#
Turbulence Measurements Downstream of a Combustor Simulator Designed for Studies on the Combustor–Turbine Interaction^{ †}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

_{duct}is computed based on the duct size, Re

_{c,swirler}is computed based on the chord of the swirler generator blades, and Re

_{d,injecotor}is computed based on the injector diameter. The calibrated nozzle of the wind tunnel is fed by compressed stored air and has a 0.08 m square exit section. According to the nozzle calibration, the open jet generated retains a wall-bounded character for an axial distance of two jet widths downstream of the nozzle. The combustor simulator is placed within a straight prolongation added downstream of the exit section (Figure 1). This device includes a swirler generator (highlighted with a circle in Figure 1) that can inject steady/unsteady temperature disturbances. Probes are traversed downstream of the device at two traversing planes: one representative of the plane where measurements are carried out upstream of the turbine stage, which is approximately one chord of the swirl generator blade downstream of the device itself, and the second at a position coincident with the turbine vane LE (in the turbine experiments). Both the planes are inside the axial extension of 2 jet widths. The characterization of the turbulence generated by the combustor simulator is carried out using a slanted hot-wire probe. In addition, a 5-hole probe is used to assess the hot-wire measurements.

#### 2.1. Generated Combustor Disturbances

#### 2.2. CFD Setup

^{+}< 1. The mesh is not further coarsened to accurately catch the mixing that occurs downstream of the injector. Among the two tested meshes, the one with 6 million cells is used, considering the small differences in the outcomes of the grid-independence analysis shown in Table 2.

#### 2.3. Measuring Technique

^{TM}XT190 transducer (Leonia, NJ, USA), which has a full scale of 5 psi. The outlet pressure is the ambient pressure that is read by a Fisher

^{TM}(Drebach, Germany) model 104 barometer with an average uncertainty of 50 Pa calibrated in the LAT n° 024. In order to phase-average the hot-wire measurements at the frequency of the injected disturbance, the pressure in injector duct 1 is used as a trigger signal and is measured using a Kulite

^{TM}XT190 transducer with a full scale of 25 psi. The transducer’s maximum uncertainty is 0.05% of its full scale. The measuring signals are acquired using a National Instrument data acquisition board (PCI 6052E) with a range of ±10 V.

#### 2.3.1. Five-Hole Probe

#### 2.3.2. Hot-Wire

_{2}):

- 1.
- The acquired voltages are used to compute $\overline{Q}$ and $\overline{q}$ by applying King’s law.
- 2.
- Assuming low-turbulence content and Q = [0, $\overline{Q}$, 0], the mean flow field is solved by iterating Equation (9) over 13 sets of rotations.
- 3.
- The first prediction of the velocity vector is used to update the rotational range and solve the Reynolds tensor (Equation (14)). The updated rotational range is centered on the nearest multiple of 20° relative to the measured yaw angle, encompassing 13 rotations spaced every 20° within the range of ±120° with respect to that closest multiple of 20°.
- 4.
- Considering that the mean velocity depends on the Reynolds stress tensor components (Equation (10)), the assumption made in step 2 is now relaxed. The mean velocity components are recalculated using a least-square regression on Equation (10), utilizing the Reynolds stresses computed in step 3.
- 5.
- With the new mean velocities, the cycle is repeated, starting from step 3 until convergence.

## 3. Results

#### 3.1. Steady Cold Streak

#### 3.2. Unsteady Cold Streaks at 110 Hz

#### 3.3. Temperature Effect

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

A, B, n | King’s coefficients |

${A}_{i}$ | Coefficients of Equation (9) |

c | Chord |

CS | Cold streak |

d | Diameter |

E | Voltage supply |

e | Fluctuating voltage supply |

EW | Entropy wave |

HS | Hot streak |

HW | Hot wire |

${k}^{2}$, ${h}^{2}$ | Jorgensen’s calibration coeff. |

LE | Leading edge |

$\widehat{n}$ | Unit vector normal to S |

M | Mach number |

MS | Mainstream |

p | Pressure |

Q | Cooling velocity |

q | Fluctuating cooling velocity |

r, Θ, z | Coordinates of polar reference system |

R | Coefficients of Equation (11) |

Re | Reynolds number |

S | Surface |

SN | Swirl number |

T | Temperature |

Ti | Turbulence intensity |

U | Velocity |

u | Fluctuating velocity |

x, y, z | ref. system coordinates |

Z | Coefficients of Equation (13) |

α | Hot-wire slanted angle |

θ | Pitch angle |

λ | Integral length scale |

φ | Yaw angle |

Subscripts | |

0 | Rest condition |

1, 2, 3 | Components on y, z, x |

corr | After temperature correction |

n, t, b | Hot-wire reference system |

rot | Motor rotation |

t | Total |

w | Wire |

Θ | Tangential component |

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**Figure 5.**Y-axis mass-average comparisons for total pressure (

**A**,

**B**) and velocity (

**C**,

**D**) at plane 1 (

**A**,

**B**) and plane 2 (

**C**,

**D**).

**Figure 6.**Absolute velocity contours at plane 1. Plane 0 refers to the plane at the swirler generator trailing edge. Numbers 1–5, indicating the different flow channels, rotate between the two planes as a consequence of the swirl components.

Duct 1 | Duct 2 | ||||||||
---|---|---|---|---|---|---|---|---|---|

Injection Case Name | Frequency (Hz) | Feed? | CFD Inlet-Plane Treatment | T_{t} (K) | Feed? | CFD Inlet-Plane Treatment | T_{t} (K) | Exp. | CFD |

HS | 0 | No | Wall | Yes | Inlet | 670 | ✓ | ||

CS | 0 | No | Wall | Yes | Inlet | 303 | ✓ | ✓ | |

EW | 110 | Yes | Inlet | 303 | Yes | Inlet | 670 | ✓ | |

Unsteady CS | 110 | Yes | Inlet | 303 | Yes | Inlet | 303 | ✓ | ✓ |

Re_{duct} | Re_{c,swirler} | Re_{d,injector} | M | T_{t} [K] | |||||

Mainstream | 2.35 × 10^{5} | 3.5 × 10^{4} | 3.8 × 10^{4} | 0.13 | 303 |

Quantity | Coarse | Fine | Δ |
---|---|---|---|

Number of cells | 6 mln | 12 mln | |

(${{P}_{t}}_{inlet}-{P}_{{t}_{outlet}})/({P}_{{t}_{inlet}}-{P}_{{s}_{inlet}})$ | 0.038 | 0.034 | 0.49% |

${T}_{{t}_{outlet}}-{T}_{{t}_{inlet}}$ [K] | 0.79 | 0.76 | 0.03 |

Variable | Mainstream | Perturbed Region |
---|---|---|

Ti | 0.07% | 5% |

U (m/s) | 0.5 | 4.8 |

U_{3} (m/s) | 1 | 8 |

$\lambda $ (m) | 2.6 × 10^{−4} | 8 × 10^{−5} |

Duct | Phase | CFD | HW |
---|---|---|---|

Streak 1 | Phase 1 | 0.087 | 0.088 |

Phase 2 | 0.084 | 0.088 | |

Phase 3 | 0.096 | 0.092 | |

Streak 2 | Phase 4 | 0.101 | 0.094 |

Phase 5 | 0.108 | 0.093 | |

Phase 6 | 0.114 | 0.092 |

Plane | Technique | SN | Ti | ||||||
---|---|---|---|---|---|---|---|---|---|

Unsteady CS | EW | CS | HS | Unsteady CS | EW | CS | HS | ||

Plane 1 | Exp | 0.12 | 0.09 | 6.5% | 6.1% | ||||

CFD | 0.12 | 0.11 | 0.10 | 0.10 | 7.2% | 7.3% | 7.2% | 7.4% | |

Plane 2 | Exp | 0.09 | 0.09 | 5.9% | 5.9% | ||||

CFD | 0.09 | 0.08 | 0.08 | 0.08 | 6.4% | 6.4% | 6.4% | 6.9% |

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**MDPI and ACS Style**

Notaristefano, A.; Persico, G.; Gaetani, P.
Turbulence Measurements Downstream of a Combustor Simulator Designed for Studies on the Combustor–Turbine Interaction. *Int. J. Turbomach. Propuls. Power* **2024**, *9*, 4.
https://doi.org/10.3390/ijtpp9010004

**AMA Style**

Notaristefano A, Persico G, Gaetani P.
Turbulence Measurements Downstream of a Combustor Simulator Designed for Studies on the Combustor–Turbine Interaction. *International Journal of Turbomachinery, Propulsion and Power*. 2024; 9(1):4.
https://doi.org/10.3390/ijtpp9010004

**Chicago/Turabian Style**

Notaristefano, Andrea, Giacomo Persico, and Paolo Gaetani.
2024. "Turbulence Measurements Downstream of a Combustor Simulator Designed for Studies on the Combustor–Turbine Interaction" *International Journal of Turbomachinery, Propulsion and Power* 9, no. 1: 4.
https://doi.org/10.3390/ijtpp9010004