1
Moscow Institute of Physics and Technology
(State University)
P
R O G R A M
of course
«
Gasdynamics of combustion
»
Speciality: 010
9
00 Applied mathematics and physics
Faculty
: Aeromec
hanics and Flight Engineering (F
AFE)
Department:
Computer modelin
g
Year: 5
Term: 9, 10
Lectures, hours:
66
Practical training (seminars), hours:
Total, hours:
66
Lecturer:
Ph.D.,
associate p
rofessor
Vlasenko V.
The program was approved in cathedr
a Computer modeling
session.
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GASDYNAMICS OF COMBUSTION
Physi
cs
of
gas
combustion
–
one
of
the
most
complex
parts of aerodynamics, with many
practical applications. This
course
is
an introduction to the problems of the gasdynamics of
combustion. The
course
occupies
one
academic
year
(
one
lecture
–
2
hours
–
per week
).
In
the
first
half
of
the
course
the
main
attention is paid to consideration of simple tasks with analytical
solutions, allowing to understand the most essential physical processes in gas flows with
combustion. This
set
of
tasks
is
culminated
with
the
ta
sk about description of turbulent diffusive
combustion in unpremixed flow. Problems of numerical simulation of reactive flows are also
considered briefly. Second
part
of
the
course
is
devoted
to
gasdynamic
theory
of
combustion
waves
in premixed flow of com
bustible gas
(
detonation
and
deflagration
)
.
As an
example of practical application, the problem of pulsing detonation engine creation is
considered.
Many
questions
,
which
are
considered
in
this
course
,
may
be
useful
not
only
for
students
,
who
want
to work
in the field of combustion, but
also
for all persons, who are interested in
physical and mathematical problems of the whole gasdynamics.
COURSE SCHEDULE
Part I
(
1
st
term)
Lecture 1.
Main terms and equations of chemical kinetics.
Lecture 2.
Heat effect
of chemical reaction.
Lecture 3.
Kinetic mechanism of hydrogen

air combustion.
Lecture 4.
Influence of stoichiometry on local combustion.
Lecture 5.
Theory of homogeneous reactor.
Lecture 6.
Flame of burners
–
combustion wave propagating due to heat condu
ctivity
.
I. Equations.
Lecture 7.
Flame of burners
–
combustion wave propagating due to heat conductivity.
II. Theory of Zeldovich
–
Frank

Kamenetsky
–
Semenov.
Lecture 8.
Laminar diffusive combustion
in unpremixed flow.
I.
E
quations.
Lecture 9.
Laminar di
ffusive combustion
in unpremixed flow.
II.
M
ethod of passive scalar.
Structure of laminar diffusive flame.
Lecture 10.
Turbulent diffusive combustion
in unpremixed flow.
I.
Qualitative representation of the structure of turbulent diffusive flame.
Time

ave
raged equations. Method of moments.
Lecture 11.
Turbulent diffusive combustion
in unpremixed flow.
II. Model of laminar flamelets.
Lecture 12.
Turbulent diffusive combustion
in unpremixed flow.
III. Method of probability density function.
Lecture 1
3
.
Tu
rbulent diffusive combustion
in unpremixed flow.
I
V
.
T
aking into account the backward reactions. Approximation of
quasi

equilibrium combustion.
Lecture 14.
Thermodynamic analysis of chemical equilibrium.
3
Lecture 1
5
.
P
roblems of numerical simulation of fin
ite

rate flows.
I. Stiffness of
chemical kinetics equation system. Comparison of implicit and
implicit schemes.
Lecture 16.
Problems of numerical simulation of finite

rate flows.
II. Analysis of numerical problems in simulation of hydrogen

air combustion.
Part II
(2
nd
term)
Lecture 1.
T
heory of quasi

1D flows with heat release.
Lecture 2.
Thermal choking.
Lecture 3.
Approximate method for
quantitative
analysis of quasi

1D reactive flows in
variable

area ducts.
Lecture
4
.
Michelson’s theory of combustion
waves.
Lecture
5
.
Classification of combustion waves (detonations and deflagrations).
Lecture
6
.
Losses and the entropy growth in combustion waves.
Lecture
7
.
Quantitative relations for combustion waves.
Lecture
8
.
Characteristic analysis and
causation
of
combustion waves.
I. Method of characteristics. Causation of shock wave.
Lecture 9.
Characteristic analysis and
causation
of combustion waves.
II. Causation of various classes of combustion waves.
Lecture
10
.
Mechanisms of realization for various classes
of combustion waves.
Lecture
11
.
Self

similar flows with combustion waves.
I. 1D non

stationary flows with overpressed detonation.
Lecture 1
2
.
Self

similar flows with combustion waves.
I
I.
1D non

stationary flows with
under
pressed detonation
and weak defla
gration
.
Lecture 1
3
.
Self

similar flows with combustion waves.
III. 2D stationary flows with
oblique detonation wave.
Lecture 14.
Influence of finite

rate kinetics on a structure of an oblique detonation wave.
Lecture 15.
Instability of 1D
structure of
det
onation and non

stationary spatial structure of
detonation
wave
s.
Lecture 1
6
.
Pulsed detonation engines
(PDE)
.
I. Thermodynamic cycle of ideal PDE in comparison with
cycle of ideal ramjet.
Lecture 17.
Pulsed detonation engines (PDE).
II. Various schemes of
PDE and analysis of problems in realization of PDE.
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