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.

Main functions

class antares.treatment.turbomachine.TreatmentThermo7.TreatmentThermo7

execute()

Compute the thermodynamic average.