thermo-fluid system level modeling for the crome and crome
TRANSCRIPT
University of Texas at El PasoDigitalCommons@UTEP
Open Access Theses & Dissertations
2019-01-01
Thermo-Fluid System Level Modeling For TheCrome And Crome-X Ground Propellant SystemUsing Generalized Fluid System SimulationProgramMariano MercadoUniversity of Texas at El Paso, [email protected]
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Recommended CitationMercado, Mariano, "Thermo-Fluid System Level Modeling For The Crome And Crome-X Ground Propellant System UsingGeneralized Fluid System Simulation Program" (2019). Open Access Theses & Dissertations. 119.https://digitalcommons.utep.edu/open_etd/119
THERMO-FLUID SYSTEM LEVEL MODELING FOR THE CROME AND CROME-X
GROUND PROPELLANT SYSTEM USING GENERALIZED FLUID SYSTEM
SIMULATION PROGRAM
MARIANO MERCADO
Master’s Program in Mechanical Engineering
APPROVED:
Jack F. Chessa, Ph.D., Chair
Yirong Lin, Ph.D.
Luis Rene Contreras-Sapien, Ph.D.
Charles Ambler, Ph.D. Dean of the Graduate School
Copyright ©
by
Mariano Mercado
2019
THERMO-FLUID SYSTEM LEVEL MODELING FOR THE CROME AND CROME-X
GROUND PROPELLANT SYSTEM USING GENERALIZED FLUID SYSTEM
SIMULATION PROGRAM
by
MARIANO MERCADO, B.S.M.E.
THESIS
Presented to the Faculty of the Graduate School of
The University of Texas at El Paso
In Partial Fulfillment
Of the Requirements
For the Degree of
MASTER OF SCIENCE
Department of Mechanical Engineering
THE UNIVERSITY OF TEXAS AT EL PASO
May 2019
iv
Abstract
A recent resurgence of interest in space exploration has given rise to a number of newcomers in the space
industry. A number of private companies like SpaceX, Blue Origin, and United Launch Alliance have
joined the likes of NASA with the goal to expand the current capabilities of space travel and exploration.
Perhaps the most ambitious of these goals is a manned mission to Mars. In order to achieve this goal, many
of these companies have taken a keen interest in liquid oxygen and methane engine technologies. Engines
like the Raptor by SpaceX and the Blue Origin BE-4 already run on methane as a propellant. Methane
offers many advantages over traditional rocket fuels such as hydrogen and RP-1, but the biggest advantage
is the capability of in situ resource utilization on the surface of Mars. The ability to produce propellant on
mars would reduce the mass and cost of space exploration architecture by reducing the amount of payload
that must be launched from Earth. In partnership with NASA, the MIRO Center for Space Exploration and
Technology Research (cSETR) at UTEP has been developing a number of methane propulsion systems
including CROME a 500 lb thrust engine and CROME-X a 2000 lb thrust engine. In order to test the
engines, the cSETR has developed the Ground Propellant System (GPS) which delivers pressurized liquid
oxygen and methane to the engines for ground testing. When designing or selecting components such as
valves, tanks, and line sizes for these complex flow systems, engineers often benefit from system level
thermo-fluid simulations to determine the performance of the system. The simulations help predict
parameters like pressure drops, flowrates, and temperatures. This paper presents system level thermo-fluid
models of the GPS system during four operational modes: tank chill, tank boiloff, line chilldown, and an
engine run case. The purpose of the paper is to introduce the Generalized Fluid System Simulation Program
(GFFSP) and verify the validity of using GFSSP for future fluid system developments.
v
Table of Contents
Abstract ............................................................................................................................................ iv
Table of Contents ...............................................................................................................................v
List of Tables ................................................................................................................................... vii
List of Figures ................................................................................................................................. viii
Chapter 1 : Introduction ......................................................................................................................1
Chapter 2 : Generalized Fluid System Simulation Program....................................................................4
2.1 Network Elements ...............................................................................................................4
2.2 Mathematical Formulations ..................................................................................................6
2.3 Solution Procedure............................................................................................................. 10
2.4 GFFSP Software ................................................................................................................ 11
2.5 Graphical User Interface..................................................................................................... 12
2.5.1 Menu Bar ................................................................................................................... 13
2.5.2 Global Options ........................................................................................................... 14
2.5.3 Flow Network Design ................................................................................................. 20
2.6 Advanced Options ............................................................................................................. 25
2.7 Running the Model ............................................................................................................ 25
2.8 Post-Processing and Visualizing Results .............................................................................. 26
2.9 User Subroutines................................................................................................................ 27
Chapter 3 : Validation Models ........................................................................................................... 32
3.1 Pressure Drop in Propellant Line......................................................................................... 32
vi
3.2 Chilldown of Short Cryogenic Pipe ..................................................................................... 33
Chapter 4 : Ground Propellant System Overview ................................................................................ 37
Chapter 5 : Propellant Feed System Models ........................................................................................ 41
5.1 Tank Chilldown and Fill..................................................................................................... 41
5.2 Tank Boiloff ...................................................................................................................... 46
5.3 Line Chill down ................................................................................................................. 52
5.4 Engine Run Case ............................................................................................................... 57
Chapter 6 : Conclusion...................................................................................................................... 62
References ....................................................................................................................................... 63
Appendix ......................................................................................................................................... 66
A.1 Pressure Drop Validation Model GFSSP Input File .............................................................. 66
A.2 Chilldown of Short Cryogenic Line GFSSP Input File .......................................................... 69
A.3 Tank Chilldown and Fill GFSSP Input File .......................................................................... 74
A.4 Tank Chilldown and Fill Custom Subroutines ...................................................................... 78
A.5 Tank Boiloff GFSSP Input File ........................................................................................... 80
A.6 Tank Boiloff Custom Subroutines ....................................................................................... 83
A.7 Line Chilldown GFSSP Input File ....................................................................................... 88
A.8 Engine Run Case GFSSP Input File .................................................................................. 101
Vita ............................................................................................................................................... 123
vii
List of Tables
Table 1.1: Fluid System Modeling Software Capabilities ......................................................................3
Table 2.1: Conservation of momentum term descriptions for branch elements........................................7
Table 2.2: Fluid properties and their corresponding governing equations used to solve them ................. 10
Table 2.3: List of Commonly Used User Subroutines ......................................................................... 28
Table 2.4: Solver Module User Subroutine Interactions ...................................................................... 28
Table 2.5: Indexing Subroutines........................................................................................................ 29
Table 5.1: Pipe Branch Geometric Properties ..................................................................................... 43
Table 5.2: Solid Node Geometric Properties ...................................................................................... 43
Table 5.3: Fluid Node Geometric Properties ...................................................................................... 49
Table 5.4: Solid Node Geometric Properties ...................................................................................... 50
Table 5.5: Branch Component Descriptions and Properties ................................................................. 54
Table 5.6: Branch Component Descriptions and Properties ................................................................. 59
viii
List of Figures
Figure 2.1: Example flow network of a cryogenic line chill down consisting of all the basic elements .....5
Figure 2.2: GFSSP Module Flowchart............................................................................................... 12
Figure 2.3: GFSSP User Interface ..................................................................................................... 12
Figure 2.4: Edit Drop-Down Menu .................................................................................................. 13
Figure 2.5: Advanced Drop-Down Menu........................................................................................... 14
Figure 2.6: Global Options Menu..................................................................................................... 15
Figure 2.7: User Information Tab in the General Information Selection ............................................... 16
Figure 2.8: Solution Control Tab in the General Information Selection................................................ 16
Figure 2.9: Output Control Tab in the General Information Selection .................................................. 17
Figure 2.10: Circuit Options Dialog Box ........................................................................................... 17
Figure 2.11: Initial Values Dialog Box Under Global Options ............................................................ 18
Figure 2.12: Unsteady Options Dialogue Box .................................................................................... 19
Figure 2.13: Fluid Options Dialogue Box .......................................................................................... 20
Figure 2.14: Available Element Creating Tools.................................................................................. 21
Figure 2.15: Node Property Window................................................................................................. 21
Figure 2.16: Branch Creation Dialogue ............................................................................................. 22
Figure 2.17: Resistance Options for Branch Elements ........................................................................ 22
Figure 2.18: Example Property Window for Restriction Resistance Option.......................................... 23
Figure 2.19: Solid Node Property Window ........................................................................................ 24
Figure 2.20: Ambient Node Property Window ................................................................................... 24
Figure 2.21: Available Conductor Options......................................................................................... 25
Figure 2.22: Example Results for Interior Node ................................................................................. 26
Figure 2.23: Example Results Plot with the Built-In Plotter ................................................................ 27
ix
Figure 2.24: Fluid Heating Using a Heated Bottom Plate in an Insulated Container (a) Representation and
(b) GFSSP Model ............................................................................................................................. 30
Figure 2.25: Example User Subroutine USRHCF............................................................................... 31
Figure 3.1: Pressure Drop Validation (a) Schematic and (b) GFSSP Model ......................................... 32
Figure 3.2: Pressure Drop Along Propellant Feed Line ....................................................................... 33
Figure 3.3: Discretized Representation of the Line Chilldown Validation Model.................................. 34
Figure 3.4: GFFSP Schematic of the Line Chilldown Validation Model .............................................. 34
Figure 3.5: Analytical and GFFSP Simulation Results for Cryogenic Pipe Chilldown .......................... 36
Figure 4.1: P&ID for the Ground Propellant System (GPS) ................................................................ 37
Figure 4.2: GPS GN2 Pressurant System ........................................................................................... 38
Figure 4.3: GPS Propellant Tank ...................................................................................................... 39
Figure 4.4: GPS Propellant Run Line (a) Propellant Trailer and (b) Engine Test Stand Trailer .............. 40
Figure 5.1: Tank Chilldown and Fill Model ....................................................................................... 42
Figure 5.2: Propellant Tank Sections................................................................................................. 43
Figure 5.3: Oxygen tank wall temperatures for a fill rate of (a) 0.5 lbm/s and (b) 1.0 lbm/s ..................... 45
Figure 5.4: Methane tank wall temperatures for a fill rate of (a) 0.5 lbm/s and (b) 1.0 lbm/s.................... 45
Figure 5.5: Oxygen fluid node quality for a fill rate of........................................................................ 46
Figure 5.6: Methane fluid node quality for a fill rate of ...................................................................... 46
Figure 5.7: Tank Boiloff GFSSP Model ............................................................................................ 47
Figure 5.8: Evaporative Mass Transfer .............................................................................................. 48
Figure 5.9: Node Volume Change Representation .............................................................................. 50
Figure 5.10: Propellant Height to Tank Wall Volume for Determining Solid Node Mass ...................... 51
Figure 5.11: Propellant Mass as a Function of Time in Boil Off Scenario ............................................ 52
Figure 5.12: Line Chill Down GFSSP Model..................................................................................... 53
Figure 5.13: P&ID of the Engine Feed System with Modeled Lines Enclosed...................................... 53
Figure 5.14: Fluid Node Qualities for the LOX Chilldown Model ....................................................... 55
x
Figure 5.15: Fluid Node Qualities for the LCH4 Chilldown Model ..................................................... 56
Figure 5.16: Flow Rates for the LOX and LCH4 Chilldown Runs ....................................................... 56
Figure 5.17: Engine Run GFSSP Model ............................................................................................ 58
Figure 5.18: Engine Run Line P&ID ................................................................................................. 58
Figure 5.19: Propellant and Ullage Node Volumes for the Engine Run Model ..................................... 60
Figure 5.20: Pressure Drop Across Propellant Run Lines for (a) LOX and (b) LCH4............................ 61
1
Chapter 1: Introduction
More than 60 years after the funding of the National Aeronautics and Space Administration
(NASA) the majority of Americans believe that the United Sates should be the forefront of global leadership
in space exploration [1]. As the private sector increasingly ventures into space through companies such as
SpaceX, Blue Origin, and Virgin Galactic, NASA still plays a vital role in research and technological
development. With these private companies emerging as major role players, increased interest has been
turned to a manned mission to Mars. Ideas that have long been only science fiction like settling on Mars
now seem closer than ever, but significant technological hurdles still need to be overcome before human
spaceflight to Mars becomes a reality. An emerging technology is the use of liquid methane (LCH4) as a
rocket propellant. Historically the most common used fuels used in rocket engines have been Hydrogen and
RP-1. Compared to hydrogen, methane holds a lower specific impulse (ISP) but offers many other
advantages. It is more stable, easier to store since the saturation temperature is much lower, and much
denser [2]. All this means that any spacecraft looking to use methane as a fuel would save considerable
amount of mass by requiring smaller tanks, less insulation, and possibly do away with active cooling.
Compared to RP-1 commonly used by SpaceX, methane boasts a higher ISP and is a much cleaner
propellant which helps towards reusability. The tradeoff for RP-1 is that methane is much less dense than
PR-1, leading to larger tanks [3]. Methane is then close to being an ideal “best of both worlds fuel” and
presents itself as a frontrunner in choice of propellants for a mission to Mars. Despite these advantages, no
LOX/LCH4 engines have ever been flown [4].
NASA, other federal space agencies, and private companies have all began development of
LOX/LCH4 engine technologies. NASA began development of engines intended for use in reaction control
systems in the early 2000’s [5]. In 2010 development of a lunar lander called Morpheus was started. The
lander was intended to demonstrate the new LOX/LCH4 technology [6]. The Raptor is a staged combustion,
LCH4 fueled rocket engine currently under development by SpaceX and is expected to power the next
generation of SpaceX launch vehicles designed for the exploration of Mars [7]. Blue Origin’s BE-4 is also
2
a methane fueled rocket engine that has been in development since 2011. The BE-4 is expected to be used
on the United Launch Alliance (ULA) Vulcan Launch vehicle [8].
With help from NASA, UTEP’s MIRO Center for Space Exploration and Technology Research
(cSETR) center has been developing a number of methane propulsion systems. Among these systems are
the CROME and CROME-X engines. CROME is a throttleable engine capable of 2000 pounds of thrust
intended for use in a vertical takeoff and landing vehicle named JANUS. CROME-X is a smaller engine
capable of 500 pounds of thrust intended to power a suborbital demonstration vehicle named DAEDALUS.
With development underway, the cSETR has established a testing facility, the Technology Research and
Innovation Acceleration Park (tRAIC), that focuses on large-scale combustion testing of LOX/LCH4
engines. The ground propellant system (GPS) was designed to provide pressurized LOX and LCH4 to the
CROME engines during ground testing.
When designing and selecting components for these complex flow systems, engineers often use
models to help predict system behavior such as pressure drops and heat transfer. Such models are often
called thermal-fluid system models. System level models often focus on entire systems rather than on
details of the flow inside specific components of the system. A system level model is modeled using a flow
network of different components each of which models a specific component of the system such as a tank,
a valve, a tank, or tubing. Computational resource requirements to perform transient CFD analysis for such
systems would be excessive and thus not practical [9]. Developing an accurate model helps teams design
systems, choose component sizes, determine operating ranges, and determine internal temperatures,
pressures, and flow rates within the system. Some commonly used thermo-fluid system modeling software
include FloMASTER, Flownex, FloCAD, and GFSSP. FloMaster is an analysis package from Matlab that
simulates one-dimensional fluid flow and heat transfer in pipes, passages, and fittings. It is used in
industries such as automotive, chemical and petroleum, as well as utilities and energy. Flownex is a
commercial network software to predict flow distributions, pressure losses, and one-dimensional
temperature distributions. FloCAD is a module for CRTech’s CAD software Thermal Desktop which
generates flow networks and calculates convective heat transfer. The module has full access to FLUINT
3
fluid network modeling capabilities with empirical inputs to common components such as pumps, flow
passages, and other loss elements. The Generalized Fluid System Simulation Program (GFSSP) was
developed at NASA Marshall Space Flight Center (MSFC) as a general fluid flow system solver as a
general-purpose customizable alternative to commercial codes [10]. The solver is capable of handling phase
changes, compressibility, mixture thermodynamics, and transient operations. Table 1.1 compares the
capabilities of the different fluid system modeling software.
Table 1.1: Fluid System Modeling Software Capabilities
Software Compressibility Phase Change Mixture Transient Conjugate Solid
Heat Transfer
CFD
Interfacing
GFFSP Yes Yes Yes Yes Yes No
FloMaster Yes Yes No Yes No Yes
Flownex Yes Yes Yes Yes No Yes
FloCAD Yes Yes No Yes Yes No
The purpose of this paper is demonstrating the capabilities of GFSSP in modeling the GPS and
other fluid flow networks going forward at the cSETR. The paper first describes the GFSSP software and
components as well as introduce the reader to using the software. Next, the paper presents validation cases
in order to verify the validity of the models and software. The subsequent chapter describes the GPS as
well as the components in the system. The last chapter is a summary of the models developed to simulate
the GPS operational modes: tank fill/chill, propellant boiloff, line chill down, and an engine test run.
4
Chapter 2: Generalized Fluid System Simulation Program
The Generalized Fluid System Simulation Program (GFSSP) was developed at NASA Marshall
Space Flight Center as a general thermal fluid system solver capable of handling steady state and transient
operations [10]. The program breaks down fluid networks into a system of nodes and branches. At each
node, the conservation of mass and energy equations are solved to obtain pressures, temperatures, and
species concentrations. At each branch, the momentum equation is solved to obtain the flow rate in that
branch. The program also uses solid nodes to represent solid masses and uses the energy conservation
equation to calculate the temperature of the solid. GFSSP uses a pressure-based finite volume method
(FVM) as the foundation of its numerical solver scheme. The finite volume method is a numerical method
for solving partial differential equations which calculates values of conserved variables such as mass and
energy averaged across a volume [11].
2.1 Network Elements
GFSSP models flow networks with three elements: boundary nodes, internal nodes, and branches.
Thermodynamic states are defined in boundary nodes by pressure, temperature, and species concentration.
At internal nodes, the software calculates all thermofluid variables such as pressure, temperature, enthalpy,
and species concentrations as well as physical properties such as viscosity. Flow rate and flow velocities
are calculated at the branches. Coupled fluid and solid heat transfer requires a network of solid nodes with
interfaces between the fluid and solid nodes. The interface models the convective and radiation heat transfer
between the fluid and solid nodes. Three elements are added to the network to integrate coupled fluid and
solid heat transfer: solid nodes, ambient nodes, and conductors. In addition to thermofluid properties, all
elements also have geometric properties. Geometric properties can be further classified into two categories.
Relational properties define the relationship of the element with the neighboring elements. Quantitative
properties include geometric quantities such as area, volume, and length. Figure 2.1 shows a typical flow
network consisting of all the different network elements: fluid boundary nodes, internal nodes, and branches
as well as solid nodes, ambient nodes, and conductors.
5
Figure 2.1: Example flow network of a cryogenic line chill down consisting of all the
basic elements
The thermofluid properties of internal and boundary nodes are: pressure, temperature, density,
species concentration, enthalpy, entropy, gas constant, viscosity, conductivity, and specific heat ratio. For
unsteady flow, each internal node also tracks the thermofluid properties of its previous time step. In
addition, internal nodes have relational and quantitative geometric properties. The relational properties of
an internal node define the number of branches connected to the node and their index. The quantitative
geometric property of an internal node is node volume, which is necessary to calculate the mass for unsteady
calculations.
The thermofluid properties of branches are flow rate, velocity, and resistance coefficient. The
relational geometric properties are the name and number of the upstream and downstream nodes, the name
and number of the upstream and downstream branches, and the index number of resistance options. The
quantitative geometric properties are the area, volume, radial resistance of the upstream and downstream
nodes, branch rotational speed, and the geometric parameters to characterize a given resistance option. For
unsteady flow, each branch includes the quantitative properties of the previous time step.
The thermophysical properties of a solid node are material, mass, and specific heat. In addition,
there are six relational properties that identify the number and names of conductors. Ambient nodes have
only two properties, name and temperature.
6
There are four types of conductors: solid to solid conduction, solid to solid radiation, solid to fluid,
and solid to ambient. The relational properties of solid to solid conductors are names of connecting solid
and fluid nodes and the geometric properties are area and distance between adjacent solid nodes. The
thermophysical properties are conductivity and effective conductance. Solid to fluid conductors’ relational
properties are names of connecting solid and fluid nodes. The geometric and thermofluid properties are
heat transfer area, heat transfer coefficient, effective conductance, and emissivity of solid and fluid nodes.
Solid to ambient conductors’ relational properties are the names of connecting solid and ambient nodes.
The geometric and thermofluid properties are heat transfer area, heat transfer coefficient, effective
conductance, and emissivity of solid and ambient.
2.2 Mathematical Formulations
GFFSP assumes a Newtonian, nonreacting and one-dimensional flow in the flow circuit. GFSSP
calculates scalar properties such as pressure and temperature at the nodes and vector properties such as
velocity and flow rate at fluid branches. Figure 2.1 shows a schematic of adjacent nodes, connecting
branches, and the indexing system. In order to solve for the unknown variables, the equations for mass
conservation, energy conservation, and fluid species conservation are written for each internal node and
flor rate equations are written for each branch.
Equation 2.1 is the mass conservation equation. In unsteady calculation, the net mass flow from a
given node must equal to the rate of change of mass in the control volume. In a steady state calculation,
the left side of the equation is zero which implies that the mass flow rate into the node must equal to the
mass flow rate out of the node.
1
j n
ij
j
m mm
=
+
=
−= −
(2.1)
Transient flow calculations require the mass in a control volume to be known. The mass is
calculated from the equation of state for real fluids and can be expressed as shown in Equation 2.2. Equation
2.2 is valid for liquid, gas, and gas-liquid mixtures. The compressibility factor, z, is zero for an ideal gas.
7
For real fluids, the compressibility factor is computed by thermodynamic routines explained in the
momentum conservation equation section.
Vm
zRT
= (2.2)
Equation 2.3 is the momentum conservation equation which represents the balance of forces acting on a
branch and is used to calculate the flow rate.
( ) ( )( ) ( ) ( ) ( ),0 ,0 ,0 ,0ij ij u ij ij u trans ij p trans ij p
c
mu muMAX m u u MAX m u u MAX m u u MAX m u u
g
+
−+ − − − − + − − − −
( )2 2
, , ,
cos p ij norm norm ij d ij ij u ijroti j ij f ij ij ij d u
c c c ij p c ij d ij u c
u u A u u AK AgVp p A K m m A u S
g g g g g
− − −= − + − + + − + − +
(2.3)
The conservation of momentum equation consists of 11 terms. There is no occasion where all 11
terms will be present in a control volume and users have the option to exclude all terms except the pressure
term. The terms in the momentum equation are shown in Table 2.1 respectively. A source term is in the
equation in order to represent a pump. If a pump is located in a given branch, all other sources are set to
zero except for pressure.
Table 2.1: Conservation of momentum term descriptions for branch elements
Term Description Unsteady The rate of change of momentum with time. For steady state this term is equal to zero.
Longitudinal Inertia This term is large when there is a substantial change in velocity in the longitudinal
direction. Flow in a nozzle is an example where this term must be active
Transverse Inertia This term accounts for any longitudinal momentum being transported by a transverse
velocity component
Pressure This term is the pressure gradient in the branch
Gravity This term is the effect of gravity
Friction This term is the frictional effect. Friction is equal to the product of Kf and the square of
the flow rate and area. For the calculation of Kf for different types of branches refer to the
GFFSP user manual [10].
Centrifugal This term represents the centrifugal force.
Shear This term represents shear force exerted on the control volume by a neighboring branch.
Moving Boundary This term represents forced exerted on the control volume by a moving boundary.
Normal Stress This term represents normal viscous force
Source This is a generic source term. Any additional force acting on the branch control volume
can be modeled through the source term.
8
The solution for the momentum conservation equation requires the density and viscosity of the
fluid within the branch. These fluid properties are dependent on the fluid temperature, pressure, and species
concentrations. GFFSP provides three thermodynamic property routines for fluid property data. GASP
provides the thermodynamic and transport properties for hydrogen, oxygen, helium, nitrogen, methane,
carbon dioxide, carbon monoxide, argon, neon, and fluorine. WASP provides the thermodynamic and
transport properties for water and steam. GASPAK provides thermodynamic properties for helium,
methane, neon, nitrogen, carbon monoxide, oxygen, argon, carbon dioxide, hydrogen, parahydrogen, water,
RP-1, isobutane, butane, deuterium, ethane, ethylene, hydrogen sulfide, krypton, propane, xenon, nitrogen
trifluoride, ammonia, hydrogen peroxide, air, and a number of refrigerants.
The energy conservation equation is solved for both fluids and solids at internal and solid nodes.
For conjugate heat transfer, the energy conservation equation of solid nodes is solved together with the
energy equation of fluid nodes. The heat transfer between the solid and fluid nodes is calculated at the
interface and used in both equations as source and sink terms.
The energy conservation for a single fluid can be expressed by either the first or second law of
thermodynamics. The first law uses enthalpy as the dependent variable while the second law uses entropy.
The first law is described in Equation 2.4. The equation states that for transient flow, the rate of increase of
internal energy in the control volume should be equal to the rate of energy transport into and out of the
control volume plus the rate of work done on the fluid by the viscous force plus the rate of heat transfer
into the control volume. For steady state, the equation states that the total energy flow from and to a given
node should be zero. The MAX operator used in Equation 2.4 is known as an upwind differencing scheme
and has been extensively employed in the numerical solution of Navier-Stokes equations in convective heat
transfer and fluid flow applications.
( ) ( )2
1
,0,0 ,0
j nij
ij j ij i i j ij ij ij i
j ij
p pm h m h
MAX mJ JMAX m h MAX m h p p K m v A Q
m
=
+
=
− − − − = − − + − + +
(2.4)
9
The energy conservation equation using second law is shown in Equation 2.5. Equation 2.5 states
that for unsteady flow, the entropy rate of increase in the control volume is equal to the rate of entropy into
the control volume plus the rate of entropy generation in all upstream branches due to the fluid friction plus
the rate of entropy added to the control volume through heat transfer. The entropy generation rate due to
fluid friction in a branch is shown in Equation 2.6.
( ) ( )
1 1
,0,0 ,0
j n j nij i
ij j ij i
j j iij
MAX mms ms QMAX m s MAX m s
Tm
= =
+
= =
−− = − − + + (2.5)
( )3
,
,
f ijij ij viscous
ij gen
u u u u
K mm pS
T J T J
= = (2.6)
In order to model fluid mixtures, energy conservation equations of fluid species are necessary.
GFFSP assumes fluid mixtures to be homogeneous, and thus the mass and momentum equations are
identical to those of a single fluid. GFFSP has three options to model the mixture and calculate the
temperature and thermophysical properties of the mixture. In the first option, the energy equation is solved
in terms of temperature. This is shown in Equation 2.7.
( ), ,
1 1
,
,
1 1
,0
,0
j n k nfi
j k j k ij i
j k
i j n k nf
j k ij
j k
mhx h MAX m Q
hm
x MAX m
= =
= =
+ = =
+
= =
− + + =
+
(2.7)
In the second option, the mixture enthalpy is calculated for the energy conservation equation from
enthalpies of fluid species, and temperature is calculated by an iterative method form the enthalpy equation.
This is shown in Equation 2.8.
1
,0 ,0
i ik i ik j nk k
ij ji ij ik ik ik
j
p pm h m h
J JMAX m h MAX m h c Q
=
+
=
− − −
= − − +
(2.8)
Where the external heat source is expressed as the external heat source times the molar
concentration of the kth species in the ith node. In the last option, separate energy equations for each species
are solved and the temperature of the mixture is calculated by averaging the thermal mass of all components.
10
Solid nodes can be connected with other solid nodes, ambient nodes, and fluid nodes. The energy
conservation for a solid node is shown in Equation 2.9. The equation states that the rate of change of
temperature of the solid node is equal to the heat transfer from the adjacent node and heat source. The heat
transfer from solid, ambient, and fluid node terms are shown in their respective order.
( )( )
( ) ( )1 1 1
sfss sa
fs s a
a a f fs
s a fs
nn njij ij ji i i
P s ij ij a a ij ij f f ij ij j jij s s
k AmC T h A T T h A T T S
T T = = =
= + − + − +
− (2.9)
Effective heat transfer coefficients for solid to fluid to ambient nodes are expresses as the sum of
convective and radiation heat transfer coefficients. GFFSP provides four options for specifying heat transfer
coefficient. The first option is for the user can provide a constant heat transfer coefficient. The second
option is using the Dittus-Boelter equation for single-phase flow. The third option is the modified
Miropolskii’s correlation for two-phase flow. The fourth option is for the user to provide a new correlation
in the user subroutine.
2.3 Solution Procedure
GFSSP uses the governing equations to solve for the fluid properties in any given circuit. The
properties and the corresponding governing equation to solve that variable are shown in Table 2.2. Pressure
is calculated in the mass conservation equation by iterating the pressure to reduce the residual error in the
mass conservation equation. This was first implemented in a semi-implicit pressure linked equation
algorithm proposed by Patankar and Spalding and is referred to as a ‘pressure based’ algorithm. The strong
coupling of pressure and flow rate requires the mass and momentum conservation equations to be solved
simultaneously.
Table 2.2: Fluid properties and their corresponding governing equations used to solve them
Variable Name Equation
1 Pressure Mass Conservation
2 Flow Rate Momentum Conservation
3 Enthalpy or Entropy Energy Conservation
4 Solid Temperature Energy Conservation
11
5 Species Concentration Species Conservation
6 Fluid Mass Thermodynamic State
GFFSP uses a combination of successive substitution and the Newton-Raphson method to solve
the sets of equations. With this method, the mass and momentum conservation equations are solved by the
Newton-Raphson method and the energy and species conservation equations are solved by the successive
substitution method. The reasoning for this scheme was that the strongly coupled equations of mass and
momentum conservation were better solved by the Newton-Raphson method. The energy and species
conservation equations are not as strongly coupled and thus can be solved by the successive substitution
method.
2.4 GFFSP Software
GFSSP consists of three major modules: the graphical user interface (GUI), the solver property
module, and the user subroutine module. The development of the flow network and the input files are done
in the GUI. The user subroutine module allows specialized inputs into the model. The GUI and the user
subroutine module supply the information to the solver and property module. The solver property module
develops the indexing system and data structure that defines the fluid and solid networks. It generates the
conservation equations and calculates the thermodynamic and thermophysical properties of the fluid and
solid nodes. The solver property module returns an output data file that can be visualized in the GUI.
Figure 2.2 shows how the three modules work together. More details on the solver property module and
the user subroutine module can be found in the GFSSP manual [10].
12
Figure 2.2: GFSSP Module Flowchart
2.5 Graphical User Interface
The GUI allows the user to create complex flow networks with a simple easy to use interface.
Figure 2.3 shows the main display window and a blank canvas. The GUI consists of the menu bar, the top
and left-hand side ribbons, and the canvas.
Figure 2.3: GFSSP User Interface
13
2.5.1 Menu Bar
The menu bar contains a variety of different menus. The File pulldown menu allows the user to
create, save, and open new models, as well as write an output file using the current model. The Edit menu
is shown in Figure 2.4. The Edit menu allows the user to delete selected items, open the global options
menu, and edit input and output files.
Figure 2.4: Edit Drop-Down Menu
The advanced menu shown in Figure 2.5 allows the user to activate dialogs for advanced options
such as transient heat, heat exchanger, tank pressurization, pump, and other branch options. Some of these
options are not available unless the option has been previously selected or turned on in the global options
menu. The advanced menu also allows the creating of conjugate heat transfer elements like the solid,
ambient, and conduction elements.
14
Figure 2.5: Advanced Drop-Down Menu
The run menu allows the user to run GFSSP, Winplot, or both programs together. Winplot is a
separate program to GFSSP and thus must be installed separately for these options to work. The Module
menu allows the user to activate the user subroutines module. The display menu allows the user to plot the
simulation results within the GUI. The canvas menu extends the canvas to two or four pages to more easily
visualize larger models. Finally, the group menu allows the user to align nodes as a group.
2.5.2 Global Options
The global options menu allows the user to set optional and required parameters for the simulation
and is shown in Figure 2.6. In order for the selections to be saved, the user must click the apply or apply-
close options before exiting the menu.
15
Figure 2.6: Global Options Menu
The general information option allows the user to input general user information, solution and
output controls. Figures 2.7-2.9 show the options available in each tab. The user information tab allows
the user to specify the title of the model, analyst name, and the location of the GFSSP executable that will
be used to run the model. The user specifies the path for the input and output files for the model. A compiler
option is available to specify either the Compaq or Intel Fortran compiler. The solution control tab allows
the user to change the solution parameters of the model. The solver method, solution scheme, and energy
equations can all be chosen here. The user can also specify the convergence criteria for the model. The
output control tab allows the user to specify the type of data to output during the GFSSP simulation as well
as to request values to be checked for debugging.
16
Figure 2.7: User Information Tab in the General Information Selection
Figure 2.8: Solution Control Tab in the General Information Selection
17
Figure 2.9: Output Control Tab in the General Information Selection
The circuit options option allows access to the circuit options and initial values tabs. The circuit
tab allows the user to specify options to be activated in the model. These options enable some of the
momentum conservation equation terms as well as other branch options. Figure 2.10 shows the options
available under the circuit tab.
Figure 2.10: Circuit Options Dialog Box
18
The initial values tab is used to set the default starting thermodynamic properties for both fluid and
solid nodes. The different options can be seen in Figure 2.11. These values will be used whenever a new
node is created.
Figure 2.11: Initial Values Dialog Box Under Global Options
The unsteady options selection allows the user to specify steady state or unsteady solutions. If the
user selects an unsteady model, they are required to select the time step and start and stop time for the
simulation. With the unsteady option selected, the user is allowed to select other options such as tank
pressurization, valve open/close, pressure regulator, flow regulator, and pressure relief valve. This menu is
shown in Figure 2.12.
19
Figure 2.12: Unsteady Options Dialogue Box
The last global options selection is fluid options and is shown in Figure 2.13. The fluid options
allow the user to choose the thermodynamic property package to be used in the model. The user can choose
constant properties, ideal gas, general fluid, or water. If the user selects constant properties, they are
prompted to input the properties in the tab. If the user selects general fluid, they are allowed to choose
which thermodynamic property package to use as well as specify the fluid.
20
Figure 2.13: Fluid Options Dialogue Box
2.5.3 Flow Network Design
The tooltip on the right-hand side of the GUI allows the creating of the different elements that make
up the flow circuit. These can be seen in Figure 2.14. The selection tool is used to select desired nodes and
branches. Selecting the circuit elements with the left mouse button allows the deletion and reposition of the
elements. Using the right mouse button brings up a special menu which allows the user to delete, align, or
access the element properties. Using the left mouse button to double click the element also allows the user
to access its properties.
21
Figure 2.14: Available Element Creating Tools
The boundary node and interior node tools allow the user to insert these nodes into the model.
Nodes are automatically given unique numeric identifiers. The node property window is shown in Figure
2.15. Within the node property window, the user can specify the node pressure, temperature, volume, and
other thermofluid and geometric properties.
Figure 2.15: Node Property Window
22
The branch tool is used to connect two nudes using a branch. Once the branch tool is selected, the
nodes in the canvas will be drawn with a series of handles denoted by green squares as seen in Figure 2.16.
The handles identify the possible locations where a branch may be attached to a specific node. There is no
limit to the number of branches that may be attached to each handle. The first node specifies the upstream
node and the second node will be the downstream node.
Figure 2.16: Branch Creation Dialogue
Newly created branches will show up with the question mark image, which indicates that the
resistance model for the branch has not been selected. Using the right mouse button, or double clicking with
the left mouse button will allow the user to specify the component. Figure 2.17 shows some of the resistance
options available. Once a resistance option has been selected, the branch will display the appropriate symbol
in the canvas.
Figure 2.17: Resistance Options for Branch Elements
23
With the resistance option selected, one can access the resistance properties by double clicking the
branch with the left mouse button. Figure 2.18 shows the properties available for a restriction type
resistance model. Descriptions of each model can be found in the GFSSP user manual [10].
Figure 2.18: Example Property Window for Restriction Resistance Option
The conjugate heat transfer tools are only available once the option has been enabled in the
Advanced drop-down menu. Adding conjugate heat transfer elements to the model is analogous to adding
the fluid elements. Solid and ambient nodes behave much the same way as boundary and interior nodes.
Figures 2.19-2.20 show the property windows for solid and ambient nodes respectively.
24
Figure 2.19: Solid Node Property Window
Figure 2.20: Ambient Node Property Window
The conductor tool is similar to the branch tool. Once selected, solid and ambient nodes will display
the handles in which the conductor will be attached to. Instead of selecting the type of resistance model, the
conductor tool will display the type of conductors available as can be seen in Figure 2.21. Accessing the
properties of the conductor will allow the user to specify the characteristics of the conductor.
25
Figure 2.21: Available Conductor Options
2.6 Advanced Options
GFSSP offers many advanced options and features including: transient heat load, heat exchanger,
tank pressurization, turbopump, valve open/close, pressure regulator, flow regulator, and pressure relief
valve. Once the advanced feature has been selected, the user can input the appropriate information by
selecting the option the option available in the Advanced menu. The dialogs for each advanced component
all operate in a similar fashion. The user can add any number of components by pressing the add button and
modify the data for any particular component. The advanced options are described in the GFSSP user
manual [10].
2.7 Running the Model
GFFSP can be directly executed from within the GUI. Selecting the GFFSP command from the
Run drop down menu will automatically write a GFSSP input file before running the solver and property
module. Once the run is complete, GFSSP automatically writes the output file and gives the user the option
of viewing the output in a text editor. Details in reading the output file can be found in the GFSSP user
manual [10].
26
2.8 Post-Processing and Visualizing Results
While the output file provides a comprehensive summary of the simulation, post-processing the
data is a much more practical way to visualize the results. For steady state simulations, each element in the
flow network will have a results dialog option available by right clicking the element. A table of results
for that element will appear with the parameters for that specific element shown, as seen in Figure 2.22.
Figure 2.22: Example Results for Interior Node
Visualizing unsteady simulation results can be done in a variety of options. The first option is to
use the built-in plotter of the GUI. This is done by selecting the results pop up option on the element of
interest. A blank plotting window should appear. In here the user has the option to plot the variable of their
choice using the properties button. This can be seen in Figure 2.23. The properties available are the ones
described in the network elements section. From here the user can select from various plotting options such
as color, labels, and scale.
27
Figure 2.23: Example Results Plot with the Built-In Plotter
The second option is to generate either comma delimited or binary plot files. This can be done by
selecting the Winplot plotting option in the Global Options menu. The comma delimited file can be opened
in Winplot or any other plotting software. If the comma delimited option is selected, each element in the
network will have its own file. If the binary option is selected, only one file will be generated. This file
will contain all the available parameters for each element in the network. The binary file can only be opened
in Winplot.
2.9 User Subroutines
User subroutines allow the user to access GFSSP solver modules. In doing so, the user can add
addition capability to the software through the use of NASTRAN code. Some examples include user-
prescribed heat transfer coefficients, user defined resistance models, variable time step, geometry, and
boundary conditions for time-dependent problems, and even customize the output files by defining
additional variables. The subroutines exist as blank blocks in the userrtrn605.for file in the GFSSP
installation folder. There is a total of 23 user subroutines provided. The most commonly used subroutines
are shown in Table 2.3. For the rest of the subroutines, refer to the GFSSP user manual [10].
28
Table 2.3: List of Commonly Used User Subroutines
Subroutine Description
BNDUSER
This subroutine allows the user to adjust
boundary conditions during transient run
such as fluid node volumes, branch areas,
and solid node masses
KFUSER(I,RHOU,EMUU,XVU,RHOUL,EMUL,AKNEW)
In this subroutine the user can define new
resistance options in a branch such that the Kf
is defined as the pressure drop divided by the
mass flow rate squared. The subroutine has
four arguments: address location of branch,
upstream node density, upstream node
viscosity, upstream node vapor quality,
upstream node liquid density, upstream node
liquid viscosity, and the new Kf for the
branch. The user must provide all arguments
to calculate Kf.
SORCEQ(IPN,TERMD)
This subroutine allows the user to introduce
a heat source or sink to any internal node.
The subroutine has two arguments: the
address location of the node, and the
linearized source term appearing in the
denominator of the enthalpy equation.
SORCETS This subroutine allows the user to add an
external heat source at any solid node
USRHCF(NUMBER,HCF)
This subroutine allows the user to define the
convective heat transfer coefficient. The
subroutine has two arguments: the address
location of the solid to fluid conductor, and
the heat transfer coefficient being defined.
The solver-user subroutine interaction is shown in Table 2.4. The solver blocks call the specified
user subroutine in order to generate the corresponding equations or to calculate properties. A small
description of each solver block is also included in Table 2.4.
Table 2.4: Solver Module User Subroutine Interactions
Solver Module User Subroutine Bound
Provides time-dependent boundary conditions from
history file
BNDUSER
EQNS
Generates mass and momentum conservation equations
SORCEM
SORCEF
ENTHALPY/ENTROPY
Generates and solves the energy conservation equation SORCEQ
MASSC
Generates and solves the species conservation equation SORCEQ
RESIST
Calculates the flow resistance coefficient KFUSER
DENSITY PRPUSER
29
Calculates the fluid properties
TSEQNS
Generates conservation equations for solid temperature SORCETS
TSOLID
Solves solid temperature equation
CONVHC
Calculates convective heat transfer coefficient USRHCF
Generates output files PRNUSER
In addition to these subroutines, there are a number of subroutines that allow the user to access
node, branch, and conductor properties. These indexing subroutines determine the pointer for each
component. The indexing subroutines are shown in Table 2.5. The input variables for each indexing
subroutine are: component number, array for storing component number, number of nodes and number of
nodes or branches. Note that the only input variable that needs to be defined is the node number, as the
other variables are global variables. The output variable is the pointer for the specified component. Once
the user has assigned a variable the component pointer, they can access component specific properties such
as temperature, pressure, volume, enthalpy, density, etc. The full list of accessible component properties is
in the GFFSP user manual [10].
Table 2.5: Indexing Subroutines
Subroutine Component INDEXI(NUMBER,NODE,NNODES,IPN) Fluid Node
INDEXI(NUMBER,IBRANCH,NBR,IB) Fluid Branch
INDEXA(NUMBER,NODEAM,NAMB,IPAN) Ambient Node
INDEXS(NUMBER,NODESL,NSOLIDX,IPSN) Solid Node
INDEXSSC(NUMBER,ICONSS,NSSC,ICSS) Solid to Solid Conductor
INDEXSFC(NUMBER,ICONSF,NSFC,ICSF) Solid to Fluid Conductor
INDEXSAC(NUMBER,ICONSA,NSAC,ICSA) Solid to Ambient Conductor
INDEXSSRC(NUMBER,ICONSSR,NSSR,ICSSR) Solid to Solid Conductor
An example of a problem that requires a user subroutine is shown in Figure 2.24. In this case a
volume of fluid is being heated by a hot plate located on the bottom of a container while the rest of the
walls are insulated. Because GFSSP is first and foremost a fluid analysis code, it is necessary to include a
fluid flow path in any GFSSP model that is being developed. In this case a relief valve with a negligible
flow area is added to create this flow path. The heat transfer between the fluid and the bottom plate is not a
30
constant value. The value varies as the thermal properties of both the plate and fluid change. It must be
calculated by natural convection correlations based on these properties.
Figure 2.24: Fluid Heating Using a Heated Bottom Plate in an Insulated Container (a)
Representation and (b) GFSSP Model
In this case the user subroutine USRHCF must be used to calculate the heat transfer coefficient.
The example user subroutine is shown in Figure 2.25. The heat transfer correlation suggested by McAdams
[12] for the upper surface of a horizontal flat plate is
1/40.54L LNu Ra= (1)
Once the user subroutine has been written in file userrtrn605.for, the file must be compiled using
a FORTRAN compiler. If the user has the Intel FORTAN compiler, one can compile the file using the
built-in module builder in GFFSP under the Module option. If the user does not have the Intel compiler, it
is recommended to use the free G95 FORTRAN compiler. In order to build a new executable file, the user
must gather the following files from the installation directory into the working directory: userrtn605.for,
comblk.for, gfssp605-G95.o, gasp605_G95.o, and gasprop605_G95.o.
In the command prompt, execute the following command:
31
g95 gfssp605_G95.o gasp605_G95.o gasprop605_G95.o userrtn605.for -i4 -r8 -O1 -malign-double
-fsloppy-char -ftrace=full -fmultiple-save -fstatic -o userrtn605.exe -cpp
The command will create a new userrtrn605.exe file which will be used to run the model. To do so, the
user must specify the GFSSP Executable under the General Information tab in the Global Options.
Figure 2.25: Example User Subroutine USRHCF
32
Chapter 3: Validation Models
Simulation models are increasingly being used to design new engineering systems and to aid in the
component selection of these systems. The accuracy of the models affects not only the analysts who make
the models, but also the engineers who use the information obtained from the results of these models, as
well as the people who operate these systems. Model verification ensures that the system models and its
implementation are correct. The main objective of this chapter is to validate GFSSP’s predictions with
analytical solutions to simple fluid and thermal systems.
3.1 Pressure Drop in Propellant Line
The first validation model is a simple pressure drop across a propellant line. In this example a cryo
methane dewar at 25 psi is feeding propellant to the propellant tank which sits 20 feet away at a pressure
of 20 psi. Figure 3.1 shows the schematic and GFFSP model. Boundary node 1 represents the cryo dewar
and boundary node 8 represents the propellant tank. Fluid nodes 2 represents the point at the exit of the
dewar and fluid node 7 represents the point right before the entrance of the tank. Each pipe branch
represents 48 inches of 1” fill line. For validation simplicity, the friction factor for each pipe branch was
set to zero.
Figure 3.1: Pressure Drop Validation (a) Schematic and (b) GFSSP Model
33
In order to solve this analytically, there were a few assumptions that had to be made. The first
assumption is that the density change of methane was small enough to be considered as incompressible.
The second assumption was to ignore entrance effects and assume fully developed flow. The Reynolds
number was determined using the equation for pressure drop for laminar flow in pipes by solving for the
average velocity [13].
2
32 avgLVP
D
= (3.1)
The Reynolds number was found to be 1846 which is below the critical Reynolds Number of 2300
for internal flow in circular pipe. Equation 3.1 was then used to determine the pressure along the tube. The
results of the analytical and GFSSP model are shown in Figure 3.2. The plot shows that the GFSSP
predictions agree well with the analytical solution. The input file for the GFSSP model is included in the
Appendix.
Figure 3.2: Pressure Drop Along Propellant Feed Line
3.2 Chilldown of Short Cryogenic Pipe
The second validation model is the chilldown of a short cryogenic pipe. Chilling down hot pipes is
an essential part of all cryogenic fluid transfers. Reducing the temperature of the pipe to near the fluid
34
saturation temperature allows for fully liquid transfers, since the heat transfer that would boil the fluid is
reduced to a minimum. In this model a 20” section of 304 SS pipe at 80 °F is cooled down using superheated
oxygen at -280 °F and 25 psi. This temperature is just above saturation temperature for the fluid, and is
chosen to simplify the analysis. The pipe has an inside diameter of 0.5” and a wall thickness of 0.125”. The
section of pipe and the corresponding model are shown in Figures 3.3 and 3.4. The pipe is discretized into
ten 2” sections. Each section is represented by a fluid node and the connecting solid node. Each connecting
branch is a flow pipe with a length of 2” and an inside diameter of 0.5”. The fluid to solid convection heat
transfer coefficient is calculated using GFSSP’s Miroposlkii equation [14].
Figure 3.3: Discretized Representation of the Line Chilldown Validation Model
Figure 3.4: GFFSP Schematic of the Line Chilldown Validation Model
35
The analytical solution to this problem was taken from Cross et al [15]. The energy balance of a fluid
control volume inside of the pipe is given by the conservation of energy equation.
dU Q W = − (3.2)
The energy conservation equation can be written in cylindrical coordinates neglecting viscous dissipation
( )1f f fz
f f r f
f
T T Pq uc u rq T
t z r r z T z
+ = − + − (3.3)
Using the following assumptions:
• Axial conduction in the fluid is neglected
• Flow work is neglected
• Fluid mass flow rate is constant
• Heat transfer coefficient is constant
• Constant solid and fluid properties
And by writing rq in terms of Newton’s law of cooling, rq hA T = , and integrating over the tube radius,
the energy conservation equation can be written as:
f
f w
TT T
− = −
(3.4)
Where and are nondimensional variables corresponding to length and time given by:
f
Dhz
mc
= and
cc f
w w
A zht
c m
= −
(3.5)
This equation can be solved to give
( ),0 ( )
0
,0 ,0 0
4w w
f w
T Te I d
T T
− +−
=− (3.6)
Using the initial and boundary condition:
@ 0 = ,0f fT T= for all
36
The integral is then integrated numerically to find the time dependent wall temperatures. The
results from the analytical model and the GFFSP model are shown in Figure 3.5. The close agreement
between the analytical and numerical model show that GFFSP is capable of modeling conjugate heat
transfer between fluid and wall and thus a suitable software for future simulations. The GFSSP input file is
included in the Appendix.
Figure 3.5: Analytical and GFFSP Simulation Results for Cryogenic Pipe Chilldown
37
Chapter 4: Ground Propellant System Overview
The Ground Propellant System (GPS) is used to deliver LCH4 and LOX to both CROME and
CROME-X engines during ground testing. The P&ID for the system is shown in Figure 4.1. The GPS is
divided into 3 parts: the pressurant system, the propellant tanks, and the propellant run lines.
Figure 4.1: P&ID for the Ground Propellant System (GPS)
The pressurant system main purpose is to pressurize the propellant tanks to 300-350 psi and
maintain this pressure during run operations. The pressurant system consists of 8 gaseous nitrogen (GN2)
k-bottles. The k-bottles are designed to store GN2 at 6000 psi and have a volume of 488 cubic feet. This
means that at 80 degrees Fahrenheit, each k-bottle can store up to 36 lb of GN2 for a total of about 292 lb
between the whole system. Each bottle is equipped with a pressure regulator that reduces the outlet
pressure to 3000 psi. From there the 8 bottles are separated into two manifolds of 4 bottles each, to
pressurize both the LOX and LCH4 tanks. Each manifold then contains its own pressure regulator which
reduces the pressure down to the propellant tank working pressure. The GN2 flows through ¼” tube until
it reaches the 1” cry check valve CV-100 or CV-101. From there the pressurant lines are 0.5” until they
reach the tank inlet fitting. A picture of the pressurant system is shown in Figure 4.2.
38
Figure 4.2: GPS GN2 Pressurant System
The propellant tanks are two identical stainless-steel tanks that are used to temporarily store
pressurized LOX and LCH4. The propellant tanks consist of the tank itself, and two manifolds which
contain all the inlet and outlet ports. Each tank is spherical with an inside diameter of 36” and a wall
thickness of 0.375”. The total weight for each tank is 610 lb. The tanks are connected at the top and bottom
by a 6” flanged pipe used as a manifold. The free side of the pipe is sealed by a blind flange. The top
manifold contains a single ½” connection for the GN2 pressurant inlet and two 1” connections for tank
pressure relief. Valve HV-102 and equivalent HV-103 are manual pressure relief valves, while valves SV-
103 and 103 are solenoid valves controlled by the data acquisition system (DAQ). In case both valves fail,
there is an additional pressure relieve valve on the pressurant line. The bottom manifold contains 3
connections: a fill, a drain, and the run line. Each of these lines is a 1” tubing line. A figure of the propellant
tanks is shown in Figure 4.3.
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Figure 4.3: GPS Propellant Tank
The propellant run lines run from the bottom tank manifold through the engine inlet. These lines
are comprised of 1” tubing and a series of 1” and ½” flex hose. The run line is separated into 2 systems,
the propellant trailer and the engine test stand trailer. The propellant trailer system runs form the tanks to
bulkhead BH-PT connected by flex hose FH-200 or FH-300. The total run length for the propellant trailer
tubing is around 67”. The propellant trailer is connected to the engine test stand trailer bulkhead BH-ET by
1” flex hose 36” in length. The engine test stand trailer runs from the bulkhead plate BH-ET to a bulkhead
plate right before the inlet of the engine test article. The engine is connected to this bulkhead plate by the
engine trailer main feature is ½” flex hose 72 inches in length. The total run length for the engine test trailer
tubing is around 145”. A picture of the individual trailers is shown in Figure 4.4.
40
Figure 4.4: GPS Propellant Run Line (a) Propellant Trailer and (b)
Engine Test Stand Trailer
In order to control the flow of the system, there are a number of hand and solenoid valves
throughout the system. Most importantly there is a venturi flowmeter and valve in the engine test stand
trailer that is used to measure the flowrate into the engine test article. This flowmeter is shown in the P&ID
as V-200 and for the LCH4 side and V-300 for the LOX side. Control of the flowrate is done by actuating
the ball valve to control the flow area through the valve. All solenoid valves are actuated by a separate
control system attached to the DAQ.
41
Chapter 5: Propellant Feed System Models
Four models were developed to simulate the more common operational modes of the propellant
feed system. The first model simulates the chilling down of the propellant tank walls in order to
successfully store liquid oxygen and methane in the tanks. Before the tank walls reach temperatures near
the saturation temperatures of the fluids, very high heat transfer evaporates most of the propellant that enters
the tanks. The model predicts how long it would take to chill the walls and how much propellant is used
before the tanks are full [16]. The second model simulates the propellant and oxidizer sitting in the tank.
The model predicts how long it takes for the propellant to fully evaporate. The third model simulates the
chilldown of the transfer lines. In order to achieve full liquid flow, the lines must reach close to saturation
temperature for the liquids. Before this, the high temperature gradient creates high heat transfer rates which
results in high evaporation rates and high qualities for the exiting fluid. The model aims to simulate the
amount of propellant used and time required for the transfer lines to reach cold enough temperatures in
order to have fully liquid flow [17]. The last model simulates the firing of the engine test and predicts the
pressure losses and system behavior during testing.
5.1 Tank Chilldown and Fill
The tank chill down and fill model simulates filling of the tank in an open vent scenario. What this
means is that the tank vent is kept open and gasified propellant is allowed to exit the tank without changing
the internal tank pressure. The model is shown in Figure 5.1. For this model the tank was divided into five
tank volumes. Each volume is modeled as a pipe branch numbered 34-78. Pipe branches have a specified
length and diameter to determine their volume. The volume is then added to the volume to the adjacent
nodes. For this model, nodes 3-8 have no volume and the entire volume of the tank is modeled in the
branches. Each fluid node is assumed to be filled with the fluid gas at -75° F. Each pipe has a height of 7.2
inches and a calculated diameter to ensure the total volume and heat transfer surface area is equal to the
original tank. A visual representation is shown in Figure 5.2 and the properties for each branch are shown
in Table 5.1. Boundary node 1 represents the fill reservoir which is set just below the saturation
42
temperature of the fluid at 100 psi. Boundary node 2 represents an atmospheric dump for the propellant and
is set to standard pressure and 80° F. Branch 82 represents the exit fitting for the propellant as is modeled
as a simple flow area restriction.
Figure 5.1: Tank Chilldown and Fill Model
43
Figure 5.2: Propellant Tank Sections
Table 5.1: Pipe Branch Geometric Properties
Branch Branch Volume [in3] Pipe Diameter [in] 34 2540.61 21.19
45 6058.39 32.73
56 7230.99 35.75
67 6058.39 32.73
78 2540.61 21.19
The solid nodes 11-16 represent the walls of the tank, and the properties for each solid node are
shown in Table 5.2. Each solid node is set at 80° F as it’s starting temperature. Fluid to solid conductors
are used to couple the fluid and solid nodes and solid to solid conductors are used to model the heat transfer
between sections of the tank wall. The GFFSP input file for this is included in the Appendix.
Table 5.2: Solid Node Geometric Properties
Solid Node Mass [lbm] FS Heat Transfer Area [in2] 11 77.16 678.58
12 74.82 678.58
13 74.82 678.58
14 74.82 678.58
15 74.82 678.58
16 77.16 678.58
44
In order to accurately model the heat transfer between the propellant and the tank walls, the heat
transfer coefficient had to be specified using a custom user subroutine. Subroutine USRHCF was used to
calculate the Nusselt number and heat transfer coefficient for each FS conductor. The user subroutine for
this model is included in the Appendix. For conductor 316 and 811, the Nusselt number correlations
suggested by McAdams [12] for horizontal plates are used.
Upper Surface of Hot Plate
1/40.54L LNu Ra= ( )4 710 10LRa (5.1)
1/30.15L LNu Ra= ( )7 1110 10LRa (5.2)
Lower Surface of Hot Plate
1/40.27L LNu Ra= ( )5 1010 10LRa (5.3)
For the rest of the conductors, the heat transfer was assumed to be between the fluid and a horizontal plate
representing the tank side walls. The correlation used was that by Churchill and Chu [18] and is show in
Equation 5.4.
2
1/6
8/279/16
0.2870.825
0.4921
Pr
LL
RaNu
= + +
(5.4)
Branch 13 is a constant flow rate branch. This branch is used to model a constant flow of propellant
that comes from the filling reservoir. The flowrates of 0.5 and 1.0 lbm/s were both modeled to determine
the effects that the flowrate had on the total amount of propellant needed to chill down the tank walls and
completely fill the tank with liquid propellant. Figures 5.3 and 5.4 show the temperature of the tank walls.
For the oxygen tanks, the higher flowrate lowers the time it takes for the tank walls to reach saturation
temperature by around 300s, from around 1300s to just below 1000s. For the methane tank, the higher
flowrate lowers the time required to reach desired temperatures by around 400s, from 1200s to around 800s.
The faster wall chilldown time for the methane runs makes sense since the thermal conductivity of methane
45
is about twice as much as that of oxygen at the same pressure and saturation conditions. The higher thermal
conductivity leads to a much higher heat transfer from the tank wall.
Figure 5.3: Oxygen tank wall temperatures for a fill rate of (a) 0.5 lbm/s
and (b) 1.0 lbm/s
Figure 5.4: Methane tank wall temperatures for a fill rate of (a) 0.5 lbm/s
and (b) 1.0 lbm/s
The qualities for each fluid node are shown in Figures 5.5 and 5.6. Compared to the tank wall
temperatures, the qualities for the fluid nodes tend to zero much faster. What this means is that the tank
walls do not have to reach the fluid saturation temperature before fully liquid fluid can exist. For the oxygen
fill, the tank reaches 90% liquid in the top most node at around 1000 seconds for a fill rate of 0.5 lbm/s and
reaches this condition much more quickly at the higher flowrate, at a time of about 400s. The methane fill
is similar in which the faster flowrate reaches mostly liquid condition at around half the time as the flower
46
flowrate. The much higher heat of vaporization of methane and the faster chilldown time explains the much
faster fill rate in the methane runs compared to the oxygen runs.
Figure 5.5: Oxygen fluid node quality for a fill rate of
(a) 0.5 lbm/s and (b) 1.0 lbm/s
Figure 5.6: Methane fluid node quality for a fill rate of
(a) 0.5 lbm/s and (b) 1.0 lbm/s
5.2 Tank Boiloff
The tank boiloff model predicts the time required to evaporate the propellant inside the tank. The
model is shown in Figure 5.7. Here node 1 represents the propellant node where only the liquid propellant
resides. The initial node temperature is set to just above the saturation temperature of the fluid. Nodes 5
and 7 represent the ullage nodes where the gaseous propellant resides. The initial temperature of the ullage
nodes sits just below saturation temperature. The tank pressure is initially set to 300 psi. Boundary node 4
is a pseudo-boundary node that exerts ullage pressure on the liquid propellant node. This is similar to the
47
tank pressurization option built into GFFSP. In this model, multiple ullage nodes are used to model tank
stratification in order to more accurately model the heat transfer between ullage to wall [19]. Boundary
node 9 represents the atmospheric propellant dump. Branch 97 is modeled as a restriction but uses the
pressure relief valve advanced option included into GFFSP. The seating pressure for the pressure relief
valve is 300 psi and becomes fully open at 350 psi. Solid nodes 2,6, and 8 represent the tank wall. Solid
node 2 represents the portion of the wall exposed to the liquid propellant and solid nodes 6 and 8 represent
the tank wall exposed to the ullage gas. The ambient node 3 is set to 80°F. The GFSSP input data file is
included in the Appendix.
Figure 5.7: Tank Boiloff GFSSP Model
The fluid solid conductors are modeled to represent the heat transfer between the fluid and tank
walls. The heat transfer coefficient used for the FS conductors is set using a custom user subroutine equal
to the one used in the tank chilldown and fill model. The heat transfer between the ambient node and the
propellant tank wall is modeled by the solid-ambient conductors 23, 63, and 83. The heat transfer coefficient
for the heat transfer between the tank and the atmosphere is modeled as a sphere inside a fluid following
the correlation by Churchill [20] shown in Equation 14. This coefficient was also adjusted using the user
subroutine BNDUSER.
48
1/4
4/99/16
0.5892
0.4691
Pr
DD
RaNu = +
+
(5.5)
In this model a user subroutine was used to model the evaporative mass transfer at the liquid-vapor interface.
Figure 5.8 shows the evaporative mass transfer process at the interface.
Figure 5.8: Evaporative Mass Transfer
It is assumed that evaporation takes place at the interface in an infinitely thin film which contains saturated
vapor at ullage pressure. The ullage contains superheated vapor at temperature UT . The interface
temperature IT is the saturation temperature at ullage pressure, and the liquid temperature is represented by
LT . The ullage to interface heat transfer UIQ can be expressed as
( )UI UI U IQ h A T T= − where UUI
kh
L= (5.6)
The liquid to interface heat transfer LIQ can be expressed as
49
( )IL IL I LQ h A T T= − where LLI
kh
L= (5.7)
The wall to liquid heat transfer WLQ can be expressed as
( )WL WL W W LQ h A T T= − (5.8)
where WA is the fluid to solid heat transfer area and
WLh is determined by Equation 5.4.
Since the thin interface layer does not accumulate mass or heat, the mass flow rate through the interface is
equal to the mass evaporated by the liquid and the heat entering the interface must be equal to the heat
exiting the interface. Thus UI ILQ Q= . Assuming the fluid accumulates no energy and all the heat is used
to evaporate the fluid, the conservation of energy equation of the fluid becomes
0 fg WL ILU mh Q Q = = − + + (5.9)
Since the liquid temperature is assumed to be at saturation temperature at all times the evaporative mass
transfer is given by
UI WL
fg
Q Qm
h
+= (5.10)
Where fgh is the heat of vaporization of the liquid. The mass transfer was computed in subroutine
SORCEM. The variation of the heat of vaporization due to pressure change was neglected in the model as
the pressure change is small due to the pressure relieve valve.
The initial fill level of the tank is set to 50%. The initial liquid node volumes are listed in Table 5.3 and
the initial solid node mass, fluid to solid heat transfer areas, and solid to ambient heat transfer areas are
shown in Table 5.4.
Table 5.3: Fluid Node Geometric Properties
Fluid Node Volume [in3] 1 12214
5 8397
7 3817
50
Table 5.4: Solid Node Geometric Properties
Solid Node Mass [lbm] FS Heat Transfer Area [in2] SA Heat Transfer Area [in2] 2 223 2035.5 2121.5 6 110 1017.9 1039.1 8 112 1246.6 1082.4
Since mass is leaving the liquid propellant node, the volume of node 1 is decreasing and the volume of node
5 is increasing. With the change in volumes, the wall in in contact with the fluid decreases and so do the
heat transfer surface areas. This can be visualized in Figure 5.9.
Figure 5.9: Node Volume Change Representation
The user subroutine BNDUSER allows the user to modify boundary conditions. In this subroutine, the new
Node 1 volume is calculated using the following equation:
mZRTV
P= (5.11)
The volume change is then added to the existing Node 5 volume to calculate the its new volume. The
volume of Node 7 is set constant. Once the new volumes are set, the new heat transfer areas for both FS
and SA conductors are calculated using the equation for the surface area of a spherical cap and spherical
segment as shown in Equation 21 where R is the overall radius of the tank and h is the height of the
segment
2capSA Rh= (5.12)
Lastly, the new solid node mass is adjusted to represent the section of wall in contact with the propellant.
To simplify the calculation of the tank wall volume, a linear correlation between the propellant height and
51
wall volume was used. Figure 5.10 shows the set of data used to come to this relationship. The volume was
then multiplied by the density of 304 Stainless Steel. The custom subroutine file for this model is included
in the Appendix.
Figure 5.10: Propellant Height to Tank Wall Volume for Determining
Solid Node Mass
The results from the simulations are shown in Figure 5.11. For the oxygen tank, at 300 psi and
50% fill, the initial mass of liquid propellant is 387 lb. In order to completely boil off the entirety of the
liquid propellant, the tank would need to sit for 10400 seconds or about 2.89 hours. For the methane tank
at the same conditions, the starting mass is 146 lb. In order to boil off all of the methane it takes only about
6760 seconds or about 1.88 hours. As expected, the methane boils off at a slower rate as seen by the less
steep decline in propellant mass. This is because it has a higher heat of vaporization and thus requires more
heat in order to evaporate. The lower density of oxygen allows for higher initial storage mass and thus a
longer complete evaporation time. While the initial oxygen mass is about 2.65 times as much as the
methane, it only takes around 1.5 times longer to fully evaporate.
52
Figure 5.11: Propellant Mass as a Function of Time in Boil Off Scenario
5.3 Line Chill down
The tank chill down model predicts the time and propellant required to lower the temperature of
the fill lines to near the saturation temperature of the fluid. Lowering the temperature of the lines reduces
the heat transfer between the hot lines and the flowing fluid and allows for full liquid flow. This is important
as the engines are designed to run on liquid-liquid. The model is shown in Figure 5.12. The model
represents the fill lines running from the propellant tanks to the inlet of the engine just after the last flex
hose as shown in Figure 5.13. Boundary node 1 represents the propellant tank with branch 13 representing
the exit fitting for the propellant line. Here branch 3263 is the last flex hose in the line with boundary node
2 representing the engine inlet. The properties and descriptions for the fluid branches are shown in Table
5.5. The initial temperature for all the nodes is 80 °F. The GFSSP input file for this model is included in
the Appendix.
53
Figure 5.12: Line Chill Down GFSSP Model
Figure 5.13: P&ID of the Engine Feed System with Modeled Lines Enclosed
54
Table 5.5: Branch Component Descriptions and Properties
Branch Number Description Length [in] Mass [lbm] 34 1" Tube (15 Deg Bend) 1.44 0.10
45 1" Swage Elbow - -
56 1" Tube 3.7 0.25
67 1" Hand Valve (Short Bonnet) - 6.61
78 1" Tube 9.8125 0.66
89 1" Swage Tee - -
910 1" Tube 10.5 0.71
1011 1" Cryo SV - 6.61
1112 1" Tube (Short) 2.7 0.18
1213 1" Flex Hose (36" Length) 36 2.44
1314 1" Swage Elbow - -
1415 1" Tube (Short) 3 0.20
1516 1" Bulkhead Union (Propellant Trailer) - -
1617 1" Tube 12 0.81
1718 1" Flex Hose (36" Length) 36 2.44
1819 1" Tube 22 1.49
1920 1" Bulkhead Union (Engine Trailer) - -
2021 1" Tube 16.5 1.12
2122 1" Swage Tee - -
2223 1" Tube 13.1875 0.89
2324 1" Cross (One side plugged) - -
2425 Oxygen Venturi (1" Swagelok Interface) - -
2526 1" Cryo Hand Valve (Long Stem) - 6.61
2627 1" Tube (One side is Swaged the other AN) 5.35 0.36
2728 1" Cryo Filter (AN interfaces) - -
2829 1" Tube (One side is Swaged the other AN) 18.25 1.24
2930 1" Elbow - -
3031 1" Tube 20.25 1.37
3132 1/2" to 1" Reducing Union - -
3263 1/2" Flex Hose (72" length) 72 1.81
For the fluid-solid conductors, the correlation by Miropolskii [14] for two phase heat tube flow was
used. This is the correlation built into GFSSP for two phase flow. The other flow correlation available in
GFFSP is the single-phase correlation by Dittus and Boelter [21]. It is shown in [22] that the correlation
by Miropolskii shows overall better results for two-phase flow compared to that of Dittus and Boelter.
55
The results for both the methane and oxygen chill lines are shown in Figures 5.14 and 5.15. The
plot shows the quality of the nodes right before and after the last flex hose, fluid nodes 32 and 63. The node
right after the venturi flow meter is fluid node 25. For the LOX case, the lines reach fully liquid at around
40 seconds into the chilldown operation. Of note is that the quality of the node right after the last flex hose
does not reach fully liquid but asymptotes at around 90% liquid. Checking the temperature and the pressure
of the fluid at that fluid node using REFPROP shows that the node is in fact fully liquid with the temperature
being below the saturation temperature. For the methane run, the fluid nodes reach fully liquid conditions
much faster, with the last node reaching fully liquid conditions at around 10s.
Figure 5.14: Fluid Node Qualities for the LOX Chilldown Model
56
Figure 5.15: Fluid Node Qualities for the LCH4 Chilldown Model
Figure 5.16 shows the flowrates for each run. The flow form these runs is entirely pressure driven by having
the propellant tanks set at a constant 300 psi and the exit reservoir at 14.7 psi. Using the measured flow
rates, it takes 60 lbm of LOX and 38 lbm of LCH4 to chill the pipes and obtain fully liquid flow into the
engine module.
Figure 5.16: Flow Rates for the LOX and LCH4 Chilldown Runs
57
5.4 Engine Run Case
The engine run model simulates the engine fire operation. In this model the engine receives a
constant propellant flowrate of 1.6 lbm/s, as it is the require flowrate to fire the engine. The GFSSP model
is shown in Figure 5.17 and a representative P&ID of the system is shown in Figure 5.18. The bottom half
of the model is an import from the Line Chilldown model. The previous boundary node representing the
propellant tank was transformed into a tank pressurization module. Fluid node 1 is the propellant volume,
and fluid node 66 becomes the ullage node. The pressurant supply system is represented by boundary node
87 and branch 8786. It is assumed that the nitrogen supply tanks have enough fluid to supply the run
operation. Instead of modeling the two-stage pressure reducer, the boundary node pressure was set to stay
at 350 psi for the duration of the run to simplify the model. The components and their corresponding
branches are shown in Table 5.6. In addition to the basic components, a flow regulator advanced option
was used to set the flowrate into the engine module of 1.6 lbm/s. The flow regulator is set at branch 2425,
the location where the flow regulating valve lies on the schematic. A pressure regulator advanced option
was added to the restriction right above the ullage. The pressure regulator was set to maintain the pressure
in fluid node 66 at 300 psi. The GFSSP input file for this model is included in the Appendix.
58
Figure 5.17: Engine Run GFSSP Model
Figure 5.18: Engine Run Line P&ID
59
Table 5.6: Branch Component Descriptions and Properties
Branch Number Description Length [in] Mass [lbm] 8685 1/4" Tube 36 0.24
8584 1/4" Swagelok Elbow - -
8483 1/4" Tube 36 0.24
8382 1/4" Elbow - -
8281 1/4" Tube (Short) 1.2 0.008
8180 1/4" Swagelok Tee - -
8079 1/4" Tube (short) 1.5 0.01
7978 1/4" Hand Valve (Quarter Turn) 2.5 1.33
7877 1/4" Tube (Short) 1.05 0.007
7776 1/4" Solenoid Valve 2.5 1.33
7675 1/4" Tube (Short) 1.15 0.00766667
7574 1/4" to 1/2" Reducing Union - -
7473 1/2" Tube (Short) 2.25 0.056625
7372 1" Cryo Check Valve 2.5 3.53
7271 1/2" Tube (Short) 2.25 0.056625
7170 1/2" Swagelok Cross - -
7069 1/2" Tube (Short) 2.25 0.056625
6968 1/2" Swagelok Tee - -
6867 1/2" Tube (Short) 1.75 0.04404167
The calculation of mass transfer from the propellant node to the ullage node is not a capability of
the pressurization option. Similar to the Tank Boiloff Model, a separate user subroutine SORCEC had to
be written to account for the mass transfer. This subroutine is called from subroutine MASSC. The user
subroutine uses the heat transfer rate from the ullage to the propellant to calculate the mass transfer rate of
vaporized propellant to the ullage. It is assumed that the propellant is vaporized from a thin interface volume
at the surface of the propellant as shown in Figure 5.8. It is also assumed that the heat transfer from the
ullage only contributes to the vaporization of the propellant. The custom subroutine file for this model is
included in the GFSSP installation folder Example 10 [10].
Following the line chill down operation, the solid nodes connected to the propellant lines in this
model are set at the saturation temperature of the fluid. The solid nodes connected to the pressurization
lines are set at 80°F. In contrast to the line chilldown model, the heat transfer coefficient option for this
60
model is set to use the Dittus Boelter correlation. This correlation has been shown to have very accurate
results when compared to single phase fluid flow.
The engine run model is mostly done to show the capabilities of the software in modeling complex
flow circuits. Figure 5.19 shows the volumes of the ullage and propellant nodes change during the run.
Initially, the tank starts at 85% full and after a 20 second run drains to 81% for the oxygen tank and 78%
for the methane tank. Additionally, it is important to get an estimate of the pressure drop across the whole
system. Figure 5.20 shows the pressure drop across various fluid nodes in the model. Fluid node 66 is the
ullage node, 01 is the propellant node, 25 is the node right after the flow meter, and node 63 is the last node
before the engine module. For the oxygen line, the total pressure drop between the propellant tanks and the
engine is 14.13 psi. For the methane line, the total pressure drop is 14.46 psi.
Figure 5.19: Propellant and Ullage Node Volumes for the Engine Run Model
61
Figure 5.20: Pressure Drop Across Propellant Run Lines for (a) LOX and (b) LCH4
62
Chapter 6: Conclusion
System level models are commonly used to design and analyze complex fluid flow systems where
performing CFD analysis would be too computationally taxing. The use of the models in development help
the designers understand the thermal and fluid behavior of the total system and each of its subcomponents
allowing them to properly size and choose components as well as determine operational ranges. Four
detailed system level models were developed for the different GPS operational modes using the GFFSP
software. The tank fill model predicts the time required to cool the tank walls and achieve fully liquid
conditions inside the tank. The tank boiloff model predicts the amount of time it takes the propellant to
completely evaporate from the tank. The line chill down predicts the amount of propellant that must be
used to lower the engine rune line temperature enough to achieve fully liquid flow. Finally, the engine test
run model predicts the behavior of the system such as pressure drop and tank fill level. Overall each model
gives reasonable results and present no indication that the models are not accurate. The validation models
presented in the paper give confidence in the ability of GFSSP to model both pressure drop and conjugate
heat transfer. The next step to ensure the accuracy of the models is to compare to test data once the system
is operational. Going forward, GFSSP should be used in developing any future flow systems at the cSETR.
63
References
[1] C. Funk and M. Strauss, "Pew Research Center," 6 June 2018. [Online]. Available:
https://www.pewresearch.org/science/2018/06/06/majority-of-americans-believe-it-is-essential-that-
the-u-s-remain-a-global-leader-in-space/. [Accessed 22 April 2019].
[2] C. Brown, "Conceptual Investigations for a Methane-Fueled Expander Rocket Engine," Pratt &
Whitney, West Palm Beach, FL, 2004.
[3] P. Pempie, "LOX/Methane and LOX/Kerosene High Thrust Engine Trade-Off," CNES Launcher
Directorate, Every, France, 2001.
[4] G. Sutton and O. Biblarz, Rocket Propulsion Elements, John Wiley & Sons Inc, 2001.
[5] E. Hurlbert, J. Mcmanamen, J. Sooknanen and J. Studak, "Advanced Development of a Compact 5-
15 lbf Lox/Methane Thruster for an Integrated Reaction Control and Main Engine Propulsion
System," in 47th AIAA/ASME/SAE/ASEE Joint Propulsoin Conference and Exhibit, 2011.
[6] J. Olansen, "Project Morpheus: Lander Techonology Development," in AIAA SPACE 2014
Conference and Exposition, 2014.
[7] D. Leone, "Space News," 25 October 2013. [Online]. Available:
https://spacenews.com/37859spacex-could-begin-testing-methane-fueled-engine-at-stennis-next-
year/. [Accessed 22 April 2019].
[8] R. DeRoy and J. Reed, "Vulcan, ACES and Beyond: Providing Launch Services for Tomorrow's
Spacecraft," Advances in the Astronautical Sciences Series, vol. 16, 2016.
[9] "Direct Coupled 1D/3D-CFD-Computation of the Flow in the Switch_over Intake System of an 8-
Cylinder SI Engine with External Exhaust Gas Recirculation," Journal of Engines, vol. 111, 2002.
64
[10] A. Majumdar, A. LeClair and R. Moore, "Generalized Fluid System Simulation Program, Version
6.0," National Aeronuatics and Space Administration, Huntsville, Alabama, 2013.
[11] E. Weisstein, "MathWorld," Wolfram, [Online]. Available:
http://mathworld.wolfram.com/FiniteVolumeMethod.html. [Accessed May 2019].
[12] M. W. H., Heat Transmission, New York: McGraw-Hill, 1954.
[13] F. Incropera, D. Dewitt, T. Bergman and A. Lavine, Fundamentals of Heat and Mass Trasnfer, John
Wiley & Sons, 2007.
[14] Z. Miropolskii, "Heat Transfer in Film Boiling of a Steam-Water Mixture in Steam Generating
Tubes," Teploenergetika, vol. 10, 1963.
[15] M. Cross, A. Majumdar, J. Bennet and R. Malla, "MOdeling of Chill Down in Cryogenic Transfer
Lines," Journal of Spacecraft and Rockets, vol. 39, 2002.
[16] A. LeClari and A. Majumbar, "Computational Model of the Chilldown and Propellant Loading of the
Space Shuttle Tanks," in American Institute of Aeronautics and Astronautics, Nashville, TN, 2010.
[17] A. Majumdar and S. Ravindran, "Numerical Prediction of Conjugate Heat Trasnfer in Fluid
Network," Journal of Propulsion and Power, vol. 27, no. 3, 2011.
[18] S. Churchill and H. Chu, International Journal of Heat and Mass Transfer, vol. 18, 1975.
[19] A. Majumdar, J. Valenzuela, A. LeClair and J. Moder, "Numerical Modeling of Self-Pressurization
and Pressure Control by a Thermodynamic Vent System in a Cryogenic Tank," Cryogenics, vol. 74,
2016.
[20] S. Churchill, "Free Convection Around Immersed Bodies," in Heat Exchanger Design Handbook,
2002.
[21] F. Dittus and L. Boelter, "Heat Transfer in Automobile Radiators of the Tubular Type," Int. Comm.
Heat Mass Transfer, vol. 12, 1985.
65
[22] M. Mercado, N. Wong and J. Hartwig, "Assessment of Two-Phase Heat Transfer Coefficient and
Critical Heat Flux Correlations for Cryogenic Flow Boiling in Pipe Heating Experiemnts,"
International Journal of Heat and Mass Transfer, vol. 133, 2018.
[23] A. Majumdar, A. LeClair and A. Hedayat, "Numerical Modeling of Pressurization of Cryogenic
Propellant Tank for Integrated Vehicle Fluid System," American Institute of Aeronautics and
Astronautics, 2016.
66
Appendix
A.1 Pressure Drop Validation Model GFSSP Input File
GFSSP VERSION
605
GFSSP INSTALLATION PATH
X:\Program Files (x86)\GFSSP\
ANALYST
Mariano Mercado
INPUT DATA FILE NAME
X:\User\My Documents\Grad School\Thesis\Validation\Pressure Drop\pressuredrop.dat
OUTPUT FILE NAME
pressuredrop.out
TITLE
Pressure Drop
USETUP
F
DENCON GRAVITY ENERGY MIXTURE THRUST STEADY TRANSV SAVER
F F T F F T F F
HEX HCOEF REACTING INERTIA CONDX ADDPROP PRINTI ROTATION
F F F F F F T F
BUOYANCY HRATE INVAL MSORCE MOVBND TPA VARGEO TVM
F T F F F F F F
SHEAR PRNTIN PRNTADD OPVALVE TRANSQ CONJUG RADIAT WINPLOT
F T T F F F F F
PRESS INSUC VARROT CYCLIC CHKVALS WINFILE DALTON NOSTATS
F F F F F F F F
NORMAL SIMUL SECONDL NRSOLVT IBDF NOPLT PRESREG FLOWREG
F T F T 1 T 0 0
TRANS_MOM USERVARS PSMG ISOLVE PLOTADD SIUNITS TECPLOT MDGEN
F F F 1 F F F F
NUM_USER_VARS IFR_MIX PRINTD SATTABL MSORIN PRELVLV LAMINAR HSTAG
1 1 F F F F F T
67
DFLI
T
NNODES NINT NBR NF
8 6 7 1
RELAXK RELAXD RELAXH CC NITER RELAXNR RELAXHC RELAXTS
1 0.5 1 0.0001 500 1 1 1
NFLUID(I), I = 1, NF
2
NODE INDEX DESCRIPTION
1 2 " BNode 1"
2 1 " INode 2"
3 1 " INode 3"
4 1 " INode 4"
5 1 " INode 5"
6 1 " INode 6"
7 1 " INode 7"
8 2 " BNode 8"
NODE PRES (PSI) TEMP(DEGF) MASS SOURC HEAT SOURC THRST AREA CONCENTRATION
1 25 -250 0 0 0
2 14.7 60 0 0 0
3 14.7 60 0 0 0
4 14.7 60 0 0 0
5 14.7 60 0 0 0
6 14.7 60 0 0 0
7 14.7 60 0 0 0
8 20 -255 0 0 0
INODE NUMBR NAMEBR
2 2 12 23
3 2 23 34
4 2 34 45
5 2 45 56
6 2 56 67
7 2 67 78
BRANCH UPNODE DNNODE OPTION DESCRIPTION
68
12 1 2 2 "Pipe 12"
23 2 3 1 "Pipe 23"
34 3 4 1 "Pipe 34"
45 4 5 1 "Pipe 45"
56 5 6 1 "Pipe 56"
67 6 7 1 "Pipe 67"
78 7 8 2 "Restrict 78"
BRANCH OPTION -2 FLOW COEFF AREA
12 0 0.79
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
23 48 1 0 0 0.7853975
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
34 48 1 0 0 0.7853975
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
45 48 1 0 0 0.7853975
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
56 48 1 0 0 0.7853975
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
67 48 1 0 0 0.7853975
BRANCH OPTION -2 FLOW COEFF AREA
78 0 0.79
69
A.2 Chilldown of Short Cryogenic Line GFSSP Input File
GFSSP VERSION
605
GFSSP INSTALLATION PATH
X:\Program Files (x86)\GFSSP\
ANALYST
Mariano Mercado
INPUT DATA FILE NAME
X:\User\My Documents\Grad School\Thesis\Validation\Cryo Line\cryoline.dat
OUTPUT FILE NAME
cryoline.out
TITLE
Cryo Line
USETUP
F
DENCON GRAVITY ENERGY MIXTURE THRUST STEADY TRANSV SAVER
F F T F F F T F
HEX HCOEF REACTING INERTIA CONDX ADDPROP PRINTI ROTATION
F F F F F F F F
BUOYANCY HRATE INVAL MSORCE MOVBND TPA VARGEO TVM
F T F F F F F F
SHEAR PRNTIN PRNTADD OPVALVE TRANSQ CONJUG RADIAT WINPLOT
F T T F F T F T
PRESS INSUC VARROT CYCLIC CHKVALS WINFILE DALTON NOSTATS
F F F F F T F F
NORMAL SIMUL SECONDL NRSOLVT IBDF NOPLT PRESREG FLOWREG
F T F T 1 T 0 0
TRANS_MOM USERVARS PSMG ISOLVE PLOTADD SIUNITS TECPLOT MDGEN
F F F 1 F F F F
NUM_USER_VARS IFR_MIX PRINTD SATTABL MSORIN PRELVLV LAMINAR HSTAG
1 1 F F F F F T
DFLI
T
NNODES NINT NBR NF
12 10 11 1
RELAXK RELAXD RELAXH CC NITER RELAXNR RELAXHC RELAXTS
1 0.5 1 0.0001 500 1 1 1
DTAU TIMEF TIMEL NPSTEP NPWSTEP WPLSTEP WPLBUFF
0.01 0 60 100 100 50 1.1
NFLUID(I), I = 1, NF
70
6
NODE INDEX DESCRIPTION
1 2 " BNode 1"
2 1 " INode 2"
3 1 " INode 3"
4 1 " INode 4"
5 1 " INode 5"
6 1 " INode 6"
7 1 " INode 7"
8 1 " INode 8"
9 1 " INode 9"
10 1 " INode 10"
11 1 " INode 11"
12 2 " BNode 12"
NODE PRES (PSI) TEMP(DEGF) MASS SOURC HEAT SOURC THRST AREA NODE-VOLUME CONCENTRATION
2 14.7 60 0 0 0 0
3 14.7 60 0 0 0 0
4 14.7 60 0 0 0 0
5 14.7 60 0 0 0 0
6 14.7 60 0 0 0 0
7 14.7 60 0 0 0 0
8 14.7 60 0 0 0 0
9 14.7 60 0 0 0 0
10 14.7 60 0 0 0 0
11 14.7 60 0 0 0 0
Hist1.dat
Hist12.dat
INODE NUMBR NAMEBR
2 2 12 23
3 2 23 34
4 2 34 45
5 2 45 56
6 2 56 67
7 2 67 78
8 2 78 89
9 2 89 910
10 2 910 1011
11 2 1011 1112
BRANCH UPNODE DNNODE OPTION DESCRIPTION
12 1 2 1 "Pipe 12"
23 2 3 1 "Pipe 23"
71
34 3 4 1 "Pipe 34"
45 4 5 1 "Pipe 45"
56 5 6 1 "Pipe 56"
67 6 7 1 "Pipe 67"
78 7 8 1 "Pipe 78"
89 8 9 1 "Pipe 89"
910 9 10 1 "Pipe 910"
1011 10 11 1 "Pipe 1011"
1112 11 12 1 "Pipe 1112"
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
12 2 0.5 0 0 0.196349375
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
23 2 0.5 0 0 0.196349375
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
34 2 0.5 0 0 0.196349375
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
45 2 0.5 0 0 0.196349375
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
56 2 0.5 0 0 0.196349375
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
67 2 0.5 0 0 0.196349375
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
78 2 0.5 0 0 0.196349375
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
89 2 0.5 0 0 0.196349375
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
910 2 0.5 0 0 0.196349375
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
1011 2 0.5 0 0 0.196349375
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
1112 2 0.5 0 0 0.196349375
INITIAL FLOWRATES IN BRANCHES FOR UNSTEADY FLOW
12 0
23 0
34 0
45 0
56 0
67 0
78 0
89 0
910 0
72
1011 0
1112 0
NSOLID NAMB NSSC NSFC NSAC NSSR
10 0 9 10 0 0
NODESL MATRL SMASS TS HtSrc NUMSS NUMSF NUMSA NUMSSR DESCRIPTION
13 29 0.1428440 80.0000000 0.0000000 1 1 0 0 "SNode 13"
NAMESS
1314
NAMESF
132
14 29 0.1428440 80.0000000 0.0000000 2 1 0 0 "SNode 14"
NAMESS
1314 1415
NAMESF
314
15 29 0.1428440 80.0000000 0.0000000 2 1 0 0 "SNode 15"
NAMESS
1415 1516
NAMESF
415
16 29 0.1428440 80.0000000 0.0000000 2 1 0 0 "SNode 16"
NAMESS
1516 1617
NAMESF
516
17 29 0.1428440 80.0000000 0.0000000 2 1 0 0 "SNode 17"
NAMESS
1617 1718
NAMESF
617
18 29 0.1428440 80.0000000 0.0000000 2 1 0 0 "SNode 18"
NAMESS
1718 1819
NAMESF
718
19 29 0.1428440 80.0000000 0.0000000 2 1 0 0 "SNode 19"
NAMESS
1819 1920
NAMESF
819
20 29 0.1428440 80.0000000 0.0000000 2 1 0 0 "SNode 20"
73
NAMESS
1920 2021
NAMESF
920
21 29 0.1428440 80.0000000 0.0000000 2 1 0 0 "SNode 21"
NAMESS
2021 2122
NAMESF
1021
22 29 0.1428440 80.0000000 0.0000000 1 1 0 0 "SNode 22"
NAMESS
2122
NAMESF
1122
ICONSS ICNSI ICNSJ ARCSIJ DISTSIJ DESCRIPTION
1314 13 14 0.24544 2.00000 "Conductor 1314"
1415 14 15 0.24544 2.00000 "Conductor 1415"
1516 15 16 0.24544 2.00000 "Conductor 1516"
1617 16 17 0.24544 2.00000 "Conductor 1617"
1718 17 18 0.24544 2.00000 "Conductor 1718"
1819 18 19 0.24544 2.00000 "Conductor 1819"
1920 19 20 0.24544 2.00000 "Conductor 1920"
2021 20 21 0.24544 2.00000 "Conductor 2021"
2122 21 22 0.24544 2.00000 "Conductor 2122"
ICONSF ICS ICF MODEL ARSF HCSF RADSF EMSFS EMSFF DESCRIPTION
132 13 2 2 3.14150e+00 0.00000e+00 F 0.00000e+00 0.00000e+00 "Convection 132"
1122 22 11 2 3.14150e+00 0.00000e+00 F 0.00000e+00 0.00000e+00 "Convection 1122"
1021 21 10 2 3.14150e+00 0.00000e+00 F 0.00000e+00 0.00000e+00 "Convection 1021"
920 20 9 2 3.14150e+00 0.00000e+00 F 0.00000e+00 0.00000e+00 "Convection 920"
819 19 8 2 3.14150e+00 0.00000e+00 F 0.00000e+00 0.00000e+00 "Convection 819"
718 18 7 2 3.14150e+00 0.00000e+00 F 0.00000e+00 0.00000e+00 "Convection 718"
617 17 6 2 3.14150e+00 0.00000e+00 F 0.00000e+00 0.00000e+00 "Convection 617"
516 16 5 2 3.14150e+00 0.00000e+00 F 0.00000e+00 0.00000e+00 "Convection 516"
415 15 4 2 3.14150e+00 0.00000e+00 F 0.00000e+00 0.00000e+00 "Convection 415"
314 14 3 2 3.14150e+00 0.00000e+00 F 0.00000e+00 0.00000e+00 "Convection 314"
74
A.3 Tank Chilldown and Fill GFSSP Input File
GFSSP VERSION
605
GFSSP INSTALLATION PATH
X:\Program Files (x86)\GFSSP\
ANALYST
Mariano Mercado
INPUT DATA FILE NAME
X:\User\My Documents\Grad School\Thesis\Tank Chilldown\Oxygen\TankChilldown.dat
OUTPUT FILE NAME
tankchilldown.out
TITLE
Tank Chilldown
USETUP
F
DENCON GRAVITY ENERGY MIXTURE THRUST STEADY TRANSV SAVER
F T T F F F T F
HEX HCOEF REACTING INERTIA CONDX ADDPROP PRINTI ROTATION
F F F F F F F F
BUOYANCY HRATE INVAL MSORCE MOVBND TPA VARGEO TVM
T T F F F F F F
SHEAR PRNTIN PRNTADD OPVALVE TRANSQ CONJUG RADIAT WINPLOT
F T F F F T F T
PRESS INSUC VARROT CYCLIC CHKVALS WINFILE DALTON NOSTATS
F F F F F T F F
NORMAL SIMUL SECONDL NRSOLVT IBDF NOPLT PRESREG FLOWREG
F T F T 1 T 0 0
TRANS_MOM USERVARS PSMG ISOLVE PLOTADD SIUNITS TECPLOT MDGEN
F F F 1 F F F F
NUM_USER_VARS IFR_MIX PRINTD SATTABL MSORIN PRELVLV LAMINAR HSTAG
1 1 F F F F F T
DFLI
T
NNODES NINT NBR NF
8 6 7 1
RELAXK RELAXD RELAXH CC NITER RELAXNR RELAXHC RELAXTS
1 0.5 1 0.0001 500 1 1 1
DTAU TIMEF TIMEL NPSTEP NPWSTEP WPLSTEP WPLBUFF
0.1 0 3600 10 10 50 1.1
NFLUID(I), I = 1, NF
75
6
NODE INDEX DESCRIPTION
1 2 " BNode 1"
3 1 " INode 3"
4 1 " INode 4"
5 1 " INode 5"
6 1 " INode 6"
7 1 " INode 7"
8 1 " INode 8"
2 2 " BNode 2"
REFERENCE NODE FOR DENSITY
3
NODE PRES (PSI) TEMP(DEGF) MASS SOURC HEAT SOURC THRST AREA NODE-VOLUME CONCENTRATION
3 14.7 -75 0 0 0 0
4 14.7 -75 0 0 0 0
5 14.7 -75 0 0 0 0
6 14.7 -75 0 0 0 0
7 14.7 -75 0 0 0 0
8 14.7 -75 0 0 0 0
Hist1.dat
Hist2.dat
INODE NUMBR NAMEBR
3 2 13 34
4 2 34 45
5 2 45 56
6 2 56 67
7 2 67 78
8 2 78 82
BRANCH UPNODE DNNODE OPTION DESCRIPTION
13 1 3 24 "FixedFlow 13"
34 3 4 1 "Pipe 34"
45 4 5 1 "Pipe 45"
56 5 6 1 "Restrict 56"
67 6 7 1 "Restrict 67"
78 7 8 1 "Restrict 78"
82 8 2 2 "Exit Fitting"
BRANCH OPTION -24 FLOW_RATE AREA HISTORY
13 0 0.79 1
FFR.dat
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
76
34 7.2 21.19 2.7869333648e-05 180
352.6561224
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
45 7.2 32.73 1.8043115796e-05 180
841.35934953
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
56 7.2 35.75 1.6518914126e-05 180
1003.7870923
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
67 7.2 32.73 1.8043115796e-05 180
841.35934953
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
78 7.2 21.19 2.7869333648e-05 180
352.6561224
BRANCH OPTION -2 FLOW COEFF AREA
82 0.6 0.19625
INITIAL FLOWRATES IN BRANCHES FOR UNSTEADY FLOW
13 0
34 0
45 0
56 0
67 0
78 0
82 0
NSOLID NAMB NSSC NSFC NSAC NSSR
6 0 5 6 0 0
NODESL MATRL SMASS TS HtSrc NUMSS NUMSF NUMSA NUMSSR DESCRIPTION
11 29 77.2000000 80.0000000 0.0000000 1 1 0 0 "SNode 11"
NAMESS
1112
NAMESF
811
12 29 74.8000000 80.0000000 0.0000000 2 1 0 0 "SNode 12"
NAMESS
1112 1213
NAMESF
712
13 29 74.8000000 80.0000000 0.0000000 2 1 0 0 "SNode 13"
NAMESS
1213 1314
NAMESF
77
613
14 29 74.8000000 80.0000000 0.0000000 2 1 0 0 "SNode 14"
NAMESS
1314 1415
NAMESF
514
15 29 74.8000000 80.0000000 0.0000000 2 1 0 0 "SNode 15"
NAMESS
1415 1516
NAMESF
415
16 29 77.2000000 80.0000000 0.0000000 1 1 0 0 "SNode 16"
NAMESS
1516
NAMESF
316
ICONSS ICNSI ICNSJ ARCSIJ DISTSIJ DESCRIPTION
1112 11 12 42.85000 6.00000 "Conductor 1112"
1213 12 13 42.85000 6.00000 "Conductor 1213"
1314 13 14 42.85000 6.00000 "Conductor 1314"
1415 14 15 42.85000 6.00000 "Conductor 1415"
1516 15 16 42.85000 6.00000 "Conductor 1516"
ICONSF ICS ICF MODEL ARSF HCSF RADSF EMSFS EMSFF DESCRIPTION
811 11 8 0 6.78600e+02 5.00000e-02 F 0.00000e+00 0.00000e+00 "Convection 811"
712 12 7 0 6.78600e+02 5.00000e-02 F 0.00000e+00 0.00000e+00 "Convection 712"
613 13 6 0 6.78600e+02 5.00000e-02 F 0.00000e+00 0.00000e+00 "Convection 613"
514 14 5 0 6.78600e+02 5.00000e-02 F 0.00000e+00 0.00000e+00 "Convection 514"
415 15 4 0 6.78600e+02 5.00000e-02 F 0.00000e+00 0.00000e+00 "Convection 415"
316 16 3 0 6.78600e+02 5.00000e-02 F 0.00000e+00 0.00000e+00 "Convection 316"
78
A.4 Tank Chilldown and Fill Custom Subroutines
C**********************************************************************
SUBROUTINE USRHCF(NUMBER,HCF)
C PURPOSE: PROVIDE HEAT TRANSFER COEFFICIENT
C***********************************************************************
INCLUDE 'comblk.for'
C**********************************************************************
C ADD CODE HERE
C Calculate the heat trasnfer coefficient
DATA HL /1.5/
NUMF = ICF(NUMBER)
CALL INDEXI(NUMF, NODE, NNODES, IPN)
NUMS = ICS(NUMBER)
CALL INDEXS(NUMS, NODESL, NSOLIDX, IPSN)
BETA = 1.0 / TF(IPN)
DELTAT = ABS(TF(IPN) - TS(IPSN))
IF (NUMBER.EQ.316) THEN
HL = 1.11
GR = HL**3 * RHO(IPN)**2 * G * BETA * DELTAT / (EMU(IPN)**2)
PRNDTL = CPNODE(IPN) * EMU(IPN) / CONDF(IPN)
RALEIGH = GR * PRNDTL
IF (RALEIGH.LT.10E+7) THEN
NUSSELT = 0.54 * RALEIGH **0.25
ELSE
NUSSELT = 0.15 * RALEIGH **0.33
END IF
HCF = NUSSELT*CONDF(IPN)/HL
ELSE
IF (NUMBER.EQ.415) THEN
HL = 1.41
ELSE IF (NUMBER.EQ.514) THEN
HL = 1.50
ELSE IF (NUMBER.EQ.613) THEN
HL = 1.41
ELSE IF (NUMBER.EQ.811) THEN
HL = 1.11
END IF
79
PRNDTL = CPNODE(IPN) * EMU(IPN) / CONDF(IPN)
GR = HL**3 * RHO(IPN)**2 * G * BETA * DELTAT / (EMU(IPN)**2)
RALEIGH = GR * PRNDTL
NUNUM = 0.387 * RALEIGH**0.16
NUDEN = (1+(0.492/PRNDTL)**0.562)**0.296
NUSSELT = (0.825 + (NUNUM/NUDEN))**2
HCF = NUSSELT*CONDF(IPN)/HL
END IF
RETURN
END
C**********************************************************************
80
A.5 Tank Boiloff GFSSP Input File
GFSSP VERSION
605
GFSSP INSTALLATION PATH
X:\Program Files (x86)\GFSSP\
ANALYST
Mariano Mercado
INPUT DATA FILE NAME
X:\User\My Documents\Grad School\Thesis\Tank Boil Off\Test 6 OXYGEN\test.dat
OUTPUT FILE NAME
test.out
TITLE
TANK BOILOFF OXYGEN
USETUP
F
DENCON GRAVITY ENERGY MIXTURE THRUST STEADY TRANSV SAVER
F F T F F F T F
HEX HCOEF REACTING INERTIA CONDX ADDPROP PRINTI ROTATION
F F F F F F F F
BUOYANCY HRATE INVAL MSORCE MOVBND TPA VARGEO TVM
F T F F F F F F
SHEAR PRNTIN PRNTADD OPVALVE TRANSQ CONJUG RADIAT WINPLOT
F T T F F T F T
PRESS INSUC VARROT CYCLIC CHKVALS WINFILE DALTON NOSTATS
F F F F F T F F
NORMAL SIMUL SECONDL NRSOLVT IBDF NOPLT PRESREG FLOWREG
F T F T 1 T 0 0
TRANS_MOM USERVARS PSMG ISOLVE PLOTADD SIUNITS TECPLOT MDGEN
F F F 1 F F F F
NUM_USER_VARS IFR_MIX PRINTD SATTABL MSORIN PRELVLV LAMINAR HSTAG
1 1 F F F T F T
DFLI
T
NNODES NINT NBR NF
5 3 3 1
RELAXK RELAXD RELAXH CC NITER RELAXNR RELAXHC RELAXTS
1 0.5 1 0.0001 500 1 1 1
DTAU TIMEF TIMEL NPSTEP NPWSTEP WPLSTEP WPLBUFF
0.2 0 12000 25 25 50 1.1
NFLUID(I), I = 1, NF
81
6
NODE INDEX DESCRIPTION
1 1 " INode 1"
4 2 " BNode 4"
5 1 " INode 5"
7 1 " INode 7"
9 2 " BNode 9"
NODE PRES (PSI) TEMP(DEGF) MASS SOURC HEAT SOURC THRST AREA NODE-VOLUME CONCENTRATION
1 300 -220 0 0 0 12214.5
5 300 -210 0 0 0 8397.48
7 300 -210 0 0 0 3817.04
Hist4.dat
Hist9.dat
INODE NUMBR NAMEBR
1 1 41
5 1 75
7 2 75 97
BRANCH UPNODE DNNODE OPTION DESCRIPTION
41 4 1 2 "Restrict 41"
75 7 5 2 "Restrict 75"
97 7 9 2 "Restrict 97"
BRANCH OPTION -2 FLOW COEFF AREA
41 0.6 1e-16
BRANCH OPTION -2 FLOW COEFF AREA
75 0 784.27
BRANCH OPTION -2 FLOW COEFF AREA
97 0.6 0.049
INITIAL FLOWRATES IN BRANCHES FOR UNSTEADY FLOW
41 0
75 0
97 0
NUMBER OF PRESSURE RELIEF ASSEMBLIES IN THE CIRCUIT
1
RELIEF VALVE BR CRACKING PRESSURE (psid)
97 10
CORRESPONDING CONTROL FILE
X:\User\My Documents\Grad School\Thesis\Tank Boil Off\Test 6 OXYGEN\PRV.DAT
NSOLID NAMB NSSC NSFC NSAC NSSR
3 1 2 3 3 0
NODESL MATRL SMASS TS HtSrc NUMSS NUMSF NUMSA NUMSSR DESCRIPTION
2 29 223.0000000 -220.0000000 0.0000000 1 1 1 0 "SNode 2"
82
NAMESS
62
NAMESF
21
NAMESA
23
6 29 110.3044800 -220.0000000 0.0000000 2 1 1 0 "SNode 6"
NAMESS
62 86
NAMESF
56
NAMESA
63
8 29 112.6100000 -220.0000000 0.0000000 1 1 1 0 "SNode 8"
NAMESS
86
NAMESF
78
NAMESA
83
NODEAM TAMB DESCRIPTION
3 80.00000 "ANode 3" 0
ICONSS ICNSI ICNSJ ARCSIJ DISTSIJ DESCRIPTION
62 6 2 42.85330 13.50000 "Conductor 62"
86 8 6 42.85330 9.00000 "Conductor 86"
ICONSF ICS ICF MODEL ARSF HCSF RADSF EMSFS EMSFF DESCRIPTION
21 2 1 0 2.03550e+03 1.00000e-02 F 0.00000e+00 0.00000e+00 "Convection 21"
56 6 5 0 1.01788e+03 1.77279e-03 F 0.00000e+00 0.00000e+00 "Convection 56"
78 8 7 0 1.24664e+03 1.77279e-03 F 0.00000e+00 0.00000e+00 "Convection 78"
ICONSA ICSAS ICSAA ARSA HCSA RADSA EMSAS EMSAA DESCRIPTION
63 6 3 1.03908e+03 3.61440e-04 F 0.00000e+00 0.00000e+00 "Convection 63"
83 8 3 1.08238e+03 3.61440e-04 F 0.00000e+00 0.00000e+00 "Convection 83"
23 2 3 2.12150e+03 3.61440e-04 F 0.00000e+00 0.00000e+00 "Convection 23"
83
A.6 Tank Boiloff Custom Subroutines
C***********************************************************************
SUBROUTINE SORCEM(IPN,TERMU)
C PURPOSE: ADD MASS SOURCES
C IPN - GFSSP INDEX NUMBER FOR NODE
C TERMU - UNSTEADY TERM IN MASS CONSERVATION EQUATION
C***********************************************************************
INCLUDE 'comblk.for'
C**********************************************************************
C ADD CODE HERE
C COMPUTE MASS TRASNFER OF PROPELLANT INTO THE ULLAGE
DATA TIL, HFGO2 / 240.13, 62.19/
DATA HL, HAREA / 1.5, 1.77/
REAL :: BETA,DELTAT,GR,PRNDTL,XNU,HLP,QDOTUP,MDOTO2
CALL INDEXI(1,NODE,NNODES,IPPRP)
CALL INDEXI(5,NODE,NNODES,IPULL)
CALL INDEXSFC(21, ICONSF,NSFC,ICSF)
BETA = 1.0 / TF(IPPRP)
DELTAT = ABS(TF(IPULL) - TF(IPPRP))
GR = HL**3 * RHO(IPPRP)**2 * G * BETA * DELTAT / (EMU(IPPRP)**2)
PRNDTL = CPNODE(IPPRP) * EMU(IPPRP) / CONDF(IPPRP)
XNU = 0.27*(GR*PRNDTL)**0.25
HLP = XNU*CONDF(IPPRP) / HL
QDOTUP = HLP*HAREA*(TF(IPULL)-TF(IPPRP))
MDOTO2 = (QDOTUP + QDOTSF(ICSF))/HFGO2
IF (NODE(IPN).EQ.1) EMS(IPN) = -MDOTO2
IF (NODE(IPN).EQ.5) EMS(IPN) = MDOTO2
RETURN
END
C***********************************************************************
C***********************************************************************
SUBROUTINE SORCEQ(IPN,TERMD)
C PURPOSE: ADD HEAT SOURCES
84
C IPN - GFSSP INDEX NUMBER FOR NODE
C TERMD - COMPONENT OF LINEARIZED SOURCE TERM APPEARING IN THE
C DENOMINATOR OF THE ENTHALPY OR ENTROPY EQUATION
C***********************************************************************
INCLUDE 'comblk.for'
C**********************************************************************
C**********************************************************************
C ADD CODE HERE
DATA TPROP /239.67/
C SET TEMPERATURE OF NODE TO PROPELLANT TEMPERATURE
IF (NODE(IPN).EQ.1) THEN
SORCEH(IPN) = SORCEMAS(IPN) * CPNODE(IPN) * TPROP
TERMD = SORCEMAS(IPN) * CPNODE(IPN)
END IF
RETURN
END
C***********************************************************************
C***********************************************************************
SUBROUTINE BNDUSER
C PURPOSE: MODIFY BOUNDARY CONDITIONS
C***********************************************************************
INCLUDE 'comblk.for'
C**********************************************************************
C ADD CODE HERE
C UPDATE NODE VOLUME
DATA TTANKVOL / 7.06858/
DATA HTCAREA / 14.137/
DATA TTANKMASS / 222.937/
DATA SAHTCAREA / 14.732/
REAL :: HL,HLOUT,CAPVOL,VRATIO,HRATIO,WALLMASS
CALL INDEXI(1, NODE, NNODES, IPPRP)
CALL INDEXI(5, NODE, NNODES, IPULL)
CALL INDEXSFC(21,ICONSF,NSFC,ICSFP)
CALL INDEXSFC(56,ICONSF,NSFC,ICSFU)
85
CALL INDEXS(2, NODESL, NSOLIDX, IPSNP)
CALL INDEXS(6, NODESL, NSOLIDX, IPSNU)
CALL INDEXS(8, NODESL, NSOLIDX, IPSNT)
CALL INDEXSAC(23,ICONSA,NSAC,ICSAP)
CALL INDEXSAC(63,ICONSA,NSAC,ICSAU)
CALL INDEXSAC(83,ICONSA,NSAC,ICSAT)
CALL INDEXA(3,NODEAM,NAMB,IPAMB)
C SET NEW VOLUME OF PROP AND ULLAGE
VOLUME(IPPRP) = EM(IPPRP)*Z(IPPRP)*RNODE(IPPRP)*TF(IPPRP)/P(IPPRP)
VOLUME(IPULL) = 4.86 + (TTANKVOL - VOLUME(IPPRP))
C CALCULATE NEW FS HEAT TRASNFER AREAS
CAPVOL = VOLUME(IPPRP)
VRATIO = CAPVOL/HTCAREA
HRATIO = 1.5537*VRATIO**3-2.3305*VRATIO**2+1.7162*VRATIO+0.0303
HL = HRATIO*3
ARSF(ICSFP) = 6.28*1.5*HL
ARSF(ICSFU) = 7.07 + (HTCAREA - ARSF(ICSFP))
C CALCULATE NEW SOLID NODE MASS
VWALL = 0.2976*HL+0.0047
WALLMASS = VWALL*494.2
SMASS(IPSNP) = WALLMASS
SMASS(IPSNU) = 110.30448 + TTANKMASS-SMASS(IPSNP)
C CALCULATE NEW SA HTA
HLOUT = HL+ 0.03125
ARSA(ICSAP) = 6.28*1.53125*HLOUT
ARSA(ICSAU) = 7.22 + SAHTCAREA - ARSA(ICSAP)
C CALCULATE NEW SA HTC
PRANDTL = 0.719642545
DELTATAMBP = ABS(TAMB(IPAMB)-TS(IPSNP))
DELTATAMBU = ABS(TAMB(IPAMB)-TS(IPSNU))
86
DELTATAMBT = ABS(TAMB(IPAMB)-TS(IPSNT))
GRASHOFFC = 79356160.60
RAP = PRANDTL*DELTATAMBP*GRASHOFFC
RAU = PRANDTL*DELTATAMBU*GRASHOFFC
RAT = PRANDTL*DELTATAMBT*GRASHOFFC
NUSSP = 2 + 0.589*RAP**0.25/(1+(0.469/PRANDTL)**0.5625)**0.444
NUSSU = 2 + 0.589*RAU**0.25/(1+(0.469/PRANDTL)**0.5625)**0.444
NUSST = 2 + 0.589*RAT**0.25/(1+(0.469/PRANDTL)**0.5625)**0.444
HCONST = 0.015018957/(3.0*3600.0)
HCSA(ICSAP) = NUSSP*HCONST
HCSA(ICSAU) = NUSSU*HCONST
HCSA(ICSAT) = NUSST*HCONST
RETURN
END
C***********************************************************************
C**********************************************************************
SUBROUTINE USRHCF(NUMBER,HCF)
C PURPOSE: PROVIDE HEAT TRANSFER COEFFICIENT
C***********************************************************************
INCLUDE 'comblk.for'
C**********************************************************************
C ADD CODE HERE
C SET HEAT TRASNFER COEFFICIENT FOR FS NODES
DATA VRAD,VDIAM /1.5, 3.0/
REAL :: VRATIO,HRATIO,HL,BETA,DELAT,GR,PRNDTL,RALEIGH
REAL :: NUNUM,NUDEN,NUSSELT,HCF
NUMF = ICF(NUMBER)
CALL INDEXI(NUMF,NODE,NNODES,IPN)
NUMS = ICS(NUMBER)
CALL INDEXS(NUMS, NODESL, NSOLIDX,IPSN)
CAPVOL = VOLUME(IPN)
VRATIO = CAPVOL/14.13716
HRATIO = 1.5537*VRATIO**3-2.3305*VRATIO**2+1.7162*VRATIO+0.0303
87
IF (NUMBER.EQ.21) THEN
HL = HRATIO*3
ELSEIF (NUMBER.EQ.56) THEN
HL = 2.25 - HRATIO*3
ELSE
HL = 0.5
ENDIF
BETA = 1.0/TF(IPN)
DELTAT = ABS(TF(IPN) - TS(IPSN))
GR = HL**3 * RHO(IPN)**2 * G * BETA * DELTAT / (EMU(IPN)**2)
PRNDTL = CPNODE(IPN) * EMU(IPN) / CONDF(IPN)
RALEIGH = GR*PRNDTL
NUNUM = 0.387 * RALEIGH**0.16
NUDEN = (1+(0.492/PRNDTL)**0.562)**0.296
NUSSELT = (0.825 + (NUNUM/NUDEN))**2
HCF = NUSSELT*CONDF(IPN)/HL
RETURN
END
C**********************************************************************
88
A.7 Line Chilldown GFSSP Input File
GFSSP VERSION
605
GFSSP INSTALLATION PATH
X:\Program Files (x86)\GFSSP\
ANALYST
Mariano Mercado
INPUT DATA FILE NAME
X:\User\My Documents\Grad School\Thesis\Line Chilldown\Oxygen\Chilldown.dat
OUTPUT FILE NAME
chilldown.out
TITLE
Line Chilldown
USETUP
F
DENCON GRAVITY ENERGY MIXTURE THRUST STEADY TRANSV SAVER
F F T F F F T F
HEX HCOEF REACTING INERTIA CONDX ADDPROP PRINTI ROTATION
F F F F F F F F
BUOYANCY HRATE INVAL MSORCE MOVBND TPA VARGEO TVM
F T F F F F F F
SHEAR PRNTIN PRNTADD OPVALVE TRANSQ CONJUG RADIAT WINPLOT
F T T F F T F T
PRESS INSUC VARROT CYCLIC CHKVALS WINFILE DALTON NOSTATS
F F F F F T F F
NORMAL SIMUL SECONDL NRSOLVT IBDF NOPLT PRESREG FLOWREG
F T F T 1 T 0 0
TRANS_MOM USERVARS PSMG ISOLVE PLOTADD SIUNITS TECPLOT MDGEN
F F F 1 F F F F
NUM_USER_VARS IFR_MIX PRINTD SATTABL MSORIN PRELVLV LAMINAR HSTAG
1 1 F F F F F T
DFLI
T
NNODES NINT NBR NF
33 31 32 1
RELAXK RELAXD RELAXH CC NITER RELAXNR RELAXHC RELAXTS
1 0.5 1 0.0001 500 1 1 1
DTAU TIMEF TIMEL NPSTEP NPWSTEP WPLSTEP WPLBUFF
0.05 0 300 100 20 50 1.1
NFLUID(I), I = 1, NF
89
6
NODE INDEX DESCRIPTION
1 2 " Oxydyzer Tank"
2 2 " EngineInlet"
3 1 " INode 3"
4 1 " INode 4"
5 1 " INode 5"
6 1 " INode 6"
7 1 " INode 7"
8 1 " INode 8"
9 1 " INode 9"
10 1 " INode 10"
11 1 " INode 11"
12 1 " INode 12"
13 1 " INode 13"
14 1 " INode 14"
15 1 " INode 15"
16 1 " INode 16"
17 1 " INode 17"
18 1 " INode 18"
19 1 " INode 19"
20 1 " INode 20"
21 1 " INode 21"
22 1 " INode 22"
23 1 " INode 23"
24 1 " INode 24"
25 1 " INode 25"
26 1 " INode 26"
27 1 " INode 27"
28 1 " INode 28"
29 1 " INode 29"
30 1 " INode 30"
31 1 " INode 31"
32 1 " INode 32"
63 1 " INode 63"
NODE PRES (PSI) TEMP(DEGF) MASS SOURC HEAT SOURC THRST AREA NODE-VOLUME CONCENTRATION
3 14.7 80 0 0 0 0
4 14.7 80 0 0 0 0
5 14.7 80 0 0 0 0
6 14.7 80 0 0 0 0
7 14.7 80 0 0 0 0
90
8 14.7 80 0 0 0 0
9 14.7 80 0 0 0 0
10 14.7 80 0 0 0 0
11 14.7 80 0 0 0 0
12 14.7 80 0 0 0 0
13 14.7 80 0 0 0 0
14 14.7 80 0 0 0 0
15 14.7 80 0 0 0 0
16 14.7 80 0 0 0 0
17 14.7 80 0 0 0 0
18 14.7 80 0 0 0 0
19 14.7 80 0 0 0 0
20 14.7 80 0 0 0 0
21 14.7 80 0 0 0 0
22 14.7 80 0 0 0 0
23 14.7 80 0 0 0 0
24 14.7 80 0 0 0 0
25 14.7 80 0 0 0 0
26 14.7 80 0 0 0 0
27 14.7 80 0 0 0 0
28 14.7 80 0 0 0 0
29 14.7 80 0 0 0 0
30 14.7 80 0 0 0 0
31 14.7 80 0 0 0 0
32 14.7 80 0 0 0 0
63 14.7 80 0 0 0 0
Hist1.dat
Hist2.dat
INODE NUMBR NAMEBR
3 2 13 34
4 2 34 45
5 2 45 56
6 2 56 67
7 2 67 78
8 2 78 89
9 2 89 910
10 2 910 1011
11 2 1011 1112
12 2 1112 1213
13 2 1213 1314
14 2 1314 1415
91
15 2 1415 1516
16 2 1516 1617
17 2 1617 1718
18 2 1718 1819
19 2 1819 1920
20 2 1920 2021
21 2 2021 2122
22 2 2122 2223
23 2 2223 2324
24 2 2324 2425
25 2 2425 2526
26 2 2526 2627
27 2 2627 2728
28 2 2728 2829
29 2 2829 2930
30 2 2930 3031
31 2 3031 3132
32 2 3132 3263
63 2 3263 632
BRANCH UPNODE DNNODE OPTION DESCRIPTION
13 1 3 2 "Restrict 13"
34 3 4 1 "Pipe 34"
45 4 5 13 "Valve 45"
56 5 6 1 "Pipe 56"
67 6 7 16 "Valve 67"
78 7 8 1 "Pipe 78"
89 8 9 13 "Valve 89"
910 9 10 1 "Pipe 910"
1011 10 11 16 "CV 1011"
1112 11 12 1 "Pipe 1112"
1213 12 13 1 "Flex Hose"
1314 13 14 13 "Valve 1314"
1415 14 15 1 "Pipe 1415"
1516 15 16 2 "Restrict 1516"
1617 16 17 1 "Pipe 1617"
1718 17 18 1 "Flex Hose"
1819 18 19 1 "Pipe 1819"
1920 19 20 2 "Restrict 1920"
2021 20 21 1 "Pipe 2021"
2122 21 22 13 "Valve 2122"
2223 22 23 1 "Pipe 2223"
92
2324 23 24 13 "Valve 2324"
2425 24 25 2 "CV 2425"
2526 25 26 16 "CV 2526"
2627 26 27 1 "Pipe 2627"
2728 27 28 2 "Restrict 2728"
2829 28 29 1 "Pipe 2829"
2930 29 30 13 "Valve 2930"
3031 30 31 1 "Pipe 3031"
3132 31 32 7 "Reduct 3132"
3263 32 63 1 "Flex Hose"
632 63 2 2 "Restrict 632"
BRANCH OPTION -2 FLOW COEFF AREA
13 0.6 0.546
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
34 1.44 0.813 0.00073800738007 0
0.51912340018
BRANCH OPTION -13 DIA K1 K2 AREA
45 0.834 800 0.4 0.54629
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
56 3.7 0.813 0.00073800738007 0
0.51912340018
BRANCH OPTION -16 CV AREA
67 32 0.5462
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
78 9.8125 0.813 0.00073800738007 0
0.51912340018
BRANCH OPTION -13 DIA K1 K2 AREA
89 0.834 200 0.1 0.54629
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
910 10.5 0.813 0.00073800738007 0
0.51912340018
BRANCH OPTION -16 CV AREA
1011 32 0.54628
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
1112 2.7 0.813 0.00073800738007 0
0.51912340018
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
1213 36 0.608 0.00098684210526 0
0.29033318144
BRANCH OPTION -13 DIA K1 K2 AREA
1314 0.834 800 0.4 0.54629
93
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
1415 3 0.813 0.00073800738007 0
0.51912340018
BRANCH OPTION -2 FLOW COEFF AREA
1516 0.6 0.546
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
1617 12 0.813 0.00073800738007 0
0.51912340018
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
1718 36 0.88 0.00068181818182 0
0.608211824
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
1819 22 0.813 0.00073800738007 0
0.51912340018
BRANCH OPTION -2 FLOW COEFF AREA
1920 0.6 0.546
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
2021 16.5 0.813 0.00073800738007 0
0.51912340018
BRANCH OPTION -13 DIA K1 K2 AREA
2122 0.834 200 0.1 0.54629
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
2223 13.1875 0.813 0.00073800738007 0
0.51912340018
BRANCH OPTION -13 DIA K1 K2 AREA
2324 0.834 200 0.1 0.54629
BRANCH OPTION -2 FLOW COEFF AREA
2425 0.985 0.546
BRANCH OPTION -16 CV AREA
2526 32 0.546
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
2627 5.35 0.813 0.00073800738007 0
0.51912340018
BRANCH OPTION -2 FLOW COEFF AREA
2728 0.9 0.546
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
2829 18.25 0.813 0.00073800738007 0
0.51912340018
BRANCH OPTION -13 DIA K1 K2 AREA
2930 0.834 800 0.4 0.54629
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
94
3031 20.25 0.813 0.00073800738007 0
0.51912340018
BRANCH OPTION -7 PIPE DIA RED. DIA AREA
3132 0.834 0.37 0.54629
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
3263 72 0.37 0.0016216216216 0
0.10752091775
BRANCH OPTION -2 FLOW COEFF AREA
632 0.6 0.302
INITIAL FLOWRATES IN BRANCHES FOR UNSTEADY FLOW
13 0
34 0
45 0
56 0
67 0
78 0
89 0
910 0
1011 0
1112 0
1213 0
1314 0
1415 0
1516 0
1617 0
1718 0
1819 0
1920 0
2021 0
2122 0
2223 0
2324 0
2425 0
2526 0
2627 0
2728 0
2829 0
2930 0
3031 0
3132 0
3263 0
95
632 0
NSOLID NAMB NSSC NSFC NSAC NSSR
31 0 30 31 0 0
NODESL MATRL SMASS TS HtSrc NUMSS NUMSF NUMSA NUMSSR DESCRIPTION
33 29 0.0487765 80.0000000 0.0000000 1 1 0 0 "SNode 33"
NAMESS
3334
NAMESF
333
34 29 0.0480000 80.0000000 0.0000000 2 1 0 0 "SNode 34"
NAMESS
3334 3435
NAMESF
344
35 29 0.1250000 80.0000000 0.0000000 2 1 0 0 "SNode 35"
NAMESS
3536 3435
NAMESF
355
36 29 3.4300000 80.0000000 0.0000000 2 1 0 0 "SNode 36"
NAMESS
3536 3637
NAMESF
366
37 29 3.6370000 80.0000000 0.0000000 2 1 0 0 "SNode 37"
NAMESS
3738 3637
NAMESF
377
38 29 0.3300000 80.0000000 0.0000000 2 1 0 0 "SNode 38"
NAMESS
3738 3839
NAMESF
388
39 29 0.3557000 80.0000000 0.0000000 2 1 0 0 "SNode 39"
NAMESS
4039 3839
NAMESF
399
40 29 3.6600000 80.0000000 0.0000000 2 1 0 0 "SNode 40"
NAMESS
96
4039 4041
NAMESF
4010
41 29 3.3960000 80.0000000 0.0000000 2 1 0 0 "SNode 41"
NAMESS
4241 4041
NAMESF
4111
42 29 1.3100000 80.0000000 0.0000000 2 1 0 0 "SNode 42"
NAMESS
4342 4241
NAMESF
4212
43 29 1.2100000 80.0000000 0.0000000 2 1 0 0 "SNode 43"
NAMESS
4342 4344
NAMESF
4313
44 29 0.1010000 80.0000000 0.0000000 2 1 0 0 "SNode 44"
NAMESS
4445 4344
NAMESF
4414
45 29 0.1016000 80.0000000 0.0000000 2 1 0 0 "SNode 45"
NAMESS
4546 4445
NAMESF
4515
46 29 0.4060000 80.0000000 0.0000000 2 1 0 0 "SNode 46"
NAMESS
4746 4546
NAMESF
1646
47 29 1.6260000 80.0000000 0.0000000 2 1 0 0 "SNode 47"
NAMESS
4847 4746
NAMESF
1747
48 29 1.9640000 80.0000000 0.0000000 2 1 0 0 "SNode 48"
NAMESS
4948 4847
97
NAMESF
1848
49 29 0.7450000 80.0000000 0.0000000 2 1 0 0 "SNode 49"
NAMESS
4948 5049
NAMESF
1949
50 29 0.5589000 80.0000000 0.0000000 2 1 0 0 "SNode 50"
NAMESS
5049 5051
NAMESF
2050
51 29 0.5589000 80.0000000 0.0000000 2 1 0 0 "SNode 51"
NAMESS
5051 5152
NAMESF
2151
52 29 0.4467000 80.0000000 0.0000000 2 1 0 0 "SNode 52"
NAMESS
5152 5253
NAMESF
2252
53 29 0.4467000 80.0000000 0.0000000 2 1 0 0 "SNode 53"
NAMESS
5253 5354
NAMESF
2353
54 29 0.1000000 80.0000000 0.0000000 2 1 0 0 "SNode 54"
NAMESS
5354 5455
NAMESF
2454
55 29 3.3050000 80.0000000 0.0000000 2 1 0 0 "SNode 55"
NAMESS
5455 5556
NAMESF
2555
56 29 3.4860000 80.0000000 0.0000000 2 1 0 0 "SNode 56"
NAMESS
5556 5657
NAMESF
98
2656
57 29 0.1810000 80.0000000 0.0000000 2 1 0 0 "SNode 57"
NAMESS
5657 5758
NAMESF
2757
58 29 0.6180000 80.0000000 0.0000000 2 1 0 0 "SNode 58"
NAMESS
5758 5859
NAMESF
2858
59 29 0.6180000 80.0000000 0.0000000 2 1 0 0 "SNode 59"
NAMESS
5859 5960
NAMESF
2959
60 29 0.6860000 80.0000000 0.0000000 2 1 0 0 "SNode 60"
NAMESS
5960 6061
NAMESF
3060
61 29 0.6860000 80.0000000 0.0000000 2 1 0 0 "SNode 61"
NAMESS
6061 6162
NAMESF
3161
62 29 0.9060000 80.0000000 0.0000000 2 1 0 0 "SNode 62"
NAMESS
6162 6264
NAMESF
6232
64 29 0.9060000 80.0000000 0.0000000 1 1 0 0 "SNode 64"
NAMESS
6264
NAMESF
6463
ICONSS ICNSI ICNSJ ARCSIJ DISTSIJ DESCRIPTION
4948 49 48 0.23900 22.00000 "0 "
4847 48 47 0.23900 36.00000 "0 "
4746 47 46 0.23900 12.00000 "0 "
4546 45 46 0.23900 1.00000 "0 "
99
4445 44 45 0.23900 3.00000 "0 "
4342 43 42 0.23900 36.00000 "0 "
4241 42 41 0.23900 2.70000 "0 "
4039 40 39 0.23900 10.50000 "0 "
3334 33 34 0.23900 1.44000 "0 "
3536 35 36 0.23900 3.70000 "0 "
3738 37 38 0.23900 9.81000 "0 "
3435 34 35 0.23900 1.00000 "0 "
3637 36 37 0.23900 1.00000 "0 "
3839 38 39 0.23900 1.00000 "0 "
4041 40 41 0.23900 1.00000 "0 "
4344 43 44 0.23900 1.00000 "0 "
5049 50 49 0.23900 1.00000 "0 "
5051 50 51 0.23900 16.50000 "0 "
5152 51 52 0.23900 1.00000 "0 "
5253 52 53 0.23900 13.19000 "0 "
5354 53 54 0.23900 1.00000 "0 "
5455 54 55 0.23900 1.00000 "0 "
5556 55 56 0.23900 1.00000 "0 "
5657 56 57 0.23900 5.35000 "0 "
5758 57 58 0.23900 1.00000 "0 "
5859 58 59 0.23900 18.25000 "0 "
5960 59 60 0.23900 1.00000 "0 "
6061 60 61 0.23900 20.25000 "0 "
6162 61 62 0.23900 1.00000 "0 "
6264 62 64 0.08880 72.00000 "0 "
ICONSF ICS ICF MODEL ARSF HCSF RADSF EMSFS EMSFF DESCRIPTION
333 33 3 2 3.77000e+00 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
344 34 4 2 3.77000e+00 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
355 35 5 2 9.69000e+00 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
366 36 6 2 9.69000e+00 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
377 37 7 2 2.57000e+01 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
388 38 8 2 2.57000e+01 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
399 39 9 2 2.75000e+01 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
4010 40 10 2 2.75000e+01 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
4111 41 11 2 7.07000e+00 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
4212 42 12 2 1.01390e+02 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
4313 43 13 2 9.43000e+01 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
4414 44 14 2 7.86000e+00 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
4515 45 15 2 7.86000e+00 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
1646 46 16 2 3.14400e+01 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
100
1747 47 17 2 1.25700e+02 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
1848 48 18 2 1.51960e+02 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
1949 49 19 2 5.76400e+01 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
6232 62 32 2 8.36900e+01 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
3161 61 31 2 5.30500e+01 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
3060 60 30 2 5.30500e+01 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
2959 59 29 2 4.78100e+01 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
2858 58 28 2 4.78000e+01 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
2757 57 27 2 1.40000e+01 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
2656 56 26 2 1.40000e+01 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
2555 55 25 2 1.00000e-01 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
2454 54 24 2 1.00000e-01 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
2353 53 23 2 3.45500e+01 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
2252 52 22 2 3.45500e+01 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
2151 51 21 2 4.32300e+01 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
2050 50 20 2 4.32300e+01 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
6463 64 63 2 8.36900e+01 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
101
A.8 Engine Run Case GFSSP Input File
GFSSP VERSION
605
GFSSP INSTALLATION PATH
X:\Program Files (x86)\GFSSP\
ANALYST
Mariano Mercado
INPUT DATA FILE NAME
X:\User\My Documents\Grad School\Thesis\Engine Run\Oxygen\run.dat
OUTPUT FILE NAME
run.out
TITLE
Engine Run
USETUP
F
DENCON GRAVITY ENERGY MIXTURE THRUST STEADY TRANSV SAVER
F F T T F F T F
HEX HCOEF REACTING INERTIA CONDX ADDPROP PRINTI ROTATION
F F F F F F F F
BUOYANCY HRATE INVAL MSORCE MOVBND TPA VARGEO TVM
F T F F F F F F
SHEAR PRNTIN PRNTADD OPVALVE TRANSQ CONJUG RADIAT WINPLOT
F T T F F T F T
PRESS INSUC VARROT CYCLIC CHKVALS WINFILE DALTON NOSTATS
T F F F F T F F
NORMAL SIMUL SECONDL NRSOLVT IBDF NOPLT PRESREG FLOWREG
F T F T 1 T 2 2
TRANS_MOM USERVARS PSMG ISOLVE PLOTADD SIUNITS TECPLOT MDGEN
F F F 1 F F F F
NUM_USER_VARS IFR_MIX PRINTD SATTABL MSORIN PRELVLV LAMINAR HSTAG
1 1 F F F F F T
DFLI
T
NNODES NINT NBR NF
56 53 54 2
RELAXK RELAXD RELAXH CC NITER RELAXNR RELAXHC RELAXTS
1 0.5 1 0.0001 500 1 1 1
DTAU TIMEF TIMEL NPSTEP NPWSTEP WPLSTEP WPLBUFF
0.05 0 300 20 20 50 1.1
NFLUID(I), I = 1, NF
102
6 4
NODE INDEX DESCRIPTION
2 2 " EngineInlet"
3 1 " INode 3"
4 1 " INode 4"
5 1 " INode 5"
6 1 " INode 6"
7 1 " INode 7"
8 1 " INode 8"
9 1 " INode 9"
10 1 " INode 10"
11 1 " INode 11"
12 1 " INode 12"
13 1 " INode 13"
14 1 " INode 14"
15 1 " INode 15"
16 1 " INode 16"
17 1 " INode 17"
18 1 " INode 18"
19 1 " INode 19"
20 1 " INode 20"
21 1 " INode 21"
22 1 " INode 22"
23 1 " INode 23"
24 1 " INode 24"
25 1 " INode 25"
26 1 " INode 26"
27 1 " INode 27"
28 1 " INode 28"
29 1 " INode 29"
30 1 " INode 30"
31 1 " INode 31"
32 1 " INode 32"
63 1 " INode 63"
1 1 " Tank Prop"
65 2 " BNode 65"
66 1 " Tank Ullage"
67 1 " INode 67"
68 1 " INode 68"
69 1 " INode 69"
70 1 " INode 70"
103
71 1 " INode 71"
72 1 " INode 72"
73 1 " INode 73"
74 1 " INode 74"
75 1 " INode 75"
76 1 " INode 76"
77 1 " INode 77"
78 1 " INode 78"
79 1 " INode 79"
80 1 " INode 80"
81 1 " INode 81"
82 1 " INode 82"
83 1 " INode 83"
84 1 " INode 84"
85 1 " INode 85"
86 1 " INode 86"
87 2 " Pressurant Tanks"
NODE PRES (PSI) TEMP(DEGF) MASS SOURC HEAT SOURC THRST AREA NODE-VOLUME CONCENTRATION
3 350 -215 0 0 0 0
1 0
4 350 -215 0 0 0 0
1 0
5 350 -215 0 0 0 0
1 0
6 350 -215 0 0 0 0
1 0
7 350 -215 0 0 0 0
1 0
8 350 -215 0 0 0 0
1 0
9 350 -215 0 0 0 0
1 0
10 350 -215 0 0 0 0
1 0
11 350 -215 0 0 0 0
1 0
12 350 -215 0 0 0 0
1 0
13 350 -215 0 0 0 0
1 0
104
14 350 -215 0 0 0 0
1 0
15 350 -215 0 0 0 0
1 0
16 350 -215 0 0 0 0
1 0
17 350 -215 0 0 0 0
1 0
18 350 -215 0 0 0 0
1 0
19 350 -215 0 0 0 0
1 0
20 350 -215 0 0 0 0
1 0
21 350 -215 0 0 0 0
1 0
22 350 -215 0 0 0 0
1 0
23 350 -215 0 0 0 0
1 0
24 350 -215 0 0 0 0
1 0
25 350 -215 0 0 0 0
1 0
26 350 -215 0 0 0 0
1 0
27 350 -215 0 0 0 0
1 0
28 350 -215 0 0 0 0
1 0
29 350 -215 0 0 0 0
1 0
30 350 -215 0 0 0 0
1 0
31 350 -215 0 0 0 0
1 0
32 350 -215 0 0 0 0
1 0
63 350 -215 0 0 0 0
1 0
105
1 350 -215 0 0 0 12214.5
1 0
66 350 -100 0 0 0 12214.51
0 1
67 400 80 0 0 0 0
0 1
68 400 80 0 0 0 0
0 1
69 400 80 0 0 0 0
0 1
70 400 80 0 0 0 0
0 1
71 400 80 0 0 0 0
0 1
72 400 80 0 0 0 0
0 1
73 400 80 0 0 0 0
0 1
74 400 80 0 0 0 0
0 1
75 400 80 0 0 0 0
0 1
76 400 80 0 0 0 0
0 1
77 400 80 0 0 0 0
0 1
78 400 80 0 0 0 0
0 1
79 400 80 0 0 0 0
0 1
80 400 80 0 0 0 0
0 1
81 400 80 0 0 0 0
0 1
82 400 80 0 0 0 0
0 1
83 400 80 0 0 0 0
0 1
84 400 80 0 0 0 0
0 1
106
85 400 80 0 0 0 0
0 1
86 400 80 0 0 0 0
0 1
Hist2.dat
Hist65.dat
Hist87.dat
INODE NUMBR NAMEBR
3 2 34 13
4 2 34 45
5 2 45 56
6 2 56 67
7 2 67 78
8 2 78 89
9 2 89 910
10 2 910 1011
11 2 1011 1112
12 2 1112 1213
13 2 1213 1314
14 2 1314 1415
15 2 1415 1516
16 2 1516 1617
17 2 1617 1718
18 2 1718 1819
19 2 1819 1920
20 2 1920 2021
21 2 2021 2122
22 2 2122 2223
23 2 2223 2324
24 2 2324 2425
25 2 2425 2526
26 2 2526 2627
27 2 2627 2728
28 2 2728 2829
29 2 2829 2930
30 2 2930 3031
31 2 3031 3132
32 2 3132 3263
63 2 3263 632
1 2 651 13
66 1 6766
107
67 2 6766 6867
68 2 6968 6867
69 2 7069 6968
70 2 7170 7069
71 2 7271 7170
72 2 7372 7271
73 2 7473 7372
74 2 7574 7473
75 2 7675 7574
76 2 7776 7675
77 2 7877 7776
78 2 7978 7877
79 2 8079 7978
80 2 8180 8079
81 2 8281 8180
82 2 8382 8281
83 2 8483 8382
84 2 8584 8483
85 2 8685 8584
86 2 8786 8685
BRANCH UPNODE DNNODE OPTION DESCRIPTION
34 3 4 1 "Pipe 34"
45 4 5 13 "Valve 45"
56 5 6 1 "Pipe 56"
67 6 7 16 "Valve 67"
78 7 8 1 "Pipe 78"
89 8 9 13 "Valve 89"
910 9 10 1 "Pipe 910"
1011 10 11 16 "CV 1011"
1112 11 12 1 "Pipe 1112"
1213 12 13 1 "Flex Hose"
1314 13 14 13 "Valve 1314"
1415 14 15 1 "Pipe 1415"
1516 15 16 2 "Restrict 1516"
1617 16 17 1 "Pipe 1617"
1718 17 18 1 "Flex Hose"
1819 18 19 1 "Pipe 1819"
1920 19 20 2 "Restrict 1920"
2021 20 21 1 "Pipe 2021"
2122 21 22 13 "Valve 2122"
2223 22 23 1 "Pipe 2223"
108
2324 23 24 13 "Valve 2324"
2425 24 25 2 "CV 2425"
2526 25 26 16 "CV 2526"
2627 26 27 1 "Pipe 2627"
2728 27 28 2 "Restrict 2728"
2829 28 29 1 "Pipe 2829"
2930 29 30 13 "Valve 2930"
3031 30 31 1 "Pipe 3031"
3132 31 32 7 "Reduct 3132"
3263 32 63 1 "Flex Hose"
632 63 2 2 "Restrict 632"
651 65 1 2 "Restrict 651"
13 1 3 2 "Restrict 13"
6766 67 66 2 "Restrict 6766"
8786 87 86 2 "Restrict 8786"
8685 86 85 1 "Pipe 8685"
8584 85 84 13 "Valve 8584"
8483 84 83 1 "Pipe 8483"
8382 83 82 13 "Valve 8382"
8281 82 81 1 "Pipe 8281"
8180 81 80 13 "Valve 8180"
8079 80 79 1 "Pipe 8079"
7978 79 78 16 "CV 7978"
7877 78 77 1 "Pipe 7877"
7776 77 76 16 "CV 7776"
7675 76 75 1 "Pipe 7675"
7574 75 74 8 "Expan 7574"
7473 74 73 1 "Pump 7473"
7372 73 72 16 "Pipe 7372"
7271 72 71 1 "Pipe 7271"
7170 71 70 13 "Valve 7170"
7069 70 69 1 "Pipe 7069"
6968 69 68 13 "Valve 6968"
6867 68 67 1 "Pipe 6867"
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
34 1.44 0.813 0.00073800738007 0
0.51912340018
BRANCH OPTION -13 DIA K1 K2 AREA
45 0.834 800 0.4 0.54629
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
109
56 3.7 0.813 0.00073800738007 0
0.51912340018
BRANCH OPTION -16 CV AREA
67 32 0.5462
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
78 9.8125 0.813 0.00073800738007 0
0.51912340018
BRANCH OPTION -13 DIA K1 K2 AREA
89 0.834 200 0.1 0.54629
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
910 10.5 0.813 0.00073800738007 0
0.51912340018
BRANCH OPTION -16 CV AREA
1011 32 0.54628
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
1112 2.7 0.813 0.00073800738007 0
0.51912340018
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
1213 36 0.608 0.00098684210526 0
0.29033318144
BRANCH OPTION -13 DIA K1 K2 AREA
1314 0.834 800 0.4 0.54629
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
1415 3 0.813 0.00073800738007 0
0.51912340018
BRANCH OPTION -2 FLOW COEFF AREA
1516 0.6 0.546
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
1617 12 0.813 0.00073800738007 0
0.51912340018
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
1718 36 0.88 0.00068181818182 0
0.608211824
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
1819 22 0.813 0.00073800738007 0
0.51912340018
BRANCH OPTION -2 FLOW COEFF AREA
1920 0.6 0.546
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
2021 16.5 0.813 0.00073800738007 0
0.51912340018
110
BRANCH OPTION -13 DIA K1 K2 AREA
2122 0.834 200 0.1 0.54629
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
2223 13.1875 0.813 0.00073800738007 0
0.51912340018
BRANCH OPTION -13 DIA K1 K2 AREA
2324 0.834 200 0.1 0.54629
BRANCH OPTION -2 FLOW COEFF AREA
2425 0.985 0.546
BRANCH OPTION -16 CV AREA
2526 32 0.546
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
2627 5.35 0.813 0.00073800738007 0
0.51912340018
BRANCH OPTION -2 FLOW COEFF AREA
2728 0.9 0.546
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
2829 18.25 0.813 0.00073800738007 0
0.51912340018
BRANCH OPTION -13 DIA K1 K2 AREA
2930 0.834 800 0.4 0.54629
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
3031 20.25 0.813 0.00073800738007 0
0.51912340018
BRANCH OPTION -7 PIPE DIA RED. DIA AREA
3132 0.834 0.37 0.54629
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
3263 72 0.37 0.0016216216216 0
0.10752091775
BRANCH OPTION -2 FLOW COEFF AREA
632 0.6 0.302
BRANCH OPTION -2 FLOW COEFF AREA
651 0 1017.9
BRANCH OPTION -2 FLOW COEFF AREA
13 0.6 0.546
BRANCH OPTION -2 FLOW COEFF AREA
6766 0.6 0.1075
BRANCH OPTION -2 FLOW COEFF AREA
8786 0.6 0.035447
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
111
8685 36 0.18 0.0033333333333 0
0.025446879
BRANCH OPTION -13 DIA K1 K2 AREA
8584 0.18 800 0.4 0.025447
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
8483 36 0.18 0.0033333333333 0
0.025446879
BRANCH OPTION -13 DIA K1 K2 AREA
8382 0.18 800 0.4 0.025447
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
8281 1.2 0.18 0.0033333333333 0
0.025446879
BRANCH OPTION -13 DIA K1 K2 AREA
8180 0.18 200 0.1 0.025447
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
8079 1.5 0.18 0.0033333333333 0
0.025446879
BRANCH OPTION -16 CV AREA
7978 3 0.0254
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
7877 1.05 0.18 0.0033333333333 0
0.025446879
BRANCH OPTION -16 CV AREA
7776 3 0.0254
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
7675 1.15 0.18 0.0033333333333 0
0.025446879
BRANCH OPTION -8 PIPE DIA EXP DIA AREA
7574 0.18 0.37 0.025447
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
7473 2.25 0.37 0.0016216216216 0
0.10752091775
BRANCH OPTION -16 CV AREA
7372 8 0.1075
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
7271 2.25 0.37 0.0016216216216 0
0.10752091775
BRANCH OPTION -13 DIA K1 K2 AREA
7170 0.37 200 0.1 0.10752
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
112
7069 2.25 0.37 0.0016216216216 0
0.10752091775
BRANCH OPTION -13 DIA K1 K2 AREA
6968 0.37 200 0.1 0.10752
BRANCH OPTION -1 LENGTH DIA EPSD ANGLE AREA
6867 1.75 0.37 0.0016216216216 0
0.10752091775
INITIAL FLOWRATES IN BRANCHES FOR UNSTEADY FLOW
34 1.6
45 1.6
56 1.6
67 1.6
78 1.6
89 1.6
910 1.6
1011 1.6
1112 1.6
1213 1.6
1314 1.6
1415 1.6
1516 1.6
1617 1.6
1718 1.6
1819 1.6
1920 1.6
2021 1.6
2122 1.6
2223 1.6
2324 1.6
2425 1.6
2526 1.6
2627 1.6
2728 1.6
2829 1.6
2930 1.6
3031 1.6
3132 1.6
3263 1.6
632 1.6
651 0
13 1.6
113
6766 0
8786 0
8685 0
8584 0
8483 0
8382 0
8281 0
8180 0
8079 0
7978 0
7877 0
7776 0
7675 0
7574 0
7473 0
7372 0
7271 0
7170 0
7069 0
6968 0
6867 0
NUMBER OF PRESSURIZATION PROPELLANT TANKS IN CIRCUIT
1
TNKTYPE NODUL NODULB NODPRP IBRPRP TNKAR TNKTH TNKRHO TNKCP TNKCON ARHC
FCTHC TNKTM CIP FNIP CIW FNIW
2 66 65 1 651 0 0.375 0.291 0.12 0.13483 0 1
-215 0.27 0.25 0.54 0.25
NUMBER OF PRESSURE REGULATOR ASSEMBLY IN THE CIRCUIT
1
PRESS REG BR HIST FILE MAX_AREA PRESSURE RELAXATION MIN_AREA
6766 0 0.1075 350 1 1e-16
NUMBER OF FLOW REGULATOR ASSEMBLY IN THE CIRCUIT
1
FLOW REG BR HIST FILE AREA REGULATOR FLOW RELAXATION
632 0 0.054 1.6 1
NSOLID NAMB NSSC NSFC NSAC NSSR
50 0 48 50 0 0
NODESL MATRL SMASS TS HtSrc NUMSS NUMSF NUMSA NUMSSR DESCRIPTION
33 29 0.0487765 -215.0000000 0.0000000 1 1 0 0 "SNode 33"
NAMESS
3334
114
NAMESF
333
34 29 0.0480000 -215.0000000 0.0000000 2 1 0 0 "SNode 34"
NAMESS
3334 3435
NAMESF
344
35 29 0.1250000 -215.0000000 0.0000000 2 1 0 0 "SNode 35"
NAMESS
3536 3435
NAMESF
355
36 29 3.4300000 -215.0000000 0.0000000 2 1 0 0 "SNode 36"
NAMESS
3536 3637
NAMESF
366
37 29 3.6370000 -215.0000000 0.0000000 2 1 0 0 "SNode 37"
NAMESS
3738 3637
NAMESF
377
38 29 0.3300000 -215.0000000 0.0000000 2 1 0 0 "SNode 38"
NAMESS
3738 3839
NAMESF
388
39 29 0.3557000 -215.0000000 0.0000000 2 1 0 0 "SNode 39"
NAMESS
4039 3839
NAMESF
399
40 29 3.6600000 -215.0000000 0.0000000 2 1 0 0 "SNode 40"
NAMESS
4039 4041
NAMESF
4010
41 29 3.3960000 -215.0000000 0.0000000 2 1 0 0 "SNode 41"
NAMESS
4241 4041
NAMESF
115
4111
42 29 1.3100000 -215.0000000 0.0000000 2 1 0 0 "SNode 42"
NAMESS
4342 4241
NAMESF
4212
43 29 1.2100000 -215.0000000 0.0000000 2 1 0 0 "SNode 43"
NAMESS
4342 4344
NAMESF
4313
44 29 0.1010000 -215.0000000 0.0000000 2 1 0 0 "SNode 44"
NAMESS
4445 4344
NAMESF
4414
45 29 0.1016000 -215.0000000 0.0000000 2 1 0 0 "SNode 45"
NAMESS
4546 4445
NAMESF
4515
46 29 0.4060000 -215.0000000 0.0000000 2 1 0 0 "SNode 46"
NAMESS
4746 4546
NAMESF
1646
47 29 1.6260000 -215.0000000 0.0000000 2 1 0 0 "SNode 47"
NAMESS
4847 4746
NAMESF
1747
48 29 1.9640000 -215.0000000 0.0000000 2 1 0 0 "SNode 48"
NAMESS
4948 4847
NAMESF
1848
49 29 0.7450000 -215.0000000 0.0000000 2 1 0 0 "SNode 49"
NAMESS
4948 5049
NAMESF
1949
116
50 29 0.5589000 -215.0000000 0.0000000 2 1 0 0 "SNode 50"
NAMESS
5049 5051
NAMESF
2050
51 29 0.5589000 -215.0000000 0.0000000 2 1 0 0 "SNode 51"
NAMESS
5051 5152
NAMESF
2151
52 29 0.4467000 -215.0000000 0.0000000 2 1 0 0 "SNode 52"
NAMESS
5152 5253
NAMESF
2252
53 29 0.4467000 -215.0000000 0.0000000 2 1 0 0 "SNode 53"
NAMESS
5253 5354
NAMESF
2353
54 29 0.1000000 -215.0000000 0.0000000 2 1 0 0 "SNode 54"
NAMESS
5354 5455
NAMESF
2454
55 29 3.3050000 -215.0000000 0.0000000 2 1 0 0 "SNode 55"
NAMESS
5455 5556
NAMESF
2555
56 29 3.4860000 -215.0000000 0.0000000 2 1 0 0 "SNode 56"
NAMESS
5556 5657
NAMESF
2656
57 29 0.1810000 -215.0000000 0.0000000 2 1 0 0 "SNode 57"
NAMESS
5657 5758
NAMESF
2757
58 29 0.6180000 -215.0000000 0.0000000 2 1 0 0 "SNode 58"
117
NAMESS
5758 5859
NAMESF
2858
59 29 0.6180000 -215.0000000 0.0000000 2 1 0 0 "SNode 59"
NAMESS
5859 5960
NAMESF
2959
60 29 0.6860000 -215.0000000 0.0000000 2 1 0 0 "SNode 60"
NAMESS
5960 6061
NAMESF
3060
61 29 0.6860000 -215.0000000 0.0000000 2 1 0 0 "SNode 61"
NAMESS
6061 6162
NAMESF
3161
62 29 0.9060000 -215.0000000 0.0000000 2 1 0 0 "SNode 62"
NAMESS
6162 6264
NAMESF
6232
64 29 0.9060000 -215.0000000 0.0000000 1 1 0 0 "SNode 64"
NAMESS
6264
NAMESF
6463
88 29 0.1200000 80.0000000 0.0000000 1 1 0 0 "SNode 88"
NAMESS
8889
NAMESF
8688
89 29 0.1200000 80.0000000 0.0000000 2 1 0 0 "SNode 89"
NAMESS
8889 8990
NAMESF
8589
90 29 0.1200000 80.0000000 0.0000000 2 1 0 0 "SNode 90"
NAMESS
118
8990 9091
NAMESF
8490
91 29 0.1200000 80.0000000 0.0000000 2 1 0 0 "SNode 91"
NAMESS
9091 9192
NAMESF
8391
92 29 0.0040000 80.0000000 0.0000000 2 1 0 0 "SNode 92"
NAMESS
9192 9293
NAMESF
8292
93 29 0.0040000 80.0000000 0.0000000 2 1 0 0 "SNode 93"
NAMESS
9293 9394
NAMESF
8193
94 29 0.0050000 80.0000000 0.0000000 2 1 0 0 "SNode 94"
NAMESS
9394 9495
NAMESF
8094
95 29 0.6700000 80.0000000 0.0000000 2 1 0 0 "SNode 95"
NAMESS
9495 9596
NAMESF
7995
96 29 0.6685000 80.0000000 0.0000000 2 1 0 0 "SNode 96"
NAMESS
9596 9697
NAMESF
7896
97 29 0.6685000 80.0000000 0.0000000 2 1 0 0 "SNode 97"
NAMESS
9697 9798
NAMESF
7797
98 29 0.6688000 80.0000000 0.0000000 2 1 0 0 "SNode 98"
NAMESS
9798 9899
119
NAMESF
7698
99 29 0.0038000 80.0000000 0.0000000 2 1 0 0 "SNode 99"
NAMESS
9899 99100
NAMESF
7599
100 29 0.0283000 80.0000000 0.0000000 2 1 0 0 "SNode 100"
NAMESS
99100 100101
NAMESF
74100
101 29 1.7930000 80.0000000 0.0000000 2 1 0 0 "SNode 101"
NAMESS
100101 101102
NAMESF
73101
102 29 1.7980000 80.0000000 0.0000000 2 1 0 0 "SNode 102"
NAMESS
101102 102103
NAMESF
72102
103 29 0.0283125 80.0000000 0.0000000 2 1 0 0 "SNode 103"
NAMESS
102103 103104
NAMESF
71103
104 29 0.0283125 80.0000000 0.0000000 2 1 0 0 "SNode 104"
NAMESS
103104 104105
NAMESF
70104
105 29 0.0283125 80.0000000 0.0000000 2 1 0 0 "SNode 105"
NAMESS
104105 105106
NAMESF
69105
106 29 0.0220208 80.0000000 0.0000000 1 1 0 0 "SNode 106"
NAMESS
105106
NAMESF
120
68106
ICONSS ICNSI ICNSJ ARCSIJ DISTSIJ DESCRIPTION
4948 49 48 0.23900 22.00000 "0 "
4847 48 47 0.23900 36.00000 "0 "
4746 47 46 0.23900 12.00000 "0 "
4546 45 46 0.23900 1.00000 "0 "
4445 44 45 0.23900 3.00000 "0 "
4342 43 42 0.23900 36.00000 "0 "
4241 42 41 0.23900 2.70000 "0 "
4039 40 39 0.23900 10.50000 "0 "
3334 33 34 0.23900 1.44000 "0 "
3536 35 36 0.23900 3.70000 "0 "
3738 37 38 0.23900 9.81000 "0 "
3435 34 35 0.23900 1.00000 "0 "
3637 36 37 0.23900 1.00000 "0 "
3839 38 39 0.23900 1.00000 "0 "
4041 40 41 0.23900 1.00000 "0 "
4344 43 44 0.23900 1.00000 "0 "
5049 50 49 0.23900 1.00000 "0 "
5051 50 51 0.23900 16.50000 "0 "
5152 51 52 0.23900 1.00000 "0 "
5253 52 53 0.23900 13.19000 "0 "
5354 53 54 0.23900 1.00000 "0 "
5455 54 55 0.23900 1.00000 "0 "
5556 55 56 0.23900 1.00000 "0 "
5657 56 57 0.23900 5.35000 "0 "
5758 57 58 0.23900 1.00000 "0 "
5859 58 59 0.23900 18.25000 "0 "
5960 59 60 0.23900 1.00000 "0 "
6061 60 61 0.23900 20.25000 "0 "
6162 61 62 0.23900 1.00000 "0 "
6264 62 64 0.08880 72.00000 "0 "
8889 88 89 0.02364 36.00000 "0 "
8990 89 90 0.02364 1.00000 "0 "
9091 90 91 0.02364 36.00000 "0 "
9192 91 92 0.02364 1.00000 "0 "
9293 92 93 0.02364 1.20000 "0 "
9394 93 94 0.02364 1.00000 "0 "
9495 94 95 0.02364 1.50000 "0 "
9596 95 96 0.02364 2.50000 "0 "
9697 96 97 0.02364 1.05000 "0 "
121
9798 97 98 0.02364 2.50000 "0 "
9899 98 99 0.02364 1.15000 "0 "
99100 99 100 0.02364 1.00000 "0 "
100101 100 101 0.08900 2.25000 "0 "
101102 101 102 0.08900 2.50000 "0 "
102103 102 103 0.89000 2.25000 "0 "
103104 103 104 0.08900 1.00000 "0 "
104105 104 105 0.08900 2.25000 "0 "
105106 105 106 0.08900 1.00000 "0 "
ICONSF ICS ICF MODEL ARSF HCSF RADSF EMSFS EMSFF DESCRIPTION
333 33 3 1 3.77000e+00 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
344 34 4 1 3.77000e+00 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
355 35 5 1 9.69000e+00 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
366 36 6 1 9.69000e+00 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
377 37 7 1 2.57000e+01 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
388 38 8 1 2.57000e+01 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
399 39 9 1 2.75000e+01 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
4010 40 10 1 2.75000e+01 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
4111 41 11 1 7.07000e+00 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
4212 42 12 1 1.01390e+02 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
4313 43 13 1 9.43000e+01 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
4414 44 14 1 7.86000e+00 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
4515 45 15 1 7.86000e+00 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
1646 46 16 1 3.14400e+01 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
1747 47 17 1 1.25700e+02 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
1848 48 18 1 1.51960e+02 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
1949 49 19 1 5.76400e+01 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
6232 62 32 1 8.36900e+01 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
3161 61 31 1 5.30500e+01 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
3060 60 30 1 5.30500e+01 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
2959 59 29 1 4.78100e+01 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
2858 58 28 1 4.78000e+01 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
2757 57 27 1 1.40000e+01 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
2656 56 26 1 1.40000e+01 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
2555 55 25 1 1.00000e-01 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
2454 54 24 1 1.00000e-01 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
2353 53 23 1 3.45500e+01 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
2252 52 22 1 3.45500e+01 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
2151 51 21 1 4.32300e+01 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
2050 50 20 1 4.32300e+01 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
6463 64 63 1 8.36900e+01 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
122
8688 88 86 1 1.01788e+01 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
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8391 91 83 1 1.01788e+01 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
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8094 94 80 1 4.24120e-01 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
7995 95 79 1 1.13097e+00 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
7896 96 78 1 1.00374e+00 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
7797 97 77 1 1.00374e+00 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
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7599 99 75 1 3.25150e-01 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
74100 100 74 1 1.30769e+00 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
73101 101 73 1 2.76067e+00 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
72102 102 72 1 2.76067e+00 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
71103 103 71 1 1.30769e+00 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
70104 104 70 1 1.30769e+00 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
69105 105 69 1 1.30769e+00 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
68106 106 68 1 1.01709e+00 0.00000e+00 F 0.00000e+00 0.00000e+00 "0 "
123
Vita
Mariano Mercado was born in Delicias, Chihuahua, Mexico but moved to the United States at an
early age where he grew up in El Paso, TX. He attended Baylor University where he received his Bachelor
of Science Degree in Mechanical Engineering with a minor in Mathematics in 2011. He then proceeded to
work as a design engineer at Diversified Product Development and later at Wild Well Control. He started
pursing a Master’s of Science in Mechanical Engineering at the University of Texas El Paso in 2016 where
he graduated in spring 2019.
At the University of Texas El Paso, he worked under the supervision of Dr. Jack F. Chessa as a
graduate research assistant at the Center for Space Exploration and Technology Research (cSETR). During
his time as a graduate student, Mariano interned at both NASA Johnson Space Center and NASA Glenn
Research Center where he published an “Assessment of two-phase heat transfer coefficient and critical heat
flux correlations for cryogenic flow boiling in pipe heating experiments” (Int. Journal of Heat and Mass
Transfer, 2019).