Mechanics of Time-Dependent Materials

, Volume 21, Issue 3, pp 455–479 | Cite as

Hyperbolic contraction measuring systems for extensional flow

  • M. Nyström
  • H. R. Tamaddon Jahromi
  • M. Stading
  • M. F. WebsterEmail author


In this paper an experimental method for extensional measurements on medium viscosity fluids in contraction flow is evaluated through numerical simulations and experimental measurements. This measuring technique measures the pressure drop over a hyperbolic contraction, caused by fluid extension and fluid shear, where the extensional component is assumed to dominate. The present evaluative work advances our previous studies on this experimental method by introducing several contraction ratios and addressing different constitutive models of varying shear and extensional response. The constitutive models included are those of the constant viscosity Oldroyd-B and FENE-CR models, and the shear-thinning LPTT model. Examining the results, the impact of shear and first normal stress difference on the measured pressure drop are studied through numerical pressure drop predictions. In addition, stream function patterns are investigated to detect vortex development and influence of contraction ratio. The numerical predictions are further related to experimental measurements for the flow through a 15:1 contraction ratio with three different test fluids. The measured pressure drops are observed to exhibit the same trends as predicted in the numerical simulations, offering close correlation and tight predictive windows for experimental data capture. This result has demonstrated that the hyperbolic contraction flow is well able to detect such elastic fluid properties and that this is matched by numerical predictions in evaluation of their flow response. The hyperbolical contraction flow technique is commended for its distinct benefits: it is straightforward and simple to perform, the Hencky strain can be set by changing contraction ratio, non-homogeneous fluids can be tested, and one can directly determine the degree of elastic fluid behaviour. Based on matching of viscometric extensional viscosity response for FENE-CR and LPTT models, a decline is predicted in pressure drop for the shear-thinning LPTT model. This would indicate a modest impact of shear in the flow since such a pressure drop decline is relatively small. It is particularly noteworthy that the increase in pressure drop gathered from the experimental measurements is relatively high despite the low Deborah number range explored.


Hyperbolic contraction Pressure-drop Viscoelastic fluid Boger fluid Extensional flow Axisymmetric contraction–expansion 


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Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  • M. Nyström
    • 1
  • H. R. Tamaddon Jahromi
    • 2
  • M. Stading
    • 1
    • 3
  • M. F. Webster
    • 2
    Email author
  1. 1.Food and BioscienceSP—Technical Research Institute of SwedenGöteborgSweden
  2. 2.Institute of Non-Newtonian Fluid Mechanics, College of EngineeringSwansea UniversitySwanseaUK
  3. 3.Department of Materials and Manufacturing TechnologyChalmers University of TechnologyGöteborgSweden

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