144 10. Conclusions
To improve the prediction of conveying limits on the basis of physical characteristics of particulate materials, which was the original objective of this investigation, it was found to be necessary to acquire a large set of data (the conveying characteristics and the characteristics of the particulate materials) to enable evaluation of existing models. This also allowed the evaluation of the new models that have been established.
Existing correlations for predicting the limit of stable conveying in suspension flow or partially suspended flow, as presented in Section 2.4.2, give poor reliability of the predictions even inside their claimed areas of validity. The errors shown in Table 6.2 vary from 116% over prediction to 77% under prediction of the limit of stable conveying. The model that is best suited for the prediction of this conveying limit is Pan's model which, with a safety factor of 31%, has been found not to give under prediction for any of the operating conditions.
Cabrejos' model is the only one for predicting pick up velocity. It has been evaluated together with the models for predicting the limit of stable conveying in suspension flow or partially suspended flow. The results show that Cabrejos' model under predicts this limit for all operating conditions (see Figures 6.2, 6.4, 6.6, 6.8, 6.9 and 6.10). This is in violation of Cabrejos' own description of the pick up velocity as a velocity above the saltation velocity. This concept is therefore not considered to be useful.
The models for predicting the velocity at minimum pressure loss give errors that vary from 111% over prediction to 85% under prediction (see Table 6.1). Matsumoto's model is the only one that does not considerably underpredict this velocity.
Part of the explanation of the poor performance of the existing models mentioned above can be found in the fact that the experimental data, on which the empirical fitting has been based, is limited to solids loading ratios below 5 for relevant pipeline sizes (see Table 2.2).
A simple model has been developed, based on the length of the mean free path for the particles in the suspension, for the prediction of whether single particle behaviour is dominant or not. As Table 2.1 shows, most industrial scale pneumatic transport systems
Ph.D. Thesis S.E.Martinussen Chapter 10, Conclusions
operate at conditions where single particle behaviour in the pipeline is not dominant. This may be yet another explanation as to why existing models, based on single particle behaviour, do not give reliable predictions of the conveying limit.
To evaluate the possibility of taking another approach towards understanding limitations in the conveying velocity in pneumatic transport systems, based on the collective behaviour rather than the single particle behaviour of the material, a set of wave propagation velocity measurements were carried out. The measurements, which were carried out on fluidized alumina, show that the propagation velocity is equal to that expected from fluid dynamic theory (Figure 8.1) in the large wavelength to bed depth region of the dispersion relation.
This explains why the Froude number is relevant for the characterisation of two phase gas solids flow where a stratified flow occurs, since the Froude number characterises such flows. It also justifies applying fluid analogies to flow of fluidized powders.
Based on the fluid analogy, a model was developed (see Section 8.4) that predicts the maximum mass flow of solids in pneumatic conveying pipelines for the Geldart type B materials to within 9 %, and for the Geldart type D materials to within 36%. It is, in all cases, too conservative and can be used for design purposes as a worst case estimate. The model, due to the assumptions on which it is based, cannot be expected to predict the maximum flow of Geldart type A and C materials. The model is purely mechanistic and requires no empirical fitting.
The fluid analogy has also been applied to develop a model for the prediction of when blockage will occur in pneumatic conveying pipelines. The model is based on the assumption that Kelvin-Helmholz instabilities on the partially settled layer of solids close to blockage, contributes to re-suspend particles and thus to prevent blockage. The absence of such instabilities is used as a criterion to identify blockage conditions. The predictions of the model are surprisingly accurate considering that the model is purely mechanistic and does not require any empirical fitting (see Table 8.2). The model, presented in Section 8.6,
Ph.D. Thesis S.E.Martinussen Chapter 10, Conclusions
146 In a collaborative project between the author at Telemark Industrial Research and Development Centre and P.E.Lia and Prof. K.H. Esbensen at Telemark College, a model, based on multivariate analysis, for predicting the pressure minimum velocity has been established (see Section 8.7) that has a root mean square error of prediction of ±1.2m/s on the average. The maximum error is -2.2m/s (or -15% of the measured value) and is obtained for PVC. The model must be validated with many more materials. It probably also needs to be expanded to include the effect of pipeline diameter.
Only marginal effects on the limit of stable conveying have been found after introducing a horizontal to horizontal bend. The bend was positioned after 15m of horizontal pipeline, as shown in Figure 3.4. The only material for which an effect was detected was rape seed.
The rape seed data showed an increase in the limit of stable conveying in suspension flow at low feed rates (see Figure 5.8). More pronounced effects of the bend might have been detected had the bend been positioned closer to the feed section.
The models that were available before the completion of this work were based on an understanding of the behaviour of the single particle in the air flow. The experimental data on which they were based, also to a large extent reflects this, because only low solids loading ratios have been considered. By computing the mean free path of the particles and comparing it to the pipeline diameter it has been shown that this approach can be used only at very low solids loading ratios. Realising the shortcomings of the single particle approach, two new mechanistic models have been devised that rely on a fluid dynamic description of the flow. These models require no empirical fitting. No model has been found previously for predicting the maximum mass flow of solids for Geldart type B materials. The predictions of the model for predicting the limit of stable conveying are more accurate than any of those provided by previous models. This model also provides new fundamental understanding of what causes blockages in pneumatic conveying pipelines.
Ph.D. Thesis S.E.Martinussen Chapter 11, Suggestions for
Further Work