Turbulent Mixing Length Inlet - Boundary Condition Description
Turbulent Mixing Length Inlet specifies the turbulent mixing length and the dissipation rate at the inlet of the computational domain. This condition is specifically designed for turbulent flows and is based on Inlet-Outlet. In case of reverse flow, Zero Gradient is applied. Unlike fixed value BC, this derives epsilon from k and mixing length for inlet conditions.
Turbulent Mixing Length Inlet - Boundary Condition Understanding Turbulent Mixing Length Inlet
The formula used in calculation of Turbulent Mixing Length Inlet is as follows:
\(\epsilon_p = \frac{C_\mu^{0.75} k^{1.5}}{L}\)
- \(\epsilon\) - dissipation rate \([m^2/s^3]\)
- \(C_\mu\) - empirical model constant retrieved from turbulence model
- \(k\) - turbulent kinetic energy \([m^2/s^2]\)
- \(l\) - mixing length scale \([m]\)
If the reversed flow appears, the boundary condition switches to zero-gradient condition:
\(\frac{d\epsilon}{dx} = 0\)
To choose proper level of mixing length \(L\), the following recommendations can be followed:
- Understanding the Physical Problem:
The first step is to have a clear understanding of the physical problem and the flow characteristics. The mixing length should correspond to the size of the largest eddies in the turbulent flow. This is often related to the geometry of the problem – for example, the distance from a wall in boundary layer flows. - Based on Flow Geometry:
In many cases, the mixing length can be estimated based on characteristic lengths of the geometry. For instance, in boundary layer flows over a flat plate, it is often estimated as a proportion of the distance from the wall. - Empirical Formulas:
There are empirical formulas to estimate the mixing length. For example, in boundary layer flows, the mixing length \(L\) is often estimated using Prandtl’s mixing length hypothesis
\(L = \kappa \cdot y\)
where: \(κ\) is the von Kármán constant (approximately 0.41)
\(y\) is the distance from the wall.
- Using Experimental Data:
Whenever possible, it’s best to use experimental data or literature values specific to the type of flow you’re studying. This can provide a more accurate estimation of the mixing length. - Adjustments and Calibration:
The chosen value might need adjustments based on simulation results. It’s common to start with a theoretical or empirical value and then calibrate it based on comparison with experimental data or desired outcomes.
Turbulent Mixing Length Inlet - Boundary Condition Application & Physical Interpretation
The Turbulent Mixing Length Inlet is applied in simulations of turbulent flows to provide an accurate initial representation of turbulence. It defines the mixing length, which is used to calculate dissipation rate at the inlet of the domain. It is typically expressed as a percentage of the mean flow velocity.
Turbulent Mixing Length Inlet in Aerodynamics applications
Example applications: car, aircraft aerodynamics, wind tunnel experiment
These types of simulations can be solved using the simpleFoam (solver) This solver has two basic independent variables: pressure and velocity. Additionally, turbulence-related variables can be defined like turbulent kinetic energy, mixing length and others. The Turbulent Mixing Length Inlet can be applied to the domain inlet to represent turbulent flow when the exact measuerments/profiles are not known..
| Physics | Pressure | Velocity | Kinetic Turbulent Energy | Turbulent Mixing Length Inlet |
|---|---|---|---|---|
Velocity Inlet | Zero Gradient | Surface Normal Fixed Value | Turbulent Mixing Length Inlet | Turbulent Mixing Length Inlet |
Outlet | Zero Gradient | Zero Gradient | Zero Gradient | Zero Gradient |
| Tutorial | Description |
|---|---|
External aerodynamic analysis based on the car example. The simulation case includes symmetry conditions and turbulence modeling. |
Turbulent Mixing Length Inlet - Boundary Condition Turbulent Mixing Length Inlet in SimFlow
Turbulent Mixing Length Inlet \(L\) is defined for turbulence-related field \(\epsilon\) available in boundary condition section. The proper option must be selected from the drop-down menu - Figure 1.
The value of \(L\) is required from the User.
Mixing Length - mixing length
Turbulent Mixing Length Inlet - Boundary Condition Turbulent Mixing Length Inlet - Alternatives
In this section, we propose boundary conditions that are alternative to Turbulent Mixing Length Inlet. While they may fulfill similar purposes, they might be better suited for a specific application and provide a better approximation of physical world conditions.
| Boundary Condition | Description |
|---|---|
fixed value of \(k\) on the patch |