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An investigation into the effect of product type when scaling for diameter in vertical pipelines
Powder Technology 112 Ž2000. 229–234 www.elsevier.comrlocaterpowtec
An investigation into the effect of product type when scaling for diameter in vertical pipelines K. Hettiaratchi, M.S.A. Bradley ) , R.J. Farnish, I. Bridle, L.M. Hyder, A.R. Reed The Wolfson Centre for Bulk Solids Handling Technology, School of Engineering, UniÕersity of Greenwich, Wellington Street, Woolwich, London SE18 6PF, UK
Abstract The prediction of pressure drop is important to pipeline design and it is often necessary to use data from one pipeline size to predict what will happen in another pipeline size. This paper looks at the effect of two different products when scaling for diameter in vertical pipelines. Data has been measured for cement and flour in two bore sizes. A means of modelling has been established to allow prediction of the operation of a pipeline of one bore size, from trials on another bore size in vertical sections. The model used to correlate pipeline diameter with pressure gradient data in vertical pneumatic conveying pipelines will be discussed along with the general data trends for the two materials. q 2000 Elsevier Science S.A. All rights reserved. Keywords: Pressure drop; Product type; Pipeline diameter; Pneumatic conveying; Vertical pipelines; Suspension density
1. Introduction The major design criteria for pneumatic conveying systems are those of pipeline bore, air mover rating, and solids feeder type. Each of these parameters is, in turn, determined to some extent by the system pipeline pressure drop. Thus, the importance of pressure drop prediction for pneumatic conveying pipelines will be self-evident. The investigations into the effect of pipeline diameter on the relationship between pressure gradient, solids flow rate and air flow rate in pneumatic conveying systems have mainly focused on pneumatic conveying in horizontal pipelines Že.g. Refs. w1,2x.. Although some work has been undertaken on vertical pipelines and the relationship to pressure drop in horizontal pipelines Že.g. Refs. w3–5x., the effect of bore size, although explored to a limited extent in vertical pipes Že.g. Ref. w6x., has not been exhaustively researched. Many of the techniques, which have been presented for pipeline design in practical situations, rely on conveying trials in a pilot scale instrumented test facility w1x. Data
) Corresponding author. Tel.: q44-181-331-8646; fax: q44-141-3318647. E-mail address: [email protected] ŽM.S.A. Bradley..
obtained from the trials is then processed by empirically determined techniques to predict the likely pressure drop in the desired plant pipeline. Clearly, the availability of a suitable pilot scale test plant is key to such a design technique, and the cost of undertaking the pilot conveying trials can be significant. Therefore, it is usual to limit such trials to a minimum, on a pilot facility as small as can be used effectively, which means it is almost always necessary to scale for pipeline bore between trials and plant. This paper presents comparisons of pressure drop data measured from two vertical pipelines of different bore sizes. The details of the test facility along with the material employed for the test programme are presented. The approach used to analyse the data is presented, followed by a discussion on the processed data and the conclusions from this study.
2. Test facility The test facility could be configured to enable tests to be carried out in either an 81-mm bore pipeline or a 53-mm bore pipeline. Both pipelines were of steel construction and a common layout was adopted to try to ensure that both pipelines were within less than 2 m of the same total length. Fig. 1 shows a schematic diagram of the
0032-5910r00r$ - see front matter q 2000 Elsevier Science S.A. All rights reserved. PII: S 0 0 3 2 - 5 9 1 0 Ž 0 0 . 0 0 2 9 1 - 6
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4. Experimental programme
Fig. 1. Schematic layout of test facility.
Tests were carried out in the two vertical pipeline sections using the cement, and wheat flour approximately 250 test runs being performed in total. The range of superficial air velocities, from 5 to 23 mrs, was covered and this was consistent with both dense and lean phase conveying regimes. A suspension density range from 10 to 300 kg of cement per cubic metre of air was covered. However, due to both the limitation of the test plant and the requirement to make the test data applicable to the most common conditions encountered in industry, only the lower suspension densities were tested at high superficial air velocities and the higher suspension densities tested at low superficial air velocities.
5. Experimental results test facility used to obtain data relating to both pipelines sections. The test material was conveyed from a top discharge blow tank, via the test pipeline section, into a receiving hopper mounted above the blow tank to facilitate recirculation of the material. The air flow rate to the plant was metered using a bank of calibrated choked flow nozzles w2x, whilst the solid flow rate was derived from load cells supporting the receiving hopper. Along each of the test sections for both pipelines, pressure tappings were installed at approximately 2-m intervals. The radii of each of the bends into both pipeline test sections were 0.75 m. Fig. 2 shows the schematic layout for the positions of the pressure tappings along the 81-mm-diameter pipeline. The pressure tappings were connected to pressure transducers, which, in turn, were connected to a computer data logging system. This allowed simultaneous logging of pressure readings from all of the transducers on the test pipeline section.
The raw data from the tests in both the 81-mm-diameter pipeline and the 53-mm pipeline was initially analysed to give pipeline pressure profiles Žas per the sample shown in Fig. 4. for each test run completed. Tangents were then fitted to the pressure profiles as indicated, in order to obtain the average pressure gradient along the pipeline straight, excluding any bend effects. Values of pipeline pressure gradient were then tabulated for each test run completed, along with the relevant suspension density and superficial air velocity at the midpoint of the tangent fitted. 5.1. Processed data The model that was adopted to analyse the data was one which stated that the experimentally measured total pres-
3. Test materials Ordinary Portland Cement and wheat flour were selected for the test programme. To assess the effect of repeated conveying on the materials, the first five tests were repeated after every thirty test runs. It was found that the change in pressure gradient with repeated conveying was not significant compared to the size of the pressure gradient. The cement that was used for the tests was a standard grade cement readily available to the building and construction industry, having a mean particle size of 17 mm. The wheat flour that was used was a variety that was commonly used in the food processing industry. The mean particle size of the flour used in the test programme was 36 mm. Fig. 3a and b shows the particle size distributions for Ordinary Portland Cement and wheat flour, respectively.
Fig. 2. Position of the pressure tappings along the 81-mm-diameter pipeline.
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Fig. 3. Ža. Particle size distribution for ordinary portland cement. Žb. Particle size distribution for wheat flour.
sure gradient comprised of three components: the solids contribution to the total pressure gradient, the air only flow contribution to the total pressure gradient and the ‘static head’ contribution to total pressure gradient. The air only flow contribution to the total pressure gradient was determined using the Darcy expression. The static head contribution was determined using the product of suspension density, acceleration due to gravity and vertical height gain; this is detailed in Appendix A. The solids flow contribution to the total pressure gradient was determined by subtracting the air only contribution and the static head contribution from the experimentally measured pressure gradient. For each velocity band, a range of suspension densities was covered in order to obtain a comprehensive set of data for each pipeline. It was found that each velocity band data set could be represented quite accurately by a linear regression curve, as shown in Fig. 5. The graphs of all velocity band data sets for cement in the 81-mm pipeline and the 53-mm pipeline are shown in Figs. 6 and 7.
Fig. 4. Pressure reading against distance along test section of 53-mm pipeline.
The graphs of all velocity band data sets for flour in the 81-mm pipeline and the 53-mm pipeline are shown in Figs. 8 and 9.
6. Discussion Figs. 6–9 show the solids flow contribution to the total pressure gradients in the 81-mm bore pipeline and the 53-mm bore pipeline for both cement and flour. It is apparent from these that the solids contribution to the pressure drop is related linearly to the suspension density for any given air velocity, for both materials and pipeline sizes. This is, in itself, a useful result in terms of characterisation of the conveyability of materials in general. However, what is more important to this particular study is that this linearity between solids contribution to
Fig. 5. Solids contribution to total pressure gradient vs. suspension density for velocity range 9.00 to 11.00 mrs for cement in 53-mm pipeline.
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Fig. 6. Solids contribution to total pressure gradient vs. suspension density for cement in the 81-mm vertical pipeline.
Fig. 8. Solids contribution to total pressure gradient vs. suspension density for flour in the 81-mm vertical pipeline.
pressure gradient and air velocity allows the data to be effectively represented in one less dimension by taking the ratio of: solids contribution to pressure gradient , suspension density
which is constant for each range of air velocity Ži.e. the slopes of the lines in Figs. 6–9. and plotting these against the air velocity.
Fig. 7. Solids contribution to total pressure gradient vs. suspension density for cement in the 53-mm vertical pipeline.
Fig. 9. Solids contribution to total pressure gradient vs. suspension density for flour in the 53-mm vertical pipeline.
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Adense phaseB conditions Ži.e. at velocities below the transition. is simply not retained in Alean phaseB conditions Žhigher velocities. even though the relationships between velocity, suspension density and pressure gradient, for the two materials, remain qualitatively the same. The effect of pipeline diameter is not clear from Figs. 6–9. However, with the slopes of these straight line models plotted against air velocity as shown in Fig. 10, it becomes clear that there is a strong similarity between the two data sets based on the same suspension density in both pipelines. For the cement, there is no clear trend for either the 53-mm pipeline or 81-mm pipeline to give higher pressure gradient, and the fact that at different velocities the two swap over, which suggests that the differences are within the bounds of repeatability for the experiments described. The situation with the flour is a little less satisfactory in that there is a fairly consistent trend for the 81-mm pipeline to give higher pressure gradients as the air velocity increases across the Alean phaseB range Ži.e. above about 12 mrs.. No clear reason for this has emerged. Fig. 10. Solids contribution to total pressure gradient per unit suspension density vs. midrange superficial air velocity.
7. Conclusions Fig. 10 shows the above ratio, plotted against the air velocity at the midpoint of the test section. Hence, all of the data from the entire test programme are shrunk onto this one graph, including both test materials and both pipeline sizes. In Fig. 10, it can be seen that there is for the cement, a strong discontinuity between the velocity band 11.50 to 13.50 mrs Žcentred on 12.5 mrs. and the velocity band 14.00 to 16.00 mrs Žcentred at 15 mrs.. This discontinuity is not so noticeable for the flour. It is interesting to note that a similar discontinuity occurs in the region where a transition between nonsuspension transport and suspension transport occurs in the horizontal conveying of cement and flour. This is apparent in both the 81-mm pipeline and the 53-mm pipeline. What changes in terms of the mechanism of transport in the vertical pipe to introduce the discontinuity at a similar velocity to that known of in the horizontal pipe is not clear; however, it could possibly be arising as a result of the behaviour of the material in the horizontal pipeline feeding the vertical section; below this discontinuity, the material would be slugging in the horizontal, whereas above it, the material would be tending to be much more dispersed and travelling in suspension in the horizontal. What is perhaps more surprising is that this discontinuity is very apparent for the cement, but hardly apparent at all for the flour. Both materials were similar in being fine powders and, hence, would be expected to exhibit a similar transition between slugging and suspended flow in horizontal transport, at about this velocity. The quantitative similarity of conveyability between cement and flour in
Two bulk solids have been conveyed over a very wide range of flow regimes Žfrom low-velocity, high-concentration dense phase flow to high-velocity, low-concentration lean phase flow. in two pipeline sizes, and the pressure gradients measured. From the results, a notional Asolids transport contribution to pressure gradientB has been obtained by subtracting the pressure drop needed to transport the air and a notional gravitational Astatic headB contribution. The conclusions of this study are that it is broadly acceptable to scale for diameter based on a model of consistent solids contribution to pressure gradient for given suspension densities and superficial air velocities, across the pipe bore range used. This approach appears to be acceptable for both suspension Žlean phase. and nonsuspension Ždense phase. flow regimes, although the correlation is especially accurate in the nonsuspension transport region. For one bulk solid, there appears to be a discontinuity in the curve of solids contribution to pressure drop vs. suspension density, at around the superficial air velocity at which saltation occurs in the horizontal pipeline. This suggests that the mode of flow in the vertical is heavily influenced by what is happening in the horizontal which feeds it. The same physical behaviour would be expected with the other bulk solid; however, the absence of an obvious discontinuity in the curve is probably only an indication that the pressure drop happens to change smoothly without a jump at the same transition in physical behaviour.
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Appendix A. Definition of static head of suspension The term Astatic head of suspensionB used in this paper is defined as the pressure exerted by a static column of the gas–solids suspension in the pneumatic conveying pipeline and was derived using the following equation: D P s Ž rs q rg . gh, where D P s static head of suspension, rs s suspension density Žsee Appendix B., rg s gas density, g s acceleration due to gravity, h s height of suspension column. It should be noted that for this to be strictly correct in theoretical terms, it should be based upon the actual average density of the mixture in the vertical pipe, whereas the Asuspension densityB as used in this paper is always lower, owing to the slip velocity between gas and solids Žsee explanation below.. However, the suspension density used here was preferred for simplicity in a practical engineering context; the fact that it is not theoretically strictly correct does not seem to compromise the usefulness of the concept in the correlations found in this work.
superficial air velocity., the difference will be small owing to the slip velocity being small; however, close to saltation conditions, the difference becomes more appreciable. In the dense phase or slug flow regime Ži.e. velocities typically under about 12 mrs., it will be very significant. In any event, the notion of an Aactual suspension densityB is probably not very useful in a dense phase flow regime since the solids travel in highly concentrated slugs with quite clean air between them. It is perfectly possible to obtain actual mixture densities by appropriate experimental means Že.g. Ref. w7x.; however, in this case, it was decided to avoid that since the objective was to obtain a relationship that could be used for the practical purposes of scaling across pipe size without the need for such complexity in the experimental setup. Hence, it is important to consider the Asuspension densityB values used here as primarily the mass of solids transported by each actual cubic metre of air and as purely a relative guide to the concentration of the particles in the air.
Appendix B. Discussion on ASuspension DensityB
References
The suspension density used in this paper is defined as the mass of solid particles transported per unit volume of gas flowing, i.e.:
w1x M.S.A. Bradley, PhD Thesis, Thames Polytechnic Žnow University of Greenwich., London, UK, 1990. w2x P.W. Wypych, P.C. Arnold, Powder Technol. 50 Ž1987. 281–294. w3x P. Marjanovic, A comparative study of the performance characteristics for horizontal and vertical pneumatic conveying in pipelines, Pneumatech 1, 1982, Stratford-upon-Avon, UK. w4x P. Marjanovic, An Investigation of The Behaviour of Gas–Solid Mixture Flow Properties for Vertical Pneumatic Conveying in Pipelines, PhD Thesis, Thames Polytechnic Žnow University of Greenwich., London, UK, 1983. w5x K. Hettiaratchi, S.R. Woodhead, A.R. Reed, Comparison between pressure drop in horizontal and vertical pneumatic conveying pipelines, Powder Technol. 95 Ž1998. 67–73. w6x K. Hettiaratchi, S.R. Woodhead, M.S.A. Bradley, M.J. Smith, A.R. Reed, The effect of pipeline bore on the conveying of cement in vertical pipelines, 6th International Conference on Bulk Materials Storage, Handling and Transportation, University of Wollongong, NSW, Australia, 1998, September. w7x H. Raaheman, V.K. Jindal, Mixture Characteristics in Pneumatic Conveying of Agricultural Grains, Powder Handling and Processing 1994, Vol. 6, No. 1.
rs s
m ˚ solid V˚gas
where m ˚ solid s mass flow rate of solids in kgrs; V˚ s actual volume flow rate of gas, i.e. at pressure obtaining in the pipeline at point of measurement, in mrs. It must be noted that this is not the actual density of the mixture of gas and solids inside the pipe. It is used as a quantity which can easily be determined from measurement, since it does not require a knowledge of any variables which cannot be obtained with simple instrumentation. In practice, this nominal suspension density will be lower than the actual density of the gas–solid mixture since there will be a slip velocity between gas and solids. At conditions of high velocity Ži.e. in a fully suspended flow regime with a fine powder, probably above 15 mrs
An investigation into the effect of product type when scaling for diameter in vertical pipelines K. Hettiaratchi, M.S.A. Bradley ) , R.J. Farnish, I. Bridle, L.M. Hyder, A.R. Reed The Wolfson Centre for Bulk Solids Handling Technology, School of Engineering, UniÕersity of Greenwich, Wellington Street, Woolwich, London SE18 6PF, UK
Abstract The prediction of pressure drop is important to pipeline design and it is often necessary to use data from one pipeline size to predict what will happen in another pipeline size. This paper looks at the effect of two different products when scaling for diameter in vertical pipelines. Data has been measured for cement and flour in two bore sizes. A means of modelling has been established to allow prediction of the operation of a pipeline of one bore size, from trials on another bore size in vertical sections. The model used to correlate pipeline diameter with pressure gradient data in vertical pneumatic conveying pipelines will be discussed along with the general data trends for the two materials. q 2000 Elsevier Science S.A. All rights reserved. Keywords: Pressure drop; Product type; Pipeline diameter; Pneumatic conveying; Vertical pipelines; Suspension density
1. Introduction The major design criteria for pneumatic conveying systems are those of pipeline bore, air mover rating, and solids feeder type. Each of these parameters is, in turn, determined to some extent by the system pipeline pressure drop. Thus, the importance of pressure drop prediction for pneumatic conveying pipelines will be self-evident. The investigations into the effect of pipeline diameter on the relationship between pressure gradient, solids flow rate and air flow rate in pneumatic conveying systems have mainly focused on pneumatic conveying in horizontal pipelines Že.g. Refs. w1,2x.. Although some work has been undertaken on vertical pipelines and the relationship to pressure drop in horizontal pipelines Že.g. Refs. w3–5x., the effect of bore size, although explored to a limited extent in vertical pipes Že.g. Ref. w6x., has not been exhaustively researched. Many of the techniques, which have been presented for pipeline design in practical situations, rely on conveying trials in a pilot scale instrumented test facility w1x. Data
) Corresponding author. Tel.: q44-181-331-8646; fax: q44-141-3318647. E-mail address: [email protected] ŽM.S.A. Bradley..
obtained from the trials is then processed by empirically determined techniques to predict the likely pressure drop in the desired plant pipeline. Clearly, the availability of a suitable pilot scale test plant is key to such a design technique, and the cost of undertaking the pilot conveying trials can be significant. Therefore, it is usual to limit such trials to a minimum, on a pilot facility as small as can be used effectively, which means it is almost always necessary to scale for pipeline bore between trials and plant. This paper presents comparisons of pressure drop data measured from two vertical pipelines of different bore sizes. The details of the test facility along with the material employed for the test programme are presented. The approach used to analyse the data is presented, followed by a discussion on the processed data and the conclusions from this study.
2. Test facility The test facility could be configured to enable tests to be carried out in either an 81-mm bore pipeline or a 53-mm bore pipeline. Both pipelines were of steel construction and a common layout was adopted to try to ensure that both pipelines were within less than 2 m of the same total length. Fig. 1 shows a schematic diagram of the
0032-5910r00r$ - see front matter q 2000 Elsevier Science S.A. All rights reserved. PII: S 0 0 3 2 - 5 9 1 0 Ž 0 0 . 0 0 2 9 1 - 6
K. Hettiaratchi et al.r Powder Technology 112 (2000) 229–234
230
4. Experimental programme
Fig. 1. Schematic layout of test facility.
Tests were carried out in the two vertical pipeline sections using the cement, and wheat flour approximately 250 test runs being performed in total. The range of superficial air velocities, from 5 to 23 mrs, was covered and this was consistent with both dense and lean phase conveying regimes. A suspension density range from 10 to 300 kg of cement per cubic metre of air was covered. However, due to both the limitation of the test plant and the requirement to make the test data applicable to the most common conditions encountered in industry, only the lower suspension densities were tested at high superficial air velocities and the higher suspension densities tested at low superficial air velocities.
5. Experimental results test facility used to obtain data relating to both pipelines sections. The test material was conveyed from a top discharge blow tank, via the test pipeline section, into a receiving hopper mounted above the blow tank to facilitate recirculation of the material. The air flow rate to the plant was metered using a bank of calibrated choked flow nozzles w2x, whilst the solid flow rate was derived from load cells supporting the receiving hopper. Along each of the test sections for both pipelines, pressure tappings were installed at approximately 2-m intervals. The radii of each of the bends into both pipeline test sections were 0.75 m. Fig. 2 shows the schematic layout for the positions of the pressure tappings along the 81-mm-diameter pipeline. The pressure tappings were connected to pressure transducers, which, in turn, were connected to a computer data logging system. This allowed simultaneous logging of pressure readings from all of the transducers on the test pipeline section.
The raw data from the tests in both the 81-mm-diameter pipeline and the 53-mm pipeline was initially analysed to give pipeline pressure profiles Žas per the sample shown in Fig. 4. for each test run completed. Tangents were then fitted to the pressure profiles as indicated, in order to obtain the average pressure gradient along the pipeline straight, excluding any bend effects. Values of pipeline pressure gradient were then tabulated for each test run completed, along with the relevant suspension density and superficial air velocity at the midpoint of the tangent fitted. 5.1. Processed data The model that was adopted to analyse the data was one which stated that the experimentally measured total pres-
3. Test materials Ordinary Portland Cement and wheat flour were selected for the test programme. To assess the effect of repeated conveying on the materials, the first five tests were repeated after every thirty test runs. It was found that the change in pressure gradient with repeated conveying was not significant compared to the size of the pressure gradient. The cement that was used for the tests was a standard grade cement readily available to the building and construction industry, having a mean particle size of 17 mm. The wheat flour that was used was a variety that was commonly used in the food processing industry. The mean particle size of the flour used in the test programme was 36 mm. Fig. 3a and b shows the particle size distributions for Ordinary Portland Cement and wheat flour, respectively.
Fig. 2. Position of the pressure tappings along the 81-mm-diameter pipeline.
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Fig. 3. Ža. Particle size distribution for ordinary portland cement. Žb. Particle size distribution for wheat flour.
sure gradient comprised of three components: the solids contribution to the total pressure gradient, the air only flow contribution to the total pressure gradient and the ‘static head’ contribution to total pressure gradient. The air only flow contribution to the total pressure gradient was determined using the Darcy expression. The static head contribution was determined using the product of suspension density, acceleration due to gravity and vertical height gain; this is detailed in Appendix A. The solids flow contribution to the total pressure gradient was determined by subtracting the air only contribution and the static head contribution from the experimentally measured pressure gradient. For each velocity band, a range of suspension densities was covered in order to obtain a comprehensive set of data for each pipeline. It was found that each velocity band data set could be represented quite accurately by a linear regression curve, as shown in Fig. 5. The graphs of all velocity band data sets for cement in the 81-mm pipeline and the 53-mm pipeline are shown in Figs. 6 and 7.
Fig. 4. Pressure reading against distance along test section of 53-mm pipeline.
The graphs of all velocity band data sets for flour in the 81-mm pipeline and the 53-mm pipeline are shown in Figs. 8 and 9.
6. Discussion Figs. 6–9 show the solids flow contribution to the total pressure gradients in the 81-mm bore pipeline and the 53-mm bore pipeline for both cement and flour. It is apparent from these that the solids contribution to the pressure drop is related linearly to the suspension density for any given air velocity, for both materials and pipeline sizes. This is, in itself, a useful result in terms of characterisation of the conveyability of materials in general. However, what is more important to this particular study is that this linearity between solids contribution to
Fig. 5. Solids contribution to total pressure gradient vs. suspension density for velocity range 9.00 to 11.00 mrs for cement in 53-mm pipeline.
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Fig. 6. Solids contribution to total pressure gradient vs. suspension density for cement in the 81-mm vertical pipeline.
Fig. 8. Solids contribution to total pressure gradient vs. suspension density for flour in the 81-mm vertical pipeline.
pressure gradient and air velocity allows the data to be effectively represented in one less dimension by taking the ratio of: solids contribution to pressure gradient , suspension density
which is constant for each range of air velocity Ži.e. the slopes of the lines in Figs. 6–9. and plotting these against the air velocity.
Fig. 7. Solids contribution to total pressure gradient vs. suspension density for cement in the 53-mm vertical pipeline.
Fig. 9. Solids contribution to total pressure gradient vs. suspension density for flour in the 53-mm vertical pipeline.
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Adense phaseB conditions Ži.e. at velocities below the transition. is simply not retained in Alean phaseB conditions Žhigher velocities. even though the relationships between velocity, suspension density and pressure gradient, for the two materials, remain qualitatively the same. The effect of pipeline diameter is not clear from Figs. 6–9. However, with the slopes of these straight line models plotted against air velocity as shown in Fig. 10, it becomes clear that there is a strong similarity between the two data sets based on the same suspension density in both pipelines. For the cement, there is no clear trend for either the 53-mm pipeline or 81-mm pipeline to give higher pressure gradient, and the fact that at different velocities the two swap over, which suggests that the differences are within the bounds of repeatability for the experiments described. The situation with the flour is a little less satisfactory in that there is a fairly consistent trend for the 81-mm pipeline to give higher pressure gradients as the air velocity increases across the Alean phaseB range Ži.e. above about 12 mrs.. No clear reason for this has emerged. Fig. 10. Solids contribution to total pressure gradient per unit suspension density vs. midrange superficial air velocity.
7. Conclusions Fig. 10 shows the above ratio, plotted against the air velocity at the midpoint of the test section. Hence, all of the data from the entire test programme are shrunk onto this one graph, including both test materials and both pipeline sizes. In Fig. 10, it can be seen that there is for the cement, a strong discontinuity between the velocity band 11.50 to 13.50 mrs Žcentred on 12.5 mrs. and the velocity band 14.00 to 16.00 mrs Žcentred at 15 mrs.. This discontinuity is not so noticeable for the flour. It is interesting to note that a similar discontinuity occurs in the region where a transition between nonsuspension transport and suspension transport occurs in the horizontal conveying of cement and flour. This is apparent in both the 81-mm pipeline and the 53-mm pipeline. What changes in terms of the mechanism of transport in the vertical pipe to introduce the discontinuity at a similar velocity to that known of in the horizontal pipe is not clear; however, it could possibly be arising as a result of the behaviour of the material in the horizontal pipeline feeding the vertical section; below this discontinuity, the material would be slugging in the horizontal, whereas above it, the material would be tending to be much more dispersed and travelling in suspension in the horizontal. What is perhaps more surprising is that this discontinuity is very apparent for the cement, but hardly apparent at all for the flour. Both materials were similar in being fine powders and, hence, would be expected to exhibit a similar transition between slugging and suspended flow in horizontal transport, at about this velocity. The quantitative similarity of conveyability between cement and flour in
Two bulk solids have been conveyed over a very wide range of flow regimes Žfrom low-velocity, high-concentration dense phase flow to high-velocity, low-concentration lean phase flow. in two pipeline sizes, and the pressure gradients measured. From the results, a notional Asolids transport contribution to pressure gradientB has been obtained by subtracting the pressure drop needed to transport the air and a notional gravitational Astatic headB contribution. The conclusions of this study are that it is broadly acceptable to scale for diameter based on a model of consistent solids contribution to pressure gradient for given suspension densities and superficial air velocities, across the pipe bore range used. This approach appears to be acceptable for both suspension Žlean phase. and nonsuspension Ždense phase. flow regimes, although the correlation is especially accurate in the nonsuspension transport region. For one bulk solid, there appears to be a discontinuity in the curve of solids contribution to pressure drop vs. suspension density, at around the superficial air velocity at which saltation occurs in the horizontal pipeline. This suggests that the mode of flow in the vertical is heavily influenced by what is happening in the horizontal which feeds it. The same physical behaviour would be expected with the other bulk solid; however, the absence of an obvious discontinuity in the curve is probably only an indication that the pressure drop happens to change smoothly without a jump at the same transition in physical behaviour.
K. Hettiaratchi et al.r Powder Technology 112 (2000) 229–234
234
Appendix A. Definition of static head of suspension The term Astatic head of suspensionB used in this paper is defined as the pressure exerted by a static column of the gas–solids suspension in the pneumatic conveying pipeline and was derived using the following equation: D P s Ž rs q rg . gh, where D P s static head of suspension, rs s suspension density Žsee Appendix B., rg s gas density, g s acceleration due to gravity, h s height of suspension column. It should be noted that for this to be strictly correct in theoretical terms, it should be based upon the actual average density of the mixture in the vertical pipe, whereas the Asuspension densityB as used in this paper is always lower, owing to the slip velocity between gas and solids Žsee explanation below.. However, the suspension density used here was preferred for simplicity in a practical engineering context; the fact that it is not theoretically strictly correct does not seem to compromise the usefulness of the concept in the correlations found in this work.
superficial air velocity., the difference will be small owing to the slip velocity being small; however, close to saltation conditions, the difference becomes more appreciable. In the dense phase or slug flow regime Ži.e. velocities typically under about 12 mrs., it will be very significant. In any event, the notion of an Aactual suspension densityB is probably not very useful in a dense phase flow regime since the solids travel in highly concentrated slugs with quite clean air between them. It is perfectly possible to obtain actual mixture densities by appropriate experimental means Že.g. Ref. w7x.; however, in this case, it was decided to avoid that since the objective was to obtain a relationship that could be used for the practical purposes of scaling across pipe size without the need for such complexity in the experimental setup. Hence, it is important to consider the Asuspension densityB values used here as primarily the mass of solids transported by each actual cubic metre of air and as purely a relative guide to the concentration of the particles in the air.
Appendix B. Discussion on ASuspension DensityB
References
The suspension density used in this paper is defined as the mass of solid particles transported per unit volume of gas flowing, i.e.:
w1x M.S.A. Bradley, PhD Thesis, Thames Polytechnic Žnow University of Greenwich., London, UK, 1990. w2x P.W. Wypych, P.C. Arnold, Powder Technol. 50 Ž1987. 281–294. w3x P. Marjanovic, A comparative study of the performance characteristics for horizontal and vertical pneumatic conveying in pipelines, Pneumatech 1, 1982, Stratford-upon-Avon, UK. w4x P. Marjanovic, An Investigation of The Behaviour of Gas–Solid Mixture Flow Properties for Vertical Pneumatic Conveying in Pipelines, PhD Thesis, Thames Polytechnic Žnow University of Greenwich., London, UK, 1983. w5x K. Hettiaratchi, S.R. Woodhead, A.R. Reed, Comparison between pressure drop in horizontal and vertical pneumatic conveying pipelines, Powder Technol. 95 Ž1998. 67–73. w6x K. Hettiaratchi, S.R. Woodhead, M.S.A. Bradley, M.J. Smith, A.R. Reed, The effect of pipeline bore on the conveying of cement in vertical pipelines, 6th International Conference on Bulk Materials Storage, Handling and Transportation, University of Wollongong, NSW, Australia, 1998, September. w7x H. Raaheman, V.K. Jindal, Mixture Characteristics in Pneumatic Conveying of Agricultural Grains, Powder Handling and Processing 1994, Vol. 6, No. 1.
rs s
m ˚ solid V˚gas
where m ˚ solid s mass flow rate of solids in kgrs; V˚ s actual volume flow rate of gas, i.e. at pressure obtaining in the pipeline at point of measurement, in mrs. It must be noted that this is not the actual density of the mixture of gas and solids inside the pipe. It is used as a quantity which can easily be determined from measurement, since it does not require a knowledge of any variables which cannot be obtained with simple instrumentation. In practice, this nominal suspension density will be lower than the actual density of the gas–solid mixture since there will be a slip velocity between gas and solids. At conditions of high velocity Ži.e. in a fully suspended flow regime with a fine powder, probably above 15 mrs