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The University of Newcastle
Pneumatic Conveying
The University of Newcastle
Pneumatic Conveying
Abstract This report is concerned with the design of a s ystem to meet a set of specified specifi ed requirements for the Pneumatic conveying of a bulk material. An important facet of design in these systems is the need to minimise cost and maintenance of the system while meeting the required system output. As such, the system will be designed around not only performance, but also with the continual maintenance of the system in mind. This report aims to make final specifications for the design of the system that best suits the above criteria. The report makes extensive use of Microsoft Excel for the generation and iteration of the calculations associated with pneumatic conveying systems. A set of data collected for a test system was provided on which to base the building of a design model. From the test data , empirical connections between system components could be generalised for si milar ‘scaled up’ versions of the test test system. A method to forward calculate the solids friction factor based on Froudes number and solids loading ratio was derived, as was an approximation of a velocity lower limit to avoid blockage. From here, a design spread sheet could be generated using these relations. The system was intended to: Convey cement meal Convey over 750 m Have 2 long radius bends with a bend factor 0.5 Use air as the conveying fluid
Contents Abstract ......................................................................................................................................2 Introduction ................................................................................................................................ 4 Steps for Analysis of Test Data ................................................................................................. 5 The Testing System ................................................................................................................ 5 Model Derivation ................................................................................................................... 5 Model Checking .....................................................................................................................6 Results of Test Data ................................................................................................................... 7 Air Alone Friction Factor .......................................................................................................7 Particle Friction Factor ...........................................................................................................8 Pick up velocity and solids loading ratio. .............................................................................. 9 Designing Process ....................................................................................................................10 System Specifications .......................................................................................................... 10 Assumptions ......................................................................................................................... 10 Method ................................................................................................................................. 11 Final Design Parameters .......................................................................................................... 13 Comparison of Stepped and non-stepped systems ............................................................... 13
Introduction Pneumatic conveying of material has widespread applications for the movement of materi al in industry. The systems are on a based on simple fundamental operating principles and are very suitable for the transport of powdered or granulated materials. The basic components of a pneumatic conveying system include an air mover to supply the conveying fluid, a feeder to introduce the solids to be conveyed, a pipeline, a receiving bin and a s eparation device to recover the solids from the fluid. (Jones, Mills, & Agarwal, 2005) The large scale of pneumatic conveyers means that cost, wear and maintenance are important aspects to be considered in their design. Pneumatic conveyors in dilute phase are best operated between 10 and 30 m/s of flow (Mills, 2004), but even within this optimal zone, wear from the moving particle on pipes and system components is a major source of maintenance requirement and spending. The pressure through the line is relatedly inductive of high wear, so efforts at the design stage must be made to minimise these parameters. This in turn minimises wear and its associated maintenance and replacement costs. An important characteristic of pneumatic conveying systems used for design in this report is that empirically derived relations between system parameters can be used for similar systems. This effectively means that provided data for a s maller testing system can be used to derive forward predictors of characteristics in the design of the final system. This report aims to use this process to derive a design model, and from there se lect a system that meets requirements while minimising cost, wear and maintenance.
Steps for Analysis of Test Data The approach taken in designing the conveying system first required data for a smaller testing system to be analysed. From this, a model could be built that would be predict the behaviour of the designed full scale system. Once the model had been derived and checked, specifications of the full scale system could be fed into the model and key characteri stics altered to optimise performance.
The Testing System -
16 samples of data* Cement meal 176m long 14 long radius bends Bend factor 0.5 53mm inner diameter Fed by a 1 cubic metre blow tank Measured pressure drops were provided for varied flow rates of air and cement meal.
*The 16th data sample was later discarded because of its incongruity with the rest of the data, inferring it was either a measurement error or transient reading.
Model Derivation The following is a stepped process of calculating s ystem variables. All equations can be found in Appendix A, along with the meaning of all variables used.
9. Hence evaluate S*= . This has no physical significance, but becomes useful because it can easily be plotted against Fr (relevant below) 10. It is know that a relationship between and Fr exists, of the form Therefore, the S* column calculated can be plotted against Fr and then curve fit to find constants ‘b’ and ‘c’
11. Using these constants, generate the formula
√
which will be the forward calculator for the design spread sheet.
Model Checking
When fitting the curve to obtain the solids loading factor, the R 2 value of the trend line should be examined, as it is an indicator of the closeness of the curve’s fit, and thus, its accuracy as a model. Acceptable curve accuracy should be 0.9; this will ensure that the error associated with using the trend line for different variables will be acceptably small. Aside from the accuracy of the trend line itself, the accuracy of the model ’s forward calculations needs to be investigated. To do this, a s pread sheet (provided in Appendix C) modelling the same system is set up identical to the first, but with two crucial differences: - λs is evaluated using Equation 16 and the derived constants, not from its f ormal
Results of Test Data As outlined by the method, characteristics of the pipe flow were determined using an excel spread sheet (supplied in Appendix B).
Air Alone Friction Factor Using Equation 7, the following table was able to be generated from the model suggested by Streeter (Streeter & Wylie, 1983):
=
Test 1 2 3 4 5 6 7 8 9
Ma (kg/s) 0.081 0.081 0.050 0.047 0.042 0.038 0.050 0.034 0.030
Ms (kg/s) 2.120 2.380 1.480 1.560 1.490 1.530 1.550 1.550 1.500
λf
0.02170 0.02170 0.02288 0.02306 0.02341 0.02373 0.02288 0.02412 0.02459
Particle Friction Factor Once the air alone friction factors were calculated, calculations of were able to proceed as outlined by the method in the previous section. Generating a graph of √ vs Fr number, a curve was fit of the appropriate form. The R 2 value was very close to unity so can be considered accurate. Figure 2 shows the relation √ or, in a more useful form
√ λs
Empirical Determination
0.9 0.8 0.7 0.6 5 . 0 ^ 0.5 * m . 0.4 s λ 0.3 0.2 0.1 0.0
y = 11.571x-1.836 R² = 0.9969
Figure 3 shows clearly that the values for pressure forward calculated with λs are about a maximum of 15% different. This is better than expected (a deviation of 20% is common), and is acceptable for use in forward calculation (Mills, 2004). Figure 3 also suggests that increasing mass flow rate and decreasing Fr number seem to adversely affect the accuracy of the results, but more testing would need be undertaken before any definitive conclusions about such a relationship are drawn.
Pick up velocity and solids loading ratio.
9
Solids Loading Ratio and Pick up Velocity
8 ) s / 7 m ( 6 y t i 5 c o l e 4 V p U3 u c i 2 P
y = -0.1687x + 10.99 R² = 0.8623
Designing Process Having developed a model useful in predicting key system characteristic s, it is now possible to design the proposed system. It should be noted that the processes outlined below are undertaken in such a way as to minimise operational cost, wear on the system and maintenance requirements.
System Specifications - Cement meal - Conveying distance of 750m - Net required delivery rate of 20 tonne/hr - 2 bends - Bend factor 0.5 - 55m of the system is to be vertical. (see Figure 5 for system schematic)
The figure above is easily constructed and forms an ef fective way of monitoring design inputs. Red colours were used to designate which constants were to be specified, and so the values in Figure 6 are not the final chosen. Note that the mass flow rate of solids is variable, in that a rate differing to the required net transfer may be needed in a batch system.
Method From here, a spread sheet is set up, identical to the one used to test the λ s relation derived. Only the system inputs are different. Again, a guess is needed to start the calculation, so the same iterative method is used as described in the test results method. Data inputs are this stage need only be rough estimates in getting the model to work appropriately. From the use of these spread sheets along with some research into general system requirements, the particular system specifications are able to be determined, and then the appropriate system components selected based on these parameter s. The process is by no means linear: given the high level of dependence between variables, the design will require constant backtracking and cross referencing with previous values to ar rive at the optimal solution. Stepped Pipelines Given the likelihood of having to use a stepped pipeline system, similar s pread sheets are set up to calculate a non-uniform bore system. In the case of a single step system, the rough schematic may be represented as:
Velocity Profile (Generalised) ) s / m ( y t i c o l e V
Length through the system (m) Figure 7: Arbitrary velocity profile for a single step pipeline (only point data evaluated, curves are approximate)
Figure 8 uses arbitrary data to show that in general, if a pipeline is not stepped, the velocity will continue to increase in the same manner through the pipeline. The figure demonstrates that stepping reduces the maximum velocity considerably, which will also have positi ve effects on the required system pressure drop and on wear in the pipes. (Jones, Mill s, & Agarwal, 2005) If this velocity profile were still to be unfavourable, the system could be stepped again. This is achieved by the same process used to introduce the first stepped pipeline. It can be noted that a generalised velocity profile would shows lower peaks and a more regular velocity
Final Design Parameters Comparison of Stepped and non-stepped systems An important aim of the design process is to minimise wear in the system. This is primarily achieved by the control of velocities through the pipe: the faste r the conveying, the more abrasive wear occurs (Jones, Mills, & Agarwal, 2005). As such, three different systems were designed using uniform pipe bore, single stepped pipelines and twice stepped pipelines. The spread sheets for uniform pipe diameter as well as single and double step systems are included in the Appendices. Figure 7 above gives the schematic for a si ngle step, while the Figure below shows the same for a two-step pipeline.
Figure 8: Schematic for the two step, three section pipeline
It is evident that the different arrangements will lead to different performances.
Comparison Of Velocity Profiles
60 50 ) 40 s / m ( y t i 30 c o l e V20
10 0 0
100
200
300
400
500
600
700
800
Length along Pipe (m) Figure 9: Comparison of Velocity Profiles for Uniform bore, single step and double step systems.
The figure above compares the different profiles i n velocity for the designed systems with uniform bore, then one and two steps. Note that in the two step s ystem, the peaks are closer to the mean value (i.e. variation is more uniform across the length). This indicates that again, velocity will be preferable in the two step system.
System Characteristics All subsequent calculations are based on the choice of a 2 step pipeline.
These values were arrived at by an iterative process of guessing and checking which standard pipe sizes yield the most favourable system outputs.
Air Flow rate Using the nominal bores above, values for air flow rate can be put into the spread sheet, and then checked for validity against C test. If the spread sheet returns that a blockage occurs, a slightly higher value for flow rate is guessed. As a lower mass flow rate of air is optimal in this system (to reduce power requirements and wear on equipment), guesses were repeated until the lowest air flow rate that did not cause blockage was found. Ultimately
̇ In volumetric terms
̇
Peak Solids flow rate In such a large system it is highly likely that large pressures will result (given the long conveying distance). This means that continuous solids conveying of 20 t/hr may be hard to achieve, and a twin feeder system will most likely need be considered. It can be seen in Figure 14 that a batch system will lead to a smaller net solid flow rate due to the down time between batches. As such, twin discharge feeders will need to be used, which will act to discharge and then refill in offset c ycles so a more continuous rate can be achieved.
Pressure Drop If the flow rate of air is set to the designated 1.9kg/s, pressure drop for t he twice stepped system selected is shown by Appendix G to be 368 kPa. The most favourable pressure drop is provided by the 2 step system (Refer to Table 2). To be conservative and to account for possible increases in pressure caused by unforseen issues in running the system, a pressure requirement of 400kPa is a saf er stipulation for the system. This equates to a 4 bar pressure drop.
Power Theoretical power can be calculated from Equation 8 in Appendix A. This calculates power based on a pressure drop and properties of the air flowing, but not of the solids properties. As such, a reliable adjustment to get a more conservative estimate of power is to double the previous calculation (Jones, Mills, & Agarwal, 2005), such that ̇ As such, for the designed system
This is the power required for conveying. It should be noted that P in needed to be converted to gauge pressure before calculation, and STP conditions are assumed.
Recommendations General Given the selected air flow rate and solids flow rate result in an m* value of around 4, the conveying mode is definitively dilute phase. Indeed, this makes the most sense, given the fa ct that over long distances dense phase flow becomes harder to achieve than dilute phase (Jones, Mills, & Agarwal, 2005). This is further corroborated by the fact that typical dilute phase velocities range from 10 to 30 m/s, a window in which the designed s ystem operates (Mills, 2004). A positive pressure design is used, as negative pressure systems are limited to around 1 bar pressure drop (Mills, 2004), which is well below the demands of the design. It is of note that cement meal is not typically combustible, so no real design needs to be amended to manage this problem. Lastly, it is clear that an assembly of twin feeders will be an optimal design feature to better achieve the specified net delivery rate, because of the ability to continuously convey.
Air Mover When considering air movers in pneumatic conveying, capacity is often quoted as volumetric flow rate. As such, a suitable air mover for this system will be capable of supplying the required 4 Bar of pressure drop and volumetric flow rate of air or 95 m 3/min. The use of a fan is almost immediately ruled out: fans are more effective over smaller conveying distances, and don’t respond well to higher pressure drops (often material can f all
Figure 12: Image of a possible screw compressor (Hibon, 2013)
There were a number of options that had max capabilit ies close to the predicted characteristics (Atlas Copco, 2013). Choosing such a component could mean that any subsequent loss of output in the component from age, extended use or wear could drop the flow rate or pressure below that required. This would likely cause pipe blockage and require costly hold ups, fault checking and pipe maintenance. Similarly, running a component at its maximum capacity for extended periods would likely shorten the lifetime and thus increase the maintenance needs of the component, or even result in the need for premature replacement. The selected component meets the demand of the designed conveying system with reasonable overshoot, and so has a reasonable factor of safety in its use. The product was also chosen as it is oil free; although being more expensive, this type of system provides better lubrication with less required maintenance and upkeep of the air mover.
Feeder A number of options exist for the type of feeder used in the design. Ultimately it is the
The only real draw back with blow tanks are their large space occupation, but this is a reasonable trade off. The best option for a blow tank in this system is to use a top discharge variety, with a fluidising membrane and valved vent line. There are a number of reasons for this: Bottom discharge tanks are not as effective at fluidising the material, meaning conveying is not as easy (especially for such fine materials as cement meal) Less room is needed for top discharging blow tanks, meaning a twin blow tank system is easy to set up A fluidising membrane is less expensive to fit in the top discharge tank, a s they don’t need to be conical Added air flows are not needed: a line of conveying air flow is diverted to fluidise the material, eventually joining the conveying line with the main air flow with no air losses. The vent line allows for fast depressurisation of the tank
Some minor draw backs include The inability to completely discharge material (not of real concern as cement meal is not really degenerative) Pressure losses associated with the discharge line (Figure 16) need be mitigated. To counter this, the shortest possible line with the least amount of vertical section are to be used to feed the conveying line The fluidising membrane must be cleaned and maintained to ensure proper fluidisation occurs
Figure 17: A similar Blow tank manufactured by Kockums Bulk Systems
This tank is advertised as being able to deliver a maximum of 200 tonnes of material an hour (very large safety factor so they machine can be operated at low repetitions, increasing its lifetime). It is able to be placed in series, and would be available for sizing to order specification. If the density of loose poured cement is 900-1000 kg/m^3 (Brabender Technologie, 2012), and two 4 cubic meter tanks are considered:
A capacity of 7.2 tonnes means that in order to attain a solids delivery rate of 20 t/hr, around
is effective only for particles >10μm. As Figure 18 indicates, cement meal is therefore too fine to rely on cyclonic separation. (Mills, 2004) The best option for gas-solids separation is therefore a filter. A filter acts to trap particles, but without regular cleaning, will block further airflow and increases the pressure loss. This means the filter needs to be flushed occasionally to clear it. In a batch system, cleaning can be achieved by shaking the filter, but given this system uses continuous conveying, time cannot be taken to shake free particulates (Jones, Mills, & Agarwal, 2005). As such reverse air pulsing is an inexpensive and easy alternative, and can be carried out while the system is still running. The type of material used is for the filter a trade-off between maintenance requirements and costs. A fabric filters are a very cheap option, but are not especially resilient to chemical degradation or especially coarse particles, and have a relatively short lifespan. As a more expensive but longer lasting alternative, glass fibre meshes or other manmade fibre matrixes can be used (Mills, 2004). Possible Component In this system, the solids are not particularly abrasive, and are chemically inert, so the use of an expensive fibre woven filter is not necessary. It is far more viable to use a cheaper but equally effective replaceable cloth filter, coupled with a reverse air pulsing system supplied by an external source of air. The extra maintenance required with occasionally replacing the cloth filter is negligible for the savings made on equally effective cloth variety.
concern, but the use of this design in a humid or tropical area may introduce excess moisture. To avoid the possible blockages and maintenance requirements incurred by this, a desiccant drying technique should be used. This requires only that the desiccant bed over which air flows be replaced occasionally. Care should be taken that the desiccant is appropriately selected to remove sufficient water, and should be able to be recycled for continued use. Pressure observation points: to aid in the maintenance process, it is suggested that multiple pressure gauges be placed around the system in key areas. This will allow the operations to be monitored and any anomalies in performance isolated with relative ease. The location of these pressure gauges should be: Before and after the pipe that draws material out of the top discharge blow tank Before the cloth filter (to ensure excessive clogging is avoided and to time cleaning) Before and after the fluidising membrane in the blow tank, to check for clogging. At the point of entry of the solids to the air and at the end of the line (for total loss measurement)
Monitoring of velocities: as increased wear is associated with higher velocities, the velocity should be monitored actively at key points (such as the inlet, a t the steps and at the exit) to ensure values close to that of design are being recorded. Pipe section and bend replacement: the pipes will eventually degrade, with the bends most likely to suffer the worst wear. Regular checking of pipes should occur so finishing roughness ε doesn’t change drastically, causing larger pressure drops. Replacement of pipes is also important in ensuring the system acts as the design intends.
Conclusion Starting with a batch of test data, statistical relations between variables in the system were able to be derived. After checking the validity of the derived model, a design model for a system similar to the subject of the test data could be built. The design process in this instance was not a linear procedure. More often than not it was an iterative approach; numbers were guessed, iterated, changed in accordance with industr y standard then finalised to define key system components. The choice for each component was justified with a mixture of literature review and results from the design data. From this process, the system design is to meet the following specifications: An overall pressure drop of 368kPa (3.68 bar) A power consumption of 553kW A steady state flow rate of cement meal of 27 tonnes/hr A flow rate of air or 1.9kg/s m* = 3.947 Positive displacement system for conveying Dilute phase conveying Schedule 40 pipes used Pipeline stepped twice. First at 250m along the horizontal section from an 8 inch nominal bore to 10 inch, then once more another 250m along the system (at the base of the vertical rise) from 10 to 14 inch nominal bore. Twin 4 m3 top discharge blow tanks in series (brand suggestion made) Continuous conveying from the twin blow tanks.
Bibliography Atlas Copco. (2013). GA 315-500: Oil-injected rotary screw compressors. Retrieved August 25, 2013, from Atlas Copco Site: http://www.atlascopco.com.au/auus/products/Product.aspx?id=1524396&productgrou pid=1473343 Brabender Technologie. (2012). Standard Material Densities. Retrieved August 25, 2013, from Conveying Feeders: http://www.lossinweightfeeder.com/standards/documents/1500-C01-2.pdf Hibon. (2013). Hibon Product Site. Retrieved August 25, 2013, from Blowers, Compressors and high Vaccum Packages: http://www.hibon.com/IS/Product.aspx-eu_en-22772 Jones, M., Mills, D., & Agarwal, V. K. (2005). Handbook of Pneumatic Conveying Engineering. New York: Marcel Dekker. Kockums Pty Ltd. (2012). Pneumatic Conveying Systems. Retrieved August 20, 2013, from Kockums Bulk Systems: http://www.kockumsbulk.com.au/system/powder_handling_product/pdf/0000/0020/D ense-Phase-Conveyor.pdf Kockums Pty Ltd. (2013). Power Handling Products. Retrieved August 20, 2013, from Kockums Bulk Systems:
Appendix A – Equations 1.
̇
2.
3.
4.
5.
6.
7.
=
8.
9.
- is solids loading ratio, ̇ is the mass flow rate of fluid (s for solid)
̇
̇
̇
- P is pressure, is pressure drop - is density, x denotes which point density is taken at, R is ideal gas constant and T is absolute temperature (°K)
- C is the velocity at point x, d is diameter - Re is Reynold’s number, is dynamic viscosity - is the fluid friction factor, roughness
is surface
Appendix B – Test Data Test 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Ma
Ms
∆P
kg/s
kg/s
kPa
0.081 0.081 0.050 0.047 0.042 0.038 0.050 0.034 0.030 0.026 0.050 0.022 0.049 0.032 0.019
2.120 2.380 1.480 1.560 1.490 1.530 1.550 1.550 1.500 1.300 1.580 1.100 1.860 1.750 0.890
315 348 249 257 247 259 260 273 275 277 267 298 285 297 259
m* 26.173 29.383 29.600 33.191 35.476 40.263 31.000 45.588 50.000 50.000 31.600 50.000 37.959 54.688 46.842
Po
Pavg
ρi
kPa
kPa
kg/m^3
101 101 101 101 101 101 101 101 101 101 101 101 101 101 101
258.5 275.0 225.5 229.5 224.5 230.5 231.0 237.5 238.5 239.5 234.5 250.0 243.5 249.5 230.5
ρo
4.947 5.340 4.162 4.257 4.139 4.281 4.293 4.448 4.472 4.495 4.376 4.745 4.590 4.733 4.281
Ci
Co
Cavg
m/s
m/s
m/s
7.421 6.876 5.445 5.004 4.600 4.023 5.279 3.465 3.041 2.622 5.179 2.102 4.838 3.064 2.012
30.567 30.567 18.868 17.736 15.849 14.340 18.868 12.831 11.321 9.812 18.868 8.302 18.491 12.076 7.170
ρavg
kg/m^3 kg/m^3 1.201 1.201 1.201 1.201 1.201 1.201 1.201 1.201 1.201 1.201 1.201 1.201 1.201 1.201 1.201
3.074 3.270 2.682 2.729 2.670 2.741 2.747 2.824 2.836 2.848 2.789 2.973 2.896 2.967 2.741
Re
λf
11.943 108105 0.02170 11.226 108105 0.02170 8.451 66732 0.02288 7.806 62728 0.02306 7.131 56055 0.02341 6.283 50716 0.02373 8.250 66732 0.02288 5.456 45377 0.02412 4.794 40039 0.02459 4.138 34700 0.02516 8.127 66732 0.02288 3.354 29362 0.02589 7.670 65397 0.02294 4.888 42708 0.02434 3.142 25358 0.02658
∆Pair
∆Pbend
kPa
kPa
15.797 14.849 7.277 6.368 5.276 4.265 7.104 3.368 2.661 2.037 6.998 1.438 6.489 2.866 1.194
41.702 43.831 20.513 19.900 17.330 15.630 20.941 13.711 11.637 8.704 21.015 5.970 23.228 13.820 4.531
λs
Fr
b*
0.01351 0.01439 0.02350 0.02518 0.02806 0.03305 0.02410 0.04021 0.04817 0.06577 0.02473 0.10465 0.02378 0.04354 0.12036
16.563 15.569 11.720 10.825 9.889 8.714 11.441 7.567 6.649 5.738 11.270 4.652 10.637 6.779 4.357
0.069 0.078 0.128 0.145 0.167 0.210 0.134 0.271 0.341 0.465 0.139 0.740 0.146 0.322 0.824
Table 4: Test Data spreadsheet. All calculations are referenced above.
Pneumatic Conveying Design
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P a g e | 26
Appendix C – Forward Calculation Ma
Ms
∆Pguess
kg/s
kg/s
kPa
0.081 0.081 0.050 0.047 0.042 0.038 0.050 0.034 0.030 0.026 0.050 0.022 0.049 0.032 0.019
2.120 2.380 1.480 1.560 1.490 1.530 1.550 1.550 1.500 1.300 1.580 1.100 1.860 1.750 0.890
303 331 245 259 258 273 254 289 298 280 258 261 297 334 234
m* 26.17 29.38 29.60 33.19 35.48 40.26 31.00 45.59 50.00 50.00 31.60 50.00 37.96 54.69 46.84
Pavg
ρi
ρavg
Ci
Co
Cavg
kPa
kg/m^3
kg/m^3
m/s
m/s
m/s
4.80 5.14 4.11 4.28 4.27 4.45 4.22 4.64 4.75 4.53 4.27 4.31 4.73 5.17 3.98
3.00 3.17 2.66 2.74 2.74 2.82 2.71 2.92 2.97 2.87 2.74 2.75 2.97 3.19 2.59
7.64 7.15 5.51 4.98 4.46 3.87 5.37 3.32 2.87 2.60 5.31 2.32 4.69 2.80 2.16
30.57 30.57 18.87 17.74 15.85 14.34 18.87 12.83 11.32 9.81 18.87 8.30 18.49 12.08 7.17
252.49 266.50 223.50 230.50 230.00 237.50 228.00 245.50 250.00 241.00 230.00 231.50 249.50 268.00 218.00
12.23 11.58 8.53 7.77 6.96 6.10 8.36 5.28 4.57 4.11 8.29 3.62 7.49 4.55 3.32
Re 108105 108105 66732 62728 56055 50716 66732 45377 40039 34700 66732 29362 65397 42708 25358
λf
0.02170 0.02170 0.02288 0.02306 0.02341 0.02373 0.02288 0.02412 0.02459 0.02516 0.02288 0.02589 0.02294 0.02434 0.02658
Fr 16.957 16.066 11.825 10.778 9.652 8.457 11.592 7.321 6.343 5.703 11.491 5.023 10.381 6.311 4.607
λs
∆Pair
∆Pfrict
∆Pbend
∆Pcalc
∆Pd/∆Pc
kPa
Pa
kPa
kPa
data/calc
0.01251 16.17 0.01304 15.32 0.02281 7.34 0.02553 6.34 0.03024 5.15 0.03618 4.14 0.02312 7.20 0.04432 3.26 0.05506 2.54 0.06695 2.02 0.02327 7.13 0.08450 1.55 0.02558 6.33 0.05314 2.67 0.10234 1.26
244.10 270.59 216.60 232.98 236.03 254.08 225.39 272.93 284.31 269.33 229.23 253.39 268.03 318.49 227.70
42.69 45.23 20.70 19.81 16.92 15.17 21.22 13.26 11.10 8.65 21.43 6.45 22.67 12.87 4.79
303 331 245 259 258 273 254 289 298 280 258 261 297 334 234
Table 5: Spreadsheet for testing of forward calculating solids friction factor
Pneumatic Conveying Design
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P a g e | 27
1.0397 1.0509 1.0178 0.9918 0.9570 0.9474 1.0244 0.9431 0.9230 0.9893 1.0357 1.1401 0.9595 0.8892 1.1080
Appendix D – System Parameters Table This table is replicated above every design spreadsheet, containing system parameters. Red font indicates a design variable.
Design Parameters Ms
Ms
Ma
t/hr
kg/s
kg/s
7.7778
1.900
27
m*
Po
Lh
D
kPa
m
m
750
0.2027
4.0936 101
N 2
B 0.5
R
T
μ
ε
J/kg °K
°K
N.s/m^s
m
286.987
293
1.80E-05
0.000046
Appendix E – Uniform Pipe Bore Design Spread sheet Design characteristics ∆Pguess
kPa 478.15
Pavg kPa 340.0 76
ρi
ρo
ρavg
kg/m3 6.887531 752
kg/m3 1.2011 36
kg/m3 4.044 33
Ci m/s 9.96 7
Ci Test m/s 10.4096
Co m/s
Cavg m/s 16.97 57.152842 4
Re
λf
7703 87
0.0195
Check No Blockage
Fr 12.05 79
λs
0.0648 39
∆Pair
∆Pbends
∆Pfrict
kPa
kPa
kPa
42.20
2.57
478.15
RESULTS
Pneumatic Conveying Design
Max C
Power (Rough)
Practical Power
57.1
323.078
646.155
523
Ctest 10.61 3
m/s
kW
kW
kPa
m/s
3146568
∆Ptot
P a g e | 28
Appendix F – Single Step Design Spread sheet Design characteristics (part 2) Lh
D
∆P
Pin=P2
Pout = P3
m
m
kPa
kpa
kpa
350
0.307
107
208
101
Pavg kPa
ρi=ρ2
ρo=ρ3
kg/m^3 kg/m^3
154.507
2.474
1.201
ρavg
Ci=C2
Co=C3
Cavg
kg/m^3
m/s
m/s
m/s
1.837
10.369 21.356 13.96
Re
437634
λf
Fr
0.0198 8.043
λs
∆Pair
∆Pbend
∆Pfrict
∆P
kPa
kPa
kPa
kPa
0.1267
4.05
0.88579
102.08 107
λs
∆Pair
∆Pbend
∆Pfrict
∆P
kPa
kPa
kPa
kPa
Design characteristics (part 1) Lh
D
∆P
Pin=P1
Pout = P2
m
m
kPa
kpa
kpa
400
0.202
293
501
208
Pavg kPa
ρi=ρ1
ρo=ρ2
kg/m^3 kg/m^3
354.688
5.962
2.474
ρavg
Ci=C1
Co=C2
Cavg
kg/m^3
m/s
m/s
m/s
4.218
9.914
24.159 14.01
Re
664348
λf
Fr
0.0196 9.948
0.0858
16
0
277.31 293
RESULTS Max C
Power (Rough)
Practical Power
∆Ptotal
Ctest
24.159
296.31
592.617
386
10.647
m/s
kW
kW
kPa
m/s
Pneumatic Conveying Design
3146568
A No Blockage
B No Blockage
P a g e | 29
