SEARCH · Search NASA
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.
Comparison of panel flutter results from approximate aerodynamic theory with results from exact inviscid theory and experiment
It is pointed out that the theory of spiral density waves, invented to explain the spiral structure of disk galaxies, has also been found useful for the study of planetary rings. The linear theory is by now well developed, while the nonlinear theory is less complete. Analytical calculations which include self-gravitation have, so far, obtained results only in the slightly nonlinear regime, or have concentrated on partial effects which are not of primary importance to the physical problem at hand. In the present paper, it is attempted to remedy these shortcomings. The simplest asymptotic ordering which can still yield useful results is adopted. Attention is given to the reduction to a nonlinear integral equation in a single variable, the use of the Wentzel-Kramers-Brillouin-Jeffreys theory, and the replacement of an equation by another which is easier to handle numerically.
A method is developed for calculating the surface load and radiated sound from a vibrating surface in a compressible viscous fluid. The method is applied to a thin two-dimensional elliptic cross-section. For large values of the viscous diffusion parameter, the surface load tends to an elliptic distribution in agreement with the results of inviscid theory when edge pressure continuity is enforced. For thin surfaces, the surface load is insensitive to variations in the thickness ratio. A three-dimensional spectral technique is developed to calculate the inviscid surface load and radiated sound from a thin vibrating airfoil. The inviscid theory predicts the correct form of the far field sound pressure and its phase. The actual levels are somewhat sensitive to the choice of theoretical spanwise surface pressure mode but are in better agreement with the experiment than the surface pressure. The comparison of theoretical and experimental surface pressure indicates that the viscous theory, used to validate the inviscid theory, is either inadequate or there is a source of experimental error.
An experiment was conducted at static conditions to determine the internal performance effects of nozzle throat contouring, the result of increasing the circular-arc throat radius. Five nonaxisymmetric converging-diverging nozzles were tested at nozzle pressure ratios up to 9.0. Data are presented as internal thrust ratios, discharge coefficients, and static-pressure distributions. Comparisons of internal performance data for the five nozzles show that throat contouring increases the value of discharge coefficient but has no significant effect on internal thrust ratio except in cases of internal flow separation. To illustrate the use of the two dimensional converging-diverging (2-D C-D) nozzle data base, a two dimensional inviscid theory was applied to the five configurations. The generally good agreement of data with theoretical results indicates that two-dimensional inviscid theory can be successfully applied to the prediction of 2-D C-D nozzle internal flow.
Growth of instabilities on the liquid/gas interface in the initial region of fuel sprays is studied by means of numerical simulations. The simulations are based on solutions of the variable-density incompressible Navier-Stokes equations, which are obtained with a new numerical algorithm. The simulations give good agreement with analytical results for the instabilities on a liquid cylinder induced by surface tension and wind-induced instabilities. The effects of boundary layers on the wind-induced instabilities are investigated. It is found that a boundary layer reduces the growth rate for a single interface, and a comparison with inviscid theory suggests that boundary layer effects may be significantly more important than surface tension effects. The results yield a better estimate than inviscid theory for the drop sizes as reported for diesel sprays. Results for the planar jet show that boundary layer effects hasten the growth of Squire's 'symmetric' mode, which is responsible for jet disintegration. This result helps explain the rapid atomization which occurs in swirl and air-blast atomizers.
A theoretical model for the interaction of a turbulent boundary layer with an oscillating wavy surface over which a fluid is flowing is developed, with an application to wind-driven water waves and to panel flutter in low supersonic flow. A systematic methodology is developed to obtain the surface pressure distribution by considering separately the effects on the perturbed flow of a mean shear velocity profile, viscous stresses, the turbulent Reynolds stresses, compressibility, and three-dimensionality. The inviscid theory is applied to the wind-water wave problem by specializing to traveling-wave disturbances, and the pressure magnitude and phase shift as a function of the wave phase speed are computed for a logarithmic mean velocity profile and compared with inviscid theory and experiment. The results agree with experimental evidence for the stabilization of the panel motion due to the influence of the unsteady boundary layer.
AA Using the existing inviscid theories, an attempt is made to explain the centering of the oscillating liquid shell. Experiments on liquid shells and liquid-core compound drops were conducted using acoustic levitation, in a low-gravity environment during a Space Shuttle flight. It was observed that their inner and outer interfaces became concentric when excited into capillary oscillations. Using the existing inviscid theories, and attempt is made to explain the centering of the oscillating liquid shell. It is concluded that viscosity needs to be considered in order to provide a realistic description of the centering process.
The wall static pressure in the vicinity of drag reducing outer layer devices in flat wall turbulent boundary layers has been measured and compared with an inviscid theory. Symmetric and cambered airfoil devices have been examined at small angles of attack and very low chord Reynolds numbers. Airfoil devices impose a sequence of strong favorable and adverse pressure gradients on the boundary layer whose drag is to be reduced. At very small angles of attack (+ or - 2 deg), this pressure field extends up to about three chord lengths downstream of the trailing edge of an airfoil device. Also examined are the pressures on the upper and lower surfaces of a symmetric airfoil device in the freestream and near the wall. The freestream pressure distribution around an airfoil section is altered by the wall proximity. The relevance of lift enhancement caused by wall proximity to drag reduction has been discussed. The pressure distributions on the flat wall beneath the symmetric airfoil devices are predicted well by the inviscid theory. However, the remaining pressure distributions are predicted only qualitatively, presumably because of strong viscous effects.
Taylor instability nonlinear oscillations, obtaining uniform solutions for wavenumbers near and larger than cut-off
A 1- by 3-meter semispan wing of taper ratio 1.0 with NACA 0012 airfoil section contours was tested in the Langley V/STOL tunnel to measure the pressure distribution at five sweep angles, 0 deg, 10 deg, 20 deg, 30 deg, and 40 deg, through an angle-of-attack range from -6 deg to 20 deg. The pressure data are presented as plots of pressure coefficients at each static-pressure tap location on the wing. Flow visualization wing-tuft photographs are also presented for a wing of 40 deg sweep. A comparison between theory and experiment using two inviscid theories and a viscous theory shows good agreement for pressure distributions, normal forces, and pitching moments for the wing at 0 deg sweep.
A systematic study is made of the approximate inviscid theory of thin bodies moving at such high supersonic speeds that nonlinearity is an essential feature of the equations of flow. The first-order small-disturbance equations are derived for three-dimensional motions involving shock waves, and estimates are obtained for the order of error involved in the approximation. The hypersonic similarity rule of Tsien and Hayes, and Hayes' unsteady analogy appear in the course of the development. It is shown that the hypersonic theory can be interpreted so that it applies also in the range of linearized supersonic flow theory. Several examples are solved according to the small-disturbance theory, and compared with the full solutions when available.
Aspects of the linear compressible stability theory are considered, with special attention given to the inviscid theory and the additional solutions that arise when there is a region of supersonic flow relative to the phase velocity. For the case of highly cooled flat-plate boundary layers at Mach number 5.8, the unstable region is found to include supersonic outgoing waves. A previously unknown neutral incoming wave has also been identified. An example of viscous multiple solutions is provided, and calculations of higher viscous discrete modes and the compressible counterpart of the Squire mode are presented. It is noted that compressible stability theory is missing a firm connection with boundary-layer transition.
An investigation of high Reynolds number stationary instabilities in the boundary layer on a rotating disc is given. It is shown that in addition to the inviscid mode at high Reynolds numbers, there is a stationary short wavelength mode. This mode has its structure fixed by a balance between viscous and Coriolis forces and cannot be described by an inviscid theory. The asymptotic structure of the wavenumber and orientation of this mode is obtained. A similar analysis is given for the inviscid mode, the expansion procedure used is capable of taking nonparallel effects into account in a self consistent manner. The results are compared to numerical calculations and experimental observations.
An investigation of high Reynolds number stationary instabilities in the boundary layer on a rotating disc is given. It is shown that in addition to the inviscid mode at high Reynolds numbers, there is a stationary short wavelength mode. This mode has its structure fixed by a balance between viscous and Coriolis forces and cannot be described by an inviscid theory. The asymptotic structure of the wavenumber and orientation of this mode is obtained. A similar analysis is given for the inviscid mode, the expansion procedure used is capable of taking nonparallel effects into account in a self consistent manner. The results are compared to numerical calculations and experimental observations.
The requirements placed on an unsteady aerodynamic theory intended for turbomachinery aeroelastic applications are discussed along with a brief description of the various theoretical models that are available to address these requirements. The main emphasis is placed on the description of a linearized inviscid theory which fully accounts for the effects of a nonuniform mean or steady flow on unsteady aerodynamic response. Although this theory has been developed primarily for blade flutter prediction, more general equations are presented which account for unsteady excitations due to incident external aerodynamic disturbances as well as those due to blade motions. The resulting equations consist of a system of three field equations along with conditions imposed at blade, wake and shock surfaces and in the far field. These equations can be solved to determine the fluctuations in all fluid dynamic properties throughout the required solution domain. Example solutions are presented to demonstrate several effects associated with nonuniform steady flows on the linearized unsteady aerodynamic response to prescribed blade motions.
The requirements placed on an unsteady aerodynamic theory intended for turbomachinery aeroelastic or aeroacoustic applications are discussed along with a brief description of the various theoretical models that are available to address these requirements. The major emphasis is placed on the description of a linearized inviscid theory which fully accounts for the affects of a nonuniform mean or steady flow on unsteady aerodynamic response. Although this linearization was developed primarily for blade flutter prediction, more general equations are presented which account for unsteady excitations due to incident external aerodynamic disturbances as well as those due to prescribed blade motions. The motivation for this linearized unsteady aerodynamic theory is focused on, its physical and mathematical formulation is outlined and examples are presented to illustrate the status of numerical solution procedures and several effects of mean flow nonuniformity on unsteady aerodynamic response.
An inviscid and viscous analysis is provided for an exposed half nozzle that is used with a scramjet for thrust generation. The analysis is based on the inviscid theory of a two-dimensional, minimum length nozzle with a curved inlet surface, where the flow may be sonic or supersonic. Inlet conditions are prescribed and the gas is assumed to be perfect. Viscous, and when appropriate inviscid, nondimensional parametric results are provided for the thrust, lift, heat transfer, pitching moment, and a variety of boundary-layer thicknesses. In addition to global results, wall distributions of pressure, heat transfer, etc., are provided. The analysis demonstrates that the nozzle produces a considerable lift force whose magnitude may exceed the thrust and a significant pitching moment. The thrust is quite sensitive to the inlet Mach number; it rapidly decreases as the inlet Mach number increases There is little loss in the thrust as the nozzle's downstream wall is truncated. The corresponding decrease in lift and the pitching moment is moderate.
In this paper the linear viscous stability theory for stably stratified parallel shear flow is reviewed and some new results are presented. Attention is focused on recent work on unbounded flows with emphasis placed on results which demonstrate apparent destabilizing effects of diffusivity which lie beyond the scope of inviscid theory. In particular it is shown that self-excited disturbances may exist with phase speeds lying outside the range of basic flow speed and that with strong thermal diffusivity, instability may occur even though the local Richardson number exceeds 0.25 throughout the flow.