Mass flow and funnel flow in the silo
In mass flow the entire bulk solid is in motion during discharge – what went in first comes out first. In funnel flow only a channel above the outlet flows, the bulk solid at the walls stays at rest. Which flow pattern develops depends on the hopper inclination, the wall friction and the internal friction of the bulk solid.
From the measured effective angle of internal friction and wall friction we calculate the hopper inclination needed for mass flow.
Advantages of mass flow over funnel flow
For cohesive bulk solids and those sensitive to segregation or ageing, mass flow is usually the design target. Funnel flow can be sufficient for free-flowing, insensitive bulk solids when height or wear rule out a steep hopper.
| Feature | Mass flow | Funnel flow |
|---|---|---|
| Bulk solid in motion | entire content | only a flow channel above the outlet |
| Residence time | uniform, first in – first out | very uneven, dead zones |
| Segregation | low, discharge in filling order | pronounced, fines and coarse material separated |
| Ratholing | not possible | possible with cohesive bulk solids |
| Emptying | complete | residual material, caking and ageing |
| Discharge | uniform and easy to meter | fluctuating, risk of fine bulk solids flooding |
| Wall loads | load peak at the transition vertical section/hopper | asymmetric with an eccentric flow channel |
| Design | steep hopper, greater height, wear on the hopper wall | flat hopper, lower height |
Limit criterion for mass flow
Critical hopper inclination
Mass flow develops when the hopper is steep enough and the wall friction low enough. The critical hopper inclination βcrit to the vertical depends on the effective angle of internal friction φe of the bulk solid, on the wall friction angle φw on the hopper material and on the hopper shape: wedge-shaped hoppers with a slot outlet reach mass flow at flatter inclinations than conical hoppers.
A margin to the limit is advisable because wall friction can increase during operation through wear, caking or time consolidation.
To EN 1991-4 and to Jenike
In its informative Annex F (Figure F.1), EN 1991-4 gives a simplified, conservative boundary between mass and funnel flow based on the hopper half-angle β and the hopper wall friction coefficient μh. Between the two boundary lines either mass or funnel flow can occur – there the flow pattern depends on further parameters.
This gap is closed by Jenike's limit criterion, which includes the measured effective angle of internal friction. The calculation tool shows both assessments for your hopper geometry.
Measurements for designing for mass flow
Decisive for the limit criterion are the internal friction of the bulk solid and the wall friction on the material the hopper is to be made of.
| Measurement | Parameters | Use |
|---|---|---|
| Yield locus | effective angle of internal friction φe, flow function σc(σ1) | critical hopper inclination, arching |
| Wall friction | wall friction angle φw, wall friction coefficient μ on the hopper material | critical hopper inclination, comparison of wall materials |
| Compression density | density function ρb(σ) | stresses in the hopper |
| Time consolidation | wall friction and yield locus after storage time (optional) | flow pattern after a standstill |
Measures to ensure mass flow
Mass flow results from the interaction of geometry, wall material, discharge and operation – if one element is missing, funnel flow develops despite a steep hopper.
- Hopper geometryHopper inclination steeper than βcrit, with a margin to the limit; wedge-shaped hoppers where height is limited.
- Wall materialSmooth, wear-resistant surfaces or coatings with low wall friction and adhesion.
- OutletLarger than the critical outlet diameter against arching.
- FeederDraw-off across the whole outlet cross-section, no one-sided or point draw-off.
- FillingConcentric filling to avoid segregation and eccentric loads.
- Product changeFor a new bulk solid, measure yield locus and wall friction and check the limit criterion for the existing silo again.
Frequently asked questions about mass flow and funnel flow
- Which measurements does the mass flow criterion need?
- Yield loci for the effective angle of internal friction φe, and wall friction on the intended hopper material for the wall friction angle φw or the wall friction coefficient μ. Several wall materials can be compared directly.
- Is a sufficiently steep hopper enough for mass flow?
- Not on its own. The feeder must draw bulk solid from the whole outlet cross-section, and the outlet must be larger than the critical outlet diameter against arching. If the feeder draws from only part of the outlet, funnel flow develops despite a steep hopper.
- Why are the loads in mass flow partly higher?
- During discharge in mass flow a load peak occurs at the transition from the vertical section to the hopper. EN 1991-4 takes this into account in the hopper loads; the calculation tool shows the loads for filling and discharge.
- Can the flow pattern change during operation?
- Yes. If the wall friction increases through wear, caking or time consolidation at the wall, a silo designed for mass flow can change to funnel flow. Wall friction measurements with time consolidation show how much margin to the limit is needed.
Designing your silo for mass flow
Describe your bulk solid, your hopper and the intended wall material – we put together the right measurements and prepare a non-binding quote for you.
- Effective angle of internal friction and wall friction on your hopper material
- Limit criterion to Jenike and to EN 1991-4, Annex F
- Comparison of several wall materials