Globe valve in single phase flow: experimental and CFD analysis

Flow-induced vibration (FIV) poses risks to engineering systems, prompting efforts for safety. Valves, crucial for fluid control, can induce turbulence-related mechanical loads, leading to vibration and potential failures. This paper combines experimental and numerical methods, using computational fluid dynamics (CFD) for flow analysis. A test loop with nine pressure sensors assesses water flow through a globe valve, testing various conditions. Dimensionless power spectral density (PSD) of pressure fluctuations is compared with CFD results. Steady simulations precede computational fluid dynamics – large eddy simulation (CFD-LES) for quantitative data. Industrial-scale valve analysis explores scalability using different protocols, contributing to design strategy improvements.


Introduction
Industrial piping networks are subjected to dynamic loadings that may lead to significant vibration levels, which in turn can possibly result in a fatigue failure.One of the loading sources responsible for piping vibration is the turbulent flow of dense fluids within the system itself.The internal flow of liquids in industrial applications is generally turbulent, the fluid-structure interaction phenomenon is much more significant around piping singularities such as sudden changes of the cross-section area or of the flow direction.At these specific locations, the flow is disturbed and becomes highly turbulent, provoking a broadband low-frequency excitation that might possess enough energy to result in a wide-range periodic displacement of thin-walled structures [1].Understanding this dynamic behavior is currently very important to the energy sector, which wants to be able to predict the flow-induced vibration phenomenon within its piping systems, among others.The accurate modelling of flow through a pipe singularity is thus critical in this process, as its unsteady pressure field serves as the excitation mechanism [2].The present study focuses on the straight globe valve singularity and is divided in two different steps.In order to be able to evaluate the excitation induced by a dense fluid flowing through a straight globe valve in a duct, a combined experimental and numerical approach was undertaken.In a first step, a closed water loop was designed to allow for the simultaneous measurement of wall-pressure fluctuations and vibrations in a test section where the valve is believed to be the only significant turbulent source.In the second part, the section was modelled and Computational Fluid Dynamics (CFD) simulations were performed to provide a clearer picture of the flow structures responsible for the excitation [3].To understand the behavior of the flow, the steady simulations (Reynolds Averaged Navier-Stokes RANS computation) of the flow have been first performed.In order to further analyse and produce quantitative numerical data for comparisons with the experiments, CFD-LES simulations have been performed.The analysis of pressure fluctuations at sensors positions and comparisons with the experimental data provide a quantitative assessment of the turbulence intensities and loads on the inner faces of the structure.

Material and Method
The experimental apparatus and the corresponding computation set-up are detailed in the present section.

2.1Valve selection
Globe valve type was selected based on two main criteria.The first criterion was to select a valve commonly used in the Oil and Gas industry.Globe valve type is one of the most used to regulate the flow.The second criterion was set from a more practical point of view: the valve should exist in diameter that can be adapted on existing VibraTec test loop (DN40).
The body and the bonnet are made of cast iron, the seat in stainless steel, the stem in AISI 304 and the packing in graphite.The studied valve is the single seat globe valve.It consists of three main components: body, trim, and actuator.The body of the valve houses the trim, which is made up of the plug and seat, and the actuator positions the plug.A view of the valve is given in Figure 1.The inside of the valve can be visualized in Figure 2. The globe valve has been cut in half to recreate precisely the internal cross section of the equipment for the simulation.

Experimental set-up
The pipe made of transparent PVC was deployed and the water was used as the working fluid.A cylindrical reservoir is followed by a centrifugal pump designed for a maximum flow rate of 50 m3/h, which means a maximum velocity of 10 m/s in the circular cross-section pipes of inner diameter  = 42.6 mm.The flow is then led to an acoustic damper consisting of a longitudinal cylindrical volume.
Therefore, one acoustic damper located upstream of the valve and another one located downstream define the limits of the test section, isolating it from parasite pressure fluctuations in the frequency range of interest to this study, which is located between 0 and 100 Hz.
Fifteen meters of straight tube, corresponding to more than 350 times the inner diameter of the pipe, connect the first damper to the valve in the test section.This length easily ensures developed turbulent flow in the valve, considering the range of diameter-based Reynolds numbers to be imposed to the flows, which are of the order of 105.The second acoustic damper is reached by a straight tube, and the end of the test section is located downstream the valve.The set-up is presented in in a schematic diagram as shown in Figure 3: A variable-frequency drive is used to control the pump rotation speed and it allows the tests to be performed in the seven flow regimes as shown in Table 1 The fluctuating pressure induced on the inner walls of the pipe was measured using 10 piezoelectric dynamic pressure sensors in the valve and in immediate downstream sections, as shown in Figure 4 and Figure 5.One pressure sensor was implemented upstream and far from the valve in order to be used for signal acoustic decontamination.The frequency response function was simultaneously measured using a triaxial accelerometer placed on the top of the valve.A SIEMENS TestLab frontal analyzer was used for the synchronous time signal acquisition.Each signal was collected over 100 seconds with a sampling frequency of 2.56 kHz.The locations of pressure sensors were determined in order to get the most relevant pressure fluctuations.The pressure sensors 8 and 9 are placed on the valve section.The pressure sensors 1, 3, and 4 are placed 51 mm from the valve end in three different axial positions to study the 3D effect of the fluctuations.The pressure sensors 2 and 5 are located 77 mm from the valve end.The pressure sensor 6 is located 97 mm from the valve end.Lastly, the pressure sensor 7 is placed 333 mm from the valve end, the lowest pressure fluctuation levels may be expected at this distance.It is important that the measured data transcribes only the physical phenomenon to be measured.In addition to the calibration of the sensors, the pressure sensor mounting is delicate because the sensor must be exactly at the same level as the inner pipe surface.Specific mounting parts were designed to reach this objective.

Computational approach
The methodology for the computational approach is described in this section.

Fluid model
Flow simulations for the globe valve case have been performed considering a domain of 0.6 m, with around 7 downwind the singularity.Figure 6 and Figure 7 represent the mesh used for these computations.

Flow dynamics
Based on the relevant conceptual model and set of equations for this specific flow through the valve, the basic idea is to use appropriate solutions and algorithms capturing the turbulent fluid motion.In the current study, where, given the flow quality and regimes, the flow is considered as isothermal and incompressible, the Navier-Stokes equations governing the fluid behaviour can be simplified as: where: , the density of the fluid , the pressure , the vector velocity , the stress tensor The Navier-Stokes equations are nonlinear partial differential equations.The nonlinearity is the main contributor to the turbulence [4].Solving the unsteady Navier-Stokes equations implies that one must take into account all the space-time scales of the solution for a result with maximum quality.Note that the discretization has to be fine enough to represent all these scales numerically.
There are several common ways of reducing the number of degrees of freedom in the numerical solution.The first one is to calculate the statistical average of the solution directly, (RANS method) which is used mostly for engineering calculations.The exact solution of the velocity  splits into the sum of its statistical average 〈〉 and a fluctuation ′.(, ) = 〈(, )〉 + ′(, ) The statistical character of the solution prevents a fine description of the physical mechanisms.On the other hand, it is an appropriate approach for analysing performances as long as the turbulence models are able to reflect the existence of the turbulent fluctuation ′ effectively.Another method mentioned in our work, is the LES method (Large eddy simulation).LES is a popular technique to simulate turbulent flows.An implication of Kolmogorov's theory of self-similarity is that the large eddies of the flow are dependent on the geometry while the smaller scales more universal.This feature allows one to explicitly solve for the large eddies in a calculation and implicitly account for the small eddies by using a subgrid-scale model (SGS model).The simulations were performed considering Fluidyn-MP and LES code softwares.

Results and discussion
The experimental and the computational fluid dynamic results are described in this section.The pressure fluctuations are measured in the time domain.The effect of the flowrate, the evolution of pressure fluctuation with distance from the source and the influence of valve opening are studied.Further in this section, a dimensionless analysis comparing both experimental and simulations are presented.

Experimental results
The pressure fluctuations measured are initially given as time signals.The first post-processing step was to evaluate the auto-spectra, the cross-spectra and the coherences through classic signal analysis.The pressure Power Spectral Densities (PSD) are given in Pa²/Hz.
In order to analyze the turbulent contribution to the excitation separately, it is important to remove the acoustic contribution from the pressure fluctuation signal.This decontamination was undertaken using two different pressure signals obtained by transducers situated at a distance greater than the typical length scale of the largest turbulent structures.At such a distance, the correlated part of the signal must come from an acoustic con)tribution, and can be eliminated.The remaining signal is considered to primarily contain the influence of the local disturbed pressure field.The correlation between the reference signal  and the signal to be decontaminated  is calculated as follows: where  is the cross-spectrum and  and  are the reference and target auto-spectra, respectively.The decontaminated target signal can be expressed as: Cavitation has been encountered for some of the regimes.This phenomenon has limited the range of flowrate studied for this configuration, cavitation inducing vibration and noise regimes that are not in the scope of this project.

Influence of flowrate
Comparison was made for all pressure sensors for different flowrates.Results are presented for sensor 8 as depicted in Figure 8 for the following flowrates: 5 m 3 /h; 10.1 m 3 /h, 15.1 m 3 /h and 20 m 3 /h.The following observation can deducted: the pressure fluctuations increase when the flow increases.Turbulent energy is higher when the flow is higher.This conclusion is valid for all sensors.

Influence of valve opening
A comparison was made for all pressure sensors for different valve openings.Results are presented for sensor 8 for the flowrate of 15.1 m 3 /h in Figure 10.Pressure fluctuations are higher when the opening is larger.

Dimensionless analysis
The dimensionless approach makes it possible to obtain reduced data depending on a minimal number of parameters as described in [5].Rendering physical quantities dimensionless has numerous advantages.It enables comparison of measurements from two different systems.It determines if behavior is associated with an acoustic or a turbulent phenomenon.It validates hypotheses such as the homogeneity of the turbulent flow.Dimensionless analysis relies on the Vashy-Buckingham theorem which specifies that a physical relation can be expressed independently from the system of units used and that the minimum number of parameters needed corresponds to the number of quantities in the relation minus the number of fundamental units in which they are expressed.
From a practical point of view, the quantities used are the frequency and the Pressure PSD.Therefore, the characteristic values that are used must be chosen as to make the pressure PSD and the frequency dimension-less.The dimensionless analysis shows a high correspondence between different flow rate configurations.The same comments can be made as for the analysis with dimensions.

Computational fluid dynamic results
The computation fluid dynamic results are described in this section.

Steady computation
To understand the behaviour of the flow, the steady simulations (RANS computation) of the flow have been performed for the three different openings and for a same mass flowrate  = 4 3 /ℎ.Figure 12, Figure 13 and Figure 14 show the pressure and the velocity vectors for the three different openings.The flow inside the globe valve is complex.The flow in upper area of the valve, (above the plug) is high for small opening meanwhile the velocity is almost null for the intermediate one.

LES Computation
In order to further analyse and produce quantitative numerical data for comparisons with the experiments, the CFD-LES simulations have been performed.The LES simulation has been produced on a global pipe + valve length of 0.45 m (equivalent resolution at the surface leading to 6.3 million cells max).
A first qualitative analysis is produced using the visualization of vortical structures onset, development and decrease downstream the valve.The vortices can be visualized for the different cases in order to gain insight on the localization of the vortices generation and mechanism.To identify the coherent structures in the LES computations, two methods were used.Each of these methods has its own advantages and drawbacks.They are exploited in order to "visualize" the vortex creation, detachment and subsequent scale cascade downstream; such qualitative analysis is then used in order to assess the flow and geometry patterns that may trigger the turbulence.The Q criterion has been proposed by Hunt et al. [6].The Q criterion gives a local equilibrium between two types of flows: a simple rotation and a simple deformation.Vortices in which the rotation is predominant take precedence over the dissipation of energy (pure deformation) are associated with a positive Q criterion.The purely dissipative zones will be associated with a negative Q criterion.
The 2 criterion has been proposed by Jeongg et al. [7].It consists in finding the eigenvalue of the symmetric tensor of the velocity gradient tensor.Area with negative eigenvalue matches with local minimum pressure induced by rotation of the fluid.However, for quantitative assessment and comparison with experimental data, the pressure fluctuations at several point locations on the wall will be preferred.The following figures show the same Q and 2 iso-contour for different geometries and configuration.The iso-contour for Q criterion is colorized by the vorticity of the fluid in the pipe direction.This coloration distinguishes clockwise and anti-clockwise rotating vortices in the pipe.The flow and the vortices generations are symmetrical to the central plane.There are as many clockwise vortices as anticlockwise vortices in all configurations.As the numerical domain is fully symmetrical and that the inlet condition is uniform, this behaviour was expected.Similarly to the previous steady state simulation, the behaviour of the flow depends drastically on the opening of the valve.When fully opened, the vortices are present in the entire region above the plug.The configuration for the fully opened valve has a flowrate superior to the other configurations, the number of vortices with energy corresponding to this threshold for  and 2 is expected to be higher.

Pressure PSD analysis
The analysis of pressure fluctuations at sensors positions and comparisons with the experimental data provide a quantitative assessment of the turbulence intensities on the inner faces of the structure.For all sensors localized in the downwind pipe (sensor 1, 3 and 6), the intensity and the variation of pressure PSD with the frequency matches between experimental and numerical results.Regarding the sensor 8, the experimental pressure PSD is constant until a specific frequency then decreases slowly similarly to others sensor.The numerical results have a same shape and intensity but the limit frequency is slightly lower.The extended flow regime  = 25 3 .ℎ−1 has exactly the same behaviour as the other flow rate but with higher energy in all frequencies.It appears that the turbulent energy as produced for the 4m 3 /h rate within the simulation is weaker when compared to the experimental data.This difference may be due to the fact that experimentally it was difficult to control the flow for low rates.The experimental rate may be larger than the sought rate of 4m 3 /h.The numerical model used in the CFD solution was developed by cutting the experimental valve and con-ducting a precise 3D point-to-point scan of its internal structure.However, the surface of the 3D CAD was smooth compared to the real one.Indeed, surface roughness seems to be larger, thereby producing higher turbulence levels.A dimensionless analysis was performed on computed pressure PSD for different pressure sensors and tested configurations.Dimensionless curves for sensor 3 are given in the following figure: The dimensionless plots collapse to a quasi-universal envelop curve regardless on the opening state of the valve and for various flow rates.The CFD Solution seems to produce more energy at very low frequencies: However, one may notice that the lowest frequencies results depend on the duration of the computation which appears to be quite short to give a correct representation for the low frequency range.The second notice is that as shown in the experimental data, the curves in this frequency range are shifting with Strouhal number.This content may therefore be related to low periods fluctuations of the mean flow (not related to turbulence).

Conclusion
Wall pressure fluctuations generated by globe valve were obtained by both experimental and computational approaches.CFD computation using Fluidyn MP and LES code enable to get a view of the vortices generation at the valve and how they will behave in its vicinity.Experimental results help to validate the CFD modeling assumptions.From CFD point of view, it appears clearly that a LES computation is mandatory to catch the mechanisms of interest.
By comparing experimental and CFD pressure fluctuations, several conclusions can be drawn.The match between experimental and computation results can be considered as satisfactory, as similar trends are observed: increase of pressure fluctuation with flowrate increase, increase of pressure fluctuations with valve opening, decrease of pressure fluctuation with distance from the valve.The dimensionless analysis presents satisfactory results for both measurements and computations.One of the major limitations of this study is that the findings are only applicable to the type of valve tested.Computations were performed using another valve design in consideration, and the findings in terms of energy intensities are substantially different.It would be interesting to investigate alternative valve designs in order to consolidate the findings.

Figure 1 .
Figure 1.Representation of the globe-valve used in the experiments.

Figure 3 .
Figure 3. Globe valve implementation in test zone.

Figure 4 .
Figure 4. Position of the sensors and the accelerometer for the Valve experiment.

Figure 6 .
Figure 6.Mesh of the Valve simulation -fully opened.

Figure 7 .
Figure 7. Zoom on the valve for the three different openings of the Valve simulation.

Figure 12 .
Figure 12.Pressure and velocity vector field on a vertical plane for the valve simulation (opening 1/3).

Figure 13 .
Figure 13.Pressure and velocity vector field on a vertical plane for the valve simulation (opening 2/3).

Figure 14 .
Figure 14.Pressure and velocity vector field on a vertical plane for the valve simulation (opening 3/3).

Figure 18 .
Figure 18.Pressure PSD for completely open valve at different flowrate (sensor 6), measurement top at CFD bottom.

Table 1 . Experimental cases description. Case number Flow Rate (m 3 /h)
: