Abstract
Flowmeters are essential components in virtually all fluid-handling infrastructure. They play an important role across all stages of the hydrogen value chain, as reliable flowmeters are vital to ensure precise measurements during production, transport, handling, and eventually end-use applications. Among the available technologies, Coriolis flowmeters offer the advantage of directly measuring the true mass flow and not just the volumetric flow. For this reason, and for their high accuracy, rangeability and repeatability, the interest in Coriolis flowmeters has been increasing steadily over the last decades [1]. The prospect of measuring true mass flow directly is especially advantageous for hydrogen applications. Hydrogen is a gas at most relevant conditions, and therefore highly compressible. Its density is also very sensitive to the presence of impurities due to the exceptionally low molar mass. Thus, it can be difficult to accurately determine the density, and thereby mass flow, of hydrogen inside volumetric flowmeters.
Unfortunately, conventional Coriolis flowmeters have an inherent trade-off between pipe stiffness pressure rating and measurement sensitivity. The pipe in a conventional Coriolis flowmeter has two functions. It must be able to withstand internal pressure, and it must be flexible enough to oscillate. This dichotomy is problematic for light gases such as hydrogen. To avoid extreme fluid velocities and large pressure drops, the gas must be pressurized. This requires the pipe to either be thick, and therefore stiff, or be divided into many smaller pipes. A thick and stiff pipe is detrimental to the sensitivity of the flowmeter, and numerous small pipes make for a costly design with a large footprint. When transporting gases, and especially hydrogen, one would like to increase their density by applying high pressure. This requires the pipe to either have a thick wall or a small diameter. Both options make the pipe stiff, and since a conventional Coriolis meter works by oscillating the fluid-carrying pipe, the stiffer pipe will inherently give a less accurate flowmeter.
Here, we present work related to a novel Coriolis flowmeter, developed by Cignus Instruments AS, that circumvents this issue by having the oscillating structure separate from the pipe, as illustrated in Figure 1. Instead of having the pipe be responsible both for withstanding the internal fluid pressure and for oscillating according to the principles of a Coriolis meter, the pipe only needs to contain the fluid. The pipe can therefore be as thick and wide as necessary. As the oscillating structure is placed inside the pipe, it is only sensitive to relative pressure changes along the structure and does not need to be stiff enough to withstand high pressures. In addition to solving the dilemma between pipe stiffness and measurement sensitivity, the freedom to choose both a large pipe diameter and a highly flexible inner structure allows the flowmeter to be completely straight and retain more than 90 % of the full pipe bore. This results in negligible pressure loss compared to conventional Coriolis meters.
The novel flowmeter is modelled using detailed computational fluid dynamics in the OpenFOAM framework [2], and the structural dynamics are modelled using a custom implementation of modal dynamic analysis, where modal decomposition is performed with CalculiX [3] prior to the simulation. This approach allows the structure to be modelled with a very detailed finite element mesh without any effect on the simulation time. In situations where the structure dynamics is governed by a finite number of modes, such as in Coriolis flowmeters, the structure dynamics become computationally trivial, and the computation time is dominated by the fluid simulation and mesh dynamics. The interactions between the fluid and the oscillating internal structure, which is driven by an external driver force, shifts the natural frequency and creates a temporal shift in the oscillations along the structure. The shift in frequency is related to the fluid density, and the temporal shift is used to measure the mass flow. Comparing the model predictions to experimental data shows good agreement, and the model is used to investigate, among other things, the effects of geometry, viscosity and compressibility. Figure 2 shows an illustration of the flowmeter with the internal oscillating structure and a 90° elbow immediately upstream. Figure 3 shows that the simulations predict very little effect of the elbow and therefore that the flowmeter is not sensitive to flow conditioning.
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latest research,” Flow Meas. Instrum., vol. 17, no. 6, pp. 317–323, Dec. 2006, doi:
10.1016/j.flowmeasinst.2006.07.004.
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using object-oriented techniques,” Comput. Phys., vol. 12, no. 6, pp. 620–631, Nov. 1998, doi:
10.1063/1.168744.
[3] G. Dhondt,. The Finite Element Method for Three-Dimensional Thermomechanical Applications, Wiley, 2004.
doi: 10.1002/0470021217