Environmental Fluid Mechanics

, Volume 10, Issue 4, pp 415–450 | Cite as

Advanced integral model for groups of interacting round turbulent buoyant jets

  • Panayotis C. Yannopoulos
Original Article


An integral model that combines all advantages of Superposition Method (SM), Entrainment Restriction Approach (ERA) and Second Order Approach (SOA) is proposed to predict the mean axial velocity and concentration fields of a group of N interacting vertical round turbulent buoyant jets. SM is successful in predicting the fields of mean axial velocity and mean concentration for a group of N interacting jets or plumes and ERA is advantageous in predicting the above fields for either two or large number (N → ∞) of interacting buoyant jets in the whole range of buoyancy. SOA takes into consideration in a dynamic way the turbulent contribution to the momentum and buoyancy fluxes and provides better accuracy than the usual procedures. A novelty of the proposed model is the production and utilisation of advanced profile distributions, convenient for the mean axial velocities and concentrations in a cross-section of the entire group of buoyant jets. These profiles are developed on the basis of flux conservation of momentum, buoyancy and kinetic energy for the mean motion. They enhance dynamic adaptation of the individual buoyant jet axes to the group centreline. Due to these profile distributions, the present model owns generality of application and better accuracy of predictions compared to usual integral models using simple Gaussian or top-hat profiles; thus it conferred the name Advanced Integral Model (AIM). AIM is herein applied to predict the mean flow properties of two different arrangement types of any number of buoyant jets: (a) linear diffusers and (b) rosette-type risers. Present results are compared to available experimental data and traditional solutions based on Gaussian profiles. Findings may be useful for design purposes and environmental impact assessment.


Multiple buoyant jets Buoyant jet merging Integral models Mean flow properties Multiport diffuser Rosette-type riser Sea outfall 


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  1. 1.
    Albertson ML, Dai YB, Jensen RA, Rouse H (1950) Diffusion of submerged jets. Trans ASCE 115: 639–664Google Scholar
  2. 2.
    Bloutsos AA, Yannopoulos PC (2005) Three round turbulent buoyant jets discharged vertically from a rosette. IASME Trans 3: 413–421Google Scholar
  3. 3.
    Bloutsos AA, Yannopoulos PC (2007) Application of a general form of the local Richardson number to interacting round buoyant jets. In: Proceedings of 32nd congress of IAHR, July 1–6 2007, Venice, Italy, vol 2, p 574 (CDROM, 9 pp)Google Scholar
  4. 4.
    Bloutsos AA, Yannopoulos PC (2009) Round turbulent buoyant jets discharged vertically upwards forming a regular polygon. J Hydraul Res 47(2): 263–274. doi: 10.3826/jhr.2009.3298 Google Scholar
  5. 5.
    Cheung SK, Leung DY, Wang W, Lee JH, Cheung V (2000) VISJET—a computer ocean outfall modeling system. IEEE 75–80Google Scholar
  6. 6.
    Hodgson JE, Moawad AK, Rajaratnam N (1999) Concentration field of multiple circular turbulent jets. J Hydraul Res 37: 249–256CrossRefGoogle Scholar
  7. 7.
    Jirka GH (2004) Integral model for turbulent buoyant jets in unbounded stratified flows—Part I: single round jet. Environ Fluid Mech 4: 1–56CrossRefGoogle Scholar
  8. 8.
    Jirka GH (2006) Integral model for turbulent buoyant jets in unbounded stratified flows. Part II: plane jet dynamics resulting from multiport diffuser jets. Environ Fluid Mech 6: 43–100CrossRefGoogle Scholar
  9. 9.
    Jirka GH, Doneker RL, Hinton SW (1996) Users manual for CORMIX: a hydrodynamic mixing zone model and decision support system for pollutant discharges into surface waters. Tech. Rep., DeFrees Hydraulics Laboratory, Cornell University, Ithaca, New YorkGoogle Scholar
  10. 10.
    Kaye NB, Linden PF (2004) Coalescing axisymmetric turbulent plumes. J Fluid Mech 502: 41–63CrossRefGoogle Scholar
  11. 11.
    Lee JH, Cheung V (1990) Generalized Langrangian model for buoyant jets in current. J Environ Eng ASCE 116: 1085–1106CrossRefGoogle Scholar
  12. 12.
    Lee JH, Cheung V, Wang W, Cheung SK (2000) Langrangian modeling and visualization of rosette outfall plumes. In: Proceedings of 4th conference on hydroinformatics (CDROM), July 23–27, University of Iowa, Iowa, 8 ppGoogle Scholar
  13. 13.
    Noutsopoulos G, Yannopoulos P (1987) The round vertical turbulent buoyant jet. J Hydraul Res 25: 481–502CrossRefGoogle Scholar
  14. 14.
    Papanicolaou PN, Papakonstantis IG, Christodoulou GC (2008) On the entrainment coefficient in negatively buoyant jets. J Fluid Mech 614: 447–470CrossRefGoogle Scholar
  15. 15.
    Papps DA, Wood IR (1997) The effect of an intermittant flapping motion on the properties of merging plumes. J Hydraul Res 35: 455–472CrossRefGoogle Scholar
  16. 16.
    Roberts PJ, Snyder WH (1993) Hydraulic model study for Boston outfall. II: environmental performance. J Hydraul Eng ASCE 119: 988–1002CrossRefGoogle Scholar
  17. 17.
    Rouse H, Yih CS, Humphreys HW (1952) Gravitational convection from a boundary source. Tellus 4: 201–210CrossRefGoogle Scholar
  18. 18.
    Tang HS, Paik J, Sotiropoulos F, Khangaonkar T (2008) Three-dimensional numerical modelling of initial mixing of thermal discharges at real-life configurations. J Hydraul Eng ASCE 134: 1210–1224CrossRefGoogle Scholar
  19. 19.
    Tian X, Roberts PJ, Daviero GJ (2004) Marine wastewater discharges from multiport diffusers. I: unstratified stationary water. J Hydraul Eng ASCE 130: 1137–1146CrossRefGoogle Scholar
  20. 20.
    Turner JS (1972) On the energy deficiency in self-preserving convective flows. J Fluid Mech 53: 217–226CrossRefGoogle Scholar
  21. 21.
    Wang H, Law AW-K (2002) Second-order integral model for a round turbulent buoyant jet. J Fluid Mech 459: 397–428Google Scholar
  22. 22.
    Wood IR, Bell RG, Wilkinson DL (1993) Ocean disposal of wastewater. World Scientific, SingaporeCrossRefGoogle Scholar
  23. 23.
    Yannopoulos PC (1984) Interaction of vertical round turbulent buoyant jets. PhD dissertation, Department of Civil Engineering, National Technical University of Athens, Athens, Greece, 457 pp (in Greek)Google Scholar
  24. 24.
    Yannopoulos PC (1996) Superposition model for multiple plumes and jets predicting end effects. J Geophys Res 101: 15153–15176CrossRefGoogle Scholar
  25. 25.
    Yannopoulos PC (2006) An improved integral model for plane and round turbulent buoyant jets. J Fluid Mech 547: 267–296CrossRefGoogle Scholar
  26. 26.
    Yannopoulos PC (2006) Attachment of two or three interacting round buoyant jets discharged vertically upwards into a quiescent environment. WSEAS Trans Fluid Mech 3: 215–220Google Scholar
  27. 27.
    Yannopoulos PC, Bekri HS (2003) A modified virtual image source technique for multiple plume discharges into a flowing ambient. In: Proceedings of XXX IAHR congress on water engineering and research in a Learning Society: modern developments and traditional concepts (Ganoulis J, Prinos, P, eds), Inland waters: research, engineering and management Theme C (Theme Nezu, I, Kotsovinos, N, eds). Aristotle University of Thessaloniki, Greece, vol I, pp 271–277Google Scholar
  28. 28.
    Yannopoulos PC, Noutsopoulos GC (2006) Interaction of vertical round turbulent buoyant jets. Part I: entrainment restriction approach. J Hydraul Res 44: 218–232CrossRefGoogle Scholar
  29. 29.
    Yannopoulos PC, Noutsopoulos GC (2006) Interaction of vertical round turbulent buoyant jets. Part II: superposition method. J Hydraul Res 44: 233–248CrossRefGoogle Scholar
  30. 30.
    Yannopoulos PC, Noutsopoulos GC (2008) Closure to the discussion by BS Pani on “Interaction of vertical round turbulent buoyant jets. Part II: superposition method”. J Hydraul Res 44(2):233–248. J Hydraul Res 46: 563–567Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Environmental Engineering Laboratory, Department of Civil EngineeringUniversity of PatrasPatrasGreece

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