A CFD SIMULATION FOR THE ULTRASONIC FLOW METER WITH A HEADER

Original scientific paper Ultrasonic flow meter has been used in natural gas metering for many years, however, the measurement accuracy of the ultrasonic flow meter is affected by the header, which leads to non-perfect fluid state in the flow meter. The objective of this research is to discuss the issues of dual-path ultrasonic flowmeter with a header. Computer fluid dynamic (CFD) method is used to simulate standard turbulent model. It is found that the flow state in the downstream is distorted by the header with secondary turbulence, swirl etc., and the velocity distribution of the gas is asymmetric; the farther the distance between the ultrasonic flow meter and the header, the smaller the distortion and the simulation error. When the downstream straight pipe length is greater than 27 − D (Diameter), the flow state will be steady. With the same diameter of the header, the shorter the meter header the greater the distortion of the gas in the downstream pipe. With the same length of the header, the smaller the diameter, the greater the distortion of the gas in the downstream. These results have a great guiding significance in the optimal design of the flow meter installation structure.


Introduction
Velocity profile refers to the distribution of velocities in the axial direction in the cross-section of the circular pipe [1].In natural gas industry, ultrasonic flowmeter is considered to be an important metering method for its accuracy, high repeatability, wide measurement range, simple operation, easy installation and other advantages [2][3][4][5].However, the accuracy of the ultrasonic flowmeter is affected by different inlet velocity distributions caused by pipe configurations upstream such as bends, headers, pressure regulators or diameter changes, resulting in erroneous measurements by up to several percent [6].For this reason, the research on the accuracy of the ultrasonic flow meter has sparked great interest in flowmeter manufacturers, and much work has been done [7][8][9][10][11][12], including experimental method, simulation and theoretical analysis.According to experimental methods, Millán et al. have studied the zero-flow offset variation caused by inhomogeneity and nonlinearity of pipe materials.They found that when using nonhomogeneous and nonlinear pipe materials, the measurement error would depend on the acoustic characteristics of the pipe material [13].In terms of simulation, Byunghad studied the completely velocity distribution of rotating and swirling turbulent flows in circular pipes by using computational fluid dynamics (CFD) simulation to investigate the effect of distorted flow profiles, especially the effect of out-ofplane double bent pipe on ultrasonic flow metering [14].Luca et al. simulated ultrasonic flow meter by modelling the wave propagation in solids with the equations of linear elasticity and the linearized Euler equations in fluids [15].As for theoretical analysis, Chen et al. proposed a novel design methodology of continuous ultrasonic flow meter [16].Furthermore, some researchers have turned their attention to the application of the ultrasonic flow meters in wet gas.Ramadas presented a finite element study with regard to fundamentally understood ultrasonic transit-time metering principles of wet-gas measurement applications [17].However, it is not known how the header affects the accuracy of ultrasonic flow meter.The purpose of this study is to assess how the header upstream affects the ultrasonic flow meter by CFD with the standard k-ε turbulent model.The influence of meter header length and diameter on metering is determined.

The mathematical method
The standard k-ε model is one of the most widely used models in the turbulence simulation for its high stability, economy and accuracy [18÷20].The model is often used for isotropic uniform turbulent flow.Two basic transport equations need to be solved for this model, the kinetic energy turbulence k, and the turbulent dissipation energy ε [21]: where ρ is density of the fluid, k is kinetic energy turbulence, ε is turbulent dissipation energy, t is time, u is mean velocity, μ is viscosity.
The quantity G k appearing in both equations is a generation term for turbulence.It contains products of velocity gradients, and also depends on the turbulent viscosity.
μ t is turbulent viscosity defined by Eq. ( 3) with the turbulent kinetic energy k and the turbulent dissipation energy ε.

Modelling
As shown in Fig. 1, the geometry model is set up by Pro/E.The size of header is DN300×4400.The pipeline length from the entrance to the header (L 3 ) is set to three times the diameter (3−D) and the length from the header to the ultrasonic flow meter (L 1 ) is 30−D.The length of metering is 4−D, the diameter of the metering pipeline is DN150.
Figure1 The geometry model for CFD simulations ANSYS-ICEM is employed to perform all geometry generation and meshing.As shown in Fig. 2, a suitable grid density is reached by repeating computations until a satisfactory independent grid is found.The number of mesh used in calculation is 252278.

Figure 2
The grid distribution of computational model

Boundary conditions
The inlet boundary condition is "Velocity-inlet", the exit boundary condition is "outflow", and the wall boundary condition is default.
A total of five groups of flow rate are collected from the minimum flow rate to the maximum flow rate, which are 39.71 m 3 /h, 215.71 m 3 /h, 558.86 m 3 /h, 875.73 m 3 /h and 2131.91 m 3 /h, respectively.The operating temperature is 12 °C, the operating pressure is set as 0.8 MPa.The gas density is 0.68 kg/m 3 , and viscosity is 1.603×10 −5 m 2 /s.The velocity of sound is 340.3 m/s.

Experimental method
Initially, experiments are carried out at a natural gas station to produce required data for boundary conditions definition and results validation of the CFD simulations.The ultrasonic flow meter used is the parallel path time-of-flight flow meter made by Daniel, whose uncertainty is less than 0.1%, and its metering range is from 35 m 3 /h to 2210 m 3 /h.
The flow medium in pipe is natural gas, the temperature is 12 °C, density is 0.68 kg/m 3 , and viscosity is 1.603×10 −5 m 2 /s.The operating pressure is 0.8 MPa.The velocity of sound is 340.3 m/s, and the minimum corresponding Reynolds number (Re) is 5802.A total of five groups of flow rate is collected: 39.71 m 3 /h, 215.71 m 3 /h, 558.86 m 3 /h, 875.73 m 3 /h and 2131.91 m 3 /h.
The numerical method used in this study has been validated against these experimental results.The flow rate simulated is compared with the real flow rate of the ultrasonic flow meter in the gas station.It is found that the maximum relative error is 3.73%, and the minimum relative error is 0.16%, all within acceptable range.Moreover, the measurement error of simulation and experimental are almost the same.

Results and discussion 3.1 The velocity distribution
Fig. 4 and Fig. 5 show the contours of the XY velocity and the velocity distributions across the crosssection of different length downstream when the flow rate is 39.71 m 3 /h.As shown in Fig. 4, the profile of the axial flow velocity is distorted by pipe header, and the distortion becomes more serious at pipe interchanges.It can be seen that the flow profile inside the pipe is significantly asymmetric due to the pressure difference.The flow state in the downstream is distorted by the header with secondary turbulence, swirl etc., and the velocity distribution of the gas is asymmetric.From the contour plots, it is concluded that the higher the Q value, the greater the axial velocity effect, the greater the distortion.On the other hand, the length downstream needed to recover the gas velocity distribution is not proportional to flow rate.When the downstream length of the meter header is typically 27 times or more than that of the pipe diameter, the flow state under five different flow rates is stable.

The influence of meter header length on metering
In order to identify the influence of meter header length on metering, two headers are simulated with the same diameter (DN300), and the lengths are 2.6 m, 4.4 m, respectively.Fig. 7 and Fig. 8 display the indication errors while the meter is located at 5D, 10D, 16D, 20D, 25D and 27D downstream the header in the pipeline, respectively.
As shown in Fig. 7 and Fig. 8, the indication errors of the shorter header vary between −0.26 % and 2.03 %, and the indication errors of the longer header at different location vary between −0.41 % and 1.84 %. the distortion is getting smaller with the longer distance between the ultrasonic flow meter and the header.It can be seen from Fig. 7 and Fig. 8 that the indication errors become smooth when the ultrasonic flow meters are located at 25D, 27D, and the indication errors of DN300×2600 are 0.50 % and 0.47 %, respectively.The indication errors of DN300×4400 are 0.47 % and 0.44 %, respectively.Fig. 9 summarizes the trends of indication errors while the meter is located at 25D downstream the header in the pipeline, the lengths of the meter headers are 2.6 m, 4.4 m, respectively, and the diameters of the headers are the same (DN300), the flow rate is collected from the minimum flow rate to the maximum flow rate, which are 39.71 m 3 /h, 215.71 m 3 /h, 558.86 m 3 /h, 875.73 m 3 /h and 2131.91 m 3 /h.As shown in Fig. 9, the indication error of DN300×2600 is bigger than DN300×4400.It means that the shorter the pipe header, the more distortion in the case of the same diameter.

Influence of diameter of meter header
Fig. 10 and Fig. 11 display the indication errors while the meter is located at 5D, 10D, 16D, 20D, 25D and 27D downstream the header in the pipeline, the diameters of the meter headers are DN300, DN550, respectively, and the length of the headers is 4.4 m.
As shown in Fig. 10 and Fig. 11, the indication errors of the larger header at different locations vary from −0.20 % to 1.20 %, the indication errors of the smaller one varied s between −0.41 % and 1.84 %; It also can be seen that the trends of indication errors vary greatly while the meter is located at 5D.When the length from the transonic flow meter to the header is greater than 10−D, the trends of indication errors of the two headers are the same, because the distortion gets smaller with shorter distance between the ultrasonic flow meter and the header.The indication errors become smooth when the ultrasonic flow meter is located at 25D, 27D, the indication errors of DN550×4400 are 0.43 % and 0.42 %, respectively.The indication errors of DN300×4400 are 0.47 % and 0.44 %, respectively.

Figure 12
Indication error with different diameters of header Fig. 12 summarizes the trends of indication errors while the meter is located at 25D downstream the header in the pipeline, the diameters of the meter headers are 300 mm, 550 mm, respectively, and the length of the headers is 4.4m, the flow rate is collected from the minimum flow rate to the maximum flow rate.As shown in Fig. 12, the indication error of DN300 is bigger than DN550.It is because the bigger the pipe manifold, the less distortion of the gas field in the case of the same length.

Conclusion
This study investigated the influence of the meter header on the measurement accuracy of a dual-path square shaped ultrasonic flowmeter by using CFD simulations.Based on standard k-ε turbulent model, a finite volume method is implemented.By analysing the velocity distribution inside the pipeline downstream the header, the effect of the header on the measurement accuracy is calculated.The results obtained from CFD simulation show that the longer the distance between the ultrasonic flow meter and the header, the smaller the distortion and the simulation error.When the downstream straight pipe length is greater than 27-D, the flow state would be steady.The shorter the meter header, the greater the distortion of the gas in the downstream pipe in the case of the same diameter of the header.With the same length of the header, the smaller the diameter, the greater the distortion of the gas in the downstream.This result has a great guiding significance in the optimal design of the flow meter installation structure.

Fig. 3 Figure 3
Figure 3The process flow diagram for metering

Figure 6
Figure 6 Contours of the XY velocity with different flow rate

Figure 7
Figure 7 The trends of indication errors at different location (DN300×2600)With the increase of distance from the flowmeter to the header, the indication error decreases.This is because

Figure 8
Figure 8 The trends of indication errors at different location (DN300×4400)

Figure 9
Figure 9 Indication error with different length of pipe manifold

Figure 10 Figure 11
Figure 10 The trends of indication errors at different location (DN300×4400)