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The mean age of air in a room validation case belongs to fluid dynamics. This test case aims to validate the following:

- Age of air using the passive scalar transport model
- Scalar mixing distribution

In this project, the age of air within a room is calculated. The SimScale results are compared to the experimental results reported by Martin et. al\(^1\).

The geometry consists of a rectangular room with one inlet and one outlet, as in Figure 1:

The center points of the inlet and outlet are placed at y = 1.8 meters. Details of the room dimensions are provided in Table 1:

Part | Length in x-direction \([m]\) | Length in y-direction \([m]\) | Length in z-direction \([m]\) |

Inlet | 1.92 | 0.30 | 0.20 |

Outlet | 0.20 | 0.30 | 1.92 |

Room | 4.20 | 3.60 | 3.00 |

In the reference study, the outlet is described to be “on the ceiling, close to the east wall (opposite to the air supply)”, however, no exact placement is given. Based on the description and the schematics of the experimental setup, a gap of 0.1 meters is assumed between the outlet and the wall opposite to the air supply:

Note

By extruding the inlet and outlet sufficiently, we can allow the flow field to develop in these sections. In this case study, the inlet and outlet are extruded by a length equal to 8 times their hydraulic diameter \(D_h\).

$$D_h = \frac {4A}{P} \tag{1}$$

In the formula above, \(A\) is the cross-section area and \(P\) is the wetted perimeter. In our case, the hydraulic diameter for the inlet and outlet is 0.24 meters.

**Tool Type**: OpenFOAM®

**Analysis Type**: Incompressible

**Turbulence Model**: k-omega SST

**Mesh and Element Types**: This validation case uses a total of 3 meshes to perform a mesh independence study. All meshes were created in SimScale with the Standard mesher algorithm. In Table 2, an overview of them is presented:

Mesh | Mesh Type | Cells | Element Type |

Coarse | Standard | 171131 | 3D tetrahedral/hexahedral |

Moderate | Standard | 573635 | 3D tetrahedral/hexahedral |

Fine | Standard | 1090381 | 3D tetrahedral/hexahedral |

Figure 2 highlights the discretization of the inlet, obtained with the fine standard mesh.

**Material**:

- Air
*Viscosity model*: Newtonian- \((\nu)\)
*Kinematic viscosity*: 1.5295e-5 \(m^2/s\) - \((\rho)\)
*Density*: 1.196 \(kg/m^3\)

**Boundary Conditions**:

Figure 3 will be used as a reference for the definition of the boundary conditions:

The exact configuration of the boundary conditions is given in the table below:

Boundary | Boundary Type | Velocity \([m/s]\) | Pressure \([Pa]\) | Turb. kinetic energy \([m^2/s^2]\) | Specific dissipation rate \([1/s]\) | Phase Fraction |

Inlet | Custom | 1.68 in the x-direction | Zero gradient | Fixed at 0.129735e-2 | Fixed at 12.48917 | Fixed at 0 |

Outlet | Custom | Inlet-outlet | Fixed at 0 | Zero gradient | Zero gradient | Zero gradient |

Walls | Custom | No-slip | Zero gradient | Wall function | Wall function | Zero gradient |

**Model:**

- \((Sc_{t})\)
*Turb. Schmidt number*= 1 *Diffusion coefficients*= 1e-9 \(m^2/s\)

Note

The *diffusion coefficient* is purposedly set to a small number. The objective is to prevent the scalar from spreading in the domain via diffusion effects, which would reduce the accuracy of the local mean age of air.

**Passive Scalar Sources**

Using Table 1 as a reference, the entire *Room* volume is defined as a *Volumetric passive scalar source*, using a cartesian box geometry primitive. Note that, in this simulation, the extrusions of the inlet and outlet are not defined as sources:

In the experimental tests, Martin et. al\(^1\) first filled the test room with a tracer gas and waited to obtain an even distribution. Afterward, fresh air is released at the inlet, which causes the tracer gas concentration to decay.

A series of gas monitors are used to measure how the concentration of the tracer gas evolves with time. The resulting mean age of air is obtained by calculating the area under the concentration *versus* time curve.

Note

The theoretical value for the mean age of fluid at the outlet is given by Equation 2:

$$Mean\ age\ of\ fluid = \frac {V}{Q} \tag{2}$$

Where \(V\) is the volume of the test environment and \(Q\) is the volumetric flow rate at the inlet. Using the data from the experimental setup in the equation above, we obtain 450 seconds.

On the other hand, the experimental result for the age of air at the outlet was 538 seconds, with a deviation of 6.5%. This discrepancy highlights errors, which are inherent to experimental studies.

The numerical simulation results for the mixing scalar are compared with experimental data presented by Martin et. al\(^1\). The authors use a dimensionless form of the mean age of air to present their results. In the present validation case, the same methodology is used:

$$\overline{\theta} = \frac{\theta}{V/Q} \tag{3}$$

Where:

- \(\overline{\theta}\) is the local mean age of air (dimensionless)
- \(\theta\) is the local mean age of air, in seconds. In the SimScale results, the local mean age is represented by the parameter
*T1* - \(V\) is the volume of the passive scalar source, in \(m^3\)
- \(Q\) is the volumetric flow rate at the inlet, in \(m^3/s\)

A comparison of the dimensionless local mean age (LMA) obtained experimentally and with SimScale is presented. The results are assessed over three lines, placed on the symmetry plane of the geometry (y = 1.8 meters). The lines are distant 1.13 m, 2.2 m, and 3.2 m from the inlet, as seen below:

To perform a mesh independence study, the results from the three meshes created in SimScale were compared. The results for both moderate and fine meshes were found to be mesh independent. Figure 6 shows the results over the line located 1.13 meters away from the inlet.

In the remaining figures, you will find the comparison between the experimental data and the fine mesh results:

In all cases, the SimScale results show the same trends as the experimental values obtained by [1]. Discrepancies are expected, due to the approximations regarding the outlet placement, as well as uncertainties in the experimental results, described in the previous sections.

The figure below shows the mean age of fluid (*T1*) on the symmetry plane of the geometry. The fresh air coming from the inlet quickly mixes with old air in the room. The mean age of air at the outlet for the fine mesh was found to be 449.97 seconds.

Last updated: September 30th, 2020

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