SIMULATION OF AIR HEAT TRANSFER IN CIRCULAR PIPES WITH TRIANGULAR AND SQUARE TURBULENCE STIMULATORS FOR HIGH REYNOLDS CRITERIA UP TO ONE MILLION

Objective. Conduct mathematical modeling of tornado zone structure systems between cyclic flow turbulence stimulators with the surface arrangement of triangular and square cross-sections based on multiblock computational techniques, based on solutions of the factorialized finite- volume procedure of the Reynolds equations (closed through the Menter shear stress transport model) and energy equations (on a multiscale  intersecting structured grid) at high Reynolds criteria Re=106 with an  exhaustive analysis of the relevant current lines.

Methods. The calculations were carried out on a mathematical foundation based on the solution of the factorized finite-volume procedure of the Reynolds equations, which are closed using the low-Reynolds Menter shear stress transport model, and the energy equations on a multiscale  intersecting structured grid (factorized finite-volume procedure).

Results. Mathematical simulations of the heat exchange process in straight
and round horizontal pipes with turbulence stimulators with d/D=0.95...0.90 and t/D=0.25...1.00 of triangular and square transverse profiles with large Reynolds numbers (Re=106) on a foundation with multiblock computing technologies, which are based on solutions of factorized and finite-volume Reynolds equations and energy equations, were conducted. It was found that the relative intensification of heat transfer [(Nu/NuGL)|Re=106]/[(Nu/NuGL)|Re=105] in round pipes with square air turbulence stimulators for large Reynolds numbers (Re=106), which may be relevant in the channels used in heat exchangers, could be higher with a large-scale increment of hydraulic resistance than for slightly smaller numbers (Re=105), for relatively high flow turbulence stimulators d/D=0.90 for the entire range under consideration for the parameter of the relative step between them t/D=0.25...1.00 a little more than 3%; for triangular turbulence stimulators, the crosssection profiles have similar  values. For lower square turbulence stimulators with d/D=0.95, this increase  in relative heat transfer for large Reynolds numbers (Re=106) compared to smaller numbers (Re=105) does not exceed 6%; for triangular cross-section turbulence stimulators, similar indicators are slightly more  than 4%. 

Conclusion. The calculated results based on the developed model can optimize the intensification by turbulence stimulators and control the processes of heat transfer intensification. It is shown that for higher square  turbulence stimulators and higher Reynolds numbers, a limited increase in  the relative Nusselt criterion Nu/NuGL is accompanied by a significant increase in the relative hydro resistance due to the very significant influence  of return currents, which can flow directly on the turbulence stimulator to  the greater extent, the higher the Reynolds number; for triangular  turbulence stimulators, the above trend persists and even deepens.

1. Dreytser G.A., Isayev S.A., Lobanov I.Ye. Raschet konvektivnogo teploobmena v trube s periodicheskimi vystupami // Problemy gazodinamiki i teplomassoobmena v energeticheskikh ustanovkakh: Trudy XIV Shkoly-seminara molodykh uchenykh i spetsialistov pod rukovodstvom akademika RAN A.I.Leont'yeva. M.: MEI, 2003. T.1. S. 57—60. [Dreitser G.A., Isaev S.A., Lobanov I.E. Calculation of convective heat transfer in a pipe with periodic protrusions // Problems of gas dynamics and heat and mass transfer in power plants: proceedings of the XIV of the School-seminar of young scientists and specialists under the leadership of academician A. I. Leontiev. M.: MPEI, 2003 V. 1. рр 57–60.(In Russ)]

2. Dreytser G.A., Isayev S.A., Lobanov I.Ye. Raschet konvektivnogo teploobmena v trube s periodicheskimi vystupami // Vestnik MAI. 2004. T. 11. № 2. S. 28—35. [Dreitser G.A., Isaev S.A., Lobanov I.E. Calculation of convective heat transfer in a pipe with periodic protrusions // Vestnik MAI. – 2004. V. 11. № 2. рр. 28–35.(In Russ)]

3. Dreytser G.A., Isayev S.A., Lobanov I.Ye. Raschet konvektivnogo teploobmena v trube s periodicheski raspolozhennymi poverkhnostnymi turbulizatorami potoka // Teplofizika vysokikh temperatur. 2005. T. 43. № 2. S. 223230. [ Dreitzer G.A., Isaev S.A., Lobanov I.E. Calculation of convective heat transfer in a pipe with periodically located surface flow turbulators // Thermophysics of high temperatures. 2005. V. 43. № 2. рр. 223–230.(In Russ)]

4. Lobanov I.Ye. Matematicheskoye modelirovaniye intensifitsirovannogo teploobmena pri turbulentnom techenii v kanalakh: Diss. na soisk. uchenoy stepeni dokt. tekhn. nauk. M., 2005. 632 s [ Lobanov I.E. Mathematical modeling of intensified heat transfer under turbulent flow in channels: Diss. on the screen. Doctor of Science degree. tech. sc. M., 2005. 632 p. (In Russ)]

5. Kalinin E.K., Dreytser G.A., Yarkho S.A. Intensifikatsiya teploobmena v kanalakh. M.: Mashinostroyeniye, 1990. 208 s. [Kalinin E.K., Dreitzer G.A., Yarkho S.A. Intensification of heat transfer in channels. M.: Mashinostroenie, 1990. 208 p. (In Russ)]

6. Effektivnyye poverkhnosti teploobmena / E.K.Kalinin, G.A.Dreytser, I.Z. Kopp i dr. M.: Energoatomizdat, 1998. 408 s. [Effective heat transfer surfaces / E.K.Kalinin, G.A.Dreitzer, I.Z.Kopp et al. M.: Energoatomizdat, 1998. 408 p. (In Russ)]

7. Lobanov I.Ye., Shteyn L.M. Perspektivnyye teploobmennyye apparaty s intensifitsirovannym teploobmenom dlya metallurgicheskogo proizvodstva. (Obshchaya teoriya intensifitsirovannogo teploobmena dlya teploobmennykh apparatov, primenyayemykh v sovremennom metallurgicheskom proizvodstve.) V 4-kh tomakh. Tom I. Matematicheskoye modelirovaniye intensifitsirovannogo teploobmena pri turbulentnom techenii v kanalakh s primeneniyem osnovnykh analiticheskikh i chislennykh metodov. M.: Izdatel'stvo Assotsiatsii stroitel'nykh vuzov, 2009. 405 s. [ Lobanov I.E., Stein L.M. Perspective heat exchangers with intensified heat exchange for metallurgical production. (General theory of intensified heat transfer for heat exchangers used in modern metallurgical production.) In 4 volumes. Volume I. Mathematical modeling of intensified heat transfer in turbulent flow in channels with the use of basic analytical and numerical methods. M.: Publishing House of the Association of Construction Universities, 2009. 405 p. (In Russ)]

8. Lobanov I.Ye., Shteyn L.M. Perspektivnyye teploobmennyye apparaty s intensifitsirovannym teploobmenom dlya metallurgicheskogo proizvodstva. (Obshchaya teoriya intensifitsirovannogo teploobmena dlya teploobmennykh apparatov, primenyayemykh v sovremennom metallurgicheskom proizvodstve.) V 4-kh tomakh. Tom II. Matematicheskoye modelirovaniye intensifitsirovannogo teploobmena pri turbulentnom techenii v kanalakh s primeneniyem neosnovnykh analiticheskikh i chislennykh metodov. M.: Izdatel'stvo Assotsiatsii stroitel'nykh vuzov, 2010. 290 s. [Lobanov I.E., Stein L.M. Perspective heat exchangers with intensified heat exchange for metallurgical production. (General theory of intensified heat transfer for heat exchangers used in modern metallurgical production.) In 4 volumes. Volume II. Mathematical modeling of intensified heat transfer in turbulent flow in channels using non-basic analytical and numerical methods. M.: Publishing House of the Association of Construction Universities, 2010. 290 p. (In Russ)]

9. Lobanov I.Ye., Shteyn L.M. Perspektivnyye teploobmennyye apparaty s intensifitsirovannym teploobmenom dlya metallurgicheskogo proizvodstva. (Obshchaya teoriya intensifitsirovannogo teploobmena dlya teploobmennykh apparatov, primenyayemykh v sovremennom metallurgicheskom proizvodstve.) V 4-kh tomakh. Tom III. Matematicheskoye modelirovaniye intensifitsirovannogo teploobmena pri turbulentnom techenii v kanalakh s primeneniyem mnogosloynykh, supermnogosloynykh i kompaundnykh modeley turbulentnogo pogranichnogo sloya. M.: MGAKKhiS, 2010. 296 s. [Lobanov I. E., Stein L. M. Perspective heat exchangers with intensified heat exchange for metallurgical production. (General theory of intensified heat transfer for heat exchangers used in modern metallurgical production.) In 4 volumes. Volume III. Mathematical modeling of intensified heat transfer in turbulent flow in channels with the use of multilayer, super-multilayer and compound models of a turbulent boundary layer. M.: MGAKHiS, 2010. 296 p. (In Russ)]

10. Chislennoye modelirovaniye vikhrevoy intensifikatsii teploobmena v paketakh trub / YU.A.Bystrov, S.A.Isayev, H.A.Kudryavtsev, A.I.Leont'yev. SPb: Sudostroyeniye, 2005. 398 s. [Numerical simulation of vortex heat transfer intensification in pipe packages / Yu.A.Bystrov, S.A.Isaev, N.A.Kudryavtsev, A.I.Leontiev. St. Petersburg: Sudostroenie, 2005. 398 p. (In Russ)]

11. Ashrafian A., Andersson H.I. Roughness Effects in Turbulent Channel Flow // Turbulence, Heat Transfer and Mass Transfer 4. New York, Wellington (UK): Begell House Inc., 2003. рр. 425–432.

12. Lobanov I.Ye. Teoreticheskoye issledovaniye struktury vikhrevykh zon mezhdu periodicheskimi, poverkhnostno raspolozhennymi turbulizatorami potoka pryamougol'nogo poperechnogo secheniya // Izvestiya vuzov. Aviatsionnaya tekhnika. 2011. № 4. S. 64—66. [Lobanov I.E. Theoretical study of the structure of vortex zones between periodic, surface-located flow turbulators of rectangular cross-section // Izvestiya vuzov. Aviation equipment. 2011. № 4. рр. 64–66. (In Russ)]

13. Lobanov I.Ye. Modelirovaniye struktury vikhrevykh zon mezhdu periodicheskimi poverkhnostno raspolozhennymi turbulizatorami potoka pryamougol'nogo poperechnogo secheniya // Matematicheskoye modelirovaniye. 2012. T. 24. № 7. S. 45—58. [Lobanov I.E. Modeling of the structure of vortex zones between periodic surface-located flow turbulators of rectangular cross-section // Mathematical modeling. 2012. V. 24. № 7. рр. 45–58. (In Russ)]

14. Lobanov I.Ye. Matematicheskoye modelirovaniye teploobmena v trubakh s turbulizatorami, a takzhe v sheroxovatykh trubakh, na vozdukhe pri bol'shikh chislakh Reynol'dsa // Otraslevyye aspekty tekhnicheskikh nauk. 2013. № 9. S. 8—18. [Lobanov I.E. Mathematical modeling of heat transfer in pipes with turbulators, as well as in rough pipes, in the air at large Reynolds numbers // Branch aspects of technical sciences. 2013. № 9. рр. 8–18. (In Russ)]

15. Lobanov I.Ye. Matematicheskoye modelirovaniye teploobmena i potoka v kruglykh trubakh s otnositel'no vysokimi vystupami polukruglogo poperechnogo secheniya pri techenii vozdukha pri bol'shikh chislakh Reynol'dsa // Elektronnyy periodicheskiy retsenziruyemyy nauchnyy zhurnal "SCI-ARTICLE.RU". 2019. № 71 (iyul'). S. 63—76. [Lobanov I.E. Mathematical modeling of heat transfer and flow in round pipes with relatively high projections of semicircular cross-section during air flow at large Reynolds numbers // Electronic periodic peer-reviewed scientific journal "SCI-ARTICLE.RU". 2019. № 71 (July). P. 63–76. (In Russ)]

16. Lobanov I.Ye. Matematicheskoye modelirovaniye teploobmena v trubakh s turbulizatorami, a takzhe v sheroxovatykh trubakh, na vozdukhe pri bol'shikh chislakh Reynol'dsa // Otraslevyye aspekty tekhnicheskikh nauk. 2013. № 9. S. 818. [Lobanov I.E. Mathematical modeling of heat transfer in pipes with turbulators, as well as in rough pipes, in the air at large Reynolds numbers // Branch aspects of technical sciences. 2013. № 9. рр. 8–18. (In Russ)]

17. Lobanov I.Ye. Teoreticheskoye matematicheskoye modelirovaniye techeniya i teploobmena v pryamykh kruglykh trubakh s turbulizatorami polukruglogo poperechnogo secheniya, a takzhe v sherokhovatykh trubakh, na vozdukhe pri bol'shikh chislakh Peynol'dsa // Veb-portal professional'nogo setevogo pedagogicheskogo soobshchestva "Ped-library.ru". 2019. [Lobanov I.E. Theoretical mathematical modeling of flow and heat transfer in a straight circular tubes with turbulators semi-circular cross section, as well as in rough tubes, in air at high Reynolds numbers // the Web portal of professional networking in the education community "Ped-library.ru". 2019. Access mode: https://pedlibrary.ru/1548529792. (In Russ)]

18. Lobanov I.Ye. Matematicheskoye nizkoreynol'dsovoye modelirovaniye teploobmena v trubakh s turbulizatorami na vozdukhe pri bol'shikh chislakh Reynol'dsa // Innovatsionnyye podkhody v otraslyakh i sferakh. 2019. Tom № 4. Bypusk № 2 (fevral', 2019). Rezhim dostupa: http://inf16.ru/vypusk-2-fevral-2019. [Lobanov I.E. Mathematical low-Reynolds simulation of heat transfer in pipes with turbulators in the air at large Reynolds numbers // Innovative approaches in industries and spheres. 2019 .V. 4. Issue № 2 (February, 2019). Access mode: http://inf16.ru/vypusk-2-fevral-2019. (In Russ)]

19. Lobanov I.Ye. Teoriya teploobmena v trubakh s turbulizatorami pri d/D=0,95÷0,90 i t/D=0,25÷1,00, a takzhe v sherokhovatykh trubakh, na vozdukhe pri bol'shikh chislakh Reynol'dsa Re=1000000 // Veb-portal professional'nogo setevogo pedagogicheskogo soobshchestva "Pedlibrary.ru". 2019. [Lobanov I.E. the Theory of heat transfer in tubes with turbulators at d/D=0,95÷0.90 and t/D=0.25÷1,00, as well as in rough tubes, in air at high Reynolds numbers Re=1000000 // Web portal network professional pedagogical community "Ped-library.ru".2019. Access mode: https://ped-library.ru/1561232054. (In Russ)]

20. Menyalkina Ye.N. Issledovaniye vliyaniya formy orebreniya na dinamiku potoka i soprotivleniye kanala // Al'manakh sovremennoy nauki i obrazovaniya. 2017. № 4–5 (118). S. 65—68. [Menyalkina E.N. A study of the influence of the shape of the fins on the dynamics of the stream and the channel resistance // Almanac of modern science and education. 2017. № 4–5 (118). рр. 65–68. (In Russ)]

21. Manca O., Nardini S., Ricci D. Numerical Analysis of Water Forced Convection in Channels with Differently Shaped Transverse Ribs // Journal of Applied Mathematics. 2011. DOI: 10.1155/2011/323485.

22. Tong-Miin Liou, Hwang J.J., Chen S.H. Simulation and measurement of enhanced turbulent heat transfer in a channel with periodic ribs on one principal wall // International Journal of Heat and Mass Transfer. 1993. № 36(2). рр. 507–517. DOI: 10.1016/0017-9310(93)80025-P.

23. Ricci D., Manca O., Manca S., Nardini S. Two-Dimensional Numerical Investigation on Forced Convection in Channels With Transversal Ribs // Conference: ASME 2009 International Mechanical Engineering Congress and Exposition, IMECE2009. 2009. DOI: 10.1115/IMECE2009-11203.

24. Chaube A., Sahu P.K., Solanki S.C., Sharma P.B. Effect of Artificial Roughness on Convective Heat Transfer // 40th Thermophysics Conference. 2008. DOI: 10.2514/6.2008-3810.

25. Ahn S,W., Son K.P. An investigation on friction factors and heat transfer coefficients in a rectangular duct with surface roughness // KSME International Journal. 2002. № 16(4). рр. 549–556.

26. Kant K., Qayoum A. Numerical investigations of fluid flow and heat transfer in a ribbed duct is heated with variable aspect ratios // Recent Trends in Fluid Mechanics. 2016. V. 3. Issue 1. рр. 23–37.

27. Kim J.-H., HeoSung-Hoo J.-N., Jeeyoung S. Numerical analysis on heat transfer and pressure drop characteristics in a horizontal channel with various ribs // DOI: 10.5916/ jkosme.2013.37.1.40.

28. Smith E., Wayo C. Analysis of turbulent heat transfer and fluid flow in channels with various ribbed internal surfaces // Journal of Thermal Science. 2011. № 20(3). рр. 260–267. DOI: 10.1007/s11630-011-0468-3.

29. Naveen S., Andallib T., Manish M. Experimental Investigation of Heat Transfer Enhancement in Rectangular Duct with Pentagonal Ribs // Heat Transfer Engineering. 2017. DOI: 10.1080/01457632.2017.1421135.

30. Lobanov I.Ye. Matematicheskoye modelirovaniye teploobmena v trubakh s kvadratnymi turbulizatorami pri d/D=0,95÷0,90 i t/D=0,25÷1,00 na vozdukhe pri bol'shikh chislakh Reynol'dsa Re=1000000 // Veb-portal professional'nogo setevogo pedagogicheskogo soobshchestva "Pedlibrary.ru". 2019. [Lobanov I.E. Mathematical modeling of heat transfer in pipes with square turbulators at d/D=0.95÷0.90 and t/D=0.25÷1.00 in air at large Reynolds numbers Re=1000000 // Web-portal of the professional network pedagogical community "Ped-library.ru". 2019. Access mode: https://ped-library.ru/1572707532. (In Russ)]