An integrated computational uid dynamics (CFD) and computational structural dynamics (CSD) method is developed for the simulation and prediction of utter. The CFD solver is based on an unsteady, parallel, multiblock, multigrid nite volume algorithm for the Euler/Navier-Stokes equations. The CSD solver is based on the time integration of modal dynamic equations extracted from full nite element analysis. A general multiblock deformation grid method is used to generate dynamically moving grids for the unsteady ow solver. The solutions of the oweld and the structural dynamics are coupled strongly in time by a fully implicit method. The coupled CFD-CSD method simulates the aeroelastic system directly on the time domain to determine the stability of the aeroelastic system. The unsteady solver with the moving grid algorithm is also used to calculate the harmonic and/or indicial responses of an aeroelastic system, in an uncoupled manner, without solving the structural equations. Flutter boundary is then determined by solving the utter equation on the frequency domain with the indicial responses as input. Computations are performed for a two-dimensional wing aeroelastic model and the three-dimensional AGARD 445.6 wing. Flutter boundary predictions by both the coupled CFD-CSD method and the indicial method are presented and compared with experimental data for the AGARD 445.6 wing.

Conditionally sampled hot-wire and ‘cold-wire’ (resistance-thermometer) measure- ments confirm the general flow picture advanced by Falco (1974, 1977, 1980; see also Smith & Abbott 1978) and by Head & Bandyopadhyay (1981; see also Smith & Abbott) on the basis of smoke observations and more limited hot-wire measurements. The probability density function of turbulent-zone lengths in the intermittent region varies rapidly with Reynolds number, supporting the above authors’ finding that the hairpin-vortex ‘typical eddies’ in the viscous superlayer scale on the viscous length ν/uτ, rather than on boundary-layer thickness. However the average turbulent-zone length, deduced as an integral moment of the probability distribution, tends to a constant fraction of the boundary-layer thickness above a momentum-thickness Reynolds number of 5000, which strongly suggests that at high Reynolds numbers the overall shape of the turbulent irrotational interface is controlled by the classical ‘large eddies’ and not by the viscosity-dependent small eddies. The intermittency profile is practically independent of Reynolds number. The second-order structural parameter $\overline{u^2}/\overline{v^2}$ increases strongly with increasing Reynolds number but the triple-product parameters, with the exception of the u-component skewness, vary only slowly with Reynolds number. This behaviour of the intermittency and velocity statistics is most simply explained by supposing that the lengthscale of the large eddies is nearly independent of Reynolds number while their intensity is somewhat lower at low Reynolds number. ‘Typical eddies’ evidently contribute to the Reynolds stresses at low Reynolds number, but it is probable that the large eddies carry most of the triple products at any Reynolds number. Our results confirm the usual finding that the mixing length and dissipation length parameter increase, while the wake component of the velocity profile decreases, as Reynolds number decreases.

A flow visualization investigation using dye-injection and laser-induced fluorescence techniques has been carried out to understand the vortex dynamics resulting from a V-notched indeterminate-origin jet with two peaks and two troughs. The laminar jet (Re=2000) was studied under forcing and nonforcing conditions to investigate the resultant dynamics of coherent large- and small-scale flow structures. Present experimental observations indicated that the effects of the nozzle peaks and troughs differ from those reported previously. Instead of the peaks producing streamwise vortex pairs which spread outwards into the ambient fluid and the troughs generating similar vortex pairs but entraining ambient fluid into the jet flows as indicated by earlier studies, the present experimental observations showed that both peaks and troughs produce outward-spreading streamwise vortex pairs. Laser cross sections further showed that the subsequent formation of azimuthal ring vortices causes these streamwise vortex pairs to be entrained. This entrainment causes the streamwise vortex pairs to “roll-up” together with the ring vortices, leading to intense flow interactions between them. Interestingly, in a comparison with the experimental study reported by Longmire et al. [“Control of jet structure by crown-shaped nozzles,” AIAA J. 30, 505 (1992)] using higher Reynolds number air jet (Re=19000), it was found that forced jet flows with four peaks and four troughs yielded practically the same flow observations as the present nozzles with two peaks and two troughs. An updated flow model based on instantaneous and time-averaged evidence is presented to explain how the interaction of the vortex structures will give rise to the present new observations.

Separation of supersonic flow in a planar convergent-divergent nozzle with moderate expansion ratio is investigated by solving the Reynolds-averaged Navier-Stokes equations with a two-equation k-! turbulence model. The focus of the study is on the structure of the fluid and wave phenomena associated with the flow separation. Computations are conducted for an exit-to-throat area ratio of 1.5 and for a range of nozzle pressure ratios. The results are compared with available experimental data in a nozzle of the same geometry. The flow separates by the action of a lambda shock, followed by a succession of expansion and compression waves. For 1:5 < NPR < 2:4, the computation reveals the possibility of asymmetric flow structure. The computationally obtained asymmetric flow structures are consistent with previous experimental flow visualizations studies. In addition, other flow features such as shock location and wall pressure distributions are also in good agreement with the experimental data. The present study provides new information that confirms earlier conjectures on the flow-wave structure relevant to the instability of the separated flow in convergent-divergent nozzles of moderate expansion ratio. Nomenclature A = nozzle cross-sectional area e = internal energy H = nozzle height h = enthalpy M = Mach number NPR = nozzle pressure ratio, P 0 =P a P = pressure P 0 = total pressure at the nozzle inlet R = gas constant T = temperature u, v, w = velocity components x = axial direction y = normal direction = ratio of specific heats = flow angle = viscosity ' = shock angle Subscripts 0 = total 1 = immediately before the Mach stem 2 = immediately after the Mach stem a = ambient c = centerline e = nozzle exit s = shock location t = throat