## Pressure Drop – Homogeneous Flow Model

The simplest approach to the prediction of two-phase flows is to treat the entire two-phase flow as if it were **all liquid**, except flowing at the two-phase **mixture velocity**. The two-phase pressure drops for flows inside pipes and channels are the sum of three contributions:

- the static pressure drop
**∆p**(elevation head)_{static} - the momentum pressure drop
**∆p**(fluid acceleration)_{mom} - the frictional pressure drop
**∆p**_{frict}

The total pressure drop of the two-phase flow is then:

**∆p _{total} = ∆p_{static} + ∆p_{mom} + ∆p_{frict}**

The static and momentum pressure drops can be calculated similarly as in case of single-phase flow and using the homogeneous mixture density:

The most problematic term is the** frictional pressure drop** **∆p _{frict}**, which is based on the single-phase pressure drop that is multiplied by the

**two-phase correction factor**(

**homogeneous friction multiplier – Φ**). By this approach the frictional component of the two-phase pressure drop is:

_{lo}^{2}where **(dP/dz) _{2f}** is frictional pressure gradient of two-phase flow and

**(dP/dz)**is frictional pressure gradient if entire flow (of total mass flow rate G) flows as liquid in the channel (standard single-phase pressure drop). The term

_{1f}**Φ**is the

_{lo}^{2 }**homogeneous friction multiplier**, that can be derived according to various methods. One of possible multipliers is equal to

**Φ**

_{lo}^{2}= (1+x_{g}(ρ_{l}/ρ_{g}– 1))**and therefore:**As can be seen this simple model suggests that the **two-phase frictional losses are in any event higher than the single-phase frictional losses.** The homogeneous friction multiplier increases rapidly with **flow quality**.

Typical** flow qualities** in** steam generators** and **BWR cores** are on the order of 10 to 20 %. The corresponding two phase frictional loss would then be** 2 – 4** times that in an equivalent single-phase system.

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