Dilip Prasad

Propagation and Decay of Shock Waves in Turbofan Engine Inlets

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 Numerical Study of Secondary Flow in Axial Turbines With Application to Radial Transport of Hot Streaks

The flow field in a low-speed turbine stage with a uniform inlet total pressure is studied numerically. A circular hot streak is superposed on the vane inlet flow. In agreement with previous experimental and numerical work, it is observed that while the streak passes through the vane unaltered, significant radial transport occurs in the rotor. Furthermore, despite the unsteady nature of the flow field, the steady theory of Hawthorne (1974) is found to predict the radial transport velocity well. Making use of this theory, it is shown that the secondary vorticity in the rotor may be attributed to the effects of density stratification, the spatial variation of the vane exit flow angle, and the relative eddy. It then follows that the extent of radial transport in the rotor may be influenced by altering the vane exit flow angle distribution. The present study examines one means by which this may be effected, viz., varying the vane twist across the span. It is shown that a reverse twist, wherein the flow angle at the vane exit is larger near the tip than it is at midspan, reduces the secondary flow (and consequently, radial transport) in the blade passage. On the other hand, positive twist, in which the vane exit flow angle decreases with span, is found to worsen the radial transport in the blade markedly. It is to be noted that varying the vane twist is but one method to obtain the desired exit flow angle; possibilities for altering other aspects of the vane geometry also exist.

Thermoacoustic Stability of Quasi-One-Dimensional Flows–Part I: Analytical and Numerical Formulation

A numerical method is developed for transient linear analysis of quasi-one-dimensional thermoacoustic systems, with emphasis on stability properties. This approach incorporates the effects of mean flow variation as well as self-excited sources such as the unsteady heat release across a flame. Working in the frequency domain, the perturbation field is represented as a superposition of local wave modes, which enables the linearized equations to be integrated in space. The problem formulation is completed by specifying appropriate boundary conditions. Here, we consider impedance boundary conditions as well as those relevant to choked and shocked flows. For choked flows, the boundary condition follows from the requirement that perturbations remain regular at the sonic point, while the boundary conditions applicable at a normal shock are obtained from the shock jump conditions. The numerical implementation of the proposed formulation is described for the system eigenvalue problem, where the natural modes are sought. The scheme is validated by comparison with analytical and numerical solutions.

Wave trapping and upstream influence in stratified flow of large depth

A theoretical study is made of continuously stratified flow of large depth over topography when small periodic vertical fluctuations are present in the Brunt-Vaisala 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.

Unsteady Aerodynamics and Aeroacoustics of a High-Bypass Ratio Fan Stage

A numerical investigation of the unsteady aerodynamics of a fan stage comprised of a transonic rotor, swept fan exit guide vane (FEGV), and low-pressure compressor inlet guide vane (IGV) is described, with emphasis on acoustics. It is shown that the effects of the two downstream stator rows on the time-mean blade flow field are negligible, permitting its investigation using isolated rotor calculations. Simulations of this type are carried out along the engine operating line to quantify the acoustic sources associated with the upstream shock field and wake turbulence-stator interaction. The shock noise achieves its maximum value near the flyover acoustic certification condition, while the wake turbulence is least at this condition owing to its proximity to the design point. The behavior of these noise sources is explained physically by carrying out a detailed examination of the rotor flow field. The unsteady interaction between the rotor and stator rows at a high-power setting is investigated next. It is shown that the time-mean IGV flow is significantly affected by this interaction. Moreover, the unsteady loading on the IGV is found to be large. The behavior of the upstream-propagating acoustic field generated by rotor-IGV interaction is examined. The interaction between the rotor and FEGV is found to be linear in nature. The FEGV surface unsteady pressure and far-field acoustic field behavior are investigated.

Thermoacoustic Stability of Quasi-One-Dimensional Flows—Part II: Application to Basic Flows

In this paper, applications of a previously developed numerical formulation (Prasad, D., and Feng, J., 2004, Thermoacoustic Stability of Quasi-One-Dimensional Flows-Part I: Analytical and Numerical Formulation, J. Turbomach., 126, pp. 636-643. for the stability analysis of spatially varying one-dimensional flows are investigated. The results are interpreted with the aid of a generalized acoustic energy equation, which shows that the stability of a flow system depends not only on the nature of the unsteady heat, mass and momentum sources but also on the mean flow gradients and on the inlet and exit boundary conditions. Specifically, it is found that subsonic diffusing flows with strongly reflecting boundary conditions are unstable, whereas flows with a favorable pressure gradient are not. Transonic flows are also investigated, including those that feature acceleration through the sonic condition and those in which a normal shock is present. In both cases, it is found that the natural modes are stable. Finally, we study a simplified ducted flame configuration. It is found that the length scale of the mean heat addition affects system stability so that the thin-flame model commonly used in studies of combustion stability may not always be applicable.

Validation of a Three-Dimensional Linearized Euler Analysis for Classical Wake/Stator Interactions

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 LINFLUX 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.Copyright

Weakly nonlinear shock propagation in slowly varying one-dimensional flows

A theoretical model for the linear and nonlinear evolution of acoustic perturbations in nonuniform one-dimensional isentropic flows is developed. On the assumption that the length scale of the mean flow greatly exceeds that of the imposed disturbances, it is shown that the propagation of linear waves can be described in a closed form that is consistent with the conservation of acoustic power. This permits the application of a “nonlinearization” procedure (Landau [J. Phys. USSR 9, 496 (1945)],Whitham [Proc. R. Soc. London, Ser. A 201, 89 (1950)]), wherein the linear functional forms are assumed to hold for weakly nonlinear simple-wave disturbances, and the effects of amplitude on the wave speed are included to leading order. When nonlinear steepening results in the formation of shocks, they are fitted into the solution using the Rankine-Hugoniot relations. The method is applicable to arbitrary waveforms and, in the present study, the evolution of hump-like and periodic disturbances through nonuniform flows...

Thermoacoustic Stability of Quasi-One-Dimensional Flows: Part II — Application to Basic Flows

In this paper, applications of a previously developed numerical formulation (Prasad and Feng 2004) for the stability analysis of spatially varying one-dimensional flows are investigated. The results are interpreted with the aid of a generalized acoustic energy equation, which shows that the stability of a flow system depends not only on the nature of the unsteady heat, mass and momentum sources but also on the mean flow gradients and on the inlet and exit boundary conditions. Specifically, it is found that subsonic diffusing flows with strongly reflecting boundary conditions are unstable, whereas flows with a favorable pressure gradient are not. Transonic flows are also investigated, including those that feature acceleration through the sonic condition and those in which a normal shock is present. In both cases, it is found that the natural modes are stable. Finally, we study a simplified ducted flame configuration. It is found that the length scale of the mean heat addition affects system stability so that the thin-flame model commonly used in studies of combustion stability may not always be applicable.© 2004 ASME

Thermoacoustic Stability of Quasi-One-Dimensional Flows: Part I — Analytical and Numerical Formulation

A numerical method is developed for transient linear analysis of quasi-one-dimensional thermoacoustic systems, with emphasis on stability properties. This approach incorporates the effects of mean flow variation as well as self-excited sources such as the unsteady heat release across a flame. Working in the frequency domain, the perturbation field is represented as a superposition of local wave modes, which enables the linearized equations to be integrated in space. The problem formulation is completed by specifying appropriate boundary conditions. Here, we consider impedance boundary conditions as well as those relevant to choked and shocked flows. For choked flows, the boundary condition follows from the requirement that perturbations remain regular at the sonic point, while the boundary conditions applicable at a normal shock are obtained from the shock jump conditions. The numerical implementation of the proposed formulation is described for the system eigenvalue problem, where the natural modes are sought. The scheme is validated by comparison with analytical and numerical solutions.Copyright