che503 two phase flow

8/19/2019 CHE503 Two Phase Flow

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CHE 503 FLUID FLOW

CHAPTER 4:TWO PHASE FLOW


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OUTLINES

1FLOW REGIMES AND PATTERNS

- HORIZONTAL PIPE

- VERTICAL PIPE

2HOLD UP

3PRESSURE, MOMENTUM & ENERGY

RELATION

4PRESSURE DROP CALCULATION


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INTRODUCTION-FLOW OF MULTIPHASE MIXTURES

1. DEFINITIONS

Multiphase flow is simultaneous flow of:

- Materials withdifferent states or phases

(eg: gas, liquid or solid)- Materials withdifferent chemical propertiesbut in

the same state or phase(eg: liquid-liquid systems such oil droplets in water)

The primary and secondary phases:- One of the phases is continuous (primary) while

the other (secondary) are dispersed within the continuous phase.


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INTRODUCTION- FLOW OF MULTIPHASE MIXTURE

IMPORTANCE OF MULTIPHASE FLOW

Important in many areas of chemical and process engineering.

- Distillation- Absorption

- Evaporation

- Condensation

- Solvent extraction in hydrocarbon and refining industries

Thebehaviour of the materialwill depend on the properties of the

components, the flowrates and the geometry of the system.

Mixed materials may be transportedhorizontally, vertically, or at an

inclination to the horizontalin pipes and, in the case of liquid-solidmixtures, in open channels.

It is important to understand the nature of the interactions between the

phases and how these influencethe flow patterns.


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INTRODUCTION- FLOW OF MULTIPHASE MIXTURE

Flow patterns — the ways in which the phases are distributed over thecross sectionof the pipe or duct.

In design, it is necessary to be able topredict pressure dropwhich,

usually, depends not only on the flow pattern, but also on the relative

velocity of the phases; this slip velocity will influence the hold-up, the fraction of the pipe volumewhich is occupied by a particular phase.

Special attention is therefore focused on three aspects of the flow of these

complex mixtures.

(1) The flow patterns.

(2) The hold-up of the individual phases and their relative velocities.

(3) The relationship between pressure gradient in a pipe and the

flowrates and physical properties of the phases


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INTRODUCTION-FLOW OF MULTIPHASE MIXTURE

The difference in density between the phases is important in determining

flow pattern.

In gas-solid and gas-liquid mixtures,ρgas < ρgas+liquid


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2. TWO-PHASE GAS (VAPOUR)-LIQUID FLOW

The possiblecombination of phases aregas/liquid, gas/solid,

liquid/solidare called two phase flow.

Because of the presence of the two phases, there are considerable

complications in describing and quantifying the nature of the flow

compared with conditions with a single phase.

In most cases the gas phase, which may be flowing with amuch greater

velocity than the liquid, continuously accelerates the liquid thus

involving a transfer of energy. Either phase may be in streamlineor inturbulent flow, though the most important case is that in which both

phases areturbulent.

If there is no heat transfer to the flowing mixture, the mass rate of flow of

each phase will remain substantially constant, though the volumetric

flowrates (and velocities) will increase progressively as the gas expands

with falling pressure.


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2.1 FLOW REGIMES AND FLOW PATTERNS

Horizontal flow.

The flow pattern is influenced by thediameter of the pipe, the

physical properties of the fluidsand their flowrates. In general, as the velocities are increased and as the gas-liquid ratio

increases, flow patterns will change from "bubble flow" through to "mist

flow“.

the principal characteristics are described in Table 5.1.


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2.1 FLOW REGIMES AND FLOW PATTERNS

Vertical flow.

Axial symmetry exists and flow patterns tend to bemore stable.

However, with slug flow in particular, oscillations in the flow can occur as

a result of sudden changes in pressure as liquid slugs are discharged

from the end of the pipe.


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TWO-PHASE GAS (VAPOUR)-LIQUID FLOW

2.2 Hold-up

Because the gas always flows at a velocity greater than that of the liquid,

thein situvolumetric fraction of liquid at any point in a pipeline will begreater than the input volume fraction of liquid; furthermore it willprogressively change along the length of the pipe as a result of expansion

of the gas.

There have been several experimental studies of two-phase flow in which

the holdup has been measured, either directly or indirectly.

LOCKHART and MARTINELLI : expressed hold-up in terms of a

parameter X, characteristic of the relative flowrates of liquid and gas,

defined as:

where∆ P L and∆ PG are the frictional pressure drops for the respective

phases on their own at the same rate.

G

L

P

P X

∆−

∆−=


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2.3 PRESSURE, MOMENTUM, AND ENERGY RELATIONS

Methods for determining the drop in pressure start with a physical model

of the two-phase system, and the analysis is developed as an extension of

that used for single-phase flow.

In the separated flow model the phases are first considered to flow separately; and theircombined effect is then examined.

The total pressure gradient in a horizontal pipe,(- dPTPF / dl), consists oftwo components which represent the frictional and the acceleration

pressure gradients respectively or:

where –dPTPF = Total pressure drop for two phase flow

-dP f = Pressure drop due to friction

-dPa = Pressure drop due to the acceleration

dl

dP

dl

dP

dl

dP a f TPF −+−

=−


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PRACTICAL METHODS FOR EVALUATING PRESSURE DROP

Probably the most widely used method for estimating the drop in

pressure due to friction is that proposed by LOCKHART and

MARTINELLI and later modified by CHISHOLM. This is based on the physical model of separated flow in which each phase

is considered separately and then a combined effect formulated.

The two-phase pressure drop due to friction -∆P TPF is taken as the

pressure drop-∆P Lor-∆P

G that would arise for either phase flowing

alone in the pipe at the stated rate, multiplied by some factor Φ

2

G orΦ2L .

This factor is presented as a function of the ratio of the individual single-

phase pressure drops.2

G

G

TPF

P

P Φ=

∆−

∆−

2

L

L

TPF

P

P Φ=

∆−

∆−


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PRACTICAL METHODS FOR EVALUATING PRESSURE DROP

The relation between ΦG and ΦL and X (defined by equation 5.1) is shown inFigure 5.4, where

it is seen that separate curves are given according to the nature of the flow of the two phases.

For mass flowrate per unit area of L' and G’ for the liquid and gas,respectively, Reynoldsnumbers Re L (L' d/ μL ) and ReG (G’d / μG ) may be used as criteriafor defining the flow regime.


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EXAMPLE 1

Steam and water flow through a75 mm i.d. pipe of flowrates of 0.05 and

1.5 kg/s respectively. If the mean temperature and pressure are 330 K

and 120 kN/m2. What is the pressure drop per unit length of pipe

assuming adiabatic conditions and the e/d= 0.00015.

Given:µsteam= 0.0113 x 10-3 N s/m2 andµwater = 0.52 x 10

-3 N s/m2.


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RECAPITULATE

Multiphase

Flow

DEFINITIONS

IMPORTANCES

GAS LIQUID

FLOW

-Material with difference

states or phases

-Materials with different

chemical properties but in

the same state or phase

-Distillation, Absorption,Evaporation, Condensation,

Solvent extraction

1. The flow patterns.

2. Thehold-up of the individual phases

and their relative velocities.

3. The relationship between pressure gradientin a pipe

andtheflowratesandphysicalpropertiesofthephases

che503 two phase flow

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