# Thermodynamic Spatial Average of type 7¶

## Description¶

This treatment computes the 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.

It must be applied on 2D surfaces resulting from a revolution cut of an axisymmetric mono-row or multi-row configuration.

This average is recommended for unsteady flows. Then, the input quantities should come from an instantaneous flow solution.

## Construction¶

```
import antares
myt = antares.Treatment('thermo7')
```

## Parameters¶

**base**:`Base`

The base on which the treatment will be applied.

**cylindrical_coordinates**:`list(str)`

, default=*[‘x’, ‘r’, ‘theta’]*The ordered coordinate names of the cylindrical 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.

**label**:`str`

, default=*‘0’*Label to append to ‘0D/Moyenne7#’ for the resulting attribute name.

**dmin**:`float`

, default=*400.e-4*This parameter is only used for logging messages if Q_abs/int_area < dmin. Its unit is kg/s. See Logging Messages to activate logging messages.

## Preconditions¶

The treatment must be applied on a mono-zone **base** containing a 2D section
resulting from a cut with a revolution surface around the ‘x’-axis of an
axisymmetric configuration.
This `Zone`

must contain only one `Instant`

(steady-state).

The specified cylindrical coordinates must be available at nodes.
The rotation axis is the given by the first component of
**cylindrical_coordinates**.

Four constants are necessary for the computation: two gas properties (ideal gas constant and specific heat ratio) and two row properties (rigid rotation of the rows in rad/s and pitch in rad). The gas properties must be available either as attributes or at cells, named respectively ‘Rgas’ or ‘Rgaz’ or ‘R_gas’ and ‘gamma’. These quantities are assumed constant: if there are taken at cells, only one value is kept within the computations. The row properties can be available as attributes in mono-row case, but must be available at cells in multi-row case.

The **conservative** variables must be available at nodes or cells and must be
expressed with the relative velocity formulation in the cartesian coordinate
system.

The `antares.treatment.turbomachine.TreatmentThermoGeom.TreatmentThermoGeom`

must have been called beforehand.
Then, the input base must contain the attribute ‘0D/Geometry’.

## Postconditions¶

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

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

**Xmin, Rmin**Coordinates (in the unit of the input data) of the hub point in the (x, r) plane.

**Xmax, Rmax**Coordinates (in the unit of the input data) of the shroud point in the (x, r) plane.

**Veine**Length (in the unit of the input data) between the hub and the shroud in the surface.

**Angle**Angle (in degrees) between the x-axis and the projection of the surface in the (x, r) plane.

The attribute ‘0D/Moyenne7#<label>’ is a dictionary with variables:

**Debit**Absolute instantaneous massflow rate in the section (kg/s) (|integral of density*normal velocity to the surface|).

**retour**Reverse instantaneous massflow rate (between 0 and 100) defined as 100*((surface integral of absolute massflow rate) - (massflow rate through the oriented surface)) / (surface integral of absolute massflow rate).

**Gcorrige****Greduit****alpha**arctan2(tangential velocity, meridional velocity norm) (in degree).

**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).

**Mv**Instantaneous absolute Mach number built from spatial mean values.

**Ts**Static temperature built from integrals.

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

**Ps**Static pressure built from integrals.

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

**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).

The Instant contained in the input **base** is extended with variables at
cells:

**VelocityX**Velocity in the first

**coordinate**direction in the absolute frame.

**VelocityY**Velocity in the second

**coordinate**direction in the absolute frame.

**VelocityZ**Velocity in the third

**coordinate**direction in the absolute frame.

**Vr**Radial velocity in the absolute frame.

**Vt**Tangential velocity in the absolute frame.

**Vn**Normal velocity in the absolute frame.

**Temperature**Static temperature.

**Tta**Total temperature in the absolute frame.

**Ttr**Total temperature in the relative frame.

**Pressure**Static pressure.

**Pta**Total pressure in the absolute frame.

**Ptr**Total pressure in the relative frame.

**Entropy**Entropy production.