Numerical simulation of velocity and temperature fields in natural circulation loop

Transcription

1 Jounal of Physics: Confeence Seies PAPER OPEN ACCESS Numeical simulation of velocity and tempeatue fields in natual ciculation loop To cite this aticle: L A Sukomel and O N Kaban kov 2017 J. Phys.: Conf. Se View the aticle online fo updates and enhancements. Related content - Veification of RELAP5-3D code in natual ciculation loop as function of the initial wate inventoy C Betani, N Falcone, A Besano et al. - Expeimental eseach of a two-phase nitogen natual ciculation loop S Reis, A Bonelli and B Baudouy - Expeimental study of themo-hydaulic chaacteistics of natual ciculation loop at wate and FC-72 boiling unde atmospheic pessue O N Kaban kov, L A Sukomel, N O Zubov et al. This content was downloaded fom IP addess on 02/03/2018 at 07:45

2 Numeical simulation of velocity and tempeatue fields in natual ciculation loop L A Sukomel 1,3, O N Kaban kov 1,2 1 Depatment of Themal Physics, National Reseach Univesity "Moscow Powe Engineeing Institute", Russia, Moscow, Kasnokaamennaya, kon09.tige@yandex.u 3 ms.las2016@mail.u Abstact. Low flow natual ciculation egimes ae ealied in many pactical applications and the existence of the eliable engineeing and design calculation methods of flows diven exclusively by buoyancy foces is an actual poblem. In paticula it is impotant fo the analysis of stat up egimes of passive safety systems of nuclea powe plants. In spite of a long yea investigations of natual ciculation loops no suitable pedicting ecommendations fo heat tansfe and fiction fo the above egimes have been poposed fo engineeing pactice and coelations fo foced flow ae commonly used which consideably ovepedicts the eal flow velocities. The 2D numeical simulation of velocity and tempeatue fields in cicula tubes fo lamina flow natual ciculation with efeence to the laboatoy expeimental loop has been caied out. The esults wee compaed with the 1D modified model and expeimental data obtained on the above loop. The 1D modified model was still based on foced flow coelations, but in these coelations the physical popeties vaiability and the existence of themal and hydodynamic entance egions ae taken into account. The compaison of 2D simulation, 1D model calculations and the expeimental data showed that even subject to influence of liquid popeties vaiability and entance egions on heat tansfe and fiction the use of 1D model with foced flow coelations do not impove the accuacy of calculations. In geneal, accoding to 2D numeical simulation the wall shea stesses ae mainly affected by the change of wall velocity gadient due to pactically continuous velocity pofiles defomation along the whole heated one. The fom of velocity pofiles and the extent of thei defomation in its tun depend upon the wall heat flux density and the hydaulic diamete. 1. Intoduction It is no need to say that natual ciculation loops o loop themosyphons ae heat emoval systems which have many industial applications of diffeent pupose. In ecent yeas natual ciculation heat emoval mechanism is consideed fo passive safety systems in new design nuclea powe plants. Besides, some advanced nuclea plant designs ely on natual ciculation to emove coe powe unde nomal opeation (statup, nomal powe opeation, and shutdown), and some designs ely on natual ciculation to povide cooling of the containment. Many applications including passive safety systems of nuclea powe plants opeate at low paametes, vey often low flow conditions of single phase heat tansfe medium ae ealied. So the availability of the eliable engineeing and design calculation methods of flows diven exclusively by buoyancy foces is an actual poblem. In paticula it is impotant fo the analysis of stat up egimes of passive safety systems of nuclea powe plants. Content fom this wok may be used unde the tems of the Ceative Commons Attibution 3.0 licence. Any futhe distibution of this wok must maintain attibution to the autho(s) and the title of the wok, jounal citation and DOI. Published unde licence by Ltd 1

3 Natual ciculation systems may have low diving foce and need to be stated fom the state of est. Stat-up fom est is one of the key issues in assessing the eliability of these systems. Thee is always a finite time lag befoe these systems attain thei optimum intended pefomance level. The pedicting models applicable fo low flow conditions can be quite diffeent fom those applicable fo high flow conditions. Fo example, in many cases unde low flow conditions the thee-dimensional flow effects occu and taditional 1D appoach may not pedict the behaviou of natual ciculation systems with easonable satisfaction. Also the pefomance of these systems is stongly dependent on the opeating conditions and system geomety [1, 2]. Being of geat pactical impotance single-phase natual ciculation loops have been investigated expeimentally, analytically and numeically fo seveal decades since ealy 1950s and emains to be the subject of eseach till today. One of the poblems having been not solved yet is the coect fiction facto calculation fo the conditions of complex velocity fields and geat vaiability of liquid popeties in the flows induced exclusively by buoyancy foces. The most complex flow fields ae in lamina flow egimes. In spite of long yea investigations of natual ciculation loops no suitable pedicting ecommendations fo heat tansfe and fiction fo the above egimes have been poposed fo engineeing pactice and coelations fo foced flow ae commonly used which to lage extent ovepedict the eal flow velocities [15]. In paticula the pedicting fiction facto coelations fo fully developed isothemal flows is vey often used in calculation of loop themosyphons [24]. To ou point of view this appoach is not fully coect because the fom of velocity pofiles in eal buoyancy-induced ciculation flows diffes fom fully developed isothemal velocity pofiles. Besides the pofile configuation can change along the heated one and it will lead to additional incease of hydodynamic dag. The pesent wok was inspied by the esults of compaison of 1D calculations with the expeimental data on two-phase natual ciculation in laboatoy loop themosyphon designed fo studying natual ciculation of boiling liquid at low pessues [6, 7]. As at low pessues boiling the single-phase convection egion can be elatively vey lage low flow expeiments fo the conditions of single-phase ciculation wee the pat of the investigation. Steady state 1D calculations of the loop wee the fist step in futhe developing of calculation method of loop behaviou fo single and twophase ciculation at low (atmospheic and subatmospheic) pessues. As it follows fom diffeent publications fiction facto coelations fo isothemal foced flows, especially fo lamina egime ae not valid fo the conditions of buoyancy diven flows, so a modified 1D model has been tied. The modified 1D model was still based on foced flow coelations, but in these coelations the physical popeties vaiability and the existence of themal and hydodynamic entance egions wee taken into consideation. Heat tansfe was calculated accoding to B.S Petuhov s and A.F. Polyakov s ecommendations fo heat tansfe and fiction fo flows with the same diection of foced and natual convection. Besides, the concuent fomation of heat and hydodynamic bounday layes in the entance egion has been taken into account. In spite of these impovements the calculated flow velocities emained ovepedicted in compaison with expeimental data. To study this poblem in moe details the 2D numeical simulation of velocity and tempeatue fields in cicula tube in model natual ciculation loop has been caied out. The pesent aticle pesents the esults fo lamina flow. 2. Expeimental loop configuation and modified 1D calculation esults The analyed expeimental data wee obtained on the natual ciculation loop of ectangula configuation the schematic diagam of which is pesented in Figue 1 [6, 7]. 2

4 The flow up (heated) 1 and flow down 3 legs of the loop ae joined to the cooling section 2 at the top of the loop. One of the stuctual featues of the loop was lage aspect atio between the down leg coss sectional aea and that of the heated leg. This detail of constuction made it possible to substantially educe pessue losses in flow down line (down come). So the flow chaacteistics can be consideed as somewhat uppe limiting case fo buoyancy diven flow fo given heat flux fo specific coss sectional geomety and hydaulic diamete of the heated leg. Two test sections have been used in the expeiments. Both 1 flow up (heated) section, 2 cooling section, 3 down come Figue 1. Configuation of the expeimental loop [6, 7]. wee electically heated stainless steel cicula tubes 1370 mm long and diffeed by inne diametes (5.4 and 9.1 mm). The test sections can be heated both along thei whole length and along the pat of it. The expeimental data having been used in pesent wok fo compaison with calculated esults wee obtained fo the loop fully filled with the woking liquid up to outlet of flow up tube in cooling section. Wate was used as woking liquid. Engineeing and design methods of pedicting themo and hydaulic chaacteistics of natual ciculation loops ae based on 1D desciption of flow and heat tansfe in channels. It is assumed accoding to this appoach that flow velocity and tempeatue vay only in steamwise diection. Substantial mathematical simplification of the poblem at 1D appoach is achieved by intoduction of such quantities as heat tansfe coefficients and hydaulic loss, which in complex way ae connected with the eal 3D flow and couldn t be detemined fom 1D theoy in pinciple. So one needs to get additional infomation fom expeimental data, 3D calculations o semiempiical theoies to detemine the values of heat tansfe coefficients and hydaulic loss. In pesent wok the modified 1D appoach was tested on the expeimental data. As it was mentioned above the velocity field patten in buoyancy diven flows vey often is in a tansfoming state at long distance in steamwise diection. Besides the flow field is foming unde the conditions of consideable vaiety of themophysical popeties of woking liquid. So the velocity field stuctue is highly complex, especially fo lamina flows, and developing of the appopiate pedictive coelations is not a tivial poblem. Futhemoe hydodynamic patten of natual convection flows is dependent upon channel coss section configuation, channel hydaulic diamete, channel length to hydaulic diamete atio and flow oientation elatively to gavity acceleation vecto. In geneal case fo the above conditions fiction facto ξ must be a function of a numbe of paametes [810]: ξ=ξ(/d h, Re, P, μ w /μ f, G), whee d h hydaulic diamete, μ w and μ f, dynamic viscosity of liquid at wall and bulk liquid tempeatue. Accoding to definition the fiction facto is u 2 w u μ, (1) 8 whee τ w is wall shea stess, ρ liquid density at bulk tempeatue, ū ciculation velocity, ( u/ ) =0 velocity gadient at the wall. Fo the foced flow the effect of physical popeties vaiability on fiction facto can be taken into account by applying the coection of the fom [8, 9] 0 w f n 0, (2) 3

5 whee ξ 0 is the fiction facto at constant popeties, n > 0. In geneal case n = n(/d h, Re, μ w /μ f ), that is n const. The most complex ξ dependence on coss-sectional viscosity vaying is at lamina flow egimes. Unfotunately not many quantitative expeimental data on fiction-viscosity vaiability dependence and a few pedictive coelations ae available fo today. All of them ae classified among foced flows. In pesent wok the following coelation fo n in the elationship (2) fo fiction facto fo flow up section of the loop wee used in 1D calculations as the fist step [8, 9]: m d h w n C Pe, (3) lt f whee C = 2.30, m = 0.3 at Pe (d h /l) 1500 and C = 0.535, m = 0.1 at Pe (d h /l) > In elationship (3) Pe is Peclet numbe, l t heated tube length. In fomulas (2) (3) isothemal flow fiction facto ξ 0 was taken as ξ 0 = 64/Re, whee in the Reynolds numbe Re physical popeties of the liquid wee taken at bulk liquid tempeatue at cuent coss-section. Fist of all it was necessay to make tests fo steady state egimes. In this case the calculation of themo-hydaulic chaacteistics of the loop is educed to solving the balance elationship elative to the ciculation velocity ΔP df = ΣΔP loss, (4) whee P g ( l) dl the diving foce, ρ(l) liquid density which vaies with tempeatue along df L l the heated one, g l pojection of gavity acceleation vecto on flow diection l, ΣΔP loss = ΔP f + ΣΔP loc total hydaulic losses, ΔP f total hydaulic losses due to fiction and ΣΔP loc total hydaulic losses due to local dag eduction. The equation (4) is solved elative to the ciculation velocity with the use of iteation pocedue. As the expeimental loop [6, 7] was designed in such a way that local dag eduction can be neglected only ΔP f emains in ight hand of (4). Fo the same diections of foced and natual convection at q w =const the local Nusselt numbe at cuent coss-section can be detemined as [9] Nu Gq 1 Re, (5) Nuv B whee Nu v is Nusselt numbe fo viscous flow with constant physical popeties; 1 B = 5,40X X 0.25 at X 0.07 and B = 240 at X > 0.07; X ; G q = gβd 4 h q w /(ν 2 λ) Pe d h Gasghof numbe. Equations (2), (3), (5) ae modified components in the 1D calculations. Accoding with the loop design Nusselt numbe Nu v was calculated with account to pactically unifom velocity and tempeatue distibutions in the inlet of the heated section and concuent fomation of heat and hydodynamic bounday layes in the entance egion [9]. Lamina expeimental egimes fo the analysis have been chosen accoding to the condition at the outlet of the heated one X lam < X c 1.3X *, (6) whee X * = 12.9(G q /Re) -0.8 adjusted coodinate of stability loss of viscous-gavitational flow and X c is adjusted coodinate of tansition to tubulence [9]. Typical example of wall tempeatue calculations with the above attempts to take into account the vaiability of physical popeties and the diffeences in tempeatue and velocity fields as elated to fully developed isothemal flow conditions is shown in figue 2. Calculated cuves fo d h = 9.1 mm fo heat flux densities of 3.7 and 17.4 kw/m 2 ae compaed with the expeimental data. As it is seen fom

6 figue 2 the calculated longitudinal wall tempeatue distibutions ae lowe than measued ones that is the pedicted flow velocities ae highe than that which actually was eached in the expeiments. It means that fo low heat fluxes actual liquid wall shea stesses must be substantially highe than that calculated accoding to coelations fo foced flow. The 2D numeical simulation showed that in low flow egimes the main effect on wall shea stess has the change of velocity pofiles and elated to it incease of thei gadients at the wall. Points expeiment, lines 1D calculations with (2), (3), (5): 1, 2 q w = 3.7 kw/m 2, T in = 23.0 o C, 3, 4 q w = 17.4 kw/m 2, T in = 34.0 o C. Figue 2. Expeimental and calculated longitudinal wall tempeatue distibutions at pue single-phase ciculation egimes 3. Numeical model A diagam of the numeical model used in 2D simulation is shown in fig. 3. The simulated loop was a closed by liquid ensemble fom annula and cicula tube. Cicula (heated) tube was placed coaxially inside the annula tube. Annula tube was the down come of the simulated loop. The heated tube height was specified equal to the loop test section height, and coss-sectional aea of annula gap was equal to coss sectional aea of the expeimental loop down leg. Thus the simulated ciculation conditions wee made moe ealistic in tems of the ciculation in expeimental loop. So the axially symmetic 2D poblem has been fomulated. Fo lamina flow the consevation equations of mass, momentum and enegy at the absence of inne heat souces and enegy dissipation being witten in cylindical coodinate system has the fom ( U and U pojections of the velocity vecto on coodinate axes, -axe is diected vetically, -axe is diected along the tube adius): 1 flow up tube, 2 coole, 3 down come Figue 3. Numeical model fo 2D simulation of the loop ( U ) ( U ) U 0 (7) U U p 1 U U U U FB (8) U U p U U U U (9) h h 1 T T U U (10) Hee ρ, h, T, p ae density, enthalpy, tempeatue and pessue, F B is the pojection of buoyancy foce vecto F B on -axe. The expession fo buoyancy foce vecto, which appeas in the system of consevation equations and which is the diving foce of motion can be witten in geneal case as F B (,) = g[ρ(,) ρ ()], whee g is vecto of gavity acceleation and ρ is local efeence density. Fo inne gavity flows (in closed space bounded by solid walls) the efeence density is 5

7 chosen accoding to the type of inne flow unde consideation [11]. In ou calculations ρ () was consideed as coss-section aveaged density at cuent coodinate in down leg of the loop. Bounday conditions wee fomulated accoding to the expeimental ones in [6, 7]. They ae the constant heat flux density on the wall of the heated section and adiabatic conditions on the othe sufaces except the coole one. The loop coole was simulated as volumetic heat sink of the cylindical shape which height was equal to the uppe gap in figue 3. The total capacity of the coole was equal to the input heat powe. The system of consevation equations (7) (10) was solved numeically with the use of contol volume method within the ANES CFD-code [12]. 4. 2D simulation esults. The 2D numeical simulation have been caied out fo distilled wate ciculation at heat flux densities which coespond to lamina flow egimes in the expeimental loop [6, 7]. The flow was consideed to be lamina along the entie length of the heated one when adjusted coodinate X at the inlet coss section was less than X c, the latte was estimated accoding to elationship (6). The calculation esults pesented in this pape have been obtained fo heating the flow up section with a length of 1300 mm fo two tube diametes: 5.4 and 9.1 mm. The calculated fiction factos fo two almost twice diffeent tube inne diametes (5.4 and 9.1 mm) and the same heat flux density q w = 2 kw/m 2 ae shown in figues b) a) a) calculated fiction factos as a function of adjusted length fo d h = 5.4 mm and q w =2 kw/m 2 ; b) change of the local Re() numbe along the tube unde heating conditions: (a): 1 isothemal fiction facto at Re = 163 (coesponds to heated one inlet), 2 isothemal fiction facto at Re = 227 (coesponds to heated one outlet), 3 numeical simulation, 4 fomula (2) with account to Re() change unde heating conditions. Figue 4. Calculated fiction factos and Re() numbes fo q w = 2 kw/m 2 and d h = 5.4 mm as a function of adjusted length. The solid lines 3 in the figues 4,a and 5,a ae the esult of numeical simulation. Dashed-point lines 4 in the same figues coespond to fomula (2) fo cuent Re() numbes. The longitudinal Re numbe change with liquid viscosity vaiation along the heated one ae shown in figues 4,b and 5,b. As the whole the Re numbe inlet and outlet values unde heating conditions can diffe fom each othe fom 20 to 40 % o moe depending on heat flux density and hydaulic diamete, the less the diamete the highe the Re numbe change. The dashed lines 1 and 2 in figues 4,a and 5,a ae fiction factos calculated fo finite length cicula pipe at constant physical popeties fo inlet and outlet liquid tempeatues unde heating conditions at given q w. As it follows fom the figues the fiction facto in buoyancy induced flows changes along the tube in a complex way and is highly influenced by the hydaulic diamete. It is also seen that fomula (2) noticeably udepedicts longitudinal ξ distibution. 6

8 b) a) a) calculated fiction factos as a function of adjusted length fo d h = 9.1 mm and q w =2 kw/m 2 ; b) change of the local Re() numbe along the tube unde heating conditions: (a): 1 isothemal fiction facto at Re = 307 (coesponds to heated one inlet), 2 isothemal fiction facto at Re = 370 (coesponds to heated one outlet), 3 numeical simulation, 4 fomula (2) with account to Re() change unde heating conditions. Figue 5. Calculated fiction factos and Re() numbes fo q w = 2 kw/m 2 and d h = 9.1 mm as a function of adjusted length In both cases simulated ξ values always emain highe than that calculated accoding to fomula (2) if the Re numbe is detemined at local bulk liquid tempeatue. The discepancy inceases downsteam and fo highe hydaulic diamete one can obseve diffeent qualitative behaviou. Local (at given coss section along the tube) ξ value is the esult of two main effects viscosity decease with tempeatue in nea wall egion and velocity gadient change due to velocity pofile defomation. Velocity pofiles calculated fo wate ciculation nea the inlet to the heated one (/d = 3.85) and almost at outlet fom it (/d = 139.0) fo the tube of d h =9.1 mm and two wall heat flux densities q w = 7.0 and 20.0 kw/m 2 ae shown in figues 6,a and 6,b. As it is seen fom figues 6,ab the fom of velocity pofiles noticeably changes along the heated one, the extent of velocity pofile defomation inceasing with the wall heat flux density incease. The velocity pofiles defomation is accompanied by the incease of velocity gadient in nea wall flow egion and the incease of the wall shea stess as a consequence. Moe ove as it follows fom fig.6,c whee the longitudinal change of absolute value of wall velocity gadient is pesented the velocity gadient incease takes place along the full length of heated tube. That is the evidence of the absence of velocity pofile stabiliation along the heated one. The wall velocity gadient incease is balanced out by the liquid viscosity decease with tempeatue in nea wall flow egion (see figue 6,d). So the esult longitudinal wall shea stess behaviou is a function of moe stong effect at cuent flow coss-section. Moe ove the esult effect depends not only on wall heat flux density but also on channel coss-section fom and hydaulic diamete. Calculated fiction factos as a function of adjusted length fo two tubes which diffes by inne diametes ae shown in figue 7,a. The heating conditions of egimes pesented in figue 7 ae chaacteied by close values of the Reynolds numbe. In the fist case (line 1 in figue 7,a) the Re numbe calculated accoding to physical popeties at local bulk liquid tempeatue fo q w = 15 kw/m 2 and d h = 5.4 mm changed fom 540 at the inlet to the heated section to 1070 at the outlet fom it. In the second case (line 3 in figue 7,a) the coesponding Re numbe vaied fo q w = 10 kw/m 2 and d h = 9.1 mm fom 720 at the inlet to 1040 at the outlet fom the heated one. 7

9 a) c) b) d) a) b) velocity pofiles at two coss sections of heated tube 9.1 mm inne diamete, calculated fo two wall heat flux densities at wate ciculation; c) longitudinal change of absolute value of wall velocity gadient coesponding to these egimes; d) change of liquid viscosity in nea wall egion due to wall tempeatue incease; a): q w = kw/m 2, 1 /d = 3.85, 2 /d = 139.0, b): q w = kw/m 2, 1 /d = 3.85, 2 /d = 139.0, c), d): 1 q w = kw/m 2, 2 q w = kw/m 2 Figue 6. Calculated longitudinal change of velocity pofiles, liquid viscosity and wall velocity gadient. One can clealy see fom figue 7,a the qualitatively diffeent ξ(χ) behaviou fo two diametes. The ξ values calculated accoding to fomula (2) ae also shown if figue 7,a (lines 2 and 4). It follows fom the compaison of cuves 1 4 that unde the conditions of exclusively buoyancy induced ciculation wall fiction changes along the heated one in a complex way and fiction facto distibution can not be descibed by a simple elationships of the fom ξ = a/re b. In most cases the effect of velocity pofiles defomation is pedominant as elated to the effect of viscosity change. The shape of velocity pofiles and the extent of thei defomation in its tun depend upon hydaulic diamete. The shape of velocity pofiles fo two tube diametes (5.4 mm and 9.1 mm) is shown in figue 7,b as an example. Though qualitatively the shape of both pofiles is M-like it is clealy seen fom figue 7,b that the defomation of the velocity pofiles becomes moe intensive with inne tube diamete incease. 8

10 5. Conclusions. With efeence to the expeimental data obtained fo laboatoy natual ciculation loop a 2D numeical simulation of velocity and tempeatue fields fo lamina low flow egimes have been caied out. I is shown that in natual ciculation loop whee fluid flow is govened exclusively by buoyancy foces wall shea stesses change along the heated one in a complex way and a) b) a) calculated fiction factos as a function of adjusted length; b) calculated velocity pofiles at the outlet fom the heated one (=1.28 m); 1 q w = 15 kw/m 2, d h = 5.4 mm, numeical simulation, 2 fomula (2) fo the egime 1 conditions;. 3 q w = 10 kw/m 2, d h = 9.1 mm, numeical simulation; 4 fomula (2) fo the egime 3 conditions; b): 5 q w =10 kw/m 2, d h = 9.1 mm; 6 qw = 15 kw/m 2, d h = 5.4 mm. Figue 7. Calculated fiction factos and velocity pofiles fo diffeent inne diametes of heated tubes. fiction facto fo use in 1D calculations can not be descibed by simple coelations in the fom of ξ = a/re b. The account of the tempeatue viscous change effect, which though is a substantial facto, does not impove pedicting accuacy. In most cases the effect of the velocity pofiles defomation, which acts oppositely to viscous decease with tempeatue, is pedominant. The fom of velocity pofiles and the extent of thei defomation in its tun depend upon the hydaulic diamete. To develop ecommendations fo 1D loop calculations at low flow egimes one needs to pefom paametic calculations with futhe genealiation. Acknowledgements The wok was suppoted by the Russian Foundation of Basic Reseach gant No a. Refeences [1] Zviin Y 1981 A eview of natual ciculation loops in pessuied wate eactos and othe systems Nuclea Engineeing and Design Vol. 67 pp [2] Kuma N, Nayak A K, Vijayan P K and Vae K K 2014 Modeling the flow chaacteistics duing stat-up of natual ciculation systems fom est state Reacto Engineeing Division Reseach Aticle ISSUE NO 336 JAN-FEB 2014 pp 1 11 [3] Kuma N, Doshi J B and Vijayan P K 2011 Investigations on the ole of mixed convection and wall fiction facto in single-phase natual ciculation loop dynamics Annals of Nuclea Enegy V. 38 pp [4] Mousavian S, Misale M, D Auia F and Salehi M A 2004 Tansient and stability analysis in single-phase natual ciculation Annals of Nuclea Enegy Vol. 31 pp [5] Misale M, Gaibaldi P, Passos J C and de Bitencout G G 2007 Expeiments in a single-phase natual ciculation mini-loop Expeimental Themal and Fluid Science Vol. 31 pp

11 [6] Kaban kov O N, Zubov N O, Sukomel L A and Yagov V V 2015 Study of flow and heat tansfe chaacteistics unde boiling conditions in natual ciculation loop Poblems in Gasodynamics and Heat and Mass Tansfe in Powe Plants. Poc. of XX Schoolsemina of young scientists and specialists unde acdemician A I Leontiev leadeship (24 29 May 2015 Zvenigood) (Moscow: MPEI Publishing House) 496 p [7] Kaban kov O N, Sukomel L A, Yagov V V and Zubov N O 2016 Unstable ciculation egimes duing wate boiling in a themosyphon loop unde atmospheic pessue Heat Pipe Science and Technology, An Int. Jounal (Begel House) Volume 7 Issue 1-2 pp [8] Yagov V V 2014 Heat Tansfe in Single Phase Media and at Phase Changes (Moscow, MPEI Publishing House) p 542 [9] Petuhov B S, Genin L G, Kovalev S A and Soloviev C L 2003 Heat Tansfe in Nuclea Powe Plants (Moscow: MPEI Publishing House) p 548 [10] Petukhov B S 1987 Selected Woks Heat Tansfe Poblems (Moscow: Publishing Nauka ) p 278 [11] Gebhat B, Jaluia Y, Mahajan R L and Sammakia B 1991 Buoyancy-induced Flows and Tanspot (Moscow: Mi Publishing House Tanslated to Russian) In 2 volumes [12] Atemov V I and Yankov G G 2010 Numeical analysis of opeating efficiency of sectional aiconditione with ai heat exchange Bulletin of Moscow Powe Engineeing Institute (Moscow: MPEI Publishing Depatment) No 6 pp