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At least 397 records · Page 22

Nonlinear interaction between the sinuous and varicose instability modes in a plane wake

The nonlinear interaction between sinuous and varicose instability modes in a plane wake is examined in the nonlinear-nonequilibrium critical layer regime. Equations governing the evolution of the instability wave amplitudes and critical layer vorticity distributions are derived. Numerical solutions for these equations are obtained for a number of wake defects and initial amplitude ratios. The results show that the primary effects of the nonlinear interaction are the suppression of the varicose mode and the downstream shift of the peak of the sinuous mode.

Leib, S. J.↗

Boundary-layer receptivity and laminar-flow airfoil design

Boundary-layer receptivity examines the way in which external disturbances generate instability waves in boundary layers. Receptivity theory is complementary to stability theory, which studies the evolution of disturbances that are already present in the boundary layer. A transition prediction method which combines receptivity with linear stability theory would directly account for the influence of free-stream disturbances and also consider the characteristics of the boundary layer upstream of the neutral stability point. The current e sup N transition prediction methods require empirical correlations for the influence of environmental disturbances, and totally ignore the boundary layer characteristics upstream of the neutral stability point. The regions where boundary-layer receptivity occurs can be separated into two classes, one near the leading edges and the other at the downstream points where the boundary layer undergoes rapid streamwise adjustments. Analyses were developed for both types of regions, and parametric studies which examine the relative importance of different mechanisms were carried out. The work presented here has focused on the low Mach number case. Extensions to high subsonic and supersonic conditions are presently underway.

Kerschen, Edward J.↗

A review of instability and noise propagation in supersonic flows

Originally analytical and numerical models were to be developed for noise production in supersonic jets, wakes and free shear layers. While the effort was concentrated initially on these aspects, other topics were also pursued, most were of interest to the Jet Noise Group of the Aeroacoustics Branch. An overview is given of subjects reviewed and the investigations that were carried out. A significant effort was devoted to numerically predicting the flow field of a turbulent supersonic wall jet. This information is necessary for computing the pressure in the far field. The wall jet was selected because it represents a generic flow that can be associated with plug nozzle in supersonic engines. It combines the characteristic of a boundary layer with that of a free shear flow. The spatially evolving flow obtained using Dash's code would form the input for the stability analysis program. This analysis would determine the large scale instability wave within the flow. The far field pressure can be computed from the shape of the evolving large scale structure by asymptotic methods. Flow characteristics obtained from a program that analyses the turbulent downstream supersonic flow in a nozzle are described and compared with experimental results.

Daudpota, Q. Isa↗

Shear stabilization of the capillary breakup of a cylindrical interface

A cylindrical interface containing a viscous liquid set into axial motion is subject to a capillary and to a surface-wave instability. Clues from previous studies suggest that, even though both mechanisms separately are destabilizing, under certain circumstances their mutual interaction can lead to a stable interface; shear can stabilize capillary breakup. Here, an axial flow through an annular cross section bounded on the inside by a rigid rod and on the outside by a deformable interface is considered. The competition between the two mechanisms is studied through the temporal growth of infinitesimal axisymmetric and nonaxisymmetric disturbances. This examination of temporal stability shows that, indeed, for geometries corresponding to thin annular layers both instabilities can be completely suppressed (disturbances of all wavelengths decay).

Russo, Mathew J.↗

Phase development and its role on subharmonic control

The conditions for resonance interaction between two instability waves in an axisymmetric jet were investigated. Considerations of the energy equation of the wave resulting from the interaction indicate that the phase angle between the wave-induced stresses and the wave-induced strains plays a crucial role in the resonance interaction. This fact is demonstrated experimentally by exciting a jet at fundamental and subharmonic frequencies. The phase angle between the waves' stresses and strains was varied by varying the initial phase-difference between the two excitation waves. The subharmonic resonance was found to be highly dependent on this angle. Favorable agreement was found between the phase angles predicted by a nonlinear theory and the measured ones. The theory is used to explain the subharmonic's resonance in terms of the phase-angles.

Mankbadi, Reda R.↗

Atomization modeling in a multiphase flow environment and comparison with experiments

An atomization model based on Reitz's instability wave analysis has been implemented into the ARICC3D multiphase CFD combustion code. Preliminary test runs with cold non-evaporating liquid jet and coaxial gas-liquid atomization cases appeared to have verified basic performance of the model, generating realistic-looking sprays. Furthermore, the extended liquid jet is explicitly resolved, and predicted jet lengths agree well with classical correlations. Fair agreement with test data is obtained for predicted spray tip penetrations and liquid mass flux radial distributions, with obvious room for improvement. Some numerical problems also appear to have resulted with the current implementation when low gas Mach number and high liquid velocities are involved.

Liang, P. Y.↗

On the receptivity and non-parallel stability of travelling disturbances in rotating disk flow

The generation and evolution of small amplitude wavelength traveling disturbances in rotating disk flow is discussed. The steady rotational speed of the disk is perturbed so as to introduce high frequency oscillations in the flow field. Secondly, surface imperfections are introduced on the disk such as roughness elements. The interaction of these two disturbances will generate the instability waves whose evolution is governed by parabolic partial differential equations that are solved numerically. For the class of disturbances considered (wavelength on the order of Reynolds number), it is found that eigensolutions exist which decay or grow algebraically in the radial direction. However, these solutions grow only for frequencies larger than 4.58 times the steady rotational speed of the disk. The computed receptivity coefficient shows that there is an optimum size of roughness for which these modes are excited the most. The width of these roughness elements in the radial direction is about .1 r(sub 0) where r(sub 0) is the radial location of the roughness. It is also found that the receptivity coefficient is larger for a negative spanwise wavenumber than for a positive one. Typical wave angles found for these disturbances are about -26 degrees.

Balakumar, P.↗

Leading-edge receptivity for blunt-nose bodies

This research program investigates boundary-layer receptivity in the leading-edge region for bodies with blunt leading edges. Receptivity theory provides the link between the unsteady distrubance environment in the free stream and the initial amplitudes of the instability waves in the boundary layer. This is a critical problem which must be addressed in order to develop more accurate prediction methods for boundary-layer transition. The first phase of this project examines the effects of leading-edge bluntness and aerodynamic loading for low Mach number flows. In the second phase of the project, the investigation is extended to supersonic Mach numbers. Singular perturbation techniques are utilized to develop an asymptotic theory for high Reynolds numbers. In the first year, the asymptotic theory was developed for leading-edge receptivity in low Mach number flows. The case of a parabolic nose is considered. Substantial progress was made on the Navier-Sotkes computations. Analytical solutions for the steady and unsteady potential flow fields were incorporated into the code, greatly expanding the types of free-stream disturbances that can be considered while also significantly reducing the the computational requirements. The time-stepping algorithm was modified so that the potential flow perturbations induced by the unsteady pressure field are directly introduced throughout the computational domain, avoiding an artificial 'numerical diffusion' of these from the outer boundary. In addition, the start-up process was modified by introducing the transient Stokes wave solution into the downstream boundary conditions.

Kerschen, Edward J.↗

Resonant triad in boundary-layer stability. Part 1: Fully nonlinear interaction

A first principles theory is developed to study the nonlinear spatial evolution of a near-resonance triad of instability waves in boundary layer transition. This triad consists of a plane wave at fundamental frequency and a pair of symmetrical, oblique waves at the subharmonic frequency. A low frequency, high Reynolds number asymptotic scaling leads to a distinct critical layer where nonlinearity first becomes important; the development of the triad's waves is determined by the critical layer's nonlinear, viscous dynamics. The resulting theory is fully nonlinear in that all nonlinearly generated oscillatory and nonoscillatory components are accounted for. The presence of the plane wave initially causes exponential of exponential growth of the oblique waves. However, the plane wave continues to follow the linear theory, even when the oblique waves' amplitude attains the same order of magnitude as that of the plane wave. A fully interactive stage then comes into effect when the oblique waves exceed a certain level compared to that of the plane wave. The oblique waves react back on the fundamental, slowing its growth rate. The oblique waves' saturation results from their self-interaction - a mechanism that does not require the presence of the plane wave. The oblique waves' saturation level is independent of their initial level, but decreases as the obliqueness angle increases.

Mankbadi, Reda R.↗

Resonant Triad in Boundary-Layer Stability: Composite Solution and Comparison with Observations - Part 2

Here, numerical results are computed from an asymptotic near-resonance triad analysis. The analysis considers a resonant triad of instability waves consisting of a plane fundamental wave and a pair of symmetrical oblique subharmonic waves. The relevant scaling ensures that nonlinearity is confined to a distinct critical layer. The analysis is first used to form a composite solution that accounts for both the flow divergence and nonlinear effects. It is shown that the backreaction on the plane Tollmien Schlichting (TS) fundamental wave, although fully accounted for, is of little significance. The observed enhancement at the fundamental frequency disturbance is not in the plane TS wave, but is caused by nonlinearly generated waves at the fundamental frequency that result from nonlinear interactions in the critical layer. The saturation of the oblique waves is caused by their self-interaction. The nonlinear phase-locking phenomenon, the location of resonance with respect to the neutral stability curve, low frequency effects, detuning in the streamwise wave numbers, and nonlinear distortion of the mode shapes are discussed. Nonlinearity modifies the initially two dimensional Blasius profile into a fuller one with spanwise periodicity. The interactions at a wide range of unstable spanwise wave numbers are considered, and the existence of a preferred spanwise wave number is explained by means of the vorticity distribution in the critical layer. Besides presenting novel features of the phenomena and explaining the delicate mechanisms of the interactions, the results of the theory are in excellent agreement with experimental and numerical observations for all stages of the development and for various input parameters.

Mankbadi, Reda R.↗

Boundary layer receptivity to unsteady free-stream pressure gradients

A linear triple-deck theory is applied to an examination of the response of a boundary layer to short-scale variations in an unsteady free-stream disturbance field. Two-dimensional incompressible flows are considered, and a locally-parallel Blasius mean flow is assumed. A simple pulsating pressure source and a traveling pressure field in the free-stream are modeled by introducing appropriate pressure sources in the upper deck of the triple-deck structure. The modification in unsteady thickness is obtained for these cases, the results are related to the Tollmien-Schlichting instability wave, and the generation of unstable Tollmien-Schlichting waves for both experiments modeled is confirmed.

Heinrich, Roland A. E.↗

Nonlinear evolution of subsonic and supersonic disturbances on a compressible free shear layer

The effects of a nonlinear-nonequilibrium-viscous critical layer on the spatial evolution of subsonic and supersonic instability modes on a compressible free shear layer is considered. It is shown that the instability wave amplitude is governed by an integrodifferential equation with cubic-type nonlinearity. Numerical and asymptotic solutions to this equation show that the amplitude either ends in a singularity at a finite downstream distance or reaches an equilibrium value, depending on the Prandtl number, viscosity law, viscous parameter and a real parameter which is determined by the linear inviscid stability theory. A necessary condition for the existence of the equilibrium solution is derived, and whether or not this condition is met is determined numerically for a wide range of physical parameters including both subsonic and supersonic disturbances. it is found that no equilibrium solution exists for the subsonic modes unless the temperature ratio of the low-to-high-speed streams exceeds a critical value, while equilibrium solutions for the most rapidly growing supersonic mode exist over most of the parameter range examined.

Leib, S. J.↗

On spatial instability of a swirling jet - Theory and experiment

The spatial instability of a swirling jet is investigated both experimentally and theoretically. A hydrodynamic stability analysis is applied to an inviscid incompressible top-hat jet, with a swirl distribution of solid-body rotation and free vortex in and outside the vortex core, respectively. Both plane and helical instability modes are examined. It is found that the top-hat jet with swirl distribution of Rankine vortex type is unstable in all the modes studied. The higher the positive helicity, the less spatially unstable the jet behavior; the higher the negative helicity, the more spatially unstable this behavior becomes. A comparison is made between theoretical results and experimental data on a low-intensity swirling jet. The trend of the initial growth of the instability waves in the near field is captured.

Wu, C.↗

Noise from turbulent shear flows

The generation of sound in turbulent shear flows with high Reynolds numbers is discussed. Solid surface effects, representation of incident turbulence, sound generation and the role of instability waves, sound generation by turbulence interacting with itself (the jet noise problem), compressible Rayleigh equations, sound generation from streamwise variations in mean flow, complex turbulent flows, and supersonic flows are among the topics discussed.

Goldstein, M. E.↗

On the mechanism of turbulence suppression in free shear flows under acoustic excitation

Acoustic excitation at certain high frequencies has been known to suppress large amplitude fluctuations otherwise occurring naturally in various free shear flows. The phenomenon has been observed in flows with initially laminar or transitional boundary layers. An experimental investigation is conducted to consider two possibilities in regards to the mechanism of the effect. (1) The natural shear layer is self excited by the instability waves already developed in the upstream boundary layer. This is overridden when the shear layer is excited at its maximally unstable mode, causing the observed decrease in the intensities downstream. (2) The upstream boundary layer is in a transitional or buffeted laminar state, characterized by large amplitude unsteady fluctuations, which force the large fluctuations downstream. Excitation trips the upstream boundary layer to full turbulence, reduces the unsteady fluctuations, and thus causes the observed suppression of the intensities throughout the flowfield. The present experimental results refute either of these possibilities to be the general mechanism of the effect.

Zaman, K. B. M. Q.↗

Leading-edge receptivity to a vortical freestream disturbance: A numerical analysis

The receptivity to freestream vorticity of the boundary layer over a flat plate with an elliptic leading edge is investigated numerically. The flow is simulated by solving the incompressible Navier-Stokes system in general curvilinear coordinates with the vorticity and stream function as dependent variables. A finite-difference scheme which is second-order accurate in both space and time is used. As a first step, the steady basic-state solution is computed. Then a small amplitude vortical disturbance is introduced at the upstream boundary and the governing equations are solved time-accurately to evaluate the spatial and temporal growth of the perturbations leading to instability waves (Tollmien-Schlichting waves) inside the boundary layer. Preliminary results for a symmetric, 2-D disturbance reveal the presence of Tollmien-Schlichting waves aft of the flat-plate/ellipse juncture.

Buter, Thomas A.↗

Leading-edge receptivity for blunt-nose bodies

Boundary-layer receptivity in the leading edge region for bodies with blunt leading edges is investigated in this research program. Receptivity theory provides the link between the unsteady disturbance environment in the freestream and the initial amplitudes of instability waves in the boundary layer. This is a critical problem which must be addressed in order to develop more accurate prediction methods for boundary-layer transition.

Hammerton, P. W.↗

High speed transition prediction

The main objective of this work period was to develop, acquire and apply state-of-the-art tools for the prediction of transition at high speeds at NASA Ames. Although various stability codes as well as basic state codes were acquired, the development of a new Parabolized Stability Equation (PSE) code was minimal. The time that was initially allocated for development was used on other tasks, in particular for the Leading Edge Suction problem, in acquiring proficiency in various graphics tools, and in applying these tools to evaluate various Navier-Stokes and Euler solutions. The second objective of this work period was to attend the Transition and Turbulence Workshop at NASA Langley in July and August, 1991. A report on the Workshop follows. From July 8, 1991 to August 2, 1991, the author participated in the Transition and Turbulence Workshop at NASA Langley. For purposes of interest here, analysis can be said to consist of solving simplified governing equations by various analytical methods, such as asymptotic methods, or by use of very meager computer resources. From the composition of the various groups at the Workshop, it can be seen that analytical methods are generally more popular in Great Britain than they are in the U.S., possibly due to historical factors and the lack of computer resources. Experimenters at the Workshop were mostly concerned with subsonic flows, and a number of demonstrations were provided, among which were a hot-wire experiment to probe the boundary layer on a rotating disc, a hot-wire rake to map a free shear layer behind a cylinder, and the use of heating strips on a flat plate to control instability waves and consequent transition. A highpoint of the demonstrations was the opportunity to observe the rather noisy 'quiet' supersonic pilot tunnel in operation.

Gasperas, Gediminis↗