Boussinesq buoyancy and reference temperature

Temperature and buoyancy

Vanellus solves the energy equation during every SIMPLE iteration, regardless of the boussinesq setting. The temperature field therefore uses the developing flow field in every simulation.

The boussinesq field controls whether temperature contributes a buoyancy force to the momentum equations:

• With boussinesq: false, coupling is one-way: flow affects temperature, but temperature does not feed back into momentum.
• With boussinesq: true, coupling is two-way: temperature and the request’s gravity vector determine a buoyancy force in the momentum equations.

Enable Boussinesq buoyancy when temperature differences should drive or alter the flow. Leave it disabled when buoyancy is negligible.

It is worth noting that very large temperature gradients can result in strong buoyancy forces, at which point the Boussinesq approximation breaks down.

Reference temperature

Vanellus derives one reference temperature for each simulation; it is not a request field. It uses the arithmetic mean of the prescribed temperatures in these boundary conditions:

• fixed_temp;
• velocity_inlet;
• ambient_pressure_inlet; and
• fan_inlet.

If the request contains none of these conditions, the reference temperature is 20 °C. Each contributing boundary condition counts once, regardless of its surface area.

Other request temperatures do not contribute. In particular, ambient_pressure_inlet_outlet only supplies a temperature when flow enters, a radiative ambient temperature does not fix the surface temperature, and a CTM junction temperature is calculated by the solver. The reference temperature is calculated once and does not change during the solve.

The reference temperature does not constrain the solution or predict its average temperature. Reported temperatures remain in °C. Vanellus uses the reference to evaluate the built-in air properties and, when boussinesq is enabled, to calculate the temperature difference that drives buoyancy.

The reference temperature also sets the properties of the built-in air model. Vanellus evaluates humid-air density at this temperature and uses its absolute value in kelvin to calculate the air thermal expansion coefficient, 1 / T_ref.

Boussinesq buoyancy

With Boussinesq buoyancy enabled, Vanellus adds a momentum source proportional to:

-density × thermal_expansion × (temperature - reference_temperature) × gravity

Consequently, fluid above the reference temperature is driven against the gravity vector, while cooler fluid is driven with it. The constant hydrostatic contribution at the reference temperature is absorbed into pressure.

The approximation keeps density constant everywhere else. The source is determined by:

• the gravity vector, which sets the direction and acceleration;
• fluid density;
• fluid thermal_expansion; and
• temperature relative to the simulation’s reference temperature.

The built-in air model resolves density and thermal expansion from the reference temperature. Water uses fixed preset values, while custom fluids use the constant material properties supplied in the request.

The Boussinesq approximation is intended for small density changes. It does not model compressibility, phase change, or strongly temperature-dependent properties.

See also

• Material properties explains density, thermal expansion, and the built-in fluid models.
• Field initialization and starting guesses explains how the reference temperature affects the initial temperature field.
• What the Vanellus solver does places buoyancy within the complete steady-state model.