Kevin Breisacher and Jeffrey Moder

Glenn Research Center, Cleveland, Ohio

Computational Fluid Dynamics (CFD) Simulations 

of Jet Mixing in Tanks of Different Scales

NASA/TM—2010-216749

July 2010
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Kevin Breisacher and Jeffrey Moder

Glenn Research Center, Cleveland, Ohio

Computational Fluid Dynamics (CFD) Simulations 

of Jet Mixing in Tanks of Different Scales

NASA/TM—2010-216749

July 2010

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared for the

57th Joint Army-Navy-NASA-Air Force (JANNAF) Propulsion Meeting

sponsored by the JANNAF Interagency Propulsion Committee

Colorado Springs, Colorado, May 3–7, 2010
Acknowledgments

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Space Administration.

Level of Review: This material has been technically reviewed by technical management. 

This report is a formal draft or working 

paper, intended to solicit comments and 

ideas from a technical peer group.

This report contains preliminary fi ndings, 

subject to revision as analysis proceeds.
NASA/TM—2010-216749 1 

Computational Fluid Dynamics (CFD) Simulations of 

Jet Mixing in Tanks of Different Scales 

Kevin Breisacher and Jeffrey Moder 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Abstract 

For long-duration in-space storage of cryogenic propellants, an axial jet mixer is one concept for 

controlling tank pressure and reducing thermal stratification. Extensive ground-test data from the 1960s to 

the present exist for tank diameters of 10 ft or less. The design of axial jet mixers for tanks on the order of 

30 ft diameter, such as those planned for the Ares V Earth Departure Stage (EDS) LH2 tank, will require 

scaling of available experimental data from much smaller tanks, as well designing for microgravity 

effects. This study will assess the ability for Computational Fluid Dynamics (CFD) to handle a change of 

scale of this magnitude by performing simulations of existing ground-based axial jet mixing experiments 

at two tank sizes differing by a factor of ten. Simulations of several axial jet configurations for an Ares V 

scale EDS LH2 tank during low Earth orbit (LEO) coast are evaluated and selected results are also 

presented. Data from jet mixing experiments performed in the 1960s by General Dynamics with water at 

two tank sizes (1 and 10 ft diameter) are used to evaluate CFD accuracy. Jet nozzle diameters ranged 

from 0.032 to 0.25 in. for the 1 ft diameter tank experiments and from 0.625 to 0.875 in. for the 

10 ft diameter tank experiments. Thermally stratified layers were created in both tanks prior to turning on 

the jet mixer. Jet mixer efficiency was determined by monitoring the temperatures on thermocouple rakes 

in the tanks to time when the stratified layer was mixed out. Dye was frequently injected into the stratified 

tank and its penetration recorded. There were no velocities or turbulence quantities available in the 

experimental data. A commercially available, time accurate, multi-dimensional CFD code with free 

surface tracking (FLOW-3D from Flow Science, Inc.) is used for the simulations presented. Comparisons 

are made between computed temperatures at various axial locations in the tank at different times and 

those observed experimentally. The affect of various modeling parameters on the agreement obtained are 

assessed. 

Introduction 

As part of the Constellation program, the Ares V is the heavy lift launcher designed to send astronauts 

back to the Moon. A part of the Ares V stack, the Earth Departure Stage (EDS) is needed to escape 

Earth’s gravity and send the crew vehicle and lunar lander on their journey to the Moon. Due to the mass 

of these vehicles and the energy required to send them to the Moon, the liquid hydrogen (LH2) and liquid 

oxygen (LO2) propellant tanks on the EDS would be very large (~10 m diameter). Due to environmental 

heat leaks into the tank, a thermodynamic vent system (TVS) including a mixing device is likely to be 

required for in-space storage durations on the order of several days to maintain tank pressure within 

design limits and maintain liquid temperatures within the limits required for engine start. One such 

mixing device is an axial jet centered along the tank axis (with respect to net acceleration) near the tank 

bottom, such as shown in Figures 1 and 2. Axial jet mixers and their incorporation into a TVS have been 

studied (Refs. 1 to 5) since the mid-1960s and there exists extensive axial jet ground test data (using noncyrogenic (Refs. 1 to 9) and cryogenic (Refs. 10 to 16) fluids), some drop tower test data using ethanol by 

Aydelott (Refs. 17 and 18), and two flight tests (Refs. 19 and 20) using Freon 113 on Shuttle (STS-43 and 

STS-52). Existing ground test data for axial jets using cryogenic propellants are limited to tank diameters 

of 3 m (10 ft) or less. There is currently no drop tower, aircraft or space flight test data available (to the 

authors’ knowledge) involving axial jets in closed tanks using subcritical cryogenic propellants. 
NASA/TM—2010-216749 2 

An axial jet is one candidate for the mixing device operating in the EDS LH2 tank during several days 

of low Earth orbit (LEO) coast. Since experimental data for axial jets operating in cryogenic storage tanks 

at proposed EDS tank scales does not exist, initial design of an axial jet TVS for EDS tanks will need to 

rely on correlations and CFD analysis anchored against existing data. This study reports current progress 

in evaluating CFD accuracy for predicting axial jet thermal destratification performance at two tank scales 

differing by an order of magnitude. CFD simulations are compared with ground-test axial jet data (Refs. 1 

to 4) using water as the working fluid. The CFD code chosen for this evaluation is the commercially 

available code FLOW-3D from Flow Science (Ref. 21), which has been used in previous analysis of 

cryogenic storage tanks and axial jets (Refs. 22 to 24). Preliminary axial jet simulations for a 

representative EDS LH2 tank in LEO are also performed for several axial jet configurations. The thermal 

destratification performance of these axial jet configurations are evaluated and selected results are 

presented. These preliminary axial jet EDS simulations are evaluating only the mixer performance for 

relatively short durations. More detailed simulations including tank heat leak, phase change, and typical 

self-pressurization (jet off)/pressure decay (jet on) cycles may be pursued in future work. 

Nomenclature 

a net acceleration acting on tank fluid

Aw total surface area of tank inner wall 

ܥ ௣liquid constant pressure specific heat 

Do diameter of the jet

Dt diameter of the tank

Gr liquid Grashof number based on Hs and qw

Hs vertical (relative to net acceleration) distance from tank bottom to liquid/gas interface

ܬொ liquid non-dimensional parameter = ܥ௣൫ܶ௦ െ ܶ௃൯ ݉ሶ⁄ܳ௪

݇ liquid thermal conductivity 

݉ሶ jet mass flow rate = ρ ܸ௃ πܦ௢

ଶ⁄4 

Pr liquid Prandtl number = ܥ ௣μ⁄݇

qw average tank wall heat flux = Qw/Aw

Qw total heat rate into tank 

Էሶ volume flow rate 

࣬Էሶ ratio of natural convection and jet volume flow rates = Էሶ

௡௖ Էሶ ൗ ௃

ReJ jet Reynolds number = ρ ܸ௃ ܦ௢⁄μ

Tb temperature in bulk liquid 

TJ temperature at jet nozzle exit 

Ts temperature along liquid/gas interface

ܸ௃ velocity of the jet 

Zb distance from jet outlet to water/air interface

 liquid thermal expansion coefficient

 liquid dynamic viscosity

 liquid density

ull ullage density 

 surface tension

T initial temperature stratification = Ts - Tb

 
NASA/TM—2010-216749 3 

Subscripts 

b bulk liquid 

J axial jet exit or axial jet flow 

nc natural convection boundary layer flow 

s liquid/gas interface 

w tank walls

Ground-Test Axial Jet Results and Discussion 

Experimental Datasets 

As part of an effort to gather data to develop correlations to be used in the design of the large 

propellant tanks anticipated for the nuclear spacecraft being studied in the 1970s, General Dynamics 

conducted jet mixing tests with simulated propellant tanks of different sizes (Refs. 1 to 4). The tests 

conducted provided data on mixing and ullage breakup for thermally stratified tanks. The scale of the 

tanks investigated in these tests ranged from test tube size tanks to tanks 3 m (10 ft) in diameter. Water 

was used as the propellant stimulant for most of the tests. 

A small tank with a 0.3053 m (1 ft) diameter by 0.6107 m (2 ft) high cylindrical section was used to 

obtain small scale jet mixing data (Refs. 1 and 2). This tank is shown schematically in Figure 1.The 

cylindrical section was installed on a steel concave or convex tank bottom. The lucite walls of the 

cylindrical section permitted visualization of the mixing process by observing the dispersion of dye 

injected into the thermally stratified layer. A jet nozzle assembly was installed in the bottom of the tank. 

Nozzle diameters ranged from 0.00081 to 0.00636 m (0.032 to 0.25 in.). A pump and flow loop were 

placed external to the tank to provide flow to the jet mixer. Liquid flow into the axial jet for the small 

scale tank experiment is provided from a source outside the test tank at a prescribed temperature. Axial 

arrays of thermocouples and pressure transducers were located at several radial locations in the tank. 

These instrumentation arrays provided temperature and pressure time histories during the tests. Both 

closed and open tank tests were conducted. 

Large scale mixing data (Refs. 3 and 4) was obtained in a 6.096 m (20 ft) high by 3.048 (10 ft) 

diameter unpressurized, cylindrical tank. The tank had a flat bottom. A schematic of the tank is shown in 

Figure 2. Jet nozzle diameters ranged from 0.016 to 0.022 m (0.625 to 0.875 in.). Thermal stratification 

was created in the tank by heating the top layer of fluid. The thermal stratification of the top layer was 

typically obtained by adding heated fluid to the top of the tank. No heat was added during mixing. Due to 

the amount of water required for the jet at this scale, a pump submerged in the tank that recycled water 

from the test tank was used to supply the jet mixer. Fluid temperature history data was obtained by four 

thermocouples placed radially outward from the tank center and located approximately 0.0127 m (1/2 in.) 

below the liquid surface. 

Simulation of Water Tank Jet Mixing 

In order to anchor the CFD simulations, the small-scale (0.3053 m diameter) water tank test with a 

0.0081 m nozzle was simulated with various modeling parameters and their affects on the calculated 

results were evaluated. The comparison of these simulations with experimental data is shown in Figure 3. 

These simulations used two-dimensional axisymmetric grids, with a baseline grid of 36 radial cells and 

170 axial cells resulting in 18,249 active cells (which include two planes of ghost cells to impose 

boundary conditions). In order to maintain a reasonable size grid with reasonable cell aspect ratios for the 

wide range of sizes of geometric features in these jet mixing problems, no attempt was made to resolve 

the flowfield within the jet. Two to four computational cells were used across the jet diameter. The 18,249 

active cell grid with 2nd order advection and the k- turbulence model produced satisfactory agreement 

with the mixing observed experimentally when compared to the temperature distribution in the fluid in 
NASA/TM—2010-216749 4 

the tank. The 8,978 active cell grid significantly underestimated the mixing occurring at the top of the 

tank. The RNG turbulence model seems to slightly over predict the mixing occurring in most parts of the 

tank. The 3rd order advection scheme with 18,249 active cells over predicts the mixing occurring at the 

mid-fluid height in comparison to the 2nd order scheme. Based on these results, subsequent CFD mixing 

simulations used a 2nd order advection scheme, the k- turbulence model, and approximately 18,000 

active cells in two-dimensional axisymmetric grids. A comparison of the computed temperature histories 

in the tank and the experimentally observed temperatures for the 0.00081 m nozzle case using the 

parameters selected above are shown in Figure 4. Reasonable agreement with experimental data is 

obtained but the simulation is still over predicting the temperature at the wall at 88 s. 

Two test cases were chosen to evaluate the scaling capabilities of the code. The cases were selected 

based on matches of relevant similarity parameters and the level of documentation of experimental 

results. The values for the relevant parameters for the two cases selected, Test 27 (Run 74) and (Run 49) 

are shown in Table 1.The scaling parameters for the two cases selected are not exact matches. The cases 

represent the best matches of scaling parameters using cases that are documented sufficiently to make 

meaningful comparisons between the simulations and experimental data. The ratio (Zb/Do) of the vertical 

distance from the jet exit to the liquid/gas interface (Zb) over the jet diameter (Do) for the two cases are 

within 29 percent of each other. The ratio (Zb/Dt) for the small tank case is more than a factor of two 

greater than that for the large tank case. The biggest mismatch is in the jet Reynolds number (ReJ) 

although both cases should be fully turbulent based on pipe and jet flow correlations. 

TABLE 1.—OPERATING PARAMETERS FOR SIMULATION TEST CASES 

Test Tank size Do = Nozzle 

diameter, 

m 

Jet velocity, 

m/s 

Zb/Dt Zb/Do ReJ Initial 

T, K 

Test 5, 

Run 50 

Small 

(Refs. 1 and 2) 

0.00081 9.6 2.00 743.8 1.15e+4 20.7 

Test 27, 

Run 74 

Small 

(Refs. 1 and 2) 

0.00636 1.48 2.03 95.2 9.60e+3 22.8 

Run 49 Large 

(Refs. 3 and 4) 

0.02226 21.7 0.89 122.0 5.08e+5 7.9 

The large water tank used a pump inside the tank to recirculate water to create a jet for mixing. A 

source/sink pair was used to model the internal pump and jet rather than a velocity inlet boundary 

condition. Other than the steady state flowrate, little information is provided on the pump transient or 

efficiency which adds uncertainty to the analysis. 

In Figure 5, a time sequence of the effectiveness of the jet mixing process is displayed in terms of the 

temperature field in the large, 3.05 m diameter tank. At time 0 s, an initial thermal stratification is setup in 

the tank based on the T quoted in the report. In the experiment, this stratification layer was setup by 

injecting heated water on the top of the water already in the tank. In the simulation, the jet source/sink 

pump model is turned on at full flow rate at time zero. The jet proceeds towards the stratified fluid as it 

spreads. As it encounters the water/air interface, it disturbs the interface slightly and is contained and 

turned (t = 6 s). It then proceeds to sweep away the stratified layer. The sweeping process continues until 

the fluid is trapped against the wall and begins to move down the tank wall and spread. As the warmer 

fluid spreads, it becomes entrained in the flow of the jet (t = 12 s). This process continues to fold and mix 

the warmer fluid. 

In the large tank tests, temperature measurements were not recorded in an axial array as in the small 

tank tests. Temperatures were measured radially in the tank approximately 0.0127 m (0.5 in.) below the 

surface of the water. A comparison between experimental data at various radial locations in the tank near 

the surface and the computed results are made in Figure 6. Qualitative trends in the time history are 

captured and reasonable quantitative agreement is obtained given the uncertainty of some of the details of 

the experiment. It is interesting to note that the tank was considered fully mixed at 36 s in the experiment. 

The simulations show (Figs. 5 and 6) that at the location of the thermocouples near the surface of the 

water in the tank, the temperature field is fairly uniform. However, Figure 5 shows that a fair amount of 

temperature striation still exists below the location of the thermocouple array. 
NASA/TM—2010-216749 5 

The simulation results for the corresponding small tank case are shown in Figure 7. Initial condition 

data from the experiment is provided at 8 s before the jet is turned on. In the simulation, 8 s are simulated 

with no jet flow to allow the stratified layer to evolve. A comparison of the simulated results with 

experimental data at 62 s shows very good agreement with the tank being mixed out. Figure 8 shows a 

time sequence of temperature contours for the jet mixing process in the small tank. Similar to the large 

tank, the jet perturbs the water interface but is contained by it and sweeps across the stratified layer (t = 

9.4 s). A portion of the stratified layer is trapped against the wall and moves down the tank. A comparison 

of Figures 5 and 8 shows that the stratified layer is entrained by the jet much sooner in the large tank with 

the higher jet Reynolds number and greater spreading of the jet. The cyclic nature of the mixing process is 

shown at times t = 16 s and t = 20 s. The warmer fluid moves down the tank wall and is entrained by the 

jet and is then propelled to the interface. The warm fluid is contained by the interface and is forced back 

down the tank wall where the process of entrainment is repeated until the tank is mixed out (t = 40 s). A 

colder layer of fluid does persist for some time at the very bottom of the tank. 

Scaling Existing LH2 Axial Jet Experiment to EDS LH2 LEO Conditions 

A representative EDS LH2 tank is shown in Figure 9 with a 9.894 m diameter, a 10.248 m total height 

and a 3.89 m high cylindrical section. Current EDS lunar missions use approximately 50 percent of EDS 

propellant for insertion of the EDS/lunar lander stack into LEO followed by several days of LEO coast 

with the EDS LH2 and LO2 tanks near 50 percent liquid fill levels. It is during this LEO coast that axial jet 

operation would be required for thermal destratification and pressure control. This study did not attempt a 

detailed axial jet mixer or thermodynamic vent system design for the EDS tanks, but did perform a simple 

analysis to scale a well-performing axial jet mixer design from a set of ground-based LH2 experiments 

(Ref. 14) to an EDS LH2 scale tank. The ground based jet mixer tests were performed at the Glenn 

Research Center’s K-site. The K-site LH2 axial jet experiments (Ref. 14) were conducted in an ellipsoidal 

tank with 2.2 m major diameter and 1.833 m minor diameter (or tank total height) at various liquid fill 

levels and axial jet flow rates. The axial jet was located along the vertical tank axis with the jet exit 51 cm 

above the tank bottom and with a jet nozzle diameter of 2.21 cm. While not geometrically equivalent to 

the representative EDS geometry, the differences in EDS and K-site experiment tank geometries are 

expected to be less important near the 50 percent fill level. The K-site test Run 449 using a liquid fill level 

of 49 percent (for which Hs = 0.93 m or Zb = 0.42 m), a jet liquid temperature 1.6 K less than the 

liquid/vapor interface temperature and a jet volume flow rate of 3.41 m3

/hr demonstrated good pressure 

reduction and thermal destratification. A scaling analysis was used to determine EDS tank values for jet 

nozzle diameter and jet mass flow rate. 

For two different scale tanks that are using the same propellant (LH2 in this case) at similar 

thermodynamic conditions and liquid fill levels (near 50 percent), the following non-dimensional liquid 

parameters were chosen to be matched (as best as possible) in order to maintain similar fluid and 

thermodynamic behavior for axial jet mixing: 

௦ܦ

௢ܦ

 and 

ܼ௕

௢ܦ

ݎܩ ൌ ܽ βρଶ ܪ௦

ସ ݍ௪

μଶ ݇ 

ReJ ൌ 

4 ݉ሶ

π μ ܦ௢

ܬொ ൌ ܥ௣൫ܶ௦ െ ܶ௃൯ ݉ሶ

ܳ௪
NASA/TM—2010-216749 6 

For the K-site test run 449 at 49 percent liquid fill level, we have 

௦ܦ

௢ܦ

ൌ 100 and 

ܼ௕

௢ܦ

ൌ 19

Which results in EDS LH2 tank values of Do = 0.09894 m and Zb = 1.88 m. This value for Zb was not 

used in the actual CFD grid since the problem setup (and jet configuration variation) was simpler with a 

jet nozzle at the tank bottom, but also a jet nozzle at the tank bottom provides the potential for more jet 

spreading before reaching the liquid/gas interface (which reduces interface distortion by the jet for a given 

jet Reynolds number relative to a jet exit closer to the interface). 

The values for net acceleration, ܽ, and total heat leak, Qw, into the EDS LH2 tank during LEO have a 

range of possible values, but for this study the following values were used for the scaling analysis: ܽ = 

10 g and Qw = 512 W (or qw = 1.43 W/m2

). For a fixed values of EDS tank dimensions, liquid fill level 

and average wall heat flux, the Grashof number for the EDS tank is fixed at Gr = 5.64e+11 compared to a 

K-site Gr = 1.80e+14, so it is not possible to match Grashof (or Rayleigh) numbers. What can be more 

important than exactly matching Gr and ReJ is matching the ratio of volume flow rate due to natural 

convection flow along the tank walls and liquid/gas interface and the axial jet volume flow rate, which 

can be expressed as (Ref. 14) 

࣬Էሶ ൌ Էሶ

௡௖

Էሶ

௃

 ܥ ൌ

௦ܦ

ܼ௕

1

Re௃

 ൬

ݎܩ

൰ݎܲ

௠

where C and m are constants. Using the expressions for the volume flow rates Էሶ

௡௖ and Էሶ௃ given by Lin, 

et al. (Ref. 14) provides the values C = 2.5614 and m = 2/7. The value of m = 1/2 is also considered here 

since Gr can be interpreted as the natural convection Reynolds number squared and m = 1/2 results in ࣬Էሶ

being directly proportional to the ratio of natural convection and axial jet Reynolds numbers. To provide a 

value for the EDS jet mass flow rate (or equivalently, EDS jet speed ܸ௃), two approaches were used: (1) 

Match the parameters ܬொ and ࣬Էሶ to the same accuracy between K-site (tank 1) and EDS (tank 2) 

ொଶܬ

ொଵܬ

ൌ ࣬Էሶଶ

Էሶଵ࣬

 ฺ EDS ܸ௃ ൌ 0.055

m

s ൬for ݉ ൌ

1

2

൰ or ܸ௃ ൌ 0.185

m

s ൬for ݉ ൌ

2

7

൰

or (2) match the parameter ࣬Էሶ exactly between the two tanks 

Էሶଶ࣬

Էሶଵ࣬

ൌ 1 ฺ EDS ܸ௃ ൌ 0.642

m

s ൬for ݉ ൌ

1

2

൰ or ܸ௃ ൌ 1.18

m

s ൬for ݉ ൌ

2

7

൰

The above analysis did not consider surface tension effects and interface breakup. One criterion 

developed provided by Thomas (Ref. 25) and used by Lin, et al. (Ref. 14) for the onset of interface 

surface breakup is given by 

Re௃ ൒ 0.46 ρଵ/ଶሺሾρ െ ρ୳୪୪ሿ a σሻଵ/ସ Zୠ ⁄μ ൌ 4.16 x 10ସ for EDS LH2 tank

For the above EDS jet speeds with a jet nozzle diameter of Do = 0.09894 m, only the jet speed of 

0.055 m/s provides a jet Reynolds number just below the above criterion (ReJ = 3.1e+04), so the other jet 

speeds are likely to result in significant interface distortion or breakup. 
NASA/TM—2010-216749 7 

Simulation of Representative EDS Hydrogen Tank Jet Mixing 

Preliminary axial jet simulations for a representative EDS LH2 tank in LEO are performed for several 

axial jet configurations. These preliminary axial jet simulations are evaluating only the mixer 

performance for relatively short durations and do not include the effects of heat leak into the tank nor 

phase change along the liquid/ullage interface. Also, the initial conditions used for these simulations 

employ zero velocity in the ullage and liquid, while fully-developed natural convection flows in the liquid 

and ullage would be expected prior to each activation of the axial jet for long duration storage in LEO. 

Future work may include these effects and simulate several cycles of pressure rise during selfpressurization periods followed by pressure decay and thermal destratification while the jet mixer is on 

(with or without TVS operation); that is, future simulations would model several complete pressure 

control cycles. 

As discussed in the previous section, the geometry used to represent an EDS class hydrogen 

propellant tank is shown schematically in Figure 9 and is defined as 9.894 m in diameter and 10.248 m 

high with a 3.89 m high cylindrical section. A 50 percent hydrogen liquid fill level was used for the 

simulations as representative of conditions in LEO since current EDS designs use approximately 

50 percent of EDS propellant for LEO insertion. A net axial acceleration of 10 g was imposed on the 

tank with a resulting Bond number based on tank radius of 93. While the actual EDS/lunar lander stack 

may experience net acceleration levels below 1 g and with a vector not necessarily aligned with the tank 

“height” axis (Ref. 26), this higher net acceleration provided a conservative estimate of the mixer flow 

rate (or pump power) likely to be required for the EDS tank mixer operation. The baseline axial jet 

configuration simulated used a jet entering from the bottom center of the tank to mix the propellant. No 

drain was simulated. 

Two-dimensional axisymmetric simulations of jet mixing were performed at various jet inlet 

velocities ranging from 0.06 to 5.50 m/s. The diameter of the jet remained fixed at 0.09894 m. As an 

initial condition, a rather conservative 2 K temperature gradient was setup in the liquid hydrogen near the 

interface. No temperature stratification was placed in the 22 K hydrogen gas that formed the ullage. The 

pressure in the tank was set to 0.142 MPa. 

The mixing sequence for a jet velocity of 0.06 m/s is shown in Figure 10. By 800 s, a significant 

curvature of the fluid interface has been established due to surface tension forces and the low gravity 

environment. At this jet velocity, the jet perturbs the interface (t = 800 s and t = 1600 s) but does not 

penetrate it. Significant mixing of the initially stratified layer occurs as the jet is turned and sweeps under 

the interface. The motion is similar to the phenomena seen in the simulation of the water tanks however, 

the curved interface at the wall provides less of a constraint for the jet (t = 2400 and t = 3200 s). 

At a jet velocity of 0.185 m/s, the jet penetrates the liquid interface (Fig. 11). There is little mixing of 

the stratified layer away from the immediate area near the jet. A comparison of the temperature contours 

at t = 600 s and t = 1000 s shows that the jet has hardly moved axially and is slowly spreading radially 

into the ullage. 

Increasing the jet velocity to 0.642 m/s permits the jet to penetrate the interface and hit the top of the 

tank (Fig. 12). The jet is diverted by the top of the tank and spills down the outside wall of the tank (t = 

400 s and t = 600 s). Significant mixing occurs but some stratification persists at the bottom of the ullage 

near the jet as the recirculated fluid does not penetrate there. 

Finally, at a jet velocity of 5.50 m/s an extreme case an order of magnitude above the values from 

scaling, (Fig. 13) the jet quickly penetrates the interface and impacts on the top of the tank. Rapid mixing 

ensues as the ullage is forced to the side of the tank and the thermal stratification of the liquid is gone by 

400 s. 

Several alternative geometries to the single straight jet mixer were explored. Imparting a swirl 

component to the jet equal to the axial velocity component did little to enhance the mixing of the stratified 

layer. The swirl component was too diminished by the time it reached the interface to effect the mixing. 

Pulsing the single jet on and off increased the mixing of the stratified layer slightly. A multiple jet 

geometry was simulated with a center jet surrounded by four jets equally spaced at a radial distance that 
NASA/TM—2010-216749 8 

roughly divided the surface area of the interface in two. The jet velocity was set at 0.06 m/s. The area of 

the central jet was equal to the total area of the four surrounding jets. The velocity of all the jets was the 

same. The five jet geometry required a three-dimensional computational domain. The computational 

domain consisted of a quarter of the tank with symmetry planes passing through the centerlines of the jets. 

The mixing resulting from the five jet geometry is shown in Figure 14. A comparison of the five jet case 

in Figure 14 with the single jet case at the same velocity in Figure 10 shows the mixing enhancement 

possible by distributing the jet flow. 

Summary and Conclusions 

CFD simulations were performed of jet mixers in tanks with diameters and jets of varying sizes. 

Modeling parameters were determined that provided reasonable agreement with the available 

experimental data for jet mixing in a 1 ft diameter water tank. The same modeling parameters were used 

to simulate the mixing in water jet mixing experiments with scales approximately an order of magnitude 

apart. The simulation results showed good agreement with experimental temperature data. A scaling 

strategy using available similarity correlations was developed to determine the appropriate jet size and 

operating condition for an EDS class jet mixer. With the modeling parameters determined from the water 

tank simulations, CFD simulations were performed of the mixing histories of an EDS class propellant 

tank using a jet mixer to control thermal stratification. The simulation results show a wide variety of 

mixing behaviors and were consistent with those expected from the use of the similarity parameters. 

These results provide some confidence that CFD simulations along with subscale testing and similarity 

correlations would permit the design of efficient jet mixers for EDS class tanks. 

References 

1. Poth, L.J., Van Hook, J.R., Wheeler, D.M. and Kee, C.R., “A Study of Cryogenic Propellant Mixing 

Techniques. Volume 1 - Mixer design and experimental investigations,” NASA CR-73908, Nov 

1968. 

2. Poth, L.J., Van Hook, J.R., Wheeler, D.M. and Kee, C.R., “A Study of Cryogenic Propellant Mixing 

Techniques. Volume 2 - Experimental data Final report,” NASA CR-73909, Nov 1968. 

3. Scale Experimental Mixing Investigations and Liquid-Oxygen Mixer Design,” NASA CR-113897, 

Sep 1970. 

4. Van Hook, J.R. and Poth, L.J., “Study of Cryogenic Fluid Mixing Techniques. Volume 1 - Large-Van 

Hook, J.R., “Study of Cryogenic Fluid Mixing Techniques. Volume 2 - Large-Scale Mixing Data,” 

NASA CR-113914, Sep 1970. 

5. Poth, L.J. and Van Hook, J.R., “Control of the Thermodynamic State of Space-Stored Cryogens by 

Jet Mixing,” J. Spacecraft, Vol. 9, No. 5, 1972. 

6. Lovrich, T.N. and Schwartz, S.H., “Development of Thermal Stratification and Destratification 

Scaling Concepts - Volume II. Stratification Experimental Data,” NASA CR-143945, 1975. 

7. Dominick, S.M., “Mixing Induced Condensation Inside Propellant Tanks,” AIAA–1984–0514. 

8. Meserole, J.S., Jones, O.S., Brennan, S.M. and Fortini, A., “Mixing-Induced Ullage Condensation 

and Fluid Destratification,” AIAA–1987–2018. 

9. Barsi, S., Kassemi, M., Panzarella, C.H. and Alexander, J.I., “A Tank Self-Pressurization Experiment 

Using a Model Fluid in Normal Gravity,” AIAA–2005–1143. 

10. Stark, J.A. and Blatt, M.H., “Cryogenic Zero-Gravity Prototype Vent System,” NAS8-20146, Convair 

Report GDC-DDB67-006, Oct 1967. 

11. Bullard, B.R., “Liquid Propellant Thermal Conditioning System Test Program,” NAS3-12033, 

Lockheed Missiles & Space Co., NASA CR-72971, July 1972. 

12. Erickson, R.C., “Space LOX Vent System,” NAS8-26972, General Dynamics Convair Report CASDNAS 75-021, April 1975. 
NASA/TM—2010-216749 9 

13. Lin, C.S., Hasan, M.M. and Nyland, T.W., “Mixing and Transient Interface Condensation of a Liquid 

Hydrogen Tank,” NASA TM-106201 (or AIAA–1993–1968), 1993. 

14. Lin, C.S., Hasan, M.M. and Van Dresar, N.T., “Experimental Investigation of Jet-Induced Mixing of 

a Large Liquid Hydrogen Storage Tank,” NASA TM-106629 (or AIAA–1994–2079), 1994. 

15. Olsen, A.D., Cady, E.C., Jenkins, D.S. and Hastings, L., “Solar Thermal Upper Stage Cryogenic 

System Engineering Checkout Test,” AIAA–1999–2604. 

16. Van Overbeke, T.J., “Thermodynamic Vent System Test in a Low Earth Orbit Simulation,” 

NASA/TM—2004-213193 (or AIAA–2004–3838), Oct 2004. 

17. Aydelott, J.C., “Axial Jet Mixing of Ethanol in Cylindrical Containers During Weightlessness,” 

NASA-TP-1487, July 1979. 

18. Aydelott, J.C., “Axial Modeling of Space Vehicle Propellant Mixing,” NASA-TP-2107, Jan 1983. 

19. Bentz, M.D., “Tank Pressure Control in Low Gravity by Jet Mixing,” NASA CR–191012, Mar. 1993. 

20. Hasan, M.M., Lin, C.S., Knoll, R.H. and Bentz, M.D., “Tank Pressure Control Experiment: Thermal 

Phenomena in Microgravity,” NASA-TP-3564, 1996. 

21. FLOW-3D User’s Manual, version 9.4, Flow Science, Inc., Santa Fe, NM 2009. 

22. Grayson, G.D., Lopez, A., Chandler, F.O., Hastings, L.J. and Tucker, S.P., “Cryogenic Tank 

Modeling for the Saturn AS-203 Experiment,” AIAA–2006–5258. 

23. Lopez, A., Grayson, G.D., Chandler, F.O., Hastings, L.J., and Hedayat, A., “Cryogenic Pressure 

Control Modeling for Ellipsoidal Space Tanks,” AIAA–2007–5552. 

24. Lopez, A., Grayson, G.D., Chandler, F.O., Hastings, L.J. and Hedayat, A., “Cryogenic Pressure 

Control Modeling for Ellipsoidal Space Tanks in Reduced Gravity,” AIAA–2008–5104. 

25. Thomas, R.M., “Condensation of Steam on Water in Turbulent Motion,” Int. J. Multiphase Flow, 

Vol. 5, No. 1, pp. 1–15, 1979. 

26. Zimmerli, G.A., Asipauskas, M., Chen, Y. and Weislogel, M.M., “A Study of Fluid Interface 

Configurations in Exploration Vehicle Propellant Tanks,” AIAA–2010–1294.

 

 

Zb 

Figure 1.—Schematic of the small water tank. Figure 2.—Schematic of the large water tank.

Dt
NASA/TM—2010-216749 10 

Figure 3.—Affect of CFD model parameters on simulation results 

for the small tank with 0.00081 m (0.032 in.) diameter nozzle. 

Figure 4.—CFD simulation of time history for the small tank with 

0.00081 m (0.032 in.) diameter nozzle. 
NASA/TM—2010-216749 11 

t = 0 s t = 6 s 

t = 12 s t = 18 s 

t = 30 s t = 36 s 

Figure 5.—Temperature contours for large tank jet mixing simulation. 

(Temperature contour range 294 to 302 K). 
NASA/TM—2010-216749 12 

Figure 6.—Time history of radial temperature profiles in the large tank. 

Figure 7.—Time history of axial temperature profiles in the small tank 

(Nozzle diameter—0.00318 m). 
NASA/TM—2010-216749 13 

t = 8 s t = 9.4 s 

t = 11 s t = 16 s 

t = 20 s t = 40 s 

Figure 8.—Temperature contours for jet mixing in the small tank. 

(Temperature contour range 291.4 to 315 K).
NASA/TM—2010-216749 14 

Figure 9.—Schematic of a representative EDS scale propellant tank. 
NASA/TM—2010-216749 15 

t = 0 s t = 800 s

t = 1600 s t = 2400 s 

t = 3200 s t = 4000 s 

Figure 10.—Temperature contour time sequence for an EDS scale propellant tank at 

a jet mixing velocity of 0.06 m/s. 
NASA/TM—2010-216749 16 

t = 0 s t = 200 s 

t = 400 s t = 600 s 

t = 800 s t = 1000 s 

Figure 11.—Temperature contour time sequence for an EDS scale propellant tank at a 

jet mixing velocity of 0.185 m/s. 
NASA/TM—2010-216749 17 

t = 0 s t = 200 s 

t = 400 s t = 600 s 

t = 800 s t = 1000 s 

Figure 12.—Temperature contour time sequence for an EDS scale propellant tank at 

a jet mixing velocity of 0.642 m/s. 
NASA/TM—2010-216749 18 

t = 0 s t = 200 s 

t = 400 s t = 600 s 

t = 800 s t = 1000 s 

Figure 13.—Temperature contour time sequence for an EDS scale propellant tank at 

a jet mixing velocity of 5.50 m/s. 
NASA/TM—2010-216749 19 

Figure 14.—Temperature contour at t = 1000 s for the five jet mixer with a 0.06 m/s jet velocity. 
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Computational Fluid Dynamics (CFD) Simulations of Jet Mixing in Tanks of Different Scales

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Breisacher, Kevin; Moder, Jeffrey 

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WBS 095240.04.03.02.36.03 

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John H. Glenn Research Center at Lewis Field 

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13. SUPPLEMENTARY NOTES

14. ABSTRACT

For long-duration in-space storage of cryogenic propellants, an axial jet mixer is one concept for controlling tank pressure and reducing 

thermal stratification. Extensive ground-test data from the 1960s to the present exist for tank diameters of 10 ft or less. The design of axial 

jet mixers for tanks on the order of 30 ft diameter, such as those planned for the Ares V Earth Departure Stage (EDS) LH2 tank, will require 

scaling of available experimental data from much smaller tanks, as well designing for microgravity effects. This study will assess the ability 

for Computational Fluid Dynamics (CFD) to handle a change of scale of this magnitude by performing simulations of existing ground-based 

axial jet mixing experiments at two tank sizes differing by a factor of ten. Simulations of several axial jet configurations for an Ares V scale 

EDS LH2 tank during low Earth orbit (LEO) coast are evaluated and selected results are also presented. Data from jet mixing experiments 

performed in the 1960s by General Dynamics with water at two tank sizes (1 and 10 ft diameter) are used to evaluate CFD accuracy. Jet 

nozzle diameters ranged from 0.032 to 0.25 in. for the 1 ft diameter tank experiments and from 0.625 to 0.875 in. for the 10 ft diameter tank 

experiments. Thermally stratified layers were created in both tanks prior to turning on the jet mixer. Jet mixer efficiency was determined by 

monitoring the temperatures on thermocouple rakes in the tanks to time when the stratified layer was mixed out. Dye was frequently injected 

into the stratified tank and its penetration recorded. There were no velocities or turbulence quantities available in the experimental data. A 

commercially available, time accurate, multi-dimensional CFD code with free surface tracking (FLOW-3D from Flow Science, Inc.) is used 

for the simulations presented. Comparisons are made between computed temperatures at various axial locations in the tank at different times 

and those observed experimentally. The affect of various modeling parameters on the agreement obtained are assessed. 

15. SUBJECT TERMS

Simulation; Jet mixing flow; Propellant tank 

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