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Study on the influence of reflecting channel position on flow velocity characteristics of ultrasonic heat meter

In this paper, LES (Large eddy simulation) method is used to study the influence of different channel positions on the flow velocity of the ultrasonic heat meter, and the variation of the average linear velocity of different channel with time is researched. Through the calculation results, the velocity characteristics of 11 channels of the U-shaped reflecting device ultrasonic heat meter are analysed. The results show that the vortex behind the reflecting cylinder affects the velocity distribution in the channel. Statistical analysis shows that the linear average velocity in different positions of the channel fluctuates with time, but the fluctuation amplitude is basically the same. The average linear velocity asymmetry of reflecting channel far from the vortex zone is smaller, and the deviation of the average velocity is less than that of the average velocity, therefore, the distribution of the velocity is more reasonable.


Introduction
It is important of the ultrasonic heat meter for the metering and charging in heating reform. Transit time ultrasonic heat meter is widely used in the market, and its measurement accuracy depends on the structure of the internal reflecting channel. The accuracy and stability of domestic meter are poor Compared with the imported, especially in the case of small flow rate. Therefore, the influence of the reflecting channel position of the ultrasonic heat meter on the flow characteristics at low Reynolds number is studies, which based on the method of LES. Many scholars have used LES method to carry out applied research, Zhang Zhao-shun [1] et al. expound the theory and application of LES; Wu Ting, Zhao Yue-zhen [2,3] et al. have studied the near wall model of LES and the method of synthesis of imported turbulence; Ai Guo-yuan, Yu Xi, Jang Hyunchul [4][5][6] et al. have applied LES method to study the wing, circle, the flow around cylinders, horizontal pipes and propellers; the previous research work of the author [7,8] also used the method of LES and PIV to study pipes and obtain some results. In conclusion, the method of LES is less used to study the ultrasonic reflection channel, but it is feasible to study the internal flow field of the ultrasonic heat meter. In this paper, LES method is used to study the influence of the position of the ultrasonic reflection channel on the flow velocity characteristics, and the relevant laws are obtained. It provides a theoretical basis for the selection of the ultrasonic heat meter, and has a certain theoretical significance and application value.

Internal structure of ultrasonic heat meter
In this paper, the structure of a U-shaped ultrasonic heat meter is studied, which is shown in Figure 1. The reflecting device is composed of two stainless steel cylinders, and a 45 degree reflecting surface located on the center of the flow. After two reflections, the acoustic wave is received by the receiving transducer, and the transmitting process is completed.

Computational domain model
In order to eliminate the influence of the inlet section, according to the literature [7,8] , the 10D-length straight pipe is taken before the inlet, and the 5D-length straight pipe after the outlet of the channel. The physical model of the computational domain is shown in Figure 2.

Grid resolution
The method of combining structured grid and unstructured grid is used for mesh generation. For the zone with complex flow in the middle, the structured grid method is adopted, and other zone adopted unstructured grid, and the grid close to the wall is refined. The mesh size of the middle reflection area is 0.8mm, and the total number of meshes is 2122545. The meshing is shown in Figure 3. The LES method requires high resolution grids, and generally requires y+<5, where y+ [1]. is the dimensionless distance from the central mass of the first layer grids to the wall. In this paper, the size of y+ is obtained via trial calculation, and the distribution of y+ is shown in Figure 4. The horizontal ordinate is the size of y+ and longitudinal coordinates is the proportion of size. It can be seen that maximum size are about 1%, which meets the requirements of LES method for grid resolution.

LES model
The mathematical equations of LES used in this paper are as follows: Where ij  is defined as Subgrid stress, and Smargorinsky model is used.

Boundary condition
Inlet conditions: when the flux is 0.05m3/h, the inlet speed is 0.01966m/s; Inlet disturbance: Inlet turbulence intensity I and hydraulic radius D are used, where I = 0.16Re -1/8 = 0.72 and D = 0.003m. Outlet conditions: Free outflow is adopted.

Numerical simulation method
Central difference scheme is used to discretize the diffusion term, and the second-order Euler difference scheme is used to discretize the time term. In this paper, the calculating time step is 0.0005s at the beginning, and then it increases according to the convergence situation. At last, the step time reaches 0.001s after stable flow. A total of 7500 steps were calculated, and the physical time was 7.3235s.

Distribution characteristics of flow field
The whole calculation is unsteady. The flow field at the time t of 7.3235s is analyzed in step 7500 of the calculation process. There are 11 reflecting channels from the two reflection surface, as shown in the Figure 5. It can be seen that there are vortices on the first reflecting cylinder from the velocity distribution in Fig.6, and the action area of the vortices covers the front of channel 7-11. The direction of the velocity vector in the middle is mainly X direction, and the flow tends to be stable. The fluid flow is impeded by the second reflecting cylinder, and velocity vector accumulates on the reflecting surface and flows out from the surface upper forming a trailing vortex area.   Vector of linear velocity of reflecting channel From the distribution of vectors, it can be seen that the velocity vector direction of channel 7-11 varies greatly after the first reflector, and then it is impeded by the second reflector, resulting in upward flow direction. The vortices generated at the top of the first reflector influence the velocity characteristics in channel 7-11, and the propagation of ultrasonic is also affected.

Analysis of the time domain characteristics of velocity in the reflecting channel of ultrasonic heat meter
It is important for the measurement stability of heat meter to the characteristics of linear average velocity in time domain. Therefore, the linear average velocity with time in the reflecting channel is calculated at each time step. Figure 8 shows the linear average velocity in 11 reflecting channels in the time range of 0-7.3235s.   Figure 9. Six channels are located in the central of the pipeline. The average velocities of 1-6 channels are gradually increasing, which is accord with the distribution of velocities in the pipe. After the seventh channel, it is shown that the velocity becomes irregularly, which increases first, then decreases, and then increases. The main reason is that the influence of the vortex region located the first reflector surface.

Conclusion
(1) The vortices generated by the reflecting cylinder of fluid flow will influence the velocity in the channel at different locations, and the velocity distribution law is not consistent with that of in pipe.
(2) The fluctuation amplitude of the average linear velocity in different positions is almost the same with time, which indicates that the reflecting device of U-shaped reflecting device is reasonable.
(3) The average linear velocity in channel 1-6 far from the vortex region is accord with the distribution of velocities in the pipe, and the distribution of the velocity is more reasonable.