### Flow and heat transfer in boiling nitrogen flow

The Japan Aerospace Exploration Agency (JAXA) is moving forward with the
development of the technology for hypersonic pre-cooled turbojet engines
that is fueled by liquid hydrogen. Because the liquid hydrogen is in a
forced convection boiling heat transfer state (vapor-liquid two-phase flow)
as it undergoes heat transfer with high-temperature air in the air pre-cooler
during high-speed flight, pressure drop and heat transfer performance are
important from a design standpoint.

As for our proposing high-efficiency hydrogen energy system, heat inleak
during pipeline transportation or heat generation induced by quenching
of superconducting equipment would cause liquid or slush hydrogen to a
forced convection boiling heat transfer state.

Accordingly, experimental studies of flow patterns, void fraction measurement,
pressure drop, and heat transfer were performed on boiling liquid nitrogen
flow with respect to circular pipe with an inner diameter of 10 or 15 mm,
square pipe with sides of 12 mm, and equilateral triangular and inverted
equilateral triangular pipes with sides of 20 mm, at each heat flux of
5, 10 or 20 kW/m^{2} [26, 27].

The above figure shows six flow patterns of bubbly, plug, slug, slug-annular, wavy-annular,
and wavy flows observed for a circular pipe with an inner diameter of 15
mm. Slug-annular flow, as suggested by the name, is a pattern incorporating
both slug and annular aspects.

Part of the work is carried out in collaboration with JAXA.

Experimentally obtained data were used in evaluation of Winterton's [34],
Khalil's [35], Butterworth's [36], Chisholm's [44], Levy's [45], Woldesemayat's
[46] and Kadambi's [47] equations for pressure drop, respectively, and
evaluation of Gungor-Winterton's [38], Liu-Winterton's [39], Schrock-Grossman's
[40], Chen's [41], Kandlikar's [48] and Steiner's [49] equations for heat
transfer coefficient, respectively.

### Pressure drop and heat transfer characteristics of boiling nitrogen in
horizontal square pipe flow

Pressure drop and heat transfer equations have been available using room
temperature fluids, such as water, primarily for flows in circular pipe.
However, empirical research on pressure drop and heat transfer in the cryogenic
boiling flow is insufficient with regards to

a) the applicability of the conventional equations to cryogenic fluids,
and

b) the applicability to pipe cross-sections that are not circular.

In the present study, boiling nitrogen two-phase flow patterns in a horizontal
square pipe are observed in terms of both visualization and void fraction
measurement. Based on the void fraction measurement results, comparison
is undertaken between experimental pressure drop results and analytical
(calculation) results using the conventionally proposed correlations between
void fraction and thermal equilibrium quality (referred to hereafter as
quality). Differences are also clarified between heat transfer coefficients
stemming from differences in quality and flow pattern, as well as differences
in heat transfer coefficients among the top, side and bottom of the heat
transfer pipe. Furthermore, evaluation is conducted on the models for pressure
drop and heat transfer [27].

The heat transfer pipe (straight) is made of phosphorus deoxidized copper,
with a side of 12 mm, a wall thickness of 1.5 mm and a heated length of
800 mm. Nichrome wire is wound around the outside of the pipe and affixed
using the Stycast. Two varieties of capacitance type void meters were used,
one having its flat plate electrodes vertically opposed (vertical type)
and the other having the electrodes horizontally opposed (horizontal type),
together with an LCR meter for void fraction measurement [12, 14]. Test
conditions were: run tank pressure *P*_{rt} = 0.1-0.15 MPa, mass flux *G* = 70-2000 kg/m^{2}-s and heat fluxes *q* = 5, 10 and 20 kW/m^{2}.

Six flow patterns were observed during experiments: bubbly, plug, slug,
slug-annular, wavy-annular and wavy flows. Slug-annular flow, as suggested
by the name, is a pattern incorporating both slug and annular aspects.

The relationship between the void fraction (as measured by void meters)
and quality is shown in the figure below. The solid lines are calculated values correspond to the homogeneous flow
model (slip ratio *s* = 1), the separation flow models for slip ratios as proposed separately
by Winterton [34] and Khalil [35], and the Butterworth’s model [36]. The portion in which quality is negative is where subcooled boiling occurs. In
the region of high quality, the separation flow model tends to show better
agreement with the actual values than the homogeneous flow model. With respect to the vertical type (V) and horizontal type (H) void meters,
the latter provides more accurate measurement of the actual void fraction. In the case of circular pipe as well, analytical results have been reported
showing that a horizontal type void meter offers better measurement accuracy
[37].

Pressure drop in a horizontal pipe is composed of acceleration loss and
friction loss. Using the homogeneous flow model (s = 1), together with
separation flow models that agree well with the void fraction obtained
from measurement results (i.e., Winterton, Khalil and Butterworth) as shown
in the figure below, pressure drop per unit length was calculated. The figureshows experimentally obtained pressure drop at heat flux of 10 kW/m^{2}, together with total pressure drop, acceleration loss and friction loss
for the homogeneous flow and separation flow models, calculated at the
representative experimental conditions indicated in the figure. For reference,
the Blasius equation of pressure drop (friction loss) for the liquid nitrogen
flow is shown in the figure.

Two figures below indicate, respectively, calculated results obtained using the homogeneous
flow model and Butterworth’s model, together with experimental results
obtained for pressure drop at heat fluxes of 5, 10 and 20 kW/m^{2}. However, in the measurement interval where quality is negative or zero,
calculation is performed using the conventional Blasius equation. Here,
let us briefly compare the four types of models. While the homogeneous
flow model can be used to evaluate experimental results for low void fractions
(bubbly and plug), experimental values are overestimated by more than 30%
when pressure drop is large (high void fraction). Because the flow velocities
for the liquid and vapor phases are assumed to be the same in the homogeneous
flow model, the liquid phase velocity tends to be overestimated, leading
in turn to overestimation of pressure drop. The calculation results for
the Butterworth’s model, indicated in the figure, are within ±30% agreement
for most of the experimental results in nearly all of the flow patterns.
Considering the experimental and calculated values in terms of the absolute
average of deviation, the Butterworth’s model delivered better results.
The calculation results for the Winterton’s and Khalil’s slip ratios, which
are not shown in the present paper, also enabled evaluation within ±30%
of the experimental values in most cases, with the separation flow model
providing good agreement with the experimental results.

The heat transfer coefficients on the side of the square pipe for heat
fluxes of *q* = 5, 10 and 20 kW/m^{2} are presented in the figure below. In the region where mass flux is large, forced convection heat transfer
in liquid phase is dominant; the heat transfer coefficient does not depend
on heat flux, depending instead on the magnitude of mass flux. The high
mass flux region is also characterized by almost no difference in terms
of heat transfer coefficient among the top, side and bottom of the pipe.
In the region of small mass flux, as designated by the arrows on the solid
lines in the figure, boiling commences and the heat transfer coefficient
increases when the mass flux becomes less. When the mass flux decreases
further, nucleate boiling heat transfer becomes dominant, and the heat
transfer coefficient increases up to a certain point. The point of mass
flux at which boiling commences (the value of *q* in the figure) becomes lower with reduced heat flux, while the amount
of increase in the heat transfer coefficient rises with greater heat flux.

In the figure, the nucleate boiling heat transfer coefficient for the
pipe side at heat flux of 20 kW/m^{2} is shown as a solid line, while the coefficients for the top and bottom
are indicated as broken lines. At the pipe bottom, following the rise in
the heat transfer coefficient to a certain level accompanying the reduction
in mass flux, this is maintained through the low mass flux region. Nucleate
boiling heat transfer becomes dominant; it is not dependent on the magnitude
of mass flux, but depends instead on the magnitude of heat flux, with the
heat transfer coefficient becoming constant. At the top of the pipe, while
the rise in the heat transfer coefficient accompanying the reduction in
mass flux exceeds that of the sides or bottom, this falls off when the
mass flux continues to decline. That is, because the bubbles formed due
to boiling are concentrated in the flow at the top of the pipe, heat transfer
is thus promoted and the heat transfer coefficient rises. When mass flux
falls further, the wall surface is subject to dry-out, and the heat transfer
coefficient is reduced. The side exhibits similar behavior to the bottom,
but the heat transfer coefficient starts to decline when dry-out occurs.
Compared to the top, the liquid phase is present even in the low mass flux
region. Because nucleate boiling heat transfer is maintained, the mass
flux point where heat transfer coefficient decline starts to occur is low,
and the rate of decline is therefore gentle.

The heat transfer coefficients for the pipe top, side and bottom are evaluated
using the heat transfer correlations proposed for room temperature fluids.
The Gungor-Winterton and Liu-Winterton equations for vapor-liquid two phase
heat transfer are used. In the measurement point where quality is zero
or negative, the flow patterns observed are liquid single-phase, bubbly
and plug, and evaluation is possible to about ±20% using the Dittus-Boelter
equation, regardless of the circumferential location of measurement. In
the case of positive quality, the flow patterns observed with slug, annular
and wavy, and results are obtained as follows. Comparison with the Gungor-Winterton
equation is presented in the figure below. At quality larger than 0.006, evaluation is possible within -20 to +30%
for most of the experimental values, regardless of the circumferential
location of measurement. While the trend of the Liu-Winterton equation,
shown in the figure below, is to underestimate the experimental values as compared with the Gungor-Winterton
equation, the difference is small even in the region where quality is low,
such that evaluation was possible within ±30% for most of the experimental
values. In terms of the absolute average of deviation between the experimental
and calculated values, the Gungor-Winterton equation provided better agreement
with the experimental results.

Pressure drop and heat transfer characteristics of boiling nitrogen in
horizontal triangular pipe flow

As the practical development of high-temperature superconducting equipment
continues, the importance of liquid nitrogen as a refrigerant is expected
to increase substantially.

Future high-temperature superconducting equipment is expected to make
use of various cross-sectional configurations in refrigerant piping and
heat exchangers, pointing to the importance of the flow and heat transfer
characteristics of cryogenic fluids in piped flow. Compared with circular
pipe having the same hydraulic diameter, triangular pipe has greater heat
transfer surface area and superior integration, and is therefore used in
applications such as plate-fin heat exchangers.

Flow and heat transfer experiments are performed on boiling liquid nitrogen
flowing in a horizontal equilateral triangular pipe having sides of 20
mm. Flow patterns are visualized, and measurements are taken of the void
fraction, pressure drop and heat transfer coefficient. Based on the void
fraction measurement results, and using conventionally proposed correlations
between void fraction and quality, comparisons are made between calculated
and experimentally obtained results for pressure drop, and the pressure
drop model is evaluated. Consideration is also given to differences in
heat transfer characteristics attributable to flow patterns, as well as
to heat transfer characteristics for the pipe sidewalls and bottom, used
in evaluation of the heat transfer model [43].

Using stycast, a nichrome wire heater is affixed to the triangular pipe (measuring 800 mm in length and 20 mm per side) made of
oxygen free copper. Pressure drop is measured along the heated length of
550 mm; inner wall temperature is analytically calculated from the outer
wall temperature as measured at 6 points along the flow orientation, while
the local heat transfer coefficient is determined from the measured bulk
temperature. Local heat transfer coefficients are evaluated with respect
to the pipe sidewall (T_{5}) and pipe bottom (T_{6}). A double-helix type static capacitance void meter and a visualization
tube are positioned downstream from the heat transfer section. During the
experiments, the inlet pressure of heat transfer pipe is 0.11-0.15 MPa,
mass flux *G* is 110-2370 kg/m^{2}-s, and heat flux *q* is 5, 10, or 20 kW/m^{2}.

Six types of flow patterns are observed, consisting of bubbly, plug, slug,
slug-annular, wavy-annular, and wavy.

The figure below shows the measured void fraction and the experimental results for thermal
equilibrium quality. Since the liquid nitrogen is in a slightly subcooled
state at the inlet of heat transfer pipe, subcooled boiling takes place
in the region of x< 0. In the pressure drop evaluation below, given
that the void fraction is required for estimation of acceleration loss
in the separated flow model, the correlation between void fraction and
quality has a major effect on the accuracy of the estimation. The figure
indicates the relationship between quality and the homogeneous flow model
(slip ratio *s* = 1), the slip ratios proposed by Winterton and Khalil [37, 38] in the
separated flow model, and the void fraction used in the Butterworth model
[39], respectively. We have found in the previous experiment of the circular
pipe that measurement values obtained using the double-helix type void
meter tend to be greater than actually measured values, and as noted below,
the pressure drop model using Khalil’s slip ratio shows good agreement
with experimental results. On the other hand, the homogeneous flow model
overestimates the actual void fraction.

Pressure drop in a horizontal pipe is composed of acceleration loss and
friction loss. Using the homogeneous flow model (s = 1), together with
separation flow models that agree well with the void fraction obtained
from measurement results (i.e., Winterton, Khalil and Butterworth) as shown
in the figure below, pressure drop per unit length is calculated. The figure shows experimentally
obtained pressure drop at heat flux of 10 kW/m^{2}, together with total pressure drop, acceleration loss and friction loss
for the homogeneous flow and separation flow models, calculated at the
representative experimental conditions indicated in the figure. For reference,
the Blasius equation of pressure drop (friction loss) for the liquid nitrogen
flow is shown in the figure.

In the experiments, since the run tank is slightly pressurized, the
quality in the pressure drop measurement section can be negative (*x*< 0), positive (*x*> 0), or a mix of negative and positive. In the negative quality, the
Blasius equation shows over 50% less than experimental values when the
effect of subcooled boiling becomes substantial. Although not presented
here, when a modified Blasius equation taking the boiling number as a parameter
is employed, pressure drop during subcooled boiling could be predicted
to within ±20%. When the quality in the pressure drop measurement section
is calculated to be either positive or a mixed negative and positive, friction
loss is evaluated using the conventional Blasius equation for the subcooled
section (*x*< 0), while the previously noted 4 types of models (homogeneous, Winterton,
Khalil, and Butterworth) are used to evaluate for the two-phase flow section
(*x*> 0).

Two figures below indicate, respectively, calculated results obtained using the homogeneous
flow model and Khalil's slip ratio, together with experimental results
obtained for pressure drop at heat fluxes of 5, 10 and 20 kW/m^{2}. As a result of comparing the calculated and experimental values, it can
be seen in the figure that the Khalil's slip ratio shows good agreement
within about ±30%.

At the heat fluxes of 5, 10 and 20 kW/m^{2}, when quality was negative at the measurement location of heat transfer
coefficient, the effect of subcooled boiling is substantial due to the
occurrence of bubbles. The conventional Dittus-Boelter equation shows over
30% less than experimental values for both the sidewall and bottom. As
with pressure drop, when a modified Dittus-Boelter equation taking the
boiling number as a parameter is employed, heat transfer coefficients could
be predicted to within ±15%.

The figure below indicates experimental results for mass flux *G* and heat transfer coefficient *h* at heat flux of 20 kW/m^{2}. In the subcooled boiling, forced convection heat transfer in liquid phase
is governing, and the difference between the heat transfer coefficients
at the pipe sidewall and bottom is small. In the case of saturated two-phase
flow (*x*> 0, *G*< 1300 kg/m^{2}-s) at the pipe bottom, accompanying reduced mass flux, the heat transfer
coefficient rises; then after reaching a constant value, a constant level
of heat transfer coefficient is maintained until the low mass flux region
is reached, subsequently falling off gently. At the sidewall, accompanying
reduced mass flux, given that nucleate boiling and the occurrence of bubbles
serve to promote heat transfer, the heat transfer coefficient increases
more than for the bottom. At even lower mass flux, wall surfaces dry out
and the heat transfer coefficient drops substantially.

A quantitative comparison is undertaken between the heat transfer coefficients
measured at the sidewall and bottom on the one hand, and 2 types of heat
transfer correlation on the other (Gunger-Winterton [38] and Liu-Winterton
[39]).

In the case of the Gunger-Winterton equation shown in the figure below, most of the pipe bottom heat transfer coefficients at quality of *x* > 0.006 could be evaluated in the range of 0-20%. On the pipe side
wall, as quality becomes greater (0.04 <*x*< 0.09) and wavy flow occurs, partial dry-out takes place at the wall
surface, and the experimentally obtained heat transfer coefficient becomes
lower. For this reason, the correlation overestimates the heat transfer
coefficient by about 30-50%.

In the case of the Liu-Winterton equation shown in the figure below, although a tendency is found to underestimate the experimental values,
the difference becomes less in the region of low quality, and, across the
entire range of experimental quality (0 <*x*< 0.09), good agreement to within approx. ±20% is seen between the calculated
and experimental values. Also in terms of the absolute average differential
and standard differential, the Liu-Winterton equation exhibits the best
fit with the experimental values.

Pressure drop and heat transfer experiments are performed for a horizontal
inverted triangular pipe having the same cross section of the triangular
pipe. A quantitative comparison is undertaken between the heat transfer
coefficients measured at the sidewall and topwall on the one hand, and
2 types of heat transfer correlation on the other (Gunger-Winterton and
Liu-Winterton) as shown in the figures below. On the topwall, as quality becomes greater (*x*> 0.05) and wavy flow occurs, partial dry-out takes place at the wall
surface, and the experimentally obtained heat transfer coefficient becomes
lower. For this reason, the correlation overestimates the heat transfer
coefficient.