Computation of the stability of the laminar compressible boundary layer.
Stability of idealized laminar boundary flow, determining phase velocity, amplification rate and wave number of all disturbances
PHASE VELOCITY↗
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Effect of Cooling on Boundary-Layer Stability at Mach Number 3
This paper describes the calculation of the effect of wall cooling on the instability of a two-dimensional, flat-plate supersonic boundary layer under stratospheric flight conditions at Mach 3 using both the inviscid and viscous linear stability theories.
wall↗
Investigation of some parameters affecting the stability of a hingeless helicopter blade in hover
Equations of motion are used to investigate the effects of the choice of the mode shape and built-in coning angle on the stability boundaries of hingeless blades in hover. The results obtained indicate that the stability boundaries are dependent upon the mode shape to a considerable degree. It was also found that positive built-in coning is usually destabilizing while a negative amount of built-in coning can be quite stabilizing.
Friedmann, P.↗
STABILITY OF THE COMPRESSIBLE LAMINAR BOUNDARY LAYER
Stability of compressible laminar boundary layer
LAMINAR BOUNDARY LAYER↗
Hydromagnetic stability of the magnetosphere boundary
Hydromagnetic stability of magnetosphere-solar wind interface
HYDRODYNAMIC STABILITY↗
Stability analysis and trend study of a balloon tethered in a wind, with experimental comparisons
A stability analysis and trend study for a balloon tethered in a steady wind are presented. The linearized, stability-derivative type analysis includes balloon aerodynamics, buoyancy, mass (including apparent mass), and static forces resulting from the tether cable. The analysis has been applied to a balloon 7.64 m in length, and the results are compared with those from tow tests of this balloon. This comparison shows that the analysis gives reasonable predictions for the damping, frequencies, modes of motion, and stability boundaries exhibited by the balloon. A trend study for the 7.64-m balloon was made to illustrate how the stability boundaries are affected by changes in individual stability parameters. The trends indicated in this study may also be applicable to many other tethered-balloon systems.
Redd, L. T.↗
The effect of small streamwise velocity distortion on the boundary layer flow over a thin flat plate with application to boundary layer stability theory
Researchers show how an initially linear spanwise disturbance in the free stream velocity field is amplified by leading edge bluntness effects and ultimately leads to a small amplitude but linear spanwise motion far downstream from the edge. This spanwise motion is imposed on the boundary layer flow and ultimately causes an order-one change in its profile shape. The modified profiles are highly unstable and can support Tollmein-Schlichting wave growth well upstream of the theoretical lower branch of the neutral stability curve for a Blasius boundary layer.
Goldstein, M. E.↗
Remarks on disputed numerical results in compressible boundary-layer stability theory
Past work on the influence of Mach number on the viscous and inviscid instability of flat-plate boundary layers is reviewed, and new spatial calculations are presented. These calculations support the previous view that viscosity is only stabilizing for both two- and three-dimensional first-mode waves above M1 = 3.0, and for second-mode waves at all Mach numbers. It is concluded that the calculations of Wazzan, Taghavi, and Keltner that show viscous instability at M1 = 6.0 for first-mode 50 deg waves, and at M1 = 3.0 for two-dimensional second-mode waves, are not correct.
Mack, L. M.↗
Analytical method for determining the stability of linear retarded systems with two delays
The stability is considered of the solution differential-difference equations of the retarded type with constant coefficients and two constant time delays. A method that makes use of analytical expressions to determine stability boundaries, and the stability of the system, is derived. The method was applied to a system represented by a second-order differential equation with constant coefficients and time delays in the velocity and displacement terms. The results obtained is in agreement with those obtained by other investigators.
Barker, L. K.↗
Sun-perturbed Earth-to-moon transfers with ballistic capture
A method is described for constructing a new type of low energy transfer trajectory from the Earth to the moon leading to ballistic capture. This is accomplished by utilizing the nonlinear Earth-moon-sun perturbations on a point mass in three dimensions. The interaction of the gravitational fields of the bodies defines transition regions in the position-velocity space where the dynamic effects on the point mass tend to balance. These are termed weak stability boundaries. The transfer is obtained by the use of trajectories connecting the weak stability boundaries. It uses approximately 18 percent less Delta-V than the Hohmann transfer to insert a spacecraft into a circular orbit about the moon. The use of this transfer has recently been demonstrated by Japan's Hiten spacecraft, which arrived at the moon on October 2, 1991. Application of the transfer method is also made to the Lunar Observer Mission.
Belbruno, Edward A.↗
Aeroelastic stability of complete rotors with application to a teetering rotor in forward flight
The derivation of a set of nonlinear coupled flap-lag-torsion equations of motion for moderately large deflections of an elastic, two bladed teetering helicopter rotor in forward flight is concisely outlined. The following degrees of freedom are included in the mathematical model: rigid body flapping, rigid body lead lag, elastic bending in flap and lead-lag blade root torsion and shaft torsion. Quasi-steady aerodynamic loads are considered and the effects of reversed flow are included. The aeroelastic stability of the complete rotor is investigated using a linearized system of equations of motion. The equilibrium position about which the equations are linearized is obtained by considering the trim state of the helicopter, in true or simulated forward flight conditions. The sensitivity of the aeroelastic stability boundaries to interblade structural and mechanical coupling is illustrated by comparing the complete rotor stability boundaries with those obtained from a single blade analysis for a number of hover and forward flight cases.
Shamie, J.↗
Aeroelastic stability of complete rotors with application to a teetering rotor in forward flight
The derivation of a set of non-linear coupled flap-lag-torsion equations of motion for moderately large deflections of an elastic, two-bladed teetering helicopter rotor in forward flight is concisely outlined. The following degrees of freedom are included in the mathematical model: rigid body flapping, rigid body lead-lag, elastic bending in flap and lead-lag, blade root torsion, and shaft torsion. Quasi-steady aerodynamic loads are considered and the effects of reversed flow are included. The aeroelastic stability of the complete rotor is investigated by using a linearized system of equations of motion. The equilibrium position about which the equations are linearized is obtained by considering the trim state of the helicopter, in true or simulated forward flight conditions. The sensitivity of the aeroelastic stability boundaries to interblade structural and mechanical coupling is illustrated by comparing the complete rotor stability boundaries with those obtained from a single blade analysis for a number of hover and forward flight cases.
Shamie, J.↗
Interactions of coupled acoustic and vortical instability
In the past, the acoustic combustion instability was studied independently of the hydrodynamic instability induced by vortex motions. This paper is intended to combine the two different sources of energy everywhere within the spatial domain and determine the effect of one upon the other. This can be achieved by calculating the mean flow velocities and vorticities and their fluctuating parts of velocities and vortices, as well as the fluctuating pressure. The Orr-Sommerfeld equation is utilized to determine the wavenumbers and unsteady stream functions from which vortically coupled acoustic instability growth constants are calculated. This process demonstrates that there are two different frequencies, acoustic and hydrodynamic, various combinations of which contribute to either damping or amplification. It is found that stability boundaries for coupled acoustic and vortical oscillations are somewhat similar to the classical hydrodynamic stability boundaries, but they occur in the form of multiple islands.
Chung, T. J.↗
Calculated blade response at high tip-speed ratios
This paper presents the initial results of a digital computer study of helicopter rotor-blade-motion stability for a broad range of forward speeds encompassing proposed conventional and compound helicopter designs. The analysis treats the general case of nonlinear, coupled flapping and lagging motions of hinged rigid blades. The results of the study to date indicate that blade-motion stability boundaries cannot be specified for a given blade design in terms of a fixed value of rotor tip-speed ratio. The stability boundaries can shift significantly within the desired operational speed range, with the stability limits depending upon the rotor loading, the magnitude of the disturbance encountered by the blade, and the blade position at the instant the external disturbance is encountered. The sample methods suggested for improving blade-motion stability include increasing the effective hinge spring restraint by incorporating pitch-flap coupling or by using hingeless or teetering rotor systems. Reducing rotor loading also has a beneficial effect on the blade-motion stability. The results indicate that methods used to deal with the blade-motion stability problem can be expected to diminish the overall vibration levels of the helicopter rotor system across the entire design speed range.
TIP SPEED↗
Boundary-layer stability analysis of Langley Research Center 8-foot LFC experimental data
An analytical study of linear-amplifying instabilities of a laminar boundary layer as found in the experimental data of the LaRC/8-foot laminar-flow control (LFC) experiment was completed and the results are presented. The LFC airfoil used for this experiment was a swept, supercritical design which removed suction air through spanwise slots. The amplification of small disturbances by linear processes on a swept surface such as this can be due to either Tollmien-Schlichting (TS) and/or crossflow (CF) mechanisms. This study consists of the examination of these two instabilities by both the commonly used incompressible (SALLY and MARIA) analysis and the more involved compressible (COSAL) analysis. A wide range of experimental test conditions with variations in Mach number, Reynolds number, and suction distributions were available for this study. Experimentally determined transition locations were found from thin-film techniques and were used to correlate the n-factors at transition for the range of test cases.
Berry, Scott↗
Effects of displacement and rate saturation on the control of statically unstable aircraft
Methodologies are presented for the analysis and design of stability augmentation control laws for aircraft in which 'hard' displacement and rate limiting are significant. Candidate control laws are derived using the linear-quadratic (LQ) regulator. Analytical and computational estimates of the stability limits imposed by control saturation are presented using state trajectories with control limiting, as well as describing functions and eigenvalue computation. Analysis also includes an investigation of the interaction of the state-space saturation and stability boundaries for various choices of LQ weighting matrices. For minimum-energy control, the saturation and stability boundaries are shown to be parallel. In this case, there is a direct relation between the solution to the matrix Riccati equation and the aircraft's open-loop dynamics.
Hanson, G. D.↗
Effect of bulges on the stability of boundary layers
The instability of flows around hump and dip imperfections is investigated. The mean flow is calculated using interacting boundary layers, thereby accounting for viscous/inviscid interaction and separation bubbles. Then, the two-dimensional linear stability of this flow is analyzed, and the amplification factors are computed. Results are obtained for several height/width ratios and locations. The theoretical results have been used to correlate the experimental results of Walker and Greening (1942). The observed transition locations are found to correspond to amplification factors varying between 7.4 and 10.0, consistent with previous results for flat plates. The method accounts for both viscous and shear-layer instabilities. Separation is found to increase significantly the amplification factor.
Nayfeh, Ali H.↗
An integrating matrix formulation for buckling of rotating beams including the effects of concentrated masses
The integrating matrix technique of computational mechanics is extended to include the effects of concentrated masses. The stability of a flexible rotating beam with discrete masses is analyzed to determine the critical rotational speeds for buckling in the inplane and out-of-plane directions. In this problem, the beam is subjected to compressive centrifugal forces arising from steady rotation about an axis which does not pass through the clamped end of the beam. To determine the eigenvalues from which stability is assessed, the differential equations of motion are solved numerically by combining the extended integrating matrix method with an eigenanalysis. Stability boundaries for a discrete mass representation of a uniform beam are shown to asymptotically approach the stability boundaries for the corresponding continuous mass beam as the number of concentrated masses is increased. An error in the literature is also noted for the discrete mass problem concerning the behavior of the critical rotational speed for inplane buckling as the radius of rotation of the clamped end of the beam is reduced.
Lakin, William D.↗