# Thermodynamic Spatial Average of type 0¶

## Description¶

This treatment computes the spatial mean of thermodynamic quantities with a type-0 formula.

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('thermo0')
```

## 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 the cartesian coordinate system, energy stagnation density. These quantities are expressed in the relative (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.

## 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.
Psta, Pta, Tsta, Tta, Ttr, alpha, beta, phi, Ma, Mr must be available at cells.

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/Moyenne0#Steady’.

The attribute ‘0D/Moyenne0#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.

**Area**The area (in the unit of the input data) of the surface on 360 degrees.

**Ep_aube**Ratio of (in %) of the blade area on the surface with blades.

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

**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).

**beta**arctan2(rotating tangential velocity, meridional velocity norm) (in degree).

**phi**arctan2(radial velocity, axial velocity) (in degree).

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

**Mw**Instantaneous relative Mach number built from spatial mean values.

**TIR_Tt1****PI_Pt1****TI_Tt1****Pt1 (Pa)****Tt1 (K)****Ps_Pt1****Ps(sect)**Static pressure (spatial integral of Ps weighted by the surface).

**ETAis****ETApoly**

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

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

**massflow**Massflow rate.

**Tsta**Static temperature.

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

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

**Psta**Static pressure.

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

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

**beta**arctan2(rotating tangential velocity, meridional velocity norm) (in degree).

**phi**arctan2(radial velocity, axial velocity) (in degree)

**Ma**Absolute Mach number.

**Mr**Relative Mach number.