Normal stress measurements

An apparatus designed to measure the dynamic viscoelastic response of polymer melts is described. Dynamic elasticity (G) and viscosity () can be measured over a frequency range 10^–2-10^–3 Hz and at temperatures up to 350 °C. The sample under test is held in a cone and plate assembly. A small strain is introduced by driving the plate with a variable speed synchronous motor and off-centre cam at low frequencies and by an electromagnetic vibrator at high frequencies. The amplitudes of the cone and plate are detected using the optical lever principle and photocell strips. The phase difference between the cone and plate is measured from a recorder trace at low frequencies and by direct reading on a meter at high frequencies.Results are described of measurements on silicone fluids, and on commercial grades of polyethylene with different molecular weight distributions and degrees of branching.A discussion is given of the correlation between the dynamic viscosity measurements and those taken under steady-flow conditions.Paper presented at the Conference on Experimental Rheology, University of Bradford, April 17–19, 1968. — Original paper published in J. Sci. Instruments Series 2,1, 1102–1112 (1968).     

Normal stress measurements

A review of the methods for obtaining the normal stress differences in simple shear flow from force measurements on the walls of apparatus in which curvilinear shear flows are generated is given. Indirect methods, for example the flow birefringence method, are considered. Some new work on normal stress measurement using cone and plate, parallel plate pressure distribution and total thrust measurements in conjunction with flow birefringence methods are reviewed. The difficulties found in obtaining consistant results are discussed.Paper presented at the Conference on Experimental Rheology, University of Bradford, April 17–19, 1968. — Original paper published in Rheo. Acta,7, 368 (1968).     

Measurements and scaling of wall shear stress fluctuations

Measurements of velocity and wall shear stress fluctuations were made in an external turbulent boundary layer developed over a towed surface-piercing flat plate. An array of eight flush-mounted wall shear stress sensors was used to compute the space-time correlation function. A methodology for in situ calibration of the sensors for ship hydrodynamic applications is presented. The intensity of the wall shear stress fluctuations, τ _rms/τ _avg was measured as 0.25 and 0.36 for R _θ =3,150 and 2,160 respectively. The probability density is shown to exhibit positive skewness, and lack of flow reversals at the wall. Correlations between velocity and wall shear stress fluctuations are shown to collapse with outer boundary layer length and velocity scales, verifying the existence of large-scale coherent structures which convect and decay along the wall at an angle of inclination varying from 10 to 13° over the range of Reynolds numbers investigated. The wall shear stress convection velocity determined from narrow band correlation measurements is shown to scale with outer variables. The space-time correlation of the wall shear is shown to exhibit a well-defined convective ridge, and to decay 80% over approximately 3δ for R _θ =3,150. Published online: 7 November 2002     

On the tangential stress anomaly in the displacement discontinuity method

It is shown that the anomaly associated with the incorrect evaluation of tangential stresses in the displacement discontinuity (DD) method, commonly used to solve crack problems, is related to the order of singularity of the fundamental solutions of linear elasticity. It is established here that a minimum of linear variation of the shear DD distribution is needed to obtain the correct tangential stress jump across a crack. Alternatively, a correction term (‘patch’) that improves tangential stresses is derived. It is also shown that need for higher functionality is a fundamental requirement rather than a convenient artifice for obtaining better accuracy.     

Shear motions of elastic fluids for a given tangential stress

Stationary and nonstationary modes of elastic fluid motion for a given constant strain rate =const were studied under simple shear conditions, theoretically in [1, 2] as compared with experiment; time dependences of the normal and tangential stresses were examined for the emergence into stationary flow and their relaxation from steady flow. These results permitted a study of the relaxation characteristics of elastic fluids. However, no less interesting are the lagging (retardation) effects in elastic fluids, which can be studied in modes giving the shear stress ₁₂(). In this paper, the two most widespread shear modes in practice are examined theoretically and experimentally for a given ₁₂: the mode of arrival at the stationary flow from the state of rest for ₁₂=const and the mode of retardation (elastic recovery) from stationary flow. Theoretical computations are performed on a model describing large elastic strains. The experiment was performed on a concentrated polymer solution. Quantitative correspondence between theory and experiment is obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 9–13, July–August, 1976.     

Normal stress measurements on drag-reducing polymer solutions

Summary The elastic properties of very dilute solutions of a number of drag-reducing polymers differing either in chemical nature or molecular weight were investigated over a range of values of shear stress using the jet thrust method. Parallel drag reduction measurements were also made with the solutions. The results indicate a general relationship between the value of the first normal stress difference at the wall, (p ₁₁-p ₂₂, and the dragreducing ability.The data tends to confirm the generality of the correlation between the value of theWeissenberg number and the drag reduction reported byMetzner for a single polymer sample.     

Normal stress effects in aqueous detergent solutions

Summary The rheological properties of a typical viscous isotropic detergent solution were investigated in steady shearing flow. The aqueous solution contained 10% of a highly soluble anionic detergent and varying amounts of sodium nitrate to produce visco-elastic behaviour. Normal stress differences were measured in the concentric cylinder and in the cone-and-plate configuration. Although the sign of the normal stress difference (S ₁₁ –S ₂₂) is opposite to that found in most other materials, the liquid climbs up at the inner cylinder due to the contribution from (S ₂₂ –S ₃₃).

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Zusammenfassung Die rheologischen Eigenschaften einer typischen viskosen isotropen Detergentlösung wurden unter stetigen ScherverhÄltnissen untersucht. Die wÄssrige Lösung enthielt 10 % eines hochlöslichen anionischen Detergents und variierende Mengen an Natriumnitrat zur Erreichung eines viskoelastischen Verhaltens. Normalspannugsunterschiede wurden im konzentrischen Zylinder- und im Platte-Kegel-Viskosimeter gemessen. Obwohl die Normalspannungsdifferenz (S₁₁–S₂₂) ein entgegengesetztes Vorzeichen hat als bei den meisten anderen Stoffen gefunden wird, steigt die Flüssigkeit am inneren Zylinder empor infolge des Beitrags von (S₂₂–S₃₃).

     

Normal stress effect in dilute polymer solutions

Rheologica Acta - The non-linear, steady flow behavior of dilute solutions of poly ethylene oxide at high shear rates is experimentally studied. The shear stress-shear rate relations at low and...     

Normal stress effects in viscoelastic fluid lubrication

Non-Newtonian flow effects are evaluated in a slider-bearing configuration. The material model taken is that of the Coleman—Noll second-order fluid. An explicit result is given for the portion of the bearing load supported by the non-Newtonian normal stresses as well as that portion resulting from the usual lubrication theory (Newtonian effect). Particular attention is given to the non-Newtonian effect of a high-polymer additive applied to a Newtonian base stock. The non-Newtonian effect has a particular dependence on the bearing geometry as well as a dependence on the relaxation time of the addtive and the amount by which the additive increases the viscosity. The strength of the non-Newtonian effect is assessed in realistic conditions of bearing operation. We find that under certain conditions the non-Newtonian effect could provide a significant load-supporting capability. However, with slight changes in the conditions of the bearing operation, the non-Newtonian load support is negligible. These results are interpreted and qualified with respect to the limitations of the second-order theory, which does not include shear thinning effects.     

Stability of wave forms of motion of a viscous fluid layer under tangential stress

We study the stability of wave flow of a viscous incompressible fluid layer subjected to tangential stress and an inclined gravity force with respect to long-wave disturbances.An asymptotic solution is constructed for the equations of the disturbed motion and the problem is reduced to the study of a second-order ordinary differential equation. It is shown that after loss of stability by a Poiseuille flow the laminar nature of the flow is not destroyed, but the form of the free surface acquires a wave-like profile. The Poiseuille regime is stable for low Reynolds numbers. The critical Reynolds number for wave flow is found, and the stability and instability regions are determined.     

Normal and shear stress gages and rosettes for orthotropic composites

Stress gages, plane-shear gages, and three-element strain rosettes have long been used in experimental-mechanics investigations on isotropic materials. This paper generalizes these concepts for applications to fiber-reinforced composite materials. Also included for the first time are data-reduction equations whichexplicitly incorporate strain-gage transverse sensitivity.Paper was presented at 1985 SEM Spring Conference on Experimental Mechanics held in Las Vegas, NV on June 9–13, 1985.     

Inner-outer decomposition of wall shear stress fluctuations in turbulent channels

Fluctuating wall shear stress in turbulent channel flows is decomposed into small-scale and large-scale components. The large-scale fluctuating wall shear stress is computed as the footprints of the outer turbulent motions, and the small-scale one is obtained by subtracting the large-scale one from the total, which fully remove the outer influences. We show that the statistics of the small-scale fluctuating wall shear stress is Reynolds number independent at the friction Reynolds number larger than 1000, while which is Reynolds number dependent or the low-Reynolds-number effect exists at the friction Reynolds number smaller than 1000. Therefore, a critical Reynolds number that defines the emergence of universal small-scale fluctuating wall shear stress is proposed to be 1000. The total and large-scale fluctuating wall shear stress intensities approximately follow logarithmic-linear relationships with Reynolds number, and empirical fitting expressions are given in this work.     

Statistical properties of wall shear stress fluctuations in turbulent channel flows

Instantaneous velocity and wall shear stress measurements are conducted in a turbulent channel flow in the Kármán number range of Re_τ = 74–400. A one-dimensional LDA system is used to measure the streamwise velocity fluctuations, and an electrochemical technique is utilized to measure the instantaneous wall shear stress. For the latter, frequency response and nonuniform correction methods are used to provide an accurate, well-resolved wall statistics database. The Reynolds number dependency of the statistical wall quantities is carefully investigated. The corrected relative wall shear stress fluctuations fit well with the best DNS data available and meet the need for clarification of the small discrepancy observed in the literature between the experimental and numerical results of such quantities. Higher-order statistics of the wall shear stress, spectra, and the turbulence kinetic energy budget at the wall are also investigated. The present paper shows that the electrochemical technique is a powerful experimental method for hydrodynamic studies involving highly unsteady flows. The study brings with it important consequences, especially in the context of the current debate regarding the appropriate scaling as well as the validation of new predictive models of near-wall turbulence.     

筒仓泄料过程中阻塞现象的数值模拟

基于颗粒材料离散颗粒模型及颗粒流方案,通过数值试验研究了筒仓泄料过程中影响颗粒流发生阻塞的若干因素,给出了阻塞概率随筒仓底部开口半径及倾角、颗粒间摩擦系数及颗粒粒径分布的关系曲线.基于颗粒簇的概念,进一步研究了颗粒形状的影响,并对颗粒材料阻塞时的力链分布特征进行简要分析.