Pipeline design for turbulent flow of non Newtonianfluids

8/10/2019 Pipeline design for turbulent flow of non Newtonianfluids

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Process Engineering Guide:GBHE-PEG-FLO-304

Pipeline Design for Isothermal,Turbulent Flow of Non-NewtonianFluids

Information contained in this publication or as otherwise supplied to Users isbelieved to be accurate and correct at time of going to press, and is given ingood faith, but it is for the User to satisfy itself of the suitability of the informationfor its own particular purpose. GBHEgives no warranty as to the fitness of thisinformation for any particular purpose and any implied warranty or condition

(statutory or otherwise) is excluded except to the extent that exclusion isprevented by law. GBHEaccepts no liability resulting from reliance on thisinformation. Freedom under Patent, Copyright and Designs cannot be assumed.


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Process Engineering Guide: Pipeline Design for Isothermal,Turbulent Flow of Non-Newtonian Fluids

CONTENTS SECTION

0 INTRODUCTION/PURPOSE 2

1 SCOPE 2

2 FIELD OF APPLICATION 2

3 DEFINITIONS 2

4 DESCRIPTION OF ANOMALOUS EFFECTS 2

4.1 Wall Slip 24.2 Drag Reduction in Polymeric Materials 24.3 Transition Delay by Polymeric Materials 34.4 Drag Reduction in Suspensions 4

5 DESIGN PROCEDURE FOR PRESSURE DROPIN TURBULENT PIPE FLOW IN THE ABSENCEOF DRAG REDUCTION 5

5.1 Pressure Drop in the Absence of Wall Slip and

Drag Reduction 55.2 Wall Slip 55.3 Pipe Roughness 55.4 Pipe Fittings 5

6 DESIGN PROCEDURE FOR DRAG REDUCINGPOLYMERIC MATERIALS 7

6.1 General 76.2 Transition Delay 8

6.3 Pipe Roughness 86.4 Pipe Fittings 9

7 DESIGN PROCEDURE FOR DRAG REDUCINGFIBRE SUSPENSIONS 9


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8 BIBLIOGRAPHY 9

9 NOMENCLATURE 10

FIGURES

1 DRAG REDUCTION PHENOMENA 3

2 TRANSITION DELAY PHENOMENA 4

3 PROCEDURE FOR THE CALCULATION OFPRESSURE DROP IN TURBULENT NON-NEWTONIANPIPE FLOW 6

4 TYPICAL RELATIONSHIP FOR VERSUS * 8

DOCUMENTS REFERRED TO IN THIS PROCESSENGINEERING GUIDE 10


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0 INTRODUCTION/PURPOSE

This Process Engineering Guide is one of a series of guides on non-Newtonianflow prepared for GBH Enterprises.

Fluid flow in chemical plants is usually turbulent, and viscosities have to be highbefore laminar flow predominates. When viscosities are high, the fluids are oftennon-Newtonian in character. In this field of non-Newtonian flow, laminar flowpredominates and this is covered by GBHE-PEG-FLO-303. There are still manyinstances when turbulent flow of non-Newtonian fluids is encountered.

1 SCOPE

This guide presents the basis for the prediction of flow rate - pressure droprelationships for the turbulent flow of non-Newtonian fluid through circular pipesunder isothermal conditions. The Guide also deals with drag reduction bypolymeric materials and fibre suspensions.

2 FIELD OF APPLICATION

This guide applies to the process engineering community in GBH Enterprisesworldwide.

3 DEFINITIONS

For the purposes of this guide, no specific definitions apply.

4 DESCRIPTION OF ANOMALOUS EFFECTS

The fluids which can exhibit non-Newtonian effects are varied, and the flow canbe complicated by the anomalous effects described in 4.1 to 4.4.

4.1 Wall Slip

Wall slip can occur with the flow of slurries. Wall slip is a misnomer, as the liquiddoes not, in fact, slip. What occurs is that under the appropriate circumstances, alayer of fluid is formed next to the wall which has a viscosity appreciably lessthan the bulk of the fluid.


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This is caused both by the wall affecting packing arrangements of particles andby the steep velocity gradients near the wall causing hydrodynamic lift effectswhich move particles away from the wall. The net effect can be considered as aneffective "slip" at the wall, hence its name.

4.2 Drag Reduction in Polymeric Materials

The addition of very small concentrations of high polymeric substances canreduce the frictional resistance in turbulent flow to as low as one quarter that ofthe pure solvent. This phenomenon, drag reduction, can occur both with fluidswhich exhibit Newtonian and non-Newtonian viscous characteristics. Dragreduction is illustrated in Figure 1.

FIGURE 1 DRAG REDUCTION PHENOMENA


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4.3 Transition Delay by Polymeric Materials

The phenomenon of transition delay is closely related to drag reduction and isillustrated in Figure 2. The behavior shown in Figure 2(a) is typical of soapsolutions (see Ref. [1]) and that in Figure 2(b) is typical of certain types ofpolymer solutions, such as polyacrylamide in water (see Ref. [2]).

With transition delayed flow, the flow does not attain turbulent flowcharacteristics.

Drag reduction and transition delay are no doubt related but, on the basis of theavailable evidence, there appear to be significant differences.

The distinction between the two phenomena is that with drag reduction the flowattains non-drag reducing fully-developed turbulent flow before it is affected bythe polymer.


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FIGURE 2 TRANSITION DELAY PHENOMENA


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4.4 Drag Reduction in Suspensions

Drag reduction can also occur with the flow of suspensions of rigid, elongatedparticles. The shape of the particles is all important, as Kerekes and Douglas(see Ref. [3]) observed that drag reduction did not occur with suspensions ofspherical particles but did with suspensions of particles having an elongatedshape.

Vaseleski and Metzner (see Ref. [4]) have reviewed the work which has beencarried out into pressure drop in fibre suspensions and have drawn a number ofimportant conclusions; viz drag reduction in fibre suspensions:

(a) Increases for a particular fibre as the fibre concentration is increased.

(b) Increases as the aspect ratio (length to diameter ratio) of the fibers isincreased at constant fibre concentration.

(c) Is not dependent upon the pipe diameter.

Much less work has been carried out on drag reduction in fibre suspensions thanpolymeric materials; this makes design procedures less reliable.

5 DESIGN PROCEDURE FOR PRESSURE DROP IN TURBULENT PIPEFLOW IN THE ABSENCE OF DRAG REDUCTION

5.1 Pressure Drop in the Absence of Wall Slip and Drag Reduction

Both slurries of approximately spherical particles and polymer solutions can,under certain circumstances, flow turbulently without exhibiting any of theanomalous effects described in Clause 4. In the absence of these effects,Newtonian friction factor correlations can be used to calculate the pressure dropin turbulent non-Newtonian pipe flow if Reynolds numbers are based on theapparent viscosity at the wall (see Ref. [5]). Unfortunately, we cannot calculatethe apparent viscosity at the wall until we know the shear stress at the wall (andhence the pressure drop); consequently an iterative calculation is required.Figure 3 shows a flow chart for the calculation of pressure drop in turbulent non-Newtonian pipe flow in the absence of any wall effects.


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Any departure of experimental data from the Newtonian friction factor correlationindicates the presence of anomalous effects. Without experimental data underturbulent conditions it is impossible to predict how a polymeric material or fibresuspension will behave under turbulent flow conditions.

5.2 Wall Slip

No procedures are currently available for estimating the effect of wall slip underturbulent flow conditions. If it is neglected in design calculations and does occurthen it is likely to lead to pressure drop predictions which are high and hence, inmost instances, a conservative design. This does not mean to say that wall slipcan also be ignored in the laminar regime. The viscometric measurementsrequired to characterize the fluid are described in GBHE-PEG-FLO-302.

5.3 Pipe Roughness

All of the experimental work which has been carried out on the turbulent flow ofnon-Newtonian fluids in the absence of wall effects has involved hydraulicallysmooth pipes. Wall roughness will no doubt affect the turbulent flow of non-Newtonian fluids as it does with Newtonian fluids. In the absence of anyinformation, it is recommended that the calculation procedure given in Figure 3still be followed and wall roughness be included in the calculations in the sameway as it would be for a Newtonian fluid but of course using a Reynolds numberbased on the apparent viscosity at the wall.

5.4 Pipe Fittings

In turbulent Newtonian flow through pipe fittings, viscous effects are not normallysignificant and pressure drops are based on a number of velocity heads lost. It isthus recommended that pressure losses for the flow of non-Newtonian fluids becalculated in the same way as for Newtonian fluids. Some data for laminarpressure drop in pipe fittings have been given in GBHE-PEG-FLO-303.

FIGURE 3 PROCEDURE FOR THE CALCULATION OF PRESSURE DROPIN TURBULENT NON-NEWTONIAN PIPE FLOW (provided walleffects are not present)


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6 DESIGN PROCEDURE FOR DRAG REDUCINGPOLYMERIC MATERIALS

6.1 General

Numerous studies have been undertaken to characterize drag reductionphenomena in polymeric materials and these have been reviewed by Hoyt,Lumley and Virk (see Refs. [6], [7] and [8] respectively). The evidence which isavailable suggests that the presence of the polymer in drag reducing flows altersthe structure of the turbulence in a complex manner. These complexities,coupled with the difficulty of defining physical properties which characterizedrag reduction, make a scaling procedure attractive for design work, i.e. beingable to scale pressure-drop measurements from one diameter of pipe to another.This would require turbulent viscometric measurements to be made, in additionto the normal laminar flow viscometric measurements required to characterizethe fluid.

In order to scale drag reduction from one flow situation to another, it is firstnecessary to define the degree of drag reduction in some way. As drag reductioncan at maximum reduce to laminar flow, it would seem logical to define it withrespect to this maximum effect. In fact, Metzner and Park (see Ref. [2])suggested a ratio of the form:


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flow and found that for a particular fluid the value was a unique function ofthe observed friction velocity and independent of pipe diameter. Thus, for aparticular fluid:

Thus, given the fluid density, the purely viscous laminar flow properties of the

fluid, the pipe diameter and bulk velocity, then v*can be calculated (hence t wand P) if f(v*)is known. This function f(v*)should be determinedexperimentally for each fluid. A typical curve is shown in Figure 4. It should benoted, however, that this method of correlation does not work with transitiondelay phenomena.

If a particular design problem does not warrant experimental measurements,then an over prediction of the pressure drop will be obtained by following the

calculation procedure shown in Figure 3. It is important to note, however, that afriction factor obtained in this manner (i.e. from Figure 3) should not be used inheat transfer calculations otherwise this could lead to a gross over-prediction ofthe heat transfer coefficient.


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FIGURE 4 TYPICAL RELATIONSHIP FOR VERSUS v*

6.2 Transition Delay

Drag reduction and transition delay behavior are no doubt related. However, themethods described for dealing with drag reduction do not apply to transitiondelay. The small amount of experimental evidence which is available suggeststhat the method recommended for correlating pressure drop data in drag

reducing flow (i.e. against v*) does not work effectively with transition delay.There are currently no reliable methods available for correlating transition delaydata.

6.3 Pipe Roughness

Polymeric materials are just as effective in reducing drag in rough pipes as theyare in smooth pipes. Virk (see Ref. [10]) carried out an extensive study into theflow of polymeric materials in roughened pipes. Although his data werecharacteristic of transition delay rather than drag reduction, one particularlyimportant result is worth noting. Virk found that the maximum drag


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reduction attainable for a given fluid had the same value for a given Reynoldsnumber in both smooth and rough pipes.

This implies that the function f(v*)in Equations (2) and (3) should be the same

for both smooth and rough pipes. However, it is recommended that turbulentpressure drop experiments to determine f(v*)be carried out using pipes with thesame relative roughness (/D)envisaged for the design.

6.4 Pipe Fittings

No investigations have been carried out into the flow of polymeric materialsthrough pipe fittings under turbulent flow conditions. If pressure drops arecalculated in the same way as for Newtonian flow, then this is likely to lead to anover-prediction of pressure drop.

7 DESIGN PROCEDURE FOR DRAG REDUCING FIBRE SUSPENSIONS

Pressure drop in drag reducing fibre suspensions is less complex to correlatethan in polymeric materials. There is no diameter effect with the flow of fibresuspensions and thus data for a particular fluid can be represented as a uniquefunction on a plot of friction factor against Reynolds number. However, thefriction factor vs Reynolds number relationship for a particular fibre suspensioncannot be predicted and can only be determined experimentally.


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8 BIBLIOGRAPHY

This Process Engineering Guide makes reference to the following:

[1] A.White, Flow characteristics of complex soap systems, Nature, London214, 585-586 (1967)

[2] A.B.Metzner and M.G.Park, Turbulent flow characteristics of viscoelasticfluids, J Fluid Mech 20,291-303 (1964)

[3] R.J.E.Kerekes and W.J.M.Douglas, Viscosity Properties of Suspensions atthe Limiting Conditions for Turbulent Drag Reduction, Can. J Chem. Eng.SO, 228-231 (1972)

[4] R.C.Vaseleski and A.B.Metzner, Drag Reduction in the Turbulent Flow ofFibre Suspensions, A.I.Ch.E.JL 20, 301-306 (1974)

[5] M.F.Edwards and R.Smith, The turbulent flow of non-Newtonian fluids inthe absence of anomalous wall effects J. Non-Newtonian Fluid Mech.7,77-90 (1980)

[6] J.W.Hoyt, The effect of additives on fluid friction, Trans ASME 94D, 258-285 (1972)

[7] J.L.Lumley, Drag reduction in turbulent flow by polymer additives, J.Polymer Sci Macromol. Rev. 7, 263-290 (1973)

[8] P.S.Virk, Drag reduction fundamentals, A.I.Ch.JL.21, 625-656 (1975)

[9] N.F.Whitsitt, L.J.Harrington and H.R.Crawford in C.S. Wells, Viscous DragReduction, Plenum Press (1969)

[10] P.S.Virk, Drag reduction in Rough Pipes, J.Fluid Mech. 45, 225-246(1971).


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9 NOMENCLATURE


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DOCUMENTS REFERRED TO IN THIS PROCESS ENGINEERING GUIDE

This Process Engineering Guide makes reference to the following documents:

PROCESS ENGINEERING GUIDES

GBHE-PEG-FLO-302 Interpretation and Correlation of Viscometric Data(referred to in 5.2)

GBHE-PEG-FLO-303 Pipeline Design for Isothermal, Laminar Flow of Non-Newtonian Fluids (referred to in Clause 0 and 5.4)


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Pipeline design for turbulent flow of non Newtonianfluids