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This paper deals with a brief description of transition problems arising on swept wings in incompressible flow. Two transition processes are discussed: the cross-flow instability, and the leading-edge contamination.
Receptivity and stability of supersonic boundary layers over a 5-degree straight cone with a blunt tip are numerically investigated at a free stream Mach number of 3.5 and at a high Reynolds number of 106/inch. Both the steady and unsteady solutions are obtained by solving the full Navier-Stokes equations using the 5th-order accurate weighted essentially non-oscillatory (WENO) scheme for space discretization and using third-order total-variation-diminishing (TVD) Runge-Kutta scheme for time integration. The linear stability results showed that bluntness has less stabilizing effects on the stability of boundary layers over cones than on flat plates and wedges. The unsteady simulations of the interaction of plane threedimensional acoustic waves with the cone showed that the modulation of wavelength and the generation of instability waves first occurred near the leading edge in the plane where the constant acoustic phase lines are perpendicular to the cone axis. Further downstream, this instability region spreads in the azimuthal direction from this plane.
The objective of this study is to determine whether or not a solid trailing edge is required to produce efficient coupling between sound and instability waves in a shear layer. Instability waves in the shear layer of a subsonic jet, excited externally by a point sound source, were first visualized by using a phase-locked flow visualization technique. Various means were adopted to shield the sound reaching the nozzle lip. It was found that the low frequency sound couples more efficiently at distances downstream of the nozzle exit. To substantiate the findings further, a supersonic screeching jet was tested such that it passed through a small opening in a baffle placed parellel to the exit plane. The measured feedback or screech frequencies, and also the excited flow disturbances, were found to change drastically on traversing the baffle axially. Similar conclusions were reached when a second baffle was placed downstream of the first baffle, and the effects of moving the first baffle on the feedback frequency of sound generated by flow impingement on the second baffle were examined. It is argued that sound waves passing through the mixing layer of a jet can excite flow instability without the benefit of assistance and coupling at the trailing edge.
In this paper we present a theoretical and numerical study of the growth of linear disturbances in the high-Reynolds-number and laminar compressible wake behind a flat plate which is aligned with a uniform stream. No ad hoc assumptions are made as to the nature of the undisturbed flow (in contrast to previous investigations) but instead the theory is developed rationally by use of proper wake-profiles which satisfy the steady equations of motion. The initial growth of near wake perturbation is governed by the compressible Rayleigh equation which is studied analytically for long- and short-waves. These solutions emphasize the asymptotic structures involved and provide a rational basis for a nonlinear development. The evolution of arbitrary wavelength perturbations is addressed numerically and spatial stability solutions are presented that account for the relative importance of the different physical mechanisms present, such as three-dimensionality, increasing Mach numbers enough (subsonic) Mach numbers, there exists a region of absolute instability very close to the trailing-edge with the majority of the wake being convectively unstable. At higher Mach numbers (but still not large-hypersonic) the absolute instability region seems to disappear and the maximum available growth-rates decrease considerably. Three-dimensional perturbations provide the highest spatial growth-rates.
Qualitative features of the inviscid instability characteristics of hypersonic boundary-layer flows over a flat plate are considered. The instability of a viscous hypersonic boundary layer which exists far downstream from the leading edge of the plate. It is shown that the vorticity mode of instability operates on a different lengthscale from that obtained using a Chapman viscosity law. The growth rate predicted by a linear viscosity law is found to overestimate the size of the growth rate. The inviscid instability of the boundary layer near the leading edge interaction zone is discussed focusing on the strong-interaction zone which occurs sufficiently close to the leading edge. The vorticity mode in this regime is found to be unstable.
Observations by the vector electron spectrometer on the ISEE 1 spacecraft are used to directly check the incompressible hydromagnetic stability condition given by Hasegawa (1975), which indicates how stability is influenced by the velocity shear, density ratio, magnetic field, and the direction of the wave vector of the unstable wave mode. The magnetopause is generally found to be stable, by a large margin. In contrast, many cases of marginal stability or instability are found across density transitions in, and at the inner edge of, the boundary layer for wave vectors in plausible directions. It thus appears that the Kelvin-Helmholtz instability is of importance at the inner edge of the magnetospheric boundary layer, as predicted by MHP theory.
The boundary layer receptivity process due to the interaction of three-dimensional slow and fast acoustic disturbances with a blunted flat plate is numerically investigated at a free stream Mach number of 3.5 and at a high Reynolds number of 106/inch. The computations are performed with and without two-dimensional isolated roughness element located near the leading edge. Both the steady and unsteady solutions are obtained by solving the full Navier-Stokes equations using the 5th-order accurate weighted essentially non-oscillatory (WENO) scheme for space discretization and using third-order total-variation-diminishing (TVD) Runge-Kutta scheme for time integration. The simulations showed that the linear instability waves are generated very close to the leading edge. The wavelength of the disturbances inside the boundary layer first increases gradually and becomes longer than the wavelength for the instability waves within a short distance from the leading edge. The wavelength then decreases gradually and merges with the wavelength for the Tollmien_Schlichting wave. The initial amplitudes of the instability waves near the neutral points, the receptivity coefficients, are about 1.20 and 0.07 times the amplitude of the free-stream disturbances for the slow and the fast waves respectively. It was also revealed that small isolated roughness element does not enhance the receptivity process for the given nose bluntness.
The boundary layer receptivity process due to the interaction of three-dimensional slow and fast acoustic disturbances with a blunted flat plate is numerically investigated at a free stream Mach number of 3.5 and at a high Reynolds number of 10(exp 6)/inch. The computations are performed with and without two-dimensional isolated roughness element located near the leading edge. Both the steady and unsteady solutions are obtained by solving the full Navier-Stokes equations using the fifth-order accurate weighted essentially non-oscillatory (WENO) scheme for space discretization and using third-order total-variation-diminishing (TVD) Runge-Kutta scheme for time integration. The simulations showed that the linear instability waves are generated very close to the leading edge. The wavelength of the disturbances inside the boundary layer first increases gradually and becomes longer than the wavelength for the instability waves within a short distance from the leading edge. The wavelength then decreases gradually and merges with the wavelength for the Tollmien-Schlichting wave. The initial amplitudes of the instability waves near the neutral points, the receptivity coefficients, are about 1.20 and 0.07 times the amplitude of the free-stream disturbances for the slow and the fast waves respectively. It was also revealed that small isolated roughness element does not enhance the receptivity process for the given nose bluntness.
The primary focus of this paper is to investigate the effect of rotor tip gap size on how the rotor unsteady tip clearance flow structure changes in a low speed one and half stage axial compressor at near stall operation (for example, where maximum pressure rise is obtained). A Large Eddy Simulation (LES) is applied to calculate the unsteady flow field at this flow condition with both a small and a large tip gaps. The numerically obtained flow fields at the small clearance matches fairly well with the available initial measurements obtained at the Johns Hopkins University with 3-D unsteady PIV in an index-matched test facility which renders the compressor blades and casing optically transparent. With this setup, the unsteady velocity field in the entire flow domain, including the flow inside the tip gap, can be measured. The numerical results are also compared with previously published measurements in a low speed single stage compressor (Maerz et al. [2002]). The current study shows that, with the smaller rotor tip gap, the tip clearance vortex moves to the leading edge plane at near stall operating condition, creating a nearly circumferentially aligned vortex that persists around the entire rotor. On the other hand, with a large tip gap, the clearance vortex stays inside the blade passage at near stall operation. With the large tip gap, flow instability and related large pressure fluctuation at the leading edge are observed in this one and a half stage compressor. Detailed examination of the unsteady flow structure in this compressor stage reveals that the flow instability is due to shed vortices near the leading edge, and not due to a three-dimensional separation vortex originating from the suction side of the blade, which is commonly referred to during a spike-type stall inception. The entire tip clearance flow is highly unsteady. Many vortex structures in the tip clearance flow, including the sheet vortex system near the casing, interact with each other. The core tip clearance vortex, which is formed with the rotor tip gap flows near the leading edge, is also highly unsteady or intermittent due to pressure oscillations near the leading edge and varies from passage to passage. For the current compressor stage, the evidence does not seem to support that a classical vortex breakup occurs in any organized way, even with the large tip gap. Although wakes from the IGV influence the tip clearance flow in the rotor, the major characteristics of rotor tip clearance flows in isolated or single stage rotors are observed in this one and a half stage axial compressor.
An optimization procedure is developed based on the responses of a system to continuous gust inputs. The procedure uses control law transfer functions which have been partially determined by using the relaxed aerodynamic energy approach. The optimization procedure yields a flutter suppression system which minimizes control surface activity in a gust environment. The procedure is applied to wing flutter of a drone aircraft to demonstrate a 44 percent increase in the basic wing flutter dynamic pressure. It is shown that a trailing edge control system suppresses the flutter instability over a wide range of subsonic mach numbers and flight altitudes. Results of this study confirm the effectiveness of the relaxed energy approach.
The radial and vertical structure of the transition zone at the magnetospheric boundary of an aligned rotating neutron star accreting matter from a Keplerian disk are calculated. The results obtained indicate that: (1) the inner edge of the disk is located where the integrated magnetic stress acting on the disk plasma becomes comparable to the integrated material stress associated with its inward radial drift and orbital motion; (2) the stellar magnetic field threads the disk near its inner edge via the Kelvin-Helmholtz instability, turbulent diffusion, and reconnection, producing a broad transition zone between the unperturbed disk flow and corotating magnetosphere; (3) the transition zone consists of two qualitatively different regions, viz., a broad outer transition zone where the motion is Keplerian and a narrow inner zone, or boundary layer, where the departure from Keplerian motion is substantial; (4) the stellar magnetic field is largely but not entirely screened by currents flowing in the boundary layer; and (5) there are no steady-flow solutions for sufficiently fast stellar rotation.
A negative-ion, positive-ion plasma produced by the release of an electron attachment chemical into the F region becomes electrically polarized by collisions with neutrals moving across magnetic field lines. The resulting electric field causes E x B drift of the two ion species and the residual electrons. The cross-field flow of the modified ionosphere is computed using a two-dimensional numerical simulation which includes electron attachment and mutual neutralization chemistry, self-consistent electric fields, and three-species plasma transport. The velocity of the plasma is initially in the direction of the neutral wind because the negative-ion cloud is a Pedersen conductivity enhancement. As the positive and negative ions react, the Pedersen conductivity becomes depressed below the ambient value and the velocity of the plasma reverses direction. A plasma hole remains after the positive and negative ions have mutually neutralized. The E x B gradient drift instability produces irregularities on the upwind edge of the hole.
Modal and nonmodal instability characteristics of cylindrically blunted flat plates with varying leading edge radii are described for Mach 4 and Mach 6 freestream conditions. The selection of leading edge radii and freestream parameters is informed by experimental conditions. The investigation of this 2D problem provides a slow entropy layer swallowing which allows for an isolated development of perturbations seeded upstream within different wall-normal regions of the flow. At both Mach numbers, a decrease in modal instability amplification was seen as the leading edge radius was increased. Nonmodal analysis reveals amplifying perturbations in the boundary layer as well as in the entropy layer. The medium bluntness regime exhibits the strongest amplification of nonmodal disturbances that is nonmonotonic in character. Small amplitude boundary forcing at the plate surface or volumetric forcing at various wall-normal heights was used to account for receptivity effects. While wall forcing effectively induced modal instabilities, only an actuation above the boundary layer captured disturbances that amplify within the entropy layer. The optimal nonmodal theory’s entropy-layer disturbance evolution exhibited outstanding agreement with controlled forcing, including receptivity effects. The evolution of entropy-layer disturbances from the optimal nonmodal theory showed excellent agreement with the results of receptivity to controlled forcing. Therefore, the nonmodal optimal growth analysis may provide a useful as well as efficient technique to identify the complete disturbance spectrum in blunt hypersonic configurations, where both modal and nonmodal disturbances can amplify in the boundary-layer and entropy-layer regions.
Modal and nonmodal instability characteristics of cylindrically blunted flat plates with varying leading edge radii are described for Mach 4 and Mach 6 freestream conditions. The selection of leading edge radii and freestream parameters is informed by experimental conditions. The investigation of this 2D problem provides a slow entropy layer swallowing which allows for an isolated development of perturbations seeded upstream within different wall-normal regions of the flow. At both Mach numbers, a decrease in modal instability amplification was seen as the leading edge radius was increased. Nonmodal analysis reveals amplifying perturbations in the boundary layer as well as in the entropy layer. The medium bluntness regime exhibits the strongest amplification of nonmodal disturbances that is nonmonotonic in character. Small amplitude boundary forcing at the plate surface or volumetric forcing at various wall-normal heights was used to account for receptivity effects. While wall forcing effectively induced modal instabilities, only an actuation above the boundary layer captured disturbances that amplify within the entropy layer. The optimal nonmodal theory’s entropy-layer disturbance evolution exhibited outstanding agreement with controlled forcing, including receptivity effects. The evolution of entropy-layer disturbances from the optimal nonmodal theory showed excellent agreement with the results of receptivity to controlled forcing. Therefore, the nonmodal optimal growth analysis may provide a useful as well as efficient technique to identify the complete disturbance spectrum in blunt hypersonic configurations, where both modal and nonmodal disturbances can amplify in the boundary-layer and entropy-layer regions.
Recent progress in vortex-control applications for alleviating the adverse consequences of three dimensional separation and vortical interactions on slender body/swept wing configurations is reported. Examples include helical separation trip to alleviate the side force due to forebody vortex asymmetry; hinged strakes to avoid vortex breakdown effects; compartmentation of swept leading edge separation to delay the pitch-up instability; under wing vortex trip and vortex trip and vortex flaps for drag reduction at high lift; and an apex-flap trimmer to fully utilize the lift capability of trailing-edge flaps for take off and landing of delta wings. Experimental results on generic wind-tunnel models are presented to illustrate the vortex-management concepts involved and to indicate their potential for enhancing the subsonic aerodynamics of supersonic-cruise type vehicles.
The instability of hypersonic boundary-layer flows over flat plates is considered. The viscosity of the fluid is taken to be governed by Sutherland's law, which gives a much more accurate representation of the temperature dependence of fluid viscosity at hypersonic speeds than Chapman's approximate linear law; although at lower speeds the temperature variation of the mean state is less pronounced so that the Chapman law can be used with some confidence. Attention is focussed on the so-called (vorticity) mode of instability of the viscous hypersonic boundary layer. This is thought to be the fastest growing inviscid disturbance at hypersonic speeds; it is also believed to have an asymptotically larger growth rate than any viscous or centrifugal instability. As a starting point the instability of the hypersonic boundary layer which exists far downstream from the leading edge of the plate is investigated. In this regime the shock that is attached to the leading edge of the plate plays no role, so that the basic boundary layer is non-interactive. It is shown that the vorticity mode of instability of this flow operates on a significantly different lengthscale than that obtained if a Chapman viscosity law is assumed. In particular, it is found that the growth rate predicted by a linear viscosity law overestimates the size of the growth rate by O(M(exp 2). Next, the development of the vorticity mode as the wavenumber decreases is described, and it is shown that acoustic modes emerge when the wavenumber has decreased from it's O(1) initial value to O(M (exp -3/2). Finally, the inviscid instability of the boundary layer near the leading edge in the interaction zone is discussed and particular attention is focussed on the strong interaction region which occurs sufficiently close to the leading edge. It is found that the vorticity mode in this regime is again unstable, and that it is concentrated in the transition layer at the edge of the boundary layer where the temperature adjusts from its large, O(M(exp 2), value in the viscous boundary layer, to its O(1) free stream value. The existence of the shock indirectly, but significantly, influences the instability problem by modifying the basic flow structure in this layer.
A purely growing electrostatic drift instability driven by the electron temperature gradient at the inner edge of the plasma sheet can grow for large enough values of the temperature gradient. The parallel electric field associated with the instability is localized near the magnetic equator. The growth of the drift instability leads to enhanced whistler noise and increased electron pitch angle diffusion. If the current limit is exceeded in the ionosphere while the parallel electric field of the drift instability exists along the field line, rapid electron precipitation (the auroral breakup) can result.
Crossflow instabilities dominate disturbance growth in the leading-edge region of swept wings. Streamwise vortices in a boundary layer strongly influence the behavior of other disturbances. Amplification of crossflow vortices near the leading edge produces a residual spanwise nonuniformity in the mid-chord regions where Tollmien-Schlichting (T-S) waves are strongly amplified. Should the T-S wave undergo double-exponential growth because of this effect, the usual transition prediction methods would fail. The crossflow/Tollmien-Schlichting wave interaction was modeled as a secondary instability. The effects of suction are included, and different stability criteria are examined. The results are applied to laminar flow control wings characteristic of energy-efficient aircraft designs.