# Characterization of Fluid Flow and Heat Transfer of Expanded Metal Meshes for Catalytic Processes

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Expanded Meshes Characterization

_{v}) and the void fraction (ε) were determined based on scans from microtomography, while the other parameters were measured.

#### 2.2. Experimental Procedure

_{0}of 0.07 ÷ 4 m/s at room temperature and ambient pressure.

_{0}entering the test section (0.2 ÷ 3 m/s).

#### 2.3. Numerical Simulation

#### 2.3.1. Computational Domain and Mesh Generation

_{0}= 1 m/s with respect to the number of elements for mesh type B. Finally, the fine grid was chosen for mesh type B, as well as for other meshes.

#### 2.3.2. Governing Equations

_{i}is the Cartesian coordinates, and u

_{i}is the velocity components.

_{ij}is the stress tensor.

_{p}is the specific heat, k is the thermal conductivity, and T is the temperature.

#### 2.3.3. Boundary Conditions

- Velocity-inlet condition with a uniform value and a static temperature equal to 300 K was defined at the inlet.
- Pressure-outlet condition with zero-gauge pressure was defined at the outlet.
- Constant heat flux and no-slip conditions were imposed on the mesh surface.
- Symmetry condition on the four side boundaries of the computational domain.

#### 2.3.4. Numerical Assumptions

- The air is defined as an ideal gas.
- The flow is in the steady state and laminar due to the maximum value of the Reynolds number, which is nearly 1100 for the arrangement with mesh type B.
- The physical properties of the fluid phase are temperature dependent because of its variations in the simulations.
- The radiative effects were not considered.

#### 2.3.5. Computational Methodology

- A commercially available CFD code, ANSYS FLUENT 21.2, was employed to simulate the fluid flow and heat transfer. The simulation procedure was:
- The pressure–velocity coupling formulation was handled with a coupled algorithm.
- The second-order upwind schemes of discretization were adopted for the momentum and energy equations.
- The residual limit was set to 1 × 10
^{−3}for the continuity and momentum equations and 1 × 10^{−6}for the energy equation.

## 3. Results and Discussion

#### 3.1. Flow Resistance

_{h}= 4ε/S

_{v}and the interstitial fluid velocity u

_{0}= u/ε:

_{y}is approximately 17.4%, 5.7%, and 18.2% for mesh types A, B, and C, respectively. The Fanning friction factor (Figure 5 right) for all meshes studied decreases when the Reynolds number increases, becoming flatter and flatter. However, the lower the Reynolds number, the smaller the discrepancies between meshes types. Computational simulations confirm this trend.

#### 3.2. Heat Transfer

_{y}is approximately 10.1%, 22.3%, and 14.7 for mesh types A, B, and C, respectively).

#### 3.3. Comparison of Different Catalyst Supports

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

A, B | constants |

c_{p} | specific heat, J·kg^{−1}·K^{−1} |

D_{p} | grain diameter, mm |

D_{h} | hydraulic diameter, mm |

d | wire diameter, mm |

e_{y} | average relative error, % |

F | surface area, m^{2} |

f | Fanning friction factor, |

h | heat transfer coefficient, W∙m^{−2}∙K^{−1} |

k | thermal conductivity, W∙m^{−1}∙K^{−1} |

L | bed length, m |

Nu | Nusselt number |

ΔP | pressure drop, Pa |

Pr | Prandtl number |

p | static pressure, Pa |

q | heat flux, W·m^{−2} |

Re | Reynolds number |

S | sheet thickness, mm |

Sc | Schmidt number |

Sh | Sherwood number |

S_{v} | specific surface area, m^{2}∙m^{−3} |

T | temperature, K |

T | strand thickness, mm |

u_{i}, u_{j} | velocity component |

u_{0} | superficial (approach) velocity, m∙s^{−1} |

W | strand width, mm |

x_{i}, x_{j} | Cartesian coordinate |

ε | porosity |

µ | viscosity, Pa∙s |

ρ | density, kg∙m^{−3} |

τ_{ij} | stress tensor |

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**Figure 3.**Experimental apparatus for pressure drop (

**A**) and heat transfer (

**B**) measurements: 1—blower; 2—flowmeter; 3—wire gauze; 4—test reactor; 5—manometer; 6—thermocouples; 7—electric current.

**Figure 4.**Computational domain for mesh type B with boundary conditions (

**left**) and numerical grid (

**right**).

**Figure 5.**Flow resistance characteristics derived from experiments (points) and modeling (lines): (

**left**)—unit pressure drop vs. superficial gas velocity; (

**right**)—Fanning friction factor vs. Reynolds number.

**Figure 6.**Comparison of Fanning friction factor derived from experiments (points) and calculated by correlations from Table 3 (lines).

**Figure 7.**Heat transfer characteristics derived from experiments (points) and modeling (lines): left—heat transfer coefficient vs. superficial gas velocity; right—Nusselt number vs. Reynolds number.

**Figure 8.**Comparison of Nusselt number derived from experiments (points) and calculated by correlations from Table 4 (lines).

**Figure 9.**Comparison of flow resistance (

**left**) and heat transfer (

**right**) of different reactor packings.

Mesh Characterization | A | B | C |
---|---|---|---|

Length of mesh, LWM [mm] | 6 (6 *) | 6 (5 *) | 4 (4 *) |

Width of mesh, SWM [mm] | 3.4 (3.4 *) | 3.5 (3.5 *) | 2.5 (2 *) |

Length of opening, LWO [mm] | 4 (4 *) | 4.5 (3 *) | 2 (2 *) |

Width of opening, SWO [mm] | 2 (2 *) | 2.5 (2 *) | 1.5 (1.5 *) |

Strand thickness, T [mm] | 0.5 (0.5 *) | 0.4 (0.5 *) | 0.3 (0.5 *) |

Strand width, W [mm] | 0.6 (0.6 *) | 0.5 (0.5 *) | 0.4 (0.6 *) |

Sheet thickness, S [mm] | 1.1 | 1 | 0.65 |

Specific surface area, S_{v} [m^{2}/m^{3}] | 1100 | 900 | 1700 |

Void fraction, ε | 0.84 | 0.9 | 0.84 |

Bed length, L [m] | 0.0295 | 0.031 | 0.0181 |

Supplier | Ann-Filters Poland | Ann-Filters Poland | NETex-POL |

Grid Size | No. of Elements | ΔP/L [Pa/m] | Difference [%] | Nu | Difference [%] |
---|---|---|---|---|---|

Coarse | 520,239 | 1952.06 | 2.5 | 58.3 | 0.87 |

Medium | 766,915 | 1928.66 | 1.3 | 58.0 | 0.35 |

Fine | 1,038,352 | 1903.90 | - | 57.8 | - |

EMM | Correlation | Correlation Factor R^{2} | Difference [%] | No of Exp. Points |
---|---|---|---|---|

A | $f=\frac{131.82}{Re}+2.4$ | 0.9988 | 3.07 | 30 |

B | $f=\frac{138.05}{Re}+1.7$ | 0.9983 | 3.35 | 30 |

C | $f=\frac{144.56}{Re}+3.1$ | 0.9987 | 3.95 | 30 |

EMM | Correlation | Correlation Factor R^{2} | Difference [%] | No of Exp. Points |
---|---|---|---|---|

A | $\mathit{Nu}=1.2{\mathit{Re}}^{0.6}{\mathit{Pr}}^{1/3}$ | 0.9956 | 4.06 | 32 |

B | $\mathit{Nu}=1.7{\mathit{Re}}^{0.68}{\mathit{Pr}}^{1/3}$ | 0.9913 | 3.55 | 24 |

C | $\mathit{Nu}=0.77{\mathit{Re}}^{0.67}{\mathit{Pr}}^{1/3}$ | 0.9802 | 4.76 | 28 |

Support Type | S_{v} [m^{2}/m^{3}] | ε | D_{h} [mm] | |
---|---|---|---|---|

EMM | A | 1100 | 0.84 | 3.05 |

B | 900 | 0.9 | 4 | |

C | 1700 | 0.84 | 1.98 | |

WWM [29] | No. 1 (d = 5 mm) | 1025 | 0.786 | 2.93 |

No. 2 (d = 1.13 mm) | 1252 | 0.754 | 2.52 | |

Monolith (L = 0.2 m) | 1339 | 0.72 | 2.15 | |

Packed bed (D_{p} = 3 mm) | 1220 | 0.39 | 1.28 |

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**MDPI and ACS Style**

Iwaniszyn, M.; Sindera, K.; Gancarczyk, A.; Leszczyński, B.; Korpyś, M.; Suwak, M.; Kołodziej, A.; Jodłowski, P.J.
Characterization of Fluid Flow and Heat Transfer of Expanded Metal Meshes for Catalytic Processes. *Energies* **2022**, *15*, 8437.
https://doi.org/10.3390/en15228437

**AMA Style**

Iwaniszyn M, Sindera K, Gancarczyk A, Leszczyński B, Korpyś M, Suwak M, Kołodziej A, Jodłowski PJ.
Characterization of Fluid Flow and Heat Transfer of Expanded Metal Meshes for Catalytic Processes. *Energies*. 2022; 15(22):8437.
https://doi.org/10.3390/en15228437

**Chicago/Turabian Style**

Iwaniszyn, Marzena, Katarzyna Sindera, Anna Gancarczyk, Bartosz Leszczyński, Mateusz Korpyś, Mikołaj Suwak, Andrzej Kołodziej, and Przemysław J. Jodłowski.
2022. "Characterization of Fluid Flow and Heat Transfer of Expanded Metal Meshes for Catalytic Processes" *Energies* 15, no. 22: 8437.
https://doi.org/10.3390/en15228437