EFFECT OF PIPE INCLINATION ON COARSE-GRAINED PARTICLE-WATER MIXTURES FLOW
DOI:10.30825/5.EJPAU.187.2020.23.2

Pavel Vlasak, Zdenek Chara, Jiri Konfrst, Jan Krupicka
Institute of Hydrodynamics CAS, Praha, Czech Republic

ABSTRACT

The effect of the mixture velocity, solid concentration, and pipe inclination on the coarse-grained particle–water mixtures flow behaviour, concentration distribution, and pressure drops were experimentally studied in horizontal, vertical, and inclined pipes of inner diameter D=100 mm. Graded basalt gravel was used as a solid phase. The local concentration distribution was studied with the application of a gamma-ray densitometer. The study revealed the stratified flow pattern of the coarse particle-water mixture in horizontal and inclined pipes. The particles moved principally close to the pipe invert, and particle saltation becomes the dominant mode of particle conveying for higher and moderate flow velocities. The frictional pressure droops in ascending pipe increases with increasing pipe inclination up to about 30 degrees, then gradually decreases. For the pipe inclination lower than about 30°, the effect of pipe inclination on local concentration distribution was not significant. The in-situ concentration reached higher values in the ascending than in the descending sections.

Key words: Solid-Liquid Mixture, Pipe Inclination, Pressure Drops, Concentration Distribution.

INTRODUCTION

Freight pipelines are commonly used for transport of different particulate solids. Pipeline conveying of bulk materials, mostly relatively fine particles, which in the turbulent flow are supported by turbulent diffusion, in the form of heterogeneous mixtures is of special interest in, e.g. dredging, building, land reclamation or mining [25]. Pipeline transport of coarse-grained material is not very frequently used due to the problems of severe wear, material degradation, high deposition velocity limit, and consequently also operational velocities, and energy requirement. A lot of theoretical or experimental studies have been carried out on the transport of particle-water mixtures in horizontal pipes. However, relatively little research has been done on hydraulic conveying of gravel or bigger particles, especially in vertical and inclined pipes. Pressure drops and operational velocity are the most important parameters for pipeline transport design and operation. Friction losses in pipeline flow of heterogeneous solid particle-water mixtures are strongly dependent on the flow pattern [8]. If the operational velocity of the mixture is close to the deposition limit, a granular bed forms at the pipe invert. The bed slide over the pipe wall at velocities above the deposition limit and it is stationary below the deposition limit. The contact bed is an important contributor to solid friction in mixture flow.  

The understanding of the slurry flow behavior makes it possible to optimize transport parameters and energy requirements, to improve quality, safety, economy and reliability of transport and/or processing of the transported material. Deep knowledge of the slurry flow behavior, deposition limit and operational velocities, and the pressure drops associated with the slurry flow in horizontal, vertical and inclined pipe sections is essential to safe and effective design and operation of such pipeline installation [11].

The flow of heterogeneous solid-liquid mixtures in a pipe may be defined as the flow with an asymmetrical velocity and concentration distribution, where a Coulomb friction contributes significantly to the friction losses. A flow pattern with a bed layer and a skewed concentration distribution generally exist for these slurries. The first mechanistic approach for coarse-grained particle slurry flow was probably that of Newitt et al. [13] , who distinguished between velocity dependent fluid friction and velocity-independent particle-wall friction of the Coulomb type and defined coarse particle conveyance as flow with a sliding bed and particle saltation.

The particles in the turbulent flow are supported by turbulent diffusion, and near the pipe wall a lift force, associated with slip velocity and concentration profile, contribute to particle lift-off, too. For coarse particles the weight cannot be balanced by buoyancy and fluid forces, they are supported mainly by inter-granular contacts to the pipe wall. For the particles with size larger than the thickness of viscous sub-layer, two forces support to particle movement. Saffman force, induced due to the shear of the fluid, supports particle movement and together with Magnus force (due to the particle rotation) could reach a significant fraction of the total weight of particles [36]. Campbell et al. [1] found, that this force, which generates from Bernoulli interaction, could be a significant fraction of the total weight of particles (about 40%).

Wilson [33] proposed a two-layer model for settling slurries with fully stratified flow pattern, where all particles were supposed to be concentrated in the lower portion of the pipe, where concentration approaches the loose-packed value. The Coulombic contribution to particle-wall friction was dominant. In the upper layer, only the carrier liquid was presented. Based on experimental data from the large test pipelines of the Saskatchewan Research Council the two-layer model was extended for finer particles [3]. The so called SRC two-layer model was based upon force balance for the upper and lower horizontal layers. When all the above-mentioned quantities, including the Reynolds number, friction factor and Coulomb type friction were defined for each layer as well as the interfacial friction factor, the flow parameters could be determined [10, 33, 35]. Because the layers differ in the solid concentration and velocity, there was a difference in the mean velocities of the particles and the liquid. Slip between the particles and the liquid resulted in a continuous transfer of energy from the fluid to the particle and from the particle to the pipe wall.

A lot of theoretical or experimental studies have been carried out on transport of sand or fine particles in horizontal pipes [2, 10, 13, 16, 21, 26, 34]. However, a relatively little research has been done on hydraulic conveying of gravel or bigger particles, especially in vertical and inclined pipes. A progress in the theoretical description of heterogeneous slurry flow was limited due to the lack of experimental data of the flow behavior and an inner structure of slurry flow [4, 20].

The study of the inner structure of such flow is very difficult, since many well-known techniques suitable to determine the inner structure of fluid flow (e.g. LDV, PIV, UVP) can be used in solid-liquid mixtures with strong limitations. Description of the slurry flow behavior and the inner structure are much more complex than measurements of overall flow parameters, e. g. the flow rate, pressure drop, mean concentration.

EXPERIMENTAL EQUIPMENT

The experimental investigation was carried out on the pipe loop of inner diameter D = 100 mm, which consisted of smooth stainless-steel pipes and transparent viewing pipe sections (7) for visual observation, situated just behind the measuring sections in the horizontal (A) and inclinable (B) sections, see Fig. 1. Slurry was prepared in a mixing tank (1) and pumped into the test loop by a centrifugal slurry pump GIW LCC-M 80-300 (2) with variable speed drive Siemens 1LG4283-2AB60-Z A11 (3).

The pressure drops were measured by the differential pressure transducers Rosemount 1151DP (8) over 2-meter long measuring sections located in the horizontal and the ascending- and descending measuring sections, which are fully inclinablefrom horizontal to vertical. The mixture flow was recorded using a high-speed digital camera NanoSence MK III+ with a frequency up to 2 000 frames per second, image resolution 1280 × 1024.

Fig. 1. Experimental test loop D = 100 mm, IH AS CR, Prague

Slurry velocity was measured by a Krohne OPTIFLUX 5000 magnetic flow meter (9) mounted in the short vertical section (C). The flow divider (11) allowed collection of slurry samples in the calibrated sampling tank (5) and measuring of the delivered concentration and flow rate. The U-tube (B) in vertical position enabled evaluating the delivered concentration of solid phase. The densities of studied mixtures, ρ_s, were 1 076, 1 142, and 1 199 kg·m^-3, respectively.

The loop was equipped with two gamma-ray density meters (10) placed on a special support controlled by the computer [31]. The support served for vertical linear positioning of both the source and the detector to measure vertical concentration profiles. To determine local concentration distribution through the pipe cross-section the parallel projections of gamma-ray beam were provided at several angles around the pipe axis (i.e. step of 15° from zero to 175°), and collected data were processed by computer tomography method. The radiometric density meters consisted of a gamma-ray source (Caesium¹³⁷Cs, activity 740 MBq) and of a detector (a scintillating crystal of NaI(Tl)). A multi-channel digital analyzer enabled an evaluation of the energy spectrum of the detected signal. The radiometric device was mounted upstream of the measuring and viewing sections in the inclinable section (B). 

Measurement of the local concentration map was rather time consuming, however it made possible to evaluate effect of the mixture velocity and mean concentration on solids distribution in pipe cross-section [6].

Fig. 2. Thegraded basalt pebbles after degradation (d50 = 11.5 mm).

The studied mixtures consisted of graded basalt pebbles of narrow particle size distribution (particle diameter, d, ranged from 8 to 16 mm, the mean diameter d₅₀ ≈ 11.5 mm, particle density ρ_p = 2 895 kg·m^-3) and water. The originally angular basalt gravel quickly degraded and formed a round shape during measurements, see Fig. 2. After short time of pumping at velocities above 3.5 m/s, the particle shape and size became practically stabilized, see particle size distribution, Fig. 3. The mean particle diameter changed from the original value d₅₀ = 11.7 mm to d₅₀ = 11.5 mm. The mass proportion of particles smaller than 5 mm did not exceed 10% even after several hours of pumping.

Fig. 3. Particle size distribution ofgraded basalt pebbles (A1, A2 – original sample, B1 – degraded after 1.5 hours, cv = 5%, B2 – degraded after 4 hours,cv= 5%, C1 – after 3 hours,cv= 9%, C2 – degraded after 3 hours,cv= 14%).

PRESSURE DROPS

Effect of mixture concentration and velocity on frictional pressure drops I_s in horizontal and vertical pipe sections was illustrated in Fig. 4. Practically parallel course of mixture pressure drop-velocity dependence I_s /V_s with that of water alone confirmed an assumption that for fully stratified mixtures the main proportion of frictional pressure drops was due to the Coulomb friction between the particles and the pipe wall. The frictional pressure drops in the horizontal pipe section were significantly higher than that in the vertical pipe due to the fact, that for stratified flow the contact load produced significant energy losses [32].

Fig. 4.   Effect of delivered volumetric concentration, cd, and mean velocity, Vs, on pressure drop, Is, in the horizontal and vertical pipe sections. Basalt pebble-water mixture, D=100 mm.

The experimental result did not confirm assumptions of some authors (e. g. Newitt et al. [12] ) about the almost negligible effect of the large particles on the frictional pressure drops in vertical pipe – when the particles moved mostly in core of the pipe, mixture behaves like carrier liquid alone and frictional pressure drops was produced mainly by pipe wall-liquid friction. Share of inner friction and drag between particles and liquid becomes less important. The present results show, that the frictional pressure drops of coarse-grained mixtures in vertical pipe increases with the increasing concentration, similarly to results of e.g. Sumardi and Chung [19]. In advance, the frictional pressure drops in vertical pipe increased with increasing mixture velocity, what confirmed effect of inner friction, inter-particles collision, and the drag due to particle-liquid slip.

The pressure drop in inclined pipe can be described by well-known Worster and Denny [37] formula, and can be divided into two parts - not recoverable frictional pressure drop, and the hydrostatic pressure difference, in principle change of potential energy. Fig. 5 illustrates effect of the pipe inclination on pressure drops in the ascending and descending pipe sections for the mean mixture delivered concentration c_d = 10.5% and three mean mixture velocities V_s = 2.2, 2.9, and 3.5 m·s^-1, and for three different values of volumetric delivered mixture concentration (c_d = 4, 8, and 12%) and mixture velocity V_s = 2.84 m·s^-1 [27, 29].

It was found that for heterogeneous and fully stratified coarse-grained mixture the frictional pressure drops were not significantly influenced by the pipe inclination, especially for low concentration values. The effect of pipe inclination decreased with increasing mixture velocity in ascending pipe section; the maximum value was reached for inclination from 20° to 40°, and then gradually decreased. Angle of inclination, where pressure drop maximum was reached increased with decreasing mixture velocity. In descending pipe section, the frictional pressure drops gradually decreased with increasing pipe section inclination. The main increase in real pressure drop was, similarly as for vertical pipe flow, due to the hydrostatic pressure difference. The effect of inclination on frictional pressure drops could be practically neglected, especially for low mixture concentration and higher flow velocities. Similar results were found by Kao and Hwang [4] for coal (d₅₀ = 1.40 mm) or glass beads (d₅₀ = 0.66 mm) in pipe of D = 50 mm and mixture velocity rangedfrom 1.3 to 2.6 m·s^-1.

Fig. 5. Effect of mixture velocity, Vs, and pipe inclination, α, on frictional pressure drop, Is. Basalt pebble-water mixture, D = 100 mm.

LOCAL CONCENTRATION DISTRIBUTION

Local concentration distribution in the pipe cross-section is important parameter for understanding of the heterogeneous mixture flow, it has a great effect on both the mixture flow behaviour and pressure drops. Various methods have been used for measurement of the local concentration, e.g. isokinetic sampling, electrical resistance and capacity or radiometric methods [7, 8, 11, 14, 15, 17, 18].

The concentration distribution was measured using a γ-ray densitometer and the effect of different flow parameters on the chord-averaged concentration profiles were analyzed. The effect of the pipe inclination a , mean mixture velocity V_s, and up and down flow on local concentration distribution in vertical chord-averaged profiles for different mixture velocities (V_s =2.05, 2.85, and 3.85 m·s^-1) and inclination angle α ranging from 0° to 90° was clearly illustrated in Fig. 6 and 7. The measured chord-averaged concentration profiles for different transport concentration c_d confirmed the stratified flow pattern of the coarse particle-water mixture in inclined pipe sections.

The concentration profiles can be divided on three parts similarly as in horizontal pipe sections [23, 27, 28]. Near the pipe invert, local concentration cv reached maximum, and for the higher mixture velocity a thin layer with nearly constant local concentration was formed, however, in inclined pipes never reached the loose-packed value. In the upper portion of the pipe, the local concentration tended to approach zero. The zero-concentration region increased for the descending flow with decreasing mixture velocity V_s and mean transport concentration c_d. A nearly linear concentration distribution was determined in the central portion of the pipe. Slope of this dependence slightly decreased with increasing mixture velocity.

Fig. 6. Chord-averaged profiles of local concentration, cv, effect of the inclination angle α and the mean mixture velocity Vs (transport concentration cd = 6%).

The effect of pipe inclination for low values of inclination angle α (see Fig. 7 - up to about 20°) was not significant, similarly as it was observed for pressure drops [23, 24, 31]. Local concentration cv at the pipe invert slightly decreased with increasing pipe inclination. For inclination angle α higher than 45°, a decrease in concentration close to the pipe invert was observed. For the vertical pipe a nearly constant concentration distribution was observed. Bed layer with thickness of about 20% of the pipe diameter were formed for moderate and higher mixture velocities. Local concentration in the bed layer decreased with increasing velocity and with increasing inclination angle α.

Fig. 7.  Effect of the inclination angle α on local concentration cv (mixture velocity Vs = 2,85 m/s, transport concentration cd = 9%)

No maximum of local concentration was observed for descending flow direction and inclination angle α = 15°, concentration profiles were nearly linear in the lower portion of the pipe. The local concentration in ascending pipe section was always higher than that in descending pipe section. It was valid also for vertical up-ward and down-ward flow, where difference between the concentration values corresponded to particle slip velocity. 

Fig. 8.  Effect of the transport concentration cd and flow direction on chord-averaged profiles of local concentration, cv

The effect of the transport concentration c_d for inclination angle α = 30° and the mixture velocity V_s = 2.85 m·s^-1 was illustrated in Fig. 8. Practically no maximum of local concentration was observed for descending flow. In the lower portion of the pipe concentration profiles were nearly linear. The zero-concentration part of the concentration profile was significantly more extended than that for the ascending flow direction due to the braking effect of gravity force on ascending flow and accelerating effect of gravity force on descending flow [23, 30]. The effect of gravity decreased and increased, respectively, the particle-liquid slip velocity.

The effect of mean mixture velocity V_s was illustrated in Fig. 9 for low values of the pipe inclination (α =15° and 30°). For moderate and higher mixture velocities bed layers with thickness of about 20% of the pipe diameter were formed. The local concentration in the bed layer decreased with increasing mixture velocity, probably due to increasing intensity of particles saltation, and more particles reached higher portion of the pipe. This effect increased with increasing inclination angle.

Fig. 9.  Effect of the mean mixture velocity Vs on local concentration cv (transport concentration cd = 6%).

During flow in horizontal and inclined pipes the coarse particles tended to occupy the bottom part of the pipe where sliding bed layer was originated. However, when mixture velocities extended enough the depositions limit, even the particles moved commonly in area up to the pipe center. Observed chord-averaged concentration profiles were in good agreement with these measured by Pugh and Wilson [15], Kaushal and Tomita [5], Matousek [9] or Sobota et al. [17,18] for heterogeneous mixtures of different solid materials with smaller particle diameters.  

LOCAL CONCENTRATION MAPS

From measured map of local concentration in horizontal pipe sections, see Fig. 10, it was evident that conveyed particles tended to move along the bottom part of the pipe. Concentration near the pipe lateral walls was slightly less than in central portion of the pipe cross-section. Some errors were detected near the pipe top due to the strong effect of pipe material on γ-ray absorption. There was no reason for increasing concentration near top of the pipe, especially for lower flow velocities. With increasing mixture velocity and concentration, even the measured coarse particles moved commonly in area above the pipe invert, up to the central portion of the pipe cross-section. 

cd = 12.0%, Vs = 2.8 m·s-1 cd = 12.1%, Vs = 3.8 m·s-1

Fig. 10. Local volumetric concentration cv distribution in horizontal pipe.

Observed concentration maps were in good agreement with these measured for mixtures of different solid materials with smaller particles [14,18].

Local concentration maps in the ascending and descending vertical pipe sections illustrated the effect of particle fall velocity on mixture concentration, see Fig. 11. The in-situ concentration reached higher values in the ascending section than in the descending section, since the fall velocity decreased the absolute particle velocity, and thus increased the particle slip velocity and in-situ concentration in the ascending pipe section.  For the descending pipe sections the opposite was valid and the in-situ concentration was less than transport concentration.

Similarly, to inclined pipe sections the concentration distribution was observed different in the ascending and descending pipe section. In the ascending pipe section, the maximum concentration was located in an annulus from about r = 0.70 D to r = 0.85 D, with increasing flow velocity the difference of local concentration in the central portion and region with a maximum concentration decreased. For the descending pipe section, the local concentration reached its maximum in the central portion of the pipe and in the direction to the pipe wall the local concentration smoothly decreased.

The concentration maps, see Fig. 12, confirmed that coarse particles tended to occupy the bottom part of the pipe in inclined pipe sections, too. However, with increasing mixture velocity and concentration, even the coarse particles lifted off the pipe bottom and moved up to the central area of the pipe, similarly as in the horizontal pipe [31].  Some differences were found for ascending and descending flow direction due to the effect of gravity force on particle movement. In descending pipe sections, the observed local concentration near lateral walls of the pipe was slightly less than that in the ascending pipe sections, where especially for higher mean concentration significantly higher local concentration values were reached close to the pipe invert, probably due to the higher slip velocity and breaking effect of the gravity force acting on the particles.

mean transport concentration cd =  6%,  mixture velocity Vs = 3.85 m·s-1                             mean transport concentration cd =  9%,  mixture velocity Vs = 2.85 m·s-1   ascending flow descending flow

Fig. 11. Local volumetric concentration cv distribution in vertical pipe.

 

mean transport concentration cd =  3%,  mixture velocity Vs = 2.85 m·s-1   mean transport concentration cd =  6%,  mixture velocity Vs = 2.85 m·s-1   mean transport concentration cd =  9%,  mixture velocity Vs = 2.85 m·s-1   mean transport concentration cd =  9%,  mixture velocity Vs = 2.05 m·s-1   ascending flow descending flow

Fig. 12. Local volumetric concentration cv distribution in inclined pipe (inclination angle α = 30°)

CONCLUSIONS

The effect of mixture velocity and mean concentration on a narrow particle size distribution basalt pebbles (mean diameter d₅₀ = 11.5 mm) – water mixtures flow behaviour in the turbulent regime was studied in horizontal, inclined, and vertical smooth pipe sections of inner diameter D = 100 mm.

The visualization and local concentration measurements revealed the stratified flow pattern of the coarse particle-water mixture in horizontal and inclined pipe sections, the particles moved principally in an area close to the pipe invert. For velocities close to deposition limit dune formations or sliding bed were formed. For moderate and higher mixture velocities, particle saltation became the dominant mode of sediment transport.

Frictional pressure drops in vertical pipe were found to be less than in horizontal pipe, due to the fact, that the contact load produced significant energy losses in horizontal pipe. Assumption about the almost negligible effect of coarse particles on the frictional pressure drops in vertical pipe was not confirmed. The main increase in real pressure drops was, for vertical and inclined pipe flow, due to the hydrostatic pressure difference.

For fully stratified coarse-grained mixture the frictional pressure drops in inclined pipes were not significantly influenced by the pipe inclination, especially for low concentration values. The frictional pressure droops in ascending pipe section increased with increasing inclination angle up to about 30 degrees, and then gradually decreased.

The effect of pipe inclination decreased with increasing mixture velocity in ascending pipe section. In descending pipe section, the frictional pressure drops gradually decreased with increasing pipe section inclination

In the inclined pipe sections, similarly to horizontal one, the chord averaged concentration profiles can be divided in three parts: a zero-concentration region in the upper portion of the pipe, a region with nearly linear concentration distribution in the central portion of the pipe, and a region with a maximum concentration near the pipe invert.

For the inclination angle α lower than about 30°, the effect of pipe inclination on local concentration distribution was not significant. The zero-concentration region increased for descending flow with decreasing mixture velocity and mean transport concentration. The zero-concentration region for descending flow was bigger than that for the ascending flow, and it was bigger than that for the ascending flow direction. Local concentration at the pipe bottom slightly decreased with increasing velocity; this effect increased with increasing inclination angle.  

The in-situ concentration reached higher values in the ascending section than in the descending section. In the vertical ascending pipe section, the maximum concentration was located in an annulus from about r = (0.70 – 0.85) D, contrary to the descending pipe section, where the local concentration reached its maximum in the central portion of the pipe.

Acknowledgements

Supports under the project P105/10/1574 and 17-14271S of the Grant Agency of the Czech Republic, and RVO: 67985874 of the Czech Academy of Sciences are gratefully acknowledged.

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Received: 5.06.2020
Reviewed: 19.06.2020
Accepted: 23.06.2020

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Pavel Vlasak
Institute of Hydrodynamics CAS, Praha, Czech Republic
Pod Patankou 30/5
166 12 Praha 6
Czech Republic
email: vlasak@ih.cas.cz

Zdenek Chara
Institute of Hydrodynamics CAS, Praha, Czech Republic
Pod Patankou 30/5
166 12 Praha 6
Czech Republic
email: chara@ih.cas.cz

Jiri Konfrst
Institute of Hydrodynamics CAS, Praha, Czech Republic
Pod Patankou 30/5
166 12 Praha 6
Czech Republic
email: konfrst@ih.cas.cz

Jan Krupicka
Institute of Hydrodynamics CAS, Praha, Czech Republic
Pod Patankou 30/5
166 12 Praha 6
Czech Republic
email: krupicka@ih.cas.cz

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