Scale-up + Pump Systems

Question 1

Why scale-up?

Answer 1

• can be too expensive or difficult to run all trials on a full scale

Question 2

Issues with scale-up

Answer 2

• many factors son’t scale linearly or with same factors
• single system will have many competing variables affecting similarity of performance at different scales
  Factors to consider:
• fluid velocities + turbulence
• shear or pressure profile
• residence or contact time
• contact mechanics
• particle to system ratio
• effect of particle size to fluid ratio

Question 3

Scaling Similarity Types

Answer 3

Geometric scale- down: hard to achieve + can cause many confounding factors
Dynamic scaling: often preferred for systems with fluid flow (dynamically similar = all forces acting at corresponding points form a constant ratio between model and prototype

Question 4

Dimensional Analysis

Answer 4

Fundamental Dimensions: not given in terms of a specific unit, instead in terms of underlying quantity
- time, mass, length, amount, temperature

Question 5

Derived Units

Answer 5

Many other units are derived from the units of fundamental dimensions
e.g. N = MLT^-2

Question 6

Buckingham Pi Theorem + Method

Answer 6

‘‘If a system is characterised by m variables, which are
completely described by n fundamental dimensions (M,
L, T, etc.), then these m variables can be grouped into
m – n independent dimensionless groups Πs which
describe the same situation.’’

Method:

• list all m variables describing problem
• find number of fundamental dimensions (n) and the number, (m-n) of dimensionless groups (pi s) that can be formed
• select n variables, the recurring set
• dimensionless groups found one at a time, take product of one of remaining variables to a known power, and recurring variables to unknown powers, determine exponents of recurring variables, using principle of dimensional homogeneity, so that group becomes dimensionless
• repeat procedure in previous step to define all m-n dimensionless groups

Question 7

Impeller Types

Answer 7

Radial Flow: discharges liquid radially outwards (high shear, good for general mixing)
Axial Flow: discharges liquid axially up or down, depending on orientation of blades (lower shear, but good for suspending solids

Question 8

Important Scale-Up Parameters

Answer 8

2 most common:
- constant impeller tip-speed 
   (N2 = N1 (D1/D2)
- constant power per unit volume 
   (N2 = N1 (D1/D2)^(2/3)

MUTUALLY EXCLUSIVE

Question 9

Pumps

Answer 9

Definition: a mechanical device for moving fluids and suspensions

• fluid liquid = pump
• fluid gas = compressor or blower/fan