LOCKHART_XTT

This function calculates the Lockhart-Martinelli two-phase parameter X_{tt}, an empirical ratio used in flow-boiling and two-phase pressure-drop modeling. It supports default exponents or deriving selected exponents from an input n value.

The standard form is:

X_{tt} = \left(\frac{1-x}{x}\right)^{0.9}\left(\frac{\rho_g}{\rho_l}\right)^{0.5}\left(\frac{\mu_l}{\mu_g}\right)^{0.1}

This parameter is dimensionless and is often used as an intermediate term in two-phase correlations.

Excel Usage

=LOCKHART_XTT(x, rhol, rhog, mul, mug, pow_x, pow_rho, pow_mu, n)

x (float, required): Quality at the tube interval (dimensionless).
rhol (float, required): Liquid density (kg/m^3).
rhog (float, required): Gas density (kg/m^3).
mul (float, required): Liquid viscosity (Pa*s).
mug (float, required): Gas viscosity (Pa*s).
pow_x (float, optional, default: 0.9): Power for phase ratio (dimensionless).
pow_rho (float, optional, default: 0.5): Power for density ratio (dimensionless).
pow_mu (float, optional, default: 0.1): Power for viscosity ratio (dimensionless).
n (float, optional, default: null): Exponent parameter to derive powers (dimensionless).

Returns (float): Lockhart-Martinelli parameter (dimensionless), or an error message if invalid.

Example 1: Example with default powers

Inputs:

x	rhol	rhog	mul	mug
0.4	800	2.5	0.001	0.00001

Excel formula:

=LOCKHART_XTT(0.4, 800, 2.5, 0.001, 0.00001)

Expected output:

0.127617

Example 2: Using n to derive powers

Inputs:

x	rhol	rhog	mul	mug	n
0.3	900	8	0.0002	0.00002	0.2

Excel formula:

=LOCKHART_XTT(0.3, 900, 8, 0.0002, 0.00002, 0.2)

Expected output:

0.25445

Example 3: Custom power values

Inputs:

x	rhol	rhog	mul	mug	pow_x	pow_rho	pow_mu
0.6	700	20	0.0003	0.000015	0.8	0.6	0.2

Excel formula:

=LOCKHART_XTT(0.6, 700, 20, 0.0003, 0.000015, 0.8, 0.6, 0.2)

Expected output:

0.155917

Example 4: Higher quality with default powers

Inputs:

x	rhol	rhog	mul	mug
0.7	950	12	0.00025	0.00002

Excel formula:

=LOCKHART_XTT(0.7, 950, 12, 0.00025, 0.00002)

Expected output:

0.0674902

Python Code

Show Code

from ht.boiling_flow import Lockhart_Martinelli_Xtt as ht_Lockhart_Martinelli_Xtt

def Lockhart_Xtt(x, rhol, rhog, mul, mug, pow_x=0.9, pow_rho=0.5, pow_mu=0.1, n=None):
    """
    Compute the Lockhart-Martinelli Xtt two-phase flow parameter.

    See: https://ht.readthedocs.io/en/latest/ht.boiling_flow.html

    This example function is provided as-is without any representation of accuracy.

    Args:
        x (float): Quality at the tube interval (dimensionless).
        rhol (float): Liquid density (kg/m^3).
        rhog (float): Gas density (kg/m^3).
        mul (float): Liquid viscosity (Pa*s).
        mug (float): Gas viscosity (Pa*s).
        pow_x (float, optional): Power for phase ratio (dimensionless). Default is 0.9.
        pow_rho (float, optional): Power for density ratio (dimensionless). Default is 0.5.
        pow_mu (float, optional): Power for viscosity ratio (dimensionless). Default is 0.1.
        n (float, optional): Exponent parameter to derive powers (dimensionless). Default is None.

    Returns:
        float: Lockhart-Martinelli parameter (dimensionless), or an error message if invalid.
    """
    try:
        return ht_Lockhart_Martinelli_Xtt(x=x, rhol=rhol, rhog=rhog, mul=mul, mug=mug,
            pow_x=pow_x, pow_rho=pow_rho, pow_mu=pow_mu, n=n)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

x *

Quality at the tube interval (dimensionless).

rhol *

Liquid density (kg/m^3).

rhog *

Gas density (kg/m^3).

mul *

Liquid viscosity (Pa*s).

mug *

Gas viscosity (Pa*s).

pow_x

Power for phase ratio (dimensionless).

pow_rho

Power for density ratio (dimensionless).

pow_mu

Power for viscosity ratio (dimensionless).

Exponent parameter to derive powers (dimensionless).