The flow through a high-bypass ratio fan stage during engine-out conditions is investigated, with the objective of quantifying the internal losses when the rotor is at “windmill”. An analysis of altitude test data at various simulated flight Mach numbers shows that the fan rotational speed scales with the engine mass flow rate. Making use of the known values of the nozzle coefficients, we deduce the stagnation pressure loss of the fan stage, which rises significantly as the mass flow rate increases. In order to better understand this behavior, numerical simulations of the fan stage were carried out. The predicted losses agree well with the test data, and it is found that the bulk of the stagnation pressure loss occurs in the stator. A detailed examination of the flow field reveals that the relative flow leaves the rotor at very nearly the metal angle. Moreover, the rotational speed of the fan is such that the inboard sections of the fan blade add work to the flow, while the outboard sections extract work from it. The overall work is essentially zero so that the absolute swirl angle at the rotor exit is small, causing the stator to operate at a severely negative incidence. A gross separation ensues and the resulting blockage of the stator passage accelerates the flow to high Mach numbers. The highly separated flow in the vane, together with the mixing of the large wakes behind it are responsible for the high losses in the vane. Based on the simulation results for the flow behavior, a simple physical model to estimate the windmill speed of the rotor is developed and is found to be in good agreement with the test data. The utility of this model is that it enables the development of a procedure to predict the internal drag at engine-out conditions, which is discussed.

The phenomenon of shelf generation by long nonlinear internal waves in stratified flows is investigated. The problem of primary interest is the case of a uniformly stratified Boussinesq fluid of finite depth. In analysing the transient evolution of a finite-amplitude long-wave disturbance, the expansion procedure of Grimshaw & Yi (1991) breaks down far downstream, and it proves expedient to follow a matched-asymptotics procedure: the main disturbance is governed by the nonlinear theory of Grimshaw & Yi (1991) in the ‘inner’ region, while the ‘outer’ region comprises multiple small-amplitude fronts, or shelves, that propagate downstream and carry O(1) mass. This picture is consistent with numerical simulations of uniformly stratified flow past an obstacle (Lamb 1994). The case of weakly nonlinear long waves in a fluid layer with general stratification is also examined, where it is found that shelves of fourth order in wave amplitude are generated. Moreover, these shelves may extend both upstream and downstream in general, and could thus lead to an upstream influence of a type that has not been previously considered. In all cases, transience of the main nonlinear wave disturbance is a necessary condition for the formation of shelves.

A theoretical study is made of continuously stratified flow of large depth over topography when small periodic vertical fluctuations are present in the Brunt–Väisälä frequency, the background flow conditions being otherwise uniform. It is known from Phillips (1968) that, owing to nonlinear interactions with such fluctuations, internal gravity waves with vertical wavelength twice that of the background variations become trapped along the vertical, suggesting a waveguide-like behaviour. Using the asymptotic theory of Kantzios & Akylas (1993), we explore the role that this interaction-trapping mechanism plays in the generation of finite-amplitude long-wave disturbances near the hydrostatic limit. As a result of vertical trapping, a resonance phenomenon occurs and the linear hydrostatic response grows unbounded when the flow speed coincides with the long-wave speed of a free propagation mode that is trapped close to the ground. Near this critical flow speed, according to weakly nonlinear analysis, the wave evolution along the streamwise direction is governed by a forced extended Korteweg–de Vries equation, which predicts upstream-propagating solitary waves and bores similar to those obtained in resonant stratified flow of finite depth. The finite-amplitude response is then studied numerically and in some cases features strong upstream influence in the form of vertically trapped solitary waves and bores. On the other hand, incipient wave breaking is often encountered during the evolution of the nonlinear resonant response, and this flow feature, which is beyond the reach of weakly nonlinear theory, arises at topography amplitudes significantly below the critical value for overturning predicted by the classical model of Long (1953) for uniformly stratified steady flow.

Numerical experiments are carried out to investigate the tone noise radiated from a turbofan engine inlet under conditions at which the relative flow past the rotor tip is supersonic. Under these conditions, the inlet tone noise is generated by the upstream-propagating rotor-locked shock wave field. The spatial evolution of this shock system is studied numerically for flows through two basic hard-walled configurations: a slender nacelle with large throat area and a thick nacelle with reduced throat area. With the flight Mach number set to 0.25, the spatial evolution of the acoustic power through the two inlets reveals that the reduced throat area inlet provides superior attenuation. This is attributed to the greater mean flow acceleration through its throat and is qualitatively in accord with one-dimensional theory, which shows that shock dissipation is enhanced at high Mach numbers. The insertion of a uniform extension upstream of the fan is shown to yield greater attenuation for the inlet with large throat area, while the acoustic performance of the reduced throat area inlet is degraded. This occurs because the interaction of the nacelle and spinner potential fields is weakened, resulting in a lower throat Mach number. The effect of forward flight on the acoustic power radiated from the two inlets is also investigated by examining a simulated static condition. It is shown that the slender nacelle radiates significantly less power at the static condition than in flight, whereas the power levels at the two conditions are comparable for the thick nacelle. The reason for this behavior is revealed to be a drastic overspeed near the leading edge of the slender nacelle, which occurs to a lesser degree in the case of the thick inlet. This has implications for ground acoustic testing of aircraft engines, which are discussed.

A comprehensive validation of the linearized Euler analysis, LINFLUX, for wake/blade row interaction is carried out. The flow configuration is that of the benchmark problem for rotor-stator interaction proposed at the Third Computational Aeroacoustics Workshop. It consists of an unstaggered, annular, flat-plate blade row excited by the vortical gusts associated with the wakes shed from an upstream rotor. The numerical results for the unsteady pressure responses of the stator are compared with semi-analytic lifting surface and lifting line solutions. The validation is first conducted for narrow-annulus flows, where the numerical results are shown to agree well with classical two-dimensional solutions over a range of frequencies. We then carry out a detailed comparison of the three-dimensional LINFLUX results with the lifting surface results of Namba and Schulten for a blade row with a hub-to-tip ratio of 0.5. This study encompasses gust excitation frequencies for which the stator responses vary from cut off to propagating, as well as gusts with varying degrees of spanwise variation. The numerical and semi-analytical analyses yield results for the stator pressure response, including the complex amplitudes of the propagating and least attenuated, evanescent, pressure modes that are in very good agreement. The effect of increasing the spanwise phase variation of the gust is generally, but not necessarily, to reduce the power associated with the acoustic response of the blade row. A comparison of the present numerical results with those obtained from a stripwise application of classical linear theory reveals that the latter approach can be erroneous and, therefore, of questionable applicability to realistic turbomachinery unsteady flows.