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Numerical Modelling of the 3D Unsteady Flow of an Inlet Particle Separator for Turboshaft Engines^{ †}

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Layout

## 3. Numerical Setup

#### 3.1. CFD Models

#### 3.2. Semi-Empirical 1D Model

## 4. Results

#### 4.1. Validation of the Numerical Models

#### 4.2. Unsteady Flow Characterization

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations and Nomenclature

## Abbreviations

IPS | Inlet Particle Separator |

DES | Detached Eddy Simulation |

VKI | von Karman Institute |

$BPR$ | Bypass Ratio |

RANS | Reynolds-Averaged Navier–Stokes |

LES | Large Eddy Simulation |

M | Million (cells) |

TKE | Turbulent Kinetic Energy |

## Nomenclature

p | pressure |

$Re$ | Reynolds number |

G | reduced mass flow rate |

m | mass |

$\mu $ | dynamic viscosity |

P | wetted perimeter |

T | temperature |

$\zeta $ | pressure loss |

$\rho $ | density |

v | velocity magnitude |

$PL$ | relative total pressure difference |

$\eta $ | separation efficiency |

k | turbulent kinetic energy |

$\epsilon $ | dissipation rate |

$\varphi $ | RANS computational time |

S | resolution factor |

${l}_{0}$ | integral length scale |

$\Delta $ | approximate grid size |

$\omega $ | vorticity magnitude |

H | inlet channel height |

L | IPS longitudinal length |

d | particle diameter |

$\Delta t$ | time step |

$\tau $ | through-flow time |

A | cross-section area |

R | air gas constant |

$\gamma $ | specific heat ratio |

${c}_{p}$ | specific heat at constant pressure |

$\beta $ | ratio of orifice to pipe diameter |

$\Delta p$ | localized pressure difference |

$\u03f5$ | compressibility factor |

${(\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}})}^{0}$ | total quantity |

${(\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}})}_{OUT}$ | outlet section |

$\dot{(\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}})}$ | flow rate |

${(\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}})}_{BY}$ | bypass section |

${(\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}})}_{IN}$ | inlet section |

${(\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}})}_{avg}$ | average |

${(\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}})}_{max}$ | maximum |

$\overline{(\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}})}$ | normalized |

${(\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}})}_{T}$ | throat |

${(\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}})}_{COLL}$ | collector |

${(\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}})}_{ORIF}$ | orifice |

${(\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}})}_{sgs}$ | sub-grid scale |

## References

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**Figure 1.**(

**Left**) Schematic test section of the IPS built at VKI: 1, upstream flap; 2, downstream flap with an L-strut supporting the flap in the deployment phase; 3, collector. (

**Right**) Numerical models presented in this paper.

**Figure 2.**(

**Left**) IPS geometry manufactured with 3D printing technologies. (

**Right**) Detail of the test geometry, instrumentation location, and measurement sections.

**Figure 5.**Normalized vorticity magnitude contours (Equation (8)) and velocity streamlines for the grids in Table 2 (50 M mesh not shown for simplicity). Preliminary RANS at $R{e}_{OUT}=580,000$, ${p}_{IN}^{0}=124,200\phantom{\rule{0.166667em}{0ex}}\mathrm{Pa}$, $BPR$ = 21% and ${G}_{OUT}=14.4\frac{\mathrm{kg}}{\mathrm{s}}\frac{{\mathrm{K}}^{0.5}}{\mathrm{bar}}$.

**Figure 6.**(

**Left**) IPS schematized as a convergent nozzle in parallel with a convergent–divergent nozzle. (

**Right**) The three main loss regions in the industrial IPS.

**Figure 7.**(

**A**): User-defined function UDF defining the regions in which the DES model switches to RANS (yellow). (

**B**,

**C**): Contours of the ratio between resolved turbulent kinetic energy and total turbulent kinetic energy (Case 9, Table 3).

**Figure 9.**Instantaneous $\overline{\omega}$ contours ($t=16.75\tau $) and velocity streamlines in the IPS regions between the two flaps from the mean of DES calculations (cases 8 and 9 Table 3) for two $R{e}_{OUT}$. (

**Left**) $R{e}_{OUT}\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}710,000$ (${v}_{IN}/H\approx 680$). (

**Right**) $R{e}_{OUT}=1,280,000$ (${v}_{IN}/H\approx 820$).

**Figure 11.**Instantaneous $\overline{\omega}$ and velocity streamlines from the DES at $R{e}_{OUT}=1,280,000$ (${v}_{IN}/H\approx 820$) during one oscillation cycle. The red arrows schematically indicate the vortical directions. (

**Upper left**) $t=16\tau $. (

**Upper right**) $t=16.25\tau $. (

**Bottom left**) $t=16.5\tau $. (

**Bottom right**) $t=16.75\tau $.

Case | Total Pressure ${\mathit{p}}_{\mathit{IN}}^{0}$[ $\mathbf{Pa}$] | Reynolds Number ${\mathit{Re}}_{\mathit{OUT}}$ | Reduced Mass Flow Rate ${\mathit{G}}_{\mathit{OUT}}\left[\frac{\mathbf{kg}}{\mathbf{s}}\frac{{\mathbf{K}}^{0.5}}{\mathbf{bar}}\right]$ | $\mathit{BPR}$ |
---|---|---|---|---|

1 | 127,700 | 580,000 | 14.2 | 28% |

2 | 126,250 | 580,000 | 14.4 | 13% |

3 | 139,804 | 710,000 | 15.9 | 6% |

4 | 137,874 | 710,000 | 16.2 | 28% |

5 | 138,793 | 710,000 | 16.0 | 13% |

6 | 125,500 | 580,000 | 14.4 | 6% |

**Table 2.**Summary of the grids generated for the IPS numerical modeling, with statistics of mesh quality: x = streamwise; y = transverse; z = spanwise; AR = aspect ratio; OQ = orthogonal quality.

Cell Count | (x,y,z) | AR | OQ | ${\mathit{y}}_{\mathit{avg}}^{+}$ | ${\mathit{y}}_{\mathit{max}}^{+}$ | ${\mathit{PL}}_{\mathit{OUT}}$ | CPU Time |
---|---|---|---|---|---|---|---|

8 M | (500,80,200) | <20 | >0.19 | 58.4 | 774 | 7.84% | $\varphi $ |

30 M | (875,125,350) | <23 | >0.20 | 45.6 | 189 | 7.90% | $5\varphi $ |

50 M | (925,150,400) | <31 | >0.12 | 41.6 | 159 | 8.05% | $13\varphi $ |

70 M | (1000,175,450) | <37 | >0.15 | 37.0 | 143 | 8.36% | $20\varphi $ |

95 M | (1100,185,475) | <${10}^{3}$ | >0.01 | 34.9 | 125 | 8.21% | $50\varphi $ |

**Table 3.**Numerical test matrix. PT = particle tracking. ${p}_{IN}^{0}$ in [Pa]; ${G}_{OUT}$ in $\left[\frac{\mathrm{kg}}{\mathrm{s}}\frac{{\mathrm{K}}^{0.5}}{\mathrm{bar}}\right]$.

Case | ${\mathit{p}}_{\mathit{IN}}^{0}$ | ${\mathit{Re}}_{\mathit{OUT}}$ | ${\mathit{G}}_{\mathit{OUT}}$ | $\mathit{BPR}$ | Mesh | Model | CPU Time |
---|---|---|---|---|---|---|---|

1 | 127,700 | 580,000 | 14.2 | 28% | 8 M | RANS, Steady PT | $\varphi $, $0.1\varphi $ |

2 | 126,250 | 580,000 | 14.4 | 13% | |||

3 | 139,804 | 710,000 | 15.9 | 6% | |||

4 | 137,874 | 710,000 | 16.2 | 28% | 8 M | RANS, Steady PT | $\varphi $, $0.1\varphi $ |

5 | 138,793 | 710,000 | 16.0 | 13% | DES | $260\varphi $–$340\varphi $ | |

6 | 125,500 | 580,000 | 14.4 | 6% | URANS, Unsteady PT | $80\varphi $, 190$\varphi $–260$\varphi $ | |

7 | 124,200 | 580,000 | 14.4 | 21% | Table 2 | RANS | Table 2 |

8 | 144,200 | 580,000 | 12.2 | 21% | 8 M | RANS DES | $\varphi $ $280\varphi $ |

9 | 247,000 | 1,280,000 | 16.5 | 21% | 8 M 70 M | RANS, URANS, DES RANS, URANS, LES | $\varphi $, $80\varphi $, $310\varphi $ $20\varphi $, $1450\varphi $, $4500\varphi $ |

**Table 4.**Validation of the numerical models with experiments. Exp. = experiments; unc. = uncertainty. Cases 1,2,6: $R{e}_{OUT}=580,000$. Cases 3,4,5: $R{e}_{OUT}=710,000$.

Case | Separation Efficiency $\mathit{\eta}$ (%) | Pressure Loss ${\mathit{PL}}_{\mathit{OUT}}$ (%) | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

# | BPR | Exp. | Unc. | SteadyTracking | UnsteadyTracking | Exp. | Unc. | 1D | RANS8 M | URANS8 M | DES8 M |

1 | 28% | 78 | ±10 | 73 | - | 7.1 | ±1.3 | 7.33 | 7.11 | - | - |

2 | 13% | 59 | ±8 | 63 | - | 6.8 | ±1.3 | 6.72 | 7.09 | - | - |

3 | 6% | 49 | ±16 | 32 | - | 7.7 | ±1.2 | 8.28 | 8.53 | - | - |

4 | 28% | 82 | ±12 | 72 | 89 | 8.5 | ±1.2 | 10.0 | 10.0 | 9.50 | 9.52 |

5 | 13% | 64 | ±11 | 58 | 68 | 7.9 | ±1.2 | 8.77 | 9.74 | 9.41 | 7.92 |

6 | 6% | 45 | ±10 | 21 | 46 | 6.7 | ±1.3 | 6.56 | 7.01 | 7.40 | 7.50 |

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## Share and Cite

**MDPI and ACS Style**

Castaldi, M.; Mayo, I.; Demolis, J.; Eulitz, F.
Numerical Modelling of the 3D Unsteady Flow of an Inlet Particle Separator for Turboshaft Engines. *Int. J. Turbomach. Propuls. Power* **2023**, *8*, 52.
https://doi.org/10.3390/ijtpp8040052

**AMA Style**

Castaldi M, Mayo I, Demolis J, Eulitz F.
Numerical Modelling of the 3D Unsteady Flow of an Inlet Particle Separator for Turboshaft Engines. *International Journal of Turbomachinery, Propulsion and Power*. 2023; 8(4):52.
https://doi.org/10.3390/ijtpp8040052

**Chicago/Turabian Style**

Castaldi, Marco, Ignacio Mayo, Jacques Demolis, and Frank Eulitz.
2023. "Numerical Modelling of the 3D Unsteady Flow of an Inlet Particle Separator for Turboshaft Engines" *International Journal of Turbomachinery, Propulsion and Power* 8, no. 4: 52.
https://doi.org/10.3390/ijtpp8040052