### High-accuracy density and mass flow rate meters for slush hydrogen.

By measuring the fluid temperature, pressure, and volumetric flow, it
is easy to determine the density or mass flow rate of single-phase fluids
such as liquid hydrogen. However, for slush hydrogen, because density varies
in accordance with the solid fraction, it is necessary to measure the solid
fraction directory.

Regardless of the method being considered, the influence of solid particles
on density and flow velocity measurement must be clarified to improve measurement
accuracies. Given the objective of high accuracy in density and mass flow
rate measurement, new density meter and mass flow meter structures are considered. These
approaches are based on changes in the specific dielectric constant, or
changes in the microwave propagation properties, due to variation in the
solid fraction [4, 5, 16].

Density meter.

In the case of solid particles mixed in a liquid, such as with slush hydrogen,
it is important to consider the behavior of the solid particles in terms
of electrode configuration if the accuracy of capacitance-type density
meter is to be improved. The above figure illustrates the principles associated with the parallel flat-plate type
for single-phase liquid, and the flat-plate and cylinder type for slush
[12].

A combination design featuring a flat-plate together with two cylinders
allows solid particles to easily enter between the electrodes, with a simple
construction that offers high accuracy. The relationship between the capacitance `C` of the capacitance-type density meter and the specific dielectric constant
*ε* is expressed in the above figure. Here, *C*_{0} and *C*_{d} are fixed constants measured in advance in liquid hydrogen. The measurement
of *C* for the density meter placed in slush hydrogen allows determination of
*ε*. The volumetric solid fraction can be calculated from the specific dielectric
constants *ε*_{s} and ε_{l} of solid and liquid hydrogen, while the density of slush hydrogen can
be determined from densities of the solid and liquid.

The figure below presents the solid fraction measurement results for two varieties of flat-plate
and cylinder type electrodes, and for a parallel flat-plate type. In the
case of the parallel flat-plate type, as the solid fraction increased,
the solid particles were unable to sufficiently enter within the electrode
structure, and the solid fraction obtained was lower than the actual density.
In contrast, almost all the measured results for the flat-plate and cylinder
type were in good agreement with the calculated value. In the cases of slush hydrogen and slush nitrogen, density measurement
accuracies were within ±0.5% and ±0.25% respectively [5, 12].

The microwave-type density meter, as shown in the above figure, consists
of micro-wave transmitter and receiver antennas, employing a network analyzer
to measure the phase shift in the microwaves propagated between the antennas.
This new type has been developed, and the measurement is done with respect
to the phase shifts Δ*ϕ*_{1}, Δ*ϕ*_{2} in the microwave propagated between the antennas in liquid and slush hydrogen,
respectively. The relationship between the phase-shift difference Δ*ϕ* = Δ*ϕ*_{2}－Δ*ϕ*_{1} and the change in the specific dielectric constant Δ*ε* for liquid and slush hydrogen on the other is expressed in the above figure.
Here, *λ* is the microwave wavelength and *L* is the distance between the transmitter and receiver antennas. In experimental
results, density measurement accuracy was obtained within ±0.5% [13].

Mass flow meter.

The new measurement principles of the capacitance-type and microwave-type
flow meters in pipe flow are shown in the above figure. These allow the determination of mass flow rate from the measurement
of density and flow velocity of slush hydrogen. A noteworthy aspect of flow velocity measurement is the slight fluctuation
in the distribution of solid particles, i.e., slush hydrogen density fluctuation
[14, 15].

First, capacitance or microwave (waveguide) -type density meters are placed
at two locations along the pipe flow, and the density is measured using
the LCR meter* or network analyzer. Then, the flow velocity *V* is calculated from the delay time *τ* where the cross-correlation function for the density measurement signals
from the two locations is at a maximum, together with the distance *L* between the density meters, such that the mass flow rate can be determined.

Since these methods do not utilize any moving parts such as turbine flow
meters, there is no need to install precooling pipes and valves.

Experimental work was performed using the capacitance and microwave-type
mass flow meters, and density measurement accuracy of ±0.5% was obtained.
Since the accuracy of the flow velocimeter used for calibration is ±5%,
the exact measurement accuracy of this method could not be immediately
confirmed. However, it is expected that the measurement of velocity using
the delay time evaluated from the cross-correlation function would be capable
of high accuracy comparable to that of density.

* LCR meter: Equipment for measuring inductance (*L*), capacitance (*C*), and resistance (*R*). In the experiment, capacitance (*C*) is measured.