### Abstract

In this short communication, we analyse the potential of the natural stress formulation (NSF) (i.e. aligning the stress basis along streamlines) for computing planar flows of an Oldroyd-B fluid around sharp corners. This is the first attempt to combine the NSF into a numerical strategy for solving a transient fluid flow problem considering the momentum equation in Navier–Stokes form (the elastic stress entering as a source term) and using the constitutive equations for natural stress variables. Preliminary results of the NSF are motivating in the sense that accuracy of the numerical solution for the extra stress tensor is improved near to the sharp corner. Comparison studies among the NSF and the Cartesian stress formulation (CSF) (i.e. using a fixed Cartesian stress basis) are conducted in a typical benchmark viscoelastic fluid flow involving a sharp corner: the 4: 1 contraction. The CSF needs a mesh approximately 10 times smaller to capture similar near singularity results to the NSF.

Language | English |
---|---|

Pages | 48-52 |

Number of pages | 5 |

Journal | Journal of Non-Newtonian Fluid Mechanics |

Volume | 249 |

DOIs | |

Status | Published - 1 Nov 2017 |

### Fingerprint

### Keywords

- Natural stress formulation
- Oldroyd-B model
- Planar contraction
- Sharp corner
- Unsteady viscoelastic flows

### ASJC Scopus subject areas

- Chemical Engineering(all)
- Materials Science(all)
- Condensed Matter Physics
- Mechanical Engineering
- Applied Mathematics

### Cite this

**Transient computations using the natural stress formulation for solving sharp corner flows.** / Evans, J. D.; Oishi, C. M.

Research output: Contribution to journal › Article

*Journal of Non-Newtonian Fluid Mechanics*, vol. 249, pp. 48-52. https://doi.org/10.1016/j.jnnfm.2017.08.012

}

TY - JOUR

T1 - Transient computations using the natural stress formulation for solving sharp corner flows

AU - Evans, J. D.

AU - Oishi, C. M.

PY - 2017/11/1

Y1 - 2017/11/1

N2 - In this short communication, we analyse the potential of the natural stress formulation (NSF) (i.e. aligning the stress basis along streamlines) for computing planar flows of an Oldroyd-B fluid around sharp corners. This is the first attempt to combine the NSF into a numerical strategy for solving a transient fluid flow problem considering the momentum equation in Navier–Stokes form (the elastic stress entering as a source term) and using the constitutive equations for natural stress variables. Preliminary results of the NSF are motivating in the sense that accuracy of the numerical solution for the extra stress tensor is improved near to the sharp corner. Comparison studies among the NSF and the Cartesian stress formulation (CSF) (i.e. using a fixed Cartesian stress basis) are conducted in a typical benchmark viscoelastic fluid flow involving a sharp corner: the 4: 1 contraction. The CSF needs a mesh approximately 10 times smaller to capture similar near singularity results to the NSF.

AB - In this short communication, we analyse the potential of the natural stress formulation (NSF) (i.e. aligning the stress basis along streamlines) for computing planar flows of an Oldroyd-B fluid around sharp corners. This is the first attempt to combine the NSF into a numerical strategy for solving a transient fluid flow problem considering the momentum equation in Navier–Stokes form (the elastic stress entering as a source term) and using the constitutive equations for natural stress variables. Preliminary results of the NSF are motivating in the sense that accuracy of the numerical solution for the extra stress tensor is improved near to the sharp corner. Comparison studies among the NSF and the Cartesian stress formulation (CSF) (i.e. using a fixed Cartesian stress basis) are conducted in a typical benchmark viscoelastic fluid flow involving a sharp corner: the 4: 1 contraction. The CSF needs a mesh approximately 10 times smaller to capture similar near singularity results to the NSF.

KW - Natural stress formulation

KW - Oldroyd-B model

KW - Planar contraction

KW - Sharp corner

KW - Unsteady viscoelastic flows

UR - http://www.scopus.com/inward/record.url?scp=85030109989&partnerID=8YFLogxK

UR - http://dx.doi.org/10.1016/j.jnnfm.2017.08.012

U2 - 10.1016/j.jnnfm.2017.08.012

DO - 10.1016/j.jnnfm.2017.08.012

M3 - Article

VL - 249

SP - 48

EP - 52

JO - Journal of Non-Newtonian Fluid Mechanics

T2 - Journal of Non-Newtonian Fluid Mechanics

JF - Journal of Non-Newtonian Fluid Mechanics

SN - 0377-0257

ER -