Choro-averaged Thermodynamic Spatial Average of Type 7¶

Thermodynamic Spatial Average of type 7 with Chorochronic Averaging.

see `antares.treatment.TreatmentChoroReconstruct.TreatmentChoroReconstruct` for the chorochronic reconstruction.

This treatment computes the time-averaged 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.

This average is recommended for unsteady flows. Then, the input quantities should include many snapshots of an unsteady flow.

It must be applied on 2D plane sections resulting from a slice of an axisymmetric configuration. The coordinates are expressed in the cylindrical coordinate system (x, r, t). The rotation axis is the Cartesian ‘x’-coordinate.

Parameters¶

• base: `Base`

The base on which the treatment will be applied.

• coordinates: list(str)

The ordered coordinate names of the Cartesian system. example: [‘x’, ‘y’, ‘z’]

• conservative: list(str), default= [‘rho’, ‘rhou’, ‘rhov’, ‘rhow’, ‘rhoE’]

Names of conservative variables. example: [‘ro’, ‘rovx’, ‘rovy’, ‘rovz’, ‘roE’]

• ref_values: (float, float), default= None

Reference values (total pressure, total temperature) for averaging. This may be the values obtained in a previous section.

• weights: str, default= ‘massflow’

Weights for the averaging. Available massflow (default) or area.

• def_points: list(tuple(float)), default= None

List of coordinates of 2 points in the cylindrical coordinate system. The first point gives the location of the hub. The second point gives the location of the shroud.

• extracts_step: int, default= 1

The number of time iterations between two instants of the base.

• nb_ite_rot: int

The number of time iterations to describe a complete rotation.

• nb_blade: int or ‘in_attr’, default= ‘in_attr’

Number of blades of the current row. If ‘in_attr’, then each zone of the base must have an attribute ‘nb_blade’.

• nb_blade_opp: int or list(int) or ‘in_attr’, default= ‘in_attr’

Number of blades of the opposite row (or list of numbers of blades of the opposite rows in the case of multiple opposite rows). If ‘in_attr’, then each zone of the base must have an attribute ‘nb_blade_opp’.

• omega_opp: float or list(float) or ‘in_attr’, default= ‘in_attr’

Rotation speed of the opposite row (or list of rotation speeds of the opposite rows in the case of multiple opposite rows) expressed in radians per second. If ‘in_attr’, then each zone of the base must have an attribute ‘omega_opp’.

• type: str, default= ‘fourier’

The type of approach (‘fourier’ or ‘least_squares’) used to determine the amplitudes and phases of each interaction mode. If ‘fourier’, a DFT is performed: in the case of a single opposite row, the base should contain enough instants to cover the associated blade passage (‘nb_ite_rot’ / ‘extracts_step’ / ‘nb_blade_opp’); in the case of multiple opposite rows, the base should contain enough instants to cover a complete rotation (‘nb_ite_rot’ / ‘extracts_step’). If ‘least_squares’, a least-squares approach is used. For robustness and accuracy reasons, it is advised to have enough instants in the base to cover at least two blade passages (2 * ‘nb_ite_rot’ / ‘extracts_step’ / ‘nb_blade_opp’).

Preconditions¶

The conservative variables must be expressed with the relative velocity formulation in the Cartesian coordinate system. The cylindrical coordinate system must already be computed.

Main functions¶

class antares.treatment.turbomachine.TreatmentThermo7ChoroAverage.TreatmentThermo7ChoroAverage
execute()

Compute the thermodynamic mean average of type 7 (choro-averaged).

Average of type 7 with chorochronic DFT averaging.

Returns:

the input base extended with 2 attributes named ‘0D/Moyenne#Steady’, ‘0D/Moyenne7#TimeAverage’

Return type:

Base

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

Xmin, Rmin: coordinates of the hub point in the meridional plane. (in m/mm, given by the input data)

Xmax, Rmax: coordinates of the shroud point in the meridional plane. (in m/mm, given by the input data)

Variables:
• Veine – Length between the hub and the shroud.

• Angle – Angle between the x-axis and the (x,r) line (in degree).

The attribute ‘0D/Moyenne7#TimeAverage’ is a dictionary with variables:

Variables:
• Debit – time-averaged massflow rate in the section (kg/s) (integral of density* normal velocity to the surface) * number of sector over 360 degrees (kg/s)

• Mv – time-averaged absolute Mach number built from spatial mean values

• 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)

• TI – absolute total temperature (spatial integral of Tta weighted by the instantaneous massflow rate)

• 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)

• Ps – static pressure built from integrals

• Ts – static temperature built from integrals

• Ps(sect) – static pressure (spatial integral of Ps weighted by the surface)