Field Histories: Pressure Time Derivative
A field history is a type of field monitor that stores a finite number of past values (or samples) of a field function, captured at moments defined by its update policy, for a given set of input regions or boundaries (or both).
This tutorial demonstrates the field histories feature of Simcenter STAR-CCM+ using the simulation file that was created in the tutorial, Rigid Body Motion: Rotating Fan.
Field histories provide the ability to compute derivatives of solution quantities, for example using turbulent kinetic energy time derivatives to identify power fluctuations. A pressure time derivative, , can help investigate acoustics, among other uses.
In this tutorial, a pressure time derivative is calculated for a rotating radial fan [1002].
From basic transport equations, the substantial or material derivative for pressure is:
Hence to obtain the pressure derivative in a simulation with mesh motion, you must evaluate:
In order to compute the
velocity-gradient term
, you must first obtain the mesh velocity
in each cell. The mesh velocity in each cell can be obtained using a field
history that samples Position, and for which the
resulting field functions are the current time-step,
HistoryofPositionSample0
, and the two previous
time-steps, HistoryofPositionSample1
and
HistoryofPositionSample2
. These are combined in a
field function MeshVelocity
as:
(3*$${HistoryofPositionSample0} - 4*$${HistoryofPositionSample1} + $${HistoryofPositionSample2})/(2*${TimeStep})
The velocity-gradient term can be
computed by a field function, Pconvective_current
:
dot($${MeshVelocity},grad(${Pressure}))
Where Pressure
is
the built-in solution field function.
For computing the final pressure
time derivative d(Pressure)/dt
, the expression is:
(3*${HistoryofPressureSample0} - 4*${HistoryofPressureSample1} + ${HistoryofPressureSample2})/(2*${TimeStep}) - ${Pconvective_current}
For MeshVelocity
and d(Pressure)/dt
, a second order backward-differencing
formulation is used. This formulation comes from [1002].