# 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.

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Filimonov, L.A., Chernukhin, V.A. (1990) Calculation

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96 p., in russian.

Bonnie, J.M., Michael, J.Z., Sanford, G. (2002)

Coefficients for Calculating Thermodynamic

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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.

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Faleev, S.V. (1997) Calculation of the thermal state of

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(2015) AA283 course, Stanford University, Stanford

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(2008) The Optimum Vacuum Nozzle: an MDO

Approach , 46th AIAA Aerospace Sciences Meeting

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Verification of Minimum Length Nozzles with

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Vasiliev, A.P., Kudryavtsev, V.M., Kuznets ov,

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V.M., Poluyan, B.Y. (1983) Fundamentals of the

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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,

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.

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in Channels of Variable Cross Section with Unsteady

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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,