Flow Induced Vibration Assessment of a Gas Piping System

Abstract

Internal fluid flow within a piping system is known to create structural vibrations when forced to pass through directional changes, T-junctions, and piping systems with a varying pipe diameter. This paper presents a numerical application example where the flow induced vibrations (FIV) of a gas transmission system containing a flow control valve (FCV) are analysed using ANSYS CFD and FEA tools, considering a one-way fluid-structure interaction (FSI). To establish the variation of the flow behaviour due to the FCV presence, three specific base cases are considered, corresponding to the maximum, average and minimum pressure drops across the FCV, determining the effects of the corresponding fluid velocities on the vibrations created. The assessment is conducted in line with the provisions included in the Energy Institute guidelines to determine the likelihood of failure of the pipework as a result of the FIV.

1 Introduction

ANSYS computational fluid dynamics and structural finite element analyses were used to investigate the response of a 24-inch diameter mainline section of a Gas Metering Train and the associated Blow Dow Valve (BDV) pipework, located downstream of a Flow Control Valve (FCV), to structural vibrations. It should be noted that the reduced diameter BDV pipework is effectively a ‘dead leg’ branch, at which the structural vibration has been observed during the normal operations. This study aims at investigating the cause of the vibration occurred in the main 24-inch pipeline as well as the BDV dead leg pipework.

The structural vibration is believed to be caused by the fluid behaviour in the piping system. Computational Fluid Dynamics (CFD) analysis was therefore implemented to establish the variation of the flow behaviour in the mainline and smaller diameter branch. Analysis of supplied process data was undertaken, resulting in the definition of three analysis cases that correspond to maximum, average and minimum pressure drops across the FCV. To simulate those conditions, three simplified local analysis models were developed, allowing for the representation of the pressure drop conditions upstream of the BDV pipework and establishing fully developed flow downstream of the FCV, without the need for resource-expensive fully detailed 3D representation of the FCV. The results from these numerical models correlated well with the supplied process data. As such, a further FIV assessment was carried out.

The three local models were integrated into a global model of the Gas Metering Train and computationally intensive steady state and transient CFD simulations were then employed to capture the variation of the internal pressure profile over 10 s. The CFD-predicted pressure profile was then mapped to a structural model of the piping system. The assessment then focused on the predicted vibration characteristics (amplitude, frequency) and associated Likelihood of Failure (LOF) index and the effects of vibration on the fatigue life of the piping system. The vibration assessment was conducted in line with the provisions included in the Energy Institute Guidelines.

2 Local Model

An initial local model was developed in ANSYS Spaceclaim [1] to represent the Flow Control Valve (FCV), which is used to adjust and control the volumetric flow of the gas within the system, and the adjacent piping components. The extent of the local model is as shown in Fig. 1.

The FCV was represented by two 24-inch diameter pipe segments with a reduced diameter central pipe segment in between. The diameter of the central pipe segment, ‘d’, was varied as required to achieve the pressure drop across the FCV for the given process conditions. As shown by Fig. 1, the larger diameter pipe segments were modelled with lengths equal to 15D, where ‘D’ is the diameter of the 24- inch pipe segments. These lengths were selected so that a fully developed flow within the system could develop, and the desired pressure for each case is matched.

Fig. 1.

Extent of local model.

The CFD analyses were conducted using the ANSYS CFX software, within ANSYS Workbench version 2022 R2 [1]. Three analyses were undertaken in order to calibrate the local model. These analyses considered a maximum, average and minimum pressure drop (∆P) cases across the FCV, as seen in Table 1.

Table 1. Field process data for validation of FCV local model

The applied boundary conditions for each analysis are summarized below:

• Upstream velocity applied at inlet

• Outlet pressure difference set to zero

• Downstream pressure used as the domain pressure

• Wall condition defined as no slip, smooth

The pressure drop across the FCV was taken to be the pressure at the inlet minus the pressure at the outlet, such that:

$$ \Delta P = P_{inlet} - P_{outlet} $$

An iterative process was then undertaken whereby the diameter of the central pipe segment was modified in the range 30 mm to 160 mm to develop the appropriate pressure drop, $\Delta P$, as given in Table 1. The results are summarized in Table 2 and agree with the target pressure drop across the FCV seen in Table 1.

Table 2. Central pipe segment diameter and corresponding pressure drop.

From the values reported in in Tables 1 and 2 it can be seen that the CFD predicted pressure drop values and field process data are well matched. The relationship of equivalent length and ID variation was established based on this benchmarking exercise, which allowed for the simplified equivalent approach to be adopted for the representation of the FCV.

3 Global Model

Three separate analysis models were subsequently generated by integrating the three local models, representing the FCV for either the maximum, average or minimum pressure drop condition, into the global model at the appropriate location, as shown by Fig. 2.

Fig. 2.

Extent of global model with integrated local model—highlighted in orange.

The pipework is fabricated from EN 3183 L450Q PSL2 carbon steel line pipe. The material yield strength and ultimate tensile strength are in accordance with ISO 3183:2019 [2] and are reproduced in Table 3.

Table 3. Summary of material properties

Note that to account for the stiffness of the FCV relative to the pipework, the Young’s modulus has been increased to 2.10 × 10⁸ MPa to the extent of the model representing the FCV. Distributed masses (kg) were also applied in accordance with provided details to represent the flange connections at the ends of pipe spools and various equipment weights.

The support boundary conditions were applied over short pipe lengths by constraining displacements in certain DOFs and allowing free displacement in others, depending on the support type at each location. A summary of the boundary conditions applied is shown in Fig. 3. For the fully constrained DOFs, at either end of the model, rigid (infinite stiffness) supports are assumed, while for the free DOFs no restrictions in displacement (e.g., friction, gaps/stops) were considered for the base cases. The two types of conditions were as follows:

• Type A—DOF: x = free, y = 0, z = free,

• Type B—DOF: x = 0, y = 0, z = 0

Fig. 3.

Definition of boundary conditions.

4 Results

An analysis time period of 10 s has been selected for each transient structural analysis. The predicted maximum deflections for Case 1 to Case 3 conditions are summarized in Table 4, with a total deformation plot for Case 3 shown in Fig. 4.

Table 4. Maximum deflections in pipework

Fig. 4.

Case 3: total deformation.

The vibration response of the pipe work was also assessed in accordance with the Energy Institute (EI) [3] guidelines to categorise the risk of fatigue. The assessment is based on the calculated frequency, the vibration velocity (RMS value) and the zones defined in Fig. 5.

The frequency of vibration and RMS values are obtained by interpreting the velocity time history from the FEA. The following equation if applied for the RMS evaluation:

$$ x_{RMS} = \sqrt {\frac{1}{n}\left( {x_{1}^{2} + x_{2}^{2} + \ldots + x_{n}^{2} } \right)} $$

where x_i corresponds to the quantity of which the RMS value is to be evaluated at the i-th time increment.

Based on the observed maximum deflections, one location on the mainline and one location on the blow down valve (BDV) pipework were selected for further consideration, as detailed in Fig. 5.

Fig. 5.

Locations for further assessment: (a) Mainline Elbow (b) BDV Elbow

The extracted velocity time histories for Location 1 and 2 are therefore as given in Figs. 6 and 7, respectively, for all cases. For Location 1, Case 3 conditions results in higher velocity amplitude compared to the other two cases. For Location 2, Case 2 conditions result in higher response in terms of vibration velocities. In both locations, the higher flow velocity appears to affect the vibration response more than the pressure drop across the FCV.

The calculated frequencies and RMS values are summarized in Table 5. These values were superimposed onto the EI Guidelines Pipework vibration criteria for the mainline and BDV pipework, as shown in Fig. 8.

Table 5. Calculated Frequencies and RMS values

Fig. 6.

Location 1, velocity time histories for mainline elbow.

Fig. 7.

Location 2, velocity time histories for BDV elbow.

Fig. 8.

Vibration assessment to EI guidelines: (a) mainline pipework (b) BDV pipework

As shown in Fig. 8, Case 1 and 2 mainline vibrations fall in the “acceptable” range but are very close to the “concern” zone. Case 3 mainline vibrations fall in the “concern area”. For the BDV pipework vibrations all cases fall in the “acceptable” range.

5 LOF Assessment

The Likelihood of Failure (LOF) calculation is a screening process in line with the Energy Institute (EI) [3] guidelines, which is used to determine the fluid velocity up to which the system can operate safely. If LOF takes a value of 0.5 or higher, a detailed analysis should be undertaken. The LOF value for each case was evaluated and the details of the calculations are presented in the following sections.

The kinetic energy of the fluid as a single-phase flow is calculated using all three of the base case velocities, as shown in Table 6, using the equation below:

$$ Kinetic\,\, energy: \rho v^{2} = \left( {actual\,\, Density} \right) \times \left( {actual\,\, Velocity} \right)^{2} $$

Table 6. Kinetic energy at three base case flow velocities

The amount of turbulent energy partially depends upon the fluid viscosity, which is taken into account by the Fluid Viscosity Factor (FVF) [2]. To determine this value, the dynamic viscosity $\left( {\mu_{gas} } \right)$ is needed.

Determining Fluid Viscosity Factor, FVF:

$$ \mu_{gas} = 1.08 \times 10^{ - 5} Pas $$

$$ FVF = \frac{{\sqrt {\mu_{gas} } }}{{\sqrt {1 \times 10^{ - 3} } }} = 0.104 $$

The FVF for the system is 0.104 and this value was used in the LOF calculation.

For each vibrational analysis, the system was split into three sections of straight pipe to be used in the calculation of LOF. The support arrangements for each length of pipe and the length between supports L_Span were used to determine the Flow Induced Vibration factors (Fv), both shown in Table 7.

Table 7. Support arrangements for each pipe length

The likelihood of failure for flow induced turbulence was then determined using the equation below:

$$ LOF = \frac{{\rho v^{2} }}{Fv}FVF $$

where $\rho v^{2}$ is shown in Table 6, FVF calculated as 0.104 and $Fv$ shown in Table 7. The results for L_Span for each case are shown in Table 8.

Table 8. LOF results

In all cases, the LOF value is less than 0.3. According to the EI guidelines, ‘A visual survey should be undertaken to check for poor construction and/or geometry and/or support for the main line and/or potential vibration transmission from other sources’.

6 Conclusions

ANSYS computational fluid dynamics and structural finite element analyses were used to investigate the response of a 24″ diameter mainline section of a Gas Metering Train and the associated BDV pipework, located downstream of the FCV, to structural vibrations.

Three local CFD models, simulating the desired maximum, average and minimum pressure drops upstream of the BDV pipework, were developed, and integrated into a global CFD model of the piping system. Steady state and transient coupled CFD and FEA simulations were then used to predict the system vibrations. The associated LOF values were also evaluated in line with the provisions included in Energy Institute Guidelines. Based on the analysis results presented, it can be concluded that the effect of higher flow velocities can be more significant in terms of the predicted line vibrations compared to the pressure drop conditions. In cases 2 and 3 where the flow velocity was above 6.0 m/s, the predicted vibration levels for the mainline section fall in and around the “concern” zone. However, the LOF values calculated for each case are lower than 0.3 meaning that the pipe system demonstrated no immediate fatigue failure concerns and requires only a visual survey to assess the pipeline.