# Large Eddy Simulations of Reactive Mixing in Jet Reactors of Varied Geometry and Size

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Jet Reactors Geometry

## 3. Experimental Setup

^{8}m

^{3}mol

^{−1}s

^{−1}[25] and ${k}_{2}$ = 0.0259 m

^{3}mol

^{−1}s

^{−1}[26].

^{−3}. Postreaction samples were taken at the exit of the reactors.

## 4. Simulation Setup

^{+}~1 condition. The mesh independence was checked at the highest tested Reynolds numbers using two quantities: average wall shear stress value at the walls and average turbulence energy dissipation rate value in the system. The results of both of these quantities were constant (less than 3% difference), even with using denser meshes than those described.

^{−6}or smaller for normalized residuals was considered as a fulfilled convergence condition. The averaged values predicted by large eddy simulations were obtained for a time interval equal to 10 residence times, $\tau $. The residence time was defined as $\tau $ = $V$/$Q$, where V is the reactor volume and $Q$ is the total flow rate in the system. The time step value was set individually to meet the $\Delta t$ ≤ $\mathsf{\Delta}$/$U$ condition [28], where $\Delta t$ is the time step value, $\mathsf{\Delta}$ is the numerical cell size (cube root of its volume), and U is the local velocity magnitude in the cell.

## 5. Results and Discussion

_{jet}), the RANS results can differ significantly from the experiments, whereas, at higher jet Reynolds numbers, the discrepancy between both the LES results and experiments decreased. The results indicated that the k-ε model failed to properly predict the flow behavior, i.e., a collision of inlet streams and resulting fluid motion around the outlet pipe and impingement zone [16]. This follows from the theory of turbulence and is related to the Reynolds-averaged approach. In this approach, the variation of time-averaged quantities occurs at relatively large scales and does not necessary resolve all small-scale phenomena, both temporal and spatial [37].

^{−3}is the density, and $\mu $ = 0.891 × 10

^{−3}Pa s is the dynamic viscosity of the inlet solutions at 298 K.

^{5}), calculations would be, at best, a million times more costly than for RANS models [38,40,41]. Of course, that makes it rather unrealistic that LES will become a major element of industrial CFD simulations; however, LES can still play a role in the detailed analysis of the elements of such flows. One possible solution for these extreme requirements can be LES hybrid methods, i.e., a combination of RANS in slender, near-wall regions and LES in regions away from walls. In near-wall regions, the turbulence is closer to having mature and repeatable behavior and is more likely to be accurately predicted by simpler models. Overall, pure LES for industrial flows is likely to be limited in the foreseeable future to free-shear flows or simpler geometries, such as jet reactors, preferentially at low to mid Reynolds numbers. Taking this into consideration, the k-ε model appears to be a reasonable choice for predicting of the course of a chemical reaction in a high Reynolds number regime ($R{e}_{jet}$ > 3000) or to determine a trend of changes in the process course depending on the process parameters.

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 3.**Geometry of: (

**a**) a symmetric T-mixer equipped with helicoidal static mixers (SP-mixer I); (

**b**) a cyclone-type mixer (L-mixer II).

**Figure 4.**The effect of the jet Reynolds number on the final selectivity of the chemical reaction: (

**a**) V-mixer I; (

**b**) V-mixer II.

**Figure 5.**Parity plot showing predictions of the large eddy simulation (LES) and Reynolds-averaged Navier–Stokes (RANS) models: (

**a**) V-mixer I; (

**b**) V-mixer II.

**Figure 6.**The effect of the jet Reynolds number on the final selectivity of the chemical reaction: (

**a**) T-mixer III; (

**b**) V-mixer III.

**Figure 7.**The effect of the jet Reynolds number on the final selectivity of the chemical reaction in: (

**a**) SP-mixer I; (

**b**) L-mixer II.

**Figure 8.**The energetic unit cost of obtaining product in different reactor types. Data for T-mixer I and T-mixer II from [15].

Reactor | Description | ${\mathit{d}}_{\mathit{j}\mathit{e}\mathit{t}},\mathbf{mm}$ | ${\mathit{d}}_{\mathit{o}\mathit{u}\mathit{t}},\mathbf{mm}$ |
---|---|---|---|

T-mixer I | symmetric T-mixer | 7.00 | 11.00 |

T-mixer II | symmetric T-mixer | 4.60 | 11.00 |

T-mixer III | symmetric T-mixer | 1.45 | 2.00 |

V-mixer I | vortex T-mixer | 7.00 | 11.00 |

V-mixer II | vortex T-mixer | 4.60 | 11.00 |

V-mixer III | vortex T-mixer | 1.45 | 2.00 |

SP-mixer I | symmetric T-mixer equipped with helicoidal static mixers | 7.00 | 11.00 |

L-mixer II | cyclone-type mixer | 4.60 | 11.00 |

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**MDPI and ACS Style**

Wojtas, K.; Orciuch, W.; Makowski, Ł.
Large Eddy Simulations of Reactive Mixing in Jet Reactors of Varied Geometry and Size. *Processes* **2020**, *8*, 1101.
https://doi.org/10.3390/pr8091101

**AMA Style**

Wojtas K, Orciuch W, Makowski Ł.
Large Eddy Simulations of Reactive Mixing in Jet Reactors of Varied Geometry and Size. *Processes*. 2020; 8(9):1101.
https://doi.org/10.3390/pr8091101

**Chicago/Turabian Style**

Wojtas, Krzysztof, Wojciech Orciuch, and Łukasz Makowski.
2020. "Large Eddy Simulations of Reactive Mixing in Jet Reactors of Varied Geometry and Size" *Processes* 8, no. 9: 1101.
https://doi.org/10.3390/pr8091101