the effect of the particle size distribution on non-newtonian turbulent ...
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the effect of the particle size distribution on non-newtonian turbulent ...

the effect of the particle size distribution on non-newtonian turbulent ... the effect of the particle size distribution on non-newtonian turbulent ...

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5.1 INTRODUCTION CHAPTERS DISCUSSION This chapter deals with discussing ong>theong> results and analysis ong>ofong> ong>theong> test data as presented in Chapter 4 and Appendix A. 5.2 PARTICLE ROUGHNESS EFFECT In Figure 4.2 it is noted that ong>theong> data points for ong>theong> kaolin tend to lie on ong>theong> line for ong>theong> law ong>ofong> ong>theong> wall for smooth pipes, with ong>theong> rock flour data points lying to ong>theong> left. The data points for ong>theong> sand tend to lie on or near ong>theong> curve ong>ofong> Nikuradse. This is not in line with what Slatter's model anticipates. The data points according to ong>theong> Slatter model should lie on or near ong>theong> horizontal asymptote (roughness function B=8,5) since ong>theong> ong>particleong>s in ong>theong> suSpensions that were tested were neiong>theong>r fixed nor uniform in ong>sizeong>, as ong>theong>y were for Nikuradse's experiments. And yet it can be seen from Figure 4.2 that ong>theong> roughness ong>effectong> ong>ofong> ong>theong> solid ong>particleong>s for mixture 2 is as great and even greater than for Nikuradse's experimental data. For smooth wall turbulent flow ong>theong> Slatter model predicts that ong>theong> data should lie on or near ong>theong> oblique asymptote (line for ong>theong> law ong>ofong> ong>theong> wall for smooth pipes) and for ong>theong> kaolin clay test sets this is certainly ong>theong> case but yet ong>theong> data points for mixture I lie to ong>theong> left. In fact most ong>ofong> ong>theong> data points lie well outside ong>theong> two asymptotes which describe ong>theong> limits ong>ofong> behaViour ong>ofong> Newtonian turbulent flow. There are many reported instances ong>ofong> similarities between ong>theong> turbulent flow ong>ofong> Newtonian and non-Newtonian fluids (section 2.12) and Slatter'S findings confirmed this trend. The data ong>ofong> Slatter (1994) matched ong>theong> limits ong>ofong> ong>theong> behaviour ong>ofong>Newtonian turbulent flow closely and hence for his correlation ong>ofong> ong>theong> roughness function for his model ong>theong> two asymptotes were chosen. However, ong>theong>se test data points :ontradict ong>theong> findings ong>ofong> Slatter and would indicate that d 85 ong>sizeong> does not give ong>theong> best representation ong>ofong> ong>theong> ong>particleong> roughness ong>effectong>.

Chapter 5 Discussion Page 5.2 Furong>theong>r investigation needs to be conducted and a large data base established to determine wheong>theong>r ong>theong> roughness ong>effectong> will: • follow ong>theong> Nikuradse trend; • continue increasing, following more closely ong>theong> oblique asymptote; • or if it does follow ong>theong> horizontal asymptote as proposed by Slatter. 5.3 ROUGHNESS FUNCTION CORRELATION USING OPTIMUM PARTICLE SIZES If, however, ong>theong> optimum ong>particleong> ong>sizeong>s are used to plot ong>theong> roughness function correlation as shown in Figure 4.11 ong>theong> data points for mixture 2 tend to lie just above ong>theong> horizontal asymptote. On ong>theong> whole ong>theong> data points tend to follow more closely ong>theong> assumptions on which ong>theong> Slatter model is based. What this does bring into question is that ong>theong> d S5 ong>sizeong> does not necessarily give ong>theong> best representative ong>particleong> ong>sizeong>. These optimum ong>particleong> ong>sizeong>s indicate that ong>theong> representative ong>particleong> ong>sizeong> will vary depending on ong>theong> PSD ong>ofong> ong>theong> slurry being transported. In fact it would seem from Table 4.1, looking at ong>theong> optimum ong>sizeong>s for kaolin clay and mixture 2, that a slurry with a steep PSD for ong>theong> smaller ong>particleong>s (eg. kaolin clay test sets) would have a higher representative ong>particleong> ong>sizeong> than a slurry which has a PSD shape that is less steep from small to large ong>particleong>s. In Table 4.1 ong>theong> kaolin clay test sets have an average ong>particleong> ong>sizeong> ong>ofong> d x =d 91 as opposed to mixture 2 tests sets which have an average representative ong>particleong> ong>sizeong> ong>ofong> d. =d 71 • Therefore ong>theong> higher fraction ong>ofong> larger Particles present in ong>theong> slurry ong>theong> lower ong>theong> representative ong>particleong> ong>sizeong>, as ong>theong> best representation ong>ofong> ong>theong> roughness ong>effectong> is reached at a lower d x value. 5.4 SLURRY TEMPERATURE As reported in section 4.2.7 an increase in temperature ong>ofong> between goC to 10°C made no significant difference and no temperature ong>effectong>s were found. It is surprising to see this trend since this would cause a decrease in ong>theong> viscosity for water ong>ofong> approximately 20%. This Could influence ong>theong> rheology ong>ofong> ong>theong> slurry and might lead one to question ong>theong> method ong>ofong>

5.1 INTRODUCTION<br />

CHAPTERS<br />

DISCUSSION<br />

This chapter deals with discussing <str<strong>on</strong>g>the</str<strong>on</strong>g> results and analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> test data as presented in<br />

Chapter 4 and Appendix A.<br />

5.2 PARTICLE ROUGHNESS EFFECT<br />

In Figure 4.2 it is noted that <str<strong>on</strong>g>the</str<strong>on</strong>g> data points for <str<strong>on</strong>g>the</str<strong>on</strong>g> kaolin tend to lie <strong>on</strong> <str<strong>on</strong>g>the</str<strong>on</strong>g> line for <str<strong>on</strong>g>the</str<strong>on</strong>g> law<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> wall for smooth pipes, with <str<strong>on</strong>g>the</str<strong>on</strong>g> rock flour data points lying to <str<strong>on</strong>g>the</str<strong>on</strong>g> left. The data<br />

points for <str<strong>on</strong>g>the</str<strong>on</strong>g> sand tend to lie <strong>on</strong> or near <str<strong>on</strong>g>the</str<strong>on</strong>g> curve <str<strong>on</strong>g>of</str<strong>on</strong>g> Nikuradse. This is not in line with<br />

what Slatter's model anticipates. The data points according to <str<strong>on</strong>g>the</str<strong>on</strong>g> Slatter model should lie<br />

<strong>on</strong> or near <str<strong>on</strong>g>the</str<strong>on</strong>g> horiz<strong>on</strong>tal asymptote (roughness functi<strong>on</strong> B=8,5) since <str<strong>on</strong>g>the</str<strong>on</strong>g> <str<strong>on</strong>g>particle</str<strong>on</strong>g>s in <str<strong>on</strong>g>the</str<strong>on</strong>g><br />

suSpensi<strong>on</strong>s that were tested were nei<str<strong>on</strong>g>the</str<strong>on</strong>g>r fixed nor uniform in <str<strong>on</strong>g>size</str<strong>on</strong>g>, as <str<strong>on</strong>g>the</str<strong>on</strong>g>y were for<br />

Nikuradse's experiments. And yet it can be seen from Figure 4.2 that <str<strong>on</strong>g>the</str<strong>on</strong>g> roughness <str<strong>on</strong>g>effect</str<strong>on</strong>g><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> solid <str<strong>on</strong>g>particle</str<strong>on</strong>g>s for mixture 2 is as great and even greater than for Nikuradse's<br />

experimental data.<br />

For smooth wall <strong>turbulent</strong> flow <str<strong>on</strong>g>the</str<strong>on</strong>g> Slatter model predicts that <str<strong>on</strong>g>the</str<strong>on</strong>g> data should lie <strong>on</strong> or near<br />

<str<strong>on</strong>g>the</str<strong>on</strong>g> oblique asymptote (line for <str<strong>on</strong>g>the</str<strong>on</strong>g> law <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> wall for smooth pipes) and for <str<strong>on</strong>g>the</str<strong>on</strong>g> kaolin clay<br />

test sets this is certainly <str<strong>on</strong>g>the</str<strong>on</strong>g> case but yet <str<strong>on</strong>g>the</str<strong>on</strong>g> data points for mixture I lie to <str<strong>on</strong>g>the</str<strong>on</strong>g> left. In fact<br />

most <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> data points lie well outside <str<strong>on</strong>g>the</str<strong>on</strong>g> two asymptotes which describe <str<strong>on</strong>g>the</str<strong>on</strong>g> limits <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

behaViour <str<strong>on</strong>g>of</str<strong>on</strong>g> Newt<strong>on</strong>ian <strong>turbulent</strong> flow. There are many reported instances <str<strong>on</strong>g>of</str<strong>on</strong>g> similarities<br />

between <str<strong>on</strong>g>the</str<strong>on</strong>g> <strong>turbulent</strong> flow <str<strong>on</strong>g>of</str<strong>on</strong>g> Newt<strong>on</strong>ian and n<strong>on</strong>-Newt<strong>on</strong>ian fluids (secti<strong>on</strong> 2.12) and<br />

Slatter'S findings c<strong>on</strong>firmed this trend. The data <str<strong>on</strong>g>of</str<strong>on</strong>g> Slatter (1994) matched <str<strong>on</strong>g>the</str<strong>on</strong>g> limits <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g><br />

behaviour <str<strong>on</strong>g>of</str<strong>on</strong>g>Newt<strong>on</strong>ian <strong>turbulent</strong> flow closely and hence for his correlati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> roughness<br />

functi<strong>on</strong> for his model <str<strong>on</strong>g>the</str<strong>on</strong>g> two asymptotes were chosen. However, <str<strong>on</strong>g>the</str<strong>on</strong>g>se test data points<br />

:<strong>on</strong>tradict <str<strong>on</strong>g>the</str<strong>on</strong>g> findings <str<strong>on</strong>g>of</str<strong>on</strong>g> Slatter and would indicate that d 85 <str<strong>on</strong>g>size</str<strong>on</strong>g> does not give <str<strong>on</strong>g>the</str<strong>on</strong>g> best<br />

representati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> <str<strong>on</strong>g>particle</str<strong>on</strong>g> roughness <str<strong>on</strong>g>effect</str<strong>on</strong>g>.

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