Skip to main content
SpringerLink
Log in

Influence of a strong density stratification on the entrainment of a turbulent axisymmetric plume

  • Originals
  • Published:
Experiments in Fluids Aims and scope Submit manuscript

Abstract

The effect of entrainment and the role of the interface during the interaction between an axisymmetric turbulent mass plume and a strong stratified layer are investigated. We describe mainly the characteristics of the plume: the change in the profiles of the density, the horizontal component of the velocity and the corresponding intensity of turbulence, the change in the entrainment co-efficient, when the plume goes through the impingement interface, assuming a self-similar Gaussian property of the axial velocity component and of the density difference. The influence of the stratification on the plume angle coefficient is studied, and compared with the results related to a homogeneous environment, obtained elsewhere. Experimental correlation on the mean entrainment coefficient in a given plume cross-section, is formulated.

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

Abbreviations

B :

specific buoyancy flux at the source \(( = {\text{g}}Q{\text{ }}(\rho _{air} - \rho _{He} )/\rho _{He} )\)

d :

diameter of the source

Fr :

Froude number = \({\text{U}}_{\text{0}}^{\text{2}} \rho _{He} {\text{/gd}}(\rho _{air} - \rho _{He} )\) (at the source)

g :

magnitude of gravitational acceleration

I :

turbulence intensity

K :

coefficient in relation with the entrainment

l m :

characteristic length (= M 0.750 B −0.5)

m :

mass flow rate

M :

momentum flux

M 0 :

specific momentum flux at the source (=QU 0)

N :

Brunt-Väisälä frequency \(\left( {N^2 = \left\{ {\frac{{ - g{\text{ }}d\rho _\infty }}{{\rho _{air} {\text{ }}d{\text{x}}}}} \right\}} \right)\)

N * :

dimensionless N (N *=N(l m/g)0.5)

Q :

volumetric flow rate (at the source = U 0 S)

r :

radial coordinate

r 1 :

radial coordinate at the point where \(\bar u/\bar u_c = \frac{1}{e}\)

r sup′inf1 :

radial coordinate at the point where \(\Delta \bar \rho /\Delta \bar \rho c = \frac{1}{e}\)

Re :

Reynolds number (at the source \(\operatorname{Re} _0 = U_0 d/v_{He} \))

Ri :

Richardson number (at the source Ri 0 = Fr1/2)

u :

vertical velocity component

U :

vertical mean velocity

v :

radial velocity component

x :

vertical coordinate distance

x v :

virtual origin of the plume

\(\hat x = \frac{x}{d}\) :

dimensionless vertical coordinate distance

X * :

dimensionless parametric group, defined in (Eq. (17))

α :

entrainment coefficient

ϱ :

fluid density

\(\Delta \rho = \rho - \rho _\infty \) :

density difference

\(\hat \tau = \frac{{\rho - \rho _{air} }}{{\rho _{He} - \rho _{air} }}\) :

dimensionless density

air:

air

c :

on the axis of the flow

He:

helium

m :

relative to minimum value or maximum value

0:

value at the source

v :

corresponding to the radial velocity

∞:

ambient conditions

∧:

dimensionless value

−:

mean value

':

fluctuation

References

  • Baines WD (1975) Entrainment by a plume or jet at a density interface J Fluid Mech 68: 309–320

    Google Scholar 

  • Bejan A (1991) Thermodynamics of an isothermal flow: the two-dimensional turbulent jet. Int J Heat Mass Transfer 34: 407–413

    Google Scholar 

  • Brahimi M (1987) Structure turbulente des panaches thermiques — Interaction. Thèse de Docteur de l'Université de Poitiers, Poitiers, France

    Google Scholar 

  • Brahimi M; Dehmani L; Son DK (1989) Structure turbulente de l'écoulement d'interaction de deux panaches thermiques. Int J Heat Mass Transfer 32: 1551–1559

    Article  Google Scholar 

  • Brahimi M; Son D-K (1986) Propagation of interacting turbulent plumes. Proceedings of the 3rd International Conference, Porto Carras, Greece

  • Brahimi M; Lamour M; Son DK (1988) Champs moyens et fluctuants des panaches thermiques isolés ou en interaction. Rev Gén Therm Fr no. 315–316: 236–243

  • Chen CJ; Rodi W (1980) Vertical turbulent buoyant jets, A review of experimental data. Pergamon Press. London

    Google Scholar 

  • Chua LP; Antonia RA (1990) Turbulent Prandtl number in a circular jet. Int J. Heat Mass Transfer 33: 331–339

    Article  Google Scholar 

  • Dehmani L (1990) Influence d'une forte stratification de masse volumique sur la structure turbulente d'un panache à symétrie axiale. Thèse de Docteur de l'Université de Poitiers, Poitiers, France

    Google Scholar 

  • Dehmani L; Rey C; Rongere FX; Son DK (1989) Etude de la pénétration d'un panache thermique dans une zone stratifiée stable. 9ème Congrès Français de Mécanique Metz

  • Douglas G Fox (1970) Forced plume in a stratified fluid. J Geophys Res 75: 6818–6835

    Google Scholar 

  • Evans DD (1983) Calculating fire plume characteristics in a two layer environment, National Bureau of Standards, Department of Commerce, Washington D.C. 20234-NBSIR 83–2670

    Google Scholar 

  • Fukui K; Nakajima M; Ueda H (1991) Coherent structure of turbulent longitudinal vortices in unstably-stratified turbulent flow. Int J Heat Mass Transfer 34: 2373–2385

    Google Scholar 

  • Gebhart B; Hilder DS; Kelleher M (1984) The diffusion of turbulent buoyant jets. Copyright by Academic Press. Inc. ISBN 0-12-020016-3, pp. 1–57

  • George WK; Alpert RL; Tamanini F (1977) Turbulence measurements in an axisymmetric buoyant plume. Int J Heat Mass Trans 20: 1145–1154

    Article  Google Scholar 

  • Guillou B (1984) Etude numérique et expérimentale de la structure turbulente d'un panache pur à symétrie axiale. Thèse de Docteur Ingénieur, Université de Poitiers, Poitiers, France

    Google Scholar 

  • Guillou B; Brahimi M; Son DK (1986) Structure turbulente d'un panache thermique. Aspect dynamique. Journal de Mécanique théorique et appliquée 5: 371–401

    Google Scholar 

  • Kapoor K; Jaluria Y (1993) Penetrative convection of a plane turbulent wall jet in a two-layer thermally stable environment: a problem in enclosure fires. Int J Heat Mass Transfer 36: 155–167

    Article  Google Scholar 

  • Kotsovinos NE (1990) Dissipation of turbulent kinetic energy in buoyant free shear flows. Int J Heat Mass Transfer 33: 393–400

    Article  Google Scholar 

  • Kotsovinos NE; List EJ (1977) Plane turbulent buoyant jets. Part I. Integral properties. J Fluid Mech 81: 25–44

    Google Scholar 

  • List EJ; Imberger J (1973) Turbulent entrainment in buoyant jets and plumes. J Hydr Div A.S.C.E. 99: 1461–1474

    Google Scholar 

  • Morton BR (1958) Forced plumes. J Fluid Mech 5: 151–163

    MathSciNet  Google Scholar 

  • Morton BR; Taylor FRS; Turner JS (1956) Turbulent gravitational convection from maintained and instantaeous sources. Proc Roy Soc A 234: 1–23

    MathSciNet  Google Scholar 

  • Papanicolaou PN; List EJ (1987) Statistical and spectral properties of tracer concentration in round buoyant jets. Int J Heat Mass Transfer 30: 2059–2071

    Article  Google Scholar 

  • Papanicolaou PN; List EJ (1988) Investigations of round vertical turbulent buoyant jets. J Fluid Mech 195: 341–391

    Google Scholar 

  • Ricou FP; Spalding DG (1961) Measurements of entrainment by axisymetrical turbulent jets. J Fluid Mech 11: 21–32

    Google Scholar 

  • Srinivasan J; Angirasa D (1990) Laminar axisymmetric multicomponent buoyant plumes in a thermally stratified medium. Int J Heat Mass Transfer 33: 1751–1757

    Article  Google Scholar 

  • Tamanini F (1977) An improved version of the k-s-g model of turbulence and its application to axisymmetric forced and buoyancy jets. F.M.R.C. Technical report, Massachussetts

  • Tamanini F (1981) An integral model of turbulent fire plumes. Eighteenth Symposium (International) on Combustion, pp. 1081–1090

  • Taylor GI (1945) Dynamics of a mass of hot gas rising in air. U.S. Atomic Energy Commission MDDC-919 LADC-276

  • Vachon M; Champion M (1986) Integral model of a flame with large buoyancy effects. Combustion and Flame 63: 269–278

    Article  Google Scholar 

  • Wygnanski I; Fiedler H (1969) Some measurements in the self-preserving jet. J Fluid Mech 38: 577–612

    Google Scholar 

  • Zukoski EE; Kubota T; Cetegen B (1981) Entrainment in fire plumes. Fire Safety Journal 3: 107–121

    Article  Google Scholar 

Download references

Author information

Author notes

  1. L. Dehmani

    Present address: Faculté des Sciences de Tunis, Département de Physique Campus Universitaire de Tunis, Tunisia

Authors and Affiliations

  1. Laboratoire d'Etudes Thermiques de l'Ecole Nationale Supérieure de Mécanique et d'Aérotechnique, BP. 109, F-86960, Futuroscope Cedex, France

    L. Dehmani, D. -K. Son & L. Gbahoué

  2. Département TTA, Centre de recherche EDF, 6 Quai Watier, F-78400, Chatou, France

    F. X. Rongère

Authors
  1. L. Dehmani
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. -K. Son
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. L. Gbahoué
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. F. X. Rongère
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dehmani, L., Son, D.K., Gbahoué, L. et al. Influence of a strong density stratification on the entrainment of a turbulent axisymmetric plume. Experiments in Fluids 21, 170–180 (1996). https://doi.org/10.1007/BF00191688

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00191688

Keywords

Search

Navigation