Predicting laminar–turbulent transition in Poiseuille pipe flow for non-Newtonian fluids

We present a new phenomenological approach for quantifying laminar–turbulent transition in pipe flow. This criterion is based on averaging a local Reynolds number to give ReG. Our localised parameter shows strong radial variations that are maximal at approximately the radial positions where puffs first appear during the first stages of turbulent transition. We present comparative data for experiments conducted with Glycerin, Xanthan and Carbopol solutions, each of which serves to demonstrate the validity of our approach.

[1]  J. Peixinho,et al.  Heat transfer of a non-Newtonian fluid (Carbopol aqueous solution) in transitional pipe flow , 2008 .

[2]  T. Mullin,et al.  Transition to turbulence in constant-mass-flux pipe flow , 1995, Journal of Fluid Mechanics.

[3]  A. B. Metzner,et al.  Flow of non‐newtonian fluids—correlation of the laminar, transition, and turbulent‐flow regions , 1955 .

[4]  G. Tripathi,et al.  Transition from laminar to turbulent flow of purely viscous non-Newtonian fluids in tubes , 1971 .

[5]  N. Ryan,et al.  Transistion from laminar to turbulent flow in pipes , 1959 .

[6]  H. Wedin,et al.  Exact coherent structures in pipe flow: travelling wave solutions , 2003, Journal of Fluid Mechanics.

[7]  Richard W. Hanks.  The laminar-turbulent transition for fluids with a yield stress , 1963 .

[8]  I. Frigaard,et al.  On three-dimensional linear stability of Poiseuille flow of Bingham fluids , 2003 .

[9]  F. Nieuwstadt,et al.  Laminar–turbulent transition in pipe flow for Newtonian and non-Newtonian fluids , 1998, Journal of Fluid Mechanics.

[10]  R. W. Hanks.  On the Flow of Bingham Plastic Slurries in Pipes and Between Parallel Plates , 1967 .

[11]  R. W. Hanks.  A theory of laminar flow stability , 1969 .

[12]  Murray Rudman,et al.  Non-Newtonian Turbulent and Transitional Pipe Flow , 2002 .

[13]  A. B. Metzner,et al.  Turbulent flow of non‐newtonian systems , 1959 .

[14]  B. Hof.  Transition to Turbulence in Pipe Flow , 2022, Annual Review of Fluid Mechanics.

[15]  Musaed N.J. Al-Awad,et al.  A new laminar-to-turbulent transition criterion for yield-pseudoplastic fluids , 1998 .

[16]  Ian A. Frigaard,et al.  Nonlinear stability of Poiseuille flow of a Bingham fluid: theoretical results and comparison with phenomenological criteria , 2001 .

[17]  C. Nouar,et al.  Transitional flow of a yield-stress fluid in a pipe: evidence of a robust coherent structure. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  P. Slatter,et al.  Laminar/turbulent transition in large pipes , 2000 .

[19]  Murray Rudman,et al.  Turbulent pipe flow of shear-thinning fluids , 2004 .

[20]  Fernando T. Pinho,et al.  Flow of non-newtonian fluids in a pipe , 1990 .

[21]  R. W. Hanks.  The laminar‐turbulent transition for flow in pipes, concentric annuli, and parallel plates , 1963 .

[22]  Robert J. Poole,et al.  Observations of asymmetrical flow behaviour in transitional pipe flow of yield-stress and other shear-thinning liquids , 2005 .

[23]  Ian A. Frigaard,et al.  On the stability of Poiseuille flow of a Bingham fluid , 1994, Journal of Fluid Mechanics.

[24]  Khalid Aziz,et al.  The Flow Of Complex Mixtures In Pipes , 2021 .

[25]  Bengt O. A. Hedstrm.  Flow of Plastic Materials in Pipes , 1952 .

[26]  C. H. Chou,et al.  Non-Newtonian flow in ducts of arbitrary cross-sectional shape , 1966 .

[27]  J. W. Hiby.  The Flow of Complex Mixtures in Pipes. Von G. W. Govier und K. Aziz. Van Nostrand Reinhold Comp., New York‐London 1972. 1. Aufl., XLVII, 792 S., zahlr. Abb., Ln. £ 17.65 , 1973 .

[28]  Kenneth C. Wilson,et al.  A new analysis of the turbulent flow of non‐newtonian fluids , 1985 .

[29]  T. Burghelea,et al.  Observation of laminar–turbulent transition of a yield stress fluid in Hagen–Poiseuille flow , 2009, Journal of Fluid Mechanics.

[30]  Robert C. Armstrong,et al.  Dynamics of polymeric liquids: Fluid mechanics , 1987 .

[31]  K. C. Wilson,et al.  Analytic Model of Laminar‐Turbulent Transition for Bingham Plastics , 2008 .

[32]  S. Park,et al.  Rheological properties and microstructures of Carbopol gel network system , 2003 .

[33]  Robert W. Serth,et al.  Generalized hydraulic calculation method using Rational polynomial model , 2005 .

[34]  Kenneth C. Wilson,et al.  New analysis of non-newtonian turbulent flowndashyield-power-law fluids , 1987 .

[35]  R. Kerswell,et al.  Recent progress in understanding the transition to turbulence in a pipe , 2005 .

[36]  R. Hayes,et al.  Properties of Carbopol solutions as models for yield-stress fluids , 2002 .

[37]  Richard W. Hanks,et al.  Theoretical analysis of the turbulent flow of non‐newtonian slurries in pipes , 1971 .

[38]  J. Peixinho,et al.  Laminar transitional and turbulent flow of yield stress fluid in a pipe , 2005 .