AIR MOVEMENT IN GRANULAR MASS

(Flow through beds of solids)

OBJECTIVE

To estimate pressure drop in a bed of granular materials (packed or grain bed) and pump power

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746

.)(

QPhpPower

ghP

FACTORS AFFECTED ON P

Porosity Particle size Exposed surface area Moisture content Surface roughness Container size Etc…3 MAIN

METHODS Ergun’s equation Leva’s equation ASAE data (American

Society of Agricultural Engineering)

KOZENY-CARMAN’S EQUATION

ERGUN’S EQUATION

Modified for specific materials Noted that Ergun uses darcy friction factor

(not fanning)

dp = average diameter of particle

2

21

v

dLP

fp

6

Moody Diagram for the Darcy friction factorMoody Diagram for the Darcy friction factor

Ergun proposed a modified friction factor E

factorfrictiondarcyf

porosity

ff

p

pE

)1(2

3

Laminar contribution

Turbulent contribution

75.1Re

)1(150

75.1,36

150

1000ReRe

)1(C 63

21

21

E

E

f

CC

for

Cf

LEVA’S EQUATION

n = 1 for laminar flow,n = 2 for turbulent flowG = mass velocity (kg/s.m2)

’ =modified fanning friction factor

SHAPE FACTOR OR SPHERICITY

For non spherical particles, is a shape factor (also called sphericity and used with symbol ), defined by:

For spheres =1 by definition. For other typical filter bed materials irregular shapes ~ 0.75

spheres of ratio surface tovolume

particles of ratio surface tovolume

’ =modified fanning friction factor

Given: Voidage = 45% Density of air = 5.239 kg/m3

Height of bed = 3 m Diameter = 0.005 m Air mass flow rate = 3000 kg/hr.m2

Entrance pressure = 5 bar Determine the pressure of exit air using Ergun Equation

Example 1

Example 2