# Computational Fluid Dynamics of Influence of Process Parameters and the Geometry of Catalyst Wires on the Ammonia Oxidation Process and Degradation of the Catalyst Gauze

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}and N

_{2}O are also produced. Motivated by its considerable industrial importance, substantial fundamental research has been directed towards the mechanistic understanding of the Ostwald process.

_{2}O selectivity. In earlier work, Haas et al. [13] used CFD methods to model an ammonia burner with a simplified catalyst gauze. Pottbacker et al. [14] conducted combined experimental and CFD research on temperature and concentration gradients. Wiser [15] applied detailed surface mechanisms in CFD simulations of ammonia oxidation. According to Wiser [15], CFD allows for an accurate model of the ammonia oxidation on platinum–rhodium gauze because this reaction is firmly heat- and mass-transfer-controlled, and the combined treatment of surface chemistry, flow, diffusion, and heat conduction should be considered.

## 2. Materials and Methods

#### 2.1. Materials

#### 2.2. Catalyst Geometry and Properties

^{2}[20]. Based on this information, a 3D geometry of a three-layer gauze was modelled and implemented in simulations. Two catalyst gauze models were created. In the first variant (Geometry A), the second layer was shifted by half the mesh size in two axes relative to the first and third layers. The second variant (Geometry B) was a novel gauze type proposed by authors. In this gauze modification, the second layer was shifted by half the mesh size on one axis and rotated 45° relative to the first and third layers. Figure 1 presents the differences and dimensions between basic and novel geometries.

#### 2.3. Computational Domain

#### 2.4. Continuous Phase Modelling

^{−8}. According to the literature [12,15], turbulence has a minor role in the process due to the slight clearances in the gauze and, therefore, has low Reynolds numbers in the catalyst wires’ vicinity. However, the k-ε model was used in calculations to improve the simulation of the gas phase outside the gauze area. Wiser [15] also proved that the k-ε model can be used to simulate flow in the vicinity of a catalyst. The following equations govern the continuity (1), momentum (2), turbulent kinetic energy (3), and the specific dissipation rate of turbulent kinetic energy (4) in the k-ε model [23]:

#### 2.5. Reaction Kinetics

_{3}+ 5 O

_{2}→ 4 NO + 6 H

_{2}O

_{r}represents the pre-exponential factor, β

_{r}is a temperature exponent, E

_{r}is the activation energy, and R is the universal gas constant. The temperature exponent was set to 0.5. The parameters used in Equations (6) and (7) are listed in Table 4.

_{wall}is the wall phase density, t is time, M

_{w,i}is the species molecular weight, ${\widehat{\mathrm{R}}}_{\mathrm{i},\mathrm{bulk}}$ is the reaction rate of the bulk phase, ρ

_{site}is the site density, and Z

_{i}is the site coverage of species. The diffusion term appearing in Equation (8) is calculated as the difference of the species mass fraction at the cell centre and wall face centre divided by the distance between these centre points.

#### 2.6. Discrete Phase Modelling

^{−3}). We assumed the following for calculations: there was no interaction and coalescence between the particles, particles did not affect the gas phase, and the gravitational forces acting on particles were negligible. Boundary conditions applied to the DPM model are described in Section 3.4.

## 3. Results

#### 3.1. Velocity and Temperature Contours

#### 3.2. Stagnation Areas

#### 3.3. NO Conversion Efficiency and Concentration Contours

_{NO_out}is the mass fraction of NO at the outlet, X

_{NH3_in}is the mass fraction of NH

_{3}at the inlet, and M

_{NH3}and M

_{NO}are molar masses of NH

_{3}and NO, respectively. Figure 7a presents the conversion efficiency as a function of contact time. Due to the construction of the second layer in Geometry B, it contained approximately 10% less mass of the catalyst than Geometry A. Figure 7b presents the conversion efficiency per 1 g of catalyst.

_{3}and NO, respectively, for the investigated geometries.

_{3}were located in the close vicinity of the wires, which confirmed that the obtained product concentration was closely related to the temperature distribution. Moreover, similar to temperature, the influence of the stagnation zones behind the last layer of gauze was observed.

#### 3.4. Platinum Particles’ Capture Efficiency

_{Pt}is the number of tracked platinum particles and N

_{Pt_loss}is the number of platinum particles that left the domain without contact with the subsequent layers of the gauze. Figure 11 presents the changes in the total and individual layer platinum capture efficiencies as a function of contact time.

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

Latin symbols: | |

A_{r} | pre-exponential factor, s^{−1} |

C_{1ε}, C_{2ε}, C_{3ε} | constants |

c_{i} | concentration of species i, mol m^{−3} |

D_{i,wall} | mass diffusion coefficient, m^{2} s^{−1} |

E_{r} | activation energy, J mol^{−1} |

G_{b} | generation of turbulence kinetic energy due to buoyancy, kg m^{−1} s^{−2} |

G_{k} | generation of turbulence kinetic energy due to the mean velocity gradients, kg m^{−1} s^{−2} |

[G_{i}]_{wall} | molar concentration of surface-adsorbed species |

H | catalyst gauze height, m |

I | unit tensor |

$\overrightarrow{{\mathrm{J}}_{\mathrm{i}}}$ | diffusion flux of species i, kg m^{−2} s^{−1} |

k | reaction rate constant, s^{−1} |

k | turbulent kinetic energy, m^{2} s^{−2} |

M_{NH3} | molar mass of NH_{3}, kg mol^{−1} |

M_{NO} | molar mass of NO_{3}, kg mol^{−1} |

M_{w,i} | molecular weight, kg mol^{−1} |

${\dot{\mathrm{m}}}_{\mathrm{dep}}$ | net rate of mass deposition as a result of the surface reaction |

N_{g} | number of gas species |

N_{s} | number of site species |

N_{Pt} | number of tracked platinum particles |

N_{Pt_loss} | number of lost platinum particles |

p | pressure, Pa |

R | universal gas constant, J mol^{−1} K^{−1} |

R_{i} | net rate of production of species i by chemical reaction |

${\widehat{\mathrm{R}}}_{\mathrm{i},\mathrm{gas}}$ | rate of reaction in the gas phase |

${\widehat{\mathrm{R}}}_{\mathrm{i},\mathrm{site}}$ | rate of reaction on the catalyst surface |

${\widehat{\mathrm{R}}}_{\mathrm{i},\mathrm{bulk}}$ | rate of reaction in the bulk phase |

r | reaction rate, mol m^{−3} s^{−1} |

S_{i} | rate of creation of species i by addition from the dispersed phase plus any user-defined sources |

[S_{i}]_{wall} | molar concentration of site species |

T | temperature, K |

t | contact time, s |

t | time, s |

u_{i} | continuous phase velocity, m s^{−1} |

$\overline{\mathrm{u}\prime}$ | average fluctuation of continuous phase velocity, m s^{−1} |

v | average velocity between wires, m s^{−1} |

$\overrightarrow{\mathrm{v}}$ | overall velocity vector, m s^{−1} |

x_{i,} x_{j} | computational domain dimensions, m |

X_{NH3_in} | mass fraction of NH_{3} at the inlet |

X_{NO_out} | mass fraction of NO at the outlet |

Y_{i} | local mass fraction of species i |

Y_{i,wall} | mass fraction at the wall of the catalyst wires |

Y_{M} | contribution of the fluctuating dilatation in compressible turbulence to the overall dissipation rate, kg m^{−1} s^{−2} |

Z_{i} | site coverage of species i |

Greek symbols: | |

α | empirical constant |

β_{r} | temperature exponent |

ε | turbulent dissipation rate, m^{2} s^{−3} |

η_{r} | NO conversion efficiency |

η_{Pt_trap} | platinum capture efficiency |

μ | continuous phase dynamic viscosity, Pa·s |

μ_{t} | continuous phase turbulent viscosity, Pa·s |

ν | continuous phase kinematic viscosity, m^{2} s^{−1} |

ρ | continuous phase density, kg m^{−3} |

ρ_{site} | site density, kg m^{−3} |

ρ_{wall} | wall phase density, kg m^{−3} |

σ_{k} | turbulent Prandtl number for k |

σ_{ε} | turbulent Prandtl number for ε |

Acronyms: | |

CFD | Computational Fluid Dynamics |

DPM | Discrete Phase Model |

SIMPLE | Semi-Implicit Method for Pressure Linked Equations |

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**Figure 2.**The visualisation of catalyst gauze: (

**a**,

**b**): typical catalyst gauze (Geometry A); (

**c**,

**d**): novel variant of catalyst gauze (Geometry B).

**Figure 4.**Velocity contours for: (

**a**) Geometry A, contact time of 0.001 s; (

**b**) Geometry A, contact time of 0.00025 s; (

**c**) Geometry B, contact time of 0.001 s; (

**d**) Geometry B, contact time of 0.00025 s.

**Figure 5.**Temperature contours for: (

**a**) Geometry A, contact time of 0.001 s; (

**b**) Geometry A, contact time of 0.00025 s; (

**c**) Geometry B, contact time of 0.001 s; (

**d**) Geometry B, contact time of 0.00025 s.

**Figure 6.**Velocity pathlines for: (

**a**) Geometry A, contact time of 0.001 s; (

**b**) Geometry A, contact time of 0.00025 s; (

**c**) Geometry B, contact time of 0.001 s; (

**d**) Geometry B, contact time of 0.00025 s.

**Figure 7.**Conversion efficiency (

**a**) and conversion efficiency per catalyst mass (

**b**) as a function of contact time for Geometries A and B.

**Figure 8.**NH

_{3}mass fraction contours for: (

**a**) Geometry A, contact time of 0.001 s; (

**b**) Geometry A, contact time of 0.00025 s; (

**c**) Geometry B, contact time of 0.001 s; (

**d**) Geometry B, contact time of 0.00025 s.

**Figure 9.**NO mass fraction contours for: (

**a**) Geometry A, contact time of 0.001 s; (

**b**) Geometry A, contact time of 0.00025 s; (

**c**) Geometry B, contact time of 0.001 s; (

**d**) Geometry B, contact time of 0.00025 s.

**Figure 10.**Surface temperature gradient on the first layer of gauze (Geometry A). Platinum particles were released from areas of higher temperature (“hot” zones shown in red).

**Figure 11.**Efficiencies of platinum capture as a function of contact time for Geometry A (

**a**) and Geometry B (

**b**).

**Figure 12.**Trajectories of platinum particles for: (

**a**) Geometry A, contact time of 0.001 s; (

**b**) Geometry A, contact time of 0.00025 s; (

**c**) Geometry B, contact time of 0.001 s; (

**d**) Geometry B, contact time of 0.00025 s.

Species Name | Concentration (Mass Fractions) |
---|---|

NH_{3} | 0.1 |

O_{2} | 0.19 |

N_{2} | 0.71 |

Name | Wire Diameter [mm] | 1st and 3rd Layer Mesh Size [mm] | 2nd Layer Mesh Size [mm] | 2nd Layer Angle Relative to the 1st and 3rd Layers | 2nd Layer Shift Relative to the 1st and 3rd Layers [mm] |
---|---|---|---|---|---|

A | 0.06 | 0.3 × 0.3 | 0.3 × 0.3 | 90° | 0.15; two axes |

B | 0.06 | 0.3 × 0.3 | 0.42 × 0.42 | 45° | 0.15; two axes |

Name | Value | Source |
---|---|---|

contact time of gas phase with a catalyst (s) | 0.001—0.0002 | [22,24] |

gas inlet velocity (m/s) | 0.22—3.17 | calculated, Equation (13) |

gas inlet temperature (K) | 453 | [12] |

operating pressure (bar) | 5 | [22] |

Symbol | Name | Unit | Value | Source |
---|---|---|---|---|

E | activation energy | J mol^{−1} | 6.28·10^{4} | [19] |

A | pre-exponential factor | s^{−1} | 5·10^{11} | [4] |

α | empirical constant | - | 0.69 | [25] |

Geometry | Contact Time [s] | Platinum Capture Efficiency [%] |
---|---|---|

A | 0.001 | 98.10% |

A | 0.00025 | 52.20% |

B | 0.001 | 68.34% |

B | 0.00025 | 92,42% |

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**MDPI and ACS Style**

Tyrański, M.; Pasik, I.; Bujalski, J.M.; Orciuch, W.; Makowski, Ł. Computational Fluid Dynamics of Influence of Process Parameters and the Geometry of Catalyst Wires on the Ammonia Oxidation Process and Degradation of the Catalyst Gauze. *Energies* **2022**, *15*, 8123.
https://doi.org/10.3390/en15218123

**AMA Style**

Tyrański M, Pasik I, Bujalski JM, Orciuch W, Makowski Ł. Computational Fluid Dynamics of Influence of Process Parameters and the Geometry of Catalyst Wires on the Ammonia Oxidation Process and Degradation of the Catalyst Gauze. *Energies*. 2022; 15(21):8123.
https://doi.org/10.3390/en15218123

**Chicago/Turabian Style**

Tyrański, Mariusz, Izabela Pasik, Jakub Michał Bujalski, Wojciech Orciuch, and Łukasz Makowski. 2022. "Computational Fluid Dynamics of Influence of Process Parameters and the Geometry of Catalyst Wires on the Ammonia Oxidation Process and Degradation of the Catalyst Gauze" *Energies* 15, no. 21: 8123.
https://doi.org/10.3390/en15218123