Centreline velocity decay characterisation in low-velocity jets downstream from an extended conical diffuser
- PDF / 981,909 Bytes
- 17 Pages / 547.087 x 737.008 pts Page_size
- 29 Downloads / 163 Views
Centreline velocity decay characterisation in low-velocity jets downstream from an extended conical diffuser X. Grandchamp · A. Van Hirtum · X. Pelorson
Received: 16 September 2011 / Accepted: 17 September 2012 / Published online: 5 October 2012 © Springer Science+Business Media Dordrecht 2012
Abstract The centreline velocity decay of round airflow jets issuing from extended conical diffusers with length-to-diameter ratio 1.2 ≤ Lt /d ≤ 20 is studied for moderate bulk Reynolds numbers 1131 ≤ Reb ≤ 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 Ub decreases for Ub < 3 m/s instead of initial mean velocity U0 < 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 Ub > 3 m/s decrease linearly when expressed as function of the initial centreline turbulence intensity u0 /U0 . Studied flow and geometrical conditions are relevant to flow through the human upper airways. Keywords Axisymmetrical jet · Moderate Reynolds number jet · Initial conditions · Centreline decay · Upper airway flow X. Grandchamp · A. Van Hirtum () · X. Pelorson GIPSA-lab, UMR CNRS 5216, Grenoble University, Grenoble, France e-mail: [email protected]
List of symbols ν kinematic viscosity of air 1.5 × 10−5 m2 /s d exit diameter of the nozzle [m] Lt length of uniform circular tube extension [m] din minimum diameter of conical diffuser [m] Ldiff length of diverging portion of conical diffuser [m] LN nozzle length LN = Ldiff + Lt [m] x longitudinal distance from nozzle exit x = 0 [m] y transverse distance from nozzle centreline y = 0 [m] x longitudinal spatial measurement step [m] y transverse spatial measurement step [m] dx/d local jet width at distance x/d from the nozzle exit x = 0 [m] θ total jet spreading angle [°] Qb volume airflow rate [m3 /s] Ub initial bulk centreline velocity at the nozzle exit x = 0 assuming an ideal fluid, Ub = (4Qb )/(πd 2 ) [m/s] U0 initial centreline mean velocity at the nozzle exit x = 0 [m/s] Reb bulk Reynolds number Reb = Ub d/ν or Reb = 4Qb /πdν Re0 initial Reynolds number Re0 = U0 d/ν Rex/d local Reynolds number Rex/d = dx/d Uc /ν Remax maximum local Reynolds number Remax (x/d) = max(Rex/d ) Uc (x) mean bulk centreline velocity [m/s]
568
Meccanica (2013) 48:567–583
U (y) mean transverse velocity at the nozzle outlet −d/2 ≤ y ≤ d/2 at x/d < 0.04 [m/s] Uc,p pth instantaneous velocity sample along the centreline [m/s] Ntot total number of instantaneous velocity samples at a given location u velocity root mean square [m/s] velocity root mean square at nozzle exit x = 0 u0 [m/s] K mean centreline
Data Loading...
