Quantification of Energy Transformation Processes Between Acoustic and Hydrodynamic Modes in Non-Compact Thermoacoustic Systems via a Helmholtz-Hodge Decomposition Approach

Solutions of the Linearized Euler Equations (LEE) are composed of acoustic, entropy and vortical perturbation types. The excitation of the latter can be provoked by a transformation of acoustic into rotational energy, which originates from the interaction between acoustics and a mean flow shear-layer. This is known as acoustically induced vortex shedding and represents the phenomenon of interest in this study. In the field of thermoacoustics, numerical eigenfrequency simulations with the LEE have moved into focus to determine the acoustic damping rates associated with vortex shedding to complete thermoacoustic stability analyses of gas turbine combustors. However, there is yet no fundamental investigation existent, which establishes the legitimation to consider these LEE damping rates for this purpose. This question arises due to the implicit presence of vortical disturbances caused by vortex shedding next to the acoustic ones in LEE eigensolutions. In conclusion, the corresponding damping rates are not expected to represent the pure acoustic damping rates, which are exclusively required for a thermoacoustic stability analysis. The main objective of this work comprises the clarification, whether damping rates obtained by straightforwardly performed LEE eigenfrequency simulations can be used for a thermoacoustic stability assessment, although their eigen-solutions are “polluted” by further disturbance types, i.e. the vortical one in this study. Therefore, a Helmholtz-Hodge decomposition approach is applied to LEE eigenmode shapes, which allows to explicitly access acoustic and vortical disturbance fields. These are used to extract the unambiguous, pure acoustic damping rates from LEE eigensolutions via evaluations of appropriate energy terms. The resulting damping rates are finally compared to the corresponding, original LEE damping rates and their experimental counterparts.

Finescale Doppler Radar Observation of a Tornado and Low-Level Misocyclones within a Winter Storm in the Japan Sea Coastal Region

Life histories of low-level misocyclones, one of which corresponded to a tornado vortex within a winter storm in the Japan Sea coastal region on 1 December 2007, were observed from close range by X-band Doppler radar of the East Japan Railway Company. Continuous plan position indicator (PPI) observations at 30-s intervals at the low-elevation angle revealed at least four cyclonic misocyclones within the head of the comma-shaped echo of the vortical disturbance under winter monsoon conditions. The meso-β-scale vortical disturbance developed within the weak frontal zone at the leading edge of cold-air outbreaks. High-resolution observation of misocyclones revealed the detailed structures of these misocyclones and their temporal evolution. As the parent storm evolved, a low-level convergence line was observed at the edge of the easternmost misocyclone. This convergence line was considered to be important for the initiation and development of the misocyclones and the tornado through vortex stretching. The strongest misocyclone gradually intensified as its diameter contracted until landfall, and then began to dissipate soon after landfall. The temporal evolution of the misocyclones through landfall is discussed. Surface wind and pressure variations suggested a cyclonic vortex passage, which was consistent with the passage of the radar-derived misocyclone. The observed pressure drop was also consistent with that computed from the cyclostrophic equation for the modified Rankine vortex. The observed behavior of two adjacent misocyclones was primarily consistent with the rotational flow associated with the other misocyclone. The generation and development processes of the tornado and misocyclones are discussed.

Response of a compressible laminar boundary layer to free-stream vortical disturbances

As a first step towards understanding the role of free-stream turbulence in laminar–turbulent transition, we calculate the fluctuations induced by free-stream vortical disturbances in a compressible laminar boundary layer. As with the incompressible case investigated by Leibet al. (J. Fluid Mech. vol. 380, 1999, p. 169), attention is focused on components with long streamwise wavelength. The boundary-layer response is governed by the linearized unsteady boundary-region equations in the typical streamwise region where the local boundary-layer thickness δ* iscomparable with the spanwise length scale Λ of the disturbances. The compressible boundary-region equations are solved numerically for a single Fourier component to obtain the boundary-layer signature. The root-mean-square of the velocity and mass-flux fluctuations induced by a continuous spectrum of free-stream disturbances are computed by an appropriate superposition of the individual Fourier components.Low-frequency vortical disturbances penetrate into the boundary layer to form slowly modulating streamwise-elongated velocity streaks. In the compressible regime, vortical disturbances are found to induce substantial temperature fluctuations so that ‘thermalstreaks’ also form. They may have a significant effect on the secondary instability. The calculations indicate that for a vortical disturbance with a relatively large Λ, the induced boundary-layer fluctuation ultimately evolves into an amplifying wave. This is due to a receptivity mechanism, in which a vortical disturbance first excites a decaying quasi-three-dimensional Lam–Rott eigensolution. The latter then undergoes wavelength shortening to generate a spanwise pressure gradient, which eventually converts the Lam–Rott mode into an exponentially growing mode. The latter is recognized to bea highly oblique Tollmien–Schlichting wave. A parametric study suggests that this receptivity mechanism could be significant when the free-stream Mach number is larger than 0.8.

Leading-edge effects in bypass transition

The effect of a blunt leading edge on bypass transition is studied by numerical simulation. A mixed direct and large-eddy simulation of a flat plate with a super-ellipse leading edge is carried out at various conditions. Onset and completion of transition is seen to move upstream with increasing bluntness. For sharper leading edges, at lower levels of turbulence, transition usually occurs through instabilities on low-speed streaks as observed by Jacobs & Durbin (2001) and Brandt et al. (2004) whereas increasing either the turbulence intensity or the leading-edge bluntness brings into play another mechanism. Free-stream vortices are amplified at the leading edge because of stretching. In the case of particularly strong vortices, this interaction induces a localized streamwise vortical disturbance in the boundary layer which then grows as it convects downstream and eventually breaks down to form a turbulent spot. These disturbances, which are localized and hence wavepacket-like, move at speeds in the range 0.55 U∞–0.65 U∞ and occur in the lower portion of the boundary layer. Simulations conducted with isolated vortices confirm such a response of the boundary layer.

On local boundary-layer receptivity to vortical disturbances in the free stream

Prompted by the recent experiments of Dietz (1999) on boundary-layer receptivity due to a local roughness interacting with a vortical disturbance in the free stream, this paper undertakes to present a second-order asymptotic theory based on the tripledeck formulation. The asymptotic approach allows us to treat vortical perturbations with a fairly general vertical distribution, and confirms Dietz's conclusion that for the convecting periodic wake in his experiments, the receptivity is independent of its vertical structure and can be fully characterized by its slip velocity at the edge of the boundary layer. As in the case of distributed vortical receptivity, dominant interactions that generate Tollmien–Schlichting waves take place in the upper deck as well as in the so-called edge layer centred at the outer reach of the boundary layer. The initial amplitude of the excited Tollmien–Schlichting wave is determined to O(R−1/8) accuracy, where R is the global Reynolds number. An appropriate superposition formula is derived for the case of multiple roughness elements. A comprehensive comparison is made with Dietz's experimental data, and an excellent quantitative agreement has been found for the first time, thereby resolving some uncertainties about this receptivity mechanism.

Receptivity of boundary layers with distributed roughness to vortical and acoustic disturbances: a second-order asymptotic theory and comparison with experiments

This paper investigates the receptivity of boundary layers due to distributed roughness interacting with free-stream disturbances. Both acoustic and vortical perturbations are considered. An asymptotic approach based on the triple-deck formulation has been developed to determine the initial amplitude of the Tollmien–Schlichting wave to the O(R−1/8) accuracy, where R is the global Reynolds number. In the case of vortical disturbances, we show that the dominant contribution to the receptivity comes from the upper deck as well as from the so-called edge layer centred at the outer reach of the boundary layer. It is found that for certain forms of disturbances, the receptivity is independent of their vertical structure and can be fully characterized by their slip velocity at the edge of the boundary layer. A typical case is the vortical disturbance in the form of a convecting wake, for which the same conclusion as above has been reached by Dietz (1999) on the basis of measurements. Our theoretical predictions are compared with the experimental data of Dietz (1999), and a good quantitative agreement has been found. Such a comparison is the first to be made for distributed vortical receptivity. Further calculations indicate that the vortical receptivity in general is much stronger than was suggested previously. In the case of acoustic disturbances, it is found that our first-order theory is in good agreement with experiments as well as with previous theoretical results. But the second-order theory over-predicts, and the possible reasons for this are discussed.

Reduction of Unsteady Blade Loading by Beneficial Use of Vortical and Potential Disturbances in an Axial Compressor With Rotor Clocking

This paper demonstrates reduction of stator unsteady loading due to forced response in a large-scale, low-speed, rotor/stator/rotor axial compressor rig by clocking the downstream rotor. Data from the rotor/stator configuration showed that the stator response due to the upstream vortical disturbance reaches a maximum when the wake impinges against the suction surface immediately downstream of the leading edge. Results from the stator/rotor configuration revealed that the stator response due to the downstream potential disturbance reaches a minimum with a slight time delay after the rotor sweeps pass the stator trailing edge. For the rotor/stator/rotor configuration, with Gap1 = 10 percent chord and Gap2 = 30 percent chord, results showed a 60 percent reduction in the stator force amplitude by clocking the downstream rotor so that the time occurrence of the maximum force due to the upstream vortical disturbance coincides with that of the minimum force due to the downstream potential disturbance. This is the first time, the authors believe, that beneficial use of flow unsteadiness is definitively demonstrated to reduce the blade unsteady loading.

Navier–Stokes and Potential Calculations of Axial Spacing Effect on Vortical and Potential Disturbances and Gust Response in an Axial Compressor

The effect of blade row axial spacing on vortical and potential disturbances and gust response is studied for a compressor stator/rotor configuration near design and at high loadings using two-dimensional incompressible Navier–Stokes and potential codes, both written for multistage calculations. First, vortical and potential disturbances downstream of the isolated stator in the moving frame are defined; these disturbances exclude blade row interaction effects. Then, vortical and potential disturbances for the stator/rotor configuration are calculated for axial gaps of 10, 20, and 30 percent chord. Results show that the potential disturbance is uncoupled locally; the potential disturbance calculated from the isolated stator configuration is a good approximation for that from the stator/rotor configuration upstream of the rotor leading edge at the locations studied. The vortical disturbance depends strongly on blade row interactions. Low-order modes of vortical disturbance are of substantial magnitude and decay much more slowly downstream than do those of potential disturbance. Vortical disturbance decays linearly with increasing mode except very close to the stator trailing edge. For a small axial gap, e.g., 10 percent chord, both vortical and potential disturbances must be included to determine the rotor gust response.