JSSSJournal of Sensors and Sensor SystemsJSSSJ. Sens. Sens. Syst.2194-878XCopernicus PublicationsGöttingen, Germany10.5194/jsss-6-135-2017Capacitive gas-phase detection in liquid nitrogenKandlbinderChristophhttps://orcid.org/0000-0001-8092-2088FischerauerAliceMöschMarioHellingTobiasFischerauerGerhardSieglMartinChair of Measurement and Control Systems, Center of Energy
Technology (ZET), University of Bayreuth, 95440 Bayreuth, GermanyInstitute of Space Systems, German Aerospace Center (DLR), 28359
Bremen, GermanyChistoph Kandlbinder (mrt@uni-bayreuth.de)2March20176113514313August20161February201712February2017This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://jsss.copernicus.org/articles/6/135/2017/jsss-6-135-2017.htmlThe full text article is available as a PDF file from https://jsss.copernicus.org/articles/6/135/2017/jsss-6-135-2017.pdf
The main and upper stages of heavy lift launchers for space applications are
often fuelled by cryogenic liquids. In order to enable the re-ignition of a
cryogenic upper stage for orbital changes, it is crucial to study the
behaviour of these fluids in microgravity. As gaseous bubbles entering the
fuel lines of the engine can cause the destruction of the engine, these
bubbles are a risk for the functionality of the re-ignition mode. To measure
an evolving gaseous phase and its volume, a capacitive measurement system for
two-phase mixtures was realised. Its electrodes are arranged in such a way
that phase changes inside a vessel can be detected without parasitic heating
under cryogenic conditions. Two cases have been investigated: a fill-level
measurement involving a large gas bubble above a homogenous liquid on the one
hand, and the identification of a bubble stream inside a liquid on the other
hand. The system concept was tested in a cryogenic environment allowing the
controlled generation of bubble streams inside liquid nitrogen and of a
contiguous gaseous volume above the liquid. The characteristics of the
measurable capacitances of different pairs of electrodes were experimentally
determined and compared with finite-element simulations (Ansys). In addition,
the electrical flux density was computed to corroborate the simulated
capacitance curves with theoretical statements. The experimental findings
closely agree with the simulated results if possible disturbances due to the
characteristics of the capacitance measurement hardware are properly taken
into account. Thus, by measuring various capacitances, it was possible to
determine the level up to which a receptacle inside a liquid-nitrogen tank
was filled with liquid (the space above the liquid being taken up by gaseous
nitrogen), to identify the existence of a bubble stream in the liquid
nitrogen and to demonstrate that the capacitance measurement results enable
one to differentiate between the two cases.
Introduction
For future space vehicles like the Ariane 6 rocket of the European Space
Agency (ESA), re-ignition of the upper stage driven by cryogenic liquids
will play a key role. Upper stages already surrounding Earth must re-ignite
their thrust engine to change into a higher orbit. This possibility could
open up new opportunities for space applications, like releasing one part of the
payload into a lower orbit and another part into a higher orbit (Stolten and
Emonts, 2016).
In order to observe fluid phenomena occurring in microgravity and to
eventually influence their behaviour, it is crucial, especially for
partially filled tanks, to determine the location of the liquid phase and
the topology of the free surface. As capillary forces are dominant under
microgravity conditions, these forces determine the shape and position of
the free surface. Additionally, gas bubbles can come into existence by
sloshing, changes in gravitational forces, or external heat input. If these
bubbles enter the fuel lines of the turbopumps, the pumps can be destroyed
by cavitation effects. This would render a re-ignition impossible. To analyse
these phenomena, experiments with suitable measurement systems are
inevitable (Stolten and Emonts, 2016; Siegl et al., 2015).
Cryostat as measurement environment. (a) Structure of the cryostat.
(b) Built-in cylindrical receptacle with foil heater and camera.
(c) Pressure–temperature (p-T) diagram of liquid nitrogen (LN2) (Span et al.,
2000).
Such measurement systems should only generate a negligible amount of heat
input into the cryogenic liquid. In addition, they are required to work
under cryogenic conditions and to determine the spatial distribution of
gaseous phases (bubbles) in a non-invasive manner.
Current measurement systems for cryogenic environments use gamma-ray-based
(Carapelle and Colette, 2005), microwave-based (Ohira, 2004), radio-frequency-based (Filippov et al., 2013), resistive, or capacitive (Jiang and
Zhang, 2011) principles. Some of them intrude into the volume under
investigation, and some can lead to a local heat input or other parasitic
effects (Mukhopadhyay, 2010). Among them, capacitive sensors promise a high potential to not only
determine the position of the surface of a liquid phase (i.e. the position
of the liquid-to-gas interface), but to also be cost-efficient, simple, and
to show fast reaction times (Carapelle and Colette, 2005; Medeova et al.,
1998; De Kerpel et al., 2013). They neither disturb the liquid movement nor
do they heat the liquid. The required electrodes can be integrated into
walls of fuel lines or smaller tanks inside space systems in such a manner
that the tank geometry need not be modified (Nurge et al., 2003). The
capacitive observability of a single gas–liquid phase boundary under
cryogenic conditions has been demonstrated by Hennes and Barnard (1964) and
Kügler et al. (1984) with liquid nitrogen (LN2) as the liquid; based on
this, a fill-level resolution of ±1 mm was reached. Successful fill-level measurements have also been reported by Matsumoto et al. (2011) with
liquid hydrogen (LH2). The earlier studies, of course, did not have access
to modern electronics and thus had to limit themselves to very specific
geometries and measurement purposes. But even the recent work in Matsumoto
et al. (2011) did not aim for a detailed investigation of the electrode
geometry, its influence on the measurable capacitances, the information
which may be extracted from these capacitances on quantities other than the
fill level, and the possibly error-producing influence of the capacitance
measurement hardware. We have designed and tested a capacitive system for
gas-phase detection under cryogenic applications. We specifically
investigated the capacitance measurement process itself and how well the
system can differentiate between single-phase boundaries (large gas bubble
above a sea of LN2 as it is assumed in fill-level measurement) and
multiple phase boundaries (stream of many small gas bubbles rising in a sea
of LN2) as such effects are likely to occur in zero-gravity
environments.
HardwareCryostat
Since the measurement system that will be described later has to be tested
in cryogenic liquids, a cryostat is used as a test environment (Fig. 1a
and b). The inner tank of the cryostat could be pressurised up to 4 bar
while the space between the inner and outer tank could be filled with LN2
for further thermal isolation from the environment. Inside the inner tank, a
foil heater was mounted for defined bubble generation by local heat input
into the LN2.
The liquid–vapour system in the cryostat was either kept on the boiling curve
or in a slightly subcooled state. By adjusting the pressure, it was then
possible to control the volume of gaseous nitrogen inside the tank. When the
pressure rose inside the cryostat upon closure of a valve, the gaseous
volume shrank because of condensation processes, and the liquid assumed a
subcooled state. This is visible in a pressure–temperature (p-T-) diagram
(Fig. 1c). The working point is marked by a red circle located on or
slightly below the boiling curve. When the pressure rises, the working point
moves upward into the region associated with the liquid state (blue circle).
As a consequence, a gaseous volume trapped in a liquid phase condensates. By
using these principles, the gas-to-liquid ratio inside this trapped volume
can be controlled.
However, the foil heater can generate bubbles by locally heating the LN2 so that subcooled nucleate or film boiling can come into existence.
These generated bubbles can rise until they reach the surface of LN2. If they are trapped while rising onto the surface by special
equipment, they coalesce and form a gaseous volume inside the LN2.
Measurement system
The exemplary configuration used in this work consists of a
circular cylindrical polycarbonate receptacle open at the bottom, with a lid
on top and mounted inside a LN2-filled cryostat. This configuration allows
the regulation of the fill level by (de-) pressurisation, as is the case in many
space systems. Bubbles rising from the liquid volume below the receptacle
are trapped by it. These local phase changes from liquid to gas are
recognised by measuring the capacitances between different electrodes
located on the inner surface of the cylinder wall and the lid. The basis of
the liquid-gas differentiation is the fact that the permittivities of liquid
and gaseous nitrogen differ from each other (εr,LN2≈1,43, εr,N2(g)≈1,0) (Murphy and Morgan, 1937).
Photograph of the circular cylindrical polycarbonate receptacle
with five electrodes of different shapes.
The geometry of the cylinder and its electrodes is shown in Fig. 2. The
receptacle has an inner diameter of 80 mm and a height of 30 mm. Electrodes
2 and 4 have areas of 900 mm2 and electrodes 1 and 3 have areas
of 1800 mm2. The circular ring electrode at the top of the
lid has inner and outer diameters of 40 and 60 mm, respectively. The
closest distance between electrodes 2 and 5 is 10 mm, and that between
electrodes 1 and 3 is 80 mm. The geometry was chosen so as to evaluate the
differences in capacitance due to different electrode geometries and their
arrangement on the one hand, and to make an optical inspection possible on
the other hand. The dashed lines shown in Fig. 2 mark the intersections of
vertical planes (planes containing the cylinder axis) and the top side of
the receptacle lid; field simulations in these planes will later be
presented to support certain statements about the characteristics of the
measurement system.
The desired capacitances were measured with integrated circuits (ICs) of the
type Acam PCap02AD. This IC calculates a capacitance by evaluating the
discharge time of the unknown capacitor in series with a known resistor
relative to the discharge time of a known capacitor–resistor combination.
The IC handles both ground capacitances (one electrode active, all other
electrodes of a multi-electrode system grounded) and mutual capacitances
(two electrodes active, all other electrodes grounded) (Acam messelectronic GmbH, 2014; Schlegl
et al., 2013). The respective advantages of these two measurement modes in
our application have been compared and will be discussed after simulation
results for the capacitances have been presented (see end of Sect. 3).
In the experiments conducted, gas bubbles were generated in LN2
in a defined way by using the foil heater as described before. These bubbles
could be accumulated under the lid inside the cylindrical receptacle and
united to form an expanding gaseous phase. By using a camera that observes
the cylinder from the side, the fractional gas-phase ratio inside the
cylinder could be observed while the capacitances were measured
simultaneously.
Modelling and simulation of capacitances
For validation and interpretation purposes, the measurements were
accompanied by finite-element (FE) simulations (Ansys). Figure 3 shows the FE
geometry model. Some care has been exercised to reproduce the real
geometry of Fig. 1 well and to use a dense mesh close to the fine structures of
the receptacle.
FE geometry of the receptacle and its environment.
Bubbles rising in the LN2 coalesce inside the receptacle, and as a
consequence the liquid fill level L inside the receptacle drops.
The results of the simulation in Fig. 4 demonstrate how selected mutual
capacitances Cij (measured between electrodes i and
j) depend on L. The numbering of the electrodes is the
same as in Fig. 2.
Simulated mutual capacitances of different pairs of electrodes as
a function of the LN2 fill level. (a)C13(b)C25.
A look at Fig. 4a reveals that the capacitance C13(L)
depends quasi-linearly on L at small fill levels (L < 20 mm).
At higher fill levels, C13 first peaks at
L≈ 23 mm and then drops again for fill levels between 23
and 30 mm. For reasons of sensitivity and uniqueness, C13 only
lends itself for the measurement of fill levels below 20 mm. In contrast,
with C25(L), the slope and therefore the sensitivity
of the characteristic curve is nearly complementary (in other words, the
functional graph C13(L) is concave from below whereas
the graph C25(L) is convex from below; Fig. 4b). This
mutual capacitance hardly changes with L at small fill levels
(L < 20 mm), but is strongly sensitive to L at
higher levels (L=20…30 mm). This makes sense as
electrode 5 is located on the lid, and is therefore more affected by the fill
level the higher the level is.
Simulated ground capacitances of different electrodes as a
function of the LN2 fill level. (a)C10(b)C50.
Similar, but not completely identical, remarks apply to ground capacitances
such as C10(L) and C50(L)
(Fig. 5). Their sensitivities (rates of change) increase with L at
high fill levels, especially when the receptacle is nearly full of LN2. The
overall change in capacitance from L= 0 to
L=Lmax=30 mm is higher for ground
capacitances than for mutual capacitances by an order of magnitude (some
0.1 pF vs. some 0.01 pF). Obviously, ground capacitances should be measured
to observe phase changes near the electrodes involved. And mutual
capacitances are needed for electrical capacitance tomography (ECT) to
identify phase interfaces in the volume between the electrodes
(Mühlbacher-Karrer and Zangl, 2015; Wang et al., 2010). The measurement
of these mutual capacitances is influenced by non-ideal ground connections.
This can be seen if Fig. 4a (C13 with perfectly grounded
electrodes 2, 4, and 5) is compared to Fig. 6 (C13 with
electrodes 2, 4, and 5 on a potential that is 2 % of the active-electrode
potential). Hence, when interpreting measured capacitances, one must take
such common imperfections into account.
Simulated mutual capacitance C13 for a ground
potential deviation of 2 % of the active-electrode potential.
Magnitude (colour-coded) and field lines of the electric flux
density in plane 1 (see Fig. 2) when electrode 3 is active. The three
figures correspond to three different LN2 fill levels. (a)L= 30 mm
(cylinder fully filled with LN2). (b)L= 25 mm.
(c)L= 10 mm. The black circle in (a) marks the region of interest
G, in which the electric flux density is further examined, as
described in the text.
Electric-field simulation
For a better understanding of the simulated capacitances, the electrostatic
field in the region close to the electrode-carrying receptacle was
investigated by FE calculations. As an example, this will first be discussed
by looking at the potential distribution associated with the measurement of
the mutual capacitance C13(L). The dashed lines in
Fig. 2 indicate the lines of intersection between the plane of projection
and the two planes, normal to the plane of projection, in which the electric
flux density D(r) has been computed.
Simulated magnitude (colour-coded) and field lines of the electric
flux density in plane 2 (see Fig. 2) when electrode 5 is active. The two
figures correspond to two different LN2 fill levels. (a)L=30 mm (cylinder
fully filled with LN2). (b)L=25 mm. The black circles mark two regions
that are further considered for analysis, as described in the text.
Figure 7 shows the magnitude and the field lines of D(r) for
three different LN2 fill levels in plane 1 (which runs through the centres
of electrodes 1 and 3) when electrode 3 is excited. Without gas inside the
receptacle (Fig. 7a), the electric field in the region G between electrodes
1 and 5 (marked by a black circle in Fig. 7a) is weaker than near the lower
part of electrode 1 (note the colour codes). The field lines starting on the
active electrode 3 end in part on electrode 1 and in part on electrode 5.
With increasing gas volume (corresponding to decreasing LN2 level), the flux
density in region G increases (Fig. 7b). Fewer field lines than before end
on electrode 5, because this electrode borders on the gaseous phase and the
field concentrates in the LN2 with its higher permittivity. As the major
part of electrode 1 reaches into the LN2, some field lines that ended on
electrode 5 in Fig. 7a now end on electrode 1, and the capacitance
C13 now is greater than in Fig. 7a. At even larger gas volumes
(lower LN2 levels), the field in region G gets weaker again (Fig. 7c). Now
the major part of electrode 1 is in contact with gaseous nitrogen, and the
electrode has lost its advantage at “catching” the field lines. As a
consequence, C13 decreases with decreasing fill level.
Another example is shown in Fig. 8. It refers to plane 2 of Fig. 2 (which
runs through the small electrodes 2 and 4), and the active electrode is
electrode 5. Without gas in the receptacle, the electric flux density is
highest in the corner regions G (marked by black circles) between the top
electrode 5 and the sidewall electrodes 2 and 4 (Fig. 8a). The situation is
similar at lower LN2 levels (Fig. 8b), but the field is somewhat weaker in
G. This explains the drop in capacitance C25: there are just
fewer field lines running from electrode 2 through the gaseous phase to
electrode 5 than before, when the volume was completely filled with LN2.
Figure 9 is an extension of Fig. 8 to even lower fill levels (half-full
receptacle in the case of Fig. 9a and completely empty receptacle in the
case of Fig. 9b). The maximum flux density is smaller than before
(0.5 vs. 1 nC m-2), and the field is
more evenly distributed inside the gaseous region than before. Also, the
field lines are almost straight inside the gaseous volume and somewhat
chaotic outside, which also shows that the field strength varies little from
the top of the receptacle to the bottom and has its highest change at the
top. The capacitance only changes very little compared to the changes
observed when the gaseous phase begins to emerge. Note that the local
density of the field lines in the figures does not represent the local field
strength (as it should, but the software used simply selects a few lines
regardless of the local field strength).
Simulated magnitude (colour-coded) and field lines of the electric
flux density in plane 2 (see Fig. 2) when electrode 5 is active. The two
figures correspond to two different LN2 fill levels. (a)L= 15 mm
(cylinder half filled with LN2). (b)L= 0 mm (no LN2 present in the
cylinder).
To visualize the variations in the region of the (left) black circle, the
mean value of the magnitude of the electrical flux density in this region is
shown in Fig. 10 for changing LN2 fill levels. The results bear some
resemblance to Fig. 4, in which the change of capacitance over the fill
level is plotted. Hence, the capacitance curves can be explained by the
change of the flux density in the region near the two electrodes making up
the measured capacitor.
Simulated electric flux density magnitude for different fill
levels in (a) plane 1, when electrode 3 is active (see Fig. 7); (b) plane 2,
when electrode 5 is active (see Figs. 8 and 9). The circles mark the
simulated data points, the dotted lines only serve to guide the eye.
Measurements and results
Different receptacle-filling and receptacle-emptying cycles were studied
experimentally. At rising LN2 fill levels, selected capacitances were
measured and the gas–liquid interface, as well as the activity of bubbles, was
optically observed by the camera. The actual fill level was determined by
using the pictures from the camera. As the resolution of the camera and the
light source in the cryostat did not suffice for precise measurements, the
fill level can only be determined with an uncertainty of ±2 mm from
the video camera images. Figure 11 shows the measured LN2 fill level
L as a function of time for a typical experiment in which the
mutual capacitances C13 and C25 were measured.
The fill level L was calculated by inverting the theoretical
characteristic curves C13(L) and
C25(L) from the results of the simulations (Fig. 6a, b).
Also, the dashed curve with the associated light “belt” shows the
fill level determined from the video camera images with an uncertainty band
of ±2 mm.
At the beginning of the measurement (t= 0 s), the receptacle was
partially filled with LN2. After a decrease of the pressure in
the cryostat, the existing gaseous phase inside the receptacle expanded
until it was eventually completely filled with gaseous nitrogen
(L= 0) at t≈ 150 s. After that point, the
pressure was increased again, and the gas–liquid phase boundary rose almost
linearly with time until the receptacle was completely filled with LN2
(L= 30 mm) at t≈ 450 s. The heater was turned
on at t≈ 650 s. After that, bubbles rose in the LN2
reservoir below the receptacle and replaced LN2 in the receptacle. After the
beginning of this replacement process, the LN2 fill level decreased with
time. As expected, C13 is sensitive to the beginning of the
bubble stream (t≈ 650 s) as the presence of bubbles leads
to a lower effective permittivity of the fluid between electrodes 1 and 3.
If one neglects this effective-permittivity effect and merely assumes a
planar interface between a gaseous phase above a liquid “sea”, one
underestimates the LN2 fill level. In contrast to this, C25 is
not influenced by the bubble stream. There is only a small amount of field
lines from electrode 5 to electrode 2 running through the bubble stream, as
can be seen from the geometry of the cylinder and the position of the heater
underneath. As mentioned before, C13(L) should be
used to estimate the LN2 fill level L in the region from 0 to 20 mm
whereas C25(L) is more suitable for L
between 15 and 30 mm. As shown by Fig. 11, the noise in the estimated
L increases dramatically if L is extracted from the
“wrong” capacitance. The two capacitively measured curves agree quite well
with the visually observed fill level, unless a bubble stream disturbs the
measurement (in which case the capacitive measurement can and must be
corrected by taking into account the results from several capacitances) and there are low fill levels (in which case the differences are attributed to reading
errors in the interpretation of the video camera images – low fill levels
were hard to make out on the images, and the uncertainty is likely to exceed
2 mm in these cases).
LN2 fill level inside the receptacle measured via electrode pair
1–3 (red curve) and via electrode pair 2–5 (black curve) compared to the
visually determined fill level (video camera images; dashed line with an
uncertainty band of ±2 mm). The photographs at the bottom are
freeze-frame images from the video camera and serve to visualize selected situations.
We would like to draw attention to the fourth photograph of the receptacle
from the left in Fig. 11, which is a freeze-frame image of the video at
t≈ 650 s. At this instant, the LN2 fill level L
was decreasing owing to the bubble stream. Because of the bubbles, the
surface of the liquid is very agitated: it “boils”.
The entire situation can be modelled by a cylinder with the permittivity of
LN2 (= receptacle full of LN2) in which there is embedded a slender
cylinder of lower permittivity (bubble stream between electrodes 1 and 3).
An effective relative permittivity of εr=1.1 was
chosen for the bubble stream region, to represent a high bubble content. The
bubble-stream region in the simulation was chosen such that it coincided
with the bubble-stream region visible in the camera-recorded video. The
simulation results are summarized in Fig. 12, where the numbering of the
electrodes and the notation for the cross-sectional planes is the same as in
Fig. 2. It is obvious that, for example, the mutual capacitance C13
and the ground capacitance C30 will respond to the presence of
the bubble stream as the associated field lines “probe” (run through) the
bubble-stream region (Fig. 12a, b). In contrast, capacitance
C25 will be hardly affected by the presence of the bubble
stream as the associated field lines do not run through the bubble-stream
region (Fig. 12c, d). Hence, not only can the fill level in a defined volume
be detected, but so too can a change in permittivity (like a bubble stream or
bubbles) inside a confined volume.
Simulated magnitude (colour-coded) and field lines of the electric
flux density in the presence of a bubble stream at the position indicated in
the center sketch. (a, b) Field in plane 1 with excitation of (a) electrode 1
and (b) electrode 3. (c, d) Field in plane 2 with excitation of (c) electrode 2
and (d) electrode 5.
As a further corroboration of the calculation and measurement results, the gas
volume increase due to a depressurization of the cryostat was observed. The
change of the fill level from full to empty was nearly linear with time, so
that the simulated capacitance curves from Fig. 6 can be superimposed on the
measured capacitance curves. For the mutual capacitances as well as for the
grounded capacitances, the simulation results and the experimental findings
agree very well (Fig. 13). The following conclusions can be drawn from these
results:
The measurement results can be correctly interpreted in a quantitative as
well as in a qualitative way by using numerical simulations (of
capacitances).
Ground-potential errors occur in practical capacitance measurements.
These are not negligible and have to be taken into account for the
interpretation of measured data. This can be done by using a model-based
approach.
The measured capacitances are noisy. The amount of noise depends on both the
capacitance and the permittivity distribution (LN2 fill level). In general,
the curves have to be smoothed. In the case of Fig. 13a, a moving average
filter with a window size of 200 was used. The measurement frequency was
25 Hz, so that 200 measured points represent a time of 8 s. With the ground
capacitances (larger than the mutual capacitances), the curves may not need
to be smoothed. In the case of Fig. 13b, no smoothing filter was used.
The measured capacitances contain an additive offset that is characteristic
for every combination of electrodes. The offset is due to cable capacitances
and has to be subtracted from the raw data.
Our specific hardware implementation could handle capacitance changes of
some femtofarads without problems.
The system can distinguish between a change in fill level and bubbles or
another source of change in permittivity occurring inside a confined volume
by using the information supplied by multi-electrode arrangements.
Measured capacitances (solid blue lines) and finite-element
simulations (dotted red lines) for a dynamic experiment with time-varying
gas volume inside the receptacle. Both curves refer to a time interval in
which the gas volume increases (decrease of the LN2 level). (a) Mutual
capacitance C13. The same ground-potential error as in Fig. 6
has been assumed in the simulation. Smoothing of the measured curve as
described in the text. (b) Ground capacitance C10.
Conclusions
It has been demonstrated that phase changes in LN2 can be
recognized in situ by measuring the electrical capacitance between different
electrodes of a multi-electrode system. The method is minimally invasive as
it does not introduce heat into the LN2 or otherwise disturb the
fluid.
This may be generalized to infer that, depending on the geometry of the
electrodes, phase changes of fluids with comparatively low changes in
relative permittivity can be detected using measured mutual and ground
capacitances. The properties of the system can be well described by using
dedicated finite-element simulations. Both the agreement between simulation
and electrical measurements and the agreement between simulation and optical
(camera-based) measurements are very good.
Original data of the publication: 10.15495/M-10150282-0001
(Kandlbinder et al., 2017). The data was used to produce Figs. 1, 4, 5, 6, 7,
8, 9, 10, 11, 12, and 13.
The authors declare that they have no conflict of
interest.
Acknowledgements
Parts of the presented work were carried out under contract from the European Space Agency (ESA),
the support of which is gratefully acknowledged.
Edited by: A. Lloyd Spetz
Reviewed by: two anonymous referees
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