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.

Main functions

class antares.treatment.turbomachine.TreatmentThermo0.TreatmentThermo0
execute()

Compute the thermodynamic average of type 0 on a surface.