Американский Научный Журнал THE THERMO-GAS-DYNAMIC DESIGN METHOD FOR THE LIQUID ROCKET ENGINE CHAMBER

Analysis of the thermodynamic and thermophysical properties of combustion products in the liquid rocket engine (LRE) chamber shows that their dissociation degree depends on temperature T, gas expansion degree ε, etc. Practically, combustion products are always chemically active working fluid, therefore the number of moles N of the products varies along the length of the LRE chamber in the entire reaction mixture. The local values of the parameters T and N depend on the specific physical conditions. Therefore, the distribution of local numbers of moles of the components of the gas mixture and its heat capacities can be represented as dependencies N~f(T) and c~g(T). For this purpose on the basis of the numerical values of the moles and the heat capacities of the gas mixture components in the main sections of the LRE chamber are formed as corresponding empirical functions through interpolation. The system of equations for the thermodynamic calculation of LRE chamber is solved by taking into account new functions. Such approach allows forming the optimal contour of the LRE chamber at the preliminary stage of engine design and improving results of the gas-dynamic calculation and nozzle profiling by modified method of characteristics. Скачать в формате PDF
American Scientific Journal № ( 32) / 2019 13

ТЕХНИЧЕСКИЕ НАУКИ

THE THERMO -GAS -DYNAM IC DESIGN METHOD FOR THE LIQUID ROCKET E NGINE
CHAMBER

Pashayev Arif Mir Jalal,
Doctor of Physical and Mathematical Sciences, Ac ademician of ANAS ,
National Aviation Academy
Samadov Adalat Soltan,
Prof., Flight Vehicles and Engines Department
Abdullay ev Parviz Shahmurad,
Prof., Head of Flight Vehic les and Engines Department
Abdulla Nijat Parviz,
MSc student, Department of Design Rocket -Space Apparatuses, NAU “KhAI”

Abstract . Analysis of the thermodynamic and thermophysical properties of combustio n products in the liquid
rocket engine (LRE) cham ber shows that their dissociation degree depends on temperature T, gas expansion degree
ε, etc. Practically, combustion products are always chemically active working fluid, therefore the number of moles
N of the products varies along the length of the LRE chamber in the entire reaction mixture. The local values of
the parameters T and N depend on the specific physical conditions. Therefore, the distribution of local numbers of
moles of the components of the gas mixture and its heat capacities can be repre sented as dependencies N~f(T) and
c~g(T). For this purpose on the basis of the numerical values of the mol es and the heat capacities of the gas mixture
components in the main sections of the LRE chamber are formed as corresponding empirical functions thr ough
interpolation. The system of equations for the thermodynamic calculation of LRE chamber is solved by ta king into
account new functions. Such approach allows forming the optimal contour of the LRE chamber at the preliminary
stage of engine design and i mproving results of the gas -dynamic calculation and nozzle profiling by modified
method of characteristics.

INTRODUCTION
As known, one of the main directions in rocket and
space technologies development is design of highly
efficient propulsion systems, w hich include liquid
rocket engines (LRE). Design of LRE and its
optimization scheme consists of choosing a
combination of parameters of the workflow, which
achieves the most advantageous combination of
traction characteristics and weight of the structure.
There accumulated a large s cientific and practical
experience in the development of various LRE.
However, determining the design parameters of a new
designed LRE camera is still a difficult process.
In LRE development their initial geometry,
pneumatic -hydr aulic scheme (PHS) of the e ngine and
parameters of these energy relations are determined.
Next, on the basis of this PHS is selected, at all
characteristic point of PHS pressures, consumption of
fuel components, required pump features and power
consumed by them and components temper atures of
working gases are determined. These engine
parameters obtained are the initial data for the design of
the LRE combustion chamber (CC), gas generator,
pumps, turbines, regulators, etc.
The pressure and the ratio of fuel components in
the CC is sel ected taking into account obtaining a
maximum specific impulse of the engine, its
dimensions and reliable cooling of the chamber. At this
design stage many parameters of LRE and its
aggregates are taken approximately based on the
experience of previous dev elopments. Therefore, great
accuracy in determining of certain engine parameters at
characteristic points of PHS and LRE chamber should
not be expected.
For determination of the thermodynamic
characteristics of combustion product s (CP) have been
done many researches and developed a number of
different software (for example, CEA (NASA, USA),
Astra.4/pc (MSTU named after N.E.Bauman, Russia),
RPA (Alexander Ponomarenko, Germany), etc.
In these applications is assumed that (for CC exi t,
the nozzle inlet):
• fuel mixing is complete,
• physical incomplete combustion missing,
• the combustion process takes place at a
constant pressure in the CC ( ),
• combustion products systems at the CC exit
are in a thermodynamic equilibr ium state,
• there is no heat exchange with CC walls,
• gas phase is described by the ideal gas state
equation,
• solubility of gases in the liquid and solid
phases is missing,
• condensed substances form one -component
immiscible phases, etc.
For the expa nsion pro cess calculating in the
nozzle, the following assumptions are made:
• the expansion process is chemically and
energetically extremely balanced,
• no fuel burnout in the nozzle,
• no heat transfer to the nozzle walls,
• there is no friction and gas -dynamic losses i n
the nozzle [ Alemasov,1989; Babkin, 1990; const pc=

14 American Scientific Journal № ( 32) / 20 19
Glushko,1976; Gurtovoy, 2016; Sutton, 2010;
Vasiliev,1983].
In the known methods, these problems are mainly
considered from general theoretical positions and
thermo -gas -dynamic features of the working pro cesses
are not taken into account. The correct accounting of
these features would allow creating the correct mass
and geometric configuration of LRE camera.
Consequently an improved technique for the
preliminary design of LRE, taking into account certain
features o f the working processes in the engine, is
considered in this paper.
THE AIM OF RESEARCHES
As known, preliminary geometry of LRE chamber
is formed both by thermodynamic models of
combustion and outflow processes and by gas -dynamic
models of the gas flow. In the engineering practice,
thermodynamic calculation precedes the gas -dynamic
design of LRE chamber. However, inaccuracies in
thermochemical modeling (for example, inco rrect
modeling of the distribution of CP thermodynamic
parameters over the chamber vol ume) of LRE’s can
lead to certain errors in the engine configuration at the
next design stages, which lead to improvements in the
basic thermodynamic models.
Therefore, t he purpose of the paper is to improve
the methodology for the correct geometry formati on of
LRE chamber (combustion chamber and nozzle) based
on the existing method refinement for thermodynamic
calculation.
SOME NOTES ON THE GAS -DYNAMIC
CALCULATION OF TH E LRE CHAMBER
As known, the task of LRE gas -dynamic
calculation is to determine the m ain geometric
dimensions in various sections of the combustion
chamber (CC), nozzle and the calculation of the
expected characteristics of the engine. The calculation
is based on the assumption of chemical inertness of the
fuel combustion products (CP) dur ing their flow
through the nozzle. Along with proposals for
adiabaticity and one -dimensional flow, this assumption
allows to use the gas -dynamic functions, which
describe the motion of a gas flow with constant
composition in an energy -insulated channel, i. e. in the
frozen expansion [ Alemasov,1989; Babkin, 1990;
Glushko,1976; Gurtovoy, 2016; Vasiliev,1983].
However, at high temperatures ( ),
the combustion products are chemically active working
fluids (medium) in which dissociation and
recombination reactions take place. During the
expansion of such working fluid in the nozzle, due to
temperature decreasing the dissoci ation decreases. In
this process there happens an increase in the
recombination phenomena that occurs with the heat
releas ing. As a result, the chemical equilibrium state is
not realized due to the short residence time of PC in the
nozzle and the final rat es of chemical reactions.
Consequently, the changing composition of the
working fluids in LRE chamber does not allow the
correct determination of engine parameters [Belov ,
2013; Babkin, 1990; Brykov, 2017; Gurtovoy, 2016].
Thus, in the classical formulatio n of this problem
the gas -dynamic calculation in separately or in the
private combination with some results of
thermodynam ic calculation does not allow the
formation of the correct geometry of LRE chamber.
This circumstance leads to improvements in the
met hodology of thermodynamic calculation for LRE,
taking into account the gas -dynamic design problems.
FEATURES OF THERMODYN AMIC
CALCULATION OF LRE
As known, at high temperatures ( ),
a thermal dissociation of the working fluids occurs in
LRE. Dissociation processes lead to a decrease in the
total conversion of the fuel chemical energy into
heat ( , in the ideal case
), which should be taken into account
during preliminary design of the engine. In addition, th e
temperature and pressure of the gas flow also decrease,
which have different effe cts on the dissociation degree.
Existing studies have shown that the temperature effect
on the gas dissociation degree is greater and at gas
temperatures the degree of dissociation
is smaller [Babkin, 1990; Gurtovoy, 2016].
Therefore , when considering the gas flow in the
nozzles, changes in the chemical composition and
chemical energy due to recombination
processes of CP are considered as small and are not
taken into account in the calculations. Analysis of
ther modynamic and thermophysical properties of CP
[Brykov, 2017; Glushko,1976] shows that the degree of
dissociation of CP also depends on the expansion
degree of PC and the oxidizer excess
ratio in the LRE chamber . For
example, for a kerosene -oxygen fuel pair at
, and temperatures
, the combusti on products are practically
a chemically active working fluids. In this case, it
would be correct to carry out a thermodynamic
calculation of the LRE, taking into account the
dependence , where
or - the relative length, -
coordinates of the point considered on the LRE
cham ber axi s, - radius of the nozzle throat (critical
section), - the relative radius of the
considered engine section.
Thus, if changes due to recombination reactions
are not taken into account, then the error of ca lculation
of thermo -gas -dynamic parameters can be several
percent. In addition, despite the change in th e
composition of the CP along the LRE chamber length
the ratio of specific heats in the
calculations is considered only in the ma in sections of
the engine. Consequently, the thermodynamic
calculatio n with some average value of the isentropic
index leads to an incorrect configuration of the LRE. K T 2000 K T 2000 chem U chem chem Q U → chem chem Q U = K T 2000 chem U e c p p / =  0 / m m K K =  30... 20 7.0  K T 2000 ,...) , , , , , ( ~ y x Tp f Qchem   cry x x / = min /x x x= x cry cry y y / = v p c c / = 

American Scientific Journal № ( 32) / 2019 15

It should be noted that the change in specific heats
and the isent ropic index along the LRE nozzle length
were considered in some previous studies [Colonno,
2008; Fu, 2016; Kestin, 1950; Kyprianidis, 2009;
Rizkalla, 1990; Zebbiche, 2011]. However, as a rule,
mathematical modeling of these changes is narrow and
does not a llow revealing the entire energy potential of
the gas flow. In these studies, changes in the isentropic
index are considered as a separate problem in order to
justify the use of the improved method of
characteristics. It is well known that the energy
forma tion of a gas stream along the LR E chamber is
extremely complex and dynamic. Consequently, it
becomes necessary to solve the problem of correctly
applying the method of characteristics, taking into
account the features of thermochemical models of
combustio n processes in the LRE chamber.
Therefore, preliminary design of LRE requires
additional researches for improving the thermodynamic
calculation, which is considered in the next paragraph
of this paper.
SOLUTION OF SOME PROBLEMS OF
THERMODYNAMIC CALCULATI ON OF THE
LRE CHAMBER
In the gen eral case, the geometric profile of the
LRE chamber and its thrust characteristics are
determined by the distribution of the moles of the gas
mixture and its components, heat capacities, isentropic
index, chemical or intern al energy over the engine
chamber length (or volume):
, , ,
or (1)
Depending on the nature of these distributions,
certain fields and isosurface s of parameters ( , ,
etc.) are formed in the LRE chamber, which affect the
engine thrust characteristics.
It should be noted that taking into account the
distribu tion of these parameters in t he LRE chamber
determines the improvement of the method of
characteristics for supersonic nozzle profiling
[Anderson, 1982 ].
As known, one of the main gas flow parameters
affecting the thrust characteristics of LRE is heat
capa city. The specific heat value s and
(respectively, other parameters) for the considered LRE
chamber section depend on the properties of indiv idual
substances (gases) and their moles in the PC mixture.
Theoretically, the specific heat capaci ties are
determined by the following formulas
[Alemasov,1989; Glushko,1976; Vasiliev,1983]
(2)
(3)
where and -are the specific heat
capacities of the -th component of CP (individual
substance of the gas mixture) for the considered
temperature, -the n umber of moles of the -th
component for the considered conditions (pressure
and te mperature ), and - the enthalpy and the
internal energy of the -th component for th e
considered temperature [Gurvich, 1982]. In the
calculations for gaseous component s of the mixture
instead of the partial pressure of the components
is used ( ). In addition, for the considered
conditions can be used, where
- the gas constant and -the molecular
mass of the -th component.
As a rule, in existing stud ies it is accepted that the
heat capacity depends on temperature in the form
or (4)
where -heat capacity at 298.15К, -
constant coefficients. Usually, coefficients and
are not taken into account because of their smallness.
However, analysis shows that for different temperature
ranges (1500 -2000K, 2000 -3000K, >3000K) and
conditions ( , , , ) changes of heat
capacities of individual substances in CP
have different effects on engine performance [Bulygin,
Rachuk, 1997] . As an example, table 1 shows changes
in the heat capacity of the CP of the kerosene -oxygen
fuel [ Glushko,1976 ]. Consequently, for different
design conditions ( , , , ) of LRE chamber
the nature of the changes of parameters and
must be taken into account.
Thus, resulting heat capacity of the gas at the
considered point of the flow is fo rmed by the variety
and number of different substances, which is almost
impossible to simulate mathematically. Therefore, on
the LRE chamber calculation the heat capacities are not
considered in the engine chamber cross s ections
between “c”, “cr” and “e” ( first approximation ),
which leads to a distortion of the nozzle geometry (Fig.
1).
) , (1 y x f Ni= ) , (2 y x f ci= ) , (3 y x f = ) , (4 y x f U chem = ) , (5 y x f U = p T w pc vc  
=


 



 + =
constp
i i i ip p T
N J N c c  
=


 



 + =
constv
i i i iv v T
N U N c c ipc ivc i iN i ip iT iJ i U i iN ip i i p N = i iv ip R c c = − i i R R / = i i ...3 2 0 dT bT aT c c + + + = aT c c +  0 0c ,... , , d b a b d  cp mK  ) ( T c   cp mK  pc vc

16 American Scientific Journal № ( 32) / 20 19
Table 1
Changes in the heat capacity of the PC of the kerosene -oxygen fuel
Case Parameters of LRE, fuels and combustion process
A) =0.5 =0.1 MPa -50 MPa =1.7 04
B) =0.5 =0.1 MPa -50 MPa =1.704
C) =1.0 =0.1 MPa -50 MPa =3.409
D) =1.0 =0.1 MPa -50 MPa =3.4 09
E) =2.0 =0.1 MPa -50 MPa =6.815
Here, the heat capacity average value is
considered unchanged due to the recombinati on
reactions between the indicated cross sections.
Accordingly, the heat can be approximately taken
constant (i.e. ). In this case, the PC
enthalpy to be calculated by the formula
[Alemasov,1989; Glushko,1976; Vasiliev,1983]

where -the reference (or initial) temperature
(298.15К), - the temperature of considered CP.
It is known that due to chemical reactions along
the LRE chamber length in the entire reacting gas
mixture the number of moles of components
changes. At the same time, the local value of this
parameter is determined by the thermophysical
conditions ( , , etc.) at the point in question.
Therefore, from the point of view of energy convers ion,
the local number of moles can be represented as a
func tion
, where (5)
Analysis of numerical studies shows that, based on
values in the main sections of the LRE chamber
using interpolation it is possible t o define a function
in the form
, ,
, . (6)
Depending on the specif ic tasks, one of these
functions can be taken into account in formulas (2) and
(3). In this case, for the formation of the LRE chamber
geometry, the thermo -gas -dynamic calculation is
repeated taking into account new dependencies (6).
This approach allows u s to obtain more refined values
of heat capacities for the considered point on the LRE
chamber axis taking into account the specific nature of
the change along the engine cross section.
Thus, in the second approximation , between the
indicated sections of the LRE chamber, changes in heat
capacities values ( or ) will be taken
into account. Then taking into account the condition
( or )
enth alpy of the combustion products should be
calculated taking into account the changing internal
thermal energy
(7)
Taking into account the above, based on the values
of the total enthalpy for two “c” and “e” sections of the
LRE chamber, we find the velocity of the gas flow in
the section “e”



Thus, if for any two "n -1" and "n" sections of the
LRE chamber the initial heat capacities are taken as
or , then

,
(8)
In order to optimize the nozzle, the value
obtained by the formula (8) is compared with the value
of a predetermined sigmoidal function as [Abdullayev,
2017]



The be st case is , i.e.

(9)

For any two "n -1" and "n" sections of the LRE
chamber, the temp erature can be found as 50  cp mK pc 50   cp mK pc 10  cp mK pc 10   cp mK pc 5000  cp mK pc const Qchem  chem
T
T
p chem Q dT c Q i J + = + = 
0 0T T iN ip iT ) (6 i i T f N = ) , (7 y x f Ti= iN ) (6 i i T f N = b aT N i i + = c aT N bi i + = b T a N i i + = ) ln( c bT aT N i i i + + = 2 iT pc pc pc const Q U chem chem   →   chem U  chem U chem
T
T
p chem chem Q dT c Q i U i J  + =  + =  + = 
0 ) ( ) ( 2 20 2 0 0 T T a T T c w e e p e − + −  = 1 0 0 −  =  np p c c np p c c 0 0  =  ) ( ) ( 2 21 2 1 0 − − − + −  = n n n n p n T T a T T c w ) ( ) (2 21 2 1 − − − +  −  = n n n n n T T a i i w ) (x wn ) ( ) ( ) ( x w x w x w n sigmoid n  −  0 ) (   x wn ) ( )] ( ) ( [ )] ( ) ( [2 ) ( 21 2 1 x w x T x Ta x i x i x w sigmoid n n n n n = − +  −  =  − −

American Scientific Journal № ( 32) / 2019 17

(10)

As can be seen, unlike the traditional
thermodynamic calculation scheme o f the engine, the
temperature and velocity of the CP can be determined
sequentially along the axis of the LRE chamber.
In view of the foregoing, we will consider a
modified thermodynamic calculation of the LRE
chamber, whi ch takes into account the average gas
dynamics of the engine.
MODIFIED TECHNIQUE FOR
THERMODYNAMIC CALCULATION OF THE
LRE CHAMBER
In general, for this technique is considered fuel
with source elements C, H, O and N. For determining
of the composition and temperature of the combustion
pro ducts in each LRE chamber section a system of
equations is composed using [ Alemasov,1989; Bonnie,
2002; Cantwell, 2019; Glushko,1976; Gordon, 1994;
Gurtovoy, 2016; Hill, 1992; Pashayev, 2018;
Vasiliev,1983]
• The chemical equilibrium law,
• The equation of mat erial balance (law of
conservation of matter),
• The Dalton's law (partial pressure balance
equation),
• The law of masses action.
The system of equations is solved accurately using
the Newton -Raphson method. Ta king into account the
main provisions of previous paragraphs sequence of
calculation will consist of the following steps (Fıg.1).
A. Combustion chamber (“c”, “c0” sections)
By the solution of equations system for a given
pressure in the CC are determined the composition
of the CP (mass or mole fraction for every -th
component), the pa rtial pressure of CP components
. Further, using the condition ( and
are the enthalpy of the fuel and combustion
products), are determined the temperature in the
CC, entropy , molecular weight , gas constant
, density , heat capacities and , the
isentropic index and speed of sound in the
initial section of the CC.
B. Nozzle exit (“e” section)
For given pressure by the solution of the
equations system are determined the composition (
) and the partial pressure of CP components.
Next, using the condition ( and are
the entropy o f the combustion products in the relevant
sections «c» and «e» of the LRE chamber) are
determined temperature , molecular mass , gas
constant , density , heat capacities and
, isentropic index , specific area and speed of
sound at th e nozzle exit.
C. Nozzle throat section (“t h” section)
Based on the solution of the equations system of
for each pressure value (from the range [ ,
], ) is set one value temperature
(from t he range [ , ], ) of the
gas mixture and are determined the composition and
entropy of the combustion products. The
temperature [ , ] for which the
condition is met is taken as final. Besides at
each solution cycle f or each value from the range
[ , ] also the composition ,
molecular mass , gas constant , density ,
heat capacities and , isentropic index ,
specific area and speed of sound of the gas
mixture are determined. The true nozzle throat section
will then when a concre tely value of the pressure
and other parameters provide the minimum specific
area . In this section will also be satisfied
the equality of v elocities .
D. Intermediate sections of the chamber with a
given length (“n” section)
The purpose of this calculation stage is adjus ting
to the gas -dynamic calculation of the LRE chamber as
close as possible. In the first approximation (parameters
calculation in the intermediate sections of the LRE
chamber) at first, based on the values , and
using interpolation are formed functions
that allow us to de termine for the
considered -th section. With the linear form of this
function for the -th section will be
. The function without
using of gas -dynamic functions allows providing
minimal difference thermodynamic and gas -dynamic
profiles of the LRE chamber using (8) and ( 10).
In the second approximation values of
thermo dynamic parameters in intermediate sections of
the LRE chamber are refined using functions for moles
and new values of and .
As noted in paragraph 3 gas -dynamic functions are
applied with an average value of the isentropic index
, which leads to certain errors in the formation o f the
LRE chamber geometry. On the other hand the 





+  − +  + =
− −
− − ) (2 ) (2 )(0
2
1 )1 (0
21 1 n n p
n
n n p
n n n aT c
w
aT c
w T T cp iñN . i icp . c F I I = FI cI cT cS c cR c cpc . cvc. c ca ep ieN . iep . e c S S = cS eS eT e eR e epc . evc. e speF . ea jthp . min.thp max.thp ,..2,1=j kthT . min.thT max.thT ,..2,1=k thS thT  min.thT max.thT c th S S = jthp . min.thp max.thp ithN . th thR th thpc . thvc. th spthF . tha thp min .) ( spthF th th w a = cpc . thpc . epc . ) (Tf cp= npc .0 n aT c c p p + = 0 n 1. .0 − = np np c c ) (Tf cp= ) (6T f N = pc vc 

18 American Scientific Journal № ( 32) / 20 19
determination of the local isentropic index by main
sectio ns (cross sections “c”, “cr” and “e” of the LRE
chamber) using thermodynamic calculation also
doesn’t allow correctly forming the gas -dynamic
structure and take into account all the properties of the
gas flow in gas -dynamic functions. Consequently, the
use of functions and allows
without use of gas -dynamic functions, maximally
match the thermodynamic and gas -dynamic profiles of
the LRE chamber using (9) and (10).
Further design is carried out using the method o f
chara cteristics, taking into account the changing values
of the isentropic index of combustion products
along the LRE chamber length. It should be noted that
such approximations allow to be improved of t he
nozzle profiling contour results using the method
characteristics. Thus, using the formulas (9) and (10)
for the -th section of the LRE chamber are
determined parameters , , , , , ,
, , etc., which allow to provide the
compatibility of the thermodynamic and gas -dynamic
profiles of the LRE chamber. Consequently, the use of
formulas (6) –(10) allows to combine these features and
to form thermo -gas -dynamic calculation technique of
the rocket engine chamber, which scheme is shown in
Fig.1.

Figure 1: The design scheme of the LRE chamber geometry based on the modified th ermo -gas -dynamic
calculation technique.

As already mentioned, the distribution of
parameters in the chamber of the LRE
, , determines the
correct application of the method of characteristic s.
Taking into account these distributions, in the next
paragraph were considered ap plying results of the
corrected method of characteristics in supersonic
nozzle profiling [Abdulla, 2019]:




where -the variable h eat capacity ratio
( , can be take as ), -
the Mach number of the gas fl ow at the mentioned
nozzle point (or at the beginning of uniform flow
region).
RESULTS AND DISCUSSION
From the above the oretical foundations of the
thermodynamic calculation of LRE, it can be concluded
that the engine nozzle must be designed with the
isentropic index values changes. As a result of the
variable application, as me ntioned, the nozzle of a
rocket engine becomes more accurate. Results of  ) (Tf cp= ) (6T f N = n n nS nI n nR n npc . nvc. n na ) , (1 y x f Ni= ) , (2 y x f ci= ) , (3 y x f =  ))1 ( arctan( 1
1 )1 ( arctan 1
1 ) , ( 2 2 − −





+
− −  −
+ = = M M M 


    ) (3T f = ) (7 x f T = ) (x T T sigmoid = M  

American Scientific Journal № ( 32) / 2019 19

different inputs can be considered in order to discuss
the effect of variable specific heat ratio implementation
to the nozzle design. In order to demonstrate the
variation, two diffe rent cases are analyzed for the
project. Fig. 2 -3 represent the outputs f or different
inputs. Two different nozzles are analyzed using the
data given in Table 2. Figures clearly show that the
nozzle contours obtained from constant and variable
specific hea t ratios are not the same. As it is observed
from the figure legends, one of the contour is
constructed based on constant , whereas another one
is constructed using variable approach. Results
yields, that the co ntours are different for two different
cases. The contour built based on constant is
inaccurate because, as mentioned previously,
thermodynamic computations of the combustion
process yield that varies along the nozzle length. On
the other hand, a more accurate contour that is build
based on varying is given in red color. As a result, it
is observed that if increases starting from the nozzle
throat until the nozzle ex it, then the nozzle contour
narrows.
Table 2
Experimental Cases with Properties
Case № Performance Parameters Spe cific Heat Ratio
Case 1
, , ,


,
Case 2
, , ,


,

Figure 2: Contour of th e LRE nozzle
Case 1: γ=const, and γ=var (γ↑)
Figure 3: Contour of the LRE nozzle
Case 2: γ=const and γ=var (γ↓)
the abscissa axis - , the ordinate axis -

On the other hand, Fig. 3 represents the nozzle
contour for Case 2, in which all the properties remain
the same as in Case 1. What differs Case 2 from Case 1
is the variation. In the first case increases from
the nozzle throat until the nozzle exit, whereas in the
second case decreases in the mentioned direction.
Thus, the LRE chamber geometry can be easily
adapted to real conditions depending on the specific
task (customer requirements for engine size and weight,
type of flight vehicle, fuel and the main parameters of
the engine work, etc.).
Based on the analysis of the results of a numerical
experiment, it can be concluded that correctly taking
into account changes in thermodynamic parameters of
combustion products along the nozzle length allows us
to sol ve the following problems:
• organize control of the LRE chamb er function
by changing the thermophysical properties of
combustion products along the nozzle length
• organize, in flight, the correct gas -dynamic
control of changes in the degree of expansion of gases
in the LRE chamber
• control the influence of the initial expansion
zone of gases on the distribution of the velocity field at
the nozzle exit
• reduce the surface area of the cooling walls o f
the LRE chamber
• to form the optimal geometry of the entire
LRE chamber
As we can see, taking into account changes in the
properties of combustion products allows us to control
the gas flow expansion in all flight conditions. This
circumstance leads to t he improvement of the pneumo -
hydraulic scheme of the LRE. Gen erally, solutions of       s m we / 2250= K Te 1500= ) /( 320 kgK J Re= 25 / *= A Ae const = = 18 . 1  16.1=i 20.1=e s m we / 2250= K Te 1500= ) /( 320 kgK J Re= 25 /
*
= A A
e const = = 18 . 1  20 . 1 =
i
 16 . 1 =
e
 x y   

20 American Scientific Journal № ( 32) / 20 19
these problems require additional researches. As can be
seen, accounting and control of thermophysical
properties of combustion products along the LRE
chamber length allows a n application of new principles
for the organization of the w orking processes of such
engines and the improvement of their design schemes.
CONCLUSION
The conducted studies show that the thermo -gas -
dynamic calculation of the LRE, taking into account the
distribution of energy parameters over the chamber
volume, allow s obtaining more accurate engine
geometry. This circumstance determines the
improvement of the constructive schemes of the LRE
with the use of elements of the formation of local values
of therm odynamic parameters in the chamber volume.
Application of these elements can be implemented in
the form of injection and afterburning of pre -burner
gases in certain sections of the LRE chamber in order
to change the local values of the main parameters.
Thu s, a modified method for determining the
optimal thermo -gas -dyn amic profile of the LRE
chamber using the results of thermodynamic
calculation has been proposed. The technique is based
on the distribution of the gas compositions and moles
of its components, heat capacities, temperatures and the
gas flow velocities alon g the length of the LRE
chamber. The proposed modified method allows to
carry out thermo -gas -dynamic calculations of LRE
with maximum consideration of the gas -dynamic
features of the PС in the engine chamber and to increase
the efficiency of thermodynamic calculation. This
approach allows forming the appropriate geometry of
the LRE chamber at the preliminary stage of engine
design and improving the nozzle profiling results by the
modified method of characteristics.

References
Abdulla, N. (2019) Implementat ion of variable
specific heat ratio in liquid rocket nozzle design using
method of characteristics , Proceedings of the IV
International Scientific and Practical Conference
“Creative Potential o f Young People in the Solving of
Aerospace Problems, February R eadings -2019”,
National Aviation Academy, Baku, Azerbaijan,
February 27 -28, 2019, p.28 –31.
Abdullayev, P.Sh., Ilyasov, M.Kh., (2017), Dual -
scheme profiling technique for the liquid rocket eng ine
nozzle . AIAC -2017 -1051, METU, 9th Ankara
International Aeros pace Conference, 2017.
Alemasov, V.E., Dregalin, A.F., Tishin, A.P.
(1989) Theory of Rocket Engines . A Textbook for High
Schools, Ed. V.P. Glushko., Moscow,
Mashinostroeniye, 464 p., in russ ian.
Anderson, J.J. (1982) Modern Compressible
Flow: With Histori cal Perspective . New York:
McGraw -Hill Book Company. 1982.
Babkin, A.I., Dorofeev, A.A., Loskutnikova, G.T.,
Filimonov, L.A., Chernukhin, V.A. (1990) Calculation
of parameters and character istics of the RE camera,
Edited by Babkin A.I. Moscow: MGTU., in ru ssian.
Belov, G.V., Trusov, B.G. (2013)
Thermodynamic modeling of chemically reacting
systems . Moscow, MSTU named after E.E. Bauman,
96 p., in russian.
Bonnie, J.M., Michael, J.Z., Sanford, G. (2002)
Coefficients for Calculating Thermodynamic
Properties of Individual Species . Glenn Research
Center, NASA TP -2002 -211556, NASA Glenn
Cleveland, Ohio, USA.
Brykov, N.A., Volkov, K.N., Emelyanov, V.N.,
and Teterina, I.V. (2017) Flows of Ideal and Real Gases
in Channels of Variable Cross Section with Unsteady
Local ized Energy Supply , Computational methods and
programming, T.18, N1, http://num -
meth.srcc.m su.ru/zhurnal/ tom_2017/pdf/v18r103.pdf,
p.20 -40., in russian.
Bulygin, Yu.A., Kretinin, A.V., Rachuk, V.S.,
Faleev, S.V. (1997) Calculation of the thermal state of
the liquid propellant rocket engine , Editor V.P.
Kozelkov, VSTU, Voronej, 1997, 90 p., in russian.
Cantwell, B.J. Aircraft and Rocket Propulsion ,
(2015) AA283 course, Stanford University, Stanford
California, 94305, https://web.stanford.edu/~cantwell/
AA28 3_Course_ Material/AA283_Course_Notes/,
January 6, 2019, viewed in 25.03.2019.
Colonno, M.R. Van der Weide, E., Alonso, J.J.
(2008) The Optimum Vacuum Nozzle: an MDO
Approach , 46th AIAA Aerospace Sciences Meeting
and Exhibit, AIAA 2008 -911, 7 - 10 January 2008,
Reno, Nevada
Fu , L., Zhang S. and Zheng, Y. (2016) Design and
Verification of Minimum Length Nozzles with
Specific/Variable Heat Ratio Based on Method of
Characteristics, International Journal of Computational
Methods V.13, N.06
Glushko, V.P., Alemasov V.E. and others. (1971 -
1976) Thermodynamic and thermophysical propert ies
of co mbustion products, A guide in 10 volumes. Under
the scientific. by the hand of V. P. Glushko, USSR
Academy of Sciences, Moscow, VINITI, Volume 1., in
russian.
Gordon, S. and McBride, B. (1994) Computer
Program for Complex Chemical Equilibrium
Com positions and Applications , Vol.1. Analysis,
NASA RP 1311.
Gurtovoy, A.A., Ivanov, A.V., Skomorokhov,
G.I., Shmatov, D.P. (2016) Calculation and design of
LPRE aggregates, Voronezh, VSTU, in russian.
Gurvich, L.V., Veitz, I.V. et al. (1978 -82)
Thermodyn amic Propert ies of Individual Substances .
in 4 volumes, Eds. V.P. Glushko et al., Nauka, M., in
russian.
Hill, P., Peterson, C. (1992) Mechanics and
Thermodynamics of Propulsion , Addison -Wesley
Publishing Company, 2nd Edition.
Kestin, J. (1950) Influenc e of Variable Specific
Heats on the High -speed Flow of Air , A.R.C. Technical
Report, C.P. No.33 (13.176), London his majesty’s
stationery office, Polish University College.
Kyprianidis, K.G., Sethi, V., Ogaji, S.O.T.,
Pilidis, P., Singh, R., Kalfas, A.I. (2009) Thermo -fluid
modelling for gas turbines -part 1: Theoretical
foundation and uncertainty analysis , GT2009 -60092,
Proceedings of ASME TURBO EXPO 2009, : Power

American Scientific Journal № ( 32) / 2019 21

for Land, Sea and Air, GT2009, June 8 -12, 2009,
Orlando, FL, USA.
Paşayev, A., Abdullayev, P. and Samedov, A .
(2018) Sıvı yakıtlı roket motorunun itme odasının
geliştirilmiş tasarım yöntemi , SAVTEK 2018,
9.Savunma Teknolojileri Kongresi, ODTÜ, Ankara,
27 -29 Haziran, 2018.
Rizkalla, O., Chinitz, W. and Erdos, J.I. (1990 )
Calculated Chemical and Vibrational Non equilibrium
Effects in Hypersonic Nozzles , Journal of propulsion
and power, pp.50 -57.
Sutton, G.P. (2010) Rocket Propulsion Elements ,
New York: John Wiley & Sons, Inc.,
Vasiliev, A.P., Kudryavtsev, V.M., Kuznets ov,
V.A., Kurpatenkov, V.D., Obelnitsky, A.M., Polyaev,
V.M., Poluyan, B.Y. (1983) Fundamentals of the
theory and calculation of liquid rocket engines,
Textbook. Edited by V.M. Kudryavtsev. Moscow,
High School, 3rd edition, revised and enlarged, 703 p.,
in russian.
Zebbiche, T. (2011) Stagnation temperature effect
on the supersonic axisymmetric minimum length
nozzle design with application for air , Adv. Space Res.
48 (10), 1656 –167 5.

DEVELOPING AN APPLIC ATION FOR FACIAL IDE NTIFICATION IN THE J AVA
PROGRAM MING LANGUAGE

Boranbayev S.N.,
Kabdulkarimov Y.Z.
Eurasian National University named after L.N. Gumilyov, Nur -Sultan

Abstract . This article describes a developed a pplication for identifying individuals in the Java programming
language. For recognition of image templates, the OpenCV library was selected. Based on the methods that the
OpenCV library classes offer, a program with a graphical user interface for detectin g faces has been developed.
Keywords: identification, recognition, image, pattern, processing, confidentiality, security.

1.Introduction
Alan Kay said: “People who are really serious
about their software must create their own hardw are”
[1]. This expressio n is also suitable for ensuring your
own safety. A country that is truly serious about its own
security must create its own security software and
hardware. This means that each country must create its
own devices for the recognition , processing,
identifica tion and analysis of data obtained from video
and photo cameras of outdoor surveillance and other
monitoring devices for private and public sectors.Since,
if these devices were purchased abroad, this can lead to
information leakage, because the device can be
controlled remotely by the manufacturers of this
device. To ensure confidentiality and complete control
of security systems by your own government agencies,
you must create your own software for the recognition,
processing, ident ification and analysis o f information.
Therefore, creating an application for recognizing and
identifying certain image patterns, such as people's
faces, partially solves this problem.
2.Development of an application for facial
identification
In the process of developing a progra m for face
recognition, the following sources were analyzed:
● Existing face recognition approaches used
by Google, Apple and Samsung to authenticate users
and face recognition in photos and videos; [2 -4]
● modern principle s of security systems for
face recogn ition and identification; [5,6]
● neural networks that are used to process and
analyze video and photos; [7.8]
Algorithms based on existing approaches have
been developed. A high -level Java programming
language is used t o create this application. The choice
of this particular programming language is that the
operating system of many devices, such as cell phones,
televisions, drones, camcorders, cameras is Android,
which is written in Java. Thus, it is possible to integrat e
the created program into a device th at uses Android.
Also programs written in Java are portable. After
compiling the program on the computer, it is possible
to run the bytecode of the program on all devices that
have a Java Virtual Machine. [9] Next, it was necessary
to choose a library that will recognize image templates.
Currently, Java does not have its own libraries for
recognizing image templates. A third -party OpenCV
library (Open Source Computer Vision Library, an
open -source computer vision librar y) was chosen - a
library of computer -vision algorithms, image
processing and general -purpose open -source numerical
algorithms. [10] Implemented in C / C ++, also
developed for Python, Java, Ruby, Matlab, Lua, and
other languages. It can be freely used for academic and
commercial purposes. The authors of this library are
Intel Corporation. [11] OpenCV includes the following
tools:
● image processing (filtering, geometric
transformations, color space conversion);
● input / output of images and videos, machine
learning models (SVM, decision trees, le arning with
stimulation);
● recognition and description of flat
primitives;
● motion analysis and object tracking (optical
flow, motion patterns, background removal);
● detection of objects in the image (finding
faces using the Viola -Jones algorithm, recognizing
HOG people), calibrating the camera, searching for
stereo matching and 3D processing elements. [12]
Next, the task was to install and connect the
OpenCV library during application development. The
tricky part was conn ecting the library to the application.
Since there was no detailed user manual. However,