Calculation Algorithm
Dear Mr. Teus,
Thank you very much for the continuous challenging and experience sharing.
Regarding the algorithm, if you not mind, i have some questions:
1. the pressure loss on the entire pipe length is not linear, i.e. is not a first degree function. How do you "slice" this ? Making constant pressure gradient ? it is undefined since it is content in itself, function and variable in the same time.
2. cloggind condition: it is not clear to me how this can be assesed from Zenz. Since in Zenz diagrams, if i'm not wrong, is given the air flow speed at open athmosphere condition and does not take into consideration the compression ratio,
Especially for the initial portion of the pipe, were, the reality is showing this, the clogging happens at air flow speed approaching floating speed.
Sincerely yours,
Tanase TANASE ■
Re: Requirements Of A Pneumatic Conveying Calculation Algorithm.
Dear Mr. Tanase,
1. the pressure loss on the entire pipe length is not linear, i.e. is not a first degree function. How do you "slice" this? Making constant pressure gradient? it is undefined since it is content in itself, function and variable in the same time.
It is correct that the pressure drop gradient is not the same for each pipeline section.
A horizontal pipeline pressure drop per meter is different from a vertical pipeline pressure drop per meter.
Around a bend, there is also a discontinuity in pressure drop, depending on the bend geometry and the bend orientation.
The pressure drop per meter is (partly) a function of the gas pressure head (changing along the pipeline) and linear for elevation and constant pressure drops (f.i. filter)
Because the velocity and the gas density (pressure dependent), the velocity head changes along the pipeline and that is exactly the reason, why an iteration algorithm is required.
The calculation itself is a numerical integration algorithm, based on a time increment (f.i. 0.001 second).
For a certain capacity calculation, the starting pressure is set, and the end pressure is known.
The first, capacity, calculation, most certainly, will not result in an end pressure equal to the known end pressure.
That is solved by an iteration algorithm (root finding).
2. clogging condition: it is not clear to me how this can be assessed from Zenz. Since in Zenz diagrams, if i'm not wrong, is given the air flow speed at open atmosphere condition and does not take into consideration the compression ratio,
Especially for the initial portion of the pipe, were, the reality is showing this, the clogging happens at air flow speed approaching floating speed.
The Zenz diagram shows the pressure drop for a certain installation operating at a certain capacity plotted against the gas velocity.
Instead, the gas velocity, the compressor gas volume can also be used as the x-axis value.
As the Zenz pressure drop (actually the compressor pressure) is calculated, the compression ratio is automatically accounted for.
Clogging/sedimentation occurs at those locations in the pipeline where the wall gas velocity drops below the required local particle suspension velocity.
That can occur at 2 locations:
-Where the pressure is too high to maintain that condition.
At the beginning of a new, bigger, pipe diameter
-In a bend, where the bend friction in combination with gravity pulls the material down to a particle velocity equaling zero or below zero.
This insight took me many years of theoretical research, mathematical modeling, software building, calculations, and field experiments to verify. ■
Teus
Requirements of a pneumatic conveying calculation algorithm.
As explained before on this forum, pneumatic conveying is a very complex technology to calculate.
This is caused by the many parameters and the interaction between those parameters.
And the available number of formulas is less than the parameters to be calculated, which results in an unsolvable set of equations.
A single calculation, resulting directly in an answer is therefore impossible and an iteration algorithm is required.
A calculation algorithm must be based on summarizing a number of partial pressure drops, whereby the iteration results in coherence between the input- and the output variables. All expressed in the Zenz diagram.
Because of the complex interactions between the particles and the pipe wall and the influence of the selected pipe diameters, air mass flow, and pressure, it is almost impossible to judge the design by intuition or experience.
Generally, a calculation algorithm is based on a material factor (K), expressing the influence the presence of material, multiplied by the gas pressure head over a certain pipeline length.
This material factor is usually derived from lab tests or from build installations.
The material velocity is assumed to be a factor times the gas velocity, from which the pressure drop for the material kinetic pressure drop is derived.
The characteristics of the compressor and pressure dependent gas leakages of equipment are often ignored.
Pressure drops of other in line equipment (also pressure dependent) are calculated separately or assumed.
All those assumptions give the K-factor the function of a fudge factor, in which several, not calculated, partial pressure drops are included.
This calculation approach blurs the pneumatic conveying information that is necessary to judge the design.
A pneumatic conveying calculation algorithm, which calculates all the partial pressure drops and gas flow changes due to temperature changes, pressure changes, compressor/vacuum pump characteristics, material velocity changes, equipment influences, leaves no room for assumptions in the calculation.
The material conveying properties are still required of which the suspension velocity and the Solid Loss Factor can be calculated and/or measured.
The relation between the SLF and the SLR and the Reynold number can be derived from these measurements and converted into a formula.
This formula expresses the statistical chance of collisions.
The found formulas for a variety of materials show a narrow band in the formula, but a wide range of SLF-values.
The algorithm must warn for possible sedimentation conditions and choking conditions.
Also, the safety factor against sedimentation and choking, both for pressure and gas flow must be a part of the calculation.
Material velocity losses in bends must be calculated, especially for the bends from horizontal to vertical, as those are likely the first ones to create a blockage.
Energy consumption per conveyed ton must be shown in the calculation output as this variable is important in the overall operating cost.
Such a sophisticated algorithm allows the selection of an optimum design and which way to change the design to obtain that goal.
In this type of pneumatic conveying calculation, the SLF (comparable to the K-factor) is no longer a fudge factor anymore.
The use of a sophisticated computerized pneumatic conveying calculation prevents input errors by illogical- or false outputs, Mistakes are hard to make without noticing.
Installations that, after commissioning are over- or underperforming, can now be analyzed in detail.
Where in the early days trial and error (hit and miss) design tactics were used, are over time improved by gained experience and mathematical approach. Today the pneumatic conveying technology can be calculated in one algorithm for both pressure and vacuum, with exactly the same formulas and material properties, including the many, existing installation types. ■
Teus