# Thermodynamic LES average weighted by mass flux¶

## Description¶

This treatment computes the spatial and temporal mean of three LES quantities. The formula of the average is weighted by mass flux.

This thermodynamic average is available for the mean flow and instantaneous flow fields of unsteady flows.

## Parameters¶

• base: antares.api.Base.Base

The base on which the treatment will be applied.

• conservative: list(str), default= [‘rhou’, ‘rhouPtotal’, ‘rhouTtotal’, ‘alpha’]

Names of turbomachinery conservative variables. The order has to be respected:

• first, the momentum in the x direction,

• then the total pressure multiplied by the x-momentum,

• then the total temperature multiplied by the x-momentum,

• and finally the gyration angle (optional).

• cell_surface_var: str, default= ‘cell_volume’

Name of the surface variable of the mesh elements in the antares.api.Instant. For instance, if the antares.treatment.turbomachine.TreatmentThermoGeom has been called beforehand, then the variable is named ‘surface’.

## 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 antares.api.Zone may contain one antares.api.Instant (steady-state) or several of them (instantaneous solutions at several instants).

For steady flows, the input quantities should directly come from the solver’s output. In fact, due to ergodicity, make sure that quantities involved are well defined in the flow solution. For instance, for the AVBP solver, the run.params file must contain at least the following options in the OUTPUT-CONTROL section:

save_average = yes
save_average.mode = packages
save_average.packages = conservative
save_average.packages = turbomachinery


For unsteady flows, the input base must contain several antares.api.Instant. Every instant will be taken into account to perform the time averaging.

The conservative variables must be available at nodes or cells.

## Postconditions¶

The input base is returned, extended with the attribute named ‘0D/MoyenneLES#Steady’.

This attribute is a dictionary with the following key:

• Ptotal

associated to the quantity $$\frac{< \overline{\rho u P_{total}} >}{< \overline{\rho u} >}$$

• Ttotal

associated to the quantity $$\frac{< \overline{\rho u T_{total}} >}{< \overline{\rho u} >}$$

• alpha

associated to the quantity $$< \overline{\alpha} >$$

where

$$<\phi(\vec{x},t)> = \frac{1}{S} \iint_S \phi(\vec{x},t).\vec{n} \ dS$$ with $$\vec{n}$$ the normal vector to the surface S and,

$$\overline{\phi(\vec{x},t)} = \frac{1}{t_f - t_0} \int_{t_0}^{t_f} \phi(\vec{x},t) \ dt$$ with $$t_0$$ and $$t_f$$ respectively the starting and ending times of the temporal averaging.

## Examples¶

We consider a LES solution averaged in time from the AVBP solver. Therefore, the conservative variables are already in the base as solver’s outputs with the names rhou, rhouPt and rhouTt. If the turbomachinery package is used, the alpha variable is also already computed under the name angle_alpha.

import antares

# if the surface variable is missing at cell centers
base.compute_cell_volume(coordinates=['x', 'y', 'z'])

myt = antares.Treatment('ThermoLES')
myt['base'] = base
myt['conservative'] = ['rhou', 'rhouPt', 'rhouTt', 'angle_alpha']
myt['cell_surface_var'] = 'cell_volume'
base = myt.execute()


We now consider several instantaneous LES solutions. Therefore, conservative variables may not be in the solver’s outputs. However, they must be in the base, hence here they are computed through antares.api.Base.Base.compute(). However, alpha must be in the base if turbomachinery package is on.

import antares

# compute the missing variable
base.compute('rhou = rho*u')
base.compute('rhouPt = rhou*Ptotal')
base.compute('rhouTt = rhou*Ttotal')

myt = antares.Treatment('ThermoLES')
myt['base'] = base
myt['conservative'] = ['rhou', 'rhouPt', 'rhouTt', 'angle_alpha']
base = myt.execute()


## Main functions¶

class antares.treatment.turbomachine.TreatmentThermoLES.TreatmentThermoLES
execute()

Compute the thermodynamic average of LES type on a surface.