A general purpose SINDA/FLUINT (S/F) stratified tank model was created and used to simulate the Ksite1 LH2 liquid self-pressurization tests as well as axial jet mixing within the liquid region of the tank. The S/F model employed the use of stratified layers, i.e. S/F lumps, in the vapor ullage as well as in the liquid region. The model was constructed to analyze a general purpose stratified tank that could incorporate the following features: Multiple or singular lumps in the liquid and vapor regions of the tank, Real gases (also mixtures) and compressible liquids, Venting, pressurizing, and draining, Condensation and evaporation/boiling, Wall heat transfer, Elliptical, cylindrical, and spherical tank geometries. Extensive user logic was used to allow for tailoring of the above features to specific cases. Most of the code input for a specific case could be done through the Registers Data Block

Sakowski, Barbara A.

NASA Technical Reports Server

 
 
 
 
 
 
 
 
 
 
 
 
 
 
SINDA/FLUINT STRATFIED TANK MODELING 
 
 
Barbara Sakowski 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
https://ntrs.nasa.gov/search.jsp?R=20150002093 2019-08-31T14:09:03+00:00Z
 2 
Introduction 
 
A general purpose SINDA/FLUINT (S/F) stratified tank model was created and used to 
simulate the Ksite1 LH2 liquid self-pressurization tests as well as axial jet mixing within 
the liquid region of the tank.  The S/F model employed the use of stratified layers, i.e. S/F 
lumps, in the vapor ullage as well as in the liquid region.  The model was constructed to 
analyze a general purpose stratified tank that could incorporate the following features: 
? Multiple or singular lumps in the liquid and vapor regions of the tank 
? Real gases (also mixtures) and compressible liquids 
? Venting, pressurizing, and draining 
? Condensation and evaporation/boiling 
? Wall heat transfer 
? Elliptical, cylindrical, and spherical tank geometries 
Extensive user logic was used to allow for tailoring of the above features to specific 
cases.  Most of the code input for a specific case could be done through the Registers 
Data Block. 
 
SINDA/FLUINT Stratifed Tank Setup 
 
The stratified tank was modeled via a series of S/F layered lumps (TANKS) in the vapor 
and liquid regions.  The number of layers in the vapor region need not be the same as the 
number of lumps in the liquid region.  The tank wall was also modeled under the same 
premise, i.e. that the number of thermal nodes in the vapor wall region need not be the 
same as the number of thermal nodes in the liquid wall region.  Furthermore the nodes 
and lumps in the vapor region need not have a one to one correspondence.  This was also 
true in the liquid region. Wall node volumes were determined by the number of thermal 
nodes input for the vapor wall and liquid wall regions respectively.  Vapor wall node 
volumes corresponded to, or were “one to one” to, the initial “equal” vapor fluid volumes 
that would be calculated based on the input number of wall vapor nodes.  Similarly, 
liquid wall node volumes corresponded to, or were “one to one” to, the initial “equal” 
liquid fluid volumes that would be calculated based on the input number of wall liquid 
nodes (Figure 1).  Therefore wall node volumes were not necessarily uniform values in 
the vapor region or liquid region.   
 
 3 
 
Figure 1:  Tank Wall Node Generation 
 
Although initial values for the lumps’ volumes were required as input in S/F, these values 
were only guesses.  Extensive logic incorporated in the S/F user logic blocks determined 
an equal volume distribution in the vapor region and an equal volume distribution in the 
liquid region.  The volumes were determined through user input in the Registers Data 
Block such as geometric tank dimensions, liquid level, as well as the input number of 
vapor and liquid lumps.  The liquid level could be input as either a volume percentage of 
fill level or actual liquid level height. 
 
The heat rate was imposed on the outer surface of the tank wall nodes.  Axial conduction 
along the tank wall was modelled (Figure 2).  Although radial conduction was ignored in 
this model, it could easily be implemented.  The heat leaves the wall and enters the fluid 
via an imposed heat rate calculated using free convection boundary layer empirical 
relations (see SINDA/FLUINT Boundary Layer Analysis). 
 
 4 
 
Figure 2:  Stratified Tank Heat Transfer 
 
Volume Flow Rate Connectors (VFRSETs) were placed between the layered lumps in 
each region.  User logic determined the volume flow rate through these connectors so that 
the volumes of the lumps in each respective region remained constant within a small 
percentage.  This process avoided lumps from becoming too small or too large relative to 
one another, and consequently avoided the problem of having very small lumps to 
somehow “disappear”.  Making a lump “disappear” was not practical or feasible to do in 
S/F.  S/F IFACES were also placed between the layered lumps in each region.  The S/F 
IFACE was a device that insured the pressure of all the lumps within the tank remained 
constant (minus buoyancy effects).  The IFACE acted like a membrane between lumps 
that allowed the lumps to expand or contract as the thermodynamics dictated.  
Maintaining constant volumes in the vapor and liquid regions respectively created a 
model that was similar to a “finite volume” approach so that the lump geometric locations 
did not dramatically fluctuate.  The volume flow rates between lumps were determined 
and set by user logic based on the flow physics of the tank, i.e., whether the tank was 
venting, pressurizing, or draining.  Other dynamics that would yield volume flow 
between the lumps included evaporation/boiling, condensation, and axial jet mixing. 
 
SINDA/FLUINT Boundary Layer Analysis 
 
The thermal boundary layer that formed along the tank wall was modeled empirically 
using correlations for convection.  These correlations could either be for forced or free 
convective flow.  The cases modeled employed only buoyancy driven flow and therefore 
the empirical relationships were for free convective flow along a vertical wall at constant 
heat flux.  Any empirical relationship could easily be employed by the user.  The logic 
also checked for turbulent or laminar conditions.  The following correlation was used1: 
 5 
 
1.a Nu   ~ 0.57 Ra (0.22)  1013  < Ra <  1016 
 
1.b Nu   ~ 0.6 Ra (0.2)  105  < Ra <  1013 
 
The Raleigh number in these correlations was based on the respective height of each 
lump.  In the vapor region this height was taken relative to the liquid level.  Correlations 
in Equation 1 were modified to have scaling factors to account for the enclosure.  These 
scaling factors were a function of liquid level and/or tank height, and vapor/liquid 
interface diameter. 
 
Although the two dimensional flow dynamics of the boundary layer could not directly be 
incorporated into the one dimensional stratified tank model, it was incorporated in a one 
dimensional sense.  Within each fluid lump the following boundary layer characteristics 
were determined: 
? Characteristic velocity 
? Boundary layer thickness 
? Buoyancy driven volume flow rate 
The characteristic velocity as well as the boundary layer thickness could be obtained by a 
general scaling analysis employing the use of Equation 12: 
 
2.a U ~ α / H Ra (2*0.2) 
 
2.b δ ~ Pr (0.5) (H Ra (-0.2)) 
 
The boundary layer was modelled as an energy exchange between the lumps using S/F 
FTIES.  This energy was equivalent to the convective heat or, mdot Cp ΔT, of the 
boundary layer.  These energy ties went only one way,”up”, along the tank wall.  Another 
set of S/F FTIES was employed to model the “mixing” of the flow.  This mixing heat 
exchange between lumps was proportional to Ra (0.33) (Figure 3). 
 6 
 
Figure 3:  Stratified Tank Heat Transfer 
 
 
SINDA/FLUINT Vapor Liquid Interface Modeling 
 
SINDA/FLUINT contained pre-built utility functions to model heat and mass transfer 
between a liquid and vapor interface (TWIN TANKS).  However to obtain modelling 
flexibility, user logic could incorporate the necessary physics to model a wide variety of 
scenarios.  The vapor/liquid interface was modelled as a S/F PLENUM, or boundary 
state.  There were actually two PLENUMS, one to represent the vapor and the other to 
represent the liquid.  The saturation state of these PLENUMS was the saturated state of 
the “top” liquid lump and updated every iteration.  A S/F FTIE was placed between the 
“bottom” vapor lump and the boundary PLENUM.  Similarly a S/F FTIE was placed 
between the “top” liquid lump and the boundary PLENUM (Figure 4).  
 
  
Figure 4:  Interface Modelling 
 7 
 
The heat rates for these FTIEs are defined as follows:  
 
3a. QVAP =   h AINTER (TVAP - TINTER ) 
3b. QLIQ =   h AINTER (TINTER - TLIQ ) 
 
where, 
 
4. h      =  k Nu / D
INTER
   
5. Nu ~ 0.04 Ra
(1/3)
  
 
Equation 5 was modified to have scaling factors to account for the enclosure.  These 
scaling factors were a function of liquid level and/or tank height, and vapor/liquid 
interface diameter. 
 
Evaporation was modeled via the process: 
? Liquid leaves the “top” liquid lump and enters the interface PLENUM via a S/F 
MFRSET connector (Set Mass Flow Rate Connector)  
? Vapor enters the “bottom” vapor lump from the vapor interface PLENUM via a 
S/F MFRSET connector 
Condensation was modeled via the process: 
? Vapor leaves the “bottom” vapor lump and enters the interface PLENUM via a 
S/F MFRSET connector 
? Liquid enters the “top” liquid lump from the liquid interface PLENUM via a S/F 
MFRSET connector 
 
The net evaporation rate at the interface is calculated to be: 
 
6. mdot
EVAP
  =   (QVAP - QLIQ) / (Hfg) 
 
The mass flow rate, whether condensing or evaporating, should be at saturated 
conditions.  However the “bottom” vapor and “top” liquid lumps may not be saturated.  
Thus when mass was removed from either of these lumps the amount of energy leaving 
these lumps needed to be adjusted to account for this discrepancy.  
 
 
 
 
 
 
 
 
 8 
Model Case Input 
 
In the Ksite model the heat load was applied uniformly through out the liquid and vapor 
regions.  The results were compared to FLUENT CFD results and test data.  Table 1 
illustrates the relevant input parameters for the Ksite model3. 
 
 
Table 1:  Ksite Input Parameters 
 
SINDA/FLUINT Results 
 
The results for the Ksite model are illustrated in the Appendix.  For the Ksite case, 49% 
fill level, a sensitivity study was performed on varying the number of lumps in the vapor 
ullage and liquid region.  For these runs the number of vapor wall nodes was 40, and the 
number of liquid wall nodes was 50.  The other fill levels used as a “baseline” 40 lumps 
in the vapor ullage, 75 lumps in the liquid region, 40 vapor wall nodes, and 50 liquid wall 
nodes.  For all three fill level at the 2.13 W/m2, FLUENT CFD results were plotted as 
well as test data results. 
 
Overall the results from the S/F stratified tank model compared well to test data and CFD 
results.  The run time of the model with only one vapor lump and one liquid lump took 
less than 10 minutes of real time to complete.  The “baseline” runs took approximately 1 
to 2 hours of real time to complete.  The run time seemed to be more dependent on the 
number of lumps in the liquid region since runs with 1 liquid lump and 80 vapor lumps 
took less than 1 hour. 
 
  
Fill Levels:    29%, 49%, 83% 
Heat Rate:    3.5 W/m2, 2.13W/m2 
Tank:     Oblate Spheroid 
              Major Diameter = 87.6 in 
              Minor Diameter = 73 in 
Volume = 4.89 m3 
Fluid:     Parahydrogen (Real Gas/Compressed Liquid) 
Initial Conditions:  20.33 Deg K Saturated 
 9 
APPENDIX  
SECTION A:  KSITE RESULTS  
                             49% FILL LEVEL  
                                 3.5 W/m2 , 2.13 W/m2 
 
Figure A.1:  Ksite 49%, 3.5 W/m2 
 
 
Figure A.2:  Ksite 49%, 2.13 W/m2, FLUENT 
 
 
  
 10 
APPENDIX  
SECTION B:  KSITE RESULTS  
                             83% FILL LEVEL  
                                 3.5 W/m2 , 2.13 W/m2 
 
Figure B.2:  Ksite 83%, 3.5 W/m2 
 
 
Figure B.2:  Ksite 83%, 2.13 W/m2, FLUENT 
 
  
 11 
APPENDIX  
SECTION C:  KSITE RESULTS  
                             29% FILL LEVEL  
                                 3.5 W/m2 , 2.13 W/m2 
 
Figure C.1:  Ksite 29%, 3.5 W/m2 
 
 
Figure C.2:  Ksite 29%, 2.13 W/m2, FLUENT 
  
 12 
 
APPENDIX  
NOMENCLATURE 
 
α     Thermal Diffusivity 
δ     Boundary Layer Thickness 
ΔT     Temperature Difference 
A     Area 
Cp     Specific Heat 
D     Diameter 
h     Heat Transfer Coefficient 
H     Height 
Hfg     Heat of Vaporization 
k     Thermal Conductivity 
mdot     Flow Rate 
Nu     Nusselt Number 
Pr     Prandtl Number 
Q     Heat Rate 
Ra     Raleigh Number 
T     Temperature 
TSAT     Saturation Temperature 
U      Velocity 
 
SUBCRIPTS 
EVAP     Evaporation 
 13 
INTER    Interface Location 
LIQ     Liquid 
VAP     Vapor 
 
 
 
 14 
REFERENCES 
 
1. Bejan, Adrian, “Convective Heat Transfer”, John Wiley & Sons Inc., 2004, pp 
216. 
 
2. Bejan, Adrian, “Convective Heat Transfer”, John Wiley & Sons Inc., 2004, pp 
188. 
3. Hasa, M.M., Lin, C.S., and Van Dresar, N.T., “Self-Pressurization of a 
Flightweight Liquid Hydrogen Storage Tank Subjected to Low Heat Flux,” 1991 
ASME/AIChE National Heat Transfer Conference ,Minneapolis, Minnesota, July 
28-31, 1991. 
  
 
 


Sinda/Fluint Stratfied Tank Modeling

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