MMSE Journal Vol.2 2016

Mechanics, Materials Science & Engineering, January 2016 – ISSN 2412-5954
MMSE Journal. Open Access www.mmse.xyz
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Sankt Lorenzen 36, 8715, Sankt Lorenzen, Austria
Mechanics, Materials Science & Engineering Journal
January 2016

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Mechanics, Materials Sciences & Engineering Journal, Austria, Sankt Lorenzen, 2015
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CONTENT
I. MATERIALS SCIENCE ................................................................................................ 5
THE CARBON-FLUORINE ADDITIVES FOR WELDING FLUXES ......................................... 5
INFLUENCE VOLTAGE PULSE ELECTRICAL DISCHARGE IN THE WATER AT THE
ENDURANCE FATIGUE OF CARBON STEEL ................................................................... 15
ALUMINUM COMPOSITES WITH SMALL NANOPARTICLES ADDITIONS: CORROSION
RESISTANCE.................................................................................................................. 25
II. MECHANICAL ENGINEERING & PHYSICS ............................................................. 31
PERFORMANCE OPTIMIZATION OF A GAS TURBINE POWER PLANT BASED ON ENERGY
AND EXERGY ANALYSIS .............................................................................................. 31
CERTAIN SOLUTIONS OF SHOCK-WAVES IN NON-IDEAL GASES .................................. 44
ANALYTICAL MODELING OF TRANSIENT PROCESS IN TERMS OF ONE-DIMENSIONAL
PROBLEM OF DYNAMICS WITH KINEMATIC ACTION .................................................... 57
ON INFLUENCE OF DESIGN PARAMETERS OF MINING RAIL TRANSPORT ON SAFETY
INDICATORS ................................................................................................................. 62
VIII. Information Technologies .............................................................................. 70
THE ASSESSMENT OF THE STABILITY OF THE ELECTRONICS INDUSTRY FACILITY IN THE
MAN-MADE EMERGENCIES WITH THE USE OF INFORMATION TECHNOLOGY .............. 70
X. Philosophy of Research and Education.............................................................. 78
TEACHING REITLINGER CYCLES TO IMPROVE STUDENTS’ KNOWLEDGE AND
COMPREHENSION OF THERMODYNAMICS .................................................................... 78
MULTIMEDIA TUTORIAL IN PHYSICS FOR FOREIGN STUDENTS OF THE ENGINEERING
FACULTY PREPARATORY DEPARTMENT ....................................................................... 84
PETRUS PEREGRINUS OF MARICOURT AND THE MEDIEVAL MAGNETISM ..................... 90
DEPLETION GILDING: AN ANCIENT METHOD FOR SURFACE
ENRICHMENT OF GOLD ALLOYS .................................................................................. 98

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I. Materials Science
The Carbon-Fluorine Additives For Welding Fluxes
R.Е. Kryukov1
, O.А. Kozyreva1,a
, N.А. Kozyrev1,b
1 – Federal State Budgetary Educational Institution of Higher Professional Education «Siberian State Industrial
University», Research and Development Center «Welding Processes and Technologies», 654007, Russia,
Novokuznetsk, 42, Kirov str.
a – kozireva-oa@yandex.ru
b – kozyrev_na@mtsp.sibsiu.ru
Keywords: welding, flux, metal, slag, gas-forming compounds.
ABSTRACT. Is carried out the thermodynamic estimation of the probability of the flow of the processes of the removal
of hydrogen from the weld with the welding in the fluorine-bearing flux in the standard states in the range of
temperatures 1700 – 2200 K. In this case, as the standard states for the substances – of reagents they were selected:
Na3AlF6L, SiO2L, SiF4g, NaAlO2s, Na2SiO3l, CaF2l, CaSiO3l, H2g, SiF2g, HFg, O2g, SiFg, Hg. As a result the calculations of
standard energy of Gibbs and equilibrium constants of reactions it is determined, that from the reactions of the direct
interaction of ftoragentov of slag with hydrogen and oxygen of the metal most probable appears the reaction with the
cryolite. In the mechanism of more complex interaction with the participation in the reaction, besides ftoragentov, silica
of slag and by the possible formation of the intermediate product of SiF4g more probable is the process with fluorite.
Calculations showed the expediency of using the connection Na3AlF6 together with fluorite for the removal of hydrogen
with the submerged welding. The carried out calculations became the basis of the development of the compositions of
the new flux- additives, protected by patents RF.
Introduction. The issue of new fluxes and their additives development has been attracting much
attention currently, as well as research into their influence on welding and technological characteristics
of a weld and on the concentration of oxygen and non-metallic impurities in a weld [1-5].
Submerged arc welding is attended by intensive mass transfer of liquid molten metal and slag,
forming from welding flux. Reactions of oxidation and deoxidation of manganese, ferrum, and
silicon, i.d. exchange processes involving oxygen are typical for this process. The most grades of
domestically produced fluxes, which are applied for welding low-alloyed steels are oxidizing ones
and ground on silicon-manganese oxidation-reduction processes. Here, the products of these
reactions are oxide compounds of silicon, manganese, ferrum, aluminum etc., which often can’t
surface and assimilate to slag, forming from welding flux, the level of impurity of weld metal by
non-metallic admixtures increases consequently; as the result, the complex of physical and
mechanical characteristics deteriorates. Apparently, restoratives, which form gaseous products of
reactions, are advisable to apply in order to avoid impurity of weld metal. It is carbon that can be a
restorative of this kind, and forms gaseous compounds CO2 and CO when reacting with oxidizers.

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Materials and methods of research. Shielding is usually provided through pushing atmospheric
gases aside from weld zone by forming gases CO2 (CO); that helps to reduce or even exclude the
probability of molten metal saturation with oxygen, nitrogen or hydrogen from atmosphere. Gas-
forming compounds of carbonates like CaCO3, MgCO3, FeCO3, MnCO3 and their derivatives are
usually used for this purpose. Gas shielding is possible due to CO2 as high-temperature
decomposition of carbonates takes place according to the following reactions and temperatures [6]:
CaCO3 → CaO + CO2 (900-1200 ºC), (1)
MgCO3 → MgO + CO2 (>650 ºC), (2)
FeCO3 → FeO + CO2 (280-490 ºC), (3)
MnCO3 → MnO + CO2 (330-500 ºC) (4)
According to stoichiometric calculations the results of decomposition are as follows: 1 kg CaCO3 –
0.224 m3
CO2, 1 kg MgCO3 – 0.267 m3
, 1 kg FeCO3 – 0.192 m3
, 1 kg MnCO3 – 0.194 m3
.
Without taking into account the costs of carbonates decomposition, MgCO3 and CaCO3 are the most
optimal components, which help to get most CO2 when decomposing 1 kg of material, succeeded
by MnCO3 и FeCO3.
Furthermore, when decomposing CaCO3 and MgCO3 basic oxides CaO and MgO are formed and
improve basicity of welding flux, and that of a forming slag, respectively, whereas, when MnCO3
and FeCO3 decomposing oxides FeO and MnO are formed, which raise the degree of oxidation in
slag systems and oxygen concentration in a weld. The latter causes all negative consequences –
increasing level of impurity by non-metallic oxide components in a weld and deterioration of
mechanical properties.
Having followed all mentioned pre-conditions we have developed a flux – ANK additive, protected
it by a patent of the Russian Federation and applied in production process at Open Joint Stock
Company “Novokuznetsk Plant of Reservoir Metalware named after N.E. Kryukov” [7]. For its
manufacturing ferrosilicon FS75 (GOST 1415-78), marble М92- М97 (GOST 4416-73 (92-97%
СаСО3)), and liquid glass (GOST 13078-81) were used. Production technology was as follows.
Marble and ferrosilicon were grinded to less than 1 mm fraction. Grinded marble and silicon were
mixed in 50 to 50% mass proportion. It was dried at temperature 100-200 0
С for 10 - 20 minutes,
succeeded by grinding and size grading to 2.5 mm. 3-5% of additive was introduced into fluxes.
Before a flux with an additive is used its 40 – 60 minutes annealing in the furnace is recommended
at temperature 250-350 0
С.
This additive is used for roll welding of tanks. The technology involves assembling, welding,
controlling and rolling plates of tanks walls, all the processes are performed on special roll facilities
with upper and down rolling. Two-side submerged arc welding of butt joints of wall plates is
applied in the process, first on the upper tier, then on the lower one, after the plate is rolled. An
additive helped to avoid pore formation and improve quality of welds.
However, shielding gases CO and CO2 can form due to carbon, added to the flux, according to the
reactions:
(C) + [O2] = {CO2}, (6)

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(C) + ½[O2] = {CO} (7)
Here 1.863 m3
CO2 and 1.864 m3
CO release per each kg of carbon (in normal conditions).
The second important issue is that of weld metal dehydrogenization. As a rule, it is carried out by
introducing fluorine-containing additives (fluorite or cryolite), hydrogen combines with fluorine
and is further removed as a compound HF.
The following chemical transformations can be considered as probable reactions of removal:
1/2 (CaF2)+ [H]+ 1/2 [O] = 1/2(CaO) + HFg, (8)
1/6(Na3AlF6)+ [H]+ 1/2 [O] = 1/6NaAlO2 s+ HFg + 1/6(Na2O), (9)
As well as reactions:
2(CaF2) + 3(SiO2) = 2CaSiO3 s + SiF4g, (10)
2/3(Na3AlF6) + 5/3(SiO2) = SiF4g + 2/3NaAlO2 s + 2/3 (Na2SiO3), (11)
succeeded by reactions of dehydrogenization with SiF4:
1/2 SiF4g + [H] = 1/2SiF2 g+ HFg (12)
1/4 SiF4g + [H]+ 1/2 [O] = 1/4 (SiО2) + HFg (13)
1/3 SiF4g + [H] = 1/3SiFg + HFg (14)
1/2 SiF4g + [H] = 1/2 SiF2g + HFg (15)
Thermodynamical characteristics in standard conditions [∆rН°(Т), ∆rS°(Т), ∆rG°(Т)] needed to
assess reaction probability were calculated by well-known methods [8] in the temperature range of
welding processes 1700 – 2200 К [9] in terms of thermodynamic properties of reagents [[Н°(Т)-
Н°(298,15 K)], S°(Т), ∆fH°(298,15 K)] [10,11]. Here, chemical states Na3AlF6l, SiO2l, SiF4g,
NaAlO2 s,Na2SiO3l, CaF2l , CaSiO3 s, H2г, SiF2g, HFg, О2g, SiFg, Hg were selected as standard ones
for substances – reagents in the range 1700 – 2200 К according to fact aggregate states of phases in
the system under consideration.
The results of calculations are provided in the Table 1.
Table 1 demonstrates that reaction (9) is thermodynamically the most probable (cryolite
dehydrogenization), the second one is reaction (8) (fluorite dehydrogenization), followed by
reactions (10, 11), where silicon tetrafluoride is formed as an intermediate product of further
reactions (12) - (15); the latter result in formation of gaseous compound HF. Here, reaction (13) is
thermodynamically the most probable (SiF4 combines with hydrogen and oxygen). The
stoichiometric reactions (15), (12), (14) are the least probable ones.

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Table 1. Standard Gibbs energy of reactions (8) – (15) and reaction equilibrium constants
according to temperature
Reaction
∆rG°(Т), kJ
К(Т)
1700К 1800К 1900К 2000К 2100К 2200К
8
-16,22 -18,61 -20,93 -23,17 -25,36 -27,47
3,2 3,5 3,8 4,0 4,3 4,5
9
-32,32 -33,82 -35,20 -36,46 -37,62 -38,68
9,8 9,6 9,3 9,0 8,6 8,3
10
41,80 35,98 30,62 25,71 21,22 17,18
0,05 0,09 0,14 0,21 0,30 0,39
11
82,41 76,11 70,40 65,22 60,56 56,38
0,003 0,006 0,012 0,020 0,031 0,046
12
86,62 78,13 69,68 61,27 52,90 44,57
0,002 0,005 0,012 0,025 0,048 0,087
13
-90,16 -89,83 -89,51 -89,21 -88,91 -88,63
589,5 404,5 289,1 213,8 162,8 127,2
14
113,04 104,93 96,86 88,82 80,80 72,82
0,0003 0,0009 0,0022 0,0048 0,0098 0,0187
15
-38,07 -40,60 -43,08 -45,49 -47,84 -50,14
14,78 15,08 15,29 15,42 15,49 15,51
Therefore, Na3AlF6 is the most reasonable to use for dehydrogenization when submerged arc
welding as if compared with fluorite.
Having taken into account the aforementioned preconditions, we have developed a technology of
submerged arc welding with carbonaceous additives. As the basis of carbon and fluorine containing
additive we took metallurgical production wastes. It was dust with the following chemical
composition (mass %): Al2O3 = 21 – 46.23; F = 18 – 27; Na2O = 8 – 15; К2O = 0.4 – 6; CaO = 0.7 –
2.3; SiO2 = 0.5 – 2.48; Fe2O3 = 2.1 – 3.27; C = 12.5 – 30.2; MnO = 0.07 – 0.9; MgO = 0.06 – 0.9; S
= 0.09 – 0.19; P = 0.1 – 0.18. Mineralogical makeup of dust was determined according to the data
of X-ray structural analysis made by difractometer DRON-2 in the mode: Fe – K α radiation,
voltage 26 kV, electrical current 30 mA.
The research into the dust of electrostatic precipitators revealed that the material consisted of bi-
dimensionally ordered carbon (d0O2=3.47Å, Lc=45.8Å), X-ray amorphous substance, cryolite,
corundum, hyolithe, and various admixtures. Diffraction patterns of roasted at 700°С material
demonstrate no indication of graphite, that is caused by nearly complete burning out of carbon-
containing mass in this temperature range, as well as significant curve flattering on the diffraction
pattern, and decrease in X-ray amorphous substance. The reason of the latter is probably chemical

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composition of X-ray amorphous substance, which carbon compounds are main components of. At
700°С the change in indication intensity of mineralizing components (cryolite, corundum, X-ray
amorphous substance, fluorite, hematite and various admixtures) was recorded.
From the theoretical point of view the additive makes possible: 1) dehydrogenization by fluorine-
containing compounds (like Na3AlF6,), decomposing at the temperatures of welding processes and
isolating fluorine, which combines with dissolved in steel hydrogen and forms gaseous HF; 2)
intensive carbon “boiling” due to forming CO and CO2, when fluoric carbon CFx (1 ≥x>0)
combines with dissolved in steel oxygen, here, as carbon is in a bound state steel carbonization is
hardly possible; 3) improvement of arc stability due to potassium and sodium, facilitating ionization
in arc column.
To make an additive to flux carbon and fluorine containing substance was mixed with liquid glass,
then this mixture was dried, cooled down and grinded. Afterwards this additive was mixed with flux
in a special mixer according to a definite, strictly determined proportion. АN-348А, АN-60, АN-67
fluxes were taken as basic ones and their mixtures with flux-additives.
The experiments were carried out on 200500 mm 09Mn2Si steel samples 16 mm in thickness.
Fay welding of butt joints was made on two sides, as when welding wall plates of tanks on roll
facility. Sv-08Mn wire 5 mm in diameter was used as a filler metal.
Submerged arc welding of samples was made in similar modes. The samples were cut of welded
plates and subject to the following tests: X-ray spectral analysis of weld metal chemical
composition, metallographic tests of welds; total concentration of oxygen in welds, mechanical
properties, strength of joint welds and impact strength of welds were determined at temperatures -
20°С and -40°С. Concentration of carbon, sulphur, phosphorus was determined in chemical
composition of weld metal by chemical methods in terms of GOST 12344-2003, GOST 12345-
2001, and GOST 12347-77, respectively. Concentration of alloying elements in weld metal; that of
calcium oxide, silicon, manganese, aluminum, magnesium, ferrum, potassium, sodium and fluorine-
compounds in fluxes with additives and slag, obtained after welding was determined by
SHIMADZU roentgen-fluorescent spectrometer XRF-1800.
The experiments demonstrated that maximum 6% carbon and fluorine containing additive provided
carbon concentration in weld similar to its concentration in original metal (Figure 1), whereas
concentration of oxygen, hydrogen and nitrogen dropped (Figures 2, 3, 4).
Fig. 1. Influence of carbon and fluorine containing additive on carbon concentration in a weld

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Metallographic research into polished sections of joint welds was carried out by optical microscope
OLYMPUS GX-51 in bright field and zooming ×100, ×500. The microstructure of metal was found
out by etching in 4 % HNO3 solution in ethanol. The structure of base metal in all samples consists
of ferrite grains and lamellar pearlite (4-5 µm). In base – to – added metal zone a fine-grain
structure occurs (1-2 µm), which was formed as the result of re-crystallizing when heating in course
of welding. In the microstructure of a weld there are ferrite grains stretched towards heat rejection
because of heating and speeded up cooling down. Structures of welds didn’t differ much
irrespectively of used fluxes. The level of impurity by non-metallic substances decreased in
samples, which were welded with fluxing agents, containing carbon and fluorine additives; it was
caused by reduction of total oxygen concentration.
Fig. 2. The change in oxygen in dependence on carbon and fluoride containing additive concentration
Fig. 3. The change in hydrogen in dependence on carbon and fluorine containing additive
The research into mechanical properties (yield point, strength, modulus of elongation, impact
strength at temperatures below zero) carried out on cut according to GOST 6996-66 samples,
demonstrated that the level of properties went beyond the values required in GOST 31385-2008 and

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increased as the concentration of carbon and fluorine containing additive rose. Increasing impact
strength KCV and KCU at temperatures -20°С and -40°С, respectively (Figures 5, 6) is worth
mentioning. Flux-additives, which were developed, have been protected by the Russian Federation
patents [12, 13].
Fig. 4. The change in nitrogen in dependence on carbon and fluorine containing additive
Fig. 5. The change in impact strength KCV at temperature -20°С in dependence on carbon and
fluorine containing additive.
Summary. 1. On the ground of made calculations and carried out experiments we can conclude that carbon
containing additives to welding fluxes are possible and promising ones in order to improve welding and
technological characteristics of welded metalware.
2. The probability of dehydrogenization of a weld in fluorine containing submerged arc welding has
been assessed thermodynamically in the temperature range 1700 – 2200 К. Here, Na3AlF6l, SiO2l,
SiF4g, NaAlO2s, Na2SiO3l, CaF2l, CaSiO3 s, H2г, SiF2g, HFg, О2g, SiFg, Hg. were selected as standard
states for substances - reagents. In terms of calculation of standard Gibbs energy reactions it has
been found out that the reaction of gaseous hydrogen fluorine direct formation by cryolite is
thermodynamically the most probable one, the second probable is the group of reactions resulting in

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formation of silicon tetrafluoride as an intermediate product for further HF formation. In this group
the most thermodynamically probable reaction is that of SiF4 with hydrogen and oxygen. In terms
of calculations Na3AlF6 is more reasonable to use for dehydrogenization when submerged arc
welding in comparison to fluorite.
Fig. 6. The change in impact strength KCV at temperature -40°С in dependence on carbon and
fluorine containing additive
3. Introduction of developed carbon and fluorine containing additive into fluxes АN-348А, АN-60
and АN-67 reduces gas content of a weld, the level of impurity by oxide non-metallic substances,
and improves required mechanical properties and impact strength (at temperatures below zero,
especially).
References
[1] Study of the relationship between the composition of a fused flux and its structure and
properties/ Amado Cruz Crespoa, Rafael Quintana Puchola, Lorenzo Perdomo Gonzáleza, Carlos R.
Gómez Péreza, Gilma Castellanosa, Eduardo Díaz Cedréa & Tamara Ortíza / Welding International.
– 2009. - Volume 23. - №2. - p. 120-131
[2] Using a new general-purpose ceramic flux SFM-101 in welding of beams/ Yu. S. Volobueva, O.
S. Volobueva, A. G. Parkhomenko, E. I. Dobrozhelac & O. S. Klimenchuk // Welding
International.– 2012.- Volume 26. - №8. - p. 649-653
[3] Special features of agglomerated (ceramic) fluxes in welding / V. V. Golovko & N. N.
Potapov // Welding International. – 2011.- Volume 25. - №11. - p. 889 - 893.
[4] The influence of the air occluded in the deposition layer of flux during automatic welding: a
technological aspect to consider in the quality of the bead / Rafael Quintana Puchola, Jeily
Rodríguez Blancoa, Lorenzo Perdomo Gonzaleza, Gilma Castellanos Hernándeza & Carlos Rene
Gómez Péreza // Welding International. – 2009.- Volume 23. - №2. - p. 132-140.
[5] Obtaining a submerged arc welding flux of the MnO–SiO2–CaO–Al2O3 – CaF2 system by
fusion / A.C. Crespoa, R.Q. Puchola, L.P. Goncaleza, L.G. Sanchezb, C.R. Gomez Pereza, E.D.

13
Cedrea, T.O. Mendeza & J.A. Pozola//Welding International.– 2007.- Volume 21. - №7. - p. 502-
511.
[6] Reaction of non-organic substances / R.А. Lidin, V.А. Molochko, L.L. Andreeva – М.: Drofa,
2007. – 637 p.
[7] Manufacture of vertical bulk –oil storage tanks for northern climates using special welding
materials/ Kryukov N.E., Koval'skii I.N., Kozyrev N.A., Igushev V.F., Kryukov R.E.// Steel in
Translation. -2012. - Т. 42. -№ 2.-P. 118-120.
[8] Thermodynamical properties of substances: Reference book. V.1. Issue 1 / Edited by V.P.
Glushko, L.V. Gurvich et al. M.: Nauka, 1978. pp. 22.
[9] Welding materials for arc welding: СReference book in 2 volumes. V. 1. Shielding gases and
welding fluxes: Konishchev B.P., Kurlanov S.А., Potapov N.N. et al. / Edited by Potapov N.N. -
М.: Machinebuilding, 1989 – pp. 104.
[10] John L. Haas, Jr., Gilpin R. Robinson, Jr., and Bruse S. Hemingway // J. Phys. Chem. Ref.
Data. – 1981. – Vol. 10. – № 3. – P. 575 – 669.
[11] NIST-JANAF Thermochemical Tables 1985. Version 1.0 [Electronic resource] : data compiled
and evaluated by M.W. Chase, Jr., C.A. Davies, J.R. Dawney, Jr., D.J. Frurip, R.A. Mc Donald, and
A.N. Syvernd. – Available at: http://kinetics.nist.gov/janaf.
[12] Patent 2467853 RF, МPК 8
V23 К35/362 Ceramic flux-additive / Kryukov N.Е., Kovalsky
I.N., Kozyrev N.А., Igushev V.F., Krykov R.Е.; Open Joint Stock Company ОАО «Novokuznetsk
Plant of Reservoir Metalware» named after N.E. Kryukov.- № 201112341602/02(034654),
Application 08.06.2011.
[13] Patent 2484936 PF, МPК 8
V23 К35/362 Ceramic flux-additive / Kozyrev N.А., Igushev V.F.,
Kryukov R.Е., Goldun S.V.; FSBEI HPE “Siberian State Industrial University”.-
№2012104939/02(007484), Application 13.02.2012.

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Influence Voltage Pulse Electrical Discharge In The Water at the Endurance
Fatigue Of Carbon Steel
I.A. Vakulenko1, a
, A.G. Lisnyak2, b
1 – Department of Materials Technology, Dnepropetrovsk National University of Railway Transport named after
Academician V. Lazarian. Street. Lazarian, 2, Dnepropetrovsk, Ukraine, 49010, Tel. 38 (056) 373 15 56, ORCID 0000-
0002-7353-1916
2 – Department "The technology of mining machinery" Dnepropetrovsk National Mining University, pr. Karl Marx, 19,
Dnepropetrovsk, Ukraine, 49027, Tel. 38 (0562) 46 99 81, ORCID 0000-0001-6701-5504
a – dnuzt_texmat@ukr.net
b – aleklisn@gmail.com
Keywords: hardness, distribution, impuls pressures, electric digit, limited endurance
ABSTRACT. Effect of pulses of electrical discharge in the water at the magnitude of the limited endurance under
cyclic loading thermally hardened carbon steel was investigated. Observed increase stamina during cyclic loading a
corresponding increase in the number of accumulated dislocations on the fracture surface. Using the equation of Cofino-
Manson has revealed a decrease of strain loading cycle after treatment discharges. For field-cycle fatigue as a result of
processing the voltage pulses carbon steel structure improvement, followed by growth of limited endurance decrease
per cycle of deformation. With increasing amplitude of the voltage loop gain stamina effect on metal processing voltage
pulses is reduced. The results can be used to extend the life of parts that are subject to cyclic loading.
Introduction. In the process of cyclic loading of carbon steel, the extent, to which the cycle
amplitude exceeds fatigue limit, affects the character of structural change considerably [2]. For this
reason, the rate of increase in the number of crystalline defects, and evenness of their distribution in
the metallic matrix are the determinants of the conditions of the fatigue damage sites formation in
metals and alloys [14]. Considering that, dislocations are basic carrier units of plastic deformation
[3], the possibility of purposeful control over the process of their growth and redistribution under
the fatigue loading can be considered a promising direction of development of the measures on
improvement of the finite life. The information on the use of electric pulse effects [6, 10] in the
carbon steel after a certain degree of plastic deformation can serve as example. As a result, there
was such a change in the internal structure of a metallic material, which was required to achieve a
desired set of properties.
Status of the problem. At the certain stage of the development of metal materials processing
technology, in the production of complex shapes, especially of plate stock of considerable size, they
detected certain difficulties in the implementation of the technical solutions. One of the ways to solve
this problem was the proposal to use the shock wave resulted by an electric discharge in liquid [4].
Based on numerous studies [4‒8], it was found that this technology allows not only the
manufacturing of products by the formation of a complex deformed state but also managing a range
of properties. Based on this, we can confidently assume that the value of the energy of pulse
loading, its momentum distribution [7, 13] may significantly change the result to be achieved.
Considering the existence of a certain threshold dependence of the impulse of voltage being formed,

15
it is possible to obtain the result of different quality, ranging from the reinforcing effect to the metal
weakening [4, 11, 12]. In most cases, the effect of hydraulic shock caused by the electric discharge
in liquid for many metallic materials has reinforcing nature [4, 5], which is supposed to be followed
by the change in the number of accumulated dislocations. Thus, if the effect has reinforcing nature,
the increase in the dislocation density may be expected. Considering that the result depends on a
large number of individual factors, the cumulative effect often leads to qualitatively opposite
results. For example, the rise of the stress wave amplitude increases the number of dislocations [4].
On the other hand, the pulse length largely determines the conditions for the movement of the
dislocation structures. Most of the known experimental data concerns the study of the influence of
the electric discharge shock waves in liquid on the properties of metallic materials under static
loading [5]. Based on this, we can confidently assume that the assessment of the impact of this
effect on the behavior of the metal under the fatigue is quite an important issue.
Purpose. Assessment of the impact of voltage impulses of the electric discharge in liquid on the
behavior pattern of carbon steel under fatigue loading.
Methodology. The carbon steel of the railway wheel pair axle with 0.45% carbon content was the
material under research. The content of other chemical elements corresponded to the grade
composition. The samples for alternating bending test under symmetric loading cycle were metal
sheets of 1 mm thick, 15 mm wide and 180 mm length. The samples were subjected to martensite
quenching and tempering at 300°C, for 1h. The analysis of the fracture surfaces was performed
using a scanning electron microscope and fractography techniques; the dislocation density was
evaluated by X-ray methods [1].
Metal fatigue testing was performed under alternating bending under symmetric loading cycle by
means of the ten-station test machine “Saturn-10”. Electrical discharge impulse action on the
samples of steel in water was performed by the “Iskra-23”, with the amplitude of the voltage to a
maximum of 2 GPa. The total number of pulses was about 10 4
, at the frequency of 2-3 Gts.
Results. Selection of the structural state of steel after martensite quenching and subsequent
tempering at 300°C was driven by the possibility of achieving, under the high density of
dislocations, enhanced values of fatigue resistance of a metal under cyclic loading. From the
analysis of the internal structure of the metal, it follows that after quenching and tempering at
300°C, there the stages occur in the process of dispersed carbide particles liberation at the
dislocations, both in the middle and at the boundaries of martensite laths. Besides, as follows from
the results of studies [9], the development of dislocation recombination processes resulting in a
decrease in their total amount should always result in the lowering of their mobility. Therefore, we
can confidently assume that most of the dislocations that have appeared in the metal as a result of
mentioned thermal treatment are immobile to different extents.
The analysis of the shock stress treatment effect on the fatigue behavior of a metal was carried out
in a particular sequence. Fatigue curve was build first, for the samples that had undergone the
thermal treatment (Fig. 1, curve 1), by which the finite life of the metal was determined. Further, the
newly prepared samples were loaded, under the corresponding amplitudes of the cycle to the level
of 0.6‒0.7 of the value of the finite life. Then they were subjected to the shock stress. Further, the
cyclic loading continued until the final destruction of the samples. Finite life value is the total
number of cycles including the number of cycles before the shock stress treatment and after it, up to
the final destruction of the sample (Fig. 1, curve 2).
The analysis of fatigue curves shows the expected difference in the evolution of the fine crystalline
structure of the metal depending on the treatment applied. Indeed, for the similar amplitudes of
loading there is a clear increase in the fatigue resistance of the metal that has been subjected to the
shock wave impulse.

16
a ,
iN 6
10 cycle.
Fig. 1. The diagrams of cyclic loading steel 45 after tempering and annealing at 300 
C (♦) and
after treatment of SS (■).(Stress straik).
To explain the observed increase in the finite life of the metal, the dislocation density was estimated
by the interference (110) and (211) on the fracture surfaces of the samples.
Regardless of the treatment (before and after the shock stress), the decrease in the amplitude of the
cycle is followed by the accumulation of the amount of dislocations in the volume of metal under
plane-strain loading. The absolute values of )(hkl are of great interest. Thus, during cyclic loading
at high amplitude the absolute values of the dislocation density at the fracture surface of the samples
are almost the same. It can be explained by the fact that under high cyclic overstress the formation
of elementary shifts within the structural element of steel causes significant plastic deformations
localization, simultaneously with the rapid transition of the metal to the plane-strain condition.
Further, during the subsequent decrease of a the increase in the accumulated number of
dislocations occurs, with the rate of increase 211 that is significantly higher than the corresponding
value 110 (Fig. 2, a).
The nature of the changes of 211 and 110 (Fig. 2, a) corresponds to the known experimental data
for metal loading under unidirectional static and cyclic loading [2].
By treatment of the metal that had been subjected to the preliminary cyclic loading (up to 0.6-0.7 of
the value of the finite life with certain a ) by shock wave impulses, we have received the
qualitative differences in the nature of the change of the dislocation density on the investigated
interference (Fig. 2, b). The received level of absolute values: 211 is less than 110 , and their
change rate with the decrease of a appeared quite unexpected.
In order to explain the nature of the observed effect of the shock stress on the finite life under cyclic
loading, we analyzed the fracture surface of the samples.
Ряд1; 0,2; 110
Ряд1; 0,25; 93
Ряд1; 0,35; 75
Ряд1; 0,7; 60
Ряд2; 0,2; 120
Ряд2; 0,25; 100
Ряд2; 0,35; 90
Ряд2; 0,7; 80
1
2

17
210
),( 10 
 смhkl
a ,
а)
210
),( 10 
 смhkl
a ,
b)
Fig.2. The change of dislocations density, estimated on interferences (110) - ♦ and (211) - ■
depending on amplitude of cyclic loading and preliminary treatment: without SS (a) and after SS
(b).
The general analysis of fracture pattern in the samples after 256 3
10 cycles with the amplitude of
950 MPa (Fig. 3) shows that the surface of fracture was formed by a mixed mechanism. It is
indicated by the presence of chips inside grains (Fig. 3, A) and formation of the faceted surfaces of
intergranular fracture (Fig. 3, B) at the fracture surface.
The mechanism of formation of the chips inside grains is associated with the high overload along
the cycle. The first phase of structural changes caused by the emergence of elementary shifts within
Ряд1; 120; 13
Ряд1; 100; 10
Ряд1; 90; 15
Ряд1; 80; 21
Ряд2; 120; 10Ряд2; 100; 10
Ряд2; 90; 11
Ряд2; 80; 14

18
the individual grains due to the movement of the unevenly distributed dislocations. Randomly
oriented shifts lead to the rapid partition of the grain into pieces, the boundaries of which are the
series of microcavities. The fatigue microcracks appear and extend along the specified boundaries
due to the local low resistance of the metal [15]. In the case of discrepancy of surfaces of the
simultaneously growing microcracks, in the places where they meet, a step or another boundary
appears that separates the other fragments (light lines in Fig. 3).
Fig.3. Fractographic investigation of the sample after the 260x. 3
10 cycles at an amplitude of
950 MPa.
Formation of the facets of intergranular fracture has a different mechanism. Instead of the chip
within the grain, due to the reduction of the cyclic overload in individual grains, the microcavities
appear near the angle boundaries, which reduces the bond between individual grains in the metal.
Moreover, the movement of dislocations near the large angular boundaries for several
crystallographic systems results in a series of vacancies. Under the influence of cyclically varying
loads in the metal, the areas accumulating the vacancies near the grain boundaries turn into volumes
with high concentrations of microcavities, along which the fatigue crack grows. The more detailed
analysis shows additional features, which indicate the participation of other failure mechanisms in
the formation of the fracture. In fact, there are dimples ( F ) on the fracture surface. These elements
of the structure of the fracture surface explain the emergence of a significant number of microcracks
( E ), which grow mostly at the ferrite grain boundaries. Based on this, it can be assumed that the
sample loading conditions with an amplitude of 950 MPa correspond to low-cycle fatigue, with the
finite life of 256 thousand of cycles.
The reduction of the amplitude to 750 MPa is followed by the expected prolongation of finite life
(up to 350 thousand of cycles). The analysis of the fracture surface (Fig. 4) testifies to the mixed
mechanism of fracture just as under higher amplitude of loading. While under 950 MPa, the fracture

19
surface is formed mainly due to the chips inside grains and formation of the faceted surfaces of
intergranular fracture, under 750 MPa the chips inside grains do not appear (Fig. 4, в, A label).
Fig.4. Fractographic investigation of the sample after 370 x10 3
cycle at an amplitude of 750 MPa.
The formation of the separation areas with the crests, which look like the light lines (Fig. 4,
A label), and the intergranular fracture facets (B label) with a significant dispersion should be
considered the dominating mechanism of the fracture surface formation. The sign that confirms the
fatigue resistance improvement is the fewer number of decompositions and microcracks. At the
same time, the number of pits of different sizes and shapes increased; this indicates an increase in
the number of microcavities in the plane of the growing crack. Moreover, on the surface of the
fracture, the occurrence of the sites with an equidistant arrangement of lines can be observed. The
lines have external characteristics similar to fatigue striations (C label). Based on the analysis of the
fracture it can be assumed that under the loading amplitude of 750 MPa the behavior of the sample
corresponds to the conditions of low-cycle fatigue with the signs explaining the increase in the
number of cycles to failure.
After the shock stress processing of the samples, the fracture surfaces have a slightly different
structure (Fig. 5).
According to the external characteristics, the elements of the fracture surface (Fig. 5) has been
formed by the mixed mechanism with almost the same range of particle dimensions as compared
to the sample that has not undergone the shock stress (Fig. 3). The fracture pattern analysis
(Fig. 5) shows the absence of the signs indicating the chip formation within the grains, which was
observed in Fig. 3. At the same time, a considerable part of the fracture surface is occupied by the
facets of intergranular fracture (Fig. 5, A label). There is approximately the same number of
micro-cracks as in the sample that has not undergone the shock stress (Fig. 3), which are located
along the grain boundaries (Fig. 5, B label), decompositions (C), separation areas with the crests
(D) and dimples (F).

20
Fig. 5. The fracture surface of the sample with an amplitude 1000 MPa, after the total number of
260 x10 3 cycle with UN interim treatment.
As for the presence of the fatigue striations as in the case of the sample shown in Fig. 3, it is quite
difficult to determine uniquely, although there are similar sections (E). By means of the
comparative analysis of the fracture surfaces and the obtained level of finite life, it is quite difficult
to determine the influence of shock stress for the high-stress low-cycle region. On the other hand, it
is known that in proportion to the degree of cyclical overload the influence of the static component
on the development of fatigue phenomena increases. The static component that determines the
effect of the deformation and precipitation hardening treatment on the structural changes, in fact,
can mask the effect of the shock stress treatment. The confirmation of the above explanations may
be received under the lower degree of the cyclic overload.
Fig. 6 presents the fracture pattern of the sample that survived 370 thousand cycles at an amplitude
of 900 MPa, which has undergone the intermediate shock stress processing. In comparison to the
sample with the same number of cycles to failure but without shock stress treatment (Fig. 4), the
degree of dispersion of the fracture elements that has undergone the shock stress is higher. Firstly,
the facets formed on the fracture surface have a more equiaxial shape (Fig. 6, a, A label). Compared
to the fracture surface of the sample shown in Fig. 4, there are large areas with very small dimples
(Fig. 6, b, B label); their formation mechanism is based on the coagulation of microcavities [2]. At
the same time, there is a certain number of facets with crests of separation (C) and equidistant
arrangement of the metal decomposition (D), with a low number of the facets of intergranular
fracture (E). In the case of reduction of the test results to the equal cycle amplitude, the finite life of
the metal after the shock stress treatment increases by about 30 %.
Summary. The voltage impulse treatment of metal produced by the electric discharge in water
contributes to the increase of finite life of the carbon steel under cyclic loading. With the rise of the
cycle amplitude, the gain in fatigue resistance resulted by the shock stress declines.

21
а)
b)
Fig. 6. The fracture surface of the sample with an amplitude of 900 MPa, after the total number of
370 x103
cycle with UN interim treatment.
References
[1] Gine A. Rentgenografiya kristallov [Roentgenography of crystals]. Moscow, Gosudarstvennoye
izdatelstvo fiziko-matematicheskoy literatury Publ., 1961, 604 p.

22
[2] Nott Dzh.F. Osnovy mekhaniki razrusheniya [Fundamentals of fracture mechanics]. Moscow,
MetallurgiyaPubl., 1978. 256 p.
[3] Yefremenko V.G., Murashkin A.V., Ivanchenko Ye.P. Sovershenstvovaniye sostava i
termicheskoy obrabotki staley dlya nozhey kholodnoy rezki listovogo prokata [Improvement of
composition and heat treatment of steels for knives for cold cutting of sheet metal]. Stal – Steel,
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[4] Meyers M.A., Murr L.B. Udarnyye volny i yavleniya vysokoskorostnoy deformatsii metallov
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[7] Ait Aissa K., Achour A., Camus J. Comparison of the structural properties and residual stress of
AIN films deposited by dc magnetron sputtering and high power impulse magnetron sputtering at
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[8] Conrad H. Effects of electric current on solid state phase transformations in metals. Materials
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5093(00)00780-2.
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aluminum alloy.Nauka ta prohres transportu. Visnyk Dnipropetrovskoho natsionalnoho
universytetu zaliznychnoho transportu– Science and Transport Progress. Bulletin of Dnipropetrovsk
National University of Railway Transport,2013, no. 4 (46), pp. 73-82. doi:10.15802/stp2013/16584.
[11] Tang G., Zhang J., Zheng M. Experimental study of electroplastic effect on stainless steel wire
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10.1016/s0921-5093(99)00708-x
[12] Morgan W.L., Rosocha L.A. Surface electrical discharges and plasma formation on electrolyte
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10.15802/stp2014/22668 [In Russian].

23
Aluminum Composites With Small Nanoparticles Additions: Corrosion
Resistance
L.E. Agureev1a
, V.I. Kostikov2
, Zh.V. Eremeeva2
, A.A. Barmin3
, S.V.Savushkina4
, B.S. Ivanov5
1 – Researcher, Department of Nanotechnology, Keldysh Research Center, Russia
2 – Doctor of Science, Associate Professor, Moscow State University of Steel and Alloys, Russia
3 – Ph.D., Leading Researcher, Department of Nanotechnology, Keldysh Research Center, Russia
4 – Ph. D., Senior Researcher, Department of Nanotechnology, Keldysh Research Center, Russia
5 – Engineer, Department of Nanotechnology, Keldysh Research Center, Russia
a – trynano@gmail.com
Keywords: nanometric particles, aluminum composites, PM method, corrosion resistance. corrosion rate
ABSTRACT. Research of corrosion resistance of the aluminum powder composites containing microadditives (0.01 –
0.15% is executed about.) zirconium oxide nanoparticles. Extreme dependence of speed of corrosion of aluminum
composites in 10-% solutions of sulfuric and nitric acid from the maintenance of nanoadditives is shown. It has been
shown the dynamics of mass loss of aluminum composites with nanoparticles of ZrO2 during corrosion tests in acids
solutions. The lowest corrosion rate of 3.36 mm/a of nitric acid was observed in the sample containing ZrO2 0.01 vol.%
nanoparticles. For the case of sulfuric acid with the best result of 2.21 mm/a showed the material with 0.05 vol.% nano-
additive.
Introduction. Nanotechnologies allow to create the strong and lightweight materials steady against
various aggressive influences. Influence of nanoparticles on structure of material is caused by high
superficial energy. There is a huge number of the works devoted to creation of composite materials,
both with metal, and with a ceramic matrix, the nanoparticles strengthened by various concentration
[1-7]. The light and strong materials, like aluminum alloys, for creation of various bearing designs
of spacecraft have high value For astronautics [8-11]. In many works, the researchers conducted the
development of aluminum composites containing nanoparticles of different nature in concentrations
of more than 5 vol.%. It is rarely possible to find work devoted to low concentrations of nano-
additives in aluminum [12-18]. This work is dedicated to the creation of aluminum composites with
small amounts (0.01-0.15 %vol.) of nano-oxide ZrO2 by powder metallurgy techniques.
Attention to small concentrations of the nanoparticles was based on the following provisions:
– high surface energy of nanoparticles;
– ease of uniform distribution of small amounts of nanoparticles and their disaggregation within the
matrix;
– high impact of nanoparticles on the structure and properties of interfacial layers (matrix-MFS-
nanoparticle).
The theory of irreversible processes and catastrophe theory say that small changes of operating
parameters can jump the most important characteristics of the system [19,20]. Nanoparticles
possessing high superficial energy, brings it in material and to interphase layer, influencing

24
functional characteristics of composite in one direction or another. In this regard, a researcher
separate issue is the determination of threshold effects of nanoparticles on the material and the
search for the optimal technology of its receipt, depending on performance requirements.
The objective of the work was creation of aluminum composites, hardened with small additions of
metal oxide nanoparticles like ZrO2, and determination of its corrosion resistance in acids solutions.
According to ideas of a number of famous scientists on the structure and properties of an interphase
layer in solids nanoparticles having a high surface energy and making changes to structure of a
matrix, even at very small concentration at the level of 0.001-0,. about. % can cardinally change
characteristics of material [21-24]. In tab. 1 influence of nanoparticles on properties of materials is
briefly explained.
1. Experimental procedure. The charge used: as a matrix - aluminum powder with mean diameter
of 4 μm (ASD-4, "SUAL", Russia), as reinforcer - nanopowder of zirconia (dav = 50 nm, Ssp = 32
m2
/g), Keldysh Research Center, Russia). The technology of preparation of composites consisted in
the following. At the beginning aluminum powder was sieved through a sieve with a cell of 14
microns, then mixed with alcohol in a ratio of 1:4. Then, placed in an ultrasonic bath while stirring
the mixture by rotary stirrer. Nanoparticles dispersed in ultrasound, after which the dispersion was
added to the stirred alumina powder in alcohol. Quantity of nanoadditives varied from 0.01 to 1.5
vol.% Mixing lasted for 20-40 min. Drying of suspensions took place on air at a temperature of 60 °
C within 24 hours. The resulting blend compressed into a cylindrical mold with a pressure of 400
MPa. Next, sintering was performed in forevacuum at 640 ° C during 120-180 minutes.
The corrosion resistance was measured as follows. The total exposure time of samples was 15
hours. Samples were weighed prior to the experiment and during the measurements on scales up to
4-th sign. Samples were immersed in 10% solution acid (nitric acid or sulfuric acid). The difference
in mass (primary - to experiment and obtained by checkweighing) was determined by mass loss of
samples and plotted on it. At each check weighing and date recorded.
By results of tests of samples of aluminum composites for corrosion resistance values of speed of
corrosion (γ) on a formula were calculated [25]:
1000
24365





x
, mm/a,
where x1 – mass loss rate, g/(m2
∙h);
ρ – density of material, g/cm3
.
2. Results and discussions. The results are shown in Fig. 1-4. Particularly interesting is the results
on corrosion resistance in a solution of nitric acid. The lowest rate of mass loss of 3.36 mm/a was
observed in the sample containing nanoparticles of ZrO2 0.01 vol.% . For the case of sulfuric acid
with the best result of 2.21 mm/a showed the material with 0.05 vol.% of the nano-additive.
The worst level of resistance in H2SO4 showed a sample with 0.15 vol.% of nanoparticles. Perhaps
this is due to the number and size of the brought defects (cavities) by mixing aluminum powder
with nano-additives . Nevertheless, it should be noted that all of the samples in comparison with
pure aluminum sintered showed considerably greater resistance to corrosion in both acid solutions.
While first (pure aluminum) at all dissolved in nitric acid after 15 hours and in sulfuric through 10.

25
Fig. 1. The dependence of the aluminum composites corrosion rate of the content nanoparticles
ZrO2 (test in a 10-% nitric acid solution).
Fig. 2. Composites mass loss over time in a solution of nitric acid.
Summary. Samples of aluminum composites with ZrO2 nanoparticles were examined for corrosion
resistance in 10-% solutions of nitric acid and sulfuric acid. The lowest corrosion rate of 3.36 mm/a
of nitric acid was observed in the sample containing ZrO2 0.01 vol.% nanoparticles. For the case of
sulfuric acid with the best result of 2.21 mm/a showed the material with 0.05 vol.% nano-additive.
Acknowledgements. Authors thank collectives NITU "MISIS" and Keldysh Research Center for
the help in development of aluminum composites.

26
Fig. 3. The dependence of the aluminum composites corrosion rate of the content nanoparticles
ZrO2 (test in a 10-% sulfuric acid solution)
Fig. 4. Composites mass loss over time in a solution of sulfuric acid.
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Directions. T. 5 (Results of Science and Technology VINITI. "-M., 1988, pp. 5-218. [In Russian]
[21] Obrazcov I.F., Lur'e S.A., Belov P.A. i dr. Osnovy teorii mezhfaznogo sloja. Mehanika
kompozicionnyh materialov i konstrukcij, 2004, t. 10, №3, s. 596-612.- Samples IF, Lurie SA,
Belov PA et al. Basic theory of the interfacial layer. Mechanics of Composite Materials and
Structures, 2004, v. 10, №3, p. 596-612. [In Russian]
[22] Tajra S., Otani R. Teorija vysokotemperaturnoj prochnosti materialov. –M.: Metallurgija,
1986. -280 s.- Taira S., R. Otani theory of high-strength materials. -M .: Metallurgy, 1986. -280 p.
[In Russian]
[23] Chuvil'deev V.N. Neravnovesnye granicy zjoren v metallah. Teorija i prilozhenija. –M.:
FIZMATLIT, 2004. -304 s.- Chuvildeev VN Non-equilibrium grain boundaries in metals. Theory
and Applications. -M .: FIZMATLIT, 2004. -304 p. [In Russian]
[24] Ohji T., Jeong Y.-K., Choa Y.-H., Niihara K. Strengtheing and toughening mechanisms of
ceramic nanocomposites .// Journal of American Ceramic Society. - 1998. - №81. - P. 1453-1460.
[25] Handbook of Corrosion Data / Ed. by B.D.Craig, D.S.Anderson. – Ohio: ASM International,
998 p.

29
II. Mechanical Engineering & Physics
Performance Optimization of a Gas Turbine Power Plant Based on Energy and
Exergy Analysis
Ghamami M.1, a
, Fayazi Barjin A.1
, Behbahani S.1
1 – Department of Mechanical Engineering, Isfahan University Technology, Isfahan, Iran
a – Mghamazi@ut.ac.ir
Keywords: Gas turbine, Exergy, Multi-objective, optimization, Fireflies algorithm, thermoflow.
ABSTRACT. The purpose of this study is energetic and exergetic analysis of combined cycle power plant, study of the
variables that affect the efficiency and performance and provide a solution to improve the efficiency and performance of
the gas turbine. Therefore, after modeling gas cycle, the impact of environmental conditions and performance of gas
turbine cycle will be checked, eventually we achieve two objective optimization of gas cycle that optimized by firefly
algorithm in six cold months of the year. The objective functions are exergy efficiency and cost of the gas cycle
maintenance, fuel cost and destroyed exergy cost. The proposed optimized result show increase in net output power of
the gas cycle, energy and exergy efficiency and decrease in air pollution amount.
Introduction. Gas turbine is one of the power generating machines that have been widely used in
various industries such as power plants, refineries and oil and gas industries. Since a high
percentage of the power requirements of the country, is provided in the gas power plants and due to
the fact that fossil fuels are the energy requirements of these power plants, thus the performance
improvement of these power plants is very important. From about 70 years before gas turbines have
been used to generate electricity, in the last twenty years the production of these type of turbines
has increased by twenty times. Thermodynamic Simulator of gas cycle and combined cycle, is a
useful tool to predict the behavior of each components of the cycle, by which the basic parameters
of the processes in the cycle can be obtained. Exergy analysis is a good way to evaluate the quality
of the energy with the aid of laws of conservation of mass and the first law of thermodynamics, and
is on the basis of the second law of thermodynamics. The tool is used for design, analysis and
optimization of thermal systems. The main objective of exergy analysis, finding solutions to
eliminate or reduce thermodynamic defects in the processes. We can reduced exergy destruction by
identifying the irreversibility factors and situation. Many studies have been done in this field,
research done in this field can be mentioned the following:
Siddiqui et al. [1] In their article they simulated a 100 MW gas cycle of one of the power plants in
Iran is hot and dry regions ,by thermoflow software ,and investigated the effect of steam injection
into the combustion chamber based on the exergy concept in order to improving gas turbine cycle.
Sadeghi et al. [2] they studied and simulated the effects of light and heavy fuel on operational
parameters of the gas turbine and combined cycle in Kazeroon power plant.
Kim and Hwang [3] examined the performance of a gas turbine with recovery in half-load situation,
by considering and comparing different mechanisms to control the turbine. Salary et al. [4] have
studied exergy analysis of 112 MW Power Plant in Ahvaz Zergan. They optimized the cycle by

30
increasing the turbine inlet temperature in terms of energy and exergy. Abdul Khaliq [5], used
exergy method to analyze gas turbine cycle with inlet air cooling and has shown that most exergy
destruction occurs in the combustion chamber, he also showed that by use of cooling the
compressor inlet air, energy efficiency and the cycle Exergy will be increased. Ehyaei et al. [6] at
the same time studied exergic, economic and enviromental analysis affected by Fog cooling system
in the gas cycle of Rajayee power plant. Sanaye and Jafari [7] work in optimizing field, they have
examined effect of inlet air cooling in gas turbine cycle by absorption refrigeration. The two-
objective optimization of the system is done by the genetic algorithm. kaviri et al. [8] have done
thermodynamic modeling and two-objective optimization of a combined cycle power plant. Ahmadi
[9] study on thermodynamic analysis of a gas cycle power plant and obtained best design
parameters by using multi-objective optimization.
In this study, energetic and exergetic analysis of gas turbine power plants have done and solutions
to improve efficiency and performance of gas turbine are suggested. Factors affecting the efficiency
of power plants have been studied and finally variables to improve the efficiency of power plants
have been selected.
Exergy (or ability to perform work). The maximum work that a system may do during a
reversible process from initial state to reach a dead end is called exergy. Exergy of a system in a
given state depends on environmental conditions and system properties, and for a control volume,
it’s equal to or reversible work with a dead end. Exergy has potential, physical and chemical
components. For the steady flow devices, kinetic and potential exergy can be assumed to be zero.
The sum of physical and chemical exergy, is called thermal exergy [10].
Ph Chex ex ex  (1)
Physical exergy is defined by Equation 2.
( ) ( )Ph o o oex h h T s s    (2)
Chemical exergy of mixtures is obtained from equation (3) [11].
̅̅̅ ∑ ̅̅̅ (̅ ) ∑ ( ), (3)
̅̅̅̅
(4)
Exergy analysis by using of the first and second laws of thermodynamics on the components of a
system, makes it possible to identify the place and production of irreversibility and unfavorable
thermodynamic process of the system, In this way, in addition to evaluate the different components
of thermodynamic cycle, approaches to increase efficiency and output are identified [13].
Efficiency of Thermodynamic Second Law (Exergic efficiency). The first law efficiency is
defined by an ideal isentropic process that never happens in practice. It makes no mention of the
best case, and isn't sufficient to measure the actual system performance alone. To assess the
deviation from the best possible processes, second law efficiency is defined. The second law
efficiency determines how much work ability or potential used in a process [11]. In fact, it
determines how much of exergy given to the system, by a process is achieved and how much of it is
wasted in the form of irreversibility. The second law efficiency is defined the ratio of useful exergy

31
to exergy input and output intensity of irreversibility is defined as (5) the difference between output
exergy and input exergy [13].
̇
(5)
̇ ̇ (6)
Thermodynamic Modeling of gas cycle and power plant. Thermodynamic modeling of gas cycle
power plant have been done by using thermodynamic relations. Plant that studied in this paper,
included 4 gas unit manufactured by Mitsubishi Japan MW-701D models with nominal capacity of
each is 128.5 MW and in total 514 megawatts. By installation of 4 retriever boilers and two steam
turbo generator that each has nominal capacity of 100 MW, power plant Transformed to combined
cycle power plant. In order to simulate the combined cycle power plant, we set the data related to
environmental conditions (Table 1).
Table 1. Environmental condition in power plant
ValueEnvironmental condition
31 centigradeTemperature
0.8964 barPressure
RH=29%Relative humidity
1022 meterAbove sea level
Thermoflow software is one of the most powerful software in design and analysis of power plant
cycles, which is capable to model various stages of the power plant, including thermodynamic
analysis, engineering design and simulating equipment. Combined cycle block consists of two gas
turbines, two recovery boilers and a steam turbine. By choosing Siemens W701 D engine which is
available in the software engines, combined cycle block is simulated in normal loads and in
software. Table 2 shows the software output.
Table 2. Power plant output in normal times (90%)
Gas oilNatural gasType of gaseous fuel cycle
520844526576
Net power output of the plant
(kW)
79487894Plant heat rate (kJ/kWh)
45.345.6Plant thermal efficiency (%)
In order to verify the results of the software simulation, the values obtained from the simulation and
actual data are compared in Table 3.
Figure 3 shows the flow of incoming and outgoing energy to one block in combined cycle of power
plant, also, it shows where the input fuel energy is intended in terms of heat value of fuel. Input
energy consists of latent and sensible energy of air and chemical energy of fuel. Most thermal losses
is related to the condenser, because discharges the heat taken from the cooling water to the
environment. After condenser most heat losses is related to the exhaust flue gas that is at about 118
Celsius degrees, which enters too much heat into the environment without using them.

32
Fig. 1. Operating parameters plant in case of 90% load
Fig. 2. Performance and placement components of HRSG plant in case of 90% load
In tables 3, net output power is expressed in kilowatts (kW) scale and heat rate is expressed in kJ /
kWh scale. The rate is expressed on a scale of kilograms per second (kg/s). By comparing the study
results provided by the simulation and power plant results it can be seen that there is a good
adaption between the results. In six cold months (October to the end of April), due to a dramatic
reduction in household electricity consumption compared with six warm months of the years, the
demand for electricity from power plants in the country declined. The main priority in the six cold
months, is increase in exergy efficiency of gas cycle and reduce the annual cost.

33
Fig. 3. Diagram of Energy flow (input and output plant power)
Table 3. Data comparing of power plant in case of 90% load
Error )%(
Power
plant
Software
simulation
Parameter
+1.08
526576532250Net power output
-0.1478947883Heat Rate
+0.1545.645.67Thermal efficiency (%)
+0.116.356.361Fuel flow
0.11338339.1Air flow
0.5712.212.27The compressor pressure ratio
0.811.211.29Turbine pressure ratio
0.2113851387.9Turbine inlet gas temperature (K)
With the increase in air temperature, the gas turbine and the compressor's power reduces, due to the
more steep decline of power in gas turbine compared with the compressor, the net output power of
the gas cycle is reduced. With the increase in air temperature, mass flow of gas turbine exhaust
gases reduces, less steam is produced in the recovery boiler and there will be a total loss in power of
steam turbine. By reducing the power of steam-gas cycle, the net output of power plant appear with
declined more sharply. For one degree Celsius rise in ambient air temperature, pure output power of
the gas cycle, steam turbine and power plant will averagely reduce 0.63 and 0.27 and 0.53,
respectively. Comparison between output powers with respect to temperature is shown in Figure 4.

34
Fig. 4. Special compressor pressure ratio and can shift with ambient temperature
Optimization. After reviewing the parameters affecting the performance of plants, defining
optimization problem based on target functions and parameters can be done. Optimization problem
in finding answers or solutions on a set of possible options aimed at improving the standard or
standards of the issue. Multi-objective optimization problem arise from the decision-making
methods in the real world that one decision maker faces a set of contradictory and conflicting
objectives and criteria. In these types of issues, unlike the single-objective optimization problems
and because of the multi-purpose (often conflicting), rather than just a solution optimized set of
questions arises.
In the multi-objective optimization, after the introduction of design variables and determine the
objective functions, optimal points are determined and the impact of design on objective functions
are provided. Many factors affect the performance of gas turbine, therefore, gas turbine cycle has
many ways to improve the performance of the industry. Each of these methods has different effects
on output power, efficiency and specific consumption of fuel. The selection of a particular method
according to plant type, climatic conditions, work area, how it affects the performance of the project
cycle, and measures will be considered. Some of the most important factors affecting the operation
of the gas turbine are:
• Pressure ratio
• Compressor inlet temperature
• Compressor efficiency
• The compressor intake
• Turbine inlet temperature
• Turbine efficiency
• Output power of turbine
• Fuel air ratio
• Mass flow rate
As can be seen in Figure 5, with increasing ambient air temperature, compressor pressure ratio
reduces. As well as the temperature increases, air density decreases, resulting in a greater volume of
air should be particularly dense, and the special power of compressor will increase.
315
320
325
330
335
340
345
350
355
360
365
5 8,5 12 15,5 19 22,5 26 29,5 33 36,5 40
Massflowrateofairentering
thecompressor[kg/s]
Environment temperature [C]

35
Fig. 5. Change in net output power cycle gas and steam turbine power plants with ambient
temperature
For one degree Celsius increase in temperature, compressor pressure ratio and special averaged
power increases 0.24 percent and 0.25 percent respectively. Gas turbine is power generation system
at constant volume. By increasing the ambient air temperature and constant air pressure in a fixed
volume, density and mass flow rate of air flow is reduced, resulting in reduced compressor inlet
mass. Figure 6 shows the compressor inlet air mass flow changes to show the changes in ambient
temperature. For one degree Celsius rise in temperature, compressor inlet air flow is reduced by an
average of 0.24 per cent.
Fig. 6. Chart compressor inlet air mass flow changes with temperature
With the increase in air temperature, gas turbine inlet gas temperature increases due to the reduced
amount of fuel and increase in air to fuel ratio. With increasing temperature due to increased
temperature of the exhaust gases from the gas turbine inlet air temperature for cooling turbine
blades increases. For one degree Celsius rise in temperature ambient air, intake and exhaust gas
330
335
340
345
350
355
360
365
370
375
380
11,4
11,6
11,8
12
12,2
12,4
12,6
12,8
13
13,2
5 8,5 12 15,5 19 22,5 26 29,5 33 36,5 40
Specialpowercompressors
[kW/kg/s]
Compressorpressureratio
Pressure ratio Special power
530
532
534
536
538
540
542
544
546
548
550
1110
1111
1112
1113
1114
1115
1116
1117
1118
1119
5 8,5 12 15,5 19 22,5 26 29,5 33 36,5 40
Exhaustturbinegastemperature[C]
Turbineinletgastemperature[C]
TIT TET

36
temperature of the turbine by an average of 0.4 degrees Celsius, respectively 0.17 ° C decrease and
increase. Figure 7 shows the change in gas turbine inlet and outlet gas temperature than the ambient
temperature shows.
Fig. 7. Gas turbine exhaust gas temperature changes graph input and ambient temperature
Differences between the energy and exergy system can be expressed as follows [12].
1. Energy just relates to the system condition and the mass flow but exergy in addition to those
conditions is dependent on environmental conditions.
2. The amount of energy in the dead system may also have an amount, but the exergy in a dead
system is always zero.
3. Energy for all the processes are subject to the law of survival, and is stated in the form of the first
law of thermodynamics but exergy is subject to survival only in reversible processes. In irreversible
processes, always exergy a destroyed. Exergy, applies a combination of the first and second laws of
thermodynamics to the review process.
4. Energy is only a quantitative measure for evaluating processes but exergy is both quantitative and
qualitative measure.
5. Energy can be calculated with respect to each case assumptions but exergy basis mode is
determined by environmental conditions.
After reading the parameters and variables on power plant performance optimization, optimization
process takes place. Because of the simultaneous search of multiple points, no need for an explicit
mathematical relationship between objective functions, the need for direct measurement and
mathematical calculations needed to optimize the methods of analysis and generalization of random
search algorithms, optimization of problem is done by random search algorithms.
The objective function. To compare the achieved considerable optimization problems we need to
have a selection criterion. Such a measure, which plan is optimized and is a function of design
variables, standard function, is called advantage function or objective function. In this study, the
objective functions, exergy efficiency and costs related to gas cycle, and the optimal points
represent the highest efficiency and lowest costs. Relation 6 and 7 show the first and second
objective function, respectively.
75
78
81
84
87
90
93
96
99
102
105
108
111
240
250
260
270
280
290
300
310
5 8,5 12 15,5 19 22,5 26 29,5 33 36,5 40
Netpoweroutput(GT-ST)
MW
Netpoweroutput(Plant)
MW
Plant Net Power GT GrossPower ST Gross Power

37
OF1:Max
̇
̇
(7)
OF2: Min ̇ ̇ ̇ ̇ (8)
̇ ( ̇ ̇ ) (9)
̇ ̇ (10)
Net Output power of the gas cycle can be obtained as above.
Decision variables. Thermodynamic modeling inputs are decision variables and numbers represent
degrees of freedom of the system. Decision variables change during the optimization process, but
the parameters are fixed, but some parameters, are dependent parameters which is determined on
the amount of basis of the decision variables. The variables which are specified in Table 4, are
selected as the decision variables. In order to stay in the recovery boiler circuit, the gas turbine load
is considered higher than 55%. Using thermoflow and EES software and range change in
environmental conditions, according to the decision of the six variables in Table 1 and also taking
into account the load percentage of the gas turbine in the range of 55 to 100% has been obtained.
Firefly algorithm. Firefly optimization algorithm or FA for short is inspired of the natural behavior
of fireflies which live together in large collections, and was introduced for the first time in late 2008
by Xin-She Yang [14], this multi-agent algorithms can be a solution of hard optimization problem
and it is a very efficient algorithm for solving combinatorial optimization problems.
In summary, the performance of the algorithm is that the number of artificial fireflies (initial
population) are randomly distributed in the range and then emits light of a firefly which intensity is
proportional to the amount of optimality point Firefly is that it is located. The light intensity of each
firefly regularly intensity compared to other fireflies and fireflies brighter too faint to be absorbed.
At the same time the brightest fireflies also aims to increase the chances of finding the optimal
solution is the global accidentally move. In this algorithm, exchange information with each other
through the light emission occurs. The composition of this combined action makes the overall trend
towards a more efficient is fireflies.
Table 4. Optimization variables and their ranges
VariableVariable interval
Compressor pressure ratio
Isentropic efficiency turbine
Isentropic efficiency compressor
̇Compressor inlet mass flow rate (kg/s)
The output of the gas turbine
combustion pressure (bar)
( )Gas turbine inlet temperature (K)
Optimization Results. Given the equations required optimization objective functions according to
the decision made and the six variables in MATLAB fireflies algorithm code was used to optimize

38
the objective function. The primary population for the first generation is considered 200. In the
multi-objective optimization instead of an optimal point, we have an optimal solution that is
optimized to the famous pareto point and the set of these points are called pareto front. Figure 8
shows the pareto front of the optimization objective functions, including optimal points. As can be
seen by increasing the efficiency of the gas cycle exergy, it also increases annual costs.
Fig. 8. Pareto Front of the first objective functions (cost) for six months
Selection the desired optimization of energy systems based on multi-objective optimization
decision-making ideas happen after the search. Each individual decision-maker may be due to
considerations in mind, their own scenario is to select the optimal point. Pareto front of the
optimization objective function shows that the costs for the six months is considered. The results,
show minimal costs during the year should be paid for a certain exergy efficiency, and most exergy
efficiency that can be achieved for a certain fee during the year. Figure 9 shows the net profit for the
six months according to exergy efficiency. Net profit, the difference between the proceeds from the
sale of electricity and the cost of the cycle ( TotC ) is obtained. The price of electricity purchased from
power plants 0.15 Dollar/kWh is considered [13]. Pareto front of net profit of the previous stage
results are plotted in Figure 9.
In Figure 10, the net profit in the six months according to exergy efficiency has been showed in gas
cycle power plant. The price of electricity purchased from power plants is intended 0.3 Dollar/kWh.
Table 5 Three optimal point A, B and C compared with each other. Given the priority of each
objective function optimal point can be selected.
In table 5, net output power and destroyed exergy are in megawatts scale (MW) and amounted net
profit is expressed in millions of dollars scale for both 0.15 and 0.3 dollar per Kilowatt hours
(dollar/kWh) of generated electricity.
Summary. The main goal of this study was to evaluate and improve the performance of gas cycle
power plant in different environmental conditions. The analysis results show that the greatest
destruction exergy of gas cycle power plant is happening in the combustion chamber. That reason is
high temperature difference between the temperature of the flame and fluid. Much of this
destruction exergy is inevitable that cannot be reduced, so exergy efficiency of power plants has
been studied and other ways use to reduce the exergy destruction.
4
4,2
4,4
4,6
4,8
5
5,2
5,4
5,6
5,8
6
6,2
6,4
6,6
6,8
0,26 0,27 0,28 0,29 0,3 0,31 0,32 0,33 0,34 0,35
(Millionsofdollars)costs
Exergy efficiency (%)
A
B
C

39
Fig. 9. The change in net profit with electricity prices 0.15 Dollar/kWh
Fig. 10. The change in net profit with electricity prices 0.3 Dollar/kWh
Table 5. Comparison of the optimum
Point CPoint BPoint A
34.531.326.7Exergy efficiency (%)
34.932.527.5Efficiency (%)
11490.768Net output power
6.44.94.3Price Six months (millions of dollars)
141120104Exergy destroyed
0.90.90.05Net profit price of electricity: 0.3
8.36.74.4Net profit price of electricity: 0.15
0
0,2
0,4
0,6
0,8
1
1,2
0,26 0,27 0,28 0,29 0,3 0,31 0,32 0,33 0,34 0,35
(Millionsofdollars)netprofit
A
B
C
3
4
5
6
7
8
9
10
0,26 0,27 0,28 0,29 0,3 0,31 0,32 0,33 0,34 0,35
(Millionsofdollars)netprofit
A
B
C

40
Firefly algorithm has been optimization algorithm in gas cycle power plant. Objective functions are
exergy efficiency and cost, cost include the gas cycle maintenance costs, fuel cost and the cost of
exergy demolition, highest efficiency exergy and lowest cost are requirements. The results show
that by increasing the efficiency of the gas cycle exergy, its cost also increased. Lower temperature
reduces emissions and steam quality in the recovery boiler and steam turbine power output is
reduced as a result. To remedy this problem, the use of gas turbine exhaust duct burner is
recommended. In this case, the temperature of the exhaust gas from the turbine should exceed the
temperature of HRSG design.
The study achievements can be cite to use of meta-heuristic algorithm in large search space, non-
linear variables and objective functions such as firefly algorithm. Because that limited studies have
been done for examine ability and capabilities of this algorithms, this study is an opportunity to
investigate the algorithm and its ability. Multi-objective optimization process has its own challenges
and advantages. In the multi-objective optimization not only efficiency but also exergy cycle costs,
including the cost of repair and maintenance, the cost of fuel and the cost of destruction exergy have
been studied. Time-consuming optimization process is very important. Less computational time and
iteration means less computational cost, by using of the optimal response of optimization algorithm,
the net power output of the gas cycle power plants by as much as 11.15 and 8.08 percent, energy
efficiency and exergy cycle gas 3.64 and 3.61 respectively percent and air emissions, 0.77 percent
decrease. This study also examines changes in environmental conditions and levels of load on the
gas cycle power plant, Technical and economic assessment, energy and exergy analysis using the
first and second law of thermodynamics can be mentioned. As well as alternative ways to reduce
destruction exergy and increase exergy efficiency are reviewed.
Thermoflow Software can calculate the pollutions of the turbine gas output. It is suggested that the
impact of changing load levels and the effect of cooling system of air entering to compressor will be
investigated in order to predict exhaust pollutions of gas turbines.
Reference
[1] Siddiqi H, Bayati Gh,Tvakoli A, Fotoohi D, "simulated cycle 100 MW gas and steam injection
into the combustion chamber 'exergetic analysis and energetic", conferences energy efficiency,
conferences Institute of Technology, Tehran, (2010).
[2] Sadeghi H, Haghighi khoshkhor V, Tanasan M, Moosavian M, "Simulation of the
thermodynamic effects of non-gaseous fuels on the performance and efficiency of combined cycle
power plant", the twenty-seventh International Conference on Electric Power Research Institute,
Inc. Tavanir, Tehran, (2012).
[3] Kim T, Hwang S.H, “Part load performance analysis of recuperated gas turbines considering
engine configuration and operation strategy”, J.of.Energy, 31, pp. 260-277, (2006),
doi: 10.1016/j.energy.2005.01.014
[4] Salari M, Hashemi Sh, Zayer noori M, "Exergy and Exergy Economic Analysis Zargan Gas
Power Plant in Ahvaz", the first International Conference on Energy Planning and Management,
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2670, (2011). doi:10.1016/j.energy.2011.02.007
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doi:10.1016/j.energy.2011.10.011

41
[7] Sanaye S, Jafari s, "Optimizing the objective cycle gas turbine inlet air cooling by absorption
chiller", Second International Conference of chiller and cooling tower, energy Ham Andyshan
Kimia, Tehran, (2011).
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42
Certain Solutions Of Shock-Waves In Non-Ideal Gases
Kanti Pandey1, a
& Kiran Singh1
1 – Department of Mathematics & Astronomy, Lucknow University, Lucknow, 226007, India
a – pandey_kanti@yahoo.co.in
Keywords: Shock waves, Non-ideal medium, AMS Classification
ABSTRACT. In present paper non similar solutions for plane, cylindrical and spherical unsteady flows of non-ideal gas
behind shock wave of arbitrary strength initiated by the instantaneous release of finite energy and propagating in a non-
ideal gas is investigated. Asymptotic analysis is applied to obtain a solution up to second order. Solution for numerical
calculation Runga-Kutta method of fourth order is applied and is concluded that for non-ideal case there is a decrease in
velocity, pressure and density for 0th and II-nd order in comparison to ideal gas but a increasing tendency in velocity,
pressure and density for Ist
order in comparison to ideal gas. The energy of explosion J0 for ideal gas is greater in
comparison to non-ideal gas for plane, cylindrical and spherical waves.
1. Introduction. The assumption that the medium is an ideal gas is no more valid when the flow
takes place in extreme conditions. Anisimov & Spiner [1] studied a problem of point explosion in
low density non ideal gas by taking the equation of state in a simplified form which describes the
behaviour of medium satisfactorily. Robert’s & Wu [2] studied the gas that obeys a simplified
Vander Waal’s equation of state.
Vishwakarma et al. [3] have investigated the one dimensional unsteady self-similar flow behind a
strong shock, driven out by a cylindrical or spherical piston in a medium which is assumed to be
non-ideal and which obey the simplified Vander-Waal’s equation of state as considered by Robert’s
& Wu [2]. However, they have assumed that the piston is moving with time according to law given
by Steiner & Hirschler [4]. Madhumita & Sharma [5] have considered the model equation for a low
density gas, which describes the behavior of the medium satisfactorily for implosion problems
where the temperature for implosion problems were the temperature attained by the gas motion in
the strong shock limit is very high. Pandey & Pathak [6] have discussed growth and decay of sonic
waves in non-ideal gases. In present paper using asymptotic expansion an attempt is made to obtain
non-self similar solution of shock-waves in non-ideal gas. For numerical calculation Runge Kutta
method is applied .In preparation of graphs Origin 7.5 is used.
2. Basic Equations
The basic equations describing a cylindrically symmetric (α= 1) or a spherically symmetric (α = 2)
motion of a non-ideal gas can be written as:
( )
0
u u
t r r
   
  
 
, (2.1)
1
0
u u p
u
t r r
  
  
   , (2.2)
( ) { ( )}
0
r E r u E p
t r
 
  
 
  , (2.3)

43
where ρ is the gas density, u is the fluid velocity, p is the pressure and
2
2
u
E e

  , (2.4)
is the total energy density with e being the internal energy density, the independent variables are the
space co-ordinate r and time t: The equation of state characterizing the non-ideal medium is taken to
be of the form
(1 )
RT
p
b




,
where b is the internal volume of the gas molecules which is known in terms of the molecular
interaction potential in high temperature gases, it is a constant with b ρ << 1. The gas constant R
and the temperature T are assumed to obey the thermodynamic relations p VR C C  and Ve C T ,
where
( 1)
V
R
C



is the specific heat at constant volume and γ is the ratio of specific heats. Thus
in view of these thermodynamic relations, the equation of state can be written as
( 1)
(1 )
e
p
b
 




. (2.5)
Expression for E, in view of equation (2.5) assumes the form
2
(1 )
( 1) 2
p b u
E
 


 

.
Using above value of E in equation (2.3), we have
0
(1 )
p p p u u
u
t r b r r
 

   
    
    
. (2.6)
Here α=0,1,2 corresponds to planar, cylindrical and spherical geometries respectively. The
assumption of the instantaneous release of constant energy 0E at time t = 0 yields the energy
balance equation:
2
0 0
0
00
(1 )1 (1 )
{ }
2 ( 1)
S
p bu p b
E K r dr



  
 
   
 
 ,

44
where Kα= 2, 2π, 4 π for α= 0, 1, 2 and S represents the shock radius which is assumed to be zero at
t = 0.
From Lagrangian equation of continuity we have
1
00
( 1)
S
S
r dr


 


 . Thus energy balance
equation transform into:
12
0 0
0
0
(1 )(1 )
2 ( 1) ( 1)( 1)
S
K S p bu p b
E K r dr





   

  
         
 . (2.7)
The conservation relations across the shock for the present problem can be written as:
0 1 1( )U U u   , (2.8)
2 2
0 0 1 1 1( )p U p U u     , (2.9)
22
0 0 0 1 1 1 1
0 0 1 1
(1 ) (1 ) ( )
( 1) 2 ( 1) 2
p p b p p b U uU 
     
  
    
 
, (2.10)
where subscripts 1 and 0 refer to values immediately behind and ahead of the shock respectively
and represents the shock velocity.
dS
U
dt
 ,
In following section we introduce the dimension less variables.
3. Transformation of Fundamental Equations in Non-Dimensional Form
To transform fundamental equations, we consider principal of similarity & introduces new variables
x and y in place of r and t as defined by 7
Sakurai
r
x
S
 (3.1)
0
2
2
y
U

 , (3.2)
u=Uf(x ,y ), (3.3)
2
0
0(1 ) ( , )
U
p b g x y



  , (3.4)
0 ( , )h x y  , (3.5)
where

45
2 0
0
0 0(1 )
p
b

 
 

,r Sx dr Sdx   . (3.6)
Thus
1
r S x
 

 
, (3.7)
( )
D U
f x y
Dt S x y

  
   
  
, (3.8)
where
dy
dSS
y

 
 
  
  
 
(3.9)
and λ is a function of y alone.
Substituting equations (3.1) to (3.8) in to fundamental equations (2.1), (2.2), (2.6), (2.7) and
boundary conditions (2.8, 2.9, 2.10), equations (2.1), (2.2), (2.6) become
( )
h h f f
f x y h
x y x x


   
     
   
, (3.10)
0(1 )
( )
2
bf f f g
h f x y
x y x



   
     
   
, (3.11)
. (3.12)
Equation (2.7) now become
1 1 22
0 0 0 0
0
(1 )(1 ) (1 )
2 ( 1) ( 1)( 1)
S g b h b b yhf
y x dx
S

  
    

    
          
 , (3.13)
where
1
1
0
0 2
0 0
E
S
K


 
  
 
. (3.14)
Equations (2.8), (2.9), (2.10) now become as
0
( )
(1 )
g g g f f
g f x y
x y b h x x
 
 

    
      
    

MMSE Journal Vol.2 2016

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