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Slender-body theory for subsonic and supersonic flow past bodies of revolution is extended to a second approximation, Methods are developed for handling the difficulties that arise at round ends, Comparison is made with experiment and with other theories for several simple shapes.
The paper presents a review of the historical development in unsteady transonic aerodynamics, along with the foundations and accomplishments of several approaches to solve the equations of unsteady transonic flow. The discussion covers the linearized unsteady flow theory, numerical solution of the exact equations for an inviscid compressible gas, nonlinear small disturbance theory of transonic flow and linearization of the unsteady component about the nonlinear solution for the steady state, local linearization solution for unsteady transonic flow, unsteady transonic flow theory for slender wings and bodies, and three-dimensional unsteady transonic flows. The relation between the calculated results and experiment is examined. It is shown that the newly emerging numerical methods are capable of solving the nonlinear equations for two-dimensional flow and can be extended to three-dimensional flows.
Results obtained through application of potential-flow theory based on a suction flow analogy for incompressible flow are compared to attached-flow theory and to experimental data acquired for sharp-edged delta wings. The error incurred in predicting structural loads on the basis of attached-flow theory is investigated. Force and moment coefficients and load distributions are used in the comparisons. The root bending moment can be estimated by assuming vortex lift concentrated at the wing leading edge. While this may entail some error at large angles of attack (owing to inboard movement of the center of vortex lift), it may furnish an upper bound in evaluating results based on other theories.
Actuator disk theory and flow field calculations for propeller induced flow with nonuniform circulation distribution
Nonconical theory of flow past slender wing bodies with leading edge separation
The highlights of a recent discussion by representatives of the fluid dynamics and structures and materials panels are reported with emphasis on the fundamental aspects of unsteady fluid mechanics. Topics include linearized potential flow theory, transonic flow calculations, unsteady boundary layers, dynamic stall, transonic buffet, and techniques for measuring unsteady pressures.
Theories of turbulent time correlations are applied to compute frequency spectra of sound radiated by isotropic turbulence and by turbulent shear flows. The hypothesis that Eulerian time correlations are dominated by the sweeping action of the most energetic scales implies that the frequency spectrum of the sound radiated by isotropic turbulence scales as omega(exp 4) for low frequencies and as omega(exp -3/4) for high frequencies. The sweeping hypothesis is applied to an approximate theory of jet noise. The high frequency noise again scales as omega(exp -3/4), but the low frequency spectrum scales as omega(exp 2). In comparison, a classical theory of jet noise based on dimensional analysis gives omega(exp -2) and omega(exp 2) scaling for these frequency ranges. It is shown that the omega(exp -2) scaling is obtained by simplifying the description of turbulent time correlations. An approximate theory of the effect of shear on turbulent time correlations is developed and applied to the frequency spectrum of sound radiated by shear turbulence. The predicted steepening of the shear dominated spectrum appears to be consistent with jet noise measurements.
Theory and experimental measurements are compared with a novel three-wire thermocouple. Signals from three wires of unequal diameters are recorded from the thermocouple suspended in constant flow with a periodic temperature fluctuation. It is demonstrated that the reconstructed signal from the three-wire thermocouple requires no compensation for omega less than or equal to 5(omega(sub 1)), where omega(sub 1) is the natural frequency of the smaller wire. The latter result represents a significant improvement compared to previous work with two-wire thermocouples. A correction factor has also been derived to account for wires of arbitrary diameter.
Theory and experimental measurements are compared with a novel three-wire thermocouple. Signals from three wires of unequal diameters arc recorded from the thermocouple suspended in constant flow with a periodic temperature fluctuation. It is demonstrated that the reconstructed signal from the three-wire thermocouple requires no compensation for omega less than or equal to 5(sub omega1), where omega, is the natural frequency of the smaller wire. The latter result represents a significant improvement compared to previous work with two-wire thermocouples. A correction factor has also been derived to account for wires of arbitrary diameter.
The purpose of this presentation is to give you a survey of a field of aerodynamics which has for a number of years been attracting an ever growing interest. The subject is the theory of flows with friction, and, within that field, particularly the theory of friction layers, or boundary layers. As you know, a great many considerations of aerodynamics are based on the so-called ideal fluid, that is, the frictionless incompressible fluid. By neglect of compressibility and friction the extensive mathematical theory of the ideal fluid (potential theory) has been made possible.
Lifting line theory is applied to describe the flow about a lifting wing at transonic speeds. The method extends that of Van Dyke (1975), in which lifting line theory is viewed as a singular perturbation problem, to transonic flows. Inner and outer expansions as the aspect ratio approaches infinity of the transonic small disturbance equations are found. It is shown that the solutions match asymptotically. A boundary value problem is formulated which describes the first aspect ratio correction to the two dimensional cross sectional transonic flow. The theory is especially applicable to wings of similar cross-sections.
A method is presented for the approximate solution of the nonlinear equations transonic flow theory. Solutions are found for two-dimensional flows at a Mach number of 1 and for purely subsonic and purely supersonic flows. Results are obtained in closed analytic form for a large and significant class of nonlifting airfoils. At a Mach number of 1 general expressions are given for the pressure distribution on an airfoil of specified geometry and for the shape of an airfoil having a prescribed pressure distribution. Extensive comparisons are made with available data, particularly for a Mach number of 1, and with existing solutions.
The flow-field characteristics beneath swept and unswept wings as determined by potential-flow theory are compared with the experimentally determined flow fields beneath swept and unswept wing-fuselage combinations. The potential-flow theory utilized considered both spanwise and chordwise distributions of vorticity as well as the wing-thickness effects. The perturbation velocities induced by a unit horseshoe vortex are included in tabular form. The results indicated that significant chordwise flow gradients existed beneath both swept and unswept wings at zero lift and throughout the lift range. The theoretical predictions of the flow-field characteristics were qualitatively correct in all cases considered, although there were indications that the magnitudes of the downwash angles tended to be overpredicted as the tip of the swept wing was approached and that the sidewash angles ahead of the unswept wing were underpredicted. The calculated effects of compressibility indicated that significant increases in the chordwise variation of flow angles and dynamic-pressure ratios should be expected in going from low to high subsonic speeds.
The flow-field characteristics beneath swept and unswept wings as determined by potential-flow theory are compared with the experimentally determined flow fields beneath swept and unswept wing-fuselage combinations. The potential-flow theory utilized considered both spanwise and chordwise distributions of vorticity as well as the wing-thickness effects. The perturbation velocities induced by a unit horseshoe vortex are included in tabular form. The theoretical predictions of the flow-field characteristics were qualitatively correct in all cases considered, although there were indications that the magnitudes of the downwash angles tended to be overpredicted as the tip of the swept wing was approached and that the sidewash angles ahead of the unswept wing were underpredicted. The calculated effects of compressibility indicated that significant increases in the chordwise variation of flow angles and dynamic-pressure ratios should be expected in going from low to high subsonic speeds.
In the theory of nonstationary flows about airfoils, the "indicial lift" function ksub1(s) of Wagner and the "alternating lift" function c(k) of Theodorsen have fundamental significance. This paper reports on some interesting relations of the nature of Fourier transforms that exist between these functions. General problems in transient flows about airfoils may be given a unified broad treatment when these functions are employed. Certain approximate results also are reported which are of notable simplicity, and an analogy with transient electrical flows is drawn.
Potential flow theory study of incompressible separated flow about circular cylinder
The theory for radiation emission, absorption, and transfer in a thermochemical nonequilibrium flow is presented. The expressions developed reduce correctly to the limit at equilibrium. To implement the theory in a practical computer code, some approximations are used, particularly the smearing of molecular radiation. Details of these approximations are presented and helpful information is included concerning the use of the computer code. This user's manual should benefit both occasional users of the Langley Optimized Radiative Nonequilibrium (LORAN) code and those who wish to use it to experiment with improved models or properties.
A method is presented for the approximate solution of the nonlinear equations of transonic flow theory. Solutions are found for two-dimensional flows at a Mach number of 1 and for purely subsonic and purely supersonic flows. Results are obtained in closed analytic form for a large and significant class of nonlifting airfoils. At a Mach number of 1 general expressions are given for the pressure distribution on an airfoil of specified geometry and for the shape of an airfoil having a prescribed pressure distribution. Extensive comparisons are made with available data, particularly for a Mach number of 1, and with existing solutions.