Ocean Engineering 125 (2016) 26–30

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Ocean Engineering
journal homepage: www.elsevier.com/locate/oceaneng

Short communication

Effect of wave boundary layer on hydrodynamic forces on small

diameter pipelines
Liang Cheng a,c,n, Hongwei An a, Scott Draper a,b, Dave White a,b
a
School of Civil, Environmental and Mining Engineering, The University of Western Australia, 35 Stirling Highway, WA, 6009 Australia
b
Centre for Offshore Foundation Systems, The University of Western Australia, 35 Stirling Highway, WA, 6009 Australia
c
State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian, China

art ic l e i nf o a b s t r a c t

Article history: Effect of wave boundary layer on hydrodynamic forces on small diameter pipelines is speculated in this
Received 22 May 2014 paper. It is found that use of the recommended calculation methods in DNV-RP-F109 leads to unrealistic
Received in revised form predictions of high specific gravity (SG) requirements for small diameter pipelines subject to wave
16 February 2016
loading. Potential reasons for such high SG requirements under wave loading are speculated based on
Accepted 11 July 2016
existing knowledge and experimental evidence, and a way forward is proposed. It is suspected that the
unrealistic predictions are because the calculation methods ignore wave boundary layer effects on hy-
Keywords: drodynamic forces.
Wave forces & 2016 Elsevier Ltd. All rights reserved.
Offshore pipeline
Stability
Wave boundary layer

1. Introduction Cheong et al. (1987) tested the effect of water depth on hydro-
dynamic force with a model diameter of 60 mm. Sorenson et al.
Small diameter submarine pipelines or cables are long cylind- (1986, DHI Report) carried out model tests to measure hydro-
rical structures laid on the seabed. The diameter of these struc- dynamic force on a model pipeline on a plane boundary. Two
tures is typically in the range of 50–200 mm. They are commonly model pipelines were used, with diameters of 200 mm and
used in offshore oil and gas developments to transport power, 400 mm. The effect of Reynolds number, Keulegan–Carpenter
control fluids or by-products of production. They are also used in number, pipe/seabed roughness and wave to current ratio was
the telecommunication and renewable energy industries – wave, examined. The test results of Sorenson et al. (1986) have been used
wind and tidal – to transmit data and power. For each of these widely in offshore engineering, including the industry re-
applications, ensuring that pipelines and cables remain stable on commended practice DNV-RP-F109 (DNV, 2010). Although design
the seabed is a significant design challenge. In Australian waters recommendations such as DNV-RP-F109 are well accepted for the
many locations experience frequent severe cyclonic storm events. on-bottom stability design of medium and large diameter oil and
Offshore renewable developments are inevitably in high energy gas pipelines, there is growing recognition among design en-
environments. Engineering the stability of submarine pipelines gineers and operators that the existing design recommendations
and cables can be so costly as to control the viability of certain appear overly conservative when applied to small diameter pipe-
projects. lines. The required on-bottom weight (or specific gravity SG, de-
The on-bottom stability design of subsea pipelines involves fined as ratio of dry weight to buoyancy) for small diameter pi-
calculating hydrodynamic forces and seabed friction on a pipeline. pelines based on current design recommendations appears un-
Sumer and Fresdøe (2001) presented a comprehensive summary realistically high, leading to very expensive stabilization measures
about the research work related to the hydrodynamics of a circular – such as concrete coating, trenching or rock dumping – and thus
cylinder under various configurations and flow conditions. high costs and large environmental footprints.
Sarpkaya and Rajabi (1980) measured the hydrodynamic force on The authors of the present work suspect that neglect of the
smooth and rough cylinders mounted on a smooth seabed. Two effect of the wave-induced boundary layer in the calculation of
cylinders with diameters of 127 mm and 165.1 mm were tested. hydrodynamic forces is the main reason for the over-conservative
design. In fluid mechanics, the boundary layer is referred to as the
n
Corresponding author. layer of fluid immediately next to a solid boundary where the
E-mail address: liang.cheng@uwa.edu.au (L. Cheng). effect of fluid viscosity is significant. It is characterized by a

http://dx.doi.org/10.1016/j.oceaneng.2016.07.016
0029-8018/& 2016 Elsevier Ltd. All rights reserved.
 L. Cheng et al. / Ocean Engineering 125 (2016) 26–30 27

velocity gradient in the direction normal to the boundary. In off- Oscillatory

Fz
shore engineering, the boundary layer profile is defined by the flow
seabed roughness and the bulk flow properties near to the seabed,
and has a significant effect on sediment transport and the hy-
drodynamic forces experienced by structures located in the Fy
boundary layer. Fredsoe and Deigaard (1992) provide a compre-
R seabed
hensive description of the boundary layer profile and seabed shear
stress under different seabed conditions.
W
It is well known that the velocity distribution in a boundary
layer induced by steady current follows a logarithmic profile with Fig. 1. Forces controlling the stability of a subsea pipeline resting on the seabed.
thickness of similar magnitude to the water depth. In oscillatory
flow, Hino et al. (1983); Sleath (1987) and Jensen et al. (1989) have
carried out experimental work to investigate the boundary layer pipeline. This forms the basis of the absolute stability design
on smooth and rough boundaries. Jensen et al. (1989) found that a analysis recommended by DNV-RP-F109, which is briefly illu-
logarithmic profile matches an oscillatory boundary layer on both strated below. Fig. 1 sketches a free-body diagram of a unit length
smooth and rough beds except at the early stage of the accelera- of submarine pipeline on a seabed. The hydrodynamic force
tion phase or the later stage of the deceleration phase. On a components in the horizontal and vertical directions are defined
smooth bed the logarithmic layer is established for a longer as Fy and Fz, respectively, the submerged weight of the pipe is Ws
duration within each wave cycle, but with a reduced thickness, as and the seabed resistance is defined as R. Since the major focus of
the Reynolds number increases. On a rough bed, the boundary this study is on the wave boundary layer effect, only lateral sta-
layer thickness increases with roughness, but is normally much bility of the pipeline is considered.
thinner than that induced by steady current because flow reversal The absolute stability of pipeline can be ensured if the fol-
prevents the development of a large boundary layer. The thickness lowing equation is satisfied:
of the boundary layer in oscillatory flow is normally in the range of γscFy + μFz
tens to hundreds millimeters on a natural seabed. ≤1
μWs (1)
Hydrodynamic force coefficients recommended in DNV-RP-
F109 assume implicitly that the boundary layer thickness in waves where γSC is a safety factor and μ is the friction coefficient between
is small compared with the pipe diameter. As a result, the effects the pipe surface and seabed. However DNV-RP-F109 recommends
of the wave boundary layer are ignored in the force calculation the following equation in the absolute stability design:
recommended by DNV-RP-F109 (in contrast the hydrodynamic
Fy + μFz
force reduction due to a steady current boundary layer has been γsc ≤1
accounted for; DNV-RP-F109 recommends the use of spatially μWs (2)
averaged velocity over the pipeline diameter to calculate the hy- It can be shown that the absolute stability can be achieved if Eq.
drodynamic force for steady current conditions only). It might be a (2) is satisfied. In the subsequent discussions, Eq. (2) is used to be
reasonable assumption to neglect the effect of wave boundary consistent with DNV-RP-F109.
layers on hydrodynamic forces for a large diameter pipeline The hydrodynamic force components can be estimated by the
(4 200 mm). However the boundary layer can have a significant following equations (DNV-RP-F109):
effect on the design of small diameter pipelines. The reduction of
hydrodynamic force can be significant for a pipeline submerged in Fy = 0. 5ρw DCy(Um + Uc )2 (3)
a wave boundary layer of similar thickness to its diameter.
If the force reduction due to the wave boundary layer is not
considered as in DNV-RP-F109, the required SG for absolute on- Fz = 0. 5ρw DCz (Um + Uc )2 (4)
bottom stability is inversely proportional to the pipeline diameter.
This means that the required SG increases dramatically as the where ρw is water density, D is pipe diameter, Cy and Cz are peak
diameter of pipeline reduces, especially for D o0.1 m. This in- force coefficients in the horizontal and vertical direction, respec-
crease is such that the required SG asymptotes to infinity as pi- tively, Um is wave velocity amplitude and Uc current velocity. The
peline diameter approaches zero. A bizarre situation is reached in force coefficients recommended in DNV-RP-F109 are based on the
which the designer finds that a pipeline ought to be covered in work by Sorenson et al. (1986). The submerged weight is a design
rock – that has a lower SG than the pipe itself – to ensure stability. parameter and can be calculated for a specific SG as:
This appears to be physically unrealistic and is an issue that puz- π D2
zles the pipeline and cable engineering communities. As men- Ws = ρw g (SG−1)
4 (5)
tioned earlier, it is suspected that the neglect of wave boundary
layer effects in estimating the hydrodynamic force is the main Substituting Eq. (3) to Eq. (5) into Eq. (2), the required SG for
reason for the extremely high SG estimated based on DNV-RP- absolute stability is obtained:
F109. In the present work, the wave boundary layer effect on the 2
2( Um + Uc ) (Cy + μCz )
hydrodynamic force on small diameter pipelines is estimated SG ≥ 1+γsc
μπgD (6)
based on a simple analysis and available data from the literature.
The force coefficients given in DNV-RP-F019 are dependent on
the wave to current ratio (Um/Uc ) and the Keulegan Carpenter (KC)
2. Absolute stability of a pipeline on the seabed number, defined as:
UmT
The absolute stability of a subsea pipeline laid on a seabed can KC =
be assured if (1) the horizontal seabed resistance to pipeline lat-
D
eral movement is always greater than the horizontal hydro- where T is the wave period. Under storm conditions the KC
dynamic force on the pipeline and (2) the submerged weight of number is normally very large for small diameter pipelines, often
the pipeline is always greater than the hydrodynamic lift on the exceeding a value of 140 (for instance, for a pipe with diameter
28 L. Cheng et al. / Ocean Engineering 125 (2016) 26–30

Table 1 Table 2
Required specific gravity for absolute stability based on DNV-RP-F109; flow con- Seabed conditions considered in the present work (roughness length estimated
ditions: Um ¼ 1 m/s and T = 1 4 s. according to Soulsby (1997)).

D (m) 0.1 0.075 0.05 0.025 Boundary type z0 (mm) kN (mm) δ (mm)
SG 4.13 5.18 7.27 13.53
Silt/sand 0.05 1.5 54
Sand (unrippled) 0.4 12.0 78
less than 0.10 m in flow conditions of Um ¼1 m/s and T ¼14 s, Gravel 3 90.0 113
Sand (rippled) 6 180.0 128
typical of modest 100-year return period storm in the North West
Shelf of Western Australia, the corresponding KC number exceeds
140). For KC numbers greater than 140 DNV-RP-F109 suggests that
the force coefficients are independent of KC number. Consequently, δ ⎛ a ⎞0.82
in the absence of steady currents (Uc ¼0.0 m/s), for example, the = 0. 086⎜ ⎟
kN ⎝ kN ⎠ (9)
force coefficients can be taken as the fixed values Cy ¼ 1.30 and
Cz ¼1.05 for small diameter pipelines. If we also assume a sandy where kN is the Nikuradse roughness height and is dependent on
seabed, the safety factor (γSC) can be taken as 1.5 for normal North seabed conditions. Under hydrodynamically rough flow condi-
West Shelf conditions and the seabed friction factor (μ) can be tions, the Nikuradse roughness height can be estimated using the
taken as 0.6 (DNV-RP-F109), neglecting any passive soil resistance following formula:
from pipe embedment. Eq. (6) can then be simplified to give:
kN = 30z 0 (10)
( Um)2
SG ≥ 1 + 0. 313
D
( using units of m/s and m for Um and D) (7)
where z0 is the seabed roughness length.
The wave boundary layer thickness is estimated for a range of
The form of Eq. (7) simply reflects the fact the hydrodynamic seabed conditions exposed to wave conditions of Um ¼ 1 m/s and
forces on a unit length of pipeline reduce linearly with the pipeline T¼ 14 s and the results are shown in Table 2. The roughness length
diameter, if boundary layer effects are ignored, whilst the weight z0 (¼ kN/30) values used in Table 2 were recommended by Soulsby
reduces with the pipeline diameter squared for a constant SG. (1997). It is seen that the wave boundary layer thickness increases
Table 1 shows the required SG values for absolute stability of pi- with the bed roughness height. For example, for a flat silt/sand
pelines of various diameters subject to a design storm with bed, the wave boundary layer thickness under the wave conditions
Um ¼1 m/s and T¼ 14 s. It can be seen that the required SG for of Um ¼ 1 m/s and T¼ 14 s is approximately 0.054 m. This is in-
absolute stability of small diameter pipelines based on DNV-RP- creased to about 0.128 m for a rippled sandy bed under the same
F109 is indeed very high. For example, the required SG for absolute wave loading. The boundary layer thicknesses for the range of
stability of a pipeline with D¼ 0.025 m is 13.53, which is higher seabed conditions are clearly comparable to the diameter of a
than the SG of a solid steel bar. In other words, it implies that even small diameter pipeline or cable (from 0.05 m to 0.20 m). If the
a solid 25 mm steel bar would not be stable under wave conditions boundary layer is not considered in estimating the hydrodynamic
that are equivalent to Um ¼1 m/s and T ¼14 s. This appears to be force on the pipeline, it could therefore lead to conservative de-
physically unrealistic. signs such as those shown in Table 1.
The effects of wave boundary layer on the hydrodynamic force
2.1. Effects of wave boundary layers on hydrodynamic forces on pipelines have been rarely investigated, to the best knowledge
of the authors. The force coefficients used in DNV-RP-F109 were
It is speculated that the neglect of the effect of the wave derived from the physical experiments reported by Sorenson et al.
boundary layer is partly attributed to the unrealistic prediction of (1986) where three different relative bed roughness heights (k/D)
the required SG for absolute stability of small diameter pipelines. It of 0.001 (fine), 0.01 (medium) and 0.05 (rough) were tested. It was
is well known from previous research that the hydrodynamic force found based on the test results that the increase of bed roughness
on a pipeline will decrease if the pipeline is fully or partially height led to reductions of drag and lift forces, but had insignif-
submerged in a boundary layer. This is because the flow velocity in icant effect on the inertia force. The reductions of the drag and lift
the boundary layer is smaller than the free stream velocity. Al- force from the fine bed to the rough bed were about 17% and 10%,
though it is not stated explicitly in DNV-RP-F109, the neglect of respectively, in the large KC value range (refer to Fig. 2). Although a
the effect of wave boundary layer on the hydrodynamic force reduction is consistent with what would be expected due to
could be justified on the basis that the wave boundary layer boundary layer effects, the relatively small force reductions re-
thickness is generally small. This treatment appears to be rea- ported by Sorenson et al. (1986) are because of the relatively large
sonable for large diameter pipelines where the ratio of the model pipe sizes (0.2 m and 0.4 m) used in the tests. The ratio of
boundary layer thickness to pipeline diameter is small, but may be the boundary layer thickness to the diameter of model pipes is
too conservative for small diameter pipelines where the ratio of relative small in those tests.
the boundary layer thickness to pipeline diameter is significant.
To confirm this, the wave boundary layer thickness on smooth 2.2. Implications for pipeline stability design
and rough beds can be estimated based on the methods in-
troduced by Fredsoe and Deigaard (1992). On a smooth boundary, Potential effect of wave boundary layer on the stability of the
the thickness of wave boundary layer (δ ) can be estimated as pipeline is examined by assuming that the spatial average velocity
over the pipeline diameter and the force coefficients re-
δ
= 0. 086Rea−0.11 commended by DNV-RP-F109 can be used to estimate the hydro-
a (8)
dynamic force on the pipeline, in a similar way to the method used
Where Rea =Uma/ν is a Reynolds number defined by water particle for steady currents in DNV-RP-F109. For small diameter pipelines,
excursion distance a, wave orbital velocity Um and the kinematic the KC values are normally very high under storm conditions.
viscosity of water ν. The water particle excursion distance a is Therefore the horizontal hydrodynamic force on the pipeline is
defined as a ¼ UmT /2π . On a rough bed, δ is related to surface dominated by drag force and it is reasonable to assume that the
roughness and can be estimated as: peak load corresponds to the peak velocity. At peak velocity during
 L. Cheng et al. / Ocean Engineering 125 (2016) 26–30 29

2 .5 5

Fine Fine
2 4
Medium Medium
Rough Rough

1 .5 3

CL
CD

1 2

0 .5 1

0 0
0 50 100 150 0 50 100 150

KC KC
Fig. 2. Drag and lift coefficients measured on a model pipe on seabeds with different roughness (reproduced based on data published in (Sorenson et al. 1986)).

a wave cycle, the velocity profile in a wave boundary layer is of z0 shown in Fig. 3 correspond to the seabed types shown in
logarithmic (Fredsøe and Deigaard, 1992; Jensen et al., 1989). The Table 2. The wave boundary layer thickness appears to have sig-
spatially averaged velocity over the pipeline diameter therefore nificant effects on the required SG for absolute stability, especially
takes the following form: when Do0.1 m. Even on a relatively smooth boundary with silt/
sand, the required SG values are significantly smaller than those
⎧ uf ⎛ D z ⎞
⎪ ⎜ ln −1+ 0 ⎟D ≤ δ predicted using DNV-RP-F109. The required SG value generally
⎪ κ ⎝ z0 D⎠ decreases as the seabed roughness increases, because the wave
U̅m = ⎨
⎪ uf ⎛ δ z0 ⎞ δ ⎛ δ⎞ boundary layer grows in thickness to influence more of the pipe-
⎪ κ ⎜⎝ ln z −1+ δ ⎟⎠ D + Um⎜ 1 − D ⎟D > δ line. It is interesting to see in Fig. 3 that the required SG values
⎩ 0 ⎝ ⎠ (11)
asymptote to constant values as D approaches to zero for two large
where uf is friction velocity and can be estimated based on an roughness heights, in contrast to the predictions based on DNV-
empirical formula such as those suggested by Soulsby (1997). In RP-F109 where SG value asymptotes to infinity. The predicted re-
this study, uf is estimated from the following equation quired SG values for small D values on a flat sand bed are still quite
high.
fw It should be noted that the results shown in Fig. 3 were ob-
uf = Um
2 (12) tained based on the assumption that the spatially averaged velo-
where fw is wave friction factor and is estimated based on a for- city over the pipeline diameter is the appropriate quantity to es-
mula suggested by Soulsby (1997): timate the hydrodynamic force on the pipeline, together with the
force coefficients recommended by DNV-RP-F109. This assumption
⎛ a ⎞−0.52 is yet to be validated against testing data and cannot be used in
fw = 0. 237⎜ ⎟
⎝ kN ⎠ (13) practice. It should be also noted that the equations used to esti-
mate boundary layer thickness and velocity distributions are em-
A series of calculations of the required SG for different D and pirical and may not be accurate enough, especially for large values
roughness values have been carried out using the spatially aver- of seabed roughness. Clearly more research is needed to quantify
aged flow velocity over the pipe diameter and the force coeffi- the effect of wave boundary layers on hydrodynamic forces on
cients from DNV-RP-F109, under the wave conditions of Um ¼1 m/ pipelines with a diameter smaller than 0.20 m.
s and T ¼14 s. The results for different roughness heights are
compared with those based on DNV-RP-F109 in Fig. 3. The values
3. Conclusions

In this work, the suitability of current design practice, embo-

died in the recommended practice DNV-RP-F109, for small dia-
meter pipelines under wave loading conditions is examined based
on a desk study. The main conclusions are given below:

– The high required SG values for absolute stability of small dia-

meter pipelines under wave loading conditions may be sub-
stantially reduced if the velocity reduction in wave boundary
layers is considered in estimating the hydrodynamic force on the
pipeline.
Fig. 3. Effect of pipe diameter on the required specific density for flow conditions – Experimental data on the effect of seabed roughness on hydro-
of Um ¼1 m/s and T ¼14 s. dynamic force on pipelines are rare. Existing experimental data
30 L. Cheng et al. / Ocean Engineering 125 (2016) 26–30

with relative large size of model pipe (D4 0.2 m) available in the References
literature appear to suggest that drag and lift forces on the pi-
peline decrease with the increase of roughness height while Cheong, H.F., Shankar, N.J., Subbiah, K., 1987. Wave forces on submarine pipelines
inertia force is barely affected by the seabed roughness. nears a plane boundary. Ocean Eng. 14 (3), 181–200.
DNV-RP-F109, On-Bottom Stability Design of Submarine Pipelines, Recommended
– More research needs to be carried out to substantiate the issue Practice, Det Norske Veritas AS, 2010.
presented in this study, especially (1) the effect of seabed Fredsoe, Deigaard, 1992. Mechanics of Coastal Sediment Transport. World Scientific,
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The authors would like to acknowledge the support from Sumer, B.M., Fresdøe, J., 2001. Hydrodynamics Around Cylindrical Structures. Ad-
Australian Research Council through LP150100249. vanced Series on Ocean Engineering Volume 26. World Scientific, Singapore.