Paper No 7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


Thermodynamic Effects on Cavitation in a Cryogenic Nozzle Flow


Kazuki Niiyama, Satoshi Hasegawa, Mitsuo Watanabe,
Shinichi Tsuda, Yoshiki Yoshida, Mamoru Oike

Japan Aerospace Exploration Agency, Space Transportation Mission Directorate,
1 Koganesawa, Kimigaya, Kakuda, Miyagi 981-1525, Japan
niiyanw kI/nki27ijr, ip



Keywords: Cavitation, Thermodynamic effect, Cryogenic fluid, Visualization



Abstract

Visualization and temperature measurement of cavitating flow in a nozzle were conducted with liquid nitrogen to investigate
the fundamental characteristics of thermodynamic effects on cavitation. Firstly, temperature depression from the inlet to the
nozzle was observed. The temperature depression became larger as the inlet cavitation number of the nozzle became smaller.
The maximum temperature depression was about 0.28 K. Meanwhile, whenever the temperature depression was observed,
cavity bubbles were observed at the nozzle. The quantity of cavity bubbles increased as the inlet cavitation number became
smaller. It was thus indicated that the temperature depression became larger with the increase in the quantity of cavity
bubbles. For the more quantitative consideration, an image analysis was applied to the pictures of the cavitating nozzle flow.
The apparent quantity and the mean diameter of cavity bubbles were calculated by the image analysis. These characteristic
parameters of cavity bubbles were considered with the inlet cavitation number and Stepanoffs factor. The consideration
showed that the quantity of cavity bubbles became larger in the straight section of the nozzle but smaller in the diffusing
section with the decrease of the inlet cavitation number, and that the mean diameter of cavity bubbles became smaller with
the decrease of the inlet cavitation number. It was concluded that these results were caused by the thermodynamic effects on
cavitation.


Introduction

Thermodynamic effects on cavitation suppress
cavitation instabilities such as cavitation surge and rotating
cavitation. Therefore, the performance of a rocket
turbopump inducer is improved if favorable
thermodynamic effects are properly applied (Kikuta 2008).
It is well-known that the degree of thermodynamic effects
becomes stronger in cryogenic propellants due to the large
vapor/liquid density ratio.
The thermodynamic effects on cavitation can be
explained as follows.
(1) As cavity bubbles grow, evaporative latent heat is taken
from the surrounding fluid of liquid/vapor boundary.
(2) The temperature of the surrounding fluid decreases and
then saturated vapor pressure becomes lower.
(3) Development of cavity bubbles is suppressed.
Therefore, temperature depression of the surrounding fluid
is a fundamental indicator for elucidation of the physics of
thermodynamic effects on cavitation.
Stepanoff (1964) considered the performance of
pumps and proposed a fundamental factor related to
temperature depression based on thermal balance around a
bubble. Hord et al. (1972-1974) measured temperature of
cavitation and visualized cavitating flow, including that in
a venturi, a hydrofoil and an ogive with liquid nitrogen and
liquid hydrogen. They proposed a method of estimating


Stepanoffs factor using reference data. Franc et al. (2'i 14)
visualized inducer cavitation with Freon-114 and
considered the degree of thermodynamic effects on
cavitation based on the cavity length. Yoshida et al. (2007)
conducted a quasi-visualization of an inducer based on the
pressure fluctuation. They considered the degree of
thermodynamic effects in a cryogenic inducer with liquid
nitrogen and estimated temperature depression based on
the difference of cavity length between water and liquid
nitrogen.
However, the physics of thermodynamic effects on
cavitation have not been elucidated and temperature
depression in a cavitating flow cannot be estimated due to
lack of an adequate model of the thermodynamic effects on
cavitation. Adequate modeling of thermodynamic effects
on cavitation requires accurate experimental data and full
visualization.
Therefore, visualization and direct temperature
measurement of a cavitating flow in liquid nitrogen were
conducted. This paper presents the results of temperature
depression as well as aspects of cryogenic cavitating flow,
and considers the degree of thermodynamic effects on
cavitating flow.

Nomenclature

B Stepanoffs factor






Paper No


C, specific heat capacity (kJ/kg-K)
D diameter (m)
L evaporative latent heat (kJ/kg)
p pressure (Pa)
Q volumetric flow rate (m3)
T temperature (K)
AT temperature difference (K)
AT characteristic temperature (K)
U flow velocity (m/s)
Greek letters
a void fraction (%)
K thermal diffusivity (m2/s)
p density (kg/m3)
a cavitation number
A flow property (in S- )
I thermodynamic property (in -
Z thermodynamic parameter
Subscripts
IN inlet section
L liquid phase
NOZ nozzle
OUT outlet section
SAT saturation point
V vapor phase

Experimental Setup


The experment was conducted using the cryogenic
cavitation tunnel shown in Fig. 1 (Niiyama 2009) at the
Kakuda Space Center of Japan Aerospace Exploration
Agency.


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

Vacuum
Heater pump
Controller DAS
Control & data
acquisition room
Vent stack
gfiA J m-


Figure 2: Schematic diagram of the cryogenic
cavitation tunnel.

Figure 3 shows the nozzle cavitation test unit, which
has a circular nozzle shown by the schematic diagram in
Fig. 4. The inner diameter of the nozzle inlet is 83.1 mm,
that of the straight section is 40.6 mm and that of the
nozzle outlet is 66.0 mm. The nozzle is made of
transparent polycarbonate for visualization of cavitating
flows and is covered with a vacuum chamber for thermal
insulation.


Figure 3: Nozzle cavitation test unit in an experiment.


Figure 1: Cryogenic cavitation tunnel.


Figure 2 shows a schematic diagram of the tunnel.
The tunnel has a run tank (20 m', vacuum insulation), a
catch tank (16 m3) and a main flow pipe (stainless, 83.1
mm in inner diameter, simple insulation). The working
fluid of the tunnel is liquid nitrogen, which flows from the
run tank to the catch tank through the main flow pipe by
pressurization of the run tank with gas nitrogen. Moreover,
the temperature of the working fluid can be risen by
pressurizing the run tank or fallen by depressurizing it with
a vacuum pump. There is a test section at the main flow
pipe. The test section can be exchanged depending on
experimental configurations. The volumetric flow rate is
measured by a turbine flowmeter installed upstream of the
test section and is controlled by a hydraulic servo valve
installed downstream of the test section.


Figure 4: Schematic diagram of the test unit.

There are four measurement ports at the inlet section,
the nozzle section and the outlet section, respectively. The
pressure and temperature were measured at each location.
In the present study, the accuracy of the temperature sensor
was the most important, and thus a miniature silicon diode
temperature sensor DT-670-SD manufactured by
Lakeshore Cryotronics Inc. was employed. The typical
accuracy of the calibrated sensor is +22 mK at 77 K, which
is sufficiently accurate to measure the temperature
depression by cavitation (Niiyama 2009). The sensor is
used as a temperature probe (Fig. 5).






Paper No


2(pN PsAT)
IN u 2
PL UNOZ


Figure 5:
probe.


DT-670-SD glued on the tip of a temperature


The experiment was conducted with the working
fluid at 89 K and the experimental sequence was as
follows:
(1) The temperature of the working fluid was set to 89 K.
(2) The run tank was pressurized at 0.4 MPa by gas
nitrogen. (Then, the working fluid began to flow from
the run tank to the catch tank.)
(3) The hydraulic servo valve was gradually opened until
cavitation was observed.
(4) Pictures were taken by the camera step by step when
the opening was changed and the flow became steady.
The pressure, temperature and volumetric flow rate
was recorded by the digital acquisition system at 50 Hz.
The aspects of the cavitating flow were captured with a
digital SLR camera D300 manufactured by Nikon. The
pictures (4288 pixels in width and 2848 pixels in height)
were taken at a rate of about 5 frames per second in
synchronization with a 9-ps flash.

Experimental Results

Figure 6 shows a time history of the pressures in run
tank and catch tank, the opening of flow control valve and
the volumetric flow rate. The pressure in run tank was at
0.4 MPa, that in catch tank was at the atmospheric pressure
and the temperature at the inlet of the test section was at 89
K during the experiment. The volumetric flow rate
increased gradually as the flow control valve was gradually
opened.


I I I I I '11
0 50 100 150 200
time t [s]


Figure 6: Time history of the pressures in run tank and
catch tank, the opening of the flow control valve and
volumetric flow rate.


ATIN-NOZ = TIN TNOz (2)


(1) (2) (3) (4) (5)


50 100 150 200
time t [s]


Figure 7: Time history of the inlet cavitation number
and the temperature difference.

Comparison between Figs. 6 and 7 shows that the
inlet cavitation number became smaller and the
temperature difference gradually increased as the opening
of the flow control valve was increased. This fact can be
considered to denote that the temperature difference is
affected by the occurrence and development of cavitation.
Aspects of the cavitating flow in the nozzle are
shown in Fig. 8 corresponding to the inlet cavitation
number GIN (Eq. (1)) the thermodynamic parameter (Eq.
(3)) and Stepanoff's factor B (Eq. (5)). The working fluid
flows from the right to the left. The timing marker of each
picture is presented in Fig. 7.


(1) oIN = 1.49, X = 1440, B = 0.03


Figure 8: Aspects of the cavitating flow in the nozzle
with the inlet cavitation number, the thermodynamic
parameter and the Stepanoffs factor. (To be continued the
next page)


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


Figure 7 shows a time history of the inlet cavitation
number and the temperature difference between the inlet
and the inside of the nozzle. The inlet cavitation number
o~ is described by Eq. (1) and the temperature difference
ATN-Noz is described by Eq. (2). The inlet cavitation
number is regarded to be almost constant in each step.






7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


C=
A


L PK


A= U OZ
A =
DNOZ


Stepanoffs factor B (Stepanoff 1964) is described by
Eq. (5), which denotes the dimensionless temperature
depression from the bubble surface to the uniform flow
around the bubble. The temperature difference calculated
by Eq. (2) is regarded as temperature depression here.


B= AT
AT*


pvL

PLCp,L


Figure 9 shows the relation between the inlet
cavitation number, the thermodynamic parameter and
Stepanoffs factor. The numbers (1) (6) in Fig. 9
correspond to those in Fig. 8.


0.10

0.05
0.05


0.00 L-
1.0


1500



1400

&


1300 "


I 1'1200
1.1 1.2 1.3 1.4 1.5


(6) oa = 1.04, 2 = 1300, B = 0.19


Figure 8 (continued): Aspects of the cavitating flow in
the nozzle with the inlet cavitation number, the
thermodynamic parameter and the Stepanoffs factor.

The thermodynamic parameter (Franc 2004,
Watanabe 2007) is described by Eq. (3), which is the ratio
of the thermodynamic property of the liquid/vapor to the
flow property and denotes the degree of thermodynamic
effects on cavitation in the flow.


inlet cavitation number a

Figure 9: Stepanoffs factor and thermodynamic
parameter corresponding to the inlet cavitation number at
the pictured timing.

From (1) to (3) shown in Fig. 8, the cavity bubbles
occurred only in the narrow area. Meanwhile, after (4), the
cavity bubbles occurred in the entire nozzle. From the
result, the cavity bubbles observed in (1) (3) can be
considered to occur at the sensor ports and those observed
after (4) can be considered to occur at the wall of the
nozzle.
Comparison between the aspect, the inlet cavitation
number, the thermodynamic parameter and Stepanoffs
factor shows that (a) the quantity of cavity bubbles
increased with the decrease of the inlet cavitation number,
(b) Stepanoffs factor became larger with the increase of
the quantity of cavity bubbles in spite of the decrease of
the thermodynamic parameter and (c) the scale of cavity
bubbles seemed to be finer with the increase of the
thermodynamic parameter in spite of the decrease of the
inlet cavitation number. Facts (a) and (b) denote that the
temperature difference was affected by the quantity of
cavity bubbles and that the temperature difference can be
regarded as an indicator of the thermodynamic effect on


Paper No






7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


cavitation. Here, the thermodynamic parameter does not
seem to affect Stepanoffs factor fully, but result (c) is
suggestive for the elucidation of the thermodynamic effect
in the cavitating flow.

Image analyses

In order to compare the visualized result with the
experimental data more quantitatively, the easy method of
image analysis detailed below was employed in the present
study. MATLAB was employed for coding of the image
analysis.
(a) The R-G-B image taken in the experiment was
converted to a grayscale image.
(b) The background image was subtracted from the target
image.
(c) The subtracted image was filtered with an edge
emphasis filter.
(d) The filtered image was binarized with the threshold
value based on that image.
(e) The characteristic properties of cavity bubbles were
evaluated from the binarized image.
The progress of the image analysis is shown in Fig.
10. The background image is given as the averaged picture
in the non-cavitating condition.


tal) largest liiage


(a2) Background image


considered to be a distinctive diameter
observed by the naked eye.


2000


S1500


S1000
Co

500
C,


which can be


0.0 0.1 0.2 0.3 0.4 0.5
diameter of cavity bubbles [mm]

Figure 11: Typical distribution of the diameter of cavity
bubbles at the binarized image of (1) and (6) shown in Fig.
8.

As shown in Fig. 11, many cavity bubbles were
detected in an image and several tens of images were taken
at each inlet cavitation number ((1) (6)). Therefore, the
mean values averaged in each location (A01 A10) of the
nozzle and at each inlet cavitation number are employed
below.

Discussion

Figure 12 shows the occupancy of cavity bubbles,
which denotes the pixel ratio of the apparent cavity
bubbles against the analyzed area in the binarized image.
Here, it is regarded as an apparent quantity of cavity
bubbles or an apparent void fraction. The location for
averaging in the nozzle is presented in Fig. 13. The area
from A01 to A04 is defined as the straight section of the
nozzle and the area from A05 to A10 is defined as the
diffusing section of the nozzle. The numbers (1) (6)
shown in Fig. 12 correspond to the pictures in Fig. 8,
respectively.


Figure 10: Typical progress of image analysis

Figure 11 shows a typical distribution of the diameter
of cavity bubbles, which is calculated from the binarized
image of (1) and (6) shown in Fig. 8. The quantity of
cavity bubbles increased as the diameter of cavity bubbles
decreased and the inlet cavitation number decreased.
Although the quantity of cavity bubbles became the largest
at the minimum diameter, the error of the image analysis
might be detected as cavity bubbles. Therefore, the rank of
the minimum diameter was not taken into account in the
following consideration. Moreover, there is a weak peak at
about 0.125 mm of the diameter. This peak can be


location in nozzle


Figure 12: Occupancy of cavity bubbles in the
analyzed area corresponding to the location in the nozzle
and the inlet cavitation number.


Paper No






Paper No


A01 A02 A03 A04 A05 A06 A07 A08 A09 A10

Figure 13: Locations of A01-A10 with the flip
horizontal image of a non-cavitating nozzle.

From Fig. 12, it can be considered that the occupancy
of cavity bubbles became gradually higher in the straight
section but became gradually lower in the diffusing section
at all inlet cavitation numbers. This is due to the variation
of local pressure in the nozzle. The local pressure, or the
local cavitation number, is kept constant in the straight
section but increases in the diffusing section. Consequently,
because the cavity bubbles keep developing in the straight
section and collapse in the diffusing section, the quantity of
cavity bubbles varies as mentioned above.
Meanwhile, as the inlet cavitation number decreased,
the occupancy became lower in the straight section but
became higher in the diffusing section. This can be
considered to be caused by the thermodynamic effect on
cavitation. In the straight section, because the cavity
bubbles develop and then the temperature depression
increases, the development of cavity bubbles is suppressed
due to the strong thermodynamic effect on cavitation.
However, in the diffusing section, because the cavity
bubbles collapse and then the temperature depression
decreases or the fluid temperature becomes higher than the
inlet temperature, the shrinkage of cavity bubbles is
suppressed. This tendency was also observed in a
cryogenic cavitating flow in an orifice (Niiyama, 2009).
Figure 14 shows the mean diameter of cavity bubbles
at each location and each inlet cavitation number. The
numbers (1) (6) shown in Fig. 14 also correspond to the
pictures in Fig. 8, respectively.


250

200

O 150

too

0
S100


o 50
rt


location in nozzle


Figure 14: Mean diameter of cavity bubbles at each
location and each inlet cavitation number.


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

The mean diameter became larger in the straight
section at all inlet cavitation numbers. However, the mean
diameter began to decrease just after the straight section at
the higher inlet cavitation number but remained larger
there at the lower inlet cavitation number. Comparing Figs.
12 and 14, there is an area in the diffusing section where
the quantity of cavity bubbles decreases but the mean
diameter of cavity bubbles increases. This may denote that
the cavity bubbles collapse sequentially from smaller to
larger ones.
Meanwhile, the mean diameter of cavity bubbles
became smaller as the inlet cavitation number became
smaller. It seems strange, but it can also be considered that
the development of cavity bubbles was suppressed due to
the thermodynamic effect on cavitation. At lower inlet
cavitation numbers, the quantity of cavity bubbles was
large in the straight section and then Stepanoffs factor also
became large. Therefore, because the thermodynamic
effect strongly suppressed the development of cavity
bubbles, the mean diameter of cavity bubbles could be
considered to become finer. On the other hand, at larger
inlet cavitation numbers, the quantity of cavity bubbles
was small and then Stepanoffs factor did not become so
large in the straight section. Consequently, because the
thermodynamic effect on cavitation could not fully
suppress the development of cavity bubbles, the mean
diameter of cavity bubbles could be considered to become
coarser.
These considerations based on the apparent quantity
and the mean diameter of cavity bubbles may suggest a
possibility which designed slight cavitation results in
suppression of development of cavity bubbles more
effectively.

Conclusions

Cryogenic cavitating flow in a nozzle was
investigated with liquid nitrogen in order to elucidate the
influence of the thermodynamic effects on the
development of cavity bubbles. Visualization and
temperature measurement of the cavitating flow were
conducted and the apparent quantity and the mean
diameter of cavity bubbles were estimated and compared
with the inlet cavitation number, Stepanoffs factor and the
thermodynamic parameter.
The results showed that (a) the quantity of cavity
bubbles increased with the decrease of the inlet cavitation
number and the increase of the Stepanoffs factor, (b) the
quantity of cavity bubbles in the straight section decreased
with the decrease of the inlet cavitation number but that in
the diffusing section increased with the decrease of the
inlet cavitation number and (c) the mean diameter of cavity
bubbles decreased with the decrease of the inlet cavitation
number. Moreover, the mean diameter decreased but the
quantity of cavity bubbles increased with the increase of
the thermodynamic parameter. Therefore, it can be
concluded that the development of cavity bubbles is
suppressed due to the thermodynamic effects on cavitation
even when the quantity of cavity bubbles increases with
the decrease of the inlet cavitation number. Consequently,
designed slight cavitation may be favorable for the
thermodynamic effects on cavitation to work more
effectively.


-o-(2)
- (3)
-- (4)







Upstream > Downstream
I I I I I A A A
A01 A02 A03 A04 A05 A06 A07 A08 A09 A10






7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


Acknowledgements

Authors would like to thank Mr. Eiichiro Sugita of
Dynax, Ltd. and Mr. Yasumasa Ogura of Kobe Steel, Ltd.
for their great helps and discussions.

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Paper No