A numerical model to predict boil-off of stored propellant in large spherical cryogenic tanks has been developed. Accurate prediction of tank boil-off rates for different thermal insulation systems was the goal of this collaboration effort. The Generalized Fluid System Simulation Program, integrating flow analysis and conjugate heat transfer for solving complex fluid system problems, was used to create the model. Calculation of tank boil-off rate requires simultaneous simulation of heat transfer processes among liquid propellant, vapor ullage space, and tank structure. The reference tank for the boil-off model was the 850,000 gallon liquid hydrogen tank at Launch Complex 39B (LC- 39B) at Kennedy Space Center, which is under study for future infrastructure improvements to support the Constellation program. The methodology employed in the numerical model was validated using a sub-scale model and tank. Experimental test data from a 1/15th scale version of the LC-39B tank using both liquid hydrogen and liquid nitrogen were used to anchor the analytical predictions of the sub-scale model. Favorable correlations between sub-scale model and experimental test data have provided confidence in full-scale tank boil-off predictions. These methods are now being used in the preliminary design for other cases including future launch vehicle

Fesmire, J. E.

Majumdar, A. K.

Maroney, J. L.

Sass, J. P.

Steadman, T. E.

NASA Technical Reports Server

NUMERICAL MODELING OF PROPELLANT BOIL-OFF IN A CRYOGENIC 
STORAGE TANK 
A.K. Majumdar', T.E. Steadman2 , J.L. Marone?, J.P. Sass 3 and J.E. Fesmire3 
'NASA Marshall Space Flight Center, ER43 
Huntsville, AL, 35812, USA 
2Jacobs Engineering, ESTS Group 
Huntsville, AL, 35806, USA 
3NASA Kennedy Space Center, KT-E 
Kennedy Space Center, FL, 32899, USA 
ABSTRACT 
A numerical model to predict boil-off of stored propellant in large spherical cryogenic 
tanks has been developed. Accurate prediction of tank boil-off rates for different thermal 
insulation systems was the goal of this collaboration effort. The Generalized Fluid 
System Simulation Program, integrating flow analysis and conjugate heat transfer for 
solving complex fluid system problems, was used to create the model. Calculation of 
tank boil-off rate requires simultaneous simulation of heat transfer processes among 
liquid propellant, vapor ullage space, and tank structure. The reference tank for the boil-
off model was the 850,000 gallon liquid hydrogen tank at Launch Complex 39B (LC-
39B) at Kennedy Space Center, which is under study for future infrastructure 
improvements to support the Constellation program. The methodology employed in the 
numerical model was validated using a sub-scale model and tank. Experimental test data 
from a l/l5t1 scale version of the LC-39B tank using both liquid hydrogen and liquid 
nitrogen were used to anchor the analytical predictions of the sub-scale model. Favorable 
correlations between sub-scale model and experimental test data have provided 
confidence in full-scale tank boil-off predictions. These methods are now being used in 
the preliminary design for other cases including future launch vehicles. 
KEYWORDS: Cryogenic tanks, thermal insulation, propellant boil-off, finite volume 
method, conjugate heat transfer 
PACS:
1
https://ntrs.nasa.gov/search.jsp?R=20120000652 2019-08-30T18:51:19+00:00Z
INTRODUCTION 
The cost of loss of propellants due to boil-off in large cryogenic storage tanks is in the 
order of one million dollar per year. One way to reduce this cost is to design a new tank 
or refurbish existing tanks by using bulk-fill insulation material with improved thermal 
performance. Such an effort was undertaken by Cryogenic Test Laboratory of Kennedy 
Space Center (KSC) to reduce the propellant boil-off in cryogenic storage tanks at 
Launch Complex 39 at KSC. The cryogenic storage tanks (Figure 1) in KSC were built 
in 1960's. The vacuumed aimulus space between the inner and outer spheres of each 
storage tank is filled with Perlite insulation. Perlite is susceptible to compaction after 
repeated thermal cycles. It is widely believed that the compaction has led to decreased 
thermal performance. 
Fesmire and Augustynowicz [1] have measured apparent thermal conductivity of several 
bulk-fill insulation materials and have found that the thermal conductivity of Glass 
Bubbles is 67% less than Perlite in vacuum. In another study Fesmire et al [2] studied the 
vibration and thermal cycling effects on several bulk-fill insulation materials and found 
that Glass Bubbles are not susceptible to compaction due to thermal cycling. As a part of 
the Independent Research and Development (IRAD) Project entitled, "New Materials and 
Technology for Cost Efficient Storage and Transfer (CESAT)", KSC [3] has built two 
1000 liter Demonstration Tanks (Figure 1) and tested to evaluate the performance of 
Perlite and Glass Bubble insulation for liquid nitrogen and hydrogen. 
The purpose of.the present paper is to develop a numerical model of the boil-off for 
cryogenic storage tank in KSC. The model developments were carried in two phases. 
First, the model was verified with the test data for Demonstration Tanks for Liquid 
Nitrogen and Hydrogen. The verified model was then extended to model the actual 
storage tank and the predictions were compared with field data. A general purpose flow 
network computer code, Generalized Fluid System Simulation Program (GFSSP) [4,5] 
was used to develop the numerical models. 
NUMERICAL APPROACH 
Boil-off calculation requires the calculation of heat leak through metal walls and 
insulation. A simple one-dimensional calculation of heat conduction through a composite 
layer consisting of metal and insulation is not adequate for estimating the boil-off 
because the heat leak process is not entirely one dimensional. The tanks are partially 
filled with vapor at a temperature higher than the liquid propellant. This vapor space, 
called the ullage, is also stratified due to gravitational effects. In addition to heat 
conduction through metal and insulation, the thermodynamics and fluid mechanics of the 
propellant also play a role in determining boil-off rate. Therefore, it is essential to use a 
code that has the capability to model all of the processes that influence boil-off. 
The Generalized Fluid System Simulation Program (GFSSP), developed at MSFC has 
been used to develop the thermal models for estimating boil-off in the Demonstration 
2
flUHFIED HY3Rc 
FLAMMABLE /
tanks and the Liquid Hydrogen Storage tank at LC-39. GFSSP is a finite volume based 
computer code for analyzing fluid flow and heat transfer in a complex network of fluid 
and solid systems. GFSSP was first developed for analyzing flow network using "node" 
and "branch". After constructing the flow network with "node" and "branch", the 
program solves for mass and energy conservation in "node" and momentum conservation 
equation in "branch". The code has been subsequently upgraded [6] to model 
simultaneously fluid and solid network with conjugate heat transfer that allows 
calculation of solid temperatures with convection and radiation heat transfer with fluid 
nodes and conduction and radiation heat transfer with other solid nodes. 
DESCRIPTION OF CRYOGENIC PROPELLANT TANKS 
Two identical 1115th scale demonstration test tanks were manufactured for the CESAT 
test program [7]. Both tanks (Figure 1) were constructed with stainless steel inner and 
outer spheres. The annular space between the two spheres in each tank can be filled with 
an insulating material and the pressure can be reduced to vacuum conditions. Both tanks 
include fill/drain lines, vent lines, support structures and anti-rotation systems that could 
contribute to heat leak. Both tanks are heavily instrumented with identical measurements 
in identical locations. Boil-off during CESAT testing was measured using either two 
flow meters installed on the vent line of each tank or by evaluating the total change in 
weight of the tank during testing. Temperature was measured at several locations on both 
the inner and outer sphere. 
r	 .. 
	
..	
. . 
u. 
	
I	 I•i•	
, 
Figure 1: Liquid Hydrogen Tank in LC-39A and Demonstration Tanks at Kennedy

Space Center 
There are two full scale liquid hydrogen tanks located at KSC LC-39. Both tanks were 
built in 1965 for the Apollo program and fabricated by Chicago Bridge and Iron of Salt 
Lake City, Utah. Both tanks (Figure 1) were constructed with austenitic stainless steel 
inner spheres and carbon steel outer spheres. The annular space between the two spheres 
in each tank can be filled with an insulating material and the pressure can be reduced to 
vacuum conditions. Both tanks include fill lines, vent lines, and support structures that 
could contribute to heat leak. Figure 5 shows the dimensions of the two full scale tanks. 
3
Asstned F 
B5% d(Tak
wall 
14 
xl Mateflal 
17 & 18 
NUMERICAL MODEL DEVELOPMENT 
Figure 2 shows a schematic that illustrates the technique that was developed for modeling 
the CESAT demonstration tanks. The figure shows that the heat path from ambient to 
propellant was broken into an ullage path and a propellant path. The heat transferred 
through the ullage path into the ullage space (Q,a-u) is used to calculate the ullage 
temperature, which is then used to calculate the heat transfer between the ullage and 
propellant (Q,u-p). The heat transferred through the propellant path (Q,a-p) is calculated 
independently. The heat transferred through the structure (Q,s-p) is assumed as a 
constant value from a separate calculation. Q,u-p, Q,a-p and Q,s-p are summed to 
determine the total heat transferred to the propellant. The total heat transfer is then used 
to calculate the propellant boil-off rate. Figure 3 shows the GFSSP model that was 
developed based on this modeling technique. The model consists of five fluid nodes 
connected by three fluid branches, as well as one ambient and twelve solid nodes joined 
to the fluid and each other by twenty conductors. 
Ambient 
Node 6	
Inne( Spflere Wall 
Figure 2 Schematic Illustrating Boil-Off Fill Level Modeling Technique 
While the model shown in Figure 3 was appropriate for modeling the CESAT 
demonstration tanks, it was found to be inadequate for modeling the LC-39 cryogenic 
storage tanks. Because of the difference in scale between the demonstration and full 
scale tank ullage spaces, using a single node to represent the ullage space led to 
unrealistic ullage temperature predictions. Therefore, the ullage space was subdivided 
into eight nodes to simulate the stratified environment. The details of the numerical 
models presented in this paper are descnbed in reference 8. 
4
Vent 
L Inc
I
Inner Wall Insulation	 Outer Wall 
12 
Ullage 
Node 102	 16 1516	 815 78 
HTC-R 
PS -DD-*D---l' 67 
HTCR 
' 1014 13 1618 
I I
1517 812 711
Zn
Ambient 
$
HTER
I 
Propellant 144	 1314	 1813 1718	 1217 1112 
Node	 46
Drain 
Line
Figure 3 GFSSP Model of CESAT Demonstration Tank 
NUMERICAL MODEL RESULTS 
All GFSSP predictions were performed at a fill level of 85% of the tank height 
(approximately 94% of the total tank volume) which was a reasonable assumption for a 
"full" storage tank. All predictions were first made as pre-test predictions. When testing 
was complete each test data set was examined to determine which boil-off test had initial 
conditions (ambient conditions and fill level) closest to the GFSSP predictions. These 
test results were then compared with GFSSP's predictions. These comparisons are 
shown in Table 1 for different liquid and insulation configurations. 
GFSSP predicts a lower ullage space skin temperature than the test data for all four cases. 
Due to the fact that the test data is a point temperature measurement, while GFSSP is 
calculating the average skin temperature for the entire ullage-exposed inner sphere, the 
differences are believed to be due to the fidelity of the model. Due to stratification there 
is a temperature variation in the ullage where as temperature of liquid propellant does not 
vary with depth and much closer agreement is obtained for liquid skin temperature. 
The predicted boil-off rates for the two liquid nitrogen comparisons are consistently 
lower than the measured test data. One factor in these discrepancies was uncertainty in 
the ullage-wall and ullage-propellant heat transfer coefficients, which were not adjusted 
to match the test data. Another possible factor is that the anti-rotation devices for both 
test tanks may have been in contact during liquid nitrogen testing. The predicted boil-off 
rates for the two liquid hydrogen comparisons match very well with measured test data. 
Initially, the liquid hydrogen comparisons were predicting much higher boil-off rates than 
5 
those seen in testing. It was found that the ullage-propellant heat transfer was 
disproportionately high for these GFSSP predictions. Because temperature stratification 
in the ullage of a liquid hydrogen tank is more pronounced than that of a liquid nitrogen 
tank, the effect of natural convection is negligible in a liquid hydrogen tank. Therefore, it 
was assumed that ullage to propellant heat transfer, Q,u-p (Figure 2) was governed by 
solely conduction heat transfer for the liquid hydrogen predictions. 
Table 1. Comparison of GFSSP Predictions with Test Data 
Propellant Insulation Boil-off Rate (sccm) Tskin.ullage (K) Tskin,propeIant (K) 
Test 
Flow Load GFSSP Test GFSSP Test GFSSP 
__________ __________ meter cell __________ 
Nitrogen Perlite 3860 4018 3468
_______ 
92
________ 
81 77 76 
3938 4206 89 77 
Nitrogen Glass 3230 3260 2493 92 80 77 76 
Bubble 
Hydrogen Perlite 20414 19182 20980 34 21 20 20 
Hydrogen Glass 13396 13242 12920 31 21 20 20 
Bubble
Based on the results of the CESAT work, a GFSSP model was developed for the LC-39 
complex liquid hydrogen storage tanks. The Full Scale Perlite GFSSP model predicts a 
boil-off of 258 gallons/day. This compares to the field measurement (approximately 300 
gal/day) [3]. The main reason for the discrepancy is uncertainty in the ullage to 
propellant heat transfer coefficient due to the size differences between CESAT and the 
full scale storage tanks. Using this model, GFSSP predicts that a full scale liquid 
hydrogen storage tank with Glass Bubbles insulation would have a boil-off rate of 182 
gallons/day. Figure 9 shows GFSSP's stratified ullage temperature prediction for the full 
scale Glass Bubbles model. Heights from the propellant surface to the "top" of each node 
location are noted in the figure. GFSSP predicts a 90 K differential between the ullage 
temperature at the propellant surface and the ullage temperature at the top of the tank. 
CONCLUSIONS 
A novel numerical modeling technique has been developed using GFSSP to predict boil-
off rate from a spherical cryogenic storage tank. The model recognizes the separation of 
liquid and the vapor space and appropriately solves for mass, momentum and energy 
conservation equations of liquid and vapor volume in the tank in conjunction with heat 
conduction equations through metallic walls and insulation material. A numerical model 
has been built for the Demonstration Tanks developed at KSC. The numerical 
predictions have compared favorably with test data for liquid nitrogen and liquid 
hydrogen with Perlite and Glass Bubble insulation. With the experience gained from the 
Demonstration Tank models, a separate numerical model was developed for the Liquid 
Hydrogen Storage Tank at LC-39 at KSC. This model has used multiple nodes in the 
ullage space to account for the effect of stratification. The numerical model of the full 
scale tank was then run using Perlite and Glass Bubble insulation. The boil-off rate using 
Perlite Insulation is in agreement with field data. When using Glass Bubble instead of 
Perlite as insulation, the numerical model predicts a) 28% reduction in boil-off rate in 
Liquid Nitrogen Demonstration Tank, b) 38% reduction in boil-off rate in Liquid 
Hydrogen Demonstration Tank, c) 30% reduction in boil-off of Liquid Hydrogen Storage 
Tank in LC-39 at KSC. 
300 
250 
50
0	 20	 40	 60	 80	 100	 120
Temperature (K) 
E
200 
C., 
C 
t 
CO 
C
150 
a. 
0 
a. 
E 
0
100 
C 
I
Figure 4 Stratified Ullage Temperature Prediction for LC-39 with Glass Bubbles

Insulation. 
ACKNOWLEDGEMENT 
Funding was provided by the NASA Space Operations Mission Directorate under the 
Internal Research and Development project New Materials and Technologies for Cost-
Efficient Storage and Transfer of Ciyogens. The authors would like to acknowledge 
Steve Sojourner and Zoltan Nagy of Cryogenic Test Laboratory at Kennedy Space Center 
for their valuable contribution to this effort through many Technical Interchange 
Meetings and discussions of Test Data.
7
REFERENES 
1. Fesmire, J. E., Augustynowicz, S. D., "Thermal Performance Testing of Glass 
Microspheres under Cryogenic Vacuum Conditions", Paper No. CEC C2-C-04, 
Cryogenic Engineering Conference, Anchorage. 
2. Fesmire, J. E., Augustynowicz, S. D.,Nagy, Z.F. , Sojourner, S. J. and Morris, D. 
L., "Vibration and Thermal Cycling Effects on Bulk-Fill Insulation Materials for 
Cryogenic Tanks", Paper No. CEC C2-T-04, Cryogenic Engineering Conference, 
Keystone. 
3. Fesmire, J.E., Sass, J.P., Nagy, Z., Sojourner, S.J., Morris, D. L. and 
Augustynowicz, S.D., "Cost-Efficient Storage of Cryogens." Cryogenic 
Engineering Conference (CEC), July 16-20, 2007 in Chattanooga, TN, USA 
(Advances in Cryogenic Engineering Publication) 
4. Majumdar, A. K., "A Second Law Based Unstructured Finite Volume Procedure 
for Generalized Flow Simulation", Paper No. AIAA 99-0934, 37th AIAA 
Aerospace Sciences Meeting Conference and Exhibit, January 11-14, 1999, Reno, 
Nevada. 
5. Majumdar, A. K. and Steadman, T., "Numerical Modeling of Pressurization of a 
Propellant Tank", Journal of Propulsion and Power, Vol. 17, No.2 pp 385-391, 
March-April, 2001. 
6. Majumdar, Alok, "Numerical Modeling of Conjugate Heat Transfer in Fluid 
Network", Thermal Fluid Analysis Workshop, August 30 - September 3, 2004, 
Jet Propulsion Laboratory, Pasadena, California 
7. Sass, J. P., Fesmire, J.E., Morris, D. L., Nagy, Z., Augustynowicz, S.D. & 
Sojourner, S. J., "Thermal Performance Comparison of Glass Microsphere and 
Perlite Insulation Systems for Liquid Hydrogen Storage Tanks". Cryogenic 
Engineering Conference (CEC), July 16-20, 2007 in Chattanooga, TN,USA 
(Advances in Cryogenic Engineering Publication) 
8. Majumdar, Alok, Steadman Todd & Maroney, Johnny, "Numerical Modeling of 
Propellant Boil-off in Cryogenic Storage Tank", CESAT Thermal Modeling 
Project Report submitted to KSC (September, 2006) to be published as NASA 
Technical Memorandum.
8


Numerical Modeling of Propellant Boil-Off in a Cryogenic Storage Tank

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