fluid/thermal modeling of a lox/propylene thruster...

Fluid/Thermal Modeling of a LOX/Propylene Thruster with Radiative

and Fuel Film Cooling

Final Report version 6 – Revised 12/1/2012

Author: Glen Guzik

Abstract

A thermal / fluid dynamic simulation for a gaseous oxygen and propylene rocket engine

with fuel film cooling is implemented via the computational fluid dynamics package

STAR-CCM+ from CD-APAPCO. The propellants are injected at a 2.27 oxidizer to fuel

mass ratio. With a chamber pressure of 2.068 MPa and 0.925 kg/s of propellant

injected, the rocket motor’s thrust is 2.224 kN (500 lbf). A steady state and non reacting

solution was obtained for the nozzle internal flow with 11.9 % of the fuel mass flow rate

injected as a film cooling layer. A reacting model without film cooling and a single step

reaction mechanism was also investigated and the validity of the resulting solution is

examined.

The engine’s combustion performance is also modeled with the one dimensional code

NASA CEA2. The results from CEA2 show that the combustion temperature for the

reaction is 3492 K and at least 7 combustion products are present in significant

quantities at the nozzle outlet including carbon monoxide, carbon dioxide, water vapor,

hydroxide, oxygen, hydrogen, and monatomic hydrogen and oxygen. The coherent

flame combustion model implemented in this study requires a “flame holder” near the

inlet to prevent the flame from exiting the nozzle and over predicts the combustion

temperature because it only considers 2 reaction products. These issues could be

resolved by implementing a more complex reaction mechanism and including the

geometry of the injector rather than assuming a uniform injection velocity at the inlet.

The nozzle wall temperature during steady state operations, a significant engine

performance metric, was found for non-reacting flows without heat transfer and with

radiation and fuel film cooling. The values obtained are conservative due to the frozen

flow assumption but heat transfer via convection from the flow, conduction through the

nozzle, and radiation from the CMC nozzle wall to space is successfully modeled. The

injection of a fuel film cooling layer reduced the inner wall temperature at the nozzle

throat to 2369 K representing a 351 K decrease from the 2720 K temperature at the

same location without film cooling.

MAE 697 Final Report

Updated 12/1/2012 1

Table of Contents

Nomenclature ........................................................................................................ 2

1. Introduction ........................................................................................................... 3

1.1. Background and Motivation .............................................................................. 3

2. Simulation Setup ................................................................................................... 7

2.1. Geometry and Configuration Description ......................................................... 7

2.2. 1D Analysis with Isentropic Expansion ............................................................. 8

2.3. Initial and Boundary Conditions ..................................................................... 13

3. Frozen Flow Simulation with STAR-CCM+......................................................... 16

3.1. Mesh Continua ............................................................................................... 16

3.2. Region Interfaces and Model Values ............................................................. 17

3.3. Physics Models .............................................................................................. 17

3.4. Solvers and Stopping Criteria ........................................................................ 20

4. Combustion Simulation ...................................................................................... 21

4.1. Combustion Model Selection and Initialization ............................................... 21

4.2. Meshing Considerations ................................................................................ 24

4.3. Model implementation .................................................................................... 25

5. Results & Analysis .............................................................................................. 28

5.1. Case 1: Non-Reacting Without Heat Transfer ................................................ 29

5.2. Case 2: Non-Reacting flow with radiative heat transfer .................................. 31

5.3. Case 3: Non-Reacting With Heat Transfer And Film Cooling ......................... 33

5.4. Case 4: Reacting Flow ................................................................................... 36

5.4.1. Verification of temperature prediction for Case 4 .................................... 38

5.4.2. Validation of Flow Field Predictions ........................................................ 41

6. Conclusion ........................................................................................................... 42

6.1. Summary ....................................................................................................... 42

6.2. Extending the Model Further .......................................................................... 43

7. Appendices .......................................................................................................... 44

7.1. Supplementary Figures, Tables, and Output .................................................. 44

7.2. CEA 2 Output................................................................................................. 44

7.3. Thermodynamic Polynomial Data .................................................................. 48

7.4. Convergence ................................................................................................. 52

8. Works Cited ......................................................................................................... 53


Updated 12/1/2012 2

Nomenclature

Table 1: Acronyms and Notation

Symbol / acronym Definition

kN 1000 N (kg/m s2)

δv

Boundary Layer Thickness (mm)

STAR-CCM+ CAD/CFD Computational Continuum Mechanics Code

CMC Ceramic Matrix Composite

CEA2 Chemical Equilibrium and Applications ( equilibrium solver)

CFM Coherent Flame Model

ρ

Density (kg/m3)

Ɛ Expansion Ratio

FFC Fuel Film Cooling

R Ideal Gas Constant (8.31446 J/mol K)

LOx Liquid Oxygen

M Mach Number

ṁ Mass Flow Rate (kg/s)

NLV Nano-satellite Launch Vehicle

n Number of Moles

o/f Oxidizer to Fuel Ratio

P Pressure (MPa)

ΔH°rxn

Reaction Enthalpy Change (kJ)

Re Reynolds Number

Cp Specific Heat (J/kg K)

γ

Specific Heat Ratio

a0

Speed of sound (m/s)

T Temperature (K)


Updated 12/1/2012 3

1. Introduction

1.1. Background and Motivation

When increased performance is required in rocket engines, incorporating a cooling

system into the design becomes necessary due to the large combustion temperatures

encountered with the use of high performance liquid propellants. It is often convenient to

circulate the cryogenic, liquid phase, or un-combusted gas propellants used in these

engines through their nozzle and chamber walls via a technique known as regenerative

cooling. For rockets that produce a large amount of thrust such as the 2000 kN kip RS-

25 used on the Space Shuttle or the 400 kN Merlin 1C used on SpaceX’s Falcon 1 and 9

the added complexity and mass penalty for implementing regenerative cooling is offset

by benefits such as the ability to make extended burns; however, for small launch

vehicles and in-space engines, those obstacles make this cooling method less attractive.

As the development timeline for large launch vehicle systems can stretch out over

years or even decades, engineers are conservative when including new technologies

within their designs. For example, the Russian Soyuz launcher’s first flight occurred in

1966 and the basic design of the R-7 family of rockets is still in use today. Small scale

programs with quick turnaround times have recently become a test bed for new

innovations. In 2009, the first flight test of a LOX/Propylene propelled rocket was

conducted by a team at California State University, Long Beach (CSULB) with the

launch of the Prospector-13 vehicle as depicted in figure 1.1 Through private and public

prizes like the X-Prize and NASA Centennial Challenges, new opportunities are

available for small businesses and academia to create niches within the aerospace

industry.

The production a nano-satellite launch vehicle (NLV) capable of delivering a 1 to 10

kg payload to low Earth orbit is one such emerging niche. The Prospector-13 was a

prototype with the potential to be evolved into an NLV 2nd stage and additional tests are

ongoing. A 2011 static test fire was conducted with a 4,500 lbf rocket engine by CSULB

with Garvey Spacecraft Corporation (GSC) towards developing the first stage of a nano-

satellite launcher for the Department of Defense’s Operationally Responsive Space

Program Office.2 For these types of applications, radiation or ablative cooling are often

implemented because of their simplicity. Radiation and ablative cooling are limited in

their utility because the thermal load can exceed the nozzle’s ability to radiate heat into

the environment and ablative cooling causes the expansion ratio to vary during firing


Updated 12/1/2012 4

making it heavy and non-reusable with suboptimal geometry. For small in-space

engines such as an NLV upper stage or the station keeping thruster for a satellite, using

fuel film cooling is worth the additional complexity of injector design and potential

reduction of specific impulse because, without convective heat transfer to the

atmosphere, thermal loading can lead to failure of the nozzle wall.

Figure 1: The author with CSULB students at the Prospector-13 test flight3

When using radiation cooled engines, it is necessary to include fuel film cooling in

order to reduce the temperature of the nozzle wall due to the high temperature of the

combustion chamber. Fuel film cooling can be implemented without increasing engine

mass as only the injector spray configuration must be modified. As depicted in figure 2,

fuel is injected near the nozzle wall to decrease the oxidizer to fuel ratio resulting in a

lower combustion temperature a subsequently less heat transfer. For maximum effect

the fuel can be injected as a liquid so thermal energy is absorbed by the phase change.

Implementing film cooling only requires the inclusion of additional ports in the injector but

determining the optimum FFC ratio is necessary in order to avoid decreasing the

engine’s specific impulse significantly.


Updated 12/1/2012 5

Figure 2: Diagram of film cooling concept (not to scale)

One prominent example of fuel film cooling augmenting a radiation cooled engine

is the primary reaction control system (PRCS) on the space shuttle. The shuttle’s RCS

thrusters use a hypergolic propellant mixture of monomethylhydrazine and nitrogen

tetroxide. When the thruster fires, a quarter of the MMH fuel that is injected enters the

chamber through orifices adjacent to the nozzle wall as a fuel film cooling layer.14

Modeling fuel film cooling for a rocket engine with heat transfer between the flow

and the rocket’s nozzle wall is a complex problem that, until recently, has been treated

primarily through empirical methods. When the dynamics of the chemical reaction

between the rocket’s propellants are taken into account, the system can only be

modeled computationally due to relatively recent advances in computer technology. For

example, the hypergolic NTO/MMH Aerojet R4-D attitude control thruster was 1st flown

during the Apollo era.15 The R4-D is radiatively and film cooled and was developed

without the aid of CFD codes. Despite this fact, variants of the thruster are still in use in

currently operating satellite constellations. Although fuel film cooling is implemented as a

mature technology in many apogee and in-space rocket systems, the ability to model

those systems computationally has the potential to drive innovation in emerging niches

such as the nano-satellite launch vehicle discussed above.

This work documents the procedure for modeling the thermal and fluid dynamics

within the nozzle of an oxygen and propylene rocket engine as a continuation of

http://en.wikipedia.org/wiki/Monomethylhydrazine

http://en.wikipedia.org/wiki/Nitrogen_tetroxide

http://en.wikipedia.org/wiki/Nitrogen_tetroxide


Updated 12/1/2012 6

previous work performed by McCall and Besnard modeling a radiation cooled ceramic

matrix composite (CMC) engine4 where, in addition to radiative cooling, gaseous fuel

film injection in the flow boundary layer is modeled. The thermal processes considered

include heat transfer from the combustion gases to the wall and radiative cooling into

space. Also, combustion is added to the model in an attempt to more completely

capture the behavior of the flow. To accomplish these tasks, the computational fluid

dynamics (CFD) application STAR-CCM+ is used to implement several test cases and

the results of those simulations are analyzed.

A variety of commercial computational fluid dynamics codes were considered

prior to the selection of CD Adapco’s STAR-CCM+ to complete this project. Siemens’

NX 6 and COSMOS FloWorks can model supersonic, compressible flows including heat

transfer but NX 6 is mainly intended for external flows and both codes lack the ability to

model combustion. Two-dimensional kinetic code (TDK) by Sierra Engineering can

model combustion inside a nozzle but would not be able to describe heat transfer

outside the flow’s control volume. The open source package OpenFOAM has some

CFD functionality but was not practical for this project as it is still a work in progress and

would require extensive software development of an algorithm capable of solving a

transport equation using a discrete, implicit, iterative numerical method for it to be

capable of modeling a combusting flow. STAR-CCM+ has built in physics models for

internal, supersonic flows with heat transfer and combustion and has a great deal of

flexibility for simulating various flow regimes making it competitive with any other

modern CFD package.5

In section 2.1, the setup of the simulation is discussed. The geometry and

configuration of the rocket engine are described in detail. Next, in section 2.2

theoretical analyses are performed to obtain a first order estimation of the rocket’s

behavior as well as provide values for the initial and boundary conditions. In section 2.3

the model’s boundary and initial conditions are described.

Section 3 covers non-reactive flow simulation with STAR-CCM+. First, the meshing

models are added and appropriate reference values are selected. Next, the previously

calculated initial and boundary conditions are used to set region physics values. Multiple

cases are run with differing physics continua and the physics models used in each

simulation are described along with their relevance to the case under consideration.


Updated 12/1/2012 7

Finally, the required relaxation factors and stopping criteria are described in order to

obtain a convergent solution in a reasonable number of iterations.

In Section 4, the methodology for modeling the flow with a single-step reaction model

is discussed. The selection of the combustion model and procedure to initialize the

model prior to iteration are described in section 4.1. Considerations that are specific to

the meshing for the combustion case are detailed in section 4.2. In section 4.3, the

setup for the Coherent Flame Model (CFM) used for modeling the reaction and related

physics continua are described in detail.

The results for the 4 test cases considered in this study are presented in section 5.

The first case presented in section 5.1 treats the flow as non-reacting and neglects heat

transfer. In section 5.2, case 2 has the same configuration as Case 1 except heat

transfer is also modeled. In section 5.3, case 3 models a non-reacting flow with heat

transfer and film cooling. The results for case 4 (a reacting flow) are shown in the final

subsection of section 5.

Conclusions are made in section 6 and options for further extending the model are

noted. Additional information that was referenced in the paper is included in the

appendices of section 7. Works cited are listed in section 8.

2. Simulation Setup

2.1. Geometry and Configuration Description

The region of the flow examined within the rocket engine is contained inside a

control volume with boundaries at the beginning of the combustion chamber or nozzle

inlet, the interior of the CMC chamber/nozzle wall, and the outlet of the nozzle. In figure

3, the relevant dimensions are delineated along a radial cross section of the nozzle in

metric units. A three-view and isometric projection of the control volume is included as

figure 25 in the appendix. In the actual motor, an injector would be located directly

upstream of the inlet with feed lines for the fuel and oxidizer attached. Injector design

and the propellant feed system are beyond the scope of this study; only the internal flow

within the nozzle is considered in the model.


Updated 12/1/2012 8

Figure 3: Nozzle Dimensions in Meters

2.2. 1D Analysis with Isentropic Expansion

Beginning with the engine characteristics specified in the analysis by McCall and

Besnard, an initial estimate of the thruster’s performance is made by treating the flow as

one-dimensional and isentropic as in the standard reference Space Propulsion Analysis

And Design.6 The rocket is designed to produce 2224 N (500 lbf) thrust with a fuel rich

oxidizer to fuel ratio of 2.27. The chamber pressure (pc) is a typical value for injection of

2.07 MPa (300 psi) and an estimated constant value for the ratio of specific heat (ɣ) is

1.14.

The first step in the procedure is to calculate the sonic velocity at the inlet so that

the mass flow rate can be determined as in equations 1 and 2. Estimating the chamber

temperature, T0 to be the LOX/Propylene combustion temperature of 3518 K the sonic

velocity is 1242 m/s at the inlet. At the chamber pressure of 2.068 MPa the mass flow

rate is 0.925 kg/s.

Sonic velocity:

00 RTa (1)


Updated 12/1/2012 9

The mass flow rate:

0

0

pAa

m t

,

12

1

1

2

(2)

The next step is to use the relationship between the expansion ratio and the

Mach number, equation 3, to determine the inlet and exit Mach number from the known

geometry. Finally the Mach number values for the chamber, throat, and exit are used in

equations 4, 5, and 6 to determine pressure, temperature, and density at each point.

The results are listed in table 1. It is important to note that the values calculated at each

station are representative of the flow properties along the axis as the analytical model is

1 dimensional.

Expansion ratio vs. Mach number:

1

1

2

2

11

1

21

M

M (3)

Pressure:

120

2

11

M

p

p (4)

Temperature:

20

2

11 M

T

T

(5)

Density:

1

1

20

2

11

M (6)


Updated 12/1/2012 10

Table 2. One Dimensional Isentropic Flow Properties for Thruster

Units Chamber Throat Exit

Expansion Ratio, Ɛ - 5.48 1 8.02

Pressure, P Pa 2.068*106 1.192*106 4.055*104

Temperature, T K 3518 3285 2171

Mach Number, M - 0.11 1 2.98

Density kg/m3 1.53 0.944 0.048

For the radiation cooled rocket engine discussed in reference 3, Two

Dimensional Kinetic Code (TDK), by Sierra Engineering was used to model combustion.

The NASA code Chemical Equilibrium with Applications version 2 (CEA2)7 is used to

verify the values calculated in table 1 and for comparison of the chamber temperature

calculated with TDK. The complete output of CEA2 is listed in the appendix and

summarized in table 2. Both codes use iterative numerical methods to obtain the

equilibrium composition of the reacting propellants. The combustion temperatures found

with TDK and CEA2 differ by less than 1% and use a multi-species 1-dimensional

combustion model. The maximum temperature found with combustion enabled in the

STAR-CCM+ model is expected to be similar however, it is important to note that a

single step reaction mechanism is used for the combustion case in this study rather than

including complex chemistry which is significantly more involved.

Table 3. Flow Properties from NASA CEA2

Unit Chamber Throat Exit

Pressure BAR 20.684 11.851 0.38311

Temperature K 3492.23 3310.57 2193.5

Density kg/m3 1.5262 9.3527-1 4.8062-2

Molar Weight kg/kmol 21.425 21.724 22.88

Specific Heat Ratio - 1.1399 1.1382 1.1967

Sonic Velocity m/s 1243 1200.9 976.7

Mach Number - 0.109 1 2.983


Updated 12/1/2012 11

It is necessary to know how far the viscous sub-layer extends from the interior

surface of the nozzle wall to ensure that a sufficient number of cells are included in the

mesh to resolve it. From Schlichting and Gersten, one approximation for the thickness

of this boundary layer is

GD

v

Re

ln(Re)122

(7)

with the Reynolds number defined as

VDRe (8)

and G corresponding to a viscous sublayer function that decreases monotonically when

the natural log of the Reynolds number increases. The value of the viscous sublayer G

function is about 1.35 for Reynolds numbers between 2300 and 107 and its limit is 1 as

the Reynolds number approaches infinity.8 Here, calculated at the inlet, the Reynolds

number is 147,947 and the boundary layer is 0.27 mm thick.

Ensuring that the specific heat of the flow is determined properly is another

important consideration. In order to calculate the specific heat of the gas species in the

flow as a function of temperature STAR-CCM+ uses thermodynamic polynomial data in

the Chemkin data format.5 This format is very similar to that of the NASA

thermodynamic polynomial database which was used for some of the first chemical

equilibrium calculations performed via computational methods.7 There are low

temperature (300 K to 1000 K) and high temperature (1000 K to 5000K) sets of 4th order

polynomial coefficients for each species in the database. Normalized by the specific gas

constant, R, the specific heat for a species at a given temperature is found via equation

9.

The specific heat in STAR-CCM+ (Chemkin12) format is:

4

5

3

4

2

321 TaTaTaTaaR

cp (9)

In CEA2 format, it is:


Updated 12/1/2012 12

4

7

3

6

2

543

1

2

2

1 TaTaTaTaaTaTaR

cp

(10)

The STAR-CCM+ thermodynamic database format uses 5 coefficient

thermodynamic polynomials. However, the NASA Chemical Equilibrium Analysis 2

program’s thermal database stores the function as a polynomial with 7 coefficients as in

equation 10. Both datasets were created by fitting empirical data to a polynomial curve

so as to determine least squares coefficients with the constraint that the function

matches the data exactly at 298.15 K. To be certain that comparisons made between

results calculated with STAR-CCM+ and CEA2 are valid equations 9 and 10 are plotted

in figure 4 using the appropriate coefficients for propylene. It is clear that despite the

differences in the formulation both curves are very similar to each other so the manner in

which the specific heat is determined is not a factor in any disagreement between results

obtained with CEA2 versus STAR-CCM+.

Figure 4: A comparison the specific heat of propylene as a function of temperature using

polynomial coefficients obtained from the STAR-CCM+ and CEA2 databases show

agreement between the two.

To further eliminate the specific heat formulation as a source of error, data from

the National Institute for Standards and Technology (NIST) for each of the species

considered in the model at 2.068 MPa was plotted along with the lower temperature

interval coefficients in the STAR-CCM+ database. Data for temperatures above 1000 K

0

50000

100000

150000

200000

250000

0 2000 4000 6000

Cp

(J/

Kg

K)

T (K)

Cea2

STAR-CCM+


Updated 12/1/2012 13

was not available for most species.9 Figures 16 through 19 in the appendix show that, at

low temperatures, the default specific heat polynomial coefficients from the STAR-CCM+

database can differ somewhat from experimentally measured data although as the

temperature increases the values approach each other. This was caused by the state

change that some of the species experience at low temperatures that is neglected in this

study due to the assumption that the flow is solely a gas.

In section 7.3 specific heat divided by the gas constant as a function of

temperature was plotted in figure 26 through 29 for propylene, oxygen, carbon dioxide,

and water showing good agreement between data available from the National Institute of

Standards and Technology. The specific gas constants required are listed in table 8.

The procedure to replace the default coefficients for the low temperature coefficients is

shown in table 9. Additional empirical studies are required to characterize completely

the behavior of the concerned species at high temperatures. Because NIST data is not

available for every species in the temperature range encountered the default coefficients

are used to avoid the complication of discontinuities in the specific heat data at 1000 K.

2.3. Initial and Boundary Conditions

Prior to activating the flow solver for a simulation, each component region’s initial

state and conditions on its boundaries must be defined. To avoid divergence, the

conditions selected must allow the solver to smoothly iterate towards convergence

without discontinuities developing in the residuals of the discretized transport equations

that are being solved. For the non-reacting flow, the initial configuration of the control

volume’s boundaries can be set to the chamber conditions calculated in the previous

section. The initial temperature and pressure for the region is 3492 K and 2.068 MPa

respectively. The initial velocity of 200 m/s is uniform, flowing from the inlet to the outlet

parallel to the axis.

For the non combusting case, the composition of the flow remains constant from

injection to exit. The results of the CEA2 analysis show that the reacted combustion gas

is composed of mainly 9 components. To best represent the properties of the flow in the

non-reacting cases the multispecies gas phase model is added to the physics continua

for the control volume. In table 4, the composition of the non-reacting combustion gas

mixture is listed in terms of mass and mole fraction.


Updated 12/1/2012 14

Table 4: Premixed Combusted Gas Composition

Mass Fraction Mol. Fraction

Carbon monoxide (CO) 0.4883 0.3688

Water vapor (H2O) 0.2340 0.2748

Carbon dioxide (CO2) 0.1922 0.0924

Hydroxide (OH) 0.0457 0.0568

Oxygen (O2) 0.0152 0.0100

Hydrogen (H2) 0.0125 0.1312

Monatomic Oxygen (O) 0.0094 0.0125

Monatomic Hydrogen (H) 0.0025 0.0534

For case 1 and 2, the mole fractions of the injected species are set to 36.7% carbon

monoxide, 27.5% water, 13.1% hydrogen gas, 9.2% carbon dioxide, 5.7% hydroxide,

5.3% monatomic hydrogen, 1.3% monatomic oxygen, and 0.5% oxygen gas. While trace

amounts of other species are present after combustion this composition is similar

enough to the actual flow to model its behavior adequately. As film cooling is

implemented in case 3 a separate boundary is included to inject the fuel. Also,

propylene must be included as a species present in the model but is not a component of

the combustion gas mixture because it has a separate inlet boundary where it is injected

along the wall. The propylene injected as a film cooling layer represents 3.6% of the

total mass flow and is equivalent to diverting 11.9% of the fuel mass flow rate towards

injection as a film cooling layer.

As the Coherent Flame Model used for modeling combustion cannot handle

multistep reactions the species composition for the reacting case is simplified. It is

instead assumed that only one reaction occurs where the combustion of propylene and

oxygen yields water and carbon dioxide. The selected o/f ratio is slightly fuel rich so

some of the propylene remains in the flow at the outlet. The mole fractions at the control

volume’s inlet and outlet boundaries for the reacting case are listed in table 5.

Table 5: Species for single step combustion

Inlet Mol. Fraction Outlet Mol. Fraction


Oxygen (O2) 0.7491 0.0000

Water vapor (H2O) 0.0000 0.4610

Propylene (C3H6) 0.2509 0.0780


Updated 12/1/2012 15

Assuming a single step reaction mechanism where only carbon dioxide and water

are produced from the combustion of the propellants and complete combustion occurs,

the species initially present in the flow are the products and the excess fuel. By mass, 11

% is propylene, 25.9 % is carbon dioxide, and the remaining 63.1 % is carbon dioxide.

The temperature of the flow at the inlet and outlet boundaries is constrained to the

chamber and exit temperatures in table 2. In section 4 the implementation of the

combusting solver is discussed in detail.

For the reacting case, an initial condition must be created to avoid divergence when

the combustion model is activated. To obtain this initial condition, the simulation is run

with the reacting physics continua model disabled and with the injected species the

same as the non-reacting case. Although it is not necessary for the solution to fully

converge, after a few hundred iterations the flow is developed sufficiently that the

combustion solver can be activated so the injected species must change from having the

composition of the reacted flow. The species mass fraction is changed to 30.6 %

propylene and 69.4 % oxygen at the inlet (a 2.27 oxidizer to fuel ratio) and the

temperature of the injected gas is lowered to 300 K.

For the cases where heat transfer to the nozzle wall is included the initial

temperature of the wall and the ambient environment is 300 K. To properly model heat

transfer, the surface orientation option for the nozzle wall must be set to outward so that

that exterior will radiate into space. The alternative option (setting surface orientation to

inward) would cause radiation from the flow to pass through the contact interface and be

intercepted by the exterior surface creating a nonphysical result.

When film cooling is included in case 3, 11.9% of the propylene mass flow is injected

near the wall unmixed with the oxidizer. To accomplish this, a field function is defined in

the tools folder such that it returns a value of 1 when evaluated within 1.25 mm of a wall.

Next a split by field function is performed on the inlet boundary to create the additional

boundary for film cooling layer injection. The case 3 control volume is represented by a

15° radial slice of the CMC nozzle’s internal volume so the total mass flow rate is 0.0385

kg/s with 0.0014 kg/s injected as the FFC layer.

Reference values are defined for each physics continuum and the default minimum

temperature of 100 K and maximum of 5000 K are unchanged. Because of the fine


Updated 12/1/2012 16

mesh near the wall, the minimum wall distance is set to 10-6 m. The reference pressure

is set to 0.1 Pa to simulate the rocket’s behavior in a void.

3. Frozen Flow Simulation with STAR-CCM+

3.1. Mesh Continua

After the simulation’s regions are created and the boundaries have been defined, the

meshing models are added so the mesh can be created. Both two and three

dimensional simulations can be created with STAR-CCM+; meshes are initially

generated in 3D and if a 2D one is required the grid on the surface of a region is be used

to create the new mesh. Individual meshes are created inside the continua folder and

can include multiple meshing models. Multiple meshes can be created so the solid

nozzle wall and internal volume can have specific meshes, with their appropriate

meshing methods defined separately. There are several meshing models available but

because of the simple geometry of the control volume only the surface remesher,

polyhedral mesher, and prism mesher are necessary for this project.

The polygons that define the geometry of the part when imported as a parasolid

are not conducive to further meshing because of their uneven size so the surface

remesher is included in the meshing continua to create a new surface mesh with more

uniform elements. The size of each cell is referenced off the base size. The simulation

was performed with various base sizes to ensure that the results were not affected by

grid dependency and a 1 mm base size was found to be sufficient.

For volume meshing both tetrahedral and polyhedral cells are available however,

the user guide states that far fewer polyhedral cells are required to fill a volume with a

given initial surface size so the polyhedral mesh can resolve the same level of detail with

less cells and subsequently less computational cost. 5 STAR-CCM+ can have trouble

meshing geometry with sharp edges so, as the control volume has a wedge angle of 150,

the target and minimum size of the cells near the surface need to be set to the same

value in order to avoid the appearance of erratic protrusions along the axis. For the non-

reacting model, 10 uniformly spaces prism layers are sufficient; in order to model


Updated 12/1/2012 17

combustion, care must be taken to fully resolve the boundary layer so 20 prism layers

with the spacing between each consecutive layer stretched by a ratio of 1.3 are used.

3.2. Region Interfaces and Model Values

No interfaces need to be setup for the two dimensional simulations because they

contain only a single region. Two kinds of interfaces are required for the three

dimensional models. The first is a periodic interface created between the two cutting

planes on the interior of the control volume. Rather than simulate an entire nozzle the

periodic interface maps the boundaries of the planes to each other creating a repeating

geometry that, as it is rotated around an axis, is equivalent to the geometry of the entire

nozzle with far fewer cells required as only a 15 degree slice is actually swept out. The

periodic interface is also included along the cutting planes of the wall as well.

The cases with heat transfer to the wall are all three dimensional because the

surface to surface radiation model only works with 3D space models. The second type

is a contact interface which is created between the gas region of the flow and solid

region of the wall allowing heat transfer between the two regions. Though composites

are usually non-isotropic materials, for this work, the ceramic matrix composites are

treated as if they were solely composed of their principal component silicon carbide.

The density is 3100 kg/m3, the specific heat is 750 J/kg-K, and the thermal conductivity

is 18 W/m-K.

It should also be noted that in addition to the inlet, outlet, and wall boundaries of the

control volume an axis type boundary must be created along the center of rotation for

the 2D axisymmetric case and the direction of the axis should be defined under the

physics values of the control volume. The 3D cases only require the direction of the axis

to be defined as a unit vector. With the centerline of the nozzle aligned along the x axis,

the direction vector for the axis’ physics value is [1,0,0].

3.3. Physics Models

The models applied to the physics continuums selected for the non-reacting cases

are summarized in Table 6. Case 1 was the simplest to verify agreement of the solver


Updated 12/1/2012 18

with the isentropic equations. Case 2 included heat transfer to the nozzle wall and case

3 added FFC to the setup for case 2.

There are three methods of representing space with STAR-CCM+ though only

the three dimensional and axisymmetric models are used here; the two dimensional

model represents flows with a unit depth. The three dimensional model is suitable

modeling the nozzle in its entirety or as a wedge. The axisymmetric model revolves a

two dimensional mesh about an axis. When a volume or area related quantity is

specified in an axisymmetric model the value is specified as if the mesh was swept

through a 1 radian angle. The three dimensional model is more computationally

expensive as there are significantly more cells in a 3d mesh than a 2d mesh.

Table 6: Physics Continua for Non-reacting Cases

Physics

Continua

Case 1 Case 2 Case 3

no FFC, heat

transfer, nor

combustion

Heat transfer, no fuel

film cooling

Heat transfer and fuel

film cooling

Geometry 2D (axisymmetric) 3D (15° wedge) 3D (15° wedge)

Combustion non-reacting non-reacting non-reacting

Turbulence standard k-ɛ standard k-ɛ standard k-ɛ

Gas Species C3H6, CO2, H2O, CO,

OH, H2, O, H

C3H6, CO2, H2O, CO,

OH, H2, O, H

C3H6, CO2, H2O, CO,

OH, H2, O, H

Time steady state steady state steady state

Flow coupled coupled coupled

Energy coupled coupled coupled

Radiation - surface to surface surface to surface

Both transient and steady state time models are available depending if the

system’s properties change with time. For this engine the steady state model is

sufficient because the boundary conditions are constant and the flow is assumed to not

be perturbed by combustion instabilities. The unsteady model would require many time

steps, each needing to converge, for the flow’s behavior to represent the rocket’s

performance during firing so the steady state model will allow a solution to be obtained

faster.


Updated 12/1/2012 19

Single component, single phase mixture, and multiphase mixture models are

available for modeling substances. The nozzle wall is treated as a single component

solid material with the isotropic properties of a ceramic matrix composite. Although the

propellants are liquids when loaded into the engine’s tanks and subsequently injected,

for simplicity they are assumed to have already vaporized before entering the control

volume so the flow is treated as a single phase mixture of gases. The multiphase

models would be much more computationally intensive because the volume of fluid

method employed requires a fine mesh to capture individual droplets.

The flow and energy models can either be segregated or coupled depending on the

anticipated flow regime. The segregated models solve the equations for momentum,

mass, and energy independently and are intended mainly for incompressible or semi

compressible flows. The coupled model solves the conservation equations

simultaneously and, as it is more suitable for flows with high Mach numbers,

compressibility, and shocks the coupled approach is used for this simulation.

The flow and energy models are always either both coupled or both segregated but

can be changed mid-simulation. After encountering problems obtaining a converged

solution for a simulation where combustion is considered, it was determined that best

practice is to solve the pressure and velocity fields initially with coupled flow solver and

then enable reaction and continue the solution with the segregated flow. The procedure

for running a combustion simulation is detailed in section 3. Only coupled flow and

energy models are required for the non-reacting test cases.

Prior to setting up turbulence, the reaction model must be defined. If the flow is

non-reactive then only the equation of state model for defining density and viscous

regime need to be defined. The density can be set to a constant, follow the ideal gas

law, or an empirical real gas relation can be used. Since the flow is high-speed and

compressible, the constant density model is not appropriate. At low temperatures and

high pressure the actual behavior of real gases differ somewhat from that predicted by

the ideal gas equation. The Redlich-Kwong and van der Waals real gas equations both

use critical temperature and pressure constants which are well defined for individual

gases. However, due to combustion the composition of the gas mixture vary through the

nozzle leading to inconstant critical values so the ideal gas model is implemented as it is

compatible with all of the cases considered.


Updated 12/1/2012 20

Because the flow is steady state the Reynolds averaged Navier-Stokes

equations are used where the flow variables are decomposed into mean and fluctuating

components. A number of turbulence models are available to close the RANS equations

by providing an averaged value for the randomly fluctuating Reynolds stress. Of these,

the k-ɛ model is the most standard solving the transport equations for the turbulent

kinetic energy and its dissipation rate. There are also many versions of the k-ɛ model

but the standard k-ɛ model is used here to avoid complexity.

The surface to surface (S2S) thermal radiation model is used to model the heat

transfer from the thruster exterior to the void due to convection from the flow to the wall

followed by conduction through the wall. For simplicity, Heat transfer is isotropic in the

model although for an actual composite the radiation would not be uniform due to the

orientation of the carbon fiber. The S2S model cannot be used on a two dimensional

mesh. It is assumed that the radiation properties of the nozzle are independent of the

wavelength of the radiation.

3.4. Solvers and Stopping Criteria

All of the non-reacting simulations will include a k-ɛ turbulence and turbulent

viscosity solver. Selecting an under-relaxation factor for these solvers is less difficult

than with the turbulent solvers in the combusting model because without reactions the

solution converges more smoothly. Both under-relaxation factors can be set to 0.9 with

no problems. Additionally, the wall distance solver is present in all of the simulations but

no configuration is necessary.

The Courant number property of the coupled implicit solver controls the number of

iterations required to achieve convergence because it controls the size of the time-steps

used in the time marching procedure employed by the solver.5 If the residuals do not

smoothly decrease, the Courant number can be set to a low value of 1 but without the

inclusion of a reaction model the solver will converge easily. For the first 3 cases a

value of 10 is sufficient to achieve good convergence.

There is a view factors calculator and an S2s solver present in cases 2 and 3

because of the inclusion of the surface to surface radiation model in the wall. To

decrease the amount of time required per iteration, the number of beams used to track


Updated 12/1/2012 21

the radiation off the surface can be reduced and the resolution of the voxel mesh used

for ray tracing can be decreased but the default settings worked fine. There is no need

to modify any of the preset values for these solvers.

Finally, the stopping criteria can be specified as a maximum number of steps.

With the prescribed Courant number, the solver should fully converge within 1500 steps

and the solver is set to halt after that many iterations. With the implementation of the

frozen flow complete the modeling of a reacting flow is next considered.

4. Combustion Simulation

4.1. Combustion Model Selection and Initialization

The combustion physics models available for simulations created with STAR-

CCM+ are suitable for either premixed, non-premixed, or partially premixed flows. For a

non-premixed flow, the fuel and oxidizer enter the control volume separately through

different boundaries. In a premixed case, the fuel and oxidizer are perfectly mixed prior

to entering the computational domain. When a partially premixed physics model is used

the reactants are premixed entering through at least one boundary while pure fuel or

oxidizer may enter the domain through a separate boundary. In this study, the flow is

considered to be premixed for the reacting case so as to avoid including the additional

complexity of injector design and the FFC may be injected through a separate (thin)

boundary.

The combustion models that are compatible with a premixed flow include the

Premixed Eddy Break-Up (PEBU), Coherent Flame Model (CFM), the Presumed

Probability Density Function (PPDF), and Homogenous Reactor Model. Due to the fact

that the Homogenous Reactor Model requires a complex chemistry definition file created

by DARSCFD or in the CHEMKIN format, additional computational tools are required for

its implementation. The PPDF model can only be used with a segregated flow model

where the velocity and pressure equations are solved in an uncoupled manner making it

unsuitable for use with a simulation when supersonic velocities are expected. The CFM

and PEBU models are compatible with the requirements for this simulation although the

CFM is limited to single step reaction chemistry. Additional reaction steps are possible

with the PEBU model; however including more than 4 reactions is not recommended in

the STAR-CCM+ documentation. One and two step reaction models are available in the

literature for the reactants considered; these simplified reaction mechanisms, however,


Updated 12/1/2012 22

inaccurately over-predict the heat of reaction and combustion temperature as multiple

species are present and dozens reactions occur in real hydrocarbon combustion.10

Because developing a simplified reaction mechanism for the PEBU model that will not

over predict the combustion temperature is impractical, the CFM is selected to model

combusting flows.

The coherent flame model tracks the flame area density and fuel mass fraction

through transport equations to determine species concentrations, enthalpy, and other

flow properties. Several built-in methods are available to calculate the flame area

density but the laminar flame speed as a function of the equivalence ratio is not

predefined in the code for oxygen and propylene combustion. In order to obtain a

functional relationship suitable for use in the coherent flame model some adjustment of

available data is required. The flame speed as a function of equivalence ratio was

determined empirically through experiment with a free stream a pressure of 1 bar and

temperature of 298 K by Davis, Law, and Wang.11

Assuming that the flame speed is not significantly influenced by free stream

temperature, the flame speed function at chamber pressure can be found via the Gülder

laminar flame speed correlation.

From the user’s guide5 the Gülder flame speed correlation is:

(11)

with Su defined as the as the laminar flame speed, Ф as the equivalence ratio, T as the

temperature, and P as the Pressure. The u and 0 denote the unburnt and reference gas

properties respectively. The remaining terms in the expression are constants with

values dependent on the fuel that is combusting. Values for these constants that were

found to fit the available data are listed specifically for propylene in Table 7. With the

above assumption regarding temperature, the data from Davis, Law, and Wang11 is used

to create the plot in Figure 5 of SU vs Ф at the chamber pressure.


Updated 12/1/2012 23

Table 7. Gülder flame speed correlation fuel dependent constants for propylene

Z W η ξ α β

1 0.46 0.15 5.1 1.8 -0.3

To use this function with the CFM physics model the resulting equation from a

curve fit is entered as a field function or the data can be entered as a table. Although it

is necessary to define a flame speed profile to initialize solution iteration, setting the

flame speed to a reasonable constant value (30 m/s) may also allow obtaining a

converged solution.

Figure 5: The flame speed versus the equivalence ratio for propylene combustion11

Performing the simulation with combustion is a two part process that requires an

initial flow field to be created prior to activating the combustion model. First, the multi-

component gas model is selected because multiple species in the gas phase are present

in the flow; the reactants will be injected at 300K so they will be above their vaporization

temperature. The reacting and premixed combustion models are enabled so that the

0

5

10

15

20

25

30

35

40

45

50

0 0.5 1 1.5 2

Flam

e Sp

eed

(m

/s)

Equivalence Ratio

1 bar

20.68 bar


Updated 12/1/2012 24

Coherent Flame Model (which models combustion) can be included. Standard k-ɛ

turbulence is used along with steady time, coupled flow, and axisymmetric space. The

High Y+ Wall Treatment model and Reynolds Averaged Navier Stokes models are

automatically added with the inclusion of the turbulence and flow models.

The process for creating the initial flow field is similar to the non-reacting case;

mass flow inlet, pressure outlet, wall, and axis boundary types must be defined at their

respective boundaries with the bluff body also treated as a wall. Again using the CEA2

results, with at 0.925 kg/s mass flow rate and chamber pressure of 2.068 MPa, the exit

pressure and temperature are set to 39.3 kPa and 2315K respectively. The initial

conditions that the solver uses to begin iteration are uniform within the control volume

and separate from the boundary conditions. A velocity of 100 m/s, 300 K temperature,

and 2.068 MPa pressure were found to work well for the initial values of the region within

the control volume. Poor initial conditions will rapidly lead to divergence because of

increasingly large corrections to the solution. The turbulence specification is set to

“Intensity +length scale” for the inlet and outlet boundaries. A turbulence intensity of

0.05 and length scale equivalent to the diameter of the nozzle at each of the boundaries

proved sufficient.

4.2. Meshing Considerations

The polyhedral cell size and prism layer thickness remain the same as in the

non-reacting case however, the geometry of the nozzle must be modified to include a

bluff body near the inlet as in Figure 6 in order for the inlet velocity to be less than the

flame speed. From the 1D model, the flow velocity at the inlet is 135 m/s which is

substantially higher than the flame velocity of 32 m/s expected at the rocket’s chamber

pressure as shown in Figure 5. The purpose of the bluff body is to create a re-

circulating zone with a slower velocity than the flame speed. Without including the bluff

body which functions essentially like a flame-holder, the flame propagates downstream

out of the nozzle after only a few iterations leading to divergence of the solution. While

adding geometry to the nozzle is not an ideal solution to the problem of obtaining a

stable flame it is sufficient for the purpose of obtaining a converged solution while

maintaining the other assumptions made during the setup of the reacting model.


Updated 12/1/2012 25

Figure 6: The bluff body near the inlet has a prism mesh along its surface to resolve the

boundary layer

4.3. Model implementation

To complete the boundary value setup for the initial run it is necessary to

consider the single step reaction that the CFM will implement. The 2.27 oxidizer to fuel

ratio implies a 0.306 fuel mass fraction but the simulation is not initialized with

combustion active because unless a stable pressure and velocity field is present first

activating the reaction will cause the solver to diverge. The propylene and oxygen

react to produce carbon dioxide and water so after complete combustion of the fuel rich

mixture the mass fraction of propylene fuel will be 0.102. This fuel mass fraction is used

at both the inlet and outlet with an injection temperature of 3500 K and exit temperature

of 2315 K.

Note that in addition to CO2 and H2O, significant quantities of CO, OH, H2, O,

and H are also present as products in the physical system. The mole fractions of the

most abundant species at the nozzle outlet are presented in the CEA2 output in Section

8.2 of the appendix. To avoid the necessity of defining a complex chemical reaction all

simulations performed in this study with STAR-CCM+ use a single step reaction

mechanism. Consequently, although the fuel mass fraction imposed as a boundary

condition at the inlet is the same for both the STAR-CCM+ and CEA2 models, the flow

will contain some un-reacted fuel at the outlet due to the simplified reaction model


Updated 12/1/2012 26

implemented with STAR-CCM+.

Listed in table 7, the mass flow rate at the inlet is a boundary condition with the

value of 0.925 kg/s. The mass flow rate remains constant throughout the simulation.

The other boundary conditions listed in table 7 including the pressure at the inlet (Pi),

pressure at the exit (Pe), and exit temperature (Te) remain at their initial values for the

duration of the simulation. After a number of iterations, on the order of 103, the inlet

temperature (Ti) is reduced from its initial value to 300 K once the CFM is activated by

disabling the frozen flow in order to allow combustion to occur in the simulation.

Table 8. Reacting Case Physics continua and initial conditions

Physics

Continua

Reacting Case Initial Conditions

Combustion, no ffc or ht

Geometry 2D (axisymmetric) ṁ 0.925 kg/s

Combustion Coherent flame model (CFM) Pi 2.068 E6 MPa

Turbulence standard k-ɛ Pe 39 KPa

Gas Species multi-component Ti 3500 K

Time steady state Te 2315 K

Flow coupled Combustion solver disabled

Energy coupled Iterations ~103

Mixing premixed

Frozen Flow Enabled for ~103 steps then

disabled.

With the geometry, mesh, boundary conditions, and physics models defined only

the solvers and stopping criteria need to be configured. The wall distance solver is

automatically included in all models with turbulence and calculates the distance from the

centroid of the mesh cells to the nearest wall; its default configuration does not need to

be altered. The CFM combustion solver updates the solution obtained by the coherent

flame model as it iterates. This solver’s under-relaxation factor property allows the user

to set the degree that the previous solution is replaced by the newly calculated solution

in the next iteration. A factor of 1 would completely replace the previous solution

whereas a factor of 0 would not allow any update of the combustion solution. It is not

necessary to change the under-relaxation factor from its default value of 0.9 because, to


Updated 12/1/2012 27

create the initial flow field, the solver frozen property is enabled to prevent combustion

from occurring while the flow is still stabilizing.

The coupled implicit solver uses a time marching procedure to update the

solution for the coupled flow and energy models by implicitly integrating the linearized

transport equations. The Courant number controls the size of the local time-steps used

for iteration of the solver and its value must be selected carefully to ensure smooth

reduction and convergence of the residuals which measure the degree to which the

discretized flow and energy equations are satisfied. A residual of zero would indicate

perfect agreement. As the steady time model was enabled, a pseudo time-step is

computed local to each cell so the converged solution is representative of a stable, non-

transient flow with the rate of convergence dependent on the Courant number. To

create the initial flow field a Courant number of 5 is suitable.

The k-ɛ turbulence and k-ɛ turbulent viscosity solvers are present due to the

inclusion of the standard k-ɛ turbulence physics model and control the update of the

turbulent kinetic energy, its rate of dissipation, and the turbulent viscosity fields. As with

the combustion solver, an under-relaxation factor controls the portion of the new solution

used in the update of the field after iterating. For smooth iteration, an under-relaxation

value of 0.7 for both solvers was practical. With the setup of these solvers complete, the

maximum number of steps under the stopping criteria is set to 1300 iterations and the

solution is initialized and then run.

After some number of iterations, the initial flow for the combusting case should

have stabilized resembling the first non-reacting test case and, the pressure and velocity

fields are close to the state anticipated in the ultimate solution. At this point, some of the

boundary conditions and physics models need to be modified in order to obtain a

solution with chemistry. The injection temperature of the premixed propellants is

reduced to 300 K although in an actual engine if the cryogenic propellants were fed

directly from the tank they would be closer to their liquid to gas phase transition

temperatures. They are injected here as room temperature gases to avoid the additional

complexity of injector design and modeling the multiphase mixing of the propellants.

In order to achieve successful convergence with this simulation the combustion

solver should not be enabled until after the coupled flow physics model has been

replaced with the segregated flow model. Despite the creation of the initial frozen flow,


Updated 12/1/2012 28

activating the coupled combustion solver may lead to the temperature near the inlet to

rapidly increase and diverge after only a few steps. This problem is solved by removing

the coupled flow and coupled energy models from the enabled models list and adding

the segregated flow model. The segregated fluid enthalpy model is added automatically.

With these changes the coupled flow and energy solvers are replaced by segregated

solvers. The segregated solver controls solution iteration using the SIMPLE algorithm

which updates the velocity, pressure, and energy separately.5 The default fluid under-

relaxation factor of 0.9 is used.

As long as none of the other physics models are disabled, the unburnt gas

components in the fluid stream manager will remain specified as 0.305 propylene and

0.695 oxygen mass fractions. As the flow will no longer be frozen, the fuel mass fraction

boundary condition at the inlet should be increased from 0.102 to 0.305. To ensure that

the combustion solver initializes correctly, an igniter must be created near the inlet in

addition to adjusting the boundary conditions at the inlet.

Since the gas in the combustion chamber is already above the ignition

temperature, if the ignitor method is set as “maximum of cell value or igniter constant”,

then the flame area density for the cells where the ignitor is defined to be triggered is set

to 500. It should be noted that the igniter uses a pulse method and only needs to be run

for 2 steps after iteration resumes. This means that the flame area density is only

temporarily a large value at the inlet for the purpose of initializing combustion. With the

modification of the setting complete the solver is again activated and the iteration

continues as depicted in figure 30 in the appendix.

5. Results & Analysis

After the initial and boundary conditions are defined and physics continua

configured for each test case, the simulation is run allowing the solver to iterate towards

a converged solution. The results from the simulation for each test case are detailed in

the following sections. In section 6.1 the first case, a non-reacting flow with heat transfer

neglected, is presented. Section 6.2 contains the results for case 2 where radiative heat

transfer was added to the simulation configuration of case 1. The results for test case 3,

where fuel film cooling was considered in addition to radiative heat transfer, are

discussed in section 6.3. Finally, in section 6.4, the results from modeling combustion in

test case 4 are described and some analysis is performed to validate the output from


Updated 12/1/2012 29

STAR-CCM+.

5.1. Case 1: Non-Reacting Without Heat Transfer

For this first case, the flow is modeled without considering film cooling,

combustion, or heat transfer. Instead, the products of the reaction are injected at the

combustion temperature of approximately 3500 K and the simulation was iterated until

achieving convergence with the fluid properties determined from NASA CEA listed

above in Table 3.

Only 1024 iterations were required to obtain a converged solution for test case 1.

The total solver CPU time was 2100 seconds. Allowing the solver to iterate further is not

necessary for the purposes of this study but continuing to run the solver after achieving

convergence only minimally decreases the residuals and has almost no effect on the

properties of the flow.

Figures 7, 8, and 9 depict the Mach number, pressure, and temperature fields

respectively. These results are close to the values listed in Table 2 expected from

performing the calculations with the 1 dimensional isentropic flow equations with some

minor exceptions. The Mach number along the centerline is 0.103 at the inlet, 1 at the

nozzle throat, and 3.25 at the outlet. The nozzle exit Mach number is slightly higher than

the 2.98 value predicted by the 1-D equations and the exit pressure is lower at 28 kPa

versus the predicted 41 kPa. Additionally the exit temperature was slightly lower than

expected with a value of 1597 K.

Figure 7: Mach number field for case 1


Updated 12/1/2012 30

Figure 8. Pressure field for case 1

Figure 9. Temperature field for case 1

Without heat transfer or combustion, the variation of the wall temperature is due

solely to isentropic expansion of the flow. In Figure 10 the temperature at the control

volume’s interface with the nozzle is plotted as a function of the distance from the inlet.

The lowest temperature along the wall is 2500 K at the exit. With only the minimum level

of complexity implemented in the problem setup, Case 1 can only yield a rough, over-

conservative model of the wall temperature.


Updated 12/1/2012 31

Figure 10: Temperature at CV wall interface without heat transfer

5.2. Case 2: Non-Reacting flow with radiative heat transfer

A non-reacting flow with radiative heat transfer through the wall but no film cooling is

then considered for Case 2. This case’s configuration is identical to case 1 except for the

inclusion of a radiative heat transfer physics model as discussed in section 4.3. The

solver converged after 947 steps but the total CPU time for the run was 3623 seconds.

The inclusion of the radiation model increased the time required per iteration from 2.4 s

to 3.9 s.

The Mach number field in Figure 11 and pressure field in Figure 12 are nearly

identical for the results obtained in Case 1. However, in figure 14 the temperature of the

wall was determined along with that of the flow. The 3000 K value for the inner wall

temperature seen near the inlet in Figure 14 is not realistic since, unlike here where we

inject the propellants fully burnt at the combustion temperature, the propellants would be

injected at cryogenic conditions and the combustion would take place some distance

downstream. From the results, a value of 2500-2600 K would probably be closer to

reality, with a subsequent increase in temperature at the throat as depicted. These high


Updated 12/1/2012 32

temperatures at the wall do present a problem as the CMC nozzle is vulnerable to burn-

through above about 1923 K for extended periods.15

Figure 11: Mach number field for case 2

Figure 12: Pressure field for case 2

Figure 13: Temperature of flow and wall for case 2

With heat transfer enabled, the thruster’s exterior surface is cooler than its

interior one where it contacts the flow within the control volume. In figure 14, the internal

and external wall temperature is plotted as a function of the distance along the nozzle’s


Updated 12/1/2012 33

central axis. It is notable that by merely including heat transfer, which does not require

any modification to the nozzle’s geometry or the injection of the flow, the maximum

temperature encountered at the CV / nozzle interface decreases 500 K.

Figure 14: Inner and outer wall Temperature with radiation physics model enabled

5.3. Case 3: Non-Reacting With Heat Transfer And Film Cooling

For Case 3, a frozen flow with heat transfer (Case 2) with the addition of fuel film

cooling is considered. The core flow is injected at 3500K and the fuel film cooling

injection temperature is 300 K. The core flow is made up of the fully reacted combustion

products and only fuel is injected near the wall. The injection mass flow rate was

selected so that the overall oxidizer to fuel ratio at the inlet was 2.27 with 11.9% of the

fuel injected in the film cooling layer. The FFC layer was injected with a thickness of

1.25 mm extending from the wall and a mass flow rate 0.034 kg/s or about 3.7 % of the

total 0.925 kg/s mass flow rate.

Test case 3 was the most computationally expensive of the 3 non-reacting cases

considered. The solver converged after 1050 iterations or 5372 seconds of CPU time or

5.1 seconds per iteration. Adding an additional boundary to inject the FFC layer did


Updated 12/1/2012 34

increase the time required to obtain a converged solution but the addition of the radiation

physics model in case 2 had the most significant impact in terms of computational cost.

While no combustion was modeled, this case demonstrates STAR-CCM+’s

capability to model convection from the flow, conduction through the nozzle wall, and

radiation out to the exterior. While the pressure and Mach number fields in figures 16

and 17 show little change when compared with Cases 1 & 2, it is clear in figure 15 that

the maximum temperature encountered by the wall has been significantly reduced by the

addition of FFC. Figure 18 depicts the mixing of the film cooling layer with the core flow

as the field of the mass fraction of the combusted gas. It is clear that the fuel film

cooling layer stays near the wall as the flow progresses downstream as desired.

Figure 15. Temperature of the flow and nozzle with film cooling

Figure 16. Pressure through the flow


Updated 12/1/2012 35

Figure 17. Mach number throughout the flow

Figure 18. Mass fraction of combustion gas showing mixing of the film cooling layer with

the core flow

With the inclusion of FFC and heat transfer, the temperature of the interior of the

combustion chamber wall at the inlet is lower than the exterior temperature. The internal

and external temperatures are plotted in figure 19 as a function of the distance along the

x axis or from the inlet. The maximum temperature experienced by the nozzle is about

2400K, 500 K lower than the temperature at which the CMC’s SiC matrix will begin to

sublimate although still significantly higher than the burn through temperature for steady

state operations. Since the core flow is still injected at 3500 K and combustion is not

modeled for Case 3, injecting 11.9% of the fuel as a FFC layer may be further reduced if

the goal is to maintain a wall temperature less than 2400K since the frozen flow model

should lead to an over prediction of the wall temperature.


Updated 12/1/2012 36

Figure 19: Temperature at CV wall interface with radiation and fuel film cooling

5.4. Case 4: Reacting Flow

In the last case considered, the flow is allowed to react using the coherent flame

combustion model discussed in Sect. 5. The combustion reaction is treated as a single

step process so the only products of the combustion of the propylene and oxygen are

carbon dioxide and water. Additionally, as discussed in Sect. 5.2, a bluff body must be

included in the geometry in order to cause circulation leading to a, injection velocity that

is lower than the flame speed of the reaction.

The CFM combustion model must be disabled while completing the first 1300

iterations of the solver because, as noted in section 5.3, a developed, frozen flow must

be present prior to initializing the combustion solver to avoid divergence. The total CPU

time required to converge case 4 is 6523 seconds after 7000 iterations although after

about 3500 iterations the residuals vary minimally in a cyclic manner as seen in Figure

30. The combustion test case required less CPU time per iteration because the mesh

used was 2 dimensional and axisymmetric rather than the 3 dimensional wedge mesh

used for the first 3 test cases.


Updated 12/1/2012 37

In figures18 and 19, the pressure and Mach number fields are within expectations

however the temperature field in figure 7 is substantially different from the values

predicted by the isentropic flow equations. Because only a single step reaction is

considered the code over predicts the combustion temperature by about 1500K.

Although this result is not representative of the actual phenomena of combustion, it is

valid for a single step reaction that yields only carbon dioxide and water as discussed in

the next section.

Figure 20: Case 4 pressure profile

Figure 21: Case 4 temperature field

Figure 22: Case 4 Mach number field


Updated 12/1/2012 38

5.4.1. Verification of temperature prediction for Case 4

Hess’s law is used in order to verify that the resulting maximum combustion

temperature of 4884 K is valid for the single step reaction that the CFM is constrained to.

The law states that the heat of reaction is equivalent to the sum of the heat of formation

of the products multiplied by their mole fraction minus the sum of the heat of formation of

the reactants multiplied by their respective mole fractions as in equation 11.

Hess’s Law

reactsfrproductsfprxn HnHnH ,, (11)

(12)

Table 9. Standard Heat of Formation for species considered

Species

Standard Heat of

Formation

Carbon dioxide (CO2) -393.522 kJ/mol

Oxygen (O2) 0 kJ/mol

Water vapor (H2O) -241.93 kJ/mol

Propylene (C3H6) 20.43 kJ/mol

Carbon monoxide (CO) -110.6 kJ/mol

Hydrogen Gas (H2) 0 kJ/mol

Hydroxyl (OH) 37.1 kJ/mol

Monatomic Hydrogen (H) 216 kJ/mol

Monatomic Oxygen (O) 246.8 kJ/mol

Table 10 lists the heat of formation, H, for the species considered for the purpose

of finding the heat of both the single step reaction and a reaction where 7 reaction

products are produced. The mole fractions for the reactants, nr, in both cases are 0.251

and 0.749 for propylene and oxygen respectively corresponding to the 2.27 o/f ratio

specified previously in this study. The mole fractions for the products, np, used in the

complex chemistry case are listed in appendix 8.2. Only the 7 most abundant products

and the 2 reactants are included. The product mole fractions for the single step reaction

are 0.078, 0.461, and 0.461 for the propylene, carbon dioxide and water respectively.


Updated 12/1/2012 39

With the heat of the reaction found from the calculation performed via equation

11, equation 12 allows the combustion temperature to be determined as the mole

fraction and specific heat as a function of temperature for the reactants and the products

are all known. The concept behind equation 12 is that the path of the reaction can be

broken down into 3 steps. First, the amount of energy released by the reactants when

cooled down to standard conditions is determined. Next reacting at standard conditions

the known heat of reaction is released. Finally, the heat required to raise the products

from standard temperature to the combustion temperature is found.

Using the thermodynamic polynomial coefficients from the STAR-CCM+

database, the specific heat as a function of temperature was integrated and evaluated

for both the decrease of the reactants from their initial temperature of 300 K to standard

temperature and the rise of the products from standard temperature to the combustion

temperature. The calculation was performed in a spreadsheet for both the single step

reaction (that of Sect. 5) and for a reaction where the 7 most abundant products from the

CEA2 model were considered including CO2, H2O, CO, OH, H2, O, and H. Additional

species were neglected in the latter case because CEA2 determined their presence to

be minute. The molar quantities for both the reactants and products were determined.

Coefficients for the specific heat polynomials for each species are also included so that

equation 12 can be evaluated numerically. The lower and upper bounds of the integral

extend from the injection to the combustion temperature respectively. As the polynomial

coefficients are provided for 2 ranges with a discontinuity at 1000 K, the specific heat

functions for each species are integrated from the injection temperature to 1000 K with

the low temperature coefficients and from 1000 k to the combustion temperature with the

high temperature coefficients.

With the contribution to the change in enthalpy of each individual product and

reactant now known, the quantities were summed to find the total enthalpy of the

reaction. The rxnH determined with equation 11 and 12 will be equal to each other if

the appropriate combustion temperature is substituted into equation12. To find this

temperature the Excel goal seek function was utilized.

The goal seek function allows a given cell to be set to a defined value by

changing another cell that the original one is dependent on. In this case, the cell that

must be modified is the location of the combustion temperature which the enthalpy

change is dependent on. The goal seek function will quickly iterate to find a combustion


Updated 12/1/2012 40

temperature where rxnH is correct but care must be taken to ensure the result is valid;

the goal seek algorithm is fairly robust but a very far off initial guess value can cause the

function to either fail or iterate towards another valid but physically meaningless solution.

This problem was avoided by running the goal seek algorithm multiple times with

a range of initial guesses. Using the spreadsheet a combustion temperature of 4876 K

was determined for the single step reaction. This was very close to the value found with

STAR-CCM+ of 4884 K. Adding 6 more species to the combustion gas’ composition in

the spreadsheet caused the combustion temperature to converge on 3560 K. This

value was much closer to the 3492 K predicted with CEA2.

Westbrook stated that when the assumption is made that the product of

hydrocarbon combustion is carbon dioxide and water the heat of the reaction and

consequently the combustion temperature will be over predicted.11 At present, the

coherent flame model included with STAR-CCM+ can only handle single step reactions

so additional methods should be considered. One example of an approach that would

be compatible with the engine considered in this study is an engine with 4 inlets for the

injection of pentane and liquid oxygen by Pandey and Yadav.12

Although the pentane fueled motor was simulated in Fluent the procedure used

could potentially be valid for STAR-CCM+ as well. For this rocket engine, the

combustion was modeled using the mixture fraction approach by injecting the

propellants unmixed and using a segregated solver. Rather than 2 products of

combustion the pentane engine simulation included 9 products or 11 total species in the

multiphase mixture. The mixture fraction tracks the oxidizer to fuel ratio locally to each

element in the model which are then substituted into a discretized transport equation. In

STAR-CCM+, the presumed probability distribution function (PPDF) model allows

simulation of a non-premixed, multi-component, reactive flow similar to the Fluent

mixture fraction model.

To run the PPDF model a PPDF equilibrium table must be created containing

information on the reactions and species required to run the model. By assuming that

the diffusion rates of the flow species are identical the mass fraction, density, and

temperature for each element in the control volume are determined by and equilibrium

routine. This routine requires an equilibrium table that contains information on the


Updated 12/1/2012 41

species and reactions required by the PPDF model which can either be created or

imported.

The PPDF look-up table can be created with the Digital Analysis of Reaction

Systems (DARS) package which was produced by LOGE AB and CD Adapco. DARS

generates the table by solving for the balance between diffusion and reaction as a

function of the dissipation rate and the mixture fraction. Any given flow variable can then

be expressed as a function of the mixture fraction and scalar dissipation rate.

5.4.2. Validation of Flow Field Predictions

Due to the assumption that the oxidizer and fuel are perfectly premixed and are

injected uniformly and normal to the inlet, a prism was inserted into the center of the

combustion chamber to act as a bluff body and create circulation as discussed in Sect.

5.2. The combustion simulation will not converge without the inclusion of the bluff body

because the circulation lowers the inlet velocity below the reaction’s flame speed. To

determine the influence of the prism on the flow the streamlines for the both the frozen

and reacting models are presented in figure 23. Circulation occurs immediately

downstream of the bluff body but adequate results are still obtained. The circulating

region ends prior to the flows entrance to the converging portion of the nozzle.

Figure 23: Streamlines for the original and modified control volume


Updated 12/1/2012 42

In figure 24, the recirculation region is depicted as a plot of the velocity vector

field. Additional length was added to the inlet to insure that the prism was placed far

enough upstream from the nozzle throat to contain the circulating vortex within the

combustion chamber. The behavior of both flows is similar beginning at the

convergence of the nozzle and continuing downstream. The model remains adequate

after the inclusion of the prism and no further modifications to the geometry of the frozen

cases were necessary to achieve convergence for case 4.

Figure 24: Recirculation downstream of the bluff body

6. Conclusion

6.1. Summary

In this work, the implementation and results of 4 simulations are presented which

demonstrate the capability of CD-Adapco’s STAR-CCM+ code at modeling heat transfer,

fuel film cooling, and combustion for a high speed flow inside a rocket nozzle. Several

assumptions had to be made in order to reduce the complexity of the modeling. The

material properties of the nozzle wall were considered isotropic; it was assumed that the

flow was injected in a premixed manner and that it was already in the gas phase at


Updated 12/1/2012 43

injection; and it was necessary to assume that the reaction yielded only 2 combustion

products which lead to an over prediction of the combustion temperature.

The first case simply verified that the behavior of a frozen flow matched the analytical

predictions made for a one dimensional isentropic flow. The second case included heat

transfer to the nozzle wall and radiation to the exterior and the third case added the

injection of a fuel film cooling layer to the setup of the second case.

To avoid the added complexity of designing an injector for the combustion

simulation, a bluff body had to be included near the inlet to introduce circulation and slow

the flow velocity to less than the flame speed at the chamber pressure. Of the

assumptions made in order to create a simulation that can be feasibly implemented, the

coherent flame model’s requirement of a single step reaction was the most detrimental

to obtaining results that are consistent with expectations of the behavior of the actual

physical phenomena because of the resulting over prediction of the combustion

temperature.

6.2. Extending the Model Further

One option for further study of this problem would be to use CD-ADAPCO’s DARS-

CFD code to create a complex chemistry definition file for use with the homogenous

reactor combustion model. This would allow results to be obtained that are more in line

with expectations for the behavior of the actual physical phenomena as many more

steps and products would be considered during the reaction. Without a complex

chemistry definition the code is limited to using simplified reaction mechanisms which

will over predict the combustion temperature.

Another avenue for further investigation is rather than using a bluff body, the next

step would be to include the injector spray pattern in the simulation by capturing the

turbulent mixing of the propellants as they are injected. It would also be useful to model

the propellants as a liquid during injection to capture their atomization and mixture in

addition to the reaction, but this latter approach would be much more involved.


Updated 12/1/2012 44

7. Appendices

7.1. Supplementary Figures, Tables, and Output

Figure 25. Nozzle Isometric view, dimensions in meters

7.2. CEA 2 Output

*******************************************************************************

NASA-GLENN CHEMICAL EQUILIBRIUM PROGRAM CEA2, MAY 21, 2004

BY BONNIE MCBRIDE AND SANFORD GORDON

REFS: NASA RP-1311, PART I, 1994 AND NASA RP-1311, PART II, 1996

*******************************************************************************

problem case=1002

rocket fac ac/at=5.48 tcest,k=3518

p,psia=300,

pi/p=53.121,


Updated 12/1/2012 45

sup,ae/at=8.02,

react

fuel=C3H6(L),propyle wt=1 t,k=225.6

oxid=O2(L) wt=2.27 t,k=90.17

output

siunits

end

OPTIONS: TP=F HP=F SP=F TV=F UV=F SV=F DETN=F SHOCK=F REFL=F INCD=F

RKT=T FROZ=F EQL=T IONS=F SIUNIT=T DEBUGF=F SHKDBG=F DETDBG=F TRNSPT=F

TRACE= 0.00E+00 S/R= 0.000000E+00 H/R= 0.000000E+00 U/R= 0.000000E+00

Pc,BAR = 20.684191

Pc/P = 53.1210

SUBSONIC AREA RATIOS = 5.4800

SUPERSONIC AREA RATIOS = 8.0200

NFZ= 1 Mdot/Ac= 0.000000E+00 Ac/At= 5.480000E+00

REACTANT WT.FRAC (ENERGY/R),K TEMP,K DENSITY

EXPLODED FORMULA

F: C3H6(L),propyle 1.000000 -0.325215E+03 225.60 0.0000

C 3.00000 H 6.00000

O: O2(L) 1.000000 -0.156101E+04 90.17 0.0000

O 2.00000

SPECIES BEING CONSIDERED IN THIS SYSTEM

(CONDENSED PHASE MAY HAVE NAME LISTED SEVERAL TIMES)

LAST thermo.inp UPDATE: 9/09/04

g 7/97 *C tpis79 *CH g 4/02 CH2

g 4/02 CH3 g11/00 CH2OH g 7/00 CH3O

g 8/99 CH4 g 7/00 CH3OH srd 01 CH3OOH

tpis79 *CO g 9/99 *CO2 tpis91 COOH

tpis91 *C2 g 6/01 C2H g 1/91 C2H2,acetylene

g 5/01 C2H2,vinylidene g 4/02 CH2CO,ketene g 3/02 O(CH)2O

srd 01 HO(CO)2OH g 7/01 C2H3,vinyl g 6/96 CH3CO,acetyl

g 1/00 C2H4 g 8/88 C2H4O,ethylen-o g 8/88 CH3CHO,ethanal

g 6/00 CH3COOH srd 01 OHCH2COOH g 7/00 C2H5

g 7/00 C2H6 g 8/88 C2H5OH g 7/00 CH3OCH3

srd 01 CH3O2CH3 g 8/00 C2O tpis79 *C3

n 4/98 C3H3,1-propynl n 4/98 C3H3,2-propynl g 2/00 C3H4,allene

g 1/00 C3H4,propyne g 5/90 C3H4,cyclo- g 3/01 C3H5,allyl

g 2/00 C3H6,propylene g 1/00 C3H6,cyclo- g 6/01 C3H6O,propylox

g 6/97 C3H6O,acetone g 1/02 C3H6O,propanal g 7/01 C3H7,n-propyl

g 9/85 C3H7,i-propyl g 2/00 C3H8 g 2/00 C3H8O,1propanol

g 2/00 C3H8O,2propanol g 7/88 C3O2 g tpis *C4

g 7/01 C4H2,butadiyne g 8/00 C4H4,1,3-cyclo- n10/92 C4H6,butadiene

n10/93 C4H6,1butyne n10/93 C4H6,2butyne g 8/00 C4H6,cyclo-

n 4/88 C4H8,1-butene n 4/88 C4H8,cis2-buten n 4/88 C4H8,tr2-butene

n 4/88 C4H8,isobutene g 8/00 C4H8,cyclo- g10/00 (CH3COOH)2

n10/84 C4H9,n-butyl n10/84 C4H9,i-butyl g 1/93 C4H9,s-butyl

g 1/93 C4H9,t-butyl g12/00 C4H10,n-butane g 8/00 C4H10,isobutane

g 8/00 *C5 g 5/90 C5H6,1,3cyclo- g 1/93 C5H8,cyclo-

n 4/87 C5H10,1-pentene g 2/01 C5H10,cyclo- n10/84 C5H11,pentyl

g 1/93 C5H11,t-pentyl n10/85 C5H12,n-pentane n10/85 C5H12,i-pentane

n10/85 CH3C(CH3)2CH3 g 2/93 C6H2 g11/00 C6H5,phenyl

g 8/00 C6H5O,phenoxy g 8/00 C6H6 g 8/00 C6H5OH,phenol

g 1/93 C6H10,cyclo- n 4/87 C6H12,1-hexene g 6/90 C6H12,cyclo-


Updated 12/1/2012 46

n10/83 C6H13,n-hexyl g 6/01 C6H14,n-hexane g 7/01 C7H7,benzyl

g 1/93 C7H8 g12/00 C7H8O,cresol-mx n 4/87 C7H14,1-heptene

n10/83 C7H15,n-heptyl n10/85 C7H16,n-heptane n10/85 C7H16,2-methylh

n 4/89 C8H8,styrene n10/86 C8H10,ethylbenz n 4/87 C8H16,1-octene

n10/83 C8H17,n-octyl n 4/85 C8H18,n-octane n 4/85 C8H18,isooctane

n10/83 C9H19,n-nonyl g 3/01 C10H8,naphthale n10/83 C10H21,n-decyl

g 8/00 C12H9,o-bipheny g 8/00 C12H10,biphenyl g 6/97 *H

g 1/01 HCO g 6/01 HCCO g 4/02 HO2

tpis78 *H2 g 5/01 HCHO,formaldehy g 6/01 HCOOH

g 8/89 H2O g 6/99 H2O2 g 6/01 (HCOOH)2

g 5/97 *O g 4/02 *OH tpis89 *O2

g 8/01 O3 n 4/83 C(gr) n 4/83 C(gr)

n 4/83 C(gr) g11/99 H2O(cr) g 8/01 H2O(L)

g 8/01 H2O(L)

O/F = 2.270000

EFFECTIVE FUEL EFFECTIVE OXIDANT MIXTURE

ENTHALPY h(2)/R h(1)/R h0/R

(KG-MOL)(K)/KG -0.77285315E+01 -0.48783267E+02 -0.36228302E+02

KG-FORM.WT./KG bi(2) bi(1) b0i

*C 0.71293216E-01 0.00000000E+00 0.21802207E-01

*H 0.14258643E+00 0.00000000E+00 0.43604414E-01

*O 0.00000000E+00 0.62502344E-01 0.43388477E-01

POINT ITN T C H O

1 22 3492.230 -15.173 -10.200 -16.339

2 2 3487.473 -15.198 -10.215 -16.350

Pinf/Pt = 1.734685

3 4 3307.129 -15.442 -10.394 -16.666

Pinf/Pt = 1.733544

3 2 3307.339 -15.441 -10.394 -16.665

4 2 3484.966 -15.201 -10.218 -16.354

4 2 3485.191 -15.201 -10.218 -16.353

4 1 3485.181 -15.201 -10.218 -16.353

2 2 3491.331 -15.178 -10.203 -16.341

Pinf/Pt = 1.734811

3 4 3310.364 -15.421 -10.381 -16.657

Pinf/Pt = 1.733683

3 2 3310.573 -15.420 -10.381 -16.657

4 2 3488.816 -15.181 -10.206 -16.345

4 2 3489.042 -15.181 -10.205 -16.345

4 1 3489.032 -15.181 -10.205 -16.345

END OF CHAMBER ITERATIONS

4 6 2199.207 -15.544 -11.303 -20.527

5 3 2168.565 -15.492 -11.319 -20.705

5 3 2193.497 -15.535 -11.306 -20.559

THEORETICAL ROCKET PERFORMANCE ASSUMING EQUILIBRIUM

COMPOSITION DURING EXPANSION FROM FINITE AREA COMBUSTOR

Pin = 300.0 PSIA

Ac/At = 5.4800 Pinj/Pinf = 1.006762

CASE = 1002

REACTANT WT FRACTION ENERGY TEMP

(SEE NOTE) KJ/KG-MOL K

FUEL C3H6(L),propyle 1.0000000 -2704.000 225.600


Updated 12/1/2012 47

OXIDANT O2(L) 1.0000000 -12979.000 90.170

O/F= 2.27000 %FUEL= 30.581040 R,EQ.RATIO= 1.507465 PHI,EQ.RATIO=

1.507465

INJECTOR COMB END THROAT EXIT EXIT

Pinj/P 1.0000 1.0137 1.7454 53.121 53.990

P, BAR 20.684 20.405 11.851 0.38938 0.38311

T, K 3492.23 3489.03 3310.57 2199.21 2193.50

RHO, KG/CU M 1.5262 0 1.5072 0 9.3527-1 4.8718-2 4.8062-2

H, KJ/KG -301.22 -310.47 -1022.31 -4533.28 -4546.23

U, KJ/KG -1656.50 -1664.37 -2289.40 -5332.53 -5343.35

G, KJ/KG -43104.2 -43083.4 -41607.4 -31493.9 -31436.8

S, KJ/(KG)(K) 12.2566 12.2592 12.2592 12.2592 12.2592

M, (1/n) 21.425 21.427 21.724 22.878 22.880

(dLV/dLP)t -1.03693 -1.03688 -1.03004 -1.00122 -1.00119

(dLV/dLT)p 1.6537 1.6535 1.5616 1.0323 1.0315

Cp, KJ/(KG)(K) 6.6457 6.6480 6.1625 2.3436 2.3358

GAMMAs 1.1399 1.1399 1.1382 1.1962 1.1967

SON VEL,M/SEC 1243.0 1242.3 1200.9 977.8 976.7

MACH NUMBER 0.000 0.109 1.000 2.975 2.983

TRANSPORT PROPERTIES (GASES ONLY)

CONDUCTIVITY IN UNITS OF MILLIWATTS/(CM)(K)

VISC,MILLIPOISE 1.0614 1.0607 0.0226 0.76711 0.76569

WITH EQUILIBRIUM REACTIONS

Cp, KJ/(KG)(K) 6.6457 6.6480 6.1625 2.3436 2.3358

CONDUCTIVITY 16.3050 16.3037 14.6036 3.4646 3.4363

PRANDTL NUMBER 0.4326 0.4325 0.4315 0.5189 0.5205

WITH FROZEN REACTIONS

Cp, KJ/(KG)(K) 2.1070 2.1068 2.0966 1.9906 1.9897

CONDUCTIVITY 3.6408 3.6379 2.4575 3.3596 2.3541

PRANDTL NUMBER 0.6142 0.6143 0.6201 0.6471 0.6472

PERFORMANCE PARAMETERS

Ae/At 5.4800 1.0000 7.9244 8.0200

CSTAR, M/SEC 1829.2 1829.2 1829.2 1829.2

CF 0.0743 0.6565 1.5905 1.5929

Ivac, M/SEC 10091.9 2256.0 3184.0 3187.3

Isp, M/SEC 136.0 1200.9 2909.3 2913.8

MOLE FRACTIONS

*CO 0.36874 0.36870 0.36699 0.34978 0.34961

*CO2 0.09834 0.09842 0.10662 0.14902 0.14922

COOH 0.00001 0.00001 0.00000 0.00000 0.00000

*H 0.04619 0.04617 0.03946 0.00352 0.00344

HCO 0.00002 0.00002 0.00001 0.00000 0.00000

HO2 0.00003 0.00003 0.00002 0.00000 0.00000

*H2 0.13073 0.13073 0.13067 0.15286 0.15308

H2O 0.28824 0.28835 0.30295 0.34356 0.34343

*O 0.00957 0.00955 0.00671 0.00002 0.00002

*OH 0.05001 0.04991 0.04052 0.00123 0.00119

*O2 0.00812 0.00811 0.00604 0.00002 0.00002


Updated 12/1/2012 48

* THERMODYNAMIC PROPERTIES FITTED TO 20000.K

PRODUCTS WHICH WERE CONSIDERED BUT WHOSE MOLE FRACTIONS

WERE LESS THAN 5.000000E-06 FOR ALL ASSIGNED CONDITIONS

*C *CH CH2 CH3 CH2OH

CH3O CH4 CH3OH CH3OOH *C2

C2H C2H2,acetylene C2H2,vinylidene CH2CO,ketene O(CH)2O

HO(CO)2OH C2H3,vinyl CH3CO,acetyl C2H4 C2H4O,ethylen-

o

CH3CHO,ethanal CH3COOH OHCH2COOH C2H5 C2H6

C2H5OH CH3OCH3 CH3O2CH3 C2O *C3

C3H3,1-propynl C3H3,2-propynl C3H4,allene C3H4,propyne C3H4,cyclo-

C3H5,allyl C3H6,propylene C3H6,cyclo- C3H6O,propylox C3H6O,acetone

C3H6O,propanal C3H7,n-propyl C3H7,i-propyl C3H8

C3H8O,1propanol

C3H8O,2propanol C3O2 *C4 C4H2,butadiyne C4H4,1,3-

cyclo-

C4H6,butadiene C4H6,1butyne C4H6,2butyne C4H6,cyclo- C4H8,1-butene

C4H8,cis2-buten C4H8,tr2-butene C4H8,isobutene C4H8,cyclo- (CH3COOH)2

C4H9,n-butyl C4H9,i-butyl C4H9,s-butyl C4H9,t-butyl C4H10,n-butane

C4H10,isobutane *C5 C5H6,1,3cyclo- C5H8,cyclo- C5H10,1-

pentene

C5H10,cyclo- C5H11,pentyl C5H11,t-pentyl C5H12,n-pentane C5H12,i-

pentane

CH3C(CH3)2CH3 C6H2 C6H5,phenyl C6H5O,phenoxy C6H6

C6H5OH,phenol C6H10,cyclo- C6H12,1-hexene C6H12,cyclo- C6H13,n-hexyl

C6H14,n-hexane C7H7,benzyl C7H8 C7H8O,cresol-mx C7H14,1-

heptene

C7H15,n-heptyl C7H16,n-heptane C7H16,2-methylh C8H8,styrene

C8H10,ethylbenz

C8H16,1-octene C8H17,n-octyl C8H18,n-octane C8H18,isooctane C9H19,n-nonyl

C10H8,naphthale C10H21,n-decyl C12H9,o-bipheny C12H10,biphenyl HCCO

HCHO,formaldehy HCOOH H2O2 (HCOOH)2 O3

C(gr) H2O(cr) H2O(L)

NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS

7.3. Thermodynamic Polynomial Data

Table 10. Specific Gas Constant, R, for figure 5 through 9

Specific Gas Constant J/(kg*K)

Mol. Weight kg/kmol


Oxygen (O2) 259.8 31.9988

Water vapor (H2O) 461.5 18.01528

Propylene (C3H6) 197.587 42.08


Updated 12/1/2012 49

Figure 26. NIST and default specific heat of oxygen at 2.068 MPa

Figure 27. NIST and default specific heat of propylene at 2.068 MPa


Updated 12/1/2012 50

Figure 28. NIST and default specific heat of carbon dioxide at 2.068 MPa

Figure 29. NIST and default specific heat of water at 2.068 MPa


Updated 12/1/2012 51

Table 11. Gas Properties for Reactants and Products

The default coefficients for the species are listed with the values to be changed highlighted:

Oxygen

[3.21294, 0.0011274899999999999, -5.75615E-7, 1.31388E-9, -8.76855E-13, -1005.25, 6.03474,

3.69758, 6.1352E-4, -1.25884E-7, 1.77528E-11, -1.13644E-15, -1233.93, 3.18917]

Propylene

[1.49331, 0.0209252, 4.48679E-6, -1.66891E-8, 7.15815E-12, 1074.83, 16.1453,

6.73226, 0.0149083, -4.9499E-6, 7.21202E-10, -3.7662E-14, -923.57, -13.3133]

CO2

[2.27572, 0.00992207, -1.04091E-5, 6.86669E-9, -2.11728E-12, -48373.1, 10.1885,

4.45362, 0.00314017, -1.27841E-6, 2.394E-10, -1.66903E-14, -48967.0, -0.955396]

H2O

[3.38684, 0.00347498, -6.3547E-6, 6.96858E-9, -2.50659E-12, -30208.1, 2.59023,

2.67215, 0.00305629, -8.73026E-7, 1.201E-10, -6.39162E-15, -29899.2, 6.86282]

The new coefficients from the polynomials calculated in figures 3 through 6 are:

Oxygen

[5.2032, -1.1600E-02, 2.9537E-05, -2.9373E-08, 1.0454E-11, -1005.25, 6.03474, 3.69758,

6.1352E-4, -1.25884E-7, 1.77528E-11, -1.13644E-15, -1233.93, 3.18917]

Propylene

[2.3248E+02, -1.8502E+00, 5.7013E-03, -7.7107E-06, 3.8890E-09, 1074.83, 16.1453,

6.73226, 0.0149083, -4.9499E-6, 7.21202E-10, -3.7662E-14, -923.57, -13.3133]

CO2

[1.7468E+01, -8.4229E-02, 2.0441E-04, -2.0545E-07, 7.4503E-11, -48373.1, 10.1885,

4.45362, 0.00314017, -1.27841E-6, 2.394E-10, -1.66903E-14, -48967.0, -0.955396]

H2O

[1.1227E+02, - 5.5264E-01, 1.0567E-03, - 8.9120E-07, 2.8007E-10, -30208.1, 2.59023,

2.67215, 0.00305629, -8.73026E-7, 1.201E-10, -6.39162E-15, -29899.2, 6.86282]


Updated 12/1/2012 52

7.4. Convergence

Figure 30. The residuals converge for the combustion model. At 1300 iterations, the

reaction solver is enabled and the coupled solver is replaced with the segregated flow

solver.


Updated 12/1/2012 53

8. Works Cited

1. Verma & Gemba. (2009). Flight Testing of a Prototype LOX/propylene Upper

Stage Engine, CSU Long Beach, website:

http://kai.gemba.org/pdf/pub/Flight_LOXProp_Engin_A1.pdf

2. Stephen Joiner. (May 2011). The Mojave Launch Lab, Air & Space Magazine.

3. Noriko Cassman. (2009). Photo Credit. FAR Test Site.

4. McCall & Besnard. (2005). Validating C/SiC Composites For Liquid Bipropellant

Thrusters: Analysis Of A 500 LBF Thrust Lox/Propylene Rocket Engine, CSU

Long Beach.

5. CD-adapco, Star-CCM+ user guide, version 6.06.

6. Humble, Henry, and Larson (1995). Space Propulsion Analysis and Design. 1st

Edition-Revised, McGraw Hill.

7. Gordon & McBride. (1994). Computer Program for Calculation of Complex

Chemical Equilibrium Compositions and Applications, NASA Reference

Publication 1311.

8. Schlichting & Gersten. (2000). Boundary Layer Theory, 8th edition, Springer.

9. "Chemistry Web Book" website: http://webbook.nist.gov

10. Westbrook (1982).Simplified reaction mechanisms for the oxidation of

hydrocarbon fuels in flames, Journal of Combustion Science and Technology.

11. S. G. Davis, C. K. Law & H. Wang. (1999). Propene Pyrolysis and Oxidation

Kinetics in a Flow Reactor and Laminar Flames, Combustion and Flame.

12. Pandey & Yadav. (2010). CFD Analysis of a Rocket Nozzle with Four Inlets at

Mach 2.1. International Journal of Chemical Engineering Applications, Vol. 1, No.

4.


Updated 12/1/2012 54

13. R.J. Kee, F.M. Rupley, and J.A. Miller, Chemkin-III: A Fortran Chemical Kinetics Package for the Analysis of Gas-Phase Chemical Kinetics and Plasma Kinetics, Sandia Report SAND96-8216.UC-405, May 1996

14. Culick, Fred E. C. and Yang, Vigor, Liquid Rocket Engine Combustion Instability. Progress in Astronautics and Aeronautics, Volume (169). American Institute of Aeronautics and Astrophysics , Washington, DC, 1995

15. Stechman, Rupert ; Harper, Steve.(2010) Performance Improvements in Small Earth Storable Rocket Engines- An Era of Approaching the Theoretical. 46th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, Nashville, TN

fluid/thermal modeling of a lox/propylene thruster...

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