# Response of Viscoelastic Turbulent Pipeflow Past Square Bar Roughness: The Effect on Mean Flow

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## Abstract

**:**

## 1. Introduction

## 2. Problem Description

**tr**(${\mathbf{\tau}}_{p}$) is the trace of the polymer stress tensor, and $\stackrel{\nabla}{{\mathbf{\tau}}_{\mathit{pk}}}$ is the upper convected derivative given as

## 3. Results and Discussion

#### 3.1. Flow Response

#### 3.2. Flow Recovery

#### 3.3. Distribution of Pressure and Wall Shear Stresses

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Comparison of the mean axial velocity profiles ($\overline{u}/{U}_{b}$) with the experimental study of Shaban et al. (2018) [29].

**Figure 4.**Streamline plot of the (

**a**) Newtonian fluid and (

**b**) viscoelastic fluid flow past a roughness element of bar height $h/D=0.05$.

**Figure 5.**Streamline plot of the (

**a**) Newtonian fluid and (

**b**) viscoelastic fluid flow past a roughness element of bar height $h/D=0.1$.

**Figure 6.**Mean axial velocity profiles ($\overline{u}/{U}_{b}$) at different axial locations ($x/h=60,80$ and 100) for $h/D=0.05$.

**Figure 7.**Mean axial velocity profiles ($\overline{u}/{U}_{b}$) at different axial locations ($x/h=60,80$ and 100) for $h/D=0.1$.

**Figure 8.**Mean pressure coefficient profile ($\overline{{C}_{p}}$) on the pipe wall behind both bar heights at $x/h=$ 0–50.

**Figure 9.**Mean pressure coefficient profile ($\overline{{C}_{p}}$) along the roughness element upstream and downstream surfaces.

**Figure 10.**Mean pressure coefficient profile ($\overline{{C}_{p}}$) along the top surface of the roughness element.

**Figure 11.**Wall shear stress distribution ($\overline{{C}_{f}}$) along the top surface of the roughness elements.

Case | $\mathit{x}/\mathit{D}\mathbf{=}$ | 1 | 2 | 5 | 8 |
---|---|---|---|---|---|

Current Case | $2.06$ | $2.27$ | $2.90$ | $3.54$ | |

Hemmati et al. (2018) [47] | $1.85$ | $2.59$ | $3.24$ | $3.97$ | |

Ashrafian et al. (2004) [48] | ≈3.2 | − | − | − | |

Dubief et al. (2013) [25] | ≈2.3 | − | − | − |

Parameter | Value |
---|---|

Extensibility of the polymer, ${L}^{2}$ | 200 |

Ratio of solvent to zero-shear viscosity, $\beta $ | $0.22$ |

Polymer relations time, $\lambda $ (s) | $0.023$ |

Reynolds number, $R{e}_{D}$ | 5000 |

Frictional Reynolds number, $R{e}_{\tau}$ | 384 |

**Table 3.**The mean recirculation length ($\overline{{L}_{r}}/h$) for Newtonian and non-Newtonian flows over roughness elements.

Study | $\mathit{h}/\mathit{D}$ | $\overline{{\mathit{L}}_{\mathit{r}}}/\mathit{h}$ | $\mathbf{\Delta}\overline{{\mathit{L}}_{\mathit{r}}}(\%)$ |
---|---|---|---|

Newtonian | $0.05$ | $23.28$ | − |

Viscoelastic | $0.05$ | $6.28$ | 73 |

Newtonian | $0.1$ | $34.18$ | − |

Viscoelastic | $0.1$ | $17.18$ | $49.74$ |

**Table 4.**The recovery locations compared between Newtonian and viscoelastic flows, for both roughness heights.

Study | $\mathit{h}/\mathit{D}$ | ${\mathit{X}}_{\mathit{r}}/\mathit{h}$ | $\mathbf{\Delta}{\mathit{X}}_{\mathit{r}}(\%)$ |
---|---|---|---|

Newtonian | $0.05$ | 350 | − |

Viscoelastic | $0.05$ | 100 | 71 |

Newtonian | $0.1$ | 200 | − |

Viscoelastic | $0.1$ | 60 | 70 |

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**MDPI and ACS Style**

Goswami, S.; Hemmati, A.
Response of Viscoelastic Turbulent Pipeflow Past Square Bar Roughness: The Effect on Mean Flow. *Computation* **2021**, *9*, 85.
https://doi.org/10.3390/computation9080085

**AMA Style**

Goswami S, Hemmati A.
Response of Viscoelastic Turbulent Pipeflow Past Square Bar Roughness: The Effect on Mean Flow. *Computation*. 2021; 9(8):85.
https://doi.org/10.3390/computation9080085

**Chicago/Turabian Style**

Goswami, Shubham, and Arman Hemmati.
2021. "Response of Viscoelastic Turbulent Pipeflow Past Square Bar Roughness: The Effect on Mean Flow" *Computation* 9, no. 8: 85.
https://doi.org/10.3390/computation9080085