### 1.2.9. Buoyancy

Natural and mixed convection flows and flows in which gravity is important can be modeled by CFX by the inclusion of buoyancy source terms. Natural convection refers to the case where convection of the fluid is driven only by local density variations, for example, in a closed box with a heat source. Mixed convection refers to the case where convection of the fluid is driven by both a pressure gradient and buoyancy forces.

Buoyancy is driven by variations in density that can arise from a number of sources:

- Local temperature variations cause changes in density; this is natural convection.

- In multicomponent flows, variations in the mass fraction cause density variations because each component usually has a different density.

- In multiphase flows, including particle transport modeling, the difference in density between the phases results in a buoyancy force. For details, see Buoyancy in Multiphase Flow.

- If density is variable for a General Fluid (that is, defined by an expression), a buoyancy force will arise.

- For ideal gases and real fluids, local pressure variations also cause changes in density. These changes are often small and the buoyancy effect is usually not important in the flow. Buoyancy does not necessarily need to be modeled if there are no other sources of buoyancy.

Therefore, for an isothermal, single phase, single component flow using a General Fluid with constant density, there are no buoyancy forces.

The relative importance of buoyancy forces due to temperature variations in a mixed convection flow can be estimated by using the ratio of Grashof and Reynolds Number,

| (1–10)

where is the thermal expansion coefficient. A value approaching or exceeding unity indicates that buoyancy effects are significant in the flow, while small values indicate that buoyancy effects can be ignored.

In purely natural convection problems, the Raleigh Number () indicates the relative strength of the buoyancy induced flow and is given by:

| (1–11)

where is the fluid Prandtl number. The laminar flow regime is generally characterized by <108, while turbulent buoyant flow is characterized by >1010.

For calculations involving buoyancy, the gravity vector components in x, y and z must be set. These are interpreted in the coordinate frame for the domain. For information on setting the gravity vector components for a rotating domain, see Buoyancy In Rotating Domains.

Buoyancy effects can be simulated using one of two available models in CFX:

- Full Buoyancy Model (Density Difference)

- Boussinesq Model

#### 1.2.9.1. Full Buoyancy Model (Density Difference)

For single phase flows, this model is used when the fluid density is a function of temperature or pressure (which includes all ideal gases and real fluids) and when a multicomponent fluid is used. For Eulerian multiphase or particle tracking, it is also set even if all phases have constant density. Significant density variations with temperature occur for most gases. You should specify a Buoyancy Reference Density as an approximate average value of the expected domain density. For multiphase simulations, other factors must be considered. For details, see Buoyancy in Multiphase Flow.

An explanation of the mathematical treatment of the Full Buoyancy model is available in Full Buoyancy Model in the CFX-Solver Theory Guide.

#### 1.2.9.2. Boussinesq Model

For many applications involving buoyancy, it is sufficient to assume a constant fluid density when the change in density over the expected range of conditions is relatively small. This is often true for many liquids. When the fluid density is not a function of pressure or temperature, the Boussinesq model is employed.

The Boussinesq model uses a constant density fluid model, but applies a local gravitational body force throughout the fluid that is a linear function of fluid thermal expansivity, , and the local temperature difference with reference to a datum called the Buoyancy Reference Temperature. You should specify the reference temperature as an approximate average value of the expected domain temperature.

The Boussinesq model can be used for the following cases:

- Single-phase, single component simulations with heat transfer, using a constant density General Fluid. This is the default usage of the Boussinesq model.

- Constant density fluids in an Eulerian or particle tracking multiphase flow with heat transfer in conjunction with the full Buoyancy Model.

. For details, see Buoyancy in Multiphase Flow. Note that the Boussinesq model is not available for multicomponent fluids and Eulerian-Eulerian multiphase flows. To include the effect of temperature on buoyancy in these cases, you must specify the components for which density is a function of temperature (for example, ideal gases).

An explanation of the mathematical treatment of the Boussinesq approximation is available in Boussinesq Model in the CFX-Solver Theory Guide.

#### 1.2.9.3. Buoyancy and Pressure

When buoyancy is activated, the pressure calculated by the solver excludes the hydrostatic pressure gradient. This modified pressure is often called motion pressure because it is responsible for driving the flow. All initial conditions and boundary conditions are interpreted in terms of this modified pressure. For details, see Buoyancy in the CFX-Solver Theory Guide.

In some situations, the true pressure is required to calculate fluid properties. For example, if the fluid is compressible, the density depends on the true pressure rather than the motion pressure. In addition, it is often useful to visualize the true pressure. For these reasons, the solver automatically includes the hydrostatic contribution in the variable called `Absolute Pressure`. The relationship between absolute pressure and the pressure calculated by the solver is available in Buoyancy in the CFX-Solver Theory Guide. When fluid properties are functions of pressure, the absolute pressure is automatically used to evaluate them. Absolute pressure is also written to the results file.

The calculation of absolute pressure requires a buoyancy reference location to be defined. By default, the solver chooses this to be the centroid of one of the pressure-specified boundaries, or if there are no pressure-specified boundaries, the pressure reference location. The pressure reference location is specified under Pressure Level Information on the Solver Control dialog box in CFX-Pre. For details, see Advanced Options Tab. You can optionally specify the buoyancy reference location directly by providing Cartesian coordinates in the domain buoyancy settings.

#### 1.2.9.4. Buoyancy In Rotating Domains

For steady-state rotating domain simulations involving buoyancy, the gravity vector must be aligned with the axis of rotation.

For transient rotating domain simulations involving buoyancy, if the gravity vector is not aligned with the vector of rotation, the solver automatically counter-rotates the relative frame gravity vector such that it has the specified value in the stationary domain.

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