# A Numerical Performance Analysis of a Rim-Driven Turbine in Real Flow Conditions

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## Abstract

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## 1. Introduction

## 2. Numerical Methods

#### 2.1. General Features

#### 2.2. Turbine Model

#### 2.3. Computational Domain

#### 2.4. Boundary Conditions

#### 2.5. Mesh Generation

^{6}. The prism layers are placed on the rotor and duct surface with smooth transition normal to the walls. The first layer height satisfies ${\mathrm{y}}^{+}=1$ condition and 10 prism layers are placed. The mesh detail on the DT and RDT are shown in Figure 7. A mesh independence assessment of three sets of meshes on RDT at 1.56 m/s and $TSR$ = 4.0 is shown in Table 1, which is carried out by analyzing ${C}_{P}$ and ${C}_{T}$. With the refinement of the mesh, the deviation becomes much smaller. The set of 8.5 million is selected for the subsequent calculations due to the consideration of calculation accuracy and efficiency.

#### 2.6. Numerical Model Validation

## 3. Results and Discussion

#### 3.1. Power and Thrust

#### 3.2. Performance Fluctuation Characteristics

#### 3.3. Wake Characteristics

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 8.**Computational model validation with experimental data at different values of current velocity and $TSR$.

**Figure 9.**${C}_{P}$ and ${C}_{T}$ versus $TSR$ for the two configurations: (

**a**) ${C}_{P}$; (

**b**) ${C}_{T}$.

**Figure 10.**Time histories of ${C}_{P}$ and ${C}_{T}$ for the two configurations at different values of $TSR$: (

**a**) ${C}_{P}$ for DT; (

**b**) ${C}_{P}$ for RDT; (

**c**) ${C}_{T}$ for DT; (

**d**) ${C}_{T}$ for RDT.

**Figure 11.**Time histories of ${C}_{P}$ and ${C}_{T}$ for the two configurations at different values of $\gamma $: (

**a**) ${C}_{P}$ for DT; (

**b**) ${C}_{P}$ for RDT; (

**c**) ${C}_{T}$ for DT; (

**d**) ${C}_{T}$ for RDT.

**Figure 12.**Velocity component contours for the two configurations in the x-y plane of z/D = 0.1: (

**a**) axial velocity contours; (

**b**) tangential velocity contours; (

**c**) radial velocity contours.

**Figure 13.**Axial velocity contours for the two configurations in the central x-z plane: (

**a**) DT for $TSR$ = 3.0; (

**b**) RDT for $TSR$ = 3.0; (

**c**) DT for $TSR$ = 4.0; (

**d**) RDT for $TSR$ = 4.0; (

**e**) DT for $TSR$ = 5.0; (

**f**) RDT for $TSR$ = 5.0.

**Figure 14.**Profiles of mean streamwise velocity for $TSR$ = 3.0 at different streamwise locations in the central x-z plane: (

**a**) z/D = 0.5; (

**b**) z/D = 1.0; (

**c**) z/D = 3.0; (

**d**) z/D = 5.0.

**Figure 15.**Profiles of mean streamwise velocity for $TSR$ = 4.0 at different streamwise locations in the central x-z plane: (

**a**) z/D = 0.5; (

**b**) z/D = 1.0; (

**c**) z/D = 3.0; (

**d**) z/D = 5.0.

**Figure 16.**Profiles of mean streamwise velocity for $TSR$ = 5.0 at different streamwise locations in the central x-z plane: (

**a**) z/D = 0.5; (

**b**) z/D = 1.0; (

**c**) z/D = 3.0; (

**d**) z/D = 5.0.

**Figure 17.**Vorticity Iso-surfaces colored by velocity for the two configurations: (

**a**) DT for $TSR$ = 3.0; (

**b**) RDT for $TSR$ = 3.0; (

**c**) DT for $TSR$ = 4.0; (

**d**) RDT for $TSR$ = 4.0; (

**e**) DT for $TSR$ = 5.0; (

**f**) RDT for $TSR$ = 5.0.

**Figure 18.**Axial velocity contours for the two configurations in the central x-z plane: (

**a**) DT for $\gamma $ = 20°; (

**b**) RDT for $\gamma $ = 20°; (

**c**) DT for $\gamma $ = 40°; (

**d**) RDT for $\gamma $ = 40°; (

**e**) DT for $\gamma $ = 60°; (

**f**) RDT for $\gamma $ = 60°.

**Figure 19.**Profiles of mean streamwise velocity for $\gamma $ = 20° at different streamwise locations in the central x-z plane: (

**a**) z/D = 0.5; (

**b**) z/D = 1.0; (

**c**) z/D = 3.0; (

**d**) z/D = 5.0.

**Figure 20.**Profiles of mean streamwise velocity for $\gamma $ = 40° at different streamwise locations in the central x-z plane: (

**a**) z/D = 0.5; (

**b**) z/D = 1.0; (

**c**) z/D = 3.0; (

**d**) z/D = 5.0.

**Figure 21.**Profiles of mean streamwise velocity for $\gamma $ = 60° at different streamwise locations in the central x-z plane: (

**a**) z/D = 0.5; (

**b**) z/D = 1.0; (

**c**) z/D = 3.0; (

**d**) z/D = 5.0.

**Figure 22.**Vorticity Iso-surfaces colored by velocity for the two configurations: (

**a**) DT for $\gamma $ = 20°; (

**b**) RDT for $\gamma $ = 20°; (

**c**) DT for $\gamma $ = 40°; (

**d**) RDT for $\gamma $ = 40°; (

**e**) DT for $\gamma $ = 60°; (

**f**) RDT for $\gamma $ = 60°.

Mesh Density | Total Cells (Million) | ${\mathit{C}}_{\mathit{P}}$ | ${\mathit{C}}_{\mathit{T}}$ |
---|---|---|---|

Coarse | 6.5 | 0.4828 | 0.8439 |

Medium | 8.5 | 0.4835 | 0.8450 |

Fine | 10.5 | 0.4863 | 0.8452 |

Cases | $\mathbf{DT}\mathbf{at}\mathit{\gamma}$ = 0° | $\mathbf{RDT}\mathbf{at}\mathit{\gamma}$ = 0° | $\mathbf{DT}\mathbf{at}\mathit{\gamma}$ = 20° | $\mathbf{RDT}\mathbf{at}\mathit{\gamma}$ = 20° | $\mathbf{DT}\mathbf{at}\mathit{\gamma}$ = 40° | $\mathbf{RDT}\mathbf{at}\mathit{\gamma}$ = 40° | $\mathbf{DT}\mathbf{at}\mathit{\gamma}$ = 60° | $\mathbf{RDT}\mathbf{at}\mathit{\gamma}$ = 60° |
---|---|---|---|---|---|---|---|---|

${S}_{{C}_{P}\mathrm{max}}$ | 12.04 | 12.70 | 12.18 | 13.18 | 12.91 | 12.65 | 9.13 | 8.62 |

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**MDPI and ACS Style**

Song, K.; Kang, Y.
A Numerical Performance Analysis of a Rim-Driven Turbine in Real Flow Conditions. *J. Mar. Sci. Eng.* **2022**, *10*, 1185.
https://doi.org/10.3390/jmse10091185

**AMA Style**

Song K, Kang Y.
A Numerical Performance Analysis of a Rim-Driven Turbine in Real Flow Conditions. *Journal of Marine Science and Engineering*. 2022; 10(9):1185.
https://doi.org/10.3390/jmse10091185

**Chicago/Turabian Style**

Song, Ke, and Yuchi Kang.
2022. "A Numerical Performance Analysis of a Rim-Driven Turbine in Real Flow Conditions" *Journal of Marine Science and Engineering* 10, no. 9: 1185.
https://doi.org/10.3390/jmse10091185