thesis draft7 introduction theory

8/13/2019 Thesis Draft7 Introduction Theory

1/36

EMBRY-RIDDLE AERONAUTICAL UNIVERSITY

Oxygen Methane Combustion

Simulation Towards Pollution FreeSolution For Industry and

Transportation

by

Arni Steingrimsson

A thesis submitted in partial fulfillment of the

degree of Master of Science

in the

Department of Aerospace Engineering

November 2012
http://www.erau.edu/http://localhost/var/www/apps/conversion/tmp/scratch_1/[email protected]://department%20of%20aerospace%20engineering.pdf/http://department%20of%20aerospace%20engineering.pdf/http://localhost/var/www/apps/conversion/tmp/scratch_1/[email protected]://www.erau.edu/


2/36

Declaration of Authorship

I, AUTHOR NAME, declare that this thesis titled, THESIS TITLE and the work

presented in it are my own. I confirm that:

This work was done wholly or mainly while in candidature for a research degree

at this University.

Where any part of this thesis has previously been submitted for a degree or any

other qualification at this University or any other institution, this has been clearly

stated.

Where I have consulted the published work of others, this is always clearly at-

tributed.

Where I have quoted from the work of others, the source is always given. With

the exception of such quotations, this thesis is entirely my own work.

I have acknowledged all main sources of help.

Where the thesis is based on work done by myself jointly with others, I have made

clear exactly what was done by others and what I have contributed myself.

Signed:

Date:

i


3/36

Write a funny quote here.

If the quote is taken from someone, their name goes here


4/36

EMBRY-RIDDLE AERONAUTICAL UNIVERSITY

Abstract

Combustion simulation of pure oxygen and pure methane using pulse injection was laid

out to investigate the combustion efficiency. The combustion system has some great

advantages over most common combustors as the fuel is inexpensive and the system can

be setup to produce zero emission. Validation of the combustion setup and numerics

was done with empirical data from Salgues et al. [1]. Initial results indicate that some

improvements are needed in mesh and combustion model.
http://www.erau.edu/http://www.erau.edu/


5/36

Acknowledgements

The acknowledgements and the people to thank go here, dont forget to include your

project advisor. . .

iv


6/36

Contents

Declaration of Authorship i

Abstract iii

Acknowledgements iv

List of Figures vii

List of Tables viii

Abbreviations ix

Physical Constants x

Symbols xi

1 Introduction 1

1.1 The System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Combustion Stability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.3 Combustion Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.4 Pulse Combustion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Governing Equations and Theory 6

2.1 Governing Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.1.1 Navier-Stokes Equation . . . . . . . . . . . . . . . . . . . . . . . . 7

2.1.2 Navier-Stokes Integral Equation . . . . . . . . . . . . . . . . . . . 9

2.1.3 Turbulence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.1.3.1 k Turbulence Model . . . . . . . . . . . . . . . . . . . 10

2.1.3.2 LES Turbulence Model . . . . . . . . . . . . . . . . . . . 11

2.1.4 Combustion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.1.4.1 Finite Rate Chemistry. . . . . . . . . . . . . . . . . . . . 12

2.1.4.2 Eddy Dissipation. . . . . . . . . . . . . . . . . . . . . . . 12

3 Method of solution 13

3.1 The Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

v


7/36

Contents vi

3.2 The Mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.3 Boundary Condition and Procedure . . . . . . . . . . . . . . . . . . . . . 17

3.3.1 Walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.3.2 Outlet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.3.3 Inlet Methane. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.3.4 Inlet Oxygen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.3.5 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

A Appendix Title Here 19

Bibliography 20


8/36

List of Figures

1.1 CES System. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Bladon Jet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.3 Natural gas prices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.4 Pulse Combustion Schematics . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.1 Flow Regime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3.1 Combustor Dimension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.2 Combustor inlet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.3 Combustor original . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.4 Combustor inlet length. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.5 Mesh. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

vii


9/36


10/36

Abbreviations

LAH List Abbreviations Here

ix


11/36

Physical Constants

Speed of Light c = 2.997 924 58 108 mss (exact)

x


12/36

Symbols

a distance m

P power W (Js1)

angular frequency rads1

xi


13/36

For/Dedicated to/To my. . .

xii


14/36

Chapter 1

Introduction

In times of depression it can be hard for businesses to justify buying green solutions,

which are most of the time more expensive. In stead the business tries to cut back and

it is natural to cut convenience before necessity. In the automotive industry the gasoline

engine is still the most popular fuel in the US even though Diesel is more efficient and

thus greener. Electric cars are getting more popular but they have a short range and

are expensive. The purpose of this study is to deliver a very efficient, inexpensive and

powerful combustion to be used in pollution free energy system.

1.1 The System

One of the most popular examples in many chemistry books, when reaction is being

discussed, is to use oxygen and hydrogen or oxygen and methane.

2H2+ O2 2H2O

or

CH4+ 2O2 CO2+ 2H2O

When combusting pure oxygen and pure methane the products are water and carbon

dioxide. At room temperature the two products are at different phases and it is a simple

process to separating them. This is the foundation for the pollution free combustion

system. Clean Energy Systems, Inc. along with Siemens Power Generation, Inc. and

Florida Turbine Technology, Inc. have tested and delivered a pollution free power plant

[4]. The heart of the system is the rocket like combustor. The concept can then be

expanded to other areas than just power plants, e.g. heavy machinery, ships and evencars as Bladon Jets has demonstrated with their micro turbine in Jaguar Limo [5].

1


15/36

Chapter 1. Chapter Title Here 2

Figure 1.1: Pollution free liquid rocket combustor power plant system made by CleanEnergy Systems

In this study the combustion chamber design is not like the traditional designs as seen

in most gas turbines. The design is much like a liquid rocket engine. In the past

most liquid rocket engine studies were focused on liquid oxygen and hydrogen as it

has the highest specific impulse [6]. Relatively recent, more emphasis has been gaining

for the liquid oxygen and methane studies. Methane has higher specific impulse than

kerosene, it is space storable, clean burning and has higher density [ 7]. Another reason

for more LOX/CH4 research attention is to use methane for human exploration of Marsas NASA at Marshall Space Flight Center has been testing LOX/CH4 injectors for [8].

Martin Marietta Corp showed also in 3 months that they could build a Mars In-Situ

propellant production unit. The unit would be able to produce methane and water from

the Maritian atmosphere [9]. With more research and test for space propulsion and

exploration it is hard to ignore the fact that the US has abundance of methane [10].

At last and one of the most important factor is that the price of Methane has been

relatively stable and low the past 40 years, see figure 1.3.


16/36


Figure 1.2: Micro turbine made by Bladon Jets are used as range extenders in up-coming Jaguar electric sport vehicles

Figure 1.3: Natural gas wellhead prices history of the past 40 years

1.2 Combustion Stability

The liquid oxygen and methane combustion stability or instability are of great impor-

tance for combustion chamber design. Rocketdyen performed numerous performance and

stability tests for NASA and results showed that many stability issues exist and more

research is needed to get full understanding[11]. The Academy of Equipment Command

& Technology performed numerical instability study on LOX/CH4 combustors and also

compared the combustion instability of LOX/H2. Low frequency instabilities are evidentwith LOX/CH4 combustion while high frequency instabilities are evident with LOX/H2


17/36


combustion. Use of baffle to control the instabilities does not have an effect on the low

frequencies as it does for the high frequencies in the LOX/H2 combustion. Extending

the combustion chamber has most dampening effect on the low frequency [12]. Experi-

mental and numerical study of combustion instability of LOX/H2 and LOX/HCH4 were

performed by the Institute of Command & Technology and the National University of

Defense Technology. Numerical models compare well with experiments. The results

show that increasing the velocity ratio suppress the instability. Optimum baffle ratio is

noticed but differ for the methane and hydrogen. Mass flow rate to chamber pressure

ratio seems to influence the combustion instability in a rectangular LOX/CH4 chamber

as noted by[13] and injection of nitrogen flow increases the pressure amplitude [14].

1.3 Combustion Models

In numerical analysis of combustion a good compromise between cost and accuracy can

be a key. Assumption of no droplets existing in truly supercritical environment using

dense gas proved successful for[15]. LES turbulence model was used to compute the

LOX/CH4 combustion at supercritical condition. Due to high Reynolds numbers the

Subgrid Scale model was computed using Fractal Model, developed by the group [15].

Simplifying the equation of state is not recommended and significant difference in results

can be expected [16]. Use of ideal gas will over-predict the temperature and pressure

[17]. Newer study shows good results using Peng-Robinson cubic equation of state and

modified subgrid chemistry is used to achieve realistic temperatures[18]. Assumption of

using calculated adiabatic flame temperature as the maximum temperature in LOX/CH4

non-premixed flames is not feasible[19]. Use of Lagrangian solver to model impingement,

droplet vaporization and combustion does not seem feasible and is not able to capture

the major flow mechanisms of LOX/CH4 combustion simulation [20].

1.4 Pulse Combustion

Unfortunately not much data is available for numerical simulation of pulsating com-

bustion[21] and none have been found using liquid oxygen. Pulse combustion has been

around for more than 75 years and its main usage has been in the area of drying [22,23].

There are many benefits of using pulsating combustors and they could proof superior

to existing designs. Some of the benefits include high thrust-to-weight ratio [24], very

high combustion efficiency [21], increased mass and heat transfer [22] and lower carbon

dioxide and nitrogen oxide emission [25]. Primary pollution prediction study was carried


18/36


out using simplified kinetic model derived from GRI-Mech3 and provided better results

than the detailed GRI-Mech2.11 [26].

Figure 1.4: Schematics of pulse combustion. Taken from reference: [27]

With all the benefits it is hard to believe that pulse combustion is not considered the

standard in combustion design. Other complexities in design and lack of understanding

has prevented its success and acceptance [28]. Experimental and numerical investiga-

tion of flow dynamics has been popular in recent years. Implementation of sub model

to simulate dynamic valve head proofs important [29] for accurate pulse combustion.

Successful flame testing methods have been investigated and will proof important for

future validation and understanding[30]. The flow effects in pulse combustors was stud-

ied using numerical models by[28] and the effects on the wall temperature and forcing

combustion frequency studied. Determination of the effect of air and fuel feed rate has

been studied and at least one of the feeding flow has to be modulated to achieve pulse

combustion[31]. In more recent application the use of pulsating rocket is being consid-

ered for hypersonic space planes. Study of pulse combustion in scramjet using ethyleneand kerosene has been tested and showed stable combustion for ethylene but not possible

for kerosene [32]. Another similar study showed that significant fuel savings is achieved

by using pulse combustor in supersonic vehicles[33]. Other research of pulse combustion

has been scaling analysis [34] and pulsating flow in axial turbine [35].


19/36

Chapter 2

Governing Equations and Theory

Computational fluid dynamics (CFD) is a tool used extensively in industry where it

can be used in fluid flow simulation of liquid fluids as well as fluid in gaseous phase.

Combustion and heat transfer are as well extensively used as it can be very expensive,

it could be illegal or even impossible to perform certain tests empirically. Another area

of use is in acoustic simulations just to name a few.

To represent the physics of flow, chemical reaction etc. the Navier Stokes equations are

used. The equations are partial differential equations named after the French mathe-

matician and civil engineer Claude Louis Navier (1758-1836) and the Irish physicist and

mathematician George Stokes (1819-1903). Navier was not able to arrive correctly to

his equation because he did not understand fully the shear stresses in fluids. Stokes on

the other hand did understand the shear stresses in fluids and published his theory of

motion of viscous fluid in 1845 [36].

Navier-Stokes equations are based on the continuum mechanics where interactions among

fluid molecules are expressed by physical constant, which is viscosity. Navier-Stokes

equations do not account for interactions at microscopic levels such as used in statistical

mechanics. To verify if your Navier-Stokes equation will qualify for your type of prob-

lem the Knudsen number can be used to verify what flow regime you are working in see

figure2.1[37].

To perform a simulation the user must create the geometry (the boundary), create the

mesh (the discretization) and define the solver conditions (set initial condition, boundary

condition, steady or unsteady and turbulence etc.) for its problem. In this study the

ANSYS CFX fluid dynamics code was used for all simulations.

6


20/36

Chapter 2. Governing Equations and Theory 7

Figure 2.1: List of flow regimes that can be used to model gas microflow

2.1 Governing Equations

For transient reacting flow the conservation of mass, momentum, energy and species

is used. Solution of complicated physics such as turbulent fluid flow, heat transfer,

chemical reaction and others are required.

2.1.1 Navier-Stokes Equation

Conservation of mass or the continuity equation can be written in general as following:

t + (u) = 0 (2.1)

It states that the rate of mass into a fluid is equal to the rate of mass out of the fluid.

The term on the left is the rate of time of the density and the term on the right is the

convective term which shows the flow of mass out of a fluid. Second law of motion, named

after Sir Isaac Newton states that the net forces acting on an element is equal to the mass

of a fluid element with an acceleration. The forces acting on the fluid element can be


21/36


split in body forces (gravity, magnetic, centrifugal and coriolis forces) and surface forces

(pressure or normal forces and viscous or shear forces). The conservation of momentum

is derived from the Newtons second law of motion and can be written in general as

follows in 3 dimensions:

Conservation of momentum, x component:

(u)

t + (uu) =

p

x+ (u) + SMx (2.2)

Conservation of momentum, y component:

(v)

t + (vu) =

p

y+ (v) + SMy (2.3)

Conservation of momentum, z component:

(w)

t + (wu) =

p

z+ (w) + SMz (2.4)

The conservation of energy describes the energy of a fluid. The transport equation

describes the rate of change of the energy inside the fluid as being equal to the flux of

heat into the element and the rate of work done on the fluid particle due to the body and

the surface forces. The equation can be written in general for compressible unsteady 3

dimensional flow as:

Conservation of energy:

(i)

t + (iu) = p u + (kT) + + Si (2.5)

where equation of state is:

p= p(, T) andi= i(, T)

perfect gasp= RT andi= CT(2.6)

and the dissipation function is:

=

2

u

x

2+

v

y

2+

w

z

2

+u

y

+v

x

2

+ u

z

+ w

x

2

+v

z

+ w

y

2

+( u)2

(2.7)


22/36


where

SM =SM+ [SM] is the source term or the body force, e.g. gravity

= dynamic viscosity

= kinematic viscosity

k= materials conductivity

(2.8)

2.1.2 Navier-Stokes Integral Equation

The most common discretization method in commercial codes is the finite volume

method. Given is the transport equation for the property

()

t + (u) = () + S (2.9)

where is the diffusion coefficient and is the conserved property.

To be useful for finite volume methods the transport equation is integrated over the

control volume as follows:

CV

()

t dV +

CV

(u)dV = CV

()dV + CV

SdV (2.10)

The first term on the left hand side represents the rate of increase of the property and

the second term is the convective term. Right hand side is the diffusive term and the

last term is the source term. Using the Gausss divergence theorem the equation above

is rewritten with the convective and diffusive term integrated over the bounding surface

of the control volume.

tCV

dV+ A

n (u)dA= A

n () CV

SdV (2.11)

then for steady state ( t = 0) problems the equation becomes:A

n (u)dA=

A

n ()

CV

SdV (2.12)

while for time-dependant problems the equation is:


23/36


t

t

CV

dV

dt+

t

A

n(u)dAdt=

t

A

n()dAdt+

t

CV

SdV dt (2.13)

2.1.3 Turbulence

Almost all fluid will experience some turbulence. In this study the so called k- model

and the large eddy simulation (LES) model were used to model the combustion physics.

Turbulence models used in computational fluid dynamics are very different and can be

very accurate like Direct numerical simulation and large eddy simulation but will take

extensive amounts of time and computer resources.

2.1.3.1 k Turbulence Model

The k- model is based on two algebraic equation, k equation which can be derived

from the Navier-Stokes equation and the equation which on the other hand cannot

be derived from the Navier-Stokes. The k equation uses the following transport

equation[38,39].

Turbulence Kinetic Energy:

k

t + (ku) =

t

+ 2tSijSij (2.14)

Dissipation Rate:

t + (u) =

tkk

+ C1

k2tSijSij C2

2

k (2.15)

where t = Ck2

is the Eddy Viscosity and the follow are the standard coefficients

C = 0.09

k = 1.00

= 1.3

C1= 1.44

C2= 1.92

(2.16)


24/36


2.1.3.2 LES Turbulence Model

Unlike the k model the Large Eddy Simulation computes the turbulence directly

at least partially. It is computationally heavy and requires very fine mesh. In short

the LES computes the eddies that are larger than the mesh spacing and models the

eddies that are smaller than the mesh spacing. The model to calculate the small eddies

is called subgrid scale model (SGS). In 1999 a new LES model was proposed by [40]

called Wall-Adapting Local Eddy-viscosity (WALE). The main improvements over the

Smagorinsky model were to account for the contribution in regions where irrational strin

is dominated by vorticity. In near wall the Smagorinsky gives a non-zero value oftwhen

velocity gradient exist and this has been improved with the new WALE model [40]. The

proposed eddy-viscosity for the WALE model is written as follows:

t= (Cw)2

(SdijSdij)

3/2

(SijSij)5/2 + (SdijSdij)

5/4 (2.17)

and the velocity gradient tensor

Sdij =1

2(g2ij+ g

2ij)

1

3ij g

2kk (2.18)

where g2ij = gikgkj and ij is the Kronecker symbol and the tensor

Sdij = SikSkj+ ikkj 13ij[SikSkj ikkj ] (2.19)

and finally the vorticity tensor

ij =1

2

uixj

ujxi

(2.20)

2.1.4 Combustion

To compute the chemical reaction the finite rate chemistry model was used in CFXfor the transient simulation. To initialize the flow and the reaction for the transient

solution the k model was used along with eddy dissipation chemistry model in the

time average simulation.


25/36


2.1.4.1 Finite Rate Chemistry

The last conservation equation needed in this study is the conservation of species and is

as follows [38,41]:

t(Yk) +

xi(uiYk) =

xi

Dk

Ykxi

+ k (2.21)

with species mass fractionYk, diffusion coefficientDk and reaction rate k. The reaction

rate equation or the source term in the transport equation is

k = (M W)kqk

qkj = dCMk

dtj

= (vk v

k) kfN

k=1

(CMk)vkj kb

N

k=1

(CMk)vkj

(2.22)

the kfis the specific reaction rate constant or the Arrhenius law

kf =AT exp(

EaRuT

) (2.23)

where

A= pre-exponent constant

= temperature exponent

Ea= activation energy

(2.24)

2.1.4.2 Eddy Dissipation

Using the transport equation of species above the reaction rate for fuel is[38,42]:

fu=

kCEDCmin

Yfu,

Yoxs

1

(2.25)

where

= 4.6v

k2

1/2=

Ypr/(1 + s)

Ymin+ Ypr/(1 + s)

(2.26)

and

Ymin= min

Yfu, Yox

(2.27)


26/36

Chapter 3

Method of solution

This chapter will cover the technical setups that are used to perform the study. The

geometry was created with the aim to match the dimensions used in the paper by Salgues

et al [1] where they performed an empirical combustion tests using liquid oxygen and

methane. Geometry was created to match[1]and meshing included a RANS mesh and

a LES mesh. All simulations were performed using ANSYS CFX and both time average

and time dependent simulation were performed. k turbulence equation and LES

were applied and Eddy Dissipation model and Finite Rate Chemistry model for the

combustion.

3.1 The Geometry

To perform this study a rocket style combustor was created using Computer Aided

Design (CAD) tool. The design and dimension were chosen to match geometry from

empirical data for validation purposes. The geometry is a simple cylinder section with

two inlets at one end of the cylinder and outlet at the other end as can be seen in figure

3.1. The cylinder section is 292.1 mm (11.5 inches) long and has a diameter of 50.8 mm(2 inches). There are two inlets, one is for the oxygen and the other for the methane.

The oxygen inlet is 3.429 mm in diameter, disk shaped, with its center at the center axis

of the main cylinder. The methane inlet is an annulus shaped with an outer diameter

of 5.182 mm and inner diameter of 4.191 mm. The center location of the methane inlet

is the same as the oxygen inlet. There is a wall annulus between the oxygen inlet and

the fuel inlet as indicated in figure 3.2with an inner diameter of 3.429 mm and outer

diameter of 4.191 mm. The outlet, nozzle throat, is an opening of 9.652 mm in diameter.

Figure3.3shows the original schematic from [1].

13


27/36

Chapter 3. Method of solution 14

Figure 3.1: Geometry created using Siemens NX showing main dimensions

Figure 3.2: Closeup on the inlet section of the CAD, showing the oxygen and fuelinlets

Due to combustion instability it was critical to model an inlet cylinder section with a

finite length to stabilize the simulation. In this study 6 different geometries were created,

all with different inlet length. Since the validation paper did not specify or show the

proper dimensions of the inlet, a trial and error approach was performed to match the

validation results. In figure 3.4(a) the geometry was modeled without a cylinder inlet

section. This proved to have very unstable characteristics and no feasible simulation

achieved. Figure3.4(b)-3.4(f)shows the geometry with a cylinder section of 20 mm, 30

mm, 10 mm, 15 mm and 17.5 mm respectfully. The walls were not given any thickness

as it was not part of this study to include any structural nor heat transfer study.


28/36


Figure 3.3: Original schematic of the validation combustor [1]

(a) Version 1, 0 mm (b) Version 2, 20 mm (c) Version 3, 30 mm

(d) Version 4, 10 mm (e) Version 5, 15 mm (f ) Version 6, 17.5 mm

Figure 3.4: Comparison of different combustor inlet length

3.2 The Mesh

Even though the geometry is simple and relatively easy to mesh using structural hexa

mesh it was decided that the geometry would be meshed using unstructured tetra mesh.

Unstructured meshes are popular in industry because they are very flexible, can fitaround very complex geometry and do not need much interaction from the user. The

drawbacks are that in most cases the solver runs slower on unstructured meshes or it

takes longer to reach convergence [add reference]. To capture all complex flow conditions,

such as wakes, the user has to pack more elements in the wake region with unstructured

meshes. The mesh was constructed by creating surface mesh on each component, i.e.

inlets, walls and outlet and then volume mesh generated from the surface mesh.

In this study there were two meshes created, one for the time-average solution or RANS

simulation and the other for the Large Eddy Simulation. Both meshes are pretty fine


29/36


Figure 3.5: Mesh created using Pointwise, LES mesh size

(over million cells) but only the LES mesh is used for the LES simulations and the mesh

sizes are set per Jiangs [3]typical mesh settings, see3.2.

The RANS mesh has 1,048,720 cells or elements and 189,206 points or nodes. Com-

parison of the different mesh sizes are listed in3.1. The LES mesh has 6,622,543 cells

and 1,149,690 points and can be seen in figure 3.5. The LES mesh uses wall model toresolve the subgrid scale eddies and that way the cost of the mesh was reduced signifi-

cantly as can be seen in3.2. The meshes have cell volume ranging from 7.28914 1013

to 7.74837 109. The mesh characteristics can be seen in table 3.1, which shows the

mesh characteristics of the mesh used in this study as well as mesh characteristics from

Boudier et. al. LES mesh sensitivity study in complex geometry combustors[2].

Coarse mesh Fine mesh My RANS mesh My LES mesh

Total num. of points 230,118 7,661,005 189,206 1,149,690Total num. of cells 1,242,086 43,949,682 1,048,720 6,622,543

Max. cell volume 3.12671 108 4.05748 109 7.74837 109 2.96836 1011

Min. cell volume 1.81795 1011 1.1828 1012 1.07624 1017 2.61382 1018

Table 3.1: Comparison of mesh sizes[2]

DNS Wall-Resolved LES LES with Wall Model

Streamwise x+ 10-15 50-150 100-600Spanwise z+ 5 10-40 100-300WEall-normal (y+) 1 1 30-150Number of points in 0< y+


30/36


3.3 Boundary Condition and Procedure

This section will describe the boundary condition used at each mesh boundary, flow

condition and initial condition used in this study as well as the simulation procedure.

3.3.1 Walls

All walls were treated as smooth with no slip condition. No slip condition tells the solver

that the velocity at the wall the nodes are zero. In sub micro and nano scale or in slip

flow conditions, see2.1, the velocity is not zero at the wall and the particles will slip.

Smooth wall condition is used to model smooth surface which will not cause disturbance

in the boundary layer like what would happen with rough surface.

3.3.2 Outlet

The flow regime in the outlet was treated subsonic but there are options to treat the

outlet flow regimes as supersonic. The outlet was set to have relative pressure of zero

and the outlet was treated as pure outflow, that is, the flow can only flow out but not

in.

3.3.3 Inlet Methane

The flow regime in the methane inlet was treated as subsonic and this was also the

case for the oxygen inlet. Mass fraction for the inlet was set to 1 for CH4 to treat the

combustion model with purse methane. The methane was given a mass flow rate of

0.03923kg/s and temperature to 300 K.

3.3.4 Inlet Oxygen

To simulate pure oxygen the mass fraction was set to 1 for the O2 only. Most combustion

simulations have atmospheric air which would only contain 21% of the mass. The oxygen

was given a mass flow rate of 0.1177kg/s. The temperature was kept constant at 300 K.

3.3.5 Procedure

In the validation phase the RANS mesh was used only for quicker solution turnaroundtime. Geometry3.4(a)through3.4(f)were tested and results compared with validation


31/36


paper[1]. The focus was to compare the velocity of RANS simulation with the validation

and change the geometry till a matching velocity was found. Boudier et. al [43] indicated

in their study that velocity, along with other variables, were not so sensitive to mesh

resolution. Once a close match was found with the RANS mesh the LES simulation

with LES mesh was ran on the same geometry and results compared. The last step

was to compare combustion instability and use a new pulsating technique to reduce the

instability and increase performance.


32/36

Appendix A

Appendix Title Here

Write your Appendix content here.

19


33/36


34/36

Bibliography 21

[10] Central Intelligence Agency. Natural gas - proved reserves, the world

factbook. http://www.cia.gov/library/publications/the-world-factbook/

rankorder/2179rank.html ,2011.

[11] R.J. Jensen, H.C. Dodson, and S.E. Claflin. Lox/hydrocarbon combustion instabil-

ity investigation. NASA Contractor Report, July 1989.

[12] Songjiang Feng, Wansheng Nie, Bo He, and Yufeng Cheng. Three-dimensional

numerical simulations of low frequency combustion instability in a lox/methane

rocket engine. American Institute of Aeronautics and Astronautics, (AIAA 2010-

8776), August 2010.

[13] F. Zhuang, W. Nie, W. Zhao, and W. Liu. Liquid rocket combustion instability

analysis methodology - methods and representative examples. American Instituteof Aeronautics and Astronautics, (AIAA 98-3690), July 1998.

[14] F. Zhuang, W. Nie, W. Zhao, and W. Liu. Liquid rocket combustion instability

analysis methodology - methods and representative examples. American Institute

of Aeronautics and Astronautics, (AIAA 98-3690), July 1998.

[15] N. Ierardo and A. Congiunti. Mixing and combustion in supercritical o2/ch 4 liquid

rocket injectors. American Institute of Aeronautics and Astronautics, (AIAA 2004-

1163), January 2004.

[16] A.Minotti and C.Bruno. Comparison between real and ideal sub and supercriti-

cal combustion simulations of lo2-ch4 lre flames at 15mpa. American Institute of

Aeronautics and Astronautics, (AIAA 2008-951), January 2008.

[17] L. Cutrone, F. Battista, G. Ranuzzi, S. Bonifacio, and J. Steelant. A cfd method for

simulation of mixing and combustion in high-pressure lox/methane rocket engines.

American Institute of Aeronautics and Astronautics, (AIAA 2008-949), January

2008.

[18] Nicolas Guezennec, Matthieu Masquelety, and Suresh Menonz. Large eddy simula-

tion of flame-turbulence interactions in a lox-ch4 shear coaxial injector. American

Institute of Aeronautics and Astronautics, (AIAA 2012-1267), January 2012.

[19] A.Minotti and C.Bruno. Flame temperatures in non-premixed flames. American

Institute of Aeronautics and Astronautics, (AIAA 2008-998), January 2008.

[20] Naimish B. Harpal, Eric Besnard, and Reza Toossi. Modeling of lox/methane

impingement, mixing and combustion. American Institute of Aeronautics and As-

tronautics, (AIAA 2010-7135), July 2010.
http://www.cia.gov/library/publications/the-world-factbook/rankorder/2179rank.htmlhttp://www.cia.gov/library/publications/the-world-factbook/rankorder/2179rank.htmlhttp://www.cia.gov/library/publications/the-world-factbook/rankorder/2179rank.htmlhttp://www.cia.gov/library/publications/the-world-factbook/rankorder/2179rank.htmlhttp://www.cia.gov/library/publications/the-world-factbook/rankorder/2179rank.html


35/36

Bibliography 22

[21] K. Tajiri and S. Menon. Les of combustion dynamics in a pulse combustor. Amer-

ican Institute of Aeronautics and Astronautics, January 2001.

[22] R. Erickson and B.T. Zinnt. One-dimensional numerical simulation of a pulse com-

bustor using the linear eddy mixing model. American Institute of Aeronautics and

Astronautics, July 2002.

[23] Subhashis Datta, Achintya Mukhopadhyay, and Dipankar Sanyal. Effects of flow

pulsations on the dynamics of a thermal pulse combustor. American Institute of

Aeronautics and Astronautics, August 2009.

[24] Mark D. Moore. Personal air vehicles: A rural/ regional and intra-urban on-demand

transportation system. American Institute of Aeronautics and Astronautics, July

2003.

[25] Ben T. Zinn. Pulse combustion: recent applications and research issues.Symposium

(International) on Combustion, 24(1):12971305, 1992.

[26] H. M. Heravi, J. R. Dawson, P. J. Bowen, and N. Syred. Primary pollutant pre-

diction from integrated thermouidkinetic pulse combustor models. JOURNAL OF

PROPULSION AND POWER, 21(6):10911097, November 2005.

[27] U.S. Department of Energy National Energy Technology Laboratory. Pulse com-

bustor design a doe assessment. Technical Report 1190, U.S. Department of Energy,July 2003.

[28] Subhashis Datta, Achintya Mukhopadhyay, and Dipankar Sanyal. Effects of flow

pulsations on the dynamics of a thermal pulse combustor. American Institute of

Aeronautics and Astronautics, (AIAA 2009-5500), August 2009.

[29] Tao Geng, Fei Zheng, Andrey V. Kuznetsov, William L. Roberts, and Daniel E.

Paxson. Comparison between numerically simulated and experimentally measured

flowfield quantities behind a pulsejet. American Institute of Aeronautics and As-

tronautics, (AIAA 2008-5046), July 2008.

[30] Michael Kowalkowski, Yu Matsutomi, and Stephen Heister. Flame sensing in pulsed

combustion using ion probes, diodes and visual indications. American Institute of

Aeronautics and Astronautics, (AIAA 2009-4945), August 2009.

[31] T. Bai, B. T. Zinn, J. I. Jagoda, B. R. Daniel, and X. Chen. Experimental study

of the effect of fuel and air feed rate modulations upon pulse combustion in a rijke

type pulse combustor. American Institute of Aeronautics and Astronautics, (AlAA

94-0216), January 1994.


36/36

Bibliography 23

[32] Taichang Zhang, Xuejun Fan, Jing Wang, Jianguo Li, and Gong Yu. Pulsed com-

bustion of hydrocarbon fuels in a supersonic model combustor. American Institute

of Aeronautics and Astronautics, (AIAA 2011-5547), August 2011.

[33] Michael Zeutzius, Toshiaki Setoguchi, Kunio Terao, and Hideo Miyanishi. Propul-

sion system for hypersonic space planes. Journal of Propulsion and Power, 16(2):

243250, March 2000.

[34] K. Tajiri and S. Menon. Les of combustion dynamics in a pulse combustor. Amer-

ican Institute of Aeronautics and Astronautics, (AlAA 2001-0194), January 2001.

[35] Andrew C. St. George and Ephraim J. Gutmark. Trends in pulsating turbine

performance: Pulse-detonation driven axial flow turbine. American Institute of

Aeronautics and Astronautics, (AIAA 2012-0769), January 2012.

[36] Uche Oteh. Mechanics of Fluids. AuthorHouse, 2008.

[37] George Karniadakis, Ali Beskok, and Narayan Aluru. Microflows and Nanoflows

Fundamentals and Simulation. Springer Science and Business Media, Inc., 2005.

[38] H K Versteeg and W Malalasekera. Introduction of Computational Fluid Dynamics

The Finite Volume Method. Pearson Education Limited, second edition, 2007.

[39] David C. Wilcox. Turbulence Modeling for CFD. DCW Industries, Inc., second

edition, 1994.

[40] F. Nicoud and F. Ducros. Subgrid-scale stress modelling based on the square of the

velocity gradient tensor. Flow, Turbulence and Combustion, 62(3):183200, April

1999.

[41] Thierry Poinsot and Denis Veynante. Theoretical And Numerical Combustion. R.

T. Edwards, Inc., second edition, 2005.

[42] Guan Heng Yeoh and Kwok Kit Yuen. Computational Fluid Dynamics in Fire

Engineering Theory, Modeling and Practice. Butterworth-Heinemann, 2009.

[43] G. Boudier, L. Y. M. Gicquel, and T. J. Poinsot. Effects of mesh resolution on large

eddy simulation of reacting ows in complex geometry combustors. Combustion and

Flame, 155(1-2):196214, October 2008.

thesis draft7 introduction theory

Documents