, Volume 48, Issue 3, pp 567–583 | Cite as

Centreline velocity decay characterisation in low-velocity jets downstream from an extended conical diffuser

  • X. Grandchamp
  • A. Van Hirtum
  • X. Pelorson


The centreline velocity decay of round airflow jets issuing from extended conical diffusers with length-to-diameter ratio 1.2≤L t /d≤20 is studied for moderate bulk Reynolds numbers 1131≤Re b ≤9054. The centreline velocity decay varies as a function of the initial conditions. The functional correlation between the centreline velocity decay coefficient and the initial centreline turbulence level observed on convergent nozzles (Malmström et al. in J. Fluid Mech. 246:363–377, 1997) breaks down as the initial centreline turbulence level exceeds 20 %. In addition, the centreline velocity decay coefficient expressed as function of the bulk velocity U b decreases for U b <3 m/s instead of initial mean velocity U 0<6 m/s as reported for convergent nozzles (Malmström et al. in J. Fluid Mech. 246:363–377, 1997). The asymptotic values of the decay coefficient for U b >3 m/s decrease linearly when expressed as function of the initial centreline turbulence intensity u 0/U 0. Studied flow and geometrical conditions are relevant to flow through the human upper airways.


Axisymmetrical jet Moderate Reynolds number jet Initial conditions Centreline decay Upper airway flow 

List of symbols


kinematic viscosity of air 1.5×10−5 m2/s


exit diameter of the nozzle [m]


length of uniform circular tube extension [m]


minimum diameter of conical diffuser [m]


length of diverging portion of conical diffuser [m]


nozzle length L N =L diff +L t [m]


longitudinal distance from nozzle exit x=0 [m]


transverse distance from nozzle centreline y=0 [m]


longitudinal spatial measurement step [m]


transverse spatial measurement step [m]


local jet width at distance x/d from the nozzle exit x=0 [m]


total jet spreading angle [°]


volume airflow rate [m3/s]


initial bulk centreline velocity at the nozzle exit x=0 assuming an ideal fluid, U b =(4Q b )/(πd 2) [m/s]


initial centreline mean velocity at the nozzle exit x=0 [m/s]


bulk Reynolds number Re b =U b d/ν or Re b =4Q b /πdν


initial Reynolds number Re 0=U 0 d/ν


local Reynolds number Re x/d =d x/d U c /ν


maximum local Reynolds number Re max(x/d)=max(Re x/d )


mean bulk centreline velocity [m/s]


mean transverse velocity at the nozzle outlet −d/2≤yd/2 at x/d<0.04 [m/s]


pth instantaneous velocity sample along the centreline [m/s]


total number of instantaneous velocity samples at a given location


velocity root mean square [m/s]


velocity root mean square at nozzle exit x=0 [m/s]


mean centreline velocity decay coefficient


mean centreline velocity decay coefficient \(K_{1}= \frac {U_{0} K}{U_{b}}\)


mean transverse velocity decay coefficient \(K_{w}= \frac {\sqrt{0.5 \ln{2}}}{\tan{\theta/2}}\)


virtual origin [m]


potential core extent [m]


centreline distance corresponding to Re max [m]


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Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  1. 1.GIPSA-lab, UMR CNRS 5216Grenoble UniversityGrenobleFrance

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