Mean Age¶

Introduction¶

Users can automatically calculate the transient mean age distribution using Mean Age under the Create menu. After selecting this option from the Menu, users will be prompted to select an age source from among the inlets, a calculation start time, and an age diffusion coefficient. The age diffusion coefficient is related to the molecular self-diffusion coefficient. The spatial variation in the mean age is printed to volume and slice output files. The mean age at each outlet is printed to output.

The transient mean age represents two physical values. First, it represents the average age of molecules at a given point inside the tank, relative to the time these molecules entered the system via the selected inlet. Second, the represents the mean residence time of molecules at a given point inside the tank. For systems with a single outlet, the mean age at the outlet is equal to the volume-averaged mean age. The volume-averaged mean age is also equal to the mean residence time of the system.

Property Grid¶

`General`¶

Start Time: s | Time at which to begin the mean age calculation.

Diffusion Coefficient Type

There are two options for defining the species diffusion coefficient: Constant and UDF.

Constant

The diffusion coefficient is a constant value that is uniform through the simulation domain.

Diffusion Coefficient: m ² /s | Diffusion coefficient of the scalar through the base fluid. Typical liquid-liquid diffusion coefficients range from \(10^{-9}\) to \(10^{-8}\) \(m^2/s\), depending on temperature and composition. Typical gas-gas diffusion coefficient ranges from \(10^{-6}\) to \(10^{-5}\), again depending on temperature and composition.

UDF

The diffusion coefficient is a user-defined function that can be time-varying and non-uniform.

Diffusion Coefficient UDF: m ² /s | This UDF defines the local species diffusion coefficient. One output must be defined within the UDF: a floating-point variable named D. This output variable defines the local species diffusion coefficient within the fluid. This is a voxel-based local UDF, calculated on a voxel-by-voxel basis using the local fluid properties.

Download Sample File: Diffusion Coefficient

Note

Scalar fields can be susceptible to numerical diffusion. Numerical diffusion occurs when the simulated fluid presents a higher diffusivity than the physical fluid. The effects of numerical diffusion can be minimized by reducing the simulation resolution, applying a flux limiter, or increasing the scalar field update interval. When running scalar fields in a simulation, resolution tests should be performed to ensure that the effects of numerical diffusion are negligibly small. This point is discussed in Application of flux limiters to passive scalar advection for the lattice Boltzmann method

`Advanced`¶

Limiter

Flux limiters are used to reduce the effects of numerical diffusion when modeling advection-diffusion processes. Flux limiters address this issue by adaptively blending high-order (accurate but oscillation-prone) and low-order (stable but diffusive) schemes, which controls the numerical flux between cells to ensure the solution remains bounded and physically realistic.

Flux limiters can be classified into both first-order and second-order schemes, each offering advantages depending on the balance needed between accuracy and stability. First-order limiters prioritize stability, introducing more numerical diffusion but remaining reliable in challenging simulations. Second-order limiters increase accuracy, particularly in smooth flow regions, though they may require adjustments to handle oscillations. In most species advection cases, a second-order scheme should be selected.

Van Leer: Blends between first-order upwind and higher-order schemes based on the gradient. Second-order accurate.
Min Mod: Uses a limited slope to prevent oscillations. Good for systems with highly oscillating concentration gradients. Second-order accurate.
MUSCL (Monotonic Upstream-centered Schemes for Conservation Laws): Captures shocks and discontinuities in concentration fields. Adaptively adjusts the flux to prevent oscillations while retaining detail in smooth regions of the flow. Second-order accurate.
Super Bee: Captures steep gradients while maintaining stability. Achieves second-order accuracy in regions where the solution is smooth, but reduces to first-order near steep transitions.
Lax Wendroff: Achieves accuracy by using a Taylor series expansion in time, combined with spatial derivatives calculated from species fluxes. Second-order accurate.
Donor Cell: Determines fluxes based on the direction of flow using values from the upwind cell. Inherently stable and simple to implement, but introduces substantial numerical diffusion. Only valid for systems with a Peclet number greater than two. First-order accurate.

Update Frequency

Updated field every N time steps. Advanced parameter that improves performance for systems with small time steps.

Mean Age Toolbar¶

Context-Specific Toolbar Forms	Description
Help	The Help command launches the M-Star reference documentation in your web browser.

For a full description of each selection on the Context-Specific Toolbar, see Toolbar Selections.