How to divide a Pneumatic Conveying Stream
How to divide a Pneumatic Conveying Stream
1.5 Calculation of the Splitter
The main calculations for the splitter are, apart from the area division in functional dependence to the number of outlets, the sinking velocity, as well as the estimation of the additional pressure loss.
1.6 Calculation of the Sedimentation Velocity of Individual Particles
The sedimentation velocity of the individual particles w is calculated from the equilibrium of the weight force F_{G} (perpendicular down) and the circulation force of the surge flow F_{W} (perpendicular), neglecting the lift forces as follows:
where:
A_{S} = projected area of the particle [m^{2}]
g = gravitational acceleration [m/s^{2}]
d_{S} = cross section of particle [m]
ρ_{S} = particle density [kg/m^{3}]
c_{W} = drag coefficient of particle [–]
It should be noted that this equation only applies to individual particles; the sedimentation velocity of particle collectives is different, depending on its composition.
Usual sedimentation velocities of fine particles are in the range of 0,5 to 2,5 m/s. These values apply to an individual particle. Practical values can be determined through experimental determination of the sedimentation velocity, e.g. in the Gonellclassifier.
1.7 Calculation of the Pressure Loss in the Splitter
The pressure loss in the described splitter is mainly due to the reacceleration of the solid particle/gas mixture. It is fairly accurately described in the following equation:
where:
Δp_{v} = Pressure loss in splitter [Pa]
K = Empiric factor (value ≈ 1,2) [–]
ρ_{L} = Gas density [kg/m^{3}]
v = Gas velocity [m/s]
μ = Load [kg solid / kg gas]
c = Solid particle velocity [m/s]
At usual velocities, system pressures, temperatures and loads, the additional pressure loss of such a splitter generally varies in the range of 8 up to approx. 50 mbar.
2 Operation of the Plant
In order to achieve the most possible even division of the mass flow, some further points need to be taken into consideration while setting up the splitter (see Fig. 7 below):
● The splitter has to be set up perpendicularly.
● Before entering the splitter, the perpendicular incident flow length must be at least 15 (20 is more favourable) times d_{E} (whereby d_{E} is the inner pipe diameter at splitter inlet).
Fig. 7: Setup of a splitter with up
and downstream lengths
An even division of the bulk mass flow rate can only be assured, if these minimum prerequisites are observed. It is recommended that a corresponding straight wake (10 to 15 times d_{A}, d_{A} = inner pipe diameter at splitter outlet) is also observed.
A disturbancefree operation of the conveying is of particular interest. The aim is to achieve accuracies in the range of ± 5 to 10%. The splitter is one part of a general plant, and in setting it up, fluidic aspects have to be observed, in addition to geometrical sizes.
It is important that the specific pressure loss occurs at the end of the conveying line, so that small differences in the lengths of feed pipes after the splitter can be neglected compared to this pressure loss. This can easiest be done by attaching a nozzle with a defined pressure loss to the end of the conveying pipe. A respective example is depicted in the diagram below (Fig. 8). Further explanations are provided in the following chapter.
Fig. 8: Typical pressure curve in a conveying system with a splitter
The splitter lengths are dependent upon material characteristics, an additional air injection and the number of exits to be supplied. Usually, these lengths are in the range of 5 to 10 times the diameter of the splitter.
3 Homogenization of the Throughput
Fluid mechanic correlation at the splitter can be well described through a simplified electric circuit. The following is valid as an analogue:
Voltage U ~ Pressure gradient
Current I ~ Material throughput
Resistance R ~ Resistance behaviour of pipe
The aim is always an evenly distributed throughput of material. Nevertheless, it often happens that due to local circumstances, the conduit after the splitter cannot necessarily be implemented absolutely even. This leads to the fact that both the resistances R_{1} to R_{4} and the throughput turn out differently, as they are directly linked with the pipe resistance (Fig. 9, below).
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