1) GEOMETRIC SIMILARITY
FILL RATIO: is defined as the ratio of Bed height and RMG Diameter (H/D ratio)
H/D Ratio (Constant fill ratio) = Powder bed height (cm)/( RMG bowl diameter (m) x 100)
Powder Bed height (cm) = (Dry mix volume (L) x 1000) / Total volume of RMG (L)
Total Volume of RMG = ¼ π D^2
Bed height (cm) = Dry mix volume (L) X 1000 / ¼ π D^2 X 10000
Bed height (cm) = 4 X Dry mix volume (L) X 1000 / π D^2 X 10000
Where,
- D = Diameter of RMG bowl in meter
- π = 3.14
Note: RMG Bowl diameter = Available from equipment manual or qualification document
2) KINETIC SIMILARITY
TIP SPEED:
RPM to be scaled down and scaled up according to Tip speed or Distance travelled by impeller tip to be kept constant.
V= 3.14 x D x N
Where,
- N = Impeller speed
- D = Impeller diameter
The tip speed represents the linear velocity at the tip of the impeller. Tip speed is responsible for the
movement within the bowl and is related to the shear forces imparted by the impeller.
3) DYNAMIC SIMILARITY
A). NEWTON’S POWER NUMBER CAN BE USED TO SCALE TORQUE:
NeP = P/ (ρ R^5N^3)
- P = Power consumption by the impeller blade = Torque* (2* π *N)
- N = Impeller RPM
- R = Impeller Radius
- ρ = Wet mass density of granules (Method to determine ρ need to be finalized)
Newton's power number relates the drag force acting on a unit area of the impeller and the inertial stress.
B). RELATIVE SWEPT VOLUME (RSV)
RSV = Volume of Material Swept per Second / Volume of the Bowl
This parameter is calculated as the volume swept by the blades per unit time vs. the bowl capacity. It is related to the work or energy imparted on the wet mass during the granulation.
Impeller swept volume = Impeller height (m) / [Bed height (cm) ÷100]
C). FROUDE- NUMBER
Tip Speed High Comparability: Tip speed scale up according to Froude- Number
Fr = N^2 x (D/g)
- N = tool speed (Impeller)
- D = tool diameter
- g = gravity acceleration
The Froude number is the ratio of the centrifugal acceleration to gravitational constant, and relates to the compaction forces experienced by the wet mass owing to centrifugal and centripetal forces generated by the plow.
Read also:
