# Influence of Propulsion Type on the Stratified Near Wake of an Axisymmetric Self-Propelled Body

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## Abstract

**:**

## 1. Introduction

## 2. Approach

#### 2.1. Governing Equations

#### 2.2. Kinetic and Potential Energy

#### 2.3. Actuator-Line Model

#### 2.4. Iowa Body

#### 2.5. Iowa Body Propeller

#### 2.6. Computational Mesh

#### 2.7. Numerical Methods

#### 2.8. Initial and Boundary Conditions

#### 2.9. Flow Field Analysis

#### 2.10. Flow Coefficients and Case Studies

## 3. Results

#### 3.1. Near-Wake Transition

#### 3.2. Velocity Profiles

#### 3.3. Velocity and Temperature Fields in the Mixed-Patch

#### 3.3.1. Velocity Field

#### 3.3.2. Temperature Field

#### 3.3.3. Comparison to a Perfectly-Mixed Temperature Field

#### 3.4. Potential and Kinetic Energy Evolution

## 4. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## Abbreviations

AL | Actuator line |

DNS | Direct Numerical Simulation |

CRP | Contra-rotating propeller |

SOWFA | Simulator fOr Wind Farm Applications |

URANS | unsteady Reynolds-Averaged Navier–Stokes |

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**Figure 1.**Non-dimensional body force on mesh slice at propeller plane $|{f}_{p}|/\left({\rho}_{0}{R}_{p}\phantom{\rule{4pt}{0ex}}{\mathrm{rps}}^{2}\right)$ for the single-propeller case.

**Figure 4.**Flow visualization for x/L ≤ 1.5 using Q-criterion visualization non-dimensionalized as (L/U

_{0})

^{2}Q = 16.9 colored by U

_{x}/U

_{0}− 1 with vertical cutting plane through mesh.

**Figure 5.**Instantaneous (

**top**); and time-averaged (

**bottom**) velocity defect ${U}_{x}/{U}_{0}-1$ for the single propeller case.

**Figure 6.**Instantaneous (

**top**); and time-averaged (

**bottom**) velocity defect ${U}_{x}/{U}_{0}-1$ for the CRP case.

**Figure 7.**Circumferentially-averaged velocity defect ${U}_{x}/{U}_{0}-1$ profiles for each configuration at various distances downstream.

**Figure 8.**Circumferentially-averaged swirl velocity ${U}_{\theta}/{U}_{0}$ profiles for each configuration at various distances downstream.

**Figure 9.**Velocity defect ${U}_{x}/{U}_{0}-1$ profiles at $x/L=1.5$ for single propeller (

**a**) and CRP (

**b**) cases.

**Figure 10.**Swirl velocity ${U}_{\theta}/{U}_{0}$ profiles at $x/L=1.5$ for single propeller (

**a**) and CRP (

**b**) cases.

**Figure 15.**Integrated energy evolution downstream of the vehicle for each configuration, with x measured from the bow of the hull and ${x}^{\prime}$ measured from the stern.

Coefficient | Value | Coefficient | Value | Coefficient | Value |
---|---|---|---|---|---|

${a}_{0}$ | $9.998425\times {10}^{2}$ | ${b}_{0}$ | $8.2449\times {10}^{-1}$ | ${c}_{0}$ | $-5.7247\times {10}^{-3}$ |

${a}_{1}$ | $6.793952\times {10}^{-2}$ | ${b}_{1}$ | $-4.0899\times {10}^{-3}$ | ${c}_{1}$ | $1.0227\times {10}^{-4}$ |

${a}_{2}$ | $-9.095290\times {10}^{-3}$ | ${b}_{2}$ | $7.6438\times {10}^{-5}$ | ${c}_{2}$ | $-1.6546\times {10}^{-6}$ |

${a}_{3}$ | $1.001685\times {10}^{-4}$ | ${b}_{3}$ | $-8.2467\times {10}^{-7}$ | ${d}_{0}$ | $4.8314\times {10}^{-4}$ |

${a}_{4}$ | $-1.120083\times {10}^{-6}$ | ${b}_{4}$ | $5.3875\times {10}^{-9}$ | ||

${a}_{5}$ | $6.536332\times {10}^{-9}$ |

Feature | Value |
---|---|

$L/D$ | 10.90 |

$D/{D}_{p}$ | 1.369 |

${D}_{p}/{D}_{h}$ | 6.266 |

Hub location | $0.9688<x/L<0.9832$ |

Propeller location | $x/L=0.9755$ |

Number of blades | 3 |

Propeller hydrofoil | NACA 66-Modified |

Mesh Feature | Value |
---|---|

Boundary layer cells | $>20$ |

Near-wall mesh spacing | ${y}^{+}<100$ |

Propulsor and wake cells/${D}_{p}$ | 100 |

Wake region extends to | $x/L=1.6$ |

Total number of cells | $2\times {10}^{7}$ |

Maximum aspect ratio | $\mathrm{AR}<170$ |

Maximum non-orthogonality | $<{45}^{\circ}$ |

Maximum skewness | $<0.8$ |

Configuration | J | ${\mathit{C}}_{\mathit{T}}$ | ${\mathit{C}}_{\mathit{T}}^{*}$ | ${\mathit{C}}_{\mathit{Q}}$ | ${\mathit{F}}_{\mathit{T}}/{\mathit{F}}_{\mathit{D}}$ |
---|---|---|---|---|---|

Single | 0.86 | 0.047 | 0.084 | 0.011 | 0.99 |

CRP (fore) | 0.90 | 0.024 | 0.041 | 0.0071 | 0.50 |

CRP (aft) | 0.86 | 0.023 | 0.041 | 0.0072 | 0.50 |

Jet | - | - | 0.082 | 0 | 1.07 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Jones, M.C.; Paterson, E.G.
Influence of Propulsion Type on the Stratified Near Wake of an Axisymmetric Self-Propelled Body. *J. Mar. Sci. Eng.* **2018**, *6*, 46.
https://doi.org/10.3390/jmse6020046

**AMA Style**

Jones MC, Paterson EG.
Influence of Propulsion Type on the Stratified Near Wake of an Axisymmetric Self-Propelled Body. *Journal of Marine Science and Engineering*. 2018; 6(2):46.
https://doi.org/10.3390/jmse6020046

**Chicago/Turabian Style**

Jones, Matthew C., and Eric G. Paterson.
2018. "Influence of Propulsion Type on the Stratified Near Wake of an Axisymmetric Self-Propelled Body" *Journal of Marine Science and Engineering* 6, no. 2: 46.
https://doi.org/10.3390/jmse6020046