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
http://www.scielo.br/scielo.php?pid=S0104-66322004000100004&script=sci_arttext
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