# Each-Phase Metering with Gas-Liquid Stratified Flow Based on the Multi-Frequency Coriolis Principle
## 3 Methodology
### The Influence of Flow Patterns on Vibration Frequency Response of the Measuring Tube  
The total mass flow inlet parameters of two-phase fluid (the real values of total mass flow) are respectively set to five conditions: 0.09120, 0.1368, 0.228, 0.3420, and 2.280 kg/s. The flow patterns are shown in Figure 3.  
Figure 3: _Cont._Figure 3 shows the simulation results of stratified flow and bubble flow. When GVF \(\leq\) 4%, the flow pattern is bubble flow with small dispersed bubbles. However, in the process of gas-containing fluid flowing through the measuring tube, due to the influence of pressure drop in the pipeline, the bubbles uniformly distributed at the back of the tube are slightly larger than those at the front. When GVF \(>\) 4%, The flow patterns change with the initial total flow at the inlet. When the total mass flow is low (0.09120-0.3420 kg/s), due to a density difference between gas and liquid, the liquid flows at the bottom of the pipe. The gas flows through the liquid and distributes it in the upper part of the pipeline. The two phases are completely separated by gas-liquid cross-section, showing stratified flow [23]. With the increase in the total mass flow of gas-containing fluid to 2.280 kg/s, bubbles are easy to break under the action of the high-speed flow of fluid, forming a bubble flow with uniform distribution.  
The deviations of vibration frequencies and phase differences of Coriolis flowmeter measuring tube are not only related to the gas content entrained by the measured fluid, but the flow patterns may also have a more significant impact on it. The vibration frequencies of high-order mode increase with the order as a multiple of the basic working vibration frequency. Therefore, the first-order frequency is extracted, as shown in Figure 4.  
Figure 3: The flow patterns in different total mass flows and Gas Volume Fractions (GVFs); (**a**) The flow patterns in different Gas Volume Fractions (GVFs) with total mass flow 0.0912 kg/s; (**b**) The flow patterns in different Gas Volume Fractions (GVFs) with total mass flow 0.1368 kg/s; (**c**) The flow patterns in different Gas Volume Fractions (GVFs) with total mass flow 0.2280 kg/s.; (**d**) The flow patterns in different Gas Volume Fractions (GVFs) with total mass flow 0.3420 kg/s; (**e**) The flow patterns in different Gas Volume Fractions (GVFs) with total mass flow 2.280 kg/s.  
It can be seen from Figure 4 that the vibration frequencies of the tube increase with the entrained gas content when the two-phase fluid with the same mass flow flows through measuring tube. Its frequencies are closely related to the mixing density and fluid-solid coupling of the measured fluid. Besides, when the total mass flow of two-phase fluid with the same density changes, the vibration frequencies of the measuring tube also change. This also means that the flow patterns affect fluid-pipeline coupling, thus influencing the vibration frequencies of the tube. The generation of stratified flow weakens the coupling between the fluid and the pipe, which may be due to the relative motion of the gas and liquid phases to form a wholly separated flow state. In bubble flow, the more uniform the bubble distribution, the stronger the coupling effect. This is because the existence of uniform bubbles only affects the change in mixing density and increase in compressibility but does not show the occupation of liquid space.