Influence of nozzle-exit boundary-layer profile on high-subsonic jets

Abstract

The influence of the nozzle-exit boundary-layer profile on high-subsonic round jets is investigated by performing compressible large-eddy simulations of four jets using lowdissipation numerical schemes. The jets are isothermal, and have a Mach number of 0.9 and a diameter-based Reynolds number of 5 × 10 4 . They originate from a pipe nozzle in which a trip-like forcing is applied. In that way, they exhibit, at the exit section, around 6% of peak turbulence intensity and boundary-layer velocity profiles characterized by a momentum thickness of about 2.8% of the nozzle radius, yielding a Reynolds number around 700, and by shape factors equal to 1.68, 1.77, 2.01 and 2.36. The results from the fourth case with a laminar velocity profile differ significantly from those from the three first cases with transitional profiles, whose accuracy is shown by a grid refinement study. Clear trends are thus identified when the shape of the exit boundary-layer profile changes from laminar to turbulent. Higher azimuthal modes and higher Strouhal numbers are found to predominate, respectively, at the pipe exit close to the wall and early on in the mixing layers. The latter appear to develop more slowly, leading to a longer potential core, and weaker velocity fluctuations are obtained in the shear layers and on the jet axis. Finally, lower noise levels are generated in the acoustic field.

Simulations of Initially Highly Disturbed Jets with Experiment-Like Exit Boundary Layers

“…Regarding the jetConic case with an inlet transitional boundarylayer profile of thickness δ T 2 0.1328r 0 and exit parameters of Re θ 1100 and u 0 e ∕u j 6.02% (see also in Sec. III.B), it can first be noted that a jet with δ T 2 0.332r 0 , Re θ 691, and u 0 e ∕u j 6.14% was recently calculated successfully on the grid mentioned previously [34]. In jetConic, the near-wall mesh spacings in the pipe expressed in wall units based on the wall friction velocity at the nozzle exit, given in Table 4, are equal to Δr 3.7, r 0 Δθ 7.4, and Δz 7.4.…”

“…with δ BL 0.0045r 0 , yielding a momentum thickness of δ θ 0.0053r 0 and a 99% velocity thickness of δ 99 0.037r 0 . In jetConic, the inlet velocity profile is transitional boundary-layer profile [34] with H 1.52 defined as…”

“…where β 2 0.423, γ 2 0.82, and δ T 2 0.1328r 0 , leading to δ θ 0.0117r 0 and δ 99 0.104r 0 . This profile was designed to fit the experimental data obtained by Schubauer and Klebanoff [44] in a flat-plate boundary layer in the region of changeover from laminar to fully turbulent conditions; refer to Appendix A of a recent paper [34]. The two jets are "tripped" using an arbitrary tripping device [45][46][47][48][49][50] whose parameters are determined by trial and error, as is usually done in laboratory experiments for boundary layers over a flat plate or in jet nozzles (e.g., in Klebanoff and Diehl [45] and Crow and Champagne [1]).…”

“…In the present jets, the forcing procedure detailed in Appendix A of Bogey et al [25] is implemented. It consists of adding random lowlevel vortical disturbances uncorrelated in the azimuthal direction in the boundary layers and has been previously applied to both laminar [25][26][27][28][29] and nonlaminar [34] velocity profiles. The position and the strength of the forcing are indicated in Table 2.…”

“…Subsequently, Sandberg et al [32] performed the simulation of a fully turbulent pipe flow at Re D 7500 exiting into a coflow, and Bühler et al [33] successfully computed a jet at Re D 18;100 with turbulent conditions at the exit of a pipe nozzle. LESs of jets at Re D 50;000 with thick transitional and turbulent boundary-layer profiles have been carried out in Bogey and Marsden [34]. Finally, Brès et al [35] and Le Bras et al [36] very recently simulated initially turbulent jets at Re D > 500;000 using wall modeling inside the nozzle.…”