Pipeline Design for Isothermal, Turbulent Flow of Non-Newtonian Fluids

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Process Engineering Guide: GBHE-PEG-FLO-304

Pipeline Design for Isothermal, Turbulent Flow of Non-Newtonian Fluids Information contained in this publication or as otherwise supplied to Users is believed to be accurate and correct at time of going to press, and is given in good faith, but it is for the User to satisfy itself of the suitability of the information for its own particular purpose. GBHE gives no warranty as to the fitness of this information for any particular purpose and any implied warranty or condition (statutory or otherwise) is excluded except to the extent that exclusion is prevented by law. GBHE accepts no liability resulting from reliance on this information. Freedom under Patent, Copyright and Designs cannot be assumed.



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 2 4.2 Drag Reduction in Polymeric Materials 2 4.3 Transition Delay by Polymeric Materials 3 4.4 Drag Reduction in Suspensions 4 5 DESIGN PROCEDURE FOR PRESSURE DROP

IN TURBULENT PIPE FLOW IN THE ABSENCE OF DRAG REDUCTION 5

5.1 Pressure Drop in the Absence of Wall Slip and

Drag Reduction 5 5.2 Wall Slip 5 5.3 Pipe Roughness 5 5.4 Pipe Fittings 5 6 DESIGN PROCEDURE FOR DRAG REDUCING

POLYMERIC MATERIALS 7

6.1 General 7 6.2 Transition Delay 8 6.3 Pipe Roughness 8 6.4 Pipe Fittings 9 7 DESIGN PROCEDURE FOR DRAG REDUCING

FIBRE SUSPENSIONS 9



8 BIBLIOGRAPHY 9 9 NOMENCLATURE 10 FIGURES 1 DRAG REDUCTION PHENOMENA 3 2 TRANSITION DELAY PHENOMENA 4 3 PROCEDURE FOR THE CALCULATION OF

PRESSURE DROP IN TURBULENT NON-NEWTONIAN PIPE FLOW 6

4 TYPICAL RELATIONSHIP FOR Ψ VERSUS ʋ* 8 DOCUMENTS REFERRED TO IN THIS PROCESS ENGINEERING GUIDE 10



0 INTRODUCTION/PURPOSE This Process Engineering Guide is one of a series of guides on non-Newtonian flow prepared for GBH Enterprises. Fluid flow in chemical plants is usually turbulent, and viscosities have to be high before laminar flow predominates. When viscosities are high, the fluids are often non-Newtonian in character. In this field of non-Newtonian flow, laminar flow predominates and this is covered by GBHE-PEG-FLO-303. There are still many instances when turbulent flow of non-Newtonian fluids is encountered. 1 SCOPE This guide presents the basis for the prediction of flow rate - pressure drop relationships for the turbulent flow of non-Newtonian fluid through circular pipes under isothermal conditions. The Guide also deals with drag reduction by polymeric materials and fibre suspensions. 2 FIELD OF APPLICATION This guide applies to the process engineering community in GBH Enterprises worldwide. 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 can be 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 liquid does not, in fact, slip. What occurs is that under the appropriate circumstances, a layer of fluid is formed next to the wall which has a viscosity appreciably less than the bulk of the fluid.



This is caused both by the wall affecting packing arrangements of particles and by the steep velocity gradients near the wall causing hydrodynamic lift effects which move particles away from the wall. The net effect can be considered as an effective "slip" at the wall, hence its name. 4.2 Drag Reduction in Polymeric Materials The addition of very small concentrations of high polymeric substances can reduce the frictional resistance in turbulent flow to as low as one quarter that of the pure solvent. This phenomenon, drag reduction, can occur both with fluids which exhibit Newtonian and non-Newtonian viscous characteristics. Drag reduction is illustrated in Figure 1. FIGURE 1 DRAG REDUCTION PHENOMENA



4.3 Transition Delay by Polymeric Materials The phenomenon of transition delay is closely related to drag reduction and is illustrated in Figure 2. The behavior shown in Figure 2(a) is typical of soap solutions (see Ref. [1]) and that in Figure 2(b) is typical of certain types of polymer solutions, such as polyacrylamide in water (see Ref. [2]). With transition delayed flow, the flow does not attain turbulent flow characteristics. Drag reduction and transition delay are no doubt related but, on the basis of the available evidence, there appear to be significant differences. The distinction between the two phenomena is that with drag reduction the flow attains non-drag reducing fully-developed turbulent flow before it is affected by the polymer.



FIGURE 2 TRANSITION DELAY PHENOMENA



4.4 Drag Reduction in Suspensions Drag reduction can also occur with the flow of suspensions of rigid, elongated particles. The shape of the particles is all important, as Kerekes and Douglas (see Ref. [3]) observed that drag reduction did not occur with suspensions of spherical particles but did with suspensions of particles having an elongated shape. Vaseleski and Metzner (see Ref. [4]) have reviewed the work which has been carried out into pressure drop in fibre suspensions and have drawn a number of important 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 is

increased 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 than polymeric materials; this makes design procedures less reliable. 5 DESIGN PROCEDURE FOR PRESSURE DROP IN TURBULENT PIPE

FLOW 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 the anomalous effects described in Clause 4. In the absence of these effects, Newtonian friction factor correlations can be used to calculate the pressure drop in turbulent non-Newtonian pipe flow if Reynolds numbers are based on the apparent viscosity at the wall (see Ref. [5]). Unfortunately, we cannot calculate the apparent viscosity at the wall until we know the shear stress at the wall (and hence 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.



Any departure of experimental data from the Newtonian friction factor correlation indicates the presence of anomalous effects. Without experimental data under turbulent conditions it is impossible to predict how a polymeric material or fibre suspension will behave under turbulent flow conditions. 5.2 Wall Slip No procedures are currently available for estimating the effect of wall slip under turbulent flow conditions. If it is neglected in design calculations and does occur then it is likely to lead to pressure drop predictions which are high and hence, in most instances, a conservative design. This does not mean to say that wall slip can also be ignored in the laminar regime. The viscometric measurements required 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 of non-Newtonian fluids in the absence of wall effects has involved hydraulically smooth pipes. Wall roughness will no doubt affect the turbulent flow of non-Newtonian fluids as it does with Newtonian fluids. In the absence of any information, it is recommended that the calculation procedure given in Figure 3 still be followed and wall roughness be included in the calculations in the same way as it would be for a Newtonian fluid but of course using a Reynolds number based on the apparent viscosity at the wall. 5.4 Pipe Fittings In turbulent Newtonian flow through pipe fittings, viscous effects are not normally significant and pressure drops are based on a number of velocity heads lost. It is thus recommended that pressure losses for the flow of non-Newtonian fluids be calculated in the same way as for Newtonian fluids. Some data for laminar pressure drop in pipe fittings have been given in GBHE-PEG-FLO-303. FIGURE 3 PROCEDURE FOR THE CALCULATION OF PRESSURE DROP

IN TURBULENT NON-NEWTONIAN PIPE FLOW (provided wall effects are not present)



6 DESIGN PROCEDURE FOR DRAG REDUCING POLYMERIC MATERIALS

6.1 General Numerous studies have been undertaken to characterize drag reduction phenomena in polymeric materials and these have been reviewed by Hoyt, Lumley and Virk (see Refs. [6], [7] and [8] respectively). The evidence which is available suggests that the presence of the polymer in drag reducing flows alters the structure of the turbulence in a complex manner. These complexities, coupled with the difficulty of defining physical properties which characterize drag reduction, make a scaling procedure attractive for design work, i.e. being able to scale pressure-drop measurements from one diameter of pipe to another. This would require turbulent viscometric measurements to be made, in addition to the normal laminar flow viscometric measurements required to characterize the fluid. In order to scale drag reduction from one flow situation to another, it is first necessary to define the degree of drag reduction in some way. As drag reduction can at maximum reduce to laminar flow, it would seem logical to define it with respect to this maximum effect. In fact, Metzner and Park (see Ref. [2]) suggested a ratio of the form:



flow and found that for a particular fluid the value Ψ was a unique function of the observed friction velocity and independent of pipe diameter. Thus, for a particular 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 w and ΔP) if f(v*) is known. This function f(v*) should be determined experimentally for each fluid. A typical curve is shown in Figure 4. It should be noted, however, that this method of correlation does not work with transition delay 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 a friction factor obtained in this manner (i.e. from Figure 3) should not be used in heat transfer calculations otherwise this could lead to a gross over-prediction of the heat transfer coefficient.



FIGURE 4 TYPICAL RELATIONSHIP FOR Ψ VERSUS v*

6.2 Transition Delay Drag reduction and transition delay behavior are no doubt related. However, the methods described for dealing with drag reduction do not apply to transition delay. The small amount of experimental evidence which is available suggests that the method recommended for correlating pressure drop data in drag reducing flow (i.e. Ψ against v*) does not work effectively with transition delay. There are currently no reliable methods available for correlating transition delay data. 6.3 Pipe Roughness Polymeric materials are just as effective in reducing drag in rough pipes as they are in smooth pipes. Virk (see Ref. [10]) carried out an extensive study into the flow of polymeric materials in roughened pipes. Although his data were characteristic of transition delay rather than drag reduction, one particularly important result is worth noting. Virk found that the maximum drag



reduction attainable for a given fluid had the same value for a given Reynolds number 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 turbulent pressure drop experiments to determine f(v*) be carried out using pipes with the same relative roughness (ε/D) envisaged for the design. 6.4 Pipe Fittings No investigations have been carried out into the flow of polymeric materials through pipe fittings under turbulent flow conditions. If pressure drops are calculated in the same way as for Newtonian flow, then this is likely to lead to an over-prediction of pressure drop. 7 DESIGN PROCEDURE FOR DRAG REDUCING FIBRE SUSPENSIONS Pressure drop in drag reducing fibre suspensions is less complex to correlate than in polymeric materials. There is no diameter effect with the flow of fibre suspensions and thus data for a particular fluid can be represented as a unique function on a plot of friction factor against Reynolds number. However, the friction factor vs Reynolds number relationship for a particular fibre suspension cannot be predicted and can only be determined experimentally.



8 BIBLIOGRAPHY This Process Engineering Guide makes reference to the following: [1] A.White, Flow characteristics of complex soap systems, Nature, London

214, 585-586 (1967) [2] A.B.Metzner and M.G.Park, Turbulent flow characteristics of viscoelastic

fluids, J Fluid Mech 20,291-303 (1964) [3] R.J.E.Kerekes and W.J.M.Douglas, Viscosity Properties of Suspensions at

the 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 of

Fibre Suspensions, A.I.Ch.E.JL 20, 301-306 (1974) [5] M.F.Edwards and R.Smith, The turbulent flow of non-Newtonian fluids in

the 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 Drag

Reduction, Plenum Press (1969) [10] P.S.Virk, Drag reduction in Rough Pipes, J.Fluid Mech. 45, 225-246

(1971).



9 NOMENCLATURE



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)

Pipeline Design for Isothermal, Turbulent Flow of Non-Newtonian Fluids

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