turboflow.axial_turbine.deviation_model module
- turboflow.axial_turbine.deviation_model.get_exit_flow_angle_ainley_mathieson(Ma_exit, Ma_crit, geometry)[source]
Calculate the flow angle using the deviation model proposed by [Ainley and Mathieson, 1951].
This model defines the gauging angle with respect to axial direction:
\[\beta_g = \cos^{-1}(A_\mathrm{throat} / A_\mathrm{out})\]For \(\mathrm{Ma_exit} < 0.50\) (low-speed), the deviation is a function of the gauging angle:
\[\delta_0 = \beta_g - (35.0 + \frac{80.0-35.0}{79.0-40.0}\cdot (\beta_g-40.0))\]For \(0.50 \leq \mathrm{Ma_exit} < \mathrm{Ma_crit}\) (medium-speed), the deviation is calculated by a linear interpolation between low and critical Mach numbers:
\[\delta = \delta_0\cdot \left(1+\frac{0.5-\mathrm{Ma_exit}}{\mathrm{Ma_crit}-0.5}\right)\]For \(\mathrm{Ma_exit} \geq \mathrm{Ma_crit}\) (supersonic), zero deviation is assumed:
\[\delta = 0.00\]The flow angle (\(\beta\)) is then computed based on the deviation and the gauging angle:
\[\beta = \beta_g - \delta\]- Parameters:
- Ma_exitfloat
Exit Mach number.
- Ma_critfloat
Critical Mach number.
- geometrydict
Dictionary containing geometric parameters. Must contain floats A_throat and A_out, representing the cascade throat and exit area respectively.
- Returns:
- float
Flow angle in degrees.
- turboflow.axial_turbine.deviation_model.get_exit_flow_angle_aungier(Ma_exit, Ma_crit, geometry)[source]
Calculate the flow angle using the deviation model proposed by [Aungier, 2006].
This model defines the gauging angle with respect to tangential axis:
\[\beta_g = 90 - \cos^{-1}\left(\frac{A_\mathrm{throat}}{A_\mathrm{out}}\right)\]The model involves a piecewise calculation depending on the mach number range:
For \(Ma_\mathrm{exit} < 0.50\), the deviation is a function of the gauging angle:
\[\delta_0 = \sin^{-1}\left(\frac{A_\mathrm{throat}}{A_\mathrm{out}} \left(1+\left(1-\frac{A_\mathrm{throat}}{A_\mathrm{out}}\right)\cdot\left(\frac{\beta_g}{90}\right)^2\right)\right)\]For \(0.50 \leq Ma_\mathrm{exit} < Ma_\mathrm{crit}\), the deviation is calculated by a fifth order interpolation between low and critical Mach numbers:
\[\begin{split}\begin{align*} X &= \frac{2\cdot Ma_\mathrm{exit}-1}{2\cdot Ma_\mathrm{crit}-1} \\ \delta &= \delta_0 \cdot (1-10X^3+15X^4-6X^5) \end{align*}\end{split}\]For \(Ma_\mathrm{exit} \geq Ma_\mathrm{crit}\), zero deviation is assumed:
\[\delta = 0.00\]The flow angle (\(\beta\)) is then computed based on the deviation and the gauging angle:
\[\beta = 90 - \beta_g - \delta\]- Parameters:
- Ma_exitfloat
Exit Mach number.
- Ma_critfloat
Critical Mach number.
- geometrydict
Dictionary containing geometric parameters. Must contain floats A_throat and A_out, representing the cascade throat and exit area respectively.
- Returns:
- float
Flow angle in degrees.
- turboflow.axial_turbine.deviation_model.get_exit_flow_angle_zero_deviation(Ma_exit, Ma_crit, geometry)[source]
Calculates the flow angle assuming zero deviation. This involves calculating the gauging angle, which is the angle of zero deviation.
The gauging angle is calculated as:
\[\beta_g = \cos^{-1}(A_\mathrm{throat} / A_\mathrm{out})\]where \(A_\mathrm{throat}\) is the cross-sectional area of the throat and \(A_\mathrm{out}\) is the cross-sectional area of the exit.
- Parameters:
- Ma_exitfloat
Exit Mach number.
- Ma_critfloat
Critical Mach number.
- geometrydict
Dictionary containing geometric parameters. Must contain floats A_throat and A_out, representing the cascade throat and exit area respectively.
- Returns:
- float
Flow angle in degrees.
- turboflow.axial_turbine.deviation_model.get_subsonic_deviation(Ma_exit, Ma_crit_throat, geometry, model)[source]
Calculate subsonic relative exit flow angle based on the selected deviation model.
Available deviation models:
“aungier”: Calculate deviation using the method proposed by [Aungier, 2006].
“ainley_mathieson”: Calculate deviation using the model proposed by [Ainley and Mathieson, 1951].
“metal_angle”: Assume the exit flow angle is given by the gauge angle (zero deviation).
- Parameters:
- deviation_modelstr
The deviation model to use (e.g., ‘aungier’, ‘ainley_mathieson’, ‘zero_deviation’).
- Ma_exitfloat or numpy.array
The exit Mach number.
- Ma_critfloat
The critical Mach number (possibly lower than one).
- opening_to_pitchfloat
The ratio of cascade opening to pitch.
- Returns:
- float
The relative exit flow angle including deviation in degrees (subsonic flow only).
- Raises:
- ValueError
If an invalid deviation model is provided.