# Time-averaged Thermodynamic Spatial Average of Type 7¶

## Description¶

This treatment computes the time-averaged spatial mean of thermodynamic quantities with a type-7 formula. This formula is a weighted mean of 5 quantities. The weight may be the mass flow or the area.

This average is recommended for unsteady flows. Then, the input quantities should include many snapshots of an unsteady flow.

## Construction¶

```
import antares
myt = antares.Treatment('thermo7timeaverage')
```

## Parameters¶

**base**:`Base`

The Base that contains the time snapshots of the unsteady flow.

**coordinates**:`list(str)`

, default=*[‘x’, ‘y’, ‘z’]*The ordered coordinate names of the Cartesian system.

**conservative**:`list(str)`

, default=*[‘rho’, ‘rhou’, ‘rhov’, ‘rhow’, ‘rhoE’]*Names of conservative variables: density, momentum components in cartesian coordinates, energy stagnation density.

**velocity_formulation**:`str`

, default=*‘relative’*If

**velocity_formulation**is ‘relative’, then the**conservative**quantities are supposed to be relative quantities in the relative (rotating) frame. If**velocity_formulation**is ‘absolute’, then the**conservative**quantities are supposed to be absolute quantities in the rotating frame.

**ref_values**:`(float, float)`

, default=*None*Reference values (total pressure, total temperature) for averaging. These values may be obtained in a previous section.

**weights**:`str`

in*[‘massflow’, ‘area’]*, default=*‘massflow’*Type of weighting to use for averaging.

**def_points**:`list(tuple(float))`

, default=*None*list of coordinates of 2 points in the cylindrical coordinate system. The first point gives the location of the hub. The second point gives the location of the shroud.

## Preconditions¶

It must be applied on 2D **plane** sections resulting from a slice of an
axisymmetric configuration.
The cylindrical coordinate system must already be computed.
The coordinates are expressed in the cylindrical coordinate system (x, r, t).
The rotation axis is the Cartesian ‘x’-coordinate.

## Postconditions¶

The input **base** is returned, extended with two attributes named
‘0D/Moyenne#Steady’ and ‘0D/Moyenne7#TimeAverage’.

The attribute ‘0D/Moyenne#Steady’ is a dictionary with variables:

**Xmin, Rmin**Coordinates of the hub point in the meridional plane. (in m/mm, given by the input data)

**Xmax, Rmax**Coordinates of the shroud point in the meridional plane. (in m/mm, given by the input data)

**Veine**Length between the hub and the shroud.

**Angle**Angle between the x-axis and the (x,r) line (in degree).

The attribute ‘0D/Moyenne7#TimeAverage’ is a dictionary with variables:

**Debit**time-averaged massflow rate in the section (kg/s) (integral of density * normal velocity to the surface) * number of sector over 360 degrees (kg/s)

**Mv**time-averaged absolute Mach number built from spatial mean values

**VelocityCylindricalX**axial absolute velocity (spatial integral of Vx weighted by the instantaneous massflow rate)

**VelocityCylindricalR**radial absolute velocity (spatial integral of Vt weighted by the instantaneous massflow rate)

**VelocityCylindricalTheta**tangential absolute velocity (spatial integral of Vr weighted by the instantaneous massflow rate)

**TI**absolute total temperature (spatial integral of Tta weighted by the instantaneous massflow rate)

**PI**absolute total pressure built from integrals

**PI(massflow)**absolute total pressure (spatial integral of Pta weighted by the instantaneous massflow rate)

**S_std**entropy (spatial integral of entropy weighted by the instantaneous massflow rate)

**Ps**static pressure built from integrals

**Ts**static temperature built from integrals

**Ps(sect)**static pressure (spatial integral of Ps weighted by the surface)