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Fanno Flow Relations

 import minuteman.cpg.fanno as fanno

This module computes 1D, calorically perfect gas with friction (Fanno flow).

High-level API

minuteman.cpg.fanno.lookup_table_by_density 

lookup_table_by_density(
    density_ratio: ArraylikeFloat, specific_heat_ratio: ArraylikeFloat = 1.4
) -> FannoFlowTable

Look up a Fanno flow table result from the density ratio, \(\rho / \rho^*\)

Parameters:

  • density_ratio (ArraylikeFloat) –

    density ratio, \(\rho / \rho^*\). Bounds: \(\left(\sqrt{\frac{\gamma-1}{\gamma+1}}, \infty \right)\)

  • specific_heat_ratio (ArraylikeFloat, default: 1.4 ) –

    ratio of specific heats, \(\gamma\). Bounds: \([1.0, 1.67]\)

Returns:

Raises:

minuteman.cpg.fanno.lookup_table_by_entropy 

lookup_table_by_entropy(
    entropy_ratio: ArraylikeFloat,
    specific_heat_ratio: ArraylikeFloat = 1.4,
    flow_regime: ArraylikeFlowSpeedRegime = FlowSpeedRegime.supersonic,
) -> FannoFlowTable

Look up a Fanno flow table result from the entropy ratio, \((s* - s) / R\)

Parameters:

  • entropy_ratio (ArraylikeFloat) –

    entropy ratio, \((s* - s) / R\). Bounds: \([0, \infty)\)

  • specific_heat_ratio (ArraylikeFloat, default: 1.4 ) –

    ratio of specific heats, \(\gamma\). Bounds: \([1.0, 1.67]\)

  • flow_regime (ArraylikeFlowSpeedRegime, default: supersonic ) –

    flow speed regime (either supersonic or subsonic).

Returns:

Raises:

minuteman.cpg.fanno.lookup_table_by_fanno_parameter 

lookup_table_by_fanno_parameter(
    fanno_parameter: ArraylikeFloat,
    specific_heat_ratio: ArraylikeFloat = 1.4,
    flow_regime: ArraylikeFlowSpeedRegime = FlowSpeedRegime.supersonic,
) -> FannoFlowTable

Look up a Fanno flow table result from the Fanno parameter, \(4 f L^* / D\)

Parameters:

  • fanno_parameter (ArraylikeFloat) –

    Fanno parameter, \(4 f L^* / D\). Subsonic Bounds: \([0, \infty)\), Supersonic Bounds: \(\left[0, -\frac{1}{\gamma} + \frac{\gamma+1}{2\gamma} \ln\left(\frac{\gamma+1}{\gamma-1}\right) \right)\)

  • specific_heat_ratio (ArraylikeFloat, default: 1.4 ) –

    ratio of specific heats, \(\gamma\). Bounds: \([1.0, 1.67]\)

  • flow_regime (ArraylikeFlowSpeedRegime, default: supersonic ) –

    flow speed regime (either supersonic or subsonic).

Returns:

Raises:

  • OutOfBoundsError –

    invalid inputs

  • InvalidArrayShapeError –

    input array shapes are incompatible

minuteman.cpg.fanno.lookup_table_by_mach 

lookup_table_by_mach(
    mach: ArraylikeFloat, specific_heat_ratio: ArraylikeFloat = 1.4
) -> FannoFlowTable

Look up a Fanno flow table result from the Mach number, \(M\)

Parameters:

  • mach (ArraylikeFloat) –

    Mach number, \(M\). Bounds: \((0, \infty)\)

  • specific_heat_ratio (ArraylikeFloat, default: 1.4 ) –

    ratio of specific heats, \(\gamma\). Bounds: \([1.0, 1.67]\)

Returns:

Raises:

minuteman.cpg.fanno.lookup_table_by_pressure 

lookup_table_by_pressure(
    pressure_ratio: ArraylikeFloat, specific_heat_ratio: ArraylikeFloat = 1.4
) -> FannoFlowTable

Look up a Fanno flow table result from the static pressure ratio, \(p / p^*\)

Parameters:

  • pressure_ratio (ArraylikeFloat) –

    static pressure ratio, \(p / p^*\). Bounds: \((0, \infty)\)

  • specific_heat_ratio (ArraylikeFloat, default: 1.4 ) –

    ratio of specific heats, \(\gamma\). Bounds: \([1.0, 1.67]\)

Returns:

Raises:

minuteman.cpg.fanno.lookup_table_by_temperature 

lookup_table_by_temperature(
    temperature_ratio: ArraylikeFloat, specific_heat_ratio: ArraylikeFloat = 1.4
) -> FannoFlowTable

Look up a Fanno flow table result from the static temperature ratio, \(T / T^*\)

Parameters:

  • temperature_ratio (ArraylikeFloat) –

    static temperature ratio, \(T / T^*\). Bounds: \(\left(0, \frac{\gamma+1}{2} \right)\)

  • specific_heat_ratio (ArraylikeFloat, default: 1.4 ) –

    ratio of specific heats, \(\gamma\). Bounds: \([1.0, 1.67]\)

Returns:

Raises:

minuteman.cpg.fanno.lookup_table_by_total_pressure 

lookup_table_by_total_pressure(
    total_pressure_ratio: ArraylikeFloat,
    specific_heat_ratio: ArraylikeFloat = 1.4,
    flow_regime: ArraylikeFlowSpeedRegime = FlowSpeedRegime.supersonic,
) -> FannoFlowTable

Look up a Fanno flow table result from the total pressure ratio, \(p_0 / p_0^*\)

Parameters:

  • total_pressure_ratio (ArraylikeFloat) –

    total pressure ratio, \(p_0 / p_0^*\). Bounds: \([1, \infty)\)

  • specific_heat_ratio (ArraylikeFloat, default: 1.4 ) –

    ratio of specific heats, \(\gamma\). Bounds: \([1.0, 1.67]\)

  • flow_regime (ArraylikeFlowSpeedRegime, default: supersonic ) –

    flow speed regime (either supersonic or subsonic).

Returns:

Raises:

Low-level API

minuteman.cpg.fanno.density_ratio_by_mach 

density_ratio_by_mach(
    mach_initial: ArraylikeFloat, mach_final: ArraylikeFloat, specific_heat_ratio: ArraylikeFloat
) -> NDArrayFloat

Compute the density ratio \(\rho_2 / \rho_1\) from the Mach number for Fanno flow.

This is equivalent to velocity ratio \(u_1 / u_2\)

Parameters:

  • mach_initial (ArraylikeFloat) –

    Initial Mach number, \(M_1\). This is the reference Mach number, \(M^*\), when equal to unity.

  • mach_final (ArraylikeFloat) –

    Final Mach number, \(M_2\). This is simply the Mach number, \(M\), when mach_initial==1.0

  • specific_heat_ratio (ArraylikeFloat) –

    ratio of specific heats, \(\gamma\)

Returns:

  • NDArrayFloat –

    Density ratio, \(\rho_2 / \rho_1\) (\(\rho / \rho^*\) if \(M_2=1.0\))

minuteman.cpg.fanno.duct_length 

duct_length(
    fanno_parameter: ArraylikeFloat,
    diameter: ArraylikeFloat,
    friction_coeff: ArraylikeFloat = 0.005,
) -> NDArrayFloat

Compute duct length \(L\) for a given Fanno parameter \(4 f L / D\).

Parameters:

  • fanno_parameter (ArraylikeFloat) –

    Fanno flow parameter, \(4 f L / D\)

  • diameter (ArraylikeFloat) –

    duct diameter, \(D\)

  • friction_coeff (ArraylikeFloat, default: 0.005 ) –

    average friction coefficient \(f\). Defaults to 0.005. The default holds for \(Re > 1e5\) and surface roughness of \(0.001 D\)

Returns:

minuteman.cpg.fanno.entropy_ratio_by_mach 

entropy_ratio_by_mach(
    mach_initial: ArraylikeFloat, mach_final: ArraylikeFloat, specific_heat_ratio: ArraylikeFloat
) -> NDArrayFloat

Compute specific entropy ratio \((s_2 - s_1) / R\) for Fanno flow.

Parameters:

  • mach_initial (ArraylikeFloat) –

    Mach number at station 1, \(M_1\) (initial or upstream Mach)

  • mach_final (ArraylikeFloat) –

    Mach number at station 2, \(M_2\) (final or downstream Mach)

  • specific_heat_ratio (ArraylikeFloat) –

    ratio of specific heats, \(\gamma\)

Returns:

  • NDArrayFloat –

    Specific entropy ratio, \((s_2 - s_1) / R\)

  • NDArrayFloat –

    (\((s - s^*) / R\) if mach_initial==1.0)

minuteman.cpg.fanno.fanno_parameter_by_mach 

fanno_parameter_by_mach(
    mach_initial: ArraylikeFloat, mach_final: ArraylikeFloat, specific_heat_ratio: ArraylikeFloat
) -> NDArrayFloat

Compute Fanno parameter, \(4L f / D\) where \(L=x_2 - x_1\)

Parameters:

  • mach_initial (ArraylikeFloat) –

    Initial Mach number, \(M_1\). This is simply the Mach number, \(M\), when mach_final==1.0

  • mach_final (ArraylikeFloat) –

    Final Mach number, \(M_2\). This is the reference Mach number, \(M^*\), when equal to unity.

  • specific_heat_ratio (ArraylikeFloat) –

    ratio of specific heats, \(\gamma\)

Returns:

  • NDArrayFloat –

    Fanno parameter, \(4L f / D\) (\(4 L^* f / D\) if \(M_2=1.0\))

minuteman.cpg.fanno.pressure_ratio_by_mach 

pressure_ratio_by_mach(
    mach_initial: ArraylikeFloat, mach_final: ArraylikeFloat, specific_heat_ratio: ArraylikeFloat
) -> NDArrayFloat

Compute the static pressure ratio \(p_2 / p_1\) from the Mach number \(M\) for Fanno flow.

Parameters:

  • mach_initial (ArraylikeFloat) –

    Initial Mach number, \(M_1\). This is the reference Mach number, \(M^*\), when equal to unity.

  • mach_final (ArraylikeFloat) –

    Final Mach number, \(M_2\). This is simply the Mach number, \(M\), when mach_initial==1.0

  • specific_heat_ratio (ArraylikeFloat) –

    ratio of specific heats, \(\gamma\)

Returns:

  • NDArrayFloat –

    Static pressure ratio, \(p_2 / p_1\) (\(p / p^*\) if \(M_2=1.0\))

minuteman.cpg.fanno.temperature_ratio_by_mach 

temperature_ratio_by_mach(
    mach_initial: ArraylikeFloat, mach_final: ArraylikeFloat, specific_heat_ratio: ArraylikeFloat
) -> NDArrayFloat

Compute the static temperature ratio \(T_2 / T_1\) from the Mach number for Fanno flow.

Parameters:

  • mach_initial (ArraylikeFloat) –

    Initial Mach number, \(M_1\). This is the reference Mach number, \(M^*\), when equal to unity.

  • mach_final (ArraylikeFloat) –

    Final Mach number, \(M_2\). This is simply the Mach number, \(M\), when mach_initial==1.0

  • specific_heat_ratio (ArraylikeFloat) –

    ratio of specific heats, \(\gamma\)

Returns:

  • NDArrayFloat –

    Static temperature ratio, \(T_2 / T_1\) (\(T / T^*\) if \(M_2=1.0\))

minuteman.cpg.fanno.total_pressure_ratio_by_mach 

total_pressure_ratio_by_mach(
    mach_initial: ArraylikeFloat, mach_final: ArraylikeFloat, specific_heat_ratio: ArraylikeFloat
) -> NDArrayFloat

Compute total pressure ratio \(p_{02} / p_{01}\) for Fanno flow.

Parameters:

  • mach_initial (ArraylikeFloat) –

    Initial Mach number, \(M_1\). This is the reference Mach number, \(M^*\), when equal to unity.

  • mach_final (ArraylikeFloat) –

    Final Mach number, \(M_2\). This is simply the Mach number, \(M\), when mach_initial==1.0

  • specific_heat_ratio (ArraylikeFloat) –

    ratio of specific heats, \(\gamma\)

Returns:

  • NDArrayFloat –

    Total pressure ratio, \(p_{02} / p_{01}\) (\(p_0 / p_0^*\) if \(M_2=1.0\))

Data Structures

minuteman.cpg.fanno.FannoFlowTable dataclass

Fanno flow table where the initial Mach number \(M_1=M^*=1.0\)

mach: NDArrayFloat instance-attribute

Mach number, \(M\)

temperature_ratio: NDArrayFloat instance-attribute

Temperature ratio, \(T / T^*\)

pressure_ratio: NDArrayFloat instance-attribute

Static pressure ratio, \(p / p^*\)

density_ratio: NDArrayFloat instance-attribute

Density ratio, \(\rho / \rho^*\)

velocity_ratio: NDArrayFloat property

Velocity ratio, \(u / u^*\)

total_pressure_ratio: NDArrayFloat instance-attribute

Total pressure ratio, \(p_0 / p_0^*\)

fanno_parameter: NDArrayFloat instance-attribute

Fanno parameter, \(4 f L^* / D\)

entropy_ratio: NDArrayFloat instance-attribute

Specific entropy ratio, \((s^* - s) / R\)

specific_heat_ratio: NDArrayFloat instance-attribute

Ratio of specific heats, \(\gamma\)