Investigations of stability and transition in rotating boundary layers.
Rotating Ekman boundary layer stability and transition for two-dimensional roll vortices superimposed upon basic boundary layer flow
BOUNDARY LAYER TRANSITION↗
SEARCH · Engineering Papers
Results for “Stability boundary”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Turbine Engine Stability/Instability With Rub Forces Axisymmetric Rotor-Support Stiffness
The stability/instability condition of a turbine rotor with axisymmetric supports is determined in the presence of gyroscopic loads and rub-induced destabilizing forces. A modal representation of the turbine engine is used, with one mode in each of the vertical and horizontal planes. The use of non-spinning rotor modes permits an explicit treatment of gyroscopic effects. The two linearized modal equations of motion of a rotor with axisymmetric supports are reduced to a single equation in a complex variable. The resulting eigenvalues yield explicit expressions at the stability boundary, for the whirl frequency as well as the required damping for stability in the presence of the available rub-induced destabilization. Conversely, the allowable destabilization in the presence of the available damping is also given.
Gallardo, Vicente↗
Improving Tiltrotor Whirl-Mode Stability with Rotor Design Variations
Further increases in tiltrotor speeds are limited by coupled wing/rotor whirl-mode aeroelastic instability. Increased power, thrust, and rotor efficiency are not enough: the whirl-mode stability boundary must also be improved. With current technology, very stiff, thick wings of limited aspect ratio are essential to meet the stability requirements, which severely limits cruise efficiency and maximum speed. Larger and more efficient tiltrotors will need longer and lighter wings, for which whirl-mode flutter is a serious design issue. Numerous approaches to improving the whirl-mode airspeed boundary have been investigated, including tailored stiffness wings, active stability augmentation, variable geometry rotors, highly swept tips, and at one extreme, folding rotors. The research reported herein began with the much simpler approach of adjusting the chordwise positions of the rotor blade aerodynamic center and center of gravity, effected by offsetting the airfoil quarter chord or structural mass with respect to the elastic axis. The research was recently extended to include variations in blade sweep, control system stiffness, and pitch-flap coupling (delta(sub 3)). As an introduction to the subject, and to establish a baseline against which to measure stability improvements, this report will first summarize results. The paper will then discuss more advanced studies of swept blades and control-system modifications.
Acree, C. W., Jr.↗
On the Stability of Three-Dimensional Boundary Layers: Linear and Nonlinear Stability - Part 1
The primary stability of incompressible three-dimensional boundary layers is investigated using the Parabolized Stability Equations (PSE). We compute the evolution of stationary and traveling disturbances in the linear and nonlinear region prior to transition. As model problems, we choose Swept Hiemenz Flow and the DLR Transition Experiment. The primary stability results for Swept Hiemenz Flow agree very well with computations by Malik et al. For the DLR Experiment, the mean flow profiles are obtained by solving the boundary layer equations for the measured pressure distribution. Both linear and nonlinear results show very good agreement with the experiment.
Janke, Erik↗
Effects of Rotor Design Variations on Tiltrotor Whirl-Mode Stability
Further increases in tiltrotor speeds are limited by coupled wing/rotor whirl-mode aeroelastic instability. Increased power, thrust, and efficiency are not enough: the whirl-mode stability boundary must also be improved. With current technology, very stiff, thick wings of limited aspect ratio are essential to meet the stability requirements, which severely limits cruise efficiency and maximum speed. Larger and more efficient tiltrotors will need longer and lighter wings, for which whirl-mode flutter is a serious design issue. Numerous approaches to improving the whirl-mode airspeed boundary have been investigated, typically focusing on wing design, active stability augmentation, and variable geometry rotors. The research reported herein applies the much simpler approach of sweeping the outboard blade sections. The effects-of control-system stiffness were also studied. Reference covers the first phase of the current research and discusses the evolution of the concept.
Acree, C. W., Jr.↗
Nonlinear dynamics near the stability margin in rotating pipe flow
The nonlinear evolution of marginally unstable wave packets in rotating pipe flow is studied. These flows depend on two control parameters, which may be taken to be the axial Reynolds number R and a Rossby number, q. Marginal stability is realized on a curve in the (R, q)-plane, and the entire marginal stability boundary is explored. As the flow passes through any point on the marginal stability curve, it undergoes a supercritical Hopf bifurcation and the steady base flow is replaced by a traveling wave. The envelope of the wave system is governed by a complex Ginzburg-Landau equation. The Ginzburg-Landau equation admits Stokes waves, which correspond to standing modulations of the linear traveling wavetrain, as well as traveling wave modulations of the linear wavetrain. Bands of wavenumbers are identified in which the nonlinear modulated waves are subject to a sideband instability.
Yang, Z.↗
The stabilizing effect of boundaries on thermal convection
Mathematical models for determining stabilizing effect of fluid boundaries on thermal convection
Gage, K. S.↗
Axisymmetric single shear element combustion instability experiment
The combustion stability characteristics of a combustor consisting of a single shear element and a cylindrical chamber utilizing LOX and gaseous hydrogen as propellants are presented. The combustor geometry and the resulting longitudinal mode instability are axisymmetric. Hydrogen injection temperature and pyrotechnic pulsing were used to determine stability boundaries. Mixture ratio, fuel annulus gap, and LOX post configuration were varied. Performance and stability data are presented for chamber pressures of 300 and 1000 psia.
Breisacher, Kevin J.↗
Axisymmetric single shear element combustion instability experiment
The combustion stability characteristics of a combustor consisting of a single shear element and a cylindrical chamber utilizing LOX and gaseous hydrogen as propellants are presented. The combustor geometry and the resulting longitudinal mode instability are axisymmetric. Hydrogen injection temperature and pyrotechnic pulsing were used to determine stability boundaries. Mixture ratio, fuel annulus gap, and LOX post configuration were varied. Performance and stability data were obtained for chamber pressures of 300 and 1000 psia.
Breisacher, Kevin J.↗
Overview of Recent Flight Flutter Testing Research at NASA Dryden
In response to the concerns of the aeroelastic community, NASA Dryden Flight Research Center, Edwards, California, is conducting research into improving the flight flutter (including aeroservoelasticity) test process with more accurate and automated techniques for stability boundary prediction. The important elements of this effort so far include the following: (1) excitation mechanisms for enhanced vibration data to reduce uncertainty levels in stability estimates; (2) investigation of a variety of frequency, time, and wavelet analysis techniques for signal processing, stability estimation, and nonlinear identification; and (3) robust flutter boundary prediction to substantially reduce the test matrix for flutter clearance. These are critical research topics addressing the concerns of a recent AGARD Specialists' Meeting on Advanced Aeroservoelastic Testing and Data Analysis. This paper addresses these items using flight test data from the F/A-18 Systems Research Aircraft and the F/A-18 High Alpha Research Vehicle.
Brenner, Martin J.↗
Nonparallel stability of three-dimensional compressible boundary layers. Part 1: Stability analysis
A compressible linear stability theory is presented for nonparallel three-dimensional boundary-layer flows, taking into account the normal velocity component as well as the streamwise and spanwise variations of the basic flow. The method of multiple scales is used to account for the nonparallelism of the basic flow, and equations are derived for the spatial evolution of the disturbance amplitude and wavenumber. The numerical procedure for obtaining the solution of the nonparallel problem is outlined.
El-Hady, N. M.↗
Viscous, resistive MHD stability computed by spectral techniques
Expansions in Chebyshev polynomials are used to study the linear stability of one dimensional magnetohydrodynamic (MHD) quasi-equilibria, in the presence of finite resistivity and viscosity. The method is modeled on the one used by Orszag in accurate computation of solutions of the Orr-Sommerfeld equation. Two Reynolds like numbers involving Alfven speeds, length scales, kinematic viscosity, and magnetic diffusivity govern the stability boundaries, which are determined by the geometric mean of the two Reynolds like numbers. Marginal stability curves, growth rates versus Reynolds like numbers, and growth rates versus parallel wave numbers are exhibited. A numerical result which appears general is that instability was found to be associated with inflection points in the current profile, though no general analytical proof has emerged. It is possible that nonlinear subcritical three dimensional instabilities may exist, similar to those in Poiseuille and Couette flow.
Dahlburg, R. B.↗
Summary of Methods for Calculating Dynamic Lateral Stability and Response and for Estimating Lateral Stability Derivatives
A summary of methods for making dynamic lateral stability and response calculations and for estimating the aerodynamic stability derivatives required for use in these calculations is presented. The processes of performing calculations of the time histories of lateral motions, of the period and damping of these motions, and of the lateral stability boundaries are presented as a series of simple straightforward steps. Existing methods for estimating the stability derivatives are summarized and, in some cases, simple new empirical formulas are presented. Reference is also made to reports presenting experimental data that should be useful in making estimates of the derivatives. Detailed estimating methods are presented for low-subsonic-speed conditions but only a brief discussion and a list of references are given for transonic- and supersonic-speed conditions.
Campbell, John P↗
Summary of methods for calculating dynamic lateral stability and response and for estimating aerodynamic stability derivatives
A summary of methods for making dynamic lateral stability and response calculations and for estimating the aerodynamic stability derivatives required for use in these calculations is presented. The processes of performing calculations of the time histories of lateral motions, of the period and damping of these motions, and of the lateral stability boundaries are presented as a series of simple straightforward steps. Existing methods for estimating the stability derivatives are summarized and, in some cases, simple new empirical formulas are presented. Detailed estimation methods are presented for low-subsonic-speed conditions but only a brief discussion and a list of references are given for transonic and supersonic speed conditions.
Campbell, John P↗
High angle-of-attack stability-and-control analysis
Methods of linear systems analysis were applied to mathematical models of aircraft flying at high angle of attack and maneuver rate. First order longitudinal and lateral directional coupling is obtained by linearizing the complete nonlinear equations of motion about a generalized (quasi steady) trim point. Open loop stability boundaries are defined using the linear dynamic equations, and pilot in the loop effects are presented. Stability augmentation structures for maneuvering flight conditions are shown to be defined readily using optimal control theory.
Stengel, R. F.↗
Viscous, resistive magnetohydrodynamic stability computed by spectral techniques
Expansions in Chebyshev polynomials are used to study the linear stability of one-dimensional magnetohydrodynamic quasi-equilibria, in the presence of finite resistivity and viscosity. The method is modeled on the one used by Orszag in accurate computation of solutions of the Orr-Sommerfeld equation. Two Reynolds-like numbers involving Alfven speeds, length scales, kinematic viscosity, and magnetic diffusivity govern the stability boundaries, which are determined by the geometric mean of the two Reynolds-like numbers. Marginal stability curves, growth rates versus Reynolds-like numbers, and growth rates versus parallel wave numbers are exhibited. A numerical result that appears general is that instability has been found to be associated with inflection points in the current profile, though no general analytical proof has emerged. It is possible that nonlinear subcritical three-dimensional instabilities may exist, similar to those in Poiseuille and Couette flow.
Dahlburg, R. B.↗
Numerical simulation of baroclinic Jovian vortices
We examine the evolution of baroclinic vortices in a time-dependent, nonlinear numerical model of a Jovian atmosphere. The model uses a normal-mode expansion in the vertical, using the barotropic and first two baroclinic modes. Results for the stability of baroclinic vortices on an f plane in the absence of a mean zonal flow are similar to results of Earth vortex models, although the presence of a fluid interior on the Jovian planets shifts the stability boundaries to smaller length scales. The presence of a barotropic mean zonal flow in the interior stabilizes vortices against instability and significantly modifies the finite amplitude form of baroclinic instabilities. The effect of a zonal flow on a form of barotropic instability produces periodic oscillations in the latitude and longitude of the vortex as observed at the level of the cloud tops. This instability may explain some, but not all, observations of longitudinal oscillations of vortices on the outer planets. Oscillations in aspect ratio and orientation of stable vortices in a zonal shear flow are observed in this baroclinic model, as in simpler two-dimensional models. Such oscillations are also observed in the atmospheres of Jupiter and Neptune. The meridional propagation and decay of vortices on a beta plane is inhibited by the presence of a mean zonal flow. The direction of propagation of a vortex relative to the mean zonal flow depends upon the sign of the meridional potential vorticity gradient; combined with observations of vortex drift rates, this may provide a constraint on model assumption for the flow in the deep interior of the Jovian planets.
Achterberg, Richard K.↗
The upper-branch stability of compressible boundary layer flows
The upper-branch linear and nonlinear stability of compressible boundary layer flows is studied using the approach of Smith and Bodonyi (1982) for a similar incompressible problem. Both pressure gradient boundary layers and Blasius flow are considered with and without heat transfer, and the neutral eigenrelations incorporating compressibility effects are obtained explicitly. The compressible nonlinear viscous critical layer equations are derived and solved numerically and the results indicate some solutions with positive phase shift across the critical layer. Various limiting cases are investigated including the case of much larger disturbance amplitudes and this indicates the structure for the strongly nonlinear critical layer of the Benney-Bergeon (1969) type. It is also shown how a match with the inviscid neutral inflexional modes arising from the generalized inflexion point criterion, is achieved.
Gajjar, J. S. B.↗