## Lockhart-Martinelli correlation

An alternate approach to calculate two-phase pressure drop is **the separated-phases model.**

In this model, the **phases** are considered to be flowing **separately** in the channel, each occupying a **given fraction** of the channel cross section and each with a **given velocity**. It is obvious the predicting of the** void fraction** is very important for these methods. Numerous methods are available for predicting the void fraction.

The method of **Lockhart and Martinelli** is the original method that predicted the **two-phase frictional pressure drop** based on a friction multiplicator for the **liquid-phase, or the vapor-phase**:

**∆p _{frict} = Φ_{ltt}^{2} . ∆p_{l}** (liquid-phase ∆p)

**∆p _{frict} = Φ_{gtt}^{2} . ∆p_{g}** (vapor-phase ∆p)

The single-phase friction factors of the liquid **f _{l} **and the vapor

**f**are based on the single phase flowing alone in the channel, in either viscous laminar (v) or turbulent (t) regimes.

_{g}**∆p _{l}** can be calculated classically, but with application of

**(1-x)**in the expression and

^{2}**∆p**with application of vapor quality

_{g}**x**respectively.

^{2}The two-phase multipliers **Φ _{ltt}^{2}** and

**Φ**are equal to:

_{gtt}^{2}where** X _{tt} **is the

**Martinelli’s parameter**defined as:

and the value of **C** in these equations depends on the flow regimes of the liquid and vapor. These values are in the following table.

**The Lockhart-Martinelli correlation** has been found to be adequate for two-phase flows at low and moderate pressures. For applications at higher pressures, the revised models of Martinelli and Nelson (1948) and Thom (1964) are recommended.

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