Jatender Datta

Sahib Sartaj Singh

Thermal Load Analysis and Comparison of Total Heat Flux and Temperature Distribution Between Carbon Graphite and Aluminum Alloy 4032 Pistons using FEA Technique (Research)

Keywords: piston analysis, thermal load on piston, cast alloy steel piston, piston properties, finite element method, analysis on piston

This paper describes the results of thermal load applied on the pistons made by aluminum alloy 4032 and carbon graphite by using finite element Analysis (FEA) .The parameters used for the simulation are operating gas temperature and material properties of pistons. The specifications used for the study of these pistons belong to four stroke 100cc hero bike engine. This paper illustrates the procedure for analytical design of aluminum alloy, and carbon graphite pistons using specifications of four stroke 100cc hero bike engine. The results predict the Total Heat Flux, Temperature distribution and critical region on all of these pistons using FEA with Temperature of 200 degree Celsius on the top of piston. It is important to locate the critical area and advantages/disadvantages of both materials. The 3D modelling of piston is done in Solidworks (Feature module) and Simulation module used to mesh the pistons, thermal analysis with temperature applied on the top of piston head.

Introduction. Piston is a cylindrical member which is placed inside cylinder and on the combustion gases exerts pressure. It is made up of cast iron or aluminium alloy. In an engine, its purpose is to transfer force from expanding gas in the cylinder to the crankshaft via a piston rod and/or connecting rod. It is the moving component that is contained by a cylinder and is made gas-tight by piston rings. It absorbs the side thrust resulting from obliquity of the connecting rod. It also dissipates the large amount of heat generated by the combustion gases form the combustion chamber to the cylinder wall. In some engines, the piston also acts as a valve by covering and uncovering ports in the cylinder wall.

FEA (Finite Element Analysis).

Finite element analysis (FEA) is the modelling of products and systems in a virtual environment, for the purpose of finding and solving potential (or existing) structural or performance issues. FEA is the practical application of the finite element method (FEM), which is used by engineers and scientist to mathematically model and numerically solve very complex structural, fluid, and multiphysics problems.

FEA software can be utilized in a wide range of industries, but is most commonly used in the aeronautical, biomechanical and automotive industries.

Volumetric Properties.

Fuel Metering Carburetion

Reverse Engineering the Piston.

With the help of measuring instruments like vernier calliper etc. the dimensions of the model piston were measured. By using this measurement 3D model of the piston were drawn using Solidworks 3D modelling software as below: Applied Temperature value of 200 degree Celsius on the top of piston. Note: Units, boundary conditions and loads will be same in both tests. Figure [START_REF] Alkidas | Experiments with an uncooled single cylinder open chamber diesel[END_REF] it shows the maximum Total heat flux in the piston due to the application of gases is 4.92 MW/m 2 which is observed on the 3 rd groove of piston ring and heat flow graphics shown till just down the piston pin hole.

Meshing of Piston.

Summary. According to the results maximum heat transfer occurs in the piston made of Carbon Graphite as compared to Aluminum alloy 4032 due to the higher thermal conductivity.Furthermore, according to volumetric properties, Carbon Graphite material is much lighter than aluminium 4032.

Moreover, other advantage of carbon graphite piston is that Carbon shows an excellent resistance to thermal shock and exhibits self -lubricant properties which increase the operational reliability of the engine and result in reduced lubricant consumption.

Carbon graphite has low thermal expansion coefficient as compared to aluminium 4032. At last, Carbon Graphite is much better than aluminium alloy 4032 as Piston material and suitable for IC engine.

Fig. 1 .

 1 Fig. 1. Model of Piston.

Figure ( 3 )

 3 Figure (3) Maximum temperature shows on the top of the piston and distribute of temperature shown until slightly down of 3 rd piston ring groove due to heat produce by the gases in block.

Figure ( 4 )

 4 Figure (4) Maximum temperature 200 deg. Сelsius shows on the top of the piston and distribute of temperature until last as 108 deg. Celsius due to heat produce by the gases in block.

Fig. 3 .

 3 Fig. 3. Temperature Distribution for Aluminum Alloy 4032.

Fig. 4 .

 4 Fig. 4. Temperature Distribution for Carbon Graphite.

Fig. 5 .

 5 Fig. 5. Total Heat Flux for Aluminum Alloy 4032.

Fig. 6 .

 6 Fig. 6. Total Heat Flux for Carbon Graphite.

Figure ( 5 )

 5 Figure[START_REF] Alkidas | Performance and emissions achievements with an uncooled heavy duty, single cylinder diesel engine[END_REF] it shows the maximum total heat flux in the piston due to the application of gases is 23.5 MW/m 2 which is observed on the 3 rd groove of piston ring and heat flow graphics shown till the holes just down the 3 rd groove.

Table 1 .

 1 Aluminum Alloy 4032.

	S. No	Properties	Value
	1	Mass	0.072 kg
	2	Volume	2.72e-005m 3
	3	Density	2680 kg/m 3
	4	Weight	0.71 N

Table 2 .

 2 Carbon Graphite.

	S. No	Properties	Value
	1	Mass	0.060 kg
	2	Volume	2.72e-005m 3
	3	Density	2240 kg/m 3
	4	Weight	0.59 N
	Mechanical Properties.

Table 3 .

 3 Aluminum Alloy 4032.

Table 4 .

 4 Carbon Graphite

	S. No	Properties	Value
	1	Poissons ratio	0.34
	2	Thermal expansion coefficient	1.94e-005/K
	3	Density	2680 kg/m 3
	4	Thermal conductivity	138 W/(m-K)
	5	Specific heat	850 J (kg-K)
	S. No	Properties	Value
	1	Poissons ratio	0.28
	2	Thermal expansion coefficient	1.3e-005/K
	3	Density	2240 kg/m 3
	4	Thermal conductivity	168 W/(m-K)
	5	Specific heat	44 J (kg-K)

Table 5 .

 5 Engine Specifications.

	Type	Air cooled, 4 -stroke single cylinder OHC
	Displacement	97.2 cc
	Max. Power	6.15kW (8.36 Ps) @8000 rpm
	Max. Torque	0.82kg -m (8.05 N-m) @5000 rpm
	Max. Speed	87 Kph
	Bore x Stroke	50.0 mm x 49.5 mm
	Carburettor	Side Draft , Variable Venturi Type with TCIS
	Compression Ratio	9.9 : 1
	Starting	Kick / Self Start
	Ignition	DC -Digital CDI
	Oil Grade	SAE 10 W 30 SJ Grade , JASO MA Grade
	Air Filtration	Dry , Pleated Paper Filter
	Fuel System	Carburettor

Table 6 .

 6 Mesh Information.

	Mesh type	Solid Mesh
	Mesher Used:	Standard mesh
	Automatic Transition:	Off
	Include Mesh Auto Loops:	Off
	Jacobian points	4 Points
	Element Size	2.94563 mm
	Tolerance	0.147281 mm
	Mesh Quality	High

Table 7 .

 7 Mesh Information -Details.

	Total Nodes	26221
	Total Elements	14224
	Maximum Aspect Ratio	90.342
	% of elements with Aspect Ratio < 3	84
	% of elements with Aspect Ratio > 10	0.443

% of distorted elements (Jacobian) 0 Time to complete mesh (hh;mm;ss): 00:00:07 Fig. 2. Meshed Model.

Table 7 .

 7 Properties Study.

	Study name	Study 1
	Analysis type	Thermal(Transient)
	Mesh type	Solid Mesh
	Solver type	Direct sparse solver
	Solution type	Transient
	Total time	1 Seconds
	Time increment	0.1 Seconds
	Contact resistance defined	No
	Result folder	SolidWorks document (C:\Users\JATENDER
		DATTA\Desktop\desk new)

Table 8 .

 8 Units.

	Unit system:	SI (MKS)
	Length/Displacement	mm
	Temperature	Kelvin
	Angular velocity	Rad/sec
	Pressure/Stress	N/m 2

Results and Discussions.


M Penchal Reddy

N Ramamanohar Reddy

K V Siva Kumar

AC Conductivity Studies of MgCuZn Ferrite 1

Keywords: AC conduction, activation energy, critical exponents, ferrites

Mg0.5-xCuxZn0.5Fe2O4 (x = 0 to 0.3) are synthesized by conventional ceramic double sintering technique. Temperature dependence of AC electrical conductivity is estimated in the temperature range of 30 to 200 o C and frequency dependence up to 1MHz. Room temperature conductivity is of the order of 10 -8 Ω -1 m -1 and increases to 10 -5 Ω -1 m -1 at higher temperatures. Temperature dependence of all the compositions follows Arrhenius law while the frequency dependence follows the double power law. The activation energies and the critical exponents evaluated supports jump relaxation model of conduction mechanism.

Introduction. Electric and magnetic characteristics of ceramic materials are of increasing importance in the fields of radio electronics, optoelectronics, microwave electronics and modern communication devices. Ferrites find vast application in these fields. An important property of these materials is their high electric resistance compared to that of other elemental magnetic materials, which generally possess low eddy current losses at high frequencies. Ferrites have very high resistivity which is one of the considerations for microwave applications. The order of magnitude of the conductivity greatly influences the electric and magnetic behavior of ferrites. This has aroused considerable interest in the study of electrical conductivity and frequency dependent electrical behavior of ferrites [START_REF] Madhuri | Transport properties of microwave sintered pure and glass added MgCuZn ferrites[END_REF][START_REF] Reddy | Structural, magnetic and electrical properties of NiCuZn ferrites prepared by microwave sintering method suitable for MLCI applications[END_REF]. The AC conductivity of a magneto-ceramic is complex. The real part of the conductivity (σ), called the polarization conductivity is a function of frequency and temperature. It is supposed to follow the power law as [START_REF] Gurusiddappa | Conductivity and dielectric behavior of polyethylene oxide-lithium perchlorate solid polymer electrolyte films[END_REF]:

2 1 ) 0 ( ) ( n n B A         (1)
where σ(0)denotes dc conductivity corresponding to frequency independent plateau at low frequency, A and B are the AC coefficient and n1 and n2 are the power exponent. with the help of a low frequency impedance analyzer Hioki LCR Hitester model 3532-50 and a computer interfaced tubular furnace. The conductivity arises as a result of charge hopping from one site to another site. The AC conductivity σ is obtained from the real part of impedance as:

A t Z Z Z ac    2 2 " ' ' ) (  (2)
where t/Ais the geometrical factor of the sample.

Results and discussion. Single phase spinel structure formation is confirmed from X-ray diffraction studies which is published in our earlier work [START_REF] Madhuri | Thermoelectric Studies of MgCuZn Ferrites[END_REF]. Fig. 1 shows the compositional variation of AC electrical conductivity of Mg0.5-xCuxZn0.5Fe2O4 samples. Within the experimental error AC conductivity is found to be independent of copper concentration. The temperature dependence of AC electrical conductivity of MgCuZn ferrites is shown in Fig. 2. The AC electrical conductivity has increased with increase in temperature. In the investigated temperature range the conductivity has increased by two orders of magnitude. Rise in temperature of the sample will help the trapped charges to be liberated and to participate in the conduction process, with the result conductivity increases, which is the normal behaviour of semiconducting materials like ferrites. Similar results were reported by, Bellad [START_REF] Bellad | Some AC electrical properties of Li-Mg ferrites[END_REF] in LiMg ferrites, by Ahmed [START_REF] Ahmed | Spectroscopic and electrical properties of Mg-Ti ferrite doped with different rare-earth elements[END_REF] in the case of Er-substituted MgTi ferrite. In the investigated temperature region AC conductivity exhibited two slope regions indicating mixed conduction mechanism in the series of ferrites. The activation energies (see Table . 1.) in the intrinsic region (high temperature region) i.e., region II are greater than those of region I. High activation energies in region II suggest polaron happing and low activation energies at low temperatures must be due to free charge carriers [START_REF] Ali | Effect of Tb-Mn substitution on DC and AC conductivity of Y-type hexagonal ferrite[END_REF]. Further, all the activation energies are found to be greater than the ionization energies (Ei = 0.1ev) of the donor or acceptors and thus the possibility of band like conduction is ruled out. The values are even higher than the Fe 2+ ↔ Fe 3+ transition energy (Ee = 0.2ev) supporting the polaron hopping in the intrinsic regions [START_REF] Madhuri | Transport properties of microwave sintered pure and glass added MgCuZn ferrites[END_REF]. Examination of compositional dependence of conductivity and activation energies reveal a good correspondence, that is samples having low conductivity have high activation energy and vice versa. The values of n1 and n2 evaluated corresponding to the two regions are tabulated in Table 1. If the values of the exponents n1 and n2 is equal to zero then the conduction is independent of frequency or DC conduction. If it is less than or equal to 1 then the conduction is frequency dependent. Physically the n value signifies the strength of carrier-lattice interactions. The n1 and n2 values less than one strongly suggest hopping conduction mechanism. The frequency response of conduction is interpreted in terms of the jump relaxation model [START_REF] Funke | Jump relaxation in solid electrolytes[END_REF][START_REF] Youssef | The Permittivity and AC Conductivity of the Layered perovskite [(CH3)(C6H5) 3P] 2HgI4[END_REF] where the conduction is due to translational hopping for n1 < 1 and localized rotational hopping for n2 ≥ 1. Frequency variation of AC electrical conductivity of all the samples is increasing with increasing temperature.

Summary. Mg0.5-xCuxZn0.5Fe2O4 (x = 0 to 0.3) are synthesized conventionally by solid state reaction route. Temperature dependence of AC electrical conductivity confirmed semiconducting behavior of these ferrites. In the temperature range of 30 to 200 o C AC conductivity has increased by two orders. Activation energy of all the samples supports hopping conduction mechanism. The frequency dependence follows the double power law. The evaluated critical exponents from the frequency dependence also support hopping conduction mechanism.

Materials and methods .

 methods Reagent grade MgO, CuO, ZnO and Fe2O3 are weighed according to the stoichiometry [Mg0.5-xCuxZn0.5Fe2O4 (x = 0 to 0.3)] and mixed and grinded. The powders are presintered at 800 o C for 2 hours. The obtained powders are milled in a ball mill for 10 hours at 300 rpm. Thus, obtained green powders are made into pellets of 1cm diameter using uniaxial press and are sintered at 1250 o C for 2 hours in Zn atmosphere. The polished pellets are given good ohmic contacts using Du Pont silver paint. The values of Z' and Z" were recorded directly at 5 o C temperature intervals in the temperature range 30 to 200 o C at different frequencies in the range 100 Hz to 1 MHz

Fig. 1 .

 1 Fig. 1. Variation of AC electrical conductivity with copper.

Fig. 2 .

 2 Fig. 2. Variation of AC electrical conductivity with reciprocal temperature.

Fig. 3 .

 3 Fig. 3. Variation of log(σ) AC with log(f) at room temperature.

Table 1 .

 1 Activation energies and critical exponents from AC conductivity studies of the series.

	Copper Content	Region I	Region II	Region I	Region II
	x	∆E1 ev	∆E2 ev	n1	n2
	0.0	0.28	0.5	0.26	0.58
	0.05	0.3	0.5	0.5	0.73
	0.1	0.26	0.42	0.22	0.53
	0.15	0.21	0.41	0.13	1
	0.2	0.24	0.63	0.64	0.34
	0.25	0.29	0.53	0.16	0.81
	0.3	0.39	0.52	0.24	0.86


Imran Shaik
email: imranshaik1414@gmail.com

Shaik Riyaaz Uddien

A Krishnaiah

Shankarachar Sutar

Shaik Riyaaz Uddien

Numerical Analysis of Clamped Fluid Conveying Pipe

Keywords: clamped-clamped, Euler Bernoulli, fluid conveying pipe, weldment, ABAQUS

  L'archive ouverte pluridisciplinaire

Introduction. The fluid conveying pipes are widely used in many industrial applications such as chemical plants, fertilizer plants, nuclear plants and pharmaceutical industries etc. The pipes are subjected to different environmental conditions such as wind forces, earthquakes, and Coriolis forces of fluid flow. Over the last sixty years, extensive studies have been carried out on pipeline systems subject to different boundary conditions and loadings. These pipes however frequently transport fluids from initial point to destination. The subject of piping vibration has attracted a lot of attention from various researchers in recent times due to vast applications. Avinash B. Kokare et.al [START_REF] Avinash | Vibration Characteristics of Pipe Conveying Fluid[END_REF], studied about vibrational characteristics of pipe conveying fluid and FE simulation to evaluate velocity and pressure distribution in a single phase fluid flow. Long Liu and Fuzhen Xuan [START_REF] Liu | Flow-Induced Vibration Analysis of Supported Pipes Conveying Pulsating Fluid Using Precise Integration Method[END_REF], presented the flow induced vibration analysis of supported pipes conveying pulsating fluid using precise integration method. Gongfa Li et.al [START_REF] Li | The nonlinear vibration analysis of the fluid conveying pipe based on finite element method[END_REF] investigated natural frequencies using Lagrangian interpolation function, the first order Hermite interpolation function and the Ritz method to obtain the element standard equation. Wentao Xiaoet.al [START_REF] Xiao | Finite element analysis of fluid conveying pipe line of nonlinear vibration response[END_REF] studied finite element analysis of nonlinear vibration response using Lagrangian interpolation function, the first order Hermit interpolation function and the Ritz method to obtain the element standard equation, and then integrated a global matrix equation, obtained the response of conveying fluid pipe with the New mark method and Matlab. Muhsin J. Jweeg et al [START_REF] Dr | Dynamic analysis of pipes conveying fluid using analytical, numerical and experimental verification with the aid of smart materials[END_REF] dynamic Analysis of Pipes Conveying Fluid Using Analytical, Numerical and Experimental Verification with the Aid of Smart Materials and the results presented in this study compared with the results performed by using analytical solution for equation of motion and also, compared with the results performed by using ANSYS Software. T.G. Ritto et.al [START_REF] Ritto | Dynamic stability of a pipe conveying fluid with an uncertain computational model[END_REF] studied about dynamic stability of a pipe conveying fluid with an uncertain computational model. Ivan Grant [START_REF] Grant | Flow induced Vibration in pipes, A Finite Element Approach[END_REF] Presented on flow induced vibrations in pipes; a finite element approach methodology is used to determine the critical fluid flow velocity that induces the threshold of pipe instability. B. Mediano-Valienteet al. [START_REF] Mediano-Valiente Et | Stability Analysis of a Clamped-Pinned Pipeline Conveying Fluid[END_REF], discussed on stability analysis of a clamped-pinned pipeline conveying fluid by means of the eigenvalues of a Hamiltonian linear system associated. From this analysis, characteristic expressions dependent on material constants have been developed. Nabeel. K. Abid et.al. [START_REF] Nabeel | Investigation into the vibration characteristics and stability of a welded pipe conveying fluid[END_REF] Investigated the stability of fluid coveying welded pipe is of practical importance because the welding induced residual stresses which effected on the vibration characteristic and stability of pipe. Singiresu S. Rao [START_REF] Singiresu | Vibrations of continuous systems[END_REF], Vibrations of Continuous Systems. Adekunle. O. Adelaja [START_REF] Adekunle | Temperature modulation of vibration responses of a flexible fluid conveying pipe[END_REF] investigated the nonlinear transverse vibration of a flexible pipe conveying hot pressurized fluid in pinned-pinned condition. M.P. Paidoussis and N.T. Issid [START_REF] Paidoussis | Dynamic and stability of flexible pipe containing flowing fluid[END_REF] studied about dynamics and stability of flexible pipe containing flowing fluid, where flow velocity is entirely constant or with a small harmonic component superposed. L.G. Oslon and D. Janison [START_REF] Oslon | Application of a General purpose Finite Element Method to Elastic Pipes Conveying Fluid[END_REF] investigated motion of elastic pipes conveying fluid for various idealized cases.

Nomenclature.

S No

Symbols Description Firstly, mathematical model for clamped clamped boundary condition was developed and then fluid motion equation and natural frequency equations were also developed accordingly.

1
The model of fluid conveying pipe is done by using I-DEAS software and the analysis of the same is done by ABAQUS software which includes standard / CFD modules to analyze fluid structural interaction. Simulation of clamped-clamped pipe performed to get the frequencies of pipe without and with welding conditions.

The FE analysis was carried out to calculate vibration characteristics of a welded pipe conveying fluid with a velocity of 5m/s and boundary conditions using a general-purpose FE package ABAQUS/Standard V6.14. The approach is divided into five parts: thermal analysis, coupled field thermal-structure analysis, computational fluid dynamics (CFD), coupled field fluid-structure analysis, and modal analysis.

The coupled field fluid-structure analysis solved the equations for the fluid and solid domains independently of each other. It transfers fluid forces and solid displacements, velocities across the fluid-solid interface. The algorithm continues to loop through the solid and fluid analyses until convergence is reached for the time step (or until the maximum number of stagger iterations is reached). Convergence in the stagger loop is based on the quantities being transferred at the fluidsolid interface.

The modal analysis was used to determine the vibration characteristics (natural frequencies and mode shapes) of a welded pipe conveying fluid. The natural frequencies and mode shapes are important parameters in the design of a structure for dynamic loading conditions. The procedure to do a prestressed modal analysis is essentially the same as a regular modal analysis, except that you first need to pre-stress the structure by doing a static analysis. Build the model and obtain a static solution with pre-stress effects turned on from thermal-structure and fluid-structure analyses A non-linear transient thermal analysis was conducted first to obtain the global temperature history generated during and after welding process (at the weld region). The basis for thermal analysis is a heat balance equation obtained from the principle of conservation of energy. The FE thermal solution employed a nonlinear (material properties depend on temperature) transient thermal analysis using two modes of heat transfer: conduction, and convection, to determine temperatures distributions that vary over time. The applied loads at the region of weld are function of time which described by divided the load-versus-time curve into load steps. For each load step, its need to specify both load and time values, along with other load step options such as stepped or ramped loads, automatic time stepping, etc. It's then written each load step to a file and solves all load steps together.

Results and Discussion.

Mathematical model, simulation and different analyses were done for fluid conveying pipe. Different cases were also considered for analysis.

Mathematical model developed for fluid conveying pipe with fixed ends.

The Fig. 1 shows the welded pipe conveying fluid, the welding is done at mid span of 1-inch Galvanized Iron pipe. Where E is young's modulus and I is moment of inertia of pipe and ρ is density of pipe material and L is length of the pipe. The governing equation of motion of a fluid conveying welded pipe by using Euler-Bernoulli's beam theory is given by:

𝐸𝐼 𝜕 4 𝑤 𝜕𝑥 4 + (𝑚 𝑝 + 𝑚 𝑓 ) 𝜕 2 𝑤 𝜕𝑡 2 + (𝑚 𝑓 𝑈 2 -𝑇) 𝜕 2 𝑤 𝜕𝑥 2 + 2𝑚 𝑓 𝑢 𝜕 2 𝑤 𝜕𝑥𝜕𝑡 0 (1)
Where the terms are as followed 𝐸𝐼 𝜕 4 𝑤 𝜕𝑥 4 = 𝑆𝑡𝑖𝑓𝑓𝑛𝑒𝑠𝑠 𝑡𝑒𝑟𝑚

(𝑚 𝑝 + 𝑚 𝑓 ) 𝜕 2 𝑤 𝜕𝑡 2 = 𝐼𝑛𝑒𝑟𝑡𝑖𝑎 𝑡𝑒𝑟𝑚 𝑚 𝑓 𝑈 2 𝜕 2 𝑤 𝜕𝑥 2 = 𝐶𝑢𝑟𝑣𝑎𝑡𝑢𝑟𝑒 𝑡𝑒𝑟𝑚 2𝑚 𝑓 𝑢 𝜕 2 𝑤 𝜕𝑥𝜕𝑡 = 𝐶𝑜𝑟𝑖𝑜𝑙𝑖𝑠 𝑓𝑜𝑟𝑐𝑒 𝑡𝑒𝑟𝑚 𝑇 = 𝑊𝑒𝑙𝑑 𝑡𝑒𝑛𝑠𝑖𝑜𝑛 𝑇𝑒𝑟𝑚

The equation of fluid motion

The equation of motion of piping vibration is given below

𝐸𝐼 𝜕 4 𝑤 𝜕𝑥 4 + (𝑚 𝑝 + 𝑚 𝑓 ) 𝜕 2 𝑤 𝜕𝑡 2 + 𝑚 𝑓 𝑈 2 𝜕 2 𝑤 𝜕𝑥 2 = 0 (2)
The Free vibration solution can be found using the method of separation of variables as

𝑊 = 𝑤(𝜉) 𝑇 (𝑡) (3)
Where T (t) is a harmonic function T (t) =𝑒 𝑖𝑤𝑡 𝜕 4 𝑤 𝜕𝜉 4 = 𝑇(𝑡) 𝜕 4 𝑤(𝜉) 𝜕𝑥 4 ;

𝜕 2 𝑤 𝜕𝜉 2 = 𝑇(𝑡) 𝜕 2 𝑤(𝜉) 𝜕𝑥 2
Natural frequency equation for clamped-clamped pipe. In the present study, we use exact method to obtain the natural frequencies of fluid conveying pipe as given below:

𝑊(𝑥) = 𝐴𝑠𝑖𝑛ℎ(𝛼𝑥) + 𝐵𝑐𝑜𝑠ℎ(𝛼𝑥) + 𝐶𝑠𝑖𝑛(𝛽𝑥) + 𝐷𝑐𝑜𝑠(𝛽𝑥) (4)
𝜕𝑤(𝑥) 𝜕𝑥 = 𝐴𝛼𝑐𝑜𝑠ℎ(𝛼𝑥) + 𝐵𝛼𝑠𝑖𝑛ℎ(𝛼𝑥) + 𝐶𝛽𝑐𝑜𝑠(𝛽𝑥) -𝐷𝛽𝑠𝑖𝑛(𝛽𝑥) (5)
𝜕 2 𝑤(𝑥)

𝜕𝑥 2 = 𝐴𝛼 2 𝑠𝑖𝑛ℎ(𝛼𝑥) + 𝐵𝛼 2 𝑐𝑜𝑠ℎ(𝛼𝑥) -𝐶𝛽 2 𝑠𝑖𝑛(𝛽𝑥) -𝐷𝛽 2 𝑐𝑜𝑠(𝛽𝑥) (6)
𝜕 3 𝑤(𝑥) 𝜕𝑥 3 = 𝐴𝛼 3 𝑐𝑜𝑠ℎ(𝛼𝑥) + 𝐵𝛼 3 𝑠𝑖𝑛ℎ(𝛼𝑥) -𝐶𝛽 2 𝑐𝑜𝑠(𝛽𝑥) + 𝐷𝛽 2 𝑐𝑜𝑠(𝛽𝑥)

Substituting in boundary condition, when W =0 at x= 0 From equation ( 7)

𝑊(𝑥) = 𝐴𝑠𝑖𝑛ℎ(𝛼𝑥) + 𝐵𝑐𝑜𝑠ℎ(𝛼𝑥) + 𝐶𝑠𝑖𝑛(𝛽𝑥) + 𝐷𝑐𝑜𝑠(𝛽𝑥) (8)
When W =0 at x= 0 From equation ( 8) Similarly,

𝑊(𝑥) = 𝐴𝑠𝑖𝑛ℎ(𝛼𝑥) + 𝐵𝑐𝑜𝑠ℎ(𝛼𝑥) + 𝐶𝑠𝑖𝑛(𝛽𝑥) + 𝐷𝑐𝑜𝑠(𝛽𝑥) (9)
𝐵 1 = -𝛽 [ 𝛼 0 𝛽 𝐶 1 𝐶 2 𝐶 3 𝐷 1 𝐷 2 𝐷 3 ]
By solving above stiffness matrix

𝐵 1 = -𝛼𝛽 2 𝑐𝑜𝑠ℎ𝛼𝑙𝑐𝑜𝑠𝛽𝑙 + 𝛼 2 𝛽𝑠𝑖𝑛𝛽𝑙𝑠𝑖𝑛ℎ𝛼𝑙 -𝛼𝛽 2 𝑠𝑖𝑛 2 ℎ𝛼𝑙 + 𝛼𝛽 2 𝑐𝑜𝑠 2 ℎ𝛼𝑙 ( 13
)
On combining and simplifying: it is applicable to a 3-D, steady-state or transient thermal analysis. Fig. 3 & Fig. 4 shows the preheating and cooling transformation during welding process. Coupled field thermal structure. A stress analysis was then developed with the temperatures obtained from the thermal analysis used as loading to the stress model. C3D20 element type was used, which can mesh irregular shape without as much loss of accuracy. C3D20 element has compatible displacement shapes and is well suited to model curved boundaries. It is defined by 20 nodes having six degree of freedom per node. The element may have any spatial orientation. C3D20 has plasticity, creep, stress stiffening, large deflection, and large strain capabilities as shown in Fig. 5. Temperature plot in degree Celsius.

𝑐𝑜𝑠ℎ𝛼𝑙𝑐𝑜𝑠𝛼𝑙 = 1 (

Fig. 5. FE analysis of clamped-clamped pipe with welding at mid span.

Cases Analysed. Fluid conveying pipe was analyzed by considering different cases and relevant analysis has been done.

(1) Pipe acts as a beam when velocity, (V) =0 and weldment effect, (T) =0

(2) Fluid flow velocity (V) =5.0 m/sec, with weldment effect (T) =0

(3) Fluid flow velocity (V) = 5.0 m/sec, without weldment Effect, (T) =10N

Case 1 when there is no velocity and no weldment effect on a pipe it behaves as a beam. The results obtained are shown in table 3. Similarly, for case 2 analysis by considering a fluid velocity 5 m/sec and weldment effect T=0 the natural frequencies were found for 3 mode shapes.

Finally, in Case 3, V=5 m/sec and T=10. Newton is applied to piping system to obtain natural frequencies using FORTRAN program code. The natural frequencies of a clamped-clamped pipe with and without welding, with and without velocity for all 3 cases mentioned above are run by ABAQUS simulation software and results were generated and compared with analytical results. The Fig. 6 and Fig. 7 show the finite element analysis of clamped ends for empty pipe with Abaqus simulation for first and second mode shapes. The first natural frequency of pipe is excited at 50.82 Hz, 2nd mode it is found to be 139.36 Hz and for 3rd mode shape 271.31Hz. For all the cases observed that the maximum deflection of the pipe is found approximately 2mm.

Similarly, harmonic analysis (sine sweep) was done on the structure by applying harmonic force of 1g acceleration to plot the Acceleration vs. Frequency. To find the frequency Peaks on the pipe as shown in Fig. 8. In case 2 fluid structure interaction is studied for clamped end pipe without welding and with fluid velocity V=5m/sec and T=0 as shown in Fig. 9 and Fig. 10. The piping vibration natural frequencies are obtained for 3 mode shapes by ABAQUS simulation the 1st mode shape is found at frequency 36.355 Hz, 2nd 99.54 Hz and 3rd Mode 192.56 Hz for all the three cases the maximum displacement was found within 0.35mm from the displacement vs. time plot. b)

The weld deposit on a pipe with c-c ends also play a major role in reduction of natural frequencies with increase in weldment. The percentage error found to be less than 3% and it is in good agreement.

c)

The frequency of first mode of vibration is computed by varying the fluid flow velocity with and without welding effects, for which critical flow velocities are obtained.

d)

In the case of c-c condition the instability region lies in the range of 32.0 to 33.56 for magnitude of 10 weld tension.

Fig. 1 .

 1 Fig. 1. Welded pipe conveying fluid with fixed ends.

4 ]

 4 𝛼𝑥) + 𝐵𝛼𝑠𝑖𝑛ℎ(𝛼𝑥) + 𝐶𝛽𝑐𝑜𝑠(𝛽𝑥) -𝐷𝛽𝑠𝑖𝑛(𝛽𝑥) x) =0 at x= l 𝑊(𝑥) = 𝐴𝑠𝑖𝑛(ℎ𝛼𝑙) + 𝐵𝑐𝑜𝑠(ℎ𝛼𝑙) + 𝐶𝑠𝑖𝑛(𝛽𝑙) + 𝐷𝑐𝑜𝑠(𝛽𝑙) Similarly, 𝜕𝑊 𝜕𝑥 = 𝛼𝐴𝑐𝑜𝑠(𝛼𝑙) + 𝛼𝐵𝑠𝑖𝑛(ℎ𝛼𝑙) + 𝛽cos (𝛽𝑙) -𝛽𝐷𝑠𝑖𝑛(𝛽𝑙) From equations We get 𝐶 1 = 𝑠𝑖𝑛ℎ𝛼𝑙, 𝐶 2 = 𝑐𝑜𝑠ℎ𝛼𝑙, 𝐶 3 = 𝑠𝑖𝑛𝛽𝑙, 𝐶 4 = 𝑐𝑜𝑠𝛽𝑙 𝐷 1 = 𝛼𝑐𝑜𝑠ℎ𝛼𝑙, 𝐷 2 = 𝛼𝑠𝑖𝑛ℎ𝛼𝑙 , 𝐷 3 = 𝛽𝑐𝑜𝑠𝛽𝑙 , 𝐷 4 = -𝛽𝑠𝑖𝑛𝛽𝑙 Stiffness matrix as follows By solving above stiffness matrix А = 𝛼 2 𝛽𝑠𝑖𝑛 2 𝛽𝑙 + 𝛼 2 𝛽𝑐𝑜𝑠 2 𝛽𝑙 -𝛼𝛽 2 𝑠𝑖𝑛ℎ𝛼𝑙𝑠𝑖𝑛𝛽𝑙 -𝛼 2 𝛽𝑐𝑜𝑠ℎ𝛼𝑙𝑐𝑜𝑠𝛽𝑙 (12)

14 )Fig. 2 .

 142 Fig. 2. (a) Finite element structural mesh model with boundary conditions, (b) finite element fluid mesh model with fixed ends.

Fig. 3 .Fig. 4 .

 34 Fig. 3. Heat cycle.

Fig. 6 .Fig . 7 .

 67 Fig. 6. Vibration analysis of clamped-clamped empty pipe ends without welding first mode shape.

Fig. 8 .

 8 Fig. 8. Acceleration vs. Frequency of an empty pipe with clamped ends without welding.

Fig. 9 .

 9 Fig. 9. Vibration analysis of clamped-clamped with velocity (V) =5m/sec without welding (T) =0.

Fig. 10 .

 10 Fig. 10. FE analysis of clamped pipe with deflection plot at V=5m/sec and T=0.

Fig. 11 .

 11 Fig. 11. Vibration analysis of clamped-clamped with velocity V =5m/sec without welding T =10N

Modelling, Simulation and Analysis of fluid conveying pipe.

		ρp	Density of pipe in (kg/m 3 )
	2	ρf	Density of fluid in (kg/m 3 )
	3	U	Fluid velocity in (m/s)
	4	E	Young's modulus in (N/m 2 )
	5	mf	Fluid mass in (kg)
	6	mp	mass of the pipe in (kg)
	7	W	Displacement component at any point in the cross section (m)
	8	Dx	Small element of the pipe
	9	f(x,t)	External transverse force per unit area
	10	w(x, t)	Transverse deflection of pipe
	11	𝑊 𝑖 (𝑥, 𝑧, 𝑡) I th normal mode shape of a pipe
	12	Z	Axial strain in Z direction
	13	𝑈 𝑖	I th mode of vibration
	14	T	Weld Tension in N
	15	K	Spring stiffness

Table 2 .

 2 Material properties of GI pipe.

	1 Inch Pipe Span	2 meters (welded at mid span)
	Pipe Material	Galvanised Iron
	Pipe Outer Diameter (OD)	0.034m
	Pipe Inner Diameter (ID)	0.0304m
	Pipe Wall Thickness (t)	0.00178m
	Density of Steel	7850 kg/m3
	Young's modulus (E)	200 Gpa
	Poisons Ratio	0.28
	Fluid Density ()	1000 kg/m3
	Mass of Pipe (mp)	3.61 kg
	Mass of Fluid (mf)	1.76kg
	Dynamic Viscosity of fluid	0.001001 pa.s at 20° C
	Analysis of simulated model. Thermal analysis.
	DC3D20 element type is used, which it is 3-D twenty nodes with a single degree of freedom,
	temperature, at each node. The 20-node elements have compatible temperature shapes and are well
	suited to model curved boundaries. It is applicable to a 3-D, steady-state or transient thermal analysis;

Table 3 .

 3 FE analysis of fluid conveying welded pipe with different conditions.

	Mode	Empty pipe V=0, T=0	Percent	Pipe without weld	Percen	Pipe with weld	Perce
	No.			age of	V=5m/sec, T=0	tage of	V=5m/sec, T=10	ntage
		Natural Freq. by	Natural Freq.	Error	Natural Freq. by	Natural Freq.	Error	Natural Freq. by	Natural Freq.	of Error
		ABAQUS	Theo. in		ABAQUS	Theo.		ABAQUS	Theo.
		Software in	Hz		Software in	in Hz		Software	in Hz
		Hz			Hz			in Hz
	1	50.82	49.58	2.43	36.35	35.76	1.6	31.36	30.71	2.07
	2	139.36	137.52	1.32	99.54	98.15	1.39	85.75	83.92	2.13
	3	271.31	265.37	2.18	192.66	187.13	2.87	166.22	163.97	1.35

©

The Authors. Published by Magnolithe GmbH. This is an open access article under the CC BY-NC-ND license http://creativecommons.org/licenses/by-nc-nd/4.0/

Acknowledgement: Shaik Imran and Shaik Riyaaz Uddien are students of Department of Mechanical Engineering, University College of Engineering, Osmania University, Hyderabad.


Yu M Mar'yinskykh
email: a-mymih44@gmail.com

The Material of the Working Fluid of the Solar Energy Heat Converter for Space Application 1

Keywords: thermal solar energy converter (TSEC), space application, power, construction, parameters, temperature

The research is dedicated to reasoning the need for creation of a functional material as an active medium of conversion of solar energy into mechanical energy with further conversion of it into electric power and using it in power plants and in projects of solar power satellites (SPSs). There have been considered the ways of generating energy from the points of view of the environment and inexhaustibility, which include photoconverting power engineering, methods of heat conversion of solar energy and the problems, restraining creation of large-sale projects. The result of the research is the development of a method of continuous generating useful mechanical energy by using the functional material (working fluid) in the process of heating it with solar radiation in the heat-absorbing zone and cooling it down in the heat-radiating zone within the optimum rated temperature range. The corresponding theoretical researches have been conducted in order to assess quantitatively the capacity of the metal segment as working fluid of the heat-converting panel while the thermal solar energy converter (TSEC) for space application is functioning. The graphic curves of segments capacity in various temperature ranges have been presented herein. The time response of the TSEC metal segment functioning cyclicity has been studied at solar concentration of n = 1.2, for different temperature ranges. A solution has been suggested that allows a significant increase of TSEC efficiency by improving the physical and technical characteristics of the segment material. The promising character of changing one of the series of parameters that define the segment material has been shown; and it leads to an opportunity to compete with photoconverting systems according to their efficiency, provided several parameters are combined in an optimum way. A variant of structure of a TSEC as an electric drive has been shown. It may also be applied on earth if modified correspondingly. The conversion method under consideration enables to construct SPSs and calculate the paths of motion so that the time of a power plant being in the subsolar zone and the shadow zone while moving around the Earth per one rotation could match the time of a TSEC cycle.

Introduction. Nowadays, such world problems of energetics as energy safety, energy efficiency and environmental protection are appended with the factor of energy pricing policy. The significance of the energy problem is worth considering due to the obvious fact that the products manufactured by any industry are purchased for money equivalent to the amount of energy expenditure. The restricted and non-renewable character of energy resources on earth as well as the increasing consumption of them caused by the people's comfortable living conditions are leading to the produced useful energy becoming more expensive, which makes us search for alternative ways of generating energy by using renewable sources.

The Price Factor of Technologies and Materials of the Photoconverting Power Engineering. The most promising among the renewable types of power engineering is the solar power engineering, particularly the photoconverting one, and the concomitant thermal energy, generated by this way of conversion, will make the increase of the environment temperature negligibly small. When getting this energy from earth energy resources, there is a direct risk of increase of the parameter values which are included into the definition of environment entropy.

In its turn, improving the photoconverting ways of generating energy causes a row of problems that are hard to solve. Thus, with significant reduction of consumption of photoconverting materials accomplished through the concentrated solar radiation method, with application of linear Fresnel lens in the module itself [START_REF] Zh | The Tendency and Prospects of Development of the Solar Power Engineering[END_REF] and because of the complexity of its structure, it is difficult to solve the problem of deployment of the system, which is based on them, in space. The 3rd-generation photoconverters using the nano-and microstructures (Vapor-Liguid-Sol: 2-VLS method) that belong to the class of devices of special industrial design with conducting quantum wires are resistant to radiation damage in space conditions, but they possess properties of metallic conductivity, because of which the applicability of the method is limited [START_REF] Nsakalakos | Silicon nanowire solar cells[END_REF]. Proceeding from the analysis of works [START_REF] Yefimov | The New-Generation Photoconverters of Solar Radiation Energy[END_REF], it follows that only the silicon photoconverters of a planar design with conducting quantum wires that belong to the 3rd generation are of a certain interest concerning their further development.

The class of multijunction (cascade) А 3 В 5 with the structure of such Cu (ZnGa)Se 2-elements, the efficiency of which reaches 33%, can be used in space. However, their production requires creating high-technology equipment, which causes their high cost. Thus, let us take the cascade photocells, the efficiency factor of which reaches 28%, and in prospect the prime cost of 1 W of capacity based on them will make USD 1.5 [START_REF] Andreev | Concentrator Solar Photo Power Engineering[END_REF]. In this connection, there are many competing companies that possess the complicated technology of epitaxial growth of multijunction photoconverters and production of solar cells using the concentrated solar radiation with the possibility of space application, though the problem of pricing policy remains actual for them.

Proceeding from the analysis of full production cycle of photoconverters for space application, starting from extraction of raw materials with creation of high-technology process of their production to their further application in large-scale projects of solar power satellites (SPS), it is obvious that the cost of generated energy after transportation onto the Earth remains sky-high. This makes us search for new ways and methods of improving the cycle. Proceeding from this fact, the method of heat conversion of solar energy into the mechanical energy with the possibility of further converting it into the electric power by using the corresponding TSEC for space application. Due to the possibility of future developing the following method of conversion of solar energy, the need has arisen to define the notion of active medium of conversion as the composition of substance that participates in converting the solar radiation energy into energy of some other type. For a thermodynamic conversion system in SPS projects based on gas or steam turbine converters, the active medium is either liquid metal with phase transformations or gas which is intended for serving as working fluid. At the stage of heating the active medium to the operation temperature and partially at cooling it down , there is no useful effect; in this case the medium is in a passive state. The active medium of the photoelectric conversion system for space application demonstrates a complex architecture based on nanoheterostructure consisting of semiconducting materials and metals. The active medium of thermoelectric systems of direct conversion of heat into electric power through physical phenomena and effects is solid bodies (metals), i.e. each conversion system needs a corresponding active medium.

The Dependence of Capacity of the Metal Segment in the Process of Its Performing Work at Heat Absorption and Radiation in Space on Parameters, Characterizing Its Physical

Properties. Let us estimate the capacity of the medium of solar energy conversion into the mechanical energy from duraluminum alloy with possible further application of it as an active medium of conversion in TSECs for SPS projects. In order to calculate the capacity of the segment in the form of a plate, which the TSEC panel consists of, the average indices of an alloy, which is not prepared specially for this purpose, are used. The mechanism of performing the continuous effective work by the active medium of the material (elastic metal plate), located in the thermal trap, lies in periodical conversion of the solar radiation, falling onto its surface, which by its thermal properties is close to a black body, as a result of thermal expansion and compression at cooling down in the shadow zone, when released from the thermal trap. The segment material must comply with its main functionality: to perform mechanical work continuously, to have the minimum specific heat capacity and density with the maximum values of the thermal expansion coefficient, the modulus of elasticity at physical loads (compression -tension), and the plates surface emissivity is close to unity with the possibility of placing them in the heat-absorbing zone of the thermal trap and beyond it in the heat-radiating zone in the shadow. The thermal trap consists of low-emission transparent with selective coating on the side of solar radiation of surface, but reflecting the heat radiation from the heated panel and preventing it from coming out in full. Nearby the opposite unlit (shadow) surface of the panel, it is possible to place specular heat-reflective foil, when it goes about the variant without using the concentration of solar radiation. To ensure rigidity, the panel segment may look like a segment of an oval line in the cross-section, so that its opposite extreme longitudinal parts could not re-radiate onto themselves. Here below, there are tabular data on the segment material, its parameters and values of constants, where the changes of values of the modulus of elasticity and the linear thermal expansion coefficient within the studied temperature ranges are negligibly small: Let us estimate the capacity of the panel segment. In the heliostationary orbit of the near-Earth space environment, where the TSEC is going to be placed, the Earth albedo is negligibly small compared to the thermal processes on the converter. The amount of thermal solar energy at irradiation of the panel segment is used for heating it, for reverse heat radiation, for insignificant reflection from the surface of the thermal trap, wherein the panel is situated, and for heat-stretch work of the segment:

ΔQ = ΔQ1+ΔQ2+ΔQ3 + ΔA. (1)
In our calculations, we shall require increasing the heat radiation from the segment to the outside through the transparent low-emission coating of the thermal trap, which it really is, by the value of the falling radiation, reflected from the upper surface of the thermal trap; then the equation ( 1) shall assume the following look:

∆𝑄 = ∆𝑄 1 + ∆𝑄 ′ 2 + ∆𝐴. (2)
∆𝑄 ′ 2 = 𝜀𝛿(𝑇 0 4 -𝑇 4 )𝑆∆𝜏 where ΔQ = GSΔτ; ΔQ1= ρVcΔT. Since the absorbing and the reflecting surface is the same.

∆𝑙 = 𝑙 0 𝛼∆𝑇segment stretch while heating; 𝐹 = 𝐸𝑆 𝑛 𝛼𝑇force close to terminal, which can suspend the segment stretch within the temperature range, where the modulus of elasticity remains the biggest (Sпsectional area of segment, 𝛼 = 0.97𝛼′).

Proceeding from the last correlations, the segment work at heat-stretch may be determined and inserted into the equation along with the previous ones [START_REF] Nsakalakos | Silicon nanowire solar cells[END_REF]. The amount of heat is coming into the thermal trap to the segment within the time dτ, and the corresponding heating occurs for the value dT. Whence the segment heating time within the temperature range from T0 to T is determined by the following expression:

𝜏 = ∫ ℎ(𝑐𝜌+2𝐸𝛼 2 𝑇) 𝑛𝐺-𝜀𝜎𝑇 4 𝑇 𝑇 0 𝑑𝑇. (3)
The highest temperature value must be lower or equal to terminal, to which the segment can be heated up, which does not cause any difficulties to determine it at a certain solar concentration. The capacity, determined by the ratio of the work performed by the segment in the process of its heating up to the time spent on this process, is determined through the following expression:

𝑃 = ∫ 2𝑉𝐸𝛼 2 𝑇𝑑𝑇 𝑇 0 ∫ ℎ(𝑐𝜌+2𝐸𝛼 2 𝑇) 𝑛𝐺-𝜀𝜎𝑇 4 𝑇 𝑇 0 𝑑𝑇 . (4)
In figure 1, there are graphs of heated segment capacity in dependence on temperature values from 250K to 430K and in the higher temperature range from 350 K to 530 K at concentrations n = 1 and n= 2 respectively.

Fig. 1. Graphs of heated segment capacity in dependence on temperature values.

In the denominator of the expression (5) for determining the time of the panel segment cooling down, the coefficient 2 indicates a two times increase of the area of the heat-radiating surface beyond the thermal trap in the shadow.

𝜏 ′ = ∫ ℎ(𝑐𝜌-2𝐸𝛼 2 𝑇) 2𝜀𝜎𝑇 4 𝑑𝑇 𝑇 0 𝑇 . (5)
The segment capacity in the process of heat-radiating (cooling down), determined by the ratio (6), is shown in figure 2. The expression in the numerator corresponds to the work of the reverse process. It is negative in relation to work at heating, then the expression (6) will be positive, if we change the limits of integration; this method covers the following expressions (7) as well:

𝑃′ = ∫ 2𝑉𝐸𝛼 2 𝑇𝑑𝑇 𝑇 𝑇 0 ∫ ℎ(𝑐𝜌-2𝐸𝛼 2 𝑇) 2ε𝜎𝑇 4 𝑇 𝑇 0 𝑑𝑇 . ( 6
)
Fig. 2. The segment capacity in the process of heat-radiating.

The capacity per one cycle of the process of heat-absorbing and heat-radiating by the segment is determined by the expression (7), and its corresponding curve is shown in figure 3. The relative curve of the segment capacity along with a value of specific heat capacity of the material decreased by 0.01 per cycle in figure 3 are shown in dotted lines. These indices increase twice, if we consider each of the directions of two-dimensional expansion. This structure variant of TSEC as an electric drive of the power plant is shown in figure 4, where (A) is the general view, (B) is the crosssection; the part of the thermal trap in the horizontal position corresponds to the heat-absorbing state, and the one in the vertical position -to the heat-radiating state in the shadow area. The Analysis of the Research Results. Based on the suggested method of conversion of solar energy, the dependence of the capacity of the segment as working fluid of TSEC on several variables has been discovered. These variables are the physical characteristics of the material, which the segment is made of. The requirements, made to the optimisation of functioning of TSEC for space application, lie in receiving an active medium of the rigid elastic material of the panel, the functionality of which is directed to obtaining the maximum capacity per heating-cooling cycle as a result of expansion and compression at minimum weight and size parameters in two perpendicular directions. This is indicated by the researches [START_REF] Xu | Size dependence of elastic mechanical properties of nanocrystal line aluminum[END_REF] that allow predicting mechanical properties of nanocrystalline materials and the scheme of their production. The possibility of a wide range of combinations of physical and technical parameters of the active medium of the segment material at its production, which are included into the analytical expression of capacity, allows choosing an optimum variant for its maximum value, which is going to be an alternative for the existing conversion systems. The advantages of TSEC are its significant service life, the safety and resistance to radiation and meteor showers, and the processability of deployment in space.

𝑃 ′′ = ∫ 4𝑉𝐸𝛼 2 𝑇𝑑𝑇 𝑇 𝑇 0 ∫ ℎ𝑐𝜌+2𝐸ℎ𝛼 2
Summary. During the accomplishment of a TSEC project, there is a problem arising: its conversion of mechanical energy into electric power. In this connection, a superconducting generator without any magnetic conductor will be an integral part of the TSEC. The low temperature value in the shadow area will allow it to function at small energy expenditure on cryostat. This conversion method enables to construct SPSs and calculate the path of motion so that the time of a power plant being in the subsolar zone and the shadow zone while moving around the Earth along the path per one rotation could match the time of a TSEC cycle. Herewith, the dimensions will be reduced, and there is no need to block the full stream of solar radiation, falling onto TSEC, with foil in order to create a heatradiating zone while shadowing.

σ = 5 .

 5 67•10 -8 W/m 2 K 4 -Boltzmann constant; c = 850 J/kgK-specific heat capacity; ρ= 2780kg/m 3density; Е = 7•10 10 Pa -Young modulus; α′ = 23.8•10 -6 K -1linear thermal expansion coefficient; k = 0.95emissivity; ε = 0.12reverse radiating capacity; G = 1360W/m 2solar constant; d = 3•10 -3 msegment thickness; m =16kgsegment mass; ι = 10msegment length; n = 1 and 2solar concentration.

Fig. 3 .

 3 Fig. 3. Capacity per one cycle of the process of heat-absorbing and heat-radiating segments.

Fig. 4 .

 4 Fig. 4. Structure variant of electric drive. (1, 5)rigid framework made of carbon, its sides and diagonals with reflecting coating serve as ways for movement of the side ends (3) of the plane (4) along them from the heat-converting segments of the active material; (2, 6)the opposite surfaces of the thermal trap in the framework (10); (7)rigid connection; (8)biaxial generator; (9)generator rods; (11)solar concentrator; (12)radiation reflector.

©

The Authors. Published by Magnolithe GmbH. This is an open access article under the CC BY-NC-ND license http://creativecommons.org/licenses/by-nc-nd/4.0/