OR2-1
極低温推進システム向けジェットミキシングを用いたサーモダイナミックベントシステムに関する研究(ジェット挙動の数値解析と検証実験)
Study on Thermodynamic Venting System with Jet
Mixing for Cryogenic Propulsion Systems (NumericalAnalysis of Jet Behavior and Verification Experiment)
氏名坪内聡汰 1, 今井良二 1, 小熊太燿 1, 河南治 2,
Sota Tsubochi 1, Ryoji IMAI 1, Taiyo OGUMA1, Osamu KAWANAMI2
121

室蘭工業大学，Graduate School of Muroran Institute of Technology,
兵庫県立大学，Graduate School of University of Hyogo

Introduction
Currently, space exploration organizations such as ISECG are planning further exploration into deep space,using the Moon as a gateway. This plan is expected to require longer missions and larger payloads fortransportation systems than conventional space exploration. To solve these problems, cryogenic propellant
propulsion systems with high specific impulse, such as those fueled by liquid hydrogen (LH2) or liquefied
natural gas (LNG) and oxidized by liquid oxygen (LOX), will be used 1). However, when these propellants,
which are classified as cryogenic liquids, are stored on long-duration missions, the propellant temperaturerises and evaporates due to sunlight and heat input from the engine, causing the tank pressure to rise.
Therefore, spacecraft operated in long-distance space transportation systems require propellant tank pressurecontrol.
Therefore, the target of this research is to develop a TVS (Thermodynamic Vent System) as a method torealize long-term storage of cryogenic propellant by managing and controlling the thermal fluid behavior
inside and outside the propellant tank2). Previous study has included ground-based experiments todemonstrate the effectiveness of jet mixing, one of the components of TVS 2).
However, as this research progresses, it will be necessary to conduct microgravity experiments to simulate
operation in a space environment. Conducting multiple such experiments is difficult due to the large amountof expense and labor required; if a model can be established that accurately predicts the behavior of jet mixing
using CFD, the development of TVS with jet mixing can be made more efficient. Therefore, the objective of
this study was to establish a CFD-based jet mixing prediction model.

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2

Theory and Methodology
Spray barFig.1

shows a schematic diagram of jetmixing. When the spacecraft receives heat fromthesun,

naturalconvection

createsaJet mixing

temperature gradient in the tank and the gas-

Dielectrophoret
ic pumpliquid interface becomes high temperature.
Whenthegas-liquidinterfaceHeat leakreachessaturation temperature, a large amount of BOG
is generated and tank pressure increases. In jet
mixing, liquid propellant taken out of the tankis subcooled by a refrigerator and injected
through a nozzle at the bottom of the tank toIon dragpump

J-T valverefrigerator

Figure.1 TVS over viewcool the gas-liquid interface by forced convection, thereby suppressing BOG (Boil Off Gas).
Jet mixing can be efficiently developed and verified by creating a model that accurately predicts jet behavior
through numerical analysis and incorporating it into development. In the previous study, a comparison wasmade between experimental values obtained from jet mixing experiments in a tank with temperature
stratification and analytical values obtained from numerical analysis based on the experiments in order toevaluate and improve the jet behavior prediction model using numerical analysis. The comparison is based on
temperature and jet behavior. However, there is a large discrepancy between the experimental and analyticalvalues, and the jet behavior is not accurately predicted. Therefore, in this study, we aimed to achieve
agreement between the experimental and analytical values by simplifying the experimental and analyticalconditions. Specifically, jet mixing was performed in a homogeneous temperature field without forming atemperature stratification in the tank, and numerical analysis was performed based on the obtained data tocompare the experimental and analytical values.
3Jet mixing experiment3.1. Experimental Apparatus and TechniquesFig.2 shows a schematic diagram of the experimental apparatus. This experimental apparatus wasdeveloped based on the one used at the University of Hyogo 3). In this experiment, after forming ahomogeneous temperature field by injecting pure water into the test tank, jet mixing is performed bysupplying a jet that has been given a subcooling degree by a heat exchanger into the test tank. As a method ofgiving subcooling to the jet, a cooling loop is constructed from the reserve tank, where the jet liquid is stored,
through the gear pump, flow meter, and heat exchanger, returning to the reservoir tank. The temperature of
the jet liquid in the cooling loop is measured by thermocouple TC-1. The right side of Fig.2 shows an overview
of the test tank. The test tank is made of copper and heat-resistant glass (Tempax float) to observe jet behavior
during jet mixing. TC-3 to TC-9 in the Fig.2 are thermocouples to measure the liquid temperature in the tank.
In the experiment, pure water is injected into the test tank to form a homogeneous temperature field, and whenthe liquid temperature in the tank and the jet temperature in the cooling loop reach a predetermined difference,
the three-way valve is switched to supply a cooling jet into the test tank. The jet liquid temperature after
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switching the three-way valve is measured by thermocouple TC-2.
Next, a visualization method for jet behavior is described. In this experiment, the backlight method is used tovisualize the jet behavior. An LED light source was installed behind the test tank, and a digital video camera
was used to capture images. The jet liquid was stained with food coloring.

Figure.2 Overview of experimental apparatus
3.2. Experimental Condition
Table 1 shows the experimental conditions. Flow rate in the table show the time-averaged value of the jet
during jet mixing, and temperature difference is the difference between the temperature near the liquid surface
and TC-1 immediately after the jet is fed.
Table.1 Experimental Conditions

Exp.NoExp-1

Flow rate [mL/min]

59.44

Jet supply time [sec]9.5

Liquid level [mm]60Temperature difference [K]

14.67

3.3 Experimental results
Figure.3, and Fig.4 shows the results of the Exp-1 experiment. Since the liquid level in this experiment was60 mm, we focused on the temperature change of thermocouples TC-4 and TC-5 in the liquid phase. As a result,
the temperature at the thermocouple TC-4, which is closer to the tank bottom, was lower than that atthermocouple TC-5, which is near the liquid surface and is considered to be most susceptible to the influenceof the low-temperature jet. The temperature of TC-5 should have dropped first because the jet diffusedthroughout the tank after reaching the liquid surface, but the temperature of TC-4 dropped after 2.0 seconds,
while the temperature of TC-5 dropped after 5.0 seconds. One possible explanation for this phenomenon is
the possibility of poor sensitivity of TC-5, but the detailed cause is unknown.

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Figure.3 Temperature change in tank during mixing experiment1.0sec5.0sec9.5secFigure.4 Images of jet behavior at each time4

Developed Numerical Analytical Model

4.1 Numerical Analysis Summary
To develop an analytical model to predict jet behavior, a numerical analysis was performed based on theexperimental values. The analytical model was based on the jet mixing analytical model developed by Kassemi
et al4). A three-dimensional model of the test tank was created using ANSYS FLUENT by ANSYS, Inc. and theexperimentally obtained values were input and analyzed.
4.2 Analysis conditions
As for the boundary conditions of the analytical model, values obtained from the experiment were inputand set. The nozzle opening in the test tank was set as the velocity inlet, and the values measured by the flow
meter during the experiment were input. As the outlet condition, the pressure outlet condition was set at theatmospheric opening of the test tank. The analytical model was created with the wall surface as the adiabatic
condition, and heat input from the outside was not taken into account.
Fluid flow and heat transfer in the liquid and vapor phase regions of the tank are defined by the equationsof motion, energy, volume fraction (VOF), and continuity. The turbulence model used was k-ωSST. Theanalysis range is from 0 second, the time when the jet begins to feed the tank, to the time when the jet feed
ends. The main analytical conditions are listed below.
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Table.2 Analysis conditions
Acceleration [m/sec]

y=-9.80665

Discretization method

VOF Model

P-V Coupling SchemeTime Discretization

Explicit

Gradient

Courant Number

0.73567

Pressure

Surface Tention Model

CSF

Momentum

Initialization

PISO
Least Squares Cell
Based
PRESTO!

Turbulent Kinetic Energy
Second Order Upwind

Temperature
Pressure

Input from

Turbulant Dissipation Rate

Experiment Data

Velocity

Energy0Volume fraction

Geo-Reconstruct

These analytical conditions were set with reference to the analysis performed by Kassemi et al 4). The time
discretization method for the volume fractions was explicit, and the Courant number was derived by thefollowing equation.

𝛥𝑡𝑉 = 𝐶𝛥𝑥𝑣𝑓𝑙𝑢𝑖𝑑(1)

Where 𝛥𝑡𝑉 is the time step width in the analysis, 𝑣𝑓𝑙𝑢𝑖𝑑 is the velocity normal to the interface, 𝛥𝑥 is the meshsize, and 𝐶 is the Courant number. In this analysis, the time step 𝛥𝑡𝑉 was set to 0.001sec in consideration of thecomputer load and the number of days required for the analysis and 𝑣𝑓𝑙𝑢𝑖𝑑 was the average flow velocity at
the time of jet supply.
As for the physical properties of the fluid, the values of density, thermal conductivity, and viscosity are
given as polynomials of temperature.
4.3 Analysis Results
A graph comparing experimental and analytical values of temperature in the tank during jet mixing isshown in Fig.5. Experimental values are plotted, and analytical values are shown as lines. The measurement
points are thermocouples TC-4 and TC-5 placed inside the tank, and the tip of the thermocouple is used as themeasurement point in the analysis. Fig.6 to 8 show the jet behavior photographed during the jet mixing
experiment and temperature contour plots obtained by numerical analysis. The points in the temperature
contour represent the temperature measurement points, TC-4 and TC-5 from the bottom of the tank. The lines
in the temperature contour indicate the liquid surface.
The graph in Fig. 5 shows that the difference between the experimental and analytical values is less than 1K.
The jet behavior taken by the experiment in Fig. 6 shows that the jet reaches the liquid surface and diffuses tothe vicinity of thermocouple TC-5. However, the temperature contourin Fig. 6 shows that the low-temperature jet does not reach the liquid surface, and the temperature graphshows no decrease in the temperature of TC-5 in both the experimental and analytical values. This is because
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the temperature of the jet increased due to heat exchange between the jet and the liquid in the tank before thejet reached the liquid surface. The jet behavior taken by the experiment in Fig. 7 and 8 shows that the jetdiffuses throughout the tank along the liquid surface and wall surfaces. The temperature contours in Fig. 7
and 8 also show that the low-temperature jet diffuses throughout the tank, resulting in a decrease in the liquid
temperature of the entire tank.

From these results, it can be said that the experimental and analytical results

are in good agreement and that a numerical model has been successfully developed to predict the jet behavior
under the experimental conditions of Exp-1.

Figure.5 Comparison of experimental and analytical values according to temperature

Figure.6 Comparison of jet behavior and temperature contour plot at 1 sec.

Figure.7 Comparison of jet behavior and temperature contour plot at 5 sec.
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Figure.8 Comparison of jet behavior and temperature contour plot at 9.5 sec.
5.

Conclusion
In order to construct a numerical model that accurately predicts jet behavior, a numerical model was built

and validation experiments were conducted. The numerical model was created based on the conducted
experiments, and numerical analysis was performed. Therefore, it can be said that we have succeeded indeveloping a numerical model that accurately predicts jet behavior under specific conditions.
In the future, we plan to conduct experiments and analyses under a variety of conditions to verify thevalidity of the numerical model developed in this study.

References
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The Global Exploration Roadmap Supplement. (2022) , ISECG , pp1-23
Kazuaki.NISHIDA, Ryoji.IMAI, Osamu.KAWANAMI, Yutaka.UMEMURA, Takehiro.HIMENO:
Ground-Based Experiment on Reducing Boil-Off Gas by Jet Mixing for Future Cryogenic Propulsion
System. IJMSA ,Vol.38 , (2021) , Issue 1 , pp.1-6
Osamu KAWANAMI , Kentaro TAKEDA , Ryoki MATSUSHIMA , Ryoji IMAI , Yutaka UMEMURA3and Takehiro HIMENO: Observation of Flow Pattern and Jet-tip Height Issuing from a Nozzle at Tank
Bottom in Microgravity. IJMSA , Vol.39 , (2022) , Issue 1 , pp1-13
O. Kartuzova , M. Kassemi : CFD Jet Mixing Model Validation against Zero-Boil-Off Tank (ZBOT)Microgravity Experiment. AIAA , (2019) , pp1-25© 2023 by the authors. Submitted for possible open access publication under theterms and conditions of the Creative Commons Attribution (CC BY) license(http://creativecommons.org/li censes/by/4.0/).

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