polykin.transport.flow

DP_GL_Mueller_Bonn

DP_GL_Mueller_Bonn(
    mdotL: float,
    mdotG: float,
    D: float,
    L: float,
    rhoL: float,
    rhoG: float,
    muL: float,
    muG: float,
) -> float

Calculate the pressure drop due to friction in two-phase liquid-gas flow through a horizontal pipe using the Mueller-Bonn correlation.

According to the authors, this correlation performs better than the classical Lockhart-Martinelli correlation, but the average error is still 40%.

References

• Müller-Steinhagen, H., Heck, K. "A simple friction pressure drop correlation for two-phase flow in pipes." Chemical Engineering and Processing: Process Intensification 20.6 (1986): 297-308.

PARAMETER	DESCRIPTION
mdotL	Mass flow rate of liquid (kg/s). TYPE: float
mdotG	Mass flow rate of gas (kg/s). TYPE: float
D	Diameter (m). TYPE: float
L	Length (m). TYPE: float
rhoL	Density of liquid (kg/m³). TYPE: float
rhoG	Density of gas (kg/m³). TYPE: float
muL	Viscosity of liquid (Pa·s). TYPE: float
muG	Viscosity of gas (Pa·s). TYPE: float

RETURNS	DESCRIPTION
float	Pressure drop (Pa).

See also

• DP_GL_Lockhart_Martinelli: alternative method.

Examples:

Calculate the pressure gradient due to friction in a 80 mm inner diameter pipe with 2 kg/s of liquid and 1 kg/s of gas. The liquid and gas have densities of 1000 and 1 kg/m³, respectively, and viscosities of 1e-3 and 2e-5 Pa·s, respectively.

>>> from polykin.transport import DP_GL_Mueller_Bonn
>>> mdotL = 2.0 # kg/s
>>> mdotG = 1.0 # kg/s 
>>> D = 80e-3   # m
>>> L = 1.0     # m
>>> rhoL = 1e3  # kg/m³
>>> rhoG = 1e0  # kg/m³
>>> muL = 1e-3  # Pa·s
>>> muG = 2e-5  # Pa·s 
>>> DP = DP_GL_Mueller_Bonn(mdotL, mdotG, D, L, rhoL, rhoG, muL, muG)
>>> print(f"DP = {DP:.1e} Pa/m")
DP = 1.1e+04 Pa/m

Source code in src/polykin/transport/flow.py

def DP_GL_Mueller_Bonn(mdotL: float,
                       mdotG: float,
                       D: float,
                       L: float,
                       rhoL: float,
                       rhoG: float,
                       muL: float,
                       muG: float
                       ) -> float:
    r"""Calculate the pressure drop due to friction in two-phase liquid-gas
    flow through a horizontal pipe using the Mueller-Bonn correlation.

    According to the authors, this correlation performs better than the
    classical Lockhart-Martinelli correlation, but the average error is still
    40%.

    **References**

    * Müller-Steinhagen, H., Heck, K. "A simple friction pressure drop
      correlation for two-phase flow in pipes." Chemical Engineering and
      Processing: Process Intensification 20.6 (1986): 297-308.

    Parameters
    ----------
    mdotL : float
        Mass flow rate of liquid (kg/s).
    mdotG : float
        Mass flow rate of gas (kg/s).
    D : float
        Diameter (m).
    L : float
        Length (m).
    rhoL : float
        Density of liquid (kg/m³).
    rhoG : float
        Density of gas (kg/m³).
    muL : float
        Viscosity of liquid (Pa·s).
    muG : float
        Viscosity of gas (Pa·s).

    Returns
    -------
    float
        Pressure drop (Pa).

    See also
    --------
    * [`DP_GL_Lockhart_Martinelli`](DP_GL_Lockhart_Martinelli.md): alternative
      method.

    Examples
    --------
    Calculate the pressure gradient due to friction in a 80 mm inner diameter
    pipe with 2 kg/s of liquid and 1 kg/s of gas. The liquid and gas have
    densities of 1000 and 1 kg/m³, respectively, and viscosities of 1e-3 and
    2e-5 Pa·s, respectively. 
    >>> from polykin.transport import DP_GL_Mueller_Bonn
    >>> mdotL = 2.0 # kg/s
    >>> mdotG = 1.0 # kg/s 
    >>> D = 80e-3   # m
    >>> L = 1.0     # m
    >>> rhoL = 1e3  # kg/m³
    >>> rhoG = 1e0  # kg/m³
    >>> muL = 1e-3  # Pa·s
    >>> muG = 2e-5  # Pa·s 
    >>> DP = DP_GL_Mueller_Bonn(mdotL, mdotG, D, L, rhoL, rhoG, muL, muG)
    >>> print(f"DP = {DP:.1e} Pa/m")
    DP = 1.1e+04 Pa/m
    """

    # Flow quality and mass flux
    mdot = mdotL + mdotG
    x = mdotG/mdot
    vm = mdot/((pi/4)*D**2)

    # Pressure gradient if total flow had liquid properties
    ReL = vm*D/muL
    fL = 64/ReL if ReL <= 1187.0 else 0.3164/ReL**0.25
    dPL0 = fL*vm**2/(2*rhoL*D)

    # Pressure gradient if total flow had gas properties
    ReG = vm*D/muG
    fG = 64/ReG if ReG <= 1187.0 else 0.3164/ReG**0.25
    dPG0 = fG*vm**2/(2*rhoG*D)

    # Two-phase pressure gradient
    dP = (dPL0 + 2*(dPG0 - dPL0)*x)*(1 - x)**(1/3) + dPG0*x**3
    DP = dP*L

    return DP