|
Home / Technical Notes / Fluid Analysis/Fluid-Thermal Analysis / Pressure in Fluid Analysis
Pressure in Fluid Analysis
An idea of pressure in the fluid analysis is explained.
1. Pressure Used in Fluid Analysis
The pressure used in the fluid analysis is explained.
1.1 Absolute Pressure and Gauge Pressure (Relative Pressure)
The pressure is expressed as relative pressure based on the environment pressure.
This is called gauge pressure notation.
For analyses conducted in other than closed domains, either natural inflow, natural outflow, or natural inflow/natural outflow boundary condition is typically applied.
The environment pressure is set to 0 [Pa] there, and pressure in the analysis domain will be calculated based on the environment pressure.
When the natural outflow boundary is set, that is, the environment pressure is set to 0 [Pa], and when the result is 10 [Pa] assuming an atmospheric pressure of 101325 1 [Pa],
then the actual pressure (absolute pressure) is 101325+10=101335 [Pa].
It should be noted that if the analysis is conducted in a closed domain or if no boundary conditions are set to specify the pressure, relative values in the analysis domain are output because no pressure reference is specified.
1.2 Corrected Pressure Excluding Effect of Gravity
The corrected pressure, which excludes the effect of gravity, is applied in Femtet.
The pressure and gravity terms in the Navie-Stokes equation can be separated into the corrected pressure and buoyancy terms using a reference density.
| Pressure and Gravity Terms Notation | Corrected Pressure and Buoyancy Terms Notation |
 |
 |
|
First Term: Pressure Term Second Term: Gravity Term |
First Term: Corrected Pressure Term Second Term: Buoyancy Term |
The corrected pressure is defined as follows.
p: Pressure [Pa]
p': Corrected Pressure [Pa]
ρ: Density [kg/m3]
ρref: Reference Density [kg/m3]
g: Gravity Acceleration Vector [m/s2] , set (0, 0, -9.8) in Femtet
x: Coordinates [m] (x,y,z)
xref:: Reference Coordinates [m] (xref, yref, zref)
See [Differential Equations Solved in the Fluid Analysis/Fluid-Thermal Analysis] for separated equations.
The reference density is defined in the section "4 External Force" in Differential Equations in Fluid Analysis/Fluid-Thermal Analysis.
Advantages of the separation are as follows. If the density is a reference density and constant, that is , the fluid is non-compressive fluid with no buoyancy taken into account,
・ As the buoyancy term becomes zero, it need not be taken into account,
・ Pressure boundary conditions can be easily set.
Given the stationary state where the gravity and pressure terms are balanced, those terms are expressed as follows.
The pressure that satisfies the equation above is expressed as follows.
pref: Pressure [Pa] at z = zref
The equation above indicates larger z coordinate will result in lower pressure and explains following experiences:
"On the higher mountains, atmosphere pressure is lower, and air is thinner", "In the deeper water, water pressure is higher."
The equilibrium between corrected pressure term and buoyancy term is explained by the following equation.
The corrected pressure that satisfies the equation above is expressed as follows.
pref': Corrected Pressure [Pa] at z = zref
The equation above indicates the corrected pressure remains constant regardless of z coordinate.
In the analysis with uncorrected pressure, the pressure of boundary conditions must be set with the slope by height taken into account.
The setting will be complex.
Contrary, in the analysis with corrected pressure, the pressure of boundary conditions can be set constant without the slope by height.
The setting will be simple.
Note that the description above may not be applicable if a fluid with a density other than the reference density flows in or out.
Note the following cases.
・In the fluid thermal analysis with buoyancy taken into account, if the fluid with a temperature other than the reference temperature flows in.
・In the diffusion analysis with weight of diffusing materials taken into account, if the fluid with a diffusion value other than an ambient value flows in.
・In the free surface analysis (VOF method) with gravity taken into account, if the fluid of a phase other than the lightest phase flows in.
For these cases, even in the analysis with corrected pressure, the slope by height must be taken into account.
If [Correct the pressure condition to balance with buoyancy] is selected in the [Detailed Setting of Fluid Analysis] dialog box, Femtet is designed to automatically correct the slope by height and set the corrected pressure.
The corrected pressure assuming the reference height is zref = 0 is applied.
Be aware that if there are multiple pressure boundary conditions, the pressures may mismatch due to the correction.