Skip to main content
SpringerLink
Log in

Advanced integral model for groups of interacting round turbulent buoyant jets

  • Original Article
  • Published:
Environmental Fluid Mechanics Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Albertson ML, Dai YB, Jensen RA, Rouse H (1950) Diffusion of submerged jets. Trans ASCE 115: 639–664

    Google Scholar 

  2. Bloutsos AA, Yannopoulos PC (2005) Three round turbulent buoyant jets discharged vertically from a rosette. IASME Trans 3: 413–421

    Google Scholar 

  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)

  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. Cheung SK, Leung DY, Wang W, Lee JH, Cheung V (2000) VISJET—a computer ocean outfall modeling system. IEEE 75–80

  6. Hodgson JE, Moawad AK, Rajaratnam N (1999) Concentration field of multiple circular turbulent jets. J Hydraul Res 37: 249–256

    Article  Google Scholar 

  7. Jirka GH (2004) Integral model for turbulent buoyant jets in unbounded stratified flows—Part I: single round jet. Environ Fluid Mech 4: 1–56

    Article  Google Scholar 

  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: 43–100

    Article  Google Scholar 

  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 York

  10. Kaye NB, Linden PF (2004) Coalescing axisymmetric turbulent plumes. J Fluid Mech 502: 41–63

    Article  Google Scholar 

  11. Lee JH, Cheung V (1990) Generalized Langrangian model for buoyant jets in current. J Environ Eng ASCE 116: 1085–1106

    Article  CAS  Google Scholar 

  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 pp

  13. Noutsopoulos G, Yannopoulos P (1987) The round vertical turbulent buoyant jet. J Hydraul Res 25: 481–502

    Article  Google Scholar 

  14. Papanicolaou PN, Papakonstantis IG, Christodoulou GC (2008) On the entrainment coefficient in negatively buoyant jets. J Fluid Mech 614: 447–470

    Article  CAS  Google Scholar 

  15. Papps DA, Wood IR (1997) The effect of an intermittant flapping motion on the properties of merging plumes. J Hydraul Res 35: 455–472

    Article  Google Scholar 

  16. Roberts PJ, Snyder WH (1993) Hydraulic model study for Boston outfall. II: environmental performance. J Hydraul Eng ASCE 119: 988–1002

    Article  Google Scholar 

  17. Rouse H, Yih CS, Humphreys HW (1952) Gravitational convection from a boundary source. Tellus 4: 201–210

    Article  Google Scholar 

  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: 1210–1224

    Article  Google Scholar 

  19. Tian X, Roberts PJ, Daviero GJ (2004) Marine wastewater discharges from multiport diffusers. I: unstratified stationary water. J Hydraul Eng ASCE 130: 1137–1146

    Article  Google Scholar 

  20. Turner JS (1972) On the energy deficiency in self-preserving convective flows. J Fluid Mech 53: 217–226

    Article  Google Scholar 

  21. Wang H, Law AW-K (2002) Second-order integral model for a round turbulent buoyant jet. J Fluid Mech 459: 397–428

    Google Scholar 

  22. Wood IR, Bell RG, Wilkinson DL (1993) Ocean disposal of wastewater. World Scientific, Singapore

    Book  Google Scholar 

  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)

  24. Yannopoulos PC (1996) Superposition model for multiple plumes and jets predicting end effects. J Geophys Res 101: 15153–15176

    Article  Google Scholar 

  25. Yannopoulos PC (2006) An improved integral model for plane and round turbulent buoyant jets. J Fluid Mech 547: 267–296

    Article  Google Scholar 

  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: 215–220

    Google Scholar 

  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 271–277

  28. Yannopoulos PC, Noutsopoulos GC (2006) Interaction of vertical round turbulent buoyant jets. Part I: entrainment restriction approach. J Hydraul Res 44: 218–232

    Article  Google Scholar 

  29. Yannopoulos PC, Noutsopoulos GC (2006) Interaction of vertical round turbulent buoyant jets. Part II: superposition method. J Hydraul Res 44: 233–248

    Article  Google Scholar 

  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: 563–567

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Environmental Engineering Laboratory, Department of Civil Engineering, University of Patras, 26504, Patras, Greece

    Panayotis C. Yannopoulos

Authors
  1. Panayotis C. Yannopoulos
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Panayotis C. Yannopoulos.

Additional information

This article is dedicated to the memory of Prof. Gerhardt H. Jirka.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yannopoulos, P.C. Advanced integral model for groups of interacting round turbulent buoyant jets. Environ Fluid Mech 10, 415–450 (2010). https://doi.org/10.1007/s10652-010-9173-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10652-010-9173-0

Keywords

Search

Navigation