Korsun A.S., Pisarevsky M.I., Pisarevskaya Yu.N., Fedoseev V.N.
National Research Nuclear University “MEPhI”, Moscow, Russia
There is roughness in the heat exchange equipment of power plants. Artificial roughness is used to intensify heat
transfer, natural roughness is formed during the operation of heat exchange
equipment. The article presents a model for the description of the mechanical
interaction of a turbulent flow with a rough wall. The model is based on the
most well-established experimentally confirmed facts. A new parameter has been
introduced, the roughness shape factor Fr, which physically
determines the speed level in the zone of the boundary with a rough wall. The
numerical value of the shape factor depends on the shape and geometry of the
roughness projections. The hydraulic characteristic of a channel with arbitrary
roughness depends not only on the number of Re and the relative height of the
protrusions Δ/d, but also on the value of the shape factor Fr. Using
the model, a equation for calculating the coefficient of hydraulic resistance
of pipes with sand roughness on the wall in all areas of the turbulent flow of
the coolant is obtained. For a wide range of relative heights of projections,
the difference from the experimental data of I. Nikuradze does not exceed 5 %. A
recommendation has been developed for calculating, in the first approximation,
the coefficient of hydraulic resistance of pipes with natural roughness. The
analysis of the existing calculation formulas for channels with artificial
roughness was carried out, which showed the need for additional research.
1. Kirillov P.L., Bobkov V.P., Zhukov A.V., Yuryev Y.S. Spravochnik
po teplogidravlicheskim raschetam v yadernoy energetike [Handbook of thermohydraulic
calculations in nuclear power engineering]. Moscow, IzdAT Publ., 2010.
Vol. 1, 771 p.
2. Idelchik I.E. Spravochnik po gidravlicheskim
soprotivleniyam [Handbook of hydraulic resistances]. Moscow,
Mashinostroyeniye Publ., 1992. 672 p.
3. Ibragimov M.H., Subbotin V.I., Bobkov V.P., Taranov G.S.,
Abelev G.I. Struktura turbulentnogo potoka i mekhanizm teploobmena v kanalakh
[Structure of turbulent flow and mechanism of heat exchange in channels]. Moscow,
Atomizdat, 1978, 294 p.
4. Millionshchikov M.D., Subbotin V.I., Ibragimov
M.H., et al. Issledovaniye poley skorosti i koeffitsiyentov gidravlicheskogo
soprotivleniya v trubakh s iskusstvennoy sherokhovatost'yu stenok
[Investigation of velocity fields and hydraulic resistance coefficients in
pipes with artificial roughness of the walls]. Preprint FEI-385 – Preprint IPPE-385,
1973, 64 p.
5. Millionshchikov
M.D., Subbotin V.I., Ibragimov M.H., et al. Profili skorosti v gladkikh i
sherokhovatykh trubakh [Velocity profiles in smooth and rough pipes]. Preprint
FEI-417 – Preprint IPPE-417, 1973. 37 p.
6. Olympiev V.V. Teplogidravlicheskiy raschet
obtekaniya sherokhovatykh tvelov, effektivnost' ikh primeneniya v reaktore
VVER-1000 [Thermohydraulic calculation of the flow of rough fuel rods, the
effectiveness of their use in the WWER-1000 reactor]. Teploenergetika –
Thermal Engineering, 1992, no. 3, pp. 48–51.
7. Olympiev V.V. Effektivnost' intensifikatsii
teploobmena posredstvom sherokhovatosti tvelov v reaktore VVER-1000 [Efficiency
of heat transfer intensification by means of fuel element roughness in the WWER-1000
reactor]. Teploenergetika – Thermal Engineering, 1993, no. 3, pp. 56–58.
8. Dalle Donne M., Mayer L. Turbulent convective heat
transfer from rough surface with two-dimensional rectangular ribs. Int.
J. Heat Mass Transfer, 1977, vol. 20, no. 6, pp. 583–620.
DOI: 10.1016/0017-9310(77)90047-3.
9. Leontiev A.I., Olympiev V.V. The effect of
intensifiers of heat transfer on the thermohydraulic
properties of channels. High Temperature, 2007, vol. 45, no. 6, pp. 844–870.
Available at: https://link.springer.com/article/10.1134/S0018151X07060168
(accessed 13.04.2022).
10. Popov I.A., Gortyshev Yu.F., Olympiev V.V. Promyshlennoye
primeneniye intensifikatorov teploobmena – sovremennoye sostoyaniye problem
[Industrial application of heat transfer intensifiers – the current state of
the problem]. Teploenergetika – Thermal Engineering, 2012, no. 1, pp. 3–14.
11. Iry S., Rafee R. Hydrothermal analysis of conventional and baffled
geothermal heat exchangers in transient mode. J. Thermal Analysis and
Calorimetry, 2021, vol. 143, issue 3, pp. 2149–2161. DOI:
10.1007/s10973-020-09582-2.
12. Oh K., Lee S., Park S., Han S., Choi H. Field experiment on heat
exchange performance of various coaxial type ground heat exchangers considering
construction conditions. Renewable Energy, 2019, vol. 144, pp. 84–96.
DOI: 10.1016/j.renene.2018.10.078.
13. Wang X., Wang R., Wu J. Experimental investigation of a new-style
double-tube heat exchanger for heating crude oil using solar hot water. Applied
Thermal Engineering, 2005, vol. 25, pp. 1753–1763. DOI:
10.1016/j.applthermaleng.2004.11.006.
14. Schlichting G. Teoriya
pogranichnogo sloya [Theory of the boundary layer]. Moscow, Nauka Publ., 1965. 711 p.
15. Nikuradse J. Gesetzmassigkeiten der Turbulenten Stromung in Glatten
Rohren. VDI-Forschungsheft, 1932, no. 356, pp. 1–36.
16. Nikuradze I. Zakonomernosti turbulentnogo dvizheniya v gladkikh
trubakh [Regularities of turbulent motion in smooth pipes]. M-L.:
ONTI NKTP Publ., 1936. pp. 75–150.
17. Nikuradse I. Stromungsges etze in rauhen Rohren. Forschungs-Heft,
1933, vol. 361, pp. 1–22.
18. Prandtl L. Rezul'taty rabot poslednego vremeni po izucheniyu turbulentnosti. Problemy turbulentnosti [The results of recent work on the
study of turbulence. Problems of turbulence]. Moscow-Leningrad, ONTI NKTP Publ., 1936. Pp. 9–35.
19. Altshul A.D. Gidravlicheskiye soprotivleniya [Hydraulic resistances]. Moscow, Nedra Publ., 1982. 224 p.
20. Landau L.D., Lifshits E.M. Teoreticheskaya fizika. T. 6. Gidrodinamika [Theoretical physics. Vol. 6. Hydrodynamics].
Moscow, Nauka Publ., 1986, 736 p.
21. Vysotsky L.I. O konstante Karmana. Chast' I [Karman’s Constant. Part I]. Izvestiya vuzov. Stroitelstvo – News of higher educational institutions. Construction, 2015, no. 6, pp.
81–89.
22. Vysotsky L.I. O konstante Karmana. Chast' II [Karman’s Constant. Part II]. Izvestiya vuzov. Stroitelstvo – News of higher educational institutions. Construction, 2015, no. 7, pp.
94–101.
23. Bailey S.C., Vallikivi M., Hultmark M., Smits A.J. Estimating the value of von Karman's constant in turbulent pipe flow. J. Fluid Mech., 2014, vol. 749, pp. 79–98.
DOI: 10.1017/jfm.2014.208.
24. McKeon B.J., Zagarola M.V., Smits A.J. A new friction factor relationship for fully developed pipe flow. J. Fluid Mech., 2005, vol. 538, pp. 429–443.
DOI: 10.1017/S0022112005005501.
25. Korsun A.S., Pisarevsky M.I., Fedoseev V.N., Kreps M.V. Velocity distribution in a turbulent flow near a rough wall. J. of Physics: Conf. Series, 2017, vol. 891, pp. 1–11.
DOI: 10.1088/1742-6596/891/1/012065.
26. Kader B.A. Teplo- i massoperenos ot stenok, pokrytykh dvumernoy sherokhovatost'yu, pri bol'shikh chislakh Reyonol'dsa i Pekle. Teoreticheskiye osnovy khimicheskikh tekhnologiy [Heat and mass transfer from walls covered with two-dimensional
roughness at high Reynolds and Pekle numbers]. Theoretical Foundations of Chemical Technologies, 1979, vol. 13, no. 5, pp. 663–675.
27. Kader B.A. Hydraulic resistance of surfaces covered with two-dimensional roughness at large Reynolds numbers. Teoreticheskiye osnovy khimicheskikh tekhnologiy – Theoretical
Foundations of Chemical Technologies, 1977, vol. 11, no. 3, pp. 393–404.
28. Petukhov B.S., Genin L.G., Kovalev S.A. Teploobmen v yadernykh energeticheskikh ustanovkakh [Heat transfer in nuclear power plants]. Moscow,
Energoatomizdat Publ., 1986. 470 p.
29. Zhukauskas A.A. Konvektivnyy perenos v teploobmennikakh [Convective transfer in heat exchangers]. Moscow: Nauka, 1982. 472 p.
30. Vilemas Yu., Shimonis V., Adomaitis I.-E. Intensifikatsiya teploobmena v gazookhlazhdayemykh kanalakh [Intensification of heat transfer in gas-cooled channels]. Vilnius, Mokslas Publ., 1989. 256 p.
31. Colebrook C.F., White C.M. Experiment with Fluid Friction in Roughened Pipes. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1937, vol. 161, issue
906, pp. 367–381.