# Study of Combustor–Turbine Interactions by Performing Coupled and Decoupled Hybrid RANS-LES Simulations under Representative Engine-like Conditions

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## Abstract

**:**

## 1. Introduction

## 2. Proper Orthogonal Decomposition

## 3. Combustion Model

## 4. Turbulence Model

## 5. Computational Model

#### 5.1. Combustor-S1N Case

#### 5.2. S1N Case

- Firstly, the recorded snapshots are employed to recreate realistic and as representative as possible unsteady boundary conditions without any further post-processing operation.
- Then, the POD technique is applied, taking into account three different POD modes:
- −
- The first thirty POD modes are identified and imposed at the S1N inlet. They represent approximately 80% of the energy with respect to the fully integrated SBES simulation, assumed as reference. It is important to point out that POD is applied individually on all the quantities prescribed at the S1N inlet as mentioned above.
- −
- The first ten POD modes are identified and imposed at the S1N inlet. They represent approximately 50% of the energy.
- −
- The first five POD modes are identified and imposed at the S1N inlet. They represent approximately 30% of the energy.

- Finally, a further SBES analysis has been included in this work, imposing as inlet boundary conditions two-dimensional maps by time-averaging the unsteady boundary conditions prescribed at the previously described S1N SBES calculations. This simulation can be considered as the application of the standard industrial practice in the case of an unsteady SBES calculation.

## 6. Operating Conditions

## 7. Results

#### 7.1. Analysis of the Application of Time-Varying Boundary Conditions at S1N Inlet

_{x}, RMS U

_{y}, RMS U

_{z}, and RMS T

_{t}are presented in Figure 7 for S1N SBES and S1N timeavg calculations, then compared with SBES CC+S1N, selected as a reference.

_{x}, RMS U

_{y}, and RMS U

_{z}, it is clear that the SBES S1N results fall very close to those from SBES CC+S1N. This confirms that the applied time-varying boundary conditions are able to successfully replicate the turbulence kinetic energy at the inlet of the stator, contrary to what happens with constant boundary conditions (SBES timeavg). Similar considerations can also be made by looking at the RMS T

_{t}results. It is, therefore, possible to conclude that the time-varying boundary conditions, applied in the manner described above, are able to satisfactorily reproduce the fluctuations of the velocity and temperature fields typical of the integrated simulation. In order to quantify the similarities between SBES CC+S1N and SBES S1N, the velocity components and their respective RMS values, the normalized total temperature, and the total temperature RMS values are reported in Table 3 by performing a spatial averaging at plane 39.5. The total temperature was normalized as follows:

_{z}. Since the obtained quantities are strictly related to the imposed inlet boundary conditions for the SBES S1N case, this confirms once again that this set of boundary conditions is able to reproduce the flow field characteristics of SBES CC+S1N in a realistic and representative way.

#### 7.2. Pod Sensitivity Analysis

#### 7.3. Interpretation of the POD Modes

_{x}, RMS U

_{y}, and RMS U

_{z}2D contours at plane 39.5, reported in Figure 7, representing the three components of the turbulent kinetic energy. Analogously, Figure 13 reports the most relevant information for the normalized total temperature, according to Equation (15), in terms of both the spatial and temporal modes for the first three coherent structures. Furthermore, in this case, in order to better quantify the results, the minimum and maximum distortions of the ${T}_{t,nd}$ field are reported with respect to the time-averaged field.

#### 7.4. Analysis of the Plane Inlet Conditions

#### 7.5. Airfoil Loads and Normalized Temperature Distributions along the Vane

#### 7.6. Analysis of the Plane Outlet Conditions

## 8. Conclusions

_{x}, RMS U

_{y}, RMS U

_{z}, and RMS T

_{t}for S1N SBES and S1N timeavg calculations are compared with SBES CC+S1N, selected as a reference. Looking at the results, it is possible to conclude that the applied time-varying boundary conditions are able to successfully replicate the turbulence kinetic energy at the inlet of the stator, contrary to what happens with constant boundary conditions (SBES timeavg).

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

C2+ | Hydrocarbons with two or more carbon atoms |

CDC | Compressor discharge chamber |

CC | Combustion chamber |

CFD | Computational fluid dynamics |

CFL | Courant–Friedrichs–Lewy |

FGM | Flamelet-generated manifolds |

DES | Detached eddy simulation |

FETT | First engine to test |

FTT | Flow Through Time |

GT | Gas turbine |

HPT | High-pressure turbine |

LE | Leading edge |

LES | Large-eddy simulation |

NGV | Nozzle guide vane |

Probability density function | |

POD | Proper orthogonal decomposition |

PODFS | Proper orthogonal decomposition and Fourier series |

PS | Pressure side |

RANS | Reynolds-averaged Navier–Stokes |

RQL | Rich quench lean |

SAS | Scale-adaptive simulation |

SBES | Stress-blended eddy simulation |

SGS | Sub-grid scale |

SS | Suction side |

SST | Shear stress transport |

S1N | First-stage nozzle |

TNH | Normalized high-pressure turbine speed |

TNL | Normalized low-pressure turbine speed |

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**Figure 1.**Schematic representation of data-driven modal analysis. (©2023 Baker Hughes Company—All rights reserved).

**Figure 2.**(

**a**) ${S}_{c}(a,\psi )$, (

**b**) ${S}_{c}(Z,a)$. (©2023 Baker Hughes Company—All rights reserved).

**Figure 3.**NOVA LT16© single sector geometry with detailed view of the simplified first-stage nozzle and platforms. (©2023 Baker Hughes Company—All rights reserved).

**Figure 4.**Mesh resolution inside the primary zone of the combustor (

**left**) and the first-stage nozzle (

**right**). (©2023 Baker Hughes Company—All rights reserved).

**Figure 6.**Visualization of two different instants of total temperature recorded at the interface plane between the combustor and turbine at (

**a**) the instant ${t}_{1}$ and (

**b**) the instant ${t}_{2}={t}_{1}+100{t}_{s}$. (©2023 Baker Hughes Company—All rights reserved).

**Figure 7.**RMS U

_{x}, RMS U

_{y}, RMS U

_{z}, and RMS T

_{t}for the SBES CC+S1N, SBES S1N and SBES timeavg calculations at plane 39.5. (©2023 Baker Hughes Company—All rights reserved).

**Figure 8.**Time-averaged normalized total temperature, swirl, and pitch angles from the SBES CC+S1N, SBES S1N, and SBES timeavg at plane 39.5. (©2023 Baker Hughes Company—All rights reserved).

**Figure 9.**Energy content with respect to the total for the first three modes of $\rho {u}_{x}$ calculated at the interface plane between the combustor and S1N by varying the total number of modes. (©2023 Baker Hughes Company—All rights reserved).

**Figure 10.**Dominant peak frequency for the first three modes of $\rho {u}_{x}$ calculated at the interface plane between the combustor and S1N by varying the total number of modes. (©2023 Baker Hughes Company—All rights reserved).

**Figure 11.**On the left, the amplitude of each mode is reported as a function of the mode number, while on the right, the energy contribution of each mode is represented. On the right axis the cumulative energy contribution is plotted. (©2023 Baker Hughes Company—All rights reserved).

**Figure 12.**Representation of the first three modes of $\rho {u}_{x}$ and their interaction with the time-averaged field. To better quantify the results, the minimum and maximum distortions of the $\rho {u}_{x}$ field are reported with respect to the time-averaged field. (©2023 Baker Hughes Company—All rights reserved).

**Figure 13.**Representation of the first three modes of normalized total temperature and their interaction with the time-averaged field. To better quantify the results, the minimum and maximum distortions of the normalized total temperature field are reported with respect to the time-averaged field. (©2023 Baker Hughes Company—All rights reserved).

**Figure 14.**Representation of RMS total temperature for all the SBES calculations at plane 39.5. (©2023 Baker Hughes Company—All rights reserved).

**Figure 15.**Isentropic Mach number on the NGV surface at 25%, 50%, and 75% of the span for all the SBES calculations. It is plotted as a function of the non-dimensional curvilinear abscissa, where x = 0 corresponds to the leading edge of the NGV, x = −1 is the trailing edge pressure side, and x = 1 is the trailing edge suction side. (©2023 Baker Hughes Company—All rights reserved).

**Figure 16.**Time-averaged normalized temperature distribution on the NGV surfaces, including also the inner and outer platforms for the SBES CC+S1N simulation (top) compared against all the S1N stand-alone simulations. (©2023 Baker Hughes Company—All rights reserved).

**Figure 17.**Normalized temperature on the NGV surface at 25%, 50%, and 75% of the span for the SBES CC+S1N simulation compared against SBES S1N and SBES S1N timeavg in terms of (

**a**) absolute values and (

**b**) relative differences. It is plotted as a function of the non-dimensional curvilinear abscissa, where x = 0 corresponds to the leading edge of the NGV, x = −1 is the trailing edge pressure side, and x = 1 is the trailing edge suction side. (©2023 Baker Hughes Company—All rights reserved).

**Figure 18.**Normalized temperature on the NGV surface at 25%, 50% and 75% of the span for the SBES CC+S1N simulation compared against SBES S1N POD30, SBES S1N POD10, and SBES S1N POD5. It is plotted as a function of the non-dimensional curvilinear abscissa, where x = 0 corresponds to the leading edge of the NGV, x = −1 is the trailing edge pressure side, and x = 1 is the trailing edge suction side. (©2023 Baker Hughes Company—All rights reserved).

**Figure 19.**Time-averaged pitch angle for all the SBES simulations extracted from the outlet plane of the S1N stator. (©2023 Baker Hughes Company—All rights reserved).

**Figure 20.**Time-averaged swirl angle for all the SBES simulations extracted from the outlet plane of the S1N stator. (©2023 Baker Hughes Company—All rights reserved).

**Figure 21.**Time-averaged (

**a**) swirl angle, (

**b**) pitch angle, and (

**c**) normalized total temperature circumference-averaged 1D profiles for all the SBES simulations extracted from the outlet plane of the S1N stator. (©2023 Baker Hughes Company—All rights reserved).

**Figure 22.**Time-averaged normalized total temperature for all the SBES simulations extracted from the outlet plane of the S1N stator. (©2023 Baker Hughes Company—All rights reserved).

**Table 1.**Summary of the main parameters of the setup of the CFD simulations. (©2023 Baker Hughes Company—All rights reserved).

CFD Simulation | CFD Domain | Inlet BCs |
---|---|---|

SBES CC+S1N | CC+S1N | Mass flow inlets |

SBES S1N | S1N | Set of instantaneous 2D maps from SBES CC+S1N |

SBES S1N 30POD | S1N | Set of instantaneous 2D maps from SBES CC+S1N (first 30 POD modes) |

SBES S1N 10POD | S1N | Set of instantaneous 2D maps from SBES CC+S1N (first 10 POD modes) |

SBES S1N 5POD | S1N | Set of instantaneous 2D maps from SBES CC+S1N (first 5 POD modes) |

SBES S1N timeavg | S1N | Time-averaged 2D maps from SBES CC+S1N |

**Table 2.**Summary of the main parameters of the operating conditions taken as reference for all the SBES calculations presented here. (©2023 Baker Hughes Company—All rights reserved).

Test Point Conditions | ||
---|---|---|

Fuel Composition (% vol.) | CH4 | 87 |

C2+ | 7.5 | |

Inert | 5.5 | |

Pilot/Premix fuel ratio (-) | 0.36 | |

Ambient Temperature (°C) | 6 | |

Firing Temperature | Design Value | |

TNH, TNL (%) | 100 |

**Table 3.**Averaged values obtained at plane 39.5 for the three velocity components and the respective RMS, normalized total temperature, and the total temperature RMS are reported for SBES CC+S1N and SBES S1N. The relative differences between the two cases are also included. (©2023 Baker Hughes Company—All rights reserved).

SBES CC+S1N | SBES S1N | Relative Difference | |
---|---|---|---|

U (m/s) | 59.848 | 60.466 | 1.032% |

RMS U (m/s) | 12.596 | 12.226 | −2.941% |

${U}_{x}$ (m/s) | 56.186 | 56.788 | 1.072% |

6.176 | 6.081 | −1.527% | |

${U}_{y}$ (m/s) | −17.417 | −17.673 | 1.471% |

RMS ${U}_{y}$ (m/s) | 6.614 | 6.518 | −1.447% |

${U}_{z}$ (m/s) | −3.543 | −3.246 | −8.390% |

RMS ${U}_{z}$ (m/s) | 8.430 | 8.027 | −4.774% |

${T}_{t,nd}$ (-) | 0.852 | 0.849 | −0.397% |

RMS ${T}_{t}$ (K) | 0.861 | 0.849 | −1.489% |

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## Share and Cite

**MDPI and ACS Style**

Tomasello, S.G.; Meloni, R.; Andrei, L.; Andreini, A.
Study of Combustor–Turbine Interactions by Performing Coupled and Decoupled Hybrid RANS-LES Simulations under Representative Engine-like Conditions. *Energies* **2023**, *16*, 5395.
https://doi.org/10.3390/en16145395

**AMA Style**

Tomasello SG, Meloni R, Andrei L, Andreini A.
Study of Combustor–Turbine Interactions by Performing Coupled and Decoupled Hybrid RANS-LES Simulations under Representative Engine-like Conditions. *Energies*. 2023; 16(14):5395.
https://doi.org/10.3390/en16145395

**Chicago/Turabian Style**

Tomasello, Stella Grazia, Roberto Meloni, Luca Andrei, and Antonio Andreini.
2023. "Study of Combustor–Turbine Interactions by Performing Coupled and Decoupled Hybrid RANS-LES Simulations under Representative Engine-like Conditions" *Energies* 16, no. 14: 5395.
https://doi.org/10.3390/en16145395