8.3. Post-Processing#

8.3.1. Non-Dimensional Outputs#

The following list shows some commonly used non-dimensional variables in the output files:

Table 8.3.1 Reference values for non-dimensional outputs in Flow360#
Property	Ref. value for non-dim.	Examples in Flow360
Length	$L_\text{gridUnit}$	{volumeOutput, surfaceOutput}->wallDistance
Density	$\rho_\infty$	{surfaceOutput, volumeOutput}->primitiveVars
Velocity	$C_\infty$	{surfaceOutput, volumeOutput}->primitiveVars
Pressure	$\rho_\infty C_\infty^2$	{surfaceOutput, volumeOutput}->primitiveVars, surfaceOutput->nodeForcesPerUnitArea
Temperature	$T_\infty$	volumeOutput->T
Force	$\rho_\infty C_\infty^2 L_\text{gridUnit}^2$	force in BET output
Moment	$\rho_\infty C_\infty^2 L_\text{gridUnit}^3$	moment in BET output

Besides the above non-dimensional quantities, there are also many coefficients commonly used in the community of computational fluid dynamics, e.g. pressure coefficient ($C_p$), skin friction coefficient ($C_f$), lift coefficient ($C_L$), drag coefficient ($C_D$), etc. Flow360 also exports the above coefficients found in volumeOutput, surfaceOutput, sliceOutput as well as the “Forces” tab of web interface.

Caution

It should be noted that the reference velocity $U_\text{ref}$ used to calculate the $C_p, C_f, C_D, C_L$ can be set via freestream/Mach or freestream/MachRef by users. Its definition can be found in case configuration. It is not the same as the reference velocity ($C_\infty$) for non-dimensionalization in Table 8.3.1.

The force coefficients and moment coefficients exported by Flow360 are listed in Table 8.3.2. These coefficients are shown in “Forces” tab of each case in Flow360 web portal. These coefficients can also be fetched by flow360client.case.GetCaseTotalForces(caseId).

Table 8.3.2 Force coefficients and moment coefficients exported by Flow360#
Property	Definition
CL	$\text{Lift}/\frac{1}{2}\rho_\infty U_\text{ref}^2 A_\text{ref}$
CD	$\text{Drag}/\frac{1}{2}\rho_\infty U_\text{ref}^2 A_\text{ref}$
CFx	$\text{Force}_x/\frac{1}{2}\rho_\infty U_\text{ref}^2 A_\text{ref}$
CFy	$\text{Force}_y/\frac{1}{2}\rho_\infty U_\text{ref}^2 A_\text{ref}$
CFz	$\text{Force}_z/\frac{1}{2}\rho_\infty U_\text{ref}^2 A_\text{ref}$
CMx	$\text{Moment}_x/\frac{1}{2}\rho_\infty U_\text{ref}^2 A_\text{ref} L_\text{ref}\left[0\right]$
CMy	$\text{Moment}_y/\frac{1}{2}\rho_\infty U_\text{ref}^2 A_\text{ref} L_\text{ref}\left[1\right]$
CMz	$\text{Moment}_z/\frac{1}{2}\rho_\infty U_\text{ref}^2 A_\text{ref} L_\text{ref}\left[2\right]$

Note

In the above table, all quantities in “Definition” column are dimensional.

$U_\text{ref} = \text{"freestream/MachRef"}\times C_\infty$.
$A_\text{ref} = \text{"geometry/refArea"}\times L_\text{gridUnit}^2$.
$L_\text{ref} = \text{"geometry/momentLength"}\times L_\text{gridUnit}$ and is an array.

The entries $\text{"freestream/MachRef"}$, $\text{"geometry/refArea"}$, $\text{"geometry/momentLength"}$ correspond to the values used in the Flow360.json file.

8.3.2. History Files#

8.3.2.1. BET Loading Output#

After the simulation is completed, a “bet_forces_v2.csv” file is created for the case, which contains the time history of the following quantities:

Integrated x-, y-, z-component of non-dimensional forces and non-dimensional moments acted on each disk, represented by “Disk[diskID]_Force_x,_y,_z” and “Disk[diskID]_Moment_x,_y,_z” in the “bet_forces_v2.csv file” respectively. The “xyz” axis is based on the inertial frame of reference. The non-dimensional force is defined as

(8.3.1)#\[\text{Force}_\text{non-dimensional} = \frac{\text{Force}_\text{physical}\text{(SI=N)}}{\rho_\infty C_\infty^2 L_{gridUnit}^2}\]

The non-dimensional moment is defined as

(8.3.2)#\[\text{Moment}_\text{non-dimensional} = \frac{\text{Moment}_\text{physical}\text{(SI=N$\cdot$m)}}{\rho_\infty C_\infty^2 L_{gridUnit}^3},\]

where the moment center is the centerOfRotation of each disk, defined in BETDisks of Flow360.json.

Note

The above Force and Moment values mean the force and moment acted on solid. If you want to know the force and moment acted on fluid, just add a negative sign in front of it.

Attention

The x-, y-, z-component of Disk[diskID]_Force and Disk[diskID]_Moment is reported in the global inertial reference frame. This reference frame is defined in the mesh file.

Sectional thrust coefficient $C_t$ and sectional torque coefficient $C_q$ on each blade at several radial locations, represented by “Disk[diskID]_Blade[bladeID]_R[radialID]” with suffix “_Radius” (non-dimensional), “_ThrustCoeff” and “_TorqueCoeff”. The number of radial locations is specified in nLoadingNodes.

The definition of $C_t$ is

(8.3.3)#\[C_t\bigl(r\bigr)=\frac{\text{Thrust per unit blade span (SI=N/m)}}{\frac{1}{2}\rho_{\infty}\left((\Omega r)^2\right)\text{chord}_{\text{ref}}}\cdot\frac{r}{R}\]

The definition of $C_q$ is

(8.3.4)#\[C_q\bigl(r\bigr)=\frac{\text{Torque per unit blade span (SI=N)}}{\frac{1}{2}\rho_{\infty}\left((\Omega r)^2\right)\text{chord}_{\text{ref}}R}\cdot\frac{r}{R}\]

where $r$ is the dimensional distance between the node to the axis of rotation. $\text{chord}_\text{ref}$ is the dimensional reference chord length. $R$ is the dimensional radius of the rotor disk.

Important

All the quantities in the right hand side of Eq.(8.3.1), Eq.(8.3.2), Eq.(8.3.3) and Eq.(8.3.4) are dimensional, which are different from the non-dimensional values in BETDisks (list) of Flow360.json. For example, at the first disk’s first blade’s first radial location $r=\text{Disk0_Blade0_R0_Radius}\times L_\text{gridUnit}$. The conventions for non-dimensional outputs can be found at Non-Dimensional Outputs.

Warning

For simulations of the steady blade disk solver, the resulting $C_t$ and $C_q$ are only saved on the first blade, named by “Blade0”. They are written as all zeros for other blades, because all the blades have the same sectional loadings in steady blade disk simulations. For the unsteady blade line solver, each blade has its own $C_t$ and $C_q$ values.

Here is an example of the header of a “bet_forces_v2.csv” file from a simulation containing two BET disks (assume nLoadingNodes = 20, numberOfBlades = 3 for each disk):

physical_step, pseudo_step,
Disk0_Force_x, Disk0_Force_y, Disk0_Force_z, Disk0_Moment_x, Disk0_Moment_y, Disk0_Moment_z,
Disk0_Blade0_R0_Radius, Disk0_Blade0_R0_ThrustCoeff, Disk0_Blade0_R0_TorqueCoeff,
Disk0_Blade0_R1_Radius, Disk0_Blade0_R1_ThrustCoeff, Disk0_Blade0_R1_TorqueCoeff,
...
Disk0_Blade0_R19_Radius, Disk0_Blade0_R19_ThrustCoeff, Disk0_Blade0_R19_TorqueCoeff,
Disk0_Blade1_R0_Radius, Disk0_Blade1_R0_ThrustCoeff, Disk0_Blade1_R0_TorqueCoeff,
Disk0_Blade1_R1_Radius, Disk0_Blade1_R1_ThrustCoeff, Disk0_Blade1_R1_TorqueCoeff,
...
Disk0_Blade1_R19_Radius, Disk0_Blade1_R19_ThrustCoeff, Disk0_Blade1_R19_TorqueCoeff,
Disk0_Blade2_R0_Radius, Disk0_Blade2_R0_ThrustCoeff, Disk0_Blade2_R0_TorqueCoeff,
Disk0_Blade2_R1_Radius, Disk0_Blade2_R1_ThrustCoeff, Disk0_Blade2_R1_TorqueCoeff,
...
Disk0_Blade2_R19_Radius, Disk0_Blade2_R19_ThrustCoeff, Disk0_Blade2_R19_TorqueCoeff,
Disk1_Force_x, Disk1_Force_y, Disk1_Force_z, Disk1_Moment_x, Disk1_Moment_y, Disk1_Moment_z,
...
...
...
Disk1_Blade2_R19_Radius, Disk1_Blade2_R19_ThrustCoeff, Disk1_Blade2_R19_TorqueCoeff

8.3.3. Visualization Files#

Visualization output formats we support are:

ParaView (.pvtu).
Tecplot (.dat and .szplt).

How to convert the non-dimensional variables in the output files are shown as follows:

8.3.3.1. Velocity#

Because the reference value of velocity is $C_\infty$ from Table 8.3.1, the dimensional velocity in X direction can be obtained by multiplying the velocityX with speed of sound of freestream. Assume the speed of sound in the freestream is 340 m/s and velocityX is 0.6 in the Paraview/Tecplot file, the dimensional velocity in X direction is $340 \text{ m/s} \times 0.6 = 204 \text{ m/s}$.

8.3.3.2. Pressure#

The reference value of pressure is $\rho_\infty C_\infty^2$ from Table 8.3.1. Assume the speed of sound in the freestream is 340 m/s, freestream density is 1.225 $\text{kg}/\text{m}^3$ and p is 0.65 in the Paraview/Tecplot file, the dimensional pressure is $0.65 \times 1.225 \, \text{kg}/\text{m}^3 \times 340^2 \, \text{m}^2/\text{s}^2 = 92046.5 \, \text{Pascal}$.