierno et al.With 16 figures and 2 tables     

An impedance method for the measurement of liquid hold-up in two-phase flow

A liquid hold-up gauge based on the measurement of the electrical impedance has been developed for application in gas-liquid pipe flow. The gauge consists of two ring electrodes mounted flush to the pipe wall. The impedance (capacitance or conductance) seen by the electrodes depends on the distance between them and on the liquid hold-up. For distances above three tube diameters, the impedance is independent of the flow configuration for all separated flow patterns and, with good approximation, also for intermittent flows. Moreover, capacitance or conductance are linearly related to the liquid hold-up. The impedance under bubble flow conditions closely follows the theoretical predictions due to Maxwell. Also for the other flow configurations (annular, stratified, intermittent) the results of static and/or dynamic calibration agree closely with theoretical models.     

An improved analysis method for cross-wire signals obtained in supersonic flow

The use of crossed-wire probes to measure simultaneously the instantaneous stream-wise and normal velocities in supersonic turbulent flows has enabled researchers to investigate the characteristics of organized structures more fully. This paper examines both the practical aspects of using crossed-wire probes in supersonic flow and several methods of converting the resulting signals into useful quantities. Three small perturbation methods are compared in a Mach 2.9 boundary layer, and it is shown that the higher-order terms neglected in the traditional first-order perturbation analysis can alter the instantaneous velocity signals. This is particularly true for regions of intense streamwise mass flux fluctuations. A fourth method, which calculates the instantaneous flow angle directly from the inclined-wire formulation of King's Law, is introduced and discussed. While this method is potentially more accurate than the small perturbation techniques, it is more sensitive to parameter drift during the period between the wire calibration and actual testing.     

An improved method for calculating flow past flapping and hovering airfoils

A method is reported here for calculating unsteady aerodynamics of hovering and flapping airfoil for two-dimensional flow via the following improved methodologies: (a) a correct formulation of the problem using stream function (ψ) and vorticity (ω) as dependent variables; (b) calculating loads and moment by a new method to solve the governing pressure Poisson equation (PPE) in a truncated part of the computational domain on a nonstaggered grid; (c) accurate solution using high accuracy compact difference scheme for the vorticity transport equation (VTE) and (d) accelerating the computations by using a high-order filter after each time step of integration. These have been used to solve Navier–Stokes equation for flow past flapping and hovering NACA 0014 and 0015 airfoils at typical Reynolds numbers relevant to the study of unsteady aerodynamics of micro air vehicle (MAV) and insect/bird flight.     

An improved Vorticity–Potential method for three-dimensional duct flow simulations

An improved Vorticity–Potential method is presented for the numerical solutions of three-dimensional duct flow problems. The solution procedure requires first a potential solution. Then the viscous effects are added through the vorticity transport equation. By using body-fitted coordinates, the method is applied to simulate the incompressible laminar flows in a square elbow and in a twisted square elbow.     

An improved unstructured WENO method for compressible multi‐fluids flow

An improved high‐order accurate WENO finite volume method based on unstructured grids for compressible multi‐fluids flow is proposed in this paper. The third‐order accuracy WENO finite volume method based on triangle cell is used to discretize the governing equations. To have higher order of accuracy, the P1 polynomial is reconstructed firstly. After that, the P2 polynomial is reconstructed from the combination of the P1. The reconstructed coefficients are calculated by analytical form of inverse matrix rather than the numerical inversion. This greatly improved the efficiency and the robustness. Four examples are presented to examine this algorithm. Numerical results show that there is no spurious oscillation of velocity and pressure across the interface and high‐order accurate result can be achieved. Copyright © 2016 John Wiley & Sons, Ltd.     

Simultaneous measurements of velocity and stress distributions in polyisobutylenes using laser-Doppler velocimetry and flow induced birefringence

An experimental device was set up for the synchronous measurement of velocities and stresses in polyisobutylenes using laser-Doppler velocimetry (LDV) and the two-colour flow-induced birefringence method (FIB). The materials investigated are three low molecular polyisobutylenes. Velocity (LDV) and stress (FIB) measurements are performed in the flow entrance region and inside a slit die with a contraction ratio of 1:10. The behaviour of the polyisobutylenes is Newtonian under the flow conditions applied. Therefore, the stresses inside the fluids can be calculated and compared to the stresses experimentally determined. A good agreement in shear and elongational flows was found between the calculated (LDV) and directly measured stresses (FIB). This result demonstrates the applicability of the experimental setup as an optical rheometer that can preferentially be used to measure elongational properties of low viscous fluids.

一种改进的姿态匹配船体变形测量方法

针对船体变形测量系统中模型不确定以及未知噪声影响导致的误差问题,分析并推导了模型偏差对滤波估计的影响,提出一种基于姿态匹配的强跟踪最大互相关熵卡尔曼滤波(STMCKF)算法,用于船体变形估计。该算法采用姿态匹配,基于两套惯性系统的姿态信息确立滤波观测量并建立线性量测方程,通过自适应在线调整多个渐消因子对多个数据通道进行渐消,减小模型失配导致的误差,并设计基于最大互相关熵准则为最优准则的滤波算法,减小量测过程中受到的非高斯噪声产生的误差。最后,在模型不匹配及噪声不确定的条件下进行了仿真验证。仿真结果表明,与传统卡尔曼滤波相比,变形估计精度提高10%～30%,提高了系统鲁棒性和环境适应性。     

An improved ghost‐cell immersed boundary method for compressible flow simulations

This study presents an improved ghost‐cell immersed boundary approach to represent a solid body in compressible flow simulations. In contrast to the commonly used approaches, in the present work, ghost cells are mirrored through the boundary described using a level‐set method to farther image points, incorporating a higher‐order extra/interpolation scheme for the ghost‐cell values. A sensor is introduced to deal with image points near the discontinuities in the flow field. Adaptive mesh refinement is used to improve the representation of the geometry efficiently in the Cartesian grid system. The improved ghost‐cell method is validated against four test cases: (a) double Mach reflections on a ramp, (b) smooth Prandtl–Meyer expansion flows, (c) supersonic flows in a wind tunnel with a forward‐facing step, and (d) supersonic flows over a circular cylinder. It is demonstrated that the improved ghost‐cell method can reach the accuracy of second order in L¹ norm and higher than first order in L^∞ norm. Direct comparisons against the cut‐cell method demonstrate that the improved ghost‐cell method is almost equally accurate with better efficiency for boundary representation in high‐fidelity compressible flow simulations. Copyright © 2016 John Wiley & Sons, Ltd.     

Simultaneous stress and birefringence measurements during uniaxial elongation of polystyrene melts with narrow molecular weight distribution

Tensile stress and flow-induced birefringence have been measured during uniaxial elongation at a constant strain rate of two polystyrene melts with narrow molecular weight distribution. For both melts, the stress- optical rule (SOR) is found to be fulfilled upto a critical stress of 2.7 MPa, independent of strain rate and temperature. Estimation of the Rouse times of the melts, from both the zero-shear viscosity and the dynamic-shear moduli at high frequency, shows that the violation of the SOR occurs when the strain rate multiplied by the Rouse time of the melt exceeds by approximately 3. The presented results indicate that in contrast to current predictions of molecular theories, the regime of extensional thinning observed by Bach et al. (2003) extends well beyond the onset of failure of the SOR, and therefore the onset of chain stretch in the non-Gaussian regime.

New apparatus for the simultaneous measurement of stresses and flow birefringence in biaxial extension of polymer melts

Summary A new apparatus is described for the measurement of the viscosity of polymer melts in biaxial extension. Use is made of the method of two impinging fluid streams. The mentioned streams are guided by lubricated trumpet shaped metal walls. The force is measured which tends to separate the trumpets. At the same time, the flow birefringence is measured in the plane of symmetry, which contains the stagnation point. The linear stress-optical relation, which is well-known from shear experiments, turns out to be valid also in the new flow geometry, at least up to the deformation rates applied. Results of the steady state measurements carried out on a polystyrene melt are evaluated. Suggestions for a better performance of the mechanical measurements are given.

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Zusammenfassung Ein neuer Apparat zur Messung der Dehnviskosität von polymeren Schmelzen unter biaxialer Dehnung wird beschrieben. Hierfür wird die Methode des Aufeinanderprallens entgegengesetzt gerichteter Ströme verwendet. Die genannten Ströme werden durch geschmierte trompetenförmige Bohrungen herangeführt. Es wird die Kraft gemessen, welche die beiden Trompeten auseinanderzudrücken sucht. Gleichzeitig wird die Strömungsdoppelbrechung in der Symmetrieebene gemessen, die den Staupunkt enthält. Die lineare spannungsoptische Regel, die bei Scherexperimenten wohlbekannt ist, scheint auch für die neue Strömungsgeometrie zu gelten, zumindest im Bereich der angewandten Deformationsgeschwindigkeiten. Ergebnisse, wie sie im stationären Strömungszustand bei einer Polystyrol-Schmelze erhalten wurden, werden ausgewertet. Vorschläge zur besseren Ausführung der mechanischen Messungen werden gemacht.

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With 11 figures     

Flow birefringence study of sharkskin and stress relaxation in polybutadiene melts

In this paper we report rheo-optical and rheological observations made through a transparent slit die attached to a capillary rheometer. We find that the flow birefringence signal oscillates periodically near the die exit when sharkskin-like extrudate distortion is present. In contrast, steady behavior is observed in the die inland region. Specifically, the flow birefringence varies at the die exit with a period identical to that measured directly from the sharkskin extrudate. We also show that the exit flow instability leading to sharkskin can be observed directly through cross-polarizers in terms of the temporal change of the retardation order. We demonstrate that the same kind of interfacial flow instability can occur at a boundary discontinuity within the die land where the upper portion of a clean die wall meets the lower portion of a polysiloxane-coated die wall. Finally, stress relaxation upon the cessation of the slit die flow of two polybutadiene melts is studied through time-dependent flow birefringence measurements. The stress relaxation is then correlated with sharkskin time scales to describe the role of relaxation in sharkskin ridge formation. Received: 8 February 1999 Accepted: 28 July 1999