American Institute of Aeronautics and Astronautics

1

Utilization of Universal Controls Analysis Tool and CFD in

Parallel for a Cold Nozzle Flow

Joel M. Faure1, Sunil Chintalapati

2, Niroshen Divitotawela

3, Daniel R. Kirk

4 and Héctor Gutiérrez

5

Florida Institute of Technology, Melbourne, FL, 32901

The NASA Kennedy Space Center Launch Services Program’s Universal Controls

Analysis Tool (UCAT) is used to analyze the flight performance of a series of specific launch

vehicles. In order to demonstrate the modeling tool as a unique Launch Services Program’s

capability, a series of non-proprietary, generic launch vehicles that are available in open

literature. Currently, the UCAT has various analytical models, and lookup tables for launch

vehicles which do not yield high fidelity. The purpose of this paper is to link UCAT with

ANSYS FLUENT which will be able to simulate a transient cold flow nozzle. This paper

explains the steps used to validate the Analytical and CFD models based on experimental

results of a conical cold flow nozzle. Then a compare the Analytical and CFD models for a

larger cold flow nozzle. Finally, link UCAT with both analytical and CFD models, and

compare their performances on a simple launch vehicle.

Nomenclature

6-DOF = Six Degrees of Freedom

CFD = Computational Fluid Dynamics

LSP = Launch Services Program

NIST = National Institute of Standards and Technology

QE = Quadrant Elevation

UCAT = Universal Controls Analysis Tool

A* = Choke area of nozzle

Ae = Exit area of nozzle

CpCV = Specific heat at constant pressure of the control volume

CvCV = Specific heat at constant volume of the control volume

dt

dTCV = Time rate change of temperature in the control volume

hCV = Specific enthalpy of the control volume

he = Exit (static) specific enthalpy

m& = Mass flow rate

mCV = Mass of control volume

Me = Exit Mach number

Pa = Ambient Pressure

PCV = Chamber, or control volume pressure

Pe = Exit (static) Pressure

R = Gas constant

T = Thrust

TCV = Chamber, or control volume temperature

Te = Exit (static) temperature of nozzle

uCV = Specific internal energy of the control volume

1 Graduate Research Assistant, Mechanical and Aerospace Engineering Department, Senior AIAA member.

2 Undergraduate Research Assistant, Mechanical and Aerospace Engineering Department, AIAA student member

3 Graduate Research Assistant, Mechanical and Aerospace Engineering Department, AIAA student member.

4 Associate Professor, Mechanical and Aerospace Engineering Department, Senior AIAA member.

5 Associate Professor, Mechanical and Aerospace Engineering Department.

46th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit25 - 28 July 2010, Nashville, TN

AIAA 2010-6558

Copyright © 2010 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

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ue = Exit velocity

V = Volume

γ = Specific heat ratio

ε = Expansion ratio of exit area to choke area

ρCV = Density of control volume

I. Introduction

he NASA Launch Service Program’s (LSP) Universal Controls Analysis Tool (UCAT) is used to analyze the

guidance, navigation, and control dynamics of launch vehicles [1]. Many launch vehicles are modeled in

UCAT, but all present vehicle models contain proprietary information which prohibits the sharing of these models

with potential users and developers or reporting the results in open literature. Florida Institute of Technology in

close collaboration with NASA LSP has developed a generic, non-proprietary version of UCAT which use launch

vehicles that are available in open literature. This model could be shared with potential users, share with potential

developers of new features and capabilities. UCAT is developed under Math Works Simulink program [2], which

enables object oriented programming which makes it easier to visualize how certain blocks of code interact with the

main program. Currently most rockets are simulated at ground level which do not take include ambient atmospheric

effects over the performance of thrust for rocket engines. Equation 1 shows that the thrust equation is directly

affected by altitude which requires a non-linear kinematic equation used in UCAT.

( )aeee PPAumT −⋅+⋅= & (1)

The purpose of this document is to prove the importance and capability of Computational Fluid Dynamics

simulation running in parallel with UCAT for high fidelity rocket simulations. As the rocket takes off, the ambient

conditions start to change, and high accelerations not seen in static test fire are encountered. The method of solution

is to create a CFD and Analytical model based on the experimental setup for a cold nozzle flow. After both the

Analytical model and CFD agree with the experimental data, the next step will be to scale the rocket with a

significantly larger storage tank, and nozzle. Compare the Analytical and CFD model together, and then simulate

both models in UCAT.

II. Validation Background

The intended procedure for validation of the CFD model was to take the initial conditions for the Florida Tech

air cylinder and compare the experimental data to the two models (Analytical, and CFD) . The Florida Tech air

cylinder is a pressurized air aluminum cylinder 8 ft long and 8 inches in diameter capable of reaching pressures up

to 3.45 MPa (gauge) as seen in Figure 1.

Figure 1. Florida Tech air cylinder fitted with a toroidal aerospike nozzle for 3.45 MPa (gauge) test fire

The tank is connected to a solenoid ball valve which is connected to a conical nozzle. The Florida Tech air

cylinder has been extensively tested on the Florida Tech 6-DOF thrust stand which measures force and torque along

the longitudinal axis, and two additional forces orthogonal to the longitudinal axis [3]. The Florida Tech air cylinder

was ideal for comparison mainly due to the large amounts of data collected, availability, and known accuracy of the

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thrust stand. The only portion of the thrust stand data of interest was the thrust in the axial (longitudinal direction).

The two computer models were developed independently and correlated well with each other, however both did not

match up to the experimental data as seen in Figure 2.

Figure 2. Comparison between CFD, Experimental, and Analytical results of the Florida Tech air cylinder

The discrepancies between the computer models and the experimental results based on the following differences:

the solenoid valve has a delay for opening and shutting, the valve orifice when the valve is open chokes the air

coming out of the tank, and unknown pressure drops across the valve. These differences which are not simulated

inside the computer models would explain these discrepancies in the results. The time for the valve to open and

close would affect the peak thrust because the pressure, temperature, and mass inside the tank has already dropped.

Because of this added complication it was decided to drop the experimental data and proceed with validation

between the Analytical and numerical models exclusively. The conceptual designs of the nozzle geometry are based

on the Florida Tech air cylinder.

After the validation of the Florida Tech air cylinder between the Analytical, and numerical models have been

made, the next step was to scale the tank, and nozzle to provide enough thrust to get it off of the ground. The nozzle

throat area and tank volume were parameters that varied, until it has attained a large altitude without making the

tank too large and provide a transition of under expansion to over expansion. The dimensions determined from the

Analytical model are used inside the CFD model, and Pro|Engineer Wildfire 5.0 to get the mass properties such as

center of gravity location, and moment of inertia at the center of gravity.

III. Analytical Setup

The Analytical model simulates the transient effects inside the pressure tank, and uses steady-state isentropic

conditions for the exit conditions such as Mach number, exit pressure, and temperature. The control volume

encompasses the tank, and the nozzle. The contact surface is only along the exit plane of the nozzle, with a ambient

pressure force being applied to it. The walls along the tank and nozzle are adiabatic for simplicity.

While many sources for the fluid properties of air exist, a decision was made to use the National Institute of

Standards and Technology (NIST). Since air is not an available material property in the NIST database, Nitrogen

was used as an analog. Several scripts have been developed at Florida Tech to extract the isobaric data from NIST

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online using MATLAB, organize the data, and use the data as a 3-D lookup table. The time to extract the data takes

too long, though robust and accepted different types of data inputs, a simplified faster program was developed for

this simulation which takes a mere fraction of the time to output the necessary data, however it requires pressure as

an input, and any other input such as temperature as an input for the lookup table function.

First some input parameters are required such as: fluid properties of nitrogen gas, expansion ratio, choke area,

volume of the control volume which all should remain as constants. The time sensitive information for the

simulation are the following: ambient pressure, mass of the control volume, and temperature of the control volume.

The assumptions are the following: ideal gas, isentropic flow inside the nozzle, single gas phase only, properties

do no change inside the nozzle (specific heat ratio does not change at any point inside the nozzle), ideal expansion,

inviscid flow, choked flow only occurs, adiabatic conditions at the walls, and 1st law of thermodynamics.

The Analytical solution is determined by first to get the molar mass, density of the gas, and total pressure in the

control volume as seen in Eqs. 2-3 [4].

V

mCVCV =ρ

(2)

CVCVCV TRP ⋅⋅= ρ

(3)

Next go into the Florida Tech-NIST lookup table function and input both pressure and temperature of the control

volume to get the specific internal energy, specific enthalpy, specific heat at constant pressure, and specific heat at

constant volume. Then calculate the specific heat ratio at constant volume as seen in Eq. 4 [4].

CV

CV

Cv

Cp=γ (4)

Next determine whether the flow is choked by checking the ambient pressure to chamber pressure ratio is greater

than the choked flow condition as seen in Eq. 5 [4] which indicates that it is no longer choked. If the flow is no

longer choked then it outputs all zeros, and exits the function, otherwise it will continue.

1

1

2 −

+

>γγ

γCV

a

P

P (5)

Then solve for the exit Mach number as seen in Eq. 6 [4] based on isentropic conditions.

( ) ( )

ee

e

MMM

⇒

⋅−

+⋅+

⋅=−⋅+ 121

2

2

11

1

21γγ

γγ

ε (6)

Mass flow of the nozzle is dependent on the following isentropic conditions at the choke point as seen in

Eq. 7 [4].

( ) ( )121*

1

2−⋅+

+

⋅⋅⋅

⋅=

γγ

γγ

CV

CV

TR

PAm& (7)

The exit pressure, and temperature, velocity and static enthalpy are determined via isentropic relations as seen in

Eqs. 8-11 [4].

γγγ −

⋅−

+⋅=1

2

2

11 eCVe MPP (8)

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1

2

2

11

−

⋅−

+⋅= eCVe MTTγ

(9)

eee TRMu ⋅⋅⋅= γ

(10)

2

2

eCVe

uhh −=

(11)

Next calculate thrust using Eq. 1, and the temperature rate change in Eq. 12 [5].

−−⋅

⋅=

2

2

eeCV

CVCV

eCV uhu

Cpm

m

dt

dT & (12)

The thrust, mass flow, time rate change of temperature are all outputted to Simulink, which will then take the

integral of the mass flow, and temperature time rate change to be inputted for the next time step. This will repeat

until criterion has been met for either of the following: time, thrust level, or choked flow condition. The interface for

the propulsion block in Figure 3 for the mask and Figure 4 for the Simulink block diagram allows the user to change

various parameters for the Analytical model.

Figure 3. Mask of Analytical propulsion block Figure 4. Analytical block at sea-level

IV. Computation Setup

The CFD simulations were performed using ANSYS FLUENT 12.1 [6]. The 2D geometry was created and

meshed using Gambit (version 2.4), preprocessor for FLUENT. Figure 5 shows the domain along with boundary

conditions. All the simulation for the current paper was axi-symmetric. A double precision, density based implicit

solver with a second order discretization for flow was preferred. Viscous model used was realizable k-epsilon (two

equation turbulence) model with standard wall function. Ideal gas was used for density formulation and Sutherland

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method was used to compute viscosity. Time-step size for the Florida Tech air cylinder simulation was 1e-05 while

a time-step size of 5e-05 was used for CFD at sea level and in-flight.

The whole tank was modeled as an adiabatic wall boundary condition and the ambient surroundings were set as

pressure outlet boundary condition. Care was taken so that the pressure outlet boundary condition was far away from

the nozzle exit and wouldn’t affect the flow downstream.

Figure 5. Domain and boundary condition

The whole computational domain was meshed using structured quad cells. The total cell count for the current

case is 424710 cells (see Figure 5). The mesh density was higher at the nozzle and the exit and spanned out to the

outlet boundary conditions. Steady state simulation with varying grid was completed prior to transient simulation to

check for grid dependency of the simulation.

A similar computational model was used in combined external and internal flow. Domain for this set-up is axi-

symmetric, double precision, density based implicit solver. Turbulence is computed using realizable k-epsilon

model. Domain of air rocket and close up feature of the rocket are given in Figure 6 . Domain was created using

structured quad with total cell count around 551960 (see Figure 6). Static pressure and temperature change due to

altitude change was incorporated by updating gage static pressure and temperature term in pressure-far field

boundary conditions at every incremental time-step.

Front end

Nozzle

Domain with air rocket Nozzle -close

Figure 6. Domain and boundary conditions with close look at rocket features

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A. Prelim Computational Results

The initial convergence criteria for steady state cases were 1e-03 but the later increased to 1e-06 to improve the

accuracy of the solution and check for grid dependency. Transient simulation were run on a eight core machine

running at 3.6 GHz with FLUENT using six cores and MATLAB using the other two core. Results from the Florida

Tech air cylinder transient simulation are shown below in Figure 7. Preliminary analysis show the results agree with

the theoretical prediction and the flow behavior is in much agreement with theory. Results of the simulation were

compared with Analytical model and experimental data given in Figure 2.

Contours of Velocity Magnitude Contours of static pressure Contours of density

Figure 7. Preliminary results; Florida Tech air cylinder transient simulation at 0.2 second flow time

V. Rocket Simulation Procedure

The method of solution differed slightly depending on whether it was a lookup table or in-flight for both

Analytical, and CFD. However the consistent outputs were mass flow, and axial thrust. The axial thrust was put into

a vector, and the mass flow was integrated and outputted to the mass properties block, the center of gravity location,

and moment of inertia are a function of mass, and are linearly interpolated. The differences vary between the inputs

for the propulsion block, if the sea-level simulations for both the Analytical and CFD are used, then time is the only

input required. However for the in-flight Analytical simulation, the ambient pressure is the only external time

dependent input required. The CFD requires the ambient Mach number, pressure and temperature as externally time

dependent inputs.

The rocket simulation program, UCAT runs inside Simulink, at a fixed time step with a major time step size of

1e-4 seconds. The solver type is Bogacki-Shampine a fixed-step solver, with minor time steps which follows the

sequence: 0, 0.5, and 0.75 of the major step size. Each minor time step repeats depending on the number of algebraic

loops, the first of these repeated time steps is used in the Analytical, and CFD propulsion module, while operating

on the assumption that any differences between repeated time steps would be too subtle, and would take

unnecessarily long to compute for less than marginally differing results.

The Analytical model develops the time rate change for both mass and temperature leaving the rocket, and

outputs the results to Simulink integrator blocks which integrates depending on the solver selected, in this case it's

the Bogacki-Shampine. The mass, and temperature of the control volume are fed back into the Analytical function,

meanwhile at any time change, the Analytical function looks into a data file which saves the outputs of the function

to a file including the sample time, if the time difference between what's recorded and sample time inputted into the

function differs by more than 1.0e-5 seconds then it calculates the output. Otherwise it outputs the values from the

data file. Due to limited operational time, the thrust is limited from 0 to 0.6 seconds, after that time has elapsed the

function outputs 0 for all outputs simulating a valve instantly closing.

The CFD model function is similar to the Analytical model; the only difference is that FLUENT does all of the

computations with the exception of thrust calculation which is calculated after convergence at every time step. The

inputs are the following: time, logical threshold, ambient Mach number, temperature and pressure. When the sample

time is 0.5e-4, (the first minor time step) and the monitor files do not exist then it initializes the CFD model using

the Florida Tech-FLUENT link.

It computes the models, and saves the data to a monitor file. Then it computes the thrust based on the data

collected from the monitor files, and outputs the results. If the sample time difference is less than 1e-5 then it

calculates thrust based on the previously iterated monitor file. Otherwise it takes the Mach number, ambient

temperature and pressure, and adjusts the time-step size to fit the difference between what was in the monitor file,

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and the current sample time, and iterates. Then the model calculates thrust and continues until the logical condition

has a non-zero value (only occurs when the sample time is greater than 0.1 seconds), and the time is greater 0.6

seconds. Once the time has exceeded 0.6 seconds a logical operator changes the output of thrust and mass flow to

zero, and outputs a 1 which is then added to a logical output in Simulink, if this is the first occurrence it outputs a

sum of 1 to the function at the next time step, which outputs zero mass flow and thrust out of the propulsion block

function, closes the CFD program, and outputs a 1 in the logical. Then the output sends a sum of 2 back into the

function where it outputs a 1 in the logical, and outputs only zero mass flow and thrust out, and no longer calls the

CFD program anymore.

VI. Results

All the simulations have the same simulation conditions, no wind, initial altitude is zero, and elevation angle set

to QE 90 degrees. The sea-level Analytical and CFD models are pre-processed and use time as an external input for

mass flow, and thrust. The Analytical in-flight model uses both time, and ambient pressure as an external input. The

CFD in-flight model uses time, Mach number, and both ambient pressure and temperature as external inputs.

The Analytical models have very little differences from each other due to the slight increase in altitude at

burnout, which was caused by the ambient pressure being lower in-flight than the sea-level case. In comparison to

the CFD results the Analytical model appears to over predict the thrust, mass flow, and exit plane pressure

difference as seen in Figure 8.

Figure 8. Thrust and Thrust components vs. Time

The Analytical model at sea-level appears to have marginally total impulse and average thrust, however their

peak thrust is the same. This is due to both models having the same altitude, and thus same conditions at the instance

in time which yield the same results. The CFD models obviously have lower total impulse, peak thrust and average

thrust. This is most likely attributed to the transient conditions in the CFD model while steady state conditions are

utilized in the Analytical model.

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Table 1. Motor performance of computational models

Model Type Total Impulse (kN·s) Peak Thrust (kN) Average Thrust (kN)

Analytical model at sea-level 30.69 89.44 51.14

Analytical model in-flight 30.70 89.44 51.15

CFD model at sea-level 28.45 72.17 47.39

CFD model in-flight 27.97 72.93 46.61

Transient air rocket simulations ran on six core machine, utilizing parallel capability of ANSYS FLUENT 12.1

[6]. Sample of qualitative results of the air rocket simulation at in-flight is given below in Figure 9, flow time in the

simulation is 0.3 seconds. The top left picture is a zoomed view of nozzle with contour of Mach number. This

picture clearly shows the formation of shocks in the nozzle at this time pressure losses that would impact the overall

performance in thrust. Monitors recording the tank pressure, tank temperature, mass flow at exit, exit velocity and

exit pressure gives the thrust and other variable for the simulation. Table 1 shows the motor performances of all four

cases. Computational run time was massive owing to the compressible nature of the simulation and based on the

alternating time-step sizes of 0.25e-04 to 0.5e-04 seconds. The total-run time for CFD in-flight case including the

interrupts and update from MATLAB was approximately 48 days on a six core machine running at 3.6GHz. The

total run-time for CFD sea level case did not include any interrupts from MATLAB was around 18 days on an eight

core machine running at 3.6GHz.

Contours of Mach number Contours of static pressure

Contours of velocity magnitude Contours of temperature

Figure 9. Simulation of air rocket at in-flight at 0.3 second flow time

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Figure 10 shows the vertical acceleration, velocity, and position, there is an obvious difference between the CFD

at sea level and those in the Analytical cases. The performances of the Analytical to CFD are higher for all cases in

Figure 10, and this is due to the performance differences, and assumptions used in each model.

Inertial Acceleration and Thrust vs. Time Altitude vs. Time

Figure 10. Inertial Acceleration, Thrust, and Altitude vs. Time

Table 2 shows that there is a marginal increase in performance for the in-flight Analytical model to the

Analytical sea-level case. The CFD model has higher performances in both altitude and peak velocity, which is due

to the higher performances in thrust over the Analytical models.

Table 2. Inertial performance of rocket

Model Type Altitude at Apogee

(m)

Percent Apogee

difference (%)

Peak Velocity (m/s)

Analytical model at sea-level 215.22 N/A 199.92

Analytical model in-flight 215.27 +0.02 199.96

CFD model at sea-level 208.81 -2.98 193.52

CFD model in-flight 207.07 -3.79 190.97

The computational time necessary to compute inside the UCAT environment as seen in Table 3 shows that pre-

processing the sea-level cases takes only a fraction of the time rather than the in-flight time which takes hours or

days.

Table 3. Computational performance inside the UCAT environment

Model Type Simulation time (s)

Analytical model at sea-level 1,106

Analytical model in-flight 51,529

CFD model at sea-level 1,195

CFD model in-flight 4,724,475

VII. Future Work

The link between MATLAB and FLUENT opens a whole new realm of possibilities for computational models.

Namely high fidelity rocket simulations, slosh dynamics, and automation routines for determining the aerodynamic

characteristics of external flows with the use of neural networks to optimize convergence. The next step for this

model at Florida Tech is to compare trajectories of a rocket based on lookup table data to the steady-state CFD data

of similar geometry, and transient CFD results for complete aerodynamic forces and torques in-flight.

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VIII. Conclusion

The purpose of this paper was to show the viability of using a CFD model inside a rocket trajectory program for

higher fidelity. The cold flow model may have been too simple of a model with little static pressure difference at the

exit plane of the nozzle which did not affect the thrust in any significant way, however even that small difference

still yielded results that varied from the sea-level cases. This means that using time as the only input parameter for

thrust does not yield the most accurate results and can be responsible to deviation of the predicted rocket's trajectory

for rocket motors that are static tested at sea-level.

Acknowledgments

We would like to thank William Benson, Dave Griffin, and Charles Walker at NASA Kennedy Space Center

Expendable Launch Vehicle Mission Analysis Branch for their continuing support.

References

1. Faure, Joel M.; Kirk, Daniel R., Gutierrez, Hector; “Validation of Universal Controls Analysis Tool Six Degree of

Freedom Kinematics”; 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum of Aerospace

Exposition; Orlando, Florida; Jan. 4-7, 2010.

2. MATLAB 7.10.0.499 (R2010a), Simulink 7.5 (R2010a), The MathWorks Inc., 3 Apple Hill Drive, Natick, MA

01760-2098, 2010.

3. Brimhall, Zack N.; Divitotawela, Niroshen; Atkinson, Joseph P.; Kirk Daniel R.; Peebles, Henry G..; “Design and

Validation of a Six Degree of Freedom Rocket Motor Test Stand”; 44th AIAA/ASME/SAE/ASEE Joint Propulsion

Conference & Exhibit; Hartford, CT; July 21-23,2008.

4. Hill, Philip G.; Peterson, Carl R.; Mechanics and Thermodynamics of Propulsion; 2nd ed.; Addison-Wesley

Publishing Company; Reading; 1992; pp. 33, 35, 68- 71.

5. Sonntag, Richard E.; Borgnakke, Claus; Van Wylen, Gordon J.; Fundamentals of Thermodynamics; 6th ed.; John

Wiley & Sons, Inc.; Hoboken; 2003; pp. 184.

6. ANSYS 12.1 FLUENT, ANSYS, Inc. Southpointe 275 Technology Drive, Canonsburg, PA, 15317

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