Total Temperature - Boundary Condition Description
Total Temperature boundary condition used to specify the total temperature on the domain boundary. The total temperature is used to compute the static temperature at the boundary, accounting for the fluid’s velocity field. The boundary condition is a wrapper around Fixed Value.
The concept of total temperature is particularly useful when dealing with high-speed flows, where the high kinetic energy of the fluid can cause the temperature to change. In such a situation, using a prescribed static temperature (with Fixed Value) is not correct and may lead to inaccurate results.
Total Temperature - Boundary Condition Understanding Total Temperature
Total Temperature allows the temperature field to adjust to the velocity field, providing a more realistic solution. This boundary condition is crucial for accurately capturing the thermal effects of fluid motion at high speeds. In such cases, considering only the static temperature would neglect the significant thermal energy contribution from the fluid’s kinetic energy.
The relation between total and static temperature is given by the following formula:
\(T_p = \frac{T_0}{1 + \frac{\gamma -1}{2 \gamma} \psi |\vec u|^2}\)
where:
\(T_0\) – total temperature \([K]\)
\(T_p\) – static temperature at the patch \([K]\)
\(\gamma\) – specific heat capacity ratio \([-]\)
\(\psi\) – flux \([-]\)
\(\vec u\) – velocity vector \([\frac{m}{s}]\)
Total Temperature - Boundary Condition Application & Physical Interpretation
The Total Temperature is the condition often used in high-speed flows (highly compressible flows). It defines static temperature on the boundary indirectly by specifying the total temperature. Total temperature accounts for the fluid’s kinetic energy, contributing to the effective thermal energy in high-speed flows. Below are a few examples demonstrating how Total Temperature can be used and how to correctly interpret its meaning.
Total Temperature in Turbo-Machinery applications
Example applications: fans, pump and turbines simulations
These types of simulations can be solved using the rhoPimpleFoam (solver). Total Temperature together with Total Pressure can be applied at the inlet.
| Physics | Pressure | Velocity | Temperature |
|---|---|---|---|
Inlet | Total Pressure | Pressure Inlet-Outlet Velocity | Total Temperature |
Outlet | Fixed Value | Inlet-Outlet | Fixed Value |
Total Temperature - Boundary Condition Total Temperature in SimFlow
Total Temperature can be selected from the drop-down menu in the Boundary Condition panel. The User needs to provide the Total Temperature \(T_0\), also called the stagnation temperature - Figure 1.
\(T_{0}\) - stagnation temperature \([K]\)
Total Temperature - Boundary Condition Total Temperature - Alternatives
In this section, we propose boundary conditions that are alternative to Total Temperature. 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 on the patch |