Test pipe

The S-HDPE test pipe was 8.5 m in length and was manufactured from a high density copolymer resin (referred to as Carbon Black). As illustrated in Figure 3.5 the test pipeline

composed of a Run-in Section and Test Section. The Run-in was 3.35 m (or 34 D) long and corresponded to the region 0.00 m < x < 3.35 m. The Test Section, which was were all the frictional measurements were recorded was 5.0 m in length and was located between 3.35 m

< x < 8.35 m. Pressure tappings, in ring formation were located at five different streamwise locations (designated P1 to P5) along the Test Section. A traversable Pitot probe was also located at the downstream end of Test Section i.e. at P5 (see Figure 3.5).

Figure 3.5 Schematic of the 8.5m test pipe of the pilot-scale pipeline, highlighting pressure tapping and Pitot probe location(s) (the flow direction is from left to right).

The test pipe had a measured outer diameter of 110.30 ± 0.28 mm and a wall thickness of 4.19 ± 0.28 mm. The inner diameter of the pipe was measured at 6 different locations along the length of the pipeline. In total 8 axial measurements were recorded at each of the 6 locations. The inner diameter at each location was at worst within ±0.68 mm of the average diameter at a given location, with the average being within ±0.44 mm. This tolerance was independent of angular and longitudinal location although, the measurements were limited to the pipe connection regions. The internal diameter of the S-HDPE pipe within the Test Section measured at 102.08 ± 0.44 mm.

The 8.5 m test pipeline consisted of four individual pipe segments, as shown in Figure 3.5.

The four discrete segment lengths measured 0.5, 3.0, 3.0 and 2.0 m respectively. The discrete pipe segments were carefully aligned and connected by flexible pipe coupling in such a manner to ensure a smooth transition between the segments. Nevertheless, it was inevitable that the joints would cause some disruption to the velocity fields in the system. Consequently, pressure tappings were positioned either side of the joints, at 0.15 m from the leading edge.

This allowed the frictional impact of the joints to be established. The pressure tappings located at the downstream end of each segment (i.e. P1, P3, and P5) were at worst 1.85 m (19 D) downstream from the nearest joint, with most being 3.35 m (34 D) downstream from a

x (m) y (m)

0.00 0.50 3.35 3.65 6.35 6.65 8.35

3.50 6.50 8.50

P1

Run-in Section, 3.35 m Test Section, 5.00 m

P2 P3 P4 P5*

Pipe Couple

S-HDPE pipe (D = 0.1 m) Flow Direction

Guide

*Pitot probe located at P5

joint. The Pitot probe was 1.85 m downstream from the nearest joint. These lengths were deemed sufficient to ensure that any disruptions caused by the respective joints had a negligible impact on the respective pressure measurements.

The flexible nature of the S-HDPE pipe meant it was unlikely that the pipe was perfectly round along its longitudinal length. Consequently, the velocity fields within the system may have been influenced by potential variations in diameter and roundness along its longitudinal length, which could have implications of on the established frictional data recorded. Due to the nature of the pipe material it was not possible to correct this anomaly, and thus any potential errors arising from it were accepted. However, it should be stated that these errors would likely have been negligible. Furthermore, the frictional data determined is likely to be more representative of the material in its natural state if these anomaly remained uncorrected.

The straightness of the pipeline was confirmed to be within acceptable limits by a basic visual interception.

The test pipe was laid at a slight positive gradient (0.18%) in the upstream to downstream direction to allow for drainage back into the storage tank. As the system was pressurised this gradient had no effect on the experimental measurements and observations documented within the current study.

3.2.3.1 Surface finish

The test pipe had an extremely smooth surface finish. The equivalent Nikuradse-styled roughness scale typically associated with a S-HDPE pipe is between 0.003-0.015 mm (based on a survey of pipe manufacturers, results not shown). However, more often than not, the ks

value of solid wall HDPE pipes is taken as 0.012 mm (Grann-Meyer 2010). A Manning’s roughness coefficient of n = 0.009 and Chezy roughness coefficient of c = 150 are also commonly used to define the effective roughness of a a S-HDPE pipe.

A surface is considered to be hydraulically smooth if ks+ is less than five viscous lengths.

Based on a ks of 0.012 mm the maximum value of ks+

, which coincides with the maximum ReD investigated (i.e. 1.30x10⁵) would be ks+

= 0.71. Therefore, theoretically the pipe can be considered to be hydraulically smooth for the full range of ReD assessed. For ReD = 3.0x10⁴ and ReD = 1.30x10⁵ the maximum allowable value of ks to satisfy the smooth flow criteria would be ks = 0.314 mm and ks = 0.084 mm, respectively.

Figure 3.6 illustrates a typical three-dimensional micro-topography of the surface of the S-HDPE test pipe. This image was captured using a Veeco FEI (Philips) XL30 ESEM in the Gaseous Secondary Electron (GSE) detection mode, at x200 magnification. The image

analysis software, commercially known as MountainsMap (developed by Digital Surf, version 7), was used to process and profile the raw ESEM image.

Figure 3.6 3-D surface topography map of the S-HDPE test pipe (Sample Size: 0.5 x 0.5 mm², Magnification: x200).

The surface roughness of a material can be defined by a number of different statistical parameters, including: mean roughness height, kav; maximum peak-to-trough height, kt (=

rmasx – rmin where r is the distance from the mean roughness height); root-mean-square roughness height, krms (=√1/ ∑^𝑁_𝑖=1𝑟²; where N is the sample number); skewness of the roughness distribution, skl (= (1/𝑁 ∑^𝑁_𝑖=1𝑟_𝑖³[(1/𝑁) ∑^𝑁_𝑖=1𝑟_𝑖²]^3/2) and kurtosis of the roughness distribution, ku (= (1/𝑁 ∑^𝑁_𝑖=1𝑟_𝑖⁴[(1/𝑁) ∑^𝑁_𝑖=1𝑟_𝑖²]²). The aforementioned parameters have been related to equivalent roughness scales, namely ks, with varying degrees of success (Hama 1954; Zagarola and Smits 1998; Shockling et al. 2006; Barton 2006; Barton et al. 2010; Andrewartha 2010; Flack and Schultz 2010). It has been documented, that an engineered surface can be related to ks using krms and skl (Flack and Schultz 2010) or using krms

on its own (Hama 1954; Zagarola and Smits 1998). However, the relationship reported by Flack and Schultz (2010) which combined both krms and skl (namely, 𝑘_𝑠≈ 4.43𝑘_𝑟𝑚𝑠 (1 + 𝑠_𝑘)^1.37) is only applicable for surfaces with relatively high ks values (ks > 500 μm). For an engineered material with a small ks value (i.e. ks < 10 μm) the following relationships are typically applied (Hama 1954; Zagarola and Smits 1998):

𝑘_𝑠 ≈ 5𝑘_𝑟𝑚𝑠 ; Equation 3.1

or 𝑘_𝑠≈ 3𝑘_𝑟𝑚𝑠 Equation 3.2

x z

y

krms = 2.35 μm kav = 1.56 μm

0.5 mm 0.5 mm

However, which relationship is used is dependent on the surface finish of the material in question. For instance, Hama (1954) suggested Equation 3.1 should be used for machine finished surfaces with an approximate Gaussian roughness distribution. Whereas, Equation 2.15 was suggested by Zagarola and Smits (1998) for materials, such as aluminium or steel which have been honed and polished. Based on Equation 3.1 and Equation 2.15 and the ks

value of 0.012 mm, the krms of the test pipe was estimated to be between 2.4-4μm.

The actual physical roughness of the test pipe was determined using ESEM imaging and the MountainsMap software. The software estimated the surface topography using a “single four image scan” approach as per the manufacturer’s specification. ESEM images captured at 8 different axial locations along the test pipe were assessed, as shown in Appendix A.2 in Figure A.2. The sample area was 0.5x0.5 mm². The results of the physical roughness evaluation are presented in Table 3.1, which presents the average values determined from the 8 images. Prior to imaging the material samples were sterilised in an 80% ethanol solution for 12 h; for the purpose of eliminating any errors casued by foreign bodies on the surface, which would distort the measured surface roughness. For improved image resolution the samples were coated with gold before imaging.

Table 3.1 Physical and Equivalent surface roughness parameters of the S-HDPE pipe.

Material kav (μm) kt (μm) krms (μm) skl

ks (μm) (Predicted)¹

ks (μm) (Actual)² S-HDPE Pipe 1.82±0.34 28.41±3.99 2.73±0.60 2.33±0.54 12.00 8.86±5.00

2 As outlined by Grann-Meyer (2010), ¹ See Chapter 4 for full details on actual ks

The analysis indicated that the kav and krms of the S-HDPE pipe was 1.82 ± 0.60 μm and 2.73

± 0.60 μm, respectively.

A hydrodynamic evaluation of the test pipe over the range of 3.15x10⁴ < ReD < 1.23x10⁵ indicated that it had a ks = 8.86 ± 5.00 (for full details see Chapter 4). Therefore, the relationship between krms and ks for the S-HDPE pipe was found to be ks = 3.25 krms, which is approximately equal to the relationship proposed by Zagarola and Smits (1998) (i.e. Equation 3.2).

The effective roughness of the 100 mm diameter, S-HDPE test pipe was found to be hydraulically equivalent to a 400 mm diameter, Structural Wall High polyethylene (Str-HDPE) pipe, as shown by Moody Diagram presented in Figure 3.7. This is despite the

inherent differences in physical roughness of the two materials. Full details of this comparative analysis are presented in in Appendix A.3.

Figure 3.7 Moody Diagram illsurating the determined friction factors for the 100 and 400 mm internal diameter HDPE pipes.

3.2.3.2 Flow development length

In order to accurately determine the test pipe’s frictional resistance, it was important to establish whether the flow in the Test Section was fully developed. A flow is considered to be fully developed to the highest criteria when all mean flow quantities (namely, velocity and pressure gradient) and all turbulence quantities are constant, independent of streamwise location. Boundary layer growth, as a result of viscous friction between the fluid and wall will commence at the entrance of the system (i.e. the pipe inlet), as shown by Figure 3.8. The development will continue in a streamwise direction until a critical threshold or thickness is reached. Typically, under idealised conditions within a pipe this coincides with the pipe’s centreline, as shown in Figure 3.8. After this point the boundary layer is considered to be fully developed. The overall development length or entrance length, Le for a zero-pressure gradient system is given as (Zagarola and Smits 1998);

𝐿_𝑒 ≈ 𝐿₀+ 𝐿₁+ 𝐿₂ Equation 3.3

where L0 is the initial boundary layer development length, L1 is the turbulent boundary layer development length and L2 is the turbulent quantities development length.

0.012 0.015 0.018 0.021 0.024 0.027 0.030

2.00E+04 2.00E+05 2.00E+06

λ

Re_D S-HDPE Pipe (D =100 mm) Str-HDPE Pipe (D = 400 mm) ks/D = 8.86E-05 (C-W eq.) Nikuradse (1933)

S-HDPE Pipe (D = 100 mm) k_s/D = 8.86x10⁵

Str-HDPE Pipe (D = 400 mm) k_s/D = 8.17x10⁵

Figure 3.8 Flow development within a typical pipe, highlighting development lengths and the fully developed flow region.

The initial boundary layer development length is dependent on the streamwise length Reynolds number, Rel. For systems with low levels of freestream turbulence a reasonable estimate of Rel is 2x10⁵. On this basis L0 is given by:

𝐿₀ 𝐷 ≈ 𝑅𝑒_𝑙

𝑅𝑒_𝐷 ≈2 × 10⁵

𝑅𝑒_𝐷 Equation 3.4

The maximum value of L0 coincides with the lowest ReD investigated and as a result, in high turbulent investigations (i.e. in the order of 10⁶) it is typically ignored. However, based on the ReD range investigated within the current study (i.e. 3.0x10⁴ < ReD < 1.30x10⁵), L0 was included in summation of the overall development length.

If the mild favourable pressure gradient and the transverse curvature of the pipe wall are neglected, then L1 is inversely proportional to the skin-friction coefficient and is given by;

𝐿₁ 𝐷 ≈𝐶₁

𝜆 Equation 3.5

where C1 is an empirical constant, taken as 0.5 for ReD in the order of 10⁵ (Dean and Bradshaw 1976.

δ=f(x) Boundary Layer

u=f(x,y) Flow

U

Developing flow, Entrance Length, Le = L0+L1+L2 Fully Developed Flow

Pressure

Linear Pressure Drop

x Entrance Pressure Drop

0.0 L0 + L1

Inviscid Core

L0 + L1 L₂

L_e Direction

A more general estimate of L1 for turbulent flow is given as a function of ReD: 𝐿₁

𝐷 ≈ 4.44(𝑅𝑒_𝐷)^1/6 Equation 3.6

The development length required to satisfy fully developed turbulence quantities is given by;

𝐿₂ 𝐷 ≈ 𝐶₂

𝜆^1/2 Equation 3.7

where C2 is empirical constant, estimated as 5.0 (Dean and Bradshaw 1976).

Previous investigations in pipes and channels have shown that for ReD in the order of 10⁵, the required overall entrance length is typically within the range of 60 D < Le < 100 D (Perry and Abell 1975). Notwithstanding, in most practical engineering cases entrance affects are typically deemed negligible after a length of 10 D (Chadwick et al. 2004). The maximum value of Le for the system, which coincides with the maximum ReD investigated (i.e. ReD = 1.30x10⁵) was found to be 6.82 m (or 69 D), as shown by Figure 3.9a. This length represents the total length required to attain fully developed flow in terms of both mean flow and turbulence quantities. For the purpose of the current study only the mean flow needs to be fully developed (i.e. L0 + L1). The maximum development length required to attain fully developed flow in terms of mean flow structure was 3.03 m (or 31 D), as shown by Figure 3.9b. Consequently, the 3.35 m Run-in Section provided sufficient length to ensure fully developed mean flow within the Test Section. Furthermore, it can be stated that the flow was fully developed to the highest criteria prior to P5, which was where local velocity data was recorded.

The boundary layer development relationship proposed by Schlichting (1979), as given by Equation 3.8 was also used to illustrate that Run-Section was sufficient in attaining fully developed flow. Figure 3.10 illustrate the results of application of Equation 3.8. In Figure 3.10a the fully developed boundary layer thickness was taken as the pipe radius (i.e. 0.05 m), whereas in Figure 3.10b, the experimentally determined values of δ were used (as given in Section 4.4 in Table 4.2).

𝛿 = 0.37𝑥 (𝑅𝑒_𝑥)^−1/5 Equation 3.8

Figure 3.9 The flow development lengths of a) Le and b) L0+L1 (only) for the pilot-scale pipeline.

Figure 3.10 Boundary layer development within the pilot-scale pipeline using a) δ = R and b) actual values of δ. Highlighting the Run-in (R) and Test (T) Sections.