Cfd Modeling of Corrugated Flexible Pipe

1

Proceedings of OMAE2010 29th International Conference on Offshore Mechanics and Arctic Engineering

June 6- June 11, 2010, Shanghai, China

OMAE2010-20509

CFD MODELING OF CORRUGATED FLEXIBLE PIPE

Rajeev K. Jaiman ACUSIM Software, Inc.

Mountain View, CA 94043

Owen H. Oakley, Jr. Chevron Energy Technology

Company

J. Dean Adkins Chevron Energy Technology

Company

ABSTRACT The objective of this paper is to present Computational Fluid Dynamics (CFD) modeling of fully developed turbulent flow through a flexible corrugated pipe and to investigate the pressure drop reduction potential of liners. This work also aims to establish a framework to be used in large scale numerical simulations of the offshore transfer of cryogenic fluids. A 3-D CFD approach is considered more appropriate than 2-D axisymmetric one, since the wavy corrugation profiles lead to a great deal of internal turbulent structures for high Reynolds number over Re > 106. Three geometries of the bellows’ (corrugation) depth are considered to determine the potential value of a cryogenic liner, corrugation filler or geometric variations for the 16” pipe. The reduction in cost and complexity of developing a robust cryogenic liner or corrugation filler, plus eventual certifications, would be significant and needs to be worth the improvement (decrease) in pressure drop. We conduct a straight pipe corrugation depth study for pressure drop (deep corrugation, shallow corrugation and liner), and include suitable mesh convergence and unsteady simulations. We also attempt to validate the friction coefficient data with the empirical formulas and recent experimental tests. Operational cryogenic transfer flow rates ranging from Q=1000 m3/h to Q=5000 m3/h are considered.

INTRODUCTION The flexible metal pipe has been used in smaller diameters for more than 30 years for all kind of cryogenic Liquid Natural Gas (LNG) transfer applications (Refs. [1,2]). Today these LNG loading systems have evolved towards large, complex industrial systems, which have to respect increasingly stringent rules and standards while continuing to maintain high levels of safety and availability. For both design and operational standpoint, the LNG from ship to ship loading is a new application of this well known technology (Ref. [2]). Such flexible LNG pipes are usually provided with corrugated walls. The basic design of a Nexans vacuum insulated LNG transfer hose is illustrated in Figure 1. Relatively minor deviations in corrugation geometry can affect the flow/pressure drop characteristics that are important from the design and operational standpoint. The relative pressure drop per unit length in a pipe differs according to the distance from the inlet, normally related to a distance of some 50 x pipe inner diameter to achieve a fully developed flow profile. After this length the flow is normally fully turbulent and the relative pressure drop per unit length is constant (and lowers than in the inlet section). Armoured metallic corrugated pipes are well known structures which can withstand tensile and internal pressure loads, as well as perform better from a fatigue and heat transfer

2

standpoints. However, series of corrugations can induce complex and undesirable flow behavior in the pipes. The wavy configuration of the corrugations promotes turbulence, which is a problem because of the extra work required to surmount the pressure drop. In a broad sense, corrugations may lead to the following flow physics phenomenon:

Large pressure head-loss Flow induced pulsations Multiphase with bubbles and cavitations Increase heat transfer

Figure 1: Nexans vacuum insulated LNG transfer hose The purpose of the modeling exercise is to assess the pressure drop and qualify the behavior of the flow in the various configurations of corrugation geometry. To estimate the variation of the pressure in the corrugations, we do not model the phase change and the bubbles cavitations but accurately evaluate the pressure drop along the pipe. The pressure drop estimation can be useful to deduce the upstream pressure which can be imposed to stay everywhere downstream above the phase change pressure. The pressure drop and friction factor are related by the following relationship (Ref. [3]):

212

4

cross - section area weighted perimeter

h

h

fp uL DAD

CA C

ρ ∆ =

=

=

(1)

, =

where pL

∆ denotes pressure drop per unit length L ,

hydraulic pipe diameter hD , the density ρ of fluid, the mean

velocity u of flow; dimensionless coefficient of friction f . In the case of a circular cross-section the hydraulic diameter is equal to the diameter of the circle. In this work, the challenge consists in making CFD modeling accurately describe the turbulent behavior of liquid flow in a corrugated hose. The macroscopic features as pressure drop and friction factor in the corrugated pipe are directly related to the wall shear stress.

To begin, it is useful to summarize briefly the essential elements of wall turbulence, mainly to establish notation and define some basic terms. From simple observations, the effect of turbulence on the mean flow is to flatten the profile relative to the parabolic profile that occurs in pipe flows. The total shear stress is sum of the Reynolds stress uvρ− and the

viscous stress ( )/du dyµ and it is defined as

( ) /du dy uvτ µ ρ= − (2) where µ denotes the dynamic viscosity of the fluid. In fully developed pipe flow in the absence of streamwise acceleration (i.e., flow no longer changing in streamwise direction), the mean equation of turbulent motion can be defined as:

0 px y

τ∂ ∂=− +

∂ ∂ (3)

Since px

∂∂ is a function of streamwise direction x and

yτ∂∂ is a function of y alone, both of them must be

constant and the stress distribution is then linearly varying

from the value at the wall wτ to zero at the centerline. The following addresses the problem of developing a CFD model to obtain an insight into the wall turbulence phenomena and

obtaining values of the pressure gradient px

∂∂ in the

corrugated pipe. In corrugated pipe applications, flow physics (e.g., recirculation, separation, mean flow three-dimensionality, streamline curvature, flow acceleration) and geometry play an important role. In this study, we show that CFD modeling can offer an accurate and powerful predictive tool for estimating the macroscopic pressure drop and complex flow phenomenon in the corrugations. In the following sections we describe the general method of solving 3D flow equations with turbulence effects. The problem of creating an optimal mesh is discussed in which the objective is to combine acceptable solution accuracy with good solution economy. We then describe simulations results and assessment of liner designs, and comparing the predicted pressure drop with the empirical formula and the water test experiments. NUMERICAL METHODOLOGY All of the solutions shown herein are produced using the AcuSolveTM finite element Navier-Stokes solver based on the Galerkin/Least-Squares formulation. Although the corrugated pipe geometry used here has cylindrical symmetry, Cartesian coordinates are employed; illustrating the potential of the solver to model complex geometries with large elbows (i.e.

3

catenary with varying curvatures) using unstructured meshes. The followings are the basic components of CFD modeling.

Turbulence Modeling The turbulence level is typically high due to the corrugations and turbulence modeling is critical to get the accurate predictions. To model the steady effects of the turbulence on the mean flow field, we employ the Spalart-Allmaras Reynolds Averaged Navier Stokes (RANS) model. This model is a general purpose model that provides reasonable results for a broad array of industrial applications. This model relies on the fact that the complete turbulence behavior has to be enclosed within an appropriate eddy viscosity variable which takes into account all turbulence scales (from the largest eddies to the Kolmogorov scale). This model solves a single transport partial differential equation (PDE) for the eddy viscosity with the appropriate boundary conditions and solver settings. For unsteady simulations, we employ Delayed Detached Eddy Simulation (DDES), a hybrid RANS model with Large Eddy Simulation (LES). In the LES based on dynamic subgrid scale estimation, an attempt is made to capture the large scale unsteady motions which carry the bulk of the mass and momentum in a flow, but the near wall turbulence behavior is treated with a wall function. In the DDES model (Refs. [6,9]), we resolve the large eddies that have the biggest effect on the wall shear stress and use the RANS equations to describe the flow near the wall. This was done not only to economize on mesh size, but also because most pipes have relatively rough walls. Wall functions reduce mesh size by providing an integrated relationship between the wall and the logarithmic region of the boundary layer.

Material Model In all simulations, the working fluid LNG is viscous and in liquid phase with constant density, that is to say incompressible flow. The flow is assumed to be isothermal, i.e., the energy equation is not solved. The flow rate and Reynolds number based on the averaged velocity are the input for the models. Table 1 summarizes the material properties of LNG.

Table 1: Summary of the properties of LNG

Property Value

Density 450 kg m -3

Dynamic viscosity 1.4 x 10-4 Pa sec

Kinematic viscosity 3.11x 10-7 kg m-1 s-1

Solver Settings

The standard solver settings were specified in AcuSolve for steady RANS calculations. When performing a steady

simulation, the time integration is automatically set to 1st order accuracy. In this configuration, the timestep size taken by AcuSolve is set to infinity (1.0x1010 s) to convect the errors through the domain and arrive at the steady solution. The mass continuity and momentum differential equations are then converged to 4 decades of the solution accuracy. This residual reduction ensured iterative convergence in all cases. For unsteady cases, we try to minimize the additional effects of finite element stabilization in both space and time integration so that numerics do not suppress the small scales of turbulent eddy motions. For the spatial integration, we switch off the discontinuity capturing operator for the DES model and we set the lumped mass fraction to zero. In time domain, we utilize an optimal high frequency damping factor to be 0.5 for the generalized second-order time integration scheme. A global time step of 1 x 10-2 sec is used to capture the unsteady turbulent motions.

Initial Conditions For steady state simulations, the flow solution for the velocity vector is initialized by the entrance averaged flow speed and pressure field is set to be zero. For unsteady calculations, the flow solution field is initialized by the steady state solution of the corresponding flow rate. The flow solution is then advanced in time to obtain the unsteady turbulent motions with fixed and small time-increment to resolve the unsteady local motions.

Boundary Conditions In various industrial applications, the flow physics and geometry can be modeled as repetitive in nature by applying periodicity. Thereby, a representative building block can be considered for computational efficiency and simplicity, while maintaining the desired accuracy of flow physics corresponding to the experiments. In this purpose, the flow profiles at exit are iteratively reported to the entrance (Ref. [7]). In AcuSolve, to simulate the large length of corrugated hose with fully developed flow, periodic conditions are applied between the outlet (exit) and inlet (entrance) of the domain. The quantity imposed at the entrance is the flow rate Q or equivalently the averaged velocity as the surface integrated boundary conditions (bulk BC). This is the only user input to define the fully developed flow and Reynolds number based on the averaged velocity. Instead of outlet condition at the exit plane, the classical periodicity on the mean velocity and the eddy viscosity are used to couple the entrance and the exit boundaries. By this way, we attempt to achieve the similar stabilized profiles of mean velocity and eddy viscosity at the entrance and the exit. For the pressure, the condition based on the constant offset is imposed to obtain the fully developed like condition. In other words, the pressure can change along the stream-wise direction and the pressure can be decomposed

4

into a variable term and a linear varying term in the streamwise direction as

dpp p xdx

= − (4)

where the fluctuating terms, p identically repeat in the periodic direction. The fully developed velocity profile typically converges to a turbulent parabolic-type profile along the iterations as it is known, except at the vicinity of the corrugation. By applying these BCs, the SA turbulence model is tied up with the fully developed Navier-Stokes flow solution and the coupled mass, momentum and eddy equations are well-posed and complete.

NUMERICAL MODELING

Model Description The first step in generating the mesh for the corrugations is to define the domain of interest. The actual corrugated hoses have a length of several tenths of meters, i.e., L/D ~ O (100) and consequently, it is not needed to model their full length in this validation exercise. It is desirable to model the shorter relevant length to save the calculations and capture the fully developed turbulent flow. Table 2 summarizes the relevant dimensions of the corrugation profiles. The assumption of 2D axi-symmetric may not be sufficient for the accurate modeling of three dimensional turbulence effects at high Reynolds number. Therefore, we consider a 3D geometry with a circular shape of corrugation profile (i.e., without any helical/spiral effects) as shown in Fig. 2.

Table 2: Dimensions of corrugation profiles

Geometry ID (m)

Pitch, P (m)

Amplitude, A (m)

A*= A/(ID+A)

Base 0.404 0.041 0.02600 0.06047 Line #1 0.404 0.041 0.00650 0.01583 Liner #2 0.404 0.041 0.00325 0.00798

Mesh Generation Obtaining an economical solution is then simply finding the minimum number of degrees of freedom in the flow solution that captures the salient fluid flow effects and predicts the pressure drop and wall shear stress accurately. We consider the length of 3D flow domain with L = 6D matching earlier work on the direct numerical simulations of fully developed pipe flow (Ref. [4]). We consider the fully developed turbulent flow in the corrugated hose with the three configurations with varying depths A*. With the CAD models shown, we discretize the geometry to form a grid that is reasonable to capture the dominant flow features. In particular, we need to pay attention in the meshing near the wall of corrugations to

resolve turbulent boundary layer and to find the optimized volumetric mesh distribution.

Figure 2: Three model geometries for corrugated hoses: Base model with A*=0.06 (top), Liner #1 model with A*=0.01583 (middle), Liner #2 with A*=0.00798 (bottom) Figure 3 shows the typical mesh distribution at a cross-sectional plane for the base model. The model has a fine mesh resolution near the wall and a gradual coarsening of the mesh away from the wall (larger elements in the core region of the pipe).

Figure 3: Typical mesh distributions (a) full domain cross-sectional mesh (b) close-up mesh

An important quality control practice while performing numerical analysis is to determine the influence of the

(a)

(b)

5

discretization parameters and to perform sensitivity analyses. For CFD, this typically entails a mesh refinement study as well as a near wall modeling sensitivity analysis. A reasonable mesh sensitivity analysis was performed for this work. An important issue in the accurate prediction of industrial turbulent flows is the formulation and the numerical treatment of equations in regions close to solid walls. The near-wall formulation determines the accuracy of the wall shear stress (friction factor) and has an important influence on the development of boundary layers and near wall turbulence structures. Typically the two following approaches are used to model the flow in the near-wall region: (a) the wall function method (b) the wall integration (low Reynolds number) method. Because of the linear variation of total stress, the wall shear stress and the Reynolds (turbulent) stresses are related, justifying the introduction of the friction velocity

wuττ

ρ= as a scale representative of the turbulent

fluctuations. The viscous length scale alluded to the viscous

boundary layer thickness is given by v uτνδ = and the

distance above the wall scaled in wall units is denoted by

v

yyδ

+ = (5)

where y is the distance from the wall and µν ρ= is

kinematic viscosity. Table 3: Mesh statistics for the base design model A*=0.06

Mesh Fine mesh (Ref.) Medium mesh (wall function)

Total no of elements 51,468,929 23,293,025

Number of nodes 8,862,821 4,025,153

The reasonable mesh sensitivity implies that we reduce the mesh about a factor of two (instead of reducing uniformly in all the directions which is equivalent to factor of 8). Tables 3-5 show the mesh statistics for the three pipe models with y+ < 10. Two successive refined grids were created for the 3D corrugated pipe model to perform a volumetric grid refinement study using the wall function approach. The results of the mesh generation study showed little sensitivity (< 2%) to the density of the volume mesh for the high Reynolds number Re=14.1 x 106. The numerical results presented for the RANS and DES models in the following sections are those on the fine reference mesh, unless noted otherwise.

Table 4: Mesh statistics for the liner #1 design model, A*=0.01583



Number of nodes 6,113,454 3,429,323

Table 5: Mesh statistics for the liner #2 design model, A*=0.00798



Number of nodes 5,728,804 3,240,773

SIMULATION RESULTS AND VISUALIZATIONS We present full-scale 3D simulations using the steady RANS and transient DDES models for the three configurations for the range of flow rates.

Base Corrugated Model We first perform 3D RANS simulations using the wall-function approach with the fine mesh. As mentioned earlier, the length of modeled domain is 6D as shown Fig. 3.

Figure 4. Streamwise variation of velocity magnitude contours in the corrugated pipe at Q=3333 m3/h for the base model RANS (top) and DDES (bottom)

6

Figures 4 (top) shows the contours of velocity magnitude (top) using the RANS model at the Reynolds number of Re=9.38 x 106 for the base model of corrugated pipe. The fully developed and time averaged steady flow behavior can be observed from the figure. As expected from the RANS model, there are no physical unsteady motions in the velocity field. Figures 4 (bottom) shows the contours of streamwise velocity at the cross section of the corrugated pipe with the DDES model. The 3D turbulence structures and unsteadiness in the flow can clearly be inferred in the image Figure 5 shows the contours of cross-stream velocity magnitude at the three cross section planes of the corrugated pipe. Significant circumferential variations in the velocity magnitude can be seen in the figure. These local variations are coupled with vorticity, which is defined as the rotation of the velocity field.

Figure 5. Instantaneous velocity magnitude contours at the cross-sectional planes for flow rate Q=3333 m3/h (Re = 9.38 x 106) Figure 6 shows complex 3D turbulent structures of low-speed streaks and in-plane streamwise vortices. These vortex topologies are identified through the Q-criterion which defines a vortex as a spatial region where

( ) ( )

2 21 0,2

1 1: ,2 2

T T

Q

where

= − >

= ∇ + ∇ = ∇ − ∇

Ω S

S v v Ω v v

The interactions between these structures are essential ingredients of wall-bounded turbulence. These fluctuating vorticity structures are somewhat organized, often called vortical flow structures.

Figure 6. Iso-surface of vorticity variable (Q-criterion) colored by velocity magnitude Figure 7 shows the quantification of instantaneous variation of velocity field in the core flow. The velocity fluctuations are normalized by the mean inlet velocity. The velocity fluctuations suggest the maximum turbulence level up to 20 % at the probe point in the core flow.

-3.00E-01

-2.00E-01

-1.00E-01

0.00E+00

1.00E-01

2.00E-01

3.00E-01

1.0E+00 1.2E+00 1.4E+00 1.6E+00 1.8E+00 2.0E+00Normalized time

Nor

mal

ized

vel

ocity

fluc

tuat

ions

v'/Uw'/Uu'/U

Figure 7. Instantaneous velocity fluctuations at a sample location in the domain

Liner Based Corrugated Models In this section, we conduct a simple straight pipe corrugation depth study with the DES model. The meshing guidelines and flow conditions are similar to those used for the base model. On further flow visualizations, Figs. 8-9 show comparison of velocity magnitude at the cross-sectional and streamwise planes. In the images, we can see a greater degree of turbulence structures (red color zone) in the liner 1 model as compared to the liner 2 model.

7

-1.5E-01

-1.0E-01

-5.0E-02

0.0E+00

5.0E-02

1.0E-01

1.5E-01


Nor

mal

ized

vel

ocity

fluc

tuat

ions

v'/Uw'/Uu'/U

-1.5E-01

-1.0E-01

-5.0E-02

0.0E+00

5.0E-02

1.0E-01

1.5E-01


Nor

mal

ized

vel

ocity

fluc

tuat

ions

v'/Uw'/Uu'/U

Figure 8. Streamwise variation of velocity magnitude contours for the liner 1 (top) and liner 2 (bottom) models at Q=3333 m3/h

Figure 9. Instantaneous velocity magnitude contours to show turbulence spatial structures at the cross-sectional planes for the two liner models for flow rate Q=3333 m3/h (Re = 9.38 x 106) Figure 10 shows the quantification of instantaneous variation of velocity field for the two liner models as a function of the time in a single point, i.e. liner 1 on top and liner 2 below.

This is equivalent to obtaining the turbulence statistics from the single-point probe. The velocity fluctuations are normalized by the mean velocity. The liner 2 model decreases the velocity fluctuations (i.e., turbulence level) by a factor of 5 compared to the liner 1 model.

Figure 10. Instantaneous velocity fluctuations at the same single-point location for the liner 1 (top) and liner 2 (bottom)

ASSESSMENT AND DISCUSSION In this section, we want to quantify the pressure loss and friction factor for the three geometries. Since there are no experimental test data for these geometries, we first attempt to compare the CFD results with the classical roughness theory and 10.5” (Ref. 3). Hydraulically smooth pipe regime: From the universal

law of friction for a smooth pipe, the friction factor can be expressed as

2.0 log 0.8huD ff υ

=

1 - (7)

This is Prandtl’s universal law of friction for smooth pipes and it has been verified with experiments and the agreement is seen to be excellent up to the Reynolds number ReD= uDh/ν=3.2x106.

8

Completely rough regime: In the present configuration, the corrugations may be considered equivalent to periodic roughness (i.e., 2k/Dh) of the diameter of pipe. A systematic investigation on the effects of Reynolds number and relative roughness k on the friction factor was performed by Nikuradse Ref. [5]). For the higher values of Reynolds number (ranging from 104 to 107), the friction factor was found to be Reynolds number independent. The theoretical estimate for the friction factor for the completely rough regime was estimated as

21

1.74 2 log2

h

fDk

= +

(8)

Base Corrugated vs. Liner Models Figure 11 shows the variation of coefficient of friction for the range of Reynolds number for the three configurations and the smooth pipe. The friction factor was determined by evaluating the pressure gradient along the pipe from the integrated pressure values. For the baseline case, the friction coefficient is consistently larger than the liner 1 & liner 2 models. The wall shear stress of the liner 2 model is converging towards the stress values corresponding to the smooth pipe. This implies that, by introducing liner materials, the coefficient of friction can be reduced by 80% with respect to the deeper metallic hose configuration. Due to complex flow behavior and recirculation in the base & liner 1 models, the friction factor changes significantly with the Reynolds numbers. For the base and liner 1 geometry at Re~10M, an inflectional behavior in the pressure drop and wall shear stress have been observed in the RANS and DDES results. This may be explained in the context of boundary layer separations along the corrugation profile and the associated effects into the pressure gradients. In other words, when the imparted shear stress dominates eddy dissipative scale, a large amount of friction occurs along the wall or vice versa. The CFD results follow an inflectional friction factor relationship rather than the monotonic relationship given by the roughness theory and the Moody diagram. Figure 11 also presents the roughness theory predictions given by the lines. For the smooth pipe, the CFD results and the theory have an excellent match. However, for the corrugated shapes the roughness theory seems to differ up to 24%.

0.00E+00

2.50E-02

5.00E-02

7.50E-02

1.00E-01

1.25E-01

1.0E+05 1.0E+06 1.0E+07 1.0E+08Reynolds number, Re

Coe

ffici

ent o

f Fric

tion

Baseline

Liner 1

Liner 2

Smooth

Base Rough. Theory

Liner1 Rough. Theory

Smooth Pipe Theory

Figure 11. Variation of friction coefficients with Reynolds number Figure 12 shows a cross plot of friction factor vs. the depth of corrugation A*, which provides another view of the impact of reducing the corrugation depth. For the range of flow rates, the friction factor increases as we increase the depth of corrugation. This suggests the potential value of liners for reducing the pressure loss. The friction factor values for the liner 1 are converging to that of the smooth pipe. The amount decrease doesn’t appear to be simply a linear function.

0

0.025

0.05

0.075

0.1

0.125

0.0E+00 2.0E-02 4.0E-02 6.0E-02 8.0E-02Ampititude/Diameter, A*

Coe

ffici

ent o

f Fric

tion

Flow rate Q=5000 m^3/hr



Figure 12. Variation of friction coefficients with respect to the depth of corrugation A*

Steady RANS vs. DES Simulations To assess the results of steady RANS with the DDES, we further conduct a comparative study on the same grids. Figure 13 shows a summary of the friction factor computed based on the pressure drop for the two CFD models. A reasonable consistency in the predictions of integrated pressure drop can be seen in the figure. By tuning the grid distributions, an

9

improved match between the RANS and DDES may be obtained. For the base and liner 1 geometry at Re~10M, an inflectional behavior in the pressure drop and wall shear stress have been observed in the RANS and DDES results. As mentioned earlier, this dip in the frictional drag may be attributed to the sudden shift in the point of separation for the base and liner 1 geometries. In this range, the laminar viscous sub-layer portion of boundary layer becomes unstable and undergoes transition to turbulence. As seen in the flow over a cylinder, the turbulent boundary layer, because of its greater energy, is able to overcome a large adverse pressure gradient. The turbulent boundary layer separates at a further downstream location along the corrugation profile, resulting in a thinner wake and a pressure distribution more similar to that of potential flow. For values of Re >10M, the separation point slowly moves upstream as the Reynolds number is increased, resulting in an increase of the friction factor. For the liner 2 and smooth pipe, the geometry is streamlined and the point of separation and the transition of boundary layer remain somewhat unchanged.

0.00E+00

2.50E-02

5.00E-02

7.50E-02

1.00E-01

1.25E-01

1.0E+06 1.0E+07 1.0E+08Reynolds number, Re

Coe

ffici

ent o

f Fric

tion

BaselineLiner 1Liner 2SmoothBaseline-DESLiner1-DESLiner2-DES

Figure 13. Variation of friction coefficients for the range of Reynolds number for the RANS and DDES models We also present a comparison with the experimental test, and perform further analysis of the results to facilitate interpretation in the commercial settings. The experiment tests were performed on a 268 mm (10.5”) ID pipe for a range of flow rates with fresh water as working fluid. All the pressure drop readings were average values taken over a period of 1 minute Figure 14 shows the comparison of CFD values with the experimental test done with water in 10.5” ID pipe (Ref. [1]). The friction factors are compared with respect the non-dimensional dynamic similarity parameter, Reynolds number. The depth and shape of the corrugation profiles are marginally different between the 16” ID pipe and 10.5” pipe. A

reasonable agreement between the CFD and experimental values can be seen.

4.00E-02

6.00E-02

8.00E-02

1.00E-01

1.20E-01

1.0E+05 1.0E+06 1.0E+07 1.0E+08Reynolds number, Re

Coe

ffici

ent o

f Fric

tion

Base CFD Model

Liner 1 CFD Model

Water Test (Ref. [1])

Figure 14. Comparison of the CFD results for A*=0.0604 of 16” ID pipe with the water test with A*=0.0513 in 10.5” ID pipe

Next, we would like to establish the relevance of friction factor in actual pipe configurations as function of pipe lengths and corrugation depths. This may be important to estimate the capacity and limitations of LNG pumps for the corrugated pipe flow. Typical LNG pumps can develop 6.6 bar differential pressure (97.3 psi) while maintaining reasonable flow rates for LNG transfer. Figure 15 shows the comparison of pressure drop as a function of flow rates for the geometries, where the pressure drop is computed based on the Equation (1).

Pressure Required vs. Flow Rate for L=100 [m]

0

10

20

30

40

50

60

‐ 2,000 4,000 6,000 8,000 10,000 12,000Flow Rate Q [m^3/hr]

Pres

sure

Dro

p [b

ar] Base

Liner 1

Liner 2

Figure 15. Pressure drop as a function of flow rates for the 16” pipe with three corrugation geometries

10

CONCLUSIONS Cryogenic flexible pipe based LNG transfer system seems to be a good candidate for CFD modeling, and to qualify the pipe system for the LNG industry requirements. Significant 3D turbulence effects were found for the pipe geometry with circular corrugations suggested by both qualitative features and quantitative information. The 3D steady RANS and DDES models provided a consistent estimate of the pressure drop and friction factor for varying flow rates. We hoped that we have done a reasonable job in predicting complex internal turbulent structures with the unsteady DDES simulations. The pressure drop results were found to be quite sensitive to the corrugation depth. By introducing the liner materials, the coefficient of friction can be reduced by 80% with respect to the deeper metallic hose configuration. The CFD results appear to be sufficiently accurate that one might seriously consider using such models to investigate relative geometric differences and perform parametric studies of various corrugation configurations. The modeling can reduce the uncertainty, offer guidance on design variations, improve the design of full scale tests and potentially eliminate some or all of such tests. CFD can add substantially to classical roughness theory (which relies on known pipe characteristics) as it can address different geometries and dimensions without additional empirical data.

REFERENCES [1] Framo Engineering AS Report, “CFD Calculations of Corrugated Flexible Pipe,” 4577-0313-D, 2006. [2] Frohne, C., Harten, F., Schippl, K., Steen, K.E., Haakonsen, R., Jorgen, E. and Høvik, J. “Innovative Pipe System for Offshore LNG Transfer,” OTC 19239, 2008.

[3] Schlichting, H., “Boundary Layer Theory,” 7th Edition, McGraw-Hill Book Company, 1975.

[4] Eggles, J. et al.,”Fully devloped turbulent pipe flow: a comparison between direct numerical simulation and experiment”, Journal of Fluid Mechanics, 268, 1994, 175-207

[5] Nikuradse., ”Laws of flow in rough pipes”, NACA TM 1292, 1933 [6] Spalart, Deck, Shur, Squires, Streletes & Travin, “A New Version of Detached-Eddy Simulation, Resistant to Ambiguous Grid Densities,” Journal of Theoretical & Computational Fluid Dynamics, 20, 181-195, 2006. [7] Patankar, S.V., Liu, C.H., and Sparrow, E.M., “Fully developed flow and heat transfer in ducts having streamwise-

periodic variations of cross-sectional area”, ASME, J. Heat Transfer, Vol. 99, pp. 180-186 [8] Piomelli U. and Balaras, E. “Annual Review of Fluid Mechanics”, Vol 34, pp 349-374, 2002 [9] Shur, M.K., Spalart, P.R., Strelets, M.K. and Travin, A.K.,”A hybrid RANS-LES approach with delayed-DES and wall-modeled LES capabilities”, International Journal of Heat and Fluid Flow, Vol 29, pp 1638-1640, 2008. [10] Allen, J.J, Shockling, M.A., Kunkel, G.J. and Smits, “Turbulent flow in smooth and rough pipes”, Philosophical Transactions of the Royal Society, vol. 365, No. 1852, 2007

Documents

Cfd Modeling of Corrugated Flexible Pipe