improving boundary conditions for multiphase cfd ... · pdf filedeveloped to model horizontal...

Xodus GroupTechnical Paper

www.xodusgroup.com 1

June 2015

AbstractFlow induced vibration (FIV) can go undetected in subsea pipework, potentially leading to fatigue failures. Although FIV screening methods have been developed, these tend to be conservative for multiphase pipe flows and are typically only validated for simple single bends. This paper investigates the usage of Computational Fluid Dynamics (CFD) to predict realistic forcing functions that could be used to analyse stress and fatigue in complex combinations of bends and tees, typically seen in subsea flow-lines, manifolds and jumpers.

When simulating multiphase flow through a complicated pipe configuration it is important to define the slug length and velocity at the inlet to correctly predict force magnitudes and frequencies. A novel approach is presented which uses a quasi-three-dimensional (Q3D) CFD method to obtain horizontal slug flow inlet boundary conditions for subsequent force prediction. The results of this approach are compared with physical tests of slug flow through a single bend and predictions based on more established slug flow correlations.

The Q3D CFD method produced slug flow inlet boundary conditions that matched correlations and test data well. The conclusion is that Q3D CFD provides improved horizontal slug flow inlet boundary conditions compared to simplistic approaches such as defining time varying square waves based on correlations. The forcing frequencies predicted using the Q3D CFD approach showed an improved distribution compared to a boundary condition based on correlation, and the magnitudes of the forces on the pipe bend compared well with published test data.

1.0 IntroductionIt is well-established that the flow of fluids through process pipework generates fluctuating forces caused by turbulence, cavitation, flashing, multiphase and acoustic effects. Under certain conditions, these forces can be sufficient to cause catastrophic fatigue failures. In the North Sea vibration and fatigue account for 21% of all pipework failures (1).

When a system is operational and accessible then these issues are typically assessed by a combination of field vibration measurements and finite element stress analysis. However, if the pipework is inaccessible (e.g. subsea), its duty is to be changed or it is yet to be

constructed then predictions of the fluid forces (typically referred to as the forcing function) are required.

The magnitude and frequencies of forces generated by the flow of liquids, gases and multiphase mixtures are not well understood. Some basic rules of thumb have been developed for the purposes of preliminary screening of new pipework designs, for example, those given in the Energy Institute Guidelines on Guidelines for the avoidance of vibration induced fatigue failure in process pipework (2). As part of the development of a new Energy Institute guidance document for subsea pipework it was highlighted that further work was required to establish improved techniques for estimating forcing functions in liquid-gas, flows. Subsequently a Joint Industry Project (JIP) funded by Aker Solutions, BP, FMC, Lundin, Shell, Statoil, Suncor and Total was established by Xodus Group in collaboration with TNO to address this issue.

Phase I of the JIP includes flow loop tests in which forces generated by water-air flow through a 6 inch bend at atmospheric conditions, over a range of flow regimes were measured. This will establish whether the results of small-scale tests (3,4,5,6) are applicable to larger pipework and help in the development of methods in which laboratory measurements are extrapolated to assess vibration in the field.

Work is also progressing to assess the ability of CFD to predict multiphase forcing functions. CFD offers a number of potential advantages over the extrapolation approach if suitably validated: › It could predict flow behaviour in complex pipework installations

such as jumpers and manifolds for which there may be no experimental information

› It could predict forces in high-pressure conditions that would be difficult and expensive to replicate experimentally

› Local, time varying forces can be exported directly to FEA software or full fluid-structural interaction simulations can be performed in which the movement of the pipework affects the fluid flow and vice versa

CFD is now being used by Xodus and others to model FIV in surface and subsea pipework and comparison with a limited number of field vibration measurements suggests that it provides realistic predictions. One of the aims of the JIP is to improve the understanding of the accuracy of CFD FIV analysis by validating it against high-quality, well-controlled laboratory measurements.4

Improving boundary conditions for multiphase CFD predictions of slug flow induced forcesPaul Emmerson, Mike Lewis and Neil Barton from Xodus Group



This will indicate when the use of CFD is most beneficial.

In initial work, CFD predictions were compared with previously published test data and good predictions were seen for a range of vertical and horizontal flow regimes. This work showed that accurate definition of inlet boundary conditions is a pre-requisite to realistic prediction of the forcing function. This is particularly true in the slug flow regime when the inlet flow velocity and liquid depth will fluctuate over time.

This paper presents a novel and effective approach that has been developed to model horizontal hydrodynamic slug flow to define inlet boundary conditions for CFD calculations to predict fluid forces on pipe bends. The work described uses STAR-CCM+ 9.04 CFD software (7) but in principle could be implemented in most general-purpose CFD codes.

It should also be noted that, although the focus of the current paper is on flow-induced vibration, the method could also be used in a variety of other types of CFD study e.g. slug catcher sizing, erosion prediction, slugging inception studies, surge control assessment, separator design and multiphase meter development.

2.0 Previous Work In principle, CFD simulation of liquid and gas flows in pipes has been possible since the 1980’s. However, the computing power required to model a typical subsea installation (e.g. a manifold) has been prohibitively expensive until relatively recently. Consequently, relatively little has been published comparing CFD predictions of FIV with flow loop tests.

Yamano et al (8) used CFD to simulate (single phase) water flow through a 410 mm ID, 1D bend. Good predictions were obtained for the frequency of dynamic pressure measurements taken immediately downstream of the bend, although the predicted fluctuation was lower than the measured value.

Sanchis and Jakobsen (9) found similar results when comparing with the same test. A comparison of single- and multi-phase URANS CFD analysis was performed. In terms of resolving the flow induced pressure loading on the pipe walls it was found that for single-phase flow, the two-equation SST turbulence model was able to correctly predict the frequency and location of the pressure fluctuations but not their amplitude nor the associated large-scale unsteady flow features. It was shown that for multiphase flow the liquid and gas could not be treated as a homogeneous mixture. The separation of the liquid and gas due to centrifugal forces travelling around the bend was important when predicting the magnitude and frequency of the forces on the pipe walls.

Hernandez-Perez (10) showed that slug generation can be accurately predicted in horizontal and inclined straight pipes using the volume of fluid (VOF) method to represent liquid and gas phases. Sharaf (11) also demonstrated reasonable agreement for vertical pipe flow.

Pontaza et al (12) used CFD in conjunction with (uncoupled) finite

element analysis (FEA) to perform FIV assessments of a subsea jumper and a subsea manifold in wet gas flow. The VOF method was used with the large eddy simulation (LES) turbulence model. No direct comparison with laboratory test was presented, although, in discussion, Pontaza stated that reasonable agreement between CFD and field measurements was achieved.

TNO performed CFD analysis (13) on a 4 inch experimental test loop which will be discussed in section 3. An inlet hold-up which varied with time in the form of a square wave was used. The square wave represented the slugs in a simplified way, with the frequency, slug length and slug velocity based on a correlations. This method was able to reasonably provide the main forcing frequency and force fluctuation. However, it is wholly dependent on the correlations from which the inlet condition is derived and the results are obtained as a direct consequence of the inlet conditions and assumed variability in slug characteristics.

3.0 Comparison of Test Results with CFD using Correlation Based Boundary ConditionsThis section gives a brief overview of the TNO water-air flow loop test set up and work which replicated their original CFD simulations (13). Subsequent sections describe the development and validation of the new improved Q3D CFD approach of providing boundary conditions for slugging flow.

3.1 Overview of TNO 4" TestsThe TNO air-water flow loop is shown in Figure 1. A mixture of water and air, at atmospheric conditions, were flowed through a long, straight 4" plastic pipe section and then through a 180 degree bend (formed by two 90 degree 1D bends). The horizontal forces caused by the flow passing round the 180 degree bend were measured using two loads cells attached to the upstream 90 degree bend. The test section pipework was not held rigidly, so it is possible that the flow behaviour was affected by pipe vibration and vice versa.

A range of multiphase flow regimes were generated during the tests. In this paper a slug flow case is considered.4

Figure 1: TNO 4" flow loop.



3.2 Preliminary CFD Simulations of the TNO 4" TestsFigure 2 shows the setup of the initial CFD simulations, which replicated the original TNO work. The main simulation parameters were as follows: › Simulations were performed using STAR-CCM+ CFD software (7).

Note: ANSYS Fluent was used in the original TNO work. › The computational domain comprised the 180 degree bend with

short straight pipe sections upstream and downstream. › The Volume of Fluid (VOF) model was used with water and air

represented as separate phases. STAR-CMM+ has a surface sharpening algorithm. In this case the sharpening factor was set to 0.6.

› The air was modelled as an ideal gas with a molecular weight of 28.97 kg/kmol and a viscosity of 1.855e-5 Pa.s. Although the pressure gradient in the system is insignificant and the flow velocity is not high, gas can accumulate in the system. This is particularly important for slugging flows, where gas compresses behind the slug and expands as the slug accelerates. Ignoring the gas compressibility would result in slugs not achieving their peak velocity.

› The liquid phase was water with a constant density of 1000 kg/m3 and a viscosity of 0.001Pa.s. The water/air surface tension was set to 0.074 N/m.

Turbulence effects were modelled using the Large Eddy Simulations (LES) approach for the 3D domain. It was found that the realizable k-epsilon model, as implemented in STAR-CCM+, increases the turbulence generation at the interface between the phases which smears the interface, damping out wave initiation. No increased turbulence generation was observed when using the LES scheme. The turbulence effects on the force fluctuations are thought to be of secondary importance compared to the multiphase effects, and although the mesh is not resolved to the expected level for a LES, the compromise appears to provide acceptable results. A mesh sensitivity study has not been performed on the cases described here, but extensive experience gained with similar cases has been applied.

Figure 2: Setup of preliminary CFD simulation.

The slug flow at the CFD model inlet was mimicked by setting a varying liquid height such that the holdup regularly stepped between 38 and 100%. The frequency of the oscillation was defined using the Fetter equation (14). The inlet velocity was set as the homogeneous mixture velocity and the slug length was defined to ensure that the total liquid and gas rates matched the test condition.

Figure 3 and Figure 4 compare the CFD predictions and the test measurements for a slug flow case in which the liquid and gas superficial velocities were 2.4 m/s and 2.2 m/s respectively. There is a reasonable match between the magnitudes of force acting on the bends. However, in reality slug sizes vary and the initial CFD boundary conditions did not account for this (as noted in the original TNO paper). Hence the predicted Power Spectral Density (PSD) plot takes the form of a series of individual frequency harmonic peaks rather than the distribution that was measured.4

Figure 3: Comparison of predicted and measured Forces (Fy) and Power

Spectral Density Plots comparing initial slug flow CFD (red) predictions

with TNO tests (black).

Figure 4: Comparison of predicted and measured Forces (Fx) and Power

Spectral Density Plots comparing initial slug flow CFD (red) predictions

with TNO tests (black).



4.0 Quasi Three Dimensional CFD MethodologyThe Quasi Three-Dimensional (Q3D CFD) approach has been developed here in STAR-CCM+, and in principle the method can be applied in any general-purpose CFD code, and is similar to that used in the Ledaflow software (15). The approach entails adding an extra section of straight, horizontal pipe onto the inlet of the 3D bend model. This Q3D CFD pipe section is treated like any other part of the CFD domain - momentum, VOF and k-epsilon equations are solved using the standard STAR-CCM+ implicit transient solver. The inlet to the Q3D CFD section is defined as being stratified with a constant inlet velocity. Slug flow spontaneously develops within the Q3D CFD section and the resulting fluctuating flow at the Q3D CFD outlet is used to define the inlet conditions for the 3D bend section.The Q3D CFD section differs from the standard CFD domain in only two ways. Firstly, the mesh in the Q3D CFD section is split vertically into a number of horizontal cells (26 in this case); each horizontal cell extends across the width of the pipe (Figure 4). Secondly a modification to Cµ is necessary to obtain the correct pressure drop along the pipe.

The advantage of this approach is that it is highly computationally efficient compared to using a fine three-dimensional mesh in a long section pipe section. It provides realistic slugging conditions without the requirement to resort to empirical correlations such as Fetter (14), whose applicability is likely be limited to specific pipe sizes, atmospheric conditions and perfectly horizontal pipes. The approach also eliminates the requirement to assume a variability in the slug length over time.

Simulation parameters were essentially identical to those described for the initial simulations in section 3.2 except that an additional 25 m straight (Q3D CFD) section was defined upstream of the bend. The liquid height and flow velocity at the inlet was fixed and unchanging with time and slug flow was spontaneously generated in the Q3D CFD section before entering the bend.

Figure 5: Q3D CFD Setup (streamwise mesh – left, cross-sectional mesh –

centre, stratified inlet – right).

The time step used was 0.5 ms; this was chosen as a balance between computational time and limiting the target Courant number below 1.0. Reducing the time step below this did not appear to give any significant improvement in the predictions.

In principle, slug flow conditions would develop in any pipe section if a sufficiently fine mesh was used. However, in practice this would result in excessive run times unless very expensive computing facilities were available. The Q3D CFD method can save considerably on computational time compared with using a fully 3D setup. For example for the Tay case described in section 6, the combined Q3D

CFD and 3D domains consisted of 820,536 cells, which took 108 minutes of computational time on 20 cores to complete 1 second of simulated time. When the previous model was converted into a fully 3D setup using the 3D cross-sectional mesh for the Q3D CFD part (and same numerical settings) it consisted of 7,105,536 cells, taking 1167 minutes on the same 20 cores to complete 1 second of simulated time. Therefore the combined Q3D CFD and 3D approach, as tested here, was over ten times faster than a fully 3D setup.

The Q3D CFD model would be expected to perform well in horizontal stratified and hydrodynamic slug flows where the large scale interface is dominantly horizontal at a given streamwise position. The applicability of the Q3D CFD approximation to high inclination and vertical flows has not been validated.

5.0 Comparison with TNO 4" Experimental Results

5.1 SetupA description of the TNO 4" experiment was given in section 3.1. Figure 6 shows the computational mesh used for the combined Q3D CFD and 3D simulation to calculate the forces on the 180 degree bend. The 3D mesh had a streamwise spacing of 7.5mm, 756 cells in the cross-sectional and a near wall spacing of 0.5mm. The total mesh count was 499,000 cells for the 3D domain. The flow parameters at the 3D inlet were interpolated from the Q3D CFD outlet at each time step.

Figure 6: Computational mesh for TNO 4" medium gas slug flow case.

5.2 Slug predictionA snapshot of the predicted slug flow using the Q3D CFD approach is shown in Figure 7. Typical slug features can be seen, such as the rolling over of the nose, drawing up liquid in front of it and the smooth tail at the rear. The variation of liquid hold-up with time is plotted in Figure 8, which shows the irregular front and sharp rear of the slugs. The minimum and maximum liquid hold-up values are reasonably consistent (~0.2 – 0.9) with time as the slugs move through, but the time period, length and shape of the slugs varies. Table 1 compares predicted slug characteristics with those based on correlations; Fetter (14) used for frequency and Oliemans (16) for velocity and length. Liquid hold-up was not measured in the experiment. The slug frequency was calculated by performing a Power Spectral Density analysis on the hold-up time history (Figure 9), and taking the dominant frequency. Slug velocity was calculated from the time taken for the tail of the slug to pass through4



two positions one metre apart and was averaged over five slugs. The average slug length was calculated from the time taken for the nose and tail (of five slugs) to pass a given point (at a level of ~0.6 hold-up) multiplied by the slug velocity. The comparison for the Q3D CFD slug characteristics with the correlations are very good, especially given that no information about the type of flow regime or details other than the superficial velocities is required.

Figure 7: Predicted slug flow using Q3D CFD for TNO 4" medium gas slug

flow case (pipe height scaled x 4).

Figure 8: Liquid hold up predicted by Q3D CFD for TNO 4" medium gas

slug flow case.

Figure 9: Power Spectral Density plot of Liquid hold up predicted by Q3D

CFD for TNO 4" medium gas slug flow case.

Table 1: Comparison of slug characteristics for TNO 4" medium slug

flow case.

Correlation Q3D CFDSlug Frequency (Hz) 1.25 1.28Slug Velocity (m/s) 5.4 5.5Slug Length (m) 1.8 1.81

5.3 Force PredictionPredicted contours of liquid volume fraction near the walls and through a vertical mid-plane along the pipe are shown in Figure

10 for the slug flow case. Table 2 summarises the measured and predicted Root Mean Squared (RMS) forces on the bend. Two CFD force predictions are given; one in which the force is calculated based on the upstream 90 degree bend only, and the other in which forces acting on the whole 180 degree bend are considered. It is unclear which of these assumptions is the most representative of the test measurement.

As expected the calculated parallel, (Fy) RMS force approximately doubles when the whole of the U-bend is considered and this compares well to the measured value. However, the predicted transverse (Fx) RMS force is significantly lower when considering the 180 degree bend because forces in the upstream 90 degree bend oppose forces in the downstream bend.

Figure 10: Liquid volume fraction near walls and through vertical mid-

section for TNO 4" medium gas slug flow case.

Table 2: RMS forces on the TNO 4" bends for slug flow case (Fx & Fy as

defined in Figure 10).

RMS Parallel RMS Transverse Force, Fy [N] Force, Fx [N]Test measurement 131.1 59.4CFD 90deg Instrumented Bend 70.0 66.3CFD whole of U bend 137.3 22.0 Figure 11 and Figure 12 compare the measured and predicted force fluctuations in the parallel and transverse flow directions. Again predicted forces are given for both 90 and 180 degree bends. When considering the whole 180 degree bend the peak-to-peak parallel (Fy) forces match well. The shape of the PSD plot compares well with the test data, having a similar range and dominant frequency. The predicted transverse (Fx) forces magnitudes and frequency ranges also match well with the test data.

The CFD simulations assumed a rigid pipe, whereas in reality the unsupported pipework flexed significantly as each slug passed through. This is believed to explain why some vibration was measured above 10 Hz in the tests but was not seen in the simulations.4



Figure 11: Measured (top) and predicted (bottom) parallel forces, Fy for the TNO 4" medium gas slug flow case.

Figure 12: Measured (top) and predicted (bottom) transverse forces, Fx for the TNO 4" medium gas slug flow case.



6.0 Comparison with Tay and Thorpe Experimental Results

6.1 SetupTay and Thorpe (17) described their experimental setup which measured the liquid heights of slug flow and the forces they generate on a horizontal 90 degree 1.5 R/D bend with an internal diameter of 70 mm with superficial velocities up to 3.89 m/s. Air and water at atmospheric pressures were mixed and slug flow allowed to develop through a 9 m horizontal run. A bend was connected to the 9 m run and a downstream horizontal pipe section via two sets of bellows, which were designed to minimise structural transmission to and from the bend. A slug flow case with a superficial gas velocity (jG) of 1.8 m/s and a superficial liquid velocity (jL) of 0.5 m/s is compared with a like-for-like Q3D CFD simulation. The computational mesh used is shown in Figure 13, comprising of a 3D mesh with 7.5 mm streamwise spacing, 864 cells in the cross-sectional and 0.5 mm near wall spacing. The total mesh count was 625,500 cells for the 3D domain. The computational time for the Q3D CFD part accounted for about 30% of the total time.

Figure 13: Computational mesh for the Tay and Thorpe slug flow case

(jL=0.5 m/s; jG=1.8 m/s).

6.2 Slug predictionA snapshot of the predicted slug flow using the Q3D CFD approach is shown in Figure 14. Again the slug features and different stages of development can be seen. The variation of liquid hold up with time is plotted in Figure 15 again showing the irregular front and sharp rear of the slugs. The slugs plotted look reasonably consistent but over a longer time period there was some variation in their frequency, length and shape. Figure 15 includes the height of liquid as measured at the inlet of the bend, and a Power Spectral Analysis (PSD) performed on the predicted hold-up time history. Table 3 compares predicted slug characteristics with those measured and those based on correlations; Fetter (14) was used for frequency, Tay and Thorpe for velocity and Taitel (18) for length. The slug frequency was calculated by performing a Power Spectral Density analysis on the hold-up time history (Figure 15), and taking the dominant frequency. Slug velocity and length was calculated in exactly the same way as for the TNO 4" case described in section 5.1. It would be beneficial to run the Q3D CFD simulations for a longer time period to collect more statistical data on the slugs; this would result in a smoother PSD distribution. Comparisons of the Q3D CFD slug characteristics with measurements and correlations are good, providing a second

validation case with different pipe diameter, inlet hold-up and superficial velocities to the first TNO 4" case.

Figure 14: Predicted slug flow using Q3D CFD for the Tay and Thorpe

case, jL = 0.5 m/s, jG = 1.8 m/s (pipe height scaled x 8).

Figure 15: Measured liquid height (top), Q3D CFD predicted liquid hold-up

(middle) and PSD (bottom) for Tay and Thorpe case (jL=0.5 m/s; jG=1.8

m/s).

Table 3: Comparison of slug characteristics for Tay and Thorpe case

(jL=0.5 m/s; jG=1.8 m/s).

Experiment Correlation Q3D CFDSlug Frequency (Hz) 0.2 0.2 0.2Slug Velocity (m/s) 3.07 - 3.29 3.2 2.8Slug Length (m) 1.55 - 1.76 2.24 1.9

6.3 Force PredictionA comparison of measured and predicted resultant forces on the bend is given in Figure 16. The measurements were taken using a quartz force sensor to provide forces in the two horizontal components. The peak magnitude of the resultant force in the experiment was about 67 N for two of the slugs, with the third slug slightly less. The peak resultant force predicted by CFD varied depending on the length and liquid content given by the Q3D CFD inlet, but the average peak magnitude was 65 N. There is significant variation in the characteristics of the slugs generated by the Q3D CFD approach as illustrated by the liquid hold-up plotted in4



Figure 16 in comparison to that in Figure 15. For the slugs illustrated in Figure 16 the peak varied from 92 N down to 18 N. There appeared to be less variation in the measured forces in the experiment though only data for three slugs were published.

Figure 16: Resultant force as measured (top) and predicted (middle) and

predicted liquid hold-up (bottom) time histories for the Tay and Thorpe

case (jL=0.5 m/s; jG=1.8 m/s).

7.0 ConclusionsFlow induced vibration (FIV) can go undetected in subsea pipework, potentially leading to fatigue failures. Although FIV screening methods have been developed, these tend to be conservative for multiphase pipe flows and are typically only validated for simple single bends at atmospheric conditions for water and air. CFD calculations offer advantages when considering complex geometries at high operating pressures and using production fluids. This paper has described the usage of CFD for prediction of flow induced forces on pipe bends in the slug flow regime.

For any subsea analysis, suitable inlet boundary conditions must be defined to obtain representative results. A novel approach has been presented which uses a quasi-three-dimensional (Q3D CFD) CFD method to obtain horizontal slug flow inlet boundary conditions. The Q3D CFD method produced slug flow inlet boundary conditions for two different test cases, namely the TNO 4" test loop with a U-bend and the Tay and Thorpe 70mm experiment with a 90 degree elbow. The slug characteristics matched correlations and test data well.

The benefits of using the Q3D CFD approach are: › the slug flow does not need to be explicitly known a priori, only the

superficial velocities of the two phases › predicted slugs vary in frequency, velocity and length, therefore

giving a distribution of forcing frequencies, rather than matching with a single slug frequency provided by a correlation

› in principle, the approach should be valid for the high-pressure conditions typically experienced subsea, for which there is little or no experimental data or correlation available

› It has been shown that Computational Fluid Dynamics (CFD) methods can predict realistic forcing functions that can be used to analyse stress and fatigue in complex combinations of bends and tees, typically seen in subsea flow-lines, manifolds and jumpers.

8.0 AcknowledgementsThe authors would like to express their thanks to the JIP sponsors Aker Solutions, BP, FMC, Lundin, Shell, Statoil, Suncor and Total as well as in-kind sponsors and software providers CD-adapco. Also thanks to TNO who provided measurement data for comparisons with the TNO 4" test loop.

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