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Hultgren, Lennart S.

Publications and source records attributed to Hultgren, Lennart S..

54 records · Page 3

Computation of Jet Screech Noise

The space-time conservation-element and solution-element method is employed to numerically study the near-field screech-tone noise of a typical underexpanded circular jet issuing from a sonic nozzle. Both axisymmetric and fully three-dimensional computations are carried out. The self-sustained feedback loop is properly simulated. The computed shock-cell structure, acoustic wave length, screech-tone frequency, and sound-pressure levels are in good agreement with existing experimental results.

Hultgren, Lennart S.↗

Boundary-Layer Separation Control under Low-Pressure Turbine Airfoil Conditions using Glow-Discharge Plasma Actuators

Modem low-pressure turbines, in general, utilize highly loaded airfoils in an effort to improve efficiency and to lower the number of airfoils needed. Typically, the airfoil boundary layers are turbulent and fully attached at takeoff conditions, whereas a substantial fraction of the boundary layers on the airfoils may be transitional at cruise conditions due to the change of density with altitude. The strong adverse pressure gradients on the suction side of these airfoils can lead to boundary-layer separation at the latter low Reynolds number conditions. Large separation bubbles, particularly those which fail to reattach, cause a significant degradation of engine efficiency. A component efficiency drop of the order 2% may occur between takeoff and cruise conditions for large commercial transport engines and could be as large as 7% for smaller engines at higher altitude. An efficient means of of separation elimination/reduction is, therefore, crucial to improved turbine design. Because the large change in the Reynolds number from takeoff to cruise leads to a distinct change in the airfoil flow physics, a separation control strategy intended for cruise conditions will need to be carefully constructed so as to incur minimum impact/penalty at takeoff. A complicating factor, but also a potential advantage in the quest for an efficient strategy, is the intricate interplay between separation and transition for the situation at hand. Volino gives a comprehensive discussion of several recent studies on transition and separation under low-pressure-turbine conditions, among them one in the present facility. Transition may begin before or after separation, depending on the Reynolds number and other flow conditions. If the transition occurs early in the boundary layer then separation may be reduced or completely eliminated. Transition in the shear layer of a separation bubble can lead to rapid reattachment. This suggests using control mechanisms to trigger and enhance early transition. Gad-el-Hak provides a review of various techniques for flow control in general and Volino discusses recent studies on separation control under low-pressure-turbine conditions utilizing passive as well as active devices. As pointed out by Volino, passive devices optimized for separation control at low Reynolds numbers tend to increase losses at high Reynolds numbers, Active devices have the attractive feature that they can be utilized only in operational regimes where they are needed and when turned off would not affect the flow. The focus in the present paper is an experimental Separation is induced on a flat plate installed in a closed-circuit wind tunnel by a shaped insert on the opposite wall. The flow conditions represent flow over the suction surface of a modem low-pressure-turbine airfoil ('Pak-B'). The Reynolds number, based on wetted plate length and nominal exit velocity, is varied from 50,000 to 300,000, covering cruise to takeoff conditions. Low (0.2%) and high (2.5%) Gee-stream turbulence intensities are set using passive grids. A spanwise-oriented phased-plasma-array actuator, fabricated on a printed circuit board, is surface- flush-mounted upstream of the separation point and can provide forcing in a wide frequency range. Static surface pressure measurements and hot-wire anemometry of the base and controlled flows are performed and indicate that the glow-discharge plasma actuator is an effective device for separation control. of active separation control using glow discharge plasma actuators.

Hultgren, Lennart S.↗

Computing Jet Screech: a Complex Aeroacoustic Feedback System

The space-time conservation-element and solution-element method is employed to numerically study the near-field axisymmetric screech-tone noise of a typical underexpanded circular jet issuing from a sonic nozzle. For the computed case, corresponding to a fully expanded Mach number of 1.19, the self-sustained feedback loop is established without artificial means. The computed shock-cell structure, acoustic wave length, screech tone frequency, and sound pressure levels are in good agreement with existing experimental results

Loh, Ching Y.↗

Experimental Investigation of Separated and Transitional Boundary Layers Under Low-Pressure Turbine Airfoil Conditions

Modern low-pressure turbine airfoils are subject to increasingly stronger pressure gradients as designers impose higher loading in an effort to improve efficiency and to reduce part count. The adverse pressure gradients on the suction side of these airfoils can lead to boundary-layer separation, particularly under cruise conditions. Separation bubbles, notably those which fail to reattach, can result in a significant degradation of engine efficiency. Accurate prediction of separation and reattachment is hence crucial to improved turbine design. This requires an improved understanding of the transition flow physics. Transition may begin before or after separation, depending on the Reynolds number and other flow conditions, has a strong influence on subsequent reattachment, and may even eliminate separation. Further complicating the problem are the high free-stream turbulence levels in a real engine environment, the strong pressure gradients along the airfoils, the curvature of the airfoils, and the unsteadiness associated with wake passing from upstream stages. Because of the complicated flow situation, transition in these devices can take many paths that can coexist, vary in importance, and possibly also interact, at different locations and instances in time. The present work was carried out in an attempt to systematically sort out some of these issues. Detailed velocity measurements were made along a flat plate subject to the same nominal dimensionless pressure gradient as the suction side of a modern low-pressure turbine airfoil ('Pak-B'). The Reynolds number based on wetted plate length and nominal exit velocity, Re, was varied from 50;000 to 300; 000, covering cruise to takeoff conditions. Low, 0.2%, and high, 7%, inlet free-stream turbulence intensities were set using passive grids. These turbulence levels correspond to about 0.2% and 2.5% turbulence intensity in the test section when normalized with the exit velocity. The Reynolds number and free-stream turbulence level do not have a significant effect on the location of boundary-layer separation unless they are high enough to induce transition upstream of separation. The location and extent of the transition zone, in contrast, depend strongly on Re and TI. The beginning of reattachment closely follows the onset of transition. Under low free-stream turbulence conditions the boundary layer is laminar at separation and then begins to exhibit fluctuations in a finite frequency band in the shear layer over the separation bubble. These fluctuations are due to instability waves. The fluctuations grow in magnitude, higher harmonics are generated, and finally lead to a breakdown to turbulence. Transition begins in the shear layer, but quickly spreads to the near wall region and causes the boundary layer to reattach. The transition is rapid and the resulting turbulence contains a full range of high and low frequencies. Under high free-stream turbulence conditions, slowly growing low-frequency fluctuations are induced in the pretransitional boundary layer by the free-stream. The separation bubbles are considerably thinner than in the low TI cases, resulting in thinner boundary layers at the end of the test wall. At Re=50,000 and 100,000, the pre-transitional boundary layer separates at about the same location as in the low TI cases. Transition occurs through a bypass mode, begins upstream of the corresponding low-TI location, and proceeds in a manner similar to that of an attached boundary layer. Under high TI at Re=200,000 and 300,000, transition begins before separation. The boundary layer may separate, but if it does the separation bubble is very short and does not significantly affect the downstream development of the boundary layer. A comparison is made to previous work in a simulated cascade.

Hultgren, Lennart S.↗

Near Field Screech Noise Computation for an Underexpanded Supersonic Jet by the CE/SE Method

The space-time conservation element and solution element (CE/SE) method is employed to numerically study the near-field axisymmetric screech-tone noise of a typical underexpanded circular jet issuing from a sonic nozzle. For the computed cases, corresponding to fully expanded Mach numbers of 1.10, 1.15 and 1.19, the self-sustained feedback loop is automatically established. The computed shock-cell structure, acoustic wave length, screech tone frequencies, and sound pressure levels are in good agreement with experimental results.

Loh, Ching Y.↗

Predictions of Separated and Transitional Boundary Layers Under Low-Pressure Turbine Airfoil Conditions Using an Intermittency Transport Equation

A new transport equation for the intermittency factor was proposed to predict separated and transitional boundary layers under low-pressure turbine airfoil conditions. The intermittent behavior of the transitional flows is taken into account and incorporated into computations by modifying the eddy viscosity, mu(sub t), with the intermittency factor, gamma. Turbulent quantities are predicted by using Menter's two-equation turbulence model (SST). The intermittency factor is obtained from a transport equation model, which not only can reproduce the experimentally observed streamwise variation of the intermittency in the transition zone, but also can provide a realistic cross-stream variation of the intermittency profile. In this paper, the intermittency model is used to predict a recent separated and transitional boundary layer experiment under low pressure turbine airfoil conditions. The experiment provides detailed measurements of velocity, turbulent kinetic energy and intermittency profiles for a number of Reynolds numbers and freestream turbulent intensity conditions and is suitable for validation purposes. Detailed comparisons of computational results with experimental data are presented and good agreements between the experiments and predictions are obtained.

Suzen, Y. Bora↗

Aeroacoustics Computation for Nearly Fully Expanded Supersonic Jets Using the CE/SE Method

In this paper, the space-time conservation element solution element (CE/SE) method is tested in the classical axisymmetric jet instability problem, rendering good agreement with the linear theory. The CE/SE method is then applied to numerical simulations of several nearly fully expanded axisymmetric jet flows and their noise fields and qualitative agreement with available experimental and theoretical results is demonstrated.

Loh, Ching Y.↗

Noise Computation of a Shock-Containing Supersonic Axisymmetric Jet by the CE/SE Method

The space-time conservation element solution element (CE/SE) method is employed to numerically study the near-field of a typical under-expanded jet. For the computed case-a circular jet with Mach number M(j) = 1.19-the shock-cell structure is in good agreement with experimental results. The computed noise field is in general agreement with the experiment, although further work is needed to properly close the screech feedback loop.

Loh, Ching Y.↗

Direct calculations of waves in fluid flows using high-order compact difference scheme

The solution of the unsteady Euler equations by a sixth-order compact difference scheme combined with a fourth-order Runge-Kutta method is investigated. Closed-form expression for the amplification factors and their corresponding dispersion correlations are obtained by Fourier analysis of the fully discretized, two-dimensional Euler equations. The numerical dissipation, dispersion, and anisotropic effects are assessed. It is found that the Courant-Friedrichs-Lewy (CFL) limit for stable calculations is about 0.8. For a CFL number equal to 0.6, the smallest wavelength which is resolved without numerical damping is about six - eight grid nodes. For phase speeds corresponding to acoustic waves, the corresponding time period is resolved by about 200 - 300 time steps. Three numerical examples of waves in compressible flow are included: (1) sound propagation in a duct with linear shear, (2) linear wave growth in a compressible free shear layer, and (3) vortex pairing in a compressible free shear layer perturbed at two frequencies.

Yu, Sheng-Tao↗

Interaction of Oblique Instability Waves with a Nonlinear Plane Wave

This paper is concerned with the downstream evolution of a resonant triad of initially non-interacting linear Instability waves in a boundary layer with a weak adverse pressure gradient. The triad consists of a two-dimensional fundamental mode and a pair of equal-amplitude oblique modes that form a subharmonic standing wave in the spanwise direction. The growth rates are small and there is a well-defined common critical layer for these waves. As in Goldstein & Lee (1992), the wave interaction takes place entirely within this critical layer and is initially of the parametric-resonance type. This enhances the spatial growth rate of the subharmonic but does not affect that of the fundamental. However, in contrast to Goldstein & Lee (1992), the initial subharmonic amplitude is assumed to be small enough so that the fundamental can become nonlinear within its own critical layer before it is affected by the subharmonic. The subharmonic evolution is then dominated by the parametric-resonance effects and occurs on a much shorter streamwise scale than that of the fundamental. The subharmonic amplitude continues to increase during this parametric-resonance stage - even as the growth rate of the fundamental approaches zero - and the subharmonic eventually becomes large enough to influence the fundamental which causes both waves to evolve on the same shorter streamwise scale.

Wundrow, David W.↗

Direct calculations of waves in fluid flows using a high-order compact difference scheme

The solution of the unsteady Euler equations by a sixth-order compact difference scheme combined with a fourth-order Runge-Kutta method is investigated. Closed-form expressions for the amplification factors and their corresponding dispersion correlations are obtained by Fourier analysis of the fully discretized, two-dimensional Euler equations, and the numerical dissipation, dispersion, and anisotropic effects are assessed. It is found that the CFL limit for stable calculations is about 0.8. For a CFL number equal to 0.6, the smallest wavelength which is resolved without numerical damping is about 6 to 8 grid nodes. For phase speeds corresponding to acoustic waves, the corresponding time period is resolved by about 200 to 300 time steps. Three numerical examples of waves in compressible flow are included.

Yu, Sheng-Tao↗

Nonlinear spatial equilibration of an externally excited instability wave in a free shear layer

A two-dimensional disturbance evolving from a strictly linear, finite-growth-rate instability wave, with nonlinear effects first becoming important in the critical layer is considered. The analysis is carried out for a general weakly nonparallel mean flow using matched asymptotic expansions. The flow in the critical layer is governed by a nonlinear vorticity equation which includes a spatial-evolution term. As in Goldstein and Hultgren (1988), the critical layer ages into a quasi-equilibrium one and the initial exponential growth of the instability wave is converted into a weak algebraic growth during the roll-up process. This leads to a next stage of evolution where the instability-wave growth is simultaneously affected by mean-flow divergence and nonlinear critical-layer effects and is eventually converted to decay. Expansions for the various streamwise regions of the flow are combined into a single composite formula accounting for both shear-layer spreading and nonlinear critical-layer effects and good agreement with the experimental results of Thomas and Chu (1989) and Freymuth (1966) is demonstrated.

Hultgren, Lennart S.↗

Boundary-layer receptivity to long-wave free-stream disturbances

The present treatment of the early stages of boundary layer-transition phenomena, where the unsteady motion is of small amplitude and can be accordingly treated as a small perturbation of an appropriate mean flow, elaborates the Heinrich et al. (1988) discussion of the role played by this 'receptivity' stage: in which the unsteady flow exhibits the same harmonic time-dependence as the externally-imposed forcing. Freestream disturbance wavelengths are noted to often be much longer than the Tollmien-Schlichting wavelength. Attention is given to the variety of wavelength-reduction mechanisms able to couple the long-wavelength, freestream disturbances to the comparatively short Tollmien-Schlichting waves.

Goldstein, M. E.↗

Nonlinear spatial evolution of an externally excited instability wave in a free shear layer

This paper considers a disturbance evolving from a strictly linear finite-growth-rate instability wave, with nonlinear effects first becoming important in the critical layer. By incorporating viscous effects into the nonlinear critical-layer analysis of Goldstein and Leib (1988), it was possible to demonstrate how an initially linear instability wave evolves as it propagates downstream and how the viscous effects eventually become important, even when the viscosity is very small, due to continually decreasing scales generated by the nonlinear effects.

Goldstein, M. E.↗

Stability of swirling gas flows

The stability of inviscid swirling gas flows to small nonaxisymmetric perturbations is considered. For small Brunt-Vaisala frequencies, the problem reduces to the classical Sturm-Liouville form and the oscillation theorem can be applied. The resulting necessary and sufficient stability condition is compared to various criteria in the literature and a limited numerical study of isothermal rigidly rotating Poiseuille flow. For given azimuthal and axial wavenumbers, it is found numerically that the higher inertial modes become unstable for successively lower Rossby numbers and that this sequence of critical values approaches the theoretical value from above.

Hultgren, Lennart S.↗

Absolute instability of the Gaussian wake profile

Linear parallel-flow stability theory has been used to investigate the effect of viscosity on the local absolute instability of a family of wake profiles with a Gaussian velocity distribution. The type of local instability, i.e., convective or absolute, is determined by the location of a branch-point singularity with zero group velocity of the complex dispersion relation for the instability waves. The effects of viscosity were found to be weak for values of the wake Reynolds number, based on the center-line velocity defect and the wake half-width, larger than about 400. Absolute instability occurs only for sufficiently large values of the center-line wake defect. The critical value of this parameter increases with decreasing wake Reynolds number, thereby indicating a shrinking region of absolute instability with decreasing wake Reynolds number. If backflow is not allowed, absolute instability does not occur for wake Reynolds numbers smaller than about 38.

Hultgren, Lennart S.↗

Higher eigenmodes in the Blasius boundary-layer stability problem

The higher spatial-stability eigenmodes for the Blasius boundary layer are examined by using asymptotic theory, and an infinite number of modes are found. The asymptotic results are shown to be in close agreement with results from a direct numerical solution of the Orr-Sommerfeld problem. The asymptotic theory would therefore provide an efficient tool in exploratory searches for the eigenvalues.

Hultgren, Lennart S.↗

A note on the generation of Tollmien-Schlichting waves by sudden surface-curvature change

This note is primarily concerned with the generation of spatially growing Tollmien-Schlichting waves by the interaction of very long-wavelength free-stream disturbances with a discontinuity in the curvature of a bounding surface (whose slope may or may not be continuous). The theory is combined with a numerical solution of the local Orr-Sommerfeld equation, and the result is used to predict the Tollmien-Schlichting amplitude in a relevant experiment carried out by Leehey and Shapiro (1980). The calculated results are in satisfactory agreement with their observations.

Goldstein, M. E.↗