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.
In the example below, we present the mean age distribution within a baffled pipe. Fluid entering the pipe is assigned an initial age of zero and accumulates age as it moves downstream. Spatial variations in the flow field, including recirculation regions behind the baffles, produce non-uniform age distributions across each pipe cross-section. Because the inlet velocity is 1 m/s and the pipe length is 1 m, the mean age of fluid exiting the pipe is 1 s. However, the exit age distribution spans a wide range, from approximately 0.6 s to over 2 s.
Download Sample File: Mean Age
Property Grid¶
General¶
- Start Time
s | Time at which to begin the mean age calculation.
- 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.
- Age Source
This selection defines the inlet boundary where fluid age is initialized to zero. This location serves as the reference point for tracking the residence time and transport history of fluid throughout the system.
Note
Mean ages 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
This blends between first-order upwind and higher-order schemes based on the gradient. Second-order accurate.
- Min Mod
This 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)
This 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
This 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
This achieves accuracy by using a Taylor series expansion in time, combined with spatial derivatives calculated from species fluxes. Second-order accurate.
- Donor Cell
This 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 Output Data¶
The mean age at each inlet or outlet will be recorded as part of the Inlet/Output statistics output. These files are data at the Statistics Output Write Interval.
In addition to the ASCII files, the variation in age across the system will be printed to the slice and volume output files .vtk file. This data can be used for rendering, visualization, and analysis within M-Star Post. These visualization files are printed at both the Plane/Probe Output Write Interval and the Volume Output Write Interval.
More information about the .vtp file structure, see the Visualization Toolkit.
Mean Age Toolbar¶
Context-Specific Toolbar Forms |
Description |
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The Help command launches the M-Star reference documentation in your web browser. |
HelpFor a full description of each selection on the Context-Specific Toolbar, see Toolbar Selections.
Additional Resources¶
Webinars¶
For more on this subject, check out the following: