Pressure

Simcenter STAR-CCM+ simulates various pressure quantities, depending on the model selection.

Reference Pressure

The reference pressure $P_{\text{ref}}$ is a device that reduces the numerical roundoff error in the numerical calculations involving pressure. For more information, see Setting Reference Values.

Working Pressure

The working pressure is the solution variable $p$ that is used in the flow models in Simcenter STAR-CCM+. In the code and in the documentation, this variable is mentioned most of the time as pressure. Its definition is a matter of computational convenience and depends on the model selection. It is always expressed relative to the reference pressure $P_{\text{ref}}$ .

In laminar flows without the influence of gravity, pressure is equal to the static gauge pressure. If the gravity model is active, pressure is equal to the piezometric pressure, as shown in Eqn. (862) for variable and constant density flows.

When a turbulence model is used, working pressure includes the contribution of $\frac{2}{3}\rho k$ . This contribution can be considered negligible in most flows of engineering interest.

Static Pressure

The static pressure $P_{\text{stat}}$ is the spherical part of the stress tensor acting in fluids (see Eqn. (946)). It happens that the static pressure is the same as the thermodynamic pressure, which is one of the state variables.

Hydrostatic Pressure

The hydrostatic pressure $P_{\text{hydro}}$ is the pressure exerted by a fluid in equilibrium at a given altitude within the fluid due to the force of gravity:

$P_{\text{hydro}}={\rho }_{\text{ref}}g(x_0-x)$

where:

• ${\rho }_{\text{ref}}$ is the reference density.
• $g$ is gravity.
• $x$ is the altitude.
• $x_0$ is the reference altitude.

Absolute Pressure

The absolute pressure $P_{\text{abs}}$ is the sum of working pressure, reference pressure, and, when gravity is present, hydrostatic pressure.

$P_{\text{abs}}=p+P_{\text{ref}}+P_{\text{hydro}}$

Relative Total Pressure

The relative total pressure is the pressure that results from isentropically bringing the flow to rest in the relative frame of motion.

Absolute Total Pressure

The absolute total pressure $P_{t,\text{abs}}$ is the pressure that results from isentropically bringing the flow to rest in the absolute frame.

For ideal gas:

$P_{\text{t,abs}}=P_{\text{abs}}{(1+\frac{\gamma -1}{2}{M}^2)}^{\gamma /(\gamma -1)}$

where $\gamma$ is the ratio of specific heats and $M$ is the Mach number.

For incompressible fluid, absolute total pressure is the sum of absolute pressure and dynamic pressure:

$P_{\text{t,abs}}=P_{\text{abs}}+\frac{1}{2}\rho v^2$

Total Pressure

The total pressure $P_t$ is the absolute total pressure minus the reference pressure and, when gravity is present, the hydrostatic pressure:

$P_t=P_{\text{t,abs}}-P_{\text{ref}}-P_{\text{hydro}}$